/usr/lib/open-axiom/algebra/interp.daase

(2994629 . 3631820570)       
((|sorted?| ((#1=(|Boolean|) #2=(|Mapping| #1# |#2| |#2|) $) 86 T ELT) ((#1# $) NIL T ELT)) (|sort!| (($ #2# $) 18 T ELT) (#3=($ $) NIL T ELT)) (|setelt| #4=((|#2| $ #5=(|Integer|) |#2|) NIL T ELT) ((|#2| $ #6=(|UniversalSegment| #5#) |#2|) 44 T ELT)) (|reverse!| (#3# 80 T ELT)) (|reduce| ((|#2| #7=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| #7# $ |#2|) 50 T ELT) ((|#2| #7# $) 49 T ELT)) (|position| ((#5# #8=(|Mapping| #1# |#2|) $) 27 T ELT) ((#5# |#2| $) NIL T ELT) ((#5# |#2| $ #5#) 96 T ELT)) (|merge| (($ #2# $ $) 64 T ELT) (#9=($ $ $) NIL T ELT)) (|members| ((#10=(|List| |#2|) $) 13 T ELT)) (|map!| (#11=($ (|Mapping| |#2| |#2|) $) 37 T ELT)) (|map| (#11# NIL T ELT) (($ #7# $ $) 60 T ELT)) (|insert| (($ |#2| $ #5#) NIL T ELT) (#12=($ $ $ #5#) 67 T ELT)) (|find| (((|Union| |#2| "failed") #8# $) 29 T ELT)) (|every?| (#13=(#1# #8# $) 23 T ELT)) (|elt| #4# ((|#2| $ #5#) NIL T ELT) (#14=($ $ #6#) 66 T ELT)) (|delete| (($ $ #5#) 76 T ELT) (#14# 75 T ELT)) (|count| ((#15=(|NonNegativeInteger|) |#2| $) NIL T ELT) ((#15# #8# $) 34 T ELT)) (|copyInto!| (#12# 69 T ELT)) (|copy| (#3# 68 T ELT)) (|construct| (($ #10#) 73 T ELT)) (|concat| (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (#9# 87 T ELT) (($ (|List| $)) 85 T ELT)) (|coerce| (((|OutputForm|) $) 92 T ELT)) (|any?| (#13# 22 T ELT)) (= (#16=(#1# $ $) 95 T ELT)) (< (#16# 99 T ELT))) 
(((|OneDimensionalArrayAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |map!| #3=(|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE < #1#) (SIGNATURE |sort!| #4=(|#1| |#1|)) (SIGNATURE |sort!| (|#1| #5=(|Mapping| #2# |#2| |#2|) |#1|)) (SIGNATURE |reverse!| #4#) (SIGNATURE |copyInto!| #6=(|#1| |#1| |#1| #7=(|Integer|))) (SIGNATURE |sorted?| (#2# |#1|)) (SIGNATURE |merge| #8=(|#1| |#1| |#1|)) (SIGNATURE |position| (#7# |#2| |#1| #7#)) (SIGNATURE |position| (#7# |#2| |#1|)) (SIGNATURE |position| (#7# #9=(|Mapping| #2# |#2|) |#1|)) (SIGNATURE |sorted?| (#2# #5# |#1|)) (SIGNATURE |merge| (|#1| #5# |#1| |#1|)) (SIGNATURE |any?| #10=(#2# #9# |#1|)) (SIGNATURE |every?| #10#) (SIGNATURE |count| (#11=(|NonNegativeInteger|) #9# |#1|)) (SIGNATURE |members| (#12=(|List| |#2|) |#1|)) (SIGNATURE |reduce| (|#2| #13=(|Mapping| |#2| |#2| |#2|) |#1|)) (SIGNATURE |reduce| (|#2| #13# |#1| |#2|)) (SIGNATURE |find| ((|Union| |#2| "failed") #9# |#1|)) (SIGNATURE |count| (#11# |#2| |#1|)) (SIGNATURE |reduce| (|#2| #13# |#1| |#2| |#2|)) (SIGNATURE |setelt| (|#2| |#1| #14=(|UniversalSegment| #7#) |#2|)) (SIGNATURE |insert| #6#) (SIGNATURE |insert| (|#1| |#2| |#1| #7#)) (SIGNATURE |delete| #15=(|#1| |#1| #14#)) (SIGNATURE |delete| (|#1| |#1| #7#)) (SIGNATURE |map| (|#1| #13# |#1| |#1|)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| #8#) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |elt| #15#) (SIGNATURE |construct| (|#1| #12#)) (SIGNATURE |elt| (|#2| |#1| #7#)) (SIGNATURE |elt| #16=(|#2| |#1| #7# |#2|)) (SIGNATURE |setelt| #16#) (SIGNATURE |map| #3#) (SIGNATURE |copy| #4#)) (|OneDimensionalArrayAggregate| |#2|) (|Type|)) (T |OneDimensionalArrayAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|swap!| (((|Void|) $ #3=(|Integer|) #3#) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#4=(|Boolean|) (|Mapping| #4# |#1| |#1|) $) 96 T ELT) ((#4# $) 90 (|has| |#1| . #5=((|OrderedSet|))) ELT)) (|sort!| (($ (|Mapping| #4# |#1| |#1|) . #6=($)) 87 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (#7=($ $) 86 (AND (|has| |#1| . #5#) (|has| $ (|ShallowlyMutableAggregate| |#1|))) ELT)) (|sort| (($ (|Mapping| #4# |#1| |#1|) . #6#) 97 T ELT) (#7# 91 (|has| |#1| . #5#) ELT)) (|setelt| ((|#1| $ #3# |#1|) 47 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #8=(|UniversalSegment| #3#) |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #9=(|Boolean|) |#1|) . #10=($)) 69 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#11=($) 6 T CONST)) (|reverse!| (#7# 88 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|reverse| (#7# 98 T ELT)) (|removeDuplicates| (($ $) 71 (AND (|has| |#1| . #12=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 70 (AND (|has| |#1| . #12#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #9# |#1|) . #10#) 68 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 110 (|has| |#1| . #13=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 106 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 105 T ELT)) (|qsetelt!| ((|#1| $ #3# |#1|) 48 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #3#) 46 T ELT)) (|position| ((#14=(|Integer|) (|Mapping| #4# |#1|) $) 95 T ELT) ((#14# |#1| $) 94 (|has| |#1| . #15=((|BasicType|))) ELT) ((#14# |#1| $ #14#) 93 (|has| |#1| . #15#) ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| ((#3# . #16=($)) 38 (|has| #3# . #17=((|OrderedSet|))) ELT)) (|min| (#18=($ $ $) 80 (|has| |#1| . #5#) ELT)) (|merge| (($ (|Mapping| #4# |#1| |#1|) $ $) 99 T ELT) (($ $ $) 92 (|has| |#1| . #5#) ELT)) (|members| (((|List| |#1|) $) 104 T ELT)) (|member?| ((#19=(|Boolean|) |#1| $) 109 (|has| |#1| . #13#) ELT)) (|maxIndex| ((#3# . #16#) 39 (|has| #3# . #17#) ELT)) (|max| (#18# 81 (|has| |#1| . #5#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 112 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 60 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #20=((|SetCategory|))) ELT)) (|insert| (($ |#1| $ #3#) 57 T ELT) (($ $ $ #3#) 56 T ELT)) (|indices| (((|List| #3#) $) 41 T ELT)) (|index?| ((#21=(|Boolean|) #3# $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #20#) ELT)) (|first| ((|#1| $) 37 (|has| #3# . #17#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #19# |#1|) $) 107 T ELT)) (|fill!| (($ $ |#1|) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|every?| ((#19# (|Mapping| #19# |#1|) . #22=($)) 102 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #20#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #20#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #20#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #20#)) ELT)) (|eq?| ((#23=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#21# |#1| $) 40 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 43 T ELT)) (|empty?| ((#23# $) 7 T ELT)) (|empty| (#11# 8 T ELT)) (|elt| ((|#1| $ #3# |#1|) 45 T ELT) ((|#1| $ #3#) 44 T ELT) (($ $ #8#) 66 T ELT)) (|delete| (($ $ #3#) 59 T ELT) (($ $ #8#) 58 T ELT)) (|count| ((#24=(|NonNegativeInteger|) |#1| $) 108 (|has| |#1| . #13#) ELT) ((#24# (|Mapping| #19# |#1|) $) 103 T ELT)) (|copyInto!| (($ $ $ #14#) 89 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#25=(|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| #25#)) ELT)) (|construct| (($ (|List| |#1|)) 67 T ELT)) (|concat| (($ $ |#1|) 64 T ELT) (($ |#1| $) 63 T ELT) (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#19# (|Mapping| #19# |#1|) . #22#) 101 T ELT)) (>= (#26=((|Boolean|) $ $) 82 (|has| |#1| . #5#) ELT)) (> (#26# 84 (|has| |#1| . #5#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (<= (#26# 83 (|has| |#1| . #5#) ELT)) (< (#26# 85 (|has| |#1| . #5#) ELT)) (|#| ((#24# $) 100 T ELT))) 
(((|OneDimensionalArrayAggregate| |#1|) (|Category|) (|Type|)) (T |OneDimensionalArrayAggregate|)) 
NIL 
(|Join| (|FiniteLinearAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|)) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|FiniteLinearAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((|subtractIfCan| (((|Union| $ "failed") $ $) 12 T ELT)) (|opposite?| (((|Boolean|) $ $) 27 T ELT)) (- (($ $) NIL T ELT) (($ $ $) 9 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) 16 T ELT) (($ (|Integer|) $) 25 T ELT))) 
(((|AbelianGroup&| |#1|) (CATEGORY |package| (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE |subtractIfCan| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |opposite?| ((|Boolean|) |#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianGroup|)) (T |AbelianGroup&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT))) 
(((|AbelianGroup|) (|Category|)) (T |AbelianGroup|)) 
((- (*1 *1 *1) (|ofCategory| *1 (|AbelianGroup|))) (- (*1 *1 *1 *1) (|ofCategory| *1 (|AbelianGroup|)))) 
(|Join| (|CancellationAbelianMonoid|) (|LeftLinearSet| (|Integer|)) (CATEGORY |domain| (SIGNATURE - ($ $)) (SIGNATURE - ($ $ $)))) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|zero?| ((#1=(|Boolean|) $) 10 T ELT)) (|sample| (($) 15 T CONST)) (|opposite?| ((#1# $ $) 22 T ELT)) (* (($ (|PositiveInteger|) $) 14 T ELT) (($ (|NonNegativeInteger|) $) 19 T ELT))) 
(((|AbelianMonoid&| |#1|) (CATEGORY |package| (SIGNATURE |opposite?| (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE |zero?| (#1# |#1|)) (SIGNATURE |sample| (|#1|) |constant|) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianMonoid|)) (T |AbelianMonoid&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| (((|Boolean|) $) 22 T ELT)) (|sample| (($) 23 T CONST)) (|opposite?| (((|Boolean|) $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (($) 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) 
(((|AbelianMonoid|) (|Category|)) (T |AbelianMonoid|)) 
((|Zero| (*1 *1) (|ofCategory| *1 (|AbelianMonoid|))) (|sample| (*1 *1) (|ofCategory| *1 (|AbelianMonoid|))) (|zero?| (*1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|Boolean|)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|opposite?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|AbelianMonoid|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|AbelianSemiGroup|) (CATEGORY |domain| (SIGNATURE |Zero| ($) |constant|) (SIGNATURE |sample| ($) |constant|) (SIGNATURE |zero?| ((|Boolean|) $)) (SIGNATURE * ($ (|NonNegativeInteger|) $)) (SIGNATURE |opposite?| ((|Boolean|) $ $)))) 
(((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((* (($ (|PositiveInteger|) $) 10 T ELT))) 
(((|AbelianSemiGroup&| |#1|) (CATEGORY |package| (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianSemiGroup|)) (T |AbelianSemiGroup&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT))) 
(((|AbelianSemiGroup|) (|Category|)) (T |AbelianSemiGroup|)) 
((+ (*1 *1 *1 *1) (|ofCategory| *1 (|AbelianSemiGroup|))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|AbelianSemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $)) (SIGNATURE * ($ (|PositiveInteger|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|zerosOf| (#1=(#2=(|List| $) #3=(|Polynomial| $)) 32 T ELT) (#4=(#2# #5=(|SparseUnivariatePolynomial| $)) 16 T ELT) (#6=(#2# #5# #7=(|Symbol|)) 20 T ELT)) (|zeroOf| (#8=($ #3#) 30 T ELT) (#9=($ #5#) 11 T ELT) (#10=($ #5# #7#) 60 T ELT)) (|rootsOf| (#1# 33 T ELT) (#4# 18 T ELT) (#6# 19 T ELT)) (|rootOf| (#8# 31 T ELT) (#9# 13 T ELT) (#10# NIL T ELT))) 
(((|AlgebraicallyClosedField&| |#1|) (CATEGORY |package| (SIGNATURE |zerosOf| #1=(#2=(|List| |#1|) #3=(|SparseUnivariatePolynomial| |#1|) #4=(|Symbol|))) (SIGNATURE |zerosOf| #5=(#2# #3#)) (SIGNATURE |zerosOf| #6=(#2# #7=(|Polynomial| |#1|))) (SIGNATURE |zeroOf| #8=(|#1| #3# #4#)) (SIGNATURE |zeroOf| #9=(|#1| #3#)) (SIGNATURE |zeroOf| #10=(|#1| #7#)) (SIGNATURE |rootsOf| #1#) (SIGNATURE |rootsOf| #5#) (SIGNATURE |rootsOf| #6#) (SIGNATURE |rootOf| #8#) (SIGNATURE |rootOf| #9#) (SIGNATURE |rootOf| #10#)) (|AlgebraicallyClosedField|)) (T |AlgebraicallyClosedField&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zerosOf| (((|List| $) (|Polynomial| $)) 98 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $)) 97 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 96 T ELT)) (|zeroOf| (($ (|Polynomial| $)) 101 T ELT) (($ (|SparseUnivariatePolynomial| $)) 100 T ELT) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 99 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sqrt| (($ $) 110 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rootsOf| (((|List| $) (|Polynomial| $)) 104 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $)) 103 T ELT) (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 102 T ELT)) (|rootOf| (($ (|Polynomial| $)) 107 T ELT) (($ (|SparseUnivariatePolynomial| $)) 106 T ELT) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 105 T ELT)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #8=(|Integer|)) 109 T ELT)) (|multiEuclidean| (((|Union| #9=(|List| $) #10="failed") #9# $) 68 T ELT)) (|lcm| (#11=($ $ $) 60 T ELT) (#12=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) 58 T ELT)) (|gcd| (#11# 62 T ELT) (#12# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #14=(|:| |coef1| $) #15=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #14# #15#) #10#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #16=(|Fraction| #17=(|Integer|))) 84 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #17#) 87 T ELT) (($ $ (|Fraction| #8#)) 108 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #18=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #16#) 86 T ELT) (($ #16# . #18#) 85 T ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|zerosOf| #1=((#2=(|List| $) #3=(|Polynomial| $)) NIL T ELT) #4=((#2# #5=(|SparseUnivariatePolynomial| $)) NIL T ELT) (#6=(#2# #5# #7=(|Symbol|)) 54 T ELT) (#8=(#2# $) 22 T ELT) (#9=(#2# $ #7#) 45 T ELT)) (|zeroOf| #10=(($ #3#) NIL T ELT) #11=(($ #5#) NIL T ELT) (#12=($ #5# #7#) 56 T ELT) (#13=($ $) 20 T ELT) (#14=($ $ #7#) 39 T ELT)) (|rootsOf| #1# #4# (#6# 52 T ELT) (#8# 18 T ELT) (#9# 47 T ELT)) (|rootOf| #10# #11# (#12# NIL T ELT) (#13# 15 T ELT) (#14# 41 T ELT))) 
(((|AlgebraicallyClosedFunctionSpace&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zerosOf| #1=(#2=(|List| |#1|) |#1| #3=(|Symbol|))) (SIGNATURE |zeroOf| #4=(|#1| |#1| #3#)) (SIGNATURE |zerosOf| #5=(#2# |#1|)) (SIGNATURE |zeroOf| #6=(|#1| |#1|)) (SIGNATURE |rootsOf| #1#) (SIGNATURE |rootOf| #4#) (SIGNATURE |rootsOf| #5#) (SIGNATURE |rootOf| #6#) (SIGNATURE |zerosOf| #7=(#2# #8=(|SparseUnivariatePolynomial| |#1|) #3#)) (SIGNATURE |zerosOf| #9=(#2# #8#)) (SIGNATURE |zerosOf| #10=(#2# #11=(|Polynomial| |#1|))) (SIGNATURE |zeroOf| #12=(|#1| #8# #3#)) (SIGNATURE |zeroOf| #13=(|#1| #8#)) (SIGNATURE |zeroOf| #14=(|#1| #11#)) (SIGNATURE |rootsOf| #7#) (SIGNATURE |rootsOf| #9#) (SIGNATURE |rootsOf| #10#) (SIGNATURE |rootOf| #12#) (SIGNATURE |rootOf| #13#) (SIGNATURE |rootOf| #14#)) (|AlgebraicallyClosedFunctionSpace| |#2|) (|IntegralDomain|)) (T |AlgebraicallyClosedFunctionSpace&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zerosOf| (#2=(#3=(|List| $) #4=(|Polynomial| $)) 98 T ELT) (#5=(#3# #6=(|SparseUnivariatePolynomial| $)) 97 T ELT) (#7=(#3# #6# #8=(|Symbol|)) 96 T ELT) (((|List| $) $) 148 T ELT) (((|List| $) $ (|Symbol|)) 146 T ELT)) (|zeroOf| (#9=($ #4#) 101 T ELT) (#10=($ #6#) 100 T ELT) (#11=($ #6# #8#) 99 T ELT) (($ $) 149 T ELT) (($ $ (|Symbol|)) 147 T ELT)) (|zero?| ((#12=(|Boolean|) $) 22 T ELT)) (|variables| ((#13=(|List| #14=(|Symbol|)) $) 217 T ELT)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ #15=(|Kernel| $)) 249 (|has| |#1| . #16=((|IntegralDomain|))) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#17=(|Boolean|) $) 52 T ELT)) (|tower| (#18=(#19=(|List| #20=(|Kernel| $)) $) 180 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|subst| (($ $ #19# #21=(|List| $)) 170 T ELT) (($ $ (|List| #22=(|Equation| $))) 169 T ELT) (($ $ #22#) 168 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#23=((|Factored| $) $) 90 T ELT)) (|sqrt| (($ $) 110 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#24=($) 23 T CONST)) (|rootsOf| (#2# 104 T ELT) (#5# 103 T ELT) (#7# 102 T ELT) (((|List| $) $) 152 T ELT) (((|List| $) $ (|Symbol|)) 150 T ELT)) (|rootOf| (#9# 107 T ELT) (#10# 106 T ELT) (#11# 105 T ELT) (($ $) 153 T ELT) (($ $ (|Symbol|)) 151 T ELT)) (|retractIfCan| (((|Union| (|Polynomial| |#1|) . #25=("failed")) . #26=($)) 268 (|has| |#1| . #27=((|Ring|))) ELT) (((|Union| (|Fraction| (|Polynomial| |#1|)) . #25#) . #26#) 251 (|has| |#1| . #16#) ELT) (((|Union| |#1| . #25#) . #26#) 213 T ELT) (((|Union| #28=(|Integer|) . #25#) . #26#) 210 (|has| |#1| . #29=((|RetractableTo| #28#))) ELT) (((|Union| #14# . #25#) . #26#) 204 T ELT) (((|Union| #20# . #25#) . #26#) 155 T ELT) (((|Union| #30=(|Fraction| #28#) . #25#) . #26#) 143 (OR (AND (|has| |#1| . #31=((|RetractableTo| #32=(|Integer|)))) (|has| |#1| . #16#)) (|has| |#1| . #33=((|RetractableTo| #30#)))) ELT)) (|retract| (((|Polynomial| |#1|) . #34=($)) 267 (|has| |#1| . #27#) ELT) (((|Fraction| (|Polynomial| |#1|)) . #34#) 250 (|has| |#1| . #16#) ELT) ((|#1| . #34#) 212 T ELT) ((#28# . #34#) 211 (|has| |#1| . #29#) ELT) ((#14# . #34#) 203 T ELT) ((#20# . #34#) 154 T ELT) ((#30# . #34#) 144 (OR (AND (|has| |#1| . #31#) (|has| |#1| . #16#)) (|has| |#1| . #33#)) ELT)) (|rem| (#35=($ $ $) 71 T ELT)) (|reducedSystem| (((|Matrix| |#1|) . #36=(#37=(|Matrix| $))) 256 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #38=(#37# #39=(|Vector| $))) 255 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| #40=(|Integer|))) (|:| |vec| (|Vector| #40#))) . #38#) 142 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41=((|LinearlyExplicitRingOver| #40#)))) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT) (((|Matrix| #40#) . #36#) 141 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41#)) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#35# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #42=(|List| $)) (|:| |generator| $)) #42#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|patternMatch| (((|PatternMatchResult| #43=(|Float|) . #44=($)) $ (|Pattern| #43#) (|PatternMatchResult| #43# . #44#)) 209 (|has| |#1| (|PatternMatchable| #43#)) ELT) (((|PatternMatchResult| #45=(|Integer|) . #44#) $ (|Pattern| #45#) (|PatternMatchResult| #45# . #44#)) 208 (|has| |#1| (|PatternMatchable| #45#)) ELT)) (|paren| (#46=($ #21#) 174 T ELT) (#47=($ $) 173 T ELT)) (|opposite?| ((#12# $ $) 20 T ELT)) (|operators| ((#48=(|List| #49=(|BasicOperator|)) $) 181 T ELT)) (|operator| ((#49# #49#) 182 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|odd?| (#50=(#51=(|Boolean|) $) 202 #52=(|has| $ (|RetractableTo| (|Integer|))) ELT)) (|numerator| (#53=($ $) 234 (|has| |#1| . #27#) ELT)) (|numer| (((|SparseMultivariatePolynomial| |#1| . #54=(#15#)) . #55=($)) 233 (|has| |#1| . #27#) ELT)) (|nthRoot| (($ $ #56=(|Integer|)) 109 T ELT)) (|multiEuclidean| (((|Union| #57=(|List| $) #58="failed") #57# $) 68 T ELT)) (|minPoly| (((|SparseUnivariatePolynomial| $) #20#) 199 #59=(|has| $ (|Ring|)) ELT)) (|map| (($ #60=(|Mapping| $ $) #20#) 188 T ELT)) (|mainKernel| (((|Union| #20# "failed") $) 178 T ELT)) (|leftReducedSystem| (((|Matrix| |#1|) . #61=(#39#)) 258 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #62=(#39# $)) 257 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| #40#)) (|:| |vec| (|Vector| #40#))) . #62#) 140 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41#)) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT) (((|Matrix| #40#) . #61#) 139 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41#)) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT)) (|lcm| (#63=($ $ $) 60 T ELT) (#64=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|kernels| (#18# 179 T ELT)) (|kernel| (#65=($ #49# #21#) 187 T ELT) (#66=($ #49# $) 186 T ELT)) (|isTimes| (#67=((|Union| #68=(|List| $) #69="failed") $) 228 (|has| |#1| . #70=((|SemiGroup|))) ELT)) (|isPower| (((|Union| (|Record| (|:| |val| $) #71=(|:| |exponent| #32#)) #69#) $) 237 (|has| |#1| . #27#) ELT)) (|isPlus| (#67# 230 (|has| |#1| . #72=((|AbelianSemiGroup|))) ELT)) (|isMult| (((|Union| (|Record| (|:| |coef| #32#) #73=(|:| |var| #15#)) #69#) $) 231 (|has| |#1| . #72#) ELT)) (|isExpt| ((#74=(|Union| (|Record| #73# #71#) #69#) $ #14#) 236 (|has| |#1| . #27#) ELT) ((#74# $ #75=(|BasicOperator|)) 235 (|has| |#1| . #27#) ELT) ((#74# $) 229 (|has| |#1| . #70#) ELT)) (|is?| (#76=(#51# $ #77=(|Symbol|)) 185 T ELT) ((#51# $ #49#) 184 T ELT)) (|inv| (($ $) 88 T ELT)) (|height| (((|NonNegativeInteger|) $) 177 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|ground?| (((|Boolean|) $) 215 T ELT)) (|ground| ((|#1| $) 216 T ELT)) (|gcdPolynomial| ((#78=(|SparseUnivariatePolynomial| $) #78# #78#) 58 T ELT)) (|gcd| (#63# 62 T ELT) (#64# 61 T ELT)) (|freeOf?| (#76# 190 T ELT) ((#51# $ $) 189 T ELT)) (|factor| (#23# 92 T ELT)) (|extendedEuclidean| (((|Record| #79=(|:| |coef1| $) #80=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #79# #80#) #58#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #42#) #42# $) 65 T ELT)) (|even?| (#50# 201 #52# ELT)) (|eval| (($ $ #14# #81=(|NonNegativeInteger|) #82=(|Mapping| $ $)) 241 (|has| |#1| . #27#) ELT) (($ $ #14# #81# #83=(|Mapping| $ #68#)) 240 (|has| |#1| . #27#) ELT) (($ $ #13# #84=(|List| #81#) (|List| #83#)) 239 (|has| |#1| . #27#) ELT) (($ $ #13# #84# (|List| #82#)) 238 (|has| |#1| . #27#) ELT) (($ $ (|List| #75#) #68# #14#) 227 (|has| |#1| . #85=((|ConvertibleTo| #86=(|InputForm|)))) ELT) (($ $ #75# $ #14#) 226 (|has| |#1| . #85#) ELT) (#53# 225 (|has| |#1| . #85#) ELT) (($ $ #13#) 224 (|has| |#1| . #85#) ELT) (($ $ #14#) 223 (|has| |#1| . #85#) ELT) (($ $ #49# #60#) 198 T ELT) (($ $ #49# #87=(|Mapping| $ #21#)) 197 T ELT) (($ $ #48# #88=(|List| #87#)) 196 T ELT) (($ $ #48# #89=(|List| #60#)) 195 T ELT) (($ $ #77# #60#) 194 T ELT) (($ $ #77# #87#) 193 T ELT) (($ $ #90=(|List| #77#) #88#) 192 T ELT) (($ $ #90# #89#) 191 T ELT) (($ $ (|List| $) (|List| $)) 162 T ELT) (($ $ $ $) 161 T ELT) (($ $ (|Equation| $)) 160 T ELT) (($ $ (|List| (|Equation| $))) 159 T ELT) (($ $ (|List| #20#) (|List| $)) 158 T ELT) (($ $ #20# $) 157 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|elt| (#65# 167 T ELT) (($ #49# $ $ $ $) 166 T ELT) (($ #49# $ $ $) 165 T ELT) (($ #49# $ $) 164 T ELT) (#66# 163 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|distribute| (($ $ $) 176 T ELT) (#47# 175 T ELT)) (|differentiate| (($ $ (|List| #14#) . #91=((|List| #92=(|NonNegativeInteger|)))) 263 (|has| |#1| . #27#) ELT) (($ $ #14# . #93=(#92#)) 262 (|has| |#1| . #27#) ELT) (($ $ (|List| #14#)) 261 (|has| |#1| . #27#) ELT) (($ $ #14#) 259 (|has| |#1| . #27#) ELT)) (|denominator| (#53# 244 (|has| |#1| . #16#) ELT)) (|denom| (((|SparseMultivariatePolynomial| |#1| . #54#) . #55#) 243 (|has| |#1| . #16#) ELT)) (|definingPolynomial| (#47# 200 #59# ELT)) (|convert| ((#86# . #94=($)) 272 (|has| |#1| . #85#) ELT) (($ (|Factored| $)) 242 (|has| |#1| . #16#) ELT) ((#95=(|Pattern| (|Float|)) . #94#) 207 (|has| |#1| (|ConvertibleTo| #95#)) ELT) ((#96=(|Pattern| (|Integer|)) . #94#) 206 (|has| |#1| (|ConvertibleTo| #96#)) ELT)) (|conjugate| (#97=($ $ $) 271 (|has| |#1| . #98=((|Group|))) ELT)) (|commutator| (#97# 270 (|has| |#1| . #98#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #99=(|Fraction| #100=(|Integer|))) 84 T ELT) (($ (|Polynomial| |#1|)) 269 (|has| |#1| . #27#) ELT) (($ (|Fraction| (|Polynomial| |#1|))) 252 (|has| |#1| . #16#) ELT) (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) 248 (|has| |#1| . #16#) ELT) (($ (|Polynomial| (|Fraction| |#1|))) 247 (|has| |#1| . #16#) ELT) (($ (|Fraction| |#1|)) 246 (|has| |#1| . #16#) ELT) (($ (|SparseMultivariatePolynomial| |#1| . #54#)) 232 (|has| |#1| . #27#) ELT) (($ |#1|) 214 T ELT) (($ #14#) 205 T ELT) (($ #20#) 156 T ELT)) (|charthRoot| (((|Maybe| $) $) 254 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|box| (#46# 172 T ELT) (#47# 171 T ELT)) (|belong?| ((#51# #49#) 183 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#17# $ $) 53 T ELT)) (|applyQuote| (($ #14# #68#) 222 T ELT) (($ #14# $ $ $ $) 221 T ELT) (($ #14# $ $ $) 220 T ELT) (($ #14# $ $) 219 T ELT) (($ #14# $) 218 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#24# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|List| #14#) . #91#) 266 (|has| |#1| . #27#) ELT) (($ $ #14# . #93#) 265 (|has| |#1| . #27#) ELT) (($ $ (|List| #14#)) 264 (|has| |#1| . #27#) ELT) (($ $ #14#) 260 (|has| |#1| . #27#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT) (($ (|SparseMultivariatePolynomial| |#1| . #54#) (|SparseMultivariatePolynomial| |#1| . #54#)) 245 (|has| |#1| . #16#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #100#) 87 T ELT) (($ $ (|Fraction| #56#)) 108 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #101=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #99#) 86 T ELT) (($ #99# . #101#) 85 T ELT) (($ $ |#1|) 253 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#1| . #101#) 145 (|has| |#1| . #27#) ELT))) 
(((|AlgebraicallyClosedFunctionSpace| |#1|) (|Category|) (|IntegralDomain|)) (T |AlgebraicallyClosedFunctionSpace|)) 
((|rootOf| (*1 *1 *1) (AND (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|rootsOf| (*1 *2 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)))) (|rootOf| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|rootsOf| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *4)))) (|zeroOf| (*1 *1 *1) (AND (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|zerosOf| (*1 *2 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)))) (|zeroOf| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedFunctionSpace| *3)) (|ofCategory| *3 (|IntegralDomain|)))) (|zerosOf| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|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| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) . T) ((|AlgebraicallyClosedField|) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) |has| |#1| (|CommutativeRing|)) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2=(|Fraction| (|Polynomial| |#1|))) |has| |#1| (|IntegralDomain|)) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #3=(|Kernel| $)) . T) ((|CoercibleFrom| #4=(|Polynomial| |#1|)) |has| |#1| (|Ring|)) ((|CoercibleFrom| #5=(|Symbol|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|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) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|CommutativeRing|))) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| #6=(|Integer|)) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LeftModule| |#1|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|CommutativeRing|))) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #6#) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|Module| #1#) . T) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #7=(|Symbol|)) |has| |#1| (|Ring|)) ((|PartialDifferentialRing| #7#) |has| |#1| (|Ring|)) ((|PartialDifferentialSpace| #7#) |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| #2#) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #3#) . T) ((|RetractableTo| #4#) |has| |#1| (|Ring|)) ((|RetractableTo| #5#) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|yRange| #1=(((|Segment| #2=(|DoubleFloat|)) $) NIL T ELT)) (|xRange| #1#) (|refine| (($ $ #2#) 164 T ELT)) (|makeSketch| (($ (|Polynomial| #3=(|Integer|)) #4=(|Symbol|) #4# #5=(|Segment| (|Fraction| #3#)) #5#) 103 T ELT)) (|listBranches| (((|List| (|List| (|Point| #2#))) $) 181 T ELT)) (|coerce| (((|OutputForm|) $) 195 T ELT))) 
(((|PlaneAlgebraicCurvePlot|) (|Join| (|PlottablePlaneCurveCategory|) (CATEGORY |domain| (SIGNATURE |makeSketch| ($ (|Polynomial| #1=(|Integer|)) #2=(|Symbol|) #2# #3=(|Segment| (|Fraction| #1#)) #3#)) (SIGNATURE |refine| ($ $ (|DoubleFloat|)))))) (T |PlaneAlgebraicCurvePlot|)) 
((|makeSketch| (*1 *1 *2 *3 *3 *4 *4) (AND (|isDomain| *2 (|Polynomial| #1=(|Integer|))) (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Segment| (|Fraction| #1#))) #2=(|isDomain| *1 (|PlaneAlgebraicCurvePlot|)))) (|refine| (*1 *1 *1 *2) (AND (|isDomain| *2 (|DoubleFloat|)) #2#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|body| (#3=((|SpadAst|) $) 12 T ELT)) (|before?| #1#) (|base| (#3# 10 T ELT)) (= #1#)) 
(((|AddAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |base| #1=((|SpadAst|) $)) (SIGNATURE |body| #1#)))) (T |AddAst|)) 
((|base| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|AddAst|)))) (|body| #1# #2#)) 
((|rootOf| ((|#2| #1=(|SparseUnivariatePolynomial| |#2|) (|Symbol|)) 39 T ELT)) (|operator| ((#2=(|BasicOperator|) #2#) 53 T ELT)) (|minPoly| ((#1# (|Kernel| |#2|)) 148 #3=(|has| |#1| (|RetractableTo| #4=(|Integer|))) ELT)) (|iroot| ((|#2| |#1| #4#) 120 #3# ELT)) (|inrootof| ((|#2| #1# |#2|) 29 T ELT)) (|droot| (((|OutputForm|) (|List| |#2|)) 87 T ELT)) (|definingPolynomial| ((|#2| |#2|) 143 #3# ELT)) (|belong?| (((|Boolean|) #2#) 17 T ELT)) (** ((|#2| |#2| (|Fraction| #4#)) 96 #3# ELT))) 
(((|AlgebraicFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rootOf| (|#2| #1=(|SparseUnivariatePolynomial| |#2|) (|Symbol|))) (SIGNATURE |operator| (#2=(|BasicOperator|) #2#)) (SIGNATURE |belong?| ((|Boolean|) #2#)) (SIGNATURE |inrootof| (|#2| #1# |#2|)) (SIGNATURE |droot| ((|OutputForm|) (|List| |#2|))) (IF (|has| |#1| (|RetractableTo| #3=(|Integer|))) (PROGN (SIGNATURE ** (|#2| |#2| (|Fraction| #3#))) (SIGNATURE |minPoly| (#1# (|Kernel| |#2|))) (SIGNATURE |definingPolynomial| (|#2| |#2|)) (SIGNATURE |iroot| (|#2| |#1| #3#))) |%noBranch|)) (|IntegralDomain|) (|FunctionSpace| |#1|)) (T |AlgebraicFunction|)) 
((|iroot| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 #2=(|Integer|)) #3=(|ofCategory| *2 #4=(|FunctionSpace| *3)) #5=(|isDomain| *1 (|AlgebraicFunction| *3 *2)) (|ofCategory| *3 (|RetractableTo| *4)) #6=(|ofCategory| *3 #7=(|IntegralDomain|)))) (|definingPolynomial| #8=(*1 *2 *2) (AND (|ofCategory| *3 #9=(|RetractableTo| #2#)) #6# #5# #3#)) (|minPoly| #10=(*1 *2 *3) (AND (|isDomain| *3 (|Kernel| *5)) #11=(|ofCategory| *5 #12=(|FunctionSpace| *4)) #13=(|ofCategory| *4 #9#) #14=(|ofCategory| *4 #7#) (|isDomain| *2 (|SparseUnivariatePolynomial| *5)) #15=(|isDomain| *1 (|AlgebraicFunction| *4 *5)))) (** (*1 *2 *2 *3) (AND (|isDomain| *3 (|Fraction| #2#)) #13# #14# #16=(|isDomain| *1 (|AlgebraicFunction| *4 *2)) #17=(|ofCategory| *2 #12#))) (|droot| #10# (AND (|isDomain| *3 (|List| *5)) #11# #14# (|isDomain| *2 (|OutputForm|)) #15#)) (|inrootof| (*1 *2 *3 *2) (AND #18=(|isDomain| *3 (|SparseUnivariatePolynomial| *2)) #17# #14# #16#)) (|belong?| #10# (AND (|isDomain| *3 #19=(|BasicOperator|)) #14# (|isDomain| *2 (|Boolean|)) #15# #11#)) (|operator| #8# (AND (|isDomain| *2 #19#) #6# (|isDomain| *1 (|AlgebraicFunction| *3 *4)) (|ofCategory| *4 #4#))) (|rootOf| #1# (AND #18# (|isDomain| *4 (|Symbol|)) (|ofCategory| *2 (|FunctionSpace| *5)) (|isDomain| *1 (|AlgebraicFunction| *5 *2)) (|ofCategory| *5 #7#)))) 
((|sample| (($) 10 T CONST)) (|eq?| (((|Boolean|) $ $) 8 T ELT))) 
(((|Aggregate&| |#1|) (CATEGORY |package| (SIGNATURE |sample| (|#1|) |constant|) (SIGNATURE |eq?| ((|Boolean|) |#1| |#1|))) (|Aggregate|)) (T |Aggregate&|)) 
NIL 
((|sample| (($) 6 T CONST)) (|eq?| (((|Boolean|) $ $) 10 T ELT)) (|empty?| (((|Boolean|) $) 7 T ELT)) (|empty| (($) 8 T ELT)) (|copy| (($ $) 9 T ELT))) 
(((|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|)))) (|sample| (*1 *1) (|ofCategory| *1 (|Aggregate|)))) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |empty| ($)) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |sample| ($) |constant|))) 
(((|Join|) . T) ((|Type|) . T)) 
((|atanh| (($ $) 11 T ELT)) (|asinh| (($ $) 10 T ELT)) (|asech| (($ $) 9 T ELT)) (|acsch| (($ $) 8 T ELT)) (|acoth| (($ $) 7 T ELT)) (|acosh| (($ $) 6 T ELT))) 
(((|ArcHyperbolicFunctionCategory|) (|Category|)) (T |ArcHyperbolicFunctionCategory|)) 
((|atanh| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|asinh| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|asech| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|acsch| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|acoth| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|acosh| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |acosh| ($ $)) (SIGNATURE |acoth| ($ $)) (SIGNATURE |acsch| ($ $)) (SIGNATURE |asech| ($ $)) (SIGNATURE |asinh| ($ $)) (SIGNATURE |atanh| ($ $)))) 
((~= (#1=((|Boolean|) $ $) 18 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2=((|BasicType|))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#) (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|value| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 136 T ELT)) (|third| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #3=($)) 159 T ELT)) (|tail| (#4=($ $) 157 T ELT)) (|table| (($) 95 T ELT) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 94 T ELT)) (|swap!| ((#5=(|Void|) $ |#1| |#1|) 82 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT) ((#5# $ #6=(|Integer|) #6#) 185 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|split!| (($ $ (|Integer|)) 170 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|sorted?| ((#7=(|Boolean|) (|Mapping| #7# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 219 T ELT) ((#7# $) 213 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8=((|OrderedSet|))) ELT)) (|sort!| (($ (|Mapping| #7# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #9=($)) 210 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (#10=($ $) 209 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT)) (|sort| (($ (|Mapping| #7# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #9#) 220 T ELT) (#10# 214 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) ELT)) (|size?| (#11=(#12=(|Boolean|) $ (|NonNegativeInteger|)) 202 T ELT)) (|setvalue!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 145 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setrest!| (#13=($ $ $) 166 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setlast!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 168 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setfirst!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 164 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setelt| ((|#2| $ |#1| |#2|) 70 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #6# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 196 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #14=(|UniversalSegment| #6#) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 171 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #15="last" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 169 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ $ #16="rest" $) 167 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #17="first" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 165 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #18="value" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 144 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setchildren!| (($ $ #19=(|List| $)) 143 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|select!| (($ (|Mapping| #20=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #21=($)) 42 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Mapping| #22=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #23=($)) 236 T ELT)) (|select| (($ (|Mapping| #24=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #25=($)) 49 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Mapping| #24# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #25#) 183 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|second| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #3#) 158 T ELT)) (|search| (((|Union| |#2| . #26=("failed")) |#1| . #27=($)) 59 T ELT)) (|sample| (#28=($) 6 T CONST)) (|reverse!| (#10# 211 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|reverse| (#10# 221 T ELT)) (|rest| (#29=($ $ #30=(|NonNegativeInteger|)) 153 T ELT) (#4# 151 T ELT)) (|removeDuplicates!| (($ $) 234 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #31=((|BasicType|))) ELT)) (|removeDuplicates| (($ $) 51 (OR (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #32=((|BasicType|))) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #32#) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))))) ELT)) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 44 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Mapping| #20# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #21#) 43 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Union| |#2| . #26#) |#1| . #27#) 60 T ELT) (($ (|Mapping| #22# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #23#) 240 T ELT) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 235 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #31#) ELT)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #33=($)) 50 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #32#) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT) (($ (|Mapping| #24# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #25#) 48 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #33#) 184 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #32#) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT) (($ (|Mapping| #24# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #25#) 182 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|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|))) 111 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #34=((|BasicType|))) ELT) (((|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|))) 107 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #35=($)) 106 T ELT) (((|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|))) 232 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #34#) ELT) (((|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|))) 228 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #35#) 227 T ELT)) (|qsetelt!| ((|#2| $ |#1| |#2|) 69 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #6# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 197 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|qelt| ((|#2| $ |#1|) 71 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #6#) 195 T ELT)) (|possiblyInfinite?| (#36=(#12# $) 199 T ELT)) (|position| ((#37=(|Integer|) (|Mapping| #7# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 218 T ELT) ((#37# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 217 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #38=((|BasicType|))) ELT) ((#37# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #37#) 216 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #38#) ELT)) (|nodes| (#39=(#19# $) 134 T ELT)) (|node?| (#40=(#41=(|Boolean|) $ $) 142 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #42=((|BasicType|))) ELT)) (|new| (($ (|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 179 T ELT)) (|more?| (#11# 201 T ELT)) (|minIndex| ((|#1| . #43=($)) 79 (|has| |#1| . #44=((|OrderedSet|))) ELT) ((#6# . #43#) 187 (|has| #6# . #44#) ELT)) (|min| (#45=($ $ $) 203 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) ELT)) (|merge!| (($ (|Mapping| #22# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ $) 237 T ELT) (#46=($ $ $) 233 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) ELT)) (|merge| (($ (|Mapping| #7# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ $) 222 T ELT) (($ $ $) 215 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) ELT)) (|members| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #47=($)) 105 T ELT) (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #47#) 226 T ELT)) (|member?| ((#48=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #49=($)) 110 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #34#) ELT) ((#48# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #49#) 231 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #34#) ELT)) (|maxIndex| ((|#1| . #43#) 78 (|has| |#1| . #44#) ELT) ((#6# . #43#) 188 (|has| #6# . #44#) ELT)) (|max| (#45# 204 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) ELT)) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #50=($)) 39 T ELT) (($ (|Mapping| |#2| |#2|) . #50#) 63 T ELT) (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #50#) 245 T ELT)) (|map| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #51=($)) 26 T ELT) (($ (|Mapping| |#2| |#2|) . #51#) 64 T ELT) (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #51#) 96 T ELT) (($ (|Mapping| |#2| |#2| |#2|) $ $) 93 T ELT) (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ $) 176 T ELT) (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #51#) 128 T ELT)) (|list| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 246 T ELT)) (|less?| (#11# 200 T ELT)) (|leaves| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 139 T ELT)) (|leaf?| (#52=(#41# $) 135 T ELT)) (|latex| (((|String|) $) 21 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53=((|SetCategory|))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#) (|has| |#2| . #53#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#)) ELT)) (|last| (#29# 156 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #3#) 154 T ELT)) (|keys| (((|List| |#1|) $) 61 T ELT)) (|key?| (((|Boolean|) |#1| $) 62 T ELT)) (|inspect| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #54=($)) 35 T ELT)) (|insert!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 36 T ELT) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #55=(|Integer|)) 239 T ELT) (($ $ $ #55#) 238 T ELT)) (|insert| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #6#) 173 T ELT) (($ $ $ #6#) 172 T ELT)) (|indices| (((|List| |#1|) . #56=($)) 76 T ELT) (((|List| #6#) . #56#) 190 T ELT)) (|index?| ((#57=(|Boolean|) |#1| . #58=($)) 75 T ELT) ((#57# #6# . #58#) 191 T ELT)) (|hash| (((|SingleInteger|) $) 20 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#) (|has| |#2| . #53#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#)) ELT)) (|first| ((|#2| $) 80 (|has| |#1| . #44#) ELT) (#29# 150 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #3#) 148 T ELT)) (|find| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #59=("failed")) (|Mapping| #48# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #60=($)) 108 T ELT) (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #59#) (|Mapping| #48# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #60#) 229 T ELT)) (|fill!| (($ $ |#2|) 81 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 186 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|extract!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #54#) 37 T ELT)) (|explicitlyFinite?| (#36# 198 T ELT)) (|every?| ((#48# (|Mapping| #48# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #61=($)) 103 T ELT) ((#48# (|Mapping| #48# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #61#) 224 T ELT)) (|eval| (($ $ (|List| (|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|)) . #53#)) ELT) (($ $ (|Equation| (|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|)) . #53#)) ELT) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|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|)) . #53#)) ELT) (($ $ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 22 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 68 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #53#)) ELT) (($ $ |#2| |#2|) 67 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #53#)) ELT) (($ $ (|Equation| |#2|)) 66 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #53#)) ELT) (($ $ (|List| (|Equation| |#2|))) 65 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #53#)) ELT) (($ $ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 100 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#)) ELT) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 99 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#)) ELT) (($ $ (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 98 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#)) ELT) (($ $ (|List| (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) 97 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#)) ELT) (($ $ (|List| 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(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #53#)) ELT)) (|eq?| ((#62=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#57# |#2| . #63=($)) 77 (AND (|has| $ (|FiniteAggregate| |#2|)) (|has| |#2| . #64=((|BasicType|)))) ELT) ((#57# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #63#) 189 (AND (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #64#)) ELT)) (|entries| (((|List| |#2|) . #65=($)) 74 T ELT) (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #65#) 192 T ELT)) (|empty?| ((#62# $) 7 T ELT)) (|empty| (#28# 8 T ELT)) (|elt| ((|#2| $ |#1|) 73 T ELT) ((|#2| $ |#1| |#2|) 72 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #6# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 194 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #6#) 193 T ELT) (($ $ #14#) 180 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #15#) 155 T ELT) (($ $ #16#) 152 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #17#) 149 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #18#) 137 T ELT)) (|distance| (((|Integer|) $ $) 140 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 45 T ELT)) (|delete!| (($ $ #55#) 242 T ELT) (($ $ (|UniversalSegment| #55#)) 241 T ELT)) (|delete| (($ $ #6#) 175 T ELT) (($ $ #14#) 174 T ELT)) (|cyclic?| (#52# 138 T ELT)) (|cycleTail| (#4# 162 T ELT)) (|cycleSplit!| (#4# 163 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|cycleLength| ((#30# $) 161 T ELT)) (|cycleEntry| (#4# 160 T ELT)) (|count| ((#66=(|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #67=($)) 109 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #34#) ELT) ((#66# (|Mapping| #48# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #68=($)) 104 T ELT) ((#66# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #67#) 230 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #34#) ELT) ((#66# (|Mapping| #48# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #68#) 225 T ELT)) (|copyInto!| (($ $ $ #37#) 212 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#69=(|InputForm|) $) 52 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #70=((|ConvertibleTo| #69#))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #70#)) ELT)) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 47 T ELT) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 181 T ELT)) (|concat!| (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 244 T ELT) (#46# 243 T ELT)) (|concat| (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 178 T ELT) (($ (|List| $)) 177 T ELT) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 147 T ELT) (#13# 146 T ELT)) (|coerce| (((|OutputForm|) $) 16 (OR 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(|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) ELT)) (> (#72# 207 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) ELT)) (= (#1# 17 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#) (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (<= (#72# 206 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) ELT)) (< (#72# 208 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) ELT)) (|#| ((#66# $) 101 T ELT))) 
(((|AssociationListAggregate| |#1| |#2|) (|Category|) (|SetCategory|) (|SetCategory|)) (T |AssociationListAggregate|)) 
((|assoc| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|AssociationListAggregate| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|Maybe| (|Record| (|:| |key| *3) (|:| |entry| *4))))))) 
(|Join| (|TableAggregate| |t#1| |t#2|) (|ListAggregate| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))) (|ShallowlyMutableAggregate| |t#2|) (CATEGORY |domain| (SIGNATURE |assoc| ((|Maybe| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))) |t#1| $)))) 
(((|Aggregate|) . T) ((|BagAggregate| #1=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|BasicType|)) (|has| |#2| (|SetCategory|)) (|has| |#2| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|CoercibleTo| (|OutputForm|))) (|has| |#2| (|SetCategory|)) (|has| |#2| (|CoercibleTo| (|OutputForm|)))) ((|Collection| #2=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))) ((|Dictionary| #1#) . T) ((|DictionaryOperations| #1#) . T) ((|Eltable| #3=(|Integer|) #2#) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| #3# #2#) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| #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| #2#) . T) ((|FiniteAggregate| #2#) . T) ((|FiniteLinearAggregate| #2#) . T) ((|Functorial| #2#) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| #2#) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| #3# #2#) . T) ((|IndexedAggregate| |#1| |#2|) . T) ((|InnerEvalable| #2# #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|))) ((|Join|) . T) ((|KeyedDictionary| |#1| |#2|) . T) ((|LinearAggregate| #2#) . T) ((|ListAggregate| #2#) . T) ((|OrderedSet|) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) ((|OrderedType|) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) ((|RecursiveAggregate| #2#) . T) ((|SetCategory|) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) (|has| |#2| (|SetCategory|))) ((|ShallowlyMutableAggregate| #2#) . T) ((|ShallowlyMutableAggregate| |#2|) . T) ((|StreamAggregate| #2#) . T) ((|TableAggregate| |#1| |#2|) . T) ((|Type|) . T) ((|UnaryRecursiveAggregate| #2#) . T)) 
((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) NIL T ELT) (($ |#2|) 10 T ELT))) 
(((|Algebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|Algebra| |#2|) (|CommutativeRing|)) (T |Algebra&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #4#) 53 T ELT))) 
(((|Algebra| |#1|) (|Category|) (|CommutativeRing|)) (T |Algebra|)) 
NIL 
(|Join| (|Ring|) (|Module| |t#1|) (|CoercibleFrom| |t#1|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|split| (#1=(#2=(|Factored| |#1|) |#1|) 41 T ELT)) (|factor| (#1# 30 T ELT) ((#2# |#1| (|List| (|AlgebraicNumber|))) 33 T ELT)) (|doublyTransitive?| (((|Boolean|) |#1|) 59 T ELT))) 
(((|AlgFactor| |#1|) (CATEGORY |package| (SIGNATURE |factor| (#1=(|Factored| |#1|) |#1| (|List| #2=(|AlgebraicNumber|)))) (SIGNATURE |factor| #3=(#1# |#1|)) (SIGNATURE |split| #3#) (SIGNATURE |doublyTransitive?| ((|Boolean|) |#1|))) (|UnivariatePolynomialCategory| #2#)) (T |AlgFactor|)) 
((|doublyTransitive?| #1=(*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) #2=(|isDomain| *1 (|AlgFactor| *3)) #3=(|ofCategory| *3 (|UnivariatePolynomialCategory| #4=(|AlgebraicNumber|))))) (|split| #1# #5=(AND #6=(|isDomain| *2 (|Factored| *3)) #2# #3#)) (|factor| #1# #5#) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| #4#)) #6# #2# #3#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|yCoordinates| (#6=((|Record| (|:| |num| #7=(|Vector| |#2|)) #8=(|:| |den| |#2|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| #10=(|Fraction| |#2|) #11=(|Field|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #9# ELT)) (|unit?| #14=(#5# NIL #9# ELT)) (|traceMatrix| #15=(#16=(#17=(|Matrix| #10#) #18=(|Vector| $)) NIL T ELT) (#19=(#17#) NIL T ELT)) (|trace| #20=((#10# $) NIL T ELT)) (|tableForDiscreteLogarithm| (((|Table| #21=(|PositiveInteger|) #22=(|NonNegativeInteger|)) #23=(|Integer|)) NIL #24=(|has| #10# (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#25=(#26=(|Union| $ #27="failed") $ $) NIL T ELT)) (|squareFreePart| #12#) (|squareFree| #28=(((|Factored| $) $) NIL #9# ELT)) (|sizeLess?| #29=(#2# NIL #9# ELT)) (|size| (#30=(#22#) NIL #31=(|has| #10# #32=(|Finite|)) ELT)) (|singularAtInfinity?| #33=(#34=(#3#) NIL T ELT)) (|singular?| #35=(#36=(#3# |#1|) NIL T ELT) #37=(#38=(#3# |#2|) NIL T ELT)) (|sample| (#39=($) NIL T CONST)) (|retractIfCan| (((|Union| #23# . #40=(#27#)) . #41=($)) NIL #42=(|has| #10# (|RetractableTo| #23#)) ELT) (((|Union| #43=(|Fraction| #23#) . #40#) . #41#) NIL #44=(|has| #10# (|RetractableTo| #43#)) ELT) (((|Union| #10# . #40#) . #41#) NIL T ELT)) (|retract| ((#23# . #45=($)) NIL #42# ELT) ((#43# . #45#) NIL #44# ELT) #20#) (|represents| (($ #46=(|Vector| #10#) #18#) NIL T ELT) (#47=($ #46#) 60 T ELT) (#48=($ #7# |#2|) 130 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #24# ELT)) (|rem| #49=(#50=($ $ $) NIL #9# ELT)) (|regularRepresentation| ((#17# $ #18#) NIL T ELT) ((#17# $) NIL T ELT)) (|reducedSystem| ((#51=(|Matrix| #23#) . #52=(#53=(|Matrix| $))) NIL #54=(|has| #10# (|LinearlyExplicitRingOver| #23#)) ELT) ((#55=(|Record| (|:| |mat| #51#) (|:| |vec| (|Vector| #23#))) . #56=(#53# #18#)) NIL #54# ELT) ((#57=(|Record| (|:| |mat| #17#) (|:| |vec| #46#)) . #56#) NIL T ELT) ((#17# . #52#) NIL T ELT)) (|reduceBasisAtInfinity| #58=(#59=(#18# #18#) NIL T ELT)) (|reduce| #60=(($ |#3|) NIL T ELT) ((#26# (|Fraction| |#3|)) NIL #9# ELT)) (|recip| ((#26# $) NIL T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| #32#) ELT)) (|rationalPoint?| ((#3# |#1| |#1|) NIL T ELT)) (|rank| ((#21#) NIL T ELT)) (|random| (#39# NIL #31# ELT)) (|ramifiedAtInfinity?| #33#) (|ramified?| #35# #37#) (|quo| #49#) (|principalIdeal| (((|Record| (|:| |coef| #61=(|List| $)) #62=(|:| |generator| $)) #61#) NIL #9# ELT)) (|primitivePart| #63=(#13# NIL T ELT)) (|primitiveElement| #64=(#39# NIL #24# ELT)) (|primitive?| (#5# NIL #24# ELT)) (|primeFrobenius| (#65=($ $ #22#) NIL #24# ELT) #66=(#13# NIL #24# ELT)) (|prime?| #14#) (|order| (#67=(#21# $) NIL #24# ELT) (((|OnePointCompletion| #21#) $) NIL #24# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfComponents| #68=(#30# NIL T ELT)) (|normalizeAtInfinity| (#59# 105 T ELT)) (|norm| #20#) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #69=(|Symbol|)) NIL (|has| |#1| #11#) ELT)) (|nextItem| (#70=((|Maybe| $) $) NIL #24# ELT)) (|multiEuclidean| (((|Union| #61# #27#) #61# $) NIL #9# ELT)) (|minimalPolynomial| (#71=(|#3| $) NIL #9# ELT)) (|lookup| (#67# NIL #31# ELT)) (|lift| #72=(#71# NIL T ELT)) (|leftReducedSystem| ((#51# #18#) NIL #54# ELT) ((#55# . #73=(#18# $)) NIL #54# ELT) ((#57# . #73#) NIL T ELT) #15#) (|lcm| #74=(($ #61#) NIL #9# ELT) #49#) (|latex| (((|String|) $) NIL T ELT)) (|knownInfBasis| (((|Void|) #22#) 83 T ELT)) (|inverseIntegralMatrixAtInfinity| (#19# 55 T ELT)) (|inverseIntegralMatrix| (#19# 48 T ELT)) (|inv| #12#) (|integralRepresents| (#48# 131 T ELT)) (|integralMatrixAtInfinity| (#19# 49 T ELT)) (|integralMatrix| (#19# 47 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) #8#) #75=(|Mapping| |#2| |#2|)) 129 T ELT)) (|integralCoordinates| (#6# 67 T ELT)) (|integralBasisAtInfinity| (#76=(#18#) 46 T ELT)) (|integralBasis| (#76# 45 T ELT)) (|integralAtInfinity?| #4#) (|integral?| #4# ((#3# $ |#1|) NIL T ELT) ((#3# $ |#2|) NIL T ELT)) (|init| (#39# NIL #24# CONST)) (|index| (($ #21#) NIL #31# ELT)) (|hyperelliptic| #77=(((|Union| |#2| #27#)) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genus| #68#) (|generator| (#39# NIL T ELT)) (|gcdPolynomial| ((#78=(|SparseUnivariatePolynomial| $) #78# #78#) NIL #9# ELT)) (|gcd| #74# #49#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #23#) (|:| |exponent| #23#)))) NIL #24# ELT)) (|factor| #28#) (|extendedEuclidean| (((|Union| (|Record| #79=(|:| |coef1| $) #80=(|:| |coef2| $)) #27#) $ $ $) NIL #9# ELT) (((|Record| #79# #80# #62#) $ $) NIL #9# ELT)) (|exquo| (#25# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #61#) #61# $) NIL #9# ELT)) (|euclideanSize| (#81=(#22# $) NIL #9# ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|elliptic| #77#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|discriminant| ((#10# #18#) NIL T ELT) ((#10#) 43 T ELT)) (|discreteLog| (#81# NIL #24# ELT) (((|Union| #22# #27#) $ $) NIL #24# ELT)) (|differentiate| #82=(($ $ #83=(|Mapping| #10# #10#)) NIL #9# ELT) #84=(($ $ #83# #22#) NIL #9# ELT) (($ $ #75#) 125 T ELT) #85=(($ $ #86=(|List| #69#) (|List| #22#)) NIL #87=(OR (AND #9# (|has| #10# (|PartialDifferentialRing| #69#))) (AND #9# (|has| #10# (|PartialDifferentialSpace| #69#)))) ELT) #88=(($ $ #69# #22#) NIL #87# ELT) #89=(($ $ #86#) NIL #87# ELT) #90=(($ $ #69#) NIL #87# ELT) #91=(#65# NIL #92=(OR (AND (|has| #10# (|DifferentialRing|)) #9#) (AND (|has| #10# (|DifferentialSpace|)) #9#) #24#) ELT) #93=(#13# NIL #92# ELT)) (|derivationCoordinates| ((#17# #18# #83#) NIL #9# ELT)) (|definingPolynomial| ((|#3|) 54 T ELT)) (|createPrimitiveElement| #64#) (|coordinates| ((#46# $ #18#) NIL T ELT) ((#17# #18# #18#) NIL T ELT) (#94=(#46# $) 61 T ELT) (#16# 106 T ELT)) (|convert| (#94# NIL T ELT) (#47# NIL T ELT) #72# #60#) (|conditionP| (((|Union| #18# #27#) #53#) NIL #24# ELT)) (|complementaryBasis| #58#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #23#) NIL T ELT) (($ #10#) NIL T ELT) (($ #43#) NIL (OR #9# #44#) ELT) #12#) (|charthRoot| #66# (#70# NIL (|has| #10# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| #72#) (|characteristic| (#30# NIL T CONST)) (|branchPointAtInfinity?| (#34# 41 T ELT)) (|branchPoint?| (#36# 53 T ELT) (#38# 137 T ELT)) (|before?| #1#) (|basis| (#76# NIL T ELT)) (|associates?| #29#) (|annihilate?| #1#) (|algSplitSimple| (((|Record| (|:| |num| $) #8# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #75#) NIL T ELT)) (|absolutelyIrreducible?| #33#) (|Zero| (#39# 17 T CONST)) (|One| (#39# 27 T CONST)) (D #82# #84# #85# #88# #89# #90# #91# #93#) (= #1#) (/ #49#) (- #63# #95=(#50# NIL T ELT)) (+ #95#) (** (($ $ #21#) NIL T ELT) (#65# NIL T ELT) (($ $ #23#) NIL #9# ELT)) (* (($ #21# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #23# . #96=($)) NIL T ELT) #95# (($ $ #10#) NIL T ELT) (($ #10# . #96#) NIL T ELT) (($ #43# . #96#) NIL #9# ELT) (($ $ #43#) NIL #9# ELT))) 
(((|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)))) 
((|rootSplit| (#1=(|#2| |#2|) 47 T ELT)) (|rootSimp| (#1# 136 #2=(AND (|has| |#2| (|FunctionSpace| |#1|)) (|has| |#1| (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))))) ELT)) (|rootProduct| (#1# 100 #2# ELT)) (|rootPower| (#1# 101 #2# ELT)) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) 80 #2# ELT)) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) 44 T ELT)) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) 18 T ELT) ((|#2| |#2| (|List| |#2|)) 20 T ELT) ((|#2| |#2| |#2|) 21 T ELT) (#1# 16 T ELT))) 
(((|AlgebraicManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rootSplit| #1=(|#2| |#2|)) (SIGNATURE |ratDenom| #1#) (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| (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)))) (IF (|has| |#2| (|FunctionSpace| |#1|)) (PROGN (SIGNATURE |rootPower| #1#) (SIGNATURE |rootProduct| #1#) (SIGNATURE |rootSimp| #1#) (SIGNATURE |rootKerSimp| (|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)))) |%noBranch|) |%noBranch|)) (|IntegralDomain|) (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| #2=(#3=(|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $)) (SIGNATURE |denom| #2#) (SIGNATURE |coerce| ($ #3#))))) (T |AlgebraicManipulations|)) 
((|rootKerSimp| (*1 *2 *3 *2 *4) (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 #1=(|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 #2=(|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *5 *2)) (|ofCategory| *2 (|FunctionSpace| *5)) (|ofCategory| *2 (|Join| #3=(|Field|) #4=(|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| #5=(#6=(|SparseMultivariatePolynomial| *5 #7=(|Kernel| $)) $)) (SIGNATURE |denom| #5#) (SIGNATURE |coerce| ($ #6#))))))) (|rootSimp| #8=(*1 *2 *2) #9=(AND (|ofCategory| *3 #1#) #10=(|ofCategory| *3 #2#) #11=(|isDomain| *1 (|AlgebraicManipulations| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)) #12=(|ofCategory| *2 (|Join| #3# #4# (CATEGORY |domain| (SIGNATURE |numer| #13=(#14=(|SparseMultivariatePolynomial| *3 #7#) $)) (SIGNATURE |denom| #13#) (SIGNATURE |coerce| ($ #14#))))))) (|rootProduct| #8# #9#) (|rootPower| #8# #9#) (|ratPoly| (*1 *2 *3) (AND #15=(|ofCategory| *4 #2#) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|isDomain| *1 (|AlgebraicManipulations| *4 *3)) (|ofCategory| *3 #16=(|Join| #3# #4# (CATEGORY |domain| (SIGNATURE |numer| #17=(#18=(|SparseMultivariatePolynomial| *4 #7#) $)) (SIGNATURE |denom| #17#) (SIGNATURE |coerce| ($ #18#))))))) (|ratDenom| #19=(*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|Kernel| *2))) #20=(|ofCategory| *2 #16#) #15# #21=(|isDomain| *1 (|AlgebraicManipulations| *4 *2)))) (|ratDenom| #19# (AND (|isDomain| *3 (|List| *2)) #20# #15# #21#)) (|ratDenom| (*1 *2 *2 *2) #22=(AND #10# #11# #12#)) (|ratDenom| #8# #22#) (|rootSplit| #8# #22#)) 
((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#3|)) #1# #2=(|List| (|AlgebraicNumber|))) 23 T ELT) (((|Factored| |#3|) |#3| #2#) 19 T ELT))) 
(((|AlgebraicMultFact| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3| #1=(|List| #2=(|AlgebraicNumber|)))) (SIGNATURE |factor| ((|Factored| #3=(|SparseUnivariatePolynomial| |#3|)) #3# #1#))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|PolynomialCategory| #2# |#2| |#1|)) (T |AlgebraicMultFact|)) 
((|factor| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *4 (|List| #3=(|AlgebraicNumber|))) #4=(|ofCategory| *5 (|OrderedSet|)) #5=(|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #6=(|PolynomialCategory| #3# *6 *5)) (|isDomain| *2 (|Factored| #7=(|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|AlgebraicMultFact| *5 *6 *7)) (|isDomain| *3 #7#))) (|factor| #1# (AND #2# #4# #5# (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|AlgebraicMultFact| *5 *6 *3)) (|ofCategory| *3 #6#)))) 
((|weakBiRank| (#1=((|NonNegativeInteger|) |#2|) 70 T ELT)) (|rightRank| (#1# 74 T ELT)) (|radicalOfLeftTraceForm| (#2=(#3=(|List| |#2|)) 37 T ELT)) (|leftRank| (#1# 73 T ELT)) (|doubleRank| (#1# 69 T ELT)) (|biRank| (#1# 72 T ELT)) (|basisOfRightNucloid| (#4=((|List| (|Matrix| |#1|))) 65 T ELT)) (|basisOfRightNucleus| (#2# 60 T ELT)) (|basisOfRightAnnihilator| (#5=(#3# |#2|) 48 T ELT)) (|basisOfNucleus| (#2# 62 T ELT)) (|basisOfMiddleNucleus| (#2# 61 T ELT)) (|basisOfLeftNucloid| (#4# 53 T ELT)) (|basisOfLeftNucleus| (#2# 59 T ELT)) (|basisOfLeftAnnihilator| (#5# 47 T ELT)) (|basisOfCommutingElements| (#2# 55 T ELT)) (|basisOfCentroid| (#4# 66 T ELT)) (|basisOfCenter| (#2# 64 T ELT)) (|basis| ((#6=(|Vector| |#2|) #6#) 99 (|has| |#1| (|EuclideanDomain|)) ELT))) 
(((|AlgebraPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftRank| #1=((|NonNegativeInteger|) |#2|)) (SIGNATURE |rightRank| #1#) (SIGNATURE |doubleRank| #1#) (SIGNATURE |weakBiRank| #1#) (SIGNATURE |biRank| #1#) (SIGNATURE |basisOfCommutingElements| #2=(#3=(|List| |#2|))) (SIGNATURE |basisOfLeftAnnihilator| #4=(#3# |#2|)) (SIGNATURE |basisOfRightAnnihilator| #4#) (SIGNATURE |basisOfLeftNucleus| #2#) (SIGNATURE |basisOfRightNucleus| #2#) (SIGNATURE |basisOfMiddleNucleus| #2#) (SIGNATURE |basisOfNucleus| #2#) (SIGNATURE |basisOfCenter| #2#) (SIGNATURE |basisOfLeftNucloid| #5=((|List| (|Matrix| |#1|)))) (SIGNATURE |basisOfRightNucloid| #5#) (SIGNATURE |basisOfCentroid| #5#) (SIGNATURE |radicalOfLeftTraceForm| #2#) (IF (|has| |#1| (|EuclideanDomain|)) (SIGNATURE |basis| (#6=(|Vector| |#2|) #6#)) |%noBranch|)) (|IntegralDomain|) (|FramedNonAssociativeAlgebra| |#1|)) (T |AlgebraPackage|)) 
((|basis| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *4)) #1=(|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|EuclideanDomain|)) #2=(|ofCategory| *3 #3=(|IntegralDomain|)) #4=(|isDomain| *1 (|AlgebraPackage| *3 *4)))) (|radicalOfLeftTraceForm| #5=(*1 *2) #6=(AND #2# (|isDomain| *2 (|List| *4)) #4# #1#)) (|basisOfCentroid| #5# #7=(AND #2# (|isDomain| *2 (|List| (|Matrix| *3))) #4# #1#)) (|basisOfRightNucloid| #5# #7#) (|basisOfLeftNucloid| #5# #7#) (|basisOfCenter| #5# #6#) (|basisOfNucleus| #5# #6#) (|basisOfMiddleNucleus| #5# #6#) (|basisOfRightNucleus| #5# #6#) (|basisOfLeftNucleus| #5# #6#) (|basisOfRightAnnihilator| #8=(*1 *2 *3) #9=(AND #10=(|ofCategory| *4 #3#) (|isDomain| *2 (|List| *3)) #11=(|isDomain| *1 (|AlgebraPackage| *4 *3)) #12=(|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|basisOfLeftAnnihilator| #8# #9#) (|basisOfCommutingElements| #5# #6#) (|biRank| #8# #13=(AND #10# (|isDomain| *2 (|NonNegativeInteger|)) #11# #12#)) (|weakBiRank| #8# #13#) (|doubleRank| #8# #13#) (|rightRank| #8# #13#) (|leftRank| #8# #13#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#7=(|Vector| #8=(|Matrix| |#1|)) #9=(|Vector| $)) NIL T ELT) ((#7#) 24 T ELT)) (|someBasis| (#10=(#9#) 52 T ELT)) (|sample| #11=(($) NIL T CONST)) (|rightUnits| #12=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #13=((#8# #9#) NIL T ELT) #14=((#8#) NIL T ELT)) (|rightTrace| #15=((|#1| $) NIL T ELT)) (|rightRegularRepresentation| #16=((#8# $ #9#) NIL T ELT) #17=((#8# $) NIL T ELT)) (|rightRecip| #18=(#19=(#4# $) NIL #6# ELT)) (|rightRankPolynomial| #20=(((|SparseUnivariatePolynomial| #21=(|Polynomial| |#1|))) NIL (|has| |#1| (|Field|)) ELT)) (|rightPower| #22=(($ $ #23=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #15#) (|rightMinimalPolynomial| #24=(#25=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #26=((|#1| #9#) NIL T ELT) #27=((|#1|) NIL T ELT)) (|rightCharacteristicPolynomial| #28=(#25# NIL T ELT)) (|rightAlternative?| (#29=(#2#) 99 T ELT)) (|represents| (($ #30=(|Vector| |#1|) #9#) NIL T ELT) #31=(#32=($ #30#) NIL T ELT)) (|recip| (#19# 14 #6# ELT)) (|rank| ((#23#) 53 T ELT)) (|powerAssociative?| #33=(#29# NIL T ELT)) (|plenaryPower| #22#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| (#29# 101 T ELT)) (|leftUnits| #12#) (|leftUnit| #3#) (|leftTraceMatrix| #13# #14#) (|leftTrace| #15#) (|leftRegularRepresentation| #16# #17#) (|leftRecip| #18#) (|leftRankPolynomial| #20#) (|leftPower| #22#) (|leftNorm| #15#) (|leftMinimalPolynomial| #24#) (|leftDiscriminant| #26# #27#) (|leftCharacteristicPolynomial| #28#) (|leftAlternative?| (#29# 98 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| (#29# 106 T ELT)) (|jordanAdmissible?| (#29# 105 T ELT)) (|jacobiIdentity?| (#29# 107 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| (#29# 100 T ELT)) (|elt| ((|#1| $ #34=(|Integer|)) 55 T ELT)) (|coordinates| ((#30# $ #9#) 48 T ELT) ((#8# #9# #9#) NIL T ELT) (#35=(#30# $) 28 T ELT) #13#) (|convert| (#35# NIL T ELT) #31#) (|conditionsForIdempotents| ((#36=(|List| #21#) #9#) NIL T ELT) ((#36#) NIL T ELT)) (|commutator| #37=(#38=($ $ $) NIL T ELT)) (|commutative?| (#29# 95 T ELT)) (|coerce| (((|OutputForm|) $) 71 T ELT) (#32# 22 T ELT)) (|before?| #1#) (|basis| (#10# 51 T ELT)) (|associatorDependence| (((|List| #30#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| (#29# 91 T ELT)) (|apply| (($ #8# $) 18 T ELT)) (|antiCommutator| #37#) (|antiCommutative?| (#29# 97 T ELT)) (|antiAssociative?| (#29# 92 T ELT)) (|alternative?| (#29# 90 T ELT)) (|Zero| #11#) (= #1#) (- (($ $) NIL T ELT) #37#) (+ #37#) (** #22#) (* (($ #23# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #34# . #39=($)) NIL T ELT) (#38# 80 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #39#) NIL T ELT) (($ (|SquareMatrix| |#2| |#1|) $) 19 T ELT))) 
(((|AlgebraGivenByStructuralConstants| |#1| |#2| |#3| |#4|) (|Join| (|FramedNonAssociativeAlgebra| |#1|) (|LeftModule| (|SquareMatrix| |#2| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|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|)))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #6=(|BasicType|)) #7=(|has| |#2| #6#)) ELT)) (|value| #8=(#9=(#5# $) NIL T ELT)) (|third| #8#) (|tail| #10=(#11=($ $) NIL T ELT)) (|table| (#12=($) NIL T ELT) #13=(#14=($ #15=(|List| #5#)) NIL T ELT)) (|swap!| ((#16=(|Void|) $ |#1| |#1|) NIL #17=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT) ((#16# $ #18=(|Integer|) #18#) NIL #19=(|has| $ (|ShallowlyMutableAggregate| #5#)) ELT)) (|split!| (#20=($ $ #18#) NIL #19# ELT)) (|sorted?| ((#3# #21=(|Mapping| #3# #5# #5#) $) NIL T ELT) (#22=(#3# $) NIL #23=(|has| #5# #24=(|OrderedSet|)) ELT)) (|sort!| (#25=($ #21# $) NIL #19# ELT) (#11# NIL (AND #19# #23#) ELT)) (|sort| (#25# NIL T ELT) (#11# NIL #23# ELT)) (|size?| #26=((#3# $ #27=(|NonNegativeInteger|)) NIL T ELT)) (|setvalue!| #28=(#29=(#5# $ #5#) NIL #19# ELT)) (|setrest!| (#30=($ $ $) 35 #19# ELT)) (|setlast!| #28#) (|setfirst!| (#29# 37 #19# ELT)) (|setelt| (#31=(|#2| $ |#1| |#2|) 60 #17# ELT) #32=(#33=(#5# $ #18# #5#) NIL #19# ELT) ((#5# $ #34=(|UniversalSegment| #18#) #5#) NIL #19# ELT) ((#5# $ #35="last" #5#) NIL #19# ELT) (($ $ #36="rest" $) NIL #19# ELT) ((#5# $ #37="first" #5#) NIL #19# ELT) ((#5# $ #38="value" #5#) NIL #19# ELT)) (|setchildren!| (($ $ #39=(|List| $)) NIL #19# ELT)) (|select!| #40=(#41=($ #42=(|Mapping| #3# #5#) $) NIL #43=(|has| $ (|FiniteAggregate| #5#)) ELT) #44=(#41# NIL T ELT)) (|select| #40# #40#) (|second| #8#) (|search| (#45=((|Union| |#2| #46="failed") |#1| $) 45 T ELT)) (|sample| (#12# NIL T CONST)) (|reverse!| #47=(#11# NIL #19# ELT)) (|reverse| #10#) (|rest| #48=(($ $ #27#) NIL T ELT) (#11# 31 T ELT)) (|removeDuplicates!| (#11# NIL #4# ELT)) (|removeDuplicates| (#11# NIL #49=(AND #43# #4#) ELT)) (|remove!| (#50=($ #5# $) NIL #43# ELT) #40# (#45# 63 T ELT) #44# (#50# NIL #4# ELT)) (|remove| #51=(#50# NIL #49# ELT) #40# #51# #40#) (|reduce| #52=((#5# #53=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) #54=((#5# #53# $ #5#) NIL T ELT) #55=((#5# #53# $) NIL T ELT) #52# #54# #55#) (|qsetelt!| (#31# NIL #17# ELT) #32#) (|qelt| #56=((|#2| $ |#1|) NIL T ELT) #57=((#5# $ #18#) NIL T ELT)) (|possiblyInfinite?| #58=(#22# NIL T ELT)) (|position| ((#18# #42# $) NIL T ELT) ((#18# #5# $) NIL #4# ELT) ((#18# #5# $ #18#) NIL #4# ELT)) (|nodes| #59=((#39# $) NIL T ELT)) (|node?| #60=(#2# NIL #4# ELT)) (|new| (($ #27# #5#) NIL T ELT)) (|more?| #26#) (|minIndex| #61=((|#1| $) NIL #62=(|has| |#1| #24#) ELT) (#63=(#18# $) 40 #64=(|has| #18# #24#) ELT)) (|min| #65=(#30# NIL #23# ELT)) (|merge!| #66=(($ #21# $ $) NIL T ELT) #65#) (|merge| #66# #65#) (|members| #67=(#68=(#15# $) 22 T ELT) #67#) (|member?| #69=(#70=(#3# #5# $) NIL #4# ELT) #69#) (|maxIndex| #61# (#63# 42 #64# ELT)) (|max| #65#) (|map!| #71=(($ (|Mapping| #5# #5#) . #72=($)) NIL T ELT) #73=(($ (|Mapping| |#2| |#2|) . #72#) NIL T ELT) #71#) (|map| #71# #73# #71# (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL T ELT) (($ #53# $ $) NIL T ELT) #71#) (|list| (($ #5#) NIL T ELT)) (|less?| #26#) (|leaves| (#68# NIL T ELT)) (|leaf?| #58#) (|latex| (((|String|) $) 51 #74=(OR #75=(|has| #5# #76=(|SetCategory|)) #77=(|has| |#2| #76#)) ELT)) (|last| #48# #8#) (|keys| (#78=((|List| |#1|) $) 24 T ELT)) (|key?| #79=((#3# |#1| $) NIL T ELT)) (|inspect| #8#) (|insert!| (#50# NIL T ELT) #80=(($ #5# $ #18#) NIL T ELT) #81=(#82=($ $ $ #18#) NIL T ELT)) (|insert| #80# #81#) (|indices| (#78# NIL T ELT) (((|List| #18#) $) NIL T ELT)) (|index?| #79# ((#3# #18# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #74# ELT)) (|first| ((|#2| $) NIL #62# ELT) #48# (#9# 29 T ELT)) (|find| #83=(((|Union| #5# #46#) #42# $) NIL T ELT) #83#) (|fill!| (($ $ |#2|) NIL #17# ELT) (#84=($ $ #5#) NIL #19# ELT)) (|extract!| #8#) (|explicitlyFinite?| #58#) (|every?| #85=((#3# #42# $) NIL T ELT) #85#) (|eval| #86=(($ $ (|List| #87=(|Equation| #5#))) NIL #88=(AND (|has| #5# (|Evalable| #5#)) #75#) ELT) #89=(($ $ #87#) NIL #88# ELT) #90=(($ $ #5# #5#) NIL #88# ELT) #91=(($ $ #15# #15#) NIL #88# ELT) (($ $ #92=(|List| |#2|) #92#) NIL #93=(AND (|has| |#2| (|Evalable| |#2|)) #77#) ELT) (($ $ |#2| |#2|) NIL #93# ELT) (($ $ #94=(|Equation| |#2|)) NIL #93# ELT) (($ $ (|List| #94#)) NIL #93# ELT) #91# #90# #89# #86# #91# #90# #89# #86#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#2| $) NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #7#) ELT) (#70# NIL #49# ELT)) (|entries| ((#92# $) NIL T ELT) (#68# 21 T ELT)) (|empty?| (#22# 20 T ELT)) (|empty| (#12# 16 T ELT)) (|elt| #56# (#31# NIL T ELT) (#33# NIL T ELT) #57# #95=(($ $ #34#) NIL T ELT) ((#5# $ #35#) NIL T ELT) (($ $ #36#) NIL T ELT) ((#5# $ #37#) NIL T ELT) ((#5# $ #38#) NIL T ELT)) (|distance| ((#18# $ $) NIL T ELT)) (|dictionary| (#12# 14 T ELT) (#14# 15 T ELT)) (|delete!| #96=(#20# NIL T ELT) #95#) (|delete| #96# #95#) (|cyclic?| #58#) (|cycleTail| #10#) (|cycleSplit!| #47#) (|cycleLength| (#97=(#27# $) NIL T ELT)) (|cycleEntry| #10#) (|count| #98=((#27# #5# $) NIL #4# ELT) #99=((#27# #42# $) NIL T ELT) #98# #99#) (|copyInto!| (#82# NIL #19# ELT)) (|copy| #10#) (|convert| ((#100=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #100#)) ELT)) (|construct| #13# #13#) (|concat!| #101=(#84# NIL T ELT) #102=(#30# NIL T ELT)) (|concat| #101# (($ #39#) NIL T ELT) (#50# 33 T ELT) #102#) (|coerce| ((#103=(|OutputForm|) $) NIL (OR (|has| #5# #104=(|CoercibleTo| #103#)) (|has| |#2| #104#)) ELT)) (|children| #59#) (|child?| #60#) (|before?| #1#) (|bag| #13#) (|assoc| (((|Maybe| #5#) |#1| $) 55 T ELT)) (|any?| #85# #85#) (>= #105=(#2# NIL #23# ELT)) (> #105#) (= #1#) (<= #105#) (< #105#) (|#| (#97# 27 T ELT))) 
(((|AssociationList| |#1| |#2|) (|AssociationListAggregate| |#1| |#2|) #1=(|SetCategory|) #1#) (T |AssociationList|)) 
NIL 
((|monomial?| (((|Boolean|) $) 12 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 21 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #1=(|Integer|) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ #2=(|Fraction| #1#) $) 25 T ELT) (($ $ #2#) NIL T ELT))) 
(((|AbelianMonoidRing&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE * (|#1| |#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE * (|#1| #1# |#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| #2# |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianMonoidRing| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |AbelianMonoidRing&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 75 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|reductum| (($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| |#2|) 82 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|leadingMonomial| (($ $) 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #3#) ELT)) (|degree| ((|#2| $) 84 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #6=(|Fraction| (|Integer|))) 78 (|has| |#1| . #7=((|Algebra| (|Fraction| (|Integer|))))) ELT) (($ $) 70 (|has| |#1| . #3#) ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 74 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #8=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #8#) 88 T ELT) (($ #6# . #8#) 77 (|has| |#1| . #7#) ELT) (($ $ #6#) 76 (|has| |#1| . #7#) ELT))) 
(((|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|)))) (|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|) (|Functorial| |t#1|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingMonomial| ($ $)) (SIGNATURE |degree| (|t#2| $)) (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| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |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|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zerosOf| #4=((#5=(|List| $) #6=(|SparseUnivariatePolynomial| $) #7=(|Symbol|)) NIL T ELT) #8=((#5# #6#) NIL T ELT) #9=((#5# #10=(|Polynomial| $)) NIL T ELT)) (|zeroOf| #11=(($ #6# #7#) NIL T ELT) #12=(($ #6#) NIL T ELT) #13=(($ #10#) NIL T ELT)) (|zero?| (#14=(#3# $) 9 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #15=(#16=($ $) NIL T ELT)) (|unit?| #17=(#14# NIL T ELT)) (|tower| #18=((#19=(|List| #20=(|Kernel| $)) $) NIL T ELT)) (|subtractIfCan| #21=((#22=(|Union| $ #23="failed") $ $) NIL T ELT)) (|subst| #24=(($ $ #25=(|Equation| $)) NIL T ELT) #26=(($ $ (|List| #25#)) NIL T ELT) #27=(($ $ #19# #5#) NIL T ELT)) (|squareFreePart| #15#) (|squareFree| #28=(((|Factored| $) $) NIL T ELT)) (|sqrt| #15#) (|sizeLess?| #1#) (|sample| (#29=($) NIL T CONST)) (|rootsOf| #4# #8# #9#) (|rootOf| #11# #12# #13#) (|retractIfCan| #30=(((|Union| #20# . #31=(#23#)) . #32=($)) NIL T ELT) (((|Union| #33=(|Integer|) . #31#) . #32#) NIL T ELT) (((|Union| #34=(|Fraction| #33#) . #31#) . #32#) NIL T ELT)) (|retract| ((#20# . #35=($)) NIL T ELT) ((#33# . #35#) NIL T ELT) ((#34# . #35#) NIL T ELT)) (|rem| #36=(($ $ $) NIL T ELT)) (|reducedSystem| ((#37=(|Record| (|:| |mat| #38=(|Matrix| #33#)) (|:| |vec| (|Vector| #33#))) . #39=(#40=(|Matrix| $) #41=(|Vector| $))) NIL T ELT) ((#38# . #42=(#40#)) NIL T ELT) ((#43=(|Record| (|:| |mat| #44=(|Matrix| #34#)) (|:| |vec| (|Vector| #34#))) . #39#) NIL T ELT) ((#44# . #42#) NIL T ELT)) (|reduce| #15#) (|recip| ((#22# $) NIL T ELT)) (|quo| #36#) (|principalIdeal| (((|Record| (|:| |coef| #5#) #45=(|:| |generator| $)) #5#) NIL T ELT)) (|prime?| #17#) (|paren| #15# #46=(($ #5#) NIL T ELT)) (|opposite?| #1#) (|operators| ((#47=(|List| #48=(|BasicOperator|)) $) NIL T ELT)) (|operator| ((#48# #48#) NIL T ELT)) (|one?| (#14# 11 T ELT)) (|odd?| #49=(#14# NIL (|has| $ (|RetractableTo| #33#)) ELT)) (|numer| #50=((#51=(|SparseMultivariatePolynomial| #33# #20#) $) NIL T ELT)) (|nthRoot| #52=(($ $ #33#) NIL T ELT)) (|norm| ((#6# #6# #20#) NIL T ELT) ((#6# #6# #19#) NIL T ELT) (($ $ #20#) NIL T ELT) (($ $ #19#) NIL T ELT)) (|multiEuclidean| (((|Union| #5# #23#) #5# $) NIL T ELT)) (|minPoly| ((#6# #20#) NIL #53=(|has| $ (|Ring|)) ELT)) (|map| (($ #54=(|Mapping| $ $) #20#) NIL T ELT)) (|mainKernel| #30#) (|leftReducedSystem| ((#37# . #55=(#41# $)) NIL T ELT) ((#38# . #56=(#41#)) NIL T ELT) ((#43# . #55#) NIL T ELT) ((#44# . #56#) NIL T ELT)) (|lcm| #46# #36#) (|latex| (((|String|) $) NIL T ELT)) (|kernels| #18#) (|kernel| #57=(($ #48# $) NIL T ELT) #58=(($ #48# #5#) NIL T ELT)) (|is?| ((#3# $ #48#) NIL T ELT) #59=((#3# $ #7#) NIL T ELT)) (|inv| #15#) (|height| #60=((#61=(|NonNegativeInteger|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#6# #6# #6#) NIL T ELT)) (|gcd| #46# #36#) (|freeOf?| #1# #59#) (|factor| #28#) (|extendedEuclidean| (((|Union| (|Record| #62=(|:| |coef1| $) #63=(|:| |coef2| $)) #23#) $ $ $) NIL T ELT) (((|Record| #62# #63# #45#) $ $) NIL T ELT)) (|exquo| #21#) (|expressIdealMember| (((|Maybe| #5#) #5# $) NIL T ELT)) (|even?| #49#) (|eval| (($ $ #20# $) NIL T ELT) #27# #26# #24# (($ $ $ $) NIL T ELT) (($ $ #5# #5#) NIL T ELT) (($ $ #64=(|List| #7#) #65=(|List| #54#)) NIL T ELT) (($ $ #64# #66=(|List| #67=(|Mapping| $ #5#))) NIL T ELT) (($ $ #7# #67#) NIL T ELT) (($ $ #7# #54#) NIL T ELT) (($ $ #47# #65#) NIL T ELT) (($ $ #47# #66#) NIL T ELT) (($ $ #48# #67#) NIL T ELT) (($ $ #48# #54#) NIL T ELT)) (|euclideanSize| #60#) (|elt| #57# (($ #48# $ $) NIL T ELT) (($ #48# $ $ $) NIL T ELT) (($ #48# $ $ $ $) NIL T ELT) #58#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|distribute| #15# #36#) (|differentiate| #15# #68=(($ $ #61#) NIL T ELT)) (|denom| #50#) (|definingPolynomial| (#16# NIL #53# ELT)) (|convert| ((#69=(|Float|) . #70=($)) NIL T ELT) (((|DoubleFloat|) . #70#) NIL T ELT) (((|Complex| #69#) . #70#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) (($ #34#) NIL T ELT) #15# (($ #33#) NIL T ELT) (($ #51#) NIL T ELT)) (|characteristic| ((#61#) NIL T CONST)) (|box| #15# #46#) (|belong?| ((#3# #48#) NIL T ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#29# 6 T CONST)) (|One| (#29# 10 T CONST)) (D #15# #68#) (= (#2# 13 T ELT)) (/ #36#) (- #36# #15#) (+ #36#) (** #71=(($ $ #34#) NIL T ELT) #52# #68# (($ $ #72=(|PositiveInteger|)) NIL T ELT)) (* (($ #34# . #73=($)) NIL T ELT) #71# #36# (($ #33# . #73#) NIL T ELT) (($ #61# $) NIL T ELT) (($ #72# $) NIL T ELT))) 
(((|AlgebraicNumber|) (|Join| (|ExpressionSpace|) (|AlgebraicallyClosedField|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| #2=(|Fraction| #1#)) (|LinearlyExplicitRingOver| #1#) (|RealConstant|) (|LinearlyExplicitRingOver| #2#) (|CharacteristicZero|) (|ConvertibleTo| (|Complex| (|Float|))) (|DifferentialRing|) (|CoercibleFrom| #3=(|SparseMultivariatePolynomial| #1# #4=(|Kernel| $))) (CATEGORY |domain| (SIGNATURE |numer| #5=(#3# $)) (SIGNATURE |denom| #5#) (SIGNATURE |reduce| ($ $)) (SIGNATURE |norm| (#6=(|SparseUnivariatePolynomial| $) #6# #4#)) (SIGNATURE |norm| (#6# #6# #7=(|List| #4#))) (SIGNATURE |norm| ($ $ #4#)) (SIGNATURE |norm| ($ $ #7#))))) (T |AlgebraicNumber|)) 
((|numer| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) #3=(|Kernel| #4=(|AlgebraicNumber|)))) #5=(|isDomain| *1 #4#))) (|denom| #1# #2#) (|reduce| (*1 *1 *1) #5#) (|norm| #6=(*1 *2 *2 *3) (AND #7=(|isDomain| *2 (|SparseUnivariatePolynomial| #4#)) (|isDomain| *3 #3#) #5#)) (|norm| #6# (AND #7# (|isDomain| *3 #8=(|List| #3#)) #5#)) (|norm| #9=(*1 *1 *1 *2) (AND (|isDomain| *2 #3#) #5#)) (|norm| #9# (AND (|isDomain| *2 #8#) #5#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|parameters| (((|List| (|Identifier|)) $) 17 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 7 T ELT)) (|body| (((|Syntax|) $) 18 T ELT)) (|before?| #1#) (= #1#)) 
(((|AnonymousFunction|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |parameters| ((|List| (|Identifier|)) $)) (SIGNATURE |body| ((|Syntax|) $))))) (T |AnonymousFunction|)) 
((|parameters| #1=(*1 *2 *1) (AND (|isDomain| *2 (|List| (|Identifier|))) #2=(|isDomain| *1 (|AnonymousFunction|)))) (|body| #1# (AND (|isDomain| *2 (|Syntax|)) #2#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) 86 T ELT)) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|retractable?| (#3# 31 T ELT)) (|retractIfCan| (((|Union| |#1| #5#) $) 34 T ELT)) (|retract| (#7=(|#1| $) 35 T ELT)) (|reductum| (#8=($ $) 41 T ELT)) (|recip| ((#4# $) NIL T ELT)) (|opposite?| #1#) (|one?| (#3# NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingCoefficient| (#7# 32 T ELT)) (|leadingBasisTerm| (#8# 75 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|homogeneous?| (#3# 44 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (($ #9=(|NonNegativeInteger|)) 73 T ELT)) (|exp| (($ (|List| #10=(|Integer|))) 74 T ELT)) (|degree| ((#9# $) 45 T ELT)) (|coerce| (((|OutputForm|) $) 92 T ELT) (($ #10#) 70 T ELT) (($ |#1|) 68 T ELT)) (|coefficient| ((|#1| $ $) 29 T ELT)) (|characteristic| ((#9#) 72 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#6# 46 T CONST)) (|One| (#6# 17 T CONST)) (= #1#) (- (#8# NIL T ELT) (#11=($ $ $) NIL T ELT)) (+ (#11# 65 T ELT)) (** (($ $ #12=(|PositiveInteger|)) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #10# . #13=($)) NIL T ELT) (#11# 66 T ELT) (($ |#1| . #13#) 59 T ELT))) 
(((|AntiSymm| |#1| |#2|) (|Join| (|LeftAlgebra| |#1|) (|RetractableTo| |#1|) (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |leadingBasisTerm| #1=($ $)) (SIGNATURE |reductum| #1#) (SIGNATURE |coefficient| (|#1| $ $)) (SIGNATURE |generator| ($ #2=(|NonNegativeInteger|))) (SIGNATURE |exp| ($ (|List| (|Integer|)))) (SIGNATURE |homogeneous?| #3=((|Boolean|) $)) (SIGNATURE |retractable?| #3#) (SIGNATURE |degree| (#2# $)))) (|Ring|) (|List| (|Symbol|))) (T |AntiSymm|)) 
((|leadingCoefficient| #1=(*1 *2 *1) #2=(AND #3=(|ofCategory| *2 #4=(|Ring|)) #5=(|isDomain| *1 (|AntiSymm| *2 *3)) #6=(|ofType| *3 #7=(|List| (|Symbol|))))) (|leadingBasisTerm| #8=(*1 *1 *1) #9=(AND #5# #3# #6#)) (|reductum| #8# #9#) (|coefficient| (*1 *2 *1 *1) #2#) (|generator| #10=(*1 *1 *2) #11=(AND (|isDomain| *2 (|NonNegativeInteger|)) #12=(|isDomain| *1 (|AntiSymm| *3 *4)) #13=(|ofCategory| *3 #4#) #14=(|ofType| *4 #7#))) (|exp| #10# (AND (|isDomain| *2 (|List| (|Integer|))) #12# #13# #14#)) (|homogeneous?| #1# #15=(AND (|isDomain| *2 (|Boolean|)) #12# #13# #14#)) (|retractable?| #1# #15#) (|degree| #1# #11#)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|obj| ((#3=(|None|) $) 8 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dom| ((#4=(|SExpression|) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 15 T ELT)) (|before?| #1#) (|any| (($ #4# #3#) 16 T ELT)) (= (#2# 12 T ELT))) 
(((|Any|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |any| ($ #1=(|SExpression|) #2=(|None|))) (SIGNATURE |dom| (#1# $)) (SIGNATURE |obj| (#2# $))))) (T |Any|)) 
((|any| (*1 *1 *2 *3) (AND #1=(|isDomain| *2 (|SExpression|)) (|isDomain| *3 #2=(|None|)) #3=(|isDomain| *1 (|Any|)))) (|dom| #4=(*1 *2 *1) (AND #1# #3#)) (|obj| #4# (AND (|isDomain| *2 #2#) #3#))) 
((|retractable?| (((|Boolean|) #1=(|Any|)) 18 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") #1#) 20 T ELT)) (|retract| ((|#1| #1#) 21 T ELT)) (|coerce| ((#1# |#1|) 14 T ELT))) 
(((|AnyFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |coerce| (#1=(|Any|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#1| "failed") #1#)) (SIGNATURE |retractable?| ((|Boolean|) #1#)) (SIGNATURE |retract| (|#1| #1#))) (|Type|)) (T |AnyFunctions1|)) 
((|retract| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|Any|)) #4=(|isDomain| *1 (|AnyFunctions1| *2)) #5=(|ofCategory| *2 #6=(|Type|)))) (|retractable?| #1# (AND #2# (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|AnyFunctions1| *4)) (|ofCategory| *4 #6#))) (|retractIfCan| #1# (|partial| AND #2# #4# #5#)) (|coerce| #1# (AND (|isDomain| *2 #3#) (|isDomain| *1 (|AnyFunctions1| *3)) (|ofCategory| *3 #6#)))) 
((|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) 16 T ELT))) 
(((|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))))) 
((|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) 44 T ELT)) (|applyRules| ((|#3| #1=(|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) 32 T ELT) ((|#3| #1# |#3|) 31 T ELT))) 
(((|ApplyRules| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |applyRules| (|#3| #1=(|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|)) (SIGNATURE |applyRules| (|#3| #1# |#3| (|PositiveInteger|))) (SIGNATURE |localUnquote| (|#3| |#3| (|List| (|Symbol|))))) (|SetCategory|) (|Join| (|Ring|) #2=(|PatternMatchable| |#1|) #3=(|ConvertibleTo| (|Pattern| |#1|))) (|Join| (|FunctionSpace| |#2|) #2# #3#)) (T |ApplyRules|)) 
((|localUnquote| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|Symbol|))) #1=(|ofCategory| *4 #2=(|SetCategory|)) #3=(|ofCategory| *5 (|Join| #4=(|Ring|) #5=(|PatternMatchable| *4) #6=(|ConvertibleTo| (|Pattern| *4)))) #7=(|isDomain| *1 (|ApplyRules| *4 *5 *2)) #8=(|ofCategory| *2 (|Join| (|FunctionSpace| *5) #5# #6#)))) (|applyRules| (*1 *2 *3 *2 *4) (AND (|isDomain| *3 (|List| (|RewriteRule| *5 *6 *2))) (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 #2#) (|ofCategory| *6 (|Join| #4# #9=(|PatternMatchable| *5) #10=(|ConvertibleTo| (|Pattern| *5)))) (|ofCategory| *2 (|Join| (|FunctionSpace| *6) #9# #10#)) (|isDomain| *1 (|ApplyRules| *5 *6 *2)))) (|applyRules| (*1 *2 *3 *2) (AND (|isDomain| *3 (|List| (|RewriteRule| *4 *5 *2))) #1# #3# #8# #7#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 13 T ELT)) (|retractIfCan| (((|Union| #5=(|NonNegativeInteger|) "failed") $) 31 T ELT)) (|retract| ((#5# $) NIL T ELT)) (|one?| (#4# 15 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) 17 T ELT)) (|coerce| (((|OutputForm|) $) 22 T ELT) (($ #5#) 28 T ELT)) (|before?| #1#) (|arbitrary| (($) 10 T CONST)) (= (#2# 19 T ELT))) 
(((|Arity|) (|Join| (|SetCategory|) (|RetractableTo| (|NonNegativeInteger|)) (CATEGORY |domain| (SIGNATURE |arbitrary| ($) |constant|) (SIGNATURE |zero?| #1=((|Boolean|) $)) (SIGNATURE |one?| #1#)))) (T |Arity|)) 
((|arbitrary| (*1 *1) #1=(|isDomain| *1 (|Arity|))) (|zero?| #2=(*1 *2 *1) #3=(AND (|isDomain| *2 (|Boolean|)) #1#)) (|one?| #2# #3#)) 
((|setRow!| (($ $ #1=(|Integer|) |#3|) 46 T ELT)) (|setColumn!| (($ $ #1# |#4|) 50 T ELT)) (|members| (((|List| |#2|) $) 41 T ELT)) (|member?| ((#2=(|Boolean|) |#2| $) 55 T ELT)) (|every?| (#3=(#2# #4=(|Mapping| #2# |#2|) $) 21 T ELT)) (|elt| ((|#2| $ #1# #1#) NIL T ELT) ((|#2| $ #1# #1# |#2|) 29 T ELT)) (|count| ((#5=(|NonNegativeInteger|) #4# $) 35 T ELT) ((#5# |#2| $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 63 T ELT)) (|any?| (#3# 20 T ELT)) (= ((#2# $ $) 54 T ELT)) (|#| ((#5# $) 26 T ELT))) 
(((|TwoDimensionalArrayCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE = (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |setColumn!| (|#1| |#1| #2=(|Integer|) |#4|)) (SIGNATURE |setRow!| (|#1| |#1| #2# |#3|)) (SIGNATURE |elt| (|#2| |#1| #2# #2# |#2|)) (SIGNATURE |elt| (|#2| |#1| #2# #2#)) (SIGNATURE |member?| (#1# |#2| |#1|)) (SIGNATURE |count| (#3=(|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |members| ((|List| |#2|) |#1|)) (SIGNATURE |count| (#3# #4=(|Mapping| #1# |#2|) |#1|)) (SIGNATURE |every?| #5=(#1# #4# |#1|)) (SIGNATURE |any?| #5#) (SIGNATURE |#| (#3# |#1|))) (|TwoDimensionalArrayCategory| |#2| |#3| |#4|) (|Type|) #6=(|FiniteLinearAggregate| |#2|) #6#) (T |TwoDimensionalArrayCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) 52 T ELT)) (|setRow!| (($ $ (|Integer|) |#2|) 50 T ELT)) (|setColumn!| (($ $ (|Integer|) |#3|) 49 T ELT)) (|sample| (#3=($) 6 T CONST)) (|row| ((|#2| $ (|Integer|)) 54 T ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 39 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 38 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 34 (|has| |#1| . #4=((|BasicType|))) ELT)) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) 51 T ELT)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) 56 T ELT)) (|nrows| (((|NonNegativeInteger|) $) 59 T ELT)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) 65 T ELT)) (|ncols| (((|NonNegativeInteger|) $) 58 T ELT)) (|minRowIndex| (((|Integer|) $) 63 T ELT)) (|minColIndex| (((|Integer|) $) 61 T ELT)) (|members| (((|List| |#1|) $) 40 T ELT)) (|member?| ((#5=(|Boolean|) |#1| $) 35 (|has| |#1| . #4#) ELT)) (|maxRowIndex| (((|Integer|) $) 62 T ELT)) (|maxColIndex| (((|Integer|) $) 60 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 66 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 48 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) 47 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #6=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #6#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #5# |#1|) $) 37 T ELT)) (|fill!| (($ $ |#1|) 64 T ELT)) (|every?| ((#5# (|Mapping| #5# |#1|) . #7=($)) 42 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#8=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#8# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) 57 T ELT) ((|#1| $ (|Integer|) (|Integer|) |#1|) 55 T ELT)) (|count| ((#9=(|NonNegativeInteger|) (|Mapping| #5# |#1|) $) 41 T ELT) ((#9# |#1| $) 36 (|has| |#1| . #4#) ELT)) (|copy| (($ $) 9 T ELT)) (|column| ((|#3| $ (|Integer|)) 53 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#5# (|Mapping| #5# |#1|) . #7#) 43 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#9# $) 44 T ELT))) 
(((|TwoDimensionalArrayCategory| |#1| |#2| |#3|) (|Category|) (|Type|) (|FiniteLinearAggregate| |t#1|) (|FiniteLinearAggregate| |t#1|)) (T |TwoDimensionalArrayCategory|)) 
((|new| (*1 *1 *2 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|fill!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *3 *4)) (|ofCategory| *2 (|Type|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|minRowIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Integer|)))) (|maxRowIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Integer|)))) (|minColIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Integer|)))) (|maxColIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Integer|)))) (|nrows| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|NonNegativeInteger|)))) (|ncols| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *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)))) (|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 *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| (|FiniteAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|) (CATEGORY |domain| (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 |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| |t#1|) $ $)) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1| |t#1|) $ $ |t#1|)))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) NIL #6=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #7=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#8=(#3# $) NIL #9=(|has| |#1| #10=(|OrderedSet|)) ELT)) (|sort!| (#11=($ #7# $) NIL #6# ELT) (#12=($ $) NIL (AND #6# #9#) ELT)) (|sort| (#11# NIL T ELT) (#12# NIL #9# ELT)) (|setelt| #13=(#14=(|#1| $ #5# |#1|) NIL #6# ELT) ((|#1| $ #15=(|UniversalSegment| #5#) |#1|) NIL #6# ELT)) (|select| #16=(($ #17=(|Mapping| #3# |#1|) $) NIL #18=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#19=($) NIL T CONST)) (|reverse!| (#12# NIL #6# ELT)) (|reverse| #20=(#12# NIL T ELT)) (|removeDuplicates| (#12# NIL #21=(AND #18# #4#) ELT)) (|remove| (#22=($ |#1| $) NIL #21# ELT) #16#) (|reduce| ((|#1| #23=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #23# $ |#1|) NIL T ELT) ((|#1| #23# $) NIL T ELT)) (|qsetelt!| #13#) (|qelt| #24=((|#1| $ #5#) NIL T ELT)) (|position| ((#5# #17# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT) ((#5# |#1| $ #5#) NIL #4# ELT)) (|oneDimensionalArray| (#25=($ #26=(|List| |#1|)) 11 T ELT) (#27=($ #28=(|NonNegativeInteger|) |#1|) 14 T ELT)) (|new| (#27# 13 T ELT)) (|minIndex| #29=((#5# $) NIL #30=(|has| #5# #10#) ELT)) (|min| #31=(#32=($ $ $) NIL #9# ELT)) (|merge| (($ #7# $ $) NIL T ELT) #31#) (|members| #33=((#26# $) NIL T ELT)) (|member?| (#34=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| #29#) (|max| #31#) (|map!| #35=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #35# (($ #23# $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #36=(|has| |#1| (|SetCategory|)) ELT)) (|insert| (($ |#1| $ #5#) NIL T ELT) (#37=($ $ $ #5#) NIL T ELT)) (|indices| (((|List| #5#) $) NIL T ELT)) (|index?| ((#3# #5# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #36# ELT)) (|first| ((|#1| $) NIL #30# ELT)) (|find| (((|Union| |#1| "failed") #17# $) NIL T ELT)) (|fill!| (#38=($ $ |#1|) NIL #6# ELT)) (|every?| #39=((#3# #17# $) NIL T ELT)) (|eval| (($ $ (|List| #40=(|Equation| |#1|))) NIL #41=(AND (|has| |#1| (|Evalable| |#1|)) #36#) ELT) (($ $ #40#) NIL #41# ELT) (($ $ |#1| |#1|) NIL #41# ELT) (($ $ #26# #26#) NIL #41# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#34# NIL #21# ELT)) (|entries| #33#) (|empty?| (#8# NIL T ELT)) (|empty| (#19# NIL T ELT)) (|elt| (#14# NIL T ELT) #24# #42=(($ $ #15#) NIL T ELT)) (|delete| (($ $ #5#) NIL T ELT) #42#) (|count| ((#28# |#1| $) NIL #4# ELT) ((#28# #17# $) NIL T ELT)) (|copyInto!| (#37# NIL #6# ELT)) (|copy| #20#) (|convert| ((#43=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #43#)) ELT)) (|construct| (#25# 10 T ELT)) (|concat| (#38# NIL T ELT) (#22# NIL T ELT) (#32# NIL T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#44=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #44#)) ELT)) (|before?| #1#) (|any?| #39#) (>= #45=(#2# NIL #9# ELT)) (> #45#) (= #1#) (<= #45#) (< #45#) (|#| ((#28# $) NIL T ELT))) 
(((|OneDimensionalArray| |#1|) (|Join| (|OneDimensionalArrayAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |oneDimensionalArray| ($ (|List| |#1|))) (SIGNATURE |oneDimensionalArray| ($ (|NonNegativeInteger|) |#1|)))) (|Type|)) (T |OneDimensionalArray|)) 
((|oneDimensionalArray| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Type|)) #2=(|isDomain| *1 (|OneDimensionalArray| *3)))) (|oneDimensionalArray| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) #2# #1#))) 
((|scan| ((#1=(|OneDimensionalArray| |#2|) #2=(|Mapping| |#2| |#1| |#2|) #3=(|OneDimensionalArray| |#1|) |#2|) 16 T ELT)) (|reduce| ((|#2| #2# #3# |#2|) 18 T ELT)) (|map| ((#1# (|Mapping| |#2| |#1|) #3#) 13 T ELT))) 
(((|OneDimensionalArrayFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |scan| (#1=(|OneDimensionalArray| |#2|) #2=(|Mapping| |#2| |#1| |#2|) #3=(|OneDimensionalArray| |#1|) |#2|)) (SIGNATURE |reduce| (|#2| #2# #3# |#2|)) (SIGNATURE |map| (#1# (|Mapping| |#2| |#1|) #3#))) #4=(|Type|) #4#) (T |OneDimensionalArrayFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) #1=(|isDomain| *4 #2=(|OneDimensionalArray| *5)) #3=(|ofCategory| *5 #4=(|Type|)) #5=(|ofCategory| *6 #4#) (|isDomain| *2 #6=(|OneDimensionalArray| *6)) (|isDomain| *1 (|OneDimensionalArrayFunctions2| *5 *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #1# #3# (|ofCategory| *2 #4#) (|isDomain| *1 (|OneDimensionalArrayFunctions2| *5 *2)))) (|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) (|isDomain| *4 #6#) #5# #3# (|isDomain| *2 #2#) (|isDomain| *1 (|OneDimensionalArrayFunctions2| *6 *5))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|setelt| #5=((|#1| $ #6=(|Integer|) #6# |#1|) NIL T ELT)) (|setRow!| #7=(($ $ #6# #8=(|OneDimensionalArray| |#1|)) NIL T ELT)) (|setColumn!| #7#) (|sample| (#9=($) NIL T CONST)) (|row| #10=((#8# $ #6#) NIL T ELT)) (|reduce| ((|#1| #11=(|Mapping| |#1| |#1| |#1|) $) NIL T ELT) ((|#1| #11# $ |#1|) NIL T ELT) ((|#1| #11# $ |#1| |#1|) NIL #4# ELT)) (|qsetelt!| #5#) (|qelt| #12=((|#1| $ #6# #6#) NIL T ELT)) (|nrows| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT)) (|new| (($ #14# #14# |#1|) NIL T ELT)) (|ncols| #13#) (|minRowIndex| #15=((#6# $) NIL T ELT)) (|minColIndex| #15#) (|members| ((#16=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|maxRowIndex| #15#) (|maxColIndex| #15#) (|map!| #17=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #17# (($ #11# $ $) NIL T ELT) (($ #11# $ $ |#1|) NIL T ELT)) (|latex| (((|String|) $) NIL #18=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) NIL #18# ELT)) (|find| (((|Union| |#1| "failed") #19=(|Mapping| #3# |#1|) $) NIL T ELT)) (|fill!| (($ $ |#1|) NIL T ELT)) (|every?| #20=((#3# #19# $) NIL T ELT)) (|eval| (($ $ (|List| #21=(|Equation| |#1|))) NIL #22=(AND (|has| |#1| (|Evalable| |#1|)) #18#) ELT) (($ $ #21#) NIL #22# ELT) (($ $ |#1| |#1|) NIL #22# ELT) (($ $ #16# #16#) NIL #22# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| (#9# NIL T ELT)) (|elt| #12# #5#) (|count| ((#14# #19# $) NIL T ELT) ((#14# |#1| $) NIL #4# ELT)) (|copy| (($ $) NIL T ELT)) (|column| #10#) (|coerce| ((#23=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #23#)) ELT)) (|before?| #1#) (|any?| #20#) (= #1#) (|#| #13#)) 
(((|TwoDimensionalArray| |#1|) (|TwoDimensionalArrayCategory| |#1| #1=(|OneDimensionalArray| |#1|) #1#) (|Type|)) (T |TwoDimensionalArray|)) 
NIL 
((|uncouplingMatrices| (((|Vector| #1=(|Matrix| |#1|)) #1#) 61 T ELT)) (|associatedSystem| (((|Record| (|:| |mat| #1#) (|:| |vec| (|Vector| #2=(|List| #3=(|PositiveInteger|))))) |#2| #3#) 49 T ELT)) (|associatedEquations| (((|Record| (|:| |minor| #2#) (|:| |eq| |#2|) (|:| |minors| (|List| #2#)) (|:| |ops| (|List| |#2|))) |#2| #3#) 72 (|has| |#1| (|Field|)) ELT))) 
(((|AssociatedEquations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |associatedSystem| ((|Record| (|:| |mat| #1=(|Matrix| |#1|)) (|:| |vec| (|Vector| #2=(|List| #3=(|PositiveInteger|))))) |#2| #3#)) (SIGNATURE |uncouplingMatrices| ((|Vector| #1#) #1#)) (IF (|has| |#1| (|Field|)) (SIGNATURE |associatedEquations| ((|Record| (|:| |minor| #2#) (|:| |eq| |#2|) (|:| |minors| (|List| #2#)) (|:| |ops| (|List| |#2|))) |#2| #3#)) |%noBranch|)) (|IntegralDomain|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |AssociatedEquations|)) 
((|associatedEquations| #1=(*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) #2=(|ofCategory| *5 #3=(|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |minor| #4=(|List| #5=(|PositiveInteger|))) (|:| |eq| *3) (|:| |minors| (|List| #4#)) (|:| |ops| (|List| *3)))) #6=(|isDomain| *1 (|AssociatedEquations| *5 *3)) #7=(|isDomain| *4 #5#) #8=(|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (|uncouplingMatrices| (*1 *2 *3) (AND (|ofCategory| *4 #3#) (|isDomain| *2 (|Vector| #9=(|Matrix| *4))) (|isDomain| *1 (|AssociatedEquations| *4 *5)) (|isDomain| *3 #9#) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *4)))) (|associatedSystem| #1# (AND #2# (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *5)) (|:| |vec| (|Vector| #4#)))) #6# #7# #8#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|top| (#5=(|#1| $) 42 T ELT)) (|sample| (#6=($) NIL T CONST)) (|reduce| ((|#1| #7=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #7# $ |#1|) NIL T ELT) ((|#1| #7# $) NIL T ELT)) (|push!| ((|#1| |#1| $) 37 T ELT)) (|pop!| (#5# 35 T ELT)) (|members| ((#8=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| #9=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #9#) (|latex| (((|String|) $) NIL #10=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#5# NIL T ELT)) (|insert!| (($ |#1| $) 38 T ELT)) (|hash| (((|SingleInteger|) $) NIL #10# ELT)) (|find| (((|Union| |#1| "failed") #11=(|Mapping| #3# |#1|) $) NIL T ELT)) (|extract!| (#5# 36 T ELT)) (|every?| #12=((#3# #11# $) NIL T ELT)) (|eval| (($ $ (|List| #13=(|Equation| |#1|))) NIL #14=(AND (|has| |#1| (|Evalable| |#1|)) #10#) ELT) (($ $ #13#) NIL #14# ELT) (($ $ |#1| |#1|) NIL #14# ELT) (($ $ #8# #8#) NIL #14# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| ((#3# $) 20 T ELT)) (|empty| (#6# 46 T ELT)) (|depth| (#15=(#16=(|NonNegativeInteger|) $) 33 T ELT)) (|count| ((#16# |#1| $) NIL #4# ELT) ((#16# #11# $) NIL T ELT)) (|copy| (($ $) 19 T ELT)) (|coerce| ((#17=(|OutputForm|) $) 32 (|has| |#1| (|CoercibleTo| #17#)) ELT)) (|before?| #1#) (|bag| (#18=($ #8#) NIL T ELT)) (|arrayStack| (#18# 44 T ELT)) (|any?| #12#) (= (#2# 17 #4# ELT)) (|#| (#15# 14 T ELT))) 
(((|ArrayStack| |#1|) (|Join| (|StackAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |arrayStack| ($ (|List| |#1|))))) (|SetCategory|)) (T |ArrayStack|)) 
((|arrayStack| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|ArrayStack| *3))))) 
((|coerce| (((|OutputForm|) $) 13 T ELT) (($ #1=(|Syntax|)) 9 T ELT) ((#1# $) 8 T ELT))) 
(((|AbstractSyntaxCategory&| |#1|) (CATEGORY |package| (SIGNATURE |coerce| (#1=(|Syntax|) |#1|)) (SIGNATURE |coerce| (|#1| #1#)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|AbstractSyntaxCategory|)) (T |AbstractSyntaxCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) . #2=($)) 13 T ELT) (($ #3=(|Syntax|)) 20 T ELT) ((#3# . #2#) 19 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|AbstractSyntaxCategory|) (|Category|)) (T |AbstractSyntaxCategory|)) 
NIL 
(|Join| (|SetCategory|) (|HomotopicTo| (|Syntax|))) 
(((|BasicType|) . T) ((|CoercibleFrom| #1=(|Syntax|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|asec| (#1=($ $) 10 T ELT)) (|acsc| (#1# 12 T ELT))) 
(((|ArcTrigonometricFunctionCategory&| |#1|) (CATEGORY |package| (SIGNATURE |acsc| #1=(|#1| |#1|)) (SIGNATURE |asec| #1#)) (|ArcTrigonometricFunctionCategory|)) (T |ArcTrigonometricFunctionCategory&|)) 
NIL 
((|atan| (($ $) 11 T ELT)) (|asin| (($ $) 10 T ELT)) (|asec| (($ $) 9 T ELT)) (|acsc| (($ $) 8 T ELT)) (|acot| (($ $) 7 T ELT)) (|acos| (($ $) 6 T ELT))) 
(((|ArcTrigonometricFunctionCategory|) (|Category|)) (T |ArcTrigonometricFunctionCategory|)) 
((|atan| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|asin| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|asec| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acsc| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acot| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acos| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |acos| ($ $)) (SIGNATURE |acot| ($ $)) (SIGNATURE |acsc| ($ $)) (SIGNATURE |asec| ($ $)) (SIGNATURE |asin| ($ $)) (SIGNATURE |atan| ($ $)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|name| (((|SpadAst|) $) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|AttributeAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |name| ((|SpadAst|) $))))) (T |AttributeAst|)) 
((|name| (*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|AttributeAst|))))) 
NIL 
(((|AttributeRegistry|) (|Category|)) (T |AttributeRegistry|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE (|commutative| "*")) (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|))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|one?| ((#3# $) NIL T ELT)) (|morphism| (($ #5=(|Mapping| |#1| |#1|)) 27 T ELT) (($ #5# #5#) 26 T ELT) (($ (|Mapping| |#1| |#1| #6=(|Integer|))) 24 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (($ $) 16 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ |#1|) 13 T ELT)) (|conjugate| #7=(#8=($ $ $) NIL T ELT)) (|commutator| #7#) (|coerce| (((|OutputForm|) $) 22 T ELT)) (|before?| #1#) (|One| (#4# 8 T CONST)) (= (#2# 10 T ELT)) (/ #7#) (** (($ $ (|PositiveInteger|)) 30 T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ #6#) 18 T ELT)) (* (#8# 31 T ELT))) 
(((|Automorphism| |#1|) (|Join| (|Group|) (|Eltable| |#1| |#1|) (CATEGORY |domain| (SIGNATURE |morphism| ($ #1=(|Mapping| |#1| |#1|))) (SIGNATURE |morphism| ($ #1# #1#)) (SIGNATURE |morphism| ($ (|Mapping| |#1| |#1| (|Integer|)))))) (|Ring|)) (T |Automorphism|)) 
((|morphism| #1=(*1 *1 *2) #2=(AND (|isDomain| *2 (|Mapping| *3 *3)) #3=(|ofCategory| *3 (|Ring|)) #4=(|isDomain| *1 (|Automorphism| *3)))) (|morphism| (*1 *1 *2 *2) #2#) (|morphism| #1# (AND (|isDomain| *2 (|Mapping| *3 *3 (|Integer|))) #3# #4#))) 
((|balancedFactorisation| ((#1=(|Factored| |#2|) |#2| (|List| |#2|)) 10 T ELT) ((#1# |#2| |#2|) 11 T ELT))) 
(((|BalancedFactorisation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |balancedFactorisation| (#1=(|Factored| |#2|) |#2| |#2|)) (SIGNATURE |balancedFactorisation| (#1# |#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 #1=(|Join| (|GcdDomain|) (|CharacteristicZero|))) #2=(|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|BalancedFactorisation| *5 *3)))) (|balancedFactorisation| (*1 *2 *3 *3) (AND (|ofCategory| *4 #1#) #2# (|isDomain| *1 (|BalancedFactorisation| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
((~= (#1=((|Boolean|) $ $) 13 T ELT)) (|before?| (#1# 14 T ELT)) (= (#1# 11 T ELT))) 
(((|BasicType&| |#1|) (CATEGORY |package| (SIGNATURE |before?| #1=((|Boolean|) |#1| |#1|)) (SIGNATURE ~= #1#) (SIGNATURE = #1#)) (|BasicType|)) (T |BasicType&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|BasicType|) (|Category|)) (T |BasicType|)) 
((= #1=(*1 *2 *1 *1) #2=(AND (|ofCategory| *1 (|BasicType|)) (|isDomain| *2 (|Boolean|)))) (~= #1# #2#) (|before?| #1# #2#)) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE = #1=((|Boolean|) $ $)) (SIGNATURE ~= #1#) (SIGNATURE |before?| #1#))) 
(((|Join|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) NIL T ELT)) (|setvalue!| ((|#1| $ |#1|) 24 #5=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| #6=(($ $ $) NIL #5# ELT)) (|setleft!| #6#) (|setleaves!| (($ $ #7=(|List| |#1|)) 30 T ELT)) (|setelt| ((|#1| $ #8="value" |#1|) NIL #5# ELT) (($ $ #9="left" $) NIL #5# ELT) (($ $ #10="right" $) NIL #5# ELT)) (|setchildren!| (($ $ #11=(|List| $)) NIL #5# ELT)) (|sample| (#12=($) NIL T CONST)) (|right| (#13=($ $) 12 T ELT)) (|reduce| ((|#1| #14=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #14# $ |#1|) NIL T ELT) ((|#1| #14# $) NIL T ELT)) (|nodes| #15=((#11# $) NIL T ELT)) (|node?| #1#) (|node| (($ $ |#1| $) 32 T ELT)) (|members| #16=((#7# $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|mapUp!| ((|#1| $ #14#) 40 T ELT) (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) 45 T ELT)) (|mapDown!| (($ $ |#1| #14#) 46 T ELT) (($ $ |#1| (|Mapping| #7# |#1| |#1| |#1|)) 49 T ELT)) (|map!| #17=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #17#) (|left| (#13# 11 T ELT)) (|leaves| #16#) (|leaf?| (#18=(#3# $) 13 T ELT)) (|latex| (((|String|) $) NIL #19=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) NIL #19# ELT)) (|find| (((|Union| |#1| "failed") #20=(|Mapping| #3# |#1|) $) NIL T ELT)) (|every?| #21=((#3# #20# $) NIL T ELT)) (|eval| (($ $ (|List| #22=(|Equation| |#1|))) NIL #23=(AND (|has| |#1| (|Evalable| |#1|)) #19#) ELT) (($ $ #22#) NIL #23# ELT) (($ $ |#1| |#1|) NIL #23# ELT) (($ $ #7# #7#) NIL #23# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| (#18# 9 T ELT)) (|empty| (#12# 31 T ELT)) (|elt| ((|#1| $ #8#) NIL T ELT) (($ $ #9#) NIL T ELT) (($ $ #10#) NIL T ELT)) (|distance| (((|Integer|) $ $) NIL T ELT)) (|cyclic?| (#18# NIL T ELT)) (|count| ((#24=(|NonNegativeInteger|) |#1| $) NIL #4# ELT) ((#24# #20# $) NIL T ELT)) (|copy| (#13# NIL T ELT)) (|coerce| ((#25=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #25#)) ELT)) (|children| #15#) (|child?| #1#) (|before?| #1#) (|balancedBinaryTree| (($ #24# |#1|) 33 T ELT)) (|any?| #21#) (= #1#) (|#| ((#24# $) NIL T ELT))) 
(((|BalancedBinaryTree| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |balancedBinaryTree| ($ (|NonNegativeInteger|) |#1|)) (SIGNATURE |setleaves!| ($ $ #1=(|List| |#1|))) (SIGNATURE |mapUp!| (|#1| $ #2=(|Mapping| |#1| |#1| |#1|))) (SIGNATURE |mapUp!| ($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|))) (SIGNATURE |mapDown!| ($ $ |#1| #2#)) (SIGNATURE |mapDown!| ($ $ |#1| (|Mapping| #1# |#1| |#1| |#1|))))) (|SetCategory|)) (T |BalancedBinaryTree|)) 
((|balancedBinaryTree| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) #1=(|isDomain| *1 (|BalancedBinaryTree| *3)) #2=(|ofCategory| *3 #3=(|SetCategory|)))) (|setleaves!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #2# #1#)) (|mapUp!| (*1 *2 *1 *3) (AND #4=(|isDomain| *3 (|Mapping| *2 *2 *2)) #5=(|isDomain| *1 (|BalancedBinaryTree| *2)) #6=(|ofCategory| *2 #3#))) (|mapUp!| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3 *3 *3 *3)) #2# #1#)) (|mapDown!| #7=(*1 *1 *1 *2 *3) (AND #4# #6# #5#)) (|mapDown!| #7# (AND (|isDomain| *3 (|Mapping| (|List| *2) *2 *2 *2)) #6# #5#))) 
((|sylvesterMatrix| (#1=(|#3| |#2| |#2|) 34 T ELT)) (|bezoutResultant| ((|#1| |#2| |#2|) 46 #2=(|has| |#1| (ATTRIBUTE (|commutative| "*"))) ELT)) (|bezoutMatrix| (#1# 36 T ELT)) (|bezoutDiscriminant| ((|#1| |#2|) 53 #2# ELT))) 
(((|BezoutMatrix| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |sylvesterMatrix| #1=(|#3| |#2| |#2|)) (SIGNATURE |bezoutMatrix| #1#) (IF (|has| |#1| (ATTRIBUTE (|commutative| "*"))) (PROGN (SIGNATURE |bezoutResultant| (|#1| |#2| |#2|)) (SIGNATURE |bezoutDiscriminant| (|#1| |#2|))) |%noBranch|)) (|Ring|) (|UnivariatePolynomialCategory| |#1|) (|MatrixCategory| |#1| |#4| |#5|) #2=(|FiniteLinearAggregate| |#1|) #2#) (T |BezoutMatrix|)) 
((|bezoutDiscriminant| (*1 *2 *3) #1=(AND (|has| *2 (ATTRIBUTE (|commutative| "*"))) (|ofCategory| *5 #2=(|FiniteLinearAggregate| *2)) (|ofCategory| *6 #2#) (|ofCategory| *2 #3=(|Ring|)) (|isDomain| *1 (|BezoutMatrix| *2 *3 *4 *5 *6)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|MatrixCategory| *2 *5 *6)))) (|bezoutResultant| #4=(*1 *2 *3 *3) #1#) (|bezoutMatrix| #4# #5=(AND (|ofCategory| *4 #3#) (|ofCategory| *2 (|MatrixCategory| *4 *5 *6)) (|isDomain| *1 (|BezoutMatrix| *4 *3 *2 *5 *6)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 #6=(|FiniteLinearAggregate| *4)) (|ofCategory| *6 #6#))) (|sylvesterMatrix| #4# #5#)) 
((|bag| (($ (|List| |#2|)) 11 T ELT))) 
(((|BagAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |bag| (|#1| (|List| |#2|)))) (|BagAggregate| |#2|) (|Type|)) (T |BagAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|sample| (#3=($) 6 T CONST)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #4=((|SetCategory|))) ELT)) (|inspect| ((|#1| $) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #4#) ELT)) (|extract!| ((|#1| $) 37 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT)) (|eq?| ((#5=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#5# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|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|) (|ShallowlyMutableAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |bag| ($ (|List| |t#1|))) (SIGNATURE |extract!| (|t#1| $)) (SIGNATURE |insert!| ($ |t#1| $)) (SIGNATURE |inspect| (|t#1| $)))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#6# NIL #19=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (#22=((|Union| #7# . #23=(#13#)) . #24=($)) NIL T ELT) (((|Union| #25=(|Symbol|) . #23#) . #24#) NIL #26=(|has| #7# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #7#) . #23#) . #24#) NIL #28=(|has| #7# (|RetractableTo| #7#)) ELT) (#22# NIL #28# ELT)) (|retract| #29=(#6# NIL T ELT) ((#25# $) NIL #26# ELT) (#30=(#27# $) NIL #28# ELT) (#6# NIL #28# ELT)) (|rem| #31=(#32=($ $ $) NIL T ELT)) (|reducedSystem| (#33=(#34=(|Matrix| #7#) #35=(|Matrix| $)) NIL #36=(|has| #7# (|LinearlyExplicitRingOver| #7#)) ELT) (#37=(#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #7#))) #35# #39=(|Vector| $)) NIL #36# ELT) (#37# NIL T ELT) (#33# NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#21# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #31#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #19# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #29#) (|nextItem| (#50=((|Maybe| $) $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #13#) #41# $) NIL T ELT)) (|min| #52=(#32# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#34# #39#) NIL #36# ELT) (#56=(#38# #39# $) NIL #36# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #31# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#21# NIL #51# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #31# #57#) (|fractionPart| (#10# NIL #8# ELT) #58=(#30# NIL T ELT)) (|floor| #59=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #60=(|:| |coef1| $) #61=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #60# #61#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #62=(|List| #7#) #62#) NIL #63=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #63# ELT) (($ $ #64=(|Equation| #7#)) NIL #63# ELT) (($ $ (|List| #64#)) NIL #63# ELT) (($ $ #65=(|List| #25#) #62#) NIL #66=(|has| #7# (|InnerEvalable| #25# #7#)) ELT) (($ $ #25# #7#) NIL #66# ELT)) (|euclideanSize| ((#67=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#68=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #69=(($ $ #54#) NIL T ELT) #70=(($ $ #54# #67#) NIL T ELT) #71=(($ $ #25#) NIL #72=(|has| #7# (|PartialDifferentialSpace| #25#)) ELT) #73=(($ $ #65#) NIL #72# ELT) #74=(($ $ #25# #67#) NIL #72# ELT) #75=(($ $ #65# (|List| #67#)) NIL #72# ELT) #76=(#10# NIL #77=(|has| #7# (|DifferentialSpace|)) ELT) #78=(#79=($ $ #67#) NIL #77# ELT)) (|denominator| #9#) (|denom| #29#) (|convert| ((#46# . #80=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #80#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#81=(|InputForm|) . #80#) NIL (|has| #7# (|ConvertibleTo| #81#)) ELT) ((#48# . #80#) NIL #82=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #80#) NIL #82# ELT)) (|conditionP| (((|Union| #39# #13#) #35#) NIL #83=(AND (|has| $ #84=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #85=(($ #7#) NIL T ELT) #9# (#86=($ #27#) 8 T ELT) #85# (($ #25#) NIL #26# ELT) #58# (((|RadixExpansion| 2) $) 10 T ELT)) (|charthRoot| (#50# NIL (OR #83# (|has| #7# #84#)) ELT)) (|characteristic| ((#67#) NIL T CONST)) (|ceiling| #59#) (|binary| (#86# 9 T ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#10# NIL #19# ELT)) (|Zero| #20#) (|One| #20#) (D #69# #70# #71# #73# #74# #75# #76# #78#) (>= #87=(#2# NIL #53# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ #31# (($ #7# #7#) NIL T ELT)) (- #9# #31#) (+ #31#) (** (($ $ #88=(|PositiveInteger|)) NIL T ELT) (#79# NIL T ELT) #89=(#68# NIL T ELT)) (* (($ #88# $) NIL T ELT) (($ #67# $) NIL T ELT) #90=(($ #7# . #91=($)) NIL T ELT) #31# (($ $ #27#) NIL T ELT) (($ #27# . #91#) NIL T ELT) #90# #89#)) 
(((|BinaryExpansion|) (|Join| (|QuotientFieldCategory| #1=(|Integer|)) (|CoercibleTo| #2=(|Fraction| #1#)) (|CoercibleTo| (|RadixExpansion| 2)) (CATEGORY |domain| (SIGNATURE |fractionPart| (#2# $)) (SIGNATURE |binary| ($ #2#))))) (T |BinaryExpansion|)) 
((|fractionPart| (*1 *2 *1) #1=(AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|BinaryExpansion|)))) (|binary| (*1 *1 *2) #1#)) 
((|properties| ((#1=(|List| (|Property|)) $) 14 T ELT)) (|name| ((#2=(|Identifier|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT)) (|binding| (($ #2# #1#) 16 T ELT))) 
(((|Binding|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |name| (#1=(|Identifier|) $)) (SIGNATURE |properties| (#2=(|List| (|Property|)) $)) (SIGNATURE |binding| ($ #1# #2#))))) (T |Binding|)) 
((|name| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Identifier|)) #3=(|isDomain| *1 (|Binding|)))) (|properties| #1# (AND (|isDomain| *2 #4=(|List| (|Property|))) #3#)) (|binding| (*1 *1 *2 *3) (AND #2# (|isDomain| *3 #4#) #3#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ |#1| |#1|) 8 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|binaryOperation| (($ (|Mapping| |#1| |#1| |#1|)) 7 T ELT)) (|before?| #1#) (= #1#)) 
(((|BinaryOperation| |#1|) (|Join| (|BinaryOperatorCategory| |#1|) (|SetCategory|) (CATEGORY |domain| (SIGNATURE |binaryOperation| ($ (|Mapping| |#1| |#1| |#1|))))) (|Type|)) (T |BinaryOperation|)) 
((|binaryOperation| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|BinaryOperation| *3))))) 
((|elt| ((|#1| $ |#1| |#1|) 6 T ELT))) 
(((|BinaryOperatorCategory| |#1|) (|Category|) (|Type|)) (T |BinaryOperatorCategory|)) 
NIL 
(|Join| (|MappingCategory| |t#1| |t#1| |t#1|)) 
(((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . T)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (~ #3=(#4=($ $) NIL T ELT)) (|xor| #5=(#6=($ $ $) NIL T ELT)) (|swap!| (((|Void|) $ #7=(|Integer|) #7#) NIL #8=(|has| $ (|ShallowlyMutableAggregate| #2#)) ELT)) (|sorted?| (#9=(#2# $) NIL #10=(|has| #2# #11=(|OrderedSet|)) ELT) #12=((#2# #13=(|Mapping| #2# #2# #2#) $) NIL T ELT)) (|sort!| (#4# NIL (AND #8# #10#) ELT) (#14=($ #13# $) NIL #8# ELT)) (|sort| (#4# NIL #10# ELT) (#14# NIL T ELT)) (|setelt| ((#2# $ #15=(|UniversalSegment| #7#) #2#) NIL #8# ELT) #16=(#17=(#2# $ #7# #2#) NIL #8# ELT)) (|select| #18=(#19=($ #20=(|Mapping| #2# #2#) $) NIL #21=(|has| $ (|FiniteAggregate| #2#)) ELT)) (|sample| (#22=($) NIL T CONST)) (|reverse!| (#4# NIL #8# ELT)) (|reverse| #3#) (|removeDuplicates| (#4# NIL #23=(AND #21# #24=(|has| #2# (|BasicType|))) ELT)) (|remove| #18# (#25=($ #2# $) NIL #23# ELT)) (|reduce| #12# ((#2# #13# $ #2#) NIL T ELT) ((#2# #13# $ #2# #2#) NIL #24# ELT)) (|qsetelt!| #16#) (|qelt| #26=((#2# $ #7#) NIL T ELT)) (|position| ((#7# #2# $ #7#) NIL #24# ELT) ((#7# #2# $) NIL #24# ELT) ((#7# #20# $) NIL T ELT)) (|or| #5#) (|not| #3#) (|nor| #5#) (|new| (#27=($ #28=(|NonNegativeInteger|) #2#) 10 T ELT)) (|nand| #5#) (|minIndex| #29=((#7# $) NIL #30=(|has| #7# #11#) ELT)) (|min| #5#) (|merge| (#6# NIL #10# ELT) #31=(($ #13# $ $) NIL T ELT)) (|members| #32=((#33=(|List| #2#) $) NIL T ELT)) (|member?| (#34=(#2# #2# $) NIL #24# ELT)) (|maxIndex| #29#) (|max| #5#) (|map!| #35=(#19# NIL T ELT)) (|map| #31# #35#) (|latex| (((|String|) $) NIL T ELT)) (|insert| (#36=($ $ $ #7#) NIL T ELT) (($ #2# $ #7#) NIL T ELT)) (|indices| (((|List| #7#) $) NIL T ELT)) (|index?| ((#2# #7# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#9# NIL #30# ELT)) (|find| (((|Union| #2# "failed") #20# $) NIL T ELT)) (|fill!| (#37=($ $ #2#) NIL #8# ELT)) (|every?| #38=((#2# #20# $) NIL T ELT)) (|eval| (($ $ #33# #33#) NIL #39=(AND (|has| #2# (|Evalable| #2#)) (|has| #2# (|SetCategory|))) ELT) (($ $ #2# #2#) NIL #39# ELT) (($ $ #40=(|Equation| #2#)) NIL #39# ELT) (($ $ (|List| #40#)) NIL #39# ELT)) (|eq?| #1#) (|entry?| (#34# NIL #23# ELT)) (|entries| #32#) (|empty?| (#9# NIL T ELT)) (|empty| (#22# NIL T ELT)) (|elt| #41=(($ $ #15#) NIL T ELT) #26# (#17# NIL T ELT)) (|delete| #41# (($ $ #7#) NIL T ELT)) (|count| ((#28# #20# $) NIL T ELT) ((#28# #2# $) NIL #24# ELT)) (|copyInto!| (#36# NIL #8# ELT)) (|copy| #3#) (|convert| ((#42=(|InputForm|) $) NIL (|has| #2# (|ConvertibleTo| #42#)) ELT)) (|construct| (($ #33#) NIL T ELT)) (|concat| (($ (|List| $)) NIL T ELT) #5# (#25# NIL T ELT) (#37# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|bits| (#27# 11 T ELT)) (|before?| #1#) (|any?| #38#) (|and| #5#) (|\\/| #5#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (|/\\| #5#) (|#| ((#28# $) NIL T ELT))) 
(((|Bits|) (|Join| (|BitAggregate|) (CATEGORY |domain| (SIGNATURE |bits| ($ (|NonNegativeInteger|) (|Boolean|)))))) (T |Bits|)) 
((|bits| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Boolean|)) (|isDomain| *1 (|Bits|))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT) (($ $ |#2|) 37 T ELT))) 
(((|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) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|or| (#1=($ $ $) 12 T ELT)) (|not| (($ $) 8 T ELT)) (|and| (#1# 10 T ELT))) 
(((|BooleanLogic&| |#1|) (CATEGORY |package| (SIGNATURE |or| #1=(|#1| |#1| |#1|)) (SIGNATURE |and| #1#) (SIGNATURE |not| (|#1| |#1|))) (|BooleanLogic|)) (T |BooleanLogic&|)) 
NIL 
((~ (($ $) 8 T ELT)) (|or| (($ $ $) 9 T ELT)) (|not| (($ $) 11 T ELT)) (|and| (($ $ $) 10 T ELT)) (|\\/| (#1=($ $ $) 6 T ELT)) (|/\\| (#1# 7 T ELT))) 
(((|BooleanLogic|) (|Category|)) (T |BooleanLogic|)) 
((|not| (*1 *1 *1) (|ofCategory| *1 (|BooleanLogic|))) (|and| (*1 *1 *1 *1) (|ofCategory| *1 (|BooleanLogic|))) (|or| (*1 *1 *1 *1) (|ofCategory| *1 (|BooleanLogic|)))) 
(|Join| (|Logic|) (CATEGORY |domain| (SIGNATURE |not| ($ $)) (SIGNATURE |and| ($ $ $)) (SIGNATURE |or| ($ $ $)))) 
(((|Join|) . T) ((|Logic|) . T) ((|Type|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (~ (#3=($ $) 9 T ELT)) (|xor| (#4=($ $ $) 14 T ELT)) (|true| (#5=($) 6 T CONST)) (|size| (((|NonNegativeInteger|)) 23 T ELT)) (|random| (#5# 31 T ELT)) (|or| (#4# 12 T ELT)) (|not| (#3# 8 T ELT)) (|nor| (#4# 15 T ELT)) (|nand| (#4# 16 T ELT)) (|min| #6=(#4# NIL T ELT) #7=(#5# NIL T CONST)) (|max| #6# #7#) (|lookup| ((#8=(|PositiveInteger|) $) 29 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #8#) 27 T ELT)) (|implies| (#4# 19 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|false| (#5# 7 T CONST)) (|equiv| (#4# 20 T ELT)) (|convert| (((|InputForm|) $) 33 T ELT)) (|coerce| (((|OutputForm|) $) 35 T ELT)) (|before?| #1#) (|and| (#4# 10 T ELT)) (|\\/| (#4# 13 T ELT)) (>= #1#) (> #1#) (= (#2# 18 T ELT)) (<= #1#) (< (#2# 21 T ELT)) (|/\\| (#4# 11 T ELT))) 
(((|Boolean|) (|Join| (|OrderedFinite|) (|PropositionalLogic|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |xor| #1=($ $ $)) (SIGNATURE |nand| #1#) (SIGNATURE |nor| #1#)))) (T |Boolean|)) 
((|xor| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|Boolean|))) (|nand| #1# #2#) (|nor| #1# #2#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|weight| ((#4=(|NonNegativeInteger|) $) 92 T ELT) (($ $ #4#) 38 T ELT)) (|unary?| (#5=(#3# $) 42 T ELT)) (|setProperty| (($ $ #6=(|String|) #7=(|None|)) 59 T ELT) (($ $ #8=(|Identifier|) #7#) 34 T ELT)) (|setProperties| (($ $ #9=(|AssociationList| #6# #7#)) 16 T ELT)) (|property| (((|Union| #7# "failed") $ #6#) 27 T ELT) (((|Maybe| #7#) $ #8#) 33 T ELT)) (|properties| ((#9# $) 15 T ELT)) (|operator| (($ #10=(|Symbol|)) 20 T ELT) (($ #10# #4#) 23 T ELT) (($ #10# #11=(|Arity|)) 24 T ELT)) (|nullary?| (#5# 40 T ELT)) (|nary?| (#5# 44 T ELT)) (|name| ((#10# $) 8 T ELT)) (|min| #12=(($ $ $) NIL T ELT)) (|max| #12#) (|latex| ((#6# $) NIL T ELT)) (|is?| ((#3# $ #10#) 11 T ELT)) (|input| (($ $ #13=(|Mapping| #14=(|InputForm|) (|List| #14#))) 65 T ELT) (((|Maybe| #13#) $) 69 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|has?| ((#3# $ #8#) 37 T ELT)) (|equality| (#15=($ $ (|Mapping| #3# $ $)) 46 T ELT)) (|display| (((|Maybe| #16=(|Mapping| #17=(|OutputForm|) (|List| #17#))) $) 67 T ELT) (($ $ #16#) 52 T ELT) (($ $ (|Mapping| #17# #17#)) 54 T ELT)) (|deleteProperty!| (($ $ #6#) 56 T ELT) (#18=($ $ #8#) 57 T ELT)) (|copy| (($ $) 75 T ELT)) (|comparison| (#15# 47 T ELT)) (|coerce| ((#17# $) 61 T ELT)) (|before?| #1#) (|assert| (#18# 35 T ELT)) (|arity| ((#11# $) 70 T ELT)) (>= #1#) (> #1#) (= (#2# 88 T ELT)) (<= #1#) (< (#2# 104 T ELT))) 
(((|BasicOperator|) (|Join| (|OrderedSet|) (|OperatorCategory| #1=(|Symbol|)) (CATEGORY |domain| (SIGNATURE |properties| (#2=(|AssociationList| #3=(|String|) #4=(|None|)) $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |operator| ($ #1#)) (SIGNATURE |operator| ($ #1# #5=(|NonNegativeInteger|))) (SIGNATURE |operator| ($ #1# (|Arity|))) (SIGNATURE |nullary?| #6=(#7=(|Boolean|) $)) (SIGNATURE |unary?| #6#) (SIGNATURE |nary?| #6#) (SIGNATURE |weight| (#5# $)) (SIGNATURE |weight| ($ $ #5#)) (SIGNATURE |equality| #8=($ $ (|Mapping| #7# $ $))) (SIGNATURE |comparison| #8#) (SIGNATURE |display| ((|Maybe| #9=(|Mapping| #10=(|OutputForm|) (|List| #10#))) $)) (SIGNATURE |display| ($ $ #9#)) (SIGNATURE |display| ($ $ (|Mapping| #10# #10#))) (SIGNATURE |input| ($ $ #11=(|Mapping| #12=(|InputForm|) (|List| #12#)))) (SIGNATURE |input| ((|Maybe| #11#) $)) (SIGNATURE |has?| (#7# $ #13=(|Identifier|))) (SIGNATURE |assert| #14=($ $ #13#)) (SIGNATURE |deleteProperty!| ($ $ #3#)) (SIGNATURE |deleteProperty!| #14#) (SIGNATURE |property| ((|Union| #4# "failed") $ #3#)) (SIGNATURE |property| ((|Maybe| #4#) $ #13#)) (SIGNATURE |setProperty| ($ $ #3# #4#)) (SIGNATURE |setProperty| ($ $ #13# #4#)) (SIGNATURE |setProperties| ($ $ #2#))))) (T |BasicOperator|)) 
((|properties| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|AssociationList| #3=(|String|) #4=(|None|))) #5=(|isDomain| *1 #6=(|BasicOperator|)))) (|copy| (*1 *1 *1) #5#) (|operator| (*1 *1 *2) (AND #7=(|isDomain| *2 (|Symbol|)) #5#)) (|operator| #8=(*1 *1 *2 *3) (AND #7# (|isDomain| *3 #9=(|NonNegativeInteger|)) #5#)) (|operator| #8# (AND #7# (|isDomain| *3 (|Arity|)) #5#)) (|nullary?| #1# #10=(AND #11=(|isDomain| *2 #12=(|Boolean|)) #5#)) (|unary?| #1# #10#) (|nary?| #1# #10#) (|weight| #1# #13=(AND (|isDomain| *2 #9#) #5#)) (|weight| #14=(*1 *1 *1 *2) #13#) (|equality| #14# #15=(AND (|isDomain| *2 (|Mapping| #12# #6# #6#)) #5#)) (|comparison| #14# #15#) (|display| #1# (AND (|isDomain| *2 (|Maybe| #16=(|Mapping| #17=(|OutputForm|) (|List| #17#)))) #5#)) (|display| #14# (AND (|isDomain| *2 #16#) #5#)) (|display| #14# (AND (|isDomain| *2 (|Mapping| #17# #17#)) #5#)) (|input| #14# (AND (|isDomain| *2 #18=(|Mapping| #19=(|InputForm|) (|List| #19#))) #5#)) (|input| #1# (AND (|isDomain| *2 (|Maybe| #18#)) #5#)) (|has?| #20=(*1 *2 *1 *3) (AND #21=(|isDomain| *3 #22=(|Identifier|)) #11# #5#)) (|assert| #14# #23=(AND #24=(|isDomain| *2 #22#) #5#)) (|deleteProperty!| #14# (AND #25=(|isDomain| *2 #3#) #5#)) (|deleteProperty!| #14# #23#) (|property| #20# (|partial| AND (|isDomain| *3 #3#) (|isDomain| *2 #4#) #5#)) (|property| #20# (AND #21# (|isDomain| *2 (|Maybe| #4#)) #5#)) (|setProperty| #26=(*1 *1 *1 *2 *3) (AND #25# #27=(|isDomain| *3 #4#) #5#)) (|setProperty| #26# (AND #24# #27# #5#)) (|setProperties| #14# #2#)) 
((|evaluate| (((|Union| #1=(|Mapping| |#1| #2=(|List| |#1|)) #3="failed") #4=(|BasicOperator|)) 23 T ELT) (#5=(#4# #4# (|Mapping| |#1| |#1|)) 13 T ELT) ((#4# #4# #1#) 11 T ELT) ((#6=(|Union| |#1| #3#) #4# #2#) 25 T ELT)) (|derivative| (((|Union| #7=(|List| #1#) #3#) #4#) 29 T ELT) (#5# 33 T ELT) ((#4# #4# #7#) 30 T ELT)) (|constantOperator| ((#4# |#1|) 63 T ELT)) (|constantOpIfCan| ((#6# #4#) 58 T ELT))) 
(((|BasicOperatorFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |evaluate| (#1=(|Union| |#1| #2="failed") #3=(|BasicOperator|) #4=(|List| |#1|))) (SIGNATURE |evaluate| (#3# #3# #5=(|Mapping| |#1| #4#))) (SIGNATURE |evaluate| #6=(#3# #3# (|Mapping| |#1| |#1|))) (SIGNATURE |evaluate| ((|Union| #5# #2#) #3#)) (SIGNATURE |derivative| (#3# #3# #7=(|List| #5#))) (SIGNATURE |derivative| #6#) (SIGNATURE |derivative| ((|Union| #7# #2#) #3#)) (SIGNATURE |constantOperator| (#3# |#1|)) (SIGNATURE |constantOpIfCan| (#1# #3#))) (|SetCategory|)) (T |BasicOperatorFunctions1|)) 
((|constantOpIfCan| #1=(*1 *2 *3) (|partial| AND #2=(|isDomain| *3 #3=(|BasicOperator|)) #4=(|isDomain| *1 (|BasicOperatorFunctions1| *2)) #5=(|ofCategory| *2 #6=(|SetCategory|)))) (|constantOperator| #1# (AND #7=(|isDomain| *2 #3#) (|isDomain| *1 (|BasicOperatorFunctions1| *3)) (|ofCategory| *3 #6#))) (|derivative| #1# (|partial| AND #2# (|isDomain| *2 #8=(|List| #9=(|Mapping| *4 (|List| *4)))) #10=(|isDomain| *1 (|BasicOperatorFunctions1| *4)) #11=(|ofCategory| *4 #6#))) (|derivative| #12=(*1 *2 *2 *3) #13=(AND #7# (|isDomain| *3 (|Mapping| *4 *4)) #11# #10#)) (|derivative| #12# (AND #7# (|isDomain| *3 #8#) #11# #10#)) (|evaluate| #1# (|partial| AND #2# (|isDomain| *2 #9#) #10# #11#)) (|evaluate| #12# #13#) (|evaluate| #12# (AND #7# (|isDomain| *3 #9#) #11# #10#)) (|evaluate| (*1 *2 *3 *4) (|partial| AND #2# (|isDomain| *4 (|List| *2)) #4# #5#))) 
((|integerBound| (((|Integer|) |#2|) 41 T ELT))) 
(((|BoundIntegerRoots| |#1| |#2|) (CATEGORY |package| (SIGNATURE |integerBound| (#1=(|Integer|) |#2|))) (|Join| (|Field|) (|RetractableTo| (|Fraction| #1#))) (|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))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| #5=((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|sqrt| #8=(($ $ #9=(|Integer|)) NIL T ELT)) (|sizeLess?| #1#) (|sample| #10=(($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| #9#) #9#) NIL T ELT)) (|rem| #11=(($ $ $) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|quotientByP| #4#) (|quo| #11#) (|principalIdeal| (((|Record| (|:| |coef| #12=(|List| $)) #13=(|:| |generator| $)) #12#) NIL T ELT)) (|order| #14=((#15=(|NonNegativeInteger|) $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #12# #7#) #12# $) NIL T ELT)) (|modulus| ((#9#) NIL T ELT)) (|moduloP| ((#9# $) NIL T ELT)) (|lcm| #11# #16=(($ #12#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#17=(|SparseUnivariatePolynomial| $) #17# #17#) NIL T ELT)) (|gcd| #11# #16#) (|extendedEuclidean| (((|Record| #18=(|:| |coef1| $) #19=(|:| |coef2| $) #13#) $ $) NIL T ELT) (((|Union| (|Record| #18# #19#) #7#) $ $ $) NIL T ELT)) (|extend| #8#) (|exquo| #5#) (|expressIdealMember| (((|Maybe| #12#) #12# $) NIL T ELT)) (|euclideanSize| #14#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (((|Stream| #9#) $) NIL T ELT)) (|complete| #4#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #9#) NIL T ELT) #4#) (|characteristic| ((#15#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| ((#9# $ #9#) NIL T ELT)) (|annihilate?| #1#) (|Zero| #10#) (|One| #10#) (= #1#) (- #4# #11#) (+ #11#) (** (($ $ #20=(|PositiveInteger|)) NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #20# $) NIL T ELT) (($ #15# $) NIL T ELT) (($ #9# $) NIL T ELT) #11#)) 
(((|BalancedPAdicInteger| |#1|) (|PAdicIntegerCategory| |#1|) (|Integer|)) (T |BalancedPAdicInteger|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|BalancedPAdicInteger| |#1|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#19=(#20=(|Integer|) $) NIL #21=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #22=(#23=($) NIL T CONST)) (|retractIfCan| (((|Union| #7# . #24=(#13#)) . #25=($)) NIL T ELT) (((|Union| #26=(|Symbol|) . #24#) . #25#) NIL #27=(|has| #7# (|RetractableTo| #26#)) ELT) (((|Union| #28=(|Fraction| #20#) . #24#) . #25#) NIL #29=(|has| #7# (|RetractableTo| #20#)) ELT) (((|Union| #20# . #24#) . #25#) NIL #29# ELT)) (|retract| #30=(#6# NIL T ELT) ((#26# . #31=($)) NIL #27# ELT) ((#28# . #31#) NIL #29# ELT) (#19# NIL #29# ELT)) (|removeZeroes| #9# #32=(($ #20# $) NIL T ELT)) (|rem| #33=(#34=($ $ $) NIL T ELT)) (|reducedSystem| ((#35=(|Matrix| #20#) . #36=(#37=(|Matrix| $))) NIL #38=(|has| #7# (|LinearlyExplicitRingOver| #20#)) ELT) ((#39=(|Record| (|:| |mat| #35#) (|:| |vec| (|Vector| #20#))) . #40=(#37# #41=(|Vector| $))) NIL #38# ELT) ((#42=(|Record| (|:| |mat| #43=(|Matrix| #7#)) (|:| |vec| (|Vector| #7#))) . #40#) NIL T ELT) ((#43# . #36#) NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#23# NIL #44=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #33#) (|principalIdeal| (((|Record| (|:| |coef| #45=(|List| $)) #46=(|:| |generator| $)) #45#) NIL T ELT)) (|prime?| #4#) (|positive?| #47=(#5# NIL #21# ELT)) (|patternMatch| ((#48=(|PatternMatchResult| #20# . #49=($)) $ #50=(|Pattern| #20#) #48#) NIL (|has| #7# (|PatternMatchable| #20#)) ELT) ((#51=(|PatternMatchResult| #52=(|Float|) . #49#) $ #53=(|Pattern| #52#) #51#) NIL (|has| #7# (|PatternMatchable| #52#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #30#) (|nextItem| (#54=((|Maybe| $) $) NIL #55=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #47#) (|multiEuclidean| (((|Union| #45# #13#) #45# $) NIL T ELT)) (|min| #56=(#34# NIL #57=(|has| #7# (|OrderedSet|)) ELT)) (|max| #56#) (|map| (($ #58=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| ((#35# . #59=(#41#)) NIL #38# ELT) ((#39# . #60=(#41# $)) NIL #38# ELT) ((#42# . #60#) NIL T ELT) ((#43# . #59#) NIL T ELT)) (|lcm| #33# #61=(($ #45#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#23# NIL #55# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #33# #61#) (|fractionPart| (#10# NIL #8# ELT)) (|floor| #62=(#6# NIL #44# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #63=(|:| |coef1| $) #64=(|:| |coef2| $) #46#) $ $) NIL T ELT) (((|Union| (|Record| #63# #64#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #45#) #45# $) NIL T ELT)) (|eval| (($ $ #65=(|List| #7#) #65#) NIL #66=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #66# ELT) (($ $ #67=(|Equation| #7#)) NIL #66# ELT) (($ $ (|List| #67#)) NIL #66# ELT) (($ $ #68=(|List| #26#) #65#) NIL #69=(|has| #7# (|InnerEvalable| #26# #7#)) ELT) (($ $ #26# #7#) NIL #69# ELT)) (|euclideanSize| ((#70=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#71=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #72=(($ $ #58#) NIL T ELT) #73=(($ $ #58# #70#) NIL T ELT) #74=(($ $ #26#) NIL #75=(|has| #7# (|PartialDifferentialSpace| #26#)) ELT) #76=(($ $ #68#) NIL #75# ELT) #77=(($ $ #26# #70#) NIL #75# ELT) #78=(($ $ #68# (|List| #70#)) NIL #75# ELT) #79=(#10# NIL #80=(|has| #7# (|DifferentialSpace|)) ELT) #81=(#82=($ $ #70#) NIL #80# ELT)) (|denominator| #9#) (|denom| #30#) (|convert| ((#50# . #83=($)) NIL (|has| #7# (|ConvertibleTo| #50#)) ELT) ((#53# . #83#) NIL (|has| #7# (|ConvertibleTo| #53#)) ELT) ((#84=(|InputForm|) . #83#) NIL (|has| #7# (|ConvertibleTo| #84#)) ELT) ((#52# . #83#) NIL #85=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #83#) NIL #85# ELT)) (|continuedFraction| (((|ContinuedFraction| #28#) $) NIL T ELT)) (|conditionP| (((|Union| #41# #13#) #37#) NIL #86=(AND (|has| $ #87=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) #9# (($ #28#) NIL T ELT) (($ #7#) NIL T ELT) (($ #26#) NIL #27# ELT)) (|charthRoot| (#54# NIL (OR #86# (|has| #7# #87#)) ELT)) (|characteristic| ((#70#) NIL T CONST)) (|ceiling| #62#) (|before?| #1#) (|associates?| #1#) (|approximate| ((#28# $ #20#) NIL T ELT)) (|annihilate?| #1#) (|abs| (#10# NIL #21# ELT)) (|Zero| #22#) (|One| #22#) (D #72# #73# #74# #76# #77# #78# #79# #81#) (>= #88=(#2# NIL #57# ELT)) (> #88#) (= #1#) (<= #88#) (< #88#) (/ #33# (($ #7# #7#) NIL T ELT)) (- #9# #33#) (+ #33#) (** (($ $ #89=(|PositiveInteger|)) NIL T ELT) (#82# NIL T ELT) (($ $ #20#) NIL T ELT)) (* (($ #89# $) NIL T ELT) (($ #70# $) NIL T ELT) #32# #33# (($ $ #28#) NIL T ELT) (($ #28# . #90=($)) NIL T ELT) (($ #7# . #90#) NIL T ELT) (#71# NIL T ELT))) 
(((|BalancedPAdicRational| |#1|) (|Join| (|QuotientFieldCategory| (|BalancedPAdicInteger| |#1|)) (CATEGORY |domain| (SIGNATURE |approximate| (#1=(|Fraction| #2=(|Integer|)) $ #2#)) (SIGNATURE |continuedFraction| ((|ContinuedFraction| #1#) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ #2# $)))) #2#) (T |BalancedPAdicRational|)) 
((|approximate| (*1 *2 *1 *3) (AND (|isDomain| *2 #1=(|Fraction| #2=(|Integer|))) (|isDomain| *1 (|BalancedPAdicRational| *4)) (|ofType| *4 *3) (|isDomain| *3 #2#))) (|continuedFraction| (*1 *2 *1) (AND (|isDomain| *2 (|ContinuedFraction| #1#)) #3=(|isDomain| *1 (|BalancedPAdicRational| *3)) (|ofType| *3 #2#))) (|removeZeroes| (*1 *1 *1) (AND (|isDomain| *1 (|BalancedPAdicRational| *2)) (|ofType| *2 #2#))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 #2#) #3# (|ofType| *3 *2)))) 
((|setelt| ((|#2| $ #1="value" |#2|) NIL T ELT) (($ $ #2="left" $) 59 T ELT) (($ $ #3="right" $) 61 T ELT)) (|nodes| (#4=((|List| $) $) 31 T ELT)) (|node?| (#5=(#6=(|Boolean|) $ $) 36 T ELT)) (|leaves| (((|List| |#2|) $) 25 T ELT)) (|leaf?| (#7=(#6# $) 18 T ELT)) (|elt| ((|#2| $ #1#) NIL T ELT) (($ $ #2#) 10 T ELT) (($ $ #3#) 13 T ELT)) (|cyclic?| (#7# 55 T ELT)) (|coerce| (((|OutputForm|) $) 46 T ELT)) (|children| (#4# 32 T ELT)) (= (#5# 38 T ELT))) 
(((|BinaryRecursiveAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |setelt| (|#1| |#1| #3="right" |#1|)) (SIGNATURE |setelt| (|#1| |#1| #4="left" |#1|)) (SIGNATURE |elt| (|#1| |#1| #3#)) (SIGNATURE |elt| (|#1| |#1| #4#)) (SIGNATURE |setelt| (|#2| |#1| #5="value" |#2|)) (SIGNATURE |node?| #1#) (SIGNATURE |leaves| ((|List| |#2|) |#1|)) (SIGNATURE |cyclic?| #6=(#2# |#1|)) (SIGNATURE |elt| (|#2| |#1| #5#)) (SIGNATURE |leaf?| #6#) (SIGNATURE |nodes| #7=((|List| |#1|) |#1|)) (SIGNATURE |children| #7#)) (|BinaryRecursiveAggregate| |#2|) (|Type|)) (T |BinaryRecursiveAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (($ $ $) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setleft!| (($ $ $) 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #3="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ "left" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ "right" $) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #4=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sample| (#5=($) 6 T CONST)) (|right| (($ $) 54 T ELT)) (|nodes| (#6=(#4# $) 45 T ELT)) (|node?| (#7=(#8=(|Boolean|) $ $) 37 (|has| |#1| . #9=((|BasicType|))) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|left| (($ $) 56 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (#10=(#8# $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #11=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #11#) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT)) (|eq?| ((#12=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#12# $) 7 T ELT)) (|empty| (#5# 8 T ELT)) (|elt| ((|#1| $ #3#) 42 T ELT) (($ $ "left") 55 T ELT) (($ $ "right") 53 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (#10# 41 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (#6# 46 T ELT)) (|child?| (#7# 38 (|has| |#1| . #9#) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|BinaryRecursiveAggregate| |#1|) (|Category|) (|Type|)) (T |BinaryRecursiveAggregate|)) 
((|left| (*1 *1 *1) (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "left") (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|right| (*1 *1 *1) (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "right") (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setelt| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 "left") (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setleft!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 "right") (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setright!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|RecursiveAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |left| ($ $)) (SIGNATURE |elt| ($ $ "left")) (SIGNATURE |right| ($ $)) (SIGNATURE |elt| ($ $ "right")) (IF (|has| $ (|ShallowlyMutableAggregate| |t#1|)) (PROGN (SIGNATURE |setelt| ($ $ "left" $)) (SIGNATURE |setleft!| ($ $ $)) (SIGNATURE |setelt| ($ $ "right" $)) (SIGNATURE |setright!| ($ $ $))) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|noLinearFactor?| (#1=(#2=(|Boolean|) |#1|) 29 T ELT)) (|brillhartTrials| ((#3=(|NonNegativeInteger|) #3#) 28 T ELT) ((#3#) 27 T ELT)) (|brillhartIrreducible?| ((#2# |#1| #2#) 30 T ELT) (#1# 31 T ELT))) 
(((|BrillhartTests| |#1|) (CATEGORY |package| (SIGNATURE |brillhartIrreducible?| #1=(#2=(|Boolean|) |#1|)) (SIGNATURE |brillhartIrreducible?| (#2# |#1| #2#)) (SIGNATURE |brillhartTrials| (#3=(|NonNegativeInteger|))) (SIGNATURE |brillhartTrials| (#3# #3#)) (SIGNATURE |noLinearFactor?| #1#)) (|UnivariatePolynomialCategory| (|Integer|))) (T |BrillhartTests|)) 
((|noLinearFactor?| #1=(*1 *2 *3) #2=(AND (|isDomain| *2 (|Boolean|)) #3=(|isDomain| *1 (|BrillhartTests| *3)) #4=(|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|brillhartTrials| (*1 *2 *2) #5=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #4#)) (|brillhartTrials| (*1 *2) #5#) (|brillhartIrreducible?| (*1 *2 *3 *2) #2#) (|brillhartIrreducible?| #1# #2#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 18 T ELT)) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) 26 T ELT)) (|setvalue!| ((|#1| $ |#1|) NIL #5=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (#6=($ $ $) 21 #5# ELT)) (|setleft!| (#6# 23 #5# ELT)) (|setelt| ((|#1| $ #7="value" |#1|) NIL #5# ELT) (($ $ #8="left" $) NIL #5# ELT) (($ $ #9="right" $) NIL #5# ELT)) (|setchildren!| (($ $ #10=(|List| $)) NIL #5# ELT)) (|sample| (#11=($) NIL T CONST)) (|right| (#12=($ $) 20 T ELT)) (|reduce| ((|#1| #13=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #13# $ |#1|) NIL T ELT) ((|#1| #13# $) NIL T ELT)) (|nodes| #14=((#10# $) NIL T ELT)) (|node?| #1#) (|node| (($ $ |#1| $) 27 T ELT)) (|members| #15=((#16=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| #17=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #17#) (|left| (#12# 22 T ELT)) (|leaves| #15#) (|leaf?| #18=(#19=(#3# $) NIL T ELT)) (|latex| (((|String|) $) NIL #20=(|has| |#1| (|SetCategory|)) ELT)) (|insertRoot!| (#21=($ |#1| $) 28 T ELT)) (|insert!| (#21# 15 T ELT)) (|hash| (((|SingleInteger|) $) NIL #20# ELT)) (|find| (((|Union| |#1| "failed") #22=(|Mapping| #3# |#1|) $) NIL T ELT)) (|every?| #23=((#3# #22# $) NIL T ELT)) (|eval| (($ $ (|List| #24=(|Equation| |#1|))) NIL #25=(AND (|has| |#1| (|Evalable| |#1|)) #20#) ELT) (($ $ #24#) NIL #25# ELT) (($ $ |#1| |#1|) NIL #25# ELT) (($ $ #16# #16#) NIL #25# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| (#19# 17 T ELT)) (|empty| (#11# 11 T ELT)) (|elt| ((|#1| $ #7#) NIL T ELT) (($ $ #8#) NIL T ELT) (($ $ #9#) NIL T ELT)) (|distance| (((|Integer|) $ $) NIL T ELT)) (|cyclic?| #18#) (|count| ((#26=(|NonNegativeInteger|) |#1| $) NIL #4# ELT) ((#26# #22# $) NIL T ELT)) (|copy| (#12# NIL T ELT)) (|coerce| ((#27=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #27#)) ELT)) (|children| #14#) (|child?| #1#) (|binarySearchTree| (($ #16#) 16 T ELT)) (|before?| #1#) (|any?| #23#) (= #1#) (|#| ((#26# $) NIL T ELT))) 
(((|BinarySearchTree| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |binarySearchTree| ($ (|List| |#1|))) (SIGNATURE |insert!| #1=($ |#1| $)) (SIGNATURE |insertRoot!| #1#) (SIGNATURE |split| ((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $)))) (|OrderedSet|)) (T |BinarySearchTree|)) 
((|binarySearchTree| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 #2=(|OrderedSet|)) #3=(|isDomain| *1 #4=(|BinarySearchTree| *3)))) (|insert!| #5=(*1 *1 *2 *1) #6=(AND (|isDomain| *1 (|BinarySearchTree| *2)) (|ofCategory| *2 #2#))) (|insertRoot!| #5# #6#) (|split| (*1 *2 *3 *1) (AND (|isDomain| *2 (|Record| (|:| |less| #4#) (|:| |greater| #4#))) #3# #1#))) 
((~ (#1=($ $) 13 T ELT)) (|not| (#1# 11 T ELT)) (|nor| (#2=($ $ $) 23 T ELT)) (|nand| (#2# 21 T ELT)) (|\\/| (#2# 19 T ELT)) (|/\\| (#2# 17 T ELT))) 
(((|BitAggregate&| |#1|) (CATEGORY |package| (SIGNATURE |nor| #1=(|#1| |#1| |#1|)) (SIGNATURE |nand| #1#) (SIGNATURE ~ #2=(|#1| |#1|)) (SIGNATURE |/\\| #1#) (SIGNATURE |\\/| #1#) (SIGNATURE |not| #2#)) (|BitAggregate|)) (T |BitAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (~ (($ $) 105 T ELT)) (|xor| (($ $ $) 34 T ELT)) (|swap!| (((|Void|) $ #2=(|Integer|) #2#) 60 (|has| $ (|ShallowlyMutableAggregate| #3=(|Boolean|))) ELT)) (|sorted?| ((#4=(|Boolean|) $) 99 (|has| #3# . #5=((|OrderedSet|))) ELT) ((#4# (|Mapping| #4# #3# #3#) $) 93 T ELT)) (|sort!| (#6=($ $) 103 (AND (|has| #3# . #5#) (|has| $ (|ShallowlyMutableAggregate| #3#))) ELT) (($ (|Mapping| #4# #3# #3#) . #7=($)) 102 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|sort| (#6# 98 (|has| #3# . #5#) ELT) (($ (|Mapping| #4# #3# #3#) . #7#) 92 T ELT)) (|setelt| ((#3# $ #8=(|UniversalSegment| #2#) #3#) 78 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT) ((#3# $ #2# #3#) 48 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|select| (($ (|Mapping| #9=(|Boolean|) #3#) . #10=($)) 64 (|has| $ (|FiniteAggregate| #3#)) ELT)) (|sample| (#11=($) 41 T CONST)) (|reverse!| (#6# 101 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|reverse| (#6# 91 T ELT)) (|removeDuplicates| (($ $) 62 (AND (|has| #3# . #12=((|BasicType|))) (|has| $ (|FiniteAggregate| #3#))) ELT)) (|remove| (($ (|Mapping| #9# #3#) . #10#) 65 (|has| $ (|FiniteAggregate| #3#)) ELT) (($ #3# $) 63 (AND (|has| #3# . #12#) (|has| $ (|FiniteAggregate| #3#))) ELT)) (|reduce| ((#3# (|Mapping| #3# #3# #3#) $) 84 T ELT) ((#3# (|Mapping| #3# #3# #3#) $ #3#) 83 T ELT) ((#3# (|Mapping| #3# #3# #3#) $ #3# #3#) 79 (|has| #3# . #13=((|BasicType|))) ELT)) (|qsetelt!| ((#3# $ #2# #3#) 47 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|qelt| ((#3# $ #2#) 49 T ELT)) (|position| ((#14=(|Integer|) #3# $ #14#) 96 (|has| #3# . #15=((|BasicType|))) ELT) ((#14# #3# $) 95 (|has| #3# . #15#) ELT) ((#14# (|Mapping| #4# #3#) $) 94 T ELT)) (|or| (#16=($ $ $) 110 T ELT)) (|not| (($ $) 108 T ELT)) (|nor| (($ $ $) 35 T ELT)) (|new| (($ (|NonNegativeInteger|) #3#) 68 T ELT)) (|nand| (($ $ $) 36 T ELT)) (|minIndex| ((#2# . #17=($)) 57 (|has| #2# . #18=((|OrderedSet|))) ELT)) (|min| (#19=($ $ $) 23 T ELT)) (|merge| (($ $ $) 97 (|has| #3# . #5#) ELT) (($ (|Mapping| #4# #3# #3#) $ $) 90 T ELT)) (|members| (((|List| #3#) $) 85 T ELT)) (|member?| ((#20=(|Boolean|) #3# $) 80 (|has| #3# . #13#) ELT)) (|maxIndex| ((#2# . #17#) 56 (|has| #2# . #18#) ELT)) (|max| (#19# 22 T ELT)) (|map!| (($ (|Mapping| #3# #3#) $) 104 T ELT)) (|map| (($ (|Mapping| #3# #3# #3#) $ $) 73 T ELT) (($ (|Mapping| #3# #3#) $) 42 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|insert| (($ $ $ #2#) 77 T ELT) (($ #3# $ #2#) 76 T ELT)) (|indices| (((|List| #2#) $) 54 T ELT)) (|index?| ((#21=(|Boolean|) #2# $) 53 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| ((#3# $) 58 (|has| #2# . #18#) ELT)) (|find| (((|Union| #3# "failed") (|Mapping| #20# #3#) $) 82 T ELT)) (|fill!| (($ $ #3#) 59 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|every?| ((#20# (|Mapping| #20# #3#) . #22=($)) 87 T ELT)) (|eval| (($ $ (|List| #3#) (|List| #3#)) 46 (AND (|has| #3# (|Evalable| #3#)) (|has| #3# . #23=((|SetCategory|)))) ELT) (($ $ #3# #3#) 45 (AND (|has| #3# (|Evalable| #3#)) (|has| #3# . #23#)) ELT) (($ $ (|Equation| #3#)) 44 (AND (|has| #3# (|Evalable| #3#)) (|has| #3# . #23#)) ELT) (($ $ (|List| (|Equation| #3#))) 43 (AND (|has| #3# (|Evalable| #3#)) (|has| #3# . #23#)) ELT)) (|eq?| ((#24=(|Boolean|) $ $) 37 T ELT)) (|entry?| ((#21# #3# $) 55 (AND (|has| $ (|FiniteAggregate| #3#)) (|has| #3# (|BasicType|))) ELT)) (|entries| (((|List| #3#) $) 52 T ELT)) (|empty?| ((#24# $) 40 T ELT)) (|empty| (#11# 39 T ELT)) (|elt| (($ $ #8#) 67 T ELT) ((#3# $ #2#) 51 T ELT) ((#3# $ #2# #3#) 50 T ELT)) (|delete| (($ $ #8#) 75 T ELT) (($ $ #2#) 74 T ELT)) (|count| ((#25=(|NonNegativeInteger|) (|Mapping| #20# #3#) $) 86 T ELT) ((#25# #3# $) 81 (|has| #3# . #13#) ELT)) (|copyInto!| (($ $ $ #14#) 100 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|copy| (($ $) 38 T ELT)) (|convert| ((#26=(|InputForm|) $) 61 (|has| #3# (|ConvertibleTo| #26#)) ELT)) (|construct| (($ (|List| #3#)) 66 T ELT)) (|concat| (($ (|List| $)) 72 T ELT) (($ $ $) 71 T ELT) (($ #3# $) 70 T ELT) (($ $ #3#) 69 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| ((#20# (|Mapping| #20# #3#) . #22#) 88 T ELT)) (|and| (#16# 109 T ELT)) (|\\/| (#27=($ $ $) 107 T ELT)) (>= (#28=((|Boolean|) $ $) 21 T ELT)) (> (#28# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#28# 20 T ELT)) (< (#28# 18 T ELT)) (|/\\| (#27# 106 T ELT)) (|#| ((#25# $) 89 T ELT))) 
(((|BitAggregate|) (|Category|)) (T |BitAggregate|)) 
((|nand| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (|nor| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (|xor| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|)))) 
(|Join| (|OrderedSet|) (|BooleanLogic|) (|Logic|) (|OneDimensionalArrayAggregate| (|Boolean|)) (CATEGORY |domain| (SIGNATURE |nand| ($ $ $)) (SIGNATURE |nor| ($ $ $)) (SIGNATURE |xor| ($ $ $)))) 
(((|Aggregate|) . T) ((|BasicType|) . T) ((|BooleanLogic|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| #1=(|Boolean|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Boolean|) (|ConvertibleTo| (|InputForm|))) ((|Eltable| #2=(|Integer|) #1#) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #2# #1#) . T) ((|Evalable| #1#) AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|))) ((|FiniteAggregate| #1#) . T) ((|FiniteLinearAggregate| #1#) . T) ((|Functorial| #1#) . T) ((|HomogeneousAggregate| #1#) . T) ((|IndexedAggregate| #2# #1#) . T) ((|InnerEvalable| #1# #1#) AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| #1#) . T) ((|Logic|) . T) ((|OneDimensionalArrayAggregate| #1#) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| #1#) . T) ((|Type|) . T)) 
((|map!| (($ (|Mapping| |#2| |#2|) $) 22 T ELT)) (|copy| (($ $) 16 T ELT)) (|#| (((|NonNegativeInteger|) $) 25 T ELT))) 
(((|BinaryTreeCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) (|BinaryTreeCategory| |#2|) (|SetCategory|)) (T |BinaryTreeCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (#3=($ $ $) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setleft!| (#3# 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #4="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ #5="left" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ #6="right" $) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #7=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sample| (#8=($) 6 T CONST)) (|right| (#9=($ $) 54 T ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 71 (|has| |#1| . #10=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 67 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 66 T ELT)) (|nodes| (#11=(#7# $) 45 T ELT)) (|node?| (#12=(#13=(|Boolean|) $ $) 37 (|has| |#1| . #14=((|BasicType|))) ELT)) (|node| (($ $ |#1| $) 59 T ELT)) (|members| (((|List| |#1|) $) 65 T ELT)) (|member?| ((#15=(|Boolean|) |#1| $) 70 (|has| |#1| . #10#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 60 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|left| (#9# 56 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (#16=(#13# $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #17=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #17#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #15# |#1|) $) 68 T ELT)) (|every?| ((#15# (|Mapping| #15# |#1|) . #18=($)) 63 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT)) (|eq?| ((#19=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#19# $) 7 T ELT)) (|empty| (#8# 8 T ELT)) (|elt| ((|#1| $ #4#) 42 T ELT) (($ $ #5#) 55 T ELT) (($ $ #6#) 53 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (#16# 41 T ELT)) (|count| ((#20=(|NonNegativeInteger|) |#1| $) 69 (|has| |#1| . #10#) ELT) ((#20# (|Mapping| #15# |#1|) $) 64 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (#11# 46 T ELT)) (|child?| (#12# 38 (|has| |#1| . #14#) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#15# (|Mapping| #15# |#1|) . #18#) 62 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#20# $) 61 T ELT))) 
(((|BinaryTreeCategory| |#1|) (|Category|) (|SetCategory|)) (T |BinaryTreeCategory|)) 
((|node| (*1 *1 *1 *2 *1) (AND (|ofCategory| *1 (|BinaryTreeCategory| *2)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|BinaryRecursiveAggregate| |t#1|) (|FiniteAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |node| ($ $ |t#1| $)))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|BinaryRecursiveAggregate| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 18 T ELT)) (|setvalue!| ((|#1| $ |#1|) 22 #5=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (#6=($ $ $) 23 #5# ELT)) (|setleft!| (#6# 21 #5# ELT)) (|setelt| ((|#1| $ #7="value" |#1|) NIL #5# ELT) (($ $ #8="left" $) NIL #5# ELT) (($ $ #9="right" $) NIL #5# ELT)) (|setchildren!| (($ $ #10=(|List| $)) NIL #5# ELT)) (|sample| (#11=($) NIL T CONST)) (|right| (#12=($ $) 24 T ELT)) (|reduce| ((|#1| #13=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #13# $ |#1|) NIL T ELT) ((|#1| #13# $) NIL T ELT)) (|nodes| #14=((#10# $) NIL T ELT)) (|node?| #1#) (|node| (($ $ |#1| $) NIL T ELT)) (|members| #15=((#16=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| #17=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #17#) (|left| (#12# NIL T ELT)) (|leaves| #15#) (|leaf?| #18=(#19=(#3# $) NIL T ELT)) (|latex| (((|String|) $) NIL #20=(|has| |#1| (|SetCategory|)) ELT)) (|insert!| (($ |#1| $) 15 T ELT)) (|hash| (((|SingleInteger|) $) NIL #20# ELT)) (|find| (((|Union| |#1| "failed") #21=(|Mapping| #3# |#1|) $) NIL T ELT)) (|every?| #22=((#3# #21# $) NIL T ELT)) (|eval| (($ $ (|List| #23=(|Equation| |#1|))) NIL #24=(AND (|has| |#1| (|Evalable| |#1|)) #20#) ELT) (($ $ #23#) NIL #24# ELT) (($ $ |#1| |#1|) NIL #24# ELT) (($ $ #16# #16#) NIL #24# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| (#19# 17 T ELT)) (|empty| (#11# 11 T ELT)) (|elt| ((|#1| $ #7#) NIL T ELT) (($ $ #8#) NIL T ELT) (($ $ #9#) NIL T ELT)) (|distance| (((|Integer|) $ $) NIL T ELT)) (|cyclic?| #18#) (|count| ((#25=(|NonNegativeInteger|) |#1| $) NIL #4# ELT) ((#25# #21# $) NIL T ELT)) (|copy| (#12# 20 T ELT)) (|coerce| ((#26=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #26#)) ELT)) (|children| #14#) (|child?| #1#) (|binaryTournament| (($ #16#) 16 T ELT)) (|before?| #1#) (|any?| #22#) (= #1#) (|#| ((#25# $) NIL T ELT))) 
(((|BinaryTournament| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |binaryTournament| ($ (|List| |#1|))) (SIGNATURE |insert!| ($ |#1| $)))) (|OrderedSet|)) (T |BinaryTournament|)) 
((|binaryTournament| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 #1=(|OrderedSet|)) (|isDomain| *1 (|BinaryTournament| *3)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|BinaryTournament| *2)) (|ofCategory| *2 #1#)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 31 T ELT)) (|setvalue!| ((|#1| $ |#1|) 33 #5=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (#6=($ $ $) 37 #5# ELT)) (|setleft!| (#6# 35 #5# ELT)) (|setelt| ((|#1| $ #7="value" |#1|) NIL #5# ELT) (($ $ #8="left" $) NIL #5# ELT) (($ $ #9="right" $) NIL #5# ELT)) (|setchildren!| (($ $ #10=(|List| $)) NIL #5# ELT)) (|sample| (#11=($) NIL T CONST)) (|right| (#12=($ $) 24 T ELT)) (|reduce| ((|#1| #13=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #13# $ |#1|) NIL T ELT) ((|#1| #13# $) NIL T ELT)) (|nodes| #14=((#10# $) NIL T ELT)) (|node?| #1#) (|node| (#15=($ $ |#1| $) 17 T ELT)) (|members| #16=((#17=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| #18=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #18#) (|left| (#12# 23 T ELT)) (|leaves| #16#) (|leaf?| (#19=(#3# $) 26 T ELT)) (|latex| (((|String|) $) NIL #20=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) NIL #20# ELT)) (|find| (((|Union| |#1| "failed") #21=(|Mapping| #3# |#1|) $) NIL T ELT)) (|every?| #22=((#3# #21# $) NIL T ELT)) (|eval| (($ $ (|List| #23=(|Equation| |#1|))) NIL #24=(AND (|has| |#1| (|Evalable| |#1|)) #20#) ELT) (($ $ #23#) NIL #24# ELT) (($ $ |#1| |#1|) NIL #24# ELT) (($ $ #17# #17#) NIL #24# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| (#19# 21 T ELT)) (|empty| (#11# 13 T ELT)) (|elt| ((|#1| $ #7#) NIL T ELT) (($ $ #8#) NIL T ELT) (($ $ #9#) NIL T ELT)) (|distance| (((|Integer|) $ $) NIL T ELT)) (|cyclic?| (#19# NIL T ELT)) (|count| ((#25=(|NonNegativeInteger|) |#1| $) NIL #4# ELT) ((#25# #21# $) NIL T ELT)) (|copy| (#12# NIL T ELT)) (|coerce| ((#26=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #26#)) ELT)) (|children| #14#) (|child?| #1#) (|binaryTree| (($ |#1|) 19 T ELT) (#15# 18 T ELT)) (|before?| #1#) (|any?| #22#) (= (#2# 12 #4# ELT)) (|#| ((#25# $) NIL T ELT))) 
(((|BinaryTree| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |binaryTree| ($ |#1|)) (SIGNATURE |binaryTree| ($ $ |#1| $)))) (|SetCategory|)) (T |BinaryTree|)) 
((|binaryTree| (*1 *1 *2) #1=(AND (|isDomain| *1 (|BinaryTree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|binaryTree| (*1 *1 *1 *2 *1) #1#)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (~ (($ $) 32 T ELT)) (|size| ((#3=(|NonNegativeInteger|)) 17 T ELT)) (|sample| (#4=($) 9 T CONST)) (|random| (#4# 27 T ELT)) (|min| #5=(#6=($ $ $) NIL T ELT) (#4# 15 T CONST)) (|max| #5# (#4# 16 T CONST)) (|lookup| ((#7=(|PositiveInteger|) $) 25 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #7#) 23 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|byte| (($ #3#) 8 T ELT)) (|bitior| (#6# 29 T ELT)) (|bitand| (#6# 28 T ELT)) (|before?| #1#) (|\\/| (#6# 31 T ELT)) (>= (#2# 14 T ELT)) (> (#2# 12 T ELT)) (= (#2# 10 T ELT)) (<= (#2# 13 T ELT)) (< (#2# 11 T ELT)) (|/\\| (#6# 30 T ELT))) 
(((|Byte|) (|Join| (|OrderedFinite|) (|Logic|) (CATEGORY |domain| (SIGNATURE |byte| ($ (|NonNegativeInteger|))) (SIGNATURE |bitand| #1=($ $ $)) (SIGNATURE |bitior| #1#) (SIGNATURE |sample| ($) |constant|)))) (T |Byte|)) 
((|byte| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) #1=(|isDomain| *1 (|Byte|)))) (|bitand| #2=(*1 *1 *1 *1) #1#) (|bitior| #2# #1#) (|sample| (*1 *1) #1#)) 
((|NonNegativeInteger|) (|%ilt| |#1| 256)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| #5=(|Byte|) (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #6=(|Integer|) #6#) NIL #7=(|has| $ (|ShallowlyMutableAggregate| #5#)) ELT)) (|sorted?| ((#3# #8=(|Mapping| #3# #5# #5#) $) NIL T ELT) (#9=(#3# $) NIL #10=(|has| #5# #11=(|OrderedSet|)) ELT)) (|sort!| (#12=($ #8# $) NIL #7# ELT) (#13=($ $) NIL (AND #7# #10#) ELT)) (|sort| (#12# NIL T ELT) (#13# NIL #10# ELT)) (|setelt| (#14=(#5# $ #6# #5#) 26 #7# ELT) ((#5# $ #15=(|UniversalSegment| #6#) #5#) NIL #7# ELT)) (|setLength!| ((#16=(|NonNegativeInteger|) $ #16#) 35 T ELT)) (|select| #17=(($ #18=(|Mapping| #3# #5#) $) NIL #19=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|sample| (#20=($) NIL T CONST)) (|reverse!| (#13# NIL #7# ELT)) (|reverse| #21=(#13# NIL T ELT)) (|removeDuplicates| (#13# NIL #22=(AND #19# #4#) ELT)) (|remove| (#23=($ #5# $) NIL #22# ELT) #17#) (|reduce| ((#5# #24=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #24# $ #5#) NIL T ELT) ((#5# #24# $) NIL T ELT)) (|qsetelt!| (#14# 25 #7# ELT)) (|qelt| (#25=(#5# $ #6#) 20 T ELT)) (|position| ((#6# #18# $) NIL T ELT) ((#6# #5# $) NIL #4# ELT) ((#6# #5# $ #6#) NIL #4# ELT)) (|new| (($ #16# #5#) 14 T ELT)) (|minIndex| (#26=(#6# $) 27 #27=(|has| #6# #11#) ELT)) (|min| #28=(#29=($ $ $) NIL #10# ELT)) (|merge| (($ #8# $ $) NIL T ELT) #28#) (|members| #30=((#31=(|List| #5#) $) NIL T ELT)) (|member?| (#32=(#3# #5# $) NIL #4# ELT)) (|maxIndex| (#26# 30 #27# ELT)) (|max| #28#) (|map!| #33=(($ (|Mapping| #5# #5#) $) NIL T ELT)) (|map| #33# (($ #24# $ $) NIL T ELT)) (|latex| (#34=((|String|) $) NIL #35=(|has| #5# (|SetCategory|)) ELT)) (|insert| (($ #5# $ #6#) NIL T ELT) (#36=($ $ $ #6#) NIL T ELT)) (|indices| (((|List| #6#) $) NIL T ELT)) (|index?| ((#3# #6# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #35# ELT)) (|first| ((#5# $) NIL #27# ELT)) (|find| (((|Union| #5# "failed") #18# $) NIL T ELT)) (|fill!| (#37=($ $ #5#) NIL #7# ELT)) (|every?| #38=((#3# #18# $) NIL T ELT)) (|eval| (($ $ (|List| #39=(|Equation| #5#))) NIL #40=(AND (|has| #5# (|Evalable| #5#)) #35#) ELT) (($ $ #39#) NIL #40# ELT) (($ $ #5# #5#) NIL #40# ELT) (($ $ #31# #31#) NIL #40# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#32# NIL #22# ELT)) (|entries| #30#) (|empty?| (#9# NIL T ELT)) (|empty| (#20# 12 T ELT)) (|elt| (#14# NIL T ELT) (#25# 23 T ELT) #41=(($ $ #15#) NIL T ELT)) (|delete| (($ $ #6#) NIL T ELT) #41#) (|count| ((#16# #5# $) NIL #4# ELT) ((#16# #18# $) NIL T ELT)) (|copyInto!| (#36# NIL #7# ELT)) (|copy| #21#) (|convert| ((#42=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #42#)) ELT)) (|construct| (($ #31#) 41 T ELT)) (|concat| (#37# NIL T ELT) (#23# NIL T ELT) (#29# 45 T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| (((|PrimitiveArray| #5#) $) 36 T ELT) (#34# 38 T ELT) ((#43=(|OutputForm|) $) NIL (|has| #5# (|CoercibleTo| #43#)) ELT)) (|capacity| (#44=(#16# $) 18 T ELT)) (|byteBuffer| (($ #16#) 8 T ELT)) (|before?| #1#) (|any?| #38#) (>= #45=(#2# NIL #10# ELT)) (> #45#) (= (#2# 33 #4# ELT)) (<= #45#) (< #45#) (|#| (#44# 15 T ELT))) 
(((|ByteBuffer|) (|Join| (|OneDimensionalArrayAggregate| #1=(|Byte|)) (|CoercibleTo| (|PrimitiveArray| #1#)) (|CoercibleTo| (|String|)) (CATEGORY |domain| (SIGNATURE |byteBuffer| ($ #2=(|NonNegativeInteger|))) (SIGNATURE |capacity| (#2# $)) (SIGNATURE |setLength!| (#2# $ #2#))))) (T |ByteBuffer|)) 
((|byteBuffer| (*1 *1 *2) #1=(AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ByteBuffer|)))) (|capacity| (*1 *2 *1) #1#) (|setLength!| (*1 *2 *1 *2) #1#)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|unknownEndian| (#3=($) 6 T CONST)) (|littleEndian| (#3# 7 T CONST)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 14 T ELT)) (|bigEndian| (#3# 8 T CONST)) (|before?| #1#) (= (#2# 10 T ELT))) 
(((|ByteOrder|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |littleEndian| #1=($) |constant|) (SIGNATURE |bigEndian| #1# |constant|) (SIGNATURE |unknownEndian| #1# |constant|)))) (T |ByteOrder|)) 
((|littleEndian| #1=(*1 *1) #2=(|isDomain| *1 (|ByteOrder|))) (|bigEndian| #1# #2#) (|unknownEndian| #1# #2#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) 
(((|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) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) 17 T ELT)) (|position| (((|NonNegativeInteger|) $) 18 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|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| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |position| ((|NonNegativeInteger|) $)) (SIGNATURE |setPosition| ((|Void|) $ (|NonNegativeInteger|))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|body| (((|List| (|SpadAst|)) $) 12 T ELT)) (|before?| #1#) (= #1#)) 
(((|CapsuleAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |body| ((|List| (|SpadAst|)) $))))) (T |CapsuleAst|)) 
((|body| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|CapsuleAst|))))) 
((~= (#1=(#2=(|Boolean|) $ $) 49 T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|retractIfCan| (((|Union| #6=(|NonNegativeInteger|) #7="failed") $) 60 T ELT)) (|retract| ((#6# $) 58 T ELT)) (|recip| ((#8=(|Union| $ #7#) $) NIL T ELT)) (|opposite?| #9=(#1# NIL T ELT)) (|one?| #3#) (|min| (#10=($ $ $) NIL T ELT)) (|max| (#10# 37 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generalizedContinuumHypothesisAssumed?| ((#2#) 61 T ELT)) (|generalizedContinuumHypothesisAssumed| ((#2# #2#) 63 T ELT)) (|finite?| (#4# 30 T ELT)) (|countable?| (#4# 57 T ELT)) (|coerce| (((|OutputForm|) $) 28 T ELT) (#11=($ #6#) 20 T ELT)) (|before?| #9#) (|Zero| (#5# 18 T CONST)) (|One| (#5# 19 T CONST)) (|Aleph| (#11# 21 T ELT)) (>= #9#) (> (#1# 40 T ELT)) (= (#1# 32 T ELT)) (<= #9#) (< (#1# 35 T ELT)) (- ((#8# $ $) 42 T ELT)) (+ (#10# 38 T ELT)) (** (($ $ #6#) NIL T ELT) (($ $ #12=(|PositiveInteger|)) NIL T ELT) (#10# 56 T ELT)) (* (($ #6# $) 48 T ELT) (($ #12# $) NIL T ELT) (#10# 45 T ELT))) 
(((|CardinalNumber|) (|Join| (|OrderedSet|) (|AbelianMonoid|) (|Monoid|) (|RetractableTo| #1=(|NonNegativeInteger|)) (CATEGORY |domain| (ATTRIBUTE (|commutative| "*")) (SIGNATURE - ((|Union| $ "failed") $ $)) (SIGNATURE ** ($ $ $)) (SIGNATURE |Aleph| ($ #1#)) (SIGNATURE |finite?| #2=(#3=(|Boolean|) $)) (SIGNATURE |countable?| #2#) (SIGNATURE |generalizedContinuumHypothesisAssumed?| (#3#)) (SIGNATURE |generalizedContinuumHypothesisAssumed| (#3# #3#))))) (T |CardinalNumber|)) 
((- #1=(*1 *1 *1 *1) (|partial| |isDomain| *1 #2=(|CardinalNumber|))) (** #1# #3=(|isDomain| *1 #2#)) (|Aleph| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) #3#)) (|finite?| #4=(*1 *2 *1) #5=(AND (|isDomain| *2 (|Boolean|)) #3#)) (|countable?| #4# #5#) (|generalizedContinuumHypothesisAssumed?| (*1 *2) #5#) (|generalizedContinuumHypothesisAssumed| (*1 *2 *2) #5#)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|unravel| (#3=($ #4=(|List| |#3|)) 63 T ELT)) (|transpose| (#5=($ $) 125 T ELT) (#6=($ $ #7=(|Integer|) #7#) 124 T ELT)) (|sample| (#8=($) 17 T ELT)) (|retractIfCan| (((|Union| |#3| "failed") $) 86 T ELT)) (|retract| (#9=(|#3| $) NIL T ELT)) (|reindex| (($ $ #10=(|List| #7#)) 126 T ELT)) (|ravel| ((#4# $) 58 T ELT)) (|rank| (#11=((|NonNegativeInteger|) $) 68 T ELT)) (|product| (#12=($ $ $) 120 T ELT)) (|leviCivitaSymbol| (#8# 67 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|kroneckerDelta| (#8# 16 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#3| $ #7#) 72 T ELT) (#9# 71 T ELT) ((|#3| $ #7# #7#) 73 T ELT) ((|#3| $ #7# #7# #7#) 74 T ELT) ((|#3| $ #7# #7# #7# #7#) 75 T ELT) ((|#3| $ #10#) 76 T ELT)) (|degree| (#11# 69 T ELT)) (|contract| (($ $ #7# $ #7#) 121 T ELT) (#6# 123 T ELT)) (|coerce| (((|OutputForm|) $) 94 T ELT) (($ |#3|) 95 T ELT) (($ (|DirectProduct| |#2| |#3|)) 102 T ELT) (($ (|SquareMatrix| |#2| |#3|)) 105 T ELT) (#3# 77 T ELT) (($ (|List| $)) 83 T ELT)) (|before?| #1#) (|Zero| (#8# 96 T CONST)) (|One| (#8# 97 T CONST)) (= (#2# 107 T ELT)) (- (#5# 113 T ELT) (#12# 111 T ELT)) (+ (#12# 109 T ELT)) (* (($ |#3| $) 118 T ELT) (($ $ |#3|) 119 T ELT) (($ $ #7#) 116 T ELT) (($ #7# $) 115 T ELT) (#12# 122 T ELT))) 
(((|CartesianTensor| |#1| |#2| |#3|) (|Join| (|GradedAlgebra| |#3| #1=(|NonNegativeInteger|)) (|GradedModule| #2=(|Integer|) #1#) (|Eltable| #2# |#3|) (|CoercibleFrom| (|DirectProduct| |#2| |#3|)) (|CoercibleFrom| (|SquareMatrix| |#2| |#3|)) (|CoercibleFrom| #3=(|List| |#3|)) (|CoercibleFrom| (|List| $)) (CATEGORY |domain| (SIGNATURE |rank| (#1# $)) (SIGNATURE |elt| (|#3| $)) (SIGNATURE |elt| (|#3| $ #2# #2#)) (SIGNATURE |elt| (|#3| $ #2# #2# #2#)) (SIGNATURE |elt| (|#3| $ #2# #2# #2# #2#)) (SIGNATURE |elt| (|#3| $ #4=(|List| #2#))) (SIGNATURE |product| #5=($ $ $)) (SIGNATURE * #5#) (SIGNATURE |contract| ($ $ #2# $ #2#)) (SIGNATURE |contract| #6=($ $ #2# #2#)) (SIGNATURE |transpose| ($ $)) (SIGNATURE |transpose| #6#) (SIGNATURE |reindex| ($ $ #4#)) (SIGNATURE |kroneckerDelta| #7=($)) (SIGNATURE |leviCivitaSymbol| #7#) (SIGNATURE |ravel| (#3# $)) (SIGNATURE |unravel| ($ #3#)) (SIGNATURE |sample| #7#))) #2# #1# (|CommutativeRing|)) (T |CartesianTensor|)) 
((|product| #1=(*1 *1 *1 *1) #2=(AND (|isDomain| *1 (|CartesianTensor| *2 *3 *4)) (|ofType| *2 #3=(|Integer|)) (|ofType| *3 #4=(|NonNegativeInteger|)) (|ofCategory| *4 #5=(|CommutativeRing|)))) (|rank| #6=(*1 *2 *1) (AND (|isDomain| *2 #4#) #7=(|isDomain| *1 (|CartesianTensor| *3 *4 *5)) #8=(|ofType| *3 #3#) (|ofType| *4 *2) #9=(|ofCategory| *5 #5#))) (|elt| #6# (AND #10=(|ofCategory| *2 #5#) (|isDomain| *1 (|CartesianTensor| *3 *4 *2)) #8# #11=(|ofType| *4 #4#))) (|elt| (*1 *2 *1 *3 *3) #12=(AND (|isDomain| *3 #3#) #10# #13=(|isDomain| *1 (|CartesianTensor| *4 *5 *2)) (|ofType| *4 *3) #14=(|ofType| *5 #4#))) (|elt| (*1 *2 *1 *3 *3 *3) #12#) (|elt| (*1 *2 *1 *3 *3 *3 *3) #12#) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 #15=(|List| #3#)) #10# #13# (|ofType| *4 #3#) #14#)) (* #1# #2#) (|contract| (*1 *1 *1 *2 *1 *2) #16=(AND (|isDomain| *2 #3#) #7# (|ofType| *3 *2) #11# #9#)) (|contract| #17=(*1 *1 *1 *2 *2) #16#) (|transpose| (*1 *1 *1) #2#) (|transpose| #17# #16#) (|reindex| (*1 *1 *1 *2) (AND (|isDomain| *2 #15#) #7# #8# #11# #9#)) (|kroneckerDelta| #18=(*1 *1) #2#) (|leviCivitaSymbol| #18# #2#) (|ravel| #6# (AND #19=(|isDomain| *2 (|List| *5)) #7# #8# #11# #9#)) (|unravel| (*1 *1 *2) (AND #19# #9# #7# #8# #11#)) (|sample| #18# #2#)) 
((|reshape| ((#1=(|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) #2=(|CartesianTensor| |#1| |#2| |#3|)) 14 T ELT)) (|map| ((#1# (|Mapping| |#4| |#3|) #2#) 18 T ELT))) 
(((|CartesianTensorFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |reshape| (#1=(|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) #2=(|CartesianTensor| |#1| |#2| |#3|))) (SIGNATURE |map| (#1# (|Mapping| |#4| |#3|) #2#))) (|Integer|) (|NonNegativeInteger|) #3=(|CommutativeRing|) #3#) (T |CartesianTensorFunctions2|)) 
((|map| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *8 *7)) #2=(|isDomain| *4 (|CartesianTensor| *5 *6 *7)) #3=(|ofType| *5 (|Integer|)) #4=(|ofType| *6 (|NonNegativeInteger|)) #5=(|ofCategory| *7 #6=(|CommutativeRing|)) #7=(|ofCategory| *8 #6#) #8=(|isDomain| *2 (|CartesianTensor| *5 *6 *8)) #9=(|isDomain| *1 (|CartesianTensorFunctions2| *5 *6 *7 *8)))) (|reshape| #1# (AND (|isDomain| *3 (|List| *8)) #2# #3# #4# #5# #7# #8# #9#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|rhs| (#2=((|SpadAst|) $) 12 T ELT)) (|lhs| (#2# 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|CaseAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |lhs| #1=((|SpadAst|) $)) (SIGNATURE |rhs| #1#)))) (T |CaseAst|)) 
((|lhs| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|CaseAst|)))) (|rhs| #1# #2#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|kind| (((|ConstructorKind|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|body| (((|List| (|SpadAst|)) $) 13 T ELT)) (|before?| #1#) (= #1#)) 
(((|CategoryAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |kind| ((|ConstructorKind|) $)) (SIGNATURE |body| ((|List| (|SpadAst|)) $))))) (T |CategoryAst|)) 
((|kind| #1=(*1 *2 *1) (AND (|isDomain| *2 (|ConstructorKind|)) #2=(|isDomain| *1 (|CategoryAst|)))) (|body| #1# (AND (|isDomain| *2 (|List| (|SpadAst|))) #2#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|operations| (((|List| (|OverloadSet|)) $) NIL T ELT)) (|name| ((#3=(|Identifier|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|kind| (((|ConstructorKind|) $) NIL T ELT)) (|is?| ((#2# $ #3#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dualSignature| (((|List| #2#) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (((|Constructor|) $) 6 T ELT)) (|before?| #1#) (|arity| (((|Arity|) $) NIL T ELT)) (= #1#)) 
(((|CategoryConstructor|) (|Join| (|ConstructorCategory|) (|CoercibleTo| (|Constructor|)))) (T |CategoryConstructor|)) 
NIL 
((|principalAncestors| (#1=((|List| (|ConstructorCall| #2=(|CategoryConstructor|))) $) 13 T ELT)) (|parents| (#1# 14 T ELT)) (|exportedOperators| (((|List| (|OperatorSignature|)) $) 10 T ELT)) (|constructor| ((#2# $) 7 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT))) 
(((|Category|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |constructor| (#1=(|CategoryConstructor|) $)) (SIGNATURE |exportedOperators| ((|List| (|OperatorSignature|)) $)) (SIGNATURE |principalAncestors| #2=((|List| (|ConstructorCall| #1#)) $)) (SIGNATURE |parents| #2#)))) (T |Category|)) 
((|constructor| #1=(*1 *2 *1) (AND (|isDomain| *2 #2=(|CategoryConstructor|)) #3=(|isDomain| *1 (|Category|)))) (|exportedOperators| #1# (AND (|isDomain| *2 (|List| (|OperatorSignature|))) #3#)) (|principalAncestors| #1# #4=(AND (|isDomain| *2 (|List| (|ConstructorCall| #2#))) #3#)) (|parents| #1# #4#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|upperCase| (#4=($) 17 T CONST)) (|universe| #5=(#4# NIL #6=(|has| #7=(|Character|) (|Finite|)) ELT)) (|union| (#8=($ $ $) 19 T ELT) #9=(($ $ #7#) NIL T ELT) (#10=($ #7# $) NIL T ELT)) (|symmetricDifference| (#8# NIL T ELT)) (|subset?| #1#) (|size| ((#11=(|NonNegativeInteger|)) NIL #6# ELT)) (|set| #12=(#4# NIL T ELT) #13=(#14=($ #15=(|List| #7#)) NIL T ELT)) (|select!| #16=(($ #17=(|Mapping| #3# #7#) $) NIL #18=(|has| $ (|FiniteAggregate| #7#)) ELT)) (|select| #16#) (|sample| (#4# NIL T CONST)) (|removeDuplicates| (#19=($ $) NIL #20=(AND #18# #21=(|has| #7# (|BasicType|))) ELT)) (|remove!| #16# (#10# 56 #18# ELT)) (|remove| #16# (#10# NIL #20# ELT)) (|reduce| ((#7# #22=(|Mapping| #7# #7# #7#) $) NIL T ELT) ((#7# #22# $ #7#) NIL T ELT) ((#7# #22# $ #7# #7#) NIL #21# ELT)) (|random| #5#) (|part?| #1#) (|min| #23=(#24=(#7# $) NIL (|has| #7# (|OrderedSet|)) ELT)) (|members| (#25=(#15# $) 65 T ELT)) (|member?| ((#3# #7# $) 29 #21# ELT)) (|max| #23#) (|map!| (#26=($ (|Mapping| #7# #7#) $) 64 T ELT)) (|map| (#26# 60 T ELT)) (|lowerCase| (#4# 18 T CONST)) (|lookup| ((#27=(|PositiveInteger|) $) NIL #6# ELT)) (|latex| (#28=(#29=(|String|) $) NIL T ELT)) (|intersect| (#8# 32 T ELT)) (|inspect| (#24# 57 T ELT)) (|insert!| (#10# 55 T ELT)) (|index| (($ #27#) NIL #6# ELT)) (|hexDigit| (#4# 16 T CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| (((|Union| #7# "failed") #17# $) NIL T ELT)) (|extract!| (#24# 58 T ELT)) (|every?| #30=((#3# #17# $) NIL T ELT)) (|eval| (($ $ #15# #15#) NIL #31=(AND (|has| #7# (|Evalable| #7#)) (|has| #7# (|SetCategory|))) ELT) (($ $ #7# #7#) NIL #31# ELT) (($ $ #32=(|Equation| #7#)) NIL #31# ELT) (($ $ (|List| #32#)) NIL #31# ELT)) (|eq?| #1#) (|empty?| ((#3# $) NIL T ELT)) (|empty| (#4# 53 T ELT)) (|digit| (#4# 15 T CONST)) (|difference| (#8# 34 T ELT) #9#) (|dictionary| #13# #12#) (|count| ((#11# #17# $) NIL T ELT) ((#11# #7# $) NIL #21# ELT)) (|copy| (#19# NIL T ELT)) (|convert| (#28# 39 T ELT) ((#33=(|InputForm|) $) NIL (|has| #7# (|ConvertibleTo| #33#)) ELT) (#25# 37 T ELT)) (|construct| #13#) (|complement| (#19# 35 #6# ELT)) (|coerce| (((|OutputForm|) $) 51 T ELT)) (|charClass| (($ #29#) 14 T ELT) (#14# 48 T ELT)) (|cardinality| (#34=(#11# $) NIL T ELT)) (|brace| (#4# 54 T ELT) #13#) (|before?| #1#) (|bag| #13#) (|any?| #30#) (|alphanumeric| (#4# 21 T CONST)) (|alphabetic| (#4# 20 T CONST)) (= (#2# 26 T ELT)) (|#| (#34# 52 T ELT))) 
(((|CharacterClass|) (|Join| (|SetCategory|) (|ConvertibleTo| #1=(|String|)) (|FiniteSetAggregate| #2=(|Character|)) (|ConvertibleTo| #3=(|List| #2#)) (CATEGORY |domain| (SIGNATURE |charClass| ($ #1#)) (SIGNATURE |charClass| ($ #3#)) (SIGNATURE |digit| #4=($) |constant|) (SIGNATURE |hexDigit| #4# |constant|) (SIGNATURE |upperCase| #4# |constant|) (SIGNATURE |lowerCase| #4# |constant|) (SIGNATURE |alphabetic| #4# |constant|) (SIGNATURE |alphanumeric| #4# |constant|)))) (T |CharacterClass|)) 
((|charClass| #1=(*1 *1 *2) (AND (|isDomain| *2 (|String|)) #2=(|isDomain| *1 (|CharacterClass|)))) (|charClass| #1# (AND (|isDomain| *2 (|List| (|Character|))) #2#)) (|digit| #3=(*1 *1) #2#) (|hexDigit| #3# #2#) (|upperCase| #3# #2#) (|lowerCase| #3# #2#) (|alphabetic| #3# #2#) (|alphanumeric| #3# #2#)) 
((|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) 17 T ELT)) (|commonDenominator| ((|#1| |#3|) 9 T ELT)) (|clearDenominator| ((|#3| |#3|) 15 T ELT))) 
(((|CommonDenominator| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| |#3|)) (SIGNATURE |clearDenominator| (|#3| |#3|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|) (|FiniteLinearAggregate| |#2|)) (T |CommonDenominator|)) 
((|splitDenominator| #1=(*1 *2 *3) (AND (|ofCategory| *4 #2=(|IntegralDomain|)) (|ofCategory| *5 (|QuotientFieldCategory| *4)) (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *4))) (|isDomain| *1 (|CommonDenominator| *4 *5 *3)) (|ofCategory| *3 (|FiniteLinearAggregate| *5)))) (|clearDenominator| (*1 *2 *2) (AND (|ofCategory| *3 #2#) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|isDomain| *1 (|CommonDenominator| *3 *4 *2)) (|ofCategory| *2 #3=(|FiniteLinearAggregate| *4)))) (|commonDenominator| #1# (AND (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 #2#) (|isDomain| *1 (|CommonDenominator| *2 *4 *3)) (|ofCategory| *3 #3#)))) 
((|permutation| (($ $ $) 8 T ELT)) (|factorial| (($ $) 7 T ELT)) (|binomial| (($ $ $) 6 T ELT))) 
(((|CombinatorialFunctionCategory|) (|Category|)) (T |CombinatorialFunctionCategory|)) 
((|permutation| (*1 *1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|))) (|factorial| (*1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|))) (|binomial| (*1 *1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |binomial| ($ $ $)) (SIGNATURE |factorial| ($ $)) (SIGNATURE |permutation| ($ $ $)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|verticalTab| (#4=($) 30 T CONST)) (|upperCase?| (#5=(#3# $) 42 T ELT)) (|upperCase| (#6=($ $) 52 T ELT)) (|underscore| (#4# 23 T CONST)) (|space| (#4# 21 T CONST)) (|size| ((#7=(|NonNegativeInteger|)) 13 T ELT)) (|random| (#4# 20 T ELT)) (|quote| (#4# 22 T CONST)) (|ord| ((#7# $) 17 T ELT)) (|newline| (#4# 24 T CONST)) (|min| #8=(($ $ $) NIL T ELT) #9=(#4# NIL T CONST)) (|max| #8# #9#) (|lowerCase?| (#5# 44 T ELT)) (|lowerCase| (#6# 53 T ELT)) (|lookup| ((#10=(|PositiveInteger|) $) 18 T ELT)) (|linefeed| (#4# 26 T CONST)) (|latex| ((#11=(|String|) $) 50 T ELT)) (|index| (($ #10#) 16 T ELT)) (|horizontalTab| (#4# 29 T CONST)) (|hexDigit?| (#5# 40 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|formfeed| (#4# 27 T CONST)) (|escape| (#4# 31 T CONST)) (|digit?| (#5# 38 T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT)) (|char| (($ #7#) 14 T ELT) (($ #11#) 51 T ELT)) (|carriageReturn| (#4# 25 T CONST)) (|before?| #1#) (|backspace| (#4# 28 T CONST)) (|alphanumeric?| (#5# 48 T ELT)) (|alphabetic?| (#5# 46 T ELT)) (>= (#2# 11 T ELT)) (> (#2# 9 T ELT)) (= (#2# 7 T ELT)) (<= (#2# 10 T ELT)) (< (#2# 8 T ELT))) 
(((|Character|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |ord| (#1=(|NonNegativeInteger|) $)) (SIGNATURE |char| ($ #1#)) (SIGNATURE |char| ($ (|String|))) (SIGNATURE |space| #2=($) |constant|) (SIGNATURE |quote| #2# |constant|) (SIGNATURE |underscore| #2# |constant|) (SIGNATURE |newline| #2# |constant|) (SIGNATURE |carriageReturn| #2# |constant|) (SIGNATURE |linefeed| #2# |constant|) (SIGNATURE |formfeed| #2# |constant|) (SIGNATURE |backspace| #2# |constant|) (SIGNATURE |horizontalTab| #2# |constant|) (SIGNATURE |verticalTab| #2# |constant|) (SIGNATURE |escape| #2# |constant|) (SIGNATURE |upperCase| #3=($ $)) (SIGNATURE |lowerCase| #3#) (SIGNATURE |digit?| #4=((|Boolean|) $)) (SIGNATURE |hexDigit?| #4#) (SIGNATURE |alphabetic?| #4#) (SIGNATURE |upperCase?| #4#) (SIGNATURE |lowerCase?| #4#) (SIGNATURE |alphanumeric?| #4#)))) (T |Character|)) 
((|ord| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3=(|isDomain| *1 (|Character|)))) (|char| #4=(*1 *1 *2) #2#) (|char| #4# (AND (|isDomain| *2 (|String|)) #3#)) (|space| #5=(*1 *1) #3#) (|quote| #5# #3#) (|underscore| #5# #3#) (|newline| #5# #3#) (|carriageReturn| #5# #3#) (|linefeed| #5# #3#) (|formfeed| #5# #3#) (|backspace| #5# #3#) (|horizontalTab| #5# #3#) (|verticalTab| #5# #3#) (|escape| #5# #3#) (|upperCase| #6=(*1 *1 *1) #3#) (|lowerCase| #6# #3#) (|digit?| #1# #7=(AND (|isDomain| *2 (|Boolean|)) #3#)) (|hexDigit?| #1# #7#) (|alphabetic?| #1# #7#) (|upperCase?| #1# #7#) (|lowerCase?| #1# #7#) (|alphanumeric?| #1# #7#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|charthRoot| (((|Maybe| $) $) 47 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|CharacteristicNonZero|) (|Category|)) (T |CharacteristicNonZero|)) 
((|charthRoot| (*1 *2 *1) (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|CharacteristicNonZero|))))) 
(|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |charthRoot| ((|Maybe| $) $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) 19 T ELT))) 
(((|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))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|CharacteristicZero|) (|Category|)) (T |CharacteristicZero|)) 
NIL 
(|Join| (|Ring|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|rootPoly| (((|Record| (|:| |exponent| #1=(|NonNegativeInteger|)) #2=(|:| |coef| #3=(|Fraction| |#2|)) (|:| |radicand| |#2|)) #3# #1#) 76 T ELT)) (|radPoly| (((|Union| (|Record| (|:| |radicand| #3#) #4=(|:| |deg| #1#)) "failed") |#3|) 56 T ELT)) (|mkIntegral| (((|Record| #2# #5=(|:| |poly| |#3|)) |#3|) 41 T ELT)) (|goodPoint| ((|#1| |#3| |#3|) 44 T ELT)) (|eval| ((|#3| |#3| #3# #3#) 20 T ELT)) (|chvar| (((|Record| (|:| |func| |#3|) #5# (|:| |c1| #3#) (|:| |c2| #3#) #4#) |#3| |#3|) 53 T ELT))) 
(((|ChangeOfVariable| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |mkIntegral| ((|Record| #1=(|:| |coef| #2=(|Fraction| |#2|)) #3=(|:| |poly| |#3|)) |#3|)) (SIGNATURE |radPoly| ((|Union| (|Record| (|:| |radicand| #2#) #4=(|:| |deg| #5=(|NonNegativeInteger|))) "failed") |#3|)) (SIGNATURE |rootPoly| ((|Record| (|:| |exponent| #5#) #1# (|:| |radicand| |#2|)) #2# #5#)) (SIGNATURE |goodPoint| (|#1| |#3| |#3|)) (SIGNATURE |eval| (|#3| |#3| #2# #2#)) (SIGNATURE |chvar| ((|Record| (|:| |func| |#3|) #3# (|:| |c1| #2#) (|:| |c2| #2#) #4#) |#3| |#3|))) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| #2#)) (T |ChangeOfVariable|)) 
((|chvar| #1=(*1 *2 *3 *3) (AND #2=(|ofCategory| *4 #3=(|UniqueFactorizationDomain|)) #4=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |func| *3) #5=(|:| |poly| *3) (|:| |c1| #6=(|Fraction| *5)) (|:| |c2| #6#) #7=(|:| |deg| #8=(|NonNegativeInteger|)))) #9=(|isDomain| *1 (|ChangeOfVariable| *4 *5 *3)) #10=(|ofCategory| *3 (|UnivariatePolynomialCategory| #6#)))) (|eval| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 #6#) #2# #4# (|isDomain| *1 (|ChangeOfVariable| *4 *5 *2)) (|ofCategory| *2 #11=(|UnivariatePolynomialCategory| *3)))) (|goodPoint| #1# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #3#) (|isDomain| *1 (|ChangeOfVariable| *2 *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|rootPoly| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| *6)) (|ofCategory| *5 #3#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |exponent| #8#) (|:| |coef| *3) (|:| |radicand| *6))) (|isDomain| *1 (|ChangeOfVariable| *5 *6 *7)) (|isDomain| *4 #8#) (|ofCategory| *7 #11#))) (|radPoly| #12=(*1 *2 *3) (|partial| AND #2# #4# (|isDomain| *2 (|Record| (|:| |radicand| #6#) #7#)) #9# #10#)) (|mkIntegral| #12# (AND #2# #4# (|isDomain| *2 (|Record| (|:| |coef| #6#) #5#)) #9# #10#))) 
((|solveLinearPolynomialEquation| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#2|)) "failed") #1# #2#) 35 T ELT))) 
(((|ComplexIntegerSolveLinearPolynomialEquation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#2|)) "failed") #1# #2#))) (|IntegerNumberSystem|) (|ComplexCategory| |#1|)) (T |ComplexIntegerSolveLinearPolynomialEquation|)) 
((|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| #1=(|SparseUnivariatePolynomial| *5))) (|isDomain| *3 #1#) (|ofCategory| *5 (|ComplexCategory| *4)) (|ofCategory| *4 (|IntegerNumberSystem|)) (|isDomain| *1 (|ComplexIntegerSolveLinearPolynomialEquation| *4 *5))))) 
((|select| (#1=($ (|Mapping| (|Boolean|) |#2|) $) 16 T ELT)) (|removeDuplicates| (($ $) 21 T ELT)) (|remove| (#1# 14 T ELT) (($ |#2| $) 19 T ELT))) 
(((|Collection&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |removeDuplicates| (|#1| |#1|)) (SIGNATURE |remove| (|#1| |#2| |#1|)) (SIGNATURE |select| #1=(|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove| #1#)) (|Collection| |#2|) (|Type|)) (T |Collection&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 38 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#3=($) 6 T CONST)) (|removeDuplicates| (($ $) 36 (AND (|has| |#1| (|BasicType|)) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) 39 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ |#1| $) 37 (AND (|has| |#1| (|BasicType|)) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #4=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #4#) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT)) (|eq?| ((#5=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#5# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| (((|InputForm|) $) 35 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT)) (|construct| (($ (|List| |#1|)) 40 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|Collection| |#1|) (|Category|) (|Type|)) (T |Collection|)) 
((|construct| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|Collection| *3)))) (|remove| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|select| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|remove| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|)))) (|removeDuplicates| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|))))) 
(|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |construct| ($ (|List| |t#1|))) (IF (|has| $ (|FiniteAggregate| |t#1|)) (PROGN (SIGNATURE |remove| ($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |select| ($ (|Mapping| (|Boolean|) |t#1|) $)) (IF (|has| |t#1| (|BasicType|)) (PROGN (SIGNATURE |remove| ($ |t#1| $)) (SIGNATURE |removeDuplicates| ($ $))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| ((#5=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|recip| ((#5# $) 113 T ELT)) (|opposite?| #1#) (|one?| #4#) (|monomial| (($ |#2| #7=(|List| #8=(|PositiveInteger|))) 72 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|e| (($ #8#) 58 T ELT)) (|dimension| (((|CardinalNumber|)) 23 T ELT)) (|coerce| (((|OutputForm|) $) 88 T ELT) (($ #9=(|Integer|)) 54 T ELT) (($ |#2|) 55 T ELT)) (|coefficient| ((|#2| $ #7#) 75 T ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) 20 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#6# 48 T CONST)) (|One| (#6# 52 T CONST)) (= (#2# 34 T ELT)) (/ #11=(($ $ |#2|) NIL T ELT)) (- (($ $) 43 T ELT) (#12=($ $ $) 41 T ELT)) (+ (#12# 39 T ELT)) (** (($ $ #8#) NIL T ELT) (($ $ #10#) NIL T ELT)) (* (($ #8# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #9# $) 45 T ELT) (#12# 64 T ELT) (($ |#2| $) 47 T ELT) #11#)) 
(((|CliffordAlgebra| |#1| |#2| |#3|) (|Join| (|Ring|) (|Algebra| |#2|) (|VectorSpace| |#2|) (CATEGORY |domain| (SIGNATURE |e| ($ #1=(|PositiveInteger|))) (SIGNATURE |monomial| ($ |#2| #2=(|List| #1#))) (SIGNATURE |coefficient| (|#2| $ #2#)) (SIGNATURE |recip| ((|Union| $ "failed") $)))) #1# (|Field|) (|QuadraticForm| |#1| |#2|)) (T |CliffordAlgebra|)) 
((|recip| (*1 *1 *1) (|partial| AND (|isDomain| *1 (|CliffordAlgebra| *2 *3 *4)) (|ofType| *2 #1=(|PositiveInteger|)) (|ofCategory| *3 #2=(|Field|)) (|ofType| *4 (|QuadraticForm| *2 *3)))) (|e| (*1 *1 *2) (AND (|isDomain| *2 #1#) (|isDomain| *1 (|CliffordAlgebra| *3 *4 *5)) (|ofType| *3 *2) (|ofCategory| *4 #2#) (|ofType| *5 (|QuadraticForm| *3 *4)))) (|monomial| (*1 *1 *2 *3) (AND #3=(|isDomain| *3 (|List| #1#)) #4=(|isDomain| *1 (|CliffordAlgebra| *4 *2 *5)) #5=(|ofType| *4 #1#) #6=(|ofCategory| *2 #2#) #7=(|ofType| *5 (|QuadraticForm| *4 *2)))) (|coefficient| (*1 *2 *1 *3) (AND #3# #6# #4# #5# #7#))) 
((|clipWithRanges| ((#1=(|Record| (|:| |brans| #2=(|List| #3=(|List| (|Point| #4=(|DoubleFloat|))))) (|:| |xValues| #5=(|Segment| #4#)) (|:| |yValues| #5#)) #2# #4# #4# #4# #4#) 59 T ELT)) (|clipParametric| (#6=(#1# #7=(|Plot|) #8=(|Fraction| (|Integer|)) #8#) 95 T ELT) (#9=(#1# #7#) 96 T ELT)) (|clip| ((#1# #2#) 99 T ELT) ((#1# #3#) 98 T ELT) (#6# 89 T ELT) (#9# 90 T ELT))) 
(((|TwoDimensionalPlotClipping|) (CATEGORY |package| (SIGNATURE |clip| #1=(#2=(|Record| (|:| |brans| #3=(|List| #4=(|List| (|Point| #5=(|DoubleFloat|))))) (|:| |xValues| #6=(|Segment| #5#)) (|:| |yValues| #6#)) #7=(|Plot|))) (SIGNATURE |clip| #8=(#2# #7# #9=(|Fraction| (|Integer|)) #9#)) (SIGNATURE |clipParametric| #1#) (SIGNATURE |clipParametric| #8#) (SIGNATURE |clipWithRanges| (#2# #3# #5# #5# #5# #5#)) (SIGNATURE |clip| (#2# #4#)) (SIGNATURE |clip| (#2# #3#)))) (T |TwoDimensionalPlotClipping|)) 
((|clip| #1=(*1 *2 *3) (AND #2=(|isDomain| *2 (|Record| (|:| |brans| #3=(|List| #4=(|List| (|Point| #5=(|DoubleFloat|))))) (|:| |xValues| #6=(|Segment| #5#)) (|:| |yValues| #6#))) #7=(|isDomain| *1 (|TwoDimensionalPlotClipping|)) (|isDomain| *3 #3#))) (|clip| #1# (AND #2# #7# (|isDomain| *3 #4#))) (|clipWithRanges| (*1 *2 *3 *4 *4 *4 *4) (AND (|isDomain| *4 #5#) (|isDomain| *2 (|Record| (|:| |brans| #8=(|List| (|List| (|Point| *4)))) (|:| |xValues| #9=(|Segment| *4)) (|:| |yValues| #9#))) #7# (|isDomain| *3 #8#))) (|clipParametric| #10=(*1 *2 *3 *4 *4) #11=(AND #12=(|isDomain| *3 (|Plot|)) (|isDomain| *4 (|Fraction| (|Integer|))) #2# #7#)) (|clipParametric| #1# #13=(AND #12# #2# #7#)) (|clip| #10# #11#) (|clip| #1# #13#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|iterators| (((|List| #2=(|SpadAst|)) $) 20 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 27 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|body| ((#2# $) 10 T ELT)) (|before?| #1#) (= #1#)) 
(((|CollectAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |iterators| ((|List| #1=(|SpadAst|)) $)) (SIGNATURE |body| (#1# $))))) (T |CollectAst|)) 
((|iterators| #1=(*1 *2 *1) (AND (|isDomain| *2 (|List| #2=(|SpadAst|))) #3=(|isDomain| *1 (|CollectAst|)))) (|body| #1# (AND (|isDomain| *2 #2#) #3#))) 
((|complexZeros| (((|List| (|Complex| |#2|)) |#1| |#2|) 50 T ELT))) 
(((|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|)))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|rhs| (((|TypeAst|) $) 13 T ELT)) (|lhs| (((|SpadAst|) $) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|ColonAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |lhs| ((|SpadAst|) $)) (SIGNATURE |rhs| ((|TypeAst|) $))))) (T |ColonAst|)) 
((|lhs| #1=(*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) #2=(|isDomain| *1 (|ColonAst|)))) (|rhs| #1# (AND (|isDomain| *2 (|TypeAst|)) #2#))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|yellow| (#3=($) 38 T ELT)) (|red| (#3# 37 T ELT)) (|numberOfHues| ((#4=(|PositiveInteger|)) 43 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hue| ((#5=(|Integer|) $) 41 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|green| (#3# 39 T ELT)) (|color| (($ #5#) 44 T ELT)) (|coerce| (((|OutputForm|) $) 50 T ELT)) (|blue| (#3# 40 T ELT)) (|before?| #1#) (= (#2# 35 T ELT)) (+ (($ $ $) 32 T ELT)) (* (($ #4# $) 42 T ELT) (($ (|DoubleFloat|) $) 11 T ELT))) 
(((|Color|) (|Join| (|AbelianSemiGroup|) (CATEGORY |domain| (SIGNATURE * ($ #1=(|PositiveInteger|) $)) (SIGNATURE * ($ (|DoubleFloat|) $)) (SIGNATURE + ($ $ $)) (SIGNATURE |red| #2=($)) (SIGNATURE |yellow| #2#) (SIGNATURE |green| #2#) (SIGNATURE |blue| #2#) (SIGNATURE |hue| (#3=(|Integer|) $)) (SIGNATURE |numberOfHues| (#1#)) (SIGNATURE |color| ($ #3#))))) (T |Color|)) 
((+ (*1 *1 *1 *1) #1=(|isDomain| *1 (|Color|))) (* #2=(*1 *1 *2 *1) #3=(AND (|isDomain| *2 (|PositiveInteger|)) #1#)) (* #2# (AND (|isDomain| *2 (|DoubleFloat|)) #1#)) (|red| #4=(*1 *1) #1#) (|yellow| #4# #1#) (|green| #4# #1#) (|blue| #4# #1#) (|hue| (*1 *2 *1) #5=(AND (|isDomain| *2 (|Integer|)) #1#)) (|numberOfHues| (*1 *2) #3#) (|color| (*1 *1 *2) #5#)) 
((|summation| (#1=(|#2| |#2| (|SegmentBinding| |#2|)) 98 T ELT) (#2=(|#2| |#2| (|Symbol|)) 75 T ELT)) (|product| (#1# 97 T ELT) (#2# 74 T ELT)) (|permutation| (#3=(|#2| |#2| |#2|) 25 T ELT)) (|operator| ((#4=(|BasicOperator|) #4#) 111 T ELT)) (|ipow| (#5=(|#2| (|List| |#2|)) 130 T ELT)) (|iipow| (#5# 150 T ELT)) (|iiperm| (#5# 138 T ELT)) (|iifact| (#6=(|#2| |#2|) 136 T ELT)) (|iidsum| (#5# 124 T ELT)) (|iidprod| (#5# 125 T ELT)) (|iibinom| (#5# 148 T ELT)) (|factorials| (#2# 63 T ELT) (#6# 62 T ELT)) (|factorial| (#6# 21 T ELT)) (|binomial| (#3# 24 T ELT)) (|belong?| (((|Boolean|) #4#) 55 T ELT)) (** (#3# 46 T ELT))) 
(((|CombinatorialFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) #1=(|BasicOperator|))) (SIGNATURE |operator| (#1# #1#)) (SIGNATURE ** #2=(|#2| |#2| |#2|)) (SIGNATURE |binomial| #2#) (SIGNATURE |permutation| #2#) (SIGNATURE |factorial| #3=(|#2| |#2|)) (SIGNATURE |factorials| #3#) (SIGNATURE |factorials| #4=(|#2| |#2| (|Symbol|))) (SIGNATURE |summation| #4#) (SIGNATURE |summation| #5=(|#2| |#2| (|SegmentBinding| |#2|))) (SIGNATURE |product| #4#) (SIGNATURE |product| #5#) (SIGNATURE |iifact| #3#) (SIGNATURE |iibinom| #6=(|#2| (|List| |#2|))) (SIGNATURE |iiperm| #6#) (SIGNATURE |iipow| #6#) (SIGNATURE |iidsum| #6#) (SIGNATURE |iidprod| #6#) (SIGNATURE |ipow| #6#)) (|IntegralDomain|) (|FunctionSpace| |#1|)) (T |CombinatorialFunction|)) 
((|ipow| #1=(*1 *2 *3) #2=(AND (|isDomain| *3 (|List| *2)) #3=(|ofCategory| *2 #4=(|FunctionSpace| *4)) #5=(|isDomain| *1 (|CombinatorialFunction| *4 *2)) #6=(|ofCategory| *4 #7=(|IntegralDomain|)))) (|iidprod| #1# #2#) (|iidsum| #1# #2#) (|iipow| #1# #2#) (|iiperm| #1# #2#) (|iibinom| #1# #2#) (|iifact| #8=(*1 *2 *2) #9=(AND #10=(|ofCategory| *3 #7#) (|isDomain| *1 (|CombinatorialFunction| *3 *2)) (|ofCategory| *2 #11=(|FunctionSpace| *3)))) (|product| #12=(*1 *2 *2 *3) #13=(AND (|isDomain| *3 (|SegmentBinding| *2)) #3# #6# #5#)) (|product| #12# #14=(AND (|isDomain| *3 (|Symbol|)) #6# #5# #3#)) (|summation| #12# #13#) (|summation| #12# #14#) (|factorials| #12# #14#) (|factorials| #8# #9#) (|factorial| #8# #9#) (|permutation| #15=(*1 *2 *2 *2) #9#) (|binomial| #15# #9#) (** #15# #9#) (|operator| #8# (AND (|isDomain| *2 #16=(|BasicOperator|)) #10# (|isDomain| *1 (|CombinatorialFunction| *3 *4)) (|ofCategory| *4 #11#))) (|belong?| #1# (AND (|isDomain| *3 #16#) #6# (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|CombinatorialFunction| *4 *5)) (|ofCategory| *5 #4#)))) 
((|stirling2| (#1=(|#1| |#1| |#1|) 66 T ELT)) (|stirling1| (#1# 63 T ELT)) (|permutation| (#1# 57 T ELT)) (|partition| (#2=(|#1| |#1|) 43 T ELT)) (|multinomial| ((|#1| |#1| (|List| |#1|)) 55 T ELT)) (|factorial| (#2# 47 T ELT)) (|binomial| (#1# 51 T ELT))) 
(((|IntegerCombinatoricFunctions| |#1|) (CATEGORY |package| (SIGNATURE |binomial| #1=(|#1| |#1| |#1|)) (SIGNATURE |factorial| #2=(|#1| |#1|)) (SIGNATURE |multinomial| (|#1| |#1| (|List| |#1|))) (SIGNATURE |partition| #2#) (SIGNATURE |permutation| #1#) (SIGNATURE |stirling1| #1#) (SIGNATURE |stirling2| #1#)) (|IntegerNumberSystem|)) (T |IntegerCombinatoricFunctions|)) 
((|stirling2| #1=(*1 *2 *2 *2) #2=(AND #3=(|isDomain| *1 (|IntegerCombinatoricFunctions| *2)) #4=(|ofCategory| *2 (|IntegerNumberSystem|)))) (|stirling1| #1# #2#) (|permutation| #1# #2#) (|partition| #5=(*1 *2 *2) #2#) (|multinomial| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) #4# #3#)) (|factorial| #5# #2#) (|binomial| #1# #2#)) 
((|summation| (($ $ (|Symbol|)) 12 T ELT) (($ $ (|SegmentBinding| $)) 11 T ELT)) (|product| (($ $ (|Symbol|)) 10 T ELT) (($ $ (|SegmentBinding| $)) 9 T ELT)) (|permutation| (#1=($ $ $) 8 T ELT)) (|factorials| (($ $) 14 T ELT) (($ $ (|Symbol|)) 13 T ELT)) (|factorial| (($ $) 7 T ELT)) (|binomial| (#1# 6 T ELT))) 
(((|CombinatorialOpsCategory|) (|Category|)) (T |CombinatorialOpsCategory|)) 
((|factorials| (*1 *1 *1) (|ofCategory| *1 (|CombinatorialOpsCategory|))) (|factorials| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|CombinatorialOpsCategory|)) (|isDomain| *2 (|Symbol|)))) (|summation| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|CombinatorialOpsCategory|)) (|isDomain| *2 (|Symbol|)))) (|summation| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SegmentBinding| *1)) (|ofCategory| *1 (|CombinatorialOpsCategory|)))) (|product| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|CombinatorialOpsCategory|)) (|isDomain| *2 (|Symbol|)))) (|product| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SegmentBinding| *1)) (|ofCategory| *1 (|CombinatorialOpsCategory|))))) 
(|Join| (|CombinatorialFunctionCategory|) (CATEGORY |domain| (SIGNATURE |factorials| ($ $)) (SIGNATURE |factorials| ($ $ (|Symbol|))) (SIGNATURE |summation| ($ $ (|Symbol|))) (SIGNATURE |summation| ($ $ (|SegmentBinding| $))) (SIGNATURE |product| ($ $ (|Symbol|))) (SIGNATURE |product| ($ $ (|SegmentBinding| $))))) 
(((|CombinatorialFunctionCategory|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|mkcomm| (($ (|Integer|)) 15 T ELT) (($ $ $) 16 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 19 T ELT)) (|before?| #1#) (= (#2# 11 T ELT))) 
(((|Commutator|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |mkcomm| ($ (|Integer|))) (SIGNATURE |mkcomm| ($ $ $))))) (T |Commutator|)) 
((|mkcomm| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #1=(|isDomain| *1 (|Commutator|)))) (|mkcomm| (*1 *1 *1 *1) #1#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|body| (((|List| (|SpadAst|)) $) 10 T ELT)) (|before?| #1#) (= #1#)) 
(((|CommaAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |body| ((|List| (|SpadAst|)) $))))) (T |CommaAst|)) 
((|body| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|CommaAst|))))) 
((|operator| (((|BasicOperator|) (|Symbol|)) 103 T ELT))) 
(((|CommonOperators|) (CATEGORY |package| (SIGNATURE |operator| ((|BasicOperator|) (|Symbol|))))) (T |CommonOperators|)) 
((|operator| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|BasicOperator|)) (|isDomain| *1 (|CommonOperators|))))) 
((|swap| ((|#3| |#3|) 19 T ELT))) 
(((|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))))) 
((|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|commutativeOperation| (($ (|Mapping| |#1| |#1| |#1|)) 9 T ELT)) (|coerce| (((|BinaryOperation| |#1|) $) 10 T ELT))) 
(((|CommutativeOperation| |#1|) (|Join| (|CommutativeOperatorCategory| |#1|) (|CoercibleTo| (|BinaryOperation| |#1|)) (CATEGORY |domain| (SIGNATURE |commutativeOperation| ($ (|Mapping| |#1| |#1| |#1|))))) (|BasicType|)) (T |CommutativeOperation|)) 
((|commutativeOperation| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|BasicType|)) (|isDomain| *1 (|CommutativeOperation| *3))))) 
((|elt| ((|#1| $ |#1| |#1|) 6 T ELT))) 
(((|CommutativeOperatorCategory| |#1|) (|Category|) (|BasicType|)) (T |CommutativeOperatorCategory|)) 
NIL 
(|Join| (|BinaryOperatorCategory| |t#1|) (CATEGORY |domain| (ATTRIBUTE (|%Rule| |commutativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|) (|:| |y| |t#1|)) (= (|f| |x| |y|) (|f| |y| |x|))))))) 
(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . T)) 
((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 222 T ELT)) (|trace| (#1=(|#2| $) 102 T ELT)) (|tanh| (#2=($ $) 255 T ELT)) (|tan| (#2# 249 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #3=(|List| #4=(|SparseUnivariatePolynomial| $)) #5="failed") #3# #4#) 47 T ELT)) (|sinh| (#2# 253 T ELT)) (|sin| (#2# 247 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) #5#) $) NIL T ELT) (#7=((|Union| #8=(|Fraction| #6#) #5#) $) NIL T ELT) (((|Union| |#2| #5#) $) 146 T ELT)) (|retract| ((#6# $) NIL T ELT) (#9=(#8# $) NIL T ELT) (#1# 144 T ELT)) (|rem| (#10=($ $ $) 228 T ELT)) (|reducedSystem| ((#11=(|Matrix| #6#) #12=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #11#) (|:| |vec| (|Vector| #6#))) #12# #13=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #14=(|Matrix| |#2|)) (|:| |vec| #15=(|Vector| |#2|))) #12# #13#) 160 T ELT) ((#14# #12#) 154 T ELT)) (|reduce| (#16=($ #17=(|SparseUnivariatePolynomial| |#2|)) 125 T ELT) ((#18=(|Union| $ #5#) (|Fraction| #17#)) NIL T ELT)) (|recip| ((#18# $) 213 T ELT)) (|rationalIfCan| (#7# 203 T ELT)) (|rational?| ((#19=(|Boolean|) $) 198 T ELT)) (|rational| (#9# 201 T ELT)) (|rank| ((#20=(|PositiveInteger|)) 96 T ELT)) (|quo| (#10# 230 T ELT)) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) 267 T ELT)) (|pi| (#21=($) 244 T ELT)) (|patternMatch| ((#22=(|PatternMatchResult| #6# $) $ #23=(|Pattern| #6#) #22#) 192 T ELT) ((#24=(|PatternMatchResult| #25=(|Float|) $) $ #26=(|Pattern| #25#) #24#) 197 T ELT)) (|norm| (#1# 100 T ELT)) (|minimalPolynomial| (#27=(#17# $) 127 T ELT)) (|map| (($ #28=(|Mapping| |#2| |#2|) $) 108 T ELT)) (|log| (#2# 246 T ELT)) (|lift| (#27# 126 T ELT)) (|inv| (#2# 206 T ELT)) (|imaginary| (#21# 103 T ELT)) (|factorSquareFreePolynomial| (#29=((|Factored| #4#) #4#) 95 T ELT)) (|factorPolynomial| (#29# 64 T ELT)) (|exquo| ((#18# $ |#2|) 208 T ELT) ((#18# $ $) 211 T ELT)) (|exp| (#2# 245 T ELT)) (|euclideanSize| ((#30=(|NonNegativeInteger|) $) 225 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 234 T ELT)) (|discriminant| ((|#2| #13#) NIL T ELT) ((|#2|) 98 T ELT)) (|differentiate| (($ $ #28#) 119 T ELT) (($ $ #28# #30#) NIL T ELT) (($ $ #31=(|List| #32=(|Symbol|)) (|List| #30#)) NIL T ELT) (($ $ #32# #30#) NIL T ELT) (($ $ #31#) NIL T ELT) (($ $ #32#) NIL T ELT) #33=(($ $ #30#) NIL T ELT) #34=(#2# NIL T ELT)) (|definingPolynomial| ((#17#) 120 T ELT)) (|cosh| (#2# 254 T ELT)) (|cos| (#2# 248 T ELT)) (|coordinates| ((#15# $ #13#) 136 T ELT) ((#14# #13# #13#) NIL T ELT) (#35=(#15# $) 116 T ELT) ((#14# #13#) NIL T ELT)) (|convert| (#35# NIL T ELT) (($ #15#) NIL T ELT) (#27# NIL T ELT) (#16# NIL T ELT) ((#23# $) 183 T ELT) ((#26# $) 187 T ELT) (((|Complex| #25#) $) 172 T ELT) (((|Complex| (|DoubleFloat|)) $) 167 T ELT) (((|InputForm|) $) 179 T ELT)) (|conjugate| (#2# 104 T ELT)) (|coerce| (((|OutputForm|) $) 143 T ELT) (($ #6#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #8#) NIL T ELT) #34#) (|characteristicPolynomial| (#27# 32 T ELT)) (|characteristic| ((#30#) 106 T CONST)) (|before?| (#36=(#19# $ $) 13 T ELT)) (|atanh| (#2# 258 T ELT)) (|atan| (#2# 252 T ELT)) (|asinh| (#2# 256 T ELT)) (|asin| (#2# 250 T ELT)) (|argument| (#1# 241 T ELT)) (|acosh| (#2# 257 T ELT)) (|acos| (#2# 251 T ELT)) (|abs| (#2# 162 T ELT)) (= (#36# 110 T ELT)) (- (#2# 112 T ELT) #37=(#10# NIL T ELT)) (+ (#10# 111 T ELT)) (** (($ $ #20#) NIL T ELT) #33# (#38=($ $ #8#) 274 T ELT) #37# (($ $ #6#) NIL T ELT)) (* (($ #20# $) NIL T ELT) (($ #30# $) NIL T ELT) (($ #6# $) 118 T ELT) (#10# 147 T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) 114 T ELT) (($ #8# $) NIL T ELT) (#38# NIL T ELT))) 
(((|ComplexCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |differentiate| #1=(|#1| |#1|)) (SIGNATURE |differentiate| #2=(|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #4=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #5=(|List| #4#))) (SIGNATURE |differentiate| (|#1| |#1| #4# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #5# (|List| #3#))) (SIGNATURE |coerce| #1#) (SIGNATURE |exquo| (#6=(|Union| |#1| #7="failed") |#1| |#1|)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |euclideanSize| (#3# |#1|)) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |quo| #8=(|#1| |#1| |#1|)) (SIGNATURE |rem| #8#) (SIGNATURE |inv| #1#) (SIGNATURE ** (|#1| |#1| #9=(|Integer|))) (SIGNATURE * #10=(|#1| |#1| #11=(|Fraction| #9#))) (SIGNATURE * (|#1| #11# |#1|)) (SIGNATURE |coerce| (|#1| #11#)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| ((|Complex| (|DoubleFloat|)) |#1|)) (SIGNATURE |convert| ((|Complex| #12=(|Float|)) |#1|)) (SIGNATURE |tan| #1#) (SIGNATURE |sin| #1#) (SIGNATURE |cos| #1#) (SIGNATURE |acos| #1#) (SIGNATURE |asin| #1#) (SIGNATURE |atan| #1#) (SIGNATURE |cosh| #1#) (SIGNATURE |sinh| #1#) (SIGNATURE |tanh| #1#) (SIGNATURE |acosh| #1#) (SIGNATURE |asinh| #1#) (SIGNATURE |atanh| #1#) (SIGNATURE |log| #1#) (SIGNATURE |exp| #1#) (SIGNATURE ** #8#) (SIGNATURE |pi| #13=(|#1|)) (SIGNATURE ** #10#) (SIGNATURE |factorPolynomial| #14=((|Factored| #15=(|SparseUnivariatePolynomial| |#1|)) #15#)) (SIGNATURE |factorSquareFreePolynomial| #14#) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #16=(|List| #15#) #7#) #16# #15#)) (SIGNATURE |rationalIfCan| #17=((|Union| #11# #7#) |#1|)) (SIGNATURE |rational| #18=(#11# |#1|)) (SIGNATURE |rational?| (#19=(|Boolean|) |#1|)) (SIGNATURE |polarCoordinates| ((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) |#1|)) (SIGNATURE |argument| #20=(|#2| |#1|)) (SIGNATURE |abs| #1#) (SIGNATURE |exquo| (#6# |#1| |#2|)) (SIGNATURE |conjugate| #1#) (SIGNATURE |imaginary| #13#) (SIGNATURE |convert| (#21=(|Pattern| #12#) |#1|)) (SIGNATURE |convert| (#22=(|Pattern| #9#) |#1|)) (SIGNATURE |patternMatch| (#23=(|PatternMatchResult| #12# |#1|) |#1| #21# #23#)) (SIGNATURE |patternMatch| (#24=(|PatternMatchResult| #9# |#1|) |#1| #22# #24#)) (SIGNATURE |map| (|#1| #25=(|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #25# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #25#)) (SIGNATURE |reduce| (#6# (|Fraction| #26=(|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |lift| #27=(#26# |#1|)) (SIGNATURE |convert| #28=(|#1| #26#)) (SIGNATURE |reduce| #28#) (SIGNATURE |definingPolynomial| (#26#)) (SIGNATURE |reducedSystem| (#29=(|Matrix| |#2|) #30=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #29#) (|:| |vec| #31=(|Vector| |#2|))) #30# #32=(|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #33=(|Matrix| #9#)) (|:| |vec| (|Vector| #9#))) #30# #32#)) (SIGNATURE |reducedSystem| (#33# #30#)) (SIGNATURE |retractIfCan| ((|Union| |#2| #7#) |#1|)) (SIGNATURE |retract| #20#) (SIGNATURE |retract| #18#) (SIGNATURE |retractIfCan| #17#) (SIGNATURE |retract| (#9# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #9# #7#) |#1|)) (SIGNATURE |convert| #27#) (SIGNATURE |discriminant| (|#2|)) (SIGNATURE |convert| (|#1| #31#)) (SIGNATURE |convert| #34=(#31# |#1|)) (SIGNATURE |coordinates| (#29# #32#)) (SIGNATURE |coordinates| #34#) (SIGNATURE |minimalPolynomial| #27#) (SIGNATURE |characteristicPolynomial| #27#) (SIGNATURE |discriminant| (|#2| #32#)) (SIGNATURE |coordinates| (#29# #32# #32#)) (SIGNATURE |coordinates| (#31# |#1| #32#)) (SIGNATURE |norm| #20#) (SIGNATURE |trace| #20#) (SIGNATURE |rank| (#35=(|PositiveInteger|))) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |characteristic| (#3#) |constant|) (SIGNATURE |coerce| (|#1| #9#)) (SIGNATURE |recip| (#6# |#1|)) (SIGNATURE ** #2#) (SIGNATURE * #8#) (SIGNATURE ** (|#1| |#1| #35#)) (SIGNATURE - #8#) (SIGNATURE - #1#) (SIGNATURE * (|#1| #9# |#1|)) (SIGNATURE * (|#1| #3# |#1|)) (SIGNATURE * (|#1| #35# |#1|)) (SIGNATURE + #8#) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |before?| #36=(#19# |#1| |#1|)) (SIGNATURE = #36#)) (|ComplexCategory| |#2|) (|CommutativeRing|)) (T |ComplexCategory&|)) 
((|characteristic| #1=(*1 *2) (AND #2=(|ofCategory| *4 #3=(|CommutativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)) #4=(|isDomain| *1 (|ComplexCategory&| *3 *4)) #5=(|ofCategory| *3 (|ComplexCategory| *4)))) (|rank| #1# (AND #2# (|isDomain| *2 (|PositiveInteger|)) #4# #5#)) (|discriminant| #1# (AND (|ofCategory| *2 #3#) (|isDomain| *1 (|ComplexCategory&| *3 *2)) (|ofCategory| *3 (|ComplexCategory| *2)))) (|definingPolynomial| #1# (AND #2# (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) #4# #5#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 114 (OR (|has| |#1| . #3=((|IntegralDomain|))) (AND (|has| |#1| . #4=((|EuclideanDomain|))) (|has| |#1| . #5=((|PolynomialFactorizationExplicit|))))) ELT)) (|unitCanonical| (($ $) 115 (OR (|has| |#1| . #3#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT)) (|unit?| ((#6=(|Boolean|) $) 117 (OR (|has| |#1| . #3#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT)) (|traceMatrix| (((|Matrix| |#1|) #7=(|Vector| $)) 61 T ELT) (((|Matrix| |#1|)) 77 T ELT)) (|trace| ((|#1| . #8=($)) 67 T ELT)) (|tanh| (#9=($ $) 250 (|has| |#1| . #10=((|TranscendentalFunctionCategory|))) ELT)) (|tan| (#11=($ $) 233 (|has| |#1| . #10#) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12=(|PositiveInteger|) #13=(|NonNegativeInteger|)) #14=(|Integer|)) 167 (|has| |#1| . #15=((|FiniteFieldCategory|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (#16=((|Factored| #17=(|SparseUnivariatePolynomial| $)) #17#) 264 (AND (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (|squareFreePart| (($ $) 134 (OR (AND (|has| |#1| . #4#) (|has| |#1| . #5#)) (|has| |#1| . #18=((|Field|)))) ELT)) (|squareFree| (#19=((|Factored| $) $) 135 (OR (AND (|has| |#1| . #4#) (|has| |#1| . #5#)) (|has| |#1| . #18#)) ELT)) (|sqrt| (($ $) 263 (AND (|has| |#1| . #20=((|RadicalCategory|))) (|has| |#1| . #21=((|TranscendentalFunctionCategory|)))) ELT)) (|solveLinearPolynomialEquation| (((|Union| #22=(|List| #17#) "failed") #22# #17#) 267 (AND (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (|sizeLess?| (((|Boolean|) $ $) 125 (|has| |#1| . #23=((|EuclideanDomain|))) ELT)) (|size| (((|NonNegativeInteger|)) 108 (|has| |#1| . #24=((|Finite|))) ELT)) (|sinh| (#9# 249 (|has| |#1| . #10#) ELT)) (|sin| (#11# 234 (|has| |#1| . #10#) ELT)) (|sech| (#9# 248 (|has| |#1| . #10#) ELT)) (|sec| (#11# 235 (|has| |#1| . #10#) ELT)) (|sample| (#25=($) 23 T CONST)) (|retractIfCan| (((|Union| #26=(|Integer|) . #27=("failed")) . #28=($)) 194 (|has| |#1| . #29=((|RetractableTo| #26#))) ELT) (((|Union| #30=(|Fraction| #26#) . #27#) . #28#) 192 (|has| |#1| . #31=((|RetractableTo| #30#))) ELT) (((|Union| |#1| . #27#) . #28#) 189 T ELT)) (|retract| ((#26# . #32=($)) 193 (|has| |#1| . #29#) ELT) ((#30# . #32#) 191 (|has| |#1| . #31#) ELT) ((|#1| . #32#) 190 T ELT)) (|represents| (($ (|Vector| |#1|) #7#) 63 T ELT) (($ (|Vector| |#1|)) 80 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 173 (|has| |#1| . #15#) ELT)) (|rem| (#33=($ $ $) 129 (|has| |#1| . #23#) ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ #7#) 68 T ELT) (((|Matrix| |#1|) $) 75 T ELT)) (|reducedSystem| (((|Matrix| #34=(|Integer|)) . #35=(#36=(|Matrix| $))) 186 (|has| |#1| . #37=((|LinearlyExplicitRingOver| #34#))) ELT) (((|Record| (|:| |mat| (|Matrix| #34#)) (|:| |vec| (|Vector| #34#))) . #38=(#36# #39=(|Vector| $))) 185 (|has| |#1| . #37#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #38#) 184 T ELT) (((|Matrix| |#1|) . #35#) 183 T ELT)) (|reduce| (($ (|SparseUnivariatePolynomial| |#1|)) 178 T ELT) (((|Union| $ "failed") (|Fraction| (|SparseUnivariatePolynomial| |#1|))) 175 (|has| |#1| . #18#) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|real| ((|#1| $) 275 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 268 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (((|Boolean|) $) 270 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational| (((|Fraction| (|Integer|)) $) 269 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rank| (((|PositiveInteger|)) 69 T ELT)) (|random| (($) 111 (|has| |#1| . #24#) ELT)) (|quo| (#33# 128 (|has| |#1| . #23#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #40=(|List| $)) (|:| |generator| $)) #40#) 123 (|has| |#1| . #23#) ELT)) (|primitiveElement| (#41=($) 169 (|has| |#1| . #15#) ELT)) (|primitive?| (((|Boolean|) $) 170 (|has| |#1| . #15#) ELT)) (|primeFrobenius| (($ $ #42=(|NonNegativeInteger|)) 161 (|has| |#1| . #15#) ELT) (($ $) 160 (|has| |#1| . #15#) ELT)) (|prime?| (((|Boolean|) $) 136 (OR (AND (|has| |#1| . #4#) (|has| |#1| . #5#)) (|has| |#1| . #18#)) ELT)) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) 271 (AND (|has| |#1| (|RealNumberSystem|)) (|has| |#1| (|TranscendentalFunctionCategory|))) ELT)) (|pi| (($) 260 (|has| |#1| . #10#) ELT)) (|patternMatch| (((|PatternMatchResult| #43=(|Integer|) . #44=($)) $ (|Pattern| #43#) (|PatternMatchResult| #43# . #44#)) 283 (|has| |#1| (|PatternMatchable| #43#)) ELT) (((|PatternMatchResult| #45=(|Float|) . #44#) $ (|Pattern| #45#) (|PatternMatchResult| #45# . #44#)) 282 (|has| |#1| (|PatternMatchable| #45#)) ELT)) (|order| ((#12# $) 172 (|has| |#1| . #15#) ELT) (((|OnePointCompletion| (|PositiveInteger|)) $) 158 (|has| |#1| . #15#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #46=(|Integer|)) 262 (AND (|has| |#1| . #20#) (|has| |#1| . #21#)) ELT)) (|norm| ((|#1| . #8#) 66 T ELT)) (|nextItem| (((|Maybe| $) $) 162 (|has| |#1| . #15#) ELT)) (|multiEuclidean| (((|Union| #47=(|List| $) #48="failed") #47# $) 132 (|has| |#1| . #23#) ELT)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #49=($)) 59 (|has| |#1| (|Field|)) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 284 T ELT)) (|lookup| ((#50=(|PositiveInteger|) $) 110 (|has| |#1| . #24#) ELT)) (|log| (#51=($ $) 257 (|has| |#1| . #10#) ELT)) (|lift| (((|SparseUnivariatePolynomial| |#1|) $) 176 T ELT)) (|leftReducedSystem| (((|Matrix| #34#) . #52=(#39#)) 188 (|has| |#1| . #37#) ELT) (((|Record| (|:| |mat| (|Matrix| #34#)) (|:| |vec| (|Vector| #34#))) . #53=(#39# $)) 187 (|has| |#1| . #37#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #53#) 182 T ELT) (((|Matrix| |#1|) . #52#) 181 T ELT)) (|lcm| (#54=($ (|List| $)) 121 (OR (|has| |#1| . #23#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT) (#55=($ $ $) 120 (OR (|has| |#1| . #23#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 137 (|has| |#1| . #18#) ELT)) (|init| (($) 163 (|has| |#1| . #15#) CONST)) (|index| (($ #50#) 109 (|has| |#1| . #24#) ELT)) (|imaginary| (($) 279 T ELT)) (|imag| ((|#1| $) 276 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (($) 180 T ELT)) (|gcdPolynomial| ((#56=(|SparseUnivariatePolynomial| $) #56# #56#) 122 (OR (|has| |#1| . #23#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT)) (|gcd| (#54# 119 (OR (|has| |#1| . #23#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT) (#55# 118 (OR (|has| |#1| . #23#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) 166 (|has| |#1| . #15#) ELT)) (|factorSquareFreePolynomial| (#16# 266 (AND (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (|factorPolynomial| (#16# 265 (AND (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (|factor| (#19# 133 (OR (AND (|has| |#1| . #4#) (|has| |#1| . #5#)) (|has| |#1| . #18#)) ELT)) (|extendedEuclidean| (((|Union| (|Record| #57=(|:| |coef1| $) #58=(|:| |coef2| $)) #48#) $ $ $) 131 (|has| |#1| . #23#) ELT) (((|Record| #57# #58# (|:| |generator| $)) $ $) 130 (|has| |#1| . #23#) ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 274 (|has| |#1| (|IntegralDomain|)) ELT) (((|Union| $ "failed") $ $) 113 (OR (|has| |#1| . #3#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT)) (|expressIdealMember| (((|Maybe| #40#) #40# $) 124 (|has| |#1| . #23#) ELT)) (|exp| (#51# 258 (|has| |#1| . #10#) ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 290 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 289 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 288 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 287 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| #59=(|Symbol|)) (|List| |#1|)) 286 (|has| |#1| (|InnerEvalable| #59# |#1|)) ELT) (($ $ 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ELT)) (|csc| (#11# 236 (|has| |#1| . #10#) ELT)) (|createPrimitiveElement| (#41# 168 (|has| |#1| . #15#) ELT)) (|coth| (#9# 246 (|has| |#1| . #10#) ELT)) (|cot| (#11# 237 (|has| |#1| . #10#) ELT)) (|cosh| (#9# 245 (|has| |#1| . #10#) ELT)) (|cos| (#11# 238 (|has| |#1| . #10#) ELT)) (|coordinates| (((|Vector| |#1|) $ #7#) 65 T ELT) (((|Matrix| |#1|) #7# #7#) 64 T ELT) (((|Vector| |#1|) . #71=($)) 82 T ELT) (((|Matrix| |#1|) #72=(|Vector| $)) 81 T ELT)) (|convert| (((|Vector| |#1|) . #71#) 79 T ELT) (($ (|Vector| |#1|)) 78 T ELT) (((|SparseUnivariatePolynomial| |#1|) . #73=($)) 195 T ELT) (($ (|SparseUnivariatePolynomial| |#1|)) 177 T ELT) ((#74=(|Pattern| (|Integer|)) . #73#) 281 (|has| |#1| (|ConvertibleTo| #74#)) ELT) ((#75=(|Pattern| (|Float|)) . #73#) 280 (|has| |#1| (|ConvertibleTo| #75#)) ELT) (((|Complex| (|Float|)) . #73#) 232 (|has| |#1| (|RealConstant|)) ELT) (((|Complex| (|DoubleFloat|)) . #73#) 231 (|has| |#1| (|RealConstant|)) ELT) (((|InputForm|) . #73#) 230 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT)) (|conjugate| (($ $) 278 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 165 (OR (|and| #76=(|has| $ (|CharacteristicNonZero|)) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) (|has| |#1| . #15#)) ELT)) (|complex| (($ |#1| |#1|) 277 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT) (($ #77=(|Fraction| #78=(|Integer|))) 107 (OR (|has| |#1| . #18#) (|has| |#1| . #31#)) ELT) (($ $) 112 (OR (|has| |#1| . #3#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT)) (|charthRoot| (($ $) 164 (|has| |#1| . #15#) ELT) (((|Maybe| $) $) 58 (OR (|and| #76# (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) (|has| |#1| (|CharacteristicNonZero|))) ELT)) (|characteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #49#) 60 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| ((#72#) 83 T ELT)) (|atanh| (#79=($ $) 256 (|has| |#1| . #10#) ELT)) (|atan| (#80=($ $) 244 (|has| |#1| . #10#) ELT)) (|associates?| ((#6# $ $) 116 (OR (|has| |#1| . #3#) (AND (|has| |#1| . #4#) (|has| |#1| . #5#))) ELT)) (|asinh| (#79# 255 (|has| |#1| . #10#) ELT)) (|asin| (#80# 243 (|has| |#1| . #10#) ELT)) (|asech| (#79# 254 (|has| |#1| . #10#) ELT)) (|asec| (#80# 242 (|has| |#1| . #10#) ELT)) (|argument| ((|#1| $) 272 (|has| |#1| (|TranscendentalFunctionCategory|)) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#79# 253 (|has| |#1| . #10#) ELT)) (|acsc| (#80# 241 (|has| |#1| . #10#) ELT)) (|acoth| (#79# 252 (|has| |#1| . #10#) ELT)) (|acot| (#80# 240 (|has| |#1| . #10#) ELT)) (|acosh| (#79# 251 (|has| |#1| . #10#) ELT)) (|acos| (#80# 239 (|has| |#1| . #10#) ELT)) (|abs| (($ $) 273 (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#25# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|Mapping| |#1| |#1|)) 143 T ELT) (($ $ (|Mapping| |#1| |#1|) . #60#) 142 T ELT) (($ $ (|List| #61#) . #62#) 153 (OR (|and| (|has| |#1| . #18#) (|has| |#1| . #64#)) (|and| (|has| |#1| . #18#) (|has| |#1| . #65#)) (|has| |#1| . #64#)) ELT) (($ $ #61# . #66#) 152 (OR (|and| (|has| |#1| . #18#) (|has| |#1| . #64#)) (|and| (|has| |#1| . #18#) (|has| |#1| . #65#)) (|has| |#1| . #64#)) ELT) (($ $ (|List| #61#)) 151 (OR (|and| (|has| |#1| . #18#) (|has| |#1| . #64#)) (|and| (|has| |#1| . #18#) (|has| |#1| . #65#)) (|has| |#1| . #64#)) ELT) (($ $ #61#) 147 (OR (|and| (|has| |#1| . #18#) (|has| |#1| . #64#)) (|and| (|has| |#1| . #18#) (|has| |#1| . #65#)) (|has| |#1| . #64#)) ELT) (#67# 157 (OR (|and| (|has| |#1| . #18#) (|has| |#1| . #68#)) (|and| (|has| |#1| . #18#) (|has| |#1| . #69#)) (|has| |#1| . #68#) (|and| (|has| |#1| . #68#) (|has| |#1| . #18#))) ELT) (($ . #70#) 155 (OR (|and| (|has| |#1| . #18#) (|has| |#1| . #68#)) (|and| (|has| |#1| . #18#) (|has| |#1| . #69#)) (|has| |#1| . #68#) (|and| (|has| |#1| . #68#) (|has| |#1| . #18#))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 141 (|has| |#1| . #18#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ (|Fraction| #46#)) 261 (AND (|has| |#1| . #20#) (|has| |#1| . #21#)) ELT) (($ $ $) 259 (|has| |#1| . #10#) ELT) (($ $ #78#) 138 (|has| |#1| . #18#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #81=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #81#) 53 T ELT) (($ #77# . #81#) 140 (|has| |#1| . #18#) ELT) (($ $ #77#) 139 (|has| |#1| . #18#) ELT))) 
(((|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| (|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| #1=(|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| #1# #1#) 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|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|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| #2=(|SparseUnivariatePolynomial| |#1|)) . T) ((|DifferentialDomain| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpace|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#1|) . T) ((|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| (|FiniteFieldCategory|)) (|has| |#1| (|Finite|))) ((|FiniteFieldCategory|) |has| |#1| (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| |#1| #2#) . T) ((|FramedAlgebra| |#1| #2#) . T) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyPatternMatchable| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#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|))) ((|Join|) . T) ((|LeftLinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftModule| #3=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LinearSet| |#1|) . T) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|LinearlyExplicitRingOver| #3#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) 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| #2#) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #4#) OR (|has| |#1| (|PartialDifferentialSpace| (|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) ((|RightLinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . 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|) 67 T ELT))) 
(((|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)))))) 
((|macroExpand| ((#1=(|SpadAst|) #1# (|Environment|)) 8 T ELT)) (|elaborateFile| (((|List| #2=(|Maybe| (|Elaboration|))) (|String|)) 81 T ELT)) (|elaborate| ((#2# #1#) 76 T ELT))) 
(((|CompilerPackage|) (|Join| (|Type|) (CATEGORY |package| (SIGNATURE |macroExpand| (#1=(|SpadAst|) #1# (|Environment|))) (SIGNATURE |elaborate| (#2=(|Maybe| (|Elaboration|)) #1#)) (SIGNATURE |elaborateFile| ((|List| #2#) (|String|)))))) (T |CompilerPackage|)) 
((|macroExpand| (*1 *2 *2 *3) (AND (|isDomain| *2 #1=(|SpadAst|)) (|isDomain| *3 (|Environment|)) #2=(|isDomain| *1 (|CompilerPackage|)))) (|elaborate| #3=(*1 *2 *3) (AND (|isDomain| *3 #1#) (|isDomain| *2 #4=(|Maybe| (|Elaboration|))) #2#)) (|elaborateFile| #3# (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|List| #4#)) #2#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 15 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(OR #6=(AND #7=(|has| |#1| (|EuclideanDomain|)) #8=(|has| |#1| (|PolynomialFactorizationExplicit|))) #9=(|has| |#1| (|IntegralDomain|))) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #5# ELT)) (|unit?| (#4# NIL #5# ELT)) (|traceMatrix| #12=((#13=(|Matrix| |#1|) #14=(|Vector| $)) NIL T ELT) ((#13#) NIL T ELT)) (|trace| #15=(#16=(|#1| $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|TranscendentalFunctionCategory|)) ELT)) (|tan| #17#) (|tableForDiscreteLogarithm| (((|Table| #19=(|PositiveInteger|) #20=(|NonNegativeInteger|)) #21=(|Integer|)) NIL #22=(|has| |#1| (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#23=(#24=(|Union| $ #25="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #26=(((|Factored| #27=(|SparseUnivariatePolynomial| $)) #27#) NIL #6# ELT)) (|squareFreePart| (#11# NIL #28=(OR #6# #29=(|has| |#1| (|Field|))) ELT)) (|squareFree| #30=(((|Factored| $) $) NIL #28# ELT)) (|sqrt| (#11# NIL #31=(AND (|has| |#1| (|RadicalCategory|)) #18#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #32=(|List| #27#) #25#) #32# #27#) NIL #6# ELT)) (|sizeLess?| (#2# NIL #7# ELT)) (|size| (#33=(#20#) NIL #34=(|has| |#1| (|Finite|)) ELT)) (|sinh| #17#) (|sin| #17#) (|sech| #17#) (|sec| #17#) (|sample| (#35=($) NIL T CONST)) (|retractIfCan| (((|Union| #21# . #36=(#25#)) . #37=($)) NIL #38=(|has| |#1| (|RetractableTo| #21#)) ELT) (#39=((|Union| #40=(|Fraction| #21#) . #36#) . #37#) NIL #41=(|has| |#1| (|RetractableTo| #40#)) ELT) (((|Union| |#1| . #36#) . #37#) NIL T ELT)) (|retract| ((#21# . #42=($)) NIL #38# ELT) (#43=(#40# . #42#) NIL #41# ELT) #15#) (|represents| (($ #44=(|Vector| |#1|) #14#) NIL T ELT) #45=(($ #44#) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #22# ELT)) (|rem| #46=(#47=($ $ $) NIL #7# ELT)) (|regularRepresentation| ((#13# $ #14#) NIL T ELT) ((#13# $) NIL T ELT)) (|reducedSystem| ((#48=(|Matrix| #21#) . #49=(#50=(|Matrix| $))) NIL #51=(|has| |#1| (|LinearlyExplicitRingOver| #21#)) ELT) ((#52=(|Record| (|:| |mat| #48#) (|:| |vec| (|Vector| #21#))) . #53=(#50# #14#)) NIL #51# ELT) ((#54=(|Record| (|:| |mat| #13#) (|:| |vec| #44#)) . #53#) NIL T ELT) ((#13# . #49#) NIL T ELT)) (|reduce| #55=(($ #56=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT) ((#24# (|Fraction| #56#)) NIL #29# ELT)) (|recip| ((#24# $) NIL T ELT)) (|real| (#16# 20 T ELT)) (|rationalIfCan| (#39# NIL #57=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#4# NIL #57# ELT)) (|rational| (#43# NIL #57# ELT)) (|rank| ((#19#) NIL T ELT)) (|random| (#35# NIL #34# ELT)) (|quo| #46#) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #7# ELT)) (|primitiveElement| #60=(#35# NIL #22# ELT)) (|primitive?| (#4# NIL #22# ELT)) (|primeFrobenius| (#61=($ $ #20#) NIL #22# ELT) #62=(#11# NIL #22# ELT)) (|prime?| (#4# NIL #28# ELT)) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) NIL (AND #63=(|has| |#1| (|RealNumberSystem|)) #18#) ELT)) (|pi| (#35# NIL #18# ELT)) (|patternMatch| ((#64=(|PatternMatchResult| #21# . #65=($)) $ #66=(|Pattern| #21#) #64#) NIL (|has| |#1| (|PatternMatchable| #21#)) ELT) ((#67=(|PatternMatchResult| #68=(|Float|) . #65#) $ #69=(|Pattern| #68#) #67#) NIL (|has| |#1| (|PatternMatchable| #68#)) ELT)) (|order| (#70=(#19# $) NIL #22# ELT) (((|OnePointCompletion| #19#) $) NIL #22# ELT)) (|opposite?| #1#) (|one?| (#4# 17 T ELT)) (|nthRoot| (#71=($ $ #21#) NIL #31# ELT)) (|norm| (#16# 30 T ELT)) (|nextItem| (#72=((|Maybe| $) $) NIL #22# ELT)) (|multiEuclidean| (((|Union| #58# #25#) #58# $) NIL #7# ELT)) (|minimalPolynomial| (#73=(#56# $) NIL #29# ELT)) (|map| (($ #74=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|lookup| (#70# NIL #34# ELT)) (|log| #17#) (|lift| #75=(#73# NIL T ELT)) (|leftReducedSystem| ((#48# #14#) NIL #51# ELT) ((#52# . #76=(#14# $)) NIL #51# ELT) ((#54# . #76#) NIL T ELT) #12#) (|lcm| #77=(($ #58#) NIL #7# ELT) #46#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#11# NIL #29# ELT)) (|init| (#35# NIL #22# CONST)) (|index| (($ #19#) NIL #34# ELT)) (|imaginary| #78=(#35# NIL T ELT)) (|imag| (#16# 21 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #78#) (|gcdPolynomial| ((#27# #27# #27#) NIL #7# ELT)) (|gcd| #77# #46#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #21#) (|:| |exponent| #21#)))) NIL #22# ELT)) (|factorSquareFreePolynomial| #26#) (|factorPolynomial| #26#) (|factor| #30#) (|extendedEuclidean| (((|Union| (|Record| #79=(|:| |coef1| $) #80=(|:| |coef2| $)) #25#) $ $ $) NIL #7# ELT) (((|Record| #79# #80# #59#) $ $) NIL #7# ELT)) (|exquo| ((#24# $ |#1|) 28 #9# ELT) (#23# 31 #5# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #7# ELT)) (|exp| #17#) (|eval| (($ $ #81=(|List| |#1|) #81#) NIL #82=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #82# ELT) (($ $ #83=(|Equation| |#1|)) NIL #82# ELT) (($ $ (|List| #83#)) NIL #82# ELT) (($ $ #84=(|List| #85=(|Symbol|)) #81#) NIL #86=(|has| |#1| (|InnerEvalable| #85# |#1|)) ELT) (($ $ #85# |#1|) NIL #86# ELT)) (|euclideanSize| (#87=(#20# $) NIL #7# ELT)) (|elt| (#88=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #7# ELT)) (|discriminant| ((|#1| #14#) NIL T ELT) ((|#1|) NIL T ELT)) (|discreteLog| (#87# NIL #22# ELT) (((|Union| #20# #25#) $ $) NIL #22# ELT)) (|differentiate| #89=(($ $ #74#) NIL T ELT) #90=(($ $ #74# #20#) NIL T ELT) #91=(($ $ #84# (|List| #20#)) NIL #92=(OR (AND #29# (|has| |#1| (|PartialDifferentialRing| #85#))) (|has| |#1| (|PartialDifferentialSpace| #85#))) ELT) #93=(($ $ #85# #20#) NIL #92# ELT) #94=(($ $ #84#) NIL #92# ELT) #95=(($ $ #85#) NIL #92# ELT) #96=(#61# NIL #97=(OR (AND (|has| |#1| (|DifferentialRing|)) #29#) (|has| |#1| (|DifferentialSpace|))) ELT) #98=(#11# NIL #97# ELT)) (|derivationCoordinates| ((#13# #14# #74#) NIL #29# ELT)) (|definingPolynomial| ((#56#) NIL T ELT)) (|csch| #17#) (|csc| #17#) (|createPrimitiveElement| #60#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|coordinates| ((#44# $ #14#) NIL T ELT) ((#13# #14# #14#) NIL T ELT) #99=((#44# $) NIL T ELT) #12#) (|convert| #99# #45# #75# #55# ((#66# . #100=($)) NIL (|has| |#1| (|ConvertibleTo| #66#)) ELT) ((#69# . #100#) NIL (|has| |#1| (|ConvertibleTo| #69#)) ELT) (((|Complex| #68#) . #100#) NIL #101=(|has| |#1| (|RealConstant|)) ELT) (((|Complex| (|DoubleFloat|)) . #100#) NIL #101# ELT) ((#102=(|InputForm|) . #100#) NIL (|has| |#1| (|ConvertibleTo| #102#)) ELT)) (|conjugate| (#11# 29 T ELT)) (|conditionP| (((|Union| #14# #25#) #50#) NIL (OR #103=(AND (|has| $ #104=(|CharacteristicNonZero|)) #7# #8#) #22#) ELT)) (|complex| (($ |#1| |#1|) 19 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #21#) NIL T ELT) (($ |#1|) 18 T ELT) (($ #40#) NIL (OR #29# #41#) ELT) #10#) (|charthRoot| #62# (#72# NIL (OR #103# (|has| |#1| #104#)) ELT)) (|characteristicPolynomial| #75#) (|characteristic| (#33# NIL T CONST)) (|before?| #1#) (|basis| ((#14#) NIL T ELT)) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #5# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|argument| (#16# NIL #18# ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|abs| (#11# NIL #63# ELT)) (|Zero| (#35# 8 T CONST)) (|One| (#35# 10 T CONST)) (D #89# #90# #91# #93# #94# #95# #96# #98#) (= #1#) (/ (#47# NIL #29# ELT)) (- (#11# NIL T ELT) (#47# NIL T ELT)) (+ (#47# 23 T ELT)) (** (($ $ #19#) NIL T ELT) (#61# NIL T ELT) (#105=($ $ #40#) NIL #31# ELT) (#47# NIL #18# ELT) (#71# NIL #29# ELT)) (* (($ #19# $) NIL T ELT) (($ #20# $) NIL T ELT) (($ #21# . #106=($)) NIL T ELT) (#47# 26 T ELT) (#88# NIL T ELT) (($ |#1| . #106#) NIL T ELT) (($ #40# . #106#) NIL #29# ELT) (#105# NIL #29# ELT))) 
(((|Complex| |#1|) (|ComplexCategory| |#1|) (|CommutativeRing|)) (T |Complex|)) 
NIL 
((|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) 14 T ELT))) 
(((|ComplexFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)))) #1=(|CommutativeRing|) #1#) (T |ComplexFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Complex| *5)) (|ofCategory| *5 #1=(|CommutativeRing|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Complex| *6)) (|isDomain| *1 (|ComplexFunctions2| *5 *6))))) 
((|convert| (((|Pattern| |#1|) |#3|) 22 T ELT))) 
(((|ComplexPattern| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |convert| (#1=(|Pattern| |#1|) |#3|))) (|SetCategory|) (|Join| (|ConvertibleTo| #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))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|solid?| (#3=(#2# $) 9 T ELT)) (|solid| (#4=(#2# $ #2#) 11 T ELT)) (|new| (($) 13 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|copy| (($ $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|closed?| (#3# 8 T ELT)) (|close| (#4# 10 T ELT)) (|before?| #1#) (= #1#)) 
(((|SubSpaceComponentProperty|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |new| ($)) (SIGNATURE |closed?| #1=(#2=(|Boolean|) $)) (SIGNATURE |solid?| #1#) (SIGNATURE |close| #3=(#2# $ #2#)) (SIGNATURE |solid| #3#) (SIGNATURE |copy| ($ $))))) (T |SubSpaceComponentProperty|)) 
((|new| (*1 *1) #1=(|isDomain| *1 (|SubSpaceComponentProperty|))) (|closed?| #2=(*1 *2 *1) #3=(AND (|isDomain| *2 (|Boolean|)) #1#)) (|solid?| #2# #3#) (|close| #4=(*1 *2 *1 *2) #3#) (|solid| #4# #3#) (|copy| (*1 *1 *1) #1#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|CommutativeRing|) (|Category|)) (T |CommutativeRing|)) 
NIL 
(|Join| (|Ring|) (|BiModule| $ $) (CATEGORY |package| (ATTRIBUTE (|commutative| "*")))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|close!| (($ $) 6 T ELT))) 
(((|Conduit|) (|Category|)) (T |Conduit|)) 
((|close!| (*1 *1 *1) (|ofCategory| *1 (|Conduit|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |close!| ($ $)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|wholePart| ((|#1| $) 79 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #7=((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #10=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#11=($) NIL T CONST)) (|rem| #12=(#13=($ $ $) NIL T ELT)) (|reducedForm| (#6# 21 T ELT)) (|reducedContinuedFraction| (($ |#1| #14=(|Stream| |#1|)) 48 T ELT)) (|recip| ((#8# $) 123 T ELT)) (|quo| #12#) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) NIL T ELT)) (|prime?| #4#) (|partialQuotients| (#17=(#14# $) 86 T ELT)) (|partialNumerators| (#17# 83 T ELT)) (|partialDenominators| (#17# 84 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numerators| (#17# 93 T ELT)) (|multiEuclidean| (((|Union| #15# #9#) #15# $) NIL T ELT)) (|lcm| #18=(($ #15#) NIL T ELT) #12#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#19=(|SparseUnivariatePolynomial| $) #19# #19#) NIL T ELT)) (|gcd| #18# #12#) (|factor| #10#) (|extendedEuclidean| (((|Union| (|Record| #20=(|:| |coef1| $) #21=(|:| |coef2| $)) #9#) $ $ $) NIL T ELT) (((|Record| #20# #21# #16#) $ $) NIL T ELT)) (|extend| (#22=($ $ #23=(|Integer|)) 96 T ELT)) (|exquo| #7#) (|expressIdealMember| (((|Maybe| #15#) #15# $) NIL T ELT)) (|euclideanSize| ((#24=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|denominators| (#17# 94 T ELT)) (|convergents| (#25=((|Stream| #26=(|Fraction| |#1|)) $) 14 T ELT)) (|continuedFraction| (#27=($ #26#) 17 T ELT) (($ |#1| #14# #14#) 38 T ELT)) (|complete| (#6# 98 T ELT)) (|coerce| (((|OutputForm|) $) 139 T ELT) (($ #23#) 51 T ELT) (($ |#1|) 52 T ELT) (#27# 36 T ELT) (($ #28=(|Fraction| #23#)) NIL T ELT) #5#) (|characteristic| ((#24#) 67 T CONST)) (|before?| #1#) (|associates?| #1#) (|approximants| (#25# 20 T ELT)) (|annihilate?| #1#) (|Zero| (#11# 103 T CONST)) (|One| (#11# 28 T CONST)) (= (#2# 35 T ELT)) (/ (#13# 121 T ELT)) (- (#6# 112 T ELT) (#13# 109 T ELT)) (+ (#13# 107 T ELT)) (** (($ $ #29=(|PositiveInteger|)) NIL T ELT) (($ $ #24#) NIL T ELT) (#22# NIL T ELT)) (* (($ #29# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #23# $) 119 T ELT) (#13# 114 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| $) 116 T ELT) (($ #26# $) 117 T ELT) (($ $ #26#) NIL T ELT) (($ #28# $) NIL T ELT) (($ $ #28#) NIL T ELT))) 
(((|ContinuedFraction| |#1|) (|Join| (|Algebra| |#1|) (|Algebra| #1=(|Fraction| |#1|)) (|Field|) (CATEGORY |domain| (SIGNATURE |continuedFraction| ($ #1#)) (SIGNATURE |continuedFraction| ($ |#1| #2=(|Stream| |#1|) #2#)) (SIGNATURE |reducedContinuedFraction| ($ |#1| #2#)) (SIGNATURE |partialNumerators| #3=(#2# $)) (SIGNATURE |partialDenominators| #3#) (SIGNATURE |partialQuotients| #3#) (SIGNATURE |wholePart| (|#1| $)) (SIGNATURE |reducedForm| #4=($ $)) (SIGNATURE |approximants| #5=((|Stream| #1#) $)) (SIGNATURE |convergents| #5#) (SIGNATURE |numerators| #3#) (SIGNATURE |denominators| #3#) (SIGNATURE |extend| ($ $ (|Integer|))) (SIGNATURE |complete| #4#))) (|EuclideanDomain|)) (T |ContinuedFraction|)) 
((|continuedFraction| (*1 *1 *2) (AND (|isDomain| *2 #1=(|Fraction| *3)) #2=(|ofCategory| *3 #3=(|EuclideanDomain|)) #4=(|isDomain| *1 (|ContinuedFraction| *3)))) (|continuedFraction| (*1 *1 *2 *3 *3) #5=(AND (|isDomain| *3 (|Stream| *2)) #6=(|ofCategory| *2 #3#) #7=(|isDomain| *1 (|ContinuedFraction| *2)))) (|reducedContinuedFraction| (*1 *1 *2 *3) #5#) (|partialNumerators| #8=(*1 *2 *1) #9=(AND (|isDomain| *2 (|Stream| *3)) #4# #2#)) (|partialDenominators| #8# #9#) (|partialQuotients| #8# #9#) (|wholePart| #8# #10=(AND #7# #6#)) (|reducedForm| #11=(*1 *1 *1) #10#) (|approximants| #8# #12=(AND (|isDomain| *2 (|Stream| #1#)) #4# #2#)) (|convergents| #8# #12#) (|numerators| #8# #9#) (|denominators| #8# #9#) (|extend| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #4# #2#)) (|complete| #11# #10#)) 
((|push| (($ #1=(|Binding|) $) 15 T ELT)) (|findBinding| (((|Maybe| #1#) (|Identifier|) $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|bindings| (((|List| #1#) $) 8 T ELT))) 
(((|Contour|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |bindings| ((|List| #1=(|Binding|)) $)) (SIGNATURE |push| ($ #1# $)) (SIGNATURE |findBinding| ((|Maybe| #1#) (|Identifier|) $))))) (T |Contour|)) 
((|bindings| (*1 *2 *1) (AND (|isDomain| *2 (|List| #1=(|Binding|))) #2=(|isDomain| *1 (|Contour|)))) (|push| (*1 *1 *2 *1) (AND (|isDomain| *2 #1#) #2#)) (|findBinding| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|Maybe| #1#)) #2#))) 
((|toroidal| (#1=(#2=(|Mapping| #3=(|Point| |#1|) #3#) |#1|) 38 T ELT)) (|spherical| (#4=(#3# #3#) 22 T ELT)) (|prolateSpheroidal| (#1# 34 T ELT)) (|polar| (#4# 20 T ELT)) (|paraboloidal| (#4# 28 T ELT)) (|parabolicCylindrical| (#4# 27 T ELT)) (|parabolic| (#4# 26 T ELT)) (|oblateSpheroidal| (#1# 35 T ELT)) (|ellipticCylindrical| (#1# 33 T ELT)) (|elliptic| (#1# 32 T ELT)) (|cylindrical| (#4# 21 T ELT)) (|conical| ((#2# |#1| |#1|) 41 T ELT)) (|cartesian| (#4# 8 T ELT)) (|bipolarCylindrical| (#1# 37 T ELT)) (|bipolar| (#1# 36 T ELT))) 
(((|CoordinateSystems| |#1|) (CATEGORY |package| (SIGNATURE |cartesian| #1=(#2=(|Point| |#1|) #2#)) (SIGNATURE |polar| #1#) (SIGNATURE |cylindrical| #1#) (SIGNATURE |spherical| #1#) (SIGNATURE |parabolic| #1#) (SIGNATURE |parabolicCylindrical| #1#) (SIGNATURE |paraboloidal| #1#) (SIGNATURE |elliptic| #3=(#4=(|Mapping| #2# #2#) |#1|)) (SIGNATURE |ellipticCylindrical| #3#) (SIGNATURE |prolateSpheroidal| #3#) (SIGNATURE |oblateSpheroidal| #3#) (SIGNATURE |bipolar| #3#) (SIGNATURE |bipolarCylindrical| #3#) (SIGNATURE |toroidal| #3#) (SIGNATURE |conical| (#4# |#1| |#1|))) (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))) (T |CoordinateSystems|)) 
((|conical| (*1 *2 *3 *3) #1=(AND (|isDomain| *2 (|Mapping| #2=(|Point| *3) #2#)) #3=(|isDomain| *1 (|CoordinateSystems| *3)) #4=(|ofCategory| *3 (|Join| (|Field|) (|TranscendentalFunctionCategory|) (|RadicalCategory|))))) (|toroidal| #5=(*1 *2 *3) #1#) (|bipolarCylindrical| #5# #1#) (|bipolar| #5# #1#) (|oblateSpheroidal| #5# #1#) (|prolateSpheroidal| #5# #1#) (|ellipticCylindrical| #5# #1#) (|elliptic| #5# #1#) (|paraboloidal| #6=(*1 *2 *2) #7=(AND (|isDomain| *2 #2#) #4# #3#)) (|parabolicCylindrical| #6# #7#) (|parabolic| #6# #7#) (|spherical| #6# #7#) (|cylindrical| #6# #7#) (|polar| #6# #7#) (|cartesian| #6# #7#)) 
((|characteristicPolynomial| ((|#2| |#3|) 28 T ELT))) 
(((|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))))) 
((|patternMatch| ((#1=(|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) #1#) 44 (|has| (|Polynomial| |#2|) (|PatternMatchable| |#1|)) ELT))) 
(((|ComplexPatternMatch| |#1| |#2| |#3|) (CATEGORY |package| (IF (|has| (|Polynomial| |#2|) #1=(|PatternMatchable| |#1|)) (SIGNATURE |patternMatch| (#2=(|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) #2#)) |%noBranch|)) (|SetCategory|) (|Join| #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) #1=(|PatternMatchable| *5)) (|ofCategory| *6 (|Join| #1# (|CommutativeRing|))) (|isDomain| *1 (|ComplexPatternMatch| *5 *6 *3))))) 
((|multiEuclideanTree| ((#1=(|List| |#1|) #1# |#1|) 41 T ELT)) (|modTree| ((#1# |#1| #1#) 20 T ELT)) (|chineseRemainder| ((#1# (|List| #1#) #1#) 36 T ELT) ((|#1| #1# #1#) 32 T ELT))) 
(((|CRApackage| |#1|) (CATEGORY |package| (SIGNATURE |modTree| (#1=(|List| |#1|) |#1| #1#)) (SIGNATURE |chineseRemainder| (|#1| #1# #1#)) (SIGNATURE |chineseRemainder| (#1# (|List| #1#) #1#)) (SIGNATURE |multiEuclideanTree| (#1# #1# |#1|))) (|EuclideanDomain|)) (T |CRApackage|)) 
((|multiEuclideanTree| (*1 *2 *2 *3) #1=(AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 #2=(|EuclideanDomain|)) (|isDomain| *1 (|CRApackage| *3)))) (|chineseRemainder| #3=(*1 *2 *3 *2) (AND (|isDomain| *3 (|List| #4=(|List| *4))) (|isDomain| *2 #4#) (|ofCategory| *4 #2#) (|isDomain| *1 (|CRApackage| *4)))) (|chineseRemainder| (*1 *2 *3 *3) (AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|CRApackage| *2)) (|ofCategory| *2 #2#))) (|modTree| #3# #1#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|target| (((|TypeAst|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|CoerceAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |expression| ((|SpadAst|) $)) (SIGNATURE |target| ((|TypeAst|) $))))) (T |CoerceAst|)) 
((|expression| #1=(*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) #2=(|isDomain| *1 (|CoerceAst|)))) (|target| #1# (AND (|isDomain| *2 (|TypeAst|)) #2#))) 
((|startPolynomial| (((|Record| (|:| |start| |#2|) (|:| |factors| #1=(|Factored| |#2|))) |#2|) 66 T ELT)) (|setErrorBound| ((|#1| |#1|) 58 T ELT)) (|schwerpunkt| ((#2=(|Complex| |#1|) |#2|) 94 T ELT)) (|rootRadius| (#3=(|#1| |#2|) 137 T ELT) ((|#1| |#2| |#1|) 90 T ELT)) (|reciprocalPolynomial| (#4=(|#2| |#2|) 91 T ELT)) (|pleskenSplit| (#5=(#1# |#2| |#1|) 119 T ELT) (#6=(#1# |#2| |#1| #7=(|Boolean|)) 88 T ELT)) (|norm| (#3# 118 T ELT)) (|graeffe| (#4# 131 T ELT)) (|factor| ((#1# |#2|) 154 T ELT) (#5# 33 T ELT) (#6# 153 T ELT)) (|divisorCascade| ((#8=(|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|) 152 T ELT) ((#8# |#2| |#2| #7#) 82 T ELT)) (|complexZeros| ((#9=(|List| #2#) |#2| |#1|) 42 T ELT) ((#9# |#2|) 43 T ELT))) 
(((|ComplexRootFindingPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |complexZeros| (#1=(|List| #2=(|Complex| |#1|)) |#2|)) (SIGNATURE |complexZeros| (#1# |#2| |#1|)) (SIGNATURE |divisorCascade| (#3=(|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| #4=(|Boolean|))) (SIGNATURE |divisorCascade| (#3# |#2| |#2|)) (SIGNATURE |factor| #5=(#6=(|Factored| |#2|) |#2| |#1| #4#)) (SIGNATURE |factor| #7=(#6# |#2| |#1|)) (SIGNATURE |factor| (#6# |#2|)) (SIGNATURE |graeffe| #8=(|#2| |#2|)) (SIGNATURE |norm| #9=(|#1| |#2|)) (SIGNATURE |pleskenSplit| #5#) (SIGNATURE |pleskenSplit| #7#) (SIGNATURE |reciprocalPolynomial| #8#) (SIGNATURE |rootRadius| (|#1| |#2| |#1|)) (SIGNATURE |rootRadius| #9#) (SIGNATURE |schwerpunkt| (#2# |#2|)) (SIGNATURE |setErrorBound| (|#1| |#1|)) (SIGNATURE |startPolynomial| ((|Record| (|:| |start| |#2|) (|:| |factors| #6#)) |#2|))) (|Join| (|Field|) (|OrderedRing|)) (|UnivariatePolynomialCategory| #2#)) (T |ComplexRootFindingPackage|)) 
((|startPolynomial| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|Join| (|Field|) (|OrderedRing|))) (|isDomain| *2 (|Record| (|:| |start| *3) (|:| |factors| #4=(|Factored| *3)))) #5=(|isDomain| *1 (|ComplexRootFindingPackage| *4 *3)) #6=(|ofCategory| *3 (|UnivariatePolynomialCategory| #7=(|Complex| *4))))) (|setErrorBound| #8=(*1 *2 *2) #9=(AND (|ofCategory| *2 #3#) (|isDomain| *1 (|ComplexRootFindingPackage| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *2))))) (|schwerpunkt| #1# (AND (|isDomain| *2 #7#) #5# #2# (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|rootRadius| #1# #9#) (|rootRadius| (*1 *2 *3 *2) #9#) (|reciprocalPolynomial| #8# #10=(AND (|ofCategory| *3 #3#) (|isDomain| *1 (|ComplexRootFindingPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Complex| *3))))) (|pleskenSplit| #11=(*1 *2 *3 *4) #12=(AND #2# #13=(|isDomain| *2 #4#) #5# #6#)) (|pleskenSplit| #14=(*1 *2 *3 *4 *5) #15=(AND (|isDomain| *5 #16=(|Boolean|)) #2# #13# #5# #6#)) (|norm| #1# #9#) (|graeffe| #8# #10#) (|factor| #1# #12#) (|factor| #11# #12#) (|factor| #14# #15#) (|divisorCascade| (*1 *2 *3 *3) (AND #2# (|isDomain| *2 (|List| (|Record| #17=(|:| |factors| (|List| *3)) (|:| |error| *4)))) #5# #6#)) (|divisorCascade| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 #16#) (|ofCategory| *5 #3#) (|isDomain| *2 (|List| (|Record| #17# (|:| |error| *5)))) (|isDomain| *1 (|ComplexRootFindingPackage| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *5))))) (|complexZeros| #11# #18=(AND #2# (|isDomain| *2 (|List| #7#)) #5# #6#)) (|complexZeros| #1# #18#)) 
((|cycleElt| (((|Union| |#2| "failed") |#2|) 16 T ELT)) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) 18 T ELT)) (|computeCycleEntry| ((|#2| |#2| |#2|) 20 T ELT))) 
(((|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 #1=(|ofCategory| *3 #2=(|Type|)) #3=(|isDomain| *1 (|CyclicStreamTools| *3 *2)) #4=(|ofCategory| *2 (|LazyStreamAggregate| *3)))) (|computeCycleLength| (*1 *2 *3) (AND (|ofCategory| *4 #2#) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|CyclicStreamTools| *4 *3)) (|ofCategory| *3 (|LazyStreamAggregate| *4)))) (|cycleElt| (*1 *2 *2) (|partial| AND #1# #3# #4#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|operations| (((|List| (|OverloadSet|)) $) NIL T ELT)) (|name| ((#3=(|Identifier|) $) 8 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|kind| (((|ConstructorKind|) $) 10 T ELT)) (|is?| ((#2# $ #3#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|findConstructor| (((|Maybe| $) #3#) 17 T ELT)) (|dualSignature| (((|List| #2#) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|arity| (((|Arity|) $) 12 T ELT)) (= #1#)) 
(((|Constructor|) (|Join| (|ConstructorCategory|) (CATEGORY |domain| (SIGNATURE |findConstructor| ((|Maybe| $) (|Identifier|)))))) (T |Constructor|)) 
((|findConstructor| (*1 *2 *3) (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|Maybe| #1=(|Constructor|))) (|isDomain| *1 #1#)))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|constructor| ((|#1| $) 7 T ELT)) (|coerce| (((|OutputForm|) $) 14 T ELT)) (|before?| #1#) (|arguments| (((|List| (|Syntax|)) $) 10 T ELT)) (= (#2# 12 T ELT))) 
(((|ConstructorCall| |#1|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |constructor| (|#1| $)) (SIGNATURE |arguments| ((|List| (|Syntax|)) $)))) (|ConstructorCategory|)) (T |ConstructorCall|)) 
((|constructor| #1=(*1 *2 *1) (AND (|isDomain| *1 (|ConstructorCall| *2)) (|ofCategory| *2 #2=(|ConstructorCategory|)))) (|arguments| #1# (AND (|isDomain| *2 (|List| (|Syntax|))) (|isDomain| *1 (|ConstructorCall| *3)) (|ofCategory| *3 #2#)))) 
((|operations| (((|List| (|OverloadSet|)) $) 16 T ELT)) (|kind| (((|ConstructorKind|) $) 8 T ELT)) (|dualSignature| (((|List| (|Boolean|)) $) 13 T ELT)) (|arity| (((|Arity|) $) 10 T ELT))) 
(((|ConstructorCategory&| |#1|) (CATEGORY |package| (SIGNATURE |operations| ((|List| (|OverloadSet|)) |#1|)) (SIGNATURE |dualSignature| ((|List| (|Boolean|)) |#1|)) (SIGNATURE |kind| ((|ConstructorKind|) |#1|)) (SIGNATURE |arity| ((|Arity|) |#1|))) (|ConstructorCategory|)) (T |ConstructorCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|operations| (((|List| (|OverloadSet|)) $) 22 T ELT)) (|name| ((#2=(|Identifier|) $) 19 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|kind| (((|ConstructorKind|) $) 24 T ELT)) (|is?| (((|Boolean|) $ #2#) 17 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|dualSignature| (((|List| (|Boolean|)) $) 23 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|arity| (((|Arity|) $) 18 T ELT)) (= (#1# 8 T ELT))) 
(((|ConstructorCategory|) (|Category|)) (T |ConstructorCategory|)) 
((|kind| (*1 *2 *1) (AND (|ofCategory| *1 (|ConstructorCategory|)) (|isDomain| *2 (|ConstructorKind|)))) (|dualSignature| (*1 *2 *1) (AND (|ofCategory| *1 (|ConstructorCategory|)) (|isDomain| *2 (|List| (|Boolean|))))) (|operations| (*1 *2 *1) (AND (|ofCategory| *1 (|ConstructorCategory|)) (|isDomain| *2 (|List| (|OverloadSet|)))))) 
(|Join| (|OperatorCategory| (|Identifier|)) (CATEGORY |domain| (SIGNATURE |kind| ((|ConstructorKind|) $)) (SIGNATURE |dualSignature| ((|List| (|Boolean|)) $)) (SIGNATURE |operations| ((|List| (|OverloadSet|)) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OperatorCategory| (|Identifier|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|package| (#3=($) 8 T CONST)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|domain| (#3# 7 T CONST)) (|coerce| (((|OutputForm|) $) 12 T ELT)) (|category| (#3# 6 T CONST)) (|before?| #1#) (= (#2# 10 T ELT))) 
(((|ConstructorKind|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |category| #1=($) |constant|) (SIGNATURE |domain| #1# |constant|) (SIGNATURE |package| #1# |constant|)))) (T |ConstructorKind|)) 
((|category| #1=(*1 *1) #2=(|isDomain| *1 (|ConstructorKind|))) (|domain| #1# #2#) (|package| #1# #2#)) 
((|trigs| (#1=(|#2| |#2|) 28 T ELT)) (|real?| (((|Boolean|) |#2|) 19 T ELT)) (|real| (#2=(#3=(|Expression| |#1|) |#2|) 12 T ELT)) (|imag| (#2# 14 T ELT)) (|complexNormalize| (#4=(|#2| |#2| (|Symbol|)) 69 T ELT) (#1# 70 T ELT)) (|complexForm| (((|Complex| #3#) |#2|) 10 T ELT)) (|complexElementary| (#4# 66 T ELT) (#1# 60 T ELT))) 
(((|ComplexTrigonometricManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |complexNormalize| #1=(|#2| |#2|)) (SIGNATURE |complexNormalize| #2=(|#2| |#2| (|Symbol|))) (SIGNATURE |complexElementary| #1#) (SIGNATURE |complexElementary| #2#) (SIGNATURE |real| #3=(#4=(|Expression| |#1|) |#2|)) (SIGNATURE |imag| #3#) (SIGNATURE |real?| ((|Boolean|) |#2|)) (SIGNATURE |trigs| #1#) (SIGNATURE |complexForm| ((|Complex| #4#) |#2|))) (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| |#1|)))) (T |ComplexTrigonometricManipulations|)) 
((|complexForm| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Complex| #4=(|Expression| *4))) #5=(|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *3)) #6=(|ofCategory| *3 #7=(|Join| #8=(|AlgebraicallyClosedField|) #9=(|TranscendentalFunctionCategory|) (|FunctionSpace| (|Complex| *4)))))) (|trigs| #10=(*1 *2 *2) #11=(AND (|ofCategory| *3 #3#) (|isDomain| *1 (|ComplexTrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| #8# #9# (|FunctionSpace| (|Complex| *3)))))) (|real?| #1# (AND #2# (|isDomain| *2 (|Boolean|)) #5# #6#)) (|imag| #1# #12=(AND #2# (|isDomain| *2 #4#) #5# #6#)) (|real| #1# #12#) (|complexElementary| #13=(*1 *2 *2 *3) #14=(AND (|isDomain| *3 (|Symbol|)) #2# (|isDomain| *1 (|ComplexTrigonometricManipulations| *4 *2)) (|ofCategory| *2 #7#))) (|complexElementary| #10# #11#) (|complexNormalize| #13# #14#) (|complexNormalize| #10# #11#)) 
((|coerceP| (((|Vector| (|Matrix| #1=(|Polynomial| |#1|))) #2=(|Vector| (|Matrix| |#1|))) 26 T ELT)) (|coerce| (((|Vector| (|Matrix| (|Fraction| #1#))) #2#) 37 T ELT))) 
(((|CoerceVectorMatrixPackage| |#1|) (CATEGORY |package| (SIGNATURE |coerceP| ((|Vector| (|Matrix| #1=(|Polynomial| |#1|))) #2=(|Vector| (|Matrix| |#1|)))) (SIGNATURE |coerce| ((|Vector| (|Matrix| (|Fraction| #1#))) #2#))) (|CommutativeRing|)) (T |CoerceVectorMatrixPackage|)) 
((|coerce| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 (|Vector| (|Matrix| *4))) #3=(|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| (|Fraction| #4=(|Polynomial| *4))))) #5=(|isDomain| *1 (|CoerceVectorMatrixPackage| *4)))) (|coerceP| #1# (AND #2# #3# (|isDomain| *2 (|Vector| (|Matrix| #4#))) #5#))) 
((|wreath| (#1=(#2=(|SymmetricPolynomial| #3=(|Fraction| #4=(|Integer|))) #2# #2#) 93 T ELT)) (|skewSFunction| ((#2# #5=(|List| #4#) #5#) 109 T ELT)) (|powerSum| (#6=(#2# #7=(|PositiveInteger|)) 54 T ELT)) (|graphs| (#6# 79 T ELT)) (|eval| ((#3# #2#) 89 T ELT)) (|elementary| (#8=(#2# (|NonNegativeInteger|)) 37 T ELT)) (|dihedral| (#6# 66 T ELT)) (|cyclic| (#6# 61 T ELT)) (|cup| (#1# 87 T ELT)) (|complete| (#8# 29 T ELT)) (|cap| ((#3# #2# #2#) 91 T ELT)) (|alternating| (#8# 35 T ELT)) (|SFunction| ((#2# (|List| #7#)) 103 T ELT))) 
(((|CycleIndicators|) (CATEGORY |package| (SIGNATURE |complete| #1=(#2=(|SymmetricPolynomial| #3=(|Fraction| #4=(|Integer|))) (|NonNegativeInteger|))) (SIGNATURE |powerSum| #5=(#2# #6=(|PositiveInteger|))) (SIGNATURE |elementary| #1#) (SIGNATURE |alternating| #1#) (SIGNATURE |cyclic| #5#) (SIGNATURE |dihedral| #5#) (SIGNATURE |graphs| #5#) (SIGNATURE |cap| (#3# #2# #2#)) (SIGNATURE |cup| #7=(#2# #2# #2#)) (SIGNATURE |eval| (#3# #2#)) (SIGNATURE |wreath| #7#) (SIGNATURE |SFunction| (#2# (|List| #6#))) (SIGNATURE |skewSFunction| (#2# #8=(|List| #4#) #8#)))) (T |CycleIndicators|)) 
((|skewSFunction| #1=(*1 *2 *3 *3) (AND (|isDomain| *3 (|List| #2=(|Integer|))) #3=(|isDomain| *2 #4=(|SymmetricPolynomial| #5=(|Fraction| #2#))) #6=(|isDomain| *1 (|CycleIndicators|)))) (|SFunction| #7=(*1 *2 *3) (AND (|isDomain| *3 (|List| #8=(|PositiveInteger|))) #3# #6#)) (|wreath| #9=(*1 *2 *2 *2) #10=(AND #3# #6#)) (|eval| #7# #11=(AND (|isDomain| *3 #4#) (|isDomain| *2 #5#) #6#)) (|cup| #9# #10#) (|cap| #1# #11#) (|graphs| #7# #12=(AND (|isDomain| *3 #8#) #3# #6#)) (|dihedral| #7# #12#) (|cyclic| #7# #12#) (|alternating| #7# #13=(AND (|isDomain| *3 (|NonNegativeInteger|)) #3# #6#)) (|elementary| #7# #13#) (|powerSum| #7# #12#) (|complete| #7# #13#)) 
((|cyclotomicFactorization| (((|Factored| #1=(|SparseUnivariatePolynomial| #2=(|Integer|))) #2#) 38 T ELT)) (|cyclotomicDecomposition| (((|List| #1#) #2#) 33 T ELT)) (|cyclotomic| ((#1# #2#) 28 T ELT))) 
(((|CyclotomicPolynomialPackage|) (CATEGORY |package| (SIGNATURE |cyclotomicDecomposition| ((|List| #1=(|SparseUnivariatePolynomial| #2=(|Integer|))) #2#)) (SIGNATURE |cyclotomic| (#1# #2#)) (SIGNATURE |cyclotomicFactorization| ((|Factored| #1#) #2#)))) (T |CyclotomicPolynomialPackage|)) 
((|cyclotomicFactorization| #1=(*1 *2 *3) (AND (|isDomain| *2 (|Factored| #2=(|SparseUnivariatePolynomial| #3=(|Integer|)))) #4=(|isDomain| *1 (|CyclotomicPolynomialPackage|)) #5=(|isDomain| *3 #3#))) (|cyclotomic| #1# (AND (|isDomain| *2 #2#) #4# #5#)) (|cyclotomicDecomposition| #1# (AND (|isDomain| *2 (|List| #2#)) #4# #5#))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|qsetelt| ((|#2| $ #3=(|NonNegativeInteger|) |#2|) 11 T ELT)) (|qelt| ((|#2| $ #3#) 10 T ELT)) (|new| (($) 8 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 23 T ELT)) (|before?| #1#) (= (#2# 13 T ELT))) 
(((|DataArray| |#1| |#2|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (SIGNATURE |new| ($)) (SIGNATURE |qelt| (|#2| $ #2=(|NonNegativeInteger|))) (SIGNATURE |qsetelt| (|#2| $ #2# |#2|)))) (|PositiveInteger|) #1#) (T |DataArray|)) 
((|new| (*1 *1) (AND (|isDomain| *1 (|DataArray| *2 *3)) (|ofType| *2 #1=(|PositiveInteger|)) (|ofCategory| *3 #2=(|SetCategory|)))) (|qelt| (*1 *2 *1 *3) (AND #3=(|isDomain| *3 (|NonNegativeInteger|)) #4=(|ofCategory| *2 #2#) #5=(|isDomain| *1 (|DataArray| *4 *2)) #6=(|ofType| *4 #1#))) (|qsetelt| (*1 *2 *1 *3 *2) (AND #3# #5# #6# #4#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| ((#2=(|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fullDisplay| (#3=(#4=(|Void|) $) 36 T ELT) ((#4# $ #5=(|PositiveInteger|) #5#) 40 T ELT)) (|elt| (($ $ (|QueryEquation|)) 19 T ELT) (((|DataList| #2#) $ (|Symbol|)) 15 T ELT)) (|display| (#3# 34 T ELT)) (|coerce| (((|OutputForm|) $) 31 T ELT) (($ (|List| |#1|)) 8 T ELT)) (|before?| #1#) (= #1#) (- (#6=($ $ $) 26 T ELT)) (+ (#6# 22 T ELT))) 
(((|Database| |#1|) (|Join| (|SetCategory|) (|CoercibleFrom| (|List| |#1|)) (CATEGORY |domain| (SIGNATURE |elt| ($ $ (|QueryEquation|))) (SIGNATURE |elt| ((|DataList| #1=(|String|)) $ #2=(|Symbol|))) (SIGNATURE + #3=($ $ $)) (SIGNATURE - #3#) #4=(SIGNATURE |display| #5=(#6=(|Void|) $)) #7=(SIGNATURE |fullDisplay| #5#) (SIGNATURE |fullDisplay| (#6# $ #8=(|PositiveInteger|) #8#)))) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |elt| (#1# $ #2#)) #4# #7#))) (T |Database|)) 
((|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 (|QueryEquation|)) #1=(|isDomain| *1 (|Database| *3)) (|ofCategory| *3 #2=(|Join| #3=(|OrderedSet|) (CATEGORY |domain| #4=(SIGNATURE |elt| (#5=(|String|) $ #6=(|Symbol|))) #7=(SIGNATURE |display| #8=(#9=(|Void|) $)) #10=(SIGNATURE |fullDisplay| #8#)))))) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 #6#) (|isDomain| *2 (|DataList| #5#)) #11=(|isDomain| *1 (|Database| *4)) (|ofCategory| *4 (|Join| #3# (CATEGORY |domain| (SIGNATURE |elt| (#5# $ *3)) #7# #10#))))) (+ #12=(*1 *1 *1 *1) #13=(AND (|isDomain| *1 (|Database| *2)) (|ofCategory| *2 #2#))) (- #12# #13#) (|display| #14=(*1 *2 *1) #15=(AND #16=(|isDomain| *2 #9#) #1# (|ofCategory| *3 #17=(|Join| #3# (CATEGORY |domain| #4# (SIGNATURE |display| #18=(*2 $)) (SIGNATURE |fullDisplay| #18#)))))) (|fullDisplay| #14# #15#) (|fullDisplay| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|PositiveInteger|)) #16# #11# (|ofCategory| *4 #17#)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|random| (#2=($) NIL T ELT)) (|min| #3=(($ $ $) NIL T ELT) #4=(#2# NIL T CONST)) (|max| #3# #4#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) 10 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dual| (($ (|LinearBasis| |#1|)) 11 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) 
(((|DualBasis| |#1|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |dual| ($ (|LinearBasis| |#1|))))) (|List| (|Symbol|))) (T |DualBasis|)) 
((|dual| (*1 *1 *2) (AND (|isDomain| *2 (|LinearBasis| *3)) (|ofType| *3 (|List| (|Symbol|))) (|isDomain| *1 (|DualBasis| *3))))) 
((|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) 49 T ELT))) 
(((|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))))) 
((|tracePowMod| (#1=(|#2| |#2| #2=(|NonNegativeInteger|) |#2|) 55 T ELT)) (|trace2PowMod| (#1# 51 T ELT)) (|separateFactors| (((|List| |#2|) #3=(|List| (|Record| (|:| |deg| #2#) (|:| |prod| |#2|)))) 79 T ELT)) (|separateDegrees| ((#3# |#2|) 72 T ELT)) (|irreducible?| ((#4=(|Boolean|) |#2|) 70 T ELT)) (|factorSquareFree| (#5=((|Factored| |#2|) |#2|) 92 T ELT)) (|factor| (#5# 91 T ELT)) (|exptMod| (#1# 49 T ELT)) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| #4#) 86 T ELT))) 
(((|DistinctDegreeFactorize| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factor| #1=((|Factored| |#2|) |#2|)) (SIGNATURE |factorSquareFree| #1#) (SIGNATURE |distdfact| ((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| #2=(|Boolean|))) (SIGNATURE |separateDegrees| (#3=(|List| (|Record| (|:| |deg| #4=(|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|)) (SIGNATURE |separateFactors| ((|List| |#2|) #3#)) (SIGNATURE |exptMod| #5=(|#2| |#2| #4# |#2|)) (SIGNATURE |trace2PowMod| #5#) (SIGNATURE |tracePowMod| #5#) (SIGNATURE |irreducible?| (#2# |#2|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|)) (T |DistinctDegreeFactorize|)) 
((|irreducible?| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|FiniteFieldCategory|)) (|isDomain| *2 #4=(|Boolean|)) #5=(|isDomain| *1 (|DistinctDegreeFactorize| *4 *3)) #6=(|ofCategory| *3 #7=(|UnivariatePolynomialCategory| *4)))) (|tracePowMod| #8=(*1 *2 *2 *3 *2) #9=(AND (|isDomain| *3 #10=(|NonNegativeInteger|)) #2# (|isDomain| *1 (|DistinctDegreeFactorize| *4 *2)) (|ofCategory| *2 #7#))) (|trace2PowMod| #8# #9#) (|exptMod| #8# #9#) (|separateFactors| #1# (AND (|isDomain| *3 (|List| (|Record| #11=(|:| |deg| #10#) (|:| |prod| *5)))) (|ofCategory| *5 #7#) #2# (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|DistinctDegreeFactorize| *4 *5)))) (|separateDegrees| #1# (AND #2# (|isDomain| *2 (|List| (|Record| #11# (|:| |prod| *3)))) #5# #6#)) (|distdfact| (*1 *2 *3 *4) (AND (|isDomain| *4 #4#) (|ofCategory| *5 #3#) (|isDomain| *2 (|Record| (|:| |cont| *5) (|:| |factors| (|List| (|Record| (|:| |irr| *3) (|:| |pow| (|Integer|))))))) (|isDomain| *1 (|DistinctDegreeFactorize| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|factorSquareFree| #1# #12=(AND #2# (|isDomain| *2 (|Factored| *3)) #5# #6#)) (|factor| #1# #12#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#6# NIL #19=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (#22=((|Union| #7# . #23=(#13#)) . #24=($)) NIL T ELT) (((|Union| #25=(|Symbol|) . #23#) . #24#) NIL #26=(|has| #7# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #7#) . #23#) . #24#) NIL #28=(|has| #7# (|RetractableTo| #7#)) ELT) (#22# NIL #28# ELT)) (|retract| #29=(#6# NIL T ELT) ((#25# $) NIL #26# ELT) (#30=(#27# $) NIL #28# ELT) (#6# NIL #28# ELT)) (|rem| #31=(#32=($ $ $) NIL T ELT)) (|reducedSystem| (#33=(#34=(|Matrix| #7#) #35=(|Matrix| $)) NIL #36=(|has| #7# (|LinearlyExplicitRingOver| #7#)) ELT) (#37=(#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #7#))) #35# #39=(|Vector| $)) NIL #36# ELT) (#37# NIL T ELT) (#33# NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#21# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #31#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #19# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #29#) (|nextItem| (#50=((|Maybe| $) $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #13#) #41# $) NIL T ELT)) (|min| #52=(#32# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#34# #39#) NIL #36# ELT) (#56=(#38# #39# $) NIL #36# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #31# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#21# NIL #51# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #31# #57#) (|fractionPart| (#10# NIL #8# ELT) #58=(#30# NIL T ELT)) (|floor| #59=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #60=(|:| |coef1| $) #61=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #60# #61#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #62=(|List| #7#) #62#) NIL #63=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #63# ELT) (($ $ #64=(|Equation| #7#)) NIL #63# ELT) (($ $ (|List| #64#)) NIL #63# ELT) (($ $ #65=(|List| #25#) #62#) NIL #66=(|has| #7# (|InnerEvalable| #25# #7#)) ELT) (($ $ #25# #7#) NIL #66# ELT)) (|euclideanSize| ((#67=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#68=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #69=(($ $ #54#) NIL T ELT) #70=(($ $ #54# #67#) NIL T ELT) #71=(($ $ #25#) NIL #72=(|has| #7# (|PartialDifferentialSpace| #25#)) ELT) #73=(($ $ #65#) NIL #72# ELT) #74=(($ $ #25# #67#) NIL #72# ELT) #75=(($ $ #65# (|List| #67#)) NIL #72# ELT) #76=(#10# NIL #77=(|has| #7# (|DifferentialSpace|)) ELT) #78=(#79=($ $ #67#) NIL #77# ELT)) (|denominator| #9#) (|denom| #29#) (|decimal| (#80=($ #27#) 9 T ELT)) (|convert| ((#46# . #81=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #81#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#82=(|InputForm|) . #81#) NIL (|has| #7# (|ConvertibleTo| #82#)) ELT) ((#48# . #81#) NIL #83=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #81#) NIL #83# ELT)) (|conditionP| (((|Union| #39# #13#) #35#) NIL #84=(AND (|has| $ #85=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #86=(($ #7#) NIL T ELT) #9# (#80# 8 T ELT) #86# (($ #25#) NIL #26# ELT) #58# (((|RadixExpansion| 10) $) 10 T ELT)) (|charthRoot| (#50# NIL (OR #84# (|has| #7# #85#)) ELT)) (|characteristic| ((#67#) NIL T CONST)) (|ceiling| #59#) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#10# NIL #19# ELT)) (|Zero| #20#) (|One| #20#) (D #69# #70# #71# #73# #74# #75# #76# #78#) (>= #87=(#2# NIL #53# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ #31# (($ #7# #7#) NIL T ELT)) (- #9# #31#) (+ 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(((|DecimalExpansion|) (|Join| (|QuotientFieldCategory| #1=(|Integer|)) (|CoercibleTo| #2=(|Fraction| #1#)) (|CoercibleTo| (|RadixExpansion| 10)) (CATEGORY |domain| (SIGNATURE |fractionPart| (#2# $)) (SIGNATURE |decimal| ($ #2#))))) (T |DecimalExpansion|)) 
((|fractionPart| (*1 *2 *1) #1=(AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|DecimalExpansion|)))) (|decimal| (*1 *1 *2) #1#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|signature| (((|Signature|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|head| (((|HeadAst|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|body| (((|SpadAst|) $) 16 T ELT)) (|before?| #1#) (= #1#)) 
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((|integrate| ((#1=(|Union| (|:| |f1| #2=(|OrderedCompletion| |#2|)) (|:| |f2| (|List| #2#)) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| #3=(|SegmentBinding| #2#) (|String|)) 29 T ELT) ((#1# |#2| #3#) 25 T ELT)) (|innerint| ((#1# |#2| (|Symbol|) #2# #2# (|Boolean|)) 17 T ELT))) 
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((|innerint| (*1 *2 *3 *4 *5 *5 *6) (AND (|isDomain| *4 (|Symbol|)) (|isDomain| *6 (|Boolean|)) (|ofCategory| *7 #1=(|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#))) (|ofCategory| *3 (|Join| #3=(|TranscendentalFunctionCategory|) #4=(|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *7))) #5=(|isDomain| *2 (|Union| (|:| |f1| #6=(|OrderedCompletion| *3)) (|:| |f2| (|List| #6#)) (|:| |fail| "failed") (|:| |pole| "potentialPole"))) (|isDomain| *1 (|ElementaryFunctionDefiniteIntegration| *7 *3)) (|isDomain| *5 #6#))) (|integrate| (*1 *2 *3 *4 *5) (AND #7=(|isDomain| *4 (|SegmentBinding| #6#)) (|isDomain| *5 (|String|)) (|ofCategory| *3 (|Join| #3# #4# (|AlgebraicallyClosedFunctionSpace| *6))) (|ofCategory| *6 #1#) #5# (|isDomain| *1 (|ElementaryFunctionDefiniteIntegration| *6 *3)))) (|integrate| (*1 *2 *3 *4) (AND #7# (|ofCategory| *3 (|Join| #3# #4# (|AlgebraicallyClosedFunctionSpace| *5))) (|ofCategory| *5 #1#) #5# (|isDomain| *1 (|ElementaryFunctionDefiniteIntegration| *5 *3))))) 
((|integrate| ((#1=(|Union| (|:| |f1| #2=(|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| #2#)) (|:| |fail| "failed") (|:| |pole| "potentialPole")) #3=(|Fraction| (|Polynomial| |#1|)) #4=(|SegmentBinding| (|OrderedCompletion| #3#)) #5=(|String|)) 49 T ELT) ((#1# #3# #4#) 46 T ELT) ((#1# #3# #6=(|SegmentBinding| #2#) #5#) 50 T ELT) ((#1# #3# #6#) 22 T ELT))) 
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((|reduce| (((|Record| (|:| |pol| #1=(|SparseUnivariatePolynomial| |#1|)) (|:| |deg| #2=(|PositiveInteger|))) #1#) 26 T ELT)) (|expand| (((|List| #3=(|Expression| |#2|)) #3# #2#) 51 T ELT))) 
(((|DegreeReductionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |reduce| ((|Record| (|:| |pol| #1=(|SparseUnivariatePolynomial| |#1|)) (|:| |deg| #2=(|PositiveInteger|))) #1#)) (SIGNATURE |expand| ((|List| #3=(|Expression| |#2|)) #3# #2#))) (|Ring|) (|IntegralDomain|)) (T |DegreeReductionPackage|)) 
((|expand| (*1 *2 *3 *4) (AND (|isDomain| *4 #1=(|PositiveInteger|)) (|ofCategory| *6 #2=(|IntegralDomain|)) (|isDomain| *2 (|List| #3=(|Expression| *6))) (|isDomain| *1 (|DegreeReductionPackage| *5 *6)) (|isDomain| *3 #3#) (|ofCategory| *5 #4=(|Ring|)))) (|reduce| (*1 *2 *3) (AND (|ofCategory| *4 #4#) (|isDomain| *2 (|Record| (|:| |pol| #5=(|SparseUnivariatePolynomial| *4)) (|:| |deg| #1#))) (|isDomain| *1 (|DegreeReductionPackage| *4 *5)) (|isDomain| *3 #5#) (|ofCategory| *5 #2#)))) 
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(((|Dequeue| |#1|) (|Join| (|DequeueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |dequeue| ($ (|List| |#1|))))) (|SetCategory|)) (T |Dequeue|)) 
((|dequeue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Dequeue| *3))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|totalDifferential| (#5=($ #6=(|Expression| |#1|)) 24 T ELT)) (|subtractIfCan| ((#7=(|Union| $ #8="failed") $ $) NIL T ELT)) (|sample| #9=(#10=($) NIL T CONST)) (|retractable?| #4#) (|retractIfCan| (((|Union| #6# #8#) $) NIL T ELT)) (|retract| #11=((#6# $) NIL T ELT)) (|reductum| (#12=($ $) 32 T ELT)) (|recip| ((#7# $) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|map| (($ (|Mapping| #6# #6#) $) NIL T ELT)) (|leadingCoefficient| #11#) (|leadingBasisTerm| (#12# 31 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|homogeneous?| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (($ #13=(|NonNegativeInteger|)) NIL T ELT)) (|exteriorDifferential| (#12# 33 T ELT)) (|degree| ((#14=(|Integer|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 65 T ELT) (($ #14#) NIL T ELT) (#5# NIL T ELT)) (|coefficient| ((#6# $ $) NIL T ELT)) (|characteristic| ((#13#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#10# 26 T CONST)) (|One| #9#) (= (#2# 29 T ELT)) (- (#12# NIL T ELT) (#15=($ $ $) NIL T ELT)) (+ (#15# 20 T ELT)) (** (($ $ #16=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) NIL T ELT)) (* (($ #16# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #14# . #17=($)) NIL T ELT) (#15# 25 T ELT) (($ #6# . #17#) 19 T ELT))) 
(((|DeRhamComplex| |#1| |#2|) (|Join| (|LeftAlgebra| #1=(|Expression| |#1|)) (|RetractableTo| #1#) (|Functorial| #1#) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (#1# $)) (SIGNATURE |leadingBasisTerm| #2=($ $)) (SIGNATURE |reductum| #2#) (SIGNATURE |coefficient| (#1# $ $)) (SIGNATURE |generator| ($ (|NonNegativeInteger|))) (SIGNATURE |homogeneous?| #3=((|Boolean|) $)) (SIGNATURE |retractable?| #3#) (SIGNATURE |degree| ((|Integer|) $)) (SIGNATURE |totalDifferential| ($ #1#)) (SIGNATURE |exteriorDifferential| #2#))) (|Join| (|Ring|) (|OrderedSet|)) (|List| (|Symbol|))) (T |DeRhamComplex|)) 
((|leadingCoefficient| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *2 (|Expression| *3)) #4=(|isDomain| *1 (|DeRhamComplex| *3 *4)) #5=(|ofCategory| *3 #6=(|Join| (|Ring|) (|OrderedSet|))) #7=(|ofType| *4 #8=(|List| (|Symbol|))))) (|leadingBasisTerm| #9=(*1 *1 *1) #10=(AND (|isDomain| *1 (|DeRhamComplex| *2 *3)) (|ofCategory| *2 #6#) (|ofType| *3 #8#))) (|reductum| #9# #10#) (|coefficient| (*1 *2 *1 *1) #2#) (|generator| #11=(*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) #4# #5# #7#)) (|homogeneous?| #1# #12=(AND (|isDomain| *2 (|Boolean|)) #4# #5# #7#)) (|retractable?| #1# #12#) (|degree| #1# (AND (|isDomain| *2 (|Integer|)) #4# #5# #7#)) (|totalDifferential| #11# (AND #3# #5# #4# #7#)) (|exteriorDifferential| #9# #10#)) 
((|ignore?| ((#1=(|Boolean|) (|String|)) 26 T ELT)) (|computeInt| (((|Union| #2=(|OrderedCompletion| |#2|) #3="failed") (|Kernel| |#2|) |#2| #2# #2# #1#) 35 T ELT)) (|checkForZero| ((#4=(|Union| #1# #3#) (|SparseUnivariatePolynomial| |#2|) #2# #2# #1#) 83 T ELT) ((#4# (|Polynomial| |#1|) (|Symbol|) #2# #2# #1#) 84 T ELT))) 
(((|DefiniteIntegrationTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ignore?| (#1=(|Boolean|) (|String|))) (SIGNATURE |computeInt| ((|Union| #2=(|OrderedCompletion| |#2|) #3="failed") (|Kernel| |#2|) |#2| #2# #2# #1#)) (SIGNATURE |checkForZero| (#4=(|Union| #1# #3#) (|Polynomial| |#1|) (|Symbol|) #2# #2# #1#)) (SIGNATURE |checkForZero| (#4# (|SparseUnivariatePolynomial| |#2|) #2# #2# #1#))) (|Join| (|GcdDomain|) (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#)) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |DefiniteIntegrationTools|)) 
((|checkForZero| (*1 *2 *3 *4 *4 *2) (|partial| AND #1=(|isDomain| *2 #2=(|Boolean|)) (|isDomain| *3 (|SparseUnivariatePolynomial| *6)) (|isDomain| *4 (|OrderedCompletion| *6)) (|ofCategory| *6 (|Join| #3=(|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *5))) (|ofCategory| *5 #4=(|Join| (|GcdDomain|) (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#))) (|isDomain| *1 (|DefiniteIntegrationTools| *5 *6)))) (|checkForZero| (*1 *2 *3 *4 *5 *5 *2) (|partial| AND #1# (|isDomain| *3 (|Polynomial| *6)) (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|OrderedCompletion| *7)) #6=(|ofCategory| *6 #4#) (|ofCategory| *7 #7=(|Join| #3# (|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 #2#) (|ofCategory| *4 #7#) #6# (|isDomain| *1 (|DefiniteIntegrationTools| *6 *4)))) (|ignore?| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *4 #4#) #1# (|isDomain| *1 (|DefiniteIntegrationTools| *4 *5)) (|ofCategory| *5 (|Join| #3# (|AlgebraicallyClosedFunctionSpace| *4)))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 86 T ELT)) (|wholePart| (#5=(#6=(|Integer|) $) 18 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #7=(#8=($ $) NIL T ELT)) (|unit?| #9=(#4# NIL T ELT)) (|truncate| #7#) (|tanh| (#8# 73 T ELT)) (|tan| (#8# 61 T ELT)) (|subtractIfCan| #10=((#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|squareFreePart| #7#) (|squareFree| #13=(((|Factored| $) $) NIL T ELT)) (|sqrt| (#8# 52 T ELT)) (|sizeLess?| #1#) (|sinh| (#8# 71 T ELT)) (|sin| (#8# 59 T ELT)) (|sign| (#5# 83 T ELT)) (|sech| (#8# 76 T ELT)) (|sec| (#8# 63 T ELT)) (|sample| (#14=($) NIL T CONST)) (|round| #7#) (|retractIfCan| (((|Union| #6# . #15=(#12#)) $) 116 T ELT) (((|Union| #16=(|Fraction| #6#) . #15#) $) 113 T ELT)) (|retract| (#5# 114 T ELT) ((#16# $) 111 T ELT)) (|rem| #17=(#18=($ $ $) NIL T ELT)) (|recip| ((#11# $) 91 T ELT)) (|rationalApproximation| ((#16# $ #19=(|NonNegativeInteger|)) 106 T ELT) ((#16# $ #19# #19#) 105 T ELT)) (|quo| #17#) (|principalIdeal| (((|Record| (|:| |coef| #20=(|List| $)) #21=(|:| |generator| $)) #20#) NIL T ELT)) (|prime?| #9#) (|precision| (#22=(#23=(|PositiveInteger|)) 12 T ELT) #24=((#23# #23#) NIL #25=(|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (#4# 107 T ELT)) (|pi| (#14# 31 T ELT)) (|patternMatch| ((#26=(|PatternMatchResult| #27=(|Float|) $) $ #28=(|Pattern| #27#) #26#) NIL T ELT)) (|order| (#5# 25 T ELT)) (|opposite?| (#2# 141 T ELT)) (|one?| (#4# 87 T ELT)) (|nthRoot| (#29=($ $ #6#) NIL T ELT)) (|norm| #7#) (|negative?| (#4# 85 T ELT)) (|nan?| (#4# 140 T ELT)) (|multiEuclidean| (((|Union| #20# #12#) #20# $) NIL T ELT)) (|min| (#18# 49 T ELT) (#14# 21 #30=(AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) (|not| #25#)) ELT)) (|max| (#18# 48 T ELT) (#14# 20 #30# ELT)) (|mantissa| (#5# 10 T ELT)) (|log2| (#8# 16 T ELT)) (|log10| (#8# 53 T ELT)) (|log| (#8# 58 T ELT)) (|lcm| #17# #31=(($ #20#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #7#) (|increasePrecision| #32=((#23# #6#) NIL #25# ELT)) (|hash| (((|SingleInteger|) $) 89 T ELT)) (|gcdPolynomial| ((#33=(|SparseUnivariatePolynomial| $) #33# #33#) NIL T ELT)) (|gcd| #17# #31#) (|fractionPart| #7#) (|floor| #7#) (|float| (($ #6# #6#) NIL T ELT) (($ #6# #6# #23#) 98 T ELT)) (|factor| #13#) (|extendedEuclidean| (((|Record| #34=(|:| |coef1| $) #35=(|:| |coef2| $) #21#) $ $) NIL T ELT) (((|Union| (|Record| #34# #35#) #12#) $ $ $) NIL T ELT)) (|exquo| #10#) (|expressIdealMember| (((|Maybe| #20#) #20# $) NIL T ELT)) (|exponent| (#5# 11 T ELT)) (|exp1| (#14# 30 T ELT)) (|exp| (#8# 57 T ELT)) (|euclideanSize| ((#19# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (#22# NIL T ELT) #24#) (|differentiate| (#8# 92 T ELT) #36=(($ $ #19#) NIL T ELT)) (|decreasePrecision| #32#) (|csch| (#8# 74 T ELT)) (|csc| (#8# 64 T ELT)) (|coth| (#8# 75 T ELT)) (|cot| (#8# 62 T ELT)) (|cosh| (#8# 72 T ELT)) (|cos| (#8# 60 T ELT)) (|convert| ((#27# $) 102 T ELT) (((|DoubleFloat|) $) 99 T ELT) ((#28# $) NIL T ELT) (((|InputForm|) $) 38 T ELT)) (|coerce| (((|OutputForm|) $) 35 T ELT) #37=(($ #6#) 56 T ELT) #7# #38=(($ #16#) NIL T ELT) #37# #38#) (|characteristic| ((#19#) NIL T CONST)) (|ceiling| #7#) (|bits| (#22# 19 T ELT) #24#) (|before?| #1#) (|base| (#22# 7 T ELT)) (|atanh| (#8# 79 T ELT)) (|atan| (#8# 67 T ELT) (#18# 109 T ELT)) (|associates?| #1#) (|asinh| (#8# 77 T ELT)) (|asin| (#8# 65 T ELT)) (|asech| (#8# 82 T ELT)) (|asec| (#8# 70 T ELT)) (|annihilate?| (#2# 143 T ELT)) (|acsch| (#8# 80 T ELT)) (|acsc| (#8# 68 T ELT)) (|acoth| (#8# 81 T ELT)) (|acot| (#8# 69 T ELT)) (|acosh| (#8# 78 T ELT)) (|acos| (#8# 66 T ELT)) (|abs| (#8# 108 T ELT)) (|Zero| (#14# 27 T CONST)) (|One| (#14# 28 T CONST)) (|Gamma| (#8# 95 T ELT)) (D #7# #36#) (|Beta| (#18# 97 T ELT)) (>= (#2# 42 T ELT)) (> (#2# 40 T ELT)) (= (#2# 50 T ELT)) (<= (#2# 41 T ELT)) (< (#2# 39 T ELT)) (/ (#18# 29 T ELT) (#29# 51 T ELT)) (- (#8# 43 T ELT) (#18# 45 T ELT)) (+ (#18# 44 T ELT)) (** (($ $ #23#) NIL T ELT) #36# (#29# 54 T ELT) (#39=($ $ #16#) 139 T ELT) (#18# 55 T ELT)) (* (($ #23# $) 17 T ELT) (($ #19# $) NIL T ELT) (($ #6# $) 47 T ELT) (#18# 46 T ELT) (#39# NIL T ELT) (($ #16# $) NIL T ELT))) 
(((|DoubleFloat|) (|Join| (|FloatingPointSystem|) (|DifferentialRing|) (|TranscendentalFunctionCategory|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE / ($ $ #1=(|Integer|))) (SIGNATURE ** #2=($ $ $)) (SIGNATURE |exp1| ($)) (SIGNATURE |log2| #3=($ $)) (SIGNATURE |log10| #3#) (SIGNATURE |atan| #2#) (SIGNATURE |Gamma| #3#) (SIGNATURE |Beta| #2#) (SIGNATURE |rationalApproximation| (#4=(|Fraction| #1#) $ #5=(|NonNegativeInteger|))) (SIGNATURE |rationalApproximation| (#4# $ #5# #5#)) (SIGNATURE |nan?| ((|Boolean|) $))))) (T |DoubleFloat|)) 
((** #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|DoubleFloat|))) (/ (*1 *1 *1 *2) (AND (|isDomain| *2 #3=(|Integer|)) #2#)) (|exp1| (*1 *1) #2#) (|log2| #4=(*1 *1 *1) #2#) (|log10| #4# #2#) (|atan| #1# #2#) (|Gamma| #4# #2#) (|Beta| #1# #2#) (|rationalApproximation| (*1 *2 *1 *3) #5=(AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| #3#)) #2#)) (|rationalApproximation| (*1 *2 *1 *3 *3) #5#) (|nan?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) #2#))) 
((|polygamma| ((#1=(|Complex| #2=(|DoubleFloat|)) #3=(|NonNegativeInteger|) #1#) 11 T ELT) ((#2# #3# #2#) 12 T ELT)) (|logGamma| (#4=(#1# #1#) 13 T ELT) (#5=(#2# #2#) 14 T ELT)) (|hypergeometric0F1| (#6=(#1# #1# #1#) 19 T ELT) (#7=(#2# #2# #2#) 22 T ELT)) (|digamma| (#4# 27 T ELT) (#5# 26 T ELT)) (|besselY| (#6# 57 T ELT) (#7# 49 T ELT)) (|besselK| (#6# 62 T ELT) (#7# 60 T ELT)) (|besselJ| (#6# 15 T ELT) (#7# 16 T ELT)) (|besselI| (#6# 17 T ELT) (#7# 18 T ELT)) (|airyBi| (#4# 74 T ELT) (#5# 73 T ELT)) (|airyAi| (#5# 68 T ELT) (#4# 72 T ELT)) (|Gamma| (#4# 8 T ELT) (#5# 9 T ELT)) (|Beta| (#6# 35 T ELT) (#7# 31 T ELT))) 
(((|DoubleFloatSpecialFunctions|) (CATEGORY |package| (SIGNATURE |Gamma| #1=(#2=(|DoubleFloat|) #2#)) (SIGNATURE |Gamma| #3=(#4=(|Complex| #2#) #4#)) (SIGNATURE |Beta| #5=(#2# #2# #2#)) (SIGNATURE |Beta| #6=(#4# #4# #4#)) (SIGNATURE |logGamma| #1#) (SIGNATURE |logGamma| #3#) (SIGNATURE |digamma| #1#) (SIGNATURE |digamma| #3#) (SIGNATURE |polygamma| (#2# #7=(|NonNegativeInteger|) #2#)) (SIGNATURE |polygamma| (#4# #7# #4#)) (SIGNATURE |besselJ| #5#) (SIGNATURE |besselJ| #6#) (SIGNATURE |besselY| #5#) (SIGNATURE |besselY| #6#) (SIGNATURE |besselI| #5#) (SIGNATURE |besselI| #6#) (SIGNATURE |besselK| #5#) (SIGNATURE |besselK| #6#) (SIGNATURE |airyAi| #3#) (SIGNATURE |airyAi| #1#) (SIGNATURE |airyBi| #1#) (SIGNATURE |airyBi| #3#) (SIGNATURE |hypergeometric0F1| #5#) (SIGNATURE |hypergeometric0F1| #6#))) (T |DoubleFloatSpecialFunctions|)) 
((|hypergeometric0F1| #1=(*1 *2 *2 *2) #2=(AND #3=(|isDomain| *2 (|Complex| #4=(|DoubleFloat|))) #5=(|isDomain| *1 (|DoubleFloatSpecialFunctions|)))) (|hypergeometric0F1| #1# #6=(AND #7=(|isDomain| *2 #4#) #5#)) (|airyBi| #8=(*1 *2 *2) #2#) (|airyBi| #8# #6#) (|airyAi| #8# #6#) (|airyAi| #8# #2#) (|besselK| #1# #2#) (|besselK| #1# #6#) (|besselI| #1# #2#) (|besselI| #1# #6#) (|besselY| #1# #2#) (|besselY| #1# #6#) (|besselJ| #1# #2#) (|besselJ| #1# #6#) (|polygamma| #9=(*1 *2 *3 *2) (AND #3# #10=(|isDomain| *3 (|NonNegativeInteger|)) #5#)) (|polygamma| #9# (AND #7# #10# #5#)) (|digamma| #8# #2#) (|digamma| #8# #6#) (|logGamma| #8# #2#) (|logGamma| #8# #6#) (|Beta| #1# #2#) (|Beta| #1# #6#) (|Gamma| #8# #2#) (|Gamma| #8# #6#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|zero| (($ #5=(|NonNegativeInteger|) #5#) NIL T ELT)) (|vertConcat| #6=(($ $ $) NIL T ELT)) (|transpose| #7=(($ #8=(|Vector| |#1|)) NIL T ELT) #9=(#10=($ $) NIL T ELT)) (|translate| (#11=($ |#1| |#1| |#1|) 33 T ELT)) (|symmetric?| #12=((#3# $) NIL T ELT)) (|swapRows!| #13=(($ $ #14=(|Integer|) #14#) NIL T ELT)) (|swapColumns!| #13#) (|subMatrix| (($ $ #14# #14# #14# #14#) NIL T ELT)) (|squareTop| #9#) (|square?| #12#) (|setsubMatrix!| (($ $ #14# #14# $) NIL T ELT)) (|setelt| #15=((|#1| $ #14# #14# |#1|) NIL T ELT) (($ $ #16=(|List| #14#) #16# $) NIL T ELT)) (|setRow!| #17=(($ $ #14# #8#) NIL T ELT)) (|setColumn!| #17#) (|scale| (#11# 32 T ELT)) (|scalarMatrix| (($ #5# |#1|) NIL T ELT)) (|sample| (#18=($) NIL T CONST)) (|rowEchelon| (#10# NIL (|has| |#1| (|EuclideanDomain|)) ELT)) (|row| #19=((#8# $ #14#) NIL T ELT)) (|rotatez| (#20=($ |#1|) 31 T ELT)) (|rotatey| (#20# 30 T ELT)) (|rotatex| (#20# 29 T ELT)) (|reduce| ((|#1| #21=(|Mapping| |#1| |#1| |#1|) $) NIL T ELT) ((|#1| #21# $ |#1|) NIL T ELT) ((|#1| #21# $ |#1| |#1|) NIL #4# ELT)) (|rank| #22=(#23=(#5# $) NIL #24=(|has| |#1| (|IntegralDomain|)) ELT)) (|qsetelt!| #15#) (|qelt| #25=((|#1| $ #14# #14#) NIL T ELT)) (|nullity| #22#) (|nullSpace| (((|List| #8#) $) NIL #24# ELT)) (|nrows| #26=(#23# NIL T ELT)) (|new| (($ #5# #5# |#1|) NIL T ELT)) (|ncols| #26#) (|minordet| #27=((|#1| $) NIL (|has| |#1| (ATTRIBUTE (|commutative| "*"))) ELT)) (|minRowIndex| #28=((#14# $) NIL T ELT)) (|minColIndex| #28#) (|members| ((#29=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|maxRowIndex| #28#) (|maxColIndex| #28#) (|matrix| (($ #30=(|List| #29#)) 11 T ELT) (($ #5# #5# (|Mapping| |#1| #14# #14#)) NIL T ELT)) (|map!| #31=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #31# (($ #21# $ $) NIL T ELT) (($ #21# $ $ |#1|) NIL T ELT)) (|listOfLists| ((#30# $) NIL T ELT)) (|latex| (((|String|) $) NIL #32=(|has| |#1| (|SetCategory|)) ELT)) (|inverse| ((#33=(|Union| $ #34="failed") $) NIL #35=(|has| |#1| (|Field|)) ELT)) (|identity| (#18# 12 T ELT)) (|horizConcat| #6#) (|hash| (((|SingleInteger|) $) NIL #32# ELT)) (|find| (((|Union| |#1| #34#) #36=(|Mapping| #3# |#1|) $) NIL T ELT)) (|fill!| #37=(#38=($ $ |#1|) NIL T ELT)) (|exquo| ((#33# $ |#1|) NIL #24# ELT)) (|every?| #39=((#3# #36# $) NIL T ELT)) (|eval| (($ $ (|List| #40=(|Equation| |#1|))) NIL #41=(AND (|has| |#1| (|Evalable| |#1|)) #32#) ELT) (($ $ #40#) NIL #41# ELT) (($ $ |#1| |#1|) NIL #41# ELT) (($ $ #29# #29#) NIL #41# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| #12#) (|empty| (#18# NIL T ELT)) (|elt| #25# #15# (($ $ #16# #16#) NIL T ELT)) (|diagonalMatrix| (($ #29#) NIL T ELT) (($ (|List| $)) NIL T ELT)) (|diagonal?| #12#) (|determinant| #27#) (|count| ((#5# #36# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT)) (|copy| #9#) (|column| #19#) (|coerce| #7# ((#42=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #42#)) ELT)) (|before?| #1#) (|any?| #39#) (|antisymmetric?| #12#) (= #1#) (/ (#38# NIL #35# ELT)) (- #6# #9#) (+ #6#) (** (($ $ #5#) NIL T ELT) (($ $ #14#) NIL #35# ELT)) (* #6# (($ |#1| $) NIL T ELT) #37# (($ #14# $) NIL T ELT) ((#8# $ #8#) 15 T ELT) ((#8# #8# $) NIL T ELT) ((#43=(|Point| |#1|) $ #43#) 21 T ELT)) (|#| #26#)) 
(((|DenavitHartenbergMatrix| |#1|) (|Join| (|MatrixCategory| |#1| #1=(|Vector| |#1|) #1#) (CATEGORY |domain| (SIGNATURE * (#2=(|Point| |#1|) $ #2#)) (SIGNATURE |identity| ($)) (SIGNATURE |rotatex| #3=($ |#1|)) (SIGNATURE |rotatey| #3#) (SIGNATURE |rotatez| #3#) (SIGNATURE |scale| #4=($ |#1| |#1| |#1|)) (SIGNATURE |translate| #4#))) (|Join| (|Field|) (|TranscendentalFunctionCategory|))) (T |DenavitHartenbergMatrix|)) 
((* (*1 *2 *1 *2) (AND (|isDomain| *2 (|Point| *3)) (|ofCategory| *3 #1=(|Join| (|Field|) (|TranscendentalFunctionCategory|))) (|isDomain| *1 (|DenavitHartenbergMatrix| *3)))) (|identity| (*1 *1) #2=(AND (|isDomain| *1 (|DenavitHartenbergMatrix| *2)) (|ofCategory| *2 #1#))) (|rotatex| #3=(*1 *1 *2) #2#) (|rotatey| #3# #2#) (|rotatez| #3# #2#) (|scale| #4=(*1 *1 *2 *2 *2) #2#) (|translate| #4# #2#)) 
((|select!| (#1=($ (|Mapping| #2=(|Boolean|) |#2|) $) 16 T ELT)) (|remove!| (($ |#2| $) NIL T ELT) (#1# 28 T ELT)) (|dictionary| (($) NIL T ELT) (($ (|List| |#2|)) 11 T ELT)) (= ((#2# $ $) 26 T ELT))) 
(((|Dictionary&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE |select!| #2=(|#1| (|Mapping| #1# |#2|) |#1|)) (SIGNATURE |remove!| #2#) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |dictionary| (|#1| (|List| |#2|))) (SIGNATURE |dictionary| (|#1|))) (|Dictionary| |#2|) (|SetCategory|)) (T |Dictionary&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|select!| (($ (|Mapping| #3=(|Boolean|) |#1|) . #4=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#7=($) 6 T CONST)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #8=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #3# |#1|) . #4#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #8#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #5# |#1|) . #6#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #9=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #10=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #9#) ELT)) (|extract!| ((|#1| . #10#) 37 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT)) (|eq?| ((#11=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#11# $) 7 T ELT)) (|empty| (#7# 8 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#12=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #12#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|Dictionary| |#1|) (|Category|) (|SetCategory|)) (T |Dictionary|)) 
NIL 
(|Join| (|DictionaryOperations| |t#1|)) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|Mapping| |#1| |#1|) . #4=((|NonNegativeInteger|))) 65 T ELT) (($ $ (|Mapping| |#1| |#1|)) 64 T ELT) (($ $ #5=(|Symbol|)) 63 (|has| |#1| . #6=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #5#)) 61 (|has| |#1| . #6#) ELT) (($ $ #5# . #7=(#8=(|NonNegativeInteger|))) 60 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#) . #9=((|List| #8#))) 59 (|has| |#1| . #6#) ELT) (($ . #10=($)) 55 (|has| |#1| . #11=((|DifferentialSpace|))) ELT) (#12=($ $ (|NonNegativeInteger|)) 53 (|has| |#1| . #11#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|Mapping| |#1| |#1|) . #4#) 67 T ELT) (($ $ (|Mapping| |#1| |#1|)) 66 T ELT) (($ $ #5#) 62 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#)) 58 (|has| |#1| . #6#) ELT) (($ $ #5# . #7#) 57 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#) . #9#) 56 (|has| |#1| . #6#) ELT) (($ . #10#) 54 (|has| |#1| . #11#) ELT) (#12# 52 (|has| |#1| . #11#) ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|DifferentialExtension| |#1|) (|Category|) (|Ring|)) (T |DifferentialExtension|)) 
NIL 
(|Join| (|Ring|) (|DifferentialSpaceExtension| |t#1|) (CATEGORY |package| (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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #1=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #1#) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((D ((|#2| $) 9 T ELT))) 
(((|DifferentialDomain&| |#1| |#2|) (CATEGORY |package| (SIGNATURE D (|#2| |#1|))) (|DifferentialDomain| |#2|) (|Type|)) (T |DifferentialDomain&|)) 
NIL 
((|differentiate| ((|#1| $) 7 T ELT)) (D ((|#1| $) 6 T ELT))) 
(((|DifferentialDomain| |#1|) (|Category|) (|Type|)) (T |DifferentialDomain|)) 
((|differentiate| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialDomain| *2)) (|ofCategory| *2 (|Type|)))) (D (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialDomain| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |differentiate| (|t#1| $)) (SIGNATURE D (|t#1| $)))) 
(((|Join|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#4=($ $ (|NonNegativeInteger|)) 43 T ELT) (($ . #5=($)) 41 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (#4# 44 T ELT) (($ . #5#) 42 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 30 T ELT) (($ |#1| . #6#) 33 T ELT) (($ $ |#1|) 37 T ELT))) 
(((|DifferentialModule| |#1|) (|Category|) (|Ring|)) (T |DifferentialModule|)) 
NIL 
(|Join| (|BiModule| |t#1| |t#1|) (|DifferentialSpace|) (CATEGORY |package| (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) ((|DifferentialDomain| $) . T) ((|DifferentialSpace|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|differentiate| #1=(($ $) NIL T ELT) (#2=($ $ (|NonNegativeInteger|)) 9 T ELT)) (D #1# (#2# 11 T ELT))) 
(((|DifferentialSpace&| |#1|) (CATEGORY |package| (SIGNATURE D #1=(|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| #1#) (SIGNATURE D #2=(|#1| |#1|)) (SIGNATURE |differentiate| #2#)) (|DifferentialSpace|)) (T |DifferentialSpace&|)) 
NIL 
((|differentiate| (($ . #1=($)) 7 T ELT) (($ $ (|NonNegativeInteger|)) 10 T ELT)) (D (($ . #1#) 6 T ELT) (($ $ (|NonNegativeInteger|)) 9 T ELT))) 
(((|DifferentialSpace|) (|Category|)) (T |DifferentialSpace|)) 
((|differentiate| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DifferentialSpace|)) (|isDomain| *2 (|NonNegativeInteger|)))) (D (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DifferentialSpace|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|DifferentialDomain| $) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $ (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|NonNegativeInteger|))))) 
(((|DifferentialDomain| $) . T) ((|Join|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#4=($ $ (|NonNegativeInteger|)) 50 T ELT) (($ . #5=($)) 48 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (#4# 51 T ELT) (($ . #5#) 49 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|DifferentialRing|) (|Category|)) (T |DifferentialRing|)) 
NIL 
(|Join| (|Ring|) (|DifferentialSpace|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) . T) ((|DifferentialSpace|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|sample| (#3=($) 30 T CONST)) (|recip| (((|Union| $ "failed") $) 36 T ELT)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|one?| (((|Boolean|) $) 38 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 29 T CONST)) (|One| (($) 39 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (+ (($ $ $) 25 T ELT)) (** (($ $ (|PositiveInteger|)) 40 T ELT) (($ $ (|NonNegativeInteger|)) 37 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ $ $) 41 T ELT))) 
(((|Dioid|) (|Category|)) (T |Dioid|)) 
NIL 
(|Join| (|OrderedAbelianMonoid|) (|SemiRing|)) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monoid|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|dictionary| (($) 12 T ELT) (#1=($ (|List| |#2|)) NIL T ELT)) (|copy| (($ $) 14 T ELT)) (|construct| (#1# 10 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT))) 
(((|DictionaryOperations&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |dictionary| #1=(|#1| (|List| |#2|))) (SIGNATURE |dictionary| (|#1|)) (SIGNATURE |construct| #1#) (SIGNATURE |copy| (|#1| |#1|))) (|DictionaryOperations| |#2|) (|SetCategory|)) (T |DictionaryOperations&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #3=(|Boolean|) |#1|) . #4=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#5=($) 6 T CONST)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #6=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| (|Boolean|) |#1|) $) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #6#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #3# |#1|) . #4#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #7=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #8=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #7#) ELT)) (|extract!| ((|#1| . #8#) 37 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #7#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #7#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #7#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #7#)) ELT)) (|eq?| ((#9=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#9# $) 7 T ELT)) (|empty| (#5# 8 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#10=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #10#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|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 (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|DictionaryOperations| *2)) (|ofCategory| *2 (|SetCategory|)))) (|remove!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *1 (|DictionaryOperations| *3)) (|ofCategory| *3 (|SetCategory|)))) (|select!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|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| $ (|FiniteAggregate| |t#1|)) (PROGN (SIGNATURE |remove!| ($ |t#1| $)) (SIGNATURE |remove!| ($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |select!| ($ (|Mapping| (|Boolean|) |t#1|) $))) |%noBranch|))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| #1=(|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| #1#)) (|Equation| (|Polynomial| (|Integer|)))) 42 T ELT))) 
(((|DiophantineSolutionPackage|) (CATEGORY |package| (SIGNATURE |dioSolve| ((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| #1=(|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| #1#)) (|Equation| (|Polynomial| (|Integer|))))))) (T |DiophantineSolutionPackage|)) 
((|dioSolve| (*1 *2 *3) (AND (|isDomain| *3 (|Equation| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| #1=(|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| #1#))) (|isDomain| *1 (|DiophantineSolutionPackage|))))) 
((|size| (#1=(#2=(|NonNegativeInteger|)) 56 T ELT)) (|reducedSystem| (((|Record| (|:| |mat| #3=(|Matrix| |#3|)) (|:| |vec| #4=(|Vector| |#3|))) #5=(|Matrix| $) #6=(|Vector| $)) 53 T ELT) ((#3# #5#) 44 T ELT) (((|Record| (|:| |mat| #7=(|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) #5# #6#) NIL T ELT) ((#7# #5#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 62 T ELT)) (|differentiate| (($ $ #9=(|Mapping| |#3| |#3|)) 18 T ELT) (($ $ #9# #2#) NIL T ELT) (($ $ #10=(|List| #11=(|Symbol|)) (|List| #2#)) NIL T ELT) (($ $ #11# #2#) NIL T ELT) (($ $ #10#) NIL T ELT) (($ $ #11#) NIL T ELT) (($ $ #2#) NIL T ELT) (($ $) NIL T ELT)) (|coerce| ((#4# $) NIL T ELT) (($ |#3|) NIL T ELT) (((|OutputForm|) $) NIL T ELT) (($ #8#) 12 T ELT) (($ (|Fraction| #8#)) NIL T ELT)) (|characteristic| (#1# 15 T CONST)) (/ (($ $ |#3|) 59 T ELT))) 
(((|DirectProductCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Fraction| #1=(|Integer|)))) (SIGNATURE |coerce| (|#1| #1#)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #2=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #4=(|List| #3#))) (SIGNATURE |differentiate| (|#1| |#1| #3# #2#)) (SIGNATURE |differentiate| (|#1| |#1| #4# (|List| #2#))) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |characteristic| #5=(#2#) |constant|) (SIGNATURE |reducedSystem| (#6=(|Matrix| #1#) #7=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #6#) (|:| |vec| (|Vector| #1#))) #7# #8=(|Vector| |#1|))) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |differentiate| (|#1| |#1| #9=(|Mapping| |#3| |#3|) #2#)) (SIGNATURE |differentiate| (|#1| |#1| #9#)) (SIGNATURE |reducedSystem| (#10=(|Matrix| |#3|) #7#)) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #10#) (|:| |vec| #11=(|Vector| |#3|))) #7# #8#)) (SIGNATURE |size| #5#) (SIGNATURE / (|#1| |#1| |#3|)) (SIGNATURE |dimension| ((|CardinalNumber|))) (SIGNATURE |coerce| (#11# |#1|))) (|DirectProductCategory| |#2| |#3|) #2# (|Type|)) (T |DirectProductCategory&|)) 
((|dimension| #1=(*1 *2) (AND (|ofType| *4 #2=(|NonNegativeInteger|)) #3=(|ofCategory| *5 (|Type|)) (|isDomain| *2 (|CardinalNumber|)) #4=(|isDomain| *1 (|DirectProductCategory&| *3 *4 *5)) #5=(|ofCategory| *3 (|DirectProductCategory| *4 *5)))) (|size| #1# #6=(AND (|ofType| *4 *2) #3# (|isDomain| *2 #2#) #4# #5#)) (|characteristic| #1# #6#)) 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#2| . #2=((|BasicType|))) ELT)) (|zero?| ((#3=(|Boolean|) $) 72 (|has| |#2| . #4=((|AbelianMonoid|))) ELT)) (|unitVector| (($ (|PositiveInteger|)) 128 (|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) 35 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (($ $ $) 124 (|has| |#2| . #6=((|OrderedAbelianMonoidSup|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 75 (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (((|NonNegativeInteger|)) 113 (|has| |#2| . #7=((|Finite|))) ELT)) (|setelt| ((|#2| $ #5# |#2|) 47 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sample| (#8=($) 6 T CONST)) (|retractIfCan| (((|Union| #9=(|Integer|) . #10=("failed")) . #11=($)) 67 (|and| (|has| |#2| . #12=((|RetractableTo| #9#))) (|has| |#2| . #13=((|SetCategory|)))) ELT) (((|Union| #14=(|Fraction| #9#) . #10#) . #11#) 64 (|and| (|has| |#2| . #15=((|RetractableTo| #14#))) (|has| |#2| . #13#)) ELT) (((|Union| |#2| . #10#) . #11#) 61 (|has| |#2| . #13#) ELT)) (|retract| ((#9# . #16=($)) 66 (|and| (|has| |#2| . #12#) (|has| |#2| . #13#)) ELT) ((#14# . #16#) 63 (|and| (|has| |#2| . #15#) (|has| |#2| . #13#)) ELT) ((|#2| . #16#) 62 (|has| |#2| . #13#) ELT)) (|reducedSystem| (((|Matrix| #17=(|Integer|)) . #18=(#19=(|Matrix| $))) 110 (|and| (|has| |#2| . #20=((|LinearlyExplicitRingOver| #17#))) (|has| |#2| . #21=((|Ring|)))) ELT) (((|Record| (|:| |mat| (|Matrix| #17#)) (|:| |vec| (|Vector| #17#))) . #22=(#19# #23=(|Vector| $))) 109 (|and| (|has| |#2| . #20#) (|has| |#2| . #21#)) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #22#) 108 (|has| |#2| . #21#) ELT) (((|Matrix| |#2|) . #18#) 107 (|has| |#2| . #21#) ELT)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 141 (|has| |#2| . #24=((|BasicType|))) ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 137 T ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $) 136 T ELT)) (|recip| (((|Union| $ "failed") $) 87 (|has| |#2| . #25=((|Ring|))) ELT)) (|random| (($) 116 (|has| |#2| . #7#) ELT)) (|qsetelt!| ((|#2| $ #5# |#2|) 48 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qelt| ((|#2| $ #5#) 46 T ELT)) (|positive?| (((|Boolean|) $) 123 (|has| |#2| . #6#) ELT)) (|opposite?| ((#3# $ $) 74 (|has| |#2| . #4#) ELT)) (|one?| (((|Boolean|) $) 85 (|has| |#2| . #25#) ELT)) (|minIndex| ((#5# . #26=($)) 38 (|has| #5# . #27=((|OrderedSet|))) ELT)) (|min| (#28=($ $ $) 117 (|has| |#2| . #29=((|OrderedSet|))) ELT)) (|members| (((|List| |#2|) $) 135 T ELT)) (|member?| ((#30=(|Boolean|) |#2| $) 140 (|has| |#2| . #24#) ELT)) (|maxIndex| ((#5# . #26#) 39 (|has| #5# . #27#) ELT)) (|max| (#28# 118 (|has| |#2| . #29#) ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 26 T ELT)) (|lookup| ((#31=(|PositiveInteger|) $) 115 (|has| |#2| . #7#) ELT)) (|leftReducedSystem| (((|Matrix| #17#) . #32=(#23#)) 112 (|and| (|has| |#2| . #20#) (|has| |#2| . #21#)) ELT) (((|Record| (|:| |mat| (|Matrix| #17#)) (|:| |vec| (|Vector| #17#))) . #33=(#23# $)) 111 (|and| (|has| |#2| . #20#) (|has| |#2| . #21#)) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #33#) 106 (|has| |#2| . #21#) ELT) (((|Matrix| |#2|) . #32#) 105 (|has| |#2| . #21#) ELT)) (|latex| (((|String|) $) 21 (|has| |#2| . #34=((|SetCategory|))) ELT)) (|indices| (((|List| #5#) $) 41 T ELT)) (|index?| ((#35=(|Boolean|) #5# $) 42 T ELT)) (|index| (($ #31#) 114 (|has| |#2| . #7#) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#2| . #34#) ELT)) (|first| ((|#2| $) 37 (|has| #5# . #27#) ELT)) (|find| (((|Union| |#2| "failed") (|Mapping| #30# |#2|) $) 138 T ELT)) (|fill!| (($ $ |#2|) 36 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|every?| ((#30# (|Mapping| #30# |#2|) . #36=($)) 133 T ELT)) (|eval| (($ $ (|List| (|Equation| |#2|))) 25 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #34#)) ELT) (($ $ (|Equation| |#2|)) 24 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #34#)) ELT) (($ $ |#2| |#2|) 23 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #34#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 22 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #34#)) ELT)) (|eq?| ((#37=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#35# |#2| $) 40 (AND (|has| $ (|FiniteAggregate| |#2|)) (|has| |#2| (|BasicType|))) ELT)) (|entries| (((|List| |#2|) $) 43 T ELT)) (|empty?| ((#37# $) 7 T ELT)) (|empty| (#8# 8 T ELT)) (|elt| ((|#2| $ #5# |#2|) 45 T ELT) ((|#2| $ #5#) 44 T ELT)) (|dot| ((|#2| $ $) 127 (|has| |#2| (|Ring|)) ELT)) (|directProduct| (($ (|Vector| |#2|)) 129 T ELT)) (|dimension| (((|CardinalNumber|)) 126 (|has| |#2| . #38=((|Field|))) ELT)) (|differentiate| (#39=($ $ (|NonNegativeInteger|)) 103 (|and| (|has| |#2| . #40=((|DifferentialSpace|))) (|has| |#2| . #25#)) ELT) (($ . #41=($)) 101 (|and| (|has| |#2| . #40#) (|has| |#2| . #25#)) ELT) (($ $ (|List| #42=(|Symbol|)) . #43=((|List| #44=(|NonNegativeInteger|)))) 97 (|and| (|has| |#2| . #45=((|PartialDifferentialSpace| (|Symbol|)))) (|has| |#2| . #25#)) ELT) (($ $ #42# . #46=(#44#)) 96 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ (|List| #42#)) 95 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ #42#) 93 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ (|Mapping| |#2| |#2|)) 92 (|has| |#2| . #25#) ELT) (($ $ (|Mapping| |#2| |#2|) . #47=((|NonNegativeInteger|))) 91 (|has| |#2| . #25#) ELT)) (|count| ((#48=(|NonNegativeInteger|) |#2| $) 139 (|has| |#2| . #24#) ELT) ((#48# (|Mapping| #30# |#2|) $) 134 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|Vector| |#2|) . #49=($)) 130 T ELT) (($ #9#) 68 (OR (|and| (|has| |#2| . #12#) (|has| |#2| . #13#)) (|has| |#2| . #25#)) ELT) (($ #14#) 65 (|and| (|has| |#2| . #15#) (|has| |#2| . #13#)) ELT) (($ |#2|) 60 (|has| |#2| . #13#) ELT) (((|OutputForm|) . #49#) 16 (|has| |#2| (|CoercibleTo| (|OutputForm|))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 88 (|has| |#2| . #25#) CONST)) (|before?| (#1# 19 (|has| |#2| . #2#) ELT)) (|any?| ((#30# (|Mapping| #30# |#2|) . #36#) 132 T ELT)) (|annihilate?| (((|Boolean|) $ $) 83 (|has| |#2| . #25#) ELT)) (|Zero| (($) 71 (|has| |#2| . #4#) CONST)) (|One| (($) 84 (|has| |#2| . #25#) CONST)) (D (#39# 104 (|and| (|has| |#2| . #40#) (|has| |#2| . #25#)) ELT) (($ . #41#) 102 (|and| (|has| |#2| . #40#) (|has| |#2| . #25#)) ELT) (($ $ (|List| #42#) . #43#) 100 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ #42# . #46#) 99 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ (|List| #42#)) 98 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ #42#) 94 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ (|Mapping| |#2| |#2|)) 90 (|has| |#2| . #25#) ELT) (($ $ (|Mapping| |#2| |#2|) . #47#) 89 (|has| |#2| . #25#) ELT)) (>= (#50=((|Boolean|) $ $) 119 (|has| |#2| . #29#) ELT)) (> (#50# 121 (|has| |#2| . #29#) ELT)) (= (#1# 17 (|has| |#2| . #2#) ELT)) (<= (#50# 120 (|has| |#2| . #29#) ELT)) (< (#50# 122 (|has| |#2| . #29#) ELT)) (/ (($ $ |#2|) 125 (|has| |#2| . #38#) ELT)) (- (($ $ $) 78 (|has| |#2| . #51=((|AbelianGroup|))) ELT) (($ $) 77 (|has| |#2| . #51#) ELT)) (+ (($ $ $) 69 (|has| |#2| . #52=((|AbelianSemiGroup|))) ELT)) (** (($ $ (|NonNegativeInteger|)) 86 (|has| |#2| . #25#) ELT) (($ $ (|PositiveInteger|)) 81 (|has| |#2| . #25#) ELT)) (* (($ $ $) 82 (|has| |#2| . #25#) ELT) (($ $ |#2|) 80 (|has| |#2| . #53=((|Monoid|))) ELT) (($ |#2| . #54=($)) 79 (|has| |#2| . #53#) ELT) (($ (|Integer|) . #54#) 76 (|has| |#2| . #51#) ELT) (($ (|NonNegativeInteger|) $) 73 (|has| |#2| . #4#) ELT) (($ (|PositiveInteger|) $) 70 (|has| |#2| . #52#) ELT)) (|#| ((#48# $) 131 T ELT))) 
(((|DirectProductCategory| |#1| |#2|) (|Category|) (|NonNegativeInteger|) (|Type|)) (T |DirectProductCategory|)) 
((|directProduct| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 (|Type|)) (|ofCategory| *1 (|DirectProductCategory| *3 *4)))) (|unitVector| (*1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|DirectProductCategory| *3 *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|Type|)))) (|dot| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Ring|))))) 
(|Join| (|IndexedAggregate| (|Integer|) |t#2|) (|FiniteAggregate| |t#2|) (|CoercibleTo| (|Vector| |t#2|)) (CATEGORY |domain| (SIGNATURE |directProduct| ($ (|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| (|AbelianMonoid|)) (ATTRIBUTE (|AbelianMonoid|)) |%noBranch|) (IF (|has| |t#2| (|AbelianGroup|)) (ATTRIBUTE (|AbelianGroup|)) |%noBranch|) (IF (|has| |t#2| (|Monoid|)) (ATTRIBUTE (|LinearSet| |t#2|)) |%noBranch|) (IF (|has| |t#2| (|Finite|)) (ATTRIBUTE (|Finite|)) |%noBranch|) (IF (|has| |t#2| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#2|)) |%noBranch|) (IF (|has| |t#2| (ATTRIBUTE |unitsKnown|)) (ATTRIBUTE |unitsKnown|) |%noBranch|) (IF (|has| |t#2| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |%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| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|AbelianGroup|))) ((|AbelianMonoid|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|AbelianSemiGroup|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|Aggregate|) . T) ((|BasicType|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|BasicType|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|BiModule| |#2| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|))) ((|CoercibleFrom| (|Integer|)) OR (|has| |#2| (|Ring|)) (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|)))) ((|CoercibleFrom| |#2|) |has| |#2| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CoercibleTo| (|OutputForm|))) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|CoercibleTo| (|Vector| |#2|)) . T) ((|DifferentialDomain| $) OR (AND (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) ((|DifferentialExtension| |#2|) |has| |#2| (|Ring|)) ((|DifferentialRing|) AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) ((|DifferentialSpace|) OR (AND (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) ((|DifferentialSpaceExtension| |#2|) |has| |#2| (|Ring|)) ((|Eltable| #2=(|Integer|) |#2|) . T) ((|EltableAggregate| #2# |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Finite|) |has| |#2| (|Finite|)) ((|FiniteAggregate| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|FullyRetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| #2# |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|AbelianGroup|))) ((|LeftLinearSet| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LeftLinearSet| $) |has| |#2| (|Ring|)) ((|LeftModule| #3=(|Integer|)) AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) ((|LeftModule| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LeftModule| $) |has| |#2| (|Ring|)) ((|LinearSet| |#2|) OR (|has| |#2| (|Monoid|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LinearlyExplicitRingOver| #3#) AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) ((|LinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|Module| |#2|) OR (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|Monoid|) |has| |#2| (|Ring|)) ((|OrderedAbelianMonoid|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedAbelianMonoidSup|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedAbelianSemiGroup|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedCancellationAbelianMonoid|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedSet|) OR (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|OrderedType|) OR (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (AND (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|))) ((|PartialDifferentialSpace| #4#) OR (AND (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|RetractableTo| #1#) AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| (|Integer|)) AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|RightLinearSet| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|RightModule| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|Ring|) |has| |#2| (|Ring|)) ((|Rng|) |has| |#2| (|Ring|)) ((|SemiGroup|) |has| |#2| (|Ring|)) ((|SemiRing|) |has| |#2| (|Ring|)) ((|SetCategory|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|Type|) . T) ((|VectorSpace| |#2|) |has| |#2| (|Field|))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) 63 #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) 69 #13=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#14=(|Union| $ #15="failed") $ $) 54 (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#16=(#17=(|NonNegativeInteger|)) NIL #18=(|has| |#2| (|Finite|)) ELT)) (|setelt| #19=(#20=(|#2| $ #10# |#2|) NIL #11# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #22=(#15#)) . #23=($)) NIL #24=(AND (|has| |#2| (|RetractableTo| #10#)) #25=(|has| |#2| (|SetCategory|))) ELT) (((|Union| #26=(|Fraction| #10#) . #22#) . #23#) NIL #27=(AND (|has| |#2| (|RetractableTo| #26#)) #25#) ELT) ((#28=(|Union| |#2| . #22#) $) 31 #25# ELT)) (|retract| (#29=(#10# . #30=($)) NIL #24# ELT) ((#26# . #30#) NIL #27# ELT) (#31=(|#2| $) 29 #25# ELT)) (|reducedSystem| ((#32=(|Matrix| #10#) . #33=(#34=(|Matrix| $))) NIL #35=(AND (|has| |#2| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #10#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#2|)) (|:| |vec| #41=(|Vector| |#2|))) . #37#) NIL #9# ELT) ((#40# . #33#) NIL #9# ELT)) (|reduce| ((|#2| #42=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) NIL #4# ELT) ((|#2| #42# $ |#2|) NIL T ELT) ((|#2| #42# $) NIL T ELT)) (|recip| ((#14# $) 59 #9# ELT)) (|random| (#21# NIL #18# ELT)) (|qsetelt!| #19#) (|qelt| (#43=(|#2| $ #10#) 57 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| (#29# 20 #44=(|has| #10# #45=(|OrderedSet|)) ELT)) (|min| #46=(#12# NIL #47=(|has| |#2| #45#) ELT)) (|members| (#48=(#49=(|List| |#2|) $) 14 T ELT)) (|member?| (#50=(#3# |#2| $) NIL #4# ELT)) (|maxIndex| (#29# NIL #44# ELT)) (|max| #46#) (|map| (($ #51=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #18# ELT)) (|leftReducedSystem| ((#32# . #52=(#38#)) NIL #35# ELT) ((#36# . #53=(#38# $)) NIL #35# ELT) ((#39# . #53#) NIL #9# ELT) ((#40# . #52#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #25# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #18# ELT)) (|hash| (((|SingleInteger|) $) NIL #25# ELT)) (|first| (#31# NIL #44# ELT)) (|find| ((#28# #54=(|Mapping| #3# |#2|) $) NIL T ELT)) (|fill!| (#55=($ $ |#2|) NIL #11# ELT)) (|every?| (#56=(#3# #54# $) 24 T ELT)) (|eval| (($ $ (|List| #57=(|Equation| |#2|))) NIL #58=(AND (|has| |#2| (|Evalable| |#2|)) #25#) ELT) (($ $ #57#) NIL #58# ELT) (($ $ |#2| |#2|) NIL #58# ELT) (($ $ #49# #49#) NIL #58# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#50# NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #4#) ELT)) (|entries| (#48# NIL T ELT)) (|empty?| (#5# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#20# NIL T ELT) (#43# 21 T ELT)) (|dot| ((|#2| $ $) NIL #9# ELT)) (|directProduct| (($ #41#) 18 T ELT)) (|dimension| (((|CardinalNumber|)) NIL #59=(|has| |#2| (|Field|)) ELT)) (|differentiate| #60=(#61=($ $ #17#) NIL #62=(AND (|has| |#2| (|DifferentialSpace|)) #9#) ELT) #63=(#64=($ $) NIL #62# ELT) #65=(($ $ #66=(|List| #67=(|Symbol|)) (|List| #17#)) NIL #68=(AND (|has| |#2| (|PartialDifferentialSpace| #67#)) #9#) ELT) #69=(($ $ #67# #17#) NIL #68# ELT) #70=(($ $ #66#) NIL #68# ELT) #71=(($ $ #67#) NIL #68# ELT) #72=(($ $ #51#) NIL #9# ELT) #73=(($ $ #51# #17#) NIL #9# ELT)) (|count| ((#17# |#2| $) NIL #4# ELT) ((#17# #54# $) NIL T ELT)) (|copy| (#64# NIL T ELT)) (|coerce| ((#41# $) 9 T ELT) (($ #10#) NIL (OR #24# #9#) ELT) (($ #26#) NIL #27# ELT) (($ |#2|) 12 #25# ELT) ((#74=(|OutputForm|) $) NIL (|has| |#2| (|CoercibleTo| #74#)) ELT)) (|characteristic| (#16# NIL #9# CONST)) (|before?| #1#) (|any?| (#56# NIL T ELT)) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#21# 37 #6# CONST)) (|One| (#21# 41 #9# CONST)) (D #60# #63# #65# #69# #70# #71# #72# #73#) (>= #75=(#2# NIL #47# ELT)) (> #75#) (= (#2# 28 #4# ELT)) (<= #75#) (< (#2# 67 #47# ELT)) (/ (#55# NIL #59# ELT)) (- (#12# NIL #76=(|has| |#2| (|AbelianGroup|)) ELT) (#64# NIL #76# ELT)) (+ (#12# 35 #77=(|has| |#2| (|AbelianSemiGroup|)) ELT)) (** (#61# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# 47 #9# ELT) (#55# 45 #78=(|has| |#2| (|Monoid|)) ELT) (($ |#2| $) 46 #78# ELT) (($ #10# $) NIL #76# ELT) (($ #17# $) NIL #6# ELT) (($ #8# $) NIL #77# ELT)) (|#| ((#17# $) NIL T ELT))) 
(((|DirectProduct| |#1| |#2|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|Type|)) (T |DirectProduct|)) 
NIL 
((|scan| ((#1=(|DirectProduct| |#1| |#3|) #2=(|Mapping| |#3| |#2| |#3|) #3=(|DirectProduct| |#1| |#2|) |#3|) 21 T ELT)) (|reduce| ((|#3| #2# #3# |#3|) 23 T ELT)) (|map| ((#1# (|Mapping| |#3| |#2|) #3#) 18 T ELT))) 
(((|DirectProductFunctions2| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |scan| (#1=(|DirectProduct| |#1| |#3|) #2=(|Mapping| |#3| |#2| |#3|) #3=(|DirectProduct| |#1| |#2|) |#3|)) (SIGNATURE |reduce| (|#3| #2# #3# |#3|)) (SIGNATURE |map| (#1# (|Mapping| |#3| |#2|) #3#))) (|NonNegativeInteger|) #4=(|Type|) #4#) (T |DirectProductFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *6)) #1=(|isDomain| *4 (|DirectProduct| *5 *6)) #2=(|ofType| *5 #3=(|NonNegativeInteger|)) #4=(|ofCategory| *6 #5=(|Type|)) #6=(|ofCategory| *7 #5#) (|isDomain| *2 (|DirectProduct| *5 *7)) (|isDomain| *1 (|DirectProductFunctions2| *5 *6 *7)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *6 *2)) #1# #2# #4# (|ofCategory| *2 #5#) (|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 #3#) #6# (|ofCategory| *5 #5#) (|isDomain| *2 (|DirectProduct| *6 *5)) (|isDomain| *1 (|DirectProductFunctions2| *6 *7 *5))))) 
((|sayLength| ((#1=(|Integer|) #2=(|List| #3=(|String|))) 36 T ELT) ((#1# #3#) 29 T ELT)) (|say| ((#4=(|Void|) #2#) 40 T ELT) ((#4# #3#) 39 T ELT)) (|newLine| ((#3#) 16 T ELT)) (|copies| ((#3# #1# #3#) 23 T ELT)) (|center| ((#2# #2# #1# #3#) 37 T ELT) ((#3# #3# #1# #3#) 35 T ELT)) (|bright| ((#2# #2#) 15 T ELT) ((#2# #3#) 11 T ELT))) 
(((|DisplayPackage|) (CATEGORY |package| (SIGNATURE |bright| (#1=(|List| #2=(|String|)) #2#)) (SIGNATURE |bright| (#1# #1#)) (SIGNATURE |newLine| (#2#)) (SIGNATURE |copies| (#2# #3=(|Integer|) #2#)) (SIGNATURE |center| (#2# #2# #3# #2#)) (SIGNATURE |center| (#1# #1# #3# #2#)) (SIGNATURE |say| (#4=(|Void|) #2#)) (SIGNATURE |say| (#4# #1#)) (SIGNATURE |sayLength| (#3# #2#)) (SIGNATURE |sayLength| (#3# #1#)))) (T |DisplayPackage|)) 
((|sayLength| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|List| #4=(|String|))) #5=(|isDomain| *2 #6=(|Integer|)) #7=(|isDomain| *1 (|DisplayPackage|)))) (|sayLength| #1# (AND #8=(|isDomain| *3 #4#) #5# #7#)) (|say| #1# (AND #2# #9=(|isDomain| *2 (|Void|)) #7#)) (|say| #1# (AND #8# #9# #7#)) (|center| (*1 *2 *2 *3 *4) (AND #10=(|isDomain| *2 #3#) #11=(|isDomain| *3 #6#) (|isDomain| *4 #4#) #7#)) (|center| (*1 *2 *2 *3 *2) #12=(AND #13=(|isDomain| *2 #4#) #11# #7#)) (|copies| (*1 *2 *3 *2) #12#) (|newLine| (*1 *2) (AND #13# #7#)) (|bright| (*1 *2 *2) (AND #10# #7#)) (|bright| #1# (AND #10# #7# #8#))) 
((** (($ $ #1=(|PositiveInteger|)) NIL T ELT) (($ $ #2=(|NonNegativeInteger|)) NIL T ELT) (($ $ #3=(|Integer|)) 18 T ELT)) (* (($ #1# $) NIL T ELT) (($ #2# $) NIL T ELT) (($ #3# $) NIL T ELT) (($ $ $) NIL T ELT) (($ #4=(|Fraction| #3#) $) 25 T ELT) (($ $ #4#) NIL T ELT))) 
(((|DivisionRing&| |#1|) (CATEGORY |package| (SIGNATURE ** (|#1| |#1| #1=(|Integer|))) (SIGNATURE * (|#1| |#1| #2=(|Fraction| #1#))) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE ** (|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE ** (|#1| |#1| #4=(|PositiveInteger|))) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE * (|#1| #3# |#1|)) (SIGNATURE * (|#1| #4# |#1|))) (|DivisionRing|)) (T |DivisionRing&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 55 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #4=(|Fraction| (|Integer|))) 59 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ (|Integer|)) 56 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #5=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ #4# . #5#) 58 T ELT) (($ $ #4#) 57 T ELT))) 
(((|DivisionRing|) (|Category|)) (T |DivisionRing|)) 
((** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DivisionRing|)) (|isDomain| *2 (|Integer|)))) (|inv| (*1 *1 *1) (|ofCategory| *1 (|DivisionRing|)))) 
(|Join| (|EntireRing|) (|Algebra| (|Fraction| #1=(|Integer|))) (CATEGORY |domain| (SIGNATURE ** ($ $ #1#)) (SIGNATURE |inv| ($ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|EntireRing|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|Module| #1#) . T) ((|Monoid|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|tail| (($ $) 54 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setprevious!| (($ $ $) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setnext!| (($ $ $) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #3="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #4=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sample| (#5=($) 6 T CONST)) (|previous| (($ $) 53 T ELT)) (|nodes| (#6=(#4# $) 45 T ELT)) (|node?| (#7=(#8=(|Boolean|) $ $) 37 (|has| |#1| . #9=((|BasicType|))) ELT)) (|next| (($ $) 52 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (#10=(#8# $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #11=((|SetCategory|))) ELT)) (|last| ((|#1| $) 56 T ELT)) (|head| (($ $) 55 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #11#) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT)) (|eq?| ((#12=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#12# $) 7 T ELT)) (|empty| (#5# 8 T ELT)) (|elt| ((|#1| $ #3#) 42 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (#10# 41 T ELT)) (|copy| (($ $) 9 T ELT)) (|concat!| (($ $ $) 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (#6# 46 T ELT)) (|child?| (#7# 38 (|has| |#1| . #9#) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|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 (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setprevious!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|DoublyLinkedAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setnext!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|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| $ (|ShallowlyMutableAggregate| |t#1|)) (PROGN (SIGNATURE |concat!| ($ $ $)) (SIGNATURE |setprevious!| ($ $ $)) (SIGNATURE |setnext!| ($ $ $))) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| #5=((|#1| $) NIL T ELT)) (|third| #5#) (|tail| #6=(#7=($ $) NIL T ELT)) (|swap!| (((|Void|) $ #8=(|Integer|) #8#) NIL #9=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|split!| (#10=($ $ #8#) NIL #9# ELT)) (|sorted?| (#11=(#3# $) NIL #12=(|has| |#1| #13=(|OrderedSet|)) ELT) ((#3# #14=(|Mapping| #3# |#1| |#1|) $) NIL T ELT)) (|sort!| (#7# NIL (AND #9# #12#) ELT) (#15=($ #14# $) NIL #9# ELT)) (|sort| (#7# 10 #12# ELT) (#15# NIL T ELT)) (|size?| #16=((#3# $ #17=(|NonNegativeInteger|)) NIL T ELT)) (|setvalue!| #18=((|#1| $ |#1|) NIL #9# ELT)) (|setrest!| (#19=($ $ $) NIL #9# ELT)) (|setlast!| #18#) (|setfirst!| #18#) (|setelt| ((|#1| $ #20="value" |#1|) NIL #9# ELT) ((|#1| $ #21="first" |#1|) NIL #9# ELT) (($ $ #22="rest" $) NIL #9# ELT) ((|#1| $ #23="last" |#1|) NIL #9# ELT) ((|#1| $ #24=(|UniversalSegment| #8#) |#1|) NIL #9# ELT) #25=(#26=(|#1| $ #8# |#1|) NIL #9# ELT)) (|setchildren!| (($ $ #27=(|List| $)) NIL #9# ELT)) (|select!| #28=(#29=($ #30=(|Mapping| #3# |#1|) $) NIL T ELT)) (|select| #31=(#29# NIL #32=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|second| #5#) (|sample| (#33=($) NIL T CONST)) (|reverse!| #34=(#7# NIL #9# ELT)) (|reverse| #6#) (|rest| #6# #35=(($ $ #17#) NIL T ELT)) (|removeDuplicates!| (#7# NIL #4# ELT)) (|removeDuplicates| (#7# 7 #36=(AND #32# #4#) ELT)) (|remove!| (#37=($ |#1| $) NIL #4# ELT) #28#) (|remove| #31# (#37# NIL #36# ELT)) (|reduce| ((|#1| #38=(|Mapping| |#1| |#1| |#1|) $) NIL T ELT) ((|#1| #38# $ |#1|) NIL T ELT) ((|#1| #38# $ |#1| |#1|) NIL #4# ELT)) (|qsetelt!| #25#) (|qelt| #39=((|#1| $ #8#) NIL T ELT)) (|possiblyInfinite?| #40=(#11# NIL T ELT)) (|position| ((#8# |#1| $ #8#) NIL #4# ELT) ((#8# |#1| $) NIL #4# ELT) ((#8# #30# $) NIL T ELT)) (|nodes| #41=((#27# $) NIL T ELT)) (|node?| #1#) (|new| (($ #17# |#1|) NIL T ELT)) (|more?| #16#) (|minIndex| #42=((#8# $) NIL (|has| #8# #13#) ELT)) (|min| #43=(#19# NIL #12# ELT)) (|merge!| #43# #44=(($ #14# $ $) NIL T ELT)) (|merge| #43# #44#) (|members| #45=(#46=(#47=(|List| |#1|) $) NIL T ELT)) (|member?| (#48=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| #42#) (|max| #43#) (|map!| #49=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #49# (($ #38# $ $) NIL T ELT)) (|list| (($ |#1|) NIL T ELT)) (|less?| #16#) (|leaves| #45#) (|leaf?| #40#) (|latex| (((|String|) $) NIL #50=(|has| |#1| (|SetCategory|)) ELT)) (|last| #5# #35#) (|insert!| #51=(#52=($ $ $ #8#) NIL T ELT) #53=(($ |#1| $ #8#) NIL T ELT)) (|insert| #51# #53#) (|indices| (((|List| #8#) $) NIL T ELT)) (|index?| ((#3# #8# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #50# ELT)) (|first| #5# #35#) (|find| (((|Union| |#1| "failed") #30# $) NIL T ELT)) (|fill!| (#54=($ $ |#1|) NIL #9# ELT)) (|explicitlyFinite?| #40#) (|every?| #55=((#3# #30# $) NIL T ELT)) (|eval| (($ $ (|List| #56=(|Equation| |#1|))) NIL #57=(AND (|has| |#1| (|Evalable| |#1|)) #50#) ELT) (($ $ #56#) NIL #57# ELT) (($ $ |#1| |#1|) NIL #57# ELT) (($ $ #47# #47#) NIL #57# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#48# NIL #36# ELT)) (|entries| #45#) (|empty?| #40#) (|empty| (#33# NIL T ELT)) (|elt| ((|#1| $ #20#) NIL T ELT) ((|#1| $ #21#) NIL T ELT) (($ $ #22#) NIL T ELT) ((|#1| $ #23#) NIL T ELT) #58=(($ $ #24#) NIL T ELT) #39# (#26# NIL T ELT) (($ $ "unique") 9 T ELT) (($ $ "sort") 12 T ELT) ((#17# $ "count") 16 T ELT)) (|distance| ((#8# $ $) NIL T ELT)) (|delete!| #58# #59=(#10# NIL T ELT)) (|delete| #58# #59#) (|datalist| (#60=($ #47#) 22 T ELT)) (|cyclic?| #40#) (|cycleTail| #6#) (|cycleSplit!| #34#) (|cycleLength| (#61=(#17# $) NIL T ELT)) (|cycleEntry| #6#) (|count| ((#17# #30# $) NIL T ELT) ((#17# |#1| $) NIL #4# ELT)) (|copyInto!| (#52# NIL #9# ELT)) (|copy| #6#) (|convert| ((#62=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #62#)) ELT)) (|construct| (#60# NIL T ELT)) (|concat!| #63=(#19# NIL T ELT) #64=(#54# NIL T ELT)) (|concat| #63# (#37# NIL T ELT) (($ #27#) NIL T ELT) #64#) (|coerce| (#60# 17 T ELT) (#46# 18 T ELT) ((#65=(|OutputForm|) $) 21 (|has| |#1| (|CoercibleTo| #65#)) ELT)) (|children| #41#) (|child?| #1#) (|before?| #1#) (|any?| #55#) (>= #66=(#2# NIL #12# ELT)) (> #66#) (= #1#) (<= #66#) (< #66#) (|#| (#61# 14 T ELT))) 
(((|DataList| |#1|) (|Join| (|ListAggregate| |#1|) (|HomotopicTo| #1=(|List| |#1|)) (CATEGORY |domain| (SIGNATURE |datalist| ($ #1#)) (SIGNATURE |elt| ($ $ "unique")) (SIGNATURE |elt| ($ $ "sort")) (SIGNATURE |elt| ((|NonNegativeInteger|) $ "count")))) (|OrderedSet|)) (T |DataList|)) 
((|datalist| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 #2=(|OrderedSet|)) #3=(|isDomain| *1 (|DataList| *3)))) (|elt| #4=(*1 *1 *1 *2) (AND (|isDomain| *2 "unique") #3# #1#)) (|elt| #4# (AND (|isDomain| *2 "sort") #3# #1#)) (|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 "count") (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DataList| *4)) (|ofCategory| *4 #2#)))) 
((|shanksDiscLogAlgorithm| (((|Union| #1=(|NonNegativeInteger|) "failed") |#1| |#1| #1#) 40 T ELT))) 
(((|DiscreteLogarithmPackage| |#1|) (CATEGORY |package| (SIGNATURE |shanksDiscLogAlgorithm| ((|Union| #1=(|NonNegativeInteger|) "failed") |#1| |#1| #1#))) (|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))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ . #4=($)) 60 (|has| |#1| . #5=((|DifferentialSpace|))) ELT) (#6=($ $ (|NonNegativeInteger|)) 58 (|has| |#1| . #5#) ELT) (($ $ #7=(|Symbol|)) 56 (|has| |#1| . #8=((|PartialDifferentialSpace| #7#))) ELT) (($ $ (|List| #7#)) 54 (|has| |#1| . #8#) ELT) (($ $ #7# . #9=(#10=(|NonNegativeInteger|))) 53 (|has| |#1| . #8#) ELT) (($ $ (|List| #7#) . #11=((|List| #10#))) 52 (|has| |#1| . #8#) ELT) (($ $ (|Mapping| |#1| |#1|) . #12=((|NonNegativeInteger|))) 46 T ELT) (($ $ (|Mapping| |#1| |#1|)) 45 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (($ . #4#) 59 (|has| |#1| . #5#) ELT) (#6# 57 (|has| |#1| . #5#) ELT) (($ $ #7#) 55 (|has| |#1| . #8#) ELT) (($ $ (|List| #7#)) 51 (|has| |#1| . #8#) ELT) (($ $ #7# . #9#) 50 (|has| |#1| . #8#) ELT) (($ $ (|List| #7#) . #11#) 49 (|has| |#1| . #8#) ELT) (($ $ (|Mapping| |#1| |#1|) . #12#) 48 T ELT) (($ $ (|Mapping| |#1| |#1|)) 47 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #13=($)) 30 T ELT) (($ |#1| . #13#) 33 T ELT) (($ $ |#1|) 37 T ELT))) 
(((|DifferentialModuleExtension| |#1|) (|Category|) (|Ring|)) (T |DifferentialModuleExtension|)) 
NIL 
(|Join| (|BiModule| |t#1| |t#1|) (|DifferentialSpaceExtension| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|DifferentialSpace|)) (ATTRIBUTE (|DifferentialModule| |t#1|)) |%noBranch|) (IF (|has| |t#1| (|PartialDifferentialSpace| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialModule| |t#1| (|Symbol|))) |%noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialModule| |#1|) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpaceExtension| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) OR (AND (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|DifferentialSpace|)))) ((|Module| |#1|) OR (AND (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|DifferentialSpace|)))) ((|PartialDifferentialDomain| $ #1=(|Symbol|)) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|PartialDifferentialModule| |#1| (|Symbol|)) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|PartialDifferentialSpace| #1#) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #8#) #8#) NIL #19=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#12# NIL #21=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #8#) #17#) #23# #8#) NIL #19# ELT)) (|sample| #24=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #25=(#17#)) . #26=($)) NIL T ELT) (((|Union| #27=(|Fraction| #28=(|Integer|)) . #25#) . #26#) NIL #29=(|has| |#2| (|RetractableTo| #27#)) ELT) (((|Union| #28# . #25#) . #26#) NIL #30=(|has| |#2| (|RetractableTo| #28#)) ELT) #31=(((|Union| #7# . #25#) . #26#) NIL T ELT)) (|retract| #32=(#33=(|#2| . #34=($)) NIL T ELT) ((#27# . #34#) NIL #29# ELT) ((#28# . #34#) NIL #30# ELT) ((#7# . #34#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #35=(|has| |#2| (|CommutativeRing|)) ELT)) (|reorder| (($ $ (|List| #28#)) NIL T ELT)) (|reductum| #36=(#12# NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #28#) . #38=(#39=(|Matrix| $))) NIL #40=(|has| |#2| (|LinearlyExplicitRingOver| #28#)) ELT) ((#41=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #28#))) . #42=(#39# #43=(|Vector| $))) NIL #40# ELT) ((#44=(|Record| (|:| |mat| #45=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #42#) NIL T ELT) ((#45# . #38#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|primitivePart| #20# #46=(#47=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#2| #50=(|DirectProduct| (|#| |#1|) #14#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#2| #55#)) ELT) ((#56=(|PatternMatchResult| #28# . #53#) $ #57=(|Pattern| #28#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #28#)) (|has| |#2| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#2| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #31#) (|leftReducedSystem| ((#37# . #65=(#43#)) NIL #40# ELT) ((#41# . #66=(#43# $)) NIL #40# ELT) ((#44# . #66#) NIL T ELT) ((#45# . #65#) NIL T ELT)) (|leadingMonomial| #36#) (|leadingCoefficient| #32#) (|lcm| #67=(($ #49#) NIL #21# ELT) #68=(#69=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #17#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #17#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #32#) (|gcdPolynomial| ((#8# #8# #8#) NIL #21# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#16# $ |#2|) NIL #10# ELT) (#15# NIL #10# ELT)) (|eval| (($ $ (|List| #71=(|Equation| $))) NIL T ELT) (($ $ #71#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#2|) NIL T ELT) (($ $ #6# #72=(|List| |#2|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #35# ELT)) (|differentiate| #60# #59# #73=(($ $ #6#) NIL T ELT) #74=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #75=($)) NIL (AND (|has| #7# #76=(|ConvertibleTo| #54#)) (|has| |#2| #76#)) ELT) ((#57# . #75#) NIL (AND (|has| #7# #77=(|ConvertibleTo| #57#)) (|has| |#2| #77#)) ELT) ((#78=(|InputForm|) . #75#) NIL (AND (|has| #7# #79=(|ConvertibleTo| #78#)) (|has| |#2| #79#)) ELT)) (|content| (#33# NIL #21# ELT) #46#) (|conditionP| (((|Union| #43# #17#) #39#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #28#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) (($ #27#) NIL (OR #82=(|has| |#2| (|Algebra| #27#)) #29#) ELT) #11#) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #82# ELT) (($ #27# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) 
(((|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|))))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|showSummary| (((|Void|) $) 17 T ELT)) (|reify| ((#3=(|ConstructorCall| #4=(|DomainConstructor|)) $) 11 T ELT)) (|reflect| (($ #3#) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|constructor| ((#4# $) 7 T ELT)) (|coerce| (((|OutputForm|) $) 9 T ELT)) (|before?| #1#) (= (#2# 15 T ELT))) 
(((|Domain|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |constructor| (#1=(|DomainConstructor|) $)) (SIGNATURE |reify| (#2=(|ConstructorCall| #1#) $)) (SIGNATURE |reflect| ($ #2#)) (SIGNATURE |showSummary| ((|Void|) $))))) (T |Domain|)) 
((|constructor| #1=(*1 *2 *1) (AND (|isDomain| *2 #2=(|DomainConstructor|)) #3=(|isDomain| *1 (|Domain|)))) (|reify| #1# #4=(AND (|isDomain| *2 (|ConstructorCall| #2#)) #3#)) (|reflect| (*1 *1 *2) #4#) (|showSummary| #1# (AND (|isDomain| *2 (|Void|)) #3#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|operations| (((|List| (|OverloadSet|)) $) NIL T ELT)) (|name| ((#3=(|Identifier|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|kind| (((|ConstructorKind|) $) NIL T ELT)) (|is?| ((#2# $ #3#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|functorData| (((|FunctorData|) $) 7 T ELT)) (|dualSignature| (((|List| #2#) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (((|Constructor|) $) 8 T ELT)) (|before?| #1#) (|arity| (((|Arity|) $) NIL T ELT)) (= #1#)) 
(((|DomainConstructor|) (|Join| (|ConstructorCategory|) (|CoercibleTo| (|Constructor|)) (CATEGORY |domain| (SIGNATURE |functorData| ((|FunctorData|) $))))) (T |DomainConstructor|)) 
((|functorData| (*1 *2 *1) (AND (|isDomain| *2 (|FunctorData|)) (|isDomain| *1 (|DomainConstructor|))))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| (((|Syntax|) $ #3=(|NonNegativeInteger|)) 14 T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT)) (|before?| #1#) (= (#2# 17 T ELT)) (|#| ((#3# $) 11 T ELT))) 
(((|DomainTemplate|) (|Join| (|SetCategory|) (|Eltable| #1=(|NonNegativeInteger|) (|Syntax|)) (CATEGORY |domain| (SIGNATURE |#| (#1# $))))) (T |DomainTemplate|)) 
((|#| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|DomainTemplate|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitVector| (#6=($ #7=(|PositiveInteger|)) NIL #8=(|has| |#4| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #9=(|Integer|) #9#) NIL #10=(|has| $ (|ShallowlyMutableAggregate| |#4|)) ELT)) (|sup| (#11=($ $ $) NIL #12=(|has| |#4| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#13=(|Union| $ #14="failed") $ $) NIL T ELT)) (|size| (#15=(#16=(|NonNegativeInteger|)) NIL #17=(|has| |#4| (|Finite|)) ELT)) (|setelt| #18=(#19=(|#4| $ #9# |#4|) NIL #10# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| ((#22=(|Union| |#4| . #23=(#14#)) . #24=($)) NIL #25=(|has| |#4| (|SetCategory|)) ELT) (((|Union| #9# . #23#) . #24#) NIL #26=(AND (|has| |#4| (|RetractableTo| #9#)) #25#) ELT) (((|Union| #27=(|Fraction| #9#) . #23#) . #24#) NIL #28=(AND (|has| |#4| (|RetractableTo| #27#)) #25#) ELT)) (|retract| (#29=(|#4| . #30=($)) NIL #25# ELT) (#31=(#9# . #30#) NIL #26# ELT) ((#27# . #30#) NIL #28# ELT)) (|reducedSystem| ((#32=(|Record| (|:| |mat| #33=(|Matrix| |#4|)) (|:| |vec| #34=(|Vector| |#4|))) . #35=(#36=(|Matrix| $) #37=(|Vector| $))) NIL #8# ELT) ((#33# . #38=(#36#)) NIL #8# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| #9#)) (|:| |vec| (|Vector| #9#))) . #35#) NIL #41=(AND (|has| |#4| (|LinearlyExplicitRingOver| #9#)) #8#) ELT) ((#40# . #38#) NIL #41# ELT)) (|reduce| ((|#4| #42=(|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) NIL #43=(|has| |#4| (|BasicType|)) ELT) ((|#4| #42# $ |#4|) NIL T ELT) ((|#4| #42# $) NIL T ELT)) (|recip| ((#13# $) NIL #8# ELT)) (|random| (#21# NIL #17# ELT)) (|qsetelt!| #18#) (|qelt| (#44=(|#4| $ #9#) NIL T ELT)) (|positive?| (#5# NIL #12# ELT)) (|opposite?| #1#) (|one?| (#5# NIL #8# ELT)) (|minIndex| #45=(#31# NIL #46=(|has| #9# #47=(|OrderedSet|)) ELT)) (|min| #48=(#11# NIL #49=(|has| |#4| #47#) ELT)) (|members| #50=((#51=(|List| |#4|) $) NIL T ELT)) (|member?| (#52=(#3# |#4| $) NIL #43# ELT)) (|maxIndex| #45#) (|max| #48#) (|map| (($ #53=(|Mapping| |#4| |#4|) $) NIL T ELT)) (|lookup| ((#7# $) NIL #17# ELT)) (|leftReducedSystem| ((#32# . #54=(#37# $)) NIL #8# ELT) ((#33# . #55=(#37#)) NIL #8# ELT) ((#39# . #54#) NIL #41# ELT) ((#40# . #55#) NIL #41# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|indices| (((|List| #9#) $) NIL T ELT)) (|index?| ((#3# #9# $) NIL T ELT)) (|index| (#6# NIL #17# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#29# NIL #46# ELT)) (|find| ((#22# #56=(|Mapping| #3# |#4|) $) NIL T ELT)) (|fill!| (#57=($ $ |#4|) NIL #10# ELT)) (|every?| #58=((#3# #56# $) NIL T ELT)) (|eval| (($ $ (|List| #59=(|Equation| |#4|))) NIL #60=(AND (|has| |#4| (|Evalable| |#4|)) #25#) ELT) (($ $ #59#) NIL #60# ELT) (($ $ |#4| |#4|) NIL #60# ELT) (($ $ #51# #51#) NIL #60# ELT)) (|eq?| #1#) (|entry?| (#52# NIL (AND (|has| $ (|FiniteAggregate| |#4|)) #43#) ELT)) (|entries| #50#) (|empty?| #4#) (|empty| (#21# NIL T ELT)) (|elt| (#19# NIL T ELT) (#44# 12 T ELT)) (|dot| ((|#4| $ $) NIL #8# ELT)) (|directProduct| (($ #34#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #61=(|has| |#4| (|Field|)) ELT)) (|differentiate| #62=(($ $ #53#) NIL #8# ELT) #63=(($ $ #53# #16#) NIL #8# ELT) #64=(($ $ #65=(|List| #66=(|Symbol|)) (|List| #16#)) NIL #67=(OR (AND (|has| |#4| (|PartialDifferentialRing| #66#)) #8#) (AND (|has| |#4| (|PartialDifferentialSpace| #66#)) #8#)) ELT) #68=(($ $ #66# #16#) NIL #67# ELT) #69=(($ $ #65#) NIL #67# ELT) #70=(($ $ #66#) NIL #67# ELT) #71=(#72=($ $ #16#) NIL #73=(OR (AND (|has| |#4| (|DifferentialRing|)) #8#) (AND (|has| |#4| (|DifferentialSpace|)) #8#)) ELT) #74=(#75=($ $) NIL #73# ELT)) (|count| ((#16# |#4| $) NIL #43# ELT) ((#16# #56# $) NIL T ELT)) (|copy| #76=(#75# NIL T ELT)) (|coerce| ((#34# . #77=($)) NIL T ELT) (($ |#4|) NIL #25# ELT) (((|OutputForm|) . #77#) NIL T ELT) (($ #9#) NIL (OR #26# #8#) ELT) (($ #27#) NIL #28# ELT)) (|characteristic| (#15# NIL #8# CONST)) (|before?| #1#) (|any?| #58#) (|annihilate?| (#2# NIL #8# ELT)) (|Zero| #20#) (|One| (#21# NIL #8# CONST)) (D #62# #63# #64# #68# #69# #70# #71# #74#) (>= #78=(#2# NIL #49# ELT)) (> #78#) (= #1#) (<= #78#) (< #78#) (/ (#57# NIL #61# ELT)) (- #79=(#11# NIL T ELT) #76#) (+ #79#) (** (#72# NIL #8# ELT) (($ $ #7#) NIL #8# ELT)) (* (($ |#2| $) 14 T ELT) (($ #9# . #80=($)) NIL T ELT) (($ #16# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ |#3| $) 18 T ELT) (#57# NIL #81=(|has| |#4| (|Monoid|)) ELT) (($ |#4| . #80#) NIL #81# ELT) (#11# NIL #8# ELT)) (|#| ((#16# $) NIL T ELT))) 
(((|DirectProductMatrixModule| |#1| |#2| |#3| |#4|) (|Join| (|DirectProductCategory| |#1| |#4|) #1=(|LeftModule| |#2|) (|LeftModule| |#3|)) (|PositiveInteger|) (|Ring|) (|SquareMatrixCategory| |#1| |#2| #2=(|DirectProduct| |#1| |#2|) #2#) #1#) (T |DirectProductMatrixModule|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitVector| (#6=($ #7=(|PositiveInteger|)) NIL #8=(|has| |#3| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #9=(|Integer|) #9#) NIL #10=(|has| $ (|ShallowlyMutableAggregate| |#3|)) ELT)) (|sup| (#11=($ $ $) NIL #12=(|has| |#3| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#13=(|Union| $ #14="failed") $ $) NIL T ELT)) (|size| (#15=(#16=(|NonNegativeInteger|)) NIL #17=(|has| |#3| (|Finite|)) ELT)) (|setelt| #18=(#19=(|#3| $ #9# |#3|) NIL #10# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| ((#22=(|Union| |#3| . #23=(#14#)) . #24=($)) NIL #25=(|has| |#3| (|SetCategory|)) ELT) (((|Union| #9# . #23#) . #24#) NIL #26=(AND (|has| |#3| (|RetractableTo| #9#)) #25#) ELT) (((|Union| #27=(|Fraction| #9#) . #23#) . #24#) NIL #28=(AND (|has| |#3| (|RetractableTo| #27#)) #25#) ELT)) (|retract| (#29=(|#3| . #30=($)) NIL #25# ELT) (#31=(#9# . #30#) NIL #26# ELT) ((#27# . #30#) NIL #28# ELT)) (|reducedSystem| ((#32=(|Record| (|:| |mat| #33=(|Matrix| |#3|)) (|:| |vec| #34=(|Vector| |#3|))) . #35=(#36=(|Matrix| $) #37=(|Vector| $))) NIL #8# ELT) ((#33# . #38=(#36#)) NIL #8# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| #9#)) (|:| |vec| (|Vector| #9#))) . #35#) NIL #41=(AND (|has| |#3| (|LinearlyExplicitRingOver| #9#)) #8#) ELT) ((#40# . #38#) NIL #41# ELT)) (|reduce| ((|#3| #42=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) NIL #43=(|has| |#3| (|BasicType|)) ELT) ((|#3| #42# $ |#3|) NIL T ELT) ((|#3| #42# $) NIL T ELT)) (|recip| ((#13# $) NIL #8# ELT)) (|random| (#21# NIL #17# ELT)) (|qsetelt!| #18#) (|qelt| (#44=(|#3| $ #9#) NIL T ELT)) (|positive?| (#5# NIL #12# ELT)) (|opposite?| #1#) (|one?| (#5# NIL #8# ELT)) (|minIndex| #45=(#31# NIL #46=(|has| #9# #47=(|OrderedSet|)) ELT)) (|min| #48=(#11# NIL #49=(|has| |#3| #47#) ELT)) (|members| #50=((#51=(|List| |#3|) $) NIL T ELT)) (|member?| (#52=(#3# |#3| $) NIL #43# ELT)) (|maxIndex| #45#) (|max| #48#) (|map| (($ #53=(|Mapping| |#3| |#3|) $) NIL T ELT)) (|lookup| ((#7# $) NIL #17# ELT)) (|leftReducedSystem| ((#32# . #54=(#37# $)) NIL #8# ELT) ((#33# . #55=(#37#)) NIL #8# ELT) ((#39# . #54#) NIL #41# ELT) ((#40# . #55#) NIL #41# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|indices| (((|List| #9#) $) NIL T ELT)) (|index?| ((#3# #9# $) NIL T ELT)) (|index| (#6# NIL #17# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#29# NIL #46# ELT)) (|find| ((#22# #56=(|Mapping| #3# |#3|) $) NIL T ELT)) (|fill!| (#57=($ $ |#3|) NIL #10# ELT)) (|every?| #58=((#3# #56# $) NIL T ELT)) (|eval| (($ $ (|List| #59=(|Equation| |#3|))) NIL #60=(AND (|has| |#3| (|Evalable| |#3|)) #25#) ELT) (($ $ #59#) NIL #60# ELT) (($ $ |#3| |#3|) NIL #60# ELT) (($ $ #51# #51#) NIL #60# ELT)) (|eq?| #1#) (|entry?| (#52# NIL (AND (|has| $ (|FiniteAggregate| |#3|)) #43#) ELT)) (|entries| #50#) (|empty?| #4#) (|empty| (#21# NIL T ELT)) (|elt| (#19# NIL T ELT) (#44# 11 T ELT)) (|dot| ((|#3| $ $) NIL #8# ELT)) (|directProduct| (($ #34#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #61=(|has| |#3| (|Field|)) ELT)) (|differentiate| #62=(($ $ #53#) NIL #8# ELT) #63=(($ $ #53# #16#) NIL #8# ELT) #64=(($ $ #65=(|List| #66=(|Symbol|)) (|List| #16#)) NIL #67=(OR (AND (|has| |#3| (|PartialDifferentialRing| #66#)) #8#) (AND (|has| |#3| (|PartialDifferentialSpace| #66#)) #8#)) ELT) #68=(($ $ #66# #16#) NIL #67# ELT) #69=(($ $ #65#) NIL #67# ELT) #70=(($ $ #66#) NIL #67# ELT) #71=(#72=($ $ #16#) NIL #73=(OR (AND (|has| |#3| (|DifferentialRing|)) #8#) (AND (|has| |#3| (|DifferentialSpace|)) #8#)) ELT) #74=(#75=($ $) NIL #73# ELT)) (|count| ((#16# |#3| $) NIL #43# ELT) ((#16# #56# $) NIL T ELT)) (|copy| #76=(#75# NIL T ELT)) (|coerce| ((#34# . #77=($)) NIL T ELT) (($ |#3|) NIL #25# ELT) (((|OutputForm|) . #77#) NIL T ELT) (($ #9#) NIL (OR #26# #8#) ELT) (($ #27#) NIL #28# ELT)) (|characteristic| (#15# NIL #8# CONST)) (|before?| #1#) (|any?| #58#) (|annihilate?| (#2# NIL #8# ELT)) (|Zero| #20#) (|One| (#21# NIL #8# CONST)) (D #62# #63# #64# #68# #69# #70# #71# #74#) (>= #78=(#2# NIL #49# ELT)) (> #78#) (= #1#) (<= #78#) (< #78#) (/ (#57# NIL #61# ELT)) (- #79=(#11# NIL T ELT) #76#) (+ #79#) (** (#72# NIL #8# ELT) (($ $ #7#) NIL #8# ELT)) (* (($ |#2| $) 13 T ELT) (($ #9# . #80=($)) NIL T ELT) (($ #16# $) NIL T ELT) (($ #7# $) NIL T ELT) (#57# NIL #81=(|has| |#3| (|Monoid|)) ELT) (($ |#3| . #80#) NIL #81# ELT) (#11# NIL #8# ELT)) (|#| ((#16# $) NIL T ELT))) 
(((|DirectProductModule| |#1| |#2| |#3|) (|Join| (|DirectProductCategory| |#1| |#3|) #1=(|LeftModule| |#2|)) (|NonNegativeInteger|) (|Ring|) #1#) (T |DirectProductModule|)) 
NIL 
((|weights| ((#1=(|List| #2=(|NonNegativeInteger|)) $) 56 T ELT) ((#1# $ |#3|) 59 T ELT)) (|weight| (#3=(#2# $) 58 T ELT) (#4=(#2# $ |#3|) 61 T ELT)) (|separant| (#5=($ $) 76 T ELT)) (|retractIfCan| (((|Union| |#2| #6="failed") $) NIL T ELT) (((|Union| #7=(|Fraction| #8=(|Integer|)) #6#) $) NIL T ELT) (((|Union| #8# #6#) $) NIL T ELT) (((|Union| |#4| #6#) $) NIL T ELT) (((|Union| |#3| #6#) $) 83 T ELT)) (|order| (#4# 43 T ELT) (#3# 38 T ELT)) (|makeVariable| ((#9=(|Mapping| $ #2#) |#3|) 15 T ELT) ((#9# $) 88 T ELT)) (|leader| ((|#4| $) 69 T ELT)) (|isobaric?| (((|Boolean|) $) 67 T ELT)) (|initial| (#5# 75 T ELT)) (|eval| (($ $ (|List| #10=(|Equation| $))) 111 T ELT) (($ $ #10#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #11=(|List| $) #11#) NIL T ELT) (($ $ |#4| |#2|) NIL T ELT) (($ $ #12=(|List| |#4|) #13=(|List| |#2|)) NIL T ELT) (($ $ |#4| $) NIL T ELT) (($ $ #12# #11#) NIL T ELT) (($ $ |#3| $) NIL T ELT) (($ $ #14=(|List| |#3|) #11#) 103 T ELT) (($ $ |#3| |#2|) NIL T ELT) (($ $ #14# #13#) 97 T ELT)) (|differentiate| (($ $ #12# #1#) NIL T ELT) (($ $ |#4| #2#) NIL T ELT) (($ $ #12#) NIL T ELT) (($ $ |#4|) NIL T ELT) (($ $ #15=(|Mapping| |#2| |#2|)) 32 T ELT) (($ $ #15# #2#) NIL T ELT) (($ $ #16=(|Symbol|)) NIL T ELT) (($ $ #17=(|List| #16#)) NIL T ELT) (($ $ #16# #2#) NIL T ELT) (($ $ #17# #1#) NIL T ELT) #18=(#5# NIL T ELT) (($ $ #2#) NIL T ELT)) (|differentialVariables| ((#14# $) 86 T ELT)) (|degree| ((|#5| $) NIL T ELT) ((#2# $ |#4|) NIL T ELT) ((#1# $ #12#) NIL T ELT) (#4# 49 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #8#) NIL T ELT) (($ |#2|) NIL T ELT) (($ |#4|) NIL T ELT) (($ |#3|) 78 T ELT) (($ #7#) NIL T ELT) #18#)) 
(((|DifferentialPolynomialCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |differentiate| (|#1| |#1| #1=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #2=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #3=(|List| #4=(|Symbol|)) #5=(|List| #1#))) (SIGNATURE |differentiate| (|#1| |#1| #4# #1#)) (SIGNATURE |differentiate| (|#1| |#1| #3#)) (SIGNATURE |differentiate| (|#1| |#1| #4#)) (SIGNATURE |coerce| #2#) (SIGNATURE |coerce| (|#1| #6=(|Fraction| #7=(|Integer|)))) (SIGNATURE |eval| (|#1| |#1| #8=(|List| |#3|) #9=(|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#3| |#2|)) (SIGNATURE |eval| (|#1| |#1| #8# #10=(|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| |#3| |#1|)) (SIGNATURE |makeVariable| (#11=(|Mapping| |#1| #1#) |#1|)) (SIGNATURE |separant| #2#) (SIGNATURE |initial| #2#) (SIGNATURE |leader| (|#4| |#1|)) (SIGNATURE |isobaric?| ((|Boolean|) |#1|)) (SIGNATURE |weight| #12=(#1# |#1| |#3|)) (SIGNATURE |weights| (#5# |#1| |#3|)) (SIGNATURE |weight| #13=(#1# |#1|)) (SIGNATURE |weights| (#5# |#1|)) (SIGNATURE |degree| #12#) (SIGNATURE |order| #13#) (SIGNATURE |order| #12#) (SIGNATURE |differentialVariables| (#8# |#1|)) (SIGNATURE |makeVariable| (#11# |#3|)) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |retractIfCan| ((|Union| |#3| #14="failed") |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #15=(|Mapping| |#2| |#2|) #1#)) (SIGNATURE |differentiate| (|#1| |#1| #15#)) (SIGNATURE |degree| (#5# |#1| #16=(|List| |#4|))) (SIGNATURE |degree| (#1# |#1| |#4|)) (SIGNATURE |coerce| (|#1| |#4|)) (SIGNATURE |retractIfCan| ((|Union| |#4| #14#) |#1|)) (SIGNATURE |eval| (|#1| |#1| #16# #10#)) (SIGNATURE |eval| (|#1| |#1| |#4| |#1|)) (SIGNATURE |eval| (|#1| |#1| #16# #9#)) (SIGNATURE |eval| (|#1| |#1| |#4| |#2|)) (SIGNATURE |eval| (|#1| |#1| #10# #10#)) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| (|#1| |#1| #17=(|Equation| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|List| #17#))) (SIGNATURE |degree| (|#5| |#1|)) (SIGNATURE |retractIfCan| ((|Union| #7# #14#) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #6# #14#) |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #14#) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |differentiate| (|#1| |#1| |#4|)) (SIGNATURE |differentiate| (|#1| |#1| #16#)) (SIGNATURE |differentiate| (|#1| |#1| |#4| #1#)) (SIGNATURE |differentiate| (|#1| |#1| #16# #5#)) (SIGNATURE |coerce| (|#1| #7#)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|DifferentialPolynomialCategory| |#2| |#3| |#4| |#5|) (|Ring|) (|OrderedSet|) (|DifferentialVariableCategory| |#3|) (|OrderedAbelianMonoidSup|)) (T |DifferentialPolynomialCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|weights| (((|List| (|NonNegativeInteger|)) $) 252 T ELT) (((|List| (|NonNegativeInteger|)) $ |#2|) 250 T ELT)) (|weight| (((|NonNegativeInteger|) $) 251 T ELT) (((|NonNegativeInteger|) $ |#2|) 249 T ELT)) (|variables| (((|List| |#3|) $) 124 T ELT)) (|univariate| ((#3=(|SparseUnivariatePolynomial| $) $ |#3|) 139 T ELT) (((|SparseUnivariatePolynomial| |#1|) $) 138 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 101 (|has| |#1| . #4=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 102 (|has| |#1| . #4#) ELT)) (|unit?| ((#5=(|Boolean|) $) 104 (|has| |#1| . #4#) ELT)) (|totalDegree| ((#6=(|NonNegativeInteger|) $) 126 T ELT) ((#6# $ (|List| |#3|)) 125 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (#7=((|Factored| #8=(|SparseUnivariatePolynomial| $)) #8#) 114 (|has| |#1| . #9=((|PolynomialFactorizationExplicit|))) ELT)) (|squareFreePart| (($ $) 112 (|has| |#1| . #10=((|GcdDomain|))) ELT)) (|squareFree| (#11=((|Factored| $) $) 111 (|has| |#1| . #10#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #12=(|List| #8#) #13="failed") #12# #8#) 117 (|has| |#1| . #9#) ELT)) (|separant| (($ $) 245 T ELT)) (|sample| (#14=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| . #15=("failed")) . #16=($)) 182 T ELT) (((|Union| #17=(|Fraction| #18=(|Integer|)) . #15#) . #16#) 179 (|has| |#1| . #19=((|RetractableTo| #17#))) ELT) (((|Union| #18# . #15#) . #16#) 177 (|has| |#1| . #20=((|RetractableTo| #18#))) ELT) (((|Union| |#3| . #15#) . #16#) 154 T ELT) (((|Union| |#2| . #15#) . #16#) 259 T ELT)) (|retract| ((|#1| . #21=($)) 181 T ELT) ((#17# . #21#) 180 (|has| |#1| . #19#) ELT) ((#18# . #21#) 178 (|has| |#1| . #20#) ELT) ((|#3| . #21#) 155 T ELT) ((|#2| . #21#) 260 T ELT)) (|resultant| (($ $ $ |#3|) 122 (|has| |#1| . #22=((|CommutativeRing|))) ELT)) (|reductum| (#23=($ $) 172 T ELT)) (|reducedSystem| (((|Matrix| #24=(|Integer|)) . #25=(#26=(|Matrix| $))) 150 (|has| |#1| . #27=((|LinearlyExplicitRingOver| #24#))) ELT) (((|Record| (|:| |mat| (|Matrix| #24#)) (|:| |vec| (|Vector| #24#))) . #28=(#26# #29=(|Vector| $))) 149 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #28#) 148 T ELT) (((|Matrix| |#1|) . #25#) 147 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (($ $) 194 (|has| |#1| . #30=((|GcdDomain|))) ELT) (($ $ |#3|) 119 (|has| |#1| . #10#) ELT)) (|primitiveMonomials| (#31=(#32=(|List| $) $) 123 T ELT)) (|prime?| (((|Boolean|) $) 110 (|has| |#1| . #9#) ELT)) (|pomopo!| (($ $ |#1| |#4| $) 190 T ELT)) (|patternMatch| (((|PatternMatchResult| #33=(|Float|) . #34=($)) $ (|Pattern| #33#) (|PatternMatchResult| #33# . #34#)) 98 (AND (|has| |#3| #35=(|PatternMatchable| #33#)) (|has| |#1| #35#)) ELT) (((|PatternMatchResult| #36=(|Integer|) . #34#) $ (|Pattern| #36#) (|PatternMatchResult| #36# . #34#)) 97 (AND (|has| |#3| #37=(|PatternMatchable| #36#)) (|has| |#1| #37#)) ELT)) (|order| (((|NonNegativeInteger|) $ |#2|) 255 T ELT) (((|NonNegativeInteger|) $) 254 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numberOfMonomials| ((#38=(|NonNegativeInteger|) $) 187 T ELT)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) |#3|) 131 T ELT) (($ #3# |#3|) 130 T ELT)) (|monomials| (#31# 140 T ELT)) (|monomial?| (((|Boolean|) $) 170 T ELT)) (|monomial| (($ |#1| |#4|) 171 T ELT) (($ $ |#3| . #39=(#6#)) 133 T ELT) (($ $ (|List| |#3|) . #40=(#41=(|List| #6#))) 132 T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) 134 T ELT)) (|minimumDegree| ((|#4| $) 188 T ELT) ((#6# $ |#3|) 136 T ELT) ((#41# $ (|List| |#3|)) 135 T ELT)) (|mapExponents| (($ (|Mapping| |#4| |#4|) $) 189 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 166 T ELT)) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) |#2|) 257 T ELT) (((|Mapping| $ (|NonNegativeInteger|)) $) 244 (|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| (((|Union| |#3| #42="failed") $) 137 T ELT)) (|leftReducedSystem| (((|Matrix| #24#) . #43=(#29#)) 152 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| #24#)) (|:| |vec| (|Vector| #24#))) . #44=(#29# $)) 151 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #44#) 146 T ELT) (((|Matrix| |#1|) . #43#) 145 T ELT)) (|leadingMonomial| (#23# 168 T ELT)) (|leadingCoefficient| ((|#1| $) 167 T ELT)) (|leader| ((|#3| $) 247 T ELT)) (|lcm| (#45=($ (|List| $)) 108 (|has| |#1| . #10#) ELT) (#46=($ $ $) 107 (|has| |#1| . #10#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|isobaric?| (((|Boolean|) $) 248 T ELT)) (|isTimes| (#47=((|Union| #32# #42#) $) 128 T ELT)) (|isPlus| (#47# 129 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| #6#)) #42#) $) 127 T ELT)) (|initial| (($ $) 246 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|ground?| (((|Boolean|) $) 184 T ELT)) (|ground| ((|#1| . #48=($)) 185 T ELT)) (|gcdPolynomial| ((#49=(|SparseUnivariatePolynomial| $) #49# #49#) 109 (|has| |#1| . #10#) ELT)) (|gcd| (#45# 106 (|has| |#1| . #10#) ELT) (#46# 105 (|has| |#1| . #10#) ELT)) (|factorSquareFreePolynomial| (#7# 116 (|has| |#1| . #9#) ELT)) (|factorPolynomial| (#7# 115 (|has| |#1| . #9#) ELT)) (|factor| (#11# 113 (|has| |#1| . #9#) ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 192 (|has| |#1| (|IntegralDomain|)) ELT) (((|Union| $ "failed") $ $) 100 (|has| |#1| . #4#) ELT)) (|eval| (($ $ (|List| (|Equation| $))) 163 T ELT) (($ $ (|Equation| $)) 162 T ELT) (($ $ $ $) 161 T ELT) (($ $ (|List| $) (|List| $)) 160 T ELT) (($ $ |#3| |#1|) 159 T ELT) (($ $ (|List| |#3|) (|List| |#1|)) 158 T ELT) (($ $ |#3| $) 157 T ELT) (($ $ (|List| |#3|) (|List| $)) 156 T ELT) (($ $ |#2| $) 243 (|has| |#1| . #50=((|DifferentialRing|))) ELT) (($ $ (|List| |#2|) (|List| $)) 242 (|has| |#1| . #50#) ELT) (($ $ |#2| |#1|) 241 (|has| |#1| . #51=((|DifferentialRing|))) ELT) (($ $ (|List| |#2|) (|List| |#1|)) 240 (|has| |#1| . #51#) ELT)) (|discriminant| (($ $ |#3|) 121 (|has| |#1| . #22#) ELT)) (|differentiate| (($ $ (|List| |#3|) . #52=((|List| #53=(|NonNegativeInteger|)))) 52 T ELT) (($ $ |#3| . #54=(#53#)) 51 T ELT) (($ $ (|List| |#3|)) 50 T ELT) (($ $ |#3|) 48 T ELT) (($ $ (|Mapping| |#1| |#1|)) 264 T ELT) (($ $ (|Mapping| |#1| |#1|) . #55=((|NonNegativeInteger|))) 263 T ELT) (($ . #56=($)) 239 (|has| |#1| . #57=((|DifferentialSpace|))) ELT) (#58=($ $ (|NonNegativeInteger|)) 237 (|has| |#1| . #57#) ELT) (($ $ #59=(|Symbol|)) 235 (|has| |#1| . #60=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #59#)) 233 (|has| |#1| . #60#) ELT) (($ $ #59# . #54#) 232 (|has| |#1| . #60#) ELT) (($ $ (|List| #59#) . #52#) 231 (|has| |#1| . #60#) ELT)) (|differentialVariables| (((|List| |#2|) $) 256 T ELT)) (|degree| ((|#4| $) 169 T ELT) ((#6# $ |#3|) 144 T ELT) ((#41# $ (|List| |#3|)) 143 T ELT) (((|NonNegativeInteger|) $ |#2|) 253 T ELT)) (|convert| 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93 (OR (|and| #68# (|has| |#1| . #9#)) (|has| |#1| (|CharacteristicNonZero|))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|binomThmExpt| (($ $ $ #38#) 191 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#5# $ $) 103 (|has| |#1| . #4#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#14# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|List| |#3|) . #52#) 55 T ELT) (($ $ |#3| . #54#) 54 T ELT) (($ $ (|List| |#3|)) 53 T ELT) (($ $ |#3|) 49 T ELT) (($ $ (|Mapping| |#1| |#1|)) 262 T ELT) (($ $ (|Mapping| |#1| |#1|) . #55#) 261 T ELT) (($ . #56#) 238 (|has| |#1| . #57#) ELT) (#58# 236 (|has| |#1| . #57#) ELT) (($ $ #59#) 234 (|has| |#1| . #60#) ELT) (($ $ (|List| #59#)) 230 (|has| |#1| . #60#) ELT) (($ $ #59# . #54#) 229 (|has| |#1| . #60#) ELT) (($ $ (|List| #59#) . #52#) 228 (|has| |#1| . #60#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 174 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #71=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #69#) 176 (|has| |#1| . #70#) ELT) (($ #69# . #71#) 175 (|has| |#1| . #70#) ELT) (($ |#1| . #71#) 165 T ELT) (($ $ |#1|) 164 T ELT))) 
(((|DifferentialPolynomialCategory| |#1| |#2| |#3| |#4|) (|Category|) (|Ring|) (|OrderedSet|) (|DifferentialVariableCategory| |t#2|) (|OrderedAbelianMonoidSup|)) (T |DifferentialPolynomialCategory|)) 
((|makeVariable| (*1 *2 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *3)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Mapping| *1 (|NonNegativeInteger|))) (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6)))) (|differentialVariables| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *4)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|List| *4)))) (|order| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *3)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *4)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|degree| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *3)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|weights| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *4)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))))) (|weight| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *4)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|weights| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *3)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|List| (|NonNegativeInteger|))))) (|weight| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *4 *3 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *3)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|isobaric?| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *4)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Boolean|)))) (|leader| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|DifferentialVariableCategory| *4)))) (|initial| (*1 *1 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|DifferentialVariableCategory| *3)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)))) (|separant| (*1 *1 *1) (AND (|ofCategory| *1 (|DifferentialPolynomialCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *4 (|DifferentialVariableCategory| *3)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)))) (|makeVariable| (*1 *2 *1) (AND (|ofCategory| *3 (|DifferentialRing|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|DifferentialVariableCategory| *4)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Mapping| *1 (|NonNegativeInteger|))) (|ofCategory| *1 (|DifferentialPolynomialCategory| *3 *4 *5 *6))))) 
(|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| #1=(|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| #1# #1#) |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|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| |#3|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|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|))))) ((|DifferentialDomain| $) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#1|) . T) ((|EntireRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| |#4|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#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|))) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialDomain| $ |#3|) . T) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialRing| |#3|) . T) ((|PartialDifferentialSpace| #3#) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialSpace| |#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) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |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) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|top!| ((|#1| $) 64 T ELT)) (|top| ((|#1| . #3=($)) 42 T ELT)) (|sample| (#4=($) 6 T CONST)) (|rotate!| (($ $) 70 T ELT)) (|reverse!| (($ $) 58 T ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 55 (|has| |#1| . #5=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 51 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 50 T ELT)) (|push!| ((|#1| |#1| $) 44 T ELT)) (|pop!| ((|#1| . #3#) 43 T ELT)) (|members| (((|List| |#1|) $) 49 T ELT)) (|member?| ((#6=(|Boolean|) |#1| $) 54 (|has| |#1| . #5#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|length| (((|NonNegativeInteger|) $) 71 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #7=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #8=($)) 35 T ELT)) (|insertTop!| ((|#1| |#1| $) 62 T ELT)) (|insertBottom!| ((|#1| |#1| $) 61 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|height| (((|NonNegativeInteger|) $) 65 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #7#) ELT)) (|front| ((|#1| . #9=($)) 72 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #6# |#1|) $) 52 T ELT)) (|extractTop!| ((|#1| $) 60 T ELT)) (|extractBottom!| ((|#1| $) 59 T ELT)) (|extract!| ((|#1| . #8#) 37 T ELT)) (|every?| ((#6# (|Mapping| #6# |#1|) . #10=($)) 47 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #7#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #7#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #7#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #7#)) ELT)) (|eq?| ((#11=(|Boolean|) $ $) 10 T ELT)) (|enqueue!| ((|#1| |#1| $) 68 T ELT)) (|empty?| ((#11# $) 7 T ELT)) (|empty| (#4# 8 T ELT)) (|dequeue!| ((|#1| . #9#) 69 T ELT)) (|dequeue| (($) 67 T ELT) (($ (|List| |#1|)) 66 T ELT)) (|depth| (((|NonNegativeInteger|) $) 41 T ELT)) (|count| ((#12=(|NonNegativeInteger|) |#1| $) 53 (|has| |#1| . #5#) ELT) ((#12# (|Mapping| #6# |#1|) $) 48 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|bottom!| ((|#1| $) 63 T ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|back| ((|#1| . #9#) 73 T ELT)) (|any?| ((#6# (|Mapping| #6# |#1|) . #10#) 46 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#12# $) 45 T ELT))) 
(((|DequeueAggregate| |#1|) (|Category|) (|Type|)) (T |DequeueAggregate|)) 
((|dequeue| (*1 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|dequeue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|DequeueAggregate| *3)))) (|height| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|top!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|bottom!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insertTop!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insertBottom!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|extractTop!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|extractBottom!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|reverse!| (*1 *1 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|StackAggregate| |t#1|) (|QueueAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |dequeue| ($)) (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|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|QueueAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|StackAggregate| |#1|) . T) ((|Type|) . T)) 
((|makeObject| ((#1=(|ThreeSpace| (|DoubleFloat|)) #2=(|ParametricSurface| |#1|) #3=(|SegmentBinding| (|Float|)) #3#) 75 T ELT) ((#1# #2# #3# #3# #4=(|List| (|DrawOption|))) 74 T ELT) ((#1# |#1| #3# #3#) 65 T ELT) ((#1# |#1| #3# #3# #4#) 64 T ELT) ((#1# #5=(|ParametricSpaceCurve| |#1|) #3#) 56 T ELT) ((#1# #5# #3# #4#) 55 T ELT)) (|draw| ((#6=(|ThreeDimensionalViewport|) #2# #3# #3#) 78 T ELT) ((#6# #2# #3# #3# #4#) 77 T ELT) ((#6# |#1| #3# #3#) 68 T ELT) ((#6# |#1| #3# #3# #4#) 67 T ELT) ((#6# #5# #3#) 60 T ELT) ((#6# #5# #3# #4#) 59 T ELT) ((#7=(|TwoDimensionalViewport|) #8=(|ParametricPlaneCurve| |#1|) #3#) 47 T ELT) ((#7# #8# #3# #4#) 46 T ELT) ((#7# |#1| #3#) 38 T ELT) ((#7# |#1| #3# #4#) 36 T ELT))) 
(((|TopLevelDrawFunctions| |#1|) (CATEGORY |package| (SIGNATURE |draw| (#1=(|TwoDimensionalViewport|) |#1| #2=(|SegmentBinding| (|Float|)) #3=(|List| (|DrawOption|)))) (SIGNATURE |draw| (#1# |#1| #2#)) (SIGNATURE |draw| (#1# #4=(|ParametricPlaneCurve| |#1|) #2# #3#)) (SIGNATURE |draw| (#1# #4# #2#)) (SIGNATURE |draw| (#5=(|ThreeDimensionalViewport|) #6=(|ParametricSpaceCurve| |#1|) #2# #3#)) (SIGNATURE |draw| (#5# #6# #2#)) (SIGNATURE |makeObject| (#7=(|ThreeSpace| (|DoubleFloat|)) #6# #2# #3#)) (SIGNATURE |makeObject| (#7# #6# #2#)) (SIGNATURE |draw| (#5# |#1| #2# #2# #3#)) (SIGNATURE |draw| (#5# |#1| #2# #2#)) (SIGNATURE |makeObject| (#7# |#1| #2# #2# #3#)) (SIGNATURE |makeObject| (#7# |#1| #2# #2#)) (SIGNATURE |draw| (#5# #8=(|ParametricSurface| |#1|) #2# #2# #3#)) (SIGNATURE |draw| (#5# #8# #2# #2#)) (SIGNATURE |makeObject| (#7# #8# #2# #2# #3#)) (SIGNATURE |makeObject| (#7# #8# #2# #2#))) (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|))) (T |TopLevelDrawFunctions|)) 
((|makeObject| #1=(*1 *2 *3 *4 *4) (AND #2=(|isDomain| *3 (|ParametricSurface| *5)) #3=(|isDomain| *4 (|SegmentBinding| (|Float|))) #4=(|ofCategory| *5 #5=(|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|))) #6=(|isDomain| *2 (|ThreeSpace| (|DoubleFloat|))) #7=(|isDomain| *1 (|TopLevelDrawFunctions| *5)))) (|makeObject| #8=(*1 *2 *3 *4 *4 *5) (AND #9=(|isDomain| *3 (|ParametricSurface| *6)) #3# #10=(|isDomain| *5 (|List| (|DrawOption|))) #11=(|ofCategory| *6 #5#) #6# #12=(|isDomain| *1 (|TopLevelDrawFunctions| *6)))) (|draw| #1# (AND #2# #3# #4# #13=(|isDomain| *2 (|ThreeDimensionalViewport|)) #7#)) (|draw| #8# (AND #9# #3# #10# #11# #13# #12#)) (|makeObject| #1# (AND #3# #6# #14=(|isDomain| *1 (|TopLevelDrawFunctions| *3)) #15=(|ofCategory| *3 #5#))) (|makeObject| #8# (AND #3# #10# #6# #14# #15#)) (|draw| #1# (AND #3# #13# #14# #15#)) (|draw| #8# (AND #3# #10# #13# #14# #15#)) (|makeObject| #16=(*1 *2 *3 *4) (AND #17=(|isDomain| *3 (|ParametricSpaceCurve| *5)) #3# #4# #6# #7#)) (|makeObject| #18=(*1 *2 *3 *4 *5) (AND #19=(|isDomain| *3 (|ParametricSpaceCurve| *6)) #3# #10# #11# #6# #12#)) (|draw| #16# (AND #17# #3# #4# #13# #7#)) (|draw| #18# (AND #19# #3# #10# #11# #13# #12#)) (|draw| #16# (AND (|isDomain| *3 (|ParametricPlaneCurve| *5)) #3# #4# #20=(|isDomain| *2 (|TwoDimensionalViewport|)) #7#)) (|draw| #18# (AND (|isDomain| *3 (|ParametricPlaneCurve| *6)) #3# #10# #11# #20# #12#)) (|draw| #16# (AND #3# #20# #14# #15#)) (|draw| #18# (AND #3# #10# #20# #14# #15#))) 
((|recolor| ((#1=(|Mapping| #2=(|Point| #3=(|DoubleFloat|)) #3# #3#) #1# (|Mapping| #3# #3# #3# #3#)) 158 T ELT)) (|makeObject| ((#4=(|ThreeSpace| #3#) #5=(|ParametricSurface| #6=(|Mapping| #3# #3# #3#)) #7=(|Segment| (|Float|)) #7#) 178 T ELT) ((#4# #5# #7# #7# #8=(|List| (|DrawOption|))) 176 T ELT) ((#4# #1# #7# #7#) 181 T ELT) ((#4# #1# #7# #7# #8#) 177 T ELT) ((#4# #6# #7# #7#) 169 T ELT) ((#4# #6# #7# #7# #8#) 168 T ELT) ((#4# #9=(|Mapping| #2# #3#) #7#) 150 T ELT) ((#4# #9# #7# #8#) 148 T ELT) ((#4# #10=(|ParametricSpaceCurve| #11=(|Mapping| #3# #3#)) #7#) 149 T ELT) ((#4# #10# #7# #8#) 146 T ELT)) (|draw| ((#12=(|ThreeDimensionalViewport|) #5# #7# #7#) 180 T ELT) ((#12# #5# #7# #7# #8#) 179 T ELT) ((#12# #1# #7# #7#) 183 T ELT) ((#12# #1# #7# #7# #8#) 182 T ELT) ((#12# #6# #7# #7#) 171 T ELT) ((#12# #6# #7# #7# #8#) 170 T ELT) ((#12# #9# #7#) 156 T ELT) ((#12# #9# #7# #8#) 155 T ELT) ((#12# #10# #7#) 154 T ELT) ((#12# #10# #7# #8#) 153 T ELT) ((#13=(|TwoDimensionalViewport|) #14=(|ParametricPlaneCurve| #11#) #7#) 118 T ELT) ((#13# #14# #7# #8#) 117 T ELT) ((#13# #11# #7#) 112 T ELT) ((#13# #11# #7# #8#) 110 T ELT))) 
(((|TopLevelDrawFunctionsForCompiledFunctions|) (CATEGORY |package| (SIGNATURE |draw| (#1=(|TwoDimensionalViewport|) #2=(|Mapping| #3=(|DoubleFloat|) #3#) #4=(|Segment| (|Float|)) #5=(|List| (|DrawOption|)))) (SIGNATURE |draw| (#1# #2# #4#)) (SIGNATURE |draw| (#1# #6=(|ParametricPlaneCurve| #2#) #4# #5#)) (SIGNATURE |draw| (#1# #6# #4#)) (SIGNATURE |draw| (#7=(|ThreeDimensionalViewport|) #8=(|ParametricSpaceCurve| #2#) #4# #5#)) (SIGNATURE |draw| (#7# #8# #4#)) (SIGNATURE |draw| (#7# #9=(|Mapping| #10=(|Point| #3#) #3#) #4# #5#)) (SIGNATURE |draw| (#7# #9# #4#)) (SIGNATURE |makeObject| (#11=(|ThreeSpace| #3#) #8# #4# #5#)) (SIGNATURE |makeObject| (#11# #8# #4#)) (SIGNATURE |makeObject| (#11# #9# #4# #5#)) (SIGNATURE |makeObject| (#11# #9# #4#)) (SIGNATURE |draw| (#7# #12=(|Mapping| #3# #3# #3#) #4# #4# #5#)) (SIGNATURE |draw| (#7# #12# #4# #4#)) (SIGNATURE |makeObject| (#11# #12# #4# #4# #5#)) (SIGNATURE |makeObject| (#11# #12# #4# #4#)) (SIGNATURE |draw| (#7# #13=(|Mapping| #10# #3# #3#) #4# #4# #5#)) (SIGNATURE |draw| (#7# #13# #4# #4#)) (SIGNATURE |makeObject| (#11# #13# #4# #4# #5#)) (SIGNATURE |makeObject| (#11# #13# #4# #4#)) (SIGNATURE |draw| (#7# #14=(|ParametricSurface| #12#) #4# #4# #5#)) (SIGNATURE |draw| (#7# #14# #4# #4#)) (SIGNATURE |makeObject| (#11# #14# #4# #4# #5#)) (SIGNATURE |makeObject| (#11# #14# #4# #4#)) (SIGNATURE |recolor| (#13# #13# (|Mapping| #3# #3# #3# #3#))))) (T |TopLevelDrawFunctionsForCompiledFunctions|)) 
((|recolor| (*1 *2 *2 *3) (AND (|isDomain| *2 #1=(|Mapping| #2=(|Point| #3=(|DoubleFloat|)) #3# #3#)) (|isDomain| *3 (|Mapping| #3# #3# #3# #3#)) #4=(|isDomain| *1 (|TopLevelDrawFunctionsForCompiledFunctions|)))) (|makeObject| #5=(*1 *2 *3 *4 *4) (AND #6=(|isDomain| *3 (|ParametricSurface| #7=(|Mapping| #3# #3# #3#))) #8=(|isDomain| *4 (|Segment| (|Float|))) #9=(|isDomain| *2 (|ThreeSpace| #3#)) #4#)) (|makeObject| #10=(*1 *2 *3 *4 *4 *5) (AND #6# #8# #11=(|isDomain| *5 (|List| (|DrawOption|))) #9# #4#)) (|draw| #5# (AND #6# #8# #12=(|isDomain| *2 (|ThreeDimensionalViewport|)) #4#)) (|draw| #10# (AND #6# #8# #11# #12# #4#)) (|makeObject| #5# (AND #13=(|isDomain| *3 #1#) #8# #9# #4#)) (|makeObject| #10# (AND #13# #8# #11# #9# #4#)) (|draw| #5# (AND #13# #8# #12# #4#)) (|draw| #10# (AND #13# #8# #11# #12# #4#)) (|makeObject| #5# (AND #14=(|isDomain| *3 #7#) #8# #9# #4#)) (|makeObject| #10# (AND #14# #8# #11# #9# #4#)) (|draw| #5# (AND #14# #8# #12# #4#)) (|draw| #10# (AND #14# #8# #11# #12# #4#)) (|makeObject| #15=(*1 *2 *3 *4) (AND #16=(|isDomain| *3 (|Mapping| #2# #3#)) #8# #9# #4#)) (|makeObject| #17=(*1 *2 *3 *4 *5) (AND #16# #8# #11# #9# #4#)) (|makeObject| #15# (AND #18=(|isDomain| *3 (|ParametricSpaceCurve| #19=(|Mapping| #3# #3#))) #8# #9# #4#)) (|makeObject| #17# (AND #18# #8# #11# #9# #4#)) (|draw| #15# (AND #16# #8# #12# #4#)) (|draw| #17# (AND #16# #8# #11# #12# #4#)) (|draw| #15# (AND #18# #8# #12# #4#)) (|draw| #17# (AND #18# #8# #11# #12# #4#)) (|draw| #15# (AND #20=(|isDomain| *3 (|ParametricPlaneCurve| #19#)) #8# #21=(|isDomain| *2 (|TwoDimensionalViewport|)) #4#)) (|draw| #17# (AND #20# #8# #11# #21# #4#)) (|draw| #15# (AND #22=(|isDomain| *3 #19#) #8# #21# #4#)) (|draw| #17# (AND #22# #8# #11# #21# #4#))) 
((|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) #1=(|Symbol|) #1# (|List| (|DrawOption|))) 102 T ELT))) 
(((|TopLevelDrawFunctionsForAlgebraicCurves| |#1| |#2|) (CATEGORY |package| (SIGNATURE |draw| ((|TwoDimensionalViewport|) (|Equation| |#2|) #1=(|Symbol|) #1# (|List| (|DrawOption|))))) (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|))) (|FunctionSpace| |#1|)) (T |TopLevelDrawFunctionsForAlgebraicCurves|)) 
((|draw| (*1 *2 *3 *4 *4 *5) (AND (|isDomain| *3 (|Equation| *7)) (|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|List| (|DrawOption|))) (|ofCategory| *7 (|FunctionSpace| *6)) (|ofCategory| *6 (|Join| (|IntegralDomain|) (|OrderedSet|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|TwoDimensionalViewport|)) (|isDomain| *1 (|TopLevelDrawFunctionsForAlgebraicCurves| *6 *7))))) 
((|setRealSteps| (#1=(#2=(|Integer|) #2#) 71 T ELT)) (|setImagSteps| (#1# 72 T ELT)) (|setClipValue| ((#3=(|DoubleFloat|) #3#) 73 T ELT)) (|drawComplexVectorField| ((#4=(|ThreeDimensionalViewport|) #5=(|Mapping| #6=(|Complex| #3#) #6#) #7=(|Segment| #3#) #7#) 70 T ELT)) (|drawComplex| ((#4# #5# #7# #7# (|Boolean|)) 68 T ELT))) 
(((|DrawComplex|) (CATEGORY |package| (SIGNATURE |drawComplex| (#1=(|ThreeDimensionalViewport|) #2=(|Mapping| #3=(|Complex| #4=(|DoubleFloat|)) #3#) #5=(|Segment| #4#) #5# (|Boolean|))) (SIGNATURE |drawComplexVectorField| (#1# #2# #5# #5#)) (SIGNATURE |setRealSteps| #6=(#7=(|Integer|) #7#)) (SIGNATURE |setImagSteps| #6#) (SIGNATURE |setClipValue| (#4# #4#)))) (T |DrawComplex|)) 
((|setClipValue| #1=(*1 *2 *2) (AND (|isDomain| *2 #2=(|DoubleFloat|)) #3=(|isDomain| *1 (|DrawComplex|)))) (|setImagSteps| #1# #4=(AND (|isDomain| *2 (|Integer|)) #3#)) (|setRealSteps| #1# #4#) (|drawComplexVectorField| (*1 *2 *3 *4 *4) (AND #5=(|isDomain| *3 (|Mapping| #6=(|Complex| #2#) #6#)) #7=(|isDomain| *4 (|Segment| #2#)) #8=(|isDomain| *2 (|ThreeDimensionalViewport|)) #3#)) (|drawComplex| (*1 *2 *3 *4 *4 *5) (AND #5# #7# (|isDomain| *5 (|Boolean|)) #8# #3#))) 
((|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) 16 T ELT))) 
(((|DrawNumericHack| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|SegmentBinding| #1=(|Float|)) (|SegmentBinding| (|Expression| |#1|))))) (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| #1#))) (T |DrawNumericHack|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|SegmentBinding| (|Expression| *4))) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| #1=(|Float|)))) (|isDomain| *2 (|SegmentBinding| #1#)) (|isDomain| *1 (|DrawNumericHack| *4))))) 
((|draw| ((#1=(|ThreeDimensionalViewport|) #2=(|List| #3=(|DoubleFloat|)) #2# #2# #4=(|List| (|DrawOption|))) 23 T ELT) ((#1# #2# #2# #2#) 24 T ELT) ((#5=(|TwoDimensionalViewport|) #6=(|List| (|Point| #3#)) #4#) 16 T ELT) ((#5# #6#) 17 T ELT) ((#5# #2# #2# #4#) 20 T ELT) ((#5# #2# #2#) 21 T ELT))) 
(((|TopLevelDrawFunctionsForPoints|) (CATEGORY |package| (SIGNATURE |draw| (#1=(|TwoDimensionalViewport|) #2=(|List| #3=(|DoubleFloat|)) #2#)) (SIGNATURE |draw| (#1# #2# #2# #4=(|List| (|DrawOption|)))) (SIGNATURE |draw| (#1# #5=(|List| (|Point| #3#)))) (SIGNATURE |draw| (#1# #5# #4#)) (SIGNATURE |draw| (#6=(|ThreeDimensionalViewport|) #2# #2# #2#)) (SIGNATURE |draw| (#6# #2# #2# #2# #4#)))) (T |TopLevelDrawFunctionsForPoints|)) 
((|draw| (*1 *2 *3 *3 *3 *4) (AND #1=(|isDomain| *3 (|List| #2=(|DoubleFloat|))) #3=(|isDomain| *4 (|List| (|DrawOption|))) #4=(|isDomain| *2 (|ThreeDimensionalViewport|)) #5=(|isDomain| *1 (|TopLevelDrawFunctionsForPoints|)))) (|draw| (*1 *2 *3 *3 *3) (AND #1# #4# #5#)) (|draw| (*1 *2 *3 *4) (AND #6=(|isDomain| *3 (|List| (|Point| #2#))) #3# #7=(|isDomain| *2 (|TwoDimensionalViewport|)) #5#)) (|draw| (*1 *2 *3) (AND #6# #7# #5#)) (|draw| (*1 *2 *3 *3 *4) (AND #1# #3# #7# #5#)) (|draw| (*1 *2 *3 *3) (AND #1# #7# #5#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|viewpoint| (($ (|Record| (|:| |theta| #4=(|DoubleFloat|)) (|:| |phi| #4#) (|:| |scale| #4#) (|:| |scaleX| #4#) (|:| |scaleY| #4#) (|:| |scaleZ| #4#) (|:| |deltaX| #4#) (|:| |deltaY| #4#))) 24 T ELT)) (|var2Steps| (#5=($ (|PositiveInteger|)) 81 T ELT)) (|var1Steps| (#5# 80 T ELT)) (|unit| (($ (|List| #6=(|Float|))) 87 T ELT)) (|tubeRadius| (#7=($ #6#) 66 T ELT)) (|tubePoints| (#5# 82 T ELT)) (|toScale| (#8=($ #3#) 33 T ELT)) (|title| (#9=($ #10=(|String|)) 28 T ELT)) (|style| (#9# 29 T ELT)) (|space| (($ (|ThreeSpace| #4#)) 76 T ELT)) (|ranges| (#11=($ (|List| (|Segment| #6#))) 72 T ELT)) (|range| (#11# 68 T ELT) (($ (|List| (|Segment| (|Fraction| (|Integer|))))) 71 T ELT)) (|pointColor| (#7# 38 T ELT) (#12=($ (|Palette|)) 42 T ELT)) (|option?| ((#3# #13=(|List| $) #14=(|Symbol|)) 100 T ELT)) (|option| (((|Union| (|Any|) "failed") #13# #14#) 102 T ELT)) (|latex| ((#10# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|curveColor| (#7# 43 T ELT) (#12# 44 T ELT)) (|coordinates| (#15=($ (|Mapping| #16=(|Point| #4#) #16#)) 65 T ELT)) (|coord| (#15# 83 T ELT)) (|colorFunction| (($ (|Mapping| #4# #4#)) 48 T ELT) (($ (|Mapping| #4# #4# #4#)) 52 T ELT) (($ (|Mapping| #4# #4# #4# #4#)) 56 T ELT)) (|coerce| (((|OutputForm|) $) 93 T ELT)) (|clip| (#8# 34 T ELT) (#11# 60 T ELT)) (|before?| #1#) (|adaptive| (#8# 35 T ELT)) (= (#2# 97 T ELT))) 
(((|DrawOption|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |adaptive| #1=($ #2=(|Boolean|))) (SIGNATURE |clip| #1#) (SIGNATURE |viewpoint| ($ (|Record| (|:| |theta| #3=(|DoubleFloat|)) (|:| |phi| #3#) (|:| |scale| #3#) (|:| |scaleX| #3#) (|:| |scaleY| #3#) (|:| |scaleZ| #3#) (|:| |deltaX| #3#) (|:| |deltaY| #3#)))) (SIGNATURE |title| #4=($ (|String|))) (SIGNATURE |style| #4#) (SIGNATURE |toScale| #1#) (SIGNATURE |clip| #5=($ (|List| (|Segment| #6=(|Float|))))) (SIGNATURE |coordinates| #7=($ (|Mapping| #8=(|Point| #3#) #8#))) (SIGNATURE |pointColor| #9=($ #6#)) (SIGNATURE |pointColor| #10=($ (|Palette|))) (SIGNATURE |curveColor| #9#) (SIGNATURE |curveColor| #10#) (SIGNATURE |colorFunction| ($ (|Mapping| #3# #3#))) (SIGNATURE |colorFunction| ($ (|Mapping| #3# #3# #3#))) (SIGNATURE |colorFunction| ($ (|Mapping| #3# #3# #3# #3#))) (SIGNATURE |tubeRadius| #9#) (SIGNATURE |range| #5#) (SIGNATURE |range| ($ (|List| (|Segment| (|Fraction| (|Integer|)))))) (SIGNATURE |ranges| #5#) (SIGNATURE |space| ($ (|ThreeSpace| #3#))) (SIGNATURE |var1Steps| #11=($ (|PositiveInteger|))) (SIGNATURE |var2Steps| #11#) (SIGNATURE |tubePoints| #11#) (SIGNATURE |coord| #7#) (SIGNATURE |unit| ($ (|List| #6#))) (SIGNATURE |option| ((|Union| (|Any|) "failed") #12=(|List| $) #13=(|Symbol|))) (SIGNATURE |option?| (#2# #12# #13#))))) (T |DrawOption|)) 
((|adaptive| #1=(*1 *1 *2) #2=(AND #3=(|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 #5=(|DrawOption|)))) (|clip| #1# #2#) (|viewpoint| #1# (AND (|isDomain| *2 (|Record| (|:| |theta| #6=(|DoubleFloat|)) (|:| |phi| #6#) (|:| |scale| #6#) (|:| |scaleX| #6#) (|:| |scaleY| #6#) (|:| |scaleZ| #6#) (|:| |deltaX| #6#) (|:| |deltaY| #6#))) #4#)) (|title| #1# #7=(AND (|isDomain| *2 (|String|)) #4#)) (|style| #1# #7#) (|toScale| #1# #2#) (|clip| #1# #8=(AND (|isDomain| *2 (|List| (|Segment| #9=(|Float|)))) #4#)) (|coordinates| #1# #10=(AND (|isDomain| *2 (|Mapping| #11=(|Point| #6#) #11#)) #4#)) (|pointColor| #1# #12=(AND (|isDomain| *2 #9#) #4#)) (|pointColor| #1# #13=(AND (|isDomain| *2 (|Palette|)) #4#)) (|curveColor| #1# #12#) (|curveColor| #1# #13#) (|colorFunction| #1# (AND (|isDomain| *2 (|Mapping| #6# #6#)) #4#)) (|colorFunction| #1# (AND (|isDomain| *2 (|Mapping| #6# #6# #6#)) #4#)) (|colorFunction| #1# (AND (|isDomain| *2 (|Mapping| #6# #6# #6# #6#)) #4#)) (|tubeRadius| #1# #12#) (|range| #1# #8#) (|range| #1# (AND (|isDomain| *2 (|List| (|Segment| (|Fraction| (|Integer|))))) #4#)) (|ranges| #1# #8#) (|space| #1# (AND (|isDomain| *2 (|ThreeSpace| #6#)) #4#)) (|var1Steps| #1# #14=(AND (|isDomain| *2 (|PositiveInteger|)) #4#)) (|var2Steps| #1# #14#) (|tubePoints| #1# #14#) (|coord| #1# #10#) (|unit| #1# (AND (|isDomain| *2 (|List| #9#)) #4#)) (|option| #15=(*1 *2 *3 *4) (|partial| AND #16=(|isDomain| *3 (|List| #5#)) #17=(|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Any|)) #4#)) (|option?| #15# (AND #16# #17# #3# #4#))) 
((|viewpoint| ((#1=(|Record| (|:| |theta| #2=(|DoubleFloat|)) (|:| |phi| #2#) (|:| |scale| #2#) (|:| |scaleX| #2#) (|:| |scaleY| #2#) (|:| |scaleZ| #2#) (|:| |deltaX| #2#) (|:| |deltaY| #2#)) #3=(|List| (|DrawOption|)) #1#) 25 T ELT)) (|var2Steps| (#4=(#5=(|PositiveInteger|) #3# #5#) 52 T ELT)) (|var1Steps| (#4# 51 T ELT)) (|units| ((#6=(|List| #7=(|Float|)) #3# #6#) 68 T ELT)) (|tubeRadius| ((#7# #3# #7#) 57 T ELT)) (|tubePoints| (#4# 53 T ELT)) (|toScale| (#8=(#9=(|Boolean|) #3# #9#) 27 T ELT)) (|title| (#10=(#11=(|String|) #3# #11#) 19 T ELT)) (|style| (#10# 26 T ELT)) (|space| (((|ThreeSpace| #2#) #3#) 46 T ELT)) (|ranges| ((#12=(|List| (|Segment| #7#)) #3# #12#) 40 T ELT)) (|pointColorPalette| (#13=(#14=(|Palette|) #3# #14#) 32 T ELT)) (|curveColorPalette| (#13# 33 T ELT)) (|coord| ((#15=(|Mapping| #16=(|Point| #2#) #16#) #3# #15#) 63 T ELT)) (|clipBoolean| (#8# 14 T ELT)) (|adaptive| (#8# 13 T ELT))) 
(((|DrawOptionFunctions0|) (CATEGORY |package| (SIGNATURE |adaptive| #1=(#2=(|Boolean|) #3=(|List| (|DrawOption|)) #2#)) (SIGNATURE |clipBoolean| #1#) (SIGNATURE |viewpoint| (#4=(|Record| (|:| |theta| #5=(|DoubleFloat|)) (|:| |phi| #5#) (|:| |scale| #5#) (|:| |scaleX| #5#) (|:| |scaleY| #5#) (|:| |scaleZ| #5#) (|:| |deltaX| #5#) (|:| |deltaY| #5#)) #3# #4#)) (SIGNATURE |title| #6=(#7=(|String|) #3# #7#)) (SIGNATURE |style| #6#) (SIGNATURE |toScale| #1#) (SIGNATURE |pointColorPalette| #8=(#9=(|Palette|) #3# #9#)) (SIGNATURE |curveColorPalette| #8#) (SIGNATURE |ranges| (#10=(|List| (|Segment| #11=(|Float|))) #3# #10#)) (SIGNATURE |var1Steps| #12=(#13=(|PositiveInteger|) #3# #13#)) (SIGNATURE |var2Steps| #12#) (SIGNATURE |space| ((|ThreeSpace| #5#) #3#)) (SIGNATURE |tubePoints| #12#) (SIGNATURE |tubeRadius| (#11# #3# #11#)) (SIGNATURE |coord| (#14=(|Mapping| #15=(|Point| #5#) #15#) #3# #14#)) (SIGNATURE |units| (#16=(|List| #11#) #3# #16#)))) (T |DrawOptionFunctions0|)) 
((|units| #1=(*1 *2 *3 *2) (AND (|isDomain| *2 (|List| #2=(|Float|))) #3=(|isDomain| *3 (|List| (|DrawOption|))) #4=(|isDomain| *1 (|DrawOptionFunctions0|)))) (|coord| #1# (AND (|isDomain| *2 (|Mapping| #5=(|Point| #6=(|DoubleFloat|)) #5#)) #3# #4#)) (|tubeRadius| #1# (AND (|isDomain| *2 #2#) #3# #4#)) (|tubePoints| #1# #7=(AND (|isDomain| *2 (|PositiveInteger|)) #3# #4#)) (|space| (*1 *2 *3) (AND #3# (|isDomain| *2 (|ThreeSpace| #6#)) #4#)) (|var2Steps| #1# #7#) (|var1Steps| #1# #7#) (|ranges| #1# (AND (|isDomain| *2 (|List| (|Segment| #2#))) #3# #4#)) (|curveColorPalette| #1# #8=(AND (|isDomain| *2 (|Palette|)) #3# #4#)) (|pointColorPalette| #1# #8#) (|toScale| #1# #9=(AND (|isDomain| *2 (|Boolean|)) #3# #4#)) (|style| #1# #10=(AND (|isDomain| *2 (|String|)) #3# #4#)) (|title| #1# #10#) (|viewpoint| #1# (AND (|isDomain| *2 (|Record| (|:| |theta| #6#) (|:| |phi| #6#) (|:| |scale| #6#) (|:| |scaleX| #6#) (|:| |scaleY| #6#) (|:| |scaleZ| #6#) (|:| |deltaX| #6#) (|:| |deltaY| #6#))) #3# #4#)) (|clipBoolean| #1# #9#) (|adaptive| #1# #9#)) 
((|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) 17 T ELT))) 
(((|DrawOptionFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |option| ((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)))) (|Type|)) (T |DrawOptionFunctions1|)) 
((|option| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|List| (|DrawOption|))) (|isDomain| *4 (|Symbol|)) (|isDomain| *1 (|DrawOptionFunctions1| *2)) (|ofCategory| *2 (|Type|))))) 
((|differentiate| (#1=($ $ #2=(|Mapping| |#2| |#2|)) NIL T ELT) (#3=($ $ #2# #4=(|NonNegativeInteger|)) 11 T ELT) #5=(($ $ #6=(|List| #7=(|Symbol|)) (|List| #4#)) NIL T ELT) #8=(($ $ #7# #4#) NIL T ELT) #9=(($ $ #6#) NIL T ELT) (#10=($ $ #7#) 19 T ELT) #11=(($ $ #4#) NIL T ELT) (#12=($ $) 16 T ELT)) (D (#1# 12 T ELT) (#3# 14 T ELT) #5# #8# #9# (#10# NIL T ELT) #11# (#12# NIL T ELT))) 
(((|DifferentialSpaceExtension&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |differentiate| #1=(|#1| |#1|)) (SIGNATURE D #1#) (SIGNATURE |differentiate| #2=(|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE D #2#) (SIGNATURE |differentiate| #4=(|#1| |#1| #5=(|Symbol|))) (SIGNATURE D #4#) (SIGNATURE |differentiate| #6=(|#1| |#1| #7=(|List| #5#))) (SIGNATURE |differentiate| #8=(|#1| |#1| #5# #3#)) (SIGNATURE |differentiate| #9=(|#1| |#1| #7# (|List| #3#))) (SIGNATURE D #6#) (SIGNATURE D #8#) (SIGNATURE D #9#) (SIGNATURE D #10=(|#1| |#1| #11=(|Mapping| |#2| |#2|) #3#)) (SIGNATURE D #12=(|#1| |#1| #11#)) (SIGNATURE |differentiate| #10#) (SIGNATURE |differentiate| #12#)) (|DifferentialSpaceExtension| |#2|) (|Type|)) (T |DifferentialSpaceExtension&|)) 
NIL 
((|differentiate| (($ $ (|Mapping| |#1| |#1|)) 23 T ELT) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 22 T ELT) (($ $ (|List| #1=(|Symbol|)) . #2=((|List| #3=(|NonNegativeInteger|)))) 16 (|has| |#1| . #4=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ #1# . #5=(#3#)) 15 (|has| |#1| . #4#) ELT) (($ $ (|List| #1#)) 14 (|has| |#1| . #4#) ELT) (($ $ #1#) 12 (|has| |#1| . #4#) ELT) (#6=($ $ (|NonNegativeInteger|)) 10 (|has| |#1| . #7=((|DifferentialSpace|))) ELT) (($ . #8=($)) 8 (|has| |#1| . #7#) ELT)) (D (($ $ (|Mapping| |#1| |#1|)) 21 T ELT) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 20 T ELT) (($ $ (|List| #1#) . #2#) 19 (|has| |#1| . #4#) ELT) (($ $ #1# . #5#) 18 (|has| |#1| . #4#) ELT) (($ $ (|List| #1#)) 17 (|has| |#1| . #4#) ELT) (($ $ #1#) 13 (|has| |#1| . #4#) ELT) (#6# 11 (|has| |#1| . #7#) ELT) (($ . #8#) 9 (|has| |#1| . #7#) ELT))) 
(((|DifferentialSpaceExtension| |#1|) (|Category|) (|Type|)) (T |DifferentialSpaceExtension|)) 
((|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|DifferentialSpaceExtension| *3)) (|ofCategory| *3 (|Type|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialSpaceExtension| *4)) (|ofCategory| *4 (|Type|)))) (D (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|DifferentialSpaceExtension| *3)) (|ofCategory| *3 (|Type|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialSpaceExtension| *4)) (|ofCategory| *4 (|Type|))))) 
(|Join| (|Type|) (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| (|DifferentialSpace|)) (ATTRIBUTE (|DifferentialSpace|)) |%noBranch|) (IF (|has| |t#1| (|PartialDifferentialSpace| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialSpace| (|Symbol|))) |%noBranch|))) 
(((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|Join|) . T) ((|PartialDifferentialDomain| $ #1=(|Symbol|)) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|PartialDifferentialSpace| #1#) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|weights| ((#6=(|List| #7=(|NonNegativeInteger|)) $) NIL T ELT) ((#6# $ |#2|) NIL T ELT)) (|weight| #8=(#9=(#7# $) NIL T ELT) #10=((#7# $ |#2|) NIL T ELT)) (|variables| ((#11=(|List| |#3|) $) NIL T ELT)) (|univariate| ((#12=(|SparseUnivariatePolynomial| $) $ |#3|) NIL T ELT) ((#13=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #15=(#16=($ $) NIL #14# ELT)) (|unit?| (#5# NIL #14# ELT)) (|totalDegree| #8# ((#7# $ #11#) NIL T ELT)) (|subtractIfCan| (#17=(#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #20=(((|Factored| #12#) #12#) NIL #21=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #22=(#16# NIL #23=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#24=((|Factored| $) $) NIL #23# ELT)) (|solveLinearPolynomialEquation| (((|Union| #25=(|List| #12#) #19#) #25# #12#) NIL #21# ELT)) (|separant| #26=(#16# NIL T ELT)) (|sample| #27=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #28=(#19#)) . #29=($)) NIL T ELT) (((|Union| #30=(|Fraction| #31=(|Integer|)) . #28#) . #29#) NIL #32=(|has| |#1| (|RetractableTo| #30#)) ELT) (((|Union| #31# . #28#) . #29#) NIL #33=(|has| |#1| (|RetractableTo| #31#)) ELT) #34=(((|Union| |#3| . #28#) . #29#) NIL T ELT) (((|Union| |#2| . #28#) . #29#) NIL T ELT) (((|Union| #35=(|SparseMultivariatePolynomial| |#1| |#2|) . #28#) $) 23 T ELT)) (|retract| #36=(#37=(|#1| $) NIL T ELT) ((#30# . #38=($)) NIL #32# ELT) ((#31# . #38#) NIL #33# ELT) #39=((|#3| . #38#) NIL T ELT) ((|#2| . #38#) NIL T ELT) ((#35# . #38#) NIL T ELT)) (|resultant| (($ $ $ |#3|) NIL #40=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #26#) (|reducedSystem| ((#41=(|Matrix| #31#) . #42=(#43=(|Matrix| $))) NIL #44=(|has| |#1| (|LinearlyExplicitRingOver| #31#)) ELT) ((#45=(|Record| (|:| |mat| #41#) (|:| |vec| (|Vector| #31#))) . #46=(#43# #47=(|Vector| $))) NIL #44# ELT) ((#48=(|Record| (|:| |mat| #49=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #46#) NIL T ELT) ((#49# . #42#) NIL T ELT)) (|recip| ((#18# $) NIL T ELT)) (|primitivePart| #22# #50=(#51=($ $ |#3|) NIL #23# ELT)) (|primitiveMonomials| #52=((#53=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #21# ELT)) (|pomopo!| (($ $ |#1| #54=(|IndexedExponents| |#3|) $) NIL T ELT)) (|patternMatch| ((#55=(|PatternMatchResult| #56=(|Float|) . #57=($)) $ #58=(|Pattern| #56#) #55#) NIL (AND (|has| |#1| #59=(|PatternMatchable| #56#)) (|has| |#3| #59#)) ELT) ((#60=(|PatternMatchResult| #31# . #57#) $ #61=(|Pattern| #31#) #60#) NIL (AND (|has| |#1| #62=(|PatternMatchable| #31#)) (|has| |#3| #62#)) ELT)) (|order| #10# (#9# 10 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #8#) (|multivariate| (($ #13# |#3|) NIL T ELT) (($ #12# |#3|) NIL T ELT)) (|monomials| #52#) (|monomial?| #4#) (|monomial| (($ |#1| #54#) NIL T ELT) #63=(($ $ |#3| #7#) NIL T ELT) #64=(($ $ #11# #6#) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) NIL T ELT)) (|minimumDegree| #65=((#54# $) NIL T ELT) #66=((#7# $ |#3|) NIL T ELT) #67=((#6# $ #11#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #54# #54#) $) NIL T ELT)) (|map| (($ #68=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeVariable| ((#69=(|Mapping| $ #7#) |#2|) NIL T ELT) ((#69# $) NIL #70=(|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| #34#) (|leftReducedSystem| ((#41# . #71=(#47#)) NIL #44# ELT) ((#45# . #72=(#47# $)) NIL #44# ELT) ((#48# . #72#) NIL T ELT) ((#49# . #71#) NIL T ELT)) (|leadingMonomial| #26#) (|leadingCoefficient| #36#) (|leader| #39#) (|lcm| #73=(($ #53#) NIL #23# ELT) #74=(#75=($ $ $) NIL #23# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #76=(((|Union| #53# #19#) $) NIL T ELT)) (|isPlus| #76#) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| #7#)) #19#) $) NIL T ELT)) (|initial| #26#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #36#) (|gcdPolynomial| ((#12# #12# #12#) NIL #23# ELT)) (|gcd| #73# #74#) (|factorSquareFreePolynomial| #20#) (|factorPolynomial| #20#) (|factor| (#24# NIL #21# ELT)) (|exquo| ((#18# $ |#1|) NIL #14# ELT) (#17# NIL #14# ELT)) (|eval| (($ $ (|List| #77=(|Equation| $))) NIL T ELT) (($ $ #77#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #53# #53#) NIL T ELT) (($ $ |#3| |#1|) NIL T ELT) (($ $ #11# #78=(|List| |#1|)) NIL T ELT) (($ $ |#3| $) NIL T ELT) (($ $ #11# #53#) NIL T ELT) (($ $ |#2| $) NIL #70# ELT) (($ $ #79=(|List| |#2|) #53#) NIL #70# ELT) (($ $ |#2| |#1|) NIL #70# ELT) (($ $ #79# #78#) NIL #70# ELT)) (|discriminant| (#51# NIL #40# ELT)) (|differentiate| #64# #63# #80=(($ $ #11#) NIL T ELT) #81=(#51# NIL T ELT) #82=(($ $ #68#) NIL T ELT) #83=(($ $ #68# #7#) NIL T ELT) #84=(($ $ #85=(|Symbol|)) NIL #86=(|has| |#1| (|PartialDifferentialSpace| #85#)) ELT) #87=(($ $ #88=(|List| #85#)) NIL #86# ELT) #89=(($ $ #85# #7#) NIL #86# ELT) #90=(($ $ #88# #6#) NIL #86# ELT) #91=(#16# NIL #92=(|has| |#1| (|DifferentialSpace|)) ELT) #93=(#94=($ $ #7#) NIL #92# ELT)) (|differentialVariables| ((#79# $) NIL T ELT)) (|degree| #65# #66# #67# #10#) (|convert| ((#58# . #95=($)) NIL (AND (|has| |#1| #96=(|ConvertibleTo| #58#)) (|has| |#3| #96#)) ELT) ((#61# . #95#) NIL (AND (|has| |#1| #97=(|ConvertibleTo| #61#)) (|has| |#3| #97#)) ELT) ((#98=(|InputForm|) . #95#) NIL (AND (|has| |#1| #99=(|ConvertibleTo| #98#)) (|has| |#3| #99#)) ELT)) (|content| (#37# NIL #23# ELT) #50#) (|conditionP| (((|Union| #47# #19#) #43#) NIL #100=(AND (|has| $ #101=(|CharacteristicNonZero|)) #21#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #31#) NIL T ELT) (($ |#1|) 26 T ELT) (($ |#3|) 25 T ELT) (($ |#2|) NIL T ELT) (($ #35#) 32 T ELT) (($ #30#) NIL (OR #102=(|has| |#1| (|Algebra| #30#)) #32#) ELT) #15#) (|coefficients| ((#78# $) NIL T ELT)) (|coefficient| ((|#1| $ #54#) NIL T ELT) #63# #64#) (|charthRoot| (((|Maybe| $) $) NIL (OR #100# (|has| |#1| #101#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #40# ELT)) (|before?| #1#) (|associates?| (#2# NIL #14# ELT)) (|annihilate?| #1#) (|Zero| #27#) (|One| #27#) (D #64# #63# #80# #81# #82# #83# #84# #87# #89# #90# #91# #93#) (= #1#) (/ (#103=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #26# #104=(#75# NIL T ELT)) (+ #104#) (** (($ $ #105=(|PositiveInteger|)) NIL T ELT) (#94# NIL T ELT)) (* (($ #105# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #31# . #106=($)) NIL T ELT) #104# (($ $ #30#) NIL #102# ELT) (($ #30# . #106#) NIL #102# ELT) (($ |#1| . #106#) NIL T ELT) (#103# NIL T ELT))) 
(((|DifferentialSparseMultivariatePolynomial| |#1| |#2| |#3|) (|Join| (|DifferentialPolynomialCategory| |#1| |#2| |#3| (|IndexedExponents| |#3|)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| |#2|))) (|Ring|) (|OrderedSet|) (|DifferentialVariableCategory| |#2|)) (T |DifferentialSparseMultivariatePolynomial|)) 
NIL 
((|weight| ((#1=(|NonNegativeInteger|) $) 37 T ELT)) (|retractIfCan| (((|Union| |#2| "failed") $) 22 T ELT)) (|retract| ((|#2| $) 33 T ELT)) (|differentiate| (($ $ #1#) 18 T ELT) (($ $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT) (($ |#2|) 11 T ELT)) (= (#2=((|Boolean|) $ $) 26 T ELT)) (< (#2# 36 T ELT))) 
(((|DifferentialVariableCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |weight| (#1=(|NonNegativeInteger|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #1#)) (SIGNATURE < #2=((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = #2#)) (|DifferentialVariableCategory| |#2|) (|OrderedSet|)) (T |DifferentialVariableCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|weight| (((|NonNegativeInteger|) $) 26 T ELT)) (|variable| ((|#1| $) 27 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 31 T ELT)) (|retract| ((|#1| $) 32 T ELT)) (|order| (((|NonNegativeInteger|) $) 28 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) 29 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#3=($ $ (|NonNegativeInteger|)) 35 T ELT) (($ . #4=($)) 33 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 30 T ELT)) (|before?| (#1# 6 T ELT)) (D (#3# 36 T ELT) (($ . #4#) 34 T ELT)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT))) 
(((|DifferentialVariableCategory| |#1|) (|Category|) (|OrderedSet|)) (T |DifferentialVariableCategory|)) 
((|makeVariable| (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|variable| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|weight| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|OrderedSet|) (|DifferentialSpace|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |makeVariable| ($ |t#1| (|NonNegativeInteger|))) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |variable| (|t#1| $)) (SIGNATURE |weight| ((|NonNegativeInteger|) $)))) 
(((|BasicType|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) . T) ((|DifferentialSpace|) . T) ((|Join|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|min| #3=(($ $ $) NIL T ELT)) (|max| #3#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exponents| ((#4=(|List| (|Integer|)) $) 28 T ELT)) (|degree| ((#5=(|NonNegativeInteger|) $) 26 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT) (($ #4#) 22 T ELT)) (|before?| #1#) (|Nul| (($ #5#) 29 T ELT)) (>= #1#) (> #1#) (= (#2# 11 T ELT)) (<= #1#) (< (#2# 18 T ELT))) 
(((|ExtAlgBasis|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1=(|List| (|Integer|)))) (SIGNATURE |degree| (#2=(|NonNegativeInteger|) $)) (SIGNATURE |exponents| (#1# $)) (SIGNATURE |Nul| ($ #2#))))) (T |ExtAlgBasis|)) 
((|coerce| #1=(*1 *1 *2) #2=(AND (|isDomain| *2 (|List| (|Integer|))) #3=(|isDomain| *1 (|ExtAlgBasis|)))) (|degree| #4=(*1 *2 *1) #5=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3#)) (|exponents| #4# #2#) (|Nul| #1# #5#)) 
((|tanh| (#1=(|#2| |#2|) 77 T ELT)) (|tan| (#1# 65 T ELT)) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| #2=(|Boolean|))))) 123 T ELT)) (|sinh| (#1# 75 T ELT)) (|sin| (#1# 63 T ELT)) (|sech| (#1# 79 T ELT)) (|sec| (#1# 67 T ELT)) (|pi| (#3=(|#2|) 46 T ELT)) (|operator| ((#4=(|BasicOperator|) #4#) 97 T ELT)) (|log| (#1# 61 T ELT)) (|localReal?| ((#2# |#2|) 146 T ELT)) (|iitanh| (#1# 193 T ELT)) (|iitan| (#1# 169 T ELT)) (|iisqrt3| (#3# 59 T ELT)) (|iisqrt2| (#3# 58 T ELT)) (|iisinh| (#1# 189 T ELT)) (|iisin| (#1# 165 T ELT)) (|iisech| (#1# 197 T ELT)) (|iisec| (#1# 173 T ELT)) (|iilog| (#1# 161 T ELT)) (|iiexp| (#1# 163 T ELT)) (|iicsch| (#1# 199 T ELT)) (|iicsc| (#1# 175 T ELT)) (|iicoth| (#1# 195 T ELT)) (|iicot| (#1# 171 T ELT)) (|iicosh| (#1# 191 T ELT)) (|iicos| (#1# 167 T ELT)) (|iiatanh| (#1# 205 T ELT)) (|iiatan| (#1# 181 T ELT)) (|iiasinh| (#1# 201 T ELT)) (|iiasin| (#1# 177 T ELT)) (|iiasech| (#1# 209 T ELT)) (|iiasec| (#1# 185 T ELT)) (|iiacsch| (#1# 211 T ELT)) (|iiacsc| (#1# 187 T ELT)) (|iiacoth| (#1# 207 T ELT)) (|iiacot| (#1# 183 T ELT)) (|iiacosh| (#1# 203 T ELT)) (|iiacos| (#1# 179 T ELT)) (|exp| (#1# 62 T ELT)) (|csch| (#1# 80 T ELT)) (|csc| (#1# 68 T ELT)) (|coth| (#1# 78 T ELT)) (|cot| (#1# 66 T ELT)) (|cosh| (#1# 76 T ELT)) (|cos| (#1# 64 T ELT)) (|belong?| ((#2# #4#) 95 T ELT)) (|atanh| (#1# 83 T ELT)) (|atan| (#1# 71 T ELT)) (|asinh| (#1# 81 T ELT)) (|asin| (#1# 69 T ELT)) (|asech| (#1# 85 T ELT)) (|asec| (#1# 73 T ELT)) (|acsch| (#1# 86 T ELT)) (|acsc| (#1# 74 T ELT)) (|acoth| (#1# 84 T ELT)) (|acot| (#1# 72 T ELT)) (|acosh| (#1# 82 T ELT)) (|acos| (#1# 70 T ELT))) 
(((|ElementaryFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |exp| #1=(|#2| |#2|)) (SIGNATURE |log| #1#) (SIGNATURE |sin| #1#) (SIGNATURE |cos| #1#) (SIGNATURE |tan| #1#) (SIGNATURE |cot| #1#) (SIGNATURE |sec| #1#) (SIGNATURE |csc| #1#) (SIGNATURE |asin| #1#) (SIGNATURE |acos| #1#) (SIGNATURE |atan| #1#) (SIGNATURE |acot| #1#) (SIGNATURE |asec| #1#) (SIGNATURE |acsc| #1#) (SIGNATURE |sinh| #1#) (SIGNATURE |cosh| #1#) (SIGNATURE |tanh| #1#) (SIGNATURE |coth| #1#) (SIGNATURE |sech| #1#) (SIGNATURE |csch| #1#) (SIGNATURE |asinh| #1#) (SIGNATURE |acosh| #1#) (SIGNATURE |atanh| #1#) (SIGNATURE |acoth| #1#) (SIGNATURE |asech| #1#) (SIGNATURE |acsch| #1#) (SIGNATURE |pi| #2=(|#2|)) (SIGNATURE |belong?| (#3=(|Boolean|) #4=(|BasicOperator|))) (SIGNATURE |operator| (#4# #4#)) (SIGNATURE |iisqrt2| #2#) (SIGNATURE |iisqrt3| #2#) (SIGNATURE |iiexp| #1#) (SIGNATURE |iilog| #1#) (SIGNATURE |iisin| #1#) (SIGNATURE |iicos| #1#) (SIGNATURE |iitan| #1#) (SIGNATURE |iicot| #1#) (SIGNATURE |iisec| #1#) (SIGNATURE |iicsc| #1#) (SIGNATURE |iiasin| #1#) (SIGNATURE |iiacos| #1#) (SIGNATURE |iiatan| #1#) (SIGNATURE |iiacot| #1#) (SIGNATURE |iiasec| #1#) (SIGNATURE |iiacsc| #1#) (SIGNATURE |iisinh| #1#) (SIGNATURE |iicosh| #1#) (SIGNATURE |iitanh| #1#) (SIGNATURE |iicoth| #1#) (SIGNATURE |iisech| #1#) (SIGNATURE |iicsch| #1#) (SIGNATURE |iiasinh| #1#) (SIGNATURE |iiacosh| #1#) (SIGNATURE |iiatanh| #1#) (SIGNATURE |iiacoth| #1#) (SIGNATURE |iiasech| #1#) (SIGNATURE |iiacsch| #1#) (SIGNATURE |specialTrigs| ((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| #3#))))) (SIGNATURE |localReal?| (#3# |#2|))) (|IntegralDomain|) (|Join| (|FunctionSpace| |#1|) (|RadicalCategory|))) (T |ElementaryFunction|)) 
((|localReal?| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|IntegralDomain|)) #4=(|isDomain| *2 #5=(|Boolean|)) (|isDomain| *1 (|ElementaryFunction| *4 *3)) (|ofCategory| *3 #6=(|Join| (|FunctionSpace| *4) #7=(|RadicalCategory|))))) (|specialTrigs| (*1 *2 *2 *3) (|partial| AND (|isDomain| *3 (|List| (|Record| (|:| |func| *2) (|:| |pole| #5#)))) (|ofCategory| *2 #6#) #2# (|isDomain| *1 (|ElementaryFunction| *4 *2)))) (|iiacsch| #8=(*1 *2 *2) #9=(AND #10=(|ofCategory| *3 #3#) #11=(|isDomain| *1 (|ElementaryFunction| *3 *2)) #12=(|ofCategory| *2 #13=(|Join| (|FunctionSpace| *3) #7#)))) (|iiasech| #8# #9#) (|iiacoth| #8# #9#) (|iiatanh| #8# #9#) (|iiacosh| #8# #9#) (|iiasinh| #8# #9#) (|iicsch| #8# #9#) (|iisech| #8# #9#) (|iicoth| #8# #9#) (|iitanh| #8# #9#) (|iicosh| #8# #9#) (|iisinh| #8# #9#) (|iiacsc| #8# #9#) (|iiasec| #8# #9#) (|iiacot| #8# #9#) (|iiatan| #8# #9#) (|iiacos| #8# #9#) (|iiasin| #8# #9#) (|iicsc| #8# #9#) (|iisec| #8# #9#) (|iicot| #8# #9#) (|iitan| #8# #9#) (|iicos| #8# #9#) (|iisin| #8# #9#) (|iilog| #8# #9#) (|iiexp| #8# #9#) (|iisqrt3| #14=(*1 *2) #15=(AND #12# #11# #10#)) (|iisqrt2| #14# #15#) (|operator| #8# (AND (|isDomain| *2 #16=(|BasicOperator|)) #10# (|isDomain| *1 (|ElementaryFunction| *3 *4)) (|ofCategory| *4 #13#))) (|belong?| #1# (AND (|isDomain| *3 #16#) #2# #4# (|isDomain| *1 (|ElementaryFunction| *4 *5)) (|ofCategory| *5 #6#))) (|pi| #14# #15#) (|acsch| #8# #9#) (|asech| #8# #9#) (|acoth| #8# #9#) (|atanh| #8# #9#) (|acosh| #8# #9#) (|asinh| #8# #9#) (|csch| #8# #9#) (|sech| #8# #9#) (|coth| #8# #9#) (|tanh| #8# #9#) (|cosh| #8# #9#) (|sinh| #8# #9#) (|acsc| #8# #9#) (|asec| #8# #9#) (|acot| #8# #9#) (|atan| #8# #9#) (|acos| #8# #9#) (|asin| #8# #9#) (|csc| #8# #9#) (|sec| #8# #9#) (|cot| #8# #9#) (|tan| #8# #9#) (|cos| #8# #9#) (|sin| #8# #9#) (|log| #8# #9#) (|exp| #8# #9#)) 
((|validExponential| (((|Union| |#2| "failed") #1=(|List| #2=(|Kernel| |#2|)) |#2| #3=(|Symbol|)) 151 T ELT)) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) 49 T ELT)) (|rootNormalize| ((|#2| |#2| #2#) 144 T ELT)) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| #1#) (|:| |vals| (|List| |#2|))) |#2| #3#) 143 T ELT)) (|realElementary| (#4=(|#2| |#2| #3#) 20 T ELT) (#5=(|#2| |#2|) 23 T ELT)) (|normalize| (#4# 157 T ELT) (#5# 155 T ELT))) 
(((|ElementaryFunctionStructurePackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |normalize| #1=(|#2| |#2|)) (SIGNATURE |normalize| #2=(|#2| |#2| #3=(|Symbol|))) (SIGNATURE |rischNormalize| ((|Record| (|:| |func| |#2|) (|:| |kers| #4=(|List| #5=(|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| #3#)) (SIGNATURE |realElementary| #1#) (SIGNATURE |realElementary| #2#) (SIGNATURE |validExponential| ((|Union| |#2| "failed") #4# |#2| #3#)) (SIGNATURE |rootNormalize| (|#2| |#2| #5#)) (SIGNATURE |tanQ| (|#2| (|Fraction| #6=(|Integer|)) |#2|))) (|Join| (|IntegralDomain|) (|RetractableTo| #6#) (|LinearlyExplicitRingOver| #6#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |ElementaryFunctionStructurePackage|)) 
((|tanQ| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Fraction| #1=(|Integer|))) #2=(|ofCategory| *4 #3=(|Join| (|IntegralDomain|) (|RetractableTo| #1#) (|LinearlyExplicitRingOver| #1#))) #4=(|isDomain| *1 (|ElementaryFunctionStructurePackage| *4 *2)) #5=(|ofCategory| *2 (|Join| #6=(|AlgebraicallyClosedField|) #7=(|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|rootNormalize| #8=(*1 *2 *2 *3) (AND (|isDomain| *3 #9=(|Kernel| *2)) #5# #2# #4#)) (|validExponential| (*1 *2 *3 *2 *4) (|partial| AND (|isDomain| *3 (|List| #9#)) #10=(|isDomain| *4 #11=(|Symbol|)) (|ofCategory| *2 #12=(|Join| #6# #7# (|FunctionSpace| *5))) #13=(|ofCategory| *5 #3#) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *5 *2)))) (|realElementary| #8# #14=(AND (|isDomain| *3 #11#) #2# #4# #5#)) (|realElementary| #15=(*1 *2 *2) #16=(AND (|ofCategory| *3 #3#) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *3 *2)) (|ofCategory| *2 (|Join| #6# #7# (|FunctionSpace| *3))))) (|rischNormalize| (*1 *2 *3 *4) (AND #10# #13# (|isDomain| *2 (|Record| (|:| |func| *3) (|:| |kers| (|List| (|Kernel| *3))) (|:| |vals| (|List| *3)))) (|isDomain| *1 (|ElementaryFunctionStructurePackage| *5 *3)) (|ofCategory| *3 #12#))) (|normalize| #8# #14#) (|normalize| #15# #16#)) 
((|tanhIfCan| (#1=(#2=(|Union| |#3| "failed") |#3|) 120 T ELT)) (|tanh| (#3=(|#3| |#3|) 142 T ELT)) (|tanIfCan| (#1# 89 T ELT)) (|tan| (#3# 132 T ELT)) (|sinhIfCan| (#1# 65 T ELT)) (|sinh| (#3# 140 T ELT)) (|sinIfCan| (#1# 53 T ELT)) (|sin| (#3# 130 T ELT)) (|sechIfCan| (#1# 122 T ELT)) (|sech| (#3# 144 T ELT)) (|secIfCan| (#1# 91 T ELT)) (|sec| (#3# 134 T ELT)) (|nthRootIfCan| ((#2# |#3| (|NonNegativeInteger|)) 41 T ELT)) (|logIfCan| (#1# 81 T ELT)) (|log| (#3# 129 T ELT)) (|expIfCan| (#1# 51 T ELT)) (|exp| (#3# 128 T ELT)) (|cschIfCan| (#1# 123 T ELT)) (|csch| (#3# 145 T ELT)) (|cscIfCan| (#1# 92 T ELT)) (|csc| (#3# 135 T ELT)) (|cothIfCan| (#1# 121 T ELT)) (|coth| (#3# 143 T ELT)) (|cotIfCan| (#1# 90 T ELT)) (|cot| (#3# 133 T ELT)) (|coshIfCan| (#1# 67 T ELT)) (|cosh| (#3# 141 T ELT)) (|cosIfCan| (#1# 55 T ELT)) (|cos| (#3# 131 T ELT)) (|atanhIfCan| (#1# 73 T ELT)) (|atanh| (#3# 148 T ELT)) (|atanIfCan| (#1# 114 T ELT)) (|atan| (#3# 152 T ELT)) (|asinhIfCan| (#1# 69 T ELT)) (|asinh| (#3# 146 T ELT)) (|asinIfCan| (#1# 57 T ELT)) (|asin| (#3# 136 T ELT)) (|asechIfCan| (#1# 77 T ELT)) (|asech| (#3# 150 T ELT)) (|asecIfCan| (#1# 61 T ELT)) (|asec| (#3# 138 T ELT)) (|acschIfCan| (#1# 79 T ELT)) (|acsch| (#3# 151 T ELT)) (|acscIfCan| (#1# 63 T ELT)) (|acsc| (#3# 139 T ELT)) (|acothIfCan| (#1# 75 T ELT)) (|acoth| (#3# 149 T ELT)) (|acotIfCan| (#1# 117 T ELT)) (|acot| (#3# 153 T ELT)) (|acoshIfCan| (#1# 71 T ELT)) (|acosh| (#3# 147 T ELT)) (|acosIfCan| (#1# 59 T ELT)) (|acos| (#3# 137 T ELT)) (** ((|#3| |#3| (|Fraction| (|Integer|))) 47 (|has| |#1| (|Field|)) ELT))) 
(((|ElementaryFunctionsUnivariateLaurentSeries| |#1| |#2| |#3|) (|Join| (|PartialTranscendentalFunctions| |#3|) (CATEGORY |package| (IF (|has| |#1| (|Field|)) (SIGNATURE ** (|#3| |#3| #1=(|Fraction| (|Integer|)))) |%noBranch|) (SIGNATURE |exp| #2=(|#3| |#3|)) (SIGNATURE |log| #2#) (SIGNATURE |sin| #2#) (SIGNATURE |cos| #2#) (SIGNATURE |tan| #2#) (SIGNATURE |cot| #2#) (SIGNATURE |sec| #2#) (SIGNATURE |csc| #2#) (SIGNATURE |asin| #2#) (SIGNATURE |acos| #2#) (SIGNATURE |atan| #2#) (SIGNATURE |acot| #2#) (SIGNATURE |asec| #2#) (SIGNATURE |acsc| #2#) (SIGNATURE |sinh| #2#) (SIGNATURE |cosh| #2#) (SIGNATURE |tanh| #2#) (SIGNATURE |coth| #2#) (SIGNATURE |sech| #2#) (SIGNATURE |csch| #2#) (SIGNATURE |asinh| #2#) (SIGNATURE |acosh| #2#) (SIGNATURE |atanh| #2#) (SIGNATURE |acoth| #2#) (SIGNATURE |asech| #2#) (SIGNATURE |acsch| #2#))) (|Algebra| #1#) (|UnivariateTaylorSeriesCategory| |#1|) (|UnivariateLaurentSeriesConstructorCategory| |#1| |#2|)) (T |ElementaryFunctionsUnivariateLaurentSeries|)) 
((** (*1 *2 *2 *3) (AND (|isDomain| *3 #1=(|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| #2=(*1 *2 *2) #3=(AND (|ofCategory| *3 (|Algebra| #1#)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariateLaurentSeries| *3 *4 *2)) (|ofCategory| *2 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)))) (|log| #2# #3#) (|sin| #2# #3#) (|cos| #2# #3#) (|tan| #2# #3#) (|cot| #2# #3#) (|sec| #2# #3#) (|csc| #2# #3#) (|asin| #2# #3#) (|acos| #2# #3#) (|atan| #2# #3#) (|acot| #2# #3#) (|asec| #2# #3#) (|acsc| #2# #3#) (|sinh| #2# #3#) (|cosh| #2# #3#) (|tanh| #2# #3#) (|coth| #2# #3#) (|sech| #2# #3#) (|csch| #2# #3#) (|asinh| #2# #3#) (|acosh| #2# #3#) (|atanh| #2# #3#) (|acoth| #2# #3#) (|asech| #2# #3#) (|acsch| #2# #3#)) 
((|tanhIfCan| (#1=(#2=(|Union| |#3| "failed") |#3|) 70 T ELT)) (|tanh| (#3=(|#3| |#3|) 137 T ELT)) (|tanIfCan| (#1# 54 T ELT)) (|tan| (#3# 125 T ELT)) (|sinhIfCan| (#1# 66 T ELT)) (|sinh| (#3# 135 T ELT)) (|sinIfCan| (#1# 50 T ELT)) (|sin| (#3# 123 T ELT)) (|sechIfCan| (#1# 74 T ELT)) (|sech| (#3# 139 T ELT)) (|secIfCan| (#1# 58 T ELT)) (|sec| (#3# 127 T ELT)) (|nthRootIfCan| ((#2# |#3| (|NonNegativeInteger|)) 38 T ELT)) (|logIfCan| (#1# 48 T ELT)) (|log| (#3# 111 T ELT)) (|expIfCan| (#1# 46 T ELT)) (|exp| (#3# 122 T ELT)) (|cschIfCan| (#1# 76 T ELT)) (|csch| (#3# 140 T ELT)) (|cscIfCan| (#1# 60 T ELT)) (|csc| (#3# 128 T ELT)) (|cothIfCan| (#1# 72 T ELT)) (|coth| (#3# 138 T ELT)) (|cotIfCan| (#1# 56 T ELT)) (|cot| (#3# 126 T ELT)) (|coshIfCan| (#1# 68 T ELT)) (|cosh| (#3# 136 T ELT)) (|cosIfCan| (#1# 52 T ELT)) (|cos| (#3# 124 T ELT)) (|atanhIfCan| (#1# 78 T ELT)) (|atanh| (#3# 143 T ELT)) (|atanIfCan| (#1# 62 T ELT)) (|atan| (#3# 131 T ELT)) (|asinhIfCan| (#1# 112 T ELT)) (|asinh| (#3# 141 T ELT)) (|asinIfCan| (#1# 100 T ELT)) (|asin| (#3# 129 T ELT)) (|asechIfCan| (#1# 116 T ELT)) (|asech| (#3# 145 T ELT)) (|asecIfCan| (#1# 107 T ELT)) (|asec| (#3# 133 T ELT)) (|acschIfCan| (#1# 117 T ELT)) (|acsch| (#3# 146 T ELT)) (|acscIfCan| (#1# 109 T ELT)) (|acsc| (#3# 134 T ELT)) (|acothIfCan| (#1# 80 T ELT)) (|acoth| (#3# 144 T ELT)) (|acotIfCan| (#1# 64 T ELT)) (|acot| (#3# 132 T ELT)) (|acoshIfCan| (#1# 113 T ELT)) (|acosh| (#3# 142 T ELT)) (|acosIfCan| (#1# 103 T ELT)) (|acos| (#3# 130 T ELT)) (** ((|#3| |#3| (|Fraction| (|Integer|))) 44 (|has| |#1| (|Field|)) ELT))) 
(((|ElementaryFunctionsUnivariatePuiseuxSeries| |#1| |#2| |#3| |#4|) (|Join| (|PartialTranscendentalFunctions| |#3|) (CATEGORY |package| (IF (|has| |#1| (|Field|)) (SIGNATURE ** (|#3| |#3| #1=(|Fraction| (|Integer|)))) |%noBranch|) (SIGNATURE |exp| #2=(|#3| |#3|)) (SIGNATURE |log| #2#) (SIGNATURE |sin| #2#) (SIGNATURE |cos| #2#) (SIGNATURE |tan| #2#) (SIGNATURE |cot| #2#) (SIGNATURE |sec| #2#) (SIGNATURE |csc| #2#) (SIGNATURE |asin| #2#) (SIGNATURE |acos| #2#) (SIGNATURE |atan| #2#) (SIGNATURE |acot| #2#) (SIGNATURE |asec| #2#) (SIGNATURE |acsc| #2#) (SIGNATURE |sinh| #2#) (SIGNATURE |cosh| #2#) (SIGNATURE |tanh| #2#) (SIGNATURE |coth| #2#) (SIGNATURE |sech| #2#) (SIGNATURE |csch| #2#) (SIGNATURE |asinh| #2#) (SIGNATURE |acosh| #2#) (SIGNATURE |atanh| #2#) (SIGNATURE |acoth| #2#) (SIGNATURE |asech| #2#) (SIGNATURE |acsch| #2#))) (|Algebra| #1#) (|UnivariateLaurentSeriesCategory| |#1|) (|UnivariatePuiseuxSeriesConstructorCategory| |#1| |#2|) (|PartialTranscendentalFunctions| |#2|)) (T |ElementaryFunctionsUnivariatePuiseuxSeries|)) 
((** (*1 *2 *2 *3) (AND (|isDomain| *3 #1=(|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| #2=(*1 *2 *2) #3=(AND (|ofCategory| *3 (|Algebra| #1#)) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *1 (|ElementaryFunctionsUnivariatePuiseuxSeries| *3 *4 *2 *5)) (|ofCategory| *2 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *5 (|PartialTranscendentalFunctions| *4)))) (|log| #2# #3#) (|sin| #2# #3#) (|cos| #2# #3#) (|tan| #2# #3#) (|cot| #2# #3#) (|sec| #2# #3#) (|csc| #2# #3#) (|asin| #2# #3#) (|acos| #2# #3#) (|atan| #2# #3#) (|acot| #2# #3#) (|asec| #2# #3#) (|acsc| #2# #3#) (|sinh| #2# #3#) (|cosh| #2# #3#) (|tanh| #2# #3#) (|coth| #2# #3#) (|sech| #2# #3#) (|csch| #2# #3#) (|asinh| #2# #3#) (|acosh| #2# #3#) (|atanh| #2# #3#) (|acoth| #2# #3#) (|asech| #2# #3#) (|acsch| #2# #3#)) 
((|variable?| (#1=((|Boolean|) $) 20 T ELT)) (|type| (((|Syntax|) $) 9 T ELT)) (|getOperator| (#2=((|Union| (|Identifier|) #3="failed") $) 15 T ELT)) (|getOperands| (((|Union| (|List| $) #3#) $) NIL T ELT)) (|getIdentifier| (#2# 21 T ELT)) (|getConstant| (((|Union| (|SExpression|) #3#) $) 19 T ELT)) (|constant?| (#1# 17 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|callForm?| (#1# 10 T ELT))) 
(((|ElaboratedExpression|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |type| ((|Syntax|) $)) (SIGNATURE |constant?| #1=((|Boolean|) $)) (SIGNATURE |getConstant| ((|Union| (|SExpression|) #2="failed") $)) (SIGNATURE |variable?| #1#) (SIGNATURE |getIdentifier| #3=((|Union| (|Identifier|) #2#) $)) (SIGNATURE |callForm?| #1#) (SIGNATURE |getOperator| #3#) (SIGNATURE |getOperands| ((|Union| (|List| $) #2#) $))))) (T |ElaboratedExpression|)) 
((|type| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Syntax|)) #2=(|isDomain| *1 #3=(|ElaboratedExpression|)))) (|constant?| #1# #4=(AND (|isDomain| *2 (|Boolean|)) #2#)) (|getConstant| #1# (|partial| AND (|isDomain| *2 (|SExpression|)) #2#)) (|variable?| #1# #4#) (|getIdentifier| #1# #5=(|partial| AND (|isDomain| *2 (|Identifier|)) #2#)) (|callForm?| #1# #4#) (|getOperator| #1# #5#) (|getOperands| #1# (|partial| AND (|isDomain| *2 (|List| #3#)) #2#))) 
((|typeForm| ((#1=(|InternalTypeForm|) $) 10 T ELT)) (|irForm| ((#2=(|InternalRepresentationForm|) $) 8 T ELT)) (|environment| ((#3=(|Environment|) $) 12 T ELT)) (|elaboration| (($ #2# #1# #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 19 T ELT))) 
(((|Elaboration|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |elaboration| ($ #1=(|InternalRepresentationForm|) #2=(|InternalTypeForm|) #3=(|Environment|))) (SIGNATURE |irForm| (#1# $)) (SIGNATURE |typeForm| (#2# $)) (SIGNATURE |environment| (#3# $))))) (T |Elaboration|)) 
((|elaboration| (*1 *1 *2 *3 *4) (AND #1=(|isDomain| *2 (|InternalRepresentationForm|)) (|isDomain| *3 #2=(|InternalTypeForm|)) (|isDomain| *4 #3=(|Environment|)) #4=(|isDomain| *1 (|Elaboration|)))) (|irForm| #5=(*1 *2 *1) (AND #1# #4#)) (|typeForm| #5# (AND (|isDomain| *2 #2#) #4#)) (|environment| #5# (AND (|isDomain| *2 #3#) #4#))) 
((|select| (#1=($ (|Mapping| #2=(|Boolean|) |#2|) $) 24 T ELT)) (|removeDuplicates| (($ $) 38 T ELT)) (|remove!| (#1# NIL T ELT) (#3=($ |#2| $) 36 T ELT)) (|remove| (#3# 34 T ELT) (#1# 18 T ELT)) (|merge!| (($ (|Mapping| #2# |#2| |#2|) $ $) NIL T ELT) (#4=($ $ $) 42 T ELT)) (|insert| (($ |#2| $ #5=(|Integer|)) 20 T ELT) (($ $ $ #5#) 22 T ELT)) (|delete| (($ $ #5#) 11 T ELT) (($ $ (|UniversalSegment| #5#)) 14 T ELT)) (|concat!| (#6=($ $ |#2|) 32 T ELT) (#4# NIL T ELT)) (|concat| (#6# 31 T ELT) (#3# NIL T ELT) (#4# 26 T ELT) (($ (|List| $)) NIL T ELT))) 
(((|ExtensibleLinearAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |merge!| #1=(|#1| |#1| |#1|)) (SIGNATURE |remove!| #2=(|#1| |#2| |#1|)) (SIGNATURE |merge!| (|#1| (|Mapping| #3=(|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |remove!| #4=(|#1| (|Mapping| #3# |#2|) |#1|)) (SIGNATURE |concat!| #1#) (SIGNATURE |concat!| #5=(|#1| |#1| |#2|)) (SIGNATURE |insert| (|#1| |#1| |#1| #6=(|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| #6#)) (SIGNATURE |delete| (|#1| |#1| (|UniversalSegment| #6#))) (SIGNATURE |delete| (|#1| |#1| #6#)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| #1#) (SIGNATURE |concat| #2#) (SIGNATURE |concat| #5#) (SIGNATURE |remove| #4#) (SIGNATURE |select| #4#) (SIGNATURE |remove| #2#) (SIGNATURE |removeDuplicates| (|#1| |#1|))) (|ExtensibleLinearAggregate| |#2|) (|Type|)) (T |ExtensibleLinearAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|swap!| (((|Void|) $ #3=(|Integer|) #3#) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #3# |#1|) 47 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #4=(|UniversalSegment| #3#) |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 83 T ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 69 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#7=($) 6 T CONST)) (|removeDuplicates!| (($ $) 81 (|has| |#1| (|BasicType|)) ELT)) (|removeDuplicates| (($ $) 71 (AND (|has| |#1| . #8=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) 87 T ELT) (($ |#1| $) 82 (|has| |#1| (|BasicType|)) ELT)) (|remove| (($ |#1| $) 70 (AND (|has| |#1| . #8#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #5# |#1|) . #6#) 68 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|qsetelt!| ((|#1| $ #3# |#1|) 48 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #3#) 46 T ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| ((#3# . #9=($)) 38 (|has| #3# . #10=((|OrderedSet|))) ELT)) (|merge!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 84 T ELT) (($ $ $) 80 (|has| |#1| (|OrderedSet|)) ELT)) (|maxIndex| ((#3# . #9#) 39 (|has| #3# . #10#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 92 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 60 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #11=((|SetCategory|))) ELT)) (|insert!| (($ |#1| $ (|Integer|)) 86 T ELT) (($ $ $ (|Integer|)) 85 T ELT)) (|insert| (($ |#1| $ #3#) 57 T ELT) (($ $ $ #3#) 56 T ELT)) (|indices| (((|List| #3#) $) 41 T ELT)) (|index?| ((#12=(|Boolean|) #3# $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #11#) ELT)) (|first| ((|#1| $) 37 (|has| #3# . #10#) ELT)) (|fill!| (($ $ |#1|) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT)) (|eq?| ((#13=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#12# |#1| $) 40 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 43 T ELT)) (|empty?| ((#13# $) 7 T ELT)) (|empty| (#7# 8 T ELT)) (|elt| ((|#1| $ #3# |#1|) 45 T ELT) ((|#1| $ #3#) 44 T ELT) (($ $ #4#) 66 T ELT)) (|delete!| (($ $ (|Integer|)) 89 T ELT) (($ $ (|UniversalSegment| (|Integer|))) 88 T ELT)) (|delete| (($ $ #3#) 59 T ELT) (($ $ #4#) 58 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#14=(|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| #14#)) ELT)) (|construct| (($ (|List| |#1|)) 67 T ELT)) (|concat!| (($ $ |#1|) 91 T ELT) (($ $ $) 90 T ELT)) (|concat| (($ $ |#1|) 64 T ELT) (($ |#1| $) 63 T ELT) (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|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 (|BasicType|)))) (|removeDuplicates!| (*1 *1 *1) (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|)))) (|merge!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|LinearAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|) (CATEGORY |domain| (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|) $)) (IF (|has| |t#1| (|BasicType|)) (PROGN (SIGNATURE |remove!| ($ |t#1| $)) (SIGNATURE |removeDuplicates!| ($ $))) |%noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (SIGNATURE |merge!| ($ $ $)) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((** (($ $ $) 10 T ELT))) 
(((|ElementaryFunctionCategory&| |#1|) (CATEGORY |package| (SIGNATURE ** (|#1| |#1| |#1|))) (|ElementaryFunctionCategory|)) (T |ElementaryFunctionCategory&|)) 
NIL 
((|log| (($ $) 6 T ELT)) (|exp| (($ $) 7 T ELT)) (** (($ $ $) 8 T ELT))) 
(((|ElementaryFunctionCategory|) (|Category|)) (T |ElementaryFunctionCategory|)) 
((** (*1 *1 *1 *1) (|ofCategory| *1 (|ElementaryFunctionCategory|))) (|exp| (*1 *1 *1) (|ofCategory| *1 (|ElementaryFunctionCategory|))) (|log| (*1 *1 *1) (|ofCategory| *1 (|ElementaryFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |log| ($ $)) (SIGNATURE |exp| ($ $)) (SIGNATURE ** ($ $ $)))) 
((|sncndn| (((|List| #1=(|Stream| |#1|)) #1# |#1|) 35 T ELT)) (|sn| (#2=(|#2| |#2| |#1|) 39 T ELT)) (|dn| (#2# 41 T ELT)) (|cn| (#2# 40 T ELT))) 
(((|EllipticFunctionsUnivariateTaylorSeries| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sn| #1=(|#2| |#2| |#1|)) (SIGNATURE |cn| #1#) (SIGNATURE |dn| #1#) (SIGNATURE |sncndn| ((|List| #2=(|Stream| |#1|)) #2# |#1|))) (|Field|) (|UnivariateTaylorSeriesCategory| |#1|)) (T |EllipticFunctionsUnivariateTaylorSeries|)) 
((|sncndn| (*1 *2 *3 *4) (AND (|ofCategory| *4 #1=(|Field|)) (|isDomain| *2 (|List| #2=(|Stream| *4))) (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *4 *5)) (|isDomain| *3 #2#) (|ofCategory| *5 (|UnivariateTaylorSeriesCategory| *4)))) (|dn| #3=(*1 *2 *2 *3) #4=(AND (|ofCategory| *3 #1#) (|isDomain| *1 (|EllipticFunctionsUnivariateTaylorSeries| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|cn| #3# #4#) (|sn| #3# #4#)) 
((|elt| ((|#2| $ |#1|) 6 T ELT))) 
(((|Eltable| |#1| |#2|) (|Category|) (|Type|) (|Type|)) (T |Eltable|)) 
((|elt| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|Eltable| *3 *2)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |elt| (|t#2| $ |t#1|)))) 
(((|Join|) . T) ((|Type|) . T)) 
((|qsetelt!| ((|#3| $ |#2| |#3|) 12 T ELT)) (|qelt| ((|#3| $ |#2|) 10 T ELT))) 
(((|EltableAggregate&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |qsetelt!| (|#3| |#1| |#2| |#3|)) (SIGNATURE |qelt| (|#3| |#1| |#2|))) (|EltableAggregate| |#2| |#3|) (|BasicType|) (|Type|)) (T |EltableAggregate&|)) 
NIL 
((|setelt| ((|#2| $ |#1| |#2|) 10 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qsetelt!| ((|#2| $ |#1| |#2|) 9 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qelt| ((|#2| $ |#1|) 11 T ELT)) (|elt| ((|#2| $ |#1|) 6 T ELT) ((|#2| $ |#1| |#2|) 12 T ELT))) 
(((|EltableAggregate| |#1| |#2|) (|Category|) (|BasicType|) (|Type|)) (T |EltableAggregate|)) 
((|elt| (*1 *2 *1 *3 *2) (AND (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|)))) (|qelt| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|)))) (|qsetelt!| (*1 *2 *1 *3 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|EltableAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|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| $ (|ShallowlyMutableAggregate| |t#2|)) (PROGN (SIGNATURE |setelt| (|t#2| $ |t#1| |t#2|)) (SIGNATURE |qsetelt!| (|t#2| $ |t#1| |t#2|))) |%noBranch|))) 
(((|Eltable| |#1| |#2|) . T) ((|Join|) . T) ((|Type|) . T)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) 37 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 44 T ELT)) (|unitCanonical| (#4=($ $) 41 T ELT)) (|unit?| #5=(#3# NIL T ELT)) (|subtractIfCan| #6=((#7=(|Union| $ #8="failed") $ $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#9=($) NIL T CONST)) (|rem| (#10=($ $ $) 35 T ELT)) (|reduce| (($ |#2| |#3|) 18 T ELT)) (|recip| ((#7# $) NIL T ELT)) (|quo| #11=(#10# NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #12=(|List| $)) #13=(|:| |generator| $)) #12#) NIL T ELT)) (|opposite?| #1#) (|one?| #5#) (|multiEuclidean| (((|Union| #12# #8#) #12# $) NIL T ELT)) (|modulus| ((|#3| $) NIL T ELT)) (|lcm| #11# #14=(($ #12#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#4# 19 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15=(|SparseUnivariatePolynomial| $) #15# #15#) NIL T ELT)) (|gcd| #11# #14#) (|extendedEuclidean| (((|Record| #16=(|:| |coef1| $) #17=(|:| |coef2| $) #13#) $ $) NIL T ELT) (((|Union| (|Record| #16# #17#) #8#) $ $ $) NIL T ELT)) (|exquo| #6#) (|expressIdealMember| (((|Maybe| #12#) #12# $) NIL T ELT)) (|exQuo| #6#) (|euclideanSize| ((#18=(|NonNegativeInteger|) $) 36 T ELT)) (|elt| ((|#2| $ |#2|) 46 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 23 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19=(|Integer|)) NIL T ELT) #20=(#4# NIL T ELT) ((|#2| $) NIL T ELT)) (|characteristic| ((#18#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#9# 31 T CONST)) (|One| (#9# 39 T CONST)) (= #1#) (- #20# #11#) (+ #11#) (** (($ $ #21=(|PositiveInteger|)) NIL T ELT) (($ $ #18#) NIL T ELT)) (* (($ #21# $) NIL T ELT) (($ #18# $) NIL T ELT) (($ #19# $) NIL T ELT) (#10# 40 T ELT))) 
(((|EuclideanModularRing| |#1| |#2| |#3| |#4| |#5| |#6|) (|Join| (|EuclideanDomain|) (|Eltable| |#2| |#2|) (CATEGORY |domain| (SIGNATURE |modulus| (|#3| $)) (SIGNATURE |coerce| (|#2| $)) (SIGNATURE |reduce| ($ |#2| |#3|)) (SIGNATURE |exQuo| (#1=(|Union| $ #2="failed") $ $)) (SIGNATURE |recip| (#1# $)) (SIGNATURE |inv| ($ $)))) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#1|) (|AbelianMonoid|) (|Mapping| |#2| |#2| |#3|) (|Mapping| (|Union| |#3| #2#) |#3| |#3|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| |#3|)) (T |EuclideanModularRing|)) 
((|recip| #1=(*1 *1 *1) #2=(|partial| AND #3=(|ofCategory| *2 #4=(|CommutativeRing|)) #5=(|isDomain| *1 (|EuclideanModularRing| *2 *3 *4 *5 *6 *7)) #6=(|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) #7=(|ofCategory| *4 #8=(|AbelianMonoid|)) #9=(|ofType| *5 (|Mapping| *3 *3 *4)) #10=(|ofType| *6 (|Mapping| #11=(|Union| *4 #12="failed") *4 *4)) #13=(|ofType| *7 (|Mapping| #14=(|Union| *3 #12#) *3 *3 *4)))) (|modulus| #15=(*1 *2 *1) (AND #16=(|ofCategory| *3 #4#) (|ofCategory| *2 #8#) (|isDomain| *1 (|EuclideanModularRing| *3 *4 *2 *5 *6 *7)) (|ofCategory| *4 #17=(|UnivariatePolynomialCategory| *3)) (|ofType| *5 (|Mapping| *4 *4 *2)) (|ofType| *6 (|Mapping| #18=(|Union| *2 #12#) *2 *2)) (|ofType| *7 (|Mapping| #11# *4 *4 *2)))) (|coerce| #15# (AND (|ofCategory| *2 #17#) (|isDomain| *1 (|EuclideanModularRing| *3 *2 *4 *5 *6 *7)) #16# #7# (|ofType| *5 (|Mapping| *2 *2 *4)) #10# (|ofType| *7 (|Mapping| #18# *2 *2 *4)))) (|reduce| (*1 *1 *2 *3) (AND (|ofCategory| *4 #4#) (|isDomain| *1 (|EuclideanModularRing| *4 *2 *3 *5 *6 *7)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *3 #8#) (|ofType| *5 (|Mapping| *2 *2 *3)) (|ofType| *6 (|Mapping| #14# *3 *3)) (|ofType| *7 (|Mapping| #18# *2 *2 *3)))) (|exQuo| (*1 *1 *1 *1) #2#) (|inv| #1# (AND #3# #5# #6# #7# #9# #10# #13#))) 
((|annihilate?| (((|Boolean|) $ $) 10 T ELT))) 
(((|EntireRing&| |#1|) (CATEGORY |package| (SIGNATURE |annihilate?| ((|Boolean|) |#1| |#1|))) (|EntireRing|)) (T |EntireRing&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|EntireRing|) (|Category|)) (T |EntireRing|)) 
NIL 
(|Join| (|Ring|) (|BiModule| $ $) (CATEGORY |package| (ATTRIBUTE |noZeroDivisors|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|scopes| (((|List| (|Scope|)) $) 10 T ELT)) (|putProperty| (($ #1=(|Identifier|) #1# #2=(|SExpression|) $) 19 T ELT)) (|putProperties| (($ #1# #3=(|List| (|Property|)) $) 23 T ELT)) (|interactiveEnv| (#4=($) 25 T ELT)) (|getProperty| (((|Maybe| #2#) #1# #1# $) 18 T ELT)) (|getProperties| ((#3# #1# $) 22 T ELT)) (|empty| (#4# 7 T ELT)) (|currentEnv| (#4# 24 T ELT)) (|coerce| (((|OutputForm|) $) 29 T ELT)) (|categoryFrame| (#4# 26 T ELT))) 
(((|Environment|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |empty| #1=($)) (SIGNATURE |scopes| ((|List| (|Scope|)) $)) (SIGNATURE |getProperty| ((|Maybe| #2=(|SExpression|)) #3=(|Identifier|) #3# $)) (SIGNATURE |putProperty| ($ #3# #3# #2# $)) (SIGNATURE |getProperties| (#4=(|List| (|Property|)) #3# $)) (SIGNATURE |putProperties| ($ #3# #4# $)) (SIGNATURE |currentEnv| #1#) (SIGNATURE |interactiveEnv| #1#) (SIGNATURE |categoryFrame| #1#)))) (T |Environment|)) 
((|empty| #1=(*1 *1) #2=(|isDomain| *1 (|Environment|))) (|scopes| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Scope|))) #2#)) (|getProperty| (*1 *2 *3 *3 *1) (AND #3=(|isDomain| *3 #4=(|Identifier|)) (|isDomain| *2 (|Maybe| #5=(|SExpression|))) #2#)) (|putProperty| (*1 *1 *2 *2 *3 *1) (AND #6=(|isDomain| *2 #4#) (|isDomain| *3 #5#) #2#)) (|getProperties| (*1 *2 *3 *1) (AND #3# (|isDomain| *2 #7=(|List| (|Property|))) #2#)) (|putProperties| (*1 *1 *2 *3 *1) (AND #6# (|isDomain| *3 #7#) #2#)) (|currentEnv| #1# #2#) (|interactiveEnv| #1# #2#) (|categoryFrame| #1# #2#)) 
((|generalizedEigenvectors| (((|List| (|Record| #1=(|:| |eigval| #2=(|Union| #3=(|Fraction| #4=(|Polynomial| |#1|)) (|SuchThat| #5=(|Symbol|) #4#))) (|:| |geneigvec| #6=(|List| #7=(|Matrix| #3#))))) #7#) 103 T ELT)) (|generalizedEigenvector| ((#6# #8=(|Record| #1# (|:| |eigmult| #9=(|NonNegativeInteger|)) (|:| |eigvec| #6#)) #7#) 98 T ELT) ((#6# #2# #7# #9# #9#) 42 T ELT)) (|eigenvectors| (((|List| #8#) #7#) 100 T ELT)) (|eigenvector| ((#6# #2# #7#) 76 T ELT)) (|eigenvalues| (((|List| #2#) #7#) 75 T ELT)) (|characteristicPolynomial| ((#4# #7#) 56 T ELT) ((#4# #7# #5#) 57 T ELT))) 
(((|EigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (#1=(|Polynomial| |#1|) #2=(|Matrix| #3=(|Fraction| #1#)) #4=(|Symbol|))) (SIGNATURE |characteristicPolynomial| (#1# #2#)) (SIGNATURE |eigenvalues| ((|List| #5=(|Union| #3# (|SuchThat| #4# #1#))) #2#)) (SIGNATURE |eigenvector| (#6=(|List| #2#) #5# #2#)) (SIGNATURE |generalizedEigenvector| (#6# #5# #2# #7=(|NonNegativeInteger|) #7#)) (SIGNATURE |generalizedEigenvector| (#6# #8=(|Record| #9=(|:| |eigval| #5#) (|:| |eigmult| #7#) (|:| |eigvec| #6#)) #2#)) (SIGNATURE |generalizedEigenvectors| ((|List| (|Record| #9# (|:| |geneigvec| #6#))) #2#)) (SIGNATURE |eigenvectors| ((|List| #8#) #2#))) (|GcdDomain|)) (T |EigenPackage|)) 
((|eigenvectors| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|GcdDomain|)) (|isDomain| *2 (|List| (|Record| #4=(|:| |eigval| #5=(|Union| #6=(|Fraction| #7=(|Polynomial| *4)) (|SuchThat| #8=(|Symbol|) #7#))) #9=(|:| |eigmult| #10=(|NonNegativeInteger|)) (|:| |eigvec| #11=(|List| #12=(|Matrix| #6#)))))) #13=(|isDomain| *1 (|EigenPackage| *4)) #14=(|isDomain| *3 #12#))) (|generalizedEigenvectors| #1# (AND #2# (|isDomain| *2 (|List| (|Record| #4# (|:| |geneigvec| #11#)))) #13# #14#)) (|generalizedEigenvector| #15=(*1 *2 *3 *4) (AND (|isDomain| *3 (|Record| (|:| |eigval| #16=(|Union| #17=(|Fraction| #18=(|Polynomial| *5)) (|SuchThat| #8# #18#))) #9# (|:| |eigvec| (|List| *4)))) #19=(|ofCategory| *5 #3#) #20=(|isDomain| *2 (|List| #21=(|Matrix| #17#))) #22=(|isDomain| *1 (|EigenPackage| *5)) #23=(|isDomain| *4 #21#))) (|generalizedEigenvector| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *3 (|Union| #24=(|Fraction| #25=(|Polynomial| *6)) (|SuchThat| #8# #25#))) (|isDomain| *5 #10#) (|ofCategory| *6 #3#) (|isDomain| *2 (|List| #26=(|Matrix| #24#))) (|isDomain| *1 (|EigenPackage| *6)) (|isDomain| *4 #26#))) (|eigenvector| #15# (AND (|isDomain| *3 #16#) #19# #20# #22# #23#)) (|eigenvalues| #1# (AND #14# #2# (|isDomain| *2 (|List| #5#)) #13#)) (|characteristicPolynomial| #1# (AND #14# (|isDomain| *2 #7#) #13# #2#)) (|characteristicPolynomial| #15# (AND (|isDomain| *3 #21#) (|isDomain| *4 #8#) (|isDomain| *2 #18#) #22# #19#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|SetCategory|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#1| (|AbelianGroup|)) ELT)) (|swap| (#7=($ $) 12 T ELT)) (|subtractIfCan| ((#8=(|Union| $ "failed") $ $) NIL #6# ELT)) (|subst| (#9=($ $ $) 95 (|has| |#1| (|ExpressionSpace|)) ELT)) (|sample| (#10=($) NIL (OR #6# #11=(|has| |#1| (|Monoid|))) CONST)) (|rightZero| (#7# 51 #6# ELT)) (|rightOne| (#12=(#8# $) 62 #11# ELT)) (|rhs| (#13=(|#1| $) 11 T ELT)) (|recip| (#12# 60 #11# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #11# ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 14 T ELT)) (|lhs| (#13# 10 T ELT)) (|leftZero| (#7# 50 #6# ELT)) (|leftOne| (#12# 61 #11# ELT)) (|latex| (((|String|) $) NIL #4# ELT)) (|inv| (#7# 64 #14=(OR #15=(|has| |#1| (|Field|)) #16=(|has| |#1| (|Group|))) ELT)) (|hash| (((|SingleInteger|) $) NIL #4# ELT)) (|factorAndSplit| ((#17=(|List| $) $) 85 (|has| |#1| (|IntegralDomain|)) ELT)) (|eval| (#9# 24 #18=(AND (|has| |#1| (|Evalable| |#1|)) #4#) ELT) (($ $ #17#) 28 #18# ELT) (($ $ #19=(|Symbol|) |#1|) 17 #20=(|has| |#1| (|InnerEvalable| #19# |#1|)) ELT) (($ $ #21=(|List| #19#) (|List| |#1|)) 21 #20# ELT)) (|equation| (#22=($ |#1| |#1|) 9 T ELT)) (|dimension| (((|CardinalNumber|)) 90 #15# ELT)) (|differentiate| (#23=($ $ #19#) 87 #24=(|has| |#1| (|PartialDifferentialRing| #19#)) ELT) #25=(($ $ #21#) NIL #24# ELT) #26=(($ $ #19# #27=(|NonNegativeInteger|)) NIL #24# ELT) #28=(($ $ #21# (|List| #27#)) NIL #24# ELT)) (|conjugate| #29=(#9# NIL #16# ELT)) (|commutator| #29#) (|coerce| (($ #30=(|Integer|)) NIL #31=(|has| |#1| (|Ring|)) ELT) (#5# 37 #4# ELT) (((|OutputForm|) $) 36 #4# ELT)) (|characteristic| ((#27#) 67 #31# CONST)) (|before?| #1#) (|annihilate?| (#2# NIL #31# ELT)) (|Zero| (#10# 47 #6# CONST)) (|One| (#10# 57 #11# CONST)) (D (#23# NIL #24# ELT) #25# #26# #28#) (= (#22# 8 T ELT) (#2# 32 #4# ELT)) (/ (#32=($ $ |#1|) NIL #15# ELT) (#9# 92 #14# ELT)) (- (#33=($ |#1| $) 45 #6# ELT) (#32# 46 #6# ELT) (#9# 44 #6# ELT) (#7# 43 #6# ELT)) (+ (#33# 40 #34=(|has| |#1| (|AbelianSemiGroup|)) ELT) (#32# 41 #34# ELT) (#9# 39 #34# ELT)) (** (($ $ #30#) NIL #16# ELT) (($ $ #27#) NIL #11# ELT) (($ $ #35=(|PositiveInteger|)) NIL #36=(|has| |#1| (|SemiGroup|)) ELT)) (* (#32# 55 #36# ELT) (#33# 54 #36# ELT) (#9# 53 #36# ELT) (($ #30# $) 70 #6# ELT) (($ #27# $) NIL #6# ELT) (($ #35# $) NIL #34# ELT))) 
(((|Equation| |#1|) (|Join| (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE = #1=($ |#1| |#1|)) (SIGNATURE |equation| #1#) (SIGNATURE |swap| #2=($ $)) (SIGNATURE |lhs| #3=(|#1| $)) (SIGNATURE |rhs| #3#) (IF (|has| |#1| #4=(|InnerEvalable| #5=(|Symbol|) |#1|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| #6=(|SetCategory|)) (PROGN (ATTRIBUTE #6#) (ATTRIBUTE (|CoercibleTo| (|Boolean|))) (IF (|has| |#1| (|Evalable| |#1|)) (PROGN (SIGNATURE |eval| #7=($ $ $)) (SIGNATURE |eval| ($ $ #8=(|List| $)))) |%noBranch|)) |%noBranch|) (IF (|has| |#1| #9=(|AbelianSemiGroup|)) (PROGN (ATTRIBUTE #9#) (SIGNATURE + #10=($ |#1| $)) (SIGNATURE + #11=($ $ |#1|))) |%noBranch|) (IF (|has| |#1| #12=(|AbelianGroup|)) (PROGN (ATTRIBUTE #12#) (SIGNATURE |leftZero| #2#) (SIGNATURE |rightZero| #2#) (SIGNATURE - #10#) (SIGNATURE - #11#)) |%noBranch|) (IF (|has| |#1| #13=(|SemiGroup|)) (PROGN (ATTRIBUTE #13#) (SIGNATURE * #10#) (SIGNATURE * #11#)) |%noBranch|) (IF (|has| |#1| #14=(|Monoid|)) (PROGN (ATTRIBUTE #14#) #15=(SIGNATURE |leftOne| #16=((|Union| $ "failed") $)) #17=(SIGNATURE |rightOne| #16#)) |%noBranch|) (IF (|has| |#1| #18=(|Group|)) (PROGN (ATTRIBUTE #18#) #15# #17#) |%noBranch|) (IF (|has| |#1| #19=(|Ring|)) (PROGN (ATTRIBUTE #19#) (ATTRIBUTE (|BiModule| |#1| |#1|))) |%noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |#1|)) |%noBranch|) (IF (|has| |#1| (|IntegralDomain|)) (SIGNATURE |factorAndSplit| (#8# $)) |%noBranch|) (IF (|has| |#1| #20=(|PartialDifferentialRing| #5#)) (ATTRIBUTE #20#) |%noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (ATTRIBUTE (|VectorSpace| |#1|)) (SIGNATURE / #7#) (SIGNATURE |inv| #2#)) |%noBranch|) (IF (|has| |#1| (|ExpressionSpace|)) (SIGNATURE |subst| #7#) |%noBranch|))) (|Type|)) (T |Equation|)) 
((= #1=(*1 *1 *2 *2) #2=(AND #3=(|isDomain| *1 (|Equation| *2)) #4=(|ofCategory| *2 #5=(|Type|)))) (|equation| #1# #2#) (|swap| #6=(*1 *1 *1) #2#) (|lhs| #7=(*1 *2 *1) #2#) (|rhs| #7# #2#) (|eval| #8=(*1 *1 *1 *1) (AND (|ofCategory| *2 (|Evalable| *2)) (|ofCategory| *2 #9=(|SetCategory|)) #4# #3#)) (|eval| #10=(*1 *1 *1 *2) (AND #11=(|isDomain| *2 (|List| #12=(|Equation| *3))) (|ofCategory| *3 (|Evalable| *3)) (|ofCategory| *3 #9#) #13=(|ofCategory| *3 #5#) #14=(|isDomain| *1 #12#))) (+ #15=(*1 *1 *2 *1) #16=(AND #3# (|ofCategory| *2 (|AbelianSemiGroup|)) #4#)) (+ #10# #16#) (|leftZero| #6# #17=(AND #3# (|ofCategory| *2 (|AbelianGroup|)) #4#)) (|rightZero| #6# #17#) (- #15# #17#) (- #10# #17#) (|leftOne| #6# #18=(|partial| AND #3# (|ofCategory| *2 (|Monoid|)) #4#)) (|rightOne| #6# #18#) (|factorAndSplit| #7# (AND #11# #14# (|ofCategory| *3 (|IntegralDomain|)) #13#)) (|subst| #8# (AND #3# (|ofCategory| *2 (|ExpressionSpace|)) #4#)) (* #10# #19=(AND #3# (|ofCategory| *2 (|SemiGroup|)) #4#)) (* #15# #19#) (/ #8# #20=(OR (AND #3# (|ofCategory| *2 (|Field|)) . #21=(#4#)) (AND #3# (|ofCategory| *2 (|Group|)) . #21#))) (|inv| #6# #20#)) 
((|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) 14 T ELT))) 
(((|EquationFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)))) #1=(|Type|) #1#) (T |EquationFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Equation| *5)) (|ofCategory| *5 #1=(|Type|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Equation| *6)) (|isDomain| *1 (|EquationFunctions2| *5 *6))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #6=(|BasicType|)) #7=(|has| |#2| #6#)) ELT)) (|table| #8=(#9=($) NIL T ELT) #10=(($ #11=(|List| #5#)) NIL T ELT)) (|swap!| (((|Void|) $ |#1| |#1|) NIL #12=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| #13=(#14=(|#2| $ |#1| |#2|) NIL #12# ELT)) (|select!| #15=(($ #16=(|Mapping| #3# #5#) $) NIL #17=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|select| #15#) (|search| #18=(((|Union| |#2| #19="failed") |#1| $) NIL T ELT)) (|sample| (#9# NIL T CONST)) (|removeDuplicates| (#20=($ $) NIL #21=(AND #17# #4#) ELT)) (|remove!| (#22=($ #5# $) NIL #17# ELT) #15# #18#) (|remove| (#22# NIL #21# ELT) #15#) (|reduce| ((#5# #23=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #23# $ #5#) NIL T ELT) ((#5# #23# $) NIL T ELT)) (|qsetelt!| #13#) (|qelt| #24=((|#2| $ |#1|) NIL T ELT)) (|minIndex| #25=((|#1| $) NIL #26=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#11# $) NIL T ELT)) (|member?| ((#3# #5# $) NIL #4# ELT)) (|maxIndex| #25#) (|map!| #27=(($ (|Mapping| #5# #5#) . #28=($)) NIL T ELT) #29=(($ (|Mapping| |#2| |#2|) . #28#) NIL T ELT)) (|map| #27# #29# #27# (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #30=(OR #31=(|has| #5# #32=(|SetCategory|)) #33=(|has| |#2| #32#)) ELT)) (|keys| #34=(((|List| |#1|) $) NIL T ELT)) (|key?| #35=((#3# |#1| $) NIL T ELT)) (|inspect| #36=((#5# $) NIL T ELT)) (|insert!| (#22# NIL T ELT)) (|indices| #34#) (|index?| #35#) (|hash| (((|SingleInteger|) $) NIL #30# ELT)) (|first| ((|#2| $) NIL #26# ELT)) (|find| (((|Union| #5# #19#) #16# $) NIL T ELT)) (|fill!| (($ $ |#2|) NIL #12# ELT)) (|extract!| #36#) (|every?| #37=((#3# #16# $) NIL T ELT)) (|eval| #38=(($ $ (|List| #39=(|Equation| #5#))) NIL #40=(AND (|has| #5# (|Evalable| #5#)) #31#) ELT) #41=(($ $ #39#) NIL #40# ELT) #42=(($ $ #5# #5#) NIL #40# ELT) #43=(($ $ #11# #11#) NIL #40# ELT) (($ $ #44=(|List| |#2|) #44#) NIL #45=(AND (|has| |#2| (|Evalable| |#2|)) #33#) ELT) (($ $ |#2| |#2|) NIL #45# ELT) (($ $ #46=(|Equation| |#2|)) NIL #45# ELT) (($ $ (|List| #46#)) NIL #45# ELT) #43# #42# #41# #38#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#2| $) NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #7#) ELT)) (|entries| ((#44# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| #8#) (|elt| #24# (#14# NIL T ELT)) (|dictionary| #8# #10#) (|count| ((#47=(|NonNegativeInteger|) #5# $) NIL #4# ELT) ((#47# #16# $) NIL T ELT)) (|copy| (#20# NIL T ELT)) (|convert| ((#48=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #48#)) ELT)) (|construct| #10#) (|coerce| ((#49=(|OutputForm|) $) NIL (OR (|has| #5# #50=(|CoercibleTo| #49#)) (|has| |#2| #50#)) ELT)) (|before?| #1#) (|bag| #10#) (|any?| #37#) (= #1#) (|#| ((#47# $) NIL T ELT))) 
(((|EqTable| |#1| |#2|) (|TableAggregate| |#1| |#2|) #1=(|SetCategory|) #1#) (T |EqTable|)) 
NIL 
((|error| ((#1=(|Exit|) #2=(|String|) #3=(|List| #2#)) 17 T ELT) ((#1# #2# #2#) 16 T ELT) ((#1# #3#) 15 T ELT) ((#1# #2#) 14 T ELT))) 
(((|ErrorFunctions|) (CATEGORY |package| (SIGNATURE |error| (#1=(|Exit|) #2=(|String|))) (SIGNATURE |error| (#1# #3=(|List| #2#))) (SIGNATURE |error| (#1# #2# #2#)) (SIGNATURE |error| (#1# #2# #3#)))) (T |ErrorFunctions|)) 
((|error| (*1 *2 *3 *4) (AND (|isDomain| *4 #1=(|List| #2=(|String|))) #3=(|isDomain| *3 #2#) #4=(|isDomain| *2 (|Exit|)) #5=(|isDomain| *1 (|ErrorFunctions|)))) (|error| (*1 *2 *3 *3) #6=(AND #3# #4# #5#)) (|error| #7=(*1 *2 *3) (AND (|isDomain| *3 #1#) #4# #5#)) (|error| #7# #6#)) 
((|tower| ((#1=(|List| #2=(|Kernel| $)) $) 27 T ELT)) (|subst| (#3=($ $ #4=(|Equation| $)) 78 T ELT) (#5=($ $ (|List| #4#)) 140 T ELT) #6=(($ $ #1# #7=(|List| $)) NIL T ELT)) (|retractIfCan| (#8=((|Union| #2# "failed") $) 128 T ELT)) (|retract| ((#2# $) 127 T ELT)) (|paren| (#9=($ $) 17 T ELT) (#10=($ #7#) 54 T ELT)) (|operators| ((#11=(|List| #12=(|BasicOperator|)) $) 35 T ELT)) (|operator| ((#12# #12#) 89 T ELT)) (|odd?| (#13=(#14=(|Boolean|) $) 151 T ELT)) (|map| (($ #15=(|Mapping| $ $) #2#) 87 T ELT)) (|mainKernel| (#8# 95 T ELT)) (|kernel| (#16=($ #12# $) 59 T ELT) (#17=($ #12# #7#) 111 T ELT)) (|is?| ((#14# $ #12#) 133 T ELT) (#18=(#14# $ #19=(|Symbol|)) 132 T ELT)) (|height| (((|NonNegativeInteger|) $) 44 T ELT)) (|freeOf?| ((#14# $ $) 57 T ELT) (#18# 49 T ELT)) (|even?| (#13# 149 T ELT)) (|eval| (($ $ #2# $) NIL T ELT) #6# (#5# 138 T ELT) (#3# NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #7# #7#) NIL T ELT) (($ $ #20=(|List| #19#) #21=(|List| #15#)) 81 T ELT) (($ $ #20# #22=(|List| #23=(|Mapping| $ #7#))) NIL T ELT) (($ $ #19# #23#) 67 T ELT) (($ $ #19# #15#) 72 T ELT) (($ $ #11# #21#) 80 T ELT) (($ $ #11# #22#) 83 T ELT) (($ $ #12# #23#) 68 T ELT) (($ $ #12# #15#) 74 T ELT)) (|elt| (#16# 60 T ELT) (($ #12# $ $) 61 T ELT) (($ #12# $ $ $) 62 T ELT) (($ #12# $ $ $ $) 63 T ELT) (#17# 124 T ELT)) (|distribute| (#9# 51 T ELT) (($ $ $) 136 T ELT)) (|box| (#9# 15 T ELT) (#10# 53 T ELT)) (|belong?| ((#14# #12#) 21 T ELT))) 
(((|ExpressionSpace&| |#1|) (CATEGORY |package| (SIGNATURE |odd?| #1=(#2=(|Boolean|) |#1|)) (SIGNATURE |even?| #1#) (SIGNATURE |eval| (|#1| |#1| #3=(|BasicOperator|) #4=(|Mapping| |#1| |#1|))) (SIGNATURE |eval| (|#1| |#1| #3# #5=(|Mapping| |#1| #6=(|List| |#1|)))) (SIGNATURE |eval| (|#1| |#1| #7=(|List| #3#) #8=(|List| #5#))) (SIGNATURE |eval| (|#1| |#1| #7# #9=(|List| #4#))) (SIGNATURE |eval| (|#1| |#1| #10=(|Symbol|) #4#)) (SIGNATURE |eval| (|#1| |#1| #10# #5#)) (SIGNATURE |eval| (|#1| |#1| #11=(|List| #10#) #8#)) (SIGNATURE |eval| (|#1| |#1| #11# #9#)) (SIGNATURE |freeOf?| #12=(#2# |#1| #10#)) (SIGNATURE |freeOf?| (#2# |#1| |#1|)) (SIGNATURE |map| (|#1| #4# #13=(|Kernel| |#1|))) (SIGNATURE |kernel| #14=(|#1| #3# #6#)) (SIGNATURE |kernel| #15=(|#1| #3# |#1|)) (SIGNATURE |is?| #12#) (SIGNATURE |is?| (#2# |#1| #3#)) (SIGNATURE |belong?| (#2# #3#)) (SIGNATURE |operator| (#3# #3#)) (SIGNATURE |operators| (#7# |#1|)) (SIGNATURE |tower| (#16=(|List| #13#) |#1|)) (SIGNATURE |mainKernel| #17=((|Union| #13# "failed") |#1|)) (SIGNATURE |height| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |distribute| (|#1| |#1| |#1|)) (SIGNATURE |distribute| #18=(|#1| |#1|)) (SIGNATURE |paren| #19=(|#1| #6#)) (SIGNATURE |paren| #18#) (SIGNATURE |box| #19#) (SIGNATURE |box| #18#) (SIGNATURE |subst| #20=(|#1| |#1| #16# #6#)) (SIGNATURE |subst| #21=(|#1| |#1| (|List| #22=(|Equation| |#1|)))) (SIGNATURE |subst| #23=(|#1| |#1| #22#)) (SIGNATURE |elt| #14#) (SIGNATURE |elt| (|#1| #3# |#1| |#1| |#1| |#1|)) (SIGNATURE |elt| (|#1| #3# |#1| |#1| |#1|)) (SIGNATURE |elt| (|#1| #3# |#1| |#1|)) (SIGNATURE |elt| #15#) (SIGNATURE |eval| (|#1| |#1| #6# #6#)) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| #23#) (SIGNATURE |eval| #21#) (SIGNATURE |eval| #20#) (SIGNATURE |eval| (|#1| |#1| #13# |#1|)) (SIGNATURE |retractIfCan| #17#) (SIGNATURE |retract| (#13# |#1|))) (|ExpressionSpace|)) (T |ExpressionSpace&|)) 
((|operator| (*1 *2 *2) (AND (|isDomain| *2 #1=(|BasicOperator|)) (|isDomain| *1 (|ExpressionSpace&| *3)) (|ofCategory| *3 #2=(|ExpressionSpace|)))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 #1#) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ExpressionSpace&| *4)) (|ofCategory| *4 #2#)))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|tower| (((|List| (|Kernel| $)) $) 42 T ELT)) (|subst| (($ $ (|Equation| $)) 54 T ELT) (($ $ (|List| (|Equation| $))) 53 T ELT) (($ $ (|List| (|Kernel| $)) (|List| $)) 52 T ELT)) (|retractIfCan| (((|Union| #2=(|Kernel| $) "failed") $) 67 T ELT)) (|retract| ((#2# $) 68 T ELT)) (|paren| (($ $) 49 T ELT) (($ (|List| $)) 48 T ELT)) (|operators| (((|List| (|BasicOperator|)) $) 41 T ELT)) (|operator| (((|BasicOperator|) (|BasicOperator|)) 40 T ELT)) (|odd?| (((|Boolean|) $) 20 (|has| $ (|RetractableTo| (|Integer|))) ELT)) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) 23 (|has| $ (|Ring|)) ELT)) (|map| (($ (|Mapping| $ $) (|Kernel| $)) 34 T ELT)) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|kernels| (((|List| (|Kernel| $)) $) 43 T ELT)) (|kernel| (($ (|BasicOperator|) $) 36 T ELT) (($ (|BasicOperator|) (|List| $)) 35 T ELT)) (|is?| (((|Boolean|) $ (|BasicOperator|)) 38 T ELT) (((|Boolean|) $ (|Symbol|)) 37 T ELT)) (|height| (((|NonNegativeInteger|) $) 45 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|freeOf?| (((|Boolean|) $ $) 33 T ELT) (((|Boolean|) $ (|Symbol|)) 32 T ELT)) (|even?| (((|Boolean|) $) 21 (|has| $ (|RetractableTo| (|Integer|))) ELT)) (|eval| (($ $ #3=(|Kernel| $) $) 65 T ELT) (($ $ (|List| #3#) (|List| $)) 64 T ELT) (($ $ (|List| (|Equation| $))) 63 T ELT) (($ $ (|Equation| $)) 62 T ELT) (($ $ $ $) 61 T ELT) (($ $ (|List| $) (|List| $)) 60 T ELT) (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) 31 T ELT) (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) 30 T ELT) (($ $ (|Symbol|) (|Mapping| $ (|List| $))) 29 T ELT) (($ $ (|Symbol|) (|Mapping| $ $)) 28 T ELT) (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) 27 T ELT) (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) 26 T ELT) (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) 25 T ELT) (($ $ (|BasicOperator|) (|Mapping| $ $)) 24 T ELT)) (|elt| (($ (|BasicOperator|) $) 59 T ELT) (($ (|BasicOperator|) $ $) 58 T ELT) (($ (|BasicOperator|) $ $ $) 57 T ELT) (($ (|BasicOperator|) $ $ $ $) 56 T ELT) (($ (|BasicOperator|) (|List| $)) 55 T ELT)) (|distribute| (($ $) 47 T ELT) (($ $ $) 46 T ELT)) (|definingPolynomial| (($ $) 22 (|has| $ (|Ring|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #2#) 66 T ELT)) (|box| (($ $) 51 T ELT) (($ (|List| $)) 50 T ELT)) (|belong?| (((|Boolean|) (|BasicOperator|)) 39 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|ExpressionSpace|) (|Category|)) (T |ExpressionSpace|)) 
((|elt| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|BasicOperator|)))) (|elt| (*1 *1 *2 *1 *1) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|BasicOperator|)))) (|elt| (*1 *1 *2 *1 *1 *1) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|BasicOperator|)))) (|elt| (*1 *1 *2 *1 *1 *1 *1) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|BasicOperator|)))) (|elt| (*1 *1 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|subst| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Equation| *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|subst| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Equation| *1))) (|ofCategory| *1 (|ExpressionSpace|)))) (|subst| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| (|Kernel| *1))) (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|box| (*1 *1 *1) (|ofCategory| *1 (|ExpressionSpace|))) (|box| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|paren| (*1 *1 *1) (|ofCategory| *1 (|ExpressionSpace|))) (|paren| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|distribute| (*1 *1 *1) (|ofCategory| *1 (|ExpressionSpace|))) (|distribute| (*1 *1 *1 *1) (|ofCategory| *1 (|ExpressionSpace|))) (|height| (*1 *2 *1) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|mainKernel| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|Kernel| *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|kernels| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Kernel| *1))) (|ofCategory| *1 (|ExpressionSpace|)))) (|tower| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Kernel| *1))) (|ofCategory| *1 (|ExpressionSpace|)))) (|operators| (*1 *2 *1) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|List| (|BasicOperator|))))) (|operator| (*1 *2 *2) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|BasicOperator|)))) (|belong?| (*1 *2 *3) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *3 (|BasicOperator|)) (|isDomain| *2 (|Boolean|)))) (|is?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *3 (|BasicOperator|)) (|isDomain| *2 (|Boolean|)))) (|is?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Boolean|)))) (|kernel| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|BasicOperator|)))) (|kernel| (*1 *1 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|map| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *1 *1)) (|isDomain| *3 (|Kernel| *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|freeOf?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|Boolean|)))) (|freeOf?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|Boolean|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *3 (|List| (|Mapping| *1 *1))) (|ofCategory| *1 (|ExpressionSpace|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| (|Symbol|))) (|isDomain| *3 (|List| (|Mapping| *1 (|List| *1)))) (|ofCategory| *1 (|ExpressionSpace|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|Mapping| *1 (|List| *1))) (|ofCategory| *1 (|ExpressionSpace|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|Mapping| *1 *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| (|BasicOperator|))) (|isDomain| *3 (|List| (|Mapping| *1 *1))) (|ofCategory| *1 (|ExpressionSpace|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| (|BasicOperator|))) (|isDomain| *3 (|List| (|Mapping| *1 (|List| *1)))) (|ofCategory| *1 (|ExpressionSpace|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Mapping| *1 (|List| *1))) (|ofCategory| *1 (|ExpressionSpace|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Mapping| *1 *1)) (|ofCategory| *1 (|ExpressionSpace|)))) (|minPoly| (*1 *2 *3) (AND (|isDomain| *3 (|Kernel| *1)) (|ofCategory| *1 (|Ring|)) (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *1)))) (|definingPolynomial| (*1 *1 *1) (AND (|ofCategory| *1 (|Ring|)) (|ofCategory| *1 (|ExpressionSpace|)))) (|even?| (*1 *2 *1) (AND (|ofCategory| *1 (|RetractableTo| (|Integer|))) (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|Boolean|)))) (|odd?| (*1 *2 *1) (AND (|ofCategory| *1 (|RetractableTo| (|Integer|))) (|ofCategory| *1 (|ExpressionSpace|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|SetCategory|) (|RetractableTo| (|Kernel| $)) (|InnerEvalable| (|Kernel| $) $) (|Evalable| $) (CATEGORY |domain| (SIGNATURE |elt| ($ (|BasicOperator|) $)) (SIGNATURE |elt| ($ (|BasicOperator|) $ $)) (SIGNATURE |elt| ($ (|BasicOperator|) $ $ $)) (SIGNATURE |elt| ($ (|BasicOperator|) $ $ $ $)) (SIGNATURE |elt| ($ (|BasicOperator|) (|List| $))) (SIGNATURE |subst| ($ $ (|Equation| $))) (SIGNATURE |subst| ($ $ (|List| (|Equation| $)))) (SIGNATURE |subst| ($ $ (|List| (|Kernel| $)) (|List| $))) (SIGNATURE |box| ($ $)) (SIGNATURE |box| ($ (|List| $))) (SIGNATURE |paren| ($ $)) (SIGNATURE |paren| ($ (|List| $))) (SIGNATURE |distribute| ($ $)) (SIGNATURE |distribute| ($ $ $)) (SIGNATURE |height| ((|NonNegativeInteger|) $)) (SIGNATURE |mainKernel| ((|Union| (|Kernel| $) "failed") $)) (SIGNATURE |kernels| ((|List| (|Kernel| $)) $)) (SIGNATURE |tower| ((|List| (|Kernel| $)) $)) (SIGNATURE |operators| ((|List| (|BasicOperator|)) $)) (SIGNATURE |operator| ((|BasicOperator|) (|BasicOperator|))) (SIGNATURE |belong?| ((|Boolean|) (|BasicOperator|))) (SIGNATURE |is?| ((|Boolean|) $ (|BasicOperator|))) (SIGNATURE |is?| ((|Boolean|) $ (|Symbol|))) (SIGNATURE |kernel| ($ (|BasicOperator|) $)) (SIGNATURE |kernel| ($ (|BasicOperator|) (|List| $))) (SIGNATURE |map| ($ (|Mapping| $ $) (|Kernel| $))) (SIGNATURE |freeOf?| ((|Boolean|) $ $)) (SIGNATURE |freeOf?| ((|Boolean|) $ (|Symbol|))) (SIGNATURE |eval| ($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $)))) (SIGNATURE |eval| ($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $))))) (SIGNATURE |eval| ($ $ (|Symbol|) (|Mapping| $ (|List| $)))) (SIGNATURE |eval| ($ $ (|Symbol|) (|Mapping| $ $))) (SIGNATURE |eval| ($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $)))) (SIGNATURE |eval| ($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $))))) (SIGNATURE |eval| ($ $ (|BasicOperator|) (|Mapping| $ (|List| $)))) (SIGNATURE |eval| ($ $ (|BasicOperator|) (|Mapping| $ $))) (IF (|has| $ (|Ring|)) (PROGN (SIGNATURE |minPoly| ((|SparseUnivariatePolynomial| $) (|Kernel| $))) (SIGNATURE |definingPolynomial| ($ $))) |%noBranch|) (IF (|has| $ (|RetractableTo| (|Integer|))) (PROGN (SIGNATURE |even?| ((|Boolean|) $)) (SIGNATURE |odd?| ((|Boolean|) $))) |%noBranch|))) 
(((|BasicType|) . T) ((|CoercibleFrom| #1=(|Kernel| $)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Evalable| $) . T) ((|InnerEvalable| (|Kernel| $) $) . T) ((|InnerEvalable| $ $) . T) ((|Join|) . T) ((|RetractableTo| #1#) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) 18 T ELT))) 
(((|ExpressionSpaceFunctions1| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| (|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)))) (|ExpressionSpace|) (|Type|)) (T |ExpressionSpaceFunctions1|)) 
((|map| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *2 *6)) (|isDomain| *4 (|String|)) (|isDomain| *5 (|Kernel| *6)) (|ofCategory| *6 (|ExpressionSpace|)) (|ofCategory| *2 (|Type|)) (|isDomain| *1 (|ExpressionSpaceFunctions1| *6 *2))))) 
((|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) 17 T ELT))) 
(((|ExpressionSpaceFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| (|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)))) #1=(|ExpressionSpace|) #1#) (T |ExpressionSpaceFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *2 *5)) (|isDomain| *4 (|Kernel| *5)) (|ofCategory| *5 #1=(|ExpressionSpace|)) (|ofCategory| *2 #1#) (|isDomain| *1 (|ExpressionSpaceFunctions2| *5 *2))))) 
((|sizeLess?| (((|Boolean|) $ $) 14 T ELT)) (|rem| (#1=($ $ $) 18 T ELT)) (|quo| (#1# 17 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #2=(|List| $)) #3=(|:| |generator| $)) #2#) 50 T ELT)) (|multiEuclidean| (((|Union| #2# #4="failed") #2# $) 67 T ELT)) (|gcd| (#1# 25 T ELT) (($ #2#) NIL T ELT)) (|extendedEuclidean| (((|Record| #5=(|:| |coef1| $) #6=(|:| |coef2| $) #3#) $ $) 35 T ELT) (((|Union| (|Record| #5# #6#) #4#) $ $ $) 40 T ELT)) (|exquo| (((|Union| $ #4#) $ $) 21 T ELT)) (|expressIdealMember| (((|Maybe| #2#) #2# $) 55 T ELT))) 
(((|EuclideanDomain&| |#1|) (CATEGORY |package| (SIGNATURE |multiEuclidean| ((|Union| #1=(|List| |#1|) #2="failed") #1# |#1|)) (SIGNATURE |extendedEuclidean| ((|Union| (|Record| #3=(|:| |coef1| |#1|) #4=(|:| |coef2| |#1|)) #2#) |#1| |#1| |#1|)) (SIGNATURE |extendedEuclidean| ((|Record| #3# #4# #5=(|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |rem| #6=(|#1| |#1| |#1|)) (SIGNATURE |quo| #6#) (SIGNATURE |sizeLess?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |expressIdealMember| ((|Maybe| #1#) #1# |#1|)) (SIGNATURE |principalIdeal| ((|Record| (|:| |coef| #1#) #5#) #1#)) (SIGNATURE |gcd| (|#1| #1#)) (SIGNATURE |gcd| #6#) (SIGNATURE |exquo| ((|Union| |#1| #2#) |#1| |#1|))) (|EuclideanDomain|)) (T |EuclideanDomain&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#4=($) 23 T CONST)) (|rem| (($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (($ $ $) 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #5=(|List| $)) (|:| |generator| $)) #5#) 66 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) 68 T ELT)) (|lcm| (#6=($ $ $) 60 T ELT) (#7=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#8=(|SparseUnivariatePolynomial| $) #8# #8#) 58 T ELT)) (|gcd| (#6# 62 T ELT) (#7# 61 T ELT)) (|extendedEuclidean| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #5#) #5# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|eval| (($ $ #1=(|List| |#2|) #1#) 14 T ELT) (($ $ |#2| |#2|) NIL T ELT) (($ $ #2=(|Equation| |#2|)) 11 T ELT) (($ $ (|List| #2#)) NIL T ELT))) 
(((|Evalable&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |eval| (|#1| |#1| (|List| #1=(|Equation| |#2|)))) (SIGNATURE |eval| (|#1| |#1| #1#)) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| #2=(|List| |#2|) #2#))) (|Evalable| |#2|) (|SetCategory|)) (T |Evalable&|)) 
NIL 
((|eval| (($ $ (|List| |#1|) (|List| |#1|)) 7 T ELT) (($ $ |#1| |#1|) 6 T ELT) (($ $ (|Equation| |#1|)) 13 T ELT) (($ $ (|List| (|Equation| |#1|))) 12 T ELT))) 
(((|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| #1=(|Integer|)) (|SymmetricPolynomial| (|Fraction| #1#))) 26 T ELT))) 
(((|EvaluateCycleIndicators| |#1|) (CATEGORY |package| (SIGNATURE |eval| (|#1| (|Mapping| |#1| #1=(|Integer|)) (|SymmetricPolynomial| #2=(|Fraction| #1#))))) (|Algebra| #2#)) (T |EvaluateCycleIndicators|)) 
((|eval| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *2 #1=(|Integer|))) (|isDomain| *4 (|SymmetricPolynomial| #2=(|Fraction| #1#))) (|isDomain| *1 (|EvaluateCycleIndicators| *2)) (|ofCategory| *2 (|Algebra| #2#))))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 7 T ELT)) (|before?| #1#) (= (#2# 9 T ELT))) 
(((|Exit|) (|SetCategory|)) (T |Exit|)) 
NIL 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|level| (((|Integer|) $) 13 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|ExitAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |expression| ((|SpadAst|) $)) (SIGNATURE |level| ((|Integer|) $))))) (T |ExitAst|)) 
((|expression| #1=(*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) #2=(|isDomain| *1 (|ExitAst|)))) (|level| #1# (AND (|isDomain| *2 (|Integer|)) #2#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 60 T ELT)) (|wholePart| (#5=(#6=(|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) $) NIL #7=(|has| #6# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #8=(#9=($ $) NIL T ELT)) (|unit?| #10=(#4# NIL T ELT)) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #6# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #8#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#19=(#20=(|Integer|) $) NIL #21=(|has| #6# (|OrderedIntegralDomain|)) ELT)) (|sample| #22=(#23=($) NIL T CONST)) (|retractIfCan| (((|Union| #6# . #24=(#13#)) . #25=($)) NIL T ELT) (((|Union| #26=(|Symbol|) . #24#) . #25#) NIL #27=(|has| #6# (|RetractableTo| #26#)) ELT) (((|Union| #28=(|Fraction| #20#) . #24#) . #25#) NIL #29=(|has| #6# (|RetractableTo| #20#)) ELT) (((|Union| #20# . #24#) . #25#) NIL #29# ELT) (((|Union| #30=(|UnivariatePuiseuxSeries| |#2| |#3| |#4|) . #24#) $) 26 T ELT)) (|retract| (#5# NIL T ELT) ((#26# . #31=($)) NIL #27# ELT) ((#28# . #31#) NIL #29# ELT) (#19# NIL #29# ELT) ((#30# . #31#) NIL T ELT)) (|rem| #32=(#33=($ $ $) NIL T ELT)) (|reducedSystem| ((#34=(|Matrix| #20#) . #35=(#36=(|Matrix| $))) NIL #37=(|has| #6# (|LinearlyExplicitRingOver| #20#)) ELT) ((#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #20#))) . #39=(#36# #40=(|Vector| $))) NIL #37# ELT) ((#41=(|Record| (|:| |mat| #42=(|Matrix| #6#)) (|:| |vec| (|Vector| #6#))) . #39#) NIL T ELT) ((#42# . #35#) NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#23# NIL #43=(|has| #6# (|IntegerNumberSystem|)) ELT)) (|quo| #32#) (|principalIdeal| (((|Record| (|:| |coef| #44=(|List| $)) #45=(|:| |generator| $)) #44#) NIL T ELT)) (|prime?| #10#) (|positive?| #46=(#4# NIL #21# ELT)) (|patternMatch| ((#47=(|PatternMatchResult| #20# . #48=($)) $ #49=(|Pattern| #20#) #47#) NIL (|has| #6# (|PatternMatchable| #20#)) ELT) ((#50=(|PatternMatchResult| #51=(|Float|) . #48#) $ #52=(|Pattern| #51#) #50#) NIL (|has| #6# (|PatternMatchable| #51#)) ELT)) (|opposite?| #1#) (|one?| #10#) (|numerator| #8#) (|numer| (#5# 22 T ELT)) (|nextItem| (#53=((|Maybe| $) $) NIL #54=(|has| #6# (|StepThrough|)) ELT)) (|negative?| #46#) (|multiEuclidean| (((|Union| #44# #13#) #44# $) NIL T ELT)) (|min| #55=(#33# NIL #56=(|has| #6# (|OrderedSet|)) ELT)) (|max| #55#) (|map| (($ #57=(|Mapping| #6# #6#) $) NIL T ELT)) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) #13#) $) 80 T ELT)) (|leftReducedSystem| ((#34# . #58=(#40#)) NIL #37# ELT) ((#38# . #59=(#40# $)) NIL #37# ELT) ((#41# . #59#) NIL T ELT) ((#42# . #58#) NIL T ELT)) (|lcm| #32# #60=(($ #44#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #8#) (|init| (#23# NIL #54# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #32# #60#) (|fractionPart| (#9# NIL #7# ELT)) (|floor| #61=(#5# NIL #43# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #62=(|:| |coef1| $) #63=(|:| |coef2| $) #45#) $ $) NIL T ELT) (((|Union| (|Record| #62# #63#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #44#) #44# $) NIL T ELT)) (|eval| (($ $ #64=(|List| #6#) #64#) NIL #65=(|has| #6# (|Evalable| #6#)) ELT) (($ $ #6# #6#) NIL #65# ELT) (($ $ #66=(|Equation| #6#)) NIL #65# ELT) (($ $ (|List| #66#)) NIL #65# ELT) (($ $ #67=(|List| #26#) #64#) NIL #68=(|has| #6# (|InnerEvalable| #26# #6#)) ELT) (($ $ #26# #6#) NIL #68# ELT)) (|euclideanSize| ((#69=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#70=($ $ #6#) NIL (|has| #6# (|Eltable| #6# #6#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #71=(($ $ #57#) NIL T ELT) #72=(($ $ #57# #69#) NIL T ELT) #73=(($ $ #26#) NIL #74=(|has| #6# (|PartialDifferentialSpace| #26#)) ELT) #75=(($ $ #67#) NIL #74# ELT) #76=(($ $ #26# #69#) NIL #74# ELT) #77=(($ $ #67# (|List| #69#)) NIL #74# ELT) #78=(#9# NIL #79=(|has| #6# (|DifferentialSpace|)) ELT) #80=(#81=($ $ #69#) NIL #79# ELT)) (|denominator| #8#) (|denom| (#5# 19 T ELT)) (|convert| ((#49# . #82=($)) NIL (|has| #6# (|ConvertibleTo| #49#)) ELT) ((#52# . #82#) NIL (|has| #6# (|ConvertibleTo| #52#)) ELT) ((#83=(|InputForm|) . #82#) NIL (|has| #6# (|ConvertibleTo| #83#)) ELT) ((#51# . #82#) NIL #84=(|has| #6# (|RealConstant|)) ELT) (((|DoubleFloat|) . #82#) NIL #84# ELT)) (|conditionP| (((|Union| #40# #13#) #36#) NIL #85=(AND (|has| $ #86=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) #8# (($ #28#) NIL T ELT) (($ #6#) 30 T ELT) (($ #26#) NIL #27# ELT) (($ #30#) 37 T ELT)) (|charthRoot| (#53# NIL (OR #85# (|has| #6# #86#)) ELT)) (|characteristic| ((#69#) NIL T CONST)) (|ceiling| #61#) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#9# NIL #21# ELT)) (|Zero| #22#) (|One| #22#) (D #71# #72# #73# #75# #76# #77# #78# #80#) (>= #87=(#2# NIL #56# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ (#33# 35 T ELT) (($ #6# #6#) 32 T ELT)) (- #8# #32#) (+ #32#) (** (($ $ #88=(|PositiveInteger|)) NIL T ELT) (#81# NIL T ELT) (($ $ #20#) NIL T ELT)) (* (($ #88# $) NIL T ELT) (($ #69# $) NIL T ELT) (($ #20# . #89=($)) NIL T ELT) #32# (($ $ #28#) NIL T ELT) (($ #28# . #89#) NIL T ELT) (($ #6# . #89#) 31 T ELT) (#70# NIL T ELT))) 
(((|ExponentialExpansion| |#1| |#2| |#3| |#4|) (|Join| (|QuotientFieldCategory| (|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|)) (|RetractableTo| #1=(|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (CATEGORY |domain| (SIGNATURE |limitPlus| ((|Union| (|OrderedCompletion| |#2|) "failed") $)) (SIGNATURE |coerce| ($ #1#)))) (|Join| (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#) (|GcdDomain|)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|)) (|Symbol|) |#2|) (T |ExponentialExpansion|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *4 *5 *6)) #1=(|ofCategory| *4 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))) #2=(|ofType| *5 (|Symbol|)) #3=(|ofType| *6 *4) #4=(|ofCategory| *3 (|Join| (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#) (|GcdDomain|))) #6=(|isDomain| *1 (|ExponentialExpansion| *3 *4 *5 *6)))) (|limitPlus| (*1 *2 *1) (|partial| AND #4# (|isDomain| *2 (|OrderedCompletion| *4)) #6# #1# #2# #3#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zerosOf| #4=((#5=(|List| $) $ #6=(|Symbol|)) NIL #7=(|has| |#1| (|IntegralDomain|)) ELT) #8=((#5# $) NIL #7# ELT) #9=((#5# #10=(|SparseUnivariatePolynomial| $) #6#) NIL #7# ELT) #11=((#5# #10#) NIL #7# ELT) #12=((#5# #13=(|Polynomial| $)) NIL #7# ELT)) (|zeroOf| #14=(#15=($ $ #6#) NIL #7# ELT) #16=(#17=($ $) NIL #7# ELT) (#18=($ #10# #6#) NIL #7# ELT) #19=(($ #10#) NIL #7# ELT) #20=(($ #13#) NIL #7# ELT)) (|zero?| (#21=(#3# $) 29 #22=(OR #23=(|has| |#1| (|AbelianSemiGroup|)) #24=(AND (|has| |#1| (|LinearlyExplicitRingOver| #25=(|Integer|))) #26=(|has| |#1| #27=(|Ring|)))) ELT)) (|variables| ((#28=(|List| #6#) $) 365 T ELT)) (|univariate| (((|Fraction| #10#) $ #29=(|Kernel| $)) NIL #7# ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #7# ELT)) (|unitCanonical| #16#) (|unit?| #30=(#21# NIL #7# ELT)) (|tower| (#31=(#32=(|List| #29#) $) NIL T ELT)) (|tanh| (#17# 170 #7# ELT)) (|tan| (#17# 146 #7# ELT)) (|summation| (#33=($ $ (|SegmentBinding| $)) 231 #7# ELT) (#15# 227 #7# ELT)) (|subtractIfCan| (#34=(#35=(|Union| $ #36="failed") $ $) NIL #37=(OR (|has| |#1| (|AbelianGroup|)) #24#) ELT)) (|subst| #38=(($ $ #39=(|Equation| $)) NIL T ELT) (#40=($ $ (|List| #39#)) 383 T ELT) (#41=($ $ #32# #5#) 438 T ELT)) (|squareFreePolynomial| (#42=((|Factored| #10#) #10#) 305 #43=(AND (|has| |#1| (|GcdDomain|)) #7#) ELT)) (|squareFreePart| #16#) (|squareFree| #44=((#45=(|Factored| $) $) NIL #7# ELT)) (|sqrt| #16#) (|sizeLess?| #46=(#2# NIL #7# ELT)) (|sinh| (#17# 166 #7# ELT)) (|sin| (#17# 142 #7# ELT)) (|simplifyPower| (#47=($ $ #25#) 68 #7# ELT)) (|sech| (#17# 174 #7# ELT)) (|sec| (#17# 150 #7# ELT)) (|sample| (#48=($) NIL (OR #23# #24# #49=(|has| |#1| (|SemiGroup|))) CONST)) (|rootsOf| #4# #8# #9# #11# #12#) (|rootOf| #14# #16# (#18# 133 #7# ELT) #19# #20#) (|retractIfCan| (#50=((|Union| #29# . #51=(#36#)) . #52=($)) 18 T ELT) (((|Union| #6# . #51#) . #52#) NIL T ELT) (((|Union| |#1| . #51#) $) 450 T ELT) (((|Union| #53=(|AlgebraicNumber|) . #51#) $) 333 #54=(AND #7# #55=(|has| |#1| #56=(|RetractableTo| #25#))) ELT) (((|Union| #25# . #51#) . #52#) NIL #55# ELT) (((|Union| #57=(|Fraction| #58=(|Polynomial| |#1|)) . #51#) . #52#) NIL #7# ELT) (((|Union| #58# . #51#) . #52#) NIL #26# ELT) (((|Union| #59=(|Fraction| #25#) . #51#) $) 48 #60=(OR #54# #61=(|has| |#1| (|RetractableTo| #59#))) ELT)) (|retract| ((#29# . #62=($)) 12 T ELT) ((#6# . #62#) NIL T ELT) (#63=(|#1| $) 429 T ELT) ((#53# . #62#) NIL #54# ELT) ((#25# . #62#) NIL #55# ELT) ((#57# . #62#) NIL #7# ELT) ((#58# . #62#) NIL #26# ELT) ((#59# $) 316 #60# ELT)) (|rem| #64=(#65=($ $ $) NIL #7# ELT)) (|reducedSystem| ((#66=(|Record| (|:| |mat| #67=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) #68=(|Matrix| $) #69=(|Vector| $)) 124 #26# ELT) ((#67# #68#) 114 #26# ELT) ((#70=(|Record| (|:| |mat| #71=(|Matrix| #25#)) (|:| |vec| (|Vector| #25#))) #68# #69#) NIL #24# ELT) ((#71# #68#) NIL #24# ELT)) (|reduce| (#17# 95 #7# ELT)) (|recip| ((#35# $) NIL #49# ELT)) (|quo| #64#) (|product| (#33# 235 #7# ELT) (#15# 233 #7# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #5#) #72=(|:| |generator| $)) #5#) NIL #7# ELT)) (|prime?| #30#) (|polygamma| (#65# 201 #7# ELT)) (|pi| (#48# 136 #7# ELT)) (|permutation| (#65# 221 #7# ELT)) (|patternMatch| ((#73=(|PatternMatchResult| #25# . #74=($)) $ #75=(|Pattern| #25#) #73#) 389 (|has| |#1| (|PatternMatchable| #25#)) ELT) ((#76=(|PatternMatchResult| #77=(|Float|) . #74#) $ #78=(|Pattern| #77#) #76#) 396 (|has| |#1| (|PatternMatchable| #77#)) ELT)) (|paren| #79=(#17# NIL T ELT) #80=(#81=($ #5#) NIL T ELT)) (|opposite?| (#2# NIL #22# ELT)) (|operators| ((#82=(|List| #83=(|BasicOperator|)) $) NIL T ELT)) (|operator| ((#83# #83#) 275 T ELT)) (|one?| (#21# 27 #49# ELT)) (|odd?| #84=(#21# NIL (|has| $ #56#) ELT)) (|numerator| (#17# 73 #26# ELT)) (|numer| (#85=(#86=(|SparseMultivariatePolynomial| |#1| #29#) $) 90 #26# ELT)) (|number?| (#21# 49 #7# ELT)) (|nthRoot| (#47# NIL #7# ELT)) (|multiEuclidean| ((#87=(|Union| #5# #36#) #5# $) NIL #7# ELT)) (|minPoly| ((#10# #29#) 276 #88=(|has| $ #27#) ELT)) (|map| (($ #89=(|Mapping| $ $) #29#) 434 T ELT)) (|mainKernel| (#50# NIL T ELT)) (|log| (#17# 140 #7# ELT)) (|li| (#17# 246 #7# ELT)) (|leftReducedSystem| ((#66# . #90=(#69# $)) NIL #26# ELT) ((#67# . #91=(#69#)) NIL #26# ELT) ((#70# . #90#) NIL #24# ELT) ((#71# . #91#) NIL #24# ELT)) (|lcm| #92=(#81# NIL #7# ELT) #64#) (|latex| (((|String|) $) NIL T ELT)) (|kernels| (#31# 51 T ELT)) (|kernel| #93=(($ #83# $) NIL T ELT) (#94=($ #83# #5#) 439 T ELT)) (|isTimes| (#95=(#87# $) NIL #49# ELT)) (|isPower| (((|Union| (|Record| (|:| |val| $) #96=(|:| |exponent| #25#)) #36#) $) NIL #26# ELT)) (|isPlus| (#95# 444 #23# ELT)) (|isMult| (((|Union| (|Record| (|:| |coef| #25#) #97=(|:| |var| #29#)) #36#) $) 448 #23# ELT)) (|isExpt| ((#98=(|Union| (|Record| #97# #96#) #36#) $) NIL #49# ELT) ((#98# $ #83#) NIL #26# ELT) ((#98# $ #6#) NIL #26# ELT)) (|is?| ((#3# $ #83#) NIL T ELT) (#99=(#3# $ #6#) 53 T ELT)) (|inv| (#17# NIL #100=(OR #101=(|has| |#1| (|Group|)) #7#) ELT)) (|integral| (#15# 250 #7# ELT) (#33# 252 #7# ELT)) (|height| (#102=(#103=(|NonNegativeInteger|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#21# 45 T ELT)) (|ground| (#63# NIL T ELT)) (|gcdPolynomial| ((#10# #10# #10#) 298 #7# ELT)) (|gcd| #92# #64#) (|freeOf?| #1# (#99# NIL T ELT)) (|factorials| (#15# 225 #7# ELT) (#17# 223 #7# ELT)) (|factorial| (#17# 217 #7# ELT)) (|factorPolynomial| (#42# 303 #43# ELT)) (|factor| #44#) (|extendedEuclidean| (((|Union| (|Record| #104=(|:| |coef1| $) #105=(|:| |coef2| $)) #36#) $ $ $) NIL #7# ELT) (((|Record| #104# #105# #72#) $ $) NIL #7# ELT)) (|exquo| (#34# NIL #7# ELT)) (|expressIdealMember| (((|Maybe| #5#) #5# $) NIL #7# ELT)) (|exp| (#17# 138 #7# ELT)) (|even?| #84#) (|eval| (($ $ #29# $) NIL T ELT) (#41# 433 T ELT) (#40# NIL T ELT) #38# (($ $ $ $) NIL T ELT) (($ $ #5# #5#) NIL T ELT) (($ $ #28# #106=(|List| #89#)) NIL T ELT) (($ $ #28# #107=(|List| #108=(|Mapping| $ #5#))) NIL T ELT) (($ $ #6# #108#) NIL T ELT) (($ $ #6# #89#) NIL T ELT) (($ $ #82# #106#) 376 T ELT) (($ $ #82# #107#) NIL T ELT) (($ $ #83# #108#) NIL T ELT) (($ $ #83# #89#) NIL T ELT) (#15# NIL #109=(|has| |#1| (|ConvertibleTo| #110=(|InputForm|))) ELT) (#111=($ $ #28#) NIL #109# ELT) (#17# NIL #109# ELT) (($ $ #83# $ #6#) 363 #109# ELT) (($ $ #82# #5# #6#) 362 #109# ELT) (($ $ #28# #112=(|List| #103#) #106#) NIL #26# ELT) (($ $ #28# #112# #107#) NIL #26# ELT) (($ $ #6# #103# #108#) NIL #26# ELT) (($ $ #6# #103# #89#) NIL #26# ELT)) (|euclideanSize| (#102# NIL #7# ELT)) (|erf| (#17# 238 #7# ELT)) (|elt| #93# (($ #83# $ $) NIL T ELT) (($ #83# $ $ $) NIL T ELT) (($ #83# $ $ $ $) NIL T ELT) (#94# NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #7# ELT)) (|distribute| #79# (#65# NIL T ELT)) (|dilog| (#17# 248 #7# ELT)) (|digamma| (#17# 199 #7# ELT)) (|differentiate| #113=(#15# NIL #26# ELT) #114=(#111# NIL #26# ELT) #115=(($ $ #6# #103#) NIL #26# ELT) #116=(($ $ #28# #112#) NIL #26# ELT)) (|denominator| (#17# 74 #7# ELT)) (|denom| (#85# 92 #7# ELT)) (|definingPolynomial| (#17# 314 #88# ELT)) (|csch| (#17# 176 #7# ELT)) (|csc| (#17# 152 #7# ELT)) (|coth| (#17# 172 #7# ELT)) (|cot| (#17# 148 #7# ELT)) (|cosh| (#17# 168 #7# ELT)) (|cos| (#17# 144 #7# ELT)) (|convert| ((#75# . #117=($)) NIL (|has| |#1| (|ConvertibleTo| #75#)) ELT) ((#78# . #117#) NIL (|has| |#1| (|ConvertibleTo| #78#)) ELT) (($ #45#) NIL #7# ELT) ((#110# $) 360 #109# ELT)) (|conjugate| #118=(#65# NIL #101# ELT)) (|commutator| #118#) (|coerce| (((|OutputForm|) $) 432 T ELT) (($ #29#) 423 T ELT) (($ #6#) 378 T ELT) (($ |#1|) 334 T ELT) #16# (($ #53#) 309 #54# ELT) (($ #86#) 94 #26# ELT) (($ #119=(|Fraction| |#1|)) NIL #7# ELT) (($ #120=(|Polynomial| #119#)) NIL #7# ELT) (($ (|Fraction| #120#)) NIL #7# ELT) (($ #57#) NIL #7# ELT) (($ #58#) NIL #26# ELT) (($ #25#) 36 (OR #55# #26#) ELT) (($ #59#) NIL (OR #7# #61#) ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#103#) NIL #26# CONST)) (|box| #79# #80#) (|binomial| (#65# 219 #7# ELT)) (|besselY| (#65# 205 #7# ELT)) (|besselK| (#65# 209 #7# ELT)) (|besselJ| (#65# 203 #7# ELT)) (|besselI| (#65# 207 #7# ELT)) (|belong?| ((#3# #83#) 10 T ELT)) (|before?| (#2# 85 T ELT)) (|atanh| (#17# 182 #7# ELT)) (|atan| (#17# 158 #7# ELT)) (|associates?| #46#) (|asinh| (#17# 178 #7# ELT)) (|asin| (#17# 154 #7# ELT)) (|asech| (#17# 186 #7# ELT)) (|asec| (#17# 162 #7# ELT)) (|applyQuote| (($ #6# $) NIL T ELT) (($ #6# $ $) NIL T ELT) (($ #6# $ $ $) NIL T ELT) (($ #6# $ $ $ $) NIL T ELT) (($ #6# #5#) NIL T ELT)) (|annihilate?| (#2# NIL #26# ELT)) (|airyBi| (#17# 213 #7# ELT)) (|airyAi| (#17# 211 #7# ELT)) (|acsch| (#17# 188 #7# ELT)) (|acsc| (#17# 164 #7# ELT)) (|acoth| (#17# 184 #7# ELT)) (|acot| (#17# 160 #7# ELT)) (|acosh| (#17# 180 #7# ELT)) (|acos| (#17# 156 #7# ELT)) (|abs| (#17# 191 #7# ELT)) (|Zero| (#48# 23 #22# CONST)) (|Si| (#17# 242 #7# ELT)) (|One| (#48# 25 #49# CONST)) (|Gamma| (#17# 193 #7# ELT) (#65# 195 #7# ELT)) (|Ei| (#17# 240 #7# ELT)) (D #113# #114# #115# #116#) (|Ci| (#17# 244 #7# ELT)) (|Beta| (#65# 197 #7# ELT)) (= (#2# 87 T ELT)) (/ (($ #86# #86#) 105 #7# ELT) (#65# 44 #100# ELT)) (- (#65# 42 #37# ELT) (#17# 31 #37# ELT)) (+ (#65# 40 #22# ELT)) (** (#65# 65 #7# ELT) (#121=($ $ #59#) 311 #7# ELT) (#47# 79 #100# ELT) (($ $ #103#) 75 #49# ELT) (($ $ #122=(|PositiveInteger|)) 83 #49# ELT)) (* (($ #59# . #123=($)) NIL #7# ELT) (#121# NIL #7# ELT) (($ $ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ |#1| . #123#) NIL #26# ELT) (#65# 38 #49# ELT) (($ #25# $) 34 #37# ELT) (($ #103# $) NIL #22# ELT) (($ #122# $) NIL #22# ELT))) 
(((|Expression| |#1|) (|Join| (|FunctionSpace| |#1|) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|AlgebraicallyClosedFunctionSpace| |#1|)) (ATTRIBUTE (|TranscendentalFunctionCategory|)) (ATTRIBUTE (|CombinatorialOpsCategory|)) (ATTRIBUTE (|LiouvillianFunctionCategory|)) (ATTRIBUTE (|SpecialFunctionCategory|)) (SIGNATURE |reduce| ($ $)) (SIGNATURE |number?| ((|Boolean|) $)) (SIGNATURE |simplifyPower| ($ $ #1=(|Integer|))) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |factorPolynomial| #2=((|Factored| #3=(|SparseUnivariatePolynomial| $)) #3#)) (SIGNATURE |squareFreePolynomial| #2#)) |%noBranch|) (IF (|has| |#1| (|RetractableTo| #1#)) (ATTRIBUTE (|RetractableTo| (|AlgebraicNumber|))) |%noBranch|)) |%noBranch|))) (|SetCategory|)) (T |Expression|)) 
((|reduce| (*1 *1 *1) (AND (|isDomain| *1 (|Expression| *2)) (|ofCategory| *2 #1=(|IntegralDomain|)) (|ofCategory| *2 #2=(|SetCategory|)))) (|number?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) #3=(|isDomain| *1 (|Expression| *3)) #4=(|ofCategory| *3 #1#) #5=(|ofCategory| *3 #2#))) (|simplifyPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #3# #4# #5#)) (|factorPolynomial| #6=(*1 *2 *3) #7=(AND (|isDomain| *2 (|Factored| #8=(|SparseUnivariatePolynomial| *1))) (|isDomain| *1 (|Expression| *4)) (|isDomain| *3 #8#) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *4 #1#) (|ofCategory| *4 #2#))) (|squareFreePolynomial| #6# #7#)) 
((|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) 13 T ELT))) 
(((|ExpressionFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)))) #1=(|SetCategory|) #1#) (T |ExpressionFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Expression| *5)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Expression| *6)) (|isDomain| *1 (|ExpressionFunctions2| *5 *6))))) 
((|taylor| ((#1=(|Any|) |#2| #2=(|Equation| |#2|) #3=(|NonNegativeInteger|)) 40 T ELT) (#4=(#1# |#2| #2#) 32 T ELT) ((#1# |#2| #3#) 35 T ELT) (#5=(#1# |#2|) 33 T ELT) (#6=(#1# (|Symbol|)) 26 T ELT)) (|series| (#7=(#1# |#2| #2# #8=(|Fraction| #9=(|Integer|))) 59 T ELT) (#4# 56 T ELT) (#10=(#1# |#2| #8#) 58 T ELT) (#5# 57 T ELT) (#6# 55 T ELT)) (|puiseux| (#7# 54 T ELT) (#4# 51 T ELT) (#10# 53 T ELT) (#5# 52 T ELT) (#6# 50 T ELT)) (|laurent| ((#1# |#2| #2# #9#) 47 T ELT) (#4# 44 T ELT) ((#1# |#2| #9#) 46 T ELT) (#5# 45 T ELT) (#6# 43 T ELT))) 
(((|ExpressionToUnivariatePowerSeries| |#1| |#2|) (CATEGORY |package| (SIGNATURE |taylor| #1=(#2=(|Any|) (|Symbol|))) (SIGNATURE |taylor| #3=(#2# |#2|)) (SIGNATURE |taylor| (#2# |#2| #4=(|NonNegativeInteger|))) (SIGNATURE |taylor| #5=(#2# |#2| #6=(|Equation| |#2|))) (SIGNATURE |taylor| (#2# |#2| #6# #4#)) (SIGNATURE |laurent| #1#) (SIGNATURE |laurent| #3#) (SIGNATURE |laurent| (#2# |#2| #7=(|Integer|))) (SIGNATURE |laurent| #5#) (SIGNATURE |laurent| (#2# |#2| #6# #7#)) (SIGNATURE |puiseux| #1#) (SIGNATURE |puiseux| #3#) (SIGNATURE |puiseux| #8=(#2# |#2| #9=(|Fraction| #7#))) (SIGNATURE |puiseux| #5#) (SIGNATURE |puiseux| #10=(#2# |#2| #6# #9#)) (SIGNATURE |series| #1#) (SIGNATURE |series| #3#) (SIGNATURE |series| #8#) (SIGNATURE |series| #5#) (SIGNATURE |series| #10#)) (|Join| (|GcdDomain|) (|RetractableTo| #7#) (|LinearlyExplicitRingOver| #7#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |ExpressionToUnivariatePowerSeries|)) 
((|series| #1=(*1 *2 *3 *4 *5) #2=(AND #3=(|isDomain| *4 (|Equation| *3)) (|isDomain| *5 #4=(|Fraction| #5=(|Integer|))) #6=(|ofCategory| *3 (|Join| #7=(|AlgebraicallyClosedField|) #8=(|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) #9=(|ofCategory| *6 #10=(|Join| #11=(|GcdDomain|) (|RetractableTo| #5#) (|LinearlyExplicitRingOver| #5#))) #12=(|isDomain| *2 (|Any|)) #13=(|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *6 *3)))) (|series| #14=(*1 *2 *3 *4) #15=(AND #3# #16=(|ofCategory| *3 (|Join| #7# #8# (|FunctionSpace| *5))) #17=(|ofCategory| *5 #10#) #12# #18=(|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *5 *3)))) (|series| #14# #19=(AND (|isDomain| *4 #4#) #17# #12# #18# #16#)) (|series| #20=(*1 *2 *3) #21=(AND #22=(|ofCategory| *4 #10#) #12# (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *3)) (|ofCategory| *3 #23=(|Join| #7# #8# (|FunctionSpace| *4))))) (|series| #20# #24=(AND (|isDomain| *3 (|Symbol|)) #22# #12# (|isDomain| *1 (|ExpressionToUnivariatePowerSeries| *4 *5)) (|ofCategory| *5 #23#))) (|puiseux| #1# #2#) (|puiseux| #14# #15#) (|puiseux| #14# #19#) (|puiseux| #20# #21#) (|puiseux| #20# #24#) (|laurent| #1# (AND #3# #6# (|ofCategory| *6 (|Join| #11# (|RetractableTo| *5) (|LinearlyExplicitRingOver| *5))) (|isDomain| *5 #5#) #12# #13#)) (|laurent| #14# #15#) (|laurent| #14# (AND (|isDomain| *4 #5#) (|ofCategory| *5 (|Join| #11# (|RetractableTo| *4) (|LinearlyExplicitRingOver| *4))) #12# #18# #16#)) (|laurent| #20# #21#) (|laurent| #20# #24#) (|taylor| #1# (AND #3# (|isDomain| *5 #25=(|NonNegativeInteger|)) #6# #9# #12# #13#)) (|taylor| #14# #15#) (|taylor| #14# (AND (|isDomain| *4 #25#) #17# #12# #18# #16#)) (|taylor| #20# #21#) (|taylor| #20# #24#)) 
((|seriesSolve| ((#1=(|Any|) |#2| #2=(|BasicOperator|) #3=(|Equation| |#2|) #4=(|List| |#2|)) 89 T ELT) ((#1# |#2| #2# #3# #3#) 85 T ELT) ((#1# |#2| #2# #3# |#2|) 87 T ELT) ((#1# #3# #2# #3# |#2|) 88 T ELT) ((#1# #4# #5=(|List| #2#) #3# #6=(|List| #3#)) 81 T ELT) ((#1# #4# #5# #3# #4#) 83 T ELT) ((#1# #6# #5# #3# #4#) 84 T ELT) ((#1# #6# #5# #3# #6#) 82 T ELT) ((#1# #3# #2# #3# #4#) 90 T ELT) ((#1# #3# #2# #3# #3#) 86 T ELT))) 
(((|ExpressionSpaceODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |seriesSolve| (#1=(|Any|) #2=(|Equation| |#2|) #3=(|BasicOperator|) #2# #2#)) (SIGNATURE |seriesSolve| (#1# #2# #3# #2# #4=(|List| |#2|))) (SIGNATURE |seriesSolve| (#1# #5=(|List| #2#) #6=(|List| #3#) #2# #5#)) (SIGNATURE |seriesSolve| (#1# #5# #6# #2# #4#)) (SIGNATURE |seriesSolve| (#1# #4# #6# #2# #4#)) (SIGNATURE |seriesSolve| (#1# #4# #6# #2# #5#)) (SIGNATURE |seriesSolve| (#1# #2# #3# #2# |#2|)) (SIGNATURE |seriesSolve| (#1# |#2| #3# #2# |#2|)) (SIGNATURE |seriesSolve| (#1# |#2| #3# #2# #2#)) (SIGNATURE |seriesSolve| (#1# |#2| #3# #2# #4#))) (|Join| (|IntegralDomain|) (|ConvertibleTo| (|InputForm|))) (|FunctionSpace| |#1|)) (T |ExpressionSpaceODESolver|)) 
((|seriesSolve| #1=(*1 *2 *3 *4 *5 *6) (AND #2=(|isDomain| *4 #3=(|BasicOperator|)) #4=(|isDomain| *5 (|Equation| *3)) (|isDomain| *6 (|List| *3)) (|ofCategory| *3 #5=(|FunctionSpace| *7)) #6=(|ofCategory| *7 #7=(|Join| (|IntegralDomain|) (|ConvertibleTo| (|InputForm|)))) #8=(|isDomain| *2 (|Any|)) (|isDomain| *1 (|ExpressionSpaceODESolver| *7 *3)))) (|seriesSolve| (*1 *2 *3 *4 *5 *5) #9=(AND #2# #4# (|ofCategory| *3 #10=(|FunctionSpace| *6)) #11=(|ofCategory| *6 #7#) #8# (|isDomain| *1 (|ExpressionSpaceODESolver| *6 *3)))) (|seriesSolve| #12=(*1 *2 *3 *4 *5 *3) #9#) (|seriesSolve| #13=(*1 *2 *3 *4 *3 *5) (AND (|isDomain| *3 (|Equation| *5)) #2# (|ofCategory| *5 #10#) #11# #8# (|isDomain| *1 (|ExpressionSpaceODESolver| *6 *5)))) (|seriesSolve| #1# (AND (|isDomain| *3 #14=(|List| *8)) #15=(|isDomain| *4 (|List| #3#)) (|isDomain| *6 #16=(|List| #17=(|Equation| *8))) #18=(|ofCategory| *8 #5#) #19=(|isDomain| *5 #17#) #6# #8# #20=(|isDomain| *1 (|ExpressionSpaceODESolver| *7 *8)))) (|seriesSolve| #12# (AND (|isDomain| *3 #21=(|List| *7)) #15# #22=(|isDomain| *5 #23=(|Equation| *7)) #24=(|ofCategory| *7 #10#) #11# #8# #25=(|isDomain| *1 (|ExpressionSpaceODESolver| *6 *7)))) (|seriesSolve| #1# (AND (|isDomain| *3 #16#) #15# #19# (|isDomain| *6 #14#) #18# #6# #8# #20#)) (|seriesSolve| #12# (AND (|isDomain| *3 (|List| #23#)) #15# #22# #24# #11# #8# #25#)) (|seriesSolve| #13# (AND (|isDomain| *3 #23#) #2# (|isDomain| *5 #21#) #24# #11# #8# #25#)) (|seriesSolve| (*1 *2 *3 *4 *3 *3) (AND (|isDomain| *3 (|Equation| *6)) #2# (|ofCategory| *6 (|FunctionSpace| *5)) (|ofCategory| *5 #7#) #8# (|isDomain| *1 (|ExpressionSpaceODESolver| *5 *6))))) 
((|tubePlot| ((#1=(|TubePlot| (|Plot3D|)) #2=(|Expression| #3=(|Integer|)) #2# #2# #4=(|Mapping| #5=(|DoubleFloat|) #5#) #6=(|Segment| #5#) #5# #3# #7=(|String|)) 67 T ELT) ((#1# #2# #2# #2# #4# #6# #5# #3#) 68 T ELT) ((#1# #2# #2# #2# #4# #6# #4# #3# #7#) 64 T ELT) ((#1# #2# #2# #2# #4# #6# #4# #3#) 65 T ELT)) (|constantToUnaryFunction| ((#4# #5#) 66 T ELT))) 
(((|ExpressionTubePlot|) (CATEGORY |package| (SIGNATURE |constantToUnaryFunction| (#1=(|Mapping| #2=(|DoubleFloat|) #2#) #2#)) (SIGNATURE |tubePlot| (#3=(|TubePlot| (|Plot3D|)) #4=(|Expression| #5=(|Integer|)) #4# #4# #1# #6=(|Segment| #2#) #1# #5#)) (SIGNATURE |tubePlot| (#3# #4# #4# #4# #1# #6# #1# #5# #7=(|String|))) (SIGNATURE |tubePlot| (#3# #4# #4# #4# #1# #6# #2# #5#)) (SIGNATURE |tubePlot| (#3# #4# #4# #4# #1# #6# #2# #5# #7#)))) (T |ExpressionTubePlot|)) 
((|tubePlot| (*1 *2 *3 *3 *3 *4 *5 *6 *7 *8) (AND #1=(|isDomain| *3 (|Expression| #2=(|Integer|))) #3=(|isDomain| *4 #4=(|Mapping| #5=(|DoubleFloat|) #5#)) #6=(|isDomain| *5 (|Segment| #5#)) #7=(|isDomain| *6 #5#) #8=(|isDomain| *7 #2#) (|isDomain| *8 #9=(|String|)) #10=(|isDomain| *2 (|TubePlot| (|Plot3D|))) #11=(|isDomain| *1 (|ExpressionTubePlot|)))) (|tubePlot| (*1 *2 *3 *3 *3 *4 *5 *6 *7) (AND #1# #3# #6# #7# #8# #10# #11#)) (|tubePlot| (*1 *2 *3 *3 *3 *4 *5 *4 *6 *7) (AND #1# #3# #6# #12=(|isDomain| *6 #2#) (|isDomain| *7 #9#) #10# #11#)) (|tubePlot| (*1 *2 *3 *3 *3 *4 *5 *4 *6) (AND #1# #3# #6# #12# #10# #11#)) (|constantToUnaryFunction| (*1 *2 *3) (AND (|isDomain| *2 #4#) #11# (|isDomain| *3 #5#)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 26 T ELT)) (|variables| ((#5=(|List| #6=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#7=(|Symbol|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|truncate| #11=(#12=($ $ #13=(|Fraction| #14=(|Integer|))) NIL T ELT) (($ $ #13# #13#) NIL T ELT)) (|terms| ((#15=(|Stream| (|Record| (|:| |k| #13#) (|:| |c| |#1|))) $) 20 T ELT)) (|tanh| #16=(#10# NIL #17=(|has| |#1| (|Algebra| #13#)) ELT)) (|tan| #16#) (|subtractIfCan| (#18=(#19=(|Union| $ #20="failed") $ $) NIL T ELT)) (|squareFreePart| #21=(#10# NIL #22=(|has| |#1| (|Field|)) ELT)) (|squareFree| #23=(((|Factored| $) $) NIL #22# ELT)) (|sqrt| #16#) (|sizeLess?| (#2# NIL #22# ELT)) (|sinh| #16#) (|sin| #16#) (|series| (($ #24=(|NonNegativeInteger|) #15#) NIL T ELT)) (|sech| #16#) (|sec| #16#) (|sample| #25=(#26=($) NIL T CONST)) (|rem| #27=(#28=($ $ $) NIL #22# ELT)) (|reductum| (#10# 36 T ELT)) (|recip| ((#19# $) NIL T ELT)) (|quo| #27#) (|principalIdeal| (((|Record| (|:| |coef| #29=(|List| $)) #30=(|:| |generator| $)) #29#) NIL #22# ELT)) (|prime?| (#4# NIL #22# ELT)) (|positive?| #31=(#4# NIL T ELT)) (|pole?| #31#) (|pi| (#26# NIL #17# ELT)) (|order| #32=(#33=(#13# $) NIL T ELT) ((#13# $ #13#) 16 T ELT)) (|opposite?| #1#) (|one?| #31#) (|nthRoot| (#34=($ $ #14#) NIL #17# ELT)) (|multiplyExponents| #35=(($ $ #36=(|PositiveInteger|)) NIL T ELT) #11#) (|multiEuclidean| (((|Union| #29# #20#) #29# $) NIL #22# ELT)) (|monomial?| #31#) (|monomial| (($ |#1| #13#) NIL T ELT) (($ $ #6# #13#) NIL T ELT) (($ $ #5# (|List| #13#)) NIL T ELT)) (|min| #37=(#28# NIL T ELT)) (|max| #37#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #16#) (|leadingMonomial| #38=(#10# NIL T ELT)) (|leadingCoefficient| #39=((|#1| $) NIL T ELT)) (|lcm| #40=(($ #29#) NIL #22# ELT) #27#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #21#) (|integrate| #16# (#41=($ $ #7#) NIL (OR (AND #17# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #14#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #17# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |variables| (#42=(|List| #7#) |#1|))))) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#43=(|SparseUnivariatePolynomial| $) #43# #43#) NIL #22# ELT)) (|gcd| #40# #27#) (|factor| #23#) (|extendedEuclidean| (((|Union| (|Record| #44=(|:| |coef1| $) #45=(|:| |coef2| $)) #20#) $ $ $) NIL #22# ELT) (((|Record| #44# #45# #30#) $ $) NIL #22# ELT)) (|extend| #11#) (|exquo| (#18# NIL #8# ELT)) (|expressIdealMember| (((|Maybe| #29#) #29# $) NIL #22# ELT)) (|exponentialOrder| (#33# 17 T ELT)) (|exponential| (($ #46=(|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) 11 T ELT)) (|exponent| ((#46# $) 12 T ELT)) (|exp| #16#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #47=(|has| |#1| (SIGNATURE ** (|#1| |#1| #13#))) ELT)) (|euclideanSize| ((#24# $) NIL #22# ELT)) (|elt| (#48=(|#1| $ #13#) NIL T ELT) (#28# NIL (|has| #13# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #22# ELT)) (|differentiate| #49=(#41# NIL #50=(AND (|has| |#1| (|PartialDifferentialRing| #7#)) #51=(|has| |#1| (SIGNATURE * (|#1| #13# |#1|)))) ELT) #52=(($ $ #42#) NIL #50# ELT) #53=(($ $ #7# #24#) NIL #50# ELT) #54=(($ $ #42# (|List| #24#)) NIL #50# ELT) #55=(#10# NIL #51# ELT) #56=(#57=($ $ #24#) NIL #51# ELT)) (|degree| #32#) (|csch| #16#) (|csc| #16#) (|coth| #16#) (|cot| #16#) (|cosh| #16#) (|cos| #16#) (|complete| (#10# 10 T ELT)) (|coerce| (((|OutputForm|) $) 42 T ELT) (($ #14#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #13#) NIL #17# ELT) #9#) (|coefficient| (#48# 34 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#24#) NIL T CONST)) (|center| #39#) (|before?| #1#) (|atanh| #16#) (|atan| #16#) (|associates?| (#2# NIL #8# ELT)) (|asinh| #16#) (|asin| #16#) (|asech| #16#) (|asec| #16#) (|approximate| (#48# NIL (AND #47# (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| #1#) (|acsch| #16#) (|acsc| #16#) (|acoth| #16#) (|acot| #16#) (|acosh| #16#) (|acos| #16#) (|Zero| #25#) (|One| #25#) (D #49# #52# #53# #54# #55# #56#) (>= #1#) (> #1#) (= (#2# 28 T ELT)) (<= #1#) (< (#2# 37 T ELT)) (/ (#58=($ $ |#1|) NIL #22# ELT) #27#) (- #38# #37#) (+ #37#) (** #35# (#57# NIL T ELT) (#34# NIL #22# ELT) (#28# NIL #17# ELT) #59=(#12# NIL #17# ELT)) (* (($ #36# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #14# . #60=($)) NIL T ELT) #37# (#58# NIL T ELT) (($ |#1| . #60#) NIL T ELT) (($ #13# . #60#) NIL #17# ELT) #59#)) 
(((|ExponentialOfUnivariatePuiseuxSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesCategory| |#1|) (|OrderedAbelianMonoid|) (CATEGORY |domain| (SIGNATURE |exponential| ($ #1=(|UnivariatePuiseuxSeries| |#1| |#2| |#3|))) (SIGNATURE |exponent| (#1# $)) (SIGNATURE |exponentialOrder| ((|Fraction| (|Integer|)) $)))) (|Field|) (|Symbol|) |#1|) (T |ExponentialOfUnivariatePuiseuxSeries|)) 
((|exponential| (*1 *1 *2) (AND #1=(|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)) #2=(|ofCategory| *3 (|Field|)) #3=(|ofType| *4 (|Symbol|)) #4=(|ofType| *5 *3) #5=(|isDomain| *1 (|ExponentialOfUnivariatePuiseuxSeries| *3 *4 *5)))) (|exponent| #6=(*1 *2 *1) (AND #1# #5# #2# #3# #4#)) (|exponentialOrder| #6# (AND (|isDomain| *2 (|Fraction| (|Integer|))) #5# #2# #3# #4#))) 
((|nthRoot| (((|Record| (|:| |exponent| #1=(|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) #2=(|Factored| |#1|) #1#) 35 T ELT)) (|log| (((|List| (|Record| (|:| |coef| #1#) (|:| |logand| |#1|))) #2#) 40 T ELT))) 
(((|FactoredFunctions| |#1|) (CATEGORY |package| (SIGNATURE |nthRoot| ((|Record| (|:| |exponent| #1=(|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) #2=(|Factored| |#1|) #1#)) (SIGNATURE |log| ((|List| (|Record| (|:| |coef| #1#) (|:| |logand| |#1|))) #2#))) (|IntegralDomain|)) (T |FactoredFunctions|)) 
((|log| (*1 *2 *3) (AND (|isDomain| *3 (|Factored| *4)) (|ofCategory| *4 #1=(|IntegralDomain|)) (|isDomain| *2 (|List| (|Record| (|:| |coef| #2=(|NonNegativeInteger|)) (|:| |logand| *4)))) (|isDomain| *1 (|FactoredFunctions| *4)))) (|nthRoot| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Factored| *5)) (|ofCategory| *5 #1#) (|isDomain| *2 (|Record| (|:| |exponent| #2#) (|:| |coef| *5) (|:| |radicand| (|List| *5)))) (|isDomain| *1 (|FactoredFunctions| *5)) (|isDomain| *4 #2#)))) 
((|variables| ((#1=(|List| |#2|) #2=(|SparseUnivariatePolynomial| |#4|)) 45 T ELT)) (|ran| ((|#3| #3=(|Integer|)) 48 T ELT)) (|raisePolynomial| ((#2# #4=(|SparseUnivariatePolynomial| |#3|)) 30 T ELT)) (|normalDeriv| ((#2# #2# #3#) 67 T ELT)) (|lowerPolynomial| ((#4# #2#) 21 T ELT)) (|degree| (((|List| (|NonNegativeInteger|)) #2# #1#) 41 T ELT)) (|completeEval| ((#4# #2# #1# (|List| |#3|)) 35 T ELT))) 
(((|FactoringUtilities| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |completeEval| (#1=(|SparseUnivariatePolynomial| |#3|) #2=(|SparseUnivariatePolynomial| |#4|) #3=(|List| |#2|) (|List| |#3|))) (SIGNATURE |degree| ((|List| (|NonNegativeInteger|)) #2# #3#)) (SIGNATURE |variables| (#3# #2#)) (SIGNATURE |lowerPolynomial| (#1# #2#)) (SIGNATURE |raisePolynomial| (#2# #1#)) (SIGNATURE |normalDeriv| (#2# #2# #4=(|Integer|))) (SIGNATURE |ran| (|#3| #4#))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Ring|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |FactoringUtilities|)) 
((|ran| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 (|Integer|)) #3=(|ofCategory| *4 #4=(|OrderedAbelianMonoidSup|)) #5=(|ofCategory| *5 #6=(|OrderedSet|)) (|ofCategory| *2 #7=(|Ring|)) (|isDomain| *1 (|FactoringUtilities| *4 *5 *2 *6)) (|ofCategory| *6 (|PolynomialCategory| *2 *4 *5)))) (|normalDeriv| (*1 *2 *2 *3) (AND #8=(|isDomain| *2 #9=(|SparseUnivariatePolynomial| *7)) #2# #10=(|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) #3# #5# #11=(|ofCategory| *6 #7#) #12=(|isDomain| *1 (|FactoringUtilities| *4 *5 *6 *7)))) (|raisePolynomial| #1# (AND (|isDomain| *3 #13=(|SparseUnivariatePolynomial| *6)) #11# #3# #5# #8# #12# #10#)) (|lowerPolynomial| #1# (AND #14=(|isDomain| *3 #9#) #10# #3# #5# #11# (|isDomain| *2 #13#) #12#)) (|variables| #1# (AND #14# #10# #3# #5# #11# (|isDomain| *2 (|List| *5)) #12#)) (|degree| (*1 *2 *3 *4) (AND (|isDomain| *3 #15=(|SparseUnivariatePolynomial| *8)) (|isDomain| *4 (|List| *6)) (|ofCategory| *6 #6#) (|ofCategory| *8 (|PolynomialCategory| *7 *5 *6)) (|ofCategory| *5 #4#) (|ofCategory| *7 #7#) (|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 #6#) (|ofCategory| *8 #7#) (|ofCategory| *9 (|PolynomialCategory| *8 *6 *7)) (|ofCategory| *6 #4#) (|isDomain| *2 #15#) (|isDomain| *1 (|FactoringUtilities| *6 *7 *8 *9))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 19 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #4=(|Integer|)))) $) 21 T ELT)) (|subtractIfCan| (((|Union| $ #5="failed") $ $) NIL T ELT)) (|size| ((#6=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| #7=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #5#) $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #4#) NIL T ELT)) (|nthCoef| ((#4# $ #4#) NIL T ELT)) (|min| #8=(#9=($ $ $) NIL #10=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #8#) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapCoef| (($ (|Mapping| #4# #4#) $) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#9# NIL (|has| #4# (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((#4# |#1| $) NIL T ELT)) (|before?| #1#) (|Zero| #7#) (>= #11=(#2# NIL #10# ELT)) (> #11#) (= #1#) (<= #11#) (< (#2# 30 #10# ELT)) (- (($ $) 12 T ELT) (#9# 29 T ELT)) (+ (#9# NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #6# $) NIL T ELT) (($ #4# $) NIL T ELT) (($ $ #4#) NIL T ELT) (($ #4# |#1|) 28 T ELT))) 
(((|FreeAbelianGroup| |#1|) (|Join| (|AbelianGroup|) (|Module| #1=(|Integer|)) (|FreeAbelianMonoidCategory| |#1| #1#) (CATEGORY |package| (IF (|has| |#1| #2=(|OrderedSet|)) (ATTRIBUTE #2#) |%noBranch|))) (|SetCategory|)) (T |FreeAbelianGroup|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 34 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|size| (((|NonNegativeInteger|) $) 35 T ELT)) (|sample| (#3=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 39 T ELT)) (|retract| ((|#1| $) 40 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|nthFactor| ((|#1| $ (|Integer|)) 32 T ELT)) (|nthCoef| ((|#2| $ (|Integer|)) 33 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 29 T ELT)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 30 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|highCommonTerms| (($ $ $) 28 (|has| |#2| (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 38 T ELT)) (|coefficient| ((|#2| |#1| $) 31 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT) (($ |#1| $) 37 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ |#2| |#1|) 36 T ELT))) 
(((|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) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #3=(|NonNegativeInteger|)))) $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|size| ((#3# $) NIL T ELT)) (|sample| #5=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #4#) $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #6=(|Integer|)) NIL T ELT)) (|nthCoef| ((#3# $ #6#) NIL T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapCoef| (($ (|Mapping| #3# #3#) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#7=($ $ $) NIL (|has| #3# (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((#3# |#1| $) NIL T ELT)) (|before?| #1#) (|Zero| #5#) (= #1#) (+ (#7# NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #3# $) NIL T ELT) (($ #3# |#1|) NIL T ELT))) 
(((|FreeAbelianMonoid| |#1|) (|FreeAbelianMonoidCategory| |#1| (|NonNegativeInteger|)) (|SetCategory|)) (T |FreeAbelianMonoid|)) 
NIL 
((|primitivePart| (($ $) 72 T ELT)) (|pomopo!| (($ $ |#2| |#3| $) 14 T ELT)) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) 51 T ELT)) (|ground?| (((|Boolean|) $) 42 T ELT)) (|ground| (#1=(|#2| $) 44 T ELT)) (|exquo| ((#2=(|Union| $ "failed") $ $) NIL T ELT) ((#2# $ |#2|) 64 T ELT)) (|content| (#1# 68 T ELT)) (|coefficients| (((|List| |#2|) $) 56 T ELT)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 37 T ELT)) (/ (($ $ |#2|) 60 T ELT))) 
(((|FiniteAbelianMonoidRing&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| #1=(|#2| |#1|)) (SIGNATURE |exquo| (#2=(|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| #1#) (SIGNATURE |ground?| ((|Boolean|) |#1|)) (SIGNATURE |exquo| (#2# |#1| |#1|)) (SIGNATURE / (|#1| |#1| |#2|))) (|FiniteAbelianMonoidRing| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |FiniteAbelianMonoidRing&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 75 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 110 (|has| |#1| . #9=((|RetractableTo| #6#))) ELT) (((|Union| #10=(|Fraction| #6#) . #7#) . #8#) 108 (|has| |#1| . #11=((|RetractableTo| #10#))) ELT) (((|Union| |#1| . #7#) . #8#) 105 T ELT)) (|retract| ((#6# . #12=($)) 109 (|has| |#1| . #9#) ELT) ((#10# . #12#) 107 (|has| |#1| . #11#) ELT) ((|#1| . #12#) 106 T ELT)) (|reductum| (#13=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (($ $) 94 (|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| |#2| $) 98 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 101 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| |#2|) 82 T ELT)) (|minimumDegree| ((|#2| $) 100 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) 99 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|leadingMonomial| (#13# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|ground?| (((|Boolean|) $) 104 T ELT)) (|ground| ((|#1| $) 103 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #3#) ELT) (((|Union| $ "failed") $ |#1|) 96 (|has| |#1| (|IntegralDomain|)) ELT)) (|degree| ((|#2| $) 84 T ELT)) (|content| ((|#1| $) 95 (|has| |#1| (|GcdDomain|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 70 (|has| |#1| . #3#) ELT) (($ |#1|) 68 T ELT) (($ #14=(|Fraction| (|Integer|))) 78 (OR (|has| |#1| . #11#) (|has| |#1| . #15=((|Algebra| #14#)))) ELT)) (|coefficients| (((|List| |#1|) $) 102 T ELT)) (|coefficient| ((|#1| $ |#2|) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 97 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 74 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #16=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #16#) 88 T ELT) (($ #14# . #16#) 77 (|has| |#1| . #15#) ELT) (($ $ #14#) 76 (|has| |#1| . #15#) ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |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|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |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) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) NIL #6=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #7=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#8=(#3# $) NIL #9=(|has| |#1| #10=(|OrderedSet|)) ELT)) (|sort!| (#11=($ #7# $) NIL #6# ELT) (#12=($ $) NIL (AND #6# #9#) ELT)) (|sort| (#11# NIL T ELT) (#12# NIL #9# ELT)) (|shrinkable| ((#3# #3#) NIL T ELT)) (|setelt| #13=(#14=(|#1| $ #5# |#1|) NIL #6# ELT) ((|#1| $ #15=(|UniversalSegment| #5#) |#1|) NIL #6# ELT)) (|select!| #16=(#17=($ #18=(|Mapping| #3# |#1|) $) NIL T ELT)) (|select| #19=(#17# NIL #20=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#21=($) NIL T CONST)) (|reverse!| (#12# NIL #6# ELT)) (|reverse| #22=(#12# NIL T ELT)) (|removeDuplicates!| (#12# NIL #4# ELT)) (|removeDuplicates| (#12# NIL #23=(AND #20# #4#) ELT)) (|remove!| (#24=($ |#1| $) NIL #4# ELT) #16#) (|remove| (#24# NIL #23# ELT) #19#) (|reduce| ((|#1| #25=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #25# $ |#1|) NIL T ELT) ((|#1| #25# $) NIL T ELT)) (|qsetelt!| #13#) (|qelt| #26=((|#1| $ #5#) NIL T ELT)) (|position| ((#5# #18# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT) ((#5# |#1| $ #5#) NIL #4# ELT)) (|physicalLength!| #27=(($ $ #5#) NIL T ELT)) (|physicalLength| #28=((#29=(|NonNegativeInteger|) $) NIL T ELT)) (|new| (($ #29# |#1|) NIL T ELT)) (|minIndex| #30=((#5# $) NIL #31=(|has| #5# #10#) ELT)) (|min| #32=(#33=($ $ $) NIL #9# ELT)) (|merge!| #32# #34=(($ #7# $ $) NIL T ELT)) (|merge| #34# #32#) (|members| #35=((#36=(|List| |#1|) $) NIL T ELT)) (|member?| (#37=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| #30#) (|max| #32#) (|map!| #38=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #38# (($ #25# $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #39=(|has| |#1| (|SetCategory|)) ELT)) (|insert!| #40=(#41=($ $ $ #5#) NIL T ELT) #42=(($ |#1| $ #5#) NIL T ELT)) (|insert| #42# #40#) (|indices| (((|List| #5#) $) NIL T ELT)) (|index?| ((#3# #5# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #39# ELT)) (|flexibleArray| #43=(($ #36#) NIL T ELT)) (|first| ((|#1| $) NIL #31# ELT)) (|find| (((|Union| |#1| "failed") #18# $) NIL T ELT)) (|fill!| (#44=($ $ |#1|) NIL #6# ELT)) (|every?| #45=((#3# #18# $) NIL T ELT)) (|eval| (($ $ (|List| #46=(|Equation| |#1|))) NIL #47=(AND (|has| |#1| (|Evalable| |#1|)) #39#) ELT) (($ $ #46#) NIL #47# ELT) (($ $ |#1| |#1|) NIL #47# ELT) (($ $ #36# #36#) NIL #47# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#37# NIL #23# ELT)) (|entries| #35#) (|empty?| (#8# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#14# NIL T ELT) #26# #48=(($ $ #15#) NIL T ELT)) (|delete!| #48# #27#) (|delete| #27# #48#) (|count| ((#29# |#1| $) NIL #4# ELT) ((#29# #18# $) NIL T ELT)) (|copyInto!| (#41# NIL #6# ELT)) (|copy| #22#) (|convert| ((#49=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #49#)) ELT)) (|construct| #43#) (|concat!| #50=(#33# NIL T ELT) #51=(#44# NIL T ELT)) (|concat| #51# (#24# NIL T ELT) #50# (($ (|List| $)) NIL T ELT)) (|coerce| ((#52=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #52#)) ELT)) (|before?| #1#) (|any?| #45#) (>= #53=(#2# NIL #9# ELT)) (> #53#) (= #1#) (<= #53#) (< #53#) (|#| #28#)) 
(((|FlexibleArray| |#1|) (|Join| (|OneDimensionalArrayAggregate| |#1|) (|ExtensibleLinearAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |flexibleArray| ($ (|List| |#1|))) (SIGNATURE |physicalLength| ((|NonNegativeInteger|) $)) (SIGNATURE |physicalLength!| ($ $ (|Integer|))) (SIGNATURE |shrinkable| (#1=(|Boolean|) #1#)))) (|Type|)) (T |FlexibleArray|)) 
((|flexibleArray| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Type|)) #2=(|isDomain| *1 (|FlexibleArray| *3)))) (|physicalLength| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) #2# #1#)) (|physicalLength!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #2# #1#)) (|shrinkable| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) #2# #1#))) 
((|transcendent?| (#1=((|Boolean|) $) 47 T ELT)) (|transcendenceDegree| (#2=((|NonNegativeInteger|)) 23 T ELT)) (|trace| (#3=(|#2| $) 51 T ELT) (#4=($ $ #5=(|PositiveInteger|)) 123 T ELT)) (|size| (#2# 124 T ELT)) (|represents| (($ #6=(|Vector| |#2|)) 20 T ELT)) (|normal?| (#1# 136 T ELT)) (|norm| (#3# 53 T ELT) (#4# 120 T ELT)) (|minimalPolynomial| (#7=(#8=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT) (((|SparseUnivariatePolynomial| $) $ #5#) 111 T ELT)) (|linearAssociatedOrder| (#7# 95 T ELT)) (|linearAssociatedLog| (#7# 91 T ELT) (((|Union| #8# "failed") $ $) 88 T ELT)) (|linearAssociatedExp| (($ $ #8#) 58 T ELT)) (|extensionDegree| ((#9=(|OnePointCompletion| #5#)) 30 T ELT) ((#5#) 48 T ELT)) (|dimension| (((|CardinalNumber|)) 27 T ELT)) (|degree| ((#9# $) 32 T ELT) ((#5# $) 139 T ELT)) (|createNormalElement| (($) 130 T ELT)) (|coordinates| ((#6# $) NIL T ELT) (((|Matrix| |#2|) (|Vector| $)) 42 T ELT)) (|charthRoot| (($ $) NIL T ELT) (((|Maybe| $) $) 100 T ELT)) (|algebraic?| (#1# 45 T ELT))) 
(((|FiniteAlgebraicExtensionField&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |charthRoot| ((|Maybe| |#1|) |#1|)) (SIGNATURE |size| #1=((|NonNegativeInteger|))) (SIGNATURE |charthRoot| (|#1| |#1|)) (SIGNATURE |linearAssociatedLog| ((|Union| #2=(|SparseUnivariatePolynomial| |#2|) "failed") |#1| |#1|)) (SIGNATURE |linearAssociatedLog| #3=(#2# |#1|)) (SIGNATURE |linearAssociatedOrder| #3#) (SIGNATURE |linearAssociatedExp| (|#1| |#1| #2#)) (SIGNATURE |normal?| #4=((|Boolean|) |#1|)) (SIGNATURE |createNormalElement| (|#1|)) (SIGNATURE |trace| #5=(|#1| |#1| #6=(|PositiveInteger|))) (SIGNATURE |norm| #5#) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |#1|) |#1| #6#)) (SIGNATURE |trace| #7=(|#2| |#1|)) (SIGNATURE |norm| #7#) (SIGNATURE |degree| (#6# |#1|)) (SIGNATURE |extensionDegree| (#6#)) (SIGNATURE |minimalPolynomial| #3#) (SIGNATURE |represents| (|#1| #8=(|Vector| |#2|))) (SIGNATURE |coordinates| ((|Matrix| |#2|) (|Vector| |#1|))) (SIGNATURE |coordinates| (#8# |#1|)) (SIGNATURE |transcendenceDegree| #1#) (SIGNATURE |extensionDegree| (#9=(|OnePointCompletion| #6#))) (SIGNATURE |degree| (#9# |#1|)) (SIGNATURE |transcendent?| #4#) (SIGNATURE |algebraic?| #4#) (SIGNATURE |dimension| ((|CardinalNumber|)))) (|FiniteAlgebraicExtensionField| |#2|) (|Field|)) (T |FiniteAlgebraicExtensionField&|)) 
((|dimension| #1=(*1 *2) (AND #2=(|ofCategory| *4 (|Field|)) (|isDomain| *2 (|CardinalNumber|)) #3=(|isDomain| *1 (|FiniteAlgebraicExtensionField&| *3 *4)) #4=(|ofCategory| *3 (|FiniteAlgebraicExtensionField| *4)))) (|extensionDegree| #1# (AND #2# (|isDomain| *2 (|OnePointCompletion| #5=(|PositiveInteger|))) #3# #4#)) (|transcendenceDegree| #1# #6=(AND #2# (|isDomain| *2 (|NonNegativeInteger|)) #3# #4#)) (|extensionDegree| #1# (AND #2# (|isDomain| *2 #5#) #3# #4#)) (|size| #1# #6#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|transcendent?| (#4=((|Boolean|) $) 114 T ELT)) (|transcendenceDegree| ((#5=(|NonNegativeInteger|)) 110 T ELT)) (|trace| ((|#1| $) 162 T ELT) (($ $ (|PositiveInteger|)) 159 (|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #6=(|PositiveInteger|) #7=(|NonNegativeInteger|)) #8=(|Integer|)) 144 (|has| |#1| . #9=((|Finite|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#10=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|size| (((|NonNegativeInteger|)) 134 (|has| |#1| . #9#) ELT)) (|sample| (#11=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 121 T ELT)) (|retract| ((|#1| $) 122 T ELT)) (|represents| (($ (|Vector| |#1|)) 168 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 150 (|has| |#1| . #9#) ELT)) (|rem| (#12=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|random| (($) 131 (|has| |#1| . #9#) ELT)) (|quo| (#12# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #13=(|List| $)) (|:| |generator| $)) #13#) 66 T ELT)) (|primitiveElement| (#14=($) 146 (|has| |#1| . #9#) ELT)) (|primitive?| (((|Boolean|) $) 147 (|has| |#1| . #9#) ELT)) (|primeFrobenius| (($ $ #15=(|NonNegativeInteger|)) 107 (OR (|has| |#1| . #16=((|CharacteristicNonZero|))) (|has| |#1| . #17=((|Finite|)))) ELT) (($ $) 106 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| ((#6# $) 149 (|has| |#1| . #9#) ELT) (((|OnePointCompletion| (|PositiveInteger|)) $) 104 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|normalElement| (($) 157 (|has| |#1| (|Finite|)) ELT)) (|normal?| (((|Boolean|) $) 156 (|has| |#1| (|Finite|)) ELT)) (|norm| ((|#1| $) 163 T ELT) (($ $ (|PositiveInteger|)) 160 (|has| |#1| (|Finite|)) ELT)) (|nextItem| (((|Maybe| $) $) 135 (|has| |#1| . #9#) ELT)) (|multiEuclidean| (((|Union| #18=(|List| $) #19="failed") #18# $) 68 T ELT)) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 167 T ELT) (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) 161 (|has| |#1| (|Finite|)) ELT)) (|lookup| ((#20=(|PositiveInteger|) $) 132 (|has| |#1| . #9#) ELT)) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) 153 (|has| |#1| (|Finite|)) ELT)) (|linearAssociatedLog| (((|SparseUnivariatePolynomial| |#1|) $) 152 (|has| |#1| (|Finite|)) ELT) (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) 151 (|has| |#1| (|Finite|)) ELT)) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) 154 (|has| |#1| (|Finite|)) ELT)) (|lcm| (#21=($ $ $) 60 T ELT) (#22=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|init| (($) 136 (|has| |#1| . #9#) CONST)) (|index| (($ #20#) 133 (|has| |#1| . #9#) ELT)) (|inGroundField?| (#4# 113 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (($) 155 (|has| |#1| (|Finite|)) ELT)) (|gcdPolynomial| ((#23=(|SparseUnivariatePolynomial| $) #23# #23#) 58 T ELT)) (|gcd| (#21# 62 T ELT) (#22# 61 T ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #8#) (|:| |exponent| #8#)))) 143 (|has| |#1| . #9#) ELT)) (|factor| (#10# 92 T ELT)) (|extensionDegree| ((#24=(|OnePointCompletion| (|PositiveInteger|))) 111 T ELT) (((|PositiveInteger|)) 165 T ELT)) (|extendedEuclidean| (((|Record| #25=(|:| |coef1| $) #26=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #25# #26#) #19#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #13#) #13# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| ((#7# $) 148 (|has| |#1| . #9#) ELT) (((|Union| #15# "failed") $ $) 105 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|dimension| (((|CardinalNumber|)) 119 T ELT)) (|differentiate| (#27=($ $ (|NonNegativeInteger|)) 139 (|has| |#1| . #9#) ELT) (($ . #28=($)) 137 (|has| |#1| . #9#) ELT)) (|degree| ((#24# $) 112 T ELT) (((|PositiveInteger|) $) 164 T ELT)) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) 166 T ELT)) (|createPrimitiveElement| (#14# 145 (|has| |#1| . #9#) ELT)) (|createNormalElement| (($) 158 (|has| |#1| (|Finite|)) ELT)) (|coordinates| (((|Vector| |#1|) $) 170 T ELT) (((|Matrix| |#1|) (|Vector| $)) 169 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 142 (|has| |#1| . #9#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #29=(|Fraction| #30=(|Integer|))) 84 T ELT) (($ |#1|) 120 T ELT)) (|charthRoot| (($ $) 141 (|has| |#1| . #9#) ELT) (((|Maybe| $) $) 103 (OR (|has| |#1| . #16#) (|has| |#1| . #17#)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 172 T ELT) (((|Vector| $) (|PositiveInteger|)) 171 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|algebraic?| (#4# 115 T ELT)) (|Zero| (#11# 24 T CONST)) (|One| (($) 45 T CONST)) (|Frobenius| (($ $) 109 (|has| |#1| . #17#) ELT) (($ $ #5#) 108 (|has| |#1| . #17#) ELT)) (D (#27# 140 (|has| |#1| . #9#) ELT) (($ . #28#) 138 (|has| |#1| . #9#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT) (($ $ |#1|) 118 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #30#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #31=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #29#) 86 T ELT) (($ #29# . #31#) 85 T ELT) (($ $ |#1|) 117 T ELT) (($ |#1| . #31#) 116 T ELT))) 
(((|FiniteAlgebraicExtensionField| |#1|) (|Category|) (|Field|)) (T |FiniteAlgebraicExtensionField|)) 
((|basis| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)))) (|basis| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)))) (|coordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)))) (|minimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|definingPolynomial| (*1 *2) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|extensionDegree| (*1 *2) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|PositiveInteger|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|PositiveInteger|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Field|)))) (|trace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Field|)))) (|minimalPolynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)))) (|norm| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)))) (|trace| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)))) (|createNormalElement| (*1 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|)))) (|normalElement| (*1 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|)))) (|normal?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|Boolean|)))) (|generator| (*1 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|)))) (|linearAssociatedExp| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Finite|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)))) (|linearAssociatedOrder| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|linearAssociatedLog| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|linearAssociatedLog| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) 
(|Join| (|ExtensionField| |t#1|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| $))) (SIGNATURE |basis| ((|Vector| $) (|PositiveInteger|))) (SIGNATURE |coordinates| ((|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|))) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |definingPolynomial| ((|SparseUnivariatePolynomial| |t#1|))) (SIGNATURE |extensionDegree| ((|PositiveInteger|))) (SIGNATURE |degree| ((|PositiveInteger|) $)) (SIGNATURE |norm| (|t#1| $)) (SIGNATURE |trace| (|t#1| $)) (IF (|has| |t#1| (|Finite|)) (PROGN (ATTRIBUTE (|FiniteFieldCategory|)) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|))) (SIGNATURE |norm| ($ $ (|PositiveInteger|))) (SIGNATURE |trace| ($ $ (|PositiveInteger|))) (SIGNATURE |createNormalElement| ($)) (SIGNATURE |normalElement| ($)) (SIGNATURE |normal?| ((|Boolean|) $)) (SIGNATURE |generator| ($)) (SIGNATURE |linearAssociatedExp| ($ $ (|SparseUnivariatePolynomial| |t#1|))) (SIGNATURE |linearAssociatedOrder| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |linearAssociatedLog| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |linearAssociatedLog| ((|Union| (|SparseUnivariatePolynomial| |t#1|) "failed") $ $))) |%noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DifferentialDomain| $) |has| |#1| (|Finite|)) ((|DifferentialRing|) |has| |#1| (|Finite|)) ((|DifferentialSpace|) |has| |#1| (|Finite|)) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|ExtensionField| |#1|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|Finite|) |has| |#1| (|Finite|)) ((|FiniteFieldCategory|) |has| |#1| (|Finite|)) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| |#1|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|Finite|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T) ((|VectorSpace| |#1|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|sin?| ((#3# $) 13 T ELT)) (|sin| (#4=($ |#1|) 10 T ELT)) (|min| #5=(($ $ $) NIL T ELT)) (|max| #5#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|cos| (#4# 12 T ELT)) (|coerce| (((|OutputForm|) $) 19 T ELT)) (|before?| #1#) (|argument| ((|#1| $) 14 T ELT)) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 21 T ELT))) 
(((|FourierComponent| |#1|) (|Join| #1=(|OrderedSet|) (CATEGORY |domain| (SIGNATURE |sin| #2=($ |#1|)) (SIGNATURE |cos| #2#) (SIGNATURE |sin?| ((|Boolean|) $)) (SIGNATURE |argument| (|#1| $)))) #1#) (T |FourierComponent|)) 
((|sin| #1=(*1 *1 *2) #2=(AND (|isDomain| *1 (|FourierComponent| *2)) (|ofCategory| *2 #3=(|OrderedSet|)))) (|cos| #1# #2#) (|sin?| #4=(*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FourierComponent| *3)) (|ofCategory| *3 #3#))) (|argument| #4# #2#)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|lookupFunction| (((|Identifier|) $) 20 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|encodingDirectory| (((|PrimitiveArray| #3=(|NonNegativeInteger|)) $) 18 T ELT)) (|domainTemplate| (((|DomainTemplate|) $) 7 T ELT)) (|coerce| (((|OutputForm|) $) 26 T ELT)) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) 16 T ELT)) (|before?| #1#) (|attributeData| (((|List| (|Pair| (|Syntax|) #3#)) $) 12 T ELT)) (= (#2# 22 T ELT))) 
(((|FunctorData|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |domainTemplate| ((|DomainTemplate|) $)) (SIGNATURE |attributeData| ((|List| (|Pair| (|Syntax|) #1=(|NonNegativeInteger|))) $)) (SIGNATURE |encodingDirectory| ((|PrimitiveArray| #1#) $)) (SIGNATURE |categories| ((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $)) (SIGNATURE |lookupFunction| ((|Identifier|) $))))) (T |FunctorData|)) 
((|domainTemplate| #1=(*1 *2 *1) (AND (|isDomain| *2 (|DomainTemplate|)) #2=(|isDomain| *1 (|FunctorData|)))) (|attributeData| #1# (AND (|isDomain| *2 (|List| (|Pair| (|Syntax|) #3=(|NonNegativeInteger|)))) #2#)) (|encodingDirectory| #1# (AND (|isDomain| *2 (|PrimitiveArray| #3#)) #2#)) (|categories| #1# (AND (|isDomain| *2 (|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|)))) #2#)) (|lookupFunction| #1# (AND (|isDomain| *2 (|Identifier|)) #2#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|reduce| (#7=($ $) 34 T ELT)) (|principal?| #4#) (|opposite?| #1#) (|latex| (((|String|) $) NIL T ELT)) (|lSpaceBasis| (#8=((|Vector| |#4|) $) 133 T ELT)) (|ideal| ((#9=(|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 32 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (((|Union| |#4| #5#) $) 37 T ELT)) (|finiteBasis| (#8# 125 T ELT)) (|divisor| (($ #9#) 42 T ELT) (($ |#4|) 44 T ELT) (($ |#1| |#1|) 46 T ELT) (($ |#1| |#1| #10=(|Integer|)) 48 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 50 T ELT)) (|decompose| (((|Record| (|:| |id| #9#) (|:| |principalPart| |#4|)) $) 40 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|before?| #1#) (|Zero| (#6# 15 T CONST)) (= (#2# 21 T ELT)) (- (#7# 28 T ELT) (#11=($ $ $) NIL T ELT)) (+ (#11# 26 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #10# $) 24 T ELT))) 
(((|FiniteDivisor| |#1| |#2| |#3| |#4|) (|Join| (|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |finiteBasis| #1=((|Vector| |#4|) $)) (SIGNATURE |lSpaceBasis| #1#))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |FiniteDivisor|)) 
((|finiteBasis| #1=(*1 *2 *1) #2=(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#)) 
((|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) 33 T ELT))) 
(((|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|)))) #1=(|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) #1# (|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 #1=(|Field|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *9 #1#) (|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))))) 
((|principal?| (((|Boolean|) $) 14 T ELT))) 
(((|FiniteDivisorCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |principal?| ((|Boolean|) |#1|))) (|FiniteDivisorCategory| |#2| |#3| |#4| |#5|) (|Field|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| (|Fraction| |#3|)) (|FunctionFieldCategory| |#2| |#3| |#4|)) (T |FiniteDivisorCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reduce| (($ $) 35 T ELT)) (|principal?| (((|Boolean|) $) 34 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 41 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (((|Union| |#4| "failed") $) 33 T ELT)) (|divisor| (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) 40 T ELT) (($ |#4|) 39 T ELT) (($ |#1| |#1|) 38 T ELT) (($ |#1| |#1| (|Integer|)) 37 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 32 T ELT)) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) 36 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT))) 
(((|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) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|eval| (($ $ #1=(|Symbol|) |#2|) NIL T ELT) (($ $ (|List| #1#) #2=(|List| |#2|)) 20 T ELT) (($ $ (|List| #3=(|Equation| |#2|))) 15 T ELT) (($ $ #3#) NIL T ELT) (($ $ |#2| |#2|) NIL T ELT) (($ $ #2# #2#) NIL T ELT)) (|elt| (($ $ |#2|) 11 T ELT))) 
(((|FullyEvalableOver&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |elt| (|#1| |#1| |#2|)) (SIGNATURE |eval| (|#1| |#1| #1=(|List| |#2|) #1#)) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| #2=(|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|List| #2#))) (SIGNATURE |eval| (|#1| |#1| (|List| #3=(|Symbol|)) #1#)) (SIGNATURE |eval| (|#1| |#1| #3# |#2|))) (|FullyEvalableOver| |#2|) (|SetCategory|)) (T |FullyEvalableOver&|)) 
NIL 
((|map| (($ (|Mapping| |#1| |#1|) $) 6 T ELT)) (|eval| (($ $ #1=(|Symbol|) |#1|) 17 (|has| |#1| (|InnerEvalable| #2=(|Symbol|) |#1|)) ELT) (($ $ (|List| #1#) (|List| |#1|)) 16 (|has| |#1| (|InnerEvalable| #2# |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 15 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 14 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 13 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 12 (|has| |#1| (|Evalable| |#1|)) ELT)) (|elt| (($ $ |#1|) 11 (|has| |#1| (|Eltable| |#1| |#1|)) ELT))) 
(((|FullyEvalableOver| |#1|) (|Category|) (|SetCategory|)) (T |FullyEvalableOver|)) 
NIL 
(|Join| (|Functorial| |t#1|) (CATEGORY |domain| (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|)) ((|Functorial| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Join|) . T) ((|Type|) . T)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((#10=(|PrimeField| |#1|) $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| #10# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #8#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #18#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #22=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| ((#17# $) NIL T ELT)) (|random| #24=(#21# NIL #14# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #8#) NIL #29=(OR (|has| #10# (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #9# #11#) (|nextItem| (#34=((|Maybe| $) $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| #10#) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #18#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #14# ELT) (((|Union| #8# #18#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#28# NIL #14# ELT) #44=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#22# $) NIL T ELT) (((|Matrix| #10#) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #18#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #46=(|Fraction| #15#)) NIL T ELT) (($ #10#) NIL T ELT)) (|charthRoot| #44# (#34# NIL #29# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #20#) (|One| #20#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #23# #47=(($ $ #10#) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #15# . #48=($)) NIL T ELT) #23# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ #10# . #48#) NIL T ELT))) 
(((|FiniteField| |#1| |#2|) (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) #1=(|PositiveInteger|) #1#) (T |FiniteField|)) 
NIL 
((|yCoordinates| (((|Record| (|:| |num| #1=(|Vector| |#3|)) #2=(|:| |den| |#3|)) $) 39 T ELT)) (|represents| (($ #3=(|Vector| #4=(|Fraction| |#3|)) #5=(|Vector| $)) NIL T ELT) (($ #3#) NIL T ELT) (($ #1# |#3|) 172 T ELT)) (|reduceBasisAtInfinity| (#6=(#5# #5#) 156 T ELT)) (|rationalPoints| (((|List| (|List| |#2|))) 126 T ELT)) (|rationalPoint?| ((#7=(|Boolean|) |#2| |#2|) 76 T ELT)) (|primitivePart| (#8=($ $) 148 T ELT)) (|numberOfComponents| (#9=(#10=(|NonNegativeInteger|)) 171 T ELT)) (|normalizeAtInfinity| (#6# 219 T ELT)) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) #11=(|Symbol|)) 115 T ELT)) (|integralAtInfinity?| (#12=(#7# $) 168 T ELT)) (|integral?| (#12# 27 T ELT) ((#7# $ |#2|) 31 T ELT) ((#7# $ |#3|) 223 T ELT)) (|hyperelliptic| (#13=((|Union| |#3| "failed")) 52 T ELT)) (|genus| (#9# 183 T ELT)) (|elt| ((|#2| $ |#2| |#2|) 140 T ELT)) (|elliptic| (#13# 71 T ELT)) (|differentiate| (($ $ #14=(|Mapping| #4# #4#)) NIL T ELT) (($ $ #14# #10#) NIL T ELT) (($ $ #15=(|Mapping| |#3| |#3|)) 227 T ELT) (($ $ #16=(|List| #11#) (|List| #10#)) NIL T ELT) (($ $ #11# #10#) NIL T ELT) (($ $ #16#) NIL T ELT) (($ $ #11#) NIL T ELT) (($ $ #10#) NIL T ELT) (#8# NIL T ELT)) (|complementaryBasis| (#6# 162 T ELT)) (|algSplitSimple| (((|Record| (|:| |num| $) #2# (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ #15#) 68 T ELT)) (|absolutelyIrreducible?| ((#7#) 34 T ELT))) 
(((|FunctionFieldCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |differentiate| #1=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #2=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #4=(|List| #3#))) (SIGNATURE |differentiate| (|#1| |#1| #3# #2#)) (SIGNATURE |differentiate| (|#1| |#1| #4# (|List| #2#))) (SIGNATURE |rationalPoints| ((|List| (|List| |#2|)))) (SIGNATURE |nonSingularModel| ((|List| (|Polynomial| |#2|)) #3#)) (SIGNATURE |algSplitSimple| ((|Record| (|:| |num| |#1|) #5=(|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) |#1| #6=(|Mapping| |#3| |#3|))) (SIGNATURE |hyperelliptic| #7=((|Union| |#3| "failed"))) (SIGNATURE |elliptic| #7#) (SIGNATURE |elt| (|#2| |#1| |#2| |#2|)) (SIGNATURE |primitivePart| #1#) (SIGNATURE |differentiate| (|#1| |#1| #6#)) (SIGNATURE |integral?| (#8=(|Boolean|) |#1| |#3|)) (SIGNATURE |integral?| (#8# |#1| |#2|)) (SIGNATURE |represents| (|#1| #9=(|Vector| |#3|) |#3|)) (SIGNATURE |yCoordinates| ((|Record| (|:| |num| #9#) #5#) |#1|)) (SIGNATURE |reduceBasisAtInfinity| #10=(#11=(|Vector| |#1|) #11#)) (SIGNATURE |normalizeAtInfinity| #10#) (SIGNATURE |complementaryBasis| #10#) (SIGNATURE |integral?| #12=(#8# |#1|)) (SIGNATURE |integralAtInfinity?| #12#) (SIGNATURE |rationalPoint?| (#8# |#2| |#2|)) (SIGNATURE |absolutelyIrreducible?| (#8#)) (SIGNATURE |genus| #13=(#2#)) (SIGNATURE |numberOfComponents| #13#) (SIGNATURE |differentiate| (|#1| |#1| #14=(|Mapping| #15=(|Fraction| |#3|) #15#) #2#)) (SIGNATURE |differentiate| (|#1| |#1| #14#)) (SIGNATURE |represents| (|#1| #16=(|Vector| #15#))) (SIGNATURE |represents| (|#1| #16# #11#))) (|FunctionFieldCategory| |#2| |#3| |#4|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| #15#)) (T |FunctionFieldCategory&|)) 
((|numberOfComponents| #1=(*1 *2) #2=(AND #3=(|ofCategory| *4 #4=(|UniqueFactorizationDomain|)) #5=(|ofCategory| *5 #6=(|UnivariatePolynomialCategory| *4)) #7=(|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|NonNegativeInteger|)) #8=(|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6)) #9=(|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6)))) (|genus| #1# #2#) (|absolutelyIrreducible?| #1# (AND #3# #5# #7# #10=(|isDomain| *2 (|Boolean|)) #8# #9#)) (|rationalPoint?| (*1 *2 *3 *3) (AND (|ofCategory| *3 #4#) (|ofCategory| *5 (|UnivariatePolynomialCategory| *3)) #7# #10# (|isDomain| *1 (|FunctionFieldCategory&| *4 *3 *5 *6)) (|ofCategory| *4 (|FunctionFieldCategory| *3 *5 *6)))) (|elliptic| #1# #11=(|partial| AND #3# (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 #6#) (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *2 *5)) (|ofCategory| *3 (|FunctionFieldCategory| *4 *2 *5)))) (|hyperelliptic| #1# #11#) (|nonSingularModel| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *5 #4#) (|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# (AND #3# #5# #7# (|isDomain| *2 (|List| (|List| *4))) #8# #9#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) 225 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 114 (|has| (|Fraction| |#2|) . #3=((|Field|))) ELT)) (|unitCanonical| (($ $) 115 (|has| (|Fraction| |#2|) . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 117 (|has| (|Fraction| |#2|) . #3#) ELT)) (|traceMatrix| (((|Matrix| (|Fraction| |#2|)) #5=(|Vector| $)) 61 T ELT) (((|Matrix| (|Fraction| |#2|))) 77 T ELT)) (|trace| (((|Fraction| |#2|) . #6=($)) 67 T ELT)) (|tableForDiscreteLogarithm| (((|Table| #7=(|PositiveInteger|) #8=(|NonNegativeInteger|)) #9=(|Integer|)) 167 (|has| (|Fraction| |#2|) . #10=((|FiniteFieldCategory|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 134 (|has| (|Fraction| |#2|) . #3#) ELT)) (|squareFree| (#11=((|Factored| $) $) 135 (|has| (|Fraction| |#2|) . #3#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 125 (|has| (|Fraction| |#2|) . #3#) ELT)) (|size| (((|NonNegativeInteger|)) 108 (|has| (|Fraction| |#2|) . #12=((|Finite|))) ELT)) (|singularAtInfinity?| (((|Boolean|)) 242 T ELT)) (|singular?| (((|Boolean|) |#1|) 241 T ELT) (((|Boolean|) |#2|) 240 T ELT)) (|sample| (#13=($) 23 T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=("failed")) . #16=($)) 194 (|has| (|Fraction| |#2|) . #17=((|RetractableTo| #14#))) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) 192 (|has| (|Fraction| |#2|) . #19=((|RetractableTo| #18#))) ELT) (((|Union| (|Fraction| |#2|) . #15#) . #16#) 189 T ELT)) (|retract| ((#14# . #20=($)) 193 (|has| (|Fraction| |#2|) . #17#) ELT) ((#18# . #20#) 191 (|has| (|Fraction| |#2|) . #19#) ELT) (((|Fraction| |#2|) . #20#) 190 T ELT)) (|represents| (($ (|Vector| (|Fraction| |#2|)) #5#) 63 T ELT) (($ (|Vector| (|Fraction| |#2|))) 80 T ELT) (($ (|Vector| |#2|) |#2|) 224 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 173 (|has| (|Fraction| |#2|) . #10#) ELT)) (|rem| (#21=($ $ $) 129 (|has| (|Fraction| |#2|) . #3#) ELT)) (|regularRepresentation| (((|Matrix| (|Fraction| |#2|)) $ #5#) 68 T ELT) (((|Matrix| (|Fraction| |#2|)) $) 75 T ELT)) (|reducedSystem| (((|Matrix| #22=(|Integer|)) . #23=(#24=(|Matrix| $))) 186 (|has| (|Fraction| |#2|) . #25=((|LinearlyExplicitRingOver| #22#))) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #26=(#24# #27=(|Vector| $))) 185 (|has| (|Fraction| |#2|) . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| (|Fraction| |#2|))) (|:| |vec| (|Vector| (|Fraction| |#2|)))) . #26#) 184 T ELT) (((|Matrix| (|Fraction| |#2|)) . #23#) 183 T ELT)) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) 230 T ELT)) (|reduce| (($ |#3|) 178 T ELT) (((|Union| $ "failed") (|Fraction| |#3|)) 175 (|has| (|Fraction| |#2|) . #3#) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) 211 (|has| |#1| (|Finite|)) ELT)) (|rationalPoint?| (((|Boolean|) |#1| |#1|) 246 T ELT)) (|rank| (((|PositiveInteger|)) 69 T ELT)) (|random| (($) 111 (|has| (|Fraction| |#2|) . #12#) ELT)) (|ramifiedAtInfinity?| (((|Boolean|)) 239 T ELT)) (|ramified?| (((|Boolean|) |#1|) 238 T ELT) (((|Boolean|) |#2|) 237 T ELT)) (|quo| (#21# 128 (|has| (|Fraction| |#2|) . #3#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #28=(|List| $)) (|:| |generator| $)) #28#) 123 (|has| (|Fraction| |#2|) . #3#) ELT)) (|primitivePart| (($ $) 217 T ELT)) (|primitiveElement| (#29=($) 169 (|has| (|Fraction| |#2|) . #10#) ELT)) (|primitive?| (((|Boolean|) $) 170 (|has| (|Fraction| |#2|) . #10#) ELT)) (|primeFrobenius| (($ $ #30=(|NonNegativeInteger|)) 161 (|has| (|Fraction| |#2|) . #10#) ELT) (($ $) 160 (|has| (|Fraction| |#2|) . #10#) ELT)) (|prime?| (((|Boolean|) $) 136 (|has| (|Fraction| |#2|) . #3#) ELT)) (|order| ((#7# $) 172 (|has| (|Fraction| |#2|) . #10#) ELT) (((|OnePointCompletion| (|PositiveInteger|)) $) 158 (|has| (|Fraction| |#2|) . #10#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numberOfComponents| (((|NonNegativeInteger|)) 249 T ELT)) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) 231 T ELT)) (|norm| (((|Fraction| |#2|) . #6#) 66 T ELT)) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) 212 (|has| |#1| (|Field|)) ELT)) (|nextItem| (((|Maybe| $) $) 162 (|has| (|Fraction| |#2|) . #10#) ELT)) (|multiEuclidean| (((|Union| #31=(|List| $) #32="failed") #31# $) 132 (|has| (|Fraction| |#2|) . #3#) ELT)) (|minimalPolynomial| ((|#3| . #33=($)) 59 (|has| (|Fraction| |#2|) (|Field|)) ELT)) (|lookup| ((#34=(|PositiveInteger|) $) 110 (|has| (|Fraction| |#2|) . #12#) ELT)) (|lift| ((|#3| $) 176 T ELT)) (|leftReducedSystem| (((|Matrix| #22#) . #35=(#27#)) 188 (|has| (|Fraction| |#2|) . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #36=(#27# $)) 187 (|has| (|Fraction| |#2|) . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| (|Fraction| |#2|))) (|:| |vec| (|Vector| (|Fraction| |#2|)))) . #36#) 182 T ELT) (((|Matrix| (|Fraction| |#2|)) . #35#) 181 T ELT)) (|lcm| (#37=($ (|List| $)) 121 (|has| (|Fraction| |#2|) . #3#) ELT) (#38=($ $ $) 120 (|has| (|Fraction| |#2|) . #3#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) 226 T ELT)) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) 228 T ELT)) (|inv| (($ $) 137 (|has| (|Fraction| |#2|) . #3#) ELT)) (|integralRepresents| (($ (|Vector| |#2|) |#2|) 222 T ELT)) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) 227 T ELT)) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) 229 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) 221 T ELT)) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) 223 T ELT)) (|integralBasisAtInfinity| (((|Vector| $)) 235 T ELT)) (|integralBasis| (((|Vector| $)) 236 T ELT)) (|integralAtInfinity?| (((|Boolean|) $) 234 T ELT)) (|integral?| (((|Boolean|) $) 233 T ELT) (((|Boolean|) $ |#1|) 220 T ELT) (((|Boolean|) $ |#2|) 219 T ELT)) (|init| (($) 163 (|has| (|Fraction| |#2|) . #10#) CONST)) (|index| (($ #34#) 109 (|has| (|Fraction| |#2|) . #12#) ELT)) (|hyperelliptic| (((|Union| |#2| "failed")) 214 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|genus| (((|NonNegativeInteger|)) 248 T ELT)) (|generator| (($) 180 T ELT)) (|gcdPolynomial| ((#39=(|SparseUnivariatePolynomial| $) #39# #39#) 122 (|has| (|Fraction| |#2|) . #3#) ELT)) (|gcd| (#37# 119 (|has| (|Fraction| |#2|) . #3#) ELT) (#38# 118 (|has| (|Fraction| |#2|) . #3#) ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #9#) (|:| |exponent| #9#)))) 166 (|has| (|Fraction| |#2|) . #10#) ELT)) (|factor| (#11# 133 (|has| (|Fraction| |#2|) . #3#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $)) #32#) $ $ $) 131 (|has| (|Fraction| |#2|) . #3#) ELT) (((|Record| #40# #41# (|:| |generator| $)) $ $) 130 (|has| (|Fraction| |#2|) . #3#) ELT)) (|exquo| (((|Union| $ "failed") $ $) 113 (|has| (|Fraction| |#2|) . #3#) ELT)) (|expressIdealMember| (((|Maybe| #28#) #28# $) 124 (|has| (|Fraction| |#2|) . #3#) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 126 (|has| (|Fraction| |#2|) . #3#) ELT)) (|elt| ((|#1| $ |#1| |#1|) 216 T ELT)) (|elliptic| (((|Union| |#2| "failed")) 215 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 127 (|has| (|Fraction| |#2|) . #3#) ELT)) (|discriminant| (((|Fraction| |#2|) #5#) 62 T ELT) (((|Fraction| |#2|)) 76 T ELT)) (|discreteLog| ((#8# $) 171 (|has| (|Fraction| |#2|) . #10#) ELT) (((|Union| #30# "failed") $ $) 159 (|has| (|Fraction| |#2|) . #10#) ELT)) (|differentiate| (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 145 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) . #42=((|NonNegativeInteger|))) 144 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ (|Mapping| |#2| |#2|)) 218 T ELT) (($ $ (|List| #43=(|Symbol|)) . #44=((|List| #45=(|NonNegativeInteger|)))) 150 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46=((|PartialDifferentialSpace| #43#)))) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47=((|PartialDifferentialRing| (|Symbol|))))) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #43# . #48=(#45#)) 149 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ (|List| #43#)) 148 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #43#) 146 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (#49=($ $ (|NonNegativeInteger|)) 156 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50=((|DifferentialSpace|)))) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51=((|DifferentialRing|)))) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#)) (|has| (|Fraction| |#2|) . #10#)) ELT) (($ . #52=($)) 154 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#)) (|has| (|Fraction| |#2|) . #10#)) ELT)) (|derivationCoordinates| (((|Matrix| (|Fraction| |#2|)) (|Vector| $) (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 174 (|has| (|Fraction| |#2|) . #3#) ELT)) (|definingPolynomial| ((|#3|) 179 T ELT)) (|createPrimitiveElement| (#29# 168 (|has| (|Fraction| |#2|) . #10#) ELT)) (|coordinates| (((|Vector| (|Fraction| |#2|)) $ #5#) 65 T ELT) (((|Matrix| (|Fraction| |#2|)) #5# #5#) 64 T ELT) (((|Vector| (|Fraction| |#2|)) . #53=($)) 82 T ELT) (((|Matrix| (|Fraction| |#2|)) #54=(|Vector| $)) 81 T ELT)) (|convert| (((|Vector| (|Fraction| |#2|)) . #53#) 79 T ELT) (($ (|Vector| (|Fraction| |#2|))) 78 T ELT) ((|#3| $) 195 T ELT) (($ |#3|) 177 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 165 (|has| (|Fraction| |#2|) . #10#) ELT)) (|complementaryBasis| (((|Vector| $) (|Vector| $)) 232 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ (|Fraction| |#2|)) 52 T ELT) (($ #55=(|Fraction| #56=(|Integer|))) 107 (OR (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #19#)) ELT) (($ $) 112 (|has| (|Fraction| |#2|) . #3#) ELT)) (|charthRoot| (($ $) 164 (|has| (|Fraction| |#2|) . #10#) ELT) (((|Maybe| $) $) 58 (|has| (|Fraction| |#2|) (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#3| . #33#) 60 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|branchPointAtInfinity?| (((|Boolean|)) 245 T ELT)) (|branchPoint?| (((|Boolean|) |#1|) 244 T ELT) (((|Boolean|) |#2|) 243 T ELT)) (|before?| (#1# 6 T ELT)) (|basis| ((#54#) 83 T ELT)) (|associates?| ((#4# $ $) 116 (|has| (|Fraction| |#2|) . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) 213 T ELT)) (|absolutelyIrreducible?| (((|Boolean|)) 247 T ELT)) (|Zero| (#13# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 143 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) . #42#) 142 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ (|List| #43#) . #44#) 153 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #43# . #48#) 152 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ (|List| #43#)) 151 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #43#) 147 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (#49# 157 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#)) (|has| (|Fraction| |#2|) . #10#)) ELT) (($ . #52#) 155 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#)) (|has| (|Fraction| |#2|) . #10#)) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 141 (|has| (|Fraction| |#2|) . #3#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #56#) 138 (|has| (|Fraction| |#2|) . #3#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #57=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ (|Fraction| |#2|)) 54 T ELT) (($ (|Fraction| |#2|) . #57#) 53 T ELT) (($ #55# . #57#) 140 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ #55#) 139 (|has| (|Fraction| |#2|) . #3#) ELT))) 
(((|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))))) (|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))))) (|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))))) (|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 |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| #1=(|Fraction| (|Integer|))) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Algebra| #2=(|Fraction| |#2|)) . T) ((|Algebra| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|BasicType|) . T) ((|BiModule| #1# #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|BiModule| #2# #2#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| (|Fraction| |#2|) (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|)))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| |#3|) . T) ((|DifferentialDomain| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (AND (|has| (|Fraction| |#2|) (|DifferentialSpace|)) (|has| (|Fraction| |#2|) (|Field|))) (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|)))) ((|DifferentialExtension| #2#) |has| (|Fraction| |#2|) (|Field|)) ((|DifferentialRing|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|)))) ((|DifferentialSpace|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (AND (|has| (|Fraction| |#2|) (|DifferentialSpace|)) (|has| (|Fraction| |#2|) (|Field|))) (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|)))) ((|DifferentialSpaceExtension| #2#) |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|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Finite|))) ((|FiniteFieldCategory|) |has| (|Fraction| |#2|) (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| #2# |#3|) . T) ((|FramedAlgebra| #2# |#3|) . T) ((|FullyLinearlyExplicitRingOver| #2#) . T) ((|FullyRetractableTo| #2#) . T) ((|GcdDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|IntegralDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LeftModule| #2#) . T) ((|LeftModule| #3=(|Integer|)) |has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| $) . T) ((|LinearSet| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LinearSet| #2#) . T) ((|LinearSet| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LinearlyExplicitRingOver| #2#) . T) ((|LinearlyExplicitRingOver| #3#) |has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|))) ((|Module| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Module| #2#) . T) ((|Module| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|MonogenicAlgebra| #2# |#3|) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialSpace| #4#) OR (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialSpace| (|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| #2#) . T) ((|RetractableTo| (|Integer|)) |has| (|Fraction| |#2|) (|RetractableTo| (|Integer|))) ((|RightLinearSet| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|RightLinearSet| #2#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|RightModule| #2#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| (|Fraction| |#2|) (|FiniteFieldCategory|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|)))) 
((|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) 19 T ELT))) 
(((|FunctionFieldCategoryFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| (|#8| (|Mapping| |#5| |#1|) |#4|))) #1=(|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) #1# (|UnivariatePolynomialCategory| |#5|) (|UnivariatePolynomialCategory| (|Fraction| |#6|)) (|FunctionFieldCategory| |#5| |#6| |#7|)) (T |FunctionFieldCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *8 *5)) (|ofCategory| *5 #1=(|UniqueFactorizationDomain|)) (|ofCategory| *8 #1#) (|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)))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((#10=(|PrimeField| |#1|) $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| #10# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #8#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #18#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #22=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| ((#17# $) NIL T ELT)) (|random| #24=(#21# NIL #14# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #8#) NIL #29=(OR (|has| #10# (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #9# #11#) (|nextItem| (#34=((|Maybe| $) $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| #10#) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #18#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| ((#40=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #40#)) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #41=(|:| |coef1| $) #42=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #41# #42#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#43=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#43# NIL #14# ELT) (((|Union| #8# #18#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #44=(#28# NIL #14# ELT) #45=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#22# $) NIL T ELT) (((|Matrix| #10#) #46=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #46# #18#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #47=(|Fraction| #15#)) NIL T ELT) (($ #10#) NIL T ELT)) (|charthRoot| #45# (#34# NIL #29# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#46#) NIL T ELT) ((#46# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #20#) (|One| #20#) (|Frobenius| #45# #44#) (D #44# #45#) (= #1#) (/ #23# #48=(($ $ #10#) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #15# . #49=($)) NIL T ELT) #23# (($ $ #47#) NIL T ELT) (($ #47# . #49#) NIL T ELT) #48# (($ #10# . #49#) NIL T ELT))) 
(((|FiniteFieldCyclicGroup| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) #1=(|PositiveInteger|) #1#) (T |FiniteFieldCyclicGroup|)) 
((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroup| *3 *4)) (|ofType| *3 #1=(|PositiveInteger|)) (|ofType| *4 #1#)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 58 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #7=(#4# NIL T ELT)) (|transcendent?| #7#) (|transcendenceDegree| (#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=(#11=(|#1| $) NIL T ELT) #12=(#13=($ $ #14=(|PositiveInteger|)) NIL #15=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #14# #9#) #16=(|Integer|)) 56 #15# ELT)) (|subtractIfCan| #17=((#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #20=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#8# NIL #15# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #19#) $) 139 T ELT)) (|retract| (#11# 111 T ELT)) (|represents| (($ #22=(|Vector| |#1|)) 128 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 119 #15# ELT)) (|rem| #23=(#24=($ $ $) NIL T ELT)) (|recip| ((#18# $) NIL T ELT)) (|random| (#21# 122 #15# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| (#21# 155 #15# ELT)) (|primitive?| (#4# 65 #15# ELT)) (|primeFrobenius| (#27=($ $ #9#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #15#) ELT) (#6# NIL #28# ELT)) (|prime?| #7#) (|order| (#29=(#14# $) 60 #15# ELT) (#30=(#31=(|OnePointCompletion| #14#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| (#4# 62 T ELT)) (|normalElement| (#21# 157 #15# ELT)) (|normal?| (#4# NIL #15# ELT)) (|norm| #10# #12#) (|nextItem| (#32=((|Maybe| $) $) NIL #15# ELT)) (|multiEuclidean| (((|Union| #25# #19#) #25# $) NIL T ELT)) (|minimalPolynomial| (#33=(#34=(|SparseUnivariatePolynomial| |#1|) $) 115 T ELT) ((#35=(|SparseUnivariatePolynomial| $) $ #14#) NIL #15# ELT)) (|lookup| (#29# 165 #15# ELT)) (|linearAssociatedOrder| #36=(#33# NIL #15# ELT)) (|linearAssociatedLog| #36# (((|Union| #34# #19#) $ $) NIL #15# ELT)) (|linearAssociatedExp| (($ $ #34#) NIL #15# ELT)) (|lcm| #23# #37=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#6# 172 T ELT)) (|init| (#21# NIL #15# CONST)) (|index| (($ #14#) 94 #15# ELT)) (|inGroundField?| (#4# 142 T ELT)) (|hash| ((#38=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #38#)) 57 T ELT)) (|generator| (#21# 153 #15# ELT)) (|gcdPolynomial| ((#35# #35# #35#) NIL T ELT)) (|gcd| #23# #37#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) 117 #15# ELT)) (|factor| #20#) (|extensionDegree| ((#31#) 88 T ELT) ((#14#) 89 T ELT)) (|extendedEuclidean| (((|Record| #39=(|:| |coef1| $) #40=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #39# #40#) #19#) $ $ $) NIL T ELT)) (|exquo| #17#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#41=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#41# 156 #15# ELT) (((|Union| #9# #19#) $ $) 149 #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #42=(#27# NIL #15# ELT) #43=(#6# NIL #15# ELT)) (|degree| (#30# NIL T ELT) (#29# NIL T ELT)) (|definingPolynomial| ((#34#) 120 T ELT)) (|createPrimitiveElement| (#21# 154 #15# ELT)) (|createNormalElement| (#21# 162 #15# ELT)) (|coordinates| ((#22# $) 76 T ELT) (((|Matrix| |#1|) #44=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #44# #19#) (|Matrix| $)) NIL #15# ELT)) (|coerce| (((|OutputForm|) $) 168 T ELT) (($ #16#) NIL T ELT) #5# (($ #45=(|Fraction| #16#)) NIL T ELT) (($ |#1|) 98 T ELT)) (|charthRoot| #43# (#32# NIL #28# ELT)) (|characteristic| (#8# 150 T CONST)) (|before?| #1#) (|basis| ((#44#) 141 T ELT) ((#44# #14#) 96 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #7#) (|Zero| (#21# 66 T CONST)) (|One| (#21# 101 T CONST)) (|Frobenius| (#6# 105 #15# ELT) #42#) (D #42# #43#) (= (#2# 64 T ELT)) (/ (#24# 170 T ELT) (#46=($ $ |#1|) 171 T ELT)) (- (#6# 152 T ELT) #23#) (+ (#24# 84 T ELT)) (** (#13# 174 T ELT) (#27# 175 T ELT) (($ $ #16#) 173 T ELT)) (* (($ #14# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #16# $) 100 T ELT) (#24# 99 T ELT) (($ $ #45#) NIL T ELT) (($ #45# $) NIL T ELT) (#46# NIL T ELT) (($ |#1| $) 169 T ELT))) 
(((|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))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((|#1| $) NIL T ELT) #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #8#) #14=(|Integer|)) NIL #13# ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #13# ELT)) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #17#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #21=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #13# ELT)) (|rem| #22=(($ $ $) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|random| #23=(#20# NIL #13# ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL T ELT)) (|primitiveElement| #23#) (|primitive?| #26=(#4# NIL #13# ELT)) (|primeFrobenius| (#27=($ $ #8#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#6# NIL #28# ELT)) (|prime?| #3#) (|order| #29=(#30=(#12# $) NIL #13# ELT) (#31=(#32=(|OnePointCompletion| #12#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #23#) (|normal?| #26#) (|norm| #9# #10#) (|nextItem| (#33=((|Maybe| $) $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #24# #17#) #24# $) NIL T ELT)) (|minimalPolynomial| (#34=(#35=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#36=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| #29#) (|linearAssociatedOrder| #37=(#34# NIL #13# ELT)) (|linearAssociatedLog| #37# (((|Union| #35# #17#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #35#) NIL #13# ELT)) (|lcm| #22# #38=(($ #24#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#20# NIL #13# CONST)) (|index| (($ #12#) NIL #13# ELT)) (|inGroundField?| #3#) (|hash| ((#39=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #39#)) NIL T ELT)) (|generator| #23#) (|gcdPolynomial| ((#36# #36# #36#) NIL T ELT)) (|gcd| #22# #38#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) NIL #13# ELT)) (|factor| #18#) (|extensionDegree| ((#32#) NIL T ELT) ((#12#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #25#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #13# ELT) (((|Union| #8# #17#) $ $) NIL #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#27# NIL #13# ELT) #44=(#6# NIL #13# ELT)) (|degree| (#31# NIL T ELT) (#30# NIL T ELT)) (|definingPolynomial| ((#35#) NIL T ELT)) (|createPrimitiveElement| #23#) (|createNormalElement| #23#) (|coordinates| ((#21# $) NIL T ELT) (((|Matrix| |#1|) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #17#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #5# (($ #46=(|Fraction| #14#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #44# (#33# NIL #28# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #12#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #19#) (|One| #19#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #22# #47=(($ $ |#1|) NIL T ELT)) (- #5# #22#) (+ #22#) (** (#11# NIL T ELT) (#27# NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #48=($)) NIL T ELT) #22# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ |#1| . #48#) NIL T ELT))) 
(((|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|))))) 
((|sizeMultiplication| (((|NonNegativeInteger|) #1=(|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #2=(|SingleInteger|)))))) 61 T ELT)) (|createZechTable| (((|PrimitiveArray| #2#) #3=(|SparseUnivariatePolynomial| |#1|)) 112 T ELT)) (|createMultiplicationTable| ((#1# #3#) 103 T ELT)) (|createMultiplicationMatrix| (((|Matrix| |#1|) #1#) 113 T ELT)) (|createLowComplexityTable| (((|Union| #1# "failed") #4=(|PositiveInteger|)) 13 T ELT)) (|createLowComplexityNormalBasis| (((|Union| #3# #1#) #4#) 18 T ELT))) 
(((|FiniteFieldFunctions| |#1|) (CATEGORY |package| (SIGNATURE |createZechTable| ((|PrimitiveArray| #1=(|SingleInteger|)) #2=(|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |createMultiplicationTable| (#3=(|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #1#)))) #2#)) (SIGNATURE |createMultiplicationMatrix| ((|Matrix| |#1|) #3#)) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|) #3#)) (SIGNATURE |createLowComplexityTable| ((|Union| #3# "failed") #4=(|PositiveInteger|))) (SIGNATURE |createLowComplexityNormalBasis| ((|Union| #2# #3#) #4#))) (|FiniteFieldCategory|)) (T |FiniteFieldFunctions|)) 
((|createLowComplexityNormalBasis| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Union| #3=(|SparseUnivariatePolynomial| *4) #4=(|Vector| (|List| (|Record| (|:| |value| *4) (|:| |index| #5=(|SingleInteger|))))))) #6=(|isDomain| *1 (|FiniteFieldFunctions| *4)) #7=(|ofCategory| *4 (|FiniteFieldCategory|)))) (|createLowComplexityTable| #1# (|partial| AND #2# #8=(|isDomain| *2 #4#) #6# #7#)) (|sizeMultiplication| #1# (AND #9=(|isDomain| *3 #4#) #7# (|isDomain| *2 (|NonNegativeInteger|)) #6#)) (|createMultiplicationMatrix| #1# (AND #9# #7# (|isDomain| *2 (|Matrix| *4)) #6#)) (|createMultiplicationTable| #1# (AND #10=(|isDomain| *3 #3#) #7# #8# #6#)) (|createZechTable| #1# (AND #10# #7# (|isDomain| *2 (|PrimitiveArray| #5#)) #6#))) 
((|coerce| ((|#1| |#3|) 104 T ELT) ((|#3| |#1|) 87 T ELT))) 
(((|FiniteFieldHomomorphisms| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |coerce| (|#3| |#1|)) (SIGNATURE |coerce| (|#1| |#3|))) #1=(|FiniteAlgebraicExtensionField| |#2|) (|FiniteFieldCategory|) #1#) (T |FiniteFieldHomomorphisms|)) 
((|coerce| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 (|FiniteFieldCategory|)) #3=(|ofCategory| *2 #4=(|FiniteAlgebraicExtensionField| *4)) (|isDomain| *1 (|FiniteFieldHomomorphisms| *2 *4 *3)) #5=(|ofCategory| *3 #4#))) (|coerce| #1# (AND #2# #3# (|isDomain| *1 (|FiniteFieldHomomorphisms| *3 *4 *2)) #5#))) 
((|primitive?| (((|Boolean|) $) 65 T ELT)) (|order| (((|OnePointCompletion| #1=(|PositiveInteger|)) $) 26 T ELT) ((#1# $) 69 T ELT)) (|nextItem| (#2=((|Maybe| $) $) 21 T ELT)) (|init| (#3=($) 9 T CONST)) (|gcdPolynomial| ((#4=(|SparseUnivariatePolynomial| $) #4# #4#) 120 T ELT)) (|discreteLog| (((|Union| #5=(|NonNegativeInteger|) #6="failed") $ $) 98 T ELT) ((#5# $) 84 T ELT)) (|differentiate| (#7=($ $) 8 T ELT) (($ $ #5#) NIL T ELT)) (|createPrimitiveElement| (#3# 58 T ELT)) (|conditionP| (((|Union| (|Vector| $) #6#) (|Matrix| $)) 41 T ELT)) (|charthRoot| (#2# 50 T ELT) (#7# 47 T ELT))) 
(((|FiniteFieldCategory&| |#1|) (CATEGORY |package| (SIGNATURE |order| (#1=(|PositiveInteger|) |#1|)) (SIGNATURE |discreteLog| (#2=(|NonNegativeInteger|) |#1|)) (SIGNATURE |primitive?| ((|Boolean|) |#1|)) (SIGNATURE |createPrimitiveElement| #3=(|#1|)) (SIGNATURE |conditionP| ((|Union| (|Vector| |#1|) #4="failed") (|Matrix| |#1|))) (SIGNATURE |charthRoot| #5=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #2#)) (SIGNATURE |differentiate| #5#) (SIGNATURE |init| #3# |constant|) (SIGNATURE |nextItem| #6=((|Maybe| |#1|) |#1|)) (SIGNATURE |discreteLog| ((|Union| #2# #4#) |#1| |#1|)) (SIGNATURE |order| ((|OnePointCompletion| #1#) |#1|)) (SIGNATURE |charthRoot| #6#) (SIGNATURE |gcdPolynomial| (#7=(|SparseUnivariatePolynomial| |#1|) #7# #7#))) (|FiniteFieldCategory|)) (T |FiniteFieldCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 113 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|size| (((|NonNegativeInteger|)) 123 T ELT)) (|sample| (#5=($) 23 T CONST)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 107 T ELT)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|random| (($) 126 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|primitiveElement| (($) 111 T ELT)) (|primitive?| (((|Boolean|) $) 110 T ELT)) (|primeFrobenius| (($ $) 97 T ELT) (($ $ #8=(|NonNegativeInteger|)) 96 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 99 T ELT) (((|PositiveInteger|) $) 108 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nextItem| (((|Maybe| $) $) 122 T ELT)) (|multiEuclidean| (((|Union| #9=(|List| $) #10="failed") #9# $) 68 T ELT)) (|lookup| ((#11=(|PositiveInteger|) $) 125 T ELT)) (|lcm| (#12=($ $ $) 60 T ELT) (#13=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|init| (($) 121 T CONST)) (|index| (($ #11#) 124 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#14=(|SparseUnivariatePolynomial| $) #14# #14#) 58 T ELT)) (|gcd| (#12# 62 T ELT) (#13# 61 T ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 114 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #15=(|:| |coef1| $) #16=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #15# #16#) #10#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| (((|Union| #8# "failed") $ $) 98 T ELT) (((|NonNegativeInteger|) $) 109 T ELT)) (|differentiate| (($ . #17=($)) 120 T ELT) (#18=($ $ (|NonNegativeInteger|)) 118 T ELT)) (|createPrimitiveElement| (($) 112 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 115 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #19=(|Fraction| #20=(|Integer|))) 84 T ELT)) (|charthRoot| (((|Maybe| $) $) 100 T ELT) (($ $) 116 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ . #17#) 119 T ELT) (#18# 117 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #20#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #21=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #19#) 86 T ELT) (($ #19# . #21#) 85 T ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DifferentialDomain| $) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) . T) ((|Finite|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|localIntegralBasis| ((#1=(|Record| (|:| |basis| #2=(|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| #2#)) |#1|) 55 T ELT)) (|integralBasis| ((#1#) 53 T ELT))) 
(((|FunctionFieldIntegralBasis| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |integralBasis| (#1=(|Record| (|:| |basis| #2=(|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| #2#)))) (SIGNATURE |localIntegralBasis| (#1# |#1|))) (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $)))) (|UnivariatePolynomialCategory| |#1|) (|FramedAlgebra| |#1| |#2|)) (T |FunctionFieldIntegralBasis|)) 
((|localIntegralBasis| (*1 *2 *3) #1=(AND (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| #2=(|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| #2#))) (|isDomain| *1 (|FunctionFieldIntegralBasis| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|integralBasis| (*1 *2) #1#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| #7=(#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=((#11=(|PrimeField| |#1|) $) NIL T ELT) #12=(#13=($ $ #14=(|PositiveInteger|)) NIL #15=(|has| #11# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #14# #9#) #16=(|Integer|)) NIL #15# ELT)) (|subtractIfCan| #17=((#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #20=(((|Factored| $) $) NIL T ELT)) (|sizeMultiplication| #7#) (|sizeLess?| #1#) (|size| (#8# NIL #15# ELT)) (|sample| #21=(#22=($) NIL T CONST)) (|retractIfCan| (((|Union| #11# #19#) $) NIL T ELT)) (|retract| #10#) (|represents| (($ #23=(|Vector| #11#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #15# ELT)) (|rem| #24=(($ $ $) NIL T ELT)) (|recip| ((#18# $) NIL T ELT)) (|random| #25=(#22# NIL #15# ELT)) (|quo| #24#) (|principalIdeal| (((|Record| (|:| |coef| #26=(|List| $)) #27=(|:| |generator| $)) #26#) NIL T ELT)) (|primitiveElement| #25#) (|primitive?| #28=(#4# NIL #15# ELT)) (|primeFrobenius| (#29=($ $ #9#) NIL #30=(OR (|has| #11# (|CharacteristicNonZero|)) #15#) ELT) (#6# NIL #30# ELT)) (|prime?| #3#) (|order| #31=(#32=(#14# $) NIL #15# ELT) (#33=(#34=(|OnePointCompletion| #14#) $) NIL #30# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #25#) (|normal?| #28#) (|norm| #10# #12#) (|nextItem| (#35=((|Maybe| $) $) NIL #15# ELT)) (|multiEuclidean| (((|Union| #26# #19#) #26# $) NIL T ELT)) (|minimalPolynomial| (#36=(#37=(|SparseUnivariatePolynomial| #11#) $) NIL T ELT) ((#38=(|SparseUnivariatePolynomial| $) $ #14#) NIL #15# ELT)) (|lookup| #31#) (|linearAssociatedOrder| #39=(#36# NIL #15# ELT)) (|linearAssociatedLog| #39# (((|Union| #37# #19#) $ $) NIL #15# ELT)) (|linearAssociatedExp| (($ $ #37#) NIL #15# ELT)) (|lcm| #24# #40=(($ #26#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#22# NIL #15# CONST)) (|index| (($ #14#) NIL #15# ELT)) (|inGroundField?| #3#) (|hash| ((#41=(|SingleInteger|) $) NIL T ELT)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| #11#) (|:| |index| #41#))))) NIL T ELT)) (|getMultiplicationMatrix| ((#42=(|Matrix| #11#)) NIL T ELT)) (|generator| #25#) (|gcdPolynomial| ((#38# #38# #38#) NIL T ELT)) (|gcd| #24# #40#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) NIL #15# ELT)) (|factor| #20#) (|extensionDegree| ((#34#) NIL T ELT) ((#14#) NIL T ELT)) (|extendedEuclidean| (((|Record| #43=(|:| |coef1| $) #44=(|:| |coef2| $) #27#) $ $) NIL T ELT) (((|Union| (|Record| #43# #44#) #19#) $ $ $) NIL T ELT)) (|exquo| #17#) (|expressIdealMember| (((|Maybe| #26#) #26# $) NIL T ELT)) (|euclideanSize| (#45=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#45# NIL #15# ELT) (((|Union| #9# #19#) $ $) NIL #30# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #46=(#29# NIL #15# ELT) #47=(#6# NIL #15# ELT)) (|degree| (#33# NIL T ELT) (#32# NIL T ELT)) (|definingPolynomial| ((#37#) NIL T ELT)) (|createPrimitiveElement| #25#) (|createNormalElement| #25#) (|coordinates| ((#23# $) NIL T ELT) ((#42# #48=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #48# #19#) (|Matrix| $)) NIL #15# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #16#) NIL T ELT) #5# (($ #49=(|Fraction| #16#)) NIL T ELT) (($ #11#) NIL T ELT)) (|charthRoot| #47# (#35# NIL #30# ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|basis| ((#48#) NIL T ELT) ((#48# #14#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #21#) (|One| #21#) (|Frobenius| #47# #46#) (D #46# #47#) (= #1#) (/ #24# #50=(($ $ #11#) NIL T ELT)) (- #5# #24#) (+ #24#) (** (#13# NIL T ELT) (#29# NIL T ELT) (($ $ #16#) NIL T ELT)) (* (($ #14# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #16# . #51=($)) NIL T ELT) #24# (($ $ #49#) NIL T ELT) (($ #49# . #51#) NIL T ELT) #50# (($ #11# . #51#) NIL T ELT))) 
(((|FiniteFieldNormalBasis| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| #1=(|PrimeField| |#1|)) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| #1#) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| #1#))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) #2=(|PositiveInteger|) #2#) (T |FiniteFieldNormalBasis|)) 
((|getMultiplicationTable| #1=(*1 *2) (AND (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| #2=(|PrimeField| *3)) (|:| |index| (|SingleInteger|)))))) #3=(|isDomain| *1 (|FiniteFieldNormalBasis| *3 *4)) #4=(|ofType| *3 #5=(|PositiveInteger|)) #6=(|ofType| *4 #5#))) (|getMultiplicationMatrix| #1# (AND (|isDomain| *2 (|Matrix| #2#)) #3# #4# #6#)) (|sizeMultiplication| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #4# #6#))) 
((~= (#1=(#2=(|Boolean|) $ $) 72 T ELT)) (|zero?| (#3=(#2# $) 87 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #6=(#3# NIL T ELT)) (|transcendent?| #6#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| (#9=(|#1| $) 105 T ELT) (#10=($ $ #11=(|PositiveInteger|)) 103 #12=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #11# #8#) #13=(|Integer|)) 168 #12# ELT)) (|subtractIfCan| #14=((#15=(|Union| $ #16="failed") $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|sizeMultiplication| (#7# 102 T ELT)) (|sizeLess?| #18=(#1# NIL T ELT)) (|size| (#7# 185 #12# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #16#) $) 126 T ELT)) (|retract| (#9# 104 T ELT)) (|represents| (($ #20=(|Vector| |#1|)) 70 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 211 #12# ELT)) (|rem| #21=(#22=($ $ $) NIL T ELT)) (|recip| ((#15# $) NIL T ELT)) (|random| (#19# 180 #12# ELT)) (|quo| #21#) (|principalIdeal| (((|Record| (|:| |coef| #23=(|List| $)) #24=(|:| |generator| $)) #23#) NIL T ELT)) (|primitiveElement| (#19# 169 #12# ELT)) (|primitive?| (#3# NIL #12# ELT)) (|primeFrobenius| (#25=($ $ #8#) NIL #26=(OR (|has| |#1| (|CharacteristicNonZero|)) #12#) ELT) (#5# NIL #26# ELT)) (|prime?| #6#) (|order| (#27=(#11# $) NIL #12# ELT) (#28=(#29=(|OnePointCompletion| #11#) $) NIL #26# ELT)) (|opposite?| #18#) (|one?| #6#) (|normalElement| (#19# 112 #12# ELT)) (|normal?| (#3# 198 #12# ELT)) (|norm| (#9# 107 T ELT) (#10# 106 #12# ELT)) (|nextItem| (#30=((|Maybe| $) $) NIL #12# ELT)) (|multiEuclidean| (((|Union| #23# #16#) #23# $) NIL T ELT)) (|minimalPolynomial| (#31=(#32=(|SparseUnivariatePolynomial| |#1|) $) 212 T ELT) ((#33=(|SparseUnivariatePolynomial| $) $ #11#) NIL #12# ELT)) (|lookup| (#27# 146 #12# ELT)) (|linearAssociatedOrder| (#31# 86 #12# ELT)) (|linearAssociatedLog| (#31# 83 #12# ELT) (((|Union| #32# #16#) $ $) 95 #12# ELT)) (|linearAssociatedExp| (($ $ #32#) 82 #12# ELT)) (|lcm| #21# #34=(($ #23#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#5# 216 T ELT)) (|init| (#19# NIL #12# CONST)) (|index| (($ #11#) 148 #12# ELT)) (|inGroundField?| (#3# 122 T ELT)) (|hash| ((#35=(|SingleInteger|) $) NIL T ELT)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #35#))))) 96 T ELT)) (|getMultiplicationMatrix| ((#36=(|Matrix| |#1|)) 100 T ELT)) (|generator| (#19# 109 #12# ELT)) (|gcdPolynomial| ((#33# #33# #33#) NIL T ELT)) (|gcd| #21# #34#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #13#) (|:| |exponent| #13#)))) 171 #12# ELT)) (|factor| #17#) (|extensionDegree| ((#29#) NIL T ELT) ((#11#) 172 T ELT)) (|extendedEuclidean| (((|Record| #37=(|:| |coef1| $) #38=(|:| |coef2| $) #24#) $ $) NIL T ELT) (((|Union| (|Record| #37# #38#) #16#) $ $ $) NIL T ELT)) (|exquo| #14#) (|expressIdealMember| (((|Maybe| #23#) #23# $) NIL T ELT)) (|euclideanSize| (#39=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#39# NIL #12# ELT) (((|Union| #8# #16#) $ $) NIL #26# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #40=(#25# NIL #12# ELT) #41=(#5# NIL #12# ELT)) (|degree| (#28# NIL T ELT) (#27# 74 T ELT)) (|definingPolynomial| ((#32#) 173 T ELT)) (|createPrimitiveElement| (#19# 145 #12# ELT)) (|createNormalElement| (#19# NIL #12# ELT)) (|coordinates| ((#20# $) 120 T ELT) ((#36# #42=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #42# #16#) (|Matrix| $)) NIL #12# ELT)) (|coerce| (((|OutputForm|) $) 138 T ELT) (($ #13#) NIL T ELT) #4# (($ #43=(|Fraction| #13#)) NIL T ELT) (($ |#1|) 69 T ELT)) (|charthRoot| #41# (#30# NIL #26# ELT)) (|characteristic| (#7# 178 T CONST)) (|before?| #18#) (|basis| ((#42#) 195 T ELT) ((#42# #11#) 115 T ELT)) (|associates?| #18#) (|annihilate?| #18#) (|algebraic?| #6#) (|Zero| (#19# 184 T CONST)) (|One| (#19# 159 T CONST)) (|Frobenius| (#5# 121 #12# ELT) (#25# 113 #12# ELT)) (D #40# #41#) (= (#1# 206 T ELT)) (/ (#22# 118 T ELT) (#44=($ $ |#1|) 119 T ELT)) (- (#5# 200 T ELT) (#22# 204 T ELT)) (+ (#22# 202 T ELT)) (** (#10# NIL T ELT) (#25# NIL T ELT) (($ $ #13#) 151 T ELT)) (* (($ #11# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #13# $) 209 T ELT) (#22# 162 T ELT) (($ $ #43#) NIL T ELT) (($ #43# $) NIL T ELT) (#44# NIL T ELT) (($ |#1| $) 117 T ELT))) 
(((|FiniteFieldNormalBasisExtensionByPolynomial| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| (#1=(|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| |#1|))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) (|FiniteFieldCategory|) (|Union| (|SparseUnivariatePolynomial| |#1|) #1#)) (T |FiniteFieldNormalBasisExtensionByPolynomial|)) 
((|getMultiplicationTable| #1=(*1 *2) (AND (|isDomain| *2 #2=(|Vector| (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|)))))) #3=(|isDomain| *1 (|FiniteFieldNormalBasisExtensionByPolynomial| *3 *4)) #4=(|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|Union| #5=(|SparseUnivariatePolynomial| *3) *2)))) (|getMultiplicationMatrix| #1# (AND (|isDomain| *2 (|Matrix| *3)) #3# #4# #6=(|ofType| *4 (|Union| #5# #2#)))) (|sizeMultiplication| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #4# #6#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| #7=(#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=((|#1| $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #9#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeMultiplication| #7#) (|sizeLess?| #1#) (|size| (#8# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #18#) $) NIL T ELT)) (|retract| #10#) (|represents| (($ #22=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| ((#17# $) NIL T ELT)) (|random| #24=(#21# NIL #14# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #9#) NIL #29=(OR (|has| |#1| (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #10# #11#) (|nextItem| (#34=((|Maybe| $) $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #18#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| ((#40=(|SingleInteger|) $) NIL T ELT)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #40#))))) NIL T ELT)) (|getMultiplicationMatrix| ((#41=(|Matrix| |#1|)) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #42=(|:| |coef1| $) #43=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #42# #43#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#44=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#44# NIL #14# ELT) (((|Union| #9# #18#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #45=(#28# NIL #14# ELT) #46=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#22# $) NIL T ELT) ((#41# #47=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #47# #18#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #48=(|Fraction| #15#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #46# (#34# NIL #29# ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|basis| ((#47#) NIL T ELT) ((#47# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #20#) (|One| #20#) (|Frobenius| #46# #45#) (D #45# #46#) (= #1#) (/ #23# #49=(($ $ |#1|) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #15# . #50=($)) NIL T ELT) #23# (($ $ #48#) NIL T ELT) (($ #48# . #50#) NIL T ELT) #49# (($ |#1| . #50#) NIL T ELT))) 
(((|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=(*1 *2) (AND (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|)))))) #2=(|isDomain| *1 (|FiniteFieldNormalBasisExtension| *3 *4)) #3=(|ofCategory| *3 (|FiniteFieldCategory|)) #4=(|ofType| *4 (|PositiveInteger|)))) (|getMultiplicationMatrix| #1# (AND (|isDomain| *2 (|Matrix| *3)) #2# #3# #4#)) (|sizeMultiplication| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #2# #3# #4#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #6=(#7=($ $) NIL T ELT)) (|unit?| #4#) (|transcendent?| #4#) (|transcendenceDegree| (#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| (#10=(|#1| $) NIL T ELT) (#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #9#) #14=(|Integer|)) 130 #13# ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#8# 156 #13# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #17#) $) 104 T ELT)) (|retract| (#10# 101 T ELT)) (|represents| (($ #20=(|Vector| |#1|)) 96 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 127 #13# ELT)) (|rem| #21=(#22=($ $ $) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|random| (#19# 93 #13# ELT)) (|quo| #21#) (|principalIdeal| (((|Record| (|:| |coef| #23=(|List| $)) #24=(|:| |generator| $)) #23#) NIL T ELT)) (|primitiveElement| (#19# 52 #13# ELT)) (|primitive?| (#5# NIL #13# ELT)) (|primeFrobenius| (#25=($ $ #9#) NIL #26=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#7# NIL #26# ELT)) (|prime?| #4#) (|order| (#27=(#12# $) NIL #13# ELT) (#28=(#29=(|OnePointCompletion| #12#) $) NIL #26# ELT)) (|opposite?| #1#) (|one?| #4#) (|normalElement| (#19# 131 #13# ELT)) (|normal?| (#5# 85 #13# ELT)) (|norm| (#10# 48 T ELT) (#11# 53 #13# ELT)) (|nextItem| (#30=((|Maybe| $) $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #23# #17#) #23# $) NIL T ELT)) (|minimalPolynomial| (#31=(#32=(|SparseUnivariatePolynomial| |#1|) $) 76 T ELT) ((#33=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| (#27# 108 #13# ELT)) (|linearAssociatedOrder| #34=(#31# NIL #13# ELT)) (|linearAssociatedLog| #34# (((|Union| #32# #17#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #32#) NIL #13# ELT)) (|lcm| #21# #35=(($ #23#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|init| (#19# NIL #13# CONST)) (|index| (($ #12#) 106 #13# ELT)) (|inGroundField?| (#5# 158 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#19# 45 #13# ELT)) (|gcdPolynomial| ((#33# #33# #33#) NIL T ELT)) (|gcd| #21# #35#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) 125 #13# ELT)) (|factor| #18#) (|extensionDegree| ((#29#) NIL T ELT) ((#12#) 155 T ELT)) (|extendedEuclidean| (((|Record| #36=(|:| |coef1| $) #37=(|:| |coef2| $) #24#) $ $) NIL T ELT) (((|Union| (|Record| #36# #37#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #23#) #23# $) NIL T ELT)) (|euclideanSize| (#38=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#38# NIL #13# ELT) (((|Union| #9# #17#) $ $) NIL #26# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #39=(#25# NIL #13# ELT) #40=(#7# NIL #13# ELT)) (|degree| (#28# NIL T ELT) (#27# 68 T ELT)) (|definingPolynomial| ((#32#) 99 T ELT)) (|createPrimitiveElement| (#19# 136 #13# ELT)) (|createNormalElement| (#19# NIL #13# ELT)) (|coordinates| ((#20# $) 64 T ELT) (((|Matrix| |#1|) #41=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #41# #17#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) 154 T ELT) (($ #14#) NIL T ELT) #6# (($ #42=(|Fraction| #14#)) NIL T ELT) (($ |#1|) 98 T ELT)) (|charthRoot| #40# (#30# NIL #26# ELT)) (|characteristic| (#8# 160 T CONST)) (|before?| (#2# 162 T ELT)) (|basis| ((#41#) 120 T ELT) ((#41# #12#) 59 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #4#) (|Zero| (#19# 122 T CONST)) (|One| (#19# 40 T CONST)) (|Frobenius| (#7# 79 #13# ELT) #39#) (D #39# #40#) (= (#2# 118 T ELT)) (/ (#22# 110 T ELT) (#43=($ $ |#1|) 111 T ELT)) (- (#7# 91 T ELT) (#22# 116 T ELT)) (+ (#22# 114 T ELT)) (** (#11# NIL T ELT) (#25# 54 T ELT) (($ $ #14#) 139 T ELT)) (* (($ #12# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #14# $) 89 T ELT) (#22# 66 T ELT) (($ $ #42#) NIL T ELT) (($ #42# $) NIL T ELT) (#43# NIL T ELT) (($ |#1| $) 87 T ELT))) 
(((|FiniteFieldExtensionByPolynomial| |#1| |#2|) (|FiniteAlgebraicExtensionField| |#1|) (|FiniteFieldCategory|) (|SparseUnivariatePolynomial| |#1|)) (T |FiniteFieldExtensionByPolynomial|)) 
NIL 
((|reducedQPowers| (((|PrimitiveArray| #1=(|SparseUnivariatePolynomial| |#1|)) #1#) 49 T ELT)) (|random| ((#1# #2=(|PositiveInteger|) #2#) 159 T ELT) (#3=(#1# #2#) 155 T ELT)) (|primitive?| (#4=((|Boolean|) #1#) 110 T ELT)) (|numberOfPrimitivePoly| (#5=(#2# #2#) 85 T ELT)) (|numberOfNormalPoly| (#5# 94 T ELT)) (|numberOfIrreduciblePoly| (#5# 83 T ELT)) (|normal?| (#4# 114 T ELT)) (|nextPrimitivePoly| (#6=((|Union| #1# "failed") #1#) 139 T ELT)) (|nextPrimitiveNormalPoly| (#6# 144 T ELT)) (|nextNormalPrimitivePoly| (#6# 143 T ELT)) (|nextNormalPoly| (#6# 142 T ELT)) (|nextIrreduciblePoly| (#6# 134 T ELT)) (|leastAffineMultiple| ((#1# #1#) 71 T ELT)) (|createPrimitivePoly| (#3# 149 T ELT)) (|createPrimitiveNormalPoly| (#3# 152 T ELT)) (|createNormalPrimitivePoly| (#3# 151 T ELT)) (|createNormalPoly| (#3# 150 T ELT)) (|createIrreduciblePoly| (#3# 147 T ELT))) 
(((|FiniteFieldPolynomialPackage| |#1|) (CATEGORY |package| (SIGNATURE |primitive?| #1=((|Boolean|) #2=(|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |normal?| #1#) (SIGNATURE |numberOfIrreduciblePoly| #3=(#4=(|PositiveInteger|) #4#)) (SIGNATURE |numberOfPrimitivePoly| #3#) (SIGNATURE |numberOfNormalPoly| #3#) (SIGNATURE |createIrreduciblePoly| #5=(#2# #4#)) (SIGNATURE |createPrimitivePoly| #5#) (SIGNATURE |createNormalPoly| #5#) (SIGNATURE |createNormalPrimitivePoly| #5#) (SIGNATURE |createPrimitiveNormalPoly| #5#) (SIGNATURE |nextIrreduciblePoly| #6=((|Union| #2# "failed") #2#)) (SIGNATURE |nextPrimitivePoly| #6#) (SIGNATURE |nextNormalPoly| #6#) (SIGNATURE |nextNormalPrimitivePoly| #6#) (SIGNATURE |nextPrimitiveNormalPoly| #6#) (SIGNATURE |random| #5#) (SIGNATURE |random| (#2# #4# #4#)) (SIGNATURE |leastAffineMultiple| (#2# #2#)) (SIGNATURE |reducedQPowers| ((|PrimitiveArray| #2#) #2#))) (|FiniteFieldCategory|)) (T |FiniteFieldPolynomialPackage|)) 
((|reducedQPowers| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|FiniteFieldCategory|)) (|isDomain| *2 (|PrimitiveArray| #4=(|SparseUnivariatePolynomial| *4))) #5=(|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) #6=(|isDomain| *3 #4#))) (|leastAffineMultiple| #7=(*1 *2 *2) (AND #8=(|isDomain| *2 (|SparseUnivariatePolynomial| *3)) #9=(|ofCategory| *3 #3#) #10=(|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)))) (|random| (*1 *2 *3 *3) #11=(AND (|isDomain| *3 #12=(|PositiveInteger|)) (|isDomain| *2 #4#) #5# #2#)) (|random| #1# #11#) (|nextPrimitiveNormalPoly| #7# #13=(|partial| AND #8# #9# #10#)) (|nextNormalPrimitivePoly| #7# #13#) (|nextNormalPoly| #7# #13#) (|nextPrimitivePoly| #7# #13#) (|nextIrreduciblePoly| #7# #13#) (|createPrimitiveNormalPoly| #1# #11#) (|createNormalPrimitivePoly| #1# #11#) (|createNormalPoly| #1# #11#) (|createPrimitivePoly| #1# #11#) (|createIrreduciblePoly| #1# #11#) (|numberOfNormalPoly| #7# #14=(AND (|isDomain| *2 #12#) #10# #9#)) (|numberOfPrimitivePoly| #7# #14#) (|numberOfIrreduciblePoly| #7# #14#) (|normal?| #1# #15=(AND #6# #2# (|isDomain| *2 (|Boolean|)) #5#)) (|primitive?| #1# #15#)) 
((|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) 60 T ELT))) 
(((|FiniteFieldPolynomialPackage2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rootOfIrreduciblePoly| (|#1| (|SparseUnivariatePolynomial| |#2|)))) (|Join| (|FieldOfPrimeCharacteristic|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |lookup| (#1=(|PositiveInteger|) |#1|)) (SIGNATURE |basis| ((|Vector| |#1|) #1#)) (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| (#1=(|PositiveInteger|) *2)) (SIGNATURE |basis| ((|Vector| *2) #1#)) (SIGNATURE |Frobenius| (*2 *2))))) (|isDomain| *1 (|FiniteFieldPolynomialPackage2| *2 *4))))) 
((|solveLinearPolynomialEquation| (((|Union| #1=(|List| |#3|) "failed") #1# |#3|) 40 T ELT))) 
(((|FiniteFieldSolveLinearPolynomialEquation| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #1=(|List| |#3|) "failed") #1# |#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))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((|#1| $) NIL T ELT) #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #8#) #14=(|Integer|)) NIL #13# ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #13# ELT)) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #17#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #21=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #13# ELT)) (|rem| #22=(($ $ $) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|random| #23=(#20# NIL #13# ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL T ELT)) (|primitiveElement| #23#) (|primitive?| #26=(#4# NIL #13# ELT)) (|primeFrobenius| (#27=($ $ #8#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#6# NIL #28# ELT)) (|prime?| #3#) (|order| #29=(#30=(#12# $) NIL #13# ELT) (#31=(#32=(|OnePointCompletion| #12#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #23#) (|normal?| #26#) (|norm| #9# #10#) (|nextItem| (#33=((|Maybe| $) $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #24# #17#) #24# $) NIL T ELT)) (|minimalPolynomial| (#34=(#35=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#36=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| #29#) (|linearAssociatedOrder| #37=(#34# NIL #13# ELT)) (|linearAssociatedLog| #37# (((|Union| #35# #17#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #35#) NIL #13# ELT)) (|lcm| #22# #38=(($ #24#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#20# NIL #13# CONST)) (|index| (($ #12#) NIL #13# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #23#) (|gcdPolynomial| ((#36# #36# #36#) NIL T ELT)) (|gcd| #22# #38#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) NIL #13# ELT)) (|factor| #18#) (|extensionDegree| ((#32#) NIL T ELT) ((#12#) NIL T ELT)) (|extendedEuclidean| (((|Record| #39=(|:| |coef1| $) #40=(|:| |coef2| $) #25#) $ $) NIL T ELT) (((|Union| (|Record| #39# #40#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL T ELT)) (|euclideanSize| (#41=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#41# NIL #13# ELT) (((|Union| #8# #17#) $ $) NIL #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #42=(#27# NIL #13# ELT) #43=(#6# NIL #13# ELT)) (|degree| (#31# NIL T ELT) (#30# NIL T ELT)) (|definingPolynomial| ((#35#) NIL T ELT)) (|createPrimitiveElement| #23#) (|createNormalElement| #23#) (|coordinates| ((#21# $) NIL T ELT) (((|Matrix| |#1|) #44=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #44# #17#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #5# (($ #45=(|Fraction| #14#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #43# (#33# NIL #28# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#44#) NIL T ELT) ((#44# #12#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #19#) (|One| #19#) (|Frobenius| #43# #42#) (D #42# #43#) (= #1#) (/ #22# #46=(($ $ |#1|) NIL T ELT)) (- #5# #22#) (+ #22#) (** (#11# NIL T ELT) (#27# NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #47=($)) NIL T ELT) #22# (($ $ #45#) NIL T ELT) (($ #45# . #47#) NIL T ELT) #46# (($ |#1| . #47#) NIL T ELT))) 
(((|FiniteFieldExtension| |#1| |#2|) (|FiniteAlgebraicExtensionField| |#1|) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldExtension|)) 
NIL 
((|zeroDimensional?| (((|Boolean|) #1=(|List| (|Polynomial| |#1|))) 41 T ELT)) (|groebner| ((#1# #1#) 53 T ELT)) (|fglmIfCan| (((|Union| #1# "failed") #1#) 48 T ELT))) 
(((|FGLMIfCanPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimensional?| ((|Boolean|) #1=(|List| (|Polynomial| |#1|)))) (SIGNATURE |fglmIfCan| ((|Union| #1# "failed") #1#)) (SIGNATURE |groebner| (#1# #1#))) (|GcdDomain|) (|List| (|Symbol|))) (T |FGLMIfCanPackage|)) 
((|groebner| #1=(*1 *2 *2) (AND #2=(|isDomain| *2 (|List| (|Polynomial| *3))) #3=(|ofCategory| *3 #4=(|GcdDomain|)) #5=(|isDomain| *1 (|FGLMIfCanPackage| *3 *4)) #6=(|ofType| *4 #7=(|List| (|Symbol|))))) (|fglmIfCan| #1# (|partial| AND #2# #3# #5# #6#)) (|zeroDimensional?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofCategory| *4 #4#) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FGLMIfCanPackage| *4 *5)) (|ofType| *5 #7#)))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|size| ((#3=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #5="failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|recip| (((|Union| $ #5#) $) NIL T ELT)) (|one?| ((#2# $) 17 T ELT)) (|nthFactor| ((|#1| $ #6=(|Integer|)) NIL T ELT)) (|nthExpon| ((#6# $ #6#) NIL T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 34 T ELT)) (|mapExpon| (($ (|Mapping| #6# #6#) $) 26 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (($ $) 28 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #6#))) $) 30 T ELT)) (|conjugate| #7=(#8=($ $ $) NIL T ELT)) (|commutator| #7#) (|coerce| (((|OutputForm|) $) 40 T ELT) (($ |#1|) NIL T ELT)) (|before?| #1#) (|One| (#4# 7 T CONST)) (= #1#) (/ #7#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #3#) NIL T ELT) (($ $ #6#) NIL T ELT) (($ |#1| #6#) 19 T ELT)) (* (#8# 53 T ELT) (($ |#1| $) 23 T ELT) (($ $ |#1|) 21 T ELT))) 
(((|FreeGroup| |#1|) (|Join| (|Group|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE ** ($ |#1| #1=(|Integer|))) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |nthExpon| (#1# $ #1#)) (SIGNATURE |nthFactor| (|#1| $ #1#)) (SIGNATURE |mapExpon| ($ (|Mapping| #1# #1#) $)) (SIGNATURE |mapGen| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |factors| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #1#))) $)))) (|SetCategory|)) (T |FreeGroup|)) 
((* #1=(*1 *1 *2 *1) #2=(AND #3=(|isDomain| *1 (|FreeGroup| *2)) #4=(|ofCategory| *2 #5=(|SetCategory|)))) (* (*1 *1 *1 *2) #2#) (** (*1 *1 *2 *3) #6=(AND (|isDomain| *3 #7=(|Integer|)) #3# #4#)) (|size| #8=(*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) #9=(|isDomain| *1 (|FreeGroup| *3)) #10=(|ofCategory| *3 #5#))) (|nthExpon| (*1 *2 *1 *2) (AND (|isDomain| *2 #7#) #9# #10#)) (|nthFactor| (*1 *2 *1 *3) #6#) (|mapExpon| #1# (AND (|isDomain| *2 (|Mapping| #7# #7#)) #9# #10#)) (|mapGen| #1# (AND (|isDomain| *2 (|Mapping| *3 *3)) #10# #9#)) (|factors| #8# (AND (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| #7#)))) #9# #10#))) 
((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 13 T ELT)) (|unitCanonical| (#1=($ $) 14 T ELT)) (|squareFree| (#2=((|Factored| $) $) 31 T ELT)) (|prime?| ((#3=(|Boolean|) $) 27 T ELT)) (|inv| (#1# 19 T ELT)) (|gcd| (#4=($ $ $) 22 T ELT) (($ (|List| $)) NIL T ELT)) (|factor| (#2# 32 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 21 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 25 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 36 T ELT)) (|associates?| ((#3# $ $) 16 T ELT)) (/ (#4# 34 T ELT))) 
(((|Field&| |#1|) (CATEGORY |package| (SIGNATURE / #1=(|#1| |#1| |#1|)) (SIGNATURE |inv| #2=(|#1| |#1|)) (SIGNATURE |prime?| (#3=(|Boolean|) |#1|)) (SIGNATURE |squareFree| #4=((|Factored| |#1|) |#1|)) (SIGNATURE |factor| #4#) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcd| #1#) (SIGNATURE |associates?| (#3# |#1| |#1|)) (SIGNATURE |unitCanonical| #2#) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|))) (|Field|)) (T |Field&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 68 T ELT)) (|lcm| (#10=($ $ $) 60 T ELT) (#11=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 58 T ELT)) (|gcd| (#10# 62 T ELT) (#11# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 84 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #16#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #15#) 86 T ELT) (($ #15# . #17#) 85 T ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|write!| ((|#1| $ |#1|) 35 T ELT)) (|reopen!| (($ $ #3=(|String|)) 23 T ELT)) (|readIfCan!| (((|Union| |#1| "failed") $) 34 T ELT)) (|read!| ((|#1| $) 32 T ELT)) (|open| (($ #4=(|FileName|)) 22 T ELT) (($ #4# #3#) 21 T ELT)) (|name| ((#4# $) 25 T ELT)) (|latex| (#5=(#3# $) NIL T ELT)) (|iomode| (#5# 26 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT)) (|close!| (($ $) 24 T ELT)) (|before?| #1#) (= (#2# 19 T ELT))) 
(((|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|))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|write!| ((|#2| $ |#2|) 17 T ELT)) (|reopen!| (($ $ (|String|)) 22 T ELT)) (|read!| ((|#2| $) 18 T ELT)) (|open| (($ |#1|) 24 T ELT) (($ |#1| (|String|)) 23 T ELT)) (|name| ((|#1| $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|iomode| (((|String|) $) 19 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|close!| (($ $) 21 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|FileCategory| |#1| |#2|) (|Category|) (|SetCategory|) (|SetCategory|)) (T |FileCategory|)) 
((|open| (*1 *1 *2) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|open| (*1 *1 *2 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *1 (|FileCategory| *2 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|reopen!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|close!| (*1 *1 *1) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|name| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|iomode| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|String|)))) (|read!| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|write!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|FileCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |open| ($ |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|)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|structuralConstants| (((|Vector| #1=(|Matrix| |#2|)) #2=(|Vector| $)) 67 T ELT)) (|rightTraceMatrix| (#3=(#1# #2#) 139 T ELT)) (|rightTrace| (#4=(|#2| $) 36 T ELT)) (|rightRegularRepresentation| (#5=(#1# $ #2#) 142 T ELT)) (|rightRecip| (#6=((|Union| $ "failed") $) 89 T ELT)) (|rightNorm| (#4# 39 T ELT)) (|rightMinimalPolynomial| (#7=((|SparseUnivariatePolynomial| |#2|) $) 98 T ELT)) (|rightDiscriminant| (#8=(|#2| #2#) 122 T ELT)) (|rightCharacteristicPolynomial| (#7# 32 T ELT)) (|rightAlternative?| (#9=((|Boolean|)) 116 T ELT)) (|represents| (($ #10=(|Vector| |#2|) #2#) 132 T ELT)) (|recip| (#6# 93 T ELT)) (|noncommutativeJordanAlgebra?| (#9# 111 T ELT)) (|lieAlgebra?| (#9# 106 T ELT)) (|lieAdmissible?| (#9# 58 T ELT)) (|leftTraceMatrix| (#3# 137 T ELT)) (|leftTrace| (#4# 35 T ELT)) (|leftRegularRepresentation| (#5# 141 T ELT)) (|leftRecip| (#6# 87 T ELT)) (|leftNorm| (#4# 38 T ELT)) (|leftMinimalPolynomial| (#7# 97 T ELT)) (|leftDiscriminant| (#8# 120 T ELT)) (|leftCharacteristicPolynomial| (#7# 30 T ELT)) (|leftAlternative?| (#9# 115 T ELT)) (|jordanAlgebra?| (#9# 108 T ELT)) (|jordanAdmissible?| (#9# 56 T ELT)) (|jacobiIdentity?| (#9# 103 T ELT)) (|flexible?| (#9# 117 T ELT)) (|coordinates| ((#10# $ #2#) NIL T ELT) ((#1# #2# #2#) 128 T ELT)) (|commutative?| (#9# 113 T ELT)) (|associatorDependence| (((|List| #10#)) 102 T ELT)) (|associative?| (#9# 114 T ELT)) (|antiCommutative?| (#9# 112 T ELT)) (|antiAssociative?| (#9# 51 T ELT)) (|alternative?| (#9# 118 T ELT))) 
(((|FiniteRankNonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rightMinimalPolynomial| #1=((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |leftMinimalPolynomial| #1#) (SIGNATURE |associatorDependence| ((|List| #2=(|Vector| |#2|)))) (SIGNATURE |rightRecip| #3=((|Union| |#1| "failed") |#1|)) (SIGNATURE |leftRecip| #3#) (SIGNATURE |recip| #3#) (SIGNATURE |lieAlgebra?| #4=((|Boolean|))) (SIGNATURE |jordanAlgebra?| #4#) (SIGNATURE |noncommutativeJordanAlgebra?| #4#) (SIGNATURE |jordanAdmissible?| #4#) (SIGNATURE |lieAdmissible?| #4#) (SIGNATURE |jacobiIdentity?| #4#) (SIGNATURE |alternative?| #4#) (SIGNATURE |flexible?| #4#) (SIGNATURE |rightAlternative?| #4#) (SIGNATURE |leftAlternative?| #4#) (SIGNATURE |antiAssociative?| #4#) (SIGNATURE |associative?| #4#) (SIGNATURE |antiCommutative?| #4#) (SIGNATURE |commutative?| #4#) (SIGNATURE |rightCharacteristicPolynomial| #1#) (SIGNATURE |leftCharacteristicPolynomial| #1#) (SIGNATURE |rightTraceMatrix| #5=(#6=(|Matrix| |#2|) #7=(|Vector| |#1|))) (SIGNATURE |leftTraceMatrix| #5#) (SIGNATURE |rightDiscriminant| #8=(|#2| #7#)) (SIGNATURE |leftDiscriminant| #8#) (SIGNATURE |represents| (|#1| #2# #7#)) (SIGNATURE |coordinates| (#6# #7# #7#)) (SIGNATURE |coordinates| (#2# |#1| #7#)) (SIGNATURE |rightNorm| #9=(|#2| |#1|)) (SIGNATURE |leftNorm| #9#) (SIGNATURE |rightTrace| #9#) (SIGNATURE |leftTrace| #9#) (SIGNATURE |rightRegularRepresentation| #10=(#6# |#1| #7#)) (SIGNATURE |leftRegularRepresentation| #10#) (SIGNATURE |structuralConstants| ((|Vector| #6#) #7#))) (|FiniteRankNonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |FiniteRankNonAssociativeAlgebra&|)) 
((|commutative?| #1=(*1 *2) #2=(AND #3=(|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) #5=(|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|antiCommutative?| #1# #2#) (|associative?| #1# #2#) (|antiAssociative?| #1# #2#) (|leftAlternative?| #1# #2#) (|rightAlternative?| #1# #2#) (|flexible?| #1# #2#) (|alternative?| #1# #2#) (|jacobiIdentity?| #1# #2#) (|lieAdmissible?| #1# #2#) (|jordanAdmissible?| #1# #2#) (|noncommutativeJordanAlgebra?| #1# #2#) (|jordanAlgebra?| #1# #2#) (|lieAlgebra?| #1# #2#) (|associatorDependence| #1# (AND #3# (|isDomain| *2 (|List| (|Vector| *4))) #4# #5#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unit| (((|Union| $ "failed")) 48 (|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) 89 T ELT)) (|someBasis| (((|Vector| $)) 92 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 51 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightUnit| (((|Union| $ "failed")) 49 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 76 T ELT)) (|rightTrace| ((|#1| $) 85 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 87 T ELT)) (|rightRecip| (((|Union| $ "failed") $) 56 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 37 T ELT)) (|rightNorm| ((|#1| $) 83 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 53 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightDiscriminant| ((|#1| (|Vector| $)) 78 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 74 T ELT)) (|rightAlternative?| (((|Boolean|)) 68 T ELT)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 80 T ELT)) (|recip| (((|Union| $ "failed") $) 58 (|has| |#1| (|IntegralDomain|)) ELT)) (|rank| (((|PositiveInteger|)) 91 T ELT)) (|powerAssociative?| (((|Boolean|)) 65 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 44 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) 61 T ELT)) (|lieAlgebra?| (((|Boolean|)) 59 T ELT)) (|lieAdmissible?| (((|Boolean|)) 63 T ELT)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 52 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftUnit| (((|Union| $ "failed")) 50 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 77 T ELT)) (|leftTrace| ((|#1| $) 86 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 88 T ELT)) (|leftRecip| (((|Union| $ "failed") $) 57 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftPower| (#4# 38 T ELT)) (|leftNorm| ((|#1| $) 84 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 54 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftDiscriminant| ((|#1| (|Vector| $)) 79 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 75 T ELT)) (|leftAlternative?| (((|Boolean|)) 69 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (((|Boolean|)) 60 T ELT)) (|jordanAdmissible?| (((|Boolean|)) 62 T ELT)) (|jacobiIdentity?| (((|Boolean|)) 64 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (((|Boolean|)) 67 T ELT)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 82 T ELT) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 81 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) 90 T ELT)) (|commutator| (#5=($ $ $) 34 T ELT)) (|commutative?| (((|Boolean|)) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 55 (|has| |#1| (|IntegralDomain|)) ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|associative?| (((|Boolean|)) 71 T ELT)) (|antiCommutator| (#5# 33 T ELT)) (|antiCommutative?| (((|Boolean|)) 72 T ELT)) (|antiAssociative?| (((|Boolean|)) 70 T ELT)) (|alternative?| (((|Boolean|)) 66 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 30 T ELT) (($ $ $) 36 T ELT) (($ $ |#1|) 46 T ELT) (($ |#1| . #6#) 45 T ELT))) 
(((|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) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeAlgebra| |#1|) . T) ((|NonAssociativeRng|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|reduce| ((|#2| #1=(|Mapping| |#2| |#2| |#2|) $) NIL T ELT) ((|#2| #1# $ |#2|) NIL T ELT) ((|#2| #1# $ |#2| |#2|) 38 T ELT)) (|member?| ((#2=(|Boolean|) |#2| $) 35 T ELT)) (|find| (((|Union| |#2| "failed") #3=(|Mapping| #2# |#2|) $) 30 T ELT)) (|every?| (#4=(#2# #3# $) 24 T ELT)) (|empty?| ((#2# $) 13 T ELT)) (|count| ((#5=(|NonNegativeInteger|) #3# $) 27 T ELT) ((#5# |#2| $) 33 T ELT)) (|coerce| (((|OutputForm|) $) 46 T ELT)) (|any?| (#4# 21 T ELT)) (= ((#2# $ $) 40 T ELT)) (|#| ((#5# $) 17 T ELT))) 
(((|FiniteAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |reduce| (|#2| #2=(|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |member?| (#1# |#2| |#1|)) (SIGNATURE |count| (#3=(|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |find| ((|Union| |#2| "failed") #4=(|Mapping| #1# |#2|) |#1|)) (SIGNATURE |reduce| (|#2| #2# |#1| |#2|)) (SIGNATURE |reduce| (|#2| #2# |#1|)) (SIGNATURE |count| (#3# #4# |#1|)) (SIGNATURE |every?| #5=(#1# #4# |#1|)) (SIGNATURE |any?| #5#) (SIGNATURE |#| (#3# |#1|)) (SIGNATURE |empty?| (#1# |#1|))) (|FiniteAggregate| |#2|) (|Type|)) (T |FiniteAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|sample| (#3=($) 6 T CONST)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 39 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 38 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 34 (|has| |#1| (|BasicType|)) ELT)) (|members| (((|List| |#1|) $) 40 T ELT)) (|member?| (((|Boolean|) |#1| $) 35 (|has| |#1| (|BasicType|)) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #4=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #4#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) 37 T ELT)) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 42 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT)) (|eq?| ((#5=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#5# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|count| (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) 41 T ELT) (((|NonNegativeInteger|) |#1| $) 36 (|has| |#1| (|BasicType|)) ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) 43 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| (((|NonNegativeInteger|) $) 44 T ELT))) 
(((|FiniteAggregate| |#1|) (|Category|) (|Type|)) (T |FiniteAggregate|)) 
((|#| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|any?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|ofCategory| *1 (|FiniteAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|every?| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|ofCategory| *1 (|FiniteAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|count| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *4)) (|ofCategory| *1 (|FiniteAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|members| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|List| *3)))) (|reduce| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|reduce| (*1 *2 *3 *1 *2) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|find| (*1 *2 *3 *1) (|partial| AND (|isDomain| *3 (|Mapping| (|Boolean|) *2)) (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|count| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|BasicType|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|member?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|BasicType|)) (|isDomain| *2 (|Boolean|)))) (|reduce| (*1 *2 *3 *1 *2 *2) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|ofCategory| *2 (|BasicType|)) (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |any?| ((|Boolean|) (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |every?| ((|Boolean|) (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |count| ((|NonNegativeInteger|) (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |members| ((|List| |t#1|) $)) (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 |find| ((|Union| |t#1| "failed") (|Mapping| (|Boolean|) |t#1|) $)) (IF (|has| |t#1| (|BasicType|)) (PROGN (SIGNATURE |count| ((|NonNegativeInteger|) |t#1| $)) (SIGNATURE |member?| ((|Boolean|) |t#1| $)) (SIGNATURE |reduce| (|t#1| (|Mapping| |t#1| |t#1| |t#1|) $ |t#1| |t#1|))) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|random| (($) 15 T ELT))) 
(((|Finite&| |#1|) (CATEGORY |package| (SIGNATURE |random| (|#1|))) (|Finite|)) (T |Finite&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|size| (((|NonNegativeInteger|)) 20 T ELT)) (|random| (($) 17 T ELT)) (|lookup| (((|PositiveInteger|) $) 18 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|index| (($ (|PositiveInteger|)) 19 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|Finite|) (|Category|)) (T |Finite|)) 
((|size| (*1 *2) (AND (|ofCategory| *1 (|Finite|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|index| (*1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|Finite|)))) (|lookup| (*1 *2 *1) (AND (|ofCategory| *1 (|Finite|)) (|isDomain| *2 (|PositiveInteger|)))) (|random| (*1 *1) (|ofCategory| *1 (|Finite|)))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE |index| ($ (|PositiveInteger|))) (SIGNATURE |lookup| ((|PositiveInteger|) $)) (SIGNATURE |random| ($)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|traceMatrix| ((#1=(|Matrix| |#2|) #2=(|Vector| $)) 45 T ELT)) (|represents| (($ #3=(|Vector| |#2|) #2#) 39 T ELT)) (|regularRepresentation| ((#1# $ #2#) 47 T ELT)) (|discriminant| ((|#2| #2#) 13 T ELT)) (|coordinates| ((#3# $ #2#) NIL T ELT) ((#1# #2# #2#) 27 T ELT))) 
(((|FiniteRankAlgebra&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |traceMatrix| (#1=(|Matrix| |#2|) #2=(|Vector| |#1|))) (SIGNATURE |discriminant| (|#2| #2#)) (SIGNATURE |represents| (|#1| #3=(|Vector| |#2|) #2#)) (SIGNATURE |coordinates| (#1# #2# #2#)) (SIGNATURE |coordinates| (#3# |#1| #2#)) (SIGNATURE |regularRepresentation| (#1# |#1| #2#))) (|FiniteRankAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |FiniteRankAlgebra&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) 61 T ELT)) (|trace| ((|#1| $) 67 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 63 T ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 68 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rank| (((|PositiveInteger|)) 69 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|norm| ((|#1| $) 66 T ELT)) (|minimalPolynomial| ((|#2| $) 59 (|has| |#1| (|Field|)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|discriminant| ((|#1| (|Vector| $)) 62 T ELT)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 65 T ELT) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 64 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT)) (|charthRoot| (((|Maybe| $) $) 58 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#2| $) 60 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #4#) 53 T ELT))) 
(((|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|)) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|sorted?| ((#1=(|Boolean|) #2=(|Mapping| #1# |#2| |#2|) $) NIL T ELT) ((#1# $) 18 T ELT)) (|sort!| (#3=($ #2# $) NIL T ELT) (#4=($ $) 28 T ELT)) (|sort| (#3# 27 T ELT) (#4# 22 T ELT)) (|reverse| (#4# 25 T ELT)) (|position| ((#5=(|Integer|) (|Mapping| #1# |#2|) $) NIL T ELT) ((#5# |#2| $) 11 T ELT) ((#5# |#2| $ #5#) NIL T ELT)) (|merge| (($ #2# $ $) NIL T ELT) (($ $ $) 20 T ELT))) 
(((|FiniteLinearAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sort!| #1=(|#1| |#1|)) (SIGNATURE |sort!| #2=(|#1| #3=(|Mapping| #4=(|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |sorted?| (#4# |#1|)) (SIGNATURE |sort| #1#) (SIGNATURE |merge| (|#1| |#1| |#1|)) (SIGNATURE |position| (#5=(|Integer|) |#2| |#1| #5#)) (SIGNATURE |position| (#5# |#2| |#1|)) (SIGNATURE |position| (#5# (|Mapping| #4# |#2|) |#1|)) (SIGNATURE |sorted?| (#4# #3# |#1|)) (SIGNATURE |sort| #2#) (SIGNATURE |reverse| #1#) (SIGNATURE |merge| (|#1| #3# |#1| |#1|))) (|FiniteLinearAggregate| |#2|) (|Type|)) (T |FiniteLinearAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|swap!| (((|Void|) $ #3=(|Integer|) #3#) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) 96 T ELT) (((|Boolean|) $) 90 (|has| |#1| (|OrderedSet|)) ELT)) (|sort!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 87 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $) 86 (AND (|has| |#1| (|OrderedSet|)) (|has| $ (|ShallowlyMutableAggregate| |#1|))) ELT)) (|sort| (($ (|Mapping| (|Boolean|) |#1| |#1|) $) 97 T ELT) (($ $) 91 (|has| |#1| (|OrderedSet|)) ELT)) (|setelt| ((|#1| $ #3# |#1|) 47 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #4=(|UniversalSegment| #3#) |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 69 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#7=($) 6 T CONST)) (|reverse!| (($ $) 88 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|reverse| (($ $) 98 T ELT)) (|removeDuplicates| (($ $) 71 (AND (|has| |#1| . #8=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 70 (AND (|has| |#1| . #8#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #5# |#1|) . #6#) 68 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 110 (|has| |#1| . #9=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 106 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 105 T ELT)) (|qsetelt!| ((|#1| $ #3# |#1|) 48 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #3#) 46 T ELT)) (|position| (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) 95 T ELT) (((|Integer|) |#1| $) 94 (|has| |#1| (|BasicType|)) ELT) (((|Integer|) |#1| $ (|Integer|)) 93 (|has| |#1| (|BasicType|)) ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| ((#3# . #10=($)) 38 (|has| #3# . #11=((|OrderedSet|))) ELT)) (|min| (#12=($ $ $) 80 (|has| |#1| . #13=((|OrderedSet|))) ELT)) (|merge| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 99 T ELT) (($ $ $) 92 (|has| |#1| (|OrderedSet|)) ELT)) (|members| (((|List| |#1|) $) 104 T ELT)) (|member?| ((#14=(|Boolean|) |#1| $) 109 (|has| |#1| . #9#) ELT)) (|maxIndex| ((#3# . #10#) 39 (|has| #3# . #11#) ELT)) (|max| (#12# 81 (|has| |#1| . #13#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 60 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #15=((|SetCategory|))) ELT)) (|insert| (($ |#1| $ #3#) 57 T ELT) (($ $ $ #3#) 56 T ELT)) (|indices| (((|List| #3#) $) 41 T ELT)) (|index?| ((#16=(|Boolean|) #3# $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #15#) ELT)) (|first| ((|#1| $) 37 (|has| #3# . #11#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #14# |#1|) $) 107 T ELT)) (|fill!| (($ $ |#1|) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|every?| ((#14# (|Mapping| #14# |#1|) . #17=($)) 102 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #15#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #15#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #15#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #15#)) ELT)) (|eq?| ((#18=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#16# |#1| $) 40 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 43 T ELT)) (|empty?| ((#18# $) 7 T ELT)) (|empty| (#7# 8 T ELT)) (|elt| ((|#1| $ #3# |#1|) 45 T ELT) ((|#1| $ #3#) 44 T ELT) (($ $ #4#) 66 T ELT)) (|delete| (($ $ #3#) 59 T ELT) (($ $ #4#) 58 T ELT)) (|count| ((#19=(|NonNegativeInteger|) |#1| $) 108 (|has| |#1| . #9#) ELT) ((#19# (|Mapping| #14# |#1|) $) 103 T ELT)) (|copyInto!| (($ $ $ (|Integer|)) 89 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#20=(|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| #20#)) ELT)) (|construct| (($ (|List| |#1|)) 67 T ELT)) (|concat| (($ $ |#1|) 64 T ELT) (($ |#1| $) 63 T ELT) (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#14# (|Mapping| #14# |#1|) . #17#) 101 T ELT)) (>= (#21=((|Boolean|) $ $) 82 (|has| |#1| . #13#) ELT)) (> (#21# 84 (|has| |#1| . #13#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (<= (#21# 83 (|has| |#1| . #13#) ELT)) (< (#21# 85 (|has| |#1| . #13#) ELT)) (|#| ((#19# $) 100 T ELT))) 
(((|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 (|BasicType|)) (|isDomain| *2 (|Integer|)))) (|position| (*1 *2 *3 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|BasicType|)))) (|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|)) (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|reverse!| (*1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|sort!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3 *3)) (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|ofCategory| *1 (|FiniteLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|sort!| (*1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|OrderedSet|))))) 
(|Join| (|LinearAggregate| |t#1|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (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| (|BasicType|)) (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| $ (|ShallowlyMutableAggregate| |t#1|)) (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|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|Type|) . T)) 
((|scan| ((|#4| #1=(|Mapping| |#3| |#1| |#3|) |#2| |#3|) 25 T ELT)) (|reduce| ((|#3| #1# |#2| |#3|) 17 T ELT)) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 23 T ELT))) 
(((|FiniteLinearAggregateFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|)) (SIGNATURE |reduce| (|#3| #1=(|Mapping| |#3| |#1| |#3|) |#2| |#3|)) (SIGNATURE |scan| (|#4| #1# |#2| |#3|))) #2=(|Type|) (|FiniteLinearAggregate| |#1|) #2# (|FiniteLinearAggregate| |#3|)) (T |FiniteLinearAggregateFunctions2|)) 
((|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) #1=(|ofCategory| *6 #2=(|Type|)) #3=(|ofCategory| *5 #2#) (|ofCategory| *2 #4=(|FiniteLinearAggregate| *5)) (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *6 *4 *5 *2)) (|ofCategory| *4 #5=(|FiniteLinearAggregate| *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #3# (|ofCategory| *2 #2#) (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *5 *4 *2 *6)) #6=(|ofCategory| *4 #4#) (|ofCategory| *6 (|FiniteLinearAggregate| *2)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) #3# #1# (|ofCategory| *2 #5#) (|isDomain| *1 (|FiniteLinearAggregateFunctions2| *5 *4 *6 *2)) #6#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|varList| (((|List| |#1|) $) 43 T ELT)) (|trunc| (($ $ (|NonNegativeInteger|)) 44 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 47 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|mirror| (($ $) 45 T ELT)) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) 48 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ |#1| $) 42 T ELT) (($ $ (|List| |#1|) (|List| $)) 41 T ELT)) (|degree| (((|NonNegativeInteger|) $) 49 T ELT)) (|construct| (($ $ $) 40 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 52 T ELT) (((|XDistributedPolynomial| |#1| |#2|) $) 51 T ELT) (((|XRecursivePolynomial| |#1| |#2|) $) 50 T ELT)) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) 53 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (|LiePoly| (($ (|LyndonWord| |#1|)) 46 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#2|) 39 (|has| |#2| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#2| . #4#) 33 T ELT) (($ $ |#2|) 37 T ELT))) 
(((|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) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#2|) . T) ((|LeftModule| |#2|) . T) ((|LieAlgebra| |#2|) . T) ((|LinearSet| |#2|) . T) ((|Module| |#2|) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|shellSort| (#1=(|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) 40 T ELT)) (|quickSort| (#1# 13 T ELT)) (|heapSort| (#1# 33 T ELT))) 
(((|FiniteLinearAggregateSort| |#1| |#2|) (CATEGORY |package| (SIGNATURE |quickSort| #1=(|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|)) (SIGNATURE |heapSort| #1#) (SIGNATURE |shellSort| #1#)) (|Type|) (|Join| (|FiniteLinearAggregate| |#1|) (|ShallowlyMutableAggregate| |#1|))) (T |FiniteLinearAggregateSort|)) 
((|shellSort| #1=(*1 *2 *3 *2) #2=(AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *1 (|FiniteLinearAggregateSort| *4 *2)) (|ofCategory| *2 (|Join| (|FiniteLinearAggregate| *4) (|ShallowlyMutableAggregate| *4))))) (|heapSort| #1# #2#) (|quickSort| #1# #2#)) 
((|reducedSystem| ((#1=(|Matrix| |#2|) #2=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #1#) (|:| |vec| (|Vector| |#2|))) #2# #3=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #4=(|Matrix| #5=(|Integer|))) (|:| |vec| (|Vector| #5#))) #2# #3#) 22 T ELT) ((#4# #2#) 14 T ELT))) 
(((|FullyLinearlyExplicitRingOver&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |reducedSystem| (#1=(|Matrix| #2=(|Integer|)) #3=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #1#) (|:| |vec| (|Vector| #2#))) #3# #4=(|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #5=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) #3# #4#)) (SIGNATURE |reducedSystem| (#5# #3#))) (|FullyLinearlyExplicitRingOver| |#2|) (|Ring|)) (T |FullyLinearlyExplicitRingOver&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reducedSystem| (((|Matrix| |#1|) . #4=(#5=(|Matrix| $))) 36 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #6=(#5# #7=(|Vector| $))) 35 T ELT) (((|Record| (|:| |mat| (|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) . #6#) 47 (|has| |#1| . #9=((|LinearlyExplicitRingOver| (|Integer|)))) ELT) (((|Matrix| #8#) . #4#) 46 (|has| |#1| . #9#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftReducedSystem| (((|Matrix| |#1|) . #10=(#7#)) 38 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #11=(#7# $)) 37 T ELT) (((|Record| (|:| |mat| (|Matrix| #8#)) (|:| |vec| (|Vector| #8#))) . #11#) 45 (|has| |#1| . #9#) ELT) (((|Matrix| #8#) . #10#) 44 (|has| |#1| . #9#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #12=($)) 30 T ELT) (($ |#1| . #12#) 33 T ELT))) 
(((|FullyLinearlyExplicitRingOver| |#1|) (|Category|) (|Ring|)) (T |FullyLinearlyExplicitRingOver|)) 
NIL 
(|Join| (|LinearlyExplicitRingOver| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|LinearlyExplicitRingOver| (|Integer|))) (ATTRIBUTE (|LinearlyExplicitRingOver| (|Integer|))) |%noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| #1=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LinearlyExplicitRingOver| #1#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 16 T ELT)) (|wholePart| (#5=(#6=(|Integer|) $) 44 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #7=(#8=($ $) NIL T ELT)) (|unit?| #9=(#4# NIL T ELT)) (|truncate| (#8# 120 T ELT)) (|tanh| (#8# 81 T ELT)) (|tan| (#8# 72 T ELT)) (|subtractIfCan| #10=((#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|squareFreePart| #7#) (|squareFree| #13=(((|Factored| $) $) NIL T ELT)) (|sqrt| (#8# 28 T ELT)) (|sizeLess?| #1#) (|sinh| (#8# 79 T ELT)) (|sin| (#8# 67 T ELT)) (|sign| (#5# 60 T ELT)) (|shift| (#14=($ $ #6#) 55 T ELT)) (|sech| #7#) (|sec| #7#) (|sample| (#15=($) NIL T CONST)) (|round| (#8# 122 T ELT)) (|retractIfCan| (((|Union| #6# . #16=(#12#)) $) 217 T ELT) (((|Union| #17=(|Fraction| #6#) . #16#) $) 213 T ELT)) (|retract| (#5# 215 T ELT) ((#17# $) 211 T ELT)) (|rem| #18=(#19=($ $ $) NIL T ELT)) (|relerror| ((#6# $ $) 110 T ELT)) (|recip| ((#11# $) 125 T ELT)) (|rationalApproximation| ((#17# $ #20=(|NonNegativeInteger|)) 218 T ELT) ((#17# $ #20# #20#) 210 T ELT)) (|quo| #18#) (|principalIdeal| (((|Record| (|:| |coef| #21=(|List| $)) #22=(|:| |generator| $)) #21#) NIL T ELT)) (|prime?| #9#) (|precision| (#23=(#24=(|PositiveInteger|)) 106 T ELT) (#25=(#24# #24#) 107 #26=(|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (#4# 38 T ELT)) (|pi| (#15# 22 T ELT)) (|patternMatch| ((#27=(|PatternMatchResult| #28=(|Float|) $) $ #29=(|Pattern| #28#) #27#) NIL T ELT)) (|outputSpacing| (#30=(#31=(|Void|) #20#) 177 T ELT)) (|outputGeneral| (#32=(#31#) 182 T ELT) (#30# 183 T ELT)) (|outputFloating| (#32# 184 T ELT) (#30# 185 T ELT)) (|outputFixed| (#32# 180 T ELT) (#30# 181 T ELT)) (|order| (#5# 50 T ELT)) (|opposite?| #1#) (|one?| (#4# 21 T ELT)) (|nthRoot| (#14# NIL T ELT)) (|normalize| (#8# 32 T ELT)) (|norm| #7#) (|negative?| (#4# 18 T ELT)) (|multiEuclidean| (((|Union| #21# #12#) #21# $) NIL T ELT)) (|min| #18# #33=(#15# NIL (AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) (|not| #26#)) ELT)) (|max| #18# #33#) (|mantissa| (#5# 112 T ELT)) (|log2| (#15# 90 T ELT) (#8# 97 T ELT)) (|log10| (#15# 96 T ELT) (#8# 98 T ELT)) (|log| (#8# 84 T ELT)) (|lcm| #18# #34=(($ #21#) NIL T ELT)) (|latex| (#35=((|String|) $) NIL T ELT)) (|inv| (#8# 127 T ELT)) (|increasePrecision| (#36=(#24# #6#) 27 #26# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#37=(|SparseUnivariatePolynomial| $) #37# #37#) NIL T ELT)) (|gcd| #18# #34#) (|fractionPart| (#8# 41 T ELT)) (|floor| (#8# 119 T ELT)) (|float| (($ #6# #6#) 115 T ELT) (($ #6# #6# #24#) 116 T ELT)) (|factor| #13#) (|extendedEuclidean| (((|Record| #38=(|:| |coef1| $) #39=(|:| |coef2| $) #22#) $ $) NIL T ELT) (((|Union| (|Record| #38# #39#) #12#) $ $ $) NIL T ELT)) (|exquo| #10#) (|expressIdealMember| (((|Maybe| #21#) #21# $) NIL T ELT)) (|exponent| (#5# 113 T ELT)) (|exp1| (#15# 99 T ELT)) (|exp| (#8# 78 T ELT)) (|euclideanSize| ((#20# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (#23# 108 T ELT) (#25# 109 #26# ELT)) (|differentiate| (#8# 126 T ELT) #40=(($ $ #20#) NIL T ELT)) (|decreasePrecision| (#36# 31 #26# ELT)) (|csch| #7#) (|csc| #7#) (|coth| #7#) (|cot| #7#) (|cosh| (#8# 80 T ELT)) (|cos| (#8# 71 T ELT)) (|convert| ((#28# $) 202 T ELT) (#41=(#42=(|DoubleFloat|) $) 204 T ELT) ((#29# $) NIL T ELT) (#35# 188 T ELT) (((|InputForm|) $) 200 T ELT) (($ #42#) 209 T ELT)) (|coerce| (((|OutputForm|) $) 192 T ELT) #43=(($ #6#) 214 T ELT) #7# #44=(($ #17#) NIL T ELT) #43# #44# (#41# 205 T ELT)) (|characteristic| ((#20#) NIL T CONST)) (|ceiling| (#8# 121 T ELT)) (|bits| (#23# 42 T ELT) (#25# 62 #26# ELT)) (|before?| #1#) (|base| (#23# 111 T ELT)) (|atanh| (#8# 87 T ELT)) (|atan| (#8# 30 T ELT) (#19# 40 T ELT)) (|associates?| #1#) (|asinh| (#8# 85 T ELT)) (|asin| (#8# 20 T ELT)) (|asech| #7#) (|asec| #7#) (|annihilate?| #1#) (|acsch| #7#) (|acsc| #7#) (|acoth| #7#) (|acot| #7#) (|acosh| (#8# 86 T ELT)) (|acos| (#8# 33 T ELT)) (|abs| (#8# 39 T ELT)) (|Zero| (#15# 17 T CONST)) (|One| (#15# 24 T CONST)) (D #7# #40#) (>= (#2# 189 T ELT)) (> (#2# 26 T ELT)) (= (#2# 37 T ELT)) (<= #1#) (< (#2# 43 T ELT)) (/ (#19# 29 T ELT) (#14# 23 T ELT)) (- (#8# 19 T ELT) (#19# 34 T ELT)) (+ (#19# 54 T ELT)) (** (($ $ #24#) 65 T ELT) #40# (#14# 91 T ELT) (#45=($ $ #17#) 137 T ELT) (#19# 129 T ELT)) (* (($ #24# $) 61 T ELT) (($ #20# $) NIL T ELT) (($ #6# $) 66 T ELT) (#19# 53 T ELT) (#45# NIL T ELT) (($ #17# $) NIL T ELT))) 
(((|Float|) (|Join| (|FloatingPointSystem|) (|DifferentialRing|) (|ConvertibleTo| (|String|)) (|CoercibleTo| #1=(|DoubleFloat|)) (|TranscendentalFunctionCategory|) (|ConvertibleTo| (|InputForm|)) (|ConvertibleFrom| #1#) (CATEGORY |domain| (SIGNATURE / #2=($ $ #3=(|Integer|))) (SIGNATURE ** #4=($ $ $)) (SIGNATURE |normalize| #5=($ $)) (SIGNATURE |relerror| (#3# $ $)) (SIGNATURE |shift| #2#) (SIGNATURE |rationalApproximation| (#6=(|Fraction| #3#) $ #7=(|NonNegativeInteger|))) (SIGNATURE |rationalApproximation| (#6# $ #7# #7#)) (SIGNATURE |log2| #8=($)) (SIGNATURE |log10| #8#) (SIGNATURE |exp1| #8#) (SIGNATURE |atan| #4#) (SIGNATURE |log2| #5#) (SIGNATURE |log10| #5#) (SIGNATURE |outputFloating| #9=(#10=(|Void|))) (SIGNATURE |outputFloating| #11=(#10# #7#)) (SIGNATURE |outputFixed| #9#) (SIGNATURE |outputFixed| #11#) (SIGNATURE |outputGeneral| #9#) (SIGNATURE |outputGeneral| #11#) (SIGNATURE |outputSpacing| #11#) (ATTRIBUTE |arbitraryPrecision|) (ATTRIBUTE |arbitraryExponent|)))) (T |Float|)) 
((** #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|Float|))) (/ #3=(*1 *1 *1 *2) #4=(AND (|isDomain| *2 #5=(|Integer|)) #2#)) (|normalize| #6=(*1 *1 *1) #2#) (|relerror| (*1 *2 *1 *1) #4#) (|shift| #3# #4#) (|rationalApproximation| (*1 *2 *1 *3) #7=(AND #8=(|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| #5#)) #2#)) (|rationalApproximation| (*1 *2 *1 *3 *3) #7#) (|log2| #9=(*1 *1) #2#) (|log10| #9# #2#) (|exp1| #9# #2#) (|atan| #1# #2#) (|log2| #6# #2#) (|log10| #6# #2#) (|outputFloating| #10=(*1 *2) #11=(AND #12=(|isDomain| *2 (|Void|)) #2#)) (|outputFloating| #13=(*1 *2 *3) #14=(AND #8# #12# #2#)) (|outputFixed| #10# #11#) (|outputFixed| #13# #14#) (|outputGeneral| #10# #11#) (|outputGeneral| #13# #14#) (|outputSpacing| #13# #14#)) 
((|complexSolve| ((#1=(|List| (|Equation| (|Polynomial| #2=(|Complex| |#1|)))) #3=(|Equation| #4=(|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) 52 T ELT) ((#1# #4# |#1|) 51 T ELT) ((#5=(|List| #1#) (|List| #3#) |#1|) 48 T ELT) ((#5# #6=(|List| #4#) |#1|) 42 T ELT)) (|complexRoots| (((|List| #7=(|List| #2#)) #6# (|List| (|Symbol|)) |#1|) 30 T ELT) ((#7# #4# |#1|) 18 T ELT))) 
(((|FloatingComplexPackage| |#1|) (CATEGORY |package| (SIGNATURE |complexSolve| (#1=(|List| #2=(|List| (|Equation| (|Polynomial| #3=(|Complex| |#1|))))) #4=(|List| #5=(|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|)) (SIGNATURE |complexSolve| (#1# (|List| #6=(|Equation| #5#)) |#1|)) (SIGNATURE |complexSolve| (#2# #5# |#1|)) (SIGNATURE |complexSolve| (#2# #6# |#1|)) (SIGNATURE |complexRoots| (#7=(|List| #3#) #5# |#1|)) (SIGNATURE |complexRoots| ((|List| #7#) #4# (|List| (|Symbol|)) |#1|))) (|Join| (|Field|) (|OrderedRing|))) (T |FloatingComplexPackage|)) 
((|complexRoots| (*1 *2 *3 *4 *5) (AND #1=(|isDomain| *3 (|List| #2=(|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| (|Complex| *5)))) (|isDomain| *1 (|FloatingComplexPackage| *5)) (|ofCategory| *5 #3=(|Join| (|Field|) (|OrderedRing|))))) (|complexRoots| #4=(*1 *2 *3 *4) (AND #5=(|isDomain| *3 #2#) (|isDomain| *2 (|List| #6=(|Complex| *4))) #7=(|isDomain| *1 (|FloatingComplexPackage| *4)) #8=(|ofCategory| *4 #3#))) (|complexSolve| #4# (AND (|isDomain| *3 #9=(|Equation| #2#)) #10=(|isDomain| *2 #11=(|List| (|Equation| (|Polynomial| #6#)))) #7# #8#)) (|complexSolve| #4# (AND #5# #10# #7# #8#)) (|complexSolve| #4# (AND (|isDomain| *3 (|List| #9#)) #12=(|isDomain| *2 (|List| #11#)) #7# #8#)) (|complexSolve| #4# (AND #1# #12# #7# #8#))) 
((|solve| ((#1=(|List| (|Equation| (|Polynomial| |#1|))) #2=(|Equation| #3=(|Fraction| (|Polynomial| (|Integer|)))) |#1|) 47 T ELT) ((#1# #3# |#1|) 46 T ELT) ((#4=(|List| #1#) (|List| #2#) |#1|) 43 T ELT) ((#4# #5=(|List| #3#) |#1|) 37 T ELT)) (|realRoots| ((#6=(|List| |#1|) #3# |#1|) 20 T ELT) (((|List| #6#) #5# (|List| (|Symbol|)) |#1|) 30 T ELT))) 
(((|FloatingRealPackage| |#1|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|List| #2=(|List| (|Equation| (|Polynomial| |#1|)))) #3=(|List| #4=(|Fraction| (|Polynomial| (|Integer|)))) |#1|)) (SIGNATURE |solve| (#1# (|List| #5=(|Equation| #4#)) |#1|)) (SIGNATURE |solve| (#2# #4# |#1|)) (SIGNATURE |solve| (#2# #5# |#1|)) (SIGNATURE |realRoots| ((|List| #6=(|List| |#1|)) #3# (|List| (|Symbol|)) |#1|)) (SIGNATURE |realRoots| (#6# #4# |#1|))) (|Join| (|OrderedRing|) (|Field|))) (T |FloatingRealPackage|)) 
((|realRoots| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 #3=(|Fraction| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|List| *4)) #4=(|isDomain| *1 (|FloatingRealPackage| *4)) #5=(|ofCategory| *4 #6=(|Join| (|OrderedRing|) (|Field|))))) (|realRoots| (*1 *2 *3 *4 *5) (AND #7=(|isDomain| *3 (|List| #3#)) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| *5))) (|isDomain| *1 (|FloatingRealPackage| *5)) (|ofCategory| *5 #6#))) (|solve| #1# (AND (|isDomain| *3 #8=(|Equation| #3#)) #9=(|isDomain| *2 #10=(|List| (|Equation| (|Polynomial| *4)))) #4# #5#)) (|solve| #1# (AND #2# #9# #4# #5#)) (|solve| #1# (AND (|isDomain| *3 (|List| #8#)) #11=(|isDomain| *2 (|List| #10#)) #4# #5#)) (|solve| #1# (AND #7# #11# #4# #5#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| |#2|)) $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|reductum| #5=(($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT)) (|before?| #1#) (|Zero| (#4# 12 T CONST)) (= #1#) (- #5# #6=(($ $ $) NIL T ELT)) (+ #6#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT) (($ |#1| $) 15 T ELT) (($ $ |#1|) 18 T ELT))) 
(((|FreeModule| |#1| |#2|) (|Join| (|BiModule| |#1| |#1|) (|IndexedDirectProductCategory| |#1| |#2|) (CATEGORY |package| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |#1|)) |%noBranch|))) (|Ring|) (|OrderedType|)) (T |FreeModule|)) 
NIL 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| #4#) $) 29 T ELT)) (|retract| (#6=(|#2| $) 31 T ELT)) (|reductum| #7=(($ $) NIL T ELT)) (|opposite?| #1#) (|numberOfMonomials| ((#8=(|NonNegativeInteger|) $) 13 T ELT)) (|monomials| (((|List| $) $) 23 T ELT)) (|monomial?| #3#) (|monom| (#9=($ |#2| |#1|) 21 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingTerm| ((#10=(|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 17 T ELT)) (|leadingMonomial| (#6# 18 T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 50 T ELT) (($ |#2|) 30 T ELT)) (|coefficients| (((|List| |#1|) $) 20 T ELT)) (|coefficient| ((|#1| $ |#2|) 54 T ELT)) (|before?| #1#) (|Zero| (#5# 32 T CONST)) (|ListOfTerms| (((|List| #10#) $) 14 T ELT)) (= #1#) (- #11=(($ $ $) NIL T ELT) #7#) (+ #11#) (* (($ $ |#1|) 36 T ELT) (($ |#1| $) 35 T ELT) (($ (|Integer|) $) NIL T ELT) (($ #8# $) NIL T ELT) (($ (|PositiveInteger|) $) NIL T ELT) (($ |#1| |#2|) 38 T ELT) (#9# 39 T ELT))) 
(((|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|))))) 
((~= (#1=((|Boolean|) $ $) 31 T ELT)) (|zero?| ((#2=(|Boolean|) $) 40 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 43 T ELT)) (|sample| (#3=($) 39 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 28 T ELT)) (|retract| ((|#2| $) 29 T ELT)) (|reductum| (($ $) 15 T ELT)) (|opposite?| ((#2# $ $) 42 T ELT)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 19 T ELT)) (|monomials| (((|List| $) $) 20 T ELT)) (|monomial?| (((|Boolean|) $) 23 T ELT)) (|monom| (($ |#2| |#1|) 24 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 6 T ELT)) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 16 T ELT)) (|leadingMonomial| ((|#2| $) 18 T ELT)) (|leadingCoefficient| ((|#1| $) 17 T ELT)) (|latex| (((|String|) $) 35 T ELT)) (|hash| (((|SingleInteger|) $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT) (($ |#2|) 27 T ELT)) (|coefficients| (((|List| |#1|) $) 21 T ELT)) (|coefficient| ((|#1| $ |#2|) 25 T ELT)) (|before?| (#1# 32 T ELT)) (|Zero| (#3# 38 T CONST)) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 22 T ELT)) (= (#1# 30 T ELT)) (- (($ $ $) 46 T ELT) (($ $) 45 T ELT)) (+ (($ $ $) 36 T ELT)) (* (($ $ |#1|) 48 T ELT) (($ |#1| . #4=($)) 47 T ELT) (($ (|Integer|) . #4#) 44 T ELT) (($ (|NonNegativeInteger|) $) 41 T ELT) (($ (|PositiveInteger|) $) 37 T ELT) (($ |#1| |#2|) 26 T ELT))) 
(((|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|)))) (|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| (|Functorial| |t#1|) (|BiModule| |t#1| |t#1|) (|RetractableTo| |t#2|) (CATEGORY |domain| (SIGNATURE * ($ |t#1| |t#2|)) (SIGNATURE |coefficient| (|t#1| $ |t#2|)) (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) ((|CoercibleFrom| |#2|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Functorial| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|size| (((|NonNegativeInteger|) $) 40 T ELT)) (|sample| (#2=($) 23 T CONST)) (|rquo| (((|Union| $ "failed") $ $) 43 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 51 T ELT)) (|retract| ((|#1| $) 52 T ELT)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) 41 T ELT)) (|one?| (((|Boolean|) $) 22 T ELT)) (|nthFactor| ((|#1| $ (|Integer|)) 37 T ELT)) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) 38 T ELT)) (|min| (#3=($ $ $) 29 (|has| |#1| . #4=((|OrderedSet|))) ELT)) (|max| (#3# 30 (|has| |#1| . #4#) ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 35 T ELT)) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) 36 T ELT)) (|lquo| (((|Union| $ "failed") $ $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hcrf| (($ $ $) 45 T ELT)) (|hclf| (($ $ $) 46 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) 39 T ELT)) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) 42 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 50 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#2# 24 T CONST)) (>= (#5=((|Boolean|) $ $) 31 (|has| |#1| . #4#) ELT)) (> (#5# 33 (|has| |#1| . #4#) ELT)) (= (#1# 8 T ELT)) (<= (#5# 32 (|has| |#1| . #4#) ELT)) (< (#5# 34 (|has| |#1| . #4#) ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT) (($ |#1| (|NonNegativeInteger|)) 47 T ELT)) (* (($ $ $) 18 T ELT) (($ |#1| $) 49 T ELT) (($ $ |#1|) 48 T ELT))) 
(((|FreeMonoidCategory| |#1|) (|Category|) (|SetCategory|)) (T |FreeMonoidCategory|)) 
((* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|FreeMonoidCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|FreeMonoidCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (** (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|FreeMonoidCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|hclf| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|FreeMonoidCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|hcrf| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|FreeMonoidCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|lquo| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *1 (|FreeMonoidCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|rquo| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *1 (|FreeMonoidCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|divide| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Record| (|:| |lm| *1) (|:| |rm| *1))) (|ofCategory| *1 (|FreeMonoidCategory| *3)))) (|overlap| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Record| (|:| |lm| *1) (|:| |mm| *1) (|:| |rm| *1))) (|ofCategory| *1 (|FreeMonoidCategory| *3)))) (|size| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeMonoidCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|factors| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeMonoidCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| (|NonNegativeInteger|))))))) (|nthExpon| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeMonoidCategory| *4)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|nthFactor| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeMonoidCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|mapExpon| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|))) (|ofCategory| *1 (|FreeMonoidCategory| *3)) (|ofCategory| *3 (|SetCategory|)))) (|mapGen| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|FreeMonoidCategory| *3)) (|ofCategory| *3 (|SetCategory|))))) 
(|Join| (|Monoid|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE * ($ |t#1| $)) (SIGNATURE * ($ $ |t#1|)) (SIGNATURE ** ($ |t#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| |t#1|) (|:| |exp| (|NonNegativeInteger|)))) $)) (SIGNATURE |nthExpon| ((|NonNegativeInteger|) $ (|Integer|))) (SIGNATURE |nthFactor| (|t#1| $ (|Integer|))) (SIGNATURE |mapExpon| ($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $)) (SIGNATURE |mapGen| ($ (|Mapping| |t#1| |t#1|) $)) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|))) 
(((|BasicType|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|RetractableTo| |#1|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|size| ((#4=(|NonNegativeInteger|) $) 74 T ELT)) (|sample| (#5=($) NIL T CONST)) (|rquo| (#6=(#7=(|Union| $ #8="failed") $ $) 77 T ELT)) (|retractIfCan| (((|Union| |#1| #8#) $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|recip| ((#7# $) NIL T ELT)) (|overlap| (((|Record| #9=(|:| |lm| $) (|:| |mm| $) #10=(|:| |rm| $)) $ $) 64 T ELT)) (|one?| ((#3# $) 17 T ELT)) (|nthFactor| ((|#1| $ #11=(|Integer|)) NIL T ELT)) (|nthExpon| ((#4# $ #11#) NIL T ELT)) (|min| #12=(#13=($ $ $) NIL #14=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #12#) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 40 T ELT)) (|mapExpon| (($ (|Mapping| #4# #4#) $) 37 T ELT)) (|lquo| (#6# 60 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hcrf| (#13# 28 T ELT)) (|hclf| (#13# 26 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #4#))) $) 34 T ELT)) (|divide| (((|Union| (|Record| #9# #10#) #8#) $ $) 70 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ |#1|) NIL T ELT)) (|before?| #1#) (|One| (#5# 7 T CONST)) (>= #15=(#2# NIL #14# ELT)) (> #15#) (= #1#) (<= #15#) (< (#2# 83 #14# ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #4#) NIL T ELT) (($ |#1| #4#) 42 T ELT)) (* (#13# 52 T ELT) (($ |#1| $) 32 T ELT) (($ $ |#1|) 30 T ELT))) 
(((|FreeMonoid| |#1|) (|FreeMonoidCategory| |#1|) (|SetCategory|)) (T |FreeMonoid|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|writable?| (#4=(#3# $) 25 T ELT)) (|readable?| (#4# 22 T ELT)) (|new| (#5=($ #6=(|String|) #6# #6#) 26 T ELT)) (|name| (#7=(#6# $) 16 T ELT)) (|latex| (#7# NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|filename| (#5# 14 T ELT)) (|extension| (#7# 17 T ELT)) (|exists?| (#4# 18 T ELT)) (|directory| (#7# 15 T ELT)) (|coerce| (((|OutputForm|) $) 12 T ELT) (($ #6#) 13 T ELT) (#7# 9 T ELT)) (|before?| #1#) (= (#2# 7 T ELT))) 
(((|FileName|) (|FileNameCategory|)) (T |FileName|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|writable?| (((|Boolean|) $) 20 T ELT)) (|readable?| (((|Boolean|) $) 21 T ELT)) (|new| (($ (|String|) (|String|) (|String|)) 19 T ELT)) (|name| (((|String|) $) 24 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|filename| (($ (|String|) (|String|) (|String|)) 26 T ELT)) (|extension| (((|String|) $) 23 T ELT)) (|exists?| (((|Boolean|) $) 22 T ELT)) (|directory| (((|String|) $) 25 T ELT)) (|coerce| (((|OutputForm|) . #2=($)) 13 T ELT) (($ #3=(|String|)) 28 T ELT) ((#3# . #2#) 27 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|FileNameCategory|) (|Category|)) (T |FileNameCategory|)) 
((|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|) (|HomotopicTo| (|String|)) (CATEGORY |domain| (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) ((|CoercibleFrom| #1=(|String|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|shallowExpand| (#4=((|OutputForm|) $) 64 T ELT)) (|sample| (#5=($) NIL T CONST)) (|rightPower| #6=(($ $ #7=(|PositiveInteger|)) NIL T ELT)) (|plenaryPower| #6#) (|opposite?| #1#) (|leftPower| #6#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (($ #8=(|NonNegativeInteger|)) 38 T ELT)) (|dimension| ((#8#) 18 T ELT)) (|deepExpand| (#4# 66 T ELT)) (|commutator| #9=(#10=($ $ $) NIL T ELT)) (|coerce| (#4# NIL T ELT)) (|before?| #1#) (|associator| (($ $ $ $) NIL T ELT)) (|antiCommutator| #9#) (|Zero| (#5# 24 T CONST)) (= (#2# 41 T ELT)) (- (($ $) 48 T ELT) (#10# 50 T ELT)) (+ (#10# 51 T ELT)) (** #6#) (* (($ #7# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ (|Integer|) . #11=($)) NIL T ELT) (#10# 52 T ELT) (($ $ |#3|) NIL T ELT) (($ |#3| . #11#) 47 T ELT))) 
(((|FreeNilpotentLie| |#1| |#2| |#3|) (|Join| (|NonAssociativeAlgebra| |#3|) (CATEGORY |domain| (SIGNATURE |dimension| (#1=(|NonNegativeInteger|))) (SIGNATURE |deepExpand| #2=((|OutputForm|) $)) (SIGNATURE |shallowExpand| #2#) (SIGNATURE |generator| ($ #1#)))) #1# #1# (|CommutativeRing|)) (T |FreeNilpotentLie|)) 
((|dimension| (*1 *2) #1=(AND (|isDomain| *2 #2=(|NonNegativeInteger|)) #3=(|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5)) (|ofType| *3 *2) (|ofType| *4 *2) #4=(|ofCategory| *5 (|CommutativeRing|)))) (|deepExpand| #5=(*1 *2 *1) #6=(AND (|isDomain| *2 (|OutputForm|)) #3# (|ofType| *3 #2#) (|ofType| *4 #2#) #4#)) (|shallowExpand| #5# #6#) (|generator| (*1 *1 *2) #1#)) 
((|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) 16 T ELT))) 
(((|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))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|polyPart| ((|#2| $) 38 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fullPartialFraction| (($ #2=(|Fraction| |#2|)) 93 T ELT)) (|fracPart| ((#3=(|List| (|Record| (|:| |exponent| #4=(|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) 39 T ELT)) (|differentiate| (#5=($ $ #4#) 36 T ELT) (#6=($ $) 34 T ELT)) (|convert| ((#2# $) 49 T ELT)) (|construct| (($ #3#) 33 T ELT)) (|coerce| (((|OutputForm|) $) 131 T ELT)) (|before?| #1#) (D (#5# 37 T ELT) (#6# 35 T ELT)) (= #1#) (+ (($ |#2| $) 41 T ELT))) 
(((|FullPartialFractionExpansion| |#1| |#2|) (|Join| (|SetCategory|) (|DifferentialSpace|) (|ConvertibleTo| #1=(|Fraction| |#2|)) (CATEGORY |domain| (SIGNATURE + ($ |#2| $)) (SIGNATURE |fullPartialFraction| ($ #1#)) (SIGNATURE |polyPart| (|#2| $)) (SIGNATURE |fracPart| (#2=(|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $)) (SIGNATURE |construct| ($ #2#)))) (|Join| (|Field|) (|CharacteristicZero|)) (|UnivariatePolynomialCategory| |#1|)) (T |FullPartialFractionExpansion|)) 
((+ (*1 *1 *2 *1) (AND #1=(|ofCategory| *3 (|Join| (|Field|) (|CharacteristicZero|))) #2=(|isDomain| *1 (|FullPartialFractionExpansion| *3 *2)) #3=(|ofCategory| *2 #4=(|UnivariatePolynomialCategory| *3)))) (|fullPartialFraction| #5=(*1 *1 *2) (AND (|isDomain| *2 (|Fraction| *4)) #6=(|ofCategory| *4 #4#) #1# #7=(|isDomain| *1 (|FullPartialFractionExpansion| *3 *4)))) (|polyPart| #8=(*1 *2 *1) (AND #3# #2# #1#)) (|fracPart| #8# (AND #1# #9=(|isDomain| *2 (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| *4) (|:| |num| *4)))) #7# #6#)) (|construct| #5# (AND #9# #6# #1# #7#))) 
((~= (#1=((|Boolean|) $ $) 10 (OR (|has| |#1| . #2=((|PatternMatchable| (|Integer|)))) (|has| |#1| . #3=((|PatternMatchable| (|Float|))))) ELT)) (|patternMatch| (((|PatternMatchResult| #4=(|Float|) . #5=($)) $ (|Pattern| #4#) (|PatternMatchResult| #4# . #5#)) 16 (|has| |#1| . #3#) ELT) (((|PatternMatchResult| #6=(|Integer|) . #5#) $ (|Pattern| #6#) (|PatternMatchResult| #6# . #5#)) 15 (|has| |#1| . #2#) ELT)) (|latex| (((|String|) $) 14 (OR (|has| |#1| . #2#) (|has| |#1| . #3#)) ELT)) (|hash| (((|SingleInteger|) $) 13 (OR (|has| |#1| . #2#) (|has| |#1| . #3#)) ELT)) (|coerce| (((|OutputForm|) $) 12 (OR (|has| |#1| . #2#) (|has| |#1| . #3#)) ELT)) (|before?| (#1# 11 (OR (|has| |#1| . #2#) (|has| |#1| . #3#)) ELT)) (= (#1# 9 (OR (|has| |#1| . #2#) (|has| |#1| . #3#)) ELT))) 
(((|FullyPatternMatchable| |#1|) (|Category|) (|Type|)) (T |FullyPatternMatchable|)) 
NIL 
(|Join| (|Type|) (CATEGORY |package| (IF (|has| |t#1| (|PatternMatchable| (|Integer|))) (ATTRIBUTE (|PatternMatchable| (|Integer|))) |%noBranch|) (IF (|has| |t#1| (|PatternMatchable| (|Float|))) (ATTRIBUTE (|PatternMatchable| (|Float|))) |%noBranch|))) 
(((|BasicType|) OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))) ((|Join|) . T) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|SetCategory|) OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))) ((|Type|) . T)) 
((|primeFrobenius| (($ $) 10 T ELT) (($ $ (|NonNegativeInteger|)) 12 T ELT))) 
(((|FieldOfPrimeCharacteristic&| |#1|) (CATEGORY |package| (SIGNATURE |primeFrobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |primeFrobenius| (|#1| |#1|))) (|FieldOfPrimeCharacteristic|)) (T |FieldOfPrimeCharacteristic&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|primeFrobenius| (($ $) 97 T ELT) (($ $ (|NonNegativeInteger|)) 96 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 99 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 68 T ELT)) (|lcm| (#10=($ $ $) 60 T ELT) (#11=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 58 T ELT)) (|gcd| (#10# 62 T ELT) (#11# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 98 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 84 T ELT)) (|charthRoot| (((|Maybe| $) $) 100 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #16#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #15#) 86 T ELT) (($ #15# . #17#) 85 T ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|float| (($ #1=(|Integer|) #1#) 11 T ELT) (($ #1# #1# #2=(|PositiveInteger|)) NIL T ELT)) (|digits| ((#2#) 19 T ELT) ((#2# #2#) NIL T ELT))) 
(((|FloatingPointSystem&| |#1|) (CATEGORY |package| (SIGNATURE |digits| (#1=(|PositiveInteger|) #1#)) (SIGNATURE |digits| (#1#)) (SIGNATURE |float| (|#1| #2=(|Integer|) #2# #1#)) (SIGNATURE |float| (|#1| #2# #2#))) (|FloatingPointSystem|)) (T |FloatingPointSystem&|)) 
((|digits| (*1 *2) #1=(AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FloatingPointSystem&| *3)) (|ofCategory| *3 (|FloatingPointSystem|)))) (|digits| (*1 *2 *2) #1#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|wholePart| ((#3=(|Integer|) $) 108 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#4=(|Boolean|) $) 52 T ELT)) (|truncate| (#5=($ $) 106 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#6=((|Factored| $) $) 90 T ELT)) (|sqrt| (($ $) 116 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sign| (((|Integer|) $) 133 T ELT)) (|sample| (#7=($) 23 T CONST)) (|round| (#5# 105 T ELT)) (|retractIfCan| (((|Union| #3# . #8=("failed")) . #9=($)) 121 T ELT) (((|Union| #10=(|Fraction| #3#) . #8#) . #9#) 118 T ELT)) (|retract| ((#3# . #11=($)) 122 T ELT) ((#10# . #11#) 119 T ELT)) (|rem| (#12=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#12# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #13=(|List| $)) (|:| |generator| $)) #13#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|precision| (((|PositiveInteger|)) 149 T ELT) (((|PositiveInteger|) (|PositiveInteger|)) 146 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (((|Boolean|) $) 131 T ELT)) (|patternMatch| (((|PatternMatchResult| #14=(|Float|) . #15=($)) $ (|Pattern| #14#) (|PatternMatchResult| #14# . #15#)) 112 T ELT)) (|order| (((|Integer|) $) 155 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #16=(|Integer|)) 115 T ELT)) (|norm| (#5# 111 T ELT)) (|negative?| (((|Boolean|) $) 132 T ELT)) (|multiEuclidean| (((|Union| #17=(|List| $) #18="failed") #17# $) 68 T ELT)) (|min| (#19=($ $ $) 125 T ELT) (($) 143 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))) ELT)) (|max| (#19# 126 T ELT) (($) 142 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))) ELT)) (|mantissa| (((|Integer|) $) 152 T ELT)) (|lcm| (#20=($ $ $) 60 T ELT) (#21=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) 145 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#22=(|SparseUnivariatePolynomial| $) #22# #22#) 58 T ELT)) (|gcd| (#20# 62 T ELT) (#21# 61 T ELT)) (|fractionPart| (#5# 107 T ELT)) (|floor| (#5# 109 T ELT)) (|float| (($ (|Integer|) (|Integer|)) 157 T ELT) (($ (|Integer|) (|Integer|) (|PositiveInteger|)) 156 T ELT)) (|factor| (#6# 92 T ELT)) (|extendedEuclidean| (((|Record| #23=(|:| |coef1| $) #24=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #23# #24#) #18#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #13#) #13# $) 65 T ELT)) (|exponent| (((|Integer|) $) 153 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|digits| (((|PositiveInteger|)) 150 T ELT) (((|PositiveInteger|) (|PositiveInteger|)) 147 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) 144 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|convert| (((|Float|) . #25=($)) 124 T ELT) (((|DoubleFloat|) . #25#) 123 T ELT) (((|Pattern| #14#) . #25#) 113 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #26=(|Fraction| #27=(|Integer|))) 84 T ELT) (($ #3#) 120 T ELT) (($ #10#) 117 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|ceiling| (#5# 110 T ELT)) (|bits| (((|PositiveInteger|)) 151 T ELT) (((|PositiveInteger|) (|PositiveInteger|)) 148 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|before?| (#1# 6 T ELT)) (|base| (((|PositiveInteger|)) 154 T ELT)) (|associates?| ((#4# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| (($ $) 134 T ELT)) (|Zero| (#7# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#28=((|Boolean|) $ $) 127 T ELT)) (> (#28# 129 T ELT)) (= (#1# 8 T ELT)) (<= (#28# 128 T ELT)) (< (#28# 130 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #27#) 87 T ELT) (($ $ (|Fraction| #16#)) 114 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #29=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #26#) 86 T ELT) (($ #26# . #29#) 85 T ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|Pattern| #2=(|Float|))) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PatternMatchable| #2#) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RealConstant|) . T) ((|RealNumberSystem|) . T) ((|RetractableTo| (|Fraction| #3=(|Integer|))) . T) ((|RetractableTo| #3#) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 59 T ELT)) (|unitNormalize| (#5=($ $) 77 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 189 T ELT)) (|unitCanonical| #6=(#5# NIL T ELT)) (|unit?| (#4# 48 T ELT)) (|unit| (#7=(|#1| $) 16 T ELT)) (|subtractIfCan| (#8=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|squareFreePart| (#5# NIL #11=(|has| |#1| (|UniqueFactorizationDomain|)) ELT)) (|squareFree| #12=(((|Factored| $) $) NIL #11# ELT)) (|sqfrFactor| (#13=($ |#1| #14=(|Integer|)) 42 T ELT)) (|sample| (#15=($) NIL T CONST)) (|retractIfCan| (((|Union| #14# . #16=(#10#)) $) NIL #17=(|has| |#1| (|RetractableTo| #14#)) ELT) (#18=((|Union| #19=(|Fraction| #14#) #10#) $) NIL #20=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| |#1| . #16#) $) 147 T ELT)) (|retract| (#21=(#14# $) NIL #17# ELT) (#22=(#19# $) NIL #20# ELT) (#7# 73 T ELT)) (|recip| ((#9# $) 163 T ELT)) (|rationalIfCan| (#18# 84 #23=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#4# 80 #23# ELT)) (|rational| (#22# 82 #23# ELT)) (|primeFactor| (#13# 44 T ELT)) (|prime?| (#4# 209 #11# ELT)) (|opposite?| #1#) (|one?| (#4# 61 T ELT)) (|numberOfFactors| ((#24=(|NonNegativeInteger|) $) 51 T ELT)) (|nthFlag| ((#25=(|Union| "nil" "sqfr" "irred" "prime") $ #14#) 174 T ELT)) (|nthFactor| ((|#1| $ #14#) 173 T ELT)) (|nthExponent| ((#14# $ #14#) 172 T ELT)) (|nilFactor| (#13# 41 T ELT)) (|map| (($ #26=(|Mapping| |#1| |#1|) $) 182 T ELT)) (|makeFR| (($ |#1| #27=(|List| (|Record| (|:| |flg| #25#) (|:| |fctr| |#1|) (|:| |xpnt| #14#)))) 78 T ELT)) (|lcm| #28=(($ #29=(|List| $)) NIL #30=(|has| |#1| (|GcdDomain|)) ELT) (#31=($ $ $) NIL #30# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|irreducibleFactor| (#13# 43 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#32=(|SparseUnivariatePolynomial| $) #32# #32#) NIL #30# ELT)) (|gcd| #28# (#31# 190 #30# ELT)) (|flagFactor| (($ |#1| #14# #25#) 40 T ELT)) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| #14#))) $) 72 T ELT)) (|factorList| ((#27# $) 12 T ELT)) (|factor| #12#) (|exquo| (#8# 175 T ELT)) (|exponent| (#21# 166 T ELT)) (|expand| (#7# 74 T ELT)) (|eval| (($ $ #33=(|List| |#1|) #33#) NIL #34=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #34# ELT) (($ $ #35=(|Equation| |#1|)) NIL #34# ELT) (($ $ (|List| #35#)) 99 #34# ELT) (($ $ #36=(|List| #37=(|Symbol|)) #33#) 105 #38=(|has| |#1| (|InnerEvalable| #37# |#1|)) ELT) (($ $ #37# |#1|) NIL #38# ELT) (($ $ #37# $) NIL #39=(|has| |#1| (|InnerEvalable| #37# $)) ELT) (($ $ #36# #29#) 106 #39# ELT) (($ $ (|List| #40=(|Equation| $))) 102 #41=(|has| |#1| (|Evalable| $)) ELT) (($ $ #40#) NIL #41# ELT) (($ $ $ $) NIL #41# ELT) (($ $ #29# #29#) NIL #41# ELT)) (|elt| (#42=($ $ |#1|) 91 (|has| |#1| (|Eltable| |#1| |#1|)) ELT) (#31# 92 (|has| |#1| (|Eltable| $ $)) ELT)) (|differentiate| (#43=($ $ #26#) 181 T ELT) #44=(($ $ #26# #24#) NIL T ELT) #45=(#5# NIL #46=(|has| |#1| (|DifferentialSpace|)) ELT) #47=(#48=($ $ #24#) NIL #46# ELT) #49=(($ $ #37#) NIL #50=(|has| |#1| (|PartialDifferentialSpace| #37#)) ELT) #51=(($ $ #36#) NIL #50# ELT) #52=(($ $ #37# #24#) NIL #50# ELT) #53=(($ $ #36# (|List| #24#)) NIL #50# ELT)) (|convert| ((#54=(|InputForm|) $) 39 (|has| |#1| (|ConvertibleTo| #54#)) ELT) (((|Float|) $) 112 #55=(|has| |#1| (|RealConstant|)) ELT) (((|DoubleFloat|) $) 118 #55# ELT)) (|coerce| (((|OutputForm|) $) 145 T ELT) (($ #14#) 64 T ELT) #6# (($ |#1|) 63 T ELT) (($ #19#) NIL #20# ELT)) (|characteristic| ((#24#) 66 T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#15# 53 T CONST)) (|One| (#15# 52 T CONST)) (D (#43# NIL T ELT) #44# #45# #47# #49# #51# #52# #53#) (= (#2# 158 T ELT)) (- (#5# 160 T ELT) (#31# NIL T ELT)) (+ (#31# 179 T ELT)) (** (($ $ #56=(|PositiveInteger|)) NIL T ELT) (#48# 124 T ELT)) (* (($ #56# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #14# $) 68 T ELT) (#31# 67 T ELT) (($ |#1| $) 69 T ELT) (#42# NIL T ELT))) 
(((|Factored| |#1|) (|Join| #1=(|IntegralDomain|) (|DifferentialExtension| |#1|) (|Algebra| |#1|) (|FullyEvalableOver| |#1|) (|FullyRetractableTo| |#1|) (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE |expand| #2=(|#1| $)) (SIGNATURE |exponent| (#3=(|Integer|) $)) (SIGNATURE |makeFR| ($ |#1| #4=(|List| (|Record| (|:| |flg| #5=(|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| #3#))))) (SIGNATURE |factorList| (#4# $)) (SIGNATURE |nilFactor| #6=($ |#1| #3#)) (SIGNATURE |factors| ((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| #3#))) $)) (SIGNATURE |irreducibleFactor| #6#) (SIGNATURE |nthExponent| (#3# $ #3#)) (SIGNATURE |nthFactor| (|#1| $ #3#)) (SIGNATURE |nthFlag| (#5# $ #3#)) (SIGNATURE |numberOfFactors| ((|NonNegativeInteger|) $)) (SIGNATURE |primeFactor| #6#) (SIGNATURE |sqfrFactor| #6#) (SIGNATURE |flagFactor| ($ |#1| #3# #5#)) (SIGNATURE |unit| #2#) (SIGNATURE |unitNormalize| ($ $)) (IF (|has| |#1| #7=(|GcdDomain|)) (ATTRIBUTE #7#) |%noBranch|) (IF (|has| |#1| #8=(|RealConstant|)) (ATTRIBUTE #8#) |%noBranch|) (IF (|has| |#1| #9=(|UniqueFactorizationDomain|)) (ATTRIBUTE #9#) |%noBranch|) (IF (|has| |#1| #10=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #10#) |%noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| (#11=(|Fraction| #3#) $)) (SIGNATURE |rationalIfCan| ((|Union| #11# "failed") $))) |%noBranch|) (IF (|has| |#1| #12=(|Eltable| $ $)) (ATTRIBUTE #12#) |%noBranch|) (IF (|has| |#1| #13=(|Evalable| $)) (ATTRIBUTE #13#) |%noBranch|) (IF (|has| |#1| #14=(|InnerEvalable| (|Symbol|) $)) (ATTRIBUTE #14#) |%noBranch|))) #1#) (T |Factored|)) 
((|expand| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *1 (|Factored| *2)) #4=(|ofCategory| *2 #5=(|IntegralDomain|)))) (|exponent| #1# #6=(AND (|isDomain| *2 #7=(|Integer|)) #8=(|isDomain| *1 (|Factored| *3)) #9=(|ofCategory| *3 #5#))) (|makeFR| #10=(*1 *1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| #11=(|:| |flg| #12=(|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| *2) #13=(|:| |xpnt| #7#)))) #4# #3#)) (|factorList| #1# (AND (|isDomain| *2 (|List| (|Record| #11# (|:| |fctr| *3) #13#))) #8# #9#)) (|nilFactor| #10# #14=(AND #15=(|isDomain| *3 #7#) #3# #4#)) (|factors| #1# (AND (|isDomain| *2 (|List| (|Record| (|:| |factor| *3) (|:| |exponent| #7#)))) #8# #9#)) (|irreducibleFactor| #10# #14#) (|nthExponent| (*1 *2 *1 *2) #6#) (|nthFactor| #16=(*1 *2 *1 *3) #14#) (|nthFlag| #16# (AND #15# (|isDomain| *2 #12#) (|isDomain| *1 (|Factored| *4)) (|ofCategory| *4 #5#))) (|numberOfFactors| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #8# #9#)) (|primeFactor| #10# #14#) (|sqfrFactor| #10# #14#) (|flagFactor| (*1 *1 *2 *3 *4) (AND #15# (|isDomain| *4 #12#) #3# #4#)) (|unit| #1# #2#) (|unitNormalize| (*1 *1 *1) #2#) (|rational?| #1# (AND (|isDomain| *2 (|Boolean|)) #8# #17=(|ofCategory| *3 (|IntegerNumberSystem|)) #9#)) (|rational| #1# (AND #18=(|isDomain| *2 (|Fraction| #7#)) #8# #17# #9#)) (|rationalIfCan| #1# (|partial| AND #18# #8# #17# #9#))) 
((|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) 20 T ELT))) 
(((|FactoredFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)))) #1=(|IntegralDomain|) #1#) (T |FactoredFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Factored| *5)) (|ofCategory| *5 #1=(|IntegralDomain|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Factored| *6)) (|isDomain| *1 (|FactoredFunctions2| *5 *6))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 13 T ELT)) (|wholePart| (#5=(|#1| $) 21 #6=(|has| |#1| (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #7=(#8=($ $) NIL T ELT)) (|unit?| #9=(#4# NIL T ELT)) (|subtractIfCan| #10=((#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|squareFreePolynomial| (#13=((|Factored| #14=(|SparseUnivariatePolynomial| $)) #14#) NIL #15=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #7#) (|squareFree| #16=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #17=(|List| #14#) #12#) #17# #14#) NIL #15# ELT)) (|sizeLess?| #1#) (|sign| (#18=(#19=(|Integer|) $) NIL #20=(|has| |#1| (|OrderedIntegralDomain|)) ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #22=(#12#)) $) 17 T ELT) (((|Union| #23=(|Symbol|) . #22#) . #24=($)) NIL #25=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| #26=(|Fraction| #19#) . #22#) $) 54 #27=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| #19# . #22#) . #24#) NIL #27# ELT)) (|retract| (#5# 15 T ELT) ((#23# $) NIL #25# ELT) ((#26# $) 51 #27# ELT) (#18# NIL #27# ELT)) (|rem| #28=(#29=($ $ $) NIL T ELT)) (|reducedSystem| ((#30=(|Matrix| #19#) . #31=(#32=(|Matrix| $))) NIL #33=(|has| |#1| (|LinearlyExplicitRingOver| #19#)) ELT) ((#34=(|Record| (|:| |mat| #30#) (|:| |vec| (|Vector| #19#))) . #35=(#32# #36=(|Vector| $))) NIL #33# ELT) ((#37=(|Record| (|:| |mat| #38=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #35#) NIL T ELT) ((#38# . #31#) NIL T ELT)) (|recip| ((#11# $) 32 T ELT)) (|random| (#21# NIL #39=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|quo| #28#) (|principalIdeal| (((|Record| (|:| |coef| #40=(|List| $)) #41=(|:| |generator| $)) #40#) NIL T ELT)) (|prime?| #9#) (|positive?| (#4# NIL #20# ELT)) (|patternMatch| ((#42=(|PatternMatchResult| #19# . #43=($)) $ #44=(|Pattern| #19#) #42#) NIL (|has| |#1| (|PatternMatchable| #19#)) ELT) ((#45=(|PatternMatchResult| #46=(|Float|) . #43#) $ #47=(|Pattern| #46#) #45#) NIL (|has| |#1| (|PatternMatchable| #46#)) ELT)) (|opposite?| #1#) (|one?| (#4# 38 T ELT)) (|numerator| #7#) (|numer| (#5# 55 T ELT)) (|nextItem| (#48=((|Maybe| $) $) NIL #49=(|has| |#1| (|StepThrough|)) ELT)) (|negative?| (#4# 22 #20# ELT)) (|multiEuclidean| (((|Union| #40# #12#) #40# $) NIL T ELT)) (|min| #50=(#29# NIL #51=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #50#) (|map| (($ #52=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|leftReducedSystem| ((#30# . #53=(#36#)) NIL #33# ELT) ((#34# . #54=(#36# $)) NIL #33# ELT) ((#37# . #54#) NIL T ELT) ((#38# . #53#) NIL T ELT)) (|lcm| #28# #55=(($ #40#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #7#) (|init| (#21# NIL #49# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#14# #14# #14#) 82 T ELT)) (|gcd| #28# #55#) (|fractionPart| (#8# NIL #6# ELT)) (|floor| (#5# 26 #39# ELT)) (|factorSquareFreePolynomial| (#13# 133 #15# ELT)) (|factorPolynomial| (#13# 128 #15# ELT)) (|factor| #16#) (|extendedEuclidean| (((|Record| #56=(|:| |coef1| $) #57=(|:| |coef2| $) #41#) $ $) NIL T ELT) (((|Union| (|Record| #56# #57#) #12#) $ $ $) NIL T ELT)) (|exquo| #10#) (|expressIdealMember| (((|Maybe| #40#) #40# $) NIL T ELT)) (|eval| (($ $ #58=(|List| |#1|) #58#) NIL #59=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #59# ELT) (($ $ #60=(|Equation| |#1|)) NIL #59# ELT) (($ $ (|List| #60#)) NIL #59# ELT) (($ $ #61=(|List| #23#) #58#) NIL #62=(|has| |#1| (|InnerEvalable| #23# |#1|)) ELT) (($ $ #23# |#1|) NIL #62# ELT)) (|euclideanSize| ((#63=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#64=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| (#65=($ $ #52#) 45 T ELT) #66=(($ $ #52# #63#) NIL T ELT) #67=(($ $ #23#) NIL #68=(|has| |#1| (|PartialDifferentialSpace| #23#)) ELT) #69=(($ $ #61#) NIL #68# ELT) #70=(($ $ #23# #63#) NIL #68# ELT) #71=(($ $ #61# (|List| #63#)) NIL #68# ELT) #72=(#8# NIL #73=(|has| |#1| (|DifferentialSpace|)) ELT) #74=(#75=($ $ #63#) NIL #73# ELT)) (|denominator| #7#) (|denom| (#5# 57 T ELT)) (|convert| ((#44# . #76=($)) NIL (|has| |#1| (|ConvertibleTo| #44#)) ELT) ((#47# . #76#) NIL (|has| |#1| (|ConvertibleTo| #47#)) ELT) ((#77=(|InputForm|) . #76#) NIL (|has| |#1| (|ConvertibleTo| #77#)) ELT) ((#46# . #76#) NIL #78=(|has| |#1| (|RealConstant|)) ELT) (((|DoubleFloat|) . #76#) NIL #78# ELT)) (|conditionP| (((|Union| #36# #12#) #32#) 112 #79=(AND (|has| $ #80=(|CharacteristicNonZero|)) #15#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) #7# (($ #26#) NIL T ELT) (($ |#1|) 10 T ELT) (($ #23#) NIL #25# ELT)) (|charthRoot| (#48# 92 (OR #79# (|has| |#1| #80#)) ELT)) (|characteristic| ((#63#) 93 T CONST)) (|ceiling| (#5# 24 #39# ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#8# NIL #20# ELT)) (|Zero| (#21# 28 T CONST)) (|One| (#21# 8 T CONST)) (D (#65# NIL T ELT) #66# #67# #69# #70# #71# #72# #74#) (>= #81=(#2# NIL #51# ELT)) (> #81#) (= (#2# 48 T ELT)) (<= #81#) (< #81#) (/ (#29# 123 T ELT) (($ |#1| |#1|) 34 T ELT)) (- (#8# 23 T ELT) (#29# 37 T ELT)) (+ (#29# 35 T ELT)) (** (($ $ #82=(|PositiveInteger|)) NIL T ELT) (#75# NIL T ELT) (($ $ #19#) 122 T ELT)) (* (($ #82# $) NIL T ELT) (($ #63# $) NIL T ELT) (($ #19# $) 42 T ELT) (#29# 39 T ELT) (($ $ #26#) NIL T ELT) (($ #26# $) NIL T ELT) (($ |#1| $) 43 T ELT) (#64# 70 T ELT))) 
(((|Fraction| |#1|) (|Join| (|QuotientFieldCategory| |#1|) (CATEGORY |package| (IF (|has| |#1| #1=(ATTRIBUTE |canonical|)) (IF (|has| |#1| (|GcdDomain|)) (IF (|has| |#1| (ATTRIBUTE |canonicalUnitNormal|)) #1# |%noBranch|) |%noBranch|) |%noBranch|))) (|IntegralDomain|)) (T |Fraction|)) 
NIL 
((|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) 13 T ELT))) 
(((|FractionFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)))) #1=(|IntegralDomain|) #1#) (T |FractionFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Fraction| *5)) (|ofCategory| *5 #1=(|IntegralDomain|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Fraction| *6)) (|isDomain| *1 (|FractionFunctions2| *5 *6))))) 
((|traceMatrix| (#1=(#2=(|Matrix| |#2|) #3=(|Vector| $)) NIL T ELT) ((#2#) 18 T ELT)) (|represents| (($ #4=(|Vector| |#2|) #3#) NIL T ELT) (#5=($ #4#) 24 T ELT)) (|regularRepresentation| ((#2# $ #3#) NIL T ELT) ((#2# $) 40 T ELT)) (|minimalPolynomial| (#6=(|#3| $) 69 T ELT)) (|discriminant| ((|#2| #3#) NIL T ELT) ((|#2|) 20 T ELT)) (|coordinates| ((#4# $ #3#) NIL T ELT) ((#2# #3# #3#) NIL T ELT) (#7=(#4# $) 22 T ELT) (#1# 38 T ELT)) (|convert| (#7# 11 T ELT) (#5# 13 T ELT)) (|characteristicPolynomial| (#6# 55 T ELT))) 
(((|FramedAlgebra&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |regularRepresentation| (#1=(|Matrix| |#2|) |#1|)) (SIGNATURE |discriminant| (|#2|)) (SIGNATURE |traceMatrix| (#1#)) (SIGNATURE |convert| #2=(|#1| #3=(|Vector| |#2|))) (SIGNATURE |convert| #4=(#3# |#1|)) (SIGNATURE |represents| #2#) (SIGNATURE |coordinates| #5=(#1# #6=(|Vector| |#1|))) (SIGNATURE |coordinates| #4#) (SIGNATURE |minimalPolynomial| #7=(|#3| |#1|)) (SIGNATURE |characteristicPolynomial| #7#) (SIGNATURE |traceMatrix| #5#) (SIGNATURE |discriminant| (|#2| #6#)) (SIGNATURE |represents| (|#1| #3# #6#)) (SIGNATURE |coordinates| (#1# #6# #6#)) (SIGNATURE |coordinates| (#3# |#1| #6#)) (SIGNATURE |regularRepresentation| (#1# |#1| #6#))) (|FramedAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |FramedAlgebra&|)) 
((|traceMatrix| #1=(*1 *2) (AND (|ofCategory| *4 #2=(|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|FramedAlgebra&| *3 *4 *5)) (|ofCategory| *3 (|FramedAlgebra| *4 *5)))) (|discriminant| #1# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #2#) (|isDomain| *1 (|FramedAlgebra&| *3 *2 *4)) (|ofCategory| *3 (|FramedAlgebra| *2 *4))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|traceMatrix| (((|Matrix| |#1|) #3=(|Vector| $)) 61 T ELT) (((|Matrix| |#1|)) 77 T ELT)) (|trace| ((|#1| . #4=($)) 67 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|represents| (($ (|Vector| |#1|) #3#) 63 T ELT) (($ (|Vector| |#1|)) 80 T ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ #3#) 68 T ELT) (((|Matrix| |#1|) $) 75 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rank| (((|PositiveInteger|)) 69 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|norm| ((|#1| . #4#) 66 T ELT)) (|minimalPolynomial| ((|#2| . #6=($)) 59 (|has| |#1| (|Field|)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|discriminant| ((|#1| #3#) 62 T ELT) ((|#1|) 76 T ELT)) (|coordinates| (((|Vector| |#1|) $ #3#) 65 T ELT) (((|Matrix| |#1|) #3# #3#) 64 T ELT) (((|Vector| |#1|) $) 82 T ELT) (((|Matrix| |#1|) (|Vector| $)) 81 T ELT)) (|convert| (((|Vector| |#1|) $) 79 T ELT) (($ (|Vector| |#1|)) 78 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT)) (|charthRoot| (((|Maybe| $) $) 58 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#2| . #6#) 60 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 83 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #7#) 53 T ELT))) 
(((|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|)) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FiniteRankAlgebra| |#1| |#2|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|retractIfCan| (((|Union| |#2| #1="failed") $) NIL T ELT) (((|Union| #2=(|Fraction| #3=(|Integer|)) #1#) $) 27 T ELT) (((|Union| #3# #1#) $) 19 T ELT)) (|retract| ((|#2| $) NIL T ELT) ((#2# $) 24 T ELT) ((#3# $) 14 T ELT)) (|coerce| (($ |#2|) NIL T ELT) (($ #2#) 22 T ELT) (($ #3#) 11 T ELT))) 
(((|FullyRetractableTo&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| #1=(|Integer|))) (SIGNATURE |retractIfCan| ((|Union| #1# #2="failed") |#1|)) (SIGNATURE |retract| (#1# |#1|)) (SIGNATURE |coerce| (|#1| #3=(|Fraction| #1#))) (SIGNATURE |retractIfCan| ((|Union| #3# #2#) |#1|)) (SIGNATURE |retract| (#3# |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #2#) |#1|)) (SIGNATURE |coerce| (|#1| |#2|))) (|FullyRetractableTo| |#2|) (|Type|)) (T |FullyRetractableTo&|)) 
NIL 
((|retractIfCan| (((|Union| |#1| . #1=("failed")) . #2=($)) 9 T ELT) (((|Union| #3=(|Fraction| (|Integer|)) . #1#) . #2#) 16 (|has| |#1| . #4=((|RetractableTo| (|Fraction| (|Integer|))))) ELT) (((|Union| #5=(|Integer|) . #1#) . #2#) 13 (|has| |#1| . #6=((|RetractableTo| (|Integer|)))) ELT)) (|retract| ((|#1| . #7=($)) 8 T ELT) ((#3# . #7#) 17 (|has| |#1| . #4#) ELT) ((#5# . #7#) 14 (|has| |#1| . #6#) ELT)) (|coerce| (($ |#1|) 6 T ELT) (($ #3#) 15 (|has| |#1| . #4#) ELT) (($ #5#) 12 (|has| |#1| . #6#) ELT))) 
(((|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|))) 
(((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2=(|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|CoercibleFrom| |#1|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|randomLC| ((|#4| #5=(|NonNegativeInteger|) #6=(|Vector| |#4|)) 55 T ELT)) (|one?| ((#3# $) NIL T ELT)) (|numer| (#7=(#6# $) 15 T ELT)) (|norm| ((|#2| $) 53 T ELT)) (|minimize| (#8=($ $) 156 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#8# 103 T ELT)) (|ideal| (($ #6#) 102 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#1| $) 16 T ELT)) (|conjugate| #9=(#10=($ $ $) NIL T ELT)) (|commutator| #9#) (|coerce| (((|OutputForm|) $) 147 T ELT)) (|before?| #1#) (|basis| (#7# 140 T ELT)) (|One| (#4# 11 T CONST)) (= (#2# 39 T ELT)) (/ #9#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #5#) NIL T ELT) (($ $ (|Integer|)) 133 T ELT)) (* (#10# 130 T ELT))) 
(((|FractionalIdeal| |#1| |#2| |#3| |#4|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |ideal| ($ #1=(|Vector| |#4|))) (SIGNATURE |basis| #2=(#1# $)) (SIGNATURE |norm| (|#2| $)) (SIGNATURE |numer| #2#) (SIGNATURE |denom| (|#1| $)) (SIGNATURE |minimize| ($ $)) (SIGNATURE |randomLC| (|#4| (|NonNegativeInteger|) #1#)))) (|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|Join| (|FramedAlgebra| |#2| |#3|) (|RetractableTo| |#2|))) (T |FractionalIdeal|)) 
((|ideal| (*1 *1 *2) (AND #1=(|isDomain| *2 (|Vector| *6)) #2=(|ofCategory| *6 (|Join| (|FramedAlgebra| *4 *5) (|RetractableTo| *4))) #3=(|ofCategory| *4 #4=(|QuotientFieldCategory| *3)) #5=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) #6=(|ofCategory| *3 #7=(|EuclideanDomain|)) #8=(|isDomain| *1 (|FractionalIdeal| *3 *4 *5 *6)))) (|basis| #9=(*1 *2 *1) #10=(AND #6# #3# #5# #1# #8# #2#)) (|norm| #9# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #4#) (|isDomain| *1 (|FractionalIdeal| *3 *2 *4 *5)) #6# (|ofCategory| *5 (|Join| (|FramedAlgebra| *2 *4) (|RetractableTo| *2))))) (|numer| #9# #10#) (|denom| #9# (AND #11=(|ofCategory| *3 (|QuotientFieldCategory| *2)) #12=(|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) #13=(|ofCategory| *2 #7#) #14=(|isDomain| *1 (|FractionalIdeal| *2 *3 *4 *5)) #15=(|ofCategory| *5 (|Join| (|FramedAlgebra| *3 *4) (|RetractableTo| *3))))) (|minimize| (*1 *1 *1) (AND #13# #11# #12# #14# #15#)) (|randomLC| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Vector| *2)) (|ofCategory| *5 #7#) (|ofCategory| *6 (|QuotientFieldCategory| *5)) (|ofCategory| *2 (|Join| (|FramedAlgebra| *6 *7) (|RetractableTo| *6))) (|isDomain| *1 (|FractionalIdeal| *5 *6 *7 *2)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))))) 
((|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) 35 T ELT))) 
(((|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|)))) #1=(|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|Join| (|FramedAlgebra| |#2| |#3|) (|RetractableTo| |#2|)) #1# (|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 #1=(|EuclideanDomain|)) (|ofCategory| *6 (|QuotientFieldCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *8 (|Join| (|FramedAlgebra| *6 *7) (|RetractableTo| *6))) (|ofCategory| *9 #1#) (|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)))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|one?| ((#2# $) NIL T ELT)) (|norm| ((|#2| $) 69 T ELT)) (|module| (($ #4=(|Vector| |#4|)) 27 T ELT) (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) 83 (|has| |#4| (|RetractableTo| |#2|)) ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 37 T ELT)) (|before?| #1#) (|basis| ((#4# $) 28 T ELT)) (|One| (#3# 26 T CONST)) (= #1#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT)) (* (($ $ $) 80 T ELT))) 
(((|FramedModule| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |basis| (#1=(|Vector| |#4|) $)) (SIGNATURE |norm| (|#2| $)) (SIGNATURE |module| ($ #1#)) (IF (|has| |#4| (|RetractableTo| |#2|)) (SIGNATURE |module| ($ (|FractionalIdeal| |#1| |#2| |#3| |#4|))) |%noBranch|))) (|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|FramedAlgebra| |#2| |#3|) #1#) (T |FramedModule|)) 
((|basis| #1=(*1 *2 *1) (AND #2=(|ofCategory| *3 (|EuclideanDomain|)) #3=(|ofCategory| *4 #4=(|QuotientFieldCategory| *3)) #5=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) #6=(|isDomain| *2 #7=(|Vector| *6)) #8=(|isDomain| *1 (|FramedModule| *3 *4 *5 *6 *7)) #9=(|ofCategory| *6 (|FramedAlgebra| *4 *5)) #10=(|ofType| *7 *2))) (|norm| #1# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #4#) (|isDomain| *1 (|FramedModule| *3 *2 *4 *5 *6)) #2# (|ofCategory| *5 (|FramedAlgebra| *2 *4)) (|ofType| *6 (|Vector| *5)))) (|module| #11=(*1 *1 *2) (AND #6# #9# #3# #5# #2# #8# #10#)) (|module| #11# (AND (|isDomain| *2 (|FractionalIdeal| *3 *4 *5 *6)) (|ofCategory| *6 (|RetractableTo| *4)) #2# #3# #5# #9# (|ofType| *7 #7#) #8#))) 
((|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) 29 T ELT))) 
(((|FramedNonAssociativeAlgebraFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) (|FramedNonAssociativeAlgebra| |#2|) #1=(|CommutativeRing|) (|FramedNonAssociativeAlgebra| |#4|) #1#) (T |FramedNonAssociativeAlgebraFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|CommutativeRing|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|FramedNonAssociativeAlgebra| *6)) (|isDomain| *1 (|FramedNonAssociativeAlgebraFunctions2| *4 *5 *2 *6)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *5))))) 
((|unit| (#1=((|Union| $ #2="failed")) 99 T ELT)) (|structuralConstants| ((#3=(|Vector| #4=(|Matrix| |#2|)) #5=(|Vector| $)) NIL T ELT) ((#3#) 104 T ELT)) (|rightUnits| (#6=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #2#)) 97 T ELT)) (|rightUnit| (#1# 96 T ELT)) (|rightTraceMatrix| #7=(#8=(#4# #5#) NIL T ELT) (#9=(#4#) 115 T ELT)) (|rightRegularRepresentation| #10=((#4# $ #5#) NIL T ELT) (#11=(#4# $) 123 T ELT)) (|rightRankPolynomial| (#12=((|SparseUnivariatePolynomial| #13=(|Polynomial| |#2|))) 64 T ELT)) (|rightDiscriminant| #14=((|#2| #5#) NIL T ELT) (#15=(|#2|) 119 T ELT)) (|represents| (($ #16=(|Vector| |#2|) #5#) NIL T ELT) (#17=($ #16#) 125 T ELT)) (|leftUnits| (#6# 95 T ELT)) (|leftUnit| (#1# 87 T ELT)) (|leftTraceMatrix| #7# (#9# 113 T ELT)) (|leftRegularRepresentation| #10# (#11# 121 T ELT)) (|leftRankPolynomial| (#12# 63 T ELT)) (|leftDiscriminant| #14# (#15# 117 T ELT)) (|coordinates| ((#16# $ #5#) NIL T ELT) ((#4# #5# #5#) NIL T ELT) (#18=(#16# $) 124 T ELT) (#8# 133 T ELT)) (|convert| (#18# 109 T ELT) (#17# 111 T ELT)) (|conditionsForIdempotents| ((#19=(|List| #13#) #5#) NIL T ELT) ((#19#) 107 T ELT)) (|apply| (($ #4# $) 103 T ELT))) 
(((|FramedNonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |apply| (|#1| #1=(|Matrix| |#2|) |#1|)) (SIGNATURE |rightRankPolynomial| #2=((|SparseUnivariatePolynomial| #3=(|Polynomial| |#2|)))) (SIGNATURE |leftRankPolynomial| #2#) (SIGNATURE |rightRegularRepresentation| #4=(#1# |#1|)) (SIGNATURE |leftRegularRepresentation| #4#) (SIGNATURE |rightTraceMatrix| #5=(#1#)) (SIGNATURE |leftTraceMatrix| #5#) (SIGNATURE |rightDiscriminant| #6=(|#2|)) (SIGNATURE |leftDiscriminant| #6#) (SIGNATURE |convert| #7=(|#1| #8=(|Vector| |#2|))) (SIGNATURE |convert| #9=(#8# |#1|)) (SIGNATURE |represents| #7#) (SIGNATURE |conditionsForIdempotents| (#10=(|List| #3#))) (SIGNATURE |structuralConstants| (#11=(|Vector| #1#))) (SIGNATURE |coordinates| #12=(#1# #13=(|Vector| |#1|))) (SIGNATURE |coordinates| #9#) (SIGNATURE |unit| #14=((|Union| |#1| #15="failed"))) (SIGNATURE |rightUnit| #14#) (SIGNATURE |leftUnit| #14#) (SIGNATURE |rightUnits| #16=((|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) #15#))) (SIGNATURE |leftUnits| #16#) (SIGNATURE |rightTraceMatrix| #12#) (SIGNATURE |leftTraceMatrix| #12#) (SIGNATURE |rightDiscriminant| #17=(|#2| #13#)) (SIGNATURE |leftDiscriminant| #17#) (SIGNATURE |represents| (|#1| #8# #13#)) (SIGNATURE |coordinates| (#1# #13# #13#)) (SIGNATURE |coordinates| (#8# |#1| #13#)) (SIGNATURE |rightRegularRepresentation| #18=(#1# |#1| #13#)) (SIGNATURE |leftRegularRepresentation| #18#) (SIGNATURE |structuralConstants| (#11# #13#)) (SIGNATURE |conditionsForIdempotents| (#10# #13#))) (|FramedNonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |FramedNonAssociativeAlgebra&|)) 
((|structuralConstants| #1=(*1 *2) (AND #2=(|ofCategory| *4 #3=(|CommutativeRing|)) (|isDomain| *2 (|Vector| #4=(|Matrix| *4))) #5=(|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4)) #6=(|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|conditionsForIdempotents| #1# (AND #2# (|isDomain| *2 (|List| #7=(|Polynomial| *4))) #5# #6#)) (|leftDiscriminant| #1# #8=(AND (|ofCategory| *2 #3#) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *2)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *2)))) (|rightDiscriminant| #1# #8#) (|leftTraceMatrix| #1# #9=(AND #2# (|isDomain| *2 #4#) #5# #6#)) (|rightTraceMatrix| #1# #9#) (|leftRankPolynomial| #1# #10=(AND #2# (|isDomain| *2 (|SparseUnivariatePolynomial| #7#)) #5# #6#)) (|rightRankPolynomial| #1# #10#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unit| (#3=(#4=(|Union| $ #5="failed")) 48 (|has| |#1| . #6=((|IntegralDomain|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) #7=(|Vector| $)) 89 T ELT) (((|Vector| (|Matrix| |#1|))) 115 T ELT)) (|someBasis| ((#7#) 92 T ELT)) (|sample| (#8=($) 23 T CONST)) (|rightUnits| (#9=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) 51 (|has| |#1| . #6#) ELT)) (|rightUnit| (#3# 49 (|has| |#1| . #6#) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) . #10=(#7#)) 76 T ELT) (((|Matrix| |#1|)) 107 T ELT)) (|rightTrace| ((|#1| . #11=($)) 85 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) . #12=($ #7#)) 87 T ELT) (((|Matrix| |#1|) $) 105 T ELT)) (|rightRecip| (#13=(#4# $) 56 (|has| |#1| . #6#) ELT)) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 103 (|has| |#1| (|Field|)) ELT)) (|rightPower| (#14=($ $ (|PositiveInteger|)) 37 T ELT)) (|rightNorm| ((|#1| . #11#) 83 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15=($)) 53 (|has| |#1| . #6#) ELT)) (|rightDiscriminant| ((|#1| . #16=(#7#)) 78 T ELT) ((|#1|) 109 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 74 T ELT)) (|rightAlternative?| (#17=((|Boolean|)) 68 T ELT)) (|represents| (($ (|Vector| |#1|) #7#) 80 T ELT) (($ (|Vector| |#1|)) 113 T ELT)) (|recip| (#13# 58 (|has| |#1| . #6#) ELT)) (|rank| (((|PositiveInteger|)) 91 T ELT)) (|powerAssociative?| (#17# 65 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 44 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (#17# 61 T ELT)) (|lieAlgebra?| (#17# 59 T ELT)) (|lieAdmissible?| (#17# 63 T ELT)) (|leftUnits| (#9# 52 (|has| |#1| . #6#) ELT)) (|leftUnit| (#3# 50 (|has| |#1| . #6#) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) . #10#) 77 T ELT) (((|Matrix| |#1|)) 108 T ELT)) (|leftTrace| ((|#1| . #11#) 86 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) . #12#) 88 T ELT) (((|Matrix| |#1|) $) 106 T ELT)) (|leftRecip| (#13# 57 (|has| |#1| . #6#) ELT)) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 104 (|has| |#1| (|Field|)) ELT)) (|leftPower| (#14# 38 T ELT)) (|leftNorm| ((|#1| . #11#) 84 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 54 (|has| |#1| . #6#) ELT)) (|leftDiscriminant| ((|#1| . #16#) 79 T ELT) ((|#1|) 110 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 75 T ELT)) (|leftAlternative?| (#17# 69 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (#17# 60 T ELT)) (|jordanAdmissible?| (#17# 62 T ELT)) (|jacobiIdentity?| (#17# 64 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (#17# 67 T ELT)) (|elt| ((|#1| $ (|Integer|)) 119 T ELT)) (|coordinates| (((|Vector| |#1|) $ #7#) 82 T ELT) (((|Matrix| |#1|) #7# #7#) 81 T ELT) (((|Vector| |#1|) $) 117 T ELT) (((|Matrix| |#1|) (|Vector| $)) 116 T ELT)) (|convert| (((|Vector| |#1|) $) 112 T ELT) (($ (|Vector| |#1|)) 111 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) #7#) 90 T ELT) (((|List| (|Polynomial| |#1|))) 114 T ELT)) (|commutator| (#18=($ $ $) 34 T ELT)) (|commutative?| (#17# 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 118 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 55 (|has| |#1| . #6#) ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|associative?| (#17# 71 T ELT)) (|apply| (($ (|Matrix| |#1|) $) 102 T ELT)) (|antiCommutator| (#18# 33 T ELT)) (|antiCommutative?| (#17# 72 T ELT)) (|antiAssociative?| (#17# 70 T ELT)) (|alternative?| (#17# 66 T ELT)) (|Zero| (#8# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#14# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #19=($)) 30 T ELT) (($ $ $) 36 T ELT) (($ $ |#1|) 46 T ELT) (($ |#1| . #19#) 45 T ELT))) 
(((|FramedNonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |FramedNonAssociativeAlgebra|)) 
((|basis| (*1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|coordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|structuralConstants| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| *3))))) (|conditionsForIdempotents| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|List| (|Polynomial| *3))))) (|represents| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|convert| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *3)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|leftDiscriminant| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightDiscriminant| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|leftTraceMatrix| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|rightTraceMatrix| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|leftRegularRepresentation| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|rightRegularRepresentation| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|leftRankPolynomial| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *3))))) (|rightRankPolynomial| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *3))))) (|apply| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|))))) 
(|Join| (|FiniteRankNonAssociativeAlgebra| |t#1|) (|Eltable| (|Integer|) |t#1|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| $))) (SIGNATURE |coordinates| ((|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |t#1|)))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |t#1|)))) (SIGNATURE |represents| ($ (|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) ((|Eltable| (|Integer|) |#1|) . T) ((|FiniteRankNonAssociativeAlgebra| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeAlgebra| |#1|) . T) ((|NonAssociativeRng|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|refine| ((#1=(|Factored| |#1|) #1# (|Mapping| #1# |#1|)) 28 T ELT)) (|mergeFactors| ((#1# #1# #1#) 17 T ELT))) 
(((|FactoredFunctionUtilities| |#1|) (CATEGORY |package| (SIGNATURE |refine| (#1=(|Factored| |#1|) #1# (|Mapping| #1# |#1|))) (SIGNATURE |mergeFactors| (#1# #1# #1#))) (|IntegralDomain|)) (T |FactoredFunctionUtilities|)) 
((|mergeFactors| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Factored| *3)) (|ofCategory| *3 #1=(|IntegralDomain|)) (|isDomain| *1 (|FactoredFunctionUtilities| *3)))) (|refine| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| #2=(|Factored| *4) *4)) (|ofCategory| *4 #1#) (|isDomain| *2 #2#) (|isDomain| *1 (|FactoredFunctionUtilities| *4))))) 
((|variables| ((#1=(|List| #2=(|Symbol|)) $) 81 T ELT)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ #3=(|Kernel| $)) 313 T ELT)) (|subst| #4=(($ $ #5=(|Equation| $)) NIL T ELT) #6=(($ $ (|List| #5#)) NIL T ELT) (#7=($ $ #8=(|List| #3#) #9=(|List| $)) 277 T ELT)) (|retractIfCan| (#10=((|Union| #3# #11="failed") $) NIL T ELT) (((|Union| #2# #11#) $) 84 T ELT) (((|Union| #12=(|Integer|) #11#) $) NIL T ELT) (((|Union| |#2| #11#) $) 273 T ELT) (((|Union| #13=(|Fraction| #14=(|Polynomial| |#2|)) #11#) $) 363 T ELT) (((|Union| #14# #11#) $) 275 T ELT) (((|Union| #15=(|Fraction| #12#) #11#) $) NIL T ELT)) (|retract| ((#3# $) NIL T ELT) ((#2# $) 28 T ELT) ((#12# $) NIL T ELT) (#16=(|#2| $) 271 T ELT) ((#13# $) 345 T ELT) ((#14# $) 272 T ELT) ((#15# $) NIL T ELT)) (|operator| ((#17=(|BasicOperator|) #17#) 47 T ELT)) (|numerator| (#18=($ $) 99 T ELT)) (|mainKernel| (#10# 268 T ELT)) (|kernels| ((#8# $) 269 T ELT)) (|isTimes| (#19=((|Union| #9# #11#) $) 287 T ELT)) (|isPower| (((|Union| (|Record| (|:| |val| $) #20=(|:| |exponent| #12#)) #11#) $) 294 T ELT)) (|isPlus| (#19# 285 T ELT)) (|isMult| (((|Union| (|Record| (|:| |coef| #12#) #21=(|:| |var| #3#)) #11#) $) 304 T ELT)) (|isExpt| ((#22=(|Union| (|Record| #21# #20#) #11#) $) 291 T ELT) ((#22# $ #17#) 255 T ELT) ((#22# $ #2#) 257 T ELT)) (|ground?| ((#23=(|Boolean|) $) 17 T ELT)) (|ground| (#16# 19 T ELT)) (|eval| (($ $ #3# $) NIL T ELT) (#7# 276 T ELT) #6# #4# (($ $ $ $) NIL T ELT) (($ $ #9# #9#) NIL T ELT) (($ $ #1# #24=(|List| #25=(|Mapping| $ $))) NIL T ELT) (($ $ #1# #26=(|List| #27=(|Mapping| $ #9#))) 109 T ELT) (($ $ #2# #27#) NIL T ELT) (($ $ #2# #25#) NIL T ELT) (($ $ #28=(|List| #17#) #24#) NIL T ELT) (($ $ #28# #26#) NIL T ELT) (($ $ #17# #27#) NIL T ELT) (($ $ #17# #25#) NIL T ELT) (#29=($ $ #2#) 62 T ELT) (#30=($ $ #1#) 280 T ELT) (#18# 281 T ELT) (($ $ #17# $ #2#) 65 T ELT) (($ $ #28# #9# #2#) 72 T ELT) (($ $ #1# #31=(|List| #32=(|NonNegativeInteger|)) #24#) 120 T ELT) (($ $ #1# #31# #26#) 282 T ELT) (($ $ #2# #32# #27#) 105 T ELT) (($ $ #2# #32# #25#) 104 T ELT)) (|elt| (($ #17# $) NIL T ELT) (($ #17# $ $) NIL T ELT) (($ #17# $ $ $) NIL T ELT) (($ #17# $ $ $ $) NIL T ELT) (($ #17# #9#) 119 T ELT)) (|differentiate| (#29# 278 T ELT) (#30# NIL T ELT) (($ $ #2# #32#) NIL T ELT) (($ $ #1# #31#) NIL T ELT)) (|denominator| (#18# 324 T ELT)) (|convert| (((|Pattern| #12#) $) 297 T ELT) (((|Pattern| (|Float|)) $) 301 T ELT) (($ (|Factored| $)) 359 T ELT) (((|InputForm|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 279 T ELT) (($ #3#) 93 T ELT) (($ #2#) 24 T ELT) (($ |#2|) NIL T ELT) (($ (|SparseMultivariatePolynomial| |#2| #3#)) NIL T ELT) (($ #33=(|Fraction| |#2|)) 329 T ELT) (($ #34=(|Polynomial| #33#)) 368 T ELT) (($ (|Fraction| #34#)) 341 T ELT) (($ #13#) 335 T ELT) (#18# NIL T ELT) (($ #14#) 216 T ELT) (($ #12#) NIL T ELT) (($ #15#) 373 T ELT)) (|characteristic| ((#32#) 88 T CONST)) (|belong?| ((#23# #17#) 42 T ELT)) (|applyQuote| (($ #2# $) 31 T ELT) (($ #2# $ $) 32 T ELT) (($ #2# $ $ $) 33 T ELT) (($ #2# $ $ $ $) 34 T ELT) (($ #2# #9#) 39 T ELT)) (* (($ #15# $) NIL T ELT) (($ $ #15#) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) 306 T ELT) (($ $ $) NIL T ELT) (($ #12# $) NIL T ELT) (($ #32# $) NIL T ELT) (($ (|PositiveInteger|) $) NIL T ELT))) 
(((|FunctionSpace&| |#1| |#2|) (CATEGORY |package| (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE * (|#1| #1=(|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| #2=(|Integer|) |#1|)) (SIGNATURE |coerce| (|#1| #3=(|Fraction| #2#))) (SIGNATURE |retractIfCan| ((|Union| #3# #4="failed") |#1|)) (SIGNATURE |retract| (#3# |#1|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE |coerce| (|#1| #2#)) (SIGNATURE |characteristic| (#1#) |constant|) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |coerce| (|#1| #5=(|Polynomial| |#2|))) (SIGNATURE |retractIfCan| ((|Union| #5# #4#) |#1|)) (SIGNATURE |retract| (#5# |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #6=(|List| #7=(|Symbol|)) #8=(|List| #1#))) (SIGNATURE |differentiate| (|#1| |#1| #7# #1#)) (SIGNATURE |differentiate| #9=(|#1| |#1| #6#)) (SIGNATURE |differentiate| #10=(|#1| |#1| #7#)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| #11=(|#1| |#1|)) (SIGNATURE * (|#1| |#1| #3#)) (SIGNATURE * (|#1| #3# |#1|)) (SIGNATURE |coerce| (|#1| #12=(|Fraction| #5#))) (SIGNATURE |retractIfCan| ((|Union| #12# #4#) |#1|)) (SIGNATURE |retract| (#12# |#1|)) (SIGNATURE |univariate| ((|Fraction| (|SparseUnivariatePolynomial| |#1|)) |#1| #13=(|Kernel| |#1|))) (SIGNATURE |coerce| (|#1| (|Fraction| #14=(|Polynomial| #15=(|Fraction| |#2|))))) (SIGNATURE |coerce| (|#1| #14#)) (SIGNATURE |coerce| (|#1| #15#)) (SIGNATURE |denominator| #11#) (SIGNATURE |convert| (|#1| (|Factored| |#1|))) (SIGNATURE |eval| (|#1| |#1| #7# #1# #16=(|Mapping| |#1| |#1|))) (SIGNATURE |eval| (|#1| |#1| #7# #1# #17=(|Mapping| |#1| #18=(|List| |#1|)))) (SIGNATURE |eval| (|#1| |#1| #6# #8# #19=(|List| #17#))) (SIGNATURE |eval| (|#1| |#1| #6# #8# #20=(|List| #16#))) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| |#1|) #21=(|:| |exponent| #2#)) #4#) |#1|)) (SIGNATURE |isExpt| (#22=(|Union| (|Record| #23=(|:| |var| #13#) #21#) #4#) |#1| #7#)) (SIGNATURE |isExpt| (#22# |#1| #24=(|BasicOperator|))) (SIGNATURE |numerator| #11#) (SIGNATURE |coerce| (|#1| (|SparseMultivariatePolynomial| |#2| #13#))) (SIGNATURE |isMult| ((|Union| (|Record| (|:| |coef| #2#) #23#) #4#) |#1|)) (SIGNATURE |isPlus| #25=((|Union| #18# #4#) |#1|)) (SIGNATURE |isExpt| (#22# |#1|)) (SIGNATURE |isTimes| #25#) (SIGNATURE |eval| (|#1| |#1| #26=(|List| #24#) #18# #7#)) (SIGNATURE |eval| (|#1| |#1| #24# |#1| #7#)) (SIGNATURE |eval| #11#) (SIGNATURE |eval| #9#) (SIGNATURE |eval| #10#) (SIGNATURE |applyQuote| (|#1| #7# #18#)) (SIGNATURE |applyQuote| (|#1| #7# |#1| |#1| |#1| |#1|)) (SIGNATURE |applyQuote| (|#1| #7# |#1| |#1| |#1|)) (SIGNATURE |applyQuote| (|#1| #7# |#1| |#1|)) (SIGNATURE |applyQuote| (|#1| #7# |#1|)) (SIGNATURE |variables| (#6# |#1|)) (SIGNATURE |ground| #27=(|#2| |#1|)) (SIGNATURE |ground?| (#28=(|Boolean|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #4#) |#1|)) (SIGNATURE |retract| #27#) (SIGNATURE |retract| (#2# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #2# #4#) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |convert| ((|Pattern| #2#) |#1|)) (SIGNATURE |coerce| (|#1| #7#)) (SIGNATURE |retractIfCan| ((|Union| #7# #4#) |#1|)) (SIGNATURE |retract| (#7# |#1|)) (SIGNATURE |eval| (|#1| |#1| #24# #16#)) (SIGNATURE |eval| (|#1| |#1| #24# #17#)) (SIGNATURE |eval| (|#1| |#1| #26# #19#)) (SIGNATURE |eval| (|#1| |#1| #26# #20#)) (SIGNATURE |eval| (|#1| |#1| #7# #16#)) (SIGNATURE |eval| (|#1| |#1| #7# #17#)) (SIGNATURE |eval| (|#1| |#1| #6# #19#)) (SIGNATURE |eval| (|#1| |#1| #6# #20#)) (SIGNATURE |belong?| (#28# #24#)) (SIGNATURE |operator| (#24# #24#)) (SIGNATURE |kernels| (#29=(|List| #13#) |#1|)) (SIGNATURE |mainKernel| #30=((|Union| #13# #4#) |#1|)) (SIGNATURE |subst| #31=(|#1| |#1| #29# #18#)) (SIGNATURE |subst| #32=(|#1| |#1| (|List| #33=(|Equation| |#1|)))) (SIGNATURE |subst| #34=(|#1| |#1| #33#)) (SIGNATURE |elt| (|#1| #24# #18#)) (SIGNATURE |elt| (|#1| #24# |#1| |#1| |#1| |#1|)) (SIGNATURE |elt| (|#1| #24# |#1| |#1| |#1|)) (SIGNATURE |elt| (|#1| #24# |#1| |#1|)) (SIGNATURE |elt| (|#1| #24# |#1|)) (SIGNATURE |eval| (|#1| |#1| #18# #18#)) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| #34#) (SIGNATURE |eval| #32#) (SIGNATURE |eval| #31#) (SIGNATURE |eval| (|#1| |#1| #13# |#1|)) (SIGNATURE |coerce| (|#1| #13#)) (SIGNATURE |retractIfCan| #30#) (SIGNATURE |retract| (#13# |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|FunctionSpace| |#2|) (|SetCategory|)) (T |FunctionSpace&|)) 
((|operator| (*1 *2 *2) (AND (|isDomain| *2 #1=(|BasicOperator|)) #2=(|ofCategory| *4 #3=(|SetCategory|)) #4=(|isDomain| *1 (|FunctionSpace&| *3 *4)) #5=(|ofCategory| *3 (|FunctionSpace| *4)))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 #1#) (|ofCategory| *5 #3#) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FunctionSpace&| *4 *5)) (|ofCategory| *4 (|FunctionSpace| *5)))) (|characteristic| (*1 *2) (AND #2# (|isDomain| *2 (|NonNegativeInteger|)) #4# #5#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 129 (|has| |#1| . #3=((|AbelianSemiGroup|))) ELT)) (|variables| (((|List| (|Symbol|)) $) 222 T ELT)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) 190 (|has| |#1| (|IntegralDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 162 (|has| |#1| . #4=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 163 (|has| |#1| . #4#) ELT)) (|unit?| ((#5=(|Boolean|) $) 165 (|has| |#1| . #4#) ELT)) (|tower| (#6=(#7=(|List| #8=(|Kernel| $)) $) 42 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 132 (|has| |#1| . #9=((|AbelianGroup|))) ELT)) (|subst| (($ $ #10=(|Equation| $)) 54 T ELT) (($ $ (|List| #10#)) 53 T ELT) (($ $ #7# #11=(|List| $)) 52 T ELT)) (|squareFreePart| (($ $) 182 (|has| |#1| . #4#) ELT)) (|squareFree| (#12=((|Factored| $) $) 183 (|has| |#1| . #4#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 173 (|has| |#1| . #4#) ELT)) (|sample| (#13=($) 117 (OR (|has| |#1| . #14=((|SemiGroup|))) (|has| |#1| . #3#)) CONST)) (|retractIfCan| (((|Union| #8# . #15=("failed")) . #16=($)) 67 T ELT) (((|Union| #17=(|Symbol|) . #15#) . #16#) 235 T ELT) (((|Union| #18=(|Integer|) . #15#) . #16#) 229 (|has| |#1| . #19=((|RetractableTo| #18#))) ELT) (((|Union| |#1| . #15#) . #16#) 226 T ELT) (((|Union| (|Fraction| (|Polynomial| |#1|)) . #15#) . #16#) 188 (|has| |#1| . #20=((|IntegralDomain|))) ELT) (((|Union| (|Polynomial| |#1|) . #15#) . #16#) 137 (|has| |#1| . #21=((|Ring|))) ELT) (((|Union| #22=(|Fraction| #18#) . #15#) . #16#) 111 (OR (AND (|has| |#1| . #23=((|RetractableTo| (|Integer|)))) (|has| |#1| . #24=((|IntegralDomain|)))) (|has| |#1| . #25=((|RetractableTo| #22#)))) ELT)) (|retract| ((#8# . #26=($)) 68 T ELT) ((#17# . #26#) 236 T ELT) ((#18# . #26#) 228 (|has| |#1| . #19#) ELT) ((|#1| . #26#) 227 T ELT) (((|Fraction| (|Polynomial| |#1|)) . #26#) 189 (|has| |#1| . #20#) ELT) (((|Polynomial| |#1|) . #26#) 138 (|has| |#1| . #21#) ELT) ((#22# . #26#) 112 (OR (AND (|has| |#1| . #23#) (|has| |#1| . #24#)) (|has| |#1| . #25#)) ELT)) (|rem| (#27=($ $ $) 177 (|has| |#1| . #4#) ELT)) (|reducedSystem| (((|Matrix| #28=(|Integer|)) . #29=(#30=(|Matrix| $))) 155 (|and| (|has| |#1| . #31=((|LinearlyExplicitRingOver| #28#))) (|has| |#1| . #32=((|Ring|)))) ELT) (((|Record| (|:| |mat| (|Matrix| #28#)) (|:| |vec| (|Vector| #28#))) . #33=(#30# #34=(|Vector| $))) 154 (|and| (|has| |#1| . #31#) (|has| |#1| . #32#)) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #33#) 153 (|has| |#1| . #32#) ELT) (((|Matrix| |#1|) . #29#) 152 (|has| |#1| . #32#) ELT)) (|recip| (((|Union| $ "failed") $) 119 (|has| |#1| . #14#) ELT)) (|quo| (#27# 176 (|has| |#1| . #4#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #35=(|List| $)) (|:| |generator| $)) #35#) 171 (|has| |#1| . #4#) ELT)) (|prime?| (((|Boolean|) $) 184 (|has| |#1| . #4#) ELT)) (|patternMatch| (((|PatternMatchResult| #36=(|Integer|) . #37=($)) $ (|Pattern| #36#) 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44 T ELT)) (|leftReducedSystem| (((|Matrix| #28#) . #50=(#34#)) 157 (|and| (|has| |#1| . #31#) (|has| |#1| . #32#)) ELT) (((|Record| (|:| |mat| (|Matrix| #28#)) (|:| |vec| (|Vector| #28#))) . #51=(#34# $)) 156 (|and| (|has| |#1| . #31#) (|has| |#1| . #32#)) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #51#) 151 (|has| |#1| . #32#) ELT) (((|Matrix| |#1|) . #50#) 150 (|has| |#1| . #32#) ELT)) (|lcm| (#52=($ (|List| $)) 169 (|has| |#1| . #4#) ELT) (#53=($ $ $) 168 (|has| |#1| . #4#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|kernels| (#6# 43 T ELT)) (|kernel| (#54=($ #42# $) 36 T ELT) (#55=($ #42# #11#) 35 T ELT)) (|isTimes| (((|Union| (|List| $) "failed") $) 211 (|has| |#1| (|SemiGroup|)) ELT)) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) 202 (|has| |#1| (|Ring|)) ELT)) (|isPlus| (((|Union| (|List| $) "failed") $) 209 (|has| |#1| (|AbelianSemiGroup|)) ELT)) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) 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. #58#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #8#) 66 T ELT) (($ #17#) 234 T ELT) (($ |#1|) 225 T ELT) (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) 207 (|has| |#1| (|Ring|)) ELT) (($ (|Fraction| |#1|)) 193 (|has| |#1| (|IntegralDomain|)) ELT) (($ (|Polynomial| (|Fraction| |#1|))) 192 (|has| |#1| (|IntegralDomain|)) ELT) (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) 191 (|has| |#1| (|IntegralDomain|)) ELT) (($ (|Fraction| (|Polynomial| |#1|))) 187 (|has| |#1| . #20#) ELT) (($ $) 160 (|has| |#1| . #4#) ELT) (($ (|Polynomial| |#1|)) 136 (|has| |#1| . #21#) ELT) (($ #22#) 110 (OR (|has| |#1| . #4#) (AND (|has| |#1| . #23#) (|has| |#1| . #24#)) (|has| |#1| . #25#)) ELT) (($ #18#) 109 (OR (|has| |#1| . #67#) (|has| |#1| . #19#)) ELT)) (|charthRoot| (((|Maybe| $) $) 158 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 140 (|has| |#1| . #67#) CONST)) (|box| (#39# 51 T ELT) (#40# 50 T ELT)) (|belong?| ((#44# #42#) 39 T ELT)) 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(((|FunctionSpace| |#1|) (|Category|) (|SetCategory|)) (T |FunctionSpace|)) 
((|ground?| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|ground| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|SetCategory|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| (|Symbol|))))) (|applyQuote| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *1 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *1 *1 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|FunctionSpace| *4)) (|ofCategory| *4 (|SetCategory|)))) (|eval| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|))))) (|eval| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Symbol|))) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *3 (|ConvertibleTo| (|InputForm|))))) (|eval| (*1 *1 *1) (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|ConvertibleTo| (|InputForm|))))) (|eval| (*1 *1 *1 *2 *1 *3) (AND (|isDomain| *2 (|BasicOperator|)) (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *4)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *4 (|ConvertibleTo| (|InputForm|))))) (|eval| (*1 *1 *1 *2 *3 *4) (AND (|isDomain| *2 (|List| (|BasicOperator|))) (|isDomain| *3 (|List| *1)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *5 (|ConvertibleTo| (|InputForm|))))) (|isTimes| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|SemiGroup|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|isExpt| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|SemiGroup|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Record| (|:| |var| (|Kernel| *1)) (|:| |exponent| (|Integer|)))) (|ofCategory| *1 (|FunctionSpace| *3)))) (|isPlus| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|AbelianSemiGroup|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|isMult| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|AbelianSemiGroup|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| *1)))) (|ofCategory| *1 (|FunctionSpace| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|numer| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1))) (|ofCategory| *1 (|FunctionSpace| *3)))) (|numerator| (*1 *1 *1) (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|Ring|)))) (|isExpt| (*1 *2 *1 *3) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|SetCategory|)) (|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 (|SetCategory|)) (|isDomain| *2 (|Record| (|:| |var| (|Kernel| *1)) (|:| |exponent| (|Integer|)))) (|ofCategory| *1 (|FunctionSpace| *4)))) (|isPower| (*1 *2 *1) (|partial| AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|SetCategory|)) (|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 (|SetCategory|)) (|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 (|SetCategory|)) (|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 (|SetCategory|)) (|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 (|SetCategory|)) (|ofCategory| *5 (|Ring|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|)))) (|denom| (*1 *2 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1))) (|ofCategory| *1 (|FunctionSpace| *3)))) (|denominator| (*1 *1 *1) (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|IntegralDomain|)))) (/ (*1 *1 *2 *2) (AND (|isDomain| *2 (|SparseMultivariatePolynomial| *3 (|Kernel| *1))) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| *3)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Fraction| *3))) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Polynomial| (|Fraction| *3)))) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|FunctionSpace| *3)))) (|univariate| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Kernel| *1)) (|ofCategory| *1 (|FunctionSpace| *4)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| *1))))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)) (|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| #1=(|Fraction| (|Integer|))) |has| |#1| (|IntegralDomain|)) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |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|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|IntegralDomain|))) ((|CoercibleFrom| #2=(|Fraction| (|Polynomial| |#1|))) |has| |#1| (|IntegralDomain|)) ((|CoercibleFrom| (|Integer|)) OR (|has| |#1| (|Ring|)) (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CoercibleFrom| #3=(|Kernel| $)) . T) ((|CoercibleFrom| #4=(|Polynomial| |#1|)) |has| |#1| (|Ring|)) ((|CoercibleFrom| #5=(|Symbol|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|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|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| (|Integer|)) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianGroup|))) ((|LeftLinearSet| |#1|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|CommutativeRing|))) ((|LeftLinearSet| $) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|LeftModule| #1#) |has| |#1| (|IntegralDomain|)) ((|LeftModule| #6=(|Integer|)) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LeftModule| |#1|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|CommutativeRing|))) ((|LeftModule| $) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|LinearSet| #1#) |has| |#1| (|IntegralDomain|)) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|LinearlyExplicitRingOver| #6#) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|Module| #1#) |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|))) ((|PartialDifferentialDomain| $ #7=(|Symbol|)) |has| |#1| (|Ring|)) ((|PartialDifferentialRing| #7#) |has| |#1| (|Ring|)) ((|PartialDifferentialSpace| #7#) |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| #2#) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #3#) . T) ((|RetractableTo| #4#) |has| |#1| (|Ring|)) ((|RetractableTo| #5#) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) |has| |#1| (|IntegralDomain|)) ((|RightLinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightLinearSet| $) |has| |#1| (|IntegralDomain|)) ((|RightModule| #1#) |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|))) ((|SemiRing|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|IntegralDomain|))) 
((|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 11 T ELT))) 
(((|FunctionSpaceFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|))) #1=(|Ring|) (|FunctionSpace| |#1|) #1# (|FunctionSpace| |#3|)) (T |FunctionSpaceFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|FunctionSpace| *6)) (|isDomain| *1 (|FunctionSpaceFunctions2| *5 *4 *6 *2)) (|ofCategory| *4 (|FunctionSpace| *5))))) 
((|localAbs| ((|#2| |#2|) 182 T ELT)) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| #1=(|String|)) (|:| |prob| #1#)))) |#2| (|Boolean|)) 60 T ELT))) 
(((|FunctionSpaceToExponentialExpansion| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |exprToXXP| ((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| #1=(|String|)) (|:| |prob| #1#)))) |#2| (|Boolean|))) (SIGNATURE |localAbs| (|#2| |#2|))) (|Join| (|GcdDomain|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|)) (|Symbol|) |#2|) (T |FunctionSpaceToExponentialExpansion|)) 
((|localAbs| (*1 *2 *2) (AND (|ofCategory| *3 #1=(|Join| (|GcdDomain|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#))) (|isDomain| *1 (|FunctionSpaceToExponentialExpansion| *3 *2 *4 *5)) (|ofCategory| *2 (|Join| #3=(|AlgebraicallyClosedField|) #4=(|TranscendentalFunctionCategory|) (|FunctionSpace| *3))) (|ofType| *4 #5=(|Symbol|)) (|ofType| *5 *2))) (|exprToXXP| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 #1#) (|isDomain| *2 (|Union| (|:| |%expansion| (|ExponentialExpansion| *5 *3 *6 *7)) (|:| |%problem| (|Record| (|:| |func| #6=(|String|)) (|:| |prob| #6#))))) (|isDomain| *1 (|FunctionSpaceToExponentialExpansion| *5 *3 *6 *7)) (|ofCategory| *3 (|Join| #3# #4# (|FunctionSpace| *5))) (|ofType| *6 #5#) (|ofType| *7 *3)))) 
((|localAbs| ((|#2| |#2|) 105 T ELT)) (|exprToUPS| (#1=((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| #2=(|String|)) (|:| |prob| #2#)))) |#2| (|Boolean|) #2#) 52 T ELT)) (|exprToGenUPS| (#1# 169 T ELT))) 
(((|FunctionSpaceToUnivariatePowerSeries| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |exprToUPS| #1=((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| #2=(|String|)) (|:| |prob| #2#)))) |#2| (|Boolean|) #2#)) (SIGNATURE |exprToGenUPS| #1#) (SIGNATURE |localAbs| (|#2| |#2|))) (|Join| (|GcdDomain|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#)) (|Join| (|AlgebraicallyClosedField|) #4=(|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#3|)))) (|OrderedRing|) (|Join| (|UnivariatePowerSeriesCategory| |#2| |#3|) (|Field|) #4# (CATEGORY |domain| (SIGNATURE |differentiate| #5=($ $)) (SIGNATURE |integrate| #5#))) (|PartialTranscendentalFunctions| |#4|) (|Symbol|)) (T |FunctionSpaceToUnivariatePowerSeries|)) 
((|localAbs| (*1 *2 *2) (AND (|ofCategory| *3 #1=(|Join| (|GcdDomain|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#))) (|ofCategory| *2 (|Join| #3=(|AlgebraicallyClosedField|) #4=(|TranscendentalFunctionCategory|) (|FunctionSpace| *3) (CATEGORY |domain| (SIGNATURE |coerce| ($ *4))))) (|ofCategory| *4 #5=(|OrderedRing|)) (|ofCategory| *5 (|Join| (|UnivariatePowerSeriesCategory| *2 *4) #6=(|Field|) #4# #7=(CATEGORY |domain| (SIGNATURE |differentiate| #8=($ $)) (SIGNATURE |integrate| #8#)))) (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *3 *2 *4 *5 *6 *7)) (|ofCategory| *6 (|PartialTranscendentalFunctions| *5)) (|ofType| *7 #9=(|Symbol|)))) (|exprToGenUPS| #10=(*1 *2 *3 *4 *5) #11=(AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *6 #1#) (|ofCategory| *3 (|Join| #3# #4# (|FunctionSpace| *6) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))))) (|ofCategory| *7 #5#) (|ofCategory| *8 (|Join| (|UnivariatePowerSeriesCategory| *3 *7) #6# #4# #7#)) (|isDomain| *2 (|Union| (|:| |%series| *8) (|:| |%problem| (|Record| (|:| |func| #12=(|String|)) (|:| |prob| #12#))))) (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *6 *3 *7 *8 *9 *10)) (|isDomain| *5 #12#) (|ofCategory| *9 (|PartialTranscendentalFunctions| *8)) (|ofType| *10 #9#))) (|exprToUPS| #10# #11#)) 
((|universe| (#1=($) 51 T ELT)) (|union| (($ |#2| $) NIL T ELT) #2=(($ $ |#2|) NIL T ELT) (#3=($ $ $) 47 T ELT)) (|symmetricDifference| (#3# 46 T ELT)) (|subset?| (#4=(#5=(|Boolean|) $ $) 35 T ELT)) (|size| ((#6=(|NonNegativeInteger|)) 55 T ELT)) (|set| (#7=($ (|List| |#2|)) 23 T ELT) #8=(#1# NIL T ELT)) (|random| (#1# 66 T ELT)) (|part?| (#4# 15 T ELT)) (|min| (#9=(|#2| $) 77 T ELT)) (|max| (#9# 75 T ELT)) (|lookup| ((#10=(|PositiveInteger|) $) 70 T ELT)) (|intersect| (#3# 42 T ELT)) (|index| (($ #10#) 60 T ELT)) (|difference| #2# (#3# 45 T ELT)) (|count| ((#6# |#2| $) 31 T ELT) ((#6# (|Mapping| #5# |#2|) $) NIL T ELT)) (|construct| (#7# 27 T ELT)) (|complement| (($ $) 53 T ELT)) (|coerce| (((|OutputForm|) $) 40 T ELT)) (|cardinality| ((#6# $) 24 T ELT)) (|brace| (#7# 22 T ELT) #8#) (= (#4# 19 T ELT))) 
(((|FiniteSetAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |size| (#1=(|NonNegativeInteger|))) (SIGNATURE |index| (|#1| #2=(|PositiveInteger|))) (SIGNATURE |lookup| (#2# |#1|)) (SIGNATURE |random| #3=(|#1|)) (SIGNATURE |min| #4=(|#2| |#1|)) (SIGNATURE |max| #4#) (SIGNATURE |universe| #3#) (SIGNATURE |complement| (|#1| |#1|)) (SIGNATURE |cardinality| (#1# |#1|)) (SIGNATURE |count| (#1# (|Mapping| #5=(|Boolean|) |#2|) |#1|)) (SIGNATURE |count| (#1# |#2| |#1|)) (SIGNATURE = #6=(#5# |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |part?| #6#) (SIGNATURE |brace| #3#) (SIGNATURE |brace| #7=(|#1| (|List| |#2|))) (SIGNATURE |set| #3#) (SIGNATURE |set| #7#) (SIGNATURE |intersect| #8=(|#1| |#1| |#1|)) (SIGNATURE |difference| #8#) (SIGNATURE |difference| #9=(|#1| |#1| |#2|)) (SIGNATURE |symmetricDifference| #8#) (SIGNATURE |subset?| #6#) (SIGNATURE |union| #8#) (SIGNATURE |union| #9#) (SIGNATURE |union| (|#1| |#2| |#1|)) (SIGNATURE |construct| #7#)) (|FiniteSetAggregate| |#2|) (|SetCategory|)) (T |FiniteSetAggregate&|)) 
((|size| (*1 *2) (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteSetAggregate&| *3 *4)) (|ofCategory| *3 (|FiniteSetAggregate| *4))))) 
((~= (#1=((|Boolean|) $ $) 18 T ELT)) (|universe| (($) 61 (|has| |#1| (|Finite|)) ELT)) (|union| (($ |#1| $) 87 T ELT) (($ $ |#1|) 86 T ELT) (#2=($ $ $) 85 T ELT)) (|symmetricDifference| (#2# 83 T ELT)) (|subset?| (#3=((|Boolean|) $ $) 84 T ELT)) (|size| (((|NonNegativeInteger|)) 55 (|has| |#1| . #4=((|Finite|))) ELT)) (|set| (($ (|List| |#1|)) 79 T ELT) (#5=($) 78 T ELT)) (|select!| (($ (|Mapping| #6=(|Boolean|) |#1|) . #7=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #8=(|Boolean|) |#1|) . #9=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#10=($) 6 T CONST)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #11=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #6# |#1|) . #7#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #11#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #8# |#1|) . #9#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 74 (|has| |#1| . #12=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 70 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 69 T ELT)) (|random| (($) 58 (|has| |#1| . #4#) ELT)) (|part?| (#3# 75 T ELT)) (|min| ((|#1| $) 59 (|has| |#1| (|OrderedSet|)) ELT)) (|members| (((|List| |#1|) $) 68 T ELT)) (|member?| ((#13=(|Boolean|) |#1| $) 73 (|has| |#1| . #12#) ELT)) (|max| ((|#1| $) 60 (|has| |#1| (|OrderedSet|)) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|lookup| ((#14=(|PositiveInteger|) $) 57 (|has| |#1| . #4#) ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#2# 80 T ELT)) (|inspect| ((|#1| . #15=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|index| (($ #14#) 56 (|has| |#1| . #4#) ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #13# |#1|) $) 71 T ELT)) (|extract!| ((|#1| . #15#) 37 T ELT)) (|every?| ((#13# (|Mapping| #13# |#1|) . #16=($)) 66 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17=((|SetCategory|)))) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT)) (|eq?| ((#18=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#18# $) 7 T ELT)) (|empty| (#10# 8 T ELT)) (|difference| (($ $ |#1|) 82 T ELT) (#2# 81 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|count| ((#19=(|NonNegativeInteger|) |#1| $) 72 (|has| |#1| . #12#) ELT) ((#19# (|Mapping| #13# |#1|) $) 67 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#20=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #20#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|complement| (($ $) 62 (|has| |#1| (|Finite|)) ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|cardinality| (((|NonNegativeInteger|) $) 63 T ELT)) (|brace| (($ (|List| |#1|)) 77 T ELT) (#5# 76 T ELT)) (|before?| (#1# 19 T ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|any?| ((#13# (|Mapping| #13# |#1|) . #16#) 65 T ELT)) (= (#1# 17 T ELT)) (|#| ((#19# $) 64 T ELT))) 
(((|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|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (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|)) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((|scan| ((|#4| #1=(|Mapping| |#3| |#1| |#3|) |#2| |#3|) 22 T ELT)) (|reduce| ((|#3| #1# |#2| |#3|) 20 T ELT)) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 17 T ELT))) 
(((|FiniteSetAggregateFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|)) (SIGNATURE |reduce| (|#3| #1=(|Mapping| |#3| |#1| |#3|) |#2| |#3|)) (SIGNATURE |scan| (|#4| #1# |#2| |#3|))) #2=(|SetCategory|) (|FiniteSetAggregate| |#1|) #2# (|FiniteSetAggregate| |#3|)) (T |FiniteSetAggregateFunctions2|)) 
((|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) #1=(|ofCategory| *6 #2=(|SetCategory|)) #3=(|ofCategory| *5 #2#) (|ofCategory| *2 #4=(|FiniteSetAggregate| *5)) (|isDomain| *1 (|FiniteSetAggregateFunctions2| *6 *4 *5 *2)) (|ofCategory| *4 #5=(|FiniteSetAggregate| *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #3# (|ofCategory| *2 #2#) (|isDomain| *1 (|FiniteSetAggregateFunctions2| *5 *4 *2 *6)) #6=(|ofCategory| *4 #4#) (|ofCategory| *6 (|FiniteSetAggregate| *2)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) #3# #1# (|ofCategory| *2 #5#) (|isDomain| *1 (|FiniteSetAggregateFunctions2| *5 *4 *6 *2)) #6#))) 
((|internalIntegrate0| (#1=((|IntegrationResult| |#2|) |#2| #2=(|Symbol|)) 36 T ELT)) (|internalIntegrate| (#1# 21 T ELT)) (|complexIntegrate| ((|#2| |#2| #2#) 26 T ELT))) 
(((|FunctionSpaceComplexIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |internalIntegrate| #1=((|IntegrationResult| |#2|) |#2| #2=(|Symbol|))) (SIGNATURE |internalIntegrate0| #1#) (SIGNATURE |complexIntegrate| (|#2| |#2| #2#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#)) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |FunctionSpaceComplexIntegration|)) 
((|complexIntegrate| (*1 *2 *2 *3) (AND (|isDomain| *3 #1=(|Symbol|)) (|ofCategory| *4 #2=(|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#))) (|isDomain| *1 (|FunctionSpaceComplexIntegration| *4 *2)) (|ofCategory| *2 (|Join| #4=(|TranscendentalFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4))))) (|internalIntegrate0| #5=(*1 *2 *3 *4) #6=(AND (|isDomain| *4 #1#) (|ofCategory| *5 #2#) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|FunctionSpaceComplexIntegration| *5 *3)) (|ofCategory| *3 (|Join| #4# (|AlgebraicallyClosedFunctionSpace| *5))))) (|internalIntegrate| #5# #6#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| ((#4=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|recip| ((#4# $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|makeSin| (#6=($ |#2| |#1|) 37 T ELT)) (|makeCos| (#6# 35 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #7=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (($ (|FourierComponent| |#2|)) 25 T ELT)) (|characteristic| ((#8=(|NonNegativeInteger|)) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#5# 10 T CONST)) (|One| (#5# 16 T CONST)) (= #1#) (- (($ $) NIL T ELT) (#9=($ $ $) NIL T ELT)) (+ (#9# 36 T ELT)) (** (($ $ #10=(|PositiveInteger|)) NIL T ELT) (($ $ #8#) NIL T ELT)) (* (($ #10# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #7# . #11=($)) NIL T ELT) (#9# 40 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #11#) NIL T ELT))) 
(((|FourierSeries| |#1| |#2|) (|Join| (|Algebra| |#1|) (CATEGORY |domain| (IF (|has| |#2| #1=(ATTRIBUTE |canonical|)) (IF (|has| |#1| #1#) #1# |%noBranch|) |%noBranch|) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |coerce| ($ (|FourierComponent| |#2|))) (SIGNATURE |makeSin| #2=($ |#2| |#1|)) (SIGNATURE |makeCos| #2#))) (|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|)))) (|Join| (|OrderedSet|) (|AbelianGroup|))) (T |FourierSeries|)) 
((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *1 (|FourierSeries| *2 *3)) (|ofCategory| *2 #2=(|Join| (|CommutativeRing|) (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 #3=(|Join| (|OrderedSet|) (|AbelianGroup|))))) (|coerce| #1# (AND (|isDomain| *2 (|FourierComponent| *4)) (|ofCategory| *4 #3#) (|isDomain| *1 (|FourierSeries| *3 *4)) #4=(|ofCategory| *3 #2#))) (|makeSin| #5=(*1 *1 *2 *3) #6=(AND (|isDomain| *1 (|FourierSeries| *3 *2)) #4# (|ofCategory| *2 #3#))) (|makeCos| #5# #6#)) 
((|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) 115 T ELT))) 
(((|FunctionSpaceIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |integrate| ((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#)) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |FunctionSpaceIntegration|)) 
((|integrate| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#))) (|isDomain| *2 (|Union| *3 (|List| *3))) (|isDomain| *1 (|FunctionSpaceIntegration| *5 *3)) (|ofCategory| *3 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *5)))))) 
((|polygamma| (#1=(|#2| |#2| |#2|) 31 T ELT)) (|operator| ((#2=(|BasicOperator|) #2#) 43 T ELT)) (|iiabs| (#3=(|#2| |#2|) 63 T ELT)) (|iiGamma| (#3# 66 T ELT)) (|digamma| (#3# 30 T ELT)) (|besselY| (#1# 33 T ELT)) (|besselK| (#1# 35 T ELT)) (|besselJ| (#1# 32 T ELT)) (|besselI| (#1# 34 T ELT)) (|belong?| (((|Boolean|) #2#) 41 T ELT)) (|airyBi| (#3# 37 T ELT)) (|airyAi| (#3# 36 T ELT)) (|abs| (#3# 25 T ELT)) (|Gamma| (#1# 28 T ELT) (#3# 26 T ELT)) (|Beta| (#1# 29 T ELT))) 
(((|FunctionalSpecialFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) #1=(|BasicOperator|))) (SIGNATURE |operator| (#1# #1#)) (SIGNATURE |abs| #2=(|#2| |#2|)) (SIGNATURE |Gamma| #2#) (SIGNATURE |Gamma| #3=(|#2| |#2| |#2|)) (SIGNATURE |Beta| #3#) (SIGNATURE |digamma| #2#) (SIGNATURE |polygamma| #3#) (SIGNATURE |besselJ| #3#) (SIGNATURE |besselY| #3#) (SIGNATURE |besselI| #3#) (SIGNATURE |besselK| #3#) (SIGNATURE |airyAi| #2#) (SIGNATURE |airyBi| #2#) (SIGNATURE |iiGamma| #2#) (SIGNATURE |iiabs| #2#)) (|IntegralDomain|) (|FunctionSpace| |#1|)) (T |FunctionalSpecialFunction|)) 
((|iiabs| #1=(*1 *2 *2) #2=(AND #3=(|ofCategory| *3 #4=(|IntegralDomain|)) (|isDomain| *1 (|FunctionalSpecialFunction| *3 *2)) (|ofCategory| *2 #5=(|FunctionSpace| *3)))) (|iiGamma| #1# #2#) (|airyBi| #1# #2#) (|airyAi| #1# #2#) (|besselK| #6=(*1 *2 *2 *2) #2#) (|besselI| #6# #2#) (|besselY| #6# #2#) (|besselJ| #6# #2#) (|polygamma| #6# #2#) (|digamma| #1# #2#) (|Beta| #6# #2#) (|Gamma| #6# #2#) (|Gamma| #1# #2#) (|abs| #1# #2#) (|operator| #1# (AND (|isDomain| *2 #7=(|BasicOperator|)) #3# (|isDomain| *1 (|FunctionalSpecialFunction| *3 *4)) (|ofCategory| *4 #5#))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 #7#) (|ofCategory| *4 #4#) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FunctionalSpecialFunction| *4 *5)) (|ofCategory| *5 (|FunctionSpace| *4))))) 
((|primitiveElement| (((|Record| #1=(|:| |primelt| |#2|) (|:| |pol1| #2=(|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| #2#) #3=(|:| |prim| #2#)) |#2| |#2|) 103 (|has| |#2| (|AlgebraicallyClosedField|)) ELT) (((|Record| #1# (|:| |poly| (|List| #2#)) #3#) (|List| |#2|)) 65 T ELT))) 
(((|FunctionSpacePrimitiveElement| |#1| |#2|) (CATEGORY |package| (SIGNATURE |primitiveElement| ((|Record| #1=(|:| |primelt| |#2|) (|:| |poly| (|List| #2=(|SparseUnivariatePolynomial| |#2|))) #3=(|:| |prim| #2#)) (|List| |#2|))) (IF (|has| |#2| (|AlgebraicallyClosedField|)) (SIGNATURE |primitiveElement| ((|Record| #1# (|:| |pol1| #2#) (|:| |pol2| #2#) #3#) |#2| |#2|)) |%noBranch|)) (|Join| (|IntegralDomain|) (|CharacteristicZero|)) (|FunctionSpace| |#1|)) (T |FunctionSpacePrimitiveElement|)) 
((|primitiveElement| (*1 *2 *3 *3) (AND #1=(|ofCategory| *4 (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |primelt| *3) (|:| |pol1| #2=(|SparseUnivariatePolynomial| *3)) (|:| |pol2| #2#) (|:| |prim| #2#))) (|isDomain| *1 (|FunctionSpacePrimitiveElement| *4 *3)) (|ofCategory| *3 (|AlgebraicallyClosedField|)) (|ofCategory| *3 #3=(|FunctionSpace| *4)))) (|primitiveElement| (*1 *2 *3) (AND (|isDomain| *3 (|List| *5)) (|ofCategory| *5 #3#) #1# (|isDomain| *2 (|Record| (|:| |primelt| *5) (|:| |poly| (|List| #4=(|SparseUnivariatePolynomial| *5))) (|:| |prim| #4#))) (|isDomain| *1 (|FunctionSpacePrimitiveElement| *4 *5))))) 
((|newReduc| (((|Void|)) 18 T ELT)) (|bringDown| (((|SparseUnivariatePolynomial| #1=(|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) 40 T ELT) ((#1# |#2|) 27 T ELT))) 
(((|FunctionSpaceReduce| |#1| |#2|) (CATEGORY |package| (SIGNATURE |bringDown| (#1=(|Fraction| #2=(|Integer|)) |#2|)) (SIGNATURE |bringDown| ((|SparseUnivariatePolynomial| #1#) |#2| (|Kernel| |#2|))) (SIGNATURE |newReduc| ((|Void|)))) (|Join| (|IntegralDomain|) (|RetractableTo| #2#)) (|FunctionSpace| |#1|)) (T |FunctionSpaceReduce|)) 
((|newReduc| (*1 *2) (AND (|ofCategory| *3 #1=(|Join| (|IntegralDomain|) (|RetractableTo| #2=(|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 #1#) (|isDomain| *2 (|SparseUnivariatePolynomial| #3=(|Fraction| #2#))) (|isDomain| *1 (|FunctionSpaceReduce| *5 *3)))) (|bringDown| (*1 *2 *3) (AND (|ofCategory| *4 #1#) (|isDomain| *2 #3#) (|isDomain| *1 (|FunctionSpaceReduce| *4 *3)) (|ofCategory| *3 (|FunctionSpace| *4))))) 
((|real?| (#1=(#2=(|Boolean|) $) 33 T ELT)) (|logical?| (#1# 35 T ELT)) (|integer?| (#1# 36 T ELT)) (|doubleComplex?| (#1# 39 T ELT)) (|double?| (#1# 34 T ELT)) (|complex?| (#1# 38 T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ (|String|)) 32 T ELT) (($ #3=(|Symbol|)) 30 T ELT) ((#3# $) 24 T ELT) (((|SExpression|) $) 23 T ELT)) (|character?| (#1# 37 T ELT)) (= ((#2# $ $) 17 T ELT))) 
(((|FortranScalarType|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|String|))) (SIGNATURE |coerce| ($ #1=(|Symbol|))) (SIGNATURE |coerce| (#1# $)) (SIGNATURE |coerce| ((|SExpression|) $)) (SIGNATURE |real?| #2=(#3=(|Boolean|) $)) (SIGNATURE |double?| #2#) (SIGNATURE |integer?| #2#) (SIGNATURE |complex?| #2#) (SIGNATURE |doubleComplex?| #2#) (SIGNATURE |character?| #2#) (SIGNATURE |logical?| #2#) (SIGNATURE = (#3# $ $))))) (T |FortranScalarType|)) 
((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *2 (|String|)) #2=(|isDomain| *1 (|FortranScalarType|)))) (|coerce| #1# #3=(AND (|isDomain| *2 (|Symbol|)) #2#)) (|coerce| #4=(*1 *2 *1) #3#) (|coerce| #4# (AND (|isDomain| *2 (|SExpression|)) #2#)) (|real?| #4# #5=(AND (|isDomain| *2 (|Boolean|)) #2#)) (|double?| #4# #5#) (|integer?| #4# #5#) (|complex?| #4# #5#) (|doubleComplex?| #4# #5#) (|character?| #4# #5#) (|logical?| #4# #5#) (= (*1 *2 *1 *1) #5#)) 
((|qfactor| (((|Union| (|Factored| #1=(|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) #2="failed") |#3|) 71 T ELT)) (|ffactor| (((|Factored| |#3|) |#3|) 34 T ELT)) (|anfactor| (((|Union| (|Factored| #3=(|SparseUnivariatePolynomial| #4=(|AlgebraicNumber|))) #2#) |#3|) 29 (|has| |#2| (|RetractableTo| #4#)) ELT)) (|UP2ifCan| (((|Union| (|:| |overq| #1#) (|:| |overan| #3#) (|:| |failed| (|Boolean|))) |#3|) 37 T ELT))) 
(((|FunctionSpaceUnivariatePolynomialFactor| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |ffactor| ((|Factored| |#3|) |#3|)) (SIGNATURE |qfactor| ((|Union| (|Factored| #1=(|SparseUnivariatePolynomial| (|Fraction| #2=(|Integer|)))) #3="failed") |#3|)) (SIGNATURE |UP2ifCan| ((|Union| (|:| |overq| #1#) (|:| |overan| #4=(|SparseUnivariatePolynomial| #5=(|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|)) (IF (|has| |#2| (|RetractableTo| #5#)) (SIGNATURE |anfactor| ((|Union| (|Factored| #4#) #3#) |#3|)) |%noBranch|)) (|Join| (|IntegralDomain|) (|RetractableTo| #2#)) (|FunctionSpace| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |FunctionSpaceUnivariatePolynomialFactor|)) 
((|anfactor| #1=(*1 *2 *3) (|partial| AND (|ofCategory| *5 (|RetractableTo| #2=(|AlgebraicNumber|))) #3=(|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| #4=(|Integer|)))) #5=(|ofCategory| *5 (|FunctionSpace| *4)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| #2#))) #7=(|isDomain| *1 (|FunctionSpaceUnivariatePolynomialFactor| *4 *5 *3)) #8=(|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|UP2ifCan| #1# (AND #3# #5# (|isDomain| *2 (|Union| (|:| |overq| #9=(|SparseUnivariatePolynomial| (|Fraction| #4#))) (|:| |overan| #6#) (|:| |failed| (|Boolean|)))) #7# #8#)) (|qfactor| #1# (|partial| AND #3# #5# (|isDomain| *2 (|Factored| #9#)) #7# #8#)) (|ffactor| #1# (AND #3# #5# (|isDomain| *2 (|Factored| *3)) #7# #8#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|scalarTypeOf| ((#3=(|Union| (|:| |fst| #4=(|FortranScalarType|)) (|:| |void| "void")) $) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fortranReal| (#5=($) 35 T ELT)) (|fortranLogical| (#5# 41 T ELT)) (|fortranInteger| (#5# 37 T ELT)) (|fortranDoubleComplex| (#5# 39 T ELT)) (|fortranDouble| (#5# 36 T ELT)) (|fortranComplex| (#5# 38 T ELT)) (|fortranCharacter| (#5# 40 T ELT)) (|external?| ((#2# $) 8 T ELT)) (|dimensionsOf| ((#6=(|List| (|Polynomial| (|Integer|))) $) 19 T ELT)) (|construct| (($ #3# (|List| (|Symbol|)) #2#) 29 T ELT) (($ #3# #6# #2#) 30 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #4#) 32 T ELT)) (|before?| #1#) (= #1#)) 
(((|FortranType|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1=(|FortranScalarType|))) (SIGNATURE |scalarTypeOf| (#2=(|Union| (|:| |fst| #1#) (|:| |void| "void")) $)) (SIGNATURE |dimensionsOf| (#3=(|List| (|Polynomial| (|Integer|))) $)) (SIGNATURE |external?| (#4=(|Boolean|) $)) (SIGNATURE |construct| ($ #2# (|List| (|Symbol|)) #4#)) (SIGNATURE |construct| ($ #2# #3# #4#)) (SIGNATURE |fortranReal| #5=($)) (SIGNATURE |fortranDouble| #5#) (SIGNATURE |fortranInteger| #5#) (SIGNATURE |fortranLogical| #5#) (SIGNATURE |fortranComplex| #5#) (SIGNATURE |fortranDoubleComplex| #5#) (SIGNATURE |fortranCharacter| #5#)))) (T |FortranType|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 #1=(|FortranScalarType|)) #2=(|isDomain| *1 (|FortranType|)))) (|scalarTypeOf| #3=(*1 *2 *1) (AND #4=(|isDomain| *2 (|Union| (|:| |fst| #1#) (|:| |void| "void"))) #2#)) (|dimensionsOf| #3# (AND (|isDomain| *2 #5=(|List| (|Polynomial| (|Integer|)))) #2#)) (|external?| #3# (AND (|isDomain| *2 #6=(|Boolean|)) #2#)) (|construct| #7=(*1 *1 *2 *3 *4) (AND #4# (|isDomain| *3 (|List| (|Symbol|))) #8=(|isDomain| *4 #6#) #2#)) (|construct| #7# (AND #4# (|isDomain| *3 #5#) #8# #2#)) (|fortranReal| #9=(*1 *1) #2#) (|fortranDouble| #9# #2#) (|fortranInteger| #9# #2#) (|fortranLogical| #9# #2#) (|fortranComplex| #9# #2#) (|fortranDoubleComplex| #9# #2#) (|fortranCharacter| #9# #2#)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|name| (((|Symbol|) $) 8 T ELT)) (|latex| (((|String|) $) 17 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT)) (|before?| #1#) (= (#2# 14 T ELT))) 
(((|FunctionCalled| |#1|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| (#1=(|Symbol|) $)))) #1#) (T |FunctionCalled|)) 
((|name| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|FunctionCalled| *3)) (|ofType| *3 *2)))) 
((|map| (($ (|Mapping| |#1| |#1|) $) 6 T ELT))) 
(((|Functorial| |#1|) (|Category|) (|Type|)) (T |Functorial|)) 
((|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|Functorial| *3)) (|ofCategory| *3 (|Type|))))) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1|) $)))) 
(((|Join|) . T) ((|Type|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|signature| (((|Signature|) $) 7 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| #1#) (= (#2# 9 T ELT))) 
(((|FunctionDescriptor|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |signature| ((|Signature|) $))))) (T |FunctionDescriptor|)) 
((|signature| (*1 *2 *1) (AND (|isDomain| *2 (|Signature|)) (|isDomain| *1 (|FunctionDescriptor|))))) 
((|useSingleFactorBound?| (#1=(#2=(|Boolean|)) 18 T ELT)) (|useSingleFactorBound| (#3=(#2# #2#) 19 T ELT)) (|useEisensteinCriterion?| (#1# 14 T ELT)) (|useEisensteinCriterion| (#3# 15 T ELT)) (|tryFunctionalDecomposition?| (#1# 16 T ELT)) (|tryFunctionalDecomposition| (#3# 17 T ELT)) (|stopMusserTrials| (#4=(#5=(|PositiveInteger|) #5#) 22 T ELT) (#6=(#5#) 21 T ELT)) (|numberOfFactors| ((#7=(|NonNegativeInteger|) #8=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #9=(|Integer|))))) 52 T ELT)) (|musserTrials| (#4# 24 T ELT) (#6# 23 T ELT)) (|modularFactor| (((|Record| (|:| |prime| #9#) (|:| |factors| (|List| |#1|))) |#1|) 94 T ELT)) (|makeFR| ((#10=(|Factored| |#1|) #11=(|Record| (|:| |contp| #9#) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #9#)))))) 176 T ELT)) (|henselFact| ((#11# |#1| #2#) 209 T ELT)) (|factorSquareFree| (#12=(#10# |#1| #7# #7#) 224 T ELT) (#13=(#10# |#1| #14=(|List| #7#) #7#) 221 T ELT) (#15=(#10# |#1| #14#) 223 T ELT) (#16=(#10# |#1| #7#) 222 T ELT) (#17=(#10# |#1|) 220 T ELT)) (|factorOfDegree| ((#18=(|Union| |#1| "failed") #5# |#1| #14# #7# #2#) 226 T ELT) ((#18# #5# |#1| #14# #7#) 227 T ELT) ((#18# #5# |#1| #14#) 229 T ELT) ((#18# #5# |#1| #7#) 228 T ELT) ((#18# #5# |#1|) 230 T ELT)) (|factor| (#12# 219 T ELT) (#13# 215 T ELT) (#15# 217 T ELT) (#16# 216 T ELT) (#17# 214 T ELT)) (|eisensteinIrreducible?| ((#2# |#1|) 43 T ELT)) (|degreePartition| (((|Multiset| #7#) #8#) 99 T ELT)) (|btwFact| ((#11# |#1| #2# (|Set| #7#) #7#) 213 T ELT))) 
(((|GaloisGroupFactorizer| |#1|) (CATEGORY |package| (SIGNATURE |makeFR| (#1=(|Factored| |#1|) #2=(|Record| (|:| |contp| #3=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #3#))))))) (SIGNATURE |degreePartition| ((|Multiset| #4=(|NonNegativeInteger|)) #5=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #3#))))) (SIGNATURE |musserTrials| #6=(#7=(|PositiveInteger|))) (SIGNATURE |musserTrials| #8=(#7# #7#)) (SIGNATURE |stopMusserTrials| #6#) (SIGNATURE |stopMusserTrials| #8#) (SIGNATURE |numberOfFactors| (#4# #5#)) (SIGNATURE |modularFactor| ((|Record| (|:| |prime| #3#) (|:| |factors| (|List| |#1|))) |#1|)) (SIGNATURE |useSingleFactorBound?| #9=(#10=(|Boolean|))) (SIGNATURE |useSingleFactorBound| #11=(#10# #10#)) (SIGNATURE |useEisensteinCriterion?| #9#) (SIGNATURE |useEisensteinCriterion| #11#) (SIGNATURE |eisensteinIrreducible?| (#10# |#1|)) (SIGNATURE |tryFunctionalDecomposition?| #9#) (SIGNATURE |tryFunctionalDecomposition| #11#) (SIGNATURE |factor| #12=(#1# |#1|)) (SIGNATURE |factor| #13=(#1# |#1| #4#)) (SIGNATURE |factor| #14=(#1# |#1| #15=(|List| #4#))) (SIGNATURE |factor| #16=(#1# |#1| #15# #4#)) (SIGNATURE |factor| #17=(#1# |#1| #4# #4#)) (SIGNATURE |factorSquareFree| #12#) (SIGNATURE |factorSquareFree| #13#) (SIGNATURE |factorSquareFree| #14#) (SIGNATURE |factorSquareFree| #16#) (SIGNATURE |factorSquareFree| #17#) (SIGNATURE |factorOfDegree| (#18=(|Union| |#1| "failed") #7# |#1|)) (SIGNATURE |factorOfDegree| (#18# #7# |#1| #4#)) (SIGNATURE |factorOfDegree| (#18# #7# |#1| #15#)) (SIGNATURE |factorOfDegree| (#18# #7# |#1| #15# #4#)) (SIGNATURE |factorOfDegree| (#18# #7# |#1| #15# #4# #10#)) (SIGNATURE |henselFact| (#2# |#1| #10#)) (SIGNATURE |btwFact| (#2# |#1| #10# (|Set| #4#) #4#))) (|UnivariatePolynomialCategory| #3#)) (T |GaloisGroupFactorizer|)) 
((|btwFact| (*1 *2 *3 *4 *5 *6) (AND #1=(|isDomain| *4 #2=(|Boolean|)) (|isDomain| *5 (|Set| #3=(|NonNegativeInteger|))) (|isDomain| *6 #3#) #4=(|isDomain| *2 (|Record| #5=(|:| |contp| #6=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| *3) #7=(|:| |pow| #6#)))))) #8=(|isDomain| *1 (|GaloisGroupFactorizer| *3)) #9=(|ofCategory| *3 #10=(|UnivariatePolynomialCategory| #6#)))) (|henselFact| #11=(*1 *2 *3 *4) (AND #1# #4# #8# #9#)) (|factorOfDegree| (*1 *2 *3 *2 *4 *5 *6) (|partial| AND #12=(|isDomain| *3 #13=(|PositiveInteger|)) #14=(|isDomain| *4 (|List| #3#)) #15=(|isDomain| *5 #3#) (|isDomain| *6 #2#) #16=(|isDomain| *1 (|GaloisGroupFactorizer| *2)) #17=(|ofCategory| *2 #10#))) (|factorOfDegree| (*1 *2 *3 *2 *4 *5) (|partial| AND #12# #14# #15# #16# #17#)) (|factorOfDegree| #18=(*1 *2 *3 *2 *4) (|partial| AND #12# #14# #16# #17#)) (|factorOfDegree| #18# (|partial| AND #12# #19=(|isDomain| *4 #3#) #16# #17#)) (|factorOfDegree| (*1 *2 *3 *2) (|partial| AND #12# #16# #17#)) (|factorSquareFree| #20=(*1 *2 *3 *4 *4) #21=(AND #19# #22=(|isDomain| *2 (|Factored| *3)) #8# #9#)) (|factorSquareFree| #23=(*1 *2 *3 *4 *5) #24=(AND #14# #15# #22# #8# #9#)) (|factorSquareFree| #11# #25=(AND #14# #22# #8# #9#)) (|factorSquareFree| #11# #21#) (|factorSquareFree| #26=(*1 *2 *3) #27=(AND #22# #8# #9#)) (|factor| #20# #21#) (|factor| #23# #24#) (|factor| #11# #25#) (|factor| #11# #21#) (|factor| #26# #27#) (|tryFunctionalDecomposition| #28=(*1 *2 *2) #29=(AND (|isDomain| *2 #2#) #8# #9#)) (|tryFunctionalDecomposition?| #30=(*1 *2) #29#) (|eisensteinIrreducible?| #26# #29#) (|useEisensteinCriterion| #28# #29#) (|useEisensteinCriterion?| #30# #29#) (|useSingleFactorBound| #28# #29#) (|useSingleFactorBound?| #30# #29#) (|modularFactor| #26# (AND (|isDomain| *2 (|Record| (|:| |prime| #6#) (|:| |factors| (|List| *3)))) #8# #9#)) (|numberOfFactors| #26# (AND #31=(|isDomain| *3 (|List| (|Record| (|:| |factor| *4) (|:| |degree| #6#)))) #32=(|ofCategory| *4 #10#) (|isDomain| *2 #3#) #33=(|isDomain| *1 (|GaloisGroupFactorizer| *4)))) (|stopMusserTrials| #28# #34=(AND (|isDomain| *2 #13#) #8# #9#)) (|stopMusserTrials| #30# #34#) (|musserTrials| #28# #34#) (|musserTrials| #30# #34#) (|degreePartition| #26# (AND #31# #32# (|isDomain| *2 (|Multiset| #3#)) #33#)) (|makeFR| #26# (AND (|isDomain| *3 (|Record| #5# (|:| |factors| (|List| (|Record| (|:| |irr| *4) #7#))))) #32# (|isDomain| *2 (|Factored| *4)) #33#))) 
((|singleFactorBound| (#1=(#2=(|Integer|) |#2|) 52 T ELT) ((#2# |#2| (|NonNegativeInteger|)) 51 T ELT)) (|rootBound| (#1# 64 T ELT)) (|quadraticNorm| (#3=(|#3| |#2|) 26 T ELT)) (|norm| (#4=(|#3| |#2| (|PositiveInteger|)) 15 T ELT)) (|length| (#3# 16 T ELT)) (|infinityNorm| (#3# 9 T ELT)) (|height| (#3# 10 T ELT)) (|bombieriNorm| (#4# 71 T ELT) (#3# 34 T ELT)) (|beauzamyBound| (#1# 66 T ELT))) 
(((|GaloisGroupFactorizationUtilities| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |beauzamyBound| #1=(#2=(|Integer|) |#2|)) (SIGNATURE |bombieriNorm| #3=(|#3| |#2|)) (SIGNATURE |bombieriNorm| #4=(|#3| |#2| (|PositiveInteger|))) (SIGNATURE |rootBound| #1#) (SIGNATURE |singleFactorBound| (#2# |#2| (|NonNegativeInteger|))) (SIGNATURE |singleFactorBound| #1#) (SIGNATURE |norm| #4#) (SIGNATURE |quadraticNorm| #3#) (SIGNATURE |infinityNorm| #3#) (SIGNATURE |height| #3#) (SIGNATURE |length| #3#)) (|Ring|) (|UnivariatePolynomialCategory| |#1|) (|Join| (|FloatingPointSystem|) (|RetractableTo| |#1|) (|Field|) (|TranscendentalFunctionCategory|) (|ElementaryFunctionCategory|))) (T |GaloisGroupFactorizationUtilities|)) 
((|length| #1=(*1 *2 *3) #2=(AND #3=(|ofCategory| *4 #4=(|Ring|)) (|ofCategory| *2 #5=(|Join| #6=(|FloatingPointSystem|) (|RetractableTo| *4) #7=(|Field|) #8=(|TranscendentalFunctionCategory|) #9=(|ElementaryFunctionCategory|))) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *2)) #10=(|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|height| #1# #2#) (|infinityNorm| #1# #2#) (|quadraticNorm| #1# #2#) (|norm| #11=(*1 *2 *3 *4) #12=(AND (|isDomain| *4 (|PositiveInteger|)) #13=(|ofCategory| *5 #4#) (|ofCategory| *2 #14=(|Join| #6# (|RetractableTo| *5) #7# #8# #9#)) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *5 *3 *2)) #15=(|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|singleFactorBound| #1# #16=(AND #3# #17=(|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *5)) #10# (|ofCategory| *5 #5#))) (|singleFactorBound| #11# (AND (|isDomain| *4 (|NonNegativeInteger|)) #13# #17# (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *5 *3 *6)) #15# (|ofCategory| *6 #14#))) (|rootBound| #1# #16#) (|bombieriNorm| #11# #12#) (|bombieriNorm| #1# #2#) (|beauzamyBound| #1# #16#)) 
((|unvectorise| ((|#2| (|Vector| |#1|)) 42 T ELT)) (|shiftRoots| (#1=(|#2| |#2| |#1|) 58 T ELT)) (|scaleRoots| (#1# 49 T ELT)) (|reverse| ((|#2| |#2|) 44 T ELT)) (|monic?| (((|Boolean|) |#2|) 32 T ELT)) (|factorsOfDegree| (((|List| |#2|) #2=(|PositiveInteger|) #3=(|Factored| |#2|)) 21 T ELT)) (|factorOfDegree| ((|#2| #2# #3#) 25 T ELT)) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) #3#) 29 T ELT))) 
(((|GaloisGroupPolynomialUtilities| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monic?| ((|Boolean|) |#2|)) (SIGNATURE |unvectorise| (|#2| (|Vector| |#1|))) (SIGNATURE |reverse| (|#2| |#2|)) (SIGNATURE |scaleRoots| #1=(|#2| |#2| |#1|)) (SIGNATURE |shiftRoots| #1#) (SIGNATURE |degreePartition| ((|Multiset| (|NonNegativeInteger|)) #2=(|Factored| |#2|))) (SIGNATURE |factorOfDegree| (|#2| #3=(|PositiveInteger|) #2#)) (SIGNATURE |factorsOfDegree| ((|List| |#2|) #3# #2#))) (|Ring|) (|UnivariatePolynomialCategory| |#1|)) (T |GaloisGroupPolynomialUtilities|)) 
((|factorsOfDegree| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Factored| *6)) (|ofCategory| *6 #3=(|UnivariatePolynomialCategory| *5)) #4=(|ofCategory| *5 #5=(|Ring|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *5 *6)))) (|factorOfDegree| #1# (AND #2# (|isDomain| *4 (|Factored| *2)) (|ofCategory| *2 #3#) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *5 *2)) #4#)) (|degreePartition| #6=(*1 *2 *3) (AND (|isDomain| *3 (|Factored| *5)) (|ofCategory| *5 #7=(|UnivariatePolynomialCategory| *4)) #8=(|ofCategory| *4 #5#) (|isDomain| *2 (|Multiset| (|NonNegativeInteger|))) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *5)))) (|shiftRoots| #9=(*1 *2 *2 *3) #10=(AND (|ofCategory| *3 #5#) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|scaleRoots| #9# #10#) (|reverse| (*1 *2 *2) #10#) (|unvectorise| #6# (AND (|isDomain| *3 (|Vector| *4)) #8# (|ofCategory| *2 #7#) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *2)))) (|monic?| #6# (AND #8# (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *3)) (|ofCategory| *3 #7#)))) 
((|sizePascalTriangle| (#1=(#2=(|NonNegativeInteger|)) 59 T ELT)) (|safetyMargin| (#1# 29 #3=(|has| |#1| (|FloatingPointSystem|)) ELT) (#4=(#2# #2#) 28 #3# ELT)) (|safeFloor| (#5=(#6=(|Integer|) |#1|) 25 #3# ELT)) (|safeCeiling| (#5# 27 #3# ELT)) (|rangePascalTriangle| (#1# 58 T ELT) (#4# 57 T ELT)) (|pascalTriangle| ((|#1| #2# #6#) 37 T ELT)) (|fillPascalTriangle| (((|Void|)) 61 T ELT))) 
(((|GaloisGroupUtilities| |#1|) (CATEGORY |package| (SIGNATURE |pascalTriangle| (|#1| #1=(|NonNegativeInteger|) #2=(|Integer|))) (SIGNATURE |rangePascalTriangle| #3=(#1# #1#)) (SIGNATURE |rangePascalTriangle| #4=(#1#)) (SIGNATURE |sizePascalTriangle| #4#) (SIGNATURE |fillPascalTriangle| ((|Void|))) (IF (|has| |#1| (|FloatingPointSystem|)) (PROGN (SIGNATURE |safeCeiling| #5=(#2# |#1|)) (SIGNATURE |safeFloor| #5#) (SIGNATURE |safetyMargin| #3#) (SIGNATURE |safetyMargin| #4#)) |%noBranch|)) (|Ring|)) (T |GaloisGroupUtilities|)) 
((|safetyMargin| #1=(*1 *2) #2=(AND #3=(|isDomain| *2 #4=(|NonNegativeInteger|)) #5=(|isDomain| *1 (|GaloisGroupUtilities| *3)) #6=(|ofCategory| *3 (|FloatingPointSystem|)) #7=(|ofCategory| *3 #8=(|Ring|)))) (|safetyMargin| #9=(*1 *2 *2) #2#) (|safeFloor| #10=(*1 *2 *3) #11=(AND (|isDomain| *2 #12=(|Integer|)) #5# #6# #7#)) (|safeCeiling| #10# #11#) (|fillPascalTriangle| #1# (AND (|isDomain| *2 (|Void|)) #5# #7#)) (|sizePascalTriangle| #1# #13=(AND #3# #5# #7#)) (|rangePascalTriangle| #1# #13#) (|rangePascalTriangle| #9# #13#) (|pascalTriangle| (*1 *2 *3 *4) (AND (|isDomain| *3 #4#) (|isDomain| *4 #12#) (|isDomain| *1 (|GaloisGroupUtilities| *2)) (|ofCategory| *2 #8#)))) 
((|sumSquares| (((|List| #1=(|Integer|)) #1#) 76 T ELT)) (|prime?| (((|Boolean|) #2=(|Complex| #1#)) 84 T ELT)) (|factor| (((|Factored| #2#) #2#) 75 T ELT))) 
(((|GaussianFactorizationPackage|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| #1=(|Complex| #2=(|Integer|))) #1#)) (SIGNATURE |sumSquares| ((|List| #2#) #2#)) (SIGNATURE |prime?| ((|Boolean|) #1#)))) (T |GaussianFactorizationPackage|)) 
((|prime?| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|Complex| #4=(|Integer|))) (|isDomain| *2 (|Boolean|)) #5=(|isDomain| *1 (|GaussianFactorizationPackage|)))) (|sumSquares| #1# (AND (|isDomain| *2 (|List| #4#)) #5# (|isDomain| *3 #4#))) (|factor| #1# (AND (|isDomain| *2 (|Factored| #3#)) #5# #2#))) 
((|normalForm| ((|#4| |#4| #1=(|List| |#4|)) 20 (|has| |#1| (|Field|)) ELT)) (|groebner| ((#1# #1# #2=(|String|) #2#) 46 T ELT) ((#1# #1# #2#) 45 T ELT) ((#1# #1#) 34 T ELT))) 
(((|GroebnerPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |groebner| (#1=(|List| |#4|) #1#)) (SIGNATURE |groebner| (#1# #1# #2=(|String|))) (SIGNATURE |groebner| (#1# #1# #2# #2#)) (IF (|has| |#1| (|Field|)) (SIGNATURE |normalForm| (|#4| |#4| #1#)) |%noBranch|)) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerPackage|)) 
((|normalForm| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #2=(|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Field|)) #3=(|ofCategory| *4 #4=(|GcdDomain|)) #5=(|ofCategory| *5 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *6 #8=(|OrderedSet|)) (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *2)))) (|groebner| (*1 *2 *2 *3 *3) #9=(AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 #2#) #3# #5# #7# (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *7)))) (|groebner| #1# #9#) (|groebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|isDomain| *1 (|GroebnerPackage| *3 *4 *5 *6))))) 
((|euclideanNormalForm| ((|#4| |#4| #1=(|List| |#4|)) 82 T ELT)) (|euclideanGroebner| ((#1# #1# #2=(|String|) #2#) 22 T ELT) ((#1# #1# #2#) 21 T ELT) ((#1# #1#) 13 T ELT))) 
(((|EuclideanGroebnerBasisPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |euclideanNormalForm| (|#4| |#4| #1=(|List| |#4|))) (SIGNATURE |euclideanGroebner| (#1# #1#)) (SIGNATURE |euclideanGroebner| (#1# #1# #2=(|String|))) (SIGNATURE |euclideanGroebner| (#1# #1# #2# #2#))) (|EuclideanDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |EuclideanGroebnerBasisPackage|)) 
((|euclideanGroebner| (*1 *2 *2 *3 *3) #1=(AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 #2=(|PolynomialCategory| *4 *5 *6)) #3=(|ofCategory| *4 #4=(|EuclideanDomain|)) #5=(|ofCategory| *5 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *6 #8=(|OrderedSet|)) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *7)))) (|euclideanGroebner| #9=(*1 *2 *2 *3) #1#) (|euclideanGroebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *3 *4 *5 *6)))) (|euclideanNormalForm| #9# (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #2#) #3# #5# #7# (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *2))))) 
((|groebnerFactorize| (#1=(#2=(|List| #3=(|List| |#4|)) #3# #4=(|Boolean|)) 90 T ELT) (#5=(#2# #3#) 89 T ELT) ((#2# #3# #3# #4#) 83 T ELT) ((#2# #3# #3#) 84 T ELT)) (|factorGroebnerBasis| (#1# 56 T ELT) (#5# 78 T ELT))) 
(((|GroebnerFactorizationPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factorGroebnerBasis| #1=(#2=(|List| #3=(|List| |#4|)) #3#)) (SIGNATURE |factorGroebnerBasis| #4=(#2# #3# #5=(|Boolean|))) (SIGNATURE |groebnerFactorize| (#2# #3# #3#)) (SIGNATURE |groebnerFactorize| (#2# #3# #3# #5#)) (SIGNATURE |groebnerFactorize| #1#) (SIGNATURE |groebnerFactorize| #4#)) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerFactorizationPackage|)) 
((|groebnerFactorize| #1=(*1 *2 *3 *4) #2=(AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 #3=(|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *6 #4=(|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #5=(|OrderedSet|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| #6=(|List| *8))) (|isDomain| *1 (|GroebnerFactorizationPackage| *5 *6 *7 *8)) (|isDomain| *3 #6#))) (|groebnerFactorize| #7=(*1 *2 *3) #8=(AND (|ofCategory| *4 #3#) (|ofCategory| *5 #4#) (|ofCategory| *6 #5#) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| #9=(|List| *7))) (|isDomain| *1 (|GroebnerFactorizationPackage| *4 *5 *6 *7)) (|isDomain| *3 #9#))) (|groebnerFactorize| (*1 *2 *3 *3 *4) #2#) (|groebnerFactorize| (*1 *2 *3 *3) #8#) (|factorGroebnerBasis| #1# #2#) (|factorGroebnerBasis| #7# #8#)) 
((|virtualDegree| ((#1=(|NonNegativeInteger|) |#4|) 12 T ELT)) (|updatF| ((#2=(|List| #3=(|Record| #4=(|:| |totdeg| #1#) (|:| |pol| |#4|))) |#4| #1# #2#) 39 T ELT)) (|updatD| ((#5=(|List| #6=(|Record| (|:| |lcmfij| |#2|) #4# (|:| |poli| |#4|) (|:| |polj| |#4|))) #5# #5#) 49 T ELT)) (|sPol| ((|#4| #6#) 52 T ELT)) (|redPol| (#7=(|#4| |#4| #8=(|List| |#4|)) 54 T ELT)) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| #8#) 96 T ELT)) (|prinshINFO| ((#9=(|Void|) |#4|) 59 T ELT)) (|prinpolINFO| ((#9# #8#) 69 T ELT)) (|prindINFO| ((#10=(|Integer|) #6# |#4| |#4| #10# #10# #10#) 66 T ELT)) (|prinb| ((#9# #10#) 110 T ELT)) (|minGbasis| ((#8# #8#) 104 T ELT)) (|makeCrit| ((#6# #3# |#4| #1#) 31 T ELT)) (|lepol| ((#10# |#4|) 109 T ELT)) (|hMonic| ((|#4| |#4|) 37 T ELT)) (|gbasis| ((#8# #8# #10# #10#) 74 T ELT)) (|fprindINFO| ((#10# #6# |#4| |#4| #10# #10# #10# #10#) 123 T ELT)) (|critpOrder| ((#11=(|Boolean|) #6# #6#) 20 T ELT)) (|critT| ((#11# #6#) 78 T ELT)) (|critMonD1| ((#5# |#2| #5#) 76 T ELT)) (|critMTonD1| ((#5# #5#) 47 T ELT)) (|critM| ((#11# |#2| |#2|) 75 T ELT)) (|critBonD| ((#5# |#4| #5#) 48 T ELT)) (|critB| ((#11# |#2| |#2| |#2| |#2|) 80 T ELT)) (|credPol| (#7# 97 T ELT))) 
(((|GroebnerInternalPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |credPol| #1=(|#4| |#4| #2=(|List| |#4|))) (SIGNATURE |redPol| #1#) (SIGNATURE |gbasis| (#2# #2# #3=(|Integer|) #3#)) (SIGNATURE |critT| (#4=(|Boolean|) #5=(|Record| (|:| |lcmfij| |#2|) #6=(|:| |totdeg| #7=(|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) (SIGNATURE |critM| (#4# |#2| |#2|)) (SIGNATURE |critB| (#4# |#2| |#2| |#2| |#2|)) (SIGNATURE |critBonD| (#8=(|List| #5#) |#4| #8#)) (SIGNATURE |critMTonD1| (#8# #8#)) (SIGNATURE |critMonD1| (#8# |#2| #8#)) (SIGNATURE |redPo| ((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| #2#)) (SIGNATURE |hMonic| (|#4| |#4|)) (SIGNATURE |updatF| (#9=(|List| #10=(|Record| #6# (|:| |pol| |#4|))) |#4| #7# #9#)) (SIGNATURE |sPol| (|#4| #5#)) (SIGNATURE |updatD| (#8# #8# #8#)) (SIGNATURE |minGbasis| (#2# #2#)) (SIGNATURE |lepol| (#3# |#4|)) (SIGNATURE |prinshINFO| (#11=(|Void|) |#4|)) (SIGNATURE |prindINFO| (#3# #5# |#4| |#4| #3# #3# #3#)) (SIGNATURE |fprindINFO| (#3# #5# |#4| |#4| #3# #3# #3# #3#)) (SIGNATURE |prinpolINFO| (#11# #2#)) (SIGNATURE |prinb| (#11# #3#)) (SIGNATURE |critpOrder| (#4# #5# #5#)) (SIGNATURE |makeCrit| (#5# #10# |#4| #7#)) (SIGNATURE |virtualDegree| (#7# |#4|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerInternalPackage|)) 
((|virtualDegree| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|GcdDomain|)) #4=(|ofCategory| *5 #5=(|OrderedAbelianMonoidSup|)) #6=(|ofCategory| *6 #7=(|OrderedSet|)) (|isDomain| *2 #8=(|NonNegativeInteger|)) #9=(|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3)) #10=(|ofCategory| *3 #11=(|PolynomialCategory| *4 *5 *6)))) (|makeCrit| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Record| #12=(|:| |totdeg| #8#) (|:| |pol| *4))) (|isDomain| *5 #8#) (|ofCategory| *4 (|PolynomialCategory| *6 *7 *8)) (|ofCategory| *6 #3#) (|ofCategory| *7 #5#) (|ofCategory| *8 #7#) (|isDomain| *2 (|Record| (|:| |lcmfij| *7) (|:| |totdeg| *5) #13=(|:| |poli| *4) #14=(|:| |polj| *4))) (|isDomain| *1 (|GroebnerInternalPackage| *6 *7 *8 *4)))) (|critpOrder| #15=(*1 *2 *3 *3) #16=(AND (|isDomain| *3 (|Record| #17=(|:| |lcmfij| *5) #12# (|:| |poli| *7) (|:| |polj| *7))) #4# #18=(|ofCategory| *7 #11#) #2# #6# #19=(|isDomain| *2 (|Boolean|)) #20=(|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7)))) (|prinb| #1# (AND #21=(|isDomain| *3 #22=(|Integer|)) #2# #4# #6# #23=(|isDomain| *2 (|Void|)) #20# #18#)) (|prinpolINFO| #1# (AND (|isDomain| *3 #24=(|List| *7)) #18# #2# #4# #6# #23# #20#)) (|fprindINFO| (*1 *2 *3 *4 *4 *2 *2 *2 *2) #25=(AND #26=(|isDomain| *2 #22#) (|isDomain| *3 (|Record| (|:| |lcmfij| *6) #12# #13# #14#)) #27=(|ofCategory| *6 #5#) (|ofCategory| *4 #28=(|PolynomialCategory| *5 *6 *7)) #29=(|ofCategory| *5 #3#) #30=(|ofCategory| *7 #7#) (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *4)))) (|prindINFO| (*1 *2 *3 *4 *4 *2 *2 *2) #25#) (|prinshINFO| #1# (AND #2# #4# #6# #23# #9# #10#)) (|lepol| #1# (AND #2# #4# #6# #26# #9# #10#)) (|minGbasis| #31=(*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) #32=(|ofCategory| *6 #33=(|PolynomialCategory| *3 *4 *5)) #34=(|ofCategory| *3 #3#) #35=(|ofCategory| *4 #5#) #36=(|ofCategory| *5 #7#) #37=(|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *6)))) (|updatD| (*1 *2 *2 *2) #38=(AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *4) #12# #39=(|:| |poli| *6) #40=(|:| |polj| *6)))) #35# #32# #34# #36# #37#)) (|sPol| #1# (AND (|isDomain| *3 (|Record| #17# #12# (|:| |poli| *2) (|:| |polj| *2))) #4# #41=(|ofCategory| *2 #11#) #42=(|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *2)) #2# #6#)) (|updatF| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|List| (|Record| #12# (|:| |pol| *3)))) (|isDomain| *4 #8#) #43=(|ofCategory| *3 #28#) #29# #27# #30# #44=(|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *3)))) (|hMonic| #31# (AND #34# #35# #36# (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *2)) (|ofCategory| *2 #33#))) (|redPo| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) #43# #29# #27# #30# (|isDomain| *2 (|Record| (|:| |poly| *3) (|:| |mult| *5))) #44#)) (|critMonD1| #45=(*1 *2 *3 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *3) #12# #39# #40#))) #46=(|ofCategory| *3 #5#) #47=(|ofCategory| *6 (|PolynomialCategory| *4 *3 *5)) #2# #36# #48=(|isDomain| *1 (|GroebnerInternalPackage| *4 *3 *5 *6)))) (|critMTonD1| #31# #38#) (|critBonD| #45# (AND (|isDomain| *2 (|List| (|Record| #17# #12# (|:| |poli| *3) (|:| |polj| *3)))) #4# #10# #2# #6# #9#)) (|critB| (*1 *2 *3 *3 *3 *3) #49=(AND #2# #46# #36# #19# #48# #47#)) (|critM| #15# #49#) (|critT| #1# #16#) (|gbasis| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 #24#) #21# #18# #2# #4# #6# #20#)) (|redPol| #50=(*1 *2 *2 *3) #51=(AND (|isDomain| *3 (|List| *2)) #41# #2# #4# #6# #42#)) (|credPol| #50# #51#)) 
((|lcm| (#1=($ $ $) 14 T ELT) (#2=($ (|List| $)) 21 T ELT)) (|gcdPolynomial| ((#3=(|SparseUnivariatePolynomial| $) #3# #3#) 45 T ELT)) (|gcd| (#1# NIL T ELT) (#2# 22 T ELT))) 
(((|GcdDomain&| |#1|) (CATEGORY |package| (SIGNATURE |gcdPolynomial| (#1=(|SparseUnivariatePolynomial| |#1|) #1# #1#)) (SIGNATURE |lcm| #2=(|#1| (|List| |#1|))) (SIGNATURE |lcm| #3=(|#1| |#1| |#1|)) (SIGNATURE |gcd| #2#) (SIGNATURE |gcd| #3#)) (|GcdDomain|)) (T |GcdDomain&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (($ $ $) 60 T ELT) (($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 58 T ELT)) (|gcd| (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|GcdDomain|) (|Category|)) (T |GcdDomain|)) 
((|gcd| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|gcd| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|lcm| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|lcm| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|GcdDomain|))))) 
(|Join| (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) (SIGNATURE |gcd| ($ (|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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(|has| #7=(|Fraction| #8=(|Polynomial| |#1|)) #9=(|IntegralDomain|)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| #7#)) #12=(|Vector| $)) NIL T ELT) ((#10#) NIL T ELT)) (|someBasis| (#13=(#12#) NIL T ELT)) (|sample| #14=(#15=($) NIL T CONST)) (|rightUnits| #16=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL T ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #17=((#11# #12#) NIL T ELT) #18=((#11#) NIL T ELT)) (|rightTrace| #19=(#20=(#7# $) NIL T ELT)) (|rightRegularRepresentation| #21=((#11# $ #12#) NIL T ELT) #22=((#11# $) NIL T ELT)) (|rightRecip| #23=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #24=(((|SparseUnivariatePolynomial| #25=(|Polynomial| #7#))) NIL (|has| #7# (|Field|)) ELT) (#26=(#27=(|SparseUnivariatePolynomial| #7#)) 89 #28=(|has| |#1| #9#) ELT)) (|rightPower| #29=(($ $ #30=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| (#31=(#27# $) 87 #6# ELT)) (|rightDiscriminant| #32=((#7# #12#) NIL T ELT) #33=(#34=(#7#) NIL T ELT)) (|rightCharacteristicPolynomial| #35=(#31# NIL T ELT)) (|rightAlternative?| #36=((#2#) NIL T ELT)) (|represents| (($ #37=(|Vector| #7#) #12#) 111 T ELT) #38=(#39=($ #37#) NIL T ELT)) (|recip| #23#) (|rank| ((#30#) NIL T ELT)) (|powerAssociative?| #36#) (|plenaryPower| #29#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #36#) (|lieAlgebra?| #36#) (|lieAdmissible?| #36#) (|leftUnits| #16#) (|leftUnit| #3#) (|leftTraceMatrix| #17# #18#) (|leftTrace| #19#) (|leftRegularRepresentation| #21# #22#) (|leftRecip| #23#) (|leftRankPolynomial| #24# (#26# 88 #28# ELT)) (|leftPower| #29#) (|leftNorm| #19#) (|leftMinimalPolynomial| (#31# 84 #6# ELT)) (|leftDiscriminant| #32# #33#) (|leftCharacteristicPolynomial| #35#) (|leftAlternative?| #36#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #36#) (|jordanAdmissible?| #36#) (|jacobiIdentity?| #36#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genericRightTraceForm| (#40=(#7# $ $) 75 #28# ELT)) (|genericRightTrace| (#20# 74 #28# ELT)) (|genericRightNorm| (#20# 101 #28# ELT)) (|genericRightMinimalPolynomial| (#31# 93 #28# ELT)) (|genericRightDiscriminant| (#34# 76 #28# ELT)) (|genericLeftTraceForm| (#40# 64 #28# ELT)) (|genericLeftTrace| (#20# 63 #28# ELT)) (|genericLeftNorm| (#20# 100 #28# ELT)) (|genericLeftMinimalPolynomial| (#31# 92 #28# ELT)) (|genericLeftDiscriminant| (#34# 73 #28# ELT)) (|generic| (#15# 107 T ELT) (($ #41=(|Symbol|)) 115 T ELT) (($ #42=(|Vector| #41#)) 114 T ELT) (($ #12#) 102 T ELT) (($ #41# #12#) 113 T ELT) (($ #42# #12#) 112 T ELT)) (|flexible?| #36#) (|elt| ((#7# $ #43=(|Integer|)) NIL T ELT)) (|coordinates| ((#37# $ #12#) 104 T ELT) ((#11# #12# #12#) NIL T ELT) (#44=(#37# $) 44 T ELT) #17#) (|convert| (#44# NIL T ELT) (#39# 41 T ELT)) (|conditionsForIdempotents| ((#45=(|List| #25#) #12#) NIL T ELT) ((#45#) NIL T ELT) ((#46=(|List| #8#) #12#) 105 #28# ELT) ((#46#) 106 #28# ELT)) (|commutator| #47=(#48=($ $ $) NIL T ELT)) (|commutative?| #36#) (|coerce| (((|OutputForm|) $) NIL T ELT) #38#) (|before?| #1#) (|basis| (#13# 66 T ELT)) (|associatorDependence| (((|List| #37#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #36#) (|apply| (($ #11# $) NIL T ELT)) (|antiCommutator| #47#) (|antiCommutative?| #36#) (|antiAssociative?| #36#) (|alternative?| #36#) (|Zero| #14#) (= #1#) (- (($ $) NIL T ELT) (#48# 103 T ELT)) (+ #47#) (** #29#) (* (($ #30# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #43# . #49=($)) NIL T ELT) (#48# 62 T ELT) (($ $ #7#) NIL T ELT) (($ #7# . #49#) NIL T ELT) (($ (|SquareMatrix| |#2| #7#) . #49#) NIL T ELT))) 
(((|GenericNonAssociativeAlgebra| |#1| |#2| |#3| |#4|) (|Join| (|FramedNonAssociativeAlgebra| #1=(|Fraction| #2=(|Polynomial| |#1|))) (|LeftModule| (|SquareMatrix| |#2| #1#)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| #1#))) (SIGNATURE |leftUnits| #3=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |rightUnits| #3#) (SIGNATURE |generic| ($)) (SIGNATURE |generic| ($ #4=(|Symbol|))) (SIGNATURE |generic| ($ #5=(|Vector| #4#))) (SIGNATURE |generic| ($ #6=(|Vector| $))) (SIGNATURE |generic| ($ #4# #6#)) (SIGNATURE |generic| ($ #5# #6#)) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |leftRankPolynomial| #7=(#8=(|SparseUnivariatePolynomial| #1#))) (SIGNATURE |genericLeftMinimalPolynomial| #9=(#8# $)) (SIGNATURE |genericLeftTrace| #10=(#1# $)) (SIGNATURE |genericLeftNorm| #10#) (SIGNATURE |rightRankPolynomial| #7#) (SIGNATURE |genericRightMinimalPolynomial| #9#) (SIGNATURE |genericRightTrace| #10#) (SIGNATURE |genericRightNorm| #10#) (SIGNATURE |genericLeftTraceForm| #11=(#1# $ $)) (SIGNATURE |genericLeftDiscriminant| #12=(#1#)) (SIGNATURE |genericRightTraceForm| #11#) (SIGNATURE |genericRightDiscriminant| #12#) (SIGNATURE |conditionsForIdempotents| (#13=(|List| #2#) #6#)) (SIGNATURE |conditionsForIdempotents| (#13#))) |%noBranch|))) (|CommutativeRing|) (|PositiveInteger|) (|List| #4#) (|Vector| (|Matrix| |#1|))) (T |GenericNonAssociativeAlgebra|)) 
((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *2 (|Vector| #2=(|Fraction| #3=(|Polynomial| *3)))) #4=(|ofCategory| *3 #5=(|CommutativeRing|)) #6=(|ofType| *6 (|Vector| (|Matrix| *3))) #7=(|isDomain| *1 #8=(|GenericNonAssociativeAlgebra| *3 *4 *5 *6)) #9=(|ofType| *4 #10=(|PositiveInteger|)) #11=(|ofType| *5 #12=(|List| #13=(|Symbol|))))) (|leftUnits| #14=(*1 *2) #15=(|partial| AND (|isDomain| *2 (|Record| (|:| |particular| #8#) (|:| |basis| (|List| #8#)))) #7# #4# #9# #11# #6#)) (|rightUnits| #14# #15#) (|generic| (*1 *1) (AND (|isDomain| *1 (|GenericNonAssociativeAlgebra| *2 *3 *4 *5)) (|ofCategory| *2 #5#) (|ofType| *3 #10#) (|ofType| *4 #12#) (|ofType| *5 (|Vector| (|Matrix| *2))))) (|generic| #1# (AND #16=(|isDomain| *2 #13#) #7# #4# #9# (|ofType| *5 #17=(|List| *2)) #6#)) (|generic| #1# (AND #18=(|isDomain| *2 (|Vector| #13#)) #7# #4# #9# #11# #6#)) (|generic| #1# (AND (|isDomain| *2 (|Vector| #8#)) #7# #4# #9# #11# #6#)) (|generic| #19=(*1 *1 *2 *3) (AND #16# #20=(|isDomain| *3 (|Vector| #21=(|GenericNonAssociativeAlgebra| *4 *5 *6 *7))) #22=(|isDomain| *1 #21#) #23=(|ofCategory| *4 #5#) #24=(|ofType| *5 #10#) (|ofType| *6 #17#) #25=(|ofType| *7 (|Vector| (|Matrix| *4))))) (|generic| #19# (AND #18# #20# #22# #23# #24# #26=(|ofType| *6 #12#) #25#)) (|leftRankPolynomial| #14# #27=(AND (|isDomain| *2 (|SparseUnivariatePolynomial| #2#)) #7# #28=(|ofCategory| *3 #29=(|IntegralDomain|)) #4# #9# #11# #6#)) (|genericLeftMinimalPolynomial| #30=(*1 *2 *1) #27#) (|genericLeftTrace| #30# #31=(AND (|isDomain| *2 #2#) #7# #28# #4# #9# #11# #6#)) (|genericLeftNorm| #30# #31#) (|rightRankPolynomial| #14# #27#) (|genericRightMinimalPolynomial| #30# #27#) (|genericRightTrace| #30# #31#) (|genericRightNorm| #30# #31#) (|genericLeftTraceForm| #32=(*1 *2 *1 *1) #31#) (|genericLeftDiscriminant| #14# #31#) (|genericRightTraceForm| #32# #31#) (|genericRightDiscriminant| #14# #31#) (|conditionsForIdempotents| (*1 *2 *3) (AND #20# (|isDomain| *2 (|List| (|Polynomial| *4))) #22# (|ofCategory| *4 #29#) #23# #24# #26# #25#)) (|conditionsForIdempotents| #14# (AND (|isDomain| *2 (|List| #3#)) #7# #28# #4# #9# #11# #6#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 19 T ELT)) (|variables| ((#5=(|List| #6=(|OrderedVariableList| |#1|)) $) 88 T ELT)) (|univariate| ((#7=(|SparseUnivariatePolynomial| $) $ #6#) 53 T ELT) ((#8=(|SparseUnivariatePolynomial| |#2|) $) 140 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#4# NIL #9# ELT)) (|totalDegree| (#12=(#13=(|NonNegativeInteger|) $) 28 T ELT) ((#13# $ #5#) NIL T ELT)) (|subtractIfCan| (#14=(#15=(|Union| $ #16="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #17=(((|Factored| #7#) #7#) NIL #18=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #19=(#11# NIL #20=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#21=((|Factored| $) $) NIL #20# ELT)) (|solveLinearPolynomialEquation| (((|Union| #22=(|List| #7#) #16#) #22# #7#) NIL #18# ELT)) (|sample| (#23=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #24=(#16#)) $) 51 T ELT) (((|Union| #25=(|Fraction| #26=(|Integer|)) . #24#) . #27=($)) NIL #28=(|has| |#2| (|RetractableTo| #25#)) ELT) (((|Union| #26# . #24#) . #27#) NIL #29=(|has| |#2| (|RetractableTo| #26#)) ELT) (#30=((|Union| #6# . #24#) . #27#) NIL T ELT)) (|retract| (#31=(|#2| $) 49 T ELT) ((#25# . #32=($)) NIL #28# ELT) ((#26# . #32#) NIL #29# ELT) ((#6# . #32#) NIL T ELT)) (|resultant| (($ $ $ #6#) NIL #33=(|has| |#2| (|CommutativeRing|)) ELT)) (|reorder| (($ $ (|List| #26#)) 95 T ELT)) (|reductum| (#11# 81 T ELT)) (|reducedSystem| ((#34=(|Matrix| #26#) . #35=(#36=(|Matrix| $))) NIL #37=(|has| |#2| (|LinearlyExplicitRingOver| #26#)) ELT) ((#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #26#))) . #39=(#36# #40=(|Vector| $))) NIL #37# ELT) ((#41=(|Record| (|:| |mat| #42=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #39#) NIL T ELT) ((#42# . #35#) NIL T ELT)) (|recip| ((#15# $) NIL T ELT)) (|primitivePart| #19# #43=(#44=($ $ #6#) NIL #20# ELT)) (|primitiveMonomials| #45=((#46=(|List| $) $) NIL T ELT)) (|prime?| (#4# NIL #18# ELT)) (|pomopo!| (($ $ |#2| |#3| $) NIL T ELT)) (|patternMatch| ((#47=(|PatternMatchResult| #48=(|Float|) . #49=($)) $ #50=(|Pattern| #48#) #47#) NIL (AND (|has| #6# #51=(|PatternMatchable| #48#)) (|has| |#2| #51#)) ELT) ((#52=(|PatternMatchResult| #26# . #49#) $ #53=(|Pattern| #26#) #52#) NIL (AND (|has| #6# #54=(|PatternMatchable| #26#)) (|has| |#2| #54#)) ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|numberOfMonomials| (#12# 66 T ELT)) (|multivariate| (($ #8# #6#) 145 T ELT) (($ #7# #6#) 59 T ELT)) (|monomials| #45#) (|monomial?| (#4# 69 T ELT)) (|monomial| (($ |#2| |#3|) 36 T ELT) (#55=($ $ #6# #13#) 38 T ELT) #56=(($ $ #5# #57=(|List| #13#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #6#) NIL T ELT)) (|minimumDegree| (#58=(|#3| $) NIL T ELT) (#59=(#13# $ #6#) 57 T ELT) (#60=(#57# $ #5#) 64 T ELT)) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| (#30# 46 T ELT)) (|leftReducedSystem| ((#34# . #61=(#40#)) NIL #37# ELT) ((#38# . #62=(#40# $)) NIL #37# ELT) ((#41# . #62#) NIL T ELT) ((#42# . #61#) NIL T ELT)) (|leadingMonomial| #63=(#11# NIL T ELT)) (|leadingCoefficient| (#31# 48 T ELT)) (|lcm| #64=(($ #46#) NIL #20# ELT) (#65=($ $ $) NIL #20# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #66=(((|Union| #46# #16#) $) NIL T ELT)) (|isPlus| #66#) (|isExpt| (((|Union| (|Record| (|:| |var| #6#) (|:| |exponent| #13#)) #16#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#4# 47 T ELT)) (|ground| (#31# 138 T ELT)) (|gcdPolynomial| ((#7# #7# #7#) NIL #20# ELT)) (|gcd| #64# (#65# 151 #20# ELT)) (|factorSquareFreePolynomial| #17#) (|factorPolynomial| #17#) (|factor| (#21# NIL #18# ELT)) (|exquo| ((#15# $ |#2|) NIL #9# ELT) (#14# NIL #9# ELT)) (|eval| (($ $ (|List| #67=(|Equation| $))) NIL T ELT) (($ $ #67#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #46# #46#) NIL T ELT) (($ $ #6# |#2|) 102 T ELT) (($ $ #5# #68=(|List| |#2|)) 108 T ELT) (($ $ #6# $) 100 T ELT) (($ $ #5# #46#) 126 T ELT)) (|discriminant| (#44# NIL #33# ELT)) (|differentiate| #56# #69=(#55# NIL T ELT) #70=(($ $ #5#) NIL T ELT) (#44# 60 T ELT)) (|degree| (#58# 80 T ELT) (#59# 43 T ELT) (#60# 63 T ELT)) (|convert| ((#50# . #71=($)) NIL (AND (|has| #6# #72=(|ConvertibleTo| #50#)) (|has| |#2| #72#)) ELT) ((#53# . #71#) NIL (AND (|has| #6# #73=(|ConvertibleTo| #53#)) (|has| |#2| #73#)) ELT) ((#74=(|InputForm|) . #71#) NIL (AND (|has| #6# #75=(|ConvertibleTo| #74#)) (|has| |#2| #75#)) ELT)) (|content| (#31# 147 #20# ELT) #43#) (|conditionP| (((|Union| #40# #16#) #36#) NIL #76=(AND (|has| $ #77=(|CharacteristicNonZero|)) #18#) ELT)) (|coerce| (((|OutputForm|) $) 175 T ELT) (($ #26#) NIL T ELT) (($ |#2|) 101 T ELT) (($ #6#) 40 T ELT) (($ #25#) NIL (OR #78=(|has| |#2| (|Algebra| #25#)) #28#) ELT) #10#) (|coefficients| ((#68# $) NIL T ELT)) (|coefficient| ((|#2| $ |#3|) NIL T ELT) #69# #56#) (|charthRoot| (((|Maybe| $) $) NIL (OR #76# (|has| |#2| #77#)) ELT)) (|characteristic| ((#13#) NIL T CONST)) (|binomThmExpt| (($ $ $ #13#) NIL #33# ELT)) (|before?| #1#) (|associates?| (#2# NIL #9# ELT)) (|annihilate?| #1#) (|Zero| (#23# 24 T CONST)) (|One| (#23# 32 T CONST)) (D #56# #69# #70# (#44# NIL T ELT)) (= #1#) (/ (#79=($ $ |#2|) 77 (|has| |#2| (|Field|)) ELT)) (- #63# (#65# NIL T ELT)) (+ (#65# 133 T ELT)) (** (($ $ #80=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) 131 T ELT)) (* (($ #80# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #26# . #81=($)) NIL T ELT) (#65# 37 T ELT) (($ $ #25#) NIL #78# ELT) (($ #25# . #81#) NIL #78# ELT) (($ |#2| . #81#) 76 T ELT) (#79# NIL T ELT))) 
(((|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|)))))) 
((|testModulus| (((|Boolean|) |#1| #1=(|List| |#2|)) 90 T ELT)) (|tablePow| (((|Union| #2=(|Vector| #1#) #3="failed") #4=(|NonNegativeInteger|) |#1| #1#) 99 T ELT)) (|solveid| (((|Union| #1# #3#) |#2| |#1| #2#) 101 T ELT)) (|reduction| ((|#2| |#2| |#1|) 35 T ELT)) (|compBound| ((#4# |#2| #1#) 26 T ELT))) 
(((|GenExEuclid| |#1| |#2|) (CATEGORY |package| (SIGNATURE |reduction| (|#2| |#2| |#1|)) (SIGNATURE |compBound| (#1=(|NonNegativeInteger|) |#2| #2=(|List| |#2|))) (SIGNATURE |tablePow| ((|Union| #3=(|Vector| #2#) #4="failed") #1# |#1| #2#)) (SIGNATURE |solveid| ((|Union| #2# #4#) |#2| |#1| #3#)) (SIGNATURE |testModulus| ((|Boolean|) |#1| #2#))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |GenExEuclid|)) 
((|testModulus| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *5)) (|ofCategory| *5 #2=(|UnivariatePolynomialCategory| *3)) #3=(|ofCategory| *3 #4=(|EuclideanDomain|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GenExEuclid| *3 *5)))) (|solveid| #5=(*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 (|Vector| #6=(|List| *3))) #7=(|ofCategory| *4 #4#) (|isDomain| *2 #6#) (|isDomain| *1 (|GenExEuclid| *4 *3)) (|ofCategory| *3 #8=(|UnivariatePolynomialCategory| *4)))) (|tablePow| #5# (|partial| AND (|isDomain| *3 #9=(|NonNegativeInteger|)) #7# (|ofCategory| *6 #8#) (|isDomain| *2 (|Vector| #10=(|List| *6))) (|isDomain| *1 (|GenExEuclid| *4 *6)) (|isDomain| *5 #10#))) (|compBound| #1# (AND (|isDomain| *4 #6#) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #4#) (|isDomain| *2 #9#) (|isDomain| *1 (|GenExEuclid| *5 *3)))) (|reduction| (*1 *2 *2 *3) (AND #3# (|isDomain| *1 (|GenExEuclid| *3 *2)) (|ofCategory| *2 #2#)))) 
((|factor| (((|Factored| |#5|) |#5|) 24 T ELT))) 
(((|GeneralizedMultivariateFactorize| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#5|) |#5|))) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#)))) (|OrderedAbelianMonoidSup|) #2=(|IntegralDomain|) #2# (|PolynomialCategory| |#4| |#2| |#1|)) (T |GeneralizedMultivariateFactorize|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#))))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #2=(|IntegralDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GeneralizedMultivariateFactorize| *4 *5 *6 *7 *3)) (|ofCategory| *6 #2#) (|ofCategory| *3 (|PolynomialCategory| *7 *5 *4))))) 
((|randomR| ((|#3|) 43 T ELT)) (|gcdPolynomial| ((#1=(|SparseUnivariatePolynomial| |#4|) #1# #1#) 34 T ELT))) 
(((|GeneralPolynomialGcdPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |gcdPolynomial| (#1=(|SparseUnivariatePolynomial| |#4|) #1# #1#)) (SIGNATURE |randomR| (|#3|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialFactorizationExplicit|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |GeneralPolynomialGcdPackage|)) 
((|randomR| (*1 *2) (AND #1=(|ofCategory| *3 (|OrderedAbelianMonoidSup|)) #2=(|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 #3=(|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)) #1# #2# (|ofCategory| *5 #3#) (|isDomain| *1 (|GeneralPolynomialGcdPackage| *3 *4 *5 *6))))) 
((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#1|)) #1#) 43 T ELT))) 
(((|GenUFactorize| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| #1=(|SparseUnivariatePolynomial| |#1|)) #1#))) (|EuclideanDomain|)) (T |GenUFactorize|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| #1=(|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|GenUFactorize| *4)) (|isDomain| *3 #1#)))) 
((|taylor| ((#1=(|Any|) |#2| #2=(|Symbol|) #3=(|Equation| |#2|) #4=(|UniversalSegment| (|NonNegativeInteger|))) 44 T ELT) ((#1# #5=(|Mapping| |#2| #6=(|Integer|)) #3# #4#) 43 T ELT) (#7=(#1# |#2| #2# #3#) 36 T ELT) (#8=(#1# #5# #3#) 29 T ELT)) (|series| (#9=(#1# |#2| #2# #3# #10=(|UniversalSegment| #11=(|Fraction| #6#)) #11#) 88 T ELT) (#12=(#1# (|Mapping| |#2| #11#) #3# #10# #11#) 87 T ELT) (#13=(#1# |#2| #2# #3# #14=(|UniversalSegment| #6#)) 86 T ELT) (#15=(#1# #5# #3# #14#) 85 T ELT) (#7# 80 T ELT) (#8# 79 T ELT)) (|puiseux| (#9# 74 T ELT) (#12# 72 T ELT)) (|laurent| (#13# 51 T ELT) (#15# 50 T ELT))) 
(((|GenerateUnivariatePowerSeries| |#1| |#2|) (CATEGORY |package| (SIGNATURE |taylor| #1=(#2=(|Any|) #3=(|Mapping| |#2| #4=(|Integer|)) #5=(|Equation| |#2|))) (SIGNATURE |taylor| #6=(#2# |#2| #7=(|Symbol|) #5#)) (SIGNATURE |taylor| (#2# #3# #5# #8=(|UniversalSegment| (|NonNegativeInteger|)))) (SIGNATURE |taylor| (#2# |#2| #7# #5# #8#)) (SIGNATURE |laurent| #9=(#2# #3# #5# #10=(|UniversalSegment| #4#))) (SIGNATURE |laurent| #11=(#2# |#2| #7# #5# #10#)) (SIGNATURE |puiseux| #12=(#2# (|Mapping| |#2| #13=(|Fraction| #4#)) #5# #14=(|UniversalSegment| #13#) #13#)) (SIGNATURE |puiseux| #15=(#2# |#2| #7# #5# #14# #13#)) (SIGNATURE |series| #1#) (SIGNATURE |series| #6#) (SIGNATURE |series| #9#) (SIGNATURE |series| #11#) (SIGNATURE |series| #12#) (SIGNATURE |series| #15#)) (|Join| (|IntegralDomain|) (|RetractableTo| #4#) (|LinearlyExplicitRingOver| #4#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |GenerateUnivariatePowerSeries|)) 
((|series| #1=(*1 *2 *3 *4 *5 *6 *7) #2=(AND #3=(|isDomain| *4 (|Symbol|)) #4=(|isDomain| *5 (|Equation| *3)) (|isDomain| *6 #5=(|UniversalSegment| #6=(|Fraction| #7=(|Integer|)))) (|isDomain| *7 #6#) (|ofCategory| *3 (|Join| #8=(|AlgebraicallyClosedField|) #9=(|TranscendentalFunctionCategory|) (|FunctionSpace| *8))) (|ofCategory| *8 #10=(|Join| (|IntegralDomain|) (|RetractableTo| #7#) (|LinearlyExplicitRingOver| #7#))) #11=(|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *8 *3)))) (|series| #12=(*1 *2 *3 *4 *5 *6) #13=(AND (|isDomain| *3 (|Mapping| *8 #6#)) (|isDomain| *4 (|Equation| *8)) (|isDomain| *5 #5#) (|isDomain| *6 #6#) (|ofCategory| *8 #14=(|Join| #8# #9# (|FunctionSpace| *7))) #15=(|ofCategory| *7 #10#) #11# (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *8)))) (|series| #12# #16=(AND #3# #4# (|isDomain| *6 #17=(|UniversalSegment| #7#)) #18=(|ofCategory| *3 #14#) #15# #11# #19=(|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *3)))) (|series| #20=(*1 *2 *3 *4 *5) #21=(AND #22=(|isDomain| *3 (|Mapping| *7 #7#)) #23=(|isDomain| *4 (|Equation| *7)) (|isDomain| *5 #17#) #24=(|ofCategory| *7 #25=(|Join| #8# #9# (|FunctionSpace| *6))) #26=(|ofCategory| *6 #10#) #11# #27=(|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *7)))) (|series| #20# #28=(AND #3# #4# (|ofCategory| *3 #25#) #26# #11# (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *3)))) (|series| #29=(*1 *2 *3 *4) #30=(AND (|isDomain| *3 (|Mapping| *6 #7#)) (|isDomain| *4 (|Equation| *6)) (|ofCategory| *6 (|Join| #8# #9# (|FunctionSpace| *5))) (|ofCategory| *5 #10#) #11# (|isDomain| *1 (|GenerateUnivariatePowerSeries| *5 *6)))) (|puiseux| #1# #2#) (|puiseux| #12# #13#) (|laurent| #12# #16#) (|laurent| #20# #21#) (|taylor| #12# (AND #3# #4# (|isDomain| *6 #31=(|UniversalSegment| (|NonNegativeInteger|))) #18# #15# #11# #19#)) (|taylor| #20# (AND #22# #23# (|isDomain| *5 #31#) #24# #26# #11# #27#)) (|taylor| #20# #28#) (|taylor| #29# #30#)) 
((|reduction| ((|#2| |#2| |#1|) 15 T ELT)) (|completeHensel| ((#1=(|List| |#2|) |#2| #1# |#1| #2=(|PositiveInteger|)) 82 T ELT)) (|HenselLift| (((|Record| (|:| |plist| #1#) (|:| |modulo| |#1|)) |#2| #1# |#1| #2#) 71 T ELT))) 
(((|GeneralHenselPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |HenselLift| ((|Record| (|:| |plist| #1=(|List| |#2|)) (|:| |modulo| |#1|)) |#2| #1# |#1| #2=(|PositiveInteger|))) (SIGNATURE |completeHensel| (#1# |#2| #1# |#1| #2#)) (SIGNATURE |reduction| (|#2| |#2| |#1|))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |GeneralHenselPackage|)) 
((|reduction| (*1 *2 *2 *3) (AND (|ofCategory| *3 #1=(|EuclideanDomain|)) (|isDomain| *1 (|GeneralHenselPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|completeHensel| (*1 *2 *3 *2 *4 *5) (AND (|isDomain| *2 #2=(|List| *3)) (|isDomain| *5 #3=(|PositiveInteger|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 #1#) (|isDomain| *1 (|GeneralHenselPackage| *4 *3)))) (|HenselLift| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *6 #3#) (|ofCategory| *5 #1#) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |plist| #2#) (|:| |modulo| *5))) (|isDomain| *1 (|GeneralHenselPackage| *5 *3)) (|isDomain| *4 #2#)))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) 28 T ELT)) (|unitVector| (($ |#3|) 25 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|reductum| (#4=($ $) 32 T ELT)) (|opposite?| #1#) (|multMonom| (($ |#2| |#4| $) 33 T ELT)) (|monomial| (($ |#2| #5=(|ModuleMonomial| |#3| |#4| |#5|)) 24 T ELT)) (|leadingMonomial| ((#5# $) 15 T ELT)) (|leadingIndex| ((|#3| $) 19 T ELT)) (|leadingExponent| ((|#4| $) 17 T ELT)) (|leadingCoefficient| ((|#2| $) 29 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|build| (($ |#2| |#3| |#4|) 26 T ELT)) (|before?| #1#) (|Zero| (#3# 36 T CONST)) (= #1#) (- (#4# NIL T ELT) (#6=($ $ $) NIL T ELT)) (+ (#6# 34 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #7=($)) NIL T ELT) (($ |#6| $) 40 T ELT) (($ $ |#6|) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #7#) NIL T ELT))) 
(((|GeneralModulePolynomial| |#1| |#2| |#3| |#4| |#5| |#6|) (|Join| (|Module| |#6|) (|Module| |#2|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|#2| $)) (SIGNATURE |leadingMonomial| (#1=(|ModuleMonomial| |#3| |#4| |#5|) $)) (SIGNATURE |leadingExponent| (|#4| $)) (SIGNATURE |leadingIndex| (|#3| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |monomial| ($ |#2| #1#)) (SIGNATURE |unitVector| ($ |#3|)) (SIGNATURE |build| ($ |#2| |#3| |#4|)) (SIGNATURE |multMonom| ($ |#2| |#4| $)) (SIGNATURE * ($ |#6| $)))) (|List| (|Symbol|)) (|CommutativeRing|) (|OrderedSet|) (|DirectProductCategory| (|#| |#1|) (|NonNegativeInteger|)) (|Mapping| (|Boolean|) #2=(|Record| (|:| |index| |#3|) (|:| |exponent| |#4|)) #2#) (|PolynomialCategory| |#2| |#4| (|OrderedVariableList| |#1|))) (T |GeneralModulePolynomial|)) 
((* (*1 *1 *2 *1) (AND #1=(|ofType| *3 #2=(|List| (|Symbol|))) #3=(|ofCategory| *4 #4=(|CommutativeRing|)) #5=(|ofCategory| *6 #6=(|DirectProductCategory| (|#| *3) #7=(|NonNegativeInteger|))) #8=(|ofType| *7 (|Mapping| #9=(|Boolean|) #10=(|Record| #11=(|:| |index| *5) (|:| |exponent| *6)) #10#)) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *2)) #12=(|ofCategory| *5 #13=(|OrderedSet|)) (|ofCategory| *2 #14=(|PolynomialCategory| *4 *6 #15=(|OrderedVariableList| *3))))) (|leadingCoefficient| #16=(*1 *2 *1) (AND #1# #17=(|ofCategory| *5 #6#) #18=(|ofType| *6 (|Mapping| #9# #19=(|Record| (|:| |index| *4) #20=(|:| |exponent| *5)) #19#)) #21=(|ofCategory| *2 #4#) (|isDomain| *1 (|GeneralModulePolynomial| *3 *2 *4 *5 *6 *7)) #22=(|ofCategory| *4 #13#) (|ofCategory| *7 (|PolynomialCategory| *2 *5 #15#)))) (|leadingMonomial| #16# (AND #1# #3# #5# #8# (|isDomain| *2 #23=(|ModuleMonomial| *5 *6 *7)) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *8)) #12# (|ofCategory| *8 #14#))) (|leadingExponent| #16# (AND #1# #3# (|ofType| *6 (|Mapping| #9# #24=(|Record| #11# (|:| |exponent| *2)) #24#)) (|ofCategory| *2 #6#) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *2 *6 *7)) #12# (|ofCategory| *7 (|PolynomialCategory| *4 *2 #15#)))) (|leadingIndex| #16# (AND #1# #3# #17# #25=(|ofType| *6 (|Mapping| #9# #26=(|Record| (|:| |index| *2) #20#) #26#)) #27=(|ofCategory| *2 #13#) #28=(|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *2 *5 *6 *7)) #29=(|ofCategory| *7 (|PolynomialCategory| *4 *5 #15#)))) (|reductum| (*1 *1 *1) (AND (|ofType| *2 #2#) (|ofCategory| *3 #4#) (|ofCategory| *5 (|DirectProductCategory| (|#| *2) #7#)) #18# (|isDomain| *1 (|GeneralModulePolynomial| *2 *3 *4 *5 *6 *7)) #22# (|ofCategory| *7 (|PolynomialCategory| *3 *5 (|OrderedVariableList| *2))))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 #23#) #12# (|ofCategory| *6 #30=(|DirectProductCategory| (|#| *4) #7#)) #8# #31=(|ofType| *4 #2#) #21# (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *6 *7 *8)) (|ofCategory| *8 (|PolynomialCategory| *2 *6 #32=(|OrderedVariableList| *4))))) (|unitVector| (*1 *1 *2) (AND #1# #3# #17# #25# #28# #27# #29#)) (|build| (*1 *1 *2 *3 *4) (AND (|ofType| *5 #2#) #21# (|ofCategory| *4 (|DirectProductCategory| (|#| *5) #7#)) (|ofType| *6 (|Mapping| #9# #33=(|Record| (|:| |index| *3) (|:| |exponent| *4)) #33#)) (|isDomain| *1 (|GeneralModulePolynomial| *5 *2 *3 *4 *6 *7)) (|ofCategory| *3 #13#) (|ofCategory| *7 (|PolynomialCategory| *2 *4 (|OrderedVariableList| *5))))) (|multMonom| (*1 *1 *2 *3 *1) (AND #31# #21# (|ofCategory| *3 #30#) (|ofType| *6 (|Mapping| #9# #34=(|Record| #11# (|:| |exponent| *3)) #34#)) (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *3 *6 *7)) #12# (|ofCategory| *7 (|PolynomialCategory| *2 *3 #32#))))) 
((|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) 39 T ELT))) 
(((|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| #1=(|#4| $)) (SIGNATURE |denom| #1#)))) (T |GosperSummationMethod|)) 
((|GospersMethod| (*1 *2 *2 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *5 *3)) (|isDomain| *1 (|GosperSummationMethod| *5 *3 *6 *7 *2)) (|ofCategory| *2 (|Join| (|RetractableTo| (|Fraction| (|Integer|))) (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| #1=(*7 $)) (SIGNATURE |denom| #1#))))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|variables| (#4=((|List| |#3|) $) 40 T ELT)) (|trivialIdeal?| (#5=(#3# $) NIL T ELT)) (|triangular?| #6=(#5# NIL #7=(|has| |#1| (|IntegralDomain|)) ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL T ELT)) (|select| #8=(($ #9=(|Mapping| #3# |#4|) $) NIL #10=(|has| $ (|FiniteAggregate| |#4|)) ELT)) (|sample| (#11=($) NIL T CONST)) (|roughUnitIdeal?| #6#) (|roughSubIdeal?| #12=(#2# NIL #7# ELT)) (|roughEqualIdeals?| #12#) (|roughBase?| #6#) (|rewriteIdealWithRemainder| #13=((#14=(|List| |#4|) #14# $) NIL #7# ELT)) (|rewriteIdealWithHeadRemainder| #13#) (|retractIfCan| (((|Union| $ #15="failed") #14#) 48 T ELT)) (|retract| (#16=($ #14#) NIL T ELT)) (|removeDuplicates| (#17=($ $) NIL #18=(AND #10# #19=(|has| |#4| (|BasicType|))) ELT)) (|remove| (($ |#4| $) NIL #18# ELT) #8#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #20=(|:| |den| |#1|)) |#4| $) NIL #7# ELT)) (|reduce| ((|#4| #21=(|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) NIL #19# ELT) ((|#4| #21# $ |#4|) NIL T ELT) ((|#4| #21# $) NIL T ELT)) (|mvar| ((|#3| $) 46 T ELT)) (|members| (#22=(#14# $) 14 T ELT)) (|member?| ((#3# |#4| $) 25 #19# ELT)) (|map!| (#23=($ (|Mapping| |#4| |#4|) $) 22 T ELT)) (|map| (#23# 20 T ELT)) (|mainVariables| (#4# NIL T ELT)) (|mainVariable?| ((#3# |#3| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) #20#) |#4| $) NIL #7# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| (((|Union| |#4| #15#) #9# $) NIL T ELT)) (|every?| #24=((#3# #9# $) NIL T ELT)) (|eval| (($ $ #14# #14#) NIL #25=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) NIL #25# ELT) (($ $ #26=(|Equation| |#4|)) NIL #25# ELT) (($ $ (|List| #26#)) NIL #25# ELT)) (|eq?| #1#) (|empty?| (#5# 38 T ELT)) (|empty| (#11# 17 T ELT)) (|count| ((#27=(|NonNegativeInteger|) |#4| $) NIL #19# ELT) ((#27# #9# $) NIL T ELT)) (|copy| (#17# 16 T ELT)) (|convert| ((#28=(|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| #28#)) ELT) (#16# 50 T ELT)) (|construct| (#16# 13 T ELT)) (|collectUpper| #29=(($ $ |#3|) NIL T ELT)) (|collectUnder| #29#) (|collect| #29#) (|coerce| (((|OutputForm|) $) 37 T ELT) (#22# 49 T ELT)) (|before?| #1#) (|any?| #24#) (= (#2# 29 T ELT)) (|#| ((#27# $) NIL T ELT))) 
(((|GeneralPolynomialSet| |#1| |#2| |#3| |#4|) (|Join| (|PolynomialSetCategory| |#1| |#2| |#3| |#4|) (|ShallowlyMutableAggregate| |#4|) (CATEGORY |domain| (SIGNATURE |convert| ($ (|List| |#4|))))) (|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))))) 
((|Zero| (#1=($) 11 T CONST)) (|One| (#1# 13 T CONST)) (* (($ |#2| $) 15 T ELT) (($ $ |#2|) 16 T ELT))) 
(((|GradedAlgebra&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |One| #1=(|#1|) |constant|) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE |Zero| #1# |constant|)) (|GradedAlgebra| |#2| |#3|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedAlgebra&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 30 T ELT)) (|retract| ((|#1| $) 31 T ELT)) (|product| (($ $ $) 27 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| ((|#2| $) 23 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 29 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (($) 22 T CONST)) (|One| (($) 28 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 19 T ELT) (#2=($ $ $) 17 T ELT)) (+ (#2# 18 T ELT)) (* (($ |#1| $) 21 T ELT) (($ $ |#1|) 20 T ELT))) 
(((|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) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|GradedModule| |#1| |#2|) . T) ((|Join|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|nextSubsetGray| ((#1=(|Vector| (|Vector| (|Integer|))) #1# #2=(|PositiveInteger|)) 26 T ELT)) (|firstSubsetGray| ((#1# #2#) 21 T ELT))) 
(((|GrayCode|) (CATEGORY |package| (SIGNATURE |nextSubsetGray| (#1=(|Vector| (|Vector| (|Integer|))) #1# #2=(|PositiveInteger|))) (SIGNATURE |firstSubsetGray| (#1# #2#)))) (T |GrayCode|)) 
((|firstSubsetGray| (*1 *2 *3) (AND #1=(|isDomain| *3 (|PositiveInteger|)) #2=(|isDomain| *2 (|Vector| (|Vector| (|Integer|)))) #3=(|isDomain| *1 (|GrayCode|)))) (|nextSubsetGray| (*1 *2 *2 *3) (AND #2# #1# #3#))) 
((|screenResolution| (#1=(#2=(|Integer|) #2#) 32 T ELT) (#3=(#2#) 24 T ELT)) (|minPoints| (#1# 28 T ELT) (#3# 20 T ELT)) (|maxPoints| (#1# 30 T ELT) (#3# 22 T ELT)) (|drawToScale| (#4=(#5=(|Boolean|) #5#) 14 T ELT) (#6=(#5#) 12 T ELT)) (|clipPointsDefault| (#4# 13 T ELT) (#6# 11 T ELT)) (|adaptive| (#4# 26 T ELT) (#6# 17 T ELT))) 
(((|GraphicsDefaults|) (CATEGORY |package| (SIGNATURE |clipPointsDefault| #1=(#2=(|Boolean|))) (SIGNATURE |drawToScale| #1#) (SIGNATURE |clipPointsDefault| #3=(#2# #2#)) (SIGNATURE |drawToScale| #3#) (SIGNATURE |adaptive| #1#) (SIGNATURE |maxPoints| #4=(#5=(|Integer|))) (SIGNATURE |minPoints| #4#) (SIGNATURE |screenResolution| #4#) (SIGNATURE |adaptive| #3#) (SIGNATURE |maxPoints| #6=(#5# #5#)) (SIGNATURE |minPoints| #6#) (SIGNATURE |screenResolution| #6#))) (T |GraphicsDefaults|)) 
((|screenResolution| #1=(*1 *2 *2) #2=(AND (|isDomain| *2 (|Integer|)) #3=(|isDomain| *1 (|GraphicsDefaults|)))) (|minPoints| #1# #2#) (|maxPoints| #1# #2#) (|adaptive| #1# #4=(AND (|isDomain| *2 (|Boolean|)) #3#)) (|screenResolution| #5=(*1 *2) #2#) (|minPoints| #5# #2#) (|maxPoints| #5# #2#) (|adaptive| #5# #4#) (|drawToScale| #1# #4#) (|clipPointsDefault| #1# #4#) (|drawToScale| #5# #4#) (|clipPointsDefault| #5# #4#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|units| ((#2=(|List| #3=(|Float|)) $) 34 T ELT) ((#2# $ #2#) 145 T ELT)) (|ranges| ((#4=(|List| (|Segment| #3#)) $) 16 T ELT) ((#4# $ #4#) 142 T ELT)) (|putColorInfo| ((#5=(|List| #6=(|List| #7=(|Point| #8=(|DoubleFloat|)))) #5# #9=(|List| #10=(|Palette|))) 58 T ELT)) (|pointLists| ((#5# $) 137 T ELT)) (|point| ((#11=(|Void|) $ #7# #10#) 162 T ELT)) (|makeGraphImage| (($ $) 136 T ELT) (#12=($ #5#) 148 T ELT) (($ #5# #9# #9# #13=(|List| #14=(|PositiveInteger|))) 147 T ELT) (($ #5# #9# #9# #13# (|List| (|DrawOption|))) 149 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|key| (((|Integer|) $) 110 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|graphImage| (($) 146 T ELT)) (|figureUnits| (((|List| #8#) #5#) 89 T ELT)) (|component| ((#11# $ #6# #10# #10# #14#) 154 T ELT) (#15=(#11# $ #7#) 156 T ELT) ((#11# $ #7# #10# #10# #14#) 155 T ELT)) (|coerce| (((|OutputForm|) $) 168 T ELT) (#12# 163 T ELT)) (|before?| #1#) (|appendPoint| (#15# 161 T ELT)) (= #1#)) 
(((|GraphImage|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |graphImage| ($)) (SIGNATURE |makeGraphImage| ($ $)) (SIGNATURE |makeGraphImage| #1=($ #2=(|List| #3=(|List| #4=(|Point| #5=(|DoubleFloat|)))))) (SIGNATURE |makeGraphImage| ($ #2# #6=(|List| #7=(|Palette|)) #6# #8=(|List| #9=(|PositiveInteger|)))) (SIGNATURE |makeGraphImage| ($ #2# #6# #6# #8# (|List| (|DrawOption|)))) (SIGNATURE |pointLists| (#2# $)) (SIGNATURE |key| ((|Integer|) $)) (SIGNATURE |ranges| (#10=(|List| (|Segment| #11=(|Float|))) $)) (SIGNATURE |ranges| (#10# $ #10#)) (SIGNATURE |units| (#12=(|List| #11#) $)) (SIGNATURE |units| (#12# $ #12#)) (SIGNATURE |component| (#13=(|Void|) $ #3# #7# #7# #9#)) (SIGNATURE |component| #14=(#13# $ #4#)) (SIGNATURE |component| (#13# $ #4# #7# #7# #9#)) (SIGNATURE |appendPoint| #14#) (SIGNATURE |point| (#13# $ #4# #7#)) (SIGNATURE |coerce| #1#) (SIGNATURE |coerce| ((|OutputForm|) $)) (SIGNATURE |putColorInfo| (#2# #2# #6#)) (SIGNATURE |figureUnits| ((|List| #5#) #2#))))) (T |GraphImage|)) 
((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) #2=(|isDomain| *1 (|GraphImage|)))) (|graphImage| (*1 *1) #2#) (|makeGraphImage| (*1 *1 *1) #2#) (|makeGraphImage| #3=(*1 *1 *2) #4=(AND #5=(|isDomain| *2 #6=(|List| #7=(|List| #8=(|Point| #9=(|DoubleFloat|))))) #2#)) (|makeGraphImage| (*1 *1 *2 *3 *3 *4) (AND #5# #10=(|isDomain| *3 (|List| #11=(|Palette|))) #12=(|isDomain| *4 (|List| #13=(|PositiveInteger|))) #2#)) (|makeGraphImage| (*1 *1 *2 *3 *3 *4 *5) (AND #5# #10# #12# (|isDomain| *5 (|List| (|DrawOption|))) #2#)) (|pointLists| #1# #4#) (|key| #1# (AND (|isDomain| *2 (|Integer|)) #2#)) (|ranges| #1# #14=(AND (|isDomain| *2 (|List| (|Segment| #15=(|Float|)))) #2#)) (|ranges| #16=(*1 *2 *1 *2) #14#) (|units| #1# #17=(AND (|isDomain| *2 (|List| #15#)) #2#)) (|units| #16# #17#) (|component| #18=(*1 *2 *1 *3 *4 *4 *5) (AND (|isDomain| *3 #7#) #19=(|isDomain| *4 #11#) #20=(|isDomain| *5 #13#) #21=(|isDomain| *2 (|Void|)) #2#)) (|component| #22=(*1 *2 *1 *3) #23=(AND #24=(|isDomain| *3 #8#) #21# #2#)) (|component| #18# (AND #24# #19# #20# #21# #2#)) (|appendPoint| #22# #23#) (|point| (*1 *2 *1 *3 *4) (AND #24# #19# #21# #2#)) (|coerce| #3# #4#) (|putColorInfo| (*1 *2 *2 *3) (AND #5# #10# #2#)) (|figureUnits| (*1 *2 *3) (AND (|isDomain| *3 #6#) (|isDomain| *2 (|List| #9#)) #2#))) 
((- (($ $) NIL T ELT) (($ $ $) 11 T ELT))) 
(((|GradedModule&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|))) (|GradedModule| |#2| |#3|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedModule&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| ((|#2| $) 23 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (($) 22 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 19 T ELT) (($ $ $) 17 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ |#1| $) 21 T ELT) (($ $ |#1|) 20 T ELT))) 
(((|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) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|testDim| (((|Union| #1=(|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") #1# #2=(|List| (|OrderedVariableList| |#1|))) 135 T ELT)) (|groebSolve| (((|List| #3=(|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) #3# #2#) 132 T ELT)) (|genericPosition| (((|Record| (|:| |dpolys| #3#) (|:| |coords| (|List| (|Integer|)))) #3# #2#) 87 T ELT))) 
(((|GroebnerSolve| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |groebSolve| ((|List| #1=(|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) #1# #2=(|List| (|OrderedVariableList| |#1|)))) (SIGNATURE |testDim| ((|Union| #3=(|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") #3# #2#)) (SIGNATURE |genericPosition| ((|Record| (|:| |dpolys| #1#) (|:| |coords| (|List| (|Integer|)))) #1# #2#))) (|List| (|Symbol|)) #4=(|GcdDomain|) #4#) (T |GroebnerSolve|)) 
((|genericPosition| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *4 (|List| (|OrderedVariableList| *5))) #3=(|ofType| *5 #4=(|List| (|Symbol|))) #5=(|ofCategory| *6 #6=(|GcdDomain|)) (|isDomain| *2 (|Record| (|:| |dpolys| #7=(|List| (|DistributedMultivariatePolynomial| *5 *6))) (|:| |coords| (|List| (|Integer|))))) #8=(|isDomain| *1 (|GroebnerSolve| *5 *6 *7)) #9=(|isDomain| *3 #7#) #10=(|ofCategory| *7 #6#))) (|testDim| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|HomogeneousDistributedMultivariatePolynomial| *4 *5))) (|isDomain| *3 (|List| (|OrderedVariableList| *4))) (|ofType| *4 #4#) (|ofCategory| *5 #6#) (|isDomain| *1 (|GroebnerSolve| *4 *5 *6)) #5#)) (|groebSolve| #1# (AND #2# #3# #5# (|isDomain| *2 (|List| #7#)) #8# #9# #10#))) 
((|recip| (((|Union| $ "failed") $) 11 T ELT)) (|conjugate| (#1=($ $ $) 22 T ELT)) (|commutator| (#1# 23 T ELT)) (/ (#1# 9 T ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ (|Integer|)) 21 T ELT))) 
(((|Group&| |#1|) (CATEGORY |package| (SIGNATURE |commutator| #1=(|#1| |#1| |#1|)) (SIGNATURE |conjugate| #1#) (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE / #1#) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|Group|)) (T |Group&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|sample| (#2=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|one?| (((|Boolean|) $) 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 30 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|conjugate| (($ $ $) 27 T ELT)) (|commutator| (($ $ $) 26 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#2# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 29 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT) (($ $ (|Integer|)) 28 T ELT)) (* (($ $ $) 18 T ELT))) 
(((|Group|) (|Category|)) (T |Group|)) 
((|inv| (*1 *1 *1) (|ofCategory| *1 (|Group|))) (/ (*1 *1 *1 *1) (|ofCategory| *1 (|Group|))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Group|)) (|isDomain| *2 (|Integer|)))) (|conjugate| (*1 *1 *1 *1) (|ofCategory| *1 (|Group|))) (|commutator| (*1 *1 *1 *1) (|ofCategory| *1 (|Group|)))) 
(|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |inv| ($ $)) (SIGNATURE / ($ $ $)) (SIGNATURE ** ($ $ (|Integer|))) (ATTRIBUTE |unitsKnown|) (SIGNATURE |conjugate| ($ $ $)) (SIGNATURE |commutator| ($ $ $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monoid|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 18 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| (#19=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|squareFreePart| #22=(#11# NIL #23=(|has| |#1| (|Field|)) ELT)) (|squareFree| #24=(((|Factored| $) $) NIL #23# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #23# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #25=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| #26=(#27=($) NIL T CONST)) (|rem| #28=(#29=($ $ $) NIL #23# ELT)) (|reductum| #30=(#11# NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|quo| #28#) (|principalIdeal| (((|Record| (|:| |coef| #31=(|List| $)) #32=(|:| |generator| $)) #31#) NIL #23# ELT)) (|prime?| (#5# NIL #23# ELT)) (|pole?| #4#) (|pi| (#27# NIL #18# ELT)) (|order| #33=((#14# $) NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#34=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #35=(($ $ #36=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #31# #21#) #31# $) NIL #23# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) NIL T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 25 T ELT)) (|log| #17#) (|leadingMonomial| #30#) (|leadingCoefficient| (#37=(|#1| $) NIL T ELT)) (|lcm| #38=(($ #31#) NIL #23# ELT) #28#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #22#) (|integrate| (#11# 29 #18# ELT) (#39=($ $ #8#) 35 (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#40=(|List| #8#) |#1|))))) ELT) (#41=($ $ #42=(|Variable| |#2|)) 30 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#43=(|SparseUnivariatePolynomial| $) #43# #43#) NIL #23# ELT)) (|gcd| #38# #28#) (|factor| #24#) (|extendedEuclidean| (((|Union| (|Record| #44=(|:| |coef1| $) #45=(|:| |coef2| $)) #21#) $ $ $) NIL #23# ELT) (((|Record| #44# #45# #32#) $ $) NIL #23# ELT)) (|extend| #12#) (|exquo| (#19# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #31#) #31# $) NIL #23# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #46=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#25# $) NIL #23# ELT)) (|elt| #47=(#48=(|#1| $ #14#) NIL T ELT) (#29# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #23# ELT)) (|differentiate| (#39# 28 #49=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #50=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #51=(($ $ #40#) NIL #49# ELT) #52=(($ $ #8# #25#) NIL #49# ELT) #53=(($ $ #40# (|List| #25#)) NIL #49# ELT) (#11# 14 #50# ELT) #54=(#55=($ $ #25#) NIL #50# ELT) (#41# 16 T ELT)) (|degree| #33#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #30#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #42#) NIL T ELT) (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) 9 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #47#) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#25#) NIL T CONST)) (|center| (#37# 21 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#48# NIL (AND #46# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| #26#) (|One| #26#) (D (#39# NIL #49# ELT) #51# #52# #53# (#11# NIL #50# ELT) #54# (#41# NIL T ELT)) (= #1#) (/ (#56=($ $ |#1|) NIL #23# ELT) #28#) (- #30# (#29# 27 T ELT)) (+ #57=(#29# NIL T ELT)) (** #35# (#55# NIL T ELT) (#34# NIL #23# ELT) (#29# NIL #18# ELT) #58=(#13# NIL #18# ELT)) (* (($ #36# $) NIL T ELT) (($ #25# $) NIL T ELT) (($ #15# . #59=($)) NIL T ELT) #57# (#56# NIL T ELT) (($ |#1| . #59#) 26 T ELT) (($ #14# . #59#) NIL #18# ELT) #58#)) 
(((|GeneralUnivariatePowerSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesCategory| |#1|) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1#)) (SIGNATURE |coerce| ($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |GeneralUnivariatePowerSeries|)) 
((|coerce| #1=(*1 *1 *2) (AND #2=(|isDomain| *2 (|Variable| *4)) #3=(|ofType| *4 (|Symbol|)) #4=(|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)) #5=(|ofCategory| *3 (|Ring|)) #6=(|ofType| *5 *3))) (|coerce| #1# (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)) #5# #3# #6# #4#)) (|integrate| (*1 *1 *1 *2) (AND #2# #3# #4# (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) #5# #6#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #6=(|BasicType|)) #7=(|has| |#2| #6#)) ELT)) (|table| #8=(#9=($) NIL T ELT) #10=(($ #11=(|List| #5#)) NIL T ELT)) (|swap!| (((|Void|) $ |#1| |#1|) NIL #12=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| (#13=(|#2| $ |#1| |#2|) 18 #12# ELT)) (|select!| #14=(($ #15=(|Mapping| #3# #5#) $) NIL #16=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|select| #14#) (|search| (#17=((|Union| |#2| #18="failed") |#1| $) 19 T ELT)) (|sample| (#9# NIL T CONST)) (|removeDuplicates| (#19=($ $) NIL #20=(AND #16# #4#) ELT)) (|remove!| (#21=($ #5# $) NIL #16# ELT) #14# (#17# 16 T ELT)) (|remove| (#21# NIL #20# ELT) #14#) (|reduce| ((#5# #22=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #22# $ #5#) NIL T ELT) ((#5# #22# $) NIL T ELT)) (|qsetelt!| (#13# NIL #12# ELT)) (|qelt| (#23=(|#2| $ |#1|) NIL T ELT)) (|minIndex| #24=((|#1| $) NIL #25=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#11# $) NIL T ELT)) (|member?| ((#3# #5# $) NIL #4# ELT)) (|maxIndex| #24#) (|map!| #26=(($ (|Mapping| #5# #5#) . #27=($)) NIL T ELT) #28=(($ (|Mapping| |#2| |#2|) . #27#) NIL T ELT)) (|map| #26# #28# #26# (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #29=(OR #30=(|has| #5# #31=(|SetCategory|)) #32=(|has| |#2| #31#)) ELT)) (|keys| #33=(((|List| |#1|) $) NIL T ELT)) (|key?| #34=((#3# |#1| $) NIL T ELT)) (|inspect| #35=((#5# $) NIL T ELT)) (|insert!| (#21# NIL T ELT)) (|indices| #33#) (|index?| #34#) (|hash| (((|SingleInteger|) $) NIL #29# ELT)) (|first| ((|#2| $) NIL #25# ELT)) (|find| (((|Union| #5# #18#) #15# $) NIL T ELT)) (|fill!| (($ $ |#2|) NIL #12# ELT)) (|extract!| #35#) (|every?| #36=((#3# #15# $) NIL T ELT)) (|eval| #37=(($ $ (|List| #38=(|Equation| #5#))) NIL #39=(AND (|has| #5# (|Evalable| #5#)) #30#) ELT) #40=(($ $ #38#) NIL #39# ELT) #41=(($ $ #5# #5#) NIL #39# ELT) #42=(($ $ #11# #11#) NIL #39# ELT) (($ $ #43=(|List| |#2|) #43#) NIL #44=(AND (|has| |#2| (|Evalable| |#2|)) #32#) ELT) (($ $ |#2| |#2|) NIL #44# ELT) (($ $ #45=(|Equation| |#2|)) NIL #44# ELT) (($ $ (|List| #45#)) NIL #44# ELT) #42# #41# #40# #37#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#2| $) NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #7#) ELT)) (|entries| ((#43# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| #8#) (|elt| (#23# 13 T ELT) (#13# NIL T ELT)) (|dictionary| #8# #10#) (|count| ((#46=(|NonNegativeInteger|) #5# $) NIL #4# ELT) ((#46# #15# $) NIL T ELT)) (|copy| (#19# NIL T ELT)) (|convert| ((#47=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #47#)) ELT)) (|construct| #10#) (|coerce| ((#48=(|OutputForm|) $) NIL (OR (|has| #5# #49=(|CoercibleTo| #48#)) (|has| |#2| #49#)) ELT)) (|before?| #1#) (|bag| #10#) (|any?| #36#) (= #1#) (|#| ((#46# $) NIL T ELT))) 
(((|GeneralSparseTable| |#1| |#2| |#3| |#4|) #1=(|TableAggregate| |#1| |#2|) #2=(|SetCategory|) #2# #1# |#2|) (T |GeneralSparseTable|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| |#4|)))) #5#) NIL T ELT)) (|zeroSetSplit| (((|List| $) #5#) NIL T ELT)) (|variables| #6=(((|List| |#3|) $) NIL T ELT)) (|trivialIdeal?| #7=(#8=(#3# $) NIL T ELT)) (|triangular?| #9=(#8# NIL #10=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #11=(#12=(#3# |#4| $) NIL T ELT) #7#) (|stronglyReduce| #13=((|#4| |#4| $) NIL T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL T ELT)) (|select| #14=(($ #15=(|Mapping| #3# |#4|) $) NIL #16=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#17=(|Union| |#4| #18="failed") $ |#3|) NIL T ELT)) (|sample| (#19=($) NIL T CONST)) (|roughUnitIdeal?| (#8# 28 #10# ELT)) (|roughSubIdeal?| #20=(#2# NIL #10# ELT)) (|roughEqualIdeals?| #20#) (|roughBase?| #9#) (|rewriteSetWithReduction| ((#5# #5# $ #21=(|Mapping| |#4| |#4| |#4|) #22=(|Mapping| #3# |#4| |#4|)) NIL T ELT)) (|rewriteIdealWithRemainder| #23=((#5# #5# $) NIL #10# ELT)) (|rewriteIdealWithHeadRemainder| #23#) (|retractIfCan| ((#24=(|Union| $ #18#) #5#) NIL T ELT)) (|retract| (#25=($ #5#) NIL T ELT)) (|rest| ((#24# $) 44 T ELT)) (|removeZero| #13#) (|removeDuplicates| (#26=($ $) NIL #27=(AND #16# #28=(|has| |#4| (|BasicType|))) ELT)) (|remove| (($ |#4| $) NIL #27# ELT) #14#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #29=(|:| |den| |#1|)) |#4| $) NIL #10# ELT)) (|reduced?| ((#3# |#4| $ #22#) NIL T ELT)) (|reduceByQuasiMonic| #13#) (|reduce| ((|#4| #21# $ |#4| |#4|) NIL #28# ELT) ((|#4| #21# $ |#4|) NIL T ELT) ((|#4| #21# $) NIL T ELT) ((|#4| |#4| $ #21# #22#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|normalized?| #11# #7#) (|mvar| ((|#3| $) 37 T ELT)) (|members| (#30=(#5# $) 18 T ELT)) (|member?| (#12# 26 #28# ELT)) (|map!| (#31=($ (|Mapping| |#4| |#4|) $) 24 T ELT)) (|map| (#31# 22 T ELT)) (|mainVariables| #6#) (|mainVariable?| #32=((#3# |#3| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|last| (#33=(#17# $) 41 T ELT)) (|initials| (#30# NIL T ELT)) (|initiallyReduced?| #11# #7#) (|initiallyReduce| #13#) (|infRittWu?| #1#) (|headRemainder| (((|Record| (|:| |num| |#4|) #29#) |#4| $) NIL #10# ELT)) (|headReduced?| #11# #7#) (|headReduce| #13#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#33# 39 T ELT)) (|find| ((#17# #15# $) NIL T ELT)) (|extendIfCan| ((#24# $ |#4|) 54 T ELT)) (|extend| (($ $ |#4|) NIL T ELT)) (|every?| #34=((#3# #15# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #35=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) NIL #35# ELT) (($ $ #36=(|Equation| |#4|)) NIL #35# ELT) (($ $ (|List| #36#)) NIL #35# ELT)) (|eq?| #1#) (|empty?| (#8# 17 T ELT)) (|empty| (#19# 14 T ELT)) (|degree| #37=(#38=(#39=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#39# |#4| $) NIL #28# ELT) ((#39# #15# $) NIL T ELT)) (|copy| (#26# 13 T ELT)) (|convert| ((#40=(|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| #40#)) ELT)) (|construct| (#25# 21 T ELT)) (|collectUpper| (#41=($ $ |#3|) 48 T ELT)) (|collectUnder| (#41# 50 T ELT)) (|collectQuasiMonic| (#26# NIL T ELT)) (|collect| (#41# NIL T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT) (#30# 45 T ELT)) (|coHeight| (#38# NIL (|has| |#3| (|Finite|)) ELT)) (|before?| #1#) (|basicSet| ((#42=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #18#) #5# #22#) NIL T ELT) ((#42# #5# #15# #22#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# |#4| #5#)) NIL T ELT)) (|any?| #34#) (|algebraicVariables| #6#) (|algebraic?| #32#) (= #1#) (|#| #37#)) 
(((|GeneralTriangularSet| |#1| |#2| |#3| |#4|) (|TriangularSetCategory| |#1| |#2| |#3| |#4|) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |GeneralTriangularSet|)) 
NIL 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| #5=((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #8=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#9=($) NIL T CONST)) (|retractIfCan| (((|Union| #10=(|Integer|) . #11=(#7#)) . #12=($)) NIL T ELT) (((|Union| #13=(|Fraction| #10#) . #11#) . #12#) NIL T ELT)) (|retract| ((#10# . #14=($)) NIL T ELT) ((#13# . #14#) NIL T ELT)) (|rem| #15=(($ $ $) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|quo| #15#) (|principalIdeal| (((|Record| (|:| |coef| #16=(|List| $)) #17=(|:| |generator| $)) #16#) NIL T ELT)) (|prime?| #3#) (|pi| (#9# 17 T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #16# #7#) #16# $) NIL T ELT)) (|lcm| #15# #18=(($ #16#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#19=(|SparseUnivariatePolynomial| $) #19# #19#) NIL T ELT)) (|gcd| #15# #18#) (|factor| #8#) (|extendedEuclidean| (((|Record| #20=(|:| |coef1| $) #21=(|:| |coef2| $) #17#) $ $) NIL T ELT) (((|Union| (|Record| #20# #21#) #7#) $ $ $) NIL T ELT)) (|exquo| #5#) (|expressIdealMember| (((|Maybe| #16#) #16# $) NIL T ELT)) (|euclideanSize| ((#22=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|convert| (#23=((|Float|) $) 21 T ELT) (#24=((|DoubleFloat|) $) 24 T ELT) (((|Fraction| (|SparseUnivariatePolynomial| #10#)) $) 18 T ELT) (((|InputForm|) $) 53 T ELT)) (|coerce| (((|OutputForm|) $) 51 T ELT) (($ #10#) NIL T ELT) #4# (($ #13#) NIL T ELT) (#24# 23 T ELT) (#23# 20 T ELT)) (|characteristic| ((#22#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#9# 37 T CONST)) (|One| (#9# 8 T CONST)) (= #1#) (/ #15#) (- #4# #15#) (+ #15#) (** (($ $ #25=(|PositiveInteger|)) NIL T ELT) (($ $ #22#) NIL T ELT) (($ $ #10#) NIL T ELT)) (* (($ #25# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #10# . #26=($)) NIL T ELT) #15# (($ $ #13#) NIL T ELT) (($ #13# . #26#) NIL T ELT))) 
(((|Pi|) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| (|Fraction| #1#)) (|RealConstant|) (|CoercibleTo| (|DoubleFloat|)) (|CoercibleTo| (|Float|)) (|ConvertibleTo| (|Fraction| (|SparseUnivariatePolynomial| #1#))) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |pi| ($))))) (T |Pi|)) 
((|pi| (*1 *1) (|isDomain| *1 (|Pi|)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|rhs| (#2=((|SpadAst|) $) 12 T ELT)) (|lhs| (#2# 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|HasAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |lhs| #1=((|SpadAst|) $)) (SIGNATURE |rhs| #1#)))) (T |HasAst|)) 
((|lhs| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|HasAst|)))) (|rhs| #1# #2#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(OR #5=(|has| #6=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #7=(|BasicType|)) #8=(|has| |#2| #7#)) ELT)) (|table| #9=(#10=($) NIL T ELT) #11=(($ #12=(|List| #6#)) NIL T ELT)) (|swap!| (((|Void|) $ |#1| |#1|) NIL #13=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| (#14=(|#2| $ |#1| |#2|) 16 #13# ELT)) (|select!| #15=(($ #16=(|Mapping| #3# #6#) $) NIL #17=(|has| $ (|FiniteAggregate| #6#)) ELT)) (|select| #15#) (|search| (#18=((|Union| |#2| #19="failed") |#1| $) 20 T ELT)) (|sample| (#10# NIL T CONST)) (|removeDuplicates| (#20=($ $) NIL #21=(AND #17# #5#) ELT)) (|remove!| (#22=($ #6# $) NIL #17# ELT) #15# (#18# 18 T ELT)) (|remove| (#22# NIL #21# ELT) #15#) (|reduce| ((#6# #23=(|Mapping| #6# #6# #6#) $ #6# #6#) NIL #5# ELT) ((#6# #23# $ #6#) NIL T ELT) ((#6# #23# $) NIL T ELT)) (|qsetelt!| (#14# NIL #13# ELT)) (|qelt| #24=((|#2| $ |#1|) NIL T ELT)) (|minIndex| #25=((|#1| $) NIL #26=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#12# $) NIL T ELT)) (|member?| ((#3# #6# $) NIL #5# ELT)) (|maxIndex| #25#) (|map!| #27=(($ (|Mapping| #6# #6#) . #28=($)) NIL T ELT) #29=(($ (|Mapping| |#2| |#2|) . #28#) NIL T ELT)) (|map| #27# #29# #27# (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #30=(OR #31=(|has| #6# #32=(|SetCategory|)) #33=(|has| |#2| #32#)) ELT)) (|keys| (#34=((|List| |#1|) $) 13 T ELT)) (|key?| #35=((#3# |#1| $) NIL T ELT)) (|inspect| #36=((#6# $) NIL T ELT)) (|insert!| (#22# NIL T ELT)) (|indices| (#34# NIL T ELT)) (|index?| #35#) (|hash| (((|SingleInteger|) $) NIL #30# ELT)) (|first| ((|#2| $) NIL #26# ELT)) (|find| (((|Union| #6# #19#) #16# $) NIL T ELT)) (|fill!| (($ $ |#2|) NIL #13# ELT)) (|extract!| #36#) (|every?| #37=((#3# #16# $) NIL T ELT)) (|eval| #38=(($ $ (|List| #39=(|Equation| #6#))) NIL #40=(AND (|has| #6# (|Evalable| #6#)) #31#) ELT) #41=(($ $ #39#) NIL #40# ELT) #42=(($ $ #6# #6#) NIL #40# ELT) #43=(($ $ #12# #12#) NIL #40# ELT) (($ $ #44=(|List| |#2|) #44#) NIL #45=(AND (|has| |#2| (|Evalable| |#2|)) #33#) ELT) (($ $ |#2| |#2|) NIL #45# ELT) (($ $ #46=(|Equation| |#2|)) NIL #45# ELT) (($ $ (|List| #46#)) NIL #45# ELT) #43# #42# #41# #38#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#2| $) NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #8#) ELT)) (|entries| ((#44# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| (#10# 19 T ELT)) (|elt| #24# (#14# NIL T ELT)) (|dictionary| #9# #11#) (|count| ((#47=(|NonNegativeInteger|) #6# $) NIL #5# ELT) ((#47# #16# $) NIL T ELT)) (|copy| (#20# NIL T ELT)) (|convert| ((#48=(|InputForm|) $) NIL (|has| #6# (|ConvertibleTo| #48#)) ELT)) (|construct| #11#) (|coerce| ((#49=(|OutputForm|) $) NIL (OR (|has| #6# #50=(|CoercibleTo| #49#)) (|has| |#2| #50#)) ELT)) (|before?| #1#) (|bag| #11#) (|any?| #37#) (= (#2# 11 #4# ELT)) (|#| ((#47# $) 15 T ELT))) 
(((|HashTable| |#1| |#2| |#3|) (|TableAggregate| |#1| |#2|) #1=(|SetCategory|) #1# (|String|)) (T |HashTable|)) 
NIL 
((|lfunc| ((#1=(|Integer|) #1# #1#) 19 T ELT)) (|inHallBasis?| (((|Boolean|) #1# #1# #1# #1#) 28 T ELT)) (|generate| (((|Vector| (|List| #1#)) #2=(|NonNegativeInteger|) #2#) 42 T ELT))) 
(((|HallBasis|) (CATEGORY |package| (SIGNATURE |lfunc| (#1=(|Integer|) #1# #1#)) (SIGNATURE |inHallBasis?| ((|Boolean|) #1# #1# #1# #1#)) (SIGNATURE |generate| ((|Vector| (|List| #1#)) #2=(|NonNegativeInteger|) #2#)))) (T |HallBasis|)) 
((|generate| (*1 *2 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Vector| (|List| #1=(|Integer|)))) #2=(|isDomain| *1 (|HallBasis|)))) (|inHallBasis?| (*1 *2 *3 *3 *3 *3) (AND (|isDomain| *3 #1#) (|isDomain| *2 (|Boolean|)) #2#)) (|lfunc| (*1 *2 *2 *2) (AND (|isDomain| *2 #1#) #2#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #8#) #8#) NIL #19=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#12# NIL #21=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #8#) #17#) #23# #8#) NIL #19# ELT)) (|sample| #24=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #25=(#17#)) . #26=($)) NIL T ELT) (((|Union| #27=(|Fraction| #28=(|Integer|)) . #25#) . #26#) NIL #29=(|has| |#2| (|RetractableTo| #27#)) ELT) (((|Union| #28# . #25#) . #26#) NIL #30=(|has| |#2| (|RetractableTo| #28#)) ELT) #31=(((|Union| #7# . #25#) . #26#) NIL T ELT)) (|retract| #32=(#33=(|#2| . #34=($)) NIL T ELT) ((#27# . #34#) NIL #29# ELT) ((#28# . #34#) NIL #30# ELT) ((#7# . #34#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #35=(|has| |#2| (|CommutativeRing|)) ELT)) (|reorder| (($ $ (|List| #28#)) NIL T ELT)) (|reductum| #36=(#12# NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #28#) . #38=(#39=(|Matrix| $))) NIL #40=(|has| |#2| (|LinearlyExplicitRingOver| #28#)) ELT) ((#41=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #28#))) . #42=(#39# #43=(|Vector| $))) NIL #40# ELT) ((#44=(|Record| (|:| |mat| #45=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #42#) NIL T ELT) ((#45# . #38#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|primitivePart| #20# #46=(#47=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#2| #50=(|HomogeneousDirectProduct| (|#| |#1|) #14#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#2| #55#)) ELT) ((#56=(|PatternMatchResult| #28# . #53#) $ #57=(|Pattern| #28#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #28#)) (|has| |#2| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#2| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #31#) (|leftReducedSystem| ((#37# . #65=(#43#)) NIL #40# ELT) ((#41# . #66=(#43# $)) NIL #40# ELT) ((#44# . #66#) NIL T ELT) ((#45# . #65#) NIL T ELT)) (|leadingMonomial| #36#) (|leadingCoefficient| #32#) (|lcm| #67=(($ #49#) NIL #21# ELT) #68=(#69=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #17#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #17#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #32#) (|gcdPolynomial| ((#8# #8# #8#) NIL #21# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#16# $ |#2|) NIL #10# ELT) (#15# NIL #10# ELT)) (|eval| (($ $ (|List| #71=(|Equation| $))) NIL T ELT) (($ $ #71#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#2|) NIL T ELT) (($ $ #6# #72=(|List| |#2|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #35# ELT)) (|differentiate| #60# #59# #73=(($ $ #6#) NIL T ELT) #74=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #75=($)) NIL (AND (|has| #7# #76=(|ConvertibleTo| #54#)) (|has| |#2| #76#)) ELT) ((#57# . #75#) NIL (AND (|has| #7# #77=(|ConvertibleTo| #57#)) (|has| |#2| #77#)) ELT) ((#78=(|InputForm|) . #75#) NIL (AND (|has| #7# #79=(|ConvertibleTo| #78#)) (|has| |#2| #79#)) ELT)) (|content| (#33# NIL #21# ELT) #46#) (|conditionP| (((|Union| #43# #17#) #39#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #28#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) (($ #27#) NIL (OR #82=(|has| |#2| (|Algebra| #27#)) #29#) ELT) #11#) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #82# ELT) (($ #27# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) 
(((|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|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) NIL #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) NIL #13=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#14=(|Union| $ #15="failed") $ $) NIL (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#16=(#17=(|NonNegativeInteger|)) NIL #18=(|has| |#2| (|Finite|)) ELT)) (|setelt| #19=(#20=(|#2| $ #10# |#2|) NIL #11# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #22=(#15#)) . #23=($)) NIL #24=(AND (|has| |#2| (|RetractableTo| #10#)) #25=(|has| |#2| (|SetCategory|))) ELT) (((|Union| #26=(|Fraction| #10#) . #22#) . #23#) NIL #27=(AND (|has| |#2| (|RetractableTo| #26#)) #25#) ELT) ((#28=(|Union| |#2| . #22#) . #23#) NIL #25# ELT)) (|retract| (#29=(#10# . #30=($)) NIL #24# ELT) ((#26# . #30#) NIL #27# ELT) (#31=(|#2| . #30#) NIL #25# ELT)) (|reducedSystem| ((#32=(|Matrix| #10#) . #33=(#34=(|Matrix| $))) NIL #35=(AND (|has| |#2| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #10#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#2|)) (|:| |vec| #41=(|Vector| |#2|))) . #37#) NIL #9# ELT) ((#40# . #33#) NIL #9# ELT)) (|reduce| ((|#2| #42=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) NIL #4# ELT) ((|#2| #42# $ |#2|) NIL T ELT) ((|#2| #42# $) NIL T ELT)) (|recip| ((#14# $) NIL #9# ELT)) (|random| (#21# NIL #18# ELT)) (|qsetelt!| #19#) (|qelt| (#43=(|#2| $ #10#) 11 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| #44=(#29# NIL #45=(|has| #10# #46=(|OrderedSet|)) ELT)) (|min| #47=(#12# NIL #48=(|has| |#2| #46#) ELT)) (|members| #49=((#50=(|List| |#2|) $) NIL T ELT)) (|member?| (#51=(#3# |#2| $) NIL #4# ELT)) (|maxIndex| #44#) (|max| #47#) (|map| (($ #52=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #18# ELT)) (|leftReducedSystem| ((#32# . #53=(#38#)) NIL #35# ELT) ((#36# . #54=(#38# $)) NIL #35# ELT) ((#39# . #54#) NIL #9# ELT) ((#40# . #53#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #25# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #18# ELT)) (|hash| (((|SingleInteger|) $) NIL #25# ELT)) (|first| (#31# NIL #45# ELT)) (|find| ((#28# #55=(|Mapping| #3# |#2|) $) NIL T ELT)) (|fill!| (#56=($ $ |#2|) NIL #11# ELT)) (|every?| #57=((#3# #55# $) NIL T ELT)) (|eval| (($ $ (|List| #58=(|Equation| |#2|))) NIL #59=(AND (|has| |#2| (|Evalable| |#2|)) #25#) ELT) (($ $ #58#) NIL #59# ELT) (($ $ |#2| |#2|) NIL #59# ELT) (($ $ #50# #50#) NIL #59# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#51# NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #4#) ELT)) (|entries| #49#) (|empty?| (#5# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#20# NIL T ELT) (#43# NIL T ELT)) (|dot| ((|#2| $ $) NIL #9# ELT)) (|directProduct| (($ #41#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #60=(|has| |#2| (|Field|)) ELT)) (|differentiate| #61=(#62=($ $ #17#) NIL #63=(AND (|has| |#2| (|DifferentialSpace|)) #9#) ELT) #64=(#65=($ $) NIL #63# ELT) #66=(($ $ #67=(|List| #68=(|Symbol|)) (|List| #17#)) NIL #69=(AND (|has| |#2| (|PartialDifferentialSpace| #68#)) #9#) ELT) #70=(($ $ #68# #17#) NIL #69# ELT) #71=(($ $ #67#) NIL #69# ELT) #72=(($ $ #68#) NIL #69# ELT) #73=(($ $ #52#) NIL #9# ELT) #74=(($ $ #52# #17#) NIL #9# ELT)) (|count| ((#17# |#2| $) NIL #4# ELT) ((#17# #55# $) NIL T ELT)) (|copy| (#65# NIL T ELT)) (|coerce| ((#41# . #75=($)) NIL T ELT) (($ #10#) NIL (OR #24# #9#) ELT) (($ #26#) NIL #27# ELT) (($ |#2|) NIL #25# ELT) ((#76=(|OutputForm|) . #75#) NIL (|has| |#2| (|CoercibleTo| #76#)) ELT)) (|characteristic| (#16# NIL #9# CONST)) (|before?| #1#) (|any?| #57#) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#21# NIL #6# CONST)) (|One| (#21# NIL #9# CONST)) (D #61# #64# #66# #70# #71# #72# #73# #74#) (>= #77=(#2# NIL #48# ELT)) (> #77#) (= #1#) (<= #77#) (< (#2# 17 #48# ELT)) (/ (#56# NIL #60# ELT)) (- (#12# NIL #78=(|has| |#2| (|AbelianGroup|)) ELT) (#65# NIL #78# ELT)) (+ (#12# NIL #79=(|has| |#2| (|AbelianSemiGroup|)) ELT)) (** (#62# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# NIL #9# ELT) (#56# NIL #80=(|has| |#2| (|Monoid|)) ELT) (($ |#2| . #81=($)) NIL #80# ELT) (($ #10# . #81#) NIL #78# ELT) (($ #17# $) NIL #6# ELT) (($ #8# $) NIL #79# ELT)) (|#| ((#17# $) NIL T ELT))) 
(((|HomogeneousDirectProduct| |#1| |#2|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|OrderedAbelianMonoidSup|)) (T |HomogeneousDirectProduct|)) 
NIL 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|parameters| ((#2=(|List| (|ParameterAst|)) $) 16 T ELT)) (|name| ((#3=(|Identifier|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|headAst| (($ #3# #2#) 12 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 23 T ELT) (($ #4=(|Syntax|)) NIL T ELT) ((#4# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|HeadAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |headAst| ($ #1=(|Identifier|) #2=(|List| (|ParameterAst|)))) (SIGNATURE |name| (#1# $)) (SIGNATURE |parameters| (#2# $))))) (T |HeadAst|)) 
((|headAst| (*1 *1 *2 *3) (AND #1=(|isDomain| *2 (|Identifier|)) (|isDomain| *3 #2=(|List| (|ParameterAst|))) #3=(|isDomain| *1 (|HeadAst|)))) (|name| #4=(*1 *2 *1) (AND #1# #3#)) (|parameters| #4# (AND (|isDomain| *2 #2#) #3#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|sample| (#5=($) NIL T CONST)) (|reduce| ((|#1| #6=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #6# $ |#1|) NIL T ELT) ((|#1| #6# $) NIL T ELT)) (|merge!| (#7=($ $ $) 48 T ELT)) (|merge| (#7# 47 T ELT)) (|members| ((#8=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|max| (#9=(|#1| $) 40 T ELT)) (|map!| #10=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #10#) (|latex| (((|String|) $) NIL #11=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#9# 41 T ELT)) (|insert!| (($ |#1| $) 18 T ELT)) (|heap| (#12=($ #8#) 19 T ELT)) (|hash| (((|SingleInteger|) $) NIL #11# ELT)) (|find| (((|Union| |#1| "failed") #13=(|Mapping| #3# |#1|) $) NIL T ELT)) (|extract!| (#9# 34 T ELT)) (|every?| #14=((#3# #13# $) NIL T ELT)) (|eval| (($ $ (|List| #15=(|Equation| |#1|))) NIL #16=(AND (|has| |#1| (|Evalable| |#1|)) #11#) ELT) (($ $ #15#) NIL #16# ELT) (($ $ |#1| |#1|) NIL #16# ELT) (($ $ #8# #8#) NIL #16# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| (#5# 11 T ELT)) (|count| ((#17=(|NonNegativeInteger|) |#1| $) NIL #4# ELT) ((#17# #13# $) NIL T ELT)) (|copy| (($ $) NIL T ELT)) (|coerce| ((#18=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #18#)) ELT)) (|before?| #1#) (|bag| (#12# 45 T ELT)) (|any?| #14#) (= #1#) (|#| ((#17# $) 29 T ELT))) 
(((|Heap| |#1|) (|Join| (|PriorityQueueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |heap| ($ (|List| |#1|))))) (|OrderedSet|)) (T |Heap|)) 
((|heap| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|Heap| *3))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|reduce| (#7=($ $) 71 T ELT)) (|principal?| #4#) (|opposite?| #1#) (|latex| (((|String|) $) NIL T ELT)) (|ideal| ((#8=(|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 45 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (((|Union| |#4| #5#) $) 117 T ELT)) (|divisor| (($ #8#) 80 T ELT) (($ |#4|) 31 T ELT) (($ |#1| |#1|) 127 T ELT) (($ |#1| |#1| #9=(|Integer|)) NIL T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 140 T ELT)) (|decompose| (((|Record| (|:| |id| #8#) (|:| |principalPart| |#4|)) $) 47 T ELT)) (|coerce| (((|OutputForm|) $) 110 T ELT)) (|before?| #1#) (|Zero| (#6# 32 T CONST)) (= (#2# 121 T ELT)) (- (#7# 76 T ELT) (#10=($ $ $) NIL T ELT)) (+ (#10# 72 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #9# $) 77 T ELT))) 
(((|HyperellipticFiniteDivisor| |#1| |#2| |#3| |#4|) (|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |HyperellipticFiniteDivisor|)) 
NIL 
((|lintgcd| ((#1=(|Integer|) #2=(|List| #1#)) 53 T ELT)) (|gcdprim| (#3=(|#1| #4=(|List| |#1|)) 94 T ELT)) (|gcdcofactprim| (#5=(#4# #4#) 95 T ELT)) (|gcdcofact| (#5# 97 T ELT)) (|gcd| (#3# 96 T ELT)) (|content| ((#2# #4#) 56 T ELT))) 
(((|HeuGcd| |#1|) (CATEGORY |package| (SIGNATURE |gcd| #1=(|#1| #2=(|List| |#1|))) (SIGNATURE |gcdprim| #1#) (SIGNATURE |gcdcofact| #3=(#2# #2#)) (SIGNATURE |gcdcofactprim| #3#) (SIGNATURE |content| (#4=(|List| #5=(|Integer|)) #2#)) (SIGNATURE |lintgcd| (#5# #4#))) (|UnivariatePolynomialCategory| #5#)) (T |HeuGcd|)) 
((|lintgcd| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|List| #3=(|Integer|))) (|isDomain| *2 #3#) #4=(|isDomain| *1 (|HeuGcd| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)))) (|content| #1# (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #5=(|UnivariatePolynomialCategory| #3#)) (|isDomain| *2 #2#) #4#)) (|gcdcofactprim| #6=(*1 *2 *2) #7=(AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 #5#) (|isDomain| *1 (|HeuGcd| *3)))) (|gcdcofact| #6# #7#) (|gcdprim| #1# #8=(AND (|isDomain| *3 (|List| *2)) (|isDomain| *1 (|HeuGcd| *2)) (|ofCategory| *2 #5#))) (|gcd| #1# #8#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#6# NIL #19=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (#22=((|Union| #7# . #23=(#13#)) . #24=($)) NIL T ELT) (((|Union| #25=(|Symbol|) . #23#) . #24#) NIL #26=(|has| #7# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #7#) . #23#) . #24#) NIL #28=(|has| #7# (|RetractableTo| #7#)) ELT) (#22# NIL #28# ELT)) (|retract| #29=(#6# NIL T ELT) ((#25# $) NIL #26# ELT) (#30=(#27# $) NIL #28# ELT) (#6# NIL #28# ELT)) (|rem| #31=(#32=($ $ $) NIL T ELT)) (|reducedSystem| (#33=(#34=(|Matrix| #7#) #35=(|Matrix| $)) NIL #36=(|has| #7# (|LinearlyExplicitRingOver| #7#)) ELT) (#37=(#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #7#))) #35# #39=(|Vector| $)) NIL #36# ELT) (#37# NIL T ELT) (#33# NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#21# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #31#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #19# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #29#) (|nextItem| (#50=((|Maybe| $) $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #13#) #41# $) NIL T ELT)) (|min| #52=(#32# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#34# #39#) NIL #36# ELT) (#56=(#38# #39# $) NIL #36# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #31# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#21# NIL #51# CONST)) (|hex| (#58=($ #27#) 9 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #31# #57#) (|fractionPart| (#10# NIL #8# ELT) #59=(#30# NIL T ELT)) (|floor| #60=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #61=(|:| |coef1| $) #62=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #61# #62#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #63=(|List| #7#) #63#) NIL #64=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #64# ELT) (($ $ #65=(|Equation| #7#)) NIL #64# ELT) (($ $ (|List| #65#)) NIL #64# ELT) (($ $ #66=(|List| #25#) #63#) NIL #67=(|has| #7# (|InnerEvalable| #25# #7#)) ELT) (($ $ #25# #7#) NIL #67# ELT)) (|euclideanSize| ((#68=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#69=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #70=(($ $ #54#) NIL T ELT) #71=(($ $ #54# #68#) NIL T ELT) #72=(($ $ #25#) NIL #73=(|has| #7# (|PartialDifferentialSpace| #25#)) ELT) #74=(($ $ #66#) NIL #73# ELT) #75=(($ $ #25# #68#) NIL #73# ELT) #76=(($ $ #66# (|List| #68#)) NIL #73# ELT) #77=(#10# NIL #78=(|has| #7# (|DifferentialSpace|)) ELT) #79=(#80=($ $ #68#) NIL #78# ELT)) (|denominator| #9#) (|denom| #29#) (|convert| ((#46# . #81=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #81#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#82=(|InputForm|) . #81#) NIL (|has| #7# (|ConvertibleTo| #82#)) ELT) ((#48# . #81#) NIL #83=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #81#) NIL #83# ELT)) (|conditionP| (((|Union| #39# #13#) #35#) NIL #84=(AND (|has| $ #85=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #86=(($ #7#) NIL T ELT) #9# (#58# 8 T ELT) #86# (($ #25#) NIL #26# ELT) #59# (((|RadixExpansion| 16) $) 10 T ELT)) (|charthRoot| (#50# NIL (OR #84# (|has| #7# #85#)) ELT)) (|characteristic| ((#68#) NIL T CONST)) (|ceiling| #60#) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#10# NIL #19# ELT)) (|Zero| #20#) (|One| #20#) (D #70# #71# #72# #74# #75# #76# #77# #79#) (>= #87=(#2# NIL #53# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ #31# (($ #7# #7#) NIL T ELT)) (- #9# #31#) (+ #31#) (** (($ $ #88=(|PositiveInteger|)) NIL T ELT) (#80# NIL T ELT) #89=(#69# NIL T ELT)) (* (($ #88# $) NIL T ELT) (($ #68# $) NIL T ELT) #90=(($ #7# . #91=($)) NIL T ELT) #31# (($ $ #27#) NIL T ELT) (($ #27# . #91#) NIL T ELT) #90# #89#)) 
(((|HexadecimalExpansion|) (|Join| (|QuotientFieldCategory| #1=(|Integer|)) (|CoercibleTo| #2=(|Fraction| #1#)) (|CoercibleTo| (|RadixExpansion| 16)) (CATEGORY |domain| (SIGNATURE |fractionPart| (#2# $)) (SIGNATURE |hex| ($ #2#))))) (T |HexadecimalExpansion|)) 
((|fractionPart| (*1 *2 *1) #1=(AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|HexadecimalExpansion|)))) (|hex| (*1 *1 *2) #1#)) 
((|eval| (($ $ (|List| #1=(|Equation| |#2|))) 13 T ELT) (($ $ #1#) NIL T ELT) (($ $ |#2| |#2|) NIL T ELT) (($ $ #2=(|List| |#2|) #2#) NIL T ELT))) 
(((|HomogeneousAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |eval| (|#1| |#1| #1=(|List| |#2|) #1#)) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| #2=(|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|List| #2#)))) (|HomogeneousAggregate| |#2|) (|Type|)) (T |HomogeneousAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|sample| (#3=($) 6 T CONST)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #4=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #4#) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #5=((|SetCategory|)))) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #5#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #5#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #5#)) ELT)) (|eq?| ((#6=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#6# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|HomogeneousAggregate| |#1|) (|Category|) (|Type|)) (T |HomogeneousAggregate|)) 
NIL 
(|Join| (|Aggregate|) (|Functorial| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|CoercibleTo| (|OutputForm|))) (ATTRIBUTE (|CoercibleTo| (|OutputForm|))) |%noBranch|) (IF (|has| |t#1| (|BasicType|)) (ATTRIBUTE (|BasicType|)) |%noBranch|) (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|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|coerce| ((|#1| $) 6 T ELT) (($ |#1|) 9 T ELT))) 
(((|HomotopicTo| |#1|) (|Category|) (|Type|)) (T |HomotopicTo|)) 
NIL 
(|Join| (|CoercibleTo| |t#1|) (|CoercibleFrom| |t#1|)) 
(((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| |#1|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (#3=(#4=(|String|) $) NIL T ELT)) (|host| (($ #4#) 8 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 15 T ELT) (#3# 12 T ELT)) (|before?| #1#) (= (#2# 11 T ELT))) 
(((|Hostname|) (|Join| (|SetCategory|) (|CoercibleTo| #1=(|String|)) (CATEGORY |domain| (SIGNATURE |host| ($ #1#))))) (T |Hostname|)) 
((|host| (*1 *1 *2) (AND (|isDomain| *2 (|String|)) (|isDomain| *1 (|Hostname|))))) 
((|tanh| (#1=($ $) 15 T ELT)) (|sinh| (#1# 24 T ELT)) (|sech| (#1# 12 T ELT)) (|csch| (#1# 10 T ELT)) (|coth| (#1# 17 T ELT)) (|cosh| (#1# 22 T ELT))) 
(((|HyperbolicFunctionCategory&| |#1|) (CATEGORY |package| (SIGNATURE |cosh| #1=(|#1| |#1|)) (SIGNATURE |coth| #1#) (SIGNATURE |csch| #1#) (SIGNATURE |sech| #1#) (SIGNATURE |sinh| #1#) (SIGNATURE |tanh| #1#)) (|HyperbolicFunctionCategory|)) (T |HyperbolicFunctionCategory&|)) 
NIL 
((|tanh| (($ $) 11 T ELT)) (|sinh| (($ $) 10 T ELT)) (|sech| (($ $) 9 T ELT)) (|csch| (($ $) 8 T ELT)) (|coth| (($ $) 7 T ELT)) (|cosh| (($ $) 6 T ELT))) 
(((|HyperbolicFunctionCategory|) (|Category|)) (T |HyperbolicFunctionCategory|)) 
((|tanh| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|sinh| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|sech| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|csch| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|coth| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|cosh| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |cosh| ($ $)) (SIGNATURE |coth| ($ $)) (SIGNATURE |csch| ($ $)) (SIGNATURE |sech| ($ $)) (SIGNATURE |sinh| ($ $)) (SIGNATURE |tanh| ($ $)))) 
((|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) 54 T ELT))) 
(((|InnerAlgFactor| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)))) #1=(|Field|) (|UnivariatePolynomialCategory| |#1|) (|Join| #1# (|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 #1=(|Field|)) (|ofCategory| *7 (|Join| #1# (|CharacteristicZero|) (|MonogenicAlgebra| *5 *6))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|InnerAlgFactor| *5 *6 *7 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *7))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zerosOf| #4=((#5=(|List| $) #6=(|SparseUnivariatePolynomial| $) #7=(|Symbol|)) NIL T ELT) #8=((#5# #6#) NIL T ELT) #9=((#5# #10=(|Polynomial| $)) NIL T ELT)) (|zeroOf| #11=(($ #6# #7#) NIL T ELT) #12=(($ #6#) NIL T ELT) #13=(($ #10#) NIL T ELT)) (|zero?| (#14=(#3# $) 39 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #15=(#16=($ $) NIL T ELT)) (|unit?| #17=(#14# NIL T ELT)) (|trueEqual| (#2# 72 T ELT)) (|tower| (#18=(#19=(|List| #20=(|Kernel| $)) $) 49 T ELT)) (|subtractIfCan| #21=((#22=(|Union| $ #23="failed") $ $) NIL T ELT)) (|subst| #24=(($ $ #25=(|Equation| $)) NIL T ELT) #26=(($ $ (|List| #25#)) NIL T ELT) #27=(($ $ #19# #5#) NIL T ELT)) (|squareFreePart| #15#) (|squareFree| #28=(((|Factored| $) $) NIL T ELT)) (|sqrt| #15#) (|sizeLess?| #1#) (|sample| (#29=($) NIL T CONST)) (|rootsOf| #4# #8# #9#) (|rootOf| #11# #12# #13#) (|retractIfCan| #30=(((|Union| #20# . #31=(#23#)) . #32=($)) NIL T ELT) (((|Union| #33=(|Integer|) . #31#) . #32#) NIL T ELT) (((|Union| #34=(|Fraction| #33#) . #31#) . #32#) NIL T ELT)) (|retract| ((#20# . #35=($)) NIL T ELT) ((#33# . #35#) NIL T ELT) ((#34# . #35#) 54 T ELT)) (|rem| #36=(#37=($ $ $) NIL T ELT)) (|reducedSystem| ((#38=(|Record| (|:| |mat| #39=(|Matrix| #33#)) (|:| |vec| (|Vector| #33#))) . #40=(#41=(|Matrix| $) #42=(|Vector| $))) NIL T ELT) ((#39# . #43=(#41#)) NIL T ELT) ((#44=(|Record| (|:| |mat| #45=(|Matrix| #34#)) (|:| |vec| (|Vector| #34#))) . #40#) NIL T ELT) ((#45# . #43#) NIL T ELT)) (|reduce| #15#) (|recip| ((#22# $) NIL T ELT)) (|quo| #36#) (|principalIdeal| (((|Record| (|:| |coef| #5#) #46=(|:| |generator| $)) #5#) NIL T ELT)) (|prime?| #17#) (|paren| #15# #47=(($ #5#) NIL T ELT)) (|opposite?| #1#) (|operators| ((#48=(|List| #49=(|BasicOperator|)) $) NIL T ELT)) (|operator| ((#49# #49#) NIL T ELT)) (|one?| (#14# 42 T ELT)) (|odd?| #50=(#14# NIL (|has| $ (|RetractableTo| #33#)) ELT)) (|numer| (#51=(#52=(|SparseMultivariatePolynomial| #33# #20#) $) 37 T ELT)) (|nthRoot| (#53=($ $ #33#) NIL T ELT)) (|norm| ((#6# #6# #20#) 86 T ELT) ((#6# #6# #19#) 61 T ELT) (($ $ #20#) 75 T ELT) (($ $ #19#) 76 T ELT)) (|multiEuclidean| (((|Union| #5# #23#) #5# $) NIL T ELT)) (|minPoly| ((#6# #20#) 73 #54=(|has| $ (|Ring|)) ELT)) (|map| (($ #55=(|Mapping| $ $) #20#) NIL T ELT)) (|mainKernel| #30#) (|leftReducedSystem| ((#38# . #56=(#42# $)) NIL T ELT) ((#39# . #57=(#42#)) NIL T ELT) ((#44# . #56#) NIL T ELT) ((#45# . #57#) NIL T ELT)) (|lcm| #47# #36#) (|latex| (((|String|) $) NIL T ELT)) (|kernels| (#18# NIL T ELT)) (|kernel| #58=(($ #49# $) NIL T ELT) #59=(($ #49# #5#) NIL T ELT)) (|is?| ((#3# $ #49#) NIL T ELT) #60=((#3# $ #7#) NIL T ELT)) (|inv| #15#) (|height| #61=((#62=(|NonNegativeInteger|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#6# #6# #6#) NIL T ELT)) (|gcd| #47# #36#) (|freeOf?| #1# #60#) (|factor| #28#) (|extendedEuclidean| (((|Union| (|Record| #63=(|:| |coef1| $) #64=(|:| |coef2| $)) #23#) $ $ $) NIL T ELT) (((|Record| #63# #64# #46#) $ $) NIL T ELT)) (|exquo| #21#) (|expressIdealMember| (((|Maybe| #5#) #5# $) NIL T ELT)) (|even?| #50#) (|eval| (($ $ #20# $) NIL T ELT) #27# #26# #24# (($ $ $ $) NIL T ELT) (($ $ #5# #5#) NIL T ELT) (($ $ #65=(|List| #7#) #66=(|List| #55#)) NIL T ELT) (($ $ #65# #67=(|List| #68=(|Mapping| $ #5#))) NIL T ELT) (($ $ #7# #68#) NIL T ELT) (($ $ #7# #55#) NIL T ELT) (($ $ #48# #66#) NIL T ELT) (($ $ #48# #67#) NIL T ELT) (($ $ #49# #68#) NIL T ELT) (($ $ #49# #55#) NIL T ELT)) (|euclideanSize| #61#) (|elt| #58# (($ #49# $ $) NIL T ELT) (($ #49# $ $ $) NIL T ELT) (($ #49# $ $ $ $) NIL T ELT) #59#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|distribute| #15# #36#) (|differentiate| (#16# 36 T ELT) #69=(($ $ #62#) NIL T ELT)) (|denom| (#51# 20 T ELT)) (|definingPolynomial| (#16# NIL #54# ELT)) (|convert| ((#70=(|Float|) $) 100 T ELT) (((|DoubleFloat|) $) 108 T ELT) (((|Complex| #70#) $) 116 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) (($ #34#) NIL T ELT) #15# (($ #33#) NIL T ELT) (($ #52#) 21 T ELT)) (|characteristic| ((#62#) NIL T CONST)) (|box| #15# #47#) (|belong?| ((#3# #49#) 92 T ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#29# 10 T CONST)) (|One| (#29# 22 T CONST)) (D #15# #69#) (= (#2# 24 T ELT)) (/ (#37# 44 T ELT)) (- #36# #15#) (+ #36#) (** #71=(($ $ #34#) NIL T ELT) (#53# 47 T ELT) #69# (($ $ #72=(|PositiveInteger|)) NIL T ELT)) (* (($ #34# . #73=($)) NIL T ELT) #71# (#37# 27 T ELT) (($ #33# . #73#) NIL T ELT) (($ #62# $) NIL T ELT) (($ #72# $) NIL T ELT))) 
(((|InnerAlgebraicNumber|) (|Join| (|ExpressionSpace|) (|AlgebraicallyClosedField|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| #2=(|Fraction| #1#)) (|LinearlyExplicitRingOver| #1#) (|RealConstant|) (|LinearlyExplicitRingOver| #2#) (|CharacteristicZero|) (|ConvertibleTo| (|Complex| (|Float|))) (|DifferentialRing|) (|CoercibleFrom| #3=(|SparseMultivariatePolynomial| #1# #4=(|Kernel| $))) (CATEGORY |domain| (SIGNATURE |numer| #5=(#3# $)) (SIGNATURE |denom| #5#) (SIGNATURE |reduce| ($ $)) (SIGNATURE |trueEqual| ((|Boolean|) $ $)) (SIGNATURE |norm| (#6=(|SparseUnivariatePolynomial| $) #6# #4#)) (SIGNATURE |norm| (#6# #6# #7=(|List| #4#))) (SIGNATURE |norm| ($ $ #4#)) (SIGNATURE |norm| ($ $ #7#))))) (T |InnerAlgebraicNumber|)) 
((|numer| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) #3=(|Kernel| #4=(|InnerAlgebraicNumber|)))) #5=(|isDomain| *1 #4#))) (|denom| #1# #2#) (|reduce| (*1 *1 *1) #5#) (|trueEqual| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) #5#)) (|norm| #6=(*1 *2 *2 *3) (AND #7=(|isDomain| *2 (|SparseUnivariatePolynomial| #4#)) (|isDomain| *3 #3#) #5#)) (|norm| #6# (AND #7# (|isDomain| *3 #8=(|List| #3#)) #5#)) (|norm| #9=(*1 *1 *1 *2) (AND (|isDomain| *2 #3#) #5#)) (|norm| #9# (AND (|isDomain| *2 #8#) #5#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) NIL #6=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #7=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#8=(#3# $) NIL #9=(|has| |#1| #10=(|OrderedSet|)) ELT)) (|sort!| (#11=($ #7# $) NIL #6# ELT) (#12=($ $) NIL (AND #6# #9#) ELT)) (|sort| (#11# NIL T ELT) (#12# NIL #9# ELT)) (|setelt| (#13=(|#1| $ #5# |#1|) 19 #6# ELT) ((|#1| $ #14=(|UniversalSegment| #5#) |#1|) NIL #6# ELT)) (|select| #15=(($ #16=(|Mapping| #3# |#1|) $) NIL #17=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#18=($) NIL T CONST)) (|reverse!| (#12# NIL #6# ELT)) (|reverse| #19=(#12# NIL T ELT)) (|removeDuplicates| (#12# NIL #20=(AND #17# #4#) ELT)) (|remove| (#21=($ |#1| $) NIL #20# ELT) #15#) (|reduce| ((|#1| #22=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #22# $ |#1|) NIL T ELT) ((|#1| #22# $) NIL T ELT)) (|qsetelt!| (#13# 14 #6# ELT)) (|qelt| (#23=(|#1| $ #5#) 13 T ELT)) (|position| ((#5# #16# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT) ((#5# |#1| $ #5#) NIL #4# ELT)) (|new| (($ #24=(|NonNegativeInteger|) |#1|) NIL T ELT)) (|minIndex| (#25=(#5# $) 9 #26=(|has| #5# #10#) ELT)) (|min| #27=(#28=($ $ $) NIL #9# ELT)) (|merge| (($ #7# $ $) NIL T ELT) #27#) (|members| #29=((#30=(|List| |#1|) $) NIL T ELT)) (|member?| (#31=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| (#25# 16 #26# ELT)) (|max| #27#) (|map!| #32=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #32# (($ #22# $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #33=(|has| |#1| (|SetCategory|)) ELT)) (|insert| (($ |#1| $ #5#) NIL T ELT) (#34=($ $ $ #5#) NIL T ELT)) (|indices| (((|List| #5#) $) NIL T ELT)) (|index?| ((#3# #5# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #33# ELT)) (|first| ((|#1| $) NIL #26# ELT)) (|find| (((|Union| |#1| "failed") #16# $) NIL T ELT)) (|fill!| (#35=($ $ |#1|) NIL #6# ELT)) (|every?| #36=((#3# #16# $) NIL T ELT)) (|eval| (($ $ (|List| #37=(|Equation| |#1|))) NIL #38=(AND (|has| |#1| (|Evalable| |#1|)) #33#) ELT) (($ $ #37#) NIL #38# ELT) (($ $ |#1| |#1|) NIL #38# ELT) (($ $ #30# #30#) NIL #38# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#31# NIL #20# ELT)) (|entries| #29#) (|empty?| (#8# NIL T ELT)) (|empty| (#18# NIL T ELT)) (|elt| (#13# NIL T ELT) (#23# 18 T ELT) #39=(($ $ #14#) NIL T ELT)) (|delete| (($ $ #5#) NIL T ELT) #39#) (|count| ((#24# |#1| $) NIL #4# ELT) ((#24# #16# $) NIL T ELT)) (|copyInto!| (#34# NIL #6# ELT)) (|copy| #19#) (|convert| ((#40=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #40#)) ELT)) (|construct| (($ #30#) NIL T ELT)) (|concat| (#35# NIL T ELT) (#21# NIL T ELT) (#28# NIL T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#41=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #41#)) ELT)) (|before?| #1#) (|any?| #36#) (>= #42=(#2# NIL #9# ELT)) (> #42#) (= #1#) (<= #42#) (< #42#) (|#| ((#24# $) NIL T ELT))) 
(((|IndexedOneDimensionalArray| |#1| |#2|) (|OneDimensionalArrayAggregate| |#1|) (|Type|) (|Integer|)) (T |IndexedOneDimensionalArray|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|setelt| (#5=(|#1| $ #6=(|Integer|) #6# |#1|) 44 T ELT)) (|setRow!| (($ $ #6# |#2|) NIL T ELT)) (|setColumn!| (($ $ #6# |#3|) NIL T ELT)) (|sample| (#7=($) NIL T CONST)) (|row| ((|#2| $ #6#) 53 T ELT)) (|reduce| ((|#1| #8=(|Mapping| |#1| |#1| |#1|) $) NIL T ELT) ((|#1| #8# $ |#1|) NIL T ELT) ((|#1| #8# $ |#1| |#1|) NIL #4# ELT)) (|qsetelt!| (#5# 43 T ELT)) (|qelt| (#9=(|#1| $ #6# #6#) 38 T ELT)) (|nrows| (#10=(#11=(|NonNegativeInteger|) $) 28 T ELT)) (|new| (($ #11# #11# |#1|) 24 T ELT)) (|ncols| (#10# 30 T ELT)) (|minRowIndex| (#12=(#6# $) 26 T ELT)) (|minColIndex| (#12# 27 T ELT)) (|members| ((#13=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|maxRowIndex| (#12# 29 T ELT)) (|maxColIndex| (#12# 31 T ELT)) (|map!| (#14=($ (|Mapping| |#1| |#1|) $) 66 T ELT)) (|map| (#14# 64 T ELT) (($ #8# $ $) 70 T ELT) (($ #8# $ $ |#1|) 74 T ELT)) (|latex| (((|String|) $) 48 #15=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) NIL #15# ELT)) (|find| (((|Union| |#1| "failed") #16=(|Mapping| #3# |#1|) $) NIL T ELT)) (|fill!| (($ $ |#1|) 61 T ELT)) (|every?| #17=((#3# #16# $) NIL T ELT)) (|eval| (($ $ (|List| #18=(|Equation| |#1|))) NIL #19=(AND (|has| |#1| (|Evalable| |#1|)) #15#) ELT) (($ $ #18#) NIL #19# ELT) (($ $ |#1| |#1|) NIL #19# ELT) (($ $ #13# #13#) NIL #19# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| ((#3# $) 33 T ELT)) (|empty| (#7# NIL T ELT)) (|elt| (#9# 41 T ELT) (#5# 72 T ELT)) (|count| ((#11# #16# $) NIL T ELT) ((#11# |#1| $) NIL #4# ELT)) (|copy| (($ $) 59 T ELT)) (|column| ((|#3| $ #6#) 55 T ELT)) (|coerce| ((#20=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #20#)) ELT)) (|before?| #1#) (|any?| #17#) (= #1#) (|#| (#10# NIL T ELT))) 
(((|InnerTwoDimensionalArray| |#1| |#2| |#3|) (|TwoDimensionalArrayCategory| |#1| |#2| |#3|) (|Type|) #1=(|FiniteLinearAggregate| |#1|) #1#) (T |InnerTwoDimensionalArray|)) 
NIL 
((|listConjugateBases| ((#1=(|List| #2=(|Record| (|:| |basis| #3=(|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| #3#))) #2# #4=(|NonNegativeInteger|) #4#) 32 T ELT)) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| #4# #4# #4#) 43 T ELT)) (|chineseRemainder| ((#2# (|List| |#3|) #1# #4#) 107 T ELT))) 
(((|ChineseRemainderToolsForIntegralBases| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |factorList| ((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| #1=(|NonNegativeInteger|) #1# #1#)) (SIGNATURE |listConjugateBases| (#2=(|List| #3=(|Record| (|:| |basis| #4=(|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| #4#))) #3# #1# #1#)) (SIGNATURE |chineseRemainder| (#3# (|List| |#3|) #2# #1#))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |ChineseRemainderToolsForIntegralBases|)) 
((|chineseRemainder| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| #1=(|Record| (|:| |basis| #2=(|Matrix| *7)) (|:| |basisDen| *7) (|:| |basisInv| #2#)))) (|isDomain| *5 #3=(|NonNegativeInteger|)) (|ofCategory| *8 (|UnivariatePolynomialCategory| *7)) #4=(|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *6 #5=(|FiniteFieldCategory|)) (|isDomain| *2 #1#) (|isDomain| *1 (|ChineseRemainderToolsForIntegralBases| *6 *7 *8)))) (|listConjugateBases| (*1 *2 *3 *4 *4) (AND #6=(|isDomain| *4 #3#) (|ofCategory| *5 #5#) #7=(|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| #8=(|Record| (|:| |basis| #9=(|Matrix| *6)) (|:| |basisDen| *6) (|:| |basisInv| #9#)))) (|isDomain| *1 (|ChineseRemainderToolsForIntegralBases| *5 *6 *7)) (|isDomain| *3 #8#) #4#)) (|factorList| (*1 *2 *3 *4 *4 *4) (AND #6# (|ofCategory| *3 #5#) (|ofCategory| *5 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *3))) (|isDomain| *1 (|ChineseRemainderToolsForIntegralBases| *3 *5 *6)) #7#))) 
((|moduleSum| ((#1=(|Record| (|:| |basis| #2=(|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| #2#)) #1# #1#) 70 T ELT)) (|matrixGcd| ((|#1| #2# |#1| #3=(|NonNegativeInteger|)) 24 T ELT)) (|leastPower| ((#3# #3# #3#) 34 T ELT)) (|idealiserMatrix| (#4=(#2# #2# #2#) 50 T ELT)) (|idealiser| ((#2# #2# #2# |#1|) 58 T ELT) (#4# 55 T ELT)) (|divideIfCan!| ((|#1| #2# #2# |#1| (|Integer|)) 28 T ELT)) (|diagonalProduct| ((|#1| #2#) 18 T ELT))) 
(((|IntegralBasisTools| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |diagonalProduct| (|#1| #1=(|Matrix| |#1|))) (SIGNATURE |matrixGcd| (|#1| #1# |#1| #2=(|NonNegativeInteger|))) (SIGNATURE |divideIfCan!| (|#1| #1# #1# |#1| (|Integer|))) (SIGNATURE |leastPower| (#2# #2# #2#)) (SIGNATURE |idealiser| #3=(#1# #1# #1#)) (SIGNATURE |idealiser| (#1# #1# #1# |#1|)) (SIGNATURE |idealiserMatrix| #3#) (SIGNATURE |moduleSum| (#4=(|Record| (|:| |basis| #1#) (|:| |basisDen| |#1|) (|:| |basisInv| #1#)) #4# #4#))) (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $)))) (|UnivariatePolynomialCategory| |#1|) (|FramedAlgebra| |#1| |#2|)) (T |IntegralBasisTools|)) 
((|moduleSum| #1=(*1 *2 *2 *2) (AND (|isDomain| *2 (|Record| (|:| |basis| #2=(|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| #2#))) #3=(|ofCategory| *3 #4=(|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) #5=(|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) #6=(|isDomain| *1 (|IntegralBasisTools| *3 *4 *5)) #7=(|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|idealiserMatrix| #1# #8=(AND (|isDomain| *2 #2#) #3# #5# #6# #7#)) (|idealiser| (*1 *2 *2 *2 *3) #8#) (|idealiser| #1# #8#) (|leastPower| #1# (AND (|isDomain| *2 #9=(|NonNegativeInteger|)) #3# #5# #6# #7#)) (|divideIfCan!| (*1 *2 *3 *3 *2 *4) (AND #10=(|isDomain| *3 (|Matrix| *2)) (|isDomain| *4 (|Integer|)) #11=(|ofCategory| *2 #4#) #12=(|ofCategory| *5 #13=(|UnivariatePolynomialCategory| *2)) #14=(|isDomain| *1 (|IntegralBasisTools| *2 *5 *6)) #15=(|ofCategory| *6 (|FramedAlgebra| *2 *5)))) (|matrixGcd| (*1 *2 *3 *2 *4) (AND #10# (|isDomain| *4 #9#) #11# #12# #14# #15#)) (|diagonalProduct| (*1 *2 *3) (AND #10# (|ofCategory| *4 #13#) #11# (|isDomain| *1 (|IntegralBasisTools| *2 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *2 *4))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (~ (#4=($ $) 53 T ELT)) (|xor| (#5=($ $ $) 51 T ELT)) (|swap!| (((|Void|) $ #6=(|Integer|) #6#) NIL #7=(|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|sorted?| (#8=(#3# $) NIL #9=(|has| #3# #10=(|OrderedSet|)) ELT) #11=((#3# #12=(|Mapping| #3# #3# #3#) $) NIL T ELT)) (|sort!| (#4# NIL (AND #7# #9#) ELT) (#13=($ #12# $) NIL #7# ELT)) (|sort| (#4# NIL #9# ELT) (#13# NIL T ELT)) (|setelt| ((#3# $ #14=(|UniversalSegment| #6#) #3#) NIL #7# ELT) (#15=(#3# $ #6# #3#) 52 #7# ELT)) (|select| #16=(#17=($ #18=(|Mapping| #3# #3#) $) NIL #19=(|has| $ (|FiniteAggregate| #3#)) ELT)) (|sample| (#20=($) NIL T CONST)) (|reverse!| (#4# NIL #7# ELT)) (|reverse| #21=(#4# NIL T ELT)) (|removeDuplicates| (#4# NIL #22=(AND #19# #23=(|has| #3# (|BasicType|))) ELT)) (|remove| #16# (#24=($ #3# $) NIL #22# ELT)) (|reduce| #11# ((#3# #12# $ #3#) NIL T ELT) ((#3# #12# $ #3# #3#) NIL #23# ELT)) (|qsetelt!| (#15# NIL #7# ELT)) (|qelt| (#25=(#3# $ #6#) NIL T ELT)) (|position| ((#6# #3# $ #6#) NIL #23# ELT) ((#6# #3# $) NIL #23# ELT) ((#6# #18# $) NIL T ELT)) (|or| (#5# 49 T ELT)) (|not| #21#) (|nor| #26=(#5# NIL T ELT)) (|new| (($ #27=(|NonNegativeInteger|) #3#) 27 T ELT)) (|nand| #26#) (|minIndex| (#28=(#6# $) 8 #29=(|has| #6# #10#) ELT)) (|min| #26#) (|merge| (#5# NIL #9# ELT) (#30=($ #12# $ $) NIL T ELT)) (|members| #31=((#32=(|List| #3#) $) NIL T ELT)) (|member?| (#33=(#3# #3# $) NIL #23# ELT)) (|maxIndex| (#28# NIL #29# ELT)) (|max| #26#) (|map!| #34=(#17# NIL T ELT)) (|map| (#30# 47 T ELT) #34#) (|latex| (((|String|) $) NIL T ELT)) (|insert| (#35=($ $ $ #6#) NIL T ELT) (($ #3# $ #6#) NIL T ELT)) (|indices| (((|List| #6#) $) NIL T ELT)) (|index?| ((#3# #6# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#8# NIL #29# ELT)) (|find| (((|Union| #3# "failed") #18# $) NIL T ELT)) (|fill!| (#36=($ $ #3#) NIL #7# ELT)) (|every?| #37=((#3# #18# $) NIL T ELT)) (|eval| (($ $ #32# #32#) NIL #38=(AND (|has| #3# (|Evalable| #3#)) (|has| #3# (|SetCategory|))) ELT) (($ $ #3# #3#) NIL #38# ELT) (($ $ #39=(|Equation| #3#)) NIL #38# ELT) (($ $ (|List| #39#)) NIL #38# ELT)) (|eq?| #1#) (|entry?| (#33# NIL #22# ELT)) (|entries| #31#) (|empty?| (#8# NIL T ELT)) (|empty| (#20# 29 T ELT)) (|elt| #40=(($ $ #14#) NIL T ELT) (#25# 22 T ELT) (#15# NIL T ELT)) (|delete| #40# (($ $ #6#) NIL T ELT)) (|count| ((#27# #18# $) NIL T ELT) ((#27# #3# $) NIL #23# ELT)) (|copyInto!| (#35# NIL #7# ELT)) (|copy| (#4# 30 T ELT)) (|convert| ((#41=(|InputForm|) $) NIL (|has| #3# (|ConvertibleTo| #41#)) ELT)) (|construct| (($ #32#) NIL T ELT)) (|concat| (($ (|List| $)) NIL T ELT) #26# (#24# NIL T ELT) (#36# NIL T ELT)) (|coerce| (((|OutputForm|) $) 26 T ELT)) (|before?| #1#) (|any?| #37#) (|and| (#5# 48 T ELT)) (|\\/| (#5# 55 T ELT)) (>= #1#) (> #1#) (= (#2# 31 T ELT)) (<= #1#) (< (#2# 43 T ELT)) (|/\\| (#5# 54 T ELT)) (|#| ((#27# $) 13 T ELT))) 
(((|IndexedBits| |#1|) (|BitAggregate|) (|Integer|)) (T |IndexedBits|)) 
NIL 
((|mapUnivariateIfCan| (((|Union| |#2| #1="failed") #2=(|Mapping| (|Union| |#1| #1#) |#4|) #3=(|SparseUnivariatePolynomial| |#4|)) 35 T ELT)) (|mapUnivariate| ((#3# #4=(|Mapping| |#4| |#1|) |#2|) 31 T ELT) ((|#2| (|Mapping| |#1| |#4|) #3#) 22 T ELT)) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) #1#) #2# (|Matrix| #3#)) 46 T ELT)) (|mapBivariate| (((|SparseUnivariatePolynomial| #3#) #4# |#3|) 55 T ELT))) 
(((|IntegralBasisPolynomialTools| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |mapUnivariate| (|#2| (|Mapping| |#1| |#4|) #1=(|SparseUnivariatePolynomial| |#4|))) (SIGNATURE |mapUnivariate| (#1# #2=(|Mapping| |#4| |#1|) |#2|)) (SIGNATURE |mapUnivariateIfCan| ((|Union| |#2| #3="failed") #4=(|Mapping| (|Union| |#1| #3#) |#4|) #1#)) (SIGNATURE |mapMatrixIfCan| ((|Union| (|Matrix| |#2|) #3#) #4# (|Matrix| #1#))) (SIGNATURE |mapBivariate| ((|SparseUnivariatePolynomial| #1#) #2# |#3|))) #5=(|Ring|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) #5#) (T |IntegralBasisPolynomialTools|)) 
((|mapBivariate| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Mapping| *7 *5)) #3=(|ofCategory| *5 #4=(|Ring|)) #5=(|ofCategory| *7 #4#) #6=(|ofCategory| *6 #7=(|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|SparseUnivariatePolynomial| #8=(|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *6 *4 *7)) (|ofCategory| *4 #9=(|UnivariatePolynomialCategory| *6)))) (|mapMatrixIfCan| #1# (|partial| AND (|isDomain| *3 (|Mapping| #10=(|Union| *5 "failed") *8)) (|isDomain| *4 (|Matrix| (|SparseUnivariatePolynomial| *8))) #3# (|ofCategory| *8 #4#) #6# (|isDomain| *2 (|Matrix| *6)) (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *6 *7 *8)) (|ofCategory| *7 #9#))) (|mapUnivariateIfCan| #1# (|partial| AND (|isDomain| *3 (|Mapping| #10# *7)) #11=(|isDomain| *4 #8#) #3# #5# #12=(|ofCategory| *2 #7#) #13=(|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *2 *6 *7)) #14=(|ofCategory| *6 (|UnivariatePolynomialCategory| *2)))) (|mapUnivariate| #1# (AND #2# #3# #5# (|ofCategory| *4 #7#) (|isDomain| *2 #8#) (|isDomain| *1 (|IntegralBasisPolynomialTools| *5 *4 *6 *7)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *4)))) (|mapUnivariate| #1# (AND (|isDomain| *3 (|Mapping| *5 *7)) #11# #3# #5# #12# #13# #14#))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|min| #3=(($ $ $) NIL T ELT)) (|max| #3#) (|latex| ((#4=(|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fullDisplay| (#5=((|Void|) $) 25 T ELT)) (|elt| ((#4# $ (|Symbol|)) 30 T ELT)) (|display| (#5# 20 T ELT)) (|coerce| (((|OutputForm|) $) 27 T ELT) (($ #4#) 26 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= (#2# 12 T ELT)) (<= #1#) (< (#2# 10 T ELT))) 
(((|IndexCard|) (|Join| (|OrderedSet|) (|CoercibleFrom| #1=(|String|)) (CATEGORY |domain| (SIGNATURE |elt| (#1# $ (|Symbol|))) (SIGNATURE |display| #2=((|Void|) $)) (SIGNATURE |fullDisplay| #2#)))) (T |IndexCard|)) 
((|elt| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 (|String|)) #1=(|isDomain| *1 (|IndexCard|)))) (|display| #2=(*1 *2 *1) #3=(AND (|isDomain| *2 (|Void|)) #1#)) (|fullDisplay| #2# #3#)) 
((|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) 19 T ELT)) (|commonDenominator| ((|#1| |#4|) 10 T ELT)) (|clearDenominator| ((|#3| |#4|) 17 T ELT))) 
(((|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=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|IntegralDomain|)) #4=(|ofCategory| *5 (|QuotientFieldCategory| *4)) (|isDomain| *2 (|Record| (|:| |num| *6) (|:| |den| *4))) (|isDomain| *1 (|InnerCommonDenominator| *4 *5 *6 *3)) (|ofCategory| *6 #5=(|FiniteLinearAggregate| *4)) #6=(|ofCategory| *3 (|FiniteLinearAggregate| *5)))) (|clearDenominator| #1# (AND #2# #4# (|ofCategory| *2 #5#) (|isDomain| *1 (|InnerCommonDenominator| *4 *5 *2 *3)) #6#)) (|commonDenominator| #1# (AND (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 #3#) (|isDomain| *1 (|InnerCommonDenominator| *2 *4 *5 *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *3 #5#)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroDim?| ((#3# $ #4=(|List| |#3|)) 127 T ELT) (#5=(#3# $) 128 T ELT)) (|zero?| (#5# 178 T ELT)) (|saturate| (#6=($ $ |#4|) 117 T ELT) (($ $ |#4| #4#) 122 T ELT)) (|relationsIdeal| (((|SuchThat| (|List| #7=(|Polynomial| |#1|)) (|List| (|Equation| #7#))) #8=(|List| |#4|)) 171 (|has| |#3| (|ConvertibleTo| (|Symbol|))) ELT)) (|quotient| (#9=($ $ $) 107 T ELT) (#6# 105 T ELT)) (|one?| (#5# 177 T ELT)) (|leadingIdeal| (#10=($ $) 132 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|intersect| (#9# 99 T ELT) (($ (|List| $)) 101 T ELT)) (|inRadical?| (#11=(#3# |#4| $) 130 T ELT)) (|in?| (#2# 82 T ELT)) (|ideal| (#12=($ #8#) 106 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|groebnerIdeal| (#12# 175 T ELT)) (|groebner?| (#5# 176 T ELT)) (|groebner| (#10# 85 T ELT)) (|generators| ((#8# $) 73 T ELT)) (|generalPosition| ((#13=(|Record| (|:| |mval| #14=(|Matrix| |#1|)) (|:| |invmval| #14#) (|:| |genIdeal| $)) $ #4#) NIL T ELT)) (|element?| (#11# 89 T ELT)) (|dimension| ((#15=(|Integer|) $ #4#) 134 T ELT) ((#15# $) 135 T ELT)) (|coerce| (((|OutputForm|) $) 174 T ELT) (#12# 102 T ELT)) (|before?| #1#) (|backOldPos| (($ #13#) NIL T ELT)) (= (#2# 84 T ELT)) (+ (#9# 109 T ELT)) (** (($ $ (|NonNegativeInteger|)) 115 T ELT)) (* (#9# 113 T ELT))) 
(((|PolynomialIdeals| |#1| |#2| |#3| |#4|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE * #1=($ $ $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE + #1#) (SIGNATURE |one?| #2=(#3=(|Boolean|) $)) (SIGNATURE |zero?| #2#) (SIGNATURE |element?| #4=(#3# |#4| $)) (SIGNATURE |in?| (#3# $ $)) (SIGNATURE |inRadical?| #4#) (SIGNATURE |zeroDim?| (#3# $ #5=(|List| |#3|))) (SIGNATURE |zeroDim?| #2#) (SIGNATURE |intersect| #1#) (SIGNATURE |intersect| ($ (|List| $))) (SIGNATURE |quotient| #1#) (SIGNATURE |quotient| #6=($ $ |#4|)) (SIGNATURE |groebner| #7=($ $)) (SIGNATURE |generalPosition| (#8=(|Record| (|:| |mval| #9=(|Matrix| |#1|)) (|:| |invmval| #9#) (|:| |genIdeal| $)) $ #5#)) (SIGNATURE |backOldPos| ($ #8#)) (SIGNATURE |dimension| (#10=(|Integer|) $ #5#)) (SIGNATURE |dimension| (#10# $)) (SIGNATURE |leadingIdeal| #7#) (SIGNATURE |ideal| #11=($ #12=(|List| |#4|))) (SIGNATURE |groebnerIdeal| #11#) (SIGNATURE |groebner?| #2#) (SIGNATURE |generators| (#12# $)) (SIGNATURE |coerce| #11#) (SIGNATURE |saturate| #6#) (SIGNATURE |saturate| ($ $ |#4| #5#)) (IF (|has| |#3| (|ConvertibleTo| (|Symbol|))) (SIGNATURE |relationsIdeal| ((|SuchThat| (|List| #13=(|Polynomial| |#1|)) (|List| (|Equation| #13#))) #12#)) |%noBranch|))) (|Field|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |PolynomialIdeals|)) 
((* #1=(*1 *1 *1 *1) #2=(AND (|ofCategory| *2 #3=(|Field|)) (|ofCategory| *3 #4=(|OrderedAbelianMonoidSup|)) (|ofCategory| *4 #5=(|OrderedSet|)) (|isDomain| *1 (|PolynomialIdeals| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (** #6=(*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) #7=(|ofCategory| *3 #3#) #8=(|ofCategory| *4 #4#) #9=(|ofCategory| *5 #5#) #10=(|isDomain| *1 #11=(|PolynomialIdeals| *3 *4 *5 *6)) #12=(|ofCategory| *6 #13=(|PolynomialCategory| *3 *4 *5)))) (+ #1# #2#) (|one?| #14=(*1 *2 *1) #15=(AND #7# #8# #9# #16=(|isDomain| *2 (|Boolean|)) #10# #12#)) (|zero?| #14# #15#) (|element?| #17=(*1 *2 *3 *1) #18=(AND #19=(|ofCategory| *4 #3#) #20=(|ofCategory| *5 #4#) #21=(|ofCategory| *6 #5#) #16# (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *3)) (|ofCategory| *3 #22=(|PolynomialCategory| *4 *5 *6)))) (|in?| (*1 *2 *1 *1) #15#) (|inRadical?| #17# #18#) (|zeroDim?| #23=(*1 *2 *1 *3) (AND #24=(|isDomain| *3 #25=(|List| *6)) #21# #19# #20# #16# #26=(|isDomain| *1 #27=(|PolynomialIdeals| *4 *5 *6 *7)) #28=(|ofCategory| *7 #22#))) (|zeroDim?| #14# #15#) (|intersect| #1# #2#) (|intersect| #29=(*1 *1 *2) (AND (|isDomain| *2 (|List| #11#)) #7# #8# #9# #10# #12#)) (|quotient| #1# #2#) (|quotient| #6# #30=(AND #7# #8# #9# (|isDomain| *1 (|PolynomialIdeals| *3 *4 *5 *2)) (|ofCategory| *2 #13#))) (|groebner| #31=(*1 *1 *1) #2#) (|generalPosition| #23# (AND #24# #21# #19# #20# (|isDomain| *2 (|Record| (|:| |mval| #32=(|Matrix| *4)) (|:| |invmval| #32#) (|:| |genIdeal| #27#))) #26# #28#)) (|backOldPos| #29# (AND (|isDomain| *2 (|Record| (|:| |mval| #33=(|Matrix| *3)) (|:| |invmval| #33#) (|:| |genIdeal| #11#))) #7# #8# #9# #10# #12#)) (|dimension| #23# (AND #24# #21# #19# #20# #34=(|isDomain| *2 (|Integer|)) #26# #28#)) (|dimension| #14# (AND #7# #8# #9# #34# #10# #12#)) (|leadingIdeal| #31# #2#) (|ideal| #29# #35=(AND #36=(|isDomain| *2 #25#) #12# #7# #8# #9# #10#)) (|groebnerIdeal| #29# #35#) (|groebner?| #14# #15#) (|generators| #14# (AND #7# #8# #9# #36# #10# #12#)) (|coerce| #29# #35#) (|saturate| #6# #30#) (|saturate| (*1 *1 *1 *2 *3) (AND #24# #21# #19# #20# (|isDomain| *1 (|PolynomialIdeals| *4 *5 *6 *2)) (|ofCategory| *2 #22#))) (|relationsIdeal| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) #28# (|ofCategory| *6 (|ConvertibleTo| (|Symbol|))) #19# #20# #21# (|isDomain| *2 (|SuchThat| (|List| #37=(|Polynomial| *4)) (|List| (|Equation| #37#)))) #26#))) 
((|zeroDimPrime?| (#1=((|Boolean|) #2=(|PolynomialIdeals| #3=(|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) #4=(|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| #3#))) 178 T ELT)) (|zeroDimPrimary?| (#1# 179 T ELT)) (|radical| ((#2# #2#) 129 T ELT)) (|prime?| (#1# NIL T ELT)) (|primaryDecomp| (((|List| #2#) #2#) 181 T ELT)) (|contract| ((#2# #2# (|List| #4#)) 197 T ELT))) 
(((|IdealDecompositionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimPrime?| #1=((|Boolean|) #2=(|PolynomialIdeals| #3=(|Fraction| (|Integer|)) (|DirectProduct| |#2| #4=(|NonNegativeInteger|)) #5=(|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| #3#)))) (SIGNATURE |zeroDimPrimary?| #1#) (SIGNATURE |prime?| #1#) (SIGNATURE |radical| (#2# #2#)) (SIGNATURE |primaryDecomp| ((|List| #2#) #2#)) (SIGNATURE |contract| (#2# #2# (|List| #5#)))) (|List| (|Symbol|)) #4#) (T |IdealDecompositionPackage|)) 
((|contract| (*1 *2 *2 *3) (AND (|isDomain| *2 #1=(|PolynomialIdeals| #2=(|Fraction| (|Integer|)) (|DirectProduct| *5 #3=(|NonNegativeInteger|)) #4=(|OrderedVariableList| *4) (|DistributedMultivariatePolynomial| *4 #2#))) (|isDomain| *3 (|List| #4#)) #5=(|ofType| *4 #6=(|List| (|Symbol|))) #7=(|ofType| *5 #3#) #8=(|isDomain| *1 (|IdealDecompositionPackage| *4 *5)))) (|primaryDecomp| #9=(*1 *2 *3) (AND #5# #7# (|isDomain| *2 (|List| #1#)) #8# #10=(|isDomain| *3 #1#))) (|radical| (*1 *2 *2) (AND (|isDomain| *2 (|PolynomialIdeals| #2# (|DirectProduct| *4 #3#) (|OrderedVariableList| *3) (|DistributedMultivariatePolynomial| *3 #2#))) (|ofType| *3 #6#) (|ofType| *4 #3#) (|isDomain| *1 (|IdealDecompositionPackage| *3 *4)))) (|prime?| #9# #11=(AND #10# #5# #7# (|isDomain| *2 (|Boolean|)) #8#)) (|zeroDimPrimary?| #9# #11#) (|zeroDimPrime?| #9# #11#)) 
((|elt| ((|#1| $ |#1| |#1|) 6 T ELT))) 
(((|IdempotentOperatorCategory| |#1|) (|Category|) (|BasicType|)) (T |IdempotentOperatorCategory|)) 
NIL 
(|Join| (|BinaryOperatorCategory| |t#1|) (CATEGORY |domain| (ATTRIBUTE (|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|)) (= (|f| |x| |x|) |x|)))))) 
(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gensym| (($) 6 T ELT)) (|coerce| (((|OutputForm|) $) 10 T ELT)) (|before?| #1#) (= (#2# 8 T ELT))) 
(((|Identifier|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |gensym| ($))))) (T |Identifier|)) 
((|gensym| (*1 *1) (|isDomain| *1 (|Identifier|)))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 10 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|reductum| (#5=($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #3#) 15 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#4# 20 T CONST)) (= #1#) (- (#5# 16 T ELT) (#6=($ $ $) 36 T ELT)) (+ (#6# NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) 25 T ELT))) 
(((|IndexedDirectProductAbelianGroup| |#1| |#2|) (|Join| #1=(|AbelianGroup|) (|IndexedDirectProductCategory| |#1| |#2|)) #1# (|OrderedType|)) (T |IndexedDirectProductAbelianGroup|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 16 T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 13 T ELT)) (|sample| (#5=($) NIL T CONST)) (|reductum| (($ $) 39 T ELT)) (|opposite?| (#2# 44 T ELT)) (|monomial| (($ |#1| |#2|) 36 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 38 T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) 41 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #4#) 11 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#5# 12 T CONST)) (= #1#) (+ (($ $ $) 30 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) 35 T ELT))) 
(((|IndexedDirectProductAbelianMonoid| |#1| |#2|) (|Join| #1=(|AbelianMonoid|) (|IndexedDirectProductCategory| |#1| |#2|)) #1# (|OrderedType|)) (T |IndexedDirectProductAbelianMonoid|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|terms| (((|List| (|IndexedProductTerm| |#1| |#2|)) $) 17 T ELT)) (|reductum| (($ $) 18 T ELT)) (|monomial| (($ |#1| |#2|) 21 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 23 T ELT)) (|leadingSupport| ((|#2| $) 19 T ELT)) (|leadingCoefficient| ((|#1| $) 20 T ELT)) (|latex| (((|String|) $) 16 (AND (|has| |#2| . #2=((|SetCategory|))) (|has| |#1| . #3=((|SetCategory|)))) ELT)) (|hash| (((|SingleInteger|) $) 15 (AND (|has| |#2| . #2#) (|has| |#1| . #3#)) ELT)) (|convert| (($ (|List| (|IndexedProductTerm| |#1| |#2|))) 22 T ELT)) (|coerce| (((|OutputForm|) $) 14 (AND (|has| |#2| . #2#) (|has| |#1| . #3#)) ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|IndexedDirectProductCategory| |#1| |#2|) (|Category|) (|BasicType|) (|OrderedType|)) (T |IndexedDirectProductCategory|)) 
((|monomial| (*1 *1 *2 *3) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) (|ofCategory| *2 (|BasicType|)) (|ofCategory| *3 (|OrderedType|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) (|ofCategory| *3 (|OrderedType|)) (|ofCategory| *2 (|BasicType|)))) (|leadingSupport| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|OrderedType|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) (|ofCategory| *2 (|BasicType|)) (|ofCategory| *3 (|OrderedType|)))) (|terms| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|OrderedType|)) (|isDomain| *2 (|List| (|IndexedProductTerm| *3 *4)))))) 
(|Join| (|BasicType|) (|Functorial| |t#1|) (|ConvertibleFrom| (|List| (|IndexedProductTerm| |t#1| |t#2|))) (CATEGORY |domain| (IF (|has| |t#1| (|SetCategory|)) (IF (|has| |t#2| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |%noBranch|) |%noBranch|) (SIGNATURE |monomial| ($ |t#1| |t#2|)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingSupport| (|t#2| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |terms| ((|List| (|IndexedProductTerm| |t#1| |t#2|)) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) AND (|has| |#1| (|SetCategory|)) (|has| |#2| (|SetCategory|))) ((|ConvertibleFrom| (|List| (|IndexedProductTerm| |#1| |#2|))) . T) ((|Functorial| |#1|) . T) ((|Join|) . T) ((|SetCategory|) AND (|has| |#1| (|SetCategory|)) (|has| |#2| (|SetCategory|))) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 33 T ELT)) (|reductum| (($ $) 28 T ELT)) (|monomial| (($ |#1| |#2|) 24 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|leadingSupport| ((|#2| $) 32 T ELT)) (|leadingCoefficient| ((|#1| $) 31 T ELT)) (|latex| (((|String|) $) NIL #5=(AND (|has| |#1| #6=(|SetCategory|)) (|has| |#2| #6#)) ELT)) (|hash| (((|SingleInteger|) $) NIL #5# ELT)) (|convert| (($ #4#) 34 T ELT)) (|combineWithIf| (($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| #3# |#1| |#1|)) 44 T ELT)) (|coerce| (((|OutputForm|) $) 18 #5# ELT)) (|before?| #1#) (= (#2# 22 T ELT))) 
(((|IndexedDirectProductObject| |#1| |#2|) (|Join| (|IndexedDirectProductCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |combineWithIf| ($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| (|Boolean|) |#1| |#1|))))) (|BasicType|) (|OrderedType|)) (T |IndexedDirectProductObject|)) 
((|combineWithIf| (*1 *1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4 *4)) (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|BasicType|)) (|isDomain| *1 (|IndexedDirectProductObject| *4 *5)) (|ofCategory| *5 (|OrderedType|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|terms| ((#5=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 10 T ELT)) (|sample| #6=(($) NIL T CONST)) (|reductum| (($ $) NIL T ELT)) (|positive?| #4#) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|min| #7=(($ $ $) NIL T ELT)) (|max| #7#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #5#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| #6#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 21 T ELT)) (+ #7#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT))) 
(((|IndexedDirectProductOrderedAbelianMonoid| |#1| |#2|) (|Join| #1=(|OrderedAbelianMonoid|) (|IndexedDirectProductCategory| |#1| |#2|)) #1# (|OrderedType|)) (T |IndexedDirectProductOrderedAbelianMonoid|)) 
NIL 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| |#1| |#2|)) $) NIL T ELT)) (|sup| (#5=($ $ $) 24 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 20 T ELT)) (|sample| #6=(($) NIL T CONST)) (|reductum| (($ $) NIL T ELT)) (|positive?| #3#) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|min| #7=(#5# NIL T ELT)) (|max| #7#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #4#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| #6#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #7#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT))) 
(((|IndexedDirectProductOrderedAbelianMonoidSup| |#1| |#2|) (|Join| #1=(|OrderedAbelianMonoidSup|) (|IndexedDirectProductCategory| |#1| |#2|)) #1# (|OrderedSet|)) (T |IndexedDirectProductOrderedAbelianMonoidSup|)) 
NIL 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|term| (($ |#2| |#1|) 9 T ELT)) (|index| ((|#2| $) 11 T ELT)) (|coerce| (((|Pair| |#2| |#1|) $) 14 T ELT)) (|coefficient| ((|#1| $) 13 T ELT)) (|before?| #1#) (= #1#)) 
(((|IndexedProductTerm| |#1| |#2|) (|Join| #1=(|BasicType|) (|CoercibleTo| (|Pair| |#2| |#1|)) (CATEGORY |domain| (SIGNATURE |term| ($ |#2| |#1|)) (SIGNATURE |index| (|#2| $)) (SIGNATURE |coefficient| (|#1| $)))) #1# (|OrderedType|)) (T |IndexedProductTerm|)) 
((|term| (*1 *1 *2 *3) (AND #1=(|isDomain| *1 (|IndexedProductTerm| *3 *2)) #2=(|ofCategory| *3 #3=(|BasicType|)) #4=(|ofCategory| *2 #5=(|OrderedType|)))) (|index| #6=(*1 *2 *1) (AND #4# #1# #2#)) (|coefficient| #6# (AND (|ofCategory| *2 #3#) (|isDomain| *1 (|IndexedProductTerm| *2 *3)) (|ofCategory| *3 #5#)))) 
((|eval| (($ $ (|List| |#2|) (|List| |#3|)) NIL T ELT) (($ $ |#2| |#3|) 12 T ELT))) 
(((|InnerEvalable&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |eval| (|#1| |#1| |#2| |#3|)) (SIGNATURE |eval| (|#1| |#1| (|List| |#2|) (|List| |#3|)))) (|InnerEvalable| |#2| |#3|) (|SetCategory|) (|Type|)) (T |InnerEvalable&|)) 
NIL 
((|eval| (($ $ (|List| |#1|) (|List| |#2|)) 7 T ELT) (($ $ |#1| |#2|) 6 T ELT))) 
(((|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|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 17 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 19 T ELT)) (|subtractIfCan| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|size| ((#5=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #4#) $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #7=(|Integer|)) 24 T ELT)) (|nthCoef| ((|#2| $ #7#) 22 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 48 T ELT)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 45 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#8=($ $ $) 55 (|has| |#2| (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 44 T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((|#2| |#1| $) 51 T ELT)) (|before?| #1#) (|Zero| (#6# 11 T CONST)) (= (#2# 30 T ELT)) (+ (#8# 28 T ELT) (($ |#1| $) 26 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #5# $) 37 T ELT) (($ |#2| |#1|) 32 T ELT))) 
(((|InnerFreeAbelianMonoid| |#1| |#2| |#3|) (|FreeAbelianMonoidCategory| |#1| |#2|) (|SetCategory|) (|CancellationAbelianMonoid|) |#2|) (T |InnerFreeAbelianMonoid|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) NIL #6=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #7=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#8=(#3# $) NIL #9=(|has| |#1| #10=(|OrderedSet|)) ELT)) (|sort!| (#11=($ #7# $) NIL #6# ELT) (#12=($ $) NIL (AND #6# #9#) ELT)) (|sort| (#11# NIL T ELT) (#12# NIL #9# ELT)) (|shrinkable| ((#3# #3#) 32 T ELT)) (|setelt| (#13=(|#1| $ #5# |#1|) 42 #6# ELT) ((|#1| $ #14=(|UniversalSegment| #5#) |#1|) NIL #6# ELT)) (|select!| (#15=($ #16=(|Mapping| #3# |#1|) $) 79 T ELT)) (|select| #17=(#15# NIL #18=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#19=($) NIL T CONST)) (|reverse!| (#12# NIL #6# ELT)) (|reverse| (#12# NIL T ELT)) (|removeDuplicates!| (#12# 83 #4# ELT)) (|removeDuplicates| (#12# NIL #20=(AND #18# #4#) ELT)) (|remove!| (#21=($ |#1| $) NIL #4# ELT) (#15# 66 T ELT)) (|remove| (#21# NIL #20# ELT) #17#) (|reduce| ((|#1| #22=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #22# $ |#1|) NIL T ELT) ((|#1| #22# $) NIL T ELT)) (|qsetelt!| (#13# NIL #6# ELT)) (|qelt| (#23=(|#1| $ #5#) NIL T ELT)) (|position| ((#5# #16# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT) ((#5# |#1| $ #5#) NIL #4# ELT)) (|physicalLength!| (#24=($ $ #5#) 19 T ELT)) (|physicalLength| (#25=(#26=(|NonNegativeInteger|) $) 13 T ELT)) (|new| (($ #26# |#1|) 31 T ELT)) (|minIndex| (#27=(#5# $) 29 #28=(|has| #5# #10#) ELT)) (|min| #29=(#30=($ $ $) NIL #9# ELT)) (|merge!| #29# (#31=($ #7# $ $) 57 T ELT)) (|merge| (#31# 58 T ELT) #29#) (|members| #32=((#33=(|List| |#1|) $) NIL T ELT)) (|member?| (#34=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| (#27# 28 #28# ELT)) (|max| #29#) (|map!| #35=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #35# (($ #22# $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #36=(|has| |#1| (|SetCategory|)) ELT)) (|insert!| (#37=($ $ $ #5#) 75 T ELT) (#38=($ |#1| $ #5#) 59 T ELT)) (|insert| (#38# NIL T ELT) (#37# NIL T ELT)) (|indices| (((|List| #5#) $) NIL T ELT)) (|index?| ((#3# #5# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #36# ELT)) (|flexibleArray| (#39=($ #33#) 43 T ELT)) (|first| ((|#1| $) NIL #28# ELT)) (|find| (((|Union| |#1| "failed") #16# $) NIL T ELT)) (|fill!| (#40=($ $ |#1|) 24 #6# ELT)) (|every?| #41=((#3# #16# $) NIL T ELT)) (|eval| (($ $ (|List| #42=(|Equation| |#1|))) NIL #43=(AND (|has| |#1| (|Evalable| |#1|)) #36#) ELT) (($ $ #42#) NIL #43# ELT) (($ $ |#1| |#1|) NIL #43# ELT) (($ $ #33# #33#) NIL #43# ELT)) (|eq?| (#2# 62 T ELT)) (|entry?| (#34# NIL #20# ELT)) (|entries| #32#) (|empty?| (#8# NIL T ELT)) (|empty| (#19# 21 T ELT)) (|elt| (#13# NIL T ELT) (#23# 55 T ELT) #44=(#45=($ $ #14#) NIL T ELT)) (|delete!| (#45# 73 T ELT) (#24# 67 T ELT)) (|delete| (#24# NIL T ELT) #44#) (|count| ((#26# |#1| $) NIL #4# ELT) ((#26# #16# $) NIL T ELT)) (|copyInto!| (#37# 63 #6# ELT)) (|copy| (#12# 53 T ELT)) (|convert| ((#46=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #46#)) ELT)) (|construct| (#39# NIL T ELT)) (|concat!| (#30# 64 T ELT) (#40# 61 T ELT)) (|concat| (#40# NIL T ELT) (#21# 60 T ELT) (#30# NIL T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#47=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #47#)) ELT)) (|before?| #1#) (|any?| #41#) (>= #48=(#2# NIL #9# ELT)) (> #48#) (= #1#) (<= #48#) (< #48#) (|#| (#25# 22 T ELT))) 
(((|IndexedFlexibleArray| |#1| |#2|) (|Join| (|OneDimensionalArrayAggregate| |#1|) (|ExtensibleLinearAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |flexibleArray| ($ (|List| |#1|))) (SIGNATURE |physicalLength| ((|NonNegativeInteger|) $)) (SIGNATURE |physicalLength!| ($ $ #1=(|Integer|))) (SIGNATURE |shrinkable| (#2=(|Boolean|) #2#)))) (|Type|) #1#) (T |IndexedFlexibleArray|)) 
((|flexibleArray| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Type|)) #2=(|isDomain| *1 (|IndexedFlexibleArray| *3 *4)) #3=(|ofType| *4 #4=(|Integer|)))) (|physicalLength| (*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) #2# #1# #3#)) (|physicalLength!| (*1 *1 *1 *2) (AND (|isDomain| *2 #4#) #2# #1# (|ofType| *4 *2))) (|shrinkable| (*1 *2 *2) (AND (|isDomain| *2 (|Boolean|)) #2# #1# #3#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|thenBranch| (#2=((|SpadAst|) $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elseBranch| (#2# 14 T ELT)) (|condition| (#2# 10 T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|IfAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |condition| #1=((|SpadAst|) $)) (SIGNATURE |thenBranch| #1#) (SIGNATURE |elseBranch| #1#)))) (T |IfAst|)) 
((|condition| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|IfAst|)))) (|thenBranch| #1# #2#) (|elseBranch| #1# #2#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((#10=(|InnerPrimeField| |#1|) $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| #10# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #8#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #18#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #22=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| ((#17# $) NIL T ELT)) (|random| #24=(#21# NIL #14# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #8#) NIL #29=(OR (|has| #10# (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #9# #11#) (|nextItem| (#34=((|Maybe| $) $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| #10#) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #18#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #14# ELT) (((|Union| #8# #18#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#28# NIL #14# ELT) #44=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#22# $) NIL T ELT) (((|Matrix| #10#) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #18#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #46=(|Fraction| #15#)) NIL T ELT) (($ #10#) NIL T ELT)) (|charthRoot| #44# (#34# NIL #29# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #20#) (|One| #20#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #23# #47=(($ $ #10#) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #15# . #48=($)) NIL T ELT) #23# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ #10# . #48#) NIL T ELT))) 
(((|InnerFiniteField| |#1| |#2|) (|FiniteAlgebraicExtensionField| (|InnerPrimeField| |#1|)) #1=(|PositiveInteger|) #1#) (T |InnerFiniteField|)) 
NIL 
((|rowEchelon| (#1=(|#4| |#4|) 38 T ELT)) (|rank| (#2=((|NonNegativeInteger|) |#4|) 45 T ELT)) (|nullity| (#2# 46 T ELT)) (|nullSpace| (((|List| |#3|) |#4|) 57 (|has| |#3| (|ShallowlyMutableAggregate| |#1|)) ELT)) (|inverse| (((|Union| |#4| "failed") |#4|) 69 T ELT)) (|generalizedInverse| (#1# 61 T ELT)) (|determinant| ((|#1| |#4|) 60 T ELT))) 
(((|InnerMatrixLinearAlgebraFunctions| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |rowEchelon| #1=(|#4| |#4|)) (SIGNATURE |rank| #2=((|NonNegativeInteger|) |#4|)) (SIGNATURE |nullity| #2#) (IF (|has| |#3| (|ShallowlyMutableAggregate| |#1|)) (SIGNATURE |nullSpace| ((|List| |#3|) |#4|)) |%noBranch|) (SIGNATURE |determinant| (|#1| |#4|)) (SIGNATURE |generalizedInverse| #1#) (SIGNATURE |inverse| ((|Union| |#4| "failed") |#4|))) (|Field|) #3=(|FiniteLinearAggregate| |#1|) #3# (|MatrixCategory| |#1| |#2| |#3|)) (T |InnerMatrixLinearAlgebraFunctions|)) 
((|inverse| #1=(*1 *2 *2) (|partial| AND #2=(|ofCategory| *3 #3=(|Field|)) #4=(|ofCategory| *4 #5=(|FiniteLinearAggregate| *3)) #6=(|ofCategory| *5 #5#) #7=(|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *3 *4 *5 *2)) #8=(|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|generalizedInverse| #1# #9=(AND #2# #4# #6# #7# #8#)) (|determinant| #10=(*1 *2 *3) (AND (|ofCategory| *4 #11=(|FiniteLinearAggregate| *2)) (|ofCategory| *5 #11#) (|ofCategory| *2 #3#) (|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *2 *4 *5 *3)) (|ofCategory| *3 (|MatrixCategory| *2 *4 *5)))) (|nullSpace| #10# (AND (|ofCategory| *6 (|ShallowlyMutableAggregate| *4)) #12=(|ofCategory| *4 #3#) #13=(|ofCategory| *5 #14=(|FiniteLinearAggregate| *4)) #15=(|ofCategory| *6 #14#) (|isDomain| *2 (|List| *6)) #16=(|isDomain| *1 (|InnerMatrixLinearAlgebraFunctions| *4 *5 *6 *3)) #17=(|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|nullity| #10# #18=(AND #12# #13# #15# (|isDomain| *2 (|NonNegativeInteger|)) #16# #17#)) (|rank| #10# #18#) (|rowEchelon| #1# #9#)) 
((|rowEchelon| ((|#8| |#4|) 20 T ELT)) (|nullSpace| (((|List| |#3|) |#4|) 29 (|has| |#7| (|ShallowlyMutableAggregate| |#5|)) ELT)) (|inverse| (((|Union| |#8| "failed") |#4|) 23 T ELT))) 
(((|InnerMatrixQuotientFieldFunctions| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |rowEchelon| (|#8| |#4|)) (SIGNATURE |inverse| ((|Union| |#8| "failed") |#4|)) (IF (|has| |#7| (|ShallowlyMutableAggregate| |#5|)) (SIGNATURE |nullSpace| ((|List| |#3|) |#4|)) |%noBranch|)) (|IntegralDomain|) #1=(|FiniteLinearAggregate| |#1|) #1# (|MatrixCategory| |#1| |#2| |#3|) (|QuotientFieldCategory| |#1|) #2=(|FiniteLinearAggregate| |#5|) #2# (|MatrixCategory| |#5| |#6| |#7|)) (T |InnerMatrixQuotientFieldFunctions|)) 
((|nullSpace| #1=(*1 *2 *3) (AND (|ofCategory| *9 (|ShallowlyMutableAggregate| *7)) #2=(|ofCategory| *4 (|IntegralDomain|)) #3=(|ofCategory| *5 #4=(|FiniteLinearAggregate| *4)) #5=(|ofCategory| *6 #4#) #6=(|ofCategory| *7 (|QuotientFieldCategory| *4)) #7=(|ofCategory| *8 #8=(|FiniteLinearAggregate| *7)) #9=(|ofCategory| *9 #8#) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|InnerMatrixQuotientFieldFunctions| *4 *5 *6 *3 *7 *8 *9 *10)) #10=(|ofCategory| *3 (|MatrixCategory| *4 *5 *6)) (|ofCategory| *10 #11=(|MatrixCategory| *7 *8 *9)))) (|inverse| #1# (|partial| AND #2# #3# #5# #6# #12=(|ofCategory| *2 #11#) #13=(|isDomain| *1 (|InnerMatrixQuotientFieldFunctions| *4 *5 *6 *3 *7 *8 *9 *2)) #10# #7# #9#)) (|rowEchelon| #1# (AND #2# #3# #5# #6# #12# #13# #10# #7# #9#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|imports| ((#2=(|List| (|TypeAst|)) $) 14 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT) (($ #2#) 12 T ELT)) (|before?| #1#) (= #1#)) 
(((|ImportAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1=(|List| (|TypeAst|)))) (SIGNATURE |imports| (#1# $))))) (T |ImportAst|)) 
((|coerce| (*1 *1 *2) #1=(AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *1 (|ImportAst|)))) (|imports| (*1 *2 *1) #1#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|sequence| (((|SpadAst|) $) 15 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|iterationVar| (((|Identifier|) $) 12 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 22 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|InAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |iterationVar| ((|Identifier|) $)) (SIGNATURE |sequence| ((|SpadAst|) $))))) (T |InAst|)) 
((|iterationVar| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) #2=(|isDomain| *1 (|InAst|)))) (|sequence| #1# (AND (|isDomain| *2 (|SpadAst|)) #2#))) 
((|readUInt8!| (((|Maybe| (|UInt8|)) $) 15 T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) 38 T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) 29 T ELT)) (|readInt8!| (((|Maybe| (|Int8|)) $) 12 T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) 42 T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) 33 T ELT)) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 54 T ELT))) 
(((|InputByteConduit&| |#1|) (CATEGORY |package| (SIGNATURE |readBytes!| ((|NonNegativeInteger|) |#1| (|ByteBuffer|))) (SIGNATURE |readUInt32!| ((|Maybe| (|UInt32|)) |#1|)) (SIGNATURE |readInt32!| ((|Maybe| (|Int32|)) |#1|)) (SIGNATURE |readUInt16!| ((|Maybe| (|UInt16|)) |#1|)) (SIGNATURE |readInt16!| ((|Maybe| (|Int16|)) |#1|)) (SIGNATURE |readUInt8!| ((|Maybe| (|UInt8|)) |#1|)) (SIGNATURE |readInt8!| ((|Maybe| (|Int8|)) |#1|))) (|InputByteConduit|)) (T |InputByteConduit&|)) 
NIL 
((|readUInt8!| (((|Maybe| (|UInt8|)) $) 12 T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) 8 T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) 10 T ELT)) (|readInt8!| (((|Maybe| (|Int8|)) $) 13 T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) 9 T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) 11 T ELT)) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 7 T ELT)) (|readByte!| (((|Maybe| (|Byte|)) $) 14 T ELT)) (|close!| (($ $) 6 T ELT))) 
(((|InputByteConduit|) (|Category|)) (T |InputByteConduit|)) 
((|readByte!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|Byte|))))) (|readInt8!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|Int8|))))) (|readUInt8!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|UInt8|))))) (|readInt16!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|Int16|))))) (|readUInt16!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|UInt16|))))) (|readInt32!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|Int32|))))) (|readUInt32!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|UInt32|))))) (|readBytes!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *3 (|ByteBuffer|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|Conduit|) (CATEGORY |domain| (SIGNATURE |readByte!| ((|Maybe| (|Byte|)) $)) (SIGNATURE |readInt8!| ((|Maybe| (|Int8|)) $)) (SIGNATURE |readUInt8!| ((|Maybe| (|UInt8|)) $)) (SIGNATURE |readInt16!| ((|Maybe| (|Int16|)) $)) (SIGNATURE |readUInt16!| ((|Maybe| (|UInt16|)) $)) (SIGNATURE |readInt32!| ((|Maybe| (|Int32|)) $)) (SIGNATURE |readUInt32!| ((|Maybe| (|UInt32|)) $)) (SIGNATURE |readBytes!| ((|NonNegativeInteger|) $ (|ByteBuffer|))))) 
(((|Conduit|) . T)) 
((|xn| ((#1=(|SparseUnivariatePolynomial| |#1|) #2=(|NonNegativeInteger|)) 114 T ELT)) (|trace| (#3=(#4=(|Vector| |#1|) #4# #5=(|PositiveInteger|)) 107 T ELT)) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #6=(|SingleInteger|))))) |#1|) 122 T ELT)) (|repSq| ((#4# #4# #2#) 53 T ELT)) (|random| (#7=(#4# #5#) 109 T ELT)) (|qPot| (#8=(#4# #4# (|Integer|)) 30 T ELT)) (|pol| (#9=(#1# #4#) 115 T ELT)) (|normalElement| (#7# 136 T ELT)) (|normal?| (((|Boolean|) #4#) 119 T ELT)) (|norm| (#3# 99 T ELT)) (|minimalPolynomial| (#9# 130 T ELT)) (|lookup| ((#5# #4#) 95 T ELT)) (|inv| ((#4# #4#) 38 T ELT)) (|index| ((#4# #5# #5#) 139 T ELT)) (|expPot| ((#4# #4# #6# #6#) 29 T ELT)) (|dAndcExp| ((#4# #4# #2# #6#) 54 T ELT)) (|basis| (((|Vector| #4#) #5#) 135 T ELT)) (/ (#10=(#4# #4# #4#) 120 T ELT)) (** (#8# 67 T ELT)) (* (#10# 31 T ELT))) 
(((|InnerNormalBasisFieldFunctions| |#1|) (CATEGORY |package| (SIGNATURE |setFieldInfo| ((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #1=(|SingleInteger|))))) |#1|)) (SIGNATURE |random| #2=(#3=(|Vector| |#1|) #4=(|PositiveInteger|))) (SIGNATURE |index| (#3# #4# #4#)) (SIGNATURE |pol| #5=(#6=(|SparseUnivariatePolynomial| |#1|) #3#)) (SIGNATURE |xn| (#6# #7=(|NonNegativeInteger|))) (SIGNATURE |dAndcExp| (#3# #3# #7# #1#)) (SIGNATURE |repSq| (#3# #3# #7#)) (SIGNATURE |expPot| (#3# #3# #1# #1#)) (SIGNATURE |qPot| #8=(#3# #3# (|Integer|))) (SIGNATURE ** #8#) (SIGNATURE * #9=(#3# #3# #3#)) (SIGNATURE / #9#) (SIGNATURE |norm| #10=(#3# #3# #4#)) (SIGNATURE |trace| #10#) (SIGNATURE |inv| (#3# #3#)) (SIGNATURE |lookup| (#4# #3#)) (SIGNATURE |normal?| ((|Boolean|) #3#)) (SIGNATURE |basis| ((|Vector| #3#) #4#)) (SIGNATURE |normalElement| #2#) (SIGNATURE |minimalPolynomial| #5#)) (|FiniteFieldCategory|)) (T |InnerNormalBasisFieldFunctions|)) 
((|minimalPolynomial| #1=(*1 *2 *3) #2=(AND #3=(|isDomain| *3 #4=(|Vector| *4)) #5=(|ofCategory| *4 #6=(|FiniteFieldCategory|)) #7=(|isDomain| *2 (|SparseUnivariatePolynomial| *4)) #8=(|isDomain| *1 (|InnerNormalBasisFieldFunctions| *4)))) (|normalElement| #1# #9=(AND #10=(|isDomain| *3 #11=(|PositiveInteger|)) #12=(|isDomain| *2 #4#) #8# #5#)) (|basis| #1# (AND #10# (|isDomain| *2 (|Vector| #4#)) #8# #5#)) (|normal?| #1# (AND #3# #5# (|isDomain| *2 (|Boolean|)) #8#)) (|lookup| #1# (AND #3# #5# (|isDomain| *2 #11#) #8#)) (|inv| (*1 *2 *2) #13=(AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 #6#) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *3)))) (|trace| #14=(*1 *2 *2 *3) #15=(AND #12# #10# #5# #8#)) (|norm| #14# #15#) (/ #16=(*1 *2 *2 *2) #13#) (* #16# #13#) (** #14# #17=(AND #12# (|isDomain| *3 (|Integer|)) #5# #8#)) (|qPot| #14# #17#) (|expPot| (*1 *2 *2 *3 *3) (AND #12# (|isDomain| *3 #18=(|SingleInteger|)) #5# #8#)) (|repSq| #14# (AND #12# #19=(|isDomain| *3 (|NonNegativeInteger|)) #5# #8#)) (|dAndcExp| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 (|Vector| *5)) #19# (|isDomain| *4 #18#) (|ofCategory| *5 #6#) (|isDomain| *1 (|InnerNormalBasisFieldFunctions| *5)))) (|xn| #1# (AND #19# #7# #8# #5#)) (|pol| #1# #2#) (|index| (*1 *2 *3 *3) #9#) (|random| #1# #9#) (|setFieldInfo| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Vector| (|List| (|Record| (|:| |value| *4) (|:| |index| #18#))))) #5# (|isDomain| *2 (|Void|)) #8#))) 
((|readUInt8!| (((|Maybe| (|UInt8|)) $) NIL T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) NIL T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) NIL T ELT)) (|readInt8!| (((|Maybe| (|Int8|)) $) NIL T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) NIL T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) NIL T ELT)) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) NIL T ELT)) (|readByte!| (((|Maybe| (|Byte|)) $) 26 T ELT)) (|position!| ((#1=(|SingleInteger|) $ #1#) 31 T ELT)) (|position| ((#1# $) 30 T ELT)) (|isOpen?| (#2=((|Boolean|) $) 20 T ELT)) (|inputBinaryFile| (($ (|FileName|)) 14 T ELT) (($ (|String|)) 16 T ELT)) (|eof?| (#2# 27 T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT)) (|close!| (($ $) 28 T ELT))) 
(((|InputBinaryFile|) (|Join| (|InputByteConduit|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |inputBinaryFile| ($ (|FileName|))) (SIGNATURE |inputBinaryFile| ($ (|String|))) (SIGNATURE |eof?| #1=((|Boolean|) $)) (SIGNATURE |isOpen?| #1#) (SIGNATURE |position| (#2=(|SingleInteger|) $)) (SIGNATURE |position!| (#2# $ #2#))))) (T |InputBinaryFile|)) 
((|inputBinaryFile| #1=(*1 *1 *2) (AND (|isDomain| *2 (|FileName|)) #2=(|isDomain| *1 (|InputBinaryFile|)))) (|inputBinaryFile| #1# (AND (|isDomain| *2 (|String|)) #2#)) (|eof?| #3=(*1 *2 *1) #4=(AND (|isDomain| *2 (|Boolean|)) #2#)) (|isOpen?| #3# #4#) (|position| #3# #5=(AND (|isDomain| *2 (|SingleInteger|)) #2#)) (|position!| (*1 *2 *1 *2) #5#)) 
((|incrementBy| ((#1=(|Mapping| |#1| |#1|) |#1|) 11 T ELT)) (|increment| ((#1#) 10 T ELT))) 
(((|IncrementingMaps| |#1|) (CATEGORY |package| (SIGNATURE |increment| (#1=(|Mapping| |#1| |#1|))) (SIGNATURE |incrementBy| (#1# |#1|))) (|Join| (|Monoid|) (|AbelianSemiGroup|))) (T |IncrementingMaps|)) 
((|incrementBy| (*1 *2 *3) #1=(AND (|isDomain| *2 (|Mapping| *3 *3)) (|isDomain| *1 (|IncrementingMaps| *3)) (|ofCategory| *3 (|Join| (|Monoid|) (|AbelianSemiGroup|))))) (|increment| (*1 *2) #1#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| #5=(|NonNegativeInteger|) |#1|)) $) NIL T ELT)) (|sup| #6=(($ $ $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| #7=(($) NIL T CONST)) (|reductum| (($ $) NIL T ELT)) (|positive?| #3#) (|opposite?| #1#) (|monomial| (($ #5# |#1|) NIL T ELT)) (|min| #6#) (|max| #6#) (|map| (($ (|Mapping| #5# #5#) $) NIL T ELT)) (|leadingSupport| ((|#1| $) NIL T ELT)) (|leadingCoefficient| ((#5# $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #4#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 28 T ELT)) (|before?| #1#) (|Zero| #7#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #6#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #5# $) NIL T ELT))) 
(((|IndexedExponents| |#1|) (|Join| (|OrderedAbelianMonoidSup|) (|IndexedDirectProductCategory| (|NonNegativeInteger|) |#1|)) (|OrderedSet|)) (T |IndexedExponents|)) 
NIL 
((|solve1| (((|List| |#2|) #1=(|SparseUnivariatePolynomial| |#1|) |#3|) 98 T ELT)) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) #2=(|Matrix| |#1|) |#3| (|Mapping| (|Factored| #1#) #1#)) 114 T ELT)) (|charpol| ((#1# #2#) 110 T ELT))) 
(((|InnerNumericEigenPackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |charpol| (#1=(|SparseUnivariatePolynomial| |#1|) #2=(|Matrix| |#1|))) (SIGNATURE |solve1| ((|List| |#2|) #1# |#3|)) (SIGNATURE |innerEigenvectors| ((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) #2# |#3| (|Mapping| (|Factored| #1#) #1#)))) #3=(|Field|) #3# (|Join| #3# (|OrderedRing|))) (T |InnerNumericEigenPackage|)) 
((|innerEigenvectors| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Matrix| *6)) (|isDomain| *5 (|Mapping| (|Factored| #1=(|SparseUnivariatePolynomial| *6)) #1#)) #2=(|ofCategory| *6 #3=(|Field|)) (|isDomain| *2 (|List| (|Record| (|:| |outval| *7) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| *7)))))) (|isDomain| *1 (|InnerNumericEigenPackage| *6 *7 *4)) (|ofCategory| *7 #3#) #4=(|ofCategory| *4 #5=(|Join| #3# (|OrderedRing|))))) (|solve1| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *5)) #6=(|ofCategory| *5 #3#) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|InnerNumericEigenPackage| *5 *6 *4)) #2# #4#)) (|charpol| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *4)) (|ofCategory| *4 #3#) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|InnerNumericEigenPackage| *4 *5 *6)) #6# (|ofCategory| *6 #5#)))) 
((|writeUInt8!| ((#1=(|Maybe| #2=(|UInt8|)) $ #2#) NIL T ELT)) (|writeInt8!| ((#3=(|Maybe| #4=(|Int8|)) $ #4#) NIL T ELT)) (|writeBytes!| (#5=((|NonNegativeInteger|) $ (|ByteBuffer|)) 39 T ELT)) (|writeByte!| ((#6=(|Maybe| #7=(|Byte|)) $ #7#) 40 T ELT)) (|readUInt8!| ((#1# $) NIL T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) NIL T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) NIL T ELT)) (|readInt8!| ((#3# $) NIL T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) NIL T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) NIL T ELT)) (|readBytes!| (#5# 35 T ELT)) (|readByte!| ((#6# $) 37 T ELT)) (|isConnected?| (((|Boolean|) $) 27 T ELT)) (|connectTo| ((#8=(|Maybe| $) (|IP4Address|) #9=(|PortNumber|)) 18 T ELT) ((#8# (|Hostname|) #9#) 24 T ELT)) (|coerce| (((|OutputForm|) $) 48 T ELT)) (|close!| (($ $) 42 T ELT))) 
(((|InetClientStreamSocket|) (|Join| (|NetworkClientSocket| (|IP4Address|)) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |connectTo| ((|Maybe| $) (|Hostname|) (|PortNumber|)))))) (T |InetClientStreamSocket|)) 
((|connectTo| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Hostname|)) (|isDomain| *4 (|PortNumber|)) (|isDomain| *2 (|Maybe| #1=(|InetClientStreamSocket|))) (|isDomain| *1 #1#)))) 
((|plusInfinity| (#1=((|OrderedCompletion| #2=(|Integer|))) 12 T ELT)) (|minusInfinity| (#1# 14 T ELT)) (|infinity| (((|OnePointCompletion| #2#)) 9 T ELT))) 
(((|Infinity|) (CATEGORY |package| (SIGNATURE |infinity| ((|OnePointCompletion| #1=(|Integer|)))) (SIGNATURE |plusInfinity| #2=((|OrderedCompletion| #1#))) (SIGNATURE |minusInfinity| #2#))) (T |Infinity|)) 
((|minusInfinity| #1=(*1 *2) #2=(AND (|isDomain| *2 (|OrderedCompletion| #3=(|Integer|))) #4=(|isDomain| *1 (|Infinity|)))) (|plusInfinity| #1# #2#) (|infinity| #1# (AND (|isDomain| *2 (|OnePointCompletion| #3#)) #4#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|unparse| (#4=(#5=(|String|) $) 55 T ELT)) (|symbol?| (#6=(#3# $) 51 T ELT)) (|symbol| ((#7=(|Symbol|) $) 52 T ELT)) (|string?| (#6# 49 T ELT)) (|string| (#4# 50 T ELT)) (|parseString| (#8=($ #5#) 56 T ELT)) (|pair?| #9=(#6# NIL T ELT)) (|null?| #9#) (|list?| #9#) (|latex| (#4# NIL T ELT)) (|lambda| (($ $ #10=(|List| #7#)) 21 T ELT)) (|interpret| (((|Any|) $) 23 T ELT)) (|integer?| #9#) (|integer| #11=((#12=(|Integer|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|function| (($ $ #10# #7#) 73 T ELT)) (|float?| #9#) (|float| ((#13=(|DoubleFloat|) $) NIL T ELT)) (|flatten| (#14=($ $) 44 T ELT)) (|expr| (#15=(#16=(|OutputForm|) $) NIL T ELT)) (|eq| #1#) (|elt| (#17=($ $ #12#) NIL T ELT) (($ $ (|List| #12#)) NIL T ELT)) (|destruct| ((#18=(|List| $) $) 30 T ELT)) (|declare| ((#7# #18#) 57 T ELT)) (|convert| (#8# NIL T ELT) (($ #7#) 19 T ELT) (($ #12#) 8 T ELT) (($ #13#) 28 T ELT) (($ #16#) NIL T ELT) (($ #18#) 65 T ELT) ((#19=(|SExpression|) $) 12 T ELT) (($ #19#) 13 T ELT)) (|compile| ((#7# #7# #18#) 60 T ELT)) (|coerce| (#15# 54 T ELT)) (|cdr| (#14# 59 T ELT)) (|car| (#14# 58 T ELT)) (|binary| (($ $ #18#) 66 T ELT)) (|before?| #1#) (|atom?| (#6# 29 T ELT)) (|Zero| (#20=($) 9 T CONST)) (|One| (#20# 11 T CONST)) (= (#2# 74 T ELT)) (/ (#21=($ $ $) 82 T ELT)) (+ (#21# 75 T ELT)) (** (($ $ (|NonNegativeInteger|)) 81 T ELT) (#17# 80 T ELT)) (* (#21# 76 T ELT)) (|#| #11#)) 
(((|InputForm|) (|Join| (|SExpressionCategory| #1=(|String|) #2=(|Symbol|) #3=(|Integer|) (|DoubleFloat|) (|OutputForm|)) (|ConvertibleTo| #4=(|SExpression|)) (CATEGORY |domain| (SIGNATURE |interpret| ((|Any|) $)) (SIGNATURE |convert| ($ #4#)) (SIGNATURE |binary| ($ $ #5=(|List| $))) (SIGNATURE |function| ($ $ #6=(|List| #2#) #2#)) (SIGNATURE |lambda| ($ $ #6#)) (SIGNATURE + #7=($ $ $)) (SIGNATURE * #7#) (SIGNATURE / #7#) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE ** ($ $ #3#)) (SIGNATURE |Zero| #8=($) |constant|) (SIGNATURE |One| #8# |constant|) (SIGNATURE |flatten| ($ $)) (SIGNATURE |unparse| (#1# $)) (SIGNATURE |parseString| ($ #1#)) (SIGNATURE |declare| (#2# #5#)) (SIGNATURE |compile| (#2# #2# #5#))))) (T |InputForm|)) 
((|interpret| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Any|)) #2=(|isDomain| *1 #3=(|InputForm|)))) (|convert| #4=(*1 *1 *2) (AND (|isDomain| *2 (|SExpression|)) #2#)) (|binary| #5=(*1 *1 *1 *2) (AND (|isDomain| *2 #6=(|List| #3#)) #2#)) (|function| (*1 *1 *1 *2 *3) (AND #7=(|isDomain| *2 (|List| #8=(|Symbol|))) (|isDomain| *3 #8#) #2#)) (|lambda| #5# (AND #7# #2#)) (+ #9=(*1 *1 *1 *1) #2#) (* #9# #2#) (/ #9# #2#) (** #5# (AND (|isDomain| *2 (|NonNegativeInteger|)) #2#)) (** #5# (AND (|isDomain| *2 (|Integer|)) #2#)) (|Zero| #10=(*1 *1) #2#) (|One| #10# #2#) (|flatten| (*1 *1 *1) #2#) (|unparse| #1# #11=(AND (|isDomain| *2 (|String|)) #2#)) (|parseString| #4# #11#) (|declare| (*1 *2 *3) (AND #12=(|isDomain| *3 #6#) #13=(|isDomain| *2 #8#) #2#)) (|compile| (*1 *2 *2 *3) (AND #13# #12# #2#))) 
((|packageCall| ((#1=(|InputForm|) (|Symbol|)) 15 T ELT)) (|interpret| ((|#1| #1#) 20 T ELT))) 
(((|InputFormFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |packageCall| (#1=(|InputForm|) (|Symbol|))) (SIGNATURE |interpret| (|#1| #1#))) (|Type|)) (T |InputFormFunctions1|)) 
((|interpret| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|InputForm|)) (|isDomain| *1 (|InputFormFunctions1| *2)) (|ofCategory| *2 #3=(|Type|)))) (|packageCall| #1# (AND (|isDomain| *3 (|Symbol|)) (|isDomain| *2 #2#) (|isDomain| *1 (|InputFormFunctions1| *4)) (|ofCategory| *4 #3#)))) 
((|oddInfiniteProduct| (#1=(|#2| |#2|) 17 T ELT)) (|infiniteProduct| (#1# 13 T ELT)) (|generalInfiniteProduct| ((|#2| |#2| #2=(|Integer|) #2#) 20 T ELT)) (|evenInfiniteProduct| (#1# 15 T ELT))) 
(((|InfiniteProductCharacteristicZero| |#1| |#2|) (CATEGORY |package| (SIGNATURE |infiniteProduct| #1=(|#2| |#2|)) (SIGNATURE |evenInfiniteProduct| #1#) (SIGNATURE |oddInfiniteProduct| #1#) (SIGNATURE |generalInfiniteProduct| (|#2| |#2| #2=(|Integer|) #2#))) (|Join| (|IntegralDomain|) (|CharacteristicZero|)) (|UnivariateTaylorSeriesCategory| |#1|)) (T |InfiniteProductCharacteristicZero|)) 
((|generalInfiniteProduct| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *4 #1=(|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|InfiniteProductCharacteristicZero| *4 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4)))) (|oddInfiniteProduct| #2=(*1 *2 *2) #3=(AND (|ofCategory| *3 #1#) (|isDomain| *1 (|InfiniteProductCharacteristicZero| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|evenInfiniteProduct| #2# #3#) (|infiniteProduct| #2# #3#)) 
((|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) #1=(|List| |#2|) #2=(|List| (|Symbol|))) 32 T ELT)) (|innerSolve1| ((#1# #3=(|Polynomial| |#1|) |#3|) 54 T ELT) ((#1# (|SparseUnivariatePolynomial| |#1|) |#3|) 53 T ELT)) (|innerSolve| (((|List| #1#) #4=(|List| #3#) #4# #2# |#3|) 106 T ELT))) 
(((|InnerNumericFloatSolvePackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |innerSolve1| (#1=(|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|)) (SIGNATURE |innerSolve1| (#1# #2=(|Polynomial| |#1|) |#3|)) (SIGNATURE |innerSolve| ((|List| #1#) #3=(|List| #2#) #3# #4=(|List| (|Symbol|)) |#3|)) (SIGNATURE |makeEq| ((|List| (|Equation| (|Polynomial| |#2|))) #1# #4#))) (|GcdDomain|) #5=(|Field|) (|Join| #5# (|OrderedRing|))) (T |InnerNumericFloatSolvePackage|)) 
((|makeEq| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 #2=(|List| *6)) #3=(|isDomain| *4 (|List| (|Symbol|))) #4=(|ofCategory| *6 #5=(|Field|)) (|isDomain| *2 (|List| (|Equation| #6=(|Polynomial| *6)))) (|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *7)) #7=(|ofCategory| *5 #8=(|GcdDomain|)) (|ofCategory| *7 #9=(|Join| #5# (|OrderedRing|))))) (|innerSolve| (*1 *2 *3 *3 *4 *5) (AND (|isDomain| *3 (|List| #6#)) #3# (|ofCategory| *6 #8#) (|isDomain| *2 (|List| (|List| *7))) (|isDomain| *1 (|InnerNumericFloatSolvePackage| *6 *7 *5)) (|ofCategory| *7 #5#) (|ofCategory| *5 #9#))) (|innerSolve1| #1# (AND (|isDomain| *3 (|Polynomial| *5)) #7# #10=(|isDomain| *2 #2#) #11=(|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *4)) #4# #12=(|ofCategory| *4 #9#))) (|innerSolve1| #1# (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *5)) #7# #10# #11# #4# #12#))) 
((|reduction| ((|#2| |#2| |#1|) 17 T ELT)) (|modularGcdPrimitive| (#1=(|#2| (|List| |#2|)) 30 T ELT)) (|modularGcd| (#1# 51 T ELT))) 
(((|InnerModularGcd| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |modularGcdPrimitive| #1=(|#2| (|List| |#2|))) (SIGNATURE |modularGcd| #1#) (SIGNATURE |reduction| (|#2| |#2| |#1|))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| |#1|) |#1| (|Mapping| |#1| |#1| (|NonNegativeInteger|))) (T |InnerModularGcd|)) 
((|reduction| (*1 *2 *2 *3) (AND (|ofCategory| *3 #1=(|EuclideanDomain|)) (|ofType| *4 *3) (|ofType| *5 (|Mapping| *3 *3 #2=(|NonNegativeInteger|))) (|isDomain| *1 (|InnerModularGcd| *3 *2 *4 *5)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|modularGcd| #3=(*1 *2 *3) #4=(AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|InnerModularGcd| *4 *2 *5 *6)) (|ofCategory| *4 #1#) (|ofType| *5 *4) (|ofType| *6 (|Mapping| *4 *4 #2#)))) (|modularGcdPrimitive| #3# #4#)) 
((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1# #2=(|Mapping| (|Factored| #3=(|SparseUnivariatePolynomial| |#3|)) #3#)) 90 T ELT) (((|Factored| |#4|) |#4| #2#) 213 T ELT))) 
(((|InnerMultFact| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4| #1=(|Mapping| (|Factored| #2=(|SparseUnivariatePolynomial| |#3|)) #2#))) (SIGNATURE |factor| ((|Factored| #3=(|SparseUnivariatePolynomial| |#4|)) #3# #1#))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|PolynomialCategory| |#3| |#2| |#1|)) (T |InnerMultFact|)) 
((|factor| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *4 (|Mapping| (|Factored| #3=(|SparseUnivariatePolynomial| *7)) #3#)) #4=(|ofCategory| *7 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) #5=(|ofCategory| *5 (|OrderedSet|)) #6=(|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 #7=(|PolynomialCategory| *7 *6 *5)) (|isDomain| *2 (|Factored| #8=(|SparseUnivariatePolynomial| *8))) (|isDomain| *1 (|InnerMultFact| *5 *6 *7 *8)) (|isDomain| *3 #8#))) (|factor| #1# (AND #2# #4# #5# #6# (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|InnerMultFact| *5 *6 *7 *3)) (|ofCategory| *3 #7#)))) 
((|oddInfiniteProduct| (#1=(|#4| |#4|) 74 T ELT)) (|infiniteProduct| (#1# 70 T ELT)) (|generalInfiniteProduct| ((|#4| |#4| #2=(|Integer|) #2#) 76 T ELT)) (|evenInfiniteProduct| (#1# 72 T ELT))) 
(((|InfiniteProductFiniteField| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |infiniteProduct| #1=(|#4| |#4|)) (SIGNATURE |evenInfiniteProduct| #1#) (SIGNATURE |oddInfiniteProduct| #1#) (SIGNATURE |generalInfiniteProduct| (|#4| |#4| #2=(|Integer|) #2#))) (|Join| (|Field|) (|Finite|) (|ConvertibleTo| #2#)) (|UnivariatePolynomialCategory| |#1|) (|MonogenicAlgebra| |#1| |#2|) (|UnivariateTaylorSeriesCategory| |#3|)) (T |InfiniteProductFiniteField|)) 
((|generalInfiniteProduct| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 #1=(|Integer|)) (|ofCategory| *4 (|Join| #2=(|Field|) #3=(|Finite|) (|ConvertibleTo| *3))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|MonogenicAlgebra| *4 *5)) (|isDomain| *1 (|InfiniteProductFiniteField| *4 *5 *6 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *6)))) (|oddInfiniteProduct| #4=(*1 *2 *2) #5=(AND (|ofCategory| *3 (|Join| #2# #3# (|ConvertibleTo| #1#))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|MonogenicAlgebra| *3 *4)) (|isDomain| *1 (|InfiniteProductFiniteField| *3 *4 *5 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *5)))) (|evenInfiniteProduct| #4# #5#) (|infiniteProduct| #4# #5#)) 
((|oddInfiniteProduct| (#1=(|#2| |#2|) 27 T ELT)) (|infiniteProduct| (#1# 23 T ELT)) (|generalInfiniteProduct| ((|#2| |#2| #2=(|Integer|) #2#) 29 T ELT)) (|evenInfiniteProduct| (#1# 25 T ELT))) 
(((|InfiniteProductPrimeField| |#1| |#2|) (CATEGORY |package| (SIGNATURE |infiniteProduct| #1=(|#2| |#2|)) (SIGNATURE |evenInfiniteProduct| #1#) (SIGNATURE |oddInfiniteProduct| #1#) (SIGNATURE |generalInfiniteProduct| (|#2| |#2| #2=(|Integer|) #2#))) (|Join| (|Field|) (|Finite|) (|ConvertibleTo| #2#)) (|UnivariateTaylorSeriesCategory| |#1|)) (T |InfiniteProductPrimeField|)) 
((|generalInfiniteProduct| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 #1=(|Integer|)) (|ofCategory| *4 (|Join| #2=(|Field|) #3=(|Finite|) (|ConvertibleTo| *3))) (|isDomain| *1 (|InfiniteProductPrimeField| *4 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *4)))) (|oddInfiniteProduct| #4=(*1 *2 *2) #5=(AND (|ofCategory| *3 (|Join| #2# #3# (|ConvertibleTo| #1#))) (|isDomain| *1 (|InfiniteProductPrimeField| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|evenInfiniteProduct| #4# #5#) (|infiniteProduct| #4# #5#)) 
((|signAround| ((#1=(|Union| #2=(|Integer|) "failed") |#2| |#1| #3=(|Mapping| #1# |#1|)) 18 T ELT) ((#1# |#2| |#1| #2# #3#) 14 T ELT) ((#1# |#2| #2# #3#) 30 T ELT))) 
(((|InnerPolySign| |#1| |#2|) (CATEGORY |package| (SIGNATURE |signAround| (#1=(|Union| #2=(|Integer|) "failed") |#2| #2# #3=(|Mapping| #1# |#1|))) (SIGNATURE |signAround| (#1# |#2| |#1| #2# #3#)) (SIGNATURE |signAround| (#1# |#2| |#1| #3#))) (|Ring|) (|UnivariatePolynomialCategory| |#1|)) (T |InnerPolySign|)) 
((|signAround| (*1 *2 *3 *4 *5) #1=(|partial| AND (|isDomain| *5 (|Mapping| #2=(|Union| #3=(|Integer|) "failed") *4)) (|ofCategory| *4 #4=(|Ring|)) #5=(|isDomain| *2 #3#) (|isDomain| *1 (|InnerPolySign| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|signAround| (*1 *2 *3 *4 *2 *5) #1#) (|signAround| (*1 *2 *3 *2 *4) (|partial| AND (|isDomain| *4 (|Mapping| #2# *5)) (|ofCategory| *5 #4#) #5# (|isDomain| *1 (|InnerPolySign| *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
((|symmetricRemainder| (#1=($ $ $) 87 T ELT)) (|squareFree| (#2=((|Factored| $) $) 50 T ELT)) (|retractIfCan| (((|Union| #3=(|Integer|) #4="failed") $) 62 T ELT)) (|retract| (#5=(#3# $) 40 T ELT)) (|rationalIfCan| (((|Union| #6=(|Fraction| #3#) #4#) $) 80 T ELT)) (|rational?| (#7=(#8=(|Boolean|) $) 24 T ELT)) (|rational| ((#6# $) 78 T ELT)) (|prime?| (#7# 53 T ELT)) (|powmod| (($ $ $ $) 94 T ELT)) (|permutation| (#1# 60 T ELT)) (|patternMatch| ((#9=(|PatternMatchResult| #3# $) $ #10=(|Pattern| #3#) #9#) 75 T ELT)) (|nextItem| (((|Maybe| $) $) 70 T ELT)) (|mask| (#11=($ $) 22 T ELT)) (|invmod| (#1# 92 T ELT)) (|init| (($) 63 T CONST)) (|factorial| (#11# 56 T ELT)) (|factor| (#2# 48 T ELT)) (|even?| (#7# 15 T ELT)) (|euclideanSize| ((#12=(|NonNegativeInteger|) $) 30 T ELT)) (|differentiate| (#11# 11 T ELT) (($ $ #12#) NIL T ELT)) (|copy| (#11# 16 T ELT)) (|convert| (#5# NIL T ELT) (((|InputForm|) $) 39 T ELT) ((#10# $) 43 T ELT) (((|Float|) $) 33 T ELT) (((|DoubleFloat|) $) 36 T ELT)) (|characteristic| ((#12#) 9 T CONST)) (|bit?| ((#8# $ $) 19 T ELT)) (|binomial| (#1# 58 T ELT))) 
(((|IntegerNumberSystem&| |#1|) (CATEGORY |package| (SIGNATURE |invmod| #1=(|#1| |#1| |#1|)) (SIGNATURE |powmod| (|#1| |#1| |#1| |#1|)) (SIGNATURE |mask| #2=(|#1| |#1|)) (SIGNATURE |copy| #2#) (SIGNATURE |rationalIfCan| ((|Union| #3=(|Fraction| #4=(|Integer|)) #5="failed") |#1|)) (SIGNATURE |rational| (#3# |#1|)) (SIGNATURE |rational?| #6=(#7=(|Boolean|) |#1|)) (SIGNATURE |symmetricRemainder| #1#) (SIGNATURE |bit?| (#7# |#1| |#1|)) (SIGNATURE |even?| #6#) (SIGNATURE |init| (|#1|) |constant|) (SIGNATURE |nextItem| ((|Maybe| |#1|) |#1|)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| ((|Float|) |#1|)) (SIGNATURE |permutation| #1#) (SIGNATURE |factorial| #2#) (SIGNATURE |binomial| #1#) (SIGNATURE |patternMatch| (#8=(|PatternMatchResult| #4# |#1|) |#1| #9=(|Pattern| #4#) #8#)) (SIGNATURE |convert| (#9# |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #4# #5#) |#1|)) (SIGNATURE |retract| #10=(#4# |#1|)) (SIGNATURE |convert| #10#) (SIGNATURE |differentiate| (|#1| |#1| #11=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #2#) (SIGNATURE |euclideanSize| (#11# |#1|)) (SIGNATURE |factor| #12=((|Factored| |#1|) |#1|)) (SIGNATURE |squareFree| #12#) (SIGNATURE |prime?| #6#) (SIGNATURE |characteristic| (#11#) |constant|)) (|IntegerNumberSystem|)) (T |IntegerNumberSystem&|)) 
((|characteristic| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|IntegerNumberSystem&| *3)) (|ofCategory| *3 (|IntegerNumberSystem|))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|symmetricRemainder| (($ $ $) 102 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|submod| (($ $ $ $) 91 T ELT)) (|squareFreePart| (($ $) 66 T ELT)) (|squareFree| (#4=((|Factored| $) $) 67 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 145 T ELT)) (|sign| (((|Integer|) $) 134 T ELT)) (|shift| (($ $ $) 105 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| #6=(|Integer|) "failed") $) 126 T ELT)) (|retract| ((#6# $) 127 T ELT)) (|rem| (#7=($ $ $) 149 T ELT)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) #9=(|Matrix| $) #10=(|Vector| $)) 124 T ELT) (((|Matrix| #8#) #9#) 123 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 99 T ELT)) (|rational?| (((|Boolean|) $) 101 T ELT)) (|rational| (((|Fraction| (|Integer|)) $) 100 T ELT)) (|random| (($) 98 T ELT) (($ $) 97 T ELT)) (|quo| (#7# 148 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) (|:| |generator| $)) #11#) 143 T ELT)) (|prime?| (((|Boolean|) $) 68 T ELT)) (|powmod| (($ $ $ $) 89 T ELT)) (|positiveRemainder| (($ $ $) 103 T ELT)) (|positive?| (((|Boolean|) $) 136 T ELT)) (|permutation| (#12=($ $ $) 114 T ELT)) (|patternMatch| (((|PatternMatchResult| #13=(|Integer|) . #14=($)) $ (|Pattern| #13#) (|PatternMatchResult| #13# . #14#)) 117 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|odd?| (((|Boolean|) $) 109 T ELT)) (|nextItem| (((|Maybe| $) $) 111 T ELT)) (|negative?| (((|Boolean|) $) 135 T ELT)) (|multiEuclidean| (((|Union| #15=(|List| $) #16="failed") #15# $) 152 T ELT)) (|mulmod| (($ $ $ $) 90 T ELT)) (|min| (#17=($ $ $) 142 T ELT)) (|max| (#17# 141 T ELT)) (|mask| (($ $) 93 T ELT)) (|length| (($ $) 106 T ELT)) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| #8#)) (|:| |vec| (|Vector| #8#))) #10# $) 122 T ELT) (((|Matrix| #8#) #10#) 121 T ELT)) (|lcm| (#18=($ $ $) 60 T ELT) (#19=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|invmod| (($ $ $) 88 T ELT)) (|init| (($) 110 T CONST)) (|inc| (($ $) 95 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#20=(|SparseUnivariatePolynomial| $) #20# #20#) 58 T ELT)) (|gcd| (#18# 62 T ELT) (#19# 61 T ELT)) (|factorial| (($ $) 115 T ELT)) (|factor| (#4# 65 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #21=(|:| |coef1| $) #22=(|:| |coef2| $)) #16#) $ $ $) 151 T ELT) (((|Record| #21# #22# (|:| |generator| $)) $ $) 150 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #11#) #11# $) 144 T ELT)) (|even?| (((|Boolean|) $) 108 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 146 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 147 T ELT)) (|differentiate| (($ . #23=($)) 132 T ELT) (#24=($ $ (|NonNegativeInteger|)) 130 T ELT)) (|dec| (($ $) 94 T ELT)) (|copy| (($ $) 96 T ELT)) (|convert| (((|Integer|) . #25=($)) 128 T ELT) (((|InputForm|) . #25#) 119 T ELT) (((|Pattern| (|Integer|)) . #25#) 118 T ELT) (((|Float|) . #25#) 113 T ELT) (((|DoubleFloat|) . #25#) 112 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #6#) 125 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|bit?| (((|Boolean|) $ $) 104 T ELT)) (|binomial| (#12# 116 T ELT)) (|before?| (#1# 6 T ELT)) (|base| (($) 107 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|addmod| (($ $ $ $) 92 T ELT)) (|abs| (($ $) 133 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ . #23#) 131 T ELT) (#24# 129 T ELT)) (>= (#26=((|Boolean|) $ $) 140 T ELT)) (> (#26# 138 T ELT)) (= (#1# 8 T ELT)) (<= (#26# 139 T ELT)) (< (#26# 137 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #27=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ #8# . #27#) 120 T ELT))) 
(((|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|))) (|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| #1=(|Integer|)) (|RetractableTo| #1#) (|LinearlyExplicitRingOver| #1#) (|ConvertibleTo| (|InputForm|)) (|ConvertibleTo| (|Pattern| #1#)) (|PatternMatchable| #1#) (|CombinatorialFunctionCategory|) (|RealConstant|) (|CharacteristicZero|) (|StepThrough|) (CATEGORY |domain| (SIGNATURE |odd?| #2=(#3=(|Boolean|) $)) (SIGNATURE |even?| #2#) (ATTRIBUTE |multiplicativeValuation|) (SIGNATURE |base| #4=($)) (SIGNATURE |length| #5=($ $)) (SIGNATURE |shift| #6=($ $ $)) (SIGNATURE |bit?| (#3# $ $)) (SIGNATURE |positiveRemainder| #6#) (SIGNATURE |symmetricRemainder| #6#) (SIGNATURE |rational?| #2#) (SIGNATURE |rational| (#7=(|Fraction| #1#) $)) (SIGNATURE |rationalIfCan| ((|Union| #7# "failed") $)) (SIGNATURE |random| #4#) (SIGNATURE |random| #5#) (SIGNATURE |copy| #5#) (SIGNATURE |inc| #5#) (SIGNATURE |dec| #5#) (SIGNATURE |mask| #5#) (SIGNATURE |addmod| #8=($ $ $ $)) (SIGNATURE |submod| #8#) (SIGNATURE |mulmod| #8#) (SIGNATURE |powmod| #8#) (SIGNATURE |invmod| #6#) (ATTRIBUTE |canonicalUnitNormal|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CombinatorialFunctionCategory|) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|InputForm|)) . T) ((|ConvertibleTo| #1=(|Integer|)) . T) ((|ConvertibleTo| (|Pattern| #1#)) . T) ((|DifferentialDomain| $) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedIntegralDomain|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PatternMatchable| #1#) . T) ((|PrincipalIdealDomain|) . T) ((|RealConstant|) . T) ((|RetractableTo| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 8 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 77 T ELT)) (|unitCanonical| (#5=($ $) 78 T ELT)) (|unit?| #6=(#4# NIL T ELT)) (|symmetricRemainder| #7=(#8=($ $ $) NIL T ELT)) (|subtractIfCan| (#9=(#10=(|Union| $ #11="failed") $ $) NIL T ELT)) (|submod| (#12=($ $ $ $) 31 T ELT)) (|squareFreePart| #13=(#5# NIL T ELT)) (|squareFree| (#14=((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sign| #15=(#16=(#17=(|Integer|) $) NIL T ELT)) (|shift| (#8# 71 T ELT)) (|sample| #18=(#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #17# #11#) $) NIL T ELT)) (|retract| #15#) (|rem| (#8# 45 T ELT)) (|reducedSystem| ((#20=(|Record| (|:| |mat| #21=(|Matrix| #17#)) (|:| |vec| (|Vector| #17#))) #22=(|Matrix| $) #23=(|Vector| $)) 53 T ELT) ((#21# #22#) 49 T ELT)) (|recip| ((#10# $) 74 T ELT)) (|rationalIfCan| (((|Union| #24=(|Fraction| #17#) #11#) $) NIL T ELT)) (|rational?| #6#) (|rational| ((#24# $) NIL T ELT)) (|random| (#19# 55 T ELT) (#5# 56 T ELT)) (|quo| (#8# 70 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|prime?| #6#) (|powmod| (#12# NIL T ELT)) (|positiveRemainder| (#8# 46 T ELT)) (|positive?| (#4# 22 T ELT)) (|permutation| #7#) (|patternMatch| ((#27=(|PatternMatchResult| #17# $) $ #28=(|Pattern| #17#) #27#) NIL T ELT)) (|opposite?| (#2# 110 T ELT)) (|one?| (#4# 9 T ELT)) (|odd?| (#4# 64 T ELT)) (|nextItem| (((|Maybe| $) $) NIL T ELT)) (|negative?| (#4# 21 T ELT)) (|multiEuclidean| (((|Union| #25# #11#) #25# $) NIL T ELT)) (|mulmod| (#12# 32 T ELT)) (|min| (#8# 67 T ELT)) (|max| (#8# 66 T ELT)) (|mask| #13#) (|length| (#5# 29 T ELT)) (|leftReducedSystem| ((#20# #23# $) NIL T ELT) ((#21# #23#) NIL T ELT)) (|lcm| #7# #29=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) 44 T ELT)) (|invmod| #7#) (|init| #18#) (|inc| (#5# 15 T ELT)) (|hash| (((|SingleInteger|) $) 19 T ELT)) (|gcdPolynomial| ((#30=(|SparseUnivariatePolynomial| $) #30# #30#) 109 T ELT)) (|gcd| (#8# 75 T ELT) #29#) (|factorial| #13#) (|factor| (#14# 95 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #31=(|:| |coef1| $) #32=(|:| |coef2| $)) #11#) $ $ $) NIL T ELT) (((|Record| #31# #32# #26#) $ $) NIL T ELT)) (|exquo| (#9# 93 T ELT)) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|even?| (#4# 65 T ELT)) (|euclideanSize| ((#33=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 69 T ELT)) (|differentiate| #13# #34=(#35=($ $ #33#) NIL T ELT)) (|dec| (#5# 17 T ELT)) (|copy| (#5# 13 T ELT)) (|convert| (#16# 28 T ELT) (((|InputForm|) $) 41 T ELT) ((#28# $) NIL T ELT) (((|Float|) $) 35 T ELT) (((|DoubleFloat|) $) 38 T ELT)) (|coerce| (((|OutputForm|) $) 26 T ELT) #36=(($ #17#) 27 T ELT) #13# #36#) (|characteristic| ((#33#) NIL T CONST)) (|bit?| #1#) (|binomial| #7#) (|before?| #1#) (|base| (#19# 12 T ELT)) (|associates?| #1#) (|annihilate?| (#2# 112 T ELT)) (|addmod| (#12# 30 T ELT)) (|abs| (#5# 54 T ELT)) (|Zero| (#19# 10 T CONST)) (|One| (#19# 11 T CONST)) (D #13# #34#) (>= (#2# 59 T ELT)) (> (#2# 57 T ELT)) (= (#2# 7 T ELT)) (<= (#2# 58 T ELT)) (< (#2# 20 T ELT)) (- (#5# 42 T ELT) (#8# 16 T ELT)) (+ (#8# 14 T ELT)) (** (($ $ #37=(|PositiveInteger|)) NIL T ELT) (#35# 63 T ELT)) (* (($ #37# $) NIL T ELT) (($ #33# $) NIL T ELT) #38=(($ #17# $) 61 T ELT) (#8# 60 T ELT) #38#)) 
(((|Integer|) (|Join| (|IntegerNumberSystem|) (CATEGORY |package| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|)))) (T |Integer|)) 
NIL 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) 
(((|Int16|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |sample| ($) |constant|)))) (T |Int16|)) 
((|sample| (*1 *1) (|isDomain| *1 (|Int16|)))) 
((|Integer|) (|%not| (|%ilt| 16 (|%ilength| |#1|)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) 
(((|Int32|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |sample| ($) |constant|)))) (T |Int32|)) 
((|sample| (*1 *1) (|isDomain| *1 (|Int32|)))) 
((|Integer|) (|%not| (|%ilt| 32 (|%ilength| |#1|)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) 
(((|Int64|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |sample| ($) |constant|)))) (T |Int64|)) 
((|sample| (*1 *1) (|isDomain| *1 (|Int64|)))) 
((|Integer|) (|%not| (|%ilt| 64 (|%ilength| |#1|)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) 
(((|Int8|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |sample| ($) |constant|)))) (T |Int8|)) 
((|sample| (*1 *1) (|isDomain| *1 (|Int8|)))) 
((|Integer|) (|%not| (|%ilt| 8 (|%ilength| |#1|)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #6=(|BasicType|)) #7=(|has| |#2| #6#)) ELT)) (|table| #8=(#9=($) NIL T ELT) #10=(($ #11=(|List| #5#)) NIL T ELT)) (|swap!| (((|Void|) $ |#1| |#1|) NIL #12=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| #13=(#14=(|#2| $ |#1| |#2|) NIL #12# ELT)) (|select!| #15=(($ #16=(|Mapping| #3# #5#) $) NIL #17=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|select| #15#) (|search| #18=(((|Union| |#2| #19="failed") |#1| $) NIL T ELT)) (|sample| (#9# NIL T CONST)) (|removeDuplicates| (#20=($ $) NIL #21=(AND #17# #4#) ELT)) (|remove!| (#22=($ #5# $) NIL #17# ELT) #15# #18#) (|remove| (#22# NIL #21# ELT) #15#) (|reduce| ((#5# #23=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #23# $ #5#) NIL T ELT) ((#5# #23# $) NIL T ELT)) (|qsetelt!| #13#) (|qelt| #24=((|#2| $ |#1|) NIL T ELT)) (|minIndex| #25=((|#1| $) NIL #26=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#11# $) NIL T ELT)) (|member?| ((#3# #5# $) NIL #4# ELT)) (|maxIndex| #25#) (|map!| #27=(($ (|Mapping| #5# #5#) . #28=($)) NIL T ELT) #29=(($ (|Mapping| |#2| |#2|) . #28#) NIL T ELT)) (|map| #27# #29# #27# (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #30=(OR #31=(|has| #5# #32=(|SetCategory|)) #33=(|has| |#2| #32#)) ELT)) (|keys| #34=(((|List| |#1|) $) NIL T ELT)) (|key?| #35=((#3# |#1| $) NIL T ELT)) (|inspect| #36=((#5# $) NIL T ELT)) (|insert!| (#22# NIL T ELT)) (|indices| #34#) (|index?| #35#) (|hash| (((|SingleInteger|) $) NIL #30# ELT)) (|first| ((|#2| $) NIL #26# ELT)) (|find| (((|Union| #5# #19#) #16# $) NIL T ELT)) (|fill!| (($ $ |#2|) NIL #12# ELT)) (|extract!| #36#) (|every?| #37=((#3# #16# $) NIL T ELT)) (|eval| #38=(($ $ (|List| #39=(|Equation| #5#))) NIL #40=(AND (|has| #5# (|Evalable| #5#)) #31#) ELT) #41=(($ $ #39#) NIL #40# ELT) #42=(($ $ #5# #5#) NIL #40# ELT) #43=(($ $ #11# #11#) NIL #40# ELT) (($ $ #44=(|List| |#2|) #44#) NIL #45=(AND (|has| |#2| (|Evalable| |#2|)) #33#) ELT) (($ $ |#2| |#2|) NIL #45# ELT) (($ $ #46=(|Equation| |#2|)) NIL #45# ELT) (($ $ (|List| #46#)) NIL #45# ELT) #43# #42# #41# #38#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#2| $) NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #7#) ELT)) (|entries| ((#44# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| #8#) (|elt| #24# (#14# NIL T ELT)) (|dictionary| #8# #10#) (|count| ((#47=(|NonNegativeInteger|) #5# $) NIL #4# ELT) ((#47# #16# $) NIL T ELT)) (|copy| (#20# NIL T ELT)) (|convert| ((#48=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #48#)) ELT)) (|construct| #10#) (|coerce| ((#49=(|OutputForm|) $) NIL (OR (|has| #5# #50=(|CoercibleTo| #49#)) (|has| |#2| #50#)) ELT)) (|before?| #1#) (|bag| #10#) (|any?| #37#) (= #1#) (|#| ((#47# $) NIL T ELT))) 
(((|InnerTable| |#1| |#2| |#3|) #1=(|TableAggregate| |#1| |#2|) #2=(|SetCategory|) #2# #1#) (T |InnerTable|)) 
NIL 
((|algint| (((|IntegrationResult| |#2|) |#2| #1=(|Kernel| |#2|) #1# (|Mapping| #2=(|SparseUnivariatePolynomial| |#2|) #2#)) 50 T ELT))) 
(((|AlgebraicIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |algint| ((|IntegrationResult| |#2|) |#2| #1=(|Kernel| |#2|) #1# (|Mapping| #2=(|SparseUnivariatePolynomial| |#2|) #2#)))) (|IntegralDomain|) (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| |#1|))) (T |AlgebraicIntegration|)) 
((|algint| (*1 *2 *3 *4 *4 *5) (AND (|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|Mapping| #1=(|SparseUnivariatePolynomial| *3) #1#)) (|ofCategory| *3 (|Join| (|AlgebraicallyClosedField|) (|FunctionSpace| *6))) (|ofCategory| *6 (|IntegralDomain|)) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|AlgebraicIntegration| *6 *3))))) 
((|palgintegrate| (#1=((|IntegrationResult| |#5|) |#5| #2=(|Mapping| |#3| |#3|)) 217 T ELT)) (|palginfieldint| (((|Union| |#5| "failed") |#5| #2#) 213 T ELT)) (|algintegrate| (#1# 221 T ELT))) 
(((|AlgebraicIntegrate| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |algintegrate| #1=((|IntegrationResult| |#5|) |#5| #2=(|Mapping| |#3| |#3|))) (SIGNATURE |palgintegrate| #1#) (SIGNATURE |palginfieldint| ((|Union| |#5| "failed") |#5| #2#))) (|Join| (|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| #1=(|AlgebraicallyClosedField|) (|FunctionSpace| *4))) (|ofCategory| *4 #2=(|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|isDomain| *1 (|AlgebraicIntegrate| *4 *5 *6 *7 *2)) (|ofCategory| *2 (|FunctionFieldCategory| *5 *6 *7)))) (|palgintegrate| #3=(*1 *2 *3 *4) #4=(AND (|isDomain| *4 (|Mapping| *7 *7)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *6 (|Join| #1# (|FunctionSpace| *5))) (|ofCategory| *5 #2#) (|ofCategory| *8 (|UnivariatePolynomialCategory| (|Fraction| *7))) (|isDomain| *2 (|IntegrationResult| *3)) (|isDomain| *1 (|AlgebraicIntegrate| *5 *6 *7 *8 *3)) (|ofCategory| *3 (|FunctionFieldCategory| *6 *7 *8)))) (|algintegrate| #3# #4#)) 
((|bitTruth| (((|Boolean|) #1=(|Integer|) #1#) 12 T ELT)) (|bitLength| ((#1# #1#) 7 T ELT)) (|bitCoef| ((#1# #1# #1#) 10 T ELT))) 
(((|IntegerBits|) (CATEGORY |package| (SIGNATURE |bitLength| (#1=(|Integer|) #1#)) (SIGNATURE |bitCoef| (#1# #1# #1#)) (SIGNATURE |bitTruth| ((|Boolean|) #1# #1#)))) (T |IntegerBits|)) 
((|bitTruth| (*1 *2 *3 *3) (AND (|isDomain| *3 #1=(|Integer|)) (|isDomain| *2 (|Boolean|)) #2=(|isDomain| *1 (|IntegerBits|)))) (|bitCoef| (*1 *2 *2 *2) #3=(AND (|isDomain| *2 #1#) #2#)) (|bitLength| (*1 *2 *2) #3#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|width| ((|#1| $) 77 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|tanh| (#4=($ $) 107 T ELT)) (|tan| (#5=($ $) 90 T ELT)) (|sup| ((|#1| $) 78 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sqrt| (($ $) 89 T ELT)) (|sinh| (#4# 106 T ELT)) (|sin| (#5# 91 T ELT)) (|sech| (#4# 105 T ELT)) (|sec| (#5# 92 T ELT)) (|sample| (#6=($) 23 T CONST)) (|retractIfCan| (((|Union| #7=(|Integer|) "failed") $) 85 T ELT)) (|retract| ((#7# $) 86 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|qinterval| (($ |#1| |#1|) 82 T ELT)) (|positive?| (((|Boolean|) $) 76 T ELT)) (|pi| (($) 117 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #8=(|Integer|)) 88 T ELT)) (|negative?| (((|Boolean|) $) 75 T ELT)) (|min| (#9=($ $ $) 118 T ELT)) (|max| (#9# 119 T ELT)) (|log| (#10=($ $) 114 T ELT)) (|lcm| (#11=($ $ $) 60 T ELT) (#12=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|interval| (($ |#1| |#1|) 83 T ELT) (($ |#1|) 81 T ELT) (($ (|Fraction| (|Integer|))) 80 T ELT)) (|inf| ((|#1| $) 79 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) 58 T ELT)) (|gcd| (#11# 62 T ELT) (#12# 61 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|exp| (#10# 115 T ELT)) (|csch| (#4# 104 T ELT)) (|csc| (#5# 93 T ELT)) (|coth| (#4# 103 T ELT)) (|cot| (#5# 94 T ELT)) (|cosh| (#4# 102 T ELT)) (|cos| (#5# 95 T ELT)) (|contains?| (((|Boolean|) $ |#1|) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #7#) 84 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|atanh| (#14=($ $) 113 T ELT)) (|atan| (#15=($ $) 101 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|asinh| (#14# 112 T ELT)) (|asin| (#15# 100 T ELT)) (|asech| (#14# 111 T ELT)) (|asec| (#15# 99 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#14# 110 T ELT)) (|acsc| (#15# 98 T ELT)) (|acoth| (#14# 109 T ELT)) (|acot| (#15# 97 T ELT)) (|acosh| (#14# 108 T ELT)) (|acos| (#15# 96 T ELT)) (|Zero| (#6# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#16=((|Boolean|) $ $) 120 T ELT)) (> (#16# 122 T ELT)) (= (#1# 8 T ELT)) (<= (#16# 121 T ELT)) (< (#16# 123 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ $) 116 T ELT) (($ $ (|Fraction| #8#)) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ElementaryFunctionCategory|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|HyperbolicFunctionCategory|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|RadicalCategory|) . T) ((|RetractableTo| (|Integer|)) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) . T) ((|TrigonometricFunctionCategory|) . T) ((|Type|) . T)) 
((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 9 T ELT)) (|unitCanonical| (($ $) 11 T ELT)) (|unit?| ((#1=(|Boolean|) $) 20 T ELT)) (|recip| (((|Union| $ "failed") $) 16 T ELT)) (|associates?| ((#1# $ $) 22 T ELT))) 
(((|IntegralDomain&| |#1|) (CATEGORY |package| (SIGNATURE |unit?| (#1=(|Boolean|) |#1|)) (SIGNATURE |associates?| (#1# |#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 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| (((|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (((|Boolean|) $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #1=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2="failed") |#2| #3=(|Symbol|) (|List| |#2|)) 38 T ELT)) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| #3#) 63 T ELT)) (|lfinfieldint| (((|Union| |#2| #2#) |#2| #3#) 156 T ELT)) (|lfextlimint| ((#4=(|Union| (|Record| (|:| |ratpart| |#2|) #1#) #2#) |#2| #3# #5=(|Kernel| |#2|) (|List| #5#)) 159 T ELT)) (|lfextendedint| ((#4# |#2| #3# |#2|) 41 T ELT))) 
(((|ElementaryIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |lfextendedint| (#1=(|Union| (|Record| (|:| |ratpart| |#2|) #2=(|:| |coeff| |#2|)) #3="failed") |#2| #4=(|Symbol|) |#2|)) (SIGNATURE |lflimitedint| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #2# (|:| |logand| |#2|))))) #3#) |#2| #4# (|List| |#2|))) (SIGNATURE |lfinfieldint| ((|Union| |#2| #3#) |#2| #4#)) (SIGNATURE |lfintegrate| ((|IntegrationResult| |#2|) |#2| #4#)) (SIGNATURE |lfextlimint| (#1# |#2| #4# #5=(|Kernel| |#2|) (|List| #5#)))) (|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| #6=(|Integer|)) (|LinearlyExplicitRingOver| #6#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |ElementaryIntegration|)) 
((|lfextlimint| (*1 *2 *3 *4 *5 *6) (|partial| AND #1=(|isDomain| *4 #2=(|Symbol|)) (|isDomain| *6 (|List| #3=(|Kernel| *3))) (|isDomain| *5 #3#) (|ofCategory| *3 (|Join| #4=(|AlgebraicallyClosedField|) #5=(|TranscendentalFunctionCategory|) (|FunctionSpace| *7))) (|ofCategory| *7 #6=(|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| #7=(|Integer|)) (|LinearlyExplicitRingOver| #7#))) #8=(|isDomain| *2 (|Record| (|:| |ratpart| *3) #9=(|:| |coeff| *3))) (|isDomain| *1 (|ElementaryIntegration| *7 *3)))) (|lfintegrate| (*1 *2 *3 *4) (AND #1# #10=(|ofCategory| *5 #6#) (|isDomain| *2 (|IntegrationResult| *3)) #11=(|isDomain| *1 (|ElementaryIntegration| *5 *3)) #12=(|ofCategory| *3 (|Join| #4# #5# (|FunctionSpace| *5))))) (|lfinfieldint| (*1 *2 *2 *3) (|partial| AND (|isDomain| *3 #2#) (|ofCategory| *4 #6#) (|isDomain| *1 (|ElementaryIntegration| *4 *2)) (|ofCategory| *2 (|Join| #4# #5# (|FunctionSpace| *4))))) (|lflimitedint| (*1 *2 *3 *4 *5) (|partial| AND #1# (|isDomain| *5 (|List| *3)) (|ofCategory| *3 (|Join| #4# #5# (|FunctionSpace| *6))) (|ofCategory| *6 #6#) (|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| #9# (|:| |logand| *3)))))) (|isDomain| *1 (|ElementaryIntegration| *6 *3)))) (|lfextendedint| (*1 *2 *3 *4 *3) (|partial| AND #1# #10# #8# #11# #12#))) 
((|squareFree| (#1=((|Factored| |#1|) |#1|) 17 T ELT)) (|factor| (#1# 32 T ELT)) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) 48 T ELT)) (|BasicMethod| (#1# 59 T ELT))) 
(((|IntegerFactorizationPackage| |#1|) (CATEGORY |package| (SIGNATURE |factor| #1=((|Factored| |#1|) |#1|)) (SIGNATURE |squareFree| #1#) (SIGNATURE |BasicMethod| #1#) (SIGNATURE |PollardSmallFactor| ((|Union| |#1| "failed") |#1|))) (|IntegerNumberSystem|)) (T |IntegerFactorizationPackage|)) 
((|PollardSmallFactor| (*1 *2 *2) (|partial| AND (|isDomain| *1 (|IntegerFactorizationPackage| *2)) (|ofCategory| *2 #1=(|IntegerNumberSystem|)))) (|BasicMethod| #2=(*1 *2 *3) #3=(AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|IntegerFactorizationPackage| *3)) (|ofCategory| *3 #1#))) (|squareFree| #2# #3#) (|factor| #2# #3#)) 
((|univariate| ((#1=(|SparseUnivariatePolynomial| #2=(|Fraction| #3=(|SparseUnivariatePolynomial| |#2|))) |#2| #4=(|Kernel| |#2|) #4# #3#) 35 T ELT)) (|palglimint0| ((#5=(|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #6=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #7="failed") |#2| #4# #4# #8=(|List| |#2|) #4# |#2| #2#) 105 T ELT) ((#5# |#2| #4# #4# #8# |#2| #3#) 115 T ELT)) (|palgint0| ((#9=(|IntegrationResult| |#2|) |#2| #4# #4# #4# |#2| #2#) 85 T ELT) ((#9# |#2| #4# #4# |#2| #3#) 55 T ELT)) (|palgextint0| ((#10=(|Union| (|Record| (|:| |ratpart| |#2|) #6#) #7#) |#2| #4# #4# |#2| #4# |#2| #2#) 92 T ELT) ((#10# |#2| #4# #4# |#2| |#2| #3#) 114 T ELT)) (|palgRDE0| ((#11=(|Union| |#2| #7#) |#2| |#2| #4# #4# #12=(|Mapping| #11# |#2| |#2| (|Symbol|)) #4# |#2| #2#) 110 T ELT) ((#11# |#2| |#2| #4# #4# #12# |#2| #3#) 116 T ELT)) (|palgLODE0| ((#13=(|Record| (|:| |particular| #11#) (|:| |basis| #8#)) |#3| |#2| #4# #4# #4# |#2| #2#) 133 #14=(|has| |#3| (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) ELT) ((#13# |#3| |#2| #4# #4# |#2| #3#) 132 #14# ELT)) (|multivariate| ((|#2| #1# #4# |#2|) 53 T ELT)) (|lift| ((#1# #3# #4#) 34 T ELT))) 
(((|GenusZeroIntegration| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |palgint0| (#1=(|IntegrationResult| |#2|) |#2| #2=(|Kernel| |#2|) #2# |#2| #3=(|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |palgint0| (#1# |#2| #2# #2# #2# |#2| #4=(|Fraction| #3#))) (SIGNATURE |palgextint0| (#5=(|Union| (|Record| (|:| |ratpart| |#2|) #6=(|:| |coeff| |#2|)) #7="failed") |#2| #2# #2# |#2| |#2| #3#)) (SIGNATURE |palgextint0| (#5# |#2| #2# #2# |#2| #2# |#2| #4#)) (SIGNATURE |palglimint0| (#8=(|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #6# (|:| |logand| |#2|))))) #7#) |#2| #2# #2# #9=(|List| |#2|) |#2| #3#)) (SIGNATURE |palglimint0| (#8# |#2| #2# #2# #9# #2# |#2| #4#)) (SIGNATURE |palgRDE0| (#10=(|Union| |#2| #7#) |#2| |#2| #2# #2# #11=(|Mapping| #10# |#2| |#2| (|Symbol|)) |#2| #3#)) (SIGNATURE |palgRDE0| (#10# |#2| |#2| #2# #2# #11# #2# |#2| #4#)) (SIGNATURE |univariate| (#12=(|SparseUnivariatePolynomial| #4#) |#2| #2# #2# #3#)) (SIGNATURE |multivariate| (|#2| #12# #2# |#2|)) (SIGNATURE |lift| (#12# #3# #2#)) (IF (|has| |#3| (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (PROGN (SIGNATURE |palgLODE0| (#13=(|Record| (|:| |particular| #10#) (|:| |basis| #9#)) |#3| |#2| #2# #2# |#2| #3#)) (SIGNATURE |palgLODE0| (#13# |#3| |#2| #2# #2# #2# |#2| #4#))) |%noBranch|)) (|Join| (|GcdDomain|) (|RetractableTo| #14=(|Integer|)) (|CharacteristicZero|) (|LinearlyExplicitRingOver| #14#)) (|Join| (|FunctionSpace| |#1|) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|)) (|SetCategory|)) (T |GenusZeroIntegration|)) 
((|palgLODE0| (*1 *2 *3 *4 *5 *5 *5 *4 *6) (AND #1=(|isDomain| *5 (|Kernel| *4)) (|isDomain| *6 (|Fraction| #2=(|SparseUnivariatePolynomial| *4))) #3=(|ofCategory| *4 #4=(|Join| (|FunctionSpace| *7) #5=(|AlgebraicallyClosedField|) #6=(|TranscendentalFunctionCategory|))) #7=(|ofCategory| *7 #8=(|Join| (|GcdDomain|) (|RetractableTo| #9=(|Integer|)) (|CharacteristicZero|) (|LinearlyExplicitRingOver| #9#))) #10=(|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 #11="failed")) (|:| |basis| (|List| *4)))) #12=(|isDomain| *1 (|GenusZeroIntegration| *7 *4 *3)) #13=(|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4)) #14=(|ofCategory| *3 #15=(|SetCategory|)))) (|palgLODE0| (*1 *2 *3 *4 *5 *5 *4 *6) (AND #1# (|isDomain| *6 #2#) #3# #7# #10# #12# #13# #14#)) (|lift| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Kernel| *6)) (|ofCategory| *6 #16=(|Join| (|FunctionSpace| *5) #5# #6#)) #17=(|ofCategory| *5 #8#) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| #18=(|SparseUnivariatePolynomial| *6)))) (|isDomain| *1 (|GenusZeroIntegration| *5 *6 *7)) (|isDomain| *3 #18#) #19=(|ofCategory| *7 #15#))) (|multivariate| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| #20=(|Fraction| #21=(|SparseUnivariatePolynomial| *2)))) (|isDomain| *4 #22=(|Kernel| *2)) (|ofCategory| *2 #16#) #17# (|isDomain| *1 (|GenusZeroIntegration| *5 *2 *6)) (|ofCategory| *6 #15#))) (|univariate| (*1 *2 *3 *4 *4 *5) (AND #23=(|isDomain| *4 (|Kernel| *3)) #24=(|ofCategory| *3 #25=(|Join| (|FunctionSpace| *6) #5# #6#)) #26=(|ofCategory| *6 #8#) (|isDomain| *2 (|SparseUnivariatePolynomial| #27=(|Fraction| #28=(|SparseUnivariatePolynomial| *3)))) #29=(|isDomain| *1 (|GenusZeroIntegration| *6 *3 *7)) #30=(|isDomain| *5 #28#) #19#)) (|palgRDE0| (*1 *2 *2 *2 *3 *3 *4 *3 *2 *5) (|partial| AND #31=(|isDomain| *3 #22#) #32=(|isDomain| *4 (|Mapping| (|Union| *2 #11#) *2 *2 (|Symbol|))) (|isDomain| *5 #20#) #33=(|ofCategory| *2 #25#) #26# #34=(|isDomain| *1 (|GenusZeroIntegration| *6 *2 *7)) #19#)) (|palgRDE0| (*1 *2 *2 *2 *3 *3 *4 *2 *5) (|partial| AND #31# #32# (|isDomain| *5 #21#) #33# #26# #34# #19#)) (|palglimint0| (*1 *2 *3 *4 *4 *5 *4 *3 *6) (|partial| AND #23# #35=(|isDomain| *5 (|List| *3)) (|isDomain| *6 #27#) #36=(|ofCategory| *3 #4#) #7# #37=(|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| #38=(|:| |coeff| *3) (|:| |logand| *3)))))) #39=(|isDomain| *1 (|GenusZeroIntegration| *7 *3 *8)) #40=(|ofCategory| *8 #15#))) (|palglimint0| (*1 *2 *3 *4 *4 *5 *3 *6) (|partial| AND #23# #35# (|isDomain| *6 #28#) #36# #7# #37# #39# #40#)) (|palgextint0| (*1 *2 *3 *4 *4 *3 *4 *3 *5) (|partial| AND #23# #41=(|isDomain| *5 #27#) #24# #26# #42=(|isDomain| *2 (|Record| (|:| |ratpart| *3) #38#)) #29# #19#)) (|palgextint0| (*1 *2 *3 *4 *4 *3 *3 *5) (|partial| AND #23# #30# #24# #26# #42# #29# #19#)) (|palgint0| (*1 *2 *3 *4 *4 *4 *3 *5) (AND #23# #41# #24# #26# #43=(|isDomain| *2 (|IntegrationResult| *3)) #29# #19#)) (|palgint0| (*1 *2 *3 *4 *4 *3 *5) (AND #23# #30# #24# #26# #43# #29# #19#))) 
((|sumOfKthPowerDivisors| ((#1=(|Integer|) #1# (|NonNegativeInteger|)) 87 T ELT)) (|sumOfDivisors| (#2=(#1# #1#) 85 T ELT)) (|numberOfDivisors| (#2# 82 T ELT)) (|moebiusMu| (#2# 89 T ELT)) (|legendre| (#3=(#1# #1# #1#) 67 T ELT)) (|jacobi| (#3# 64 T ELT)) (|harmonic| (#4=((|Fraction| #1#) #1#) 29 T ELT)) (|fibonacci| (#2# 34 T ELT)) (|eulerPhi| (#2# 76 T ELT)) (|euler| (#2# 47 T ELT)) (|divisors| (((|List| #1#) #1#) 81 T ELT)) (|chineseRemainder| ((#1# #1# #1# #1# #1#) 60 T ELT)) (|bernoulli| (#4# 56 T ELT))) 
(((|IntegerNumberTheoryFunctions|) (CATEGORY |package| (SIGNATURE |bernoulli| #1=((|Fraction| #2=(|Integer|)) #2#)) (SIGNATURE |chineseRemainder| (#2# #2# #2# #2# #2#)) (SIGNATURE |divisors| ((|List| #2#) #2#)) (SIGNATURE |euler| #3=(#2# #2#)) (SIGNATURE |eulerPhi| #3#) (SIGNATURE |fibonacci| #3#) (SIGNATURE |harmonic| #1#) (SIGNATURE |jacobi| #4=(#2# #2# #2#)) (SIGNATURE |legendre| #4#) (SIGNATURE |moebiusMu| #3#) (SIGNATURE |numberOfDivisors| #3#) (SIGNATURE |sumOfDivisors| #3#) (SIGNATURE |sumOfKthPowerDivisors| (#2# #2# (|NonNegativeInteger|))))) (T |IntegerNumberTheoryFunctions|)) 
((|sumOfKthPowerDivisors| (*1 *2 *2 *3) (AND #1=(|isDomain| *2 #2=(|Integer|)) (|isDomain| *3 (|NonNegativeInteger|)) #3=(|isDomain| *1 (|IntegerNumberTheoryFunctions|)))) (|sumOfDivisors| #4=(*1 *2 *2) #5=(AND #1# #3#)) (|numberOfDivisors| #4# #5#) (|moebiusMu| #4# #5#) (|legendre| #6=(*1 *2 *2 *2) #5#) (|jacobi| #6# #5#) (|harmonic| #7=(*1 *2 *3) #8=(AND (|isDomain| *2 (|Fraction| #2#)) #3# #9=(|isDomain| *3 #2#))) (|fibonacci| #4# #5#) (|eulerPhi| #4# #5#) (|euler| #4# #5#) (|divisors| #7# (AND (|isDomain| *2 (|List| #2#)) #3# #9#)) (|chineseRemainder| (*1 *2 *2 *2 *2 *2) #5#) (|bernoulli| #7# #8#)) 
((|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) 56 T ELT))) 
(((|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))))) 
((|HermiteIntegrate| (((|Record| (|:| |answer| #1=(|Fraction| |#2|)) (|:| |logpart| #1#) (|:| |specpart| #1#) (|:| |polypart| |#2|)) #1# (|Mapping| |#2| |#2|)) 18 T ELT))) 
(((|TranscendentalHermiteIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |HermiteIntegrate| ((|Record| (|:| |answer| #1=(|Fraction| |#2|)) (|:| |logpart| #1#) (|:| |specpart| #1#) (|:| |polypart| |#2|)) #1# (|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| #1=(|Fraction| *6)) (|:| |logpart| #1#) (|:| |specpart| #1#) (|:| |polypart| *6))) (|isDomain| *1 (|TranscendentalHermiteIntegration| *5 *6)) (|isDomain| *3 #1#)))) 
((|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #1=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2="failed") |#2| #3=(|Kernel| |#2|) #3# #4=(|List| |#2|)) 195 T ELT)) (|palgint| (((|IntegrationResult| |#2|) |#2| #3# #3#) 97 T ELT)) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) #1#) #2#) |#2| #3# #3# |#2|) 191 T ELT)) (|palgRDE| ((#5=(|Union| |#2| #2#) |#2| |#2| |#2| #3# #3# (|Mapping| #5# |#2| |#2| #6=(|Symbol|))) 200 T ELT)) (|palgLODE| (((|Record| (|:| |particular| #5#) (|:| |basis| #4#)) |#3| |#2| #3# #3# #6#) 209 (|has| |#3| (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) ELT))) 
(((|PureAlgebraicIntegration| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |palgint| ((|IntegrationResult| |#2|) |#2| #1=(|Kernel| |#2|) #1#)) (SIGNATURE |palgextint| ((|Union| (|Record| (|:| |ratpart| |#2|) #2=(|:| |coeff| |#2|)) #3="failed") |#2| #1# #1# |#2|)) (SIGNATURE |palglimint| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #2# (|:| |logand| |#2|))))) #3#) |#2| #1# #1# #4=(|List| |#2|))) (SIGNATURE |palgRDE| (#5=(|Union| |#2| #3#) |#2| |#2| |#2| #1# #1# (|Mapping| #5# |#2| |#2| #6=(|Symbol|)))) (IF (|has| |#3| (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (SIGNATURE |palgLODE| ((|Record| (|:| |particular| #5#) (|:| |basis| #4#)) |#3| |#2| #1# #1# #6#)) |%noBranch|)) (|Join| (|GcdDomain|) (|RetractableTo| #7=(|Integer|)) (|CharacteristicZero|) (|LinearlyExplicitRingOver| #7#)) (|Join| (|FunctionSpace| |#1|) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|)) (|SetCategory|)) (T |PureAlgebraicIntegration|)) 
((|palgLODE| (*1 *2 *3 *4 *5 *5 *6) (AND (|isDomain| *5 (|Kernel| *4)) (|isDomain| *6 #1=(|Symbol|)) (|ofCategory| *4 (|Join| (|FunctionSpace| *7) #2=(|AlgebraicallyClosedField|) #3=(|TranscendentalFunctionCategory|))) (|ofCategory| *7 #4=(|Join| (|GcdDomain|) (|RetractableTo| #5=(|Integer|)) (|CharacteristicZero|) (|LinearlyExplicitRingOver| #5#))) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 #6="failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|PureAlgebraicIntegration| *7 *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4)) (|ofCategory| *3 #7=(|SetCategory|)))) (|palgRDE| (*1 *2 *2 *2 *2 *3 *3 *4) (|partial| AND (|isDomain| *3 (|Kernel| *2)) (|isDomain| *4 (|Mapping| (|Union| *2 #6#) *2 *2 #1#)) (|ofCategory| *2 #8=(|Join| (|FunctionSpace| *5) #2# #3#)) #9=(|ofCategory| *5 #4#) (|isDomain| *1 (|PureAlgebraicIntegration| *5 *2 *6)) #10=(|ofCategory| *6 #7#))) (|palglimint| (*1 *2 *3 *4 *4 *5) (|partial| AND #11=(|isDomain| *4 (|Kernel| *3)) (|isDomain| *5 (|List| *3)) (|ofCategory| *3 (|Join| (|FunctionSpace| *6) #2# #3#)) (|ofCategory| *6 #4#) (|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| #12=(|:| |coeff| *3) (|:| |logand| *3)))))) (|isDomain| *1 (|PureAlgebraicIntegration| *6 *3 *7)) (|ofCategory| *7 #7#))) (|palgextint| (*1 *2 *3 *4 *4 *3) (|partial| AND #11# #13=(|ofCategory| *3 #8#) #9# (|isDomain| *2 (|Record| (|:| |ratpart| *3) #12#)) #14=(|isDomain| *1 (|PureAlgebraicIntegration| *5 *3 *6)) #10#)) (|palgint| (*1 *2 *3 *4 *4) (AND #11# #13# #9# (|isDomain| *2 (|IntegrationResult| *3)) #14# #10#))) 
((|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| #1=(|Symbol|)) 64 T ELT)) (|pmintegrate| (((|Union| |#2| #2="failed") |#2| #1# #3=(|OrderedCompletion| |#2|) #3#) 174 (AND (|has| |#2| (|SpecialFunctionCategory|)) #4=(|has| |#1| (|ConvertibleTo| (|Pattern| #5=(|Integer|)))) #6=(|has| |#1| (|PatternMatchable| #5#))) ELT) (#7=((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) #2#) |#2| #1#) 145 #8=(AND (|has| |#2| (|LiouvillianFunctionCategory|)) #4# #6#) ELT)) (|pmComplexintegrate| (#7# 156 #8# ELT))) 
(((|PatternMatchIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |splitConstant| ((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| #1=(|Symbol|))) (IF (|has| |#1| (|ConvertibleTo| (|Pattern| #2=(|Integer|)))) (IF (|has| |#1| (|PatternMatchable| #2#)) (PROGN (IF (|has| |#2| (|LiouvillianFunctionCategory|)) (PROGN (SIGNATURE |pmComplexintegrate| #3=((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) #4="failed") |#2| #1#)) (SIGNATURE |pmintegrate| #3#)) |%noBranch|) (IF (|has| |#2| (|SpecialFunctionCategory|)) (SIGNATURE |pmintegrate| ((|Union| |#2| #4#) |#2| #1# #5=(|OrderedCompletion| |#2|) #5#)) |%noBranch|)) |%noBranch|) |%noBranch|)) (|Join| (|RetractableTo| #2#) (|GcdDomain|) (|LinearlyExplicitRingOver| #2#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |PatternMatchIntegration|)) 
((|pmintegrate| (*1 *2 *2 *3 *4 *4) (|partial| AND (|isDomain| *3 #1=(|Symbol|)) (|isDomain| *4 (|OrderedCompletion| *2)) (|ofCategory| *2 (|SpecialFunctionCategory|)) (|ofCategory| *2 #2=(|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *5))) #3=(|ofCategory| *5 (|ConvertibleTo| (|Pattern| #4=(|Integer|)))) #5=(|ofCategory| *5 (|PatternMatchable| #4#)) #6=(|ofCategory| *5 (|Join| (|RetractableTo| #4#) (|GcdDomain|) (|LinearlyExplicitRingOver| #4#))) (|isDomain| *1 (|PatternMatchIntegration| *5 *2)))) (|pmintegrate| #7=(*1 *2 *3 *4) #8=(|partial| AND #9=(|isDomain| *4 #1#) #3# #5# #6# (|isDomain| *2 (|Record| (|:| |special| *3) (|:| |integrand| *3))) #10=(|isDomain| *1 (|PatternMatchIntegration| *5 *3)) (|ofCategory| *3 (|LiouvillianFunctionCategory|)) #11=(|ofCategory| *3 #2#))) (|pmComplexintegrate| #7# #8#) (|splitConstant| #7# (AND #9# #6# (|isDomain| *2 (|Record| (|:| |const| *3) (|:| |nconst| *3))) #10# #11#))) 
((|limitedint| (((|Union| (|Record| (|:| |mainpart| #1=(|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| #2=(|:| |coeff| #1#) (|:| |logand| #1#))))) #3="failed") #1# (|List| #1#)) 41 T ELT)) (|integrate| (((|IntegrationResult| #1#) #1#) 28 T ELT)) (|infieldint| (((|Union| #1# #3#) #1#) 17 T ELT)) (|extendedint| (((|Union| (|Record| (|:| |ratpart| #1#) #2#) #3#) #1# #1#) 48 T ELT))) 
(((|RationalIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |integrate| ((|IntegrationResult| #1=(|Fraction| |#2|)) #1#)) (SIGNATURE |infieldint| ((|Union| #1# #2="failed") #1#)) (SIGNATURE |extendedint| ((|Union| (|Record| (|:| |ratpart| #1#) #3=(|:| |coeff| #1#)) #2#) #1# #1#)) (SIGNATURE |limitedint| ((|Union| (|Record| (|:| |mainpart| #1#) (|:| |limitedlogs| (|List| (|Record| #3# (|:| |logand| #1#))))) #2#) #1# (|List| #1#)))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|))) (|UnivariatePolynomialCategory| |#1|)) (T |RationalIntegration|)) 
((|limitedint| (*1 *2 *3 *4) (|partial| AND (|isDomain| *4 (|List| #1=(|Fraction| *6))) (|isDomain| *3 #1#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #2=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3)))))) (|isDomain| *1 (|RationalIntegration| *5 *6)))) (|extendedint| (*1 *2 *3 *3) (|partial| AND #3=(|ofCategory| *4 #2#) #4=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |ratpart| #5=(|Fraction| *5)) (|:| |coeff| #5#))) #6=(|isDomain| *1 (|RationalIntegration| *4 *5)) #7=(|isDomain| *3 #5#))) (|infieldint| (*1 *2 *2) (|partial| AND (|isDomain| *2 (|Fraction| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 #2#) (|isDomain| *1 (|RationalIntegration| *3 *4)))) (|integrate| (*1 *2 *3) (AND #3# #4# (|isDomain| *2 (|IntegrationResult| #5#)) #6# #7#))) 
((|integerIfCan| (((|Union| #1=(|Integer|) "failed") |#1|) 14 T ELT)) (|integer?| (((|Boolean|) |#1|) 13 T ELT)) (|integer| ((#1# |#1|) 9 T ELT))) 
(((|IntegerRetractions| |#1|) (CATEGORY |package| (SIGNATURE |integer| (#1=(|Integer|) |#1|)) (SIGNATURE |integer?| ((|Boolean|) |#1|)) (SIGNATURE |integerIfCan| ((|Union| #1# "failed") |#1|))) (|RetractableTo| #1#)) (T |IntegerRetractions|)) 
((|integerIfCan| #1=(*1 *2 *3) (|partial| AND #2=(|isDomain| *2 #3=(|Integer|)) #4=(|isDomain| *1 (|IntegerRetractions| *3)) #5=(|ofCategory| *3 (|RetractableTo| *2)))) (|integer?| #1# (AND (|isDomain| *2 (|Boolean|)) #4# (|ofCategory| *3 (|RetractableTo| #3#)))) (|integer| #1# (AND #2# #4# #5#))) 
((|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| #1=(|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| #2=(|:| |coeff| #1#) (|:| |logand| #1#))))) #3="failed") #1# #4=(|Symbol|) (|List| #1#)) 48 T ELT)) (|internalIntegrate| (((|IntegrationResult| #1#) #1# #4#) 28 T ELT)) (|infieldIntegrate| (((|Union| #1# #3#) #1# #4#) 23 T ELT)) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| #1#) #2#) #3#) #1# #4# #1#) 35 T ELT))) 
(((|RationalFunctionIntegration| |#1|) (CATEGORY |package| (SIGNATURE |internalIntegrate| ((|IntegrationResult| #1=(|Fraction| (|Polynomial| |#1|))) #1# #2=(|Symbol|))) (SIGNATURE |infieldIntegrate| ((|Union| #1# #3="failed") #1# #2#)) (SIGNATURE |limitedIntegrate| ((|Union| (|Record| (|:| |mainpart| #1#) (|:| |limitedlogs| (|List| (|Record| #4=(|:| |coeff| #1#) (|:| |logand| #1#))))) #3#) #1# #2# (|List| #1#))) (SIGNATURE |extendedIntegrate| ((|Union| (|Record| (|:| |ratpart| #1#) #4#) #3#) #1# #2# #1#))) (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)) (|CharacteristicZero|))) (T |RationalFunctionIntegration|)) 
((|extendedIntegrate| (*1 *2 *3 *4 *3) (|partial| AND #1=(|isDomain| *4 #2=(|Symbol|)) #3=(|ofCategory| *5 #4=(|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)) (|CharacteristicZero|))) (|isDomain| *2 (|Record| (|:| |ratpart| #5=(|Fraction| (|Polynomial| *5))) (|:| |coeff| #5#))) #6=(|isDomain| *1 (|RationalFunctionIntegration| *5)) #7=(|isDomain| *3 #5#))) (|limitedIntegrate| (*1 *2 *3 *4 *5) (|partial| AND #1# (|isDomain| *5 (|List| #8=(|Fraction| (|Polynomial| *6)))) (|isDomain| *3 #8#) (|ofCategory| *6 #4#) (|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 #2#) (|ofCategory| *4 #4#) (|isDomain| *1 (|RationalFunctionIntegration| *4)))) (|internalIntegrate| (*1 *2 *3 *4) (AND #1# #3# (|isDomain| *2 (|IntegrationResult| #5#)) #6# #7#))) 
((~= (#1=(#2=(|Boolean|) $ $) 77 T ELT)) (|zero?| (#3=(#2# $) 49 T ELT)) (|width| (#4=(|#1| $) 39 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| (#3# 81 T ELT)) (|tanh| (#6# 142 T ELT)) (|tan| (#6# 120 T ELT)) (|sup| (#4# 37 T ELT)) (|subtractIfCan| (#7=(#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|sqrt| #5#) (|sinh| (#6# 144 T ELT)) (|sin| (#6# 116 T ELT)) (|sech| (#6# 146 T ELT)) (|sec| (#6# 124 T ELT)) (|sample| (#10=($) NIL T CONST)) (|retractIfCan| (((|Union| #11=(|Integer|) #9#) $) 95 T ELT)) (|retract| ((#11# $) 97 T ELT)) (|recip| ((#8# $) 80 T ELT)) (|qinterval| (#12=($ |#1| |#1|) 35 T ELT)) (|positive?| (#3# 44 T ELT)) (|pi| (#10# 106 T ELT)) (|opposite?| #13=(#1# NIL T ELT)) (|one?| (#3# 56 T ELT)) (|nthRoot| (($ $ #11#) NIL T ELT)) (|negative?| (#3# 46 T ELT)) (|min| #14=(#15=($ $ $) NIL T ELT)) (|max| #14#) (|log| (#6# 108 T ELT)) (|lcm| #14# #16=(($ (|List| $)) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|interval| (#12# 29 T ELT) (($ |#1|) 34 T ELT) (($ #17=(|Fraction| #11#)) 94 T ELT)) (|inf| (#4# 36 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#18=(|SparseUnivariatePolynomial| $) #18# #18#) NIL T ELT)) (|gcd| (#15# 83 T ELT) #16#) (|exquo| (#7# 82 T ELT)) (|exp| (#6# 110 T ELT)) (|csch| (#6# 150 T ELT)) (|csc| (#6# 122 T ELT)) (|coth| (#6# 152 T ELT)) (|cot| (#6# 126 T ELT)) (|cosh| (#6# 148 T ELT)) (|cos| (#6# 118 T ELT)) (|contains?| ((#2# $ |#1|) 42 T ELT)) (|coerce| (((|OutputForm|) $) 102 T ELT) #19=(($ #11#) 85 T ELT) #5# #19#) (|characteristic| ((#20=(|NonNegativeInteger|)) 104 T CONST)) (|before?| #13#) (|atanh| (#6# 164 T ELT)) (|atan| (#6# 132 T ELT)) (|associates?| #13#) (|asinh| (#6# 162 T ELT)) (|asin| (#6# 128 T ELT)) (|asech| (#6# 160 T ELT)) (|asec| (#6# 140 T ELT)) (|annihilate?| #13#) (|acsch| (#6# 158 T ELT)) (|acsc| (#6# 138 T ELT)) (|acoth| (#6# 156 T ELT)) (|acot| (#6# 134 T ELT)) (|acosh| (#6# 154 T ELT)) (|acos| (#6# 130 T ELT)) (|Zero| (#10# 30 T CONST)) (|One| (#10# 10 T CONST)) (>= #13#) (> #13#) (= (#1# 50 T ELT)) (<= #13#) (< (#1# 48 T ELT)) (- (#6# 54 T ELT) (#15# 55 T ELT)) (+ (#15# 53 T ELT)) (** (($ $ #21=(|PositiveInteger|)) 73 T ELT) (($ $ #20#) NIL T ELT) (#15# 112 T ELT) (($ $ #17#) 166 T ELT)) (* (($ #21# $) 67 T ELT) (($ #20# $) NIL T ELT) (($ #11# $) 66 T ELT) (#15# 62 T ELT))) 
(((|Interval| |#1|) (|IntervalCategory| |#1|) (|Join| (|FloatingPointSystem|) (|TranscendentalFunctionCategory|))) (T |Interval|)) 
NIL 
((|solveLinearPolynomialEquation| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| (|Integer|))) "failed") #1# #2#) 27 T ELT))) 
(((|IntegerSolveLinearPolynomialEquation|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| (|Integer|))) "failed") #1# #2#)))) (T |IntegerSolveLinearPolynomialEquation|)) 
((|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| #1=(|SparseUnivariatePolynomial| (|Integer|)))) (|isDomain| *3 #1#) (|isDomain| *1 (|IntegerSolveLinearPolynomialEquation|))))) 
((|varselect| ((#1=(|List| #2=(|Kernel| |#2|)) #1# #3=(|Symbol|)) 19 T ELT)) (|vark| ((#1# (|List| |#2|) #3#) 23 T ELT)) (|union| ((#1# #1# #1#) 11 T ELT)) (|removeConstantTerm| (#4=(|#2| |#2| #3#) 59 (|has| |#1| (|IntegralDomain|)) ELT)) (|mkPrim| (#4# 87 (AND #5=(|has| |#2| (|ElementaryFunctionCategory|)) #6=(|has| |#1| (|GcdDomain|))) ELT)) (|ksec| ((#2# #2# #1# #3#) 25 T ELT)) (|kmax| ((#2# #1#) 24 T ELT)) (|intPatternMatch| ((#7=(|IntegrationResult| |#2|) |#2| #3# (|Mapping| #7# |#2| #3#) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| #3#)) 115 (AND #5# (|has| |#2| (|LiouvillianFunctionCategory|)) (|has| |#2| (|RetractableTo| #3#)) (|has| |#1| (|ConvertibleTo| (|Pattern| #8=(|Integer|)))) #6# (|has| |#1| (|PatternMatchable| #8#))) ELT))) 
(((|IntegrationTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |varselect| (#1=(|List| #2=(|Kernel| |#2|)) #1# #3=(|Symbol|))) (SIGNATURE |kmax| (#2# #1#)) (SIGNATURE |ksec| (#2# #2# #1# #3#)) (SIGNATURE |union| (#1# #1# #1#)) (SIGNATURE |vark| (#1# (|List| |#2|) #3#)) (IF (|has| |#1| (|IntegralDomain|)) (SIGNATURE |removeConstantTerm| #4=(|#2| |#2| #3#)) |%noBranch|) (IF (|has| |#1| (|GcdDomain|)) (IF (|has| |#2| (|ElementaryFunctionCategory|)) (PROGN (SIGNATURE |mkPrim| #4#) (IF (|has| |#1| (|ConvertibleTo| (|Pattern| #5=(|Integer|)))) (IF (|has| |#1| (|PatternMatchable| #5#)) (IF (|has| |#2| (|LiouvillianFunctionCategory|)) (IF (|has| |#2| (|RetractableTo| #3#)) (SIGNATURE |intPatternMatch| (#6=(|IntegrationResult| |#2|) |#2| #3# (|Mapping| #6# |#2| #3#) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| #3#))) |%noBranch|) |%noBranch|) |%noBranch|) |%noBranch|)) |%noBranch|) |%noBranch|)) (|SetCategory|) (|FunctionSpace| |#1|)) (T |IntegrationTools|)) 
((|intPatternMatch| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *5 (|Mapping| #1=(|IntegrationResult| *3) *3 #2=(|Symbol|))) (|isDomain| *6 (|Mapping| (|Union| (|Record| (|:| |special| *3) (|:| |integrand| *3)) "failed") *3 #2#)) (|ofCategory| *3 #3=(|ElementaryFunctionCategory|)) (|ofCategory| *3 (|LiouvillianFunctionCategory|)) (|ofCategory| *3 (|RetractableTo| *4)) (|ofCategory| *3 (|FunctionSpace| *7)) #4=(|isDomain| *4 #2#) (|ofCategory| *7 (|ConvertibleTo| (|Pattern| #5=(|Integer|)))) (|ofCategory| *7 #6=(|GcdDomain|)) (|ofCategory| *7 (|PatternMatchable| #5#)) (|ofCategory| *7 #7=(|SetCategory|)) (|isDomain| *2 #1#) (|isDomain| *1 (|IntegrationTools| *7 *3)))) (|mkPrim| #8=(*1 *2 *2 *3) (AND #9=(|isDomain| *3 #2#) (|ofCategory| *4 #6#) #10=(|ofCategory| *4 #7#) #11=(|isDomain| *1 (|IntegrationTools| *4 *2)) (|ofCategory| *2 #3#) #12=(|ofCategory| *2 #13=(|FunctionSpace| *4)))) (|removeConstantTerm| #8# (AND #9# (|ofCategory| *4 (|IntegralDomain|)) #10# #11# #12#)) (|vark| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) #4# #14=(|ofCategory| *6 (|FunctionSpace| *5)) #15=(|ofCategory| *5 #7#) (|isDomain| *2 #16=(|List| #17=(|Kernel| *6))) #18=(|isDomain| *1 (|IntegrationTools| *5 *6)))) (|union| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| (|Kernel| *4))) (|ofCategory| *4 (|FunctionSpace| *3)) (|ofCategory| *3 #7#) (|isDomain| *1 (|IntegrationTools| *3 *4)))) (|ksec| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 #16#) #4# (|isDomain| *2 #17#) #14# #15# #18#)) (|kmax| (*1 *2 *3) (AND (|isDomain| *3 #19=(|List| #20=(|Kernel| *5))) #10# (|isDomain| *2 #20#) #21=(|isDomain| *1 (|IntegrationTools| *4 *5)) #22=(|ofCategory| *5 #13#))) (|varselect| #8# (AND (|isDomain| *2 #19#) #9# #22# #10# #21#))) 
((|tanintegrate| ((#1=(|Record| (|:| |answer| #2=(|IntegrationResult| #3=(|Fraction| |#2|))) #4=(|:| |a0| |#1|)) #3# #5=(|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) #6="failed") #7=(|Integer|) |#1| |#1|)) 199 T ELT)) (|primlimitedint| ((#8=(|Union| (|Record| (|:| |answer| #9=(|Record| (|:| |mainpart| #3#) (|:| |limitedlogs| (|List| (|Record| #10=(|:| |coeff| #3#) (|:| |logand| #3#)))))) #4#) #6#) #3# #5# #11=(|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #6#) |#1|) #12=(|List| #3#)) 174 T ELT)) (|primlimintfrac| (((|Union| #9# #6#) #3# #5# #12#) 171 T ELT)) (|primintfldpoly| (((|Union| |#2| #6#) |#2| #11# |#1|) 162 T ELT)) (|primintegrate| ((#1# #3# #5# #11#) 185 T ELT)) (|primextintfrac| (((|Union| #13=(|Record| (|:| |ratpart| #3#) #10#) #6#) #3# #5# #3#) 202 T ELT)) (|primextendedint| ((#14=(|Union| (|Record| (|:| |answer| #3#) #4#) #13# #6#) #3# #5# #11# #3#) 205 T ELT)) (|monomialIntegrate| (((|Record| (|:| |ir| #2#) (|:| |specpart| #3#) #15=(|:| |polypart| |#2|)) #3# #5#) 88 T ELT)) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) #15#) |#2| #5#) 100 T ELT)) (|explimitedint| ((#8# #3# #5# #16=(|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) #7# |#1|) #12#) 178 T ELT)) (|expintfldpoly| (((|Union| #17=(|LaurentPolynomial| |#1| |#2|) #6#) #17# #16#) 166 T ELT)) (|expintegrate| ((#1# #3# #5# #16#) 189 T ELT)) (|expextendedint| ((#14# #3# #5# #16# #3#) 210 T ELT))) 
(((|TranscendentalIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |primintegrate| (#1=(|Record| (|:| |answer| #2=(|IntegrationResult| #3=(|Fraction| |#2|))) #4=(|:| |a0| |#1|)) #3# #5=(|Mapping| |#2| |#2|) #6=(|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #7="failed") |#1|))) (SIGNATURE |expintegrate| (#1# #3# #5# #8=(|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) #9=(|Integer|) |#1|))) (SIGNATURE |tanintegrate| (#1# #3# #5# (|Mapping| (|Union| (|List| |#1|) #7#) #9# |#1| |#1|))) (SIGNATURE |primextendedint| (#10=(|Union| (|Record| (|:| |answer| #3#) #4#) #11=(|Record| (|:| |ratpart| #3#) #12=(|:| |coeff| #3#)) #7#) #3# #5# #6# #3#)) (SIGNATURE |expextendedint| (#10# #3# #5# #8# #3#)) (SIGNATURE |primlimitedint| (#13=(|Union| (|Record| (|:| |answer| #14=(|Record| (|:| |mainpart| #3#) (|:| |limitedlogs| (|List| (|Record| #12# (|:| |logand| #3#)))))) #4#) #7#) #3# #5# #6# #15=(|List| #3#))) (SIGNATURE |explimitedint| (#13# #3# #5# #8# #15#)) (SIGNATURE |primextintfrac| ((|Union| #11# #7#) #3# #5# #3#)) (SIGNATURE |primlimintfrac| ((|Union| #14# #7#) #3# #5# #15#)) (SIGNATURE |primintfldpoly| ((|Union| |#2| #7#) |#2| #6# |#1|)) (SIGNATURE |expintfldpoly| ((|Union| #16=(|LaurentPolynomial| |#1| |#2|) #7#) #16# #8#)) (SIGNATURE |monomialIntegrate| ((|Record| (|:| |ir| #2#) (|:| |specpart| #3#) #17=(|:| |polypart| |#2|)) #3# #5#)) (SIGNATURE |monomialIntPoly| ((|Record| (|:| |answer| |#2|) #17#) |#2| #5#))) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |TranscendentalIntegration|)) 
((|monomialIntPoly| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *3 *3)) (|ofCategory| *3 #2=(|UnivariatePolynomialCategory| *5)) #3=(|ofCategory| *5 #4=(|Field|)) (|isDomain| *2 (|Record| (|:| |answer| *3) (|:| |polypart| *3))) (|isDomain| *1 (|TranscendentalIntegration| *5 *3)))) (|monomialIntegrate| #1# (AND #5=(|isDomain| *4 (|Mapping| *6 *6)) #6=(|ofCategory| *6 #2#) #3# (|isDomain| *2 (|Record| (|:| |ir| (|IntegrationResult| #7=(|Fraction| *6))) (|:| |specpart| #7#) (|:| |polypart| *6))) #8=(|isDomain| *1 (|TranscendentalIntegration| *5 *6)) #9=(|isDomain| *3 #7#))) (|expintfldpoly| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|LaurentPolynomial| *4 *5)) (|isDomain| *3 (|Mapping| (|Record| (|:| |ans| *4) (|:| |right| *4) #10=(|:| |sol?| (|Boolean|))) #11=(|Integer|) *4)) #12=(|ofCategory| *4 #4#) (|ofCategory| *5 #13=(|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|TranscendentalIntegration| *4 *5)))) (|primintfldpoly| (*1 *2 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| (|Union| (|Record| (|:| |ratpart| *4) (|:| |coeff| *4)) #14="failed") *4)) #12# (|isDomain| *1 (|TranscendentalIntegration| *4 *2)) (|ofCategory| *2 #13#))) (|primlimintfrac| #15=(*1 *2 *3 *4 *5) (|partial| AND #16=(|isDomain| *4 (|Mapping| *7 *7)) (|isDomain| *5 (|List| #17=(|Fraction| *7))) #18=(|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) #19=(|isDomain| *3 #17#) #20=(|ofCategory| *6 #4#) (|isDomain| *2 #21=(|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| *3) (|:| |logand| *3)))))) #22=(|isDomain| *1 (|TranscendentalIntegration| *6 *7)))) (|primextintfrac| (*1 *2 *3 *4 *3) (|partial| AND #5# #6# #3# (|isDomain| *2 (|Record| (|:| |ratpart| #7#) (|:| |coeff| #7#))) #8# #9#)) (|explimitedint| #23=(*1 *2 *3 *4 *5 *6) (|partial| AND #24=(|isDomain| *4 (|Mapping| *8 *8)) (|isDomain| *5 (|Mapping| (|Record| (|:| |ans| *7) (|:| |right| *7) #10#) #11# *7)) #25=(|isDomain| *6 (|List| #26=(|Fraction| *8))) #27=(|ofCategory| *7 #4#) #28=(|ofCategory| *8 (|UnivariatePolynomialCategory| *7)) #29=(|isDomain| *3 #26#) #30=(|isDomain| *2 (|Record| (|:| |answer| #21#) (|:| |a0| *7))) #31=(|isDomain| *1 (|TranscendentalIntegration| *7 *8)))) (|primlimitedint| #23# (|partial| AND #24# (|isDomain| *5 (|Mapping| (|Union| (|Record| (|:| |ratpart| *7) (|:| |coeff| *7)) #14#) *7)) #25# #27# #28# #29# #30# #31#)) (|expextendedint| #32=(*1 *2 *3 *4 *5 *3) (AND #16# #33=(|isDomain| *5 (|Mapping| (|Record| (|:| |ans| *6) (|:| |right| *6) #10#) #11# *6)) #20# #18# #34=(|isDomain| *2 (|Union| (|Record| (|:| |answer| #17#) #35=(|:| |a0| *6)) (|Record| (|:| |ratpart| #17#) (|:| |coeff| #17#)) #14#)) #22# #19#)) (|primextendedint| #32# (AND #16# #36=(|isDomain| *5 (|Mapping| (|Union| (|Record| (|:| |ratpart| *6) (|:| |coeff| *6)) #14#) *6)) #20# #18# #34# #22# #19#)) (|tanintegrate| #15# (AND #16# (|isDomain| *5 (|Mapping| (|Union| (|List| *6) #14#) #11# *6 *6)) #20# #18# #37=(|isDomain| *2 (|Record| (|:| |answer| (|IntegrationResult| #17#)) #35#)) #22# #19#)) (|expintegrate| #15# (AND #16# #33# #20# #18# #37# #22# #19#)) (|primintegrate| #15# (AND #16# #36# #20# #18# #37# #22# #19#))) 
((|inverseLaplace| (((|Union| |#2| "failed") |#2| #1=(|Symbol|) #1#) 10 T ELT))) 
(((|InverseLaplaceTransform| |#1| |#2|) (CATEGORY |package| (SIGNATURE |inverseLaplace| ((|Union| |#2| "failed") |#2| #1=(|Symbol|) #1#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#)) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|SpecialFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |InverseLaplaceTransform|)) 
((|inverseLaplace| (*1 *2 *2 *3 *3) (|partial| AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#))) (|isDomain| *1 (|InverseLaplaceTransform| *4 *2)) (|ofCategory| *2 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|SpecialFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4)))))) 
((|writeUInt8!| (((|Maybe| #1=(|UInt8|)) $ #1#) 27 T ELT)) (|writeInt8!| (((|Maybe| #2=(|Int8|)) $ #2#) 26 T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 28 T ELT)) (|writeByte!| (((|Maybe| #3=(|Byte|)) $ #3#) 25 T ELT)) (|readUInt8!| (((|Maybe| (|UInt8|)) $) 12 T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) 8 T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) 10 T ELT)) (|readInt8!| (((|Maybe| (|Int8|)) $) 13 T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) 9 T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) 11 T ELT)) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 7 T ELT)) (|readByte!| (((|Maybe| (|Byte|)) $) 14 T ELT)) (|close!| (($ $) 6 T ELT))) 
(((|InputOutputByteConduit|) (|Category|)) (T |InputOutputByteConduit|)) 
NIL 
(|Join| (|InputByteConduit|) (|OutputByteConduit|)) 
(((|Conduit|) . T) ((|InputByteConduit|) . T) ((|OutputByteConduit|) . T)) 
((|writeUInt8!| ((#1=(|Maybe| #2=(|UInt8|)) $ #2#) NIL T ELT)) (|writeInt8!| ((#3=(|Maybe| #4=(|Int8|)) $ #4#) NIL T ELT)) (|writeBytes!| #5=(((|NonNegativeInteger|) $ (|ByteBuffer|)) NIL T ELT)) (|writeByte!| ((#6=(|Maybe| #7=(|Byte|)) $ #7#) NIL T ELT)) (|readUInt8!| ((#1# $) NIL T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) NIL T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) NIL T ELT)) (|readInt8!| ((#3# $) NIL T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) NIL T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) NIL T ELT)) (|readBytes!| #5#) (|readByte!| ((#6# $) NIL T ELT)) (|isOpen?| (((|Boolean|) $) NIL T ELT)) (|inputOutputBinaryFile| (($ (|FileName|)) 14 T ELT) (($ (|String|)) 16 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|close!| (($ $) NIL T ELT))) 
(((|InputOutputBinaryFile|) (|Join| (|InputOutputByteConduit|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |inputOutputBinaryFile| ($ (|FileName|))) (SIGNATURE |inputOutputBinaryFile| ($ (|String|))) (SIGNATURE |isOpen?| ((|Boolean|) $))))) (T |InputOutputBinaryFile|)) 
((|inputOutputBinaryFile| #1=(*1 *1 *2) (AND (|isDomain| *2 (|FileName|)) #2=(|isDomain| *1 (|InputOutputBinaryFile|)))) (|inputOutputBinaryFile| #1# (AND (|isDomain| *2 (|String|)) #2#)) (|isOpen?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) #2#))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|output| (#3=($) 7 T CONST)) (|latex| (((|String|) $) NIL T ELT)) (|input| (#3# 6 T CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 15 T ELT)) (|closed| (#3# 9 T CONST)) (|bothWays| (#3# 8 T CONST)) (|before?| #1#) (= (#2# 11 T ELT))) 
(((|IOMode|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |input| #1=($) |constant|) (SIGNATURE |output| #1# |constant|) (SIGNATURE |bothWays| #1# |constant|) (SIGNATURE |closed| #1# |constant|)))) (T |IOMode|)) 
((|input| #1=(*1 *1) #2=(|isDomain| *1 (|IOMode|))) (|output| #1# #2#) (|bothWays| #1# #2#) (|closed| #1# #2#)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|resolve| (((|Maybe| $) (|Hostname|)) 23 T ELT)) (|latex| ((#3=(|String|) $) NIL T ELT)) (|ip4Address| (($ #3#) 16 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT)) (|bytes| (((|DataArray| 4 (|Byte|)) $) 24 T ELT)) (|before?| #1#) (= (#2# 26 T ELT))) 
(((|IP4Address|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |ip4Address| ($ (|String|))) (SIGNATURE |bytes| ((|DataArray| 4 (|Byte|)) $)) (SIGNATURE |resolve| ((|Maybe| $) (|Hostname|)))))) (T |IP4Address|)) 
((|ip4Address| (*1 *1 *2) (AND (|isDomain| *2 (|String|)) #1=(|isDomain| *1 #2=(|IP4Address|)))) (|bytes| (*1 *2 *1) (AND (|isDomain| *2 (|DataArray| 4 (|Byte|))) #1#)) (|resolve| (*1 *2 *3) (AND (|isDomain| *3 (|Hostname|)) (|isDomain| *2 (|Maybe| #2#)) #1#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| (#7=(#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|sqrt| (#10=($ $ #11=(|Integer|)) 73 T ELT)) (|sizeLess?| #1#) (|sample| (#12=($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| #11#) #11#) 79 T ELT)) (|rem| #13=(#14=($ $ $) NIL T ELT)) (|recip| ((#8# $) 64 T ELT)) (|quotientByP| (#6# 43 T ELT)) (|quo| #13#) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) NIL T ELT)) (|order| (#17=(#18=(|NonNegativeInteger|) $) 16 T ELT)) (|opposite?| #1#) (|one?| #4#) (|multiEuclidean| (((|Union| #15# #9#) #15# $) NIL T ELT)) (|modulus| ((#11#) 37 T ELT)) (|moduloP| ((#11# $) 41 T ELT)) (|lcm| #13# #19=(($ #15#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#20=(|SparseUnivariatePolynomial| $) #20# #20#) NIL T ELT)) (|gcd| #13# #19#) (|extendedEuclidean| (((|Record| #21=(|:| |coef1| $) #22=(|:| |coef2| $) #16#) $ $) NIL T ELT) (((|Union| (|Record| #21# #22#) #9#) $ $ $) NIL T ELT)) (|extend| (#10# 24 T ELT)) (|exquo| (#7# 70 T ELT)) (|expressIdealMember| (((|Maybe| #15#) #15# $) NIL T ELT)) (|euclideanSize| (#17# 17 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 71 T ELT)) (|digits| (((|Stream| #11#) $) 19 T ELT)) (|complete| (#6# 26 T ELT)) (|coerce| (((|OutputForm|) $) 100 T ELT) (($ #11#) 59 T ELT) #5#) (|characteristic| ((#18#) 15 T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| ((#11# $ #11#) 46 T ELT)) (|annihilate?| #1#) (|Zero| (#12# 44 T CONST)) (|One| (#12# 21 T CONST)) (= (#2# 51 T ELT)) (- (#6# 58 T ELT) (#14# 48 T ELT)) (+ (#14# 57 T ELT)) (** (($ $ #23=(|PositiveInteger|)) NIL T ELT) (($ $ #18#) NIL T ELT)) (* (($ #23# $) NIL T ELT) (($ #18# $) NIL T ELT) (($ #11# $) 60 T ELT) (#14# 61 T ELT))) 
(((|InnerPAdicInteger| |#1| |#2|) (|PAdicIntegerCategory| |#1|) (|Integer|) (|Boolean|)) (T |InnerPAdicInteger|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 30 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #7=(#4# NIL T ELT)) (|transcendent?| #7#) (|transcendenceDegree| #8=(#9=(#10=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| $ (|Finite|)) ELT) #5#) (|tableForDiscreteLogarithm| (((|Table| #13# #10#) #15=(|Integer|)) 59 T ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| #8#) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (#22=(#17# $) 95 T ELT)) (|retract| (#6# 94 T ELT)) (|represents| (($ #23=(|Vector| $)) 93 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 56 T ELT)) (|rem| #24=(#25=($ $ $) NIL T ELT)) (|recip| (#22# 47 T ELT)) (|random| (#21# NIL T ELT)) (|quo| #24#) (|principalIdeal| (((|Record| (|:| |coef| #26=(|List| $)) #27=(|:| |generator| $)) #26#) NIL T ELT)) (|primitiveElement| (#21# 61 T ELT)) (|primitive?| #7#) (|primeFrobenius| #5# #28=(#29=($ $ #10#) NIL T ELT)) (|prime?| #7#) (|order| #30=((#31=(|OnePointCompletion| #13#) $) NIL T ELT) (#32=(#13# $) NIL T ELT)) (|opposite?| #1#) (|one?| #7#) (|normalElement| (#21# 49 #14# ELT)) (|normal?| (#4# NIL #14# ELT)) (|norm| #11# #5#) (|nextItem| #33=(((|Maybe| $) $) NIL T ELT)) (|multiEuclidean| (((|Union| #26# #18#) #26# $) NIL T ELT)) (|minimalPolynomial| ((#34=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT) (#35=(#34# $) 104 T ELT)) (|lookup| (#32# 67 T ELT)) (|linearAssociatedOrder| #36=(#35# NIL #14# ELT)) (|linearAssociatedLog| (((|Union| #34# #18#) $ $) NIL #14# ELT) #36#) (|linearAssociatedExp| (($ $ #34#) NIL #14# ELT)) (|lcm| #24# #37=(($ #26#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| #20#) (|index| (($ #13#) 60 T ELT)) (|inGroundField?| (#4# 87 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#21# 28 #14# ELT)) (|gcdPolynomial| ((#34# #34# #34#) NIL T ELT)) (|gcd| #24# #37#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) 54 T ELT)) (|factor| #19#) (|extensionDegree| ((#13#) 86 T ELT) ((#31#) NIL T ELT)) (|extendedEuclidean| (((|Record| #38=(|:| |coef1| $) #39=(|:| |coef2| $) #27#) $ $) NIL T ELT) (((|Union| (|Record| #38# #39#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #26#) #26# $) NIL T ELT)) (|euclideanSize| #40=((#10# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (((|Union| #10# #18#) $ $) NIL T ELT) #40#) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #5# #28#) (|degree| (#32# 85 T ELT) #30#) (|definingPolynomial| ((#34#) 102 T ELT)) (|createPrimitiveElement| (#21# 66 T ELT)) (|createNormalElement| (#21# 50 #14# ELT)) (|coordinates| ((#41=(|Matrix| $) #23#) NIL T ELT) ((#23# $) 91 T ELT)) (|convert| ((#15# $) 42 T ELT)) (|conditionP| (((|Union| #23# #18#) #41#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) 45 T ELT) #5# (($ #42=(|Fraction| #15#)) NIL T ELT)) (|charthRoot| #33# (#6# 105 T ELT)) (|characteristic| (#9# 51 T CONST)) (|before?| (#2# 107 T ELT)) (|basis| ((#23# #13#) 97 T ELT) ((#23#) 96 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #7#) (|Zero| (#21# 31 T CONST)) (|One| (#21# 27 T CONST)) (|Frobenius| (#29# NIL #14# ELT) (#6# NIL #14# ELT)) (D #5# #28#) (= #1#) (/ #24#) (- #5# #24#) (+ #24#) (** (#12# NIL T ELT) #28# (($ $ #15#) 34 T ELT)) (* (($ #13# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #15# . #43=($)) NIL T ELT) (#25# 81 T ELT) (($ $ #42#) NIL T ELT) (($ #42# . #43#) NIL T ELT))) 
(((|InnerPrimeField| |#1|) (|Join| (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| $) (|ConvertibleTo| (|Integer|))) (|PositiveInteger|)) (T |InnerPrimeField|)) 
NIL 
((|iprint| (((|Void|) (|String|)) 10 T ELT))) 
(((|InternalPrintPackage|) (CATEGORY |package| (SIGNATURE |iprint| ((|Void|) (|String|))))) (T |InternalPrintPackage|)) 
((|iprint| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|InternalPrintPackage|))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #4#) $) 77 T ELT)) (|retract| (#6=(|#1| $) NIL T ELT)) (|ratpart| (#6# 30 T ELT)) (|opposite?| #1#) (|notelem| ((#7=(|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) 32 T ELT)) (|mkAnswer| (($ |#1| #8=(|List| (|Record| (|:| |scalar| #9=(|Fraction| #10=(|Integer|))) (|:| |coeff| #11=(|SparseUnivariatePolynomial| |#1|)) (|:| |logand| #11#))) #7#) 28 T ELT)) (|logpart| ((#8# $) 31 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integral| (($ |#1| |#1|) 38 T ELT) (($ |#1| #12=(|Symbol|)) 49 (|has| |#1| (|RetractableTo| #12#)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elem?| (#3# 35 T ELT)) (|differentiate| ((|#1| $ (|Mapping| |#1| |#1|)) 89 T ELT) ((|#1| $ #12#) 90 (|has| |#1| (|PartialDifferentialRing| #12#)) ELT)) (|coerce| (((|OutputForm|) $) 113 T ELT) (($ |#1|) 29 T ELT)) (|before?| #1#) (|Zero| (#5# 18 T CONST)) (= #1#) (- (($ $) 17 T ELT) (#13=($ $ $) NIL T ELT)) (+ (#13# 86 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #10# $) 16 T ELT) (($ #9# $) 41 T ELT) (($ $ #9#) NIL T ELT))) 
(((|IntegrationResult| |#1|) (|Join| (|Module| #1=(|Fraction| (|Integer|))) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |mkAnswer| ($ |#1| #2=(|List| (|Record| (|:| |scalar| #1#) (|:| |coeff| #3=(|SparseUnivariatePolynomial| |#1|)) (|:| |logand| #3#))) #4=(|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))))) (SIGNATURE |ratpart| (|#1| $)) (SIGNATURE |logpart| (#2# $)) (SIGNATURE |notelem| (#4# $)) (SIGNATURE |elem?| ((|Boolean|) $)) (SIGNATURE |integral| ($ |#1| |#1|)) (SIGNATURE |differentiate| (|#1| $ (|Mapping| |#1| |#1|))) (IF (|has| |#1| (|PartialDifferentialRing| #5=(|Symbol|))) (SIGNATURE |differentiate| (|#1| $ #5#)) |%noBranch|) (IF (|has| |#1| (|RetractableTo| #5#)) (SIGNATURE |integral| ($ |#1| #5#)) |%noBranch|))) (|Field|)) (T |IntegrationResult|)) 
((|mkAnswer| (*1 *1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| #1=(|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| #2=(|SparseUnivariatePolynomial| *2)) (|:| |logand| #2#)))) (|isDomain| *4 (|List| (|Record| (|:| |integrand| *2) (|:| |intvar| *2)))) #3=(|ofCategory| *2 #4=(|Field|)) #5=(|isDomain| *1 (|IntegrationResult| *2)))) (|ratpart| #6=(*1 *2 *1) #7=(AND #5# #3#)) (|logpart| #6# (AND (|isDomain| *2 (|List| (|Record| #1# (|:| |coeff| #8=(|SparseUnivariatePolynomial| *3)) (|:| |logand| #8#)))) #9=(|isDomain| *1 (|IntegrationResult| *3)) #10=(|ofCategory| *3 #4#))) (|notelem| #6# (AND (|isDomain| *2 (|List| (|Record| (|:| |integrand| *3) (|:| |intvar| *3)))) #9# #10#)) (|elem?| #6# (AND (|isDomain| *2 (|Boolean|)) #9# #10#)) (|integral| (*1 *1 *2 *2) #7#) (|differentiate| #11=(*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| *2 *2)) #5# #3#)) (|differentiate| #11# (AND #3# (|ofCategory| *2 (|PartialDifferentialRing| *3)) #5# #12=(|isDomain| *3 (|Symbol|)))) (|integral| (*1 *1 *2 *3) (AND #12# #5# (|ofCategory| *2 (|RetractableTo| *3)) #3#))) 
((|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #1=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2="failed") #3=(|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| #4=(|:| |coeff| |#1|) (|:| |logand| |#1|))))) #2#)) 44 T ELT) (((|Union| |#2| #2#) #3# (|Union| |#1| #2#)) 11 T ELT) (((|Union| (|Record| (|:| |ratpart| |#2|) #1#) #2#) #3# (|Union| (|Record| (|:| |ratpart| |#1|) #4#) #2#)) 35 T ELT) (((|IntegrationResult| |#2|) #3# (|IntegrationResult| |#1|)) 30 T ELT))) 
(((|IntegrationResultFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|IntegrationResult| |#2|) #1=(|Mapping| |#2| |#1|) (|IntegrationResult| |#1|))) (SIGNATURE |map| ((|Union| (|Record| (|:| |ratpart| |#2|) #2=(|:| |coeff| |#2|)) #3="failed") #1# (|Union| (|Record| (|:| |ratpart| |#1|) #4=(|:| |coeff| |#1|)) #3#))) (SIGNATURE |map| ((|Union| |#2| #3#) #1# (|Union| |#1| #3#))) (SIGNATURE |map| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #2# (|:| |logand| |#2|))))) #3#) #1# (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| #4# (|:| |logand| |#1|))))) #3#)))) #5=(|Field|) #5#) (T |IntegrationResultFunctions2|)) 
((|map| #1=(*1 *2 *3 *4) (|partial| AND #2=(|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Union| (|Record| (|:| |mainpart| *5) (|:| |limitedlogs| (|List| (|Record| #3=(|:| |coeff| *5) (|:| |logand| *5))))) #4="failed")) #5=(|ofCategory| *5 #6=(|Field|)) #7=(|ofCategory| *6 #6#) (|isDomain| *2 (|Record| (|:| |mainpart| *6) (|:| |limitedlogs| (|List| (|Record| #8=(|:| |coeff| *6) (|:| |logand| *6)))))) #9=(|isDomain| *1 (|IntegrationResultFunctions2| *5 *6)))) (|map| #1# (|partial| AND (|isDomain| *3 (|Mapping| *2 *5)) (|isDomain| *4 (|Union| *5 #4#)) #5# (|ofCategory| *2 #6#) (|isDomain| *1 (|IntegrationResultFunctions2| *5 *2)))) (|map| #1# (|partial| AND #2# (|isDomain| *4 (|Union| (|Record| (|:| |ratpart| *5) #3#) #4#)) #5# #7# (|isDomain| *2 (|Record| (|:| |ratpart| *6) #8#)) #9#)) (|map| #1# (AND #2# (|isDomain| *4 (|IntegrationResult| *5)) #5# #7# (|isDomain| *2 (|IntegrationResult| *6)) #9#))) 
((|split| ((#1=(|IntegrationResult| |#2|) #1#) 42 T ELT)) (|expand| (((|List| |#2|) #1#) 44 T ELT)) (|complexExpand| ((|#2| #1#) 50 T ELT))) 
(((|IntegrationResultToFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |split| (#1=(|IntegrationResult| |#2|) #1#)) (SIGNATURE |expand| ((|List| |#2|) #1#)) (SIGNATURE |complexExpand| (|#2| #1#))) (|Join| (|GcdDomain|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|))) (T |IntegrationResultToFunction|)) 
((|complexExpand| #1=(*1 *2 *3) (AND (|isDomain| *3 (|IntegrationResult| *2)) (|ofCategory| *2 #2=(|Join| (|AlgebraicallyClosedFunctionSpace| *4) #3=(|TranscendentalFunctionCategory|))) (|isDomain| *1 (|IntegrationResultToFunction| *4 *2)) #4=(|ofCategory| *4 #5=(|Join| (|GcdDomain|) (|RetractableTo| #6=(|Integer|)) (|LinearlyExplicitRingOver| #6#))))) (|expand| #1# (AND (|isDomain| *3 (|IntegrationResult| *5)) (|ofCategory| *5 #2#) #4# (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|IntegrationResultToFunction| *4 *5)))) (|split| (*1 *2 *2) (AND (|isDomain| *2 (|IntegrationResult| *4)) (|ofCategory| *4 (|Join| (|AlgebraicallyClosedFunctionSpace| *3) #3#)) (|ofCategory| *3 #5#) (|isDomain| *1 (|IntegrationResultToFunction| *3 *4))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|irVar| (#2=($ #3=(|Identifier|) #4=(|InternalTypeForm|)) 14 T ELT)) (|irDef| (($ #3# #4# $) 16 T ELT)) (|irCtor| (#2# 15 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #5=(|Syntax|)) 7 T ELT) ((#5# $) 6 T ELT)) (|before?| #1#) (= #1#)) 
(((|InternalRepresentationForm|) (|Join| (|SetCategory|) (|HomotopicTo| (|Syntax|)) (CATEGORY |domain| (SIGNATURE |irVar| #1=($ #2=(|Identifier|) #3=(|InternalTypeForm|))) (SIGNATURE |irCtor| #1#) (SIGNATURE |irDef| ($ #2# #3# $))))) (T |InternalRepresentationForm|)) 
((|irVar| #1=(*1 *1 *2 *3) #2=(AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|InternalTypeForm|)) (|isDomain| *1 (|InternalRepresentationForm|)))) (|irCtor| #1# #2#) (|irDef| (*1 *1 *2 *3 *1) #2#)) 
((|perfectSquare?| ((#1=(|Boolean|) |#1|) 16 T ELT)) (|perfectSqrt| ((#2=(|Union| |#1| "failed") |#1|) 14 T ELT)) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| #3=(|NonNegativeInteger|))) |#1|) 37 T ELT) ((#2# |#1| #3#) 18 T ELT)) (|perfectNthPower?| ((#1# |#1| #3#) 19 T ELT)) (|approxSqrt| ((|#1| |#1|) 41 T ELT)) (|approxNthRoot| ((|#1| |#1| #3#) 44 T ELT))) 
(((|IntegerRoots| |#1|) (CATEGORY |package| (SIGNATURE |perfectNthPower?| (#1=(|Boolean|) |#1| #2=(|NonNegativeInteger|))) (SIGNATURE |perfectNthRoot| (#3=(|Union| |#1| "failed") |#1| #2#)) (SIGNATURE |perfectNthRoot| ((|Record| (|:| |base| |#1|) (|:| |exponent| #2#)) |#1|)) (SIGNATURE |approxNthRoot| (|#1| |#1| #2#)) (SIGNATURE |perfectSquare?| (#1# |#1|)) (SIGNATURE |perfectSqrt| (#3# |#1|)) (SIGNATURE |approxSqrt| (|#1| |#1|))) (|IntegerNumberSystem|)) (T |IntegerRoots|)) 
((|approxSqrt| #1=(*1 *2 *2) (AND #2=(|isDomain| *1 (|IntegerRoots| *2)) #3=(|ofCategory| *2 #4=(|IntegerNumberSystem|)))) (|perfectSqrt| #1# (|partial| AND #2# #3#)) (|perfectSquare?| #5=(*1 *2 *3) (AND #6=(|isDomain| *2 (|Boolean|)) #7=(|isDomain| *1 (|IntegerRoots| *3)) #8=(|ofCategory| *3 #4#))) (|approxNthRoot| #9=(*1 *2 *2 *3) (AND #10=(|isDomain| *3 #11=(|NonNegativeInteger|)) #2# #3#)) (|perfectNthRoot| #5# (AND (|isDomain| *2 (|Record| (|:| |base| *3) (|:| |exponent| #11#))) #7# #8#)) (|perfectNthRoot| #9# (|partial| AND #10# #2# #3#)) (|perfectNthPower?| (*1 *2 *3 *4) (AND (|isDomain| *4 #11#) #6# #7# #8#))) 
((|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) 44 T ELT))) 
(((|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|))))) 
((|split| ((#1=(|IntegrationResult| #2=(|Fraction| (|Polynomial| |#1|))) #1#) 27 T ELT)) (|integrate| (((|Union| #3=(|Expression| |#1|) #4=(|List| #3#)) #2# #5=(|Symbol|)) 33 #6=(|has| |#1| (|CharacteristicZero|)) ELT)) (|expand| ((#4# #1#) 19 T ELT)) (|complexIntegrate| ((#3# #2# #5#) 31 #6# ELT)) (|complexExpand| ((#3# #1#) 21 T ELT))) 
(((|IntegrationResultRFToFunction| |#1|) (CATEGORY |package| (SIGNATURE |split| (#1=(|IntegrationResult| #2=(|Fraction| (|Polynomial| |#1|))) #1#)) (SIGNATURE |expand| (#3=(|List| #4=(|Expression| |#1|)) #1#)) (SIGNATURE |complexExpand| (#4# #1#)) (IF (|has| |#1| (|CharacteristicZero|)) (PROGN (SIGNATURE |integrate| ((|Union| #4# #3#) #2# #5=(|Symbol|))) (SIGNATURE |complexIntegrate| (#4# #2# #5#))) |%noBranch|)) (|Join| (|GcdDomain|) (|RetractableTo| #6=(|Integer|)) (|LinearlyExplicitRingOver| #6#))) (T |IntegrationResultRFToFunction|)) 
((|complexIntegrate| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Fraction| (|Polynomial| *5))) #3=(|isDomain| *4 (|Symbol|)) #4=(|ofCategory| *5 (|CharacteristicZero|)) #5=(|ofCategory| *5 #6=(|Join| (|GcdDomain|) (|RetractableTo| #7=(|Integer|)) (|LinearlyExplicitRingOver| #7#))) (|isDomain| *2 #8=(|Expression| *5)) #9=(|isDomain| *1 (|IntegrationResultRFToFunction| *5)))) (|integrate| #1# (AND #2# #3# #4# #5# (|isDomain| *2 (|Union| #8# (|List| #8#))) #9#)) (|complexExpand| #10=(*1 *2 *3) (AND #11=(|isDomain| *3 (|IntegrationResult| (|Fraction| (|Polynomial| *4)))) #12=(|ofCategory| *4 #6#) (|isDomain| *2 #13=(|Expression| *4)) #14=(|isDomain| *1 (|IntegrationResultRFToFunction| *4)))) (|expand| #10# (AND #11# #12# (|isDomain| *2 (|List| #13#)) #14#)) (|split| (*1 *2 *2) (AND (|isDomain| *2 (|IntegrationResult| (|Fraction| (|Polynomial| *3)))) (|ofCategory| *3 #6#) (|isDomain| *1 (|IntegrationResultRFToFunction| *3))))) 
((|irreducibleRepresentation| ((#1=(|List| #2=(|Matrix| #3=(|Integer|))) #4=(|List| (|PositiveInteger|)) (|List| #5=(|Permutation| #3#))) 80 T ELT) ((#1# #4#) 81 T ELT) ((#2# #4# #5#) 74 T ELT)) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) #4#) 71 T ELT))) 
(((|IrrRepSymNatPackage|) (CATEGORY |package| (SIGNATURE |dimensionOfIrreducibleRepresentation| ((|NonNegativeInteger|) #1=(|List| (|PositiveInteger|)))) (SIGNATURE |irreducibleRepresentation| (#2=(|Matrix| #3=(|Integer|)) #1# #4=(|Permutation| #3#))) (SIGNATURE |irreducibleRepresentation| (#5=(|List| #2#) #1#)) (SIGNATURE |irreducibleRepresentation| (#5# #1# (|List| #4#))))) (T |IrrRepSymNatPackage|)) 
((|irreducibleRepresentation| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|List| (|PositiveInteger|))) (|isDomain| *4 (|List| #3=(|Permutation| #4=(|Integer|)))) #5=(|isDomain| *2 (|List| #6=(|Matrix| #4#))) #7=(|isDomain| *1 (|IrrRepSymNatPackage|)))) (|irreducibleRepresentation| #8=(*1 *2 *3) (AND #2# #5# #7#)) (|irreducibleRepresentation| #1# (AND #2# (|isDomain| *4 #3#) (|isDomain| *2 #6#) #7#)) (|dimensionOfIrreducibleRepresentation| #8# (AND #2# (|isDomain| *2 (|NonNegativeInteger|)) #7#))) 
((|rur| ((#1=(|List| |#5|) |#5| #2=(|Boolean|)) 97 T ELT)) (|checkRur| ((#2# |#5| #1#) 34 T ELT))) 
(((|InternalRationalUnivariateRepresentationPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |rur| (#1=(|List| |#5|) |#5| #2=(|Boolean|))) (SIGNATURE |checkRur| (#2# |#5| #1#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |InternalRationalUnivariateRepresentationPackage|)) 
((|checkRur| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 #2=(|List| *3)) #3=(|ofCategory| *3 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)) #4=(|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) #5=(|ofCategory| *6 (|OrderedAbelianMonoidSup|)) #6=(|ofCategory| *7 (|OrderedSet|)) #7=(|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 #8=(|Boolean|)) #9=(|isDomain| *1 (|InternalRationalUnivariateRepresentationPackage| *5 *6 *7 *8 *3)))) (|rur| #1# (AND (|isDomain| *4 #8#) #4# #5# #6# #7# (|isDomain| *2 #2#) #9# #3#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|rhs| (#2=((|SpadAst|) $) 12 T ELT)) (|lhs| (#2# 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|IsAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |lhs| #1=((|SpadAst|) $)) (SIGNATURE |rhs| #1#)))) (T |IsAst|)) 
((|lhs| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|IsAst|)))) (|rhs| #1# #2#)) 
((|sum| ((#1=(|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) 23 T ELT) ((#1# |#4| |#2| (|Segment| |#4|)) 32 T ELT))) 
(((|InnerPolySum| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |sum| (#1=(|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|))) (SIGNATURE |sum| (#1# |#4| |#2|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|IntegralDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |InnerPolySum|)) 
((|sum| (*1 *2 *3 *4) (AND (|ofCategory| *5 #1=(|OrderedAbelianMonoidSup|)) #2=(|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 #3=(|IntegralDomain|)) #4=(|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 #1#) #2# (|ofCategory| *7 #3#) #4# (|isDomain| *1 (|InnerPolySum| *6 *4 *7 *3))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 71 T ELT)) (|variables| ((#5=(|List| #6=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#7=(|Symbol|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|truncate| (#11=($ $ #12=(|Integer|)) 58 T ELT) (($ $ #12# #12#) 59 T ELT)) (|terms| (#13=(#14=(|Stream| (|Record| (|:| |k| #12#) (|:| |c| |#1|))) $) 65 T ELT)) (|taylorQuoByVar| (#10# 109 T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ "failed") $ $) NIL T ELT)) (|seriesToOutputForm| ((#17=(|OutputForm|) #14# #18=(|Reference| (|OrderedCompletion| #12#)) #7# |#1| #19=(|Fraction| #12#)) 232 T ELT)) (|series| (($ #14#) 36 T ELT)) (|sample| (#20=($) NIL T CONST)) (|reductum| #21=(#10# NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|pole?| #22=(#4# NIL T ELT)) (|order| (#23=(#12# $) 63 T ELT) ((#12# $ #12#) 64 T ELT)) (|opposite?| #1#) (|one?| #22#) (|multiplyExponents| (#24=($ $ #25=(|PositiveInteger|)) 83 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #12#) $) 80 T ELT)) (|monomial?| (#4# 26 T ELT)) (|monomial| (($ |#1| #12#) 22 T ELT) (($ $ #6# #12#) NIL T ELT) (($ $ #5# (|List| #12#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 75 T ELT)) (|makeSeries| (($ #18# #14#) 13 T ELT)) (|leadingMonomial| #21#) (|leadingCoefficient| #26=((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#10# 120 #27=(|has| |#1| (|Algebra| #19#)) ELT)) (|iExquo| ((#16# $ $ #3#) 108 T ELT)) (|iCompose| (#28=($ $ $) 116 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|getStream| (#13# 15 T ELT)) (|getRef| ((#18# $) 14 T ELT)) (|extend| (#11# 47 T ELT)) (|exquo| (#15# NIL #8# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) NIL #29=(|has| |#1| (SIGNATURE ** (|#1| |#1| #12#))) ELT)) (|elt| (#30=(|#1| $ #12#) 62 T ELT) (#28# NIL (|has| #12# (|SemiGroup|)) ELT)) (|differentiate| #31=(($ $ #7#) NIL #32=(AND (|has| |#1| (|PartialDifferentialRing| #7#)) #33=(|has| |#1| (SIGNATURE * (|#1| #12# |#1|)))) ELT) #34=(($ $ #35=(|List| #7#)) NIL #32# ELT) #36=(($ $ #7# #37=(|NonNegativeInteger|)) NIL #32# ELT) #38=(($ $ #35# (|List| #37#)) NIL #32# ELT) (#10# 77 #33# ELT) #39=(#40=($ $ #37#) NIL #33# ELT)) (|degree| (#23# NIL T ELT)) (|complete| (#10# 48 T ELT)) (|coerce| ((#17# $) NIL T ELT) (($ #12#) 29 T ELT) (($ #19#) NIL #27# ELT) #9# (($ |#1|) 28 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| (#30# 61 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#37#) 39 T CONST)) (|center| #26#) (|cTanh| (#10# 192 #27# ELT)) (|cTan| (#10# 167 #27# ELT)) (|cSinh| (#10# 189 #27# ELT)) (|cSin| (#10# 164 #27# ELT)) (|cSech| (#10# 194 #27# ELT)) (|cSec| (#10# 170 #27# ELT)) (|cRationalPower| (#41=($ $ #19#) 157 #27# ELT)) (|cPower| (#42=($ $ |#1|) 128 #27# ELT)) (|cLog| (#10# 161 #27# ELT)) (|cExp| (#10# 159 #27# ELT)) (|cCsch| (#10# 195 #27# ELT)) (|cCsc| (#10# 171 #27# ELT)) (|cCoth| (#10# 193 #27# ELT)) (|cCot| (#10# 169 #27# ELT)) (|cCosh| (#10# 190 #27# ELT)) (|cCos| (#10# 165 #27# ELT)) (|cAtanh| (#10# 200 #27# ELT)) (|cAtan| (#10# 180 #27# ELT)) (|cAsinh| (#10# 197 #27# ELT)) (|cAsin| (#10# 176 #27# ELT)) (|cAsech| (#10# 204 #27# ELT)) (|cAsec| (#10# 184 #27# ELT)) (|cAcsch| (#10# 206 #27# ELT)) (|cAcsc| (#10# 186 #27# ELT)) (|cAcoth| (#10# 202 #27# ELT)) (|cAcot| (#10# 182 #27# ELT)) (|cAcosh| (#10# 199 #27# ELT)) (|cAcos| (#10# 178 #27# ELT)) (|before?| #1#) (|associates?| (#2# NIL #8# ELT)) (|approximate| (#30# NIL (AND #29# (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| #1#) (|Zero| (#20# 30 T CONST)) (|One| (#20# 40 T CONST)) (D #31# #34# #36# #38# (#10# NIL #33# ELT) #39#) (= (#2# 73 T ELT)) (/ (#42# NIL (|has| |#1| (|Field|)) ELT)) (- (#10# 91 T ELT) (#28# 72 T ELT)) (+ (#28# 88 T ELT)) (** (#24# NIL T ELT) (#40# 111 T ELT)) (* (($ #25# $) 98 T ELT) (($ #37# $) 96 T ELT) (($ #12# $) 93 T ELT) (#28# 104 T ELT) (#42# NIL T ELT) (($ |#1| . #43=($)) 123 T ELT) (($ #19# . #43#) NIL #27# ELT) (#41# NIL #27# ELT))) 
(((|InnerSparseUnivariatePowerSeries| |#1|) (|Join| (|UnivariatePowerSeriesCategory| |#1| #1=(|Integer|)) (CATEGORY |domain| (SIGNATURE |makeSeries| ($ #2=(|Reference| (|OrderedCompletion| #1#)) #3=(|Stream| (|Record| (|:| |k| #1#) (|:| |c| |#1|))))) (SIGNATURE |getRef| (#2# $)) (SIGNATURE |getStream| (#3# $)) (SIGNATURE |series| ($ #3#)) (SIGNATURE |monomial?| (#4=(|Boolean|) $)) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |#1| #1#) $)) (SIGNATURE |iExquo| ((|Union| $ "failed") $ $ #4#)) (SIGNATURE |taylorQuoByVar| #5=($ $)) (SIGNATURE |iCompose| ($ $ $)) (SIGNATURE |seriesToOutputForm| ((|OutputForm|) #3# #2# (|Symbol|) |#1| #6=(|Fraction| #1#))) (IF (|has| |#1| (|Algebra| #6#)) (PROGN (SIGNATURE |integrate| #5#) (SIGNATURE |cPower| ($ $ |#1|)) (SIGNATURE |cRationalPower| ($ $ #6#)) (SIGNATURE |cExp| #5#) (SIGNATURE |cLog| #5#) (SIGNATURE |cSin| #5#) (SIGNATURE |cCos| #5#) (SIGNATURE |cTan| #5#) (SIGNATURE |cCot| #5#) (SIGNATURE |cSec| #5#) (SIGNATURE |cCsc| #5#) (SIGNATURE |cAsin| #5#) (SIGNATURE |cAcos| #5#) (SIGNATURE |cAtan| #5#) (SIGNATURE |cAcot| #5#) (SIGNATURE |cAsec| #5#) (SIGNATURE |cAcsc| #5#) (SIGNATURE |cSinh| #5#) (SIGNATURE |cCosh| #5#) (SIGNATURE |cTanh| #5#) (SIGNATURE |cCoth| #5#) (SIGNATURE |cSech| #5#) (SIGNATURE |cCsch| #5#) (SIGNATURE |cAsinh| #5#) (SIGNATURE |cAcosh| #5#) (SIGNATURE |cAtanh| #5#) (SIGNATURE |cAcoth| #5#) (SIGNATURE |cAsech| #5#) (SIGNATURE |cAcsch| #5#)) |%noBranch|))) (|Ring|)) (T |InnerSparseUnivariatePowerSeries|)) 
((|monomial?| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Boolean|)) #3=(|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3)) #4=(|ofCategory| *3 #5=(|Ring|)))) (|makeSeries| (*1 *1 *2 *3) (AND #6=(|isDomain| *2 #7=(|Reference| (|OrderedCompletion| #8=(|Integer|)))) (|isDomain| *3 (|Stream| (|Record| #9=(|:| |k| #8#) (|:| |c| *4)))) (|ofCategory| *4 #5#) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *4)))) (|getRef| #1# (AND #6# #3# #4#)) (|getStream| #1# (AND #10=(|isDomain| *2 (|Stream| (|Record| #9# (|:| |c| *3)))) #3# #4#)) (|series| (*1 *1 *2) (AND #10# #4# #3#)) (|multiplyCoefficients| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 #8#)) #4# #3#)) (|iExquo| (*1 *1 *1 *1 *2) (|partial| AND #2# #3# #4#)) (|taylorQuoByVar| #11=(*1 *1 *1) #12=(AND #13=(|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) #14=(|ofCategory| *2 #5#))) (|iCompose| (*1 *1 *1 *1) #12#) (|seriesToOutputForm| (*1 *2 *3 *4 *5 *6 *7) (AND (|isDomain| *3 (|Stream| (|Record| #9# (|:| |c| *6)))) (|isDomain| *4 #7#) (|isDomain| *5 (|Symbol|)) (|isDomain| *7 #15=(|Fraction| #8#)) (|ofCategory| *6 #5#) (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *6)))) (|integrate| #11# #16=(AND #13# (|ofCategory| *2 (|Algebra| #15#)) #14#)) (|cPower| #17=(*1 *1 *1 *2) #16#) (|cRationalPower| #17# (AND (|isDomain| *2 #15#) #3# (|ofCategory| *3 (|Algebra| *2)) #4#)) (|cExp| #11# #16#) (|cLog| #11# #16#) (|cSin| #11# #16#) (|cCos| #11# #16#) (|cTan| #11# #16#) (|cCot| #11# #16#) (|cSec| #11# #16#) (|cCsc| #11# #16#) (|cAsin| #11# #16#) (|cAcos| #11# #16#) (|cAtan| #11# #16#) (|cAcot| #11# #16#) (|cAsec| #11# #16#) (|cAcsc| #11# #16#) (|cSinh| #11# #16#) (|cCosh| #11# #16#) (|cTanh| #11# #16#) (|cCoth| #11# #16#) (|cSech| #11# #16#) (|cCsch| #11# #16#) (|cAsinh| #11# #16#) (|cAcosh| #11# #16#) (|cAtanh| #11# #16#) (|cAcoth| #11# #16#) (|cAsech| #11# #16#) (|cAcsch| #11# #16#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 62 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #6=(#7=($ $) NIL #5# ELT)) (|unit?| (#4# NIL #5# ELT)) (|subtractIfCan| (#8=(#9=(|Union| $ "failed") $ $) NIL T ELT)) (|series| (($ #10=(|Stream| |#1|)) 9 T ELT)) (|sample| (#11=($) NIL T CONST)) (|recip| ((#9# $) 44 T ELT)) (|pole?| (#4# 56 T ELT)) (|order| ((#12=(|NonNegativeInteger|) $) 61 T ELT) ((#12# $ #12#) 60 T ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| (#8# 46 #5# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #13=(|Integer|)) NIL T ELT) #6#) (|coefficients| ((#10# $) 25 T ELT)) (|characteristic| ((#12#) 55 T CONST)) (|before?| #1#) (|associates?| (#2# NIL #5# ELT)) (|annihilate?| #1#) (|Zero| (#11# 10 T CONST)) (|One| (#11# 14 T CONST)) (= (#2# 24 T ELT)) (- (#7# 32 T ELT) (#14=($ $ $) 16 T ELT)) (+ (#14# 27 T ELT)) (** (($ $ #15=(|PositiveInteger|)) NIL T ELT) (($ $ #12#) 53 T ELT)) (* (($ #15# $) NIL T ELT) (($ #12# $) NIL T ELT) (($ #13# $) 36 T ELT) (#14# 30 T ELT) (($ $ |#1|) 40 T ELT) (($ |#1| $) 39 T ELT) (($ $ #13#) 38 T ELT))) 
(((|InnerTaylorSeries| |#1|) (|Join| #1=(|Ring|) (|BiModule| |#1| |#1|) (CATEGORY |domain| (SIGNATURE |coefficients| (#2=(|Stream| |#1|) $)) (SIGNATURE |series| ($ #2#)) (SIGNATURE |pole?| ((|Boolean|) $)) (SIGNATURE |order| (#3=(|NonNegativeInteger|) $)) (SIGNATURE |order| (#3# $ #3#)) (SIGNATURE * ($ $ (|Integer|))) (IF (|has| |#1| #4=(|IntegralDomain|)) (ATTRIBUTE #4#) |%noBranch|))) #1#) (T |InnerTaylorSeries|)) 
((|coefficients| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Stream| *3)) #3=(|isDomain| *1 (|InnerTaylorSeries| *3)) #4=(|ofCategory| *3 (|Ring|)))) (|series| (*1 *1 *2) (AND #2# #4# #3#)) (|pole?| #1# (AND (|isDomain| *2 (|Boolean|)) #3# #4#)) (|order| #1# #5=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #4#)) (|order| (*1 *2 *1 *2) #5#) (* (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #3# #4#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|voidMode| (#2=($) 8 T CONST)) (|noValueMode| (#2# 7 T CONST)) (|mappingMode| (($ $ (|List| $)) 16 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jokerMode| (#2# 6 T CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #3=($)) NIL T ELT) (($ #4=(|Syntax|)) 15 T ELT) ((#4# . #3#) 10 T ELT)) (|categoryMode| (#2# NIL T CONST)) (|before?| #1#) (= #1#)) 
(((|InternalTypeForm|) (|Join| (|SetCategory|) (|HomotopicTo| (|Syntax|)) (CATEGORY |domain| (SIGNATURE |jokerMode| #1=($) |constant|) (SIGNATURE |noValueMode| #1# |constant|) (SIGNATURE |voidMode| #1# |constant|) (SIGNATURE |categoryMode| #1# |constant|) (SIGNATURE |mappingMode| ($ $ (|List| $)))))) (T |InternalTypeForm|)) 
((|jokerMode| #1=(*1 *1) #2=(|isDomain| *1 #3=(|InternalTypeForm|))) (|noValueMode| #1# #2#) (|voidMode| #1# #2#) (|categoryMode| #1# #2#) (|mappingMode| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| #3#)) #2#))) 
((|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) 15 T ELT))) 
(((|InfiniteTupleFunctions2| |#1| |#2|) (|Join| #1=(|Type|) (CATEGORY |package| (SIGNATURE |map| ((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|))))) #1# #1#) (T |InfiniteTupleFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|InfiniteTuple| *5)) (|ofCategory| *5 #1=(|Type|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|InfiniteTuple| *6)) (|isDomain| *1 (|InfiniteTupleFunctions2| *5 *6))))) 
((|map| ((#1=(|Stream| |#3|) #2=(|Mapping| |#3| |#1| |#2|) #3=(|InfiniteTuple| |#1|) (|Stream| |#2|)) 20 T ELT) ((#1# #2# (|Stream| |#1|) #4=(|InfiniteTuple| |#2|)) 19 T ELT) (((|InfiniteTuple| |#3|) #2# #3# #4#) 18 T ELT))) 
(((|InfiniteTupleFunctions3| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|InfiniteTuple| |#3|) #1=(|Mapping| |#3| |#1| |#2|) #2=(|InfiniteTuple| |#1|) #3=(|InfiniteTuple| |#2|))) (SIGNATURE |map| (#4=(|Stream| |#3|) #1# (|Stream| |#1|) #3#)) (SIGNATURE |map| (#4# #1# #2# (|Stream| |#2|)))) #5=(|Type|) #5# #5#) (T |InfiniteTupleFunctions3|)) 
((|map| #1=(*1 *2 *3 *4 *5) (AND #2=(|isDomain| *3 (|Mapping| *8 *6 *7)) #3=(|isDomain| *4 (|InfiniteTuple| *6)) (|isDomain| *5 (|Stream| *7)) #4=(|ofCategory| *6 #5=(|Type|)) #6=(|ofCategory| *7 #5#) #7=(|ofCategory| *8 #5#) #8=(|isDomain| *2 (|Stream| *8)) #9=(|isDomain| *1 (|InfiniteTupleFunctions3| *6 *7 *8)))) (|map| #1# (AND #2# (|isDomain| *4 (|Stream| *6)) #10=(|isDomain| *5 (|InfiniteTuple| *7)) #4# #6# #7# #8# #9#)) (|map| #1# (AND #2# #3# #10# #4# #6# #7# (|isDomain| *2 (|InfiniteTuple| *8)) #9#))) 
((|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) 57 T ELT)) (|explogs2trigs| ((#1=(|Complex| |#2|) |#3|) 122 T ELT)) (GF2FG ((|#3| #1#) 46 T ELT)) (FG2F ((|#2| |#3|) 21 T ELT)) (F2FG ((|#3| |#2|) 35 T ELT))) 
(((|InnerTrigonometricManipulations| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE GF2FG (|#3| #1=(|Complex| |#2|))) (SIGNATURE FG2F (|#2| |#3|)) (SIGNATURE F2FG (|#3| |#2|)) (SIGNATURE |explogs2trigs| (#1# |#3|)) (SIGNATURE |trigs2explogs| (|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))))) (|IntegralDomain|) (|Join| (|FunctionSpace| |#1|) #2=(|RadicalCategory|) #3=(|TranscendentalFunctionCategory|)) (|Join| (|FunctionSpace| (|Complex| |#1|)) #2# #3#)) (T |InnerTrigonometricManipulations|)) 
((|trigs2explogs| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Kernel| *2))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *2 (|Join| (|FunctionSpace| #1=(|Complex| *5)) #2=(|RadicalCategory|) #3=(|TranscendentalFunctionCategory|))) (|ofCategory| *5 #4=(|IntegralDomain|)) (|isDomain| *1 (|InnerTrigonometricManipulations| *5 *6 *2)) (|ofCategory| *6 (|Join| (|FunctionSpace| *5) #2# #3#)))) (|explogs2trigs| #5=(*1 *2 *3) (AND #6=(|ofCategory| *4 #4#) (|isDomain| *2 #1#) (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *5 *3)) #7=(|ofCategory| *5 #8=(|Join| (|FunctionSpace| *4) #2# #3#)) #9=(|ofCategory| *3 #10=(|Join| (|FunctionSpace| (|Complex| *4)) #2# #3#)))) (F2FG #5# (AND #6# #11=(|ofCategory| *2 #10#) (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *3 *2)) (|ofCategory| *3 #8#))) (FG2F #5# (AND #6# (|ofCategory| *2 #8#) (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *2 *3)) #9#)) (GF2FG #5# (AND (|isDomain| *3 #1#) #7# #6# #11# (|isDomain| *1 (|InnerTrigonometricManipulations| *4 *5 *2))))) 
((|select| (#1=($ (|Mapping| (|Boolean|) |#1|) $) 19 T ELT)) (|map| (($ #2=(|Mapping| |#1| |#1|) $) 22 T ELT)) (|generate| (($ #2# |#1|) 11 T ELT)) (|filterWhile| (#1# 15 T ELT)) (|filterUntil| (#1# 17 T ELT)) (|construct| (((|Stream| |#1|) $) 20 T ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT))) 
(((|InfiniteTuple| |#1|) (|Join| (|Functorial| |#1|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |filterWhile| #1=($ (|Mapping| (|Boolean|) |#1|) $)) (SIGNATURE |filterUntil| #1#) (SIGNATURE |select| #1#) (SIGNATURE |generate| ($ (|Mapping| |#1| |#1|) |#1|)) (SIGNATURE |construct| ((|Stream| |#1|) $)))) (|Type|)) (T |InfiniteTuple|)) 
((|filterWhile| #1=(*1 *1 *2 *1) #2=(AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) #3=(|ofCategory| *3 (|Type|)) #4=(|isDomain| *1 (|InfiniteTuple| *3)))) (|filterUntil| #1# #2#) (|select| #1# #2#) (|generate| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3 *3)) #3# #4#)) (|construct| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) #4# #3#))) 
((|swap!| (((|Void|) $ |#2| |#2|) 34 T ELT)) (|minIndex| (#1=(|#2| $) 23 T ELT)) (|maxIndex| (#1# 21 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) 30 T ELT)) (|first| ((|#3| $) 26 T ELT)) (|fill!| (($ $ |#3|) 32 T ELT)) (|entry?| (((|Boolean|) |#3| $) 17 T ELT)) (|entries| (((|List| |#3|) $) 15 T ELT)) (|elt| ((|#3| $ |#2| |#3|) 12 T ELT) ((|#3| $ |#2|) NIL T ELT))) 
(((|IndexedAggregate&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |swap!| ((|Void|) |#1| |#2| |#2|)) (SIGNATURE |fill!| (|#1| |#1| |#3|)) (SIGNATURE |first| (|#3| |#1|)) (SIGNATURE |minIndex| #1=(|#2| |#1|)) (SIGNATURE |maxIndex| #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|))) (|IndexedAggregate| |#2| |#3|) (|BasicType|) (|Type|)) (T |IndexedAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#2| . #2=((|BasicType|))) ELT)) (|swap!| (((|Void|) $ |#1| |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| ((|#2| $ |#1| |#2|) 47 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sample| (#3=($) 6 T CONST)) (|qsetelt!| ((|#2| $ |#1| |#2|) 48 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qelt| ((|#2| $ |#1|) 46 T ELT)) (|minIndex| ((|#1| $) 38 (|has| |#1| (|OrderedSet|)) ELT)) (|maxIndex| ((|#1| $) 39 (|has| |#1| (|OrderedSet|)) ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#2| . #4=((|SetCategory|))) ELT)) (|indices| (((|List| |#1|) $) 41 T ELT)) (|index?| (((|Boolean|) |#1| $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#2| . #4#) ELT)) (|first| ((|#2| $) 37 (|has| |#1| (|OrderedSet|)) ELT)) (|fill!| (($ $ |#2|) 36 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|eval| (($ $ (|List| (|Equation| |#2|))) 25 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #4#)) ELT) (($ $ (|Equation| |#2|)) 24 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #4#)) ELT) (($ $ |#2| |#2|) 23 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #4#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 22 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #4#)) ELT)) (|eq?| ((#5=(|Boolean|) $ $) 10 T ELT)) (|entry?| (((|Boolean|) |#2| $) 40 (AND (|has| $ (|FiniteAggregate| |#2|)) (|has| |#2| (|BasicType|))) ELT)) (|entries| (((|List| |#2|) $) 43 T ELT)) (|empty?| ((#5# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|elt| ((|#2| $ |#1| |#2|) 45 T ELT) ((|#2| $ |#1|) 44 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#2| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#2| . #2#) ELT)) (= (#1# 17 (|has| |#2| . #2#) ELT))) 
(((|IndexedAggregate| |#1| |#2|) (|Category|) (|BasicType|) (|Type|)) (T |IndexedAggregate|)) 
((|entries| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|List| *4)))) (|index?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|indices| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|List| *3)))) (|entry?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *1 (|IndexedAggregate| *4 *3)) (|ofCategory| *4 (|BasicType|)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|maxIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|BasicType|)) (|ofCategory| *2 (|OrderedSet|)))) (|minIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|BasicType|)) (|ofCategory| *2 (|OrderedSet|)))) (|first| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Type|)))) (|fill!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|IndexedAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|)))) (|swap!| (*1 *2 *1 *3 *3) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *4)) (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|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| (|BasicType|)) (IF (|has| $ (|FiniteAggregate| |t#2|)) (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| $ (|ShallowlyMutableAggregate| |t#2|)) (PROGN (SIGNATURE |fill!| ($ $ |t#2|)) (SIGNATURE |swap!| ((|Void|) $ |t#1| |t#1|))) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|CoercibleTo| (|OutputForm|)))) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#2| (|SetCategory|)) ((|Type|) . T)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #2=($)) NIL T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# . #2#) NIL T ELT) ((#4=(|TypeAst|) $) 15 T ELT) (($ #5=(|List| #4#)) 14 T ELT)) (|categories| ((#5# $) 12 T ELT)) (|before?| #1#) (= #1#)) 
(((|JoinAst|) (|Join| (|SpadSyntaxCategory|) (|CoercibleTo| #1=(|TypeAst|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #2=(|List| #1#))) (SIGNATURE |categories| (#2# $))))) (T |JoinAst|)) 
((|coerce| (*1 *1 *2) #1=(AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *1 (|JoinAst|)))) (|categories| (*1 *2 *1) #1#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(OR (AND #7=(|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #8=(|has| |#1| (|IntegralDomain|))) (AND #9=(|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #8#)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#1|))) NIL #9# ELT) ((#10# #12=(|Vector| $)) NIL #7# ELT)) (|someBasis| (#13=(#12#) NIL #7# ELT)) (|sample| #14=(($) NIL T CONST)) (|rightUnits| #15=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #16=((#11#) NIL #9# ELT) #17=(#18=(#11# #12#) NIL #7# ELT)) (|rightTrace| #19=((|#1| $) NIL #7# ELT)) (|rightRegularRepresentation| #20=((#11# $) NIL #9# ELT) #21=((#11# $ #12#) NIL #7# ELT)) (|rightRecip| #22=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #23=(((|SparseUnivariatePolynomial| #24=(|Polynomial| |#1|))) NIL (AND #9# (|has| |#1| (|Field|))) ELT)) (|rightPower| #25=(#26=($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| #28=(#29=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #30=((|#1|) NIL #9# ELT) #31=((|#1| #12#) NIL #7# ELT)) (|rightCharacteristicPolynomial| #32=(#29# NIL #7# ELT)) (|rightAlternative?| #33=((#2#) NIL #7# ELT)) (|represents| #34=(($ #35=(|Vector| |#1|)) NIL #9# ELT) (($ #35# #12#) NIL #7# ELT)) (|recip| #22#) (|rank| ((#27#) NIL #7# ELT)) (|powerAssociative?| #33#) (|plenaryPower| #25#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| #33#) (|leftUnits| #15#) (|leftUnit| #3#) (|leftTraceMatrix| #16# #17#) (|leftTrace| #19#) (|leftRegularRepresentation| #20# #21#) (|leftRecip| #22#) (|leftRankPolynomial| #23#) (|leftPower| #25#) (|leftNorm| #19#) (|leftMinimalPolynomial| #28#) (|leftDiscriminant| #30# #31#) (|leftCharacteristicPolynomial| #32#) (|leftAlternative?| #33#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #33#) (|jordanAdmissible?| #33#) (|jacobiIdentity?| #33#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| #33#) (|elt| ((|#1| $ #36=(|Integer|)) NIL #9# ELT)) (|coordinates| (#18# NIL #9# ELT) #37=((#35# $) NIL #9# ELT) ((#11# #12# #12#) NIL #7# ELT) ((#35# $ #12#) NIL #7# ELT)) (|convert| #34# #37#) (|conditionsForIdempotents| ((#38=(|List| #24#)) NIL #9# ELT) ((#38# #12#) NIL #7# ELT)) (|commutator| #39=(#40=($ $ $) NIL T ELT)) (|commutative?| #33#) (|coerce| (((|OutputForm|) $) NIL T ELT) ((|#2| $) 21 T ELT) (($ |#2|) 22 T ELT)) (|before?| #1#) (|basis| (#13# NIL #9# ELT)) (|associatorDependence| (((|List| #35#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #33#) (|apply| (($ #11# $) NIL #9# ELT)) (|antiCommutator| #39#) (|antiCommutative?| #33#) (|antiAssociative?| #33#) (|alternative?| #33#) (|Zero| #14#) (= #1#) (- (($ $) NIL T ELT) #39#) (+ #39#) (** (#26# 24 T ELT)) (* (($ #27# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #36# . #41=($)) NIL T ELT) (#40# 20 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #41#) NIL T ELT))) 
(((|AssociatedJordanAlgebra| |#1| |#2|) (|Join| #1=(|NonAssociativeAlgebra| |#1|) (|CoercibleTo| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#2|)) (IF (|has| |#2| #2=(|FramedNonAssociativeAlgebra| |#1|)) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |#2| #3=(|FiniteRankNonAssociativeAlgebra| |#1|)) (ATTRIBUTE #3#) |%noBranch|))) (|CommutativeRing|) #1#) (T |AssociatedJordanAlgebra|)) 
((|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|AssociatedJordanAlgebra| *3 *2)) (|ofCategory| *2 (|NonAssociativeAlgebra| *3))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #2=(|Byte|)) 6 T ELT) ((#2# $) 7 T ELT)) (|before?| #1#) (= #1#)) 
(((|JVMBytecode|) (|Join| (|SetCategory|) (|HomotopicTo| (|Byte|)))) (T |JVMBytecode|)) 
NIL 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (($ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jvmSuper| (#2=($) 10 T CONST)) (|jvmPublic| (#2# 8 T CONST)) (|jvmInterface| (#2# 11 T CONST)) (|jvmFinal| (#2# 9 T CONST)) (|jvmAbstract| (#2# 12 T CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|\\/| #3=(($ $ $) NIL T ELT)) (= #1#) (|/\\| #3#)) 
(((|JVMClassFileAccess|) (|Join| (|SetCategory|) (|Logic|) (CATEGORY |domain| (SIGNATURE |jvmPublic| #1=($) |constant|) (SIGNATURE |jvmFinal| #1# |constant|) (SIGNATURE |jvmSuper| #1# |constant|) (SIGNATURE |jvmInterface| #1# |constant|) (SIGNATURE |jvmAbstract| #1# |constant|)))) (T |JVMClassFileAccess|)) 
((|jvmPublic| #1=(*1 *1) #2=(|isDomain| *1 (|JVMClassFileAccess|))) (|jvmFinal| #1# #2#) (|jvmSuper| #1# #2#) (|jvmInterface| #1# #2#) (|jvmAbstract| #1# #2#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jvmUTF8ConstantTag| (#2=($) 11 T CONST)) (|jvmStringConstantTag| (#2# 17 T CONST)) (|jvmNameAndTypeConstantTag| (#2# 21 T CONST)) (|jvmMethodrefConstantTag| (#2# 19 T CONST)) (|jvmLongConstantTag| (#2# 14 T CONST)) (|jvmInterfaceMethodConstantTag| (#2# 20 T CONST)) (|jvmIntegerConstantTag| (#2# 12 T CONST)) (|jvmFloatConstantTag| (#2# 13 T CONST)) (|jvmFieldrefConstantTag| (#2# 18 T CONST)) (|jvmDoubleConstantTag| (#2# 15 T CONST)) (|jvmClassConstantTag| (#2# 16 T CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #3=($)) NIL T ELT) (((|Byte|) . #3#) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|JVMConstantTag|) (|Join| (|SetCategory|) (|CoercibleTo| (|Byte|)) (CATEGORY |domain| (SIGNATURE |jvmUTF8ConstantTag| #1=($) |constant|) (SIGNATURE |jvmIntegerConstantTag| #1# |constant|) (SIGNATURE |jvmFloatConstantTag| #1# |constant|) (SIGNATURE |jvmLongConstantTag| #1# |constant|) (SIGNATURE |jvmDoubleConstantTag| #1# |constant|) (SIGNATURE |jvmClassConstantTag| #1# |constant|) (SIGNATURE |jvmStringConstantTag| #1# |constant|) (SIGNATURE |jvmFieldrefConstantTag| #1# |constant|) (SIGNATURE |jvmMethodrefConstantTag| #1# |constant|) (SIGNATURE |jvmInterfaceMethodConstantTag| #1# |constant|) (SIGNATURE |jvmNameAndTypeConstantTag| #1# |constant|)))) (T |JVMConstantTag|)) 
((|jvmUTF8ConstantTag| #1=(*1 *1) #2=(|isDomain| *1 (|JVMConstantTag|))) (|jvmIntegerConstantTag| #1# #2#) (|jvmFloatConstantTag| #1# #2#) (|jvmLongConstantTag| #1# #2#) (|jvmDoubleConstantTag| #1# #2#) (|jvmClassConstantTag| #1# #2#) (|jvmStringConstantTag| #1# #2#) (|jvmFieldrefConstantTag| #1# #2#) (|jvmMethodrefConstantTag| #1# #2#) (|jvmInterfaceMethodConstantTag| #1# #2#) (|jvmNameAndTypeConstantTag| #1# #2#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (($ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jvmVolatile| (#2=($) 13 T CONST)) (|jvmTransient| (#2# 14 T CONST)) (|jvmStatic| (#2# 11 T CONST)) (|jvmPublic| (#2# 8 T CONST)) (|jvmProtected| (#2# 10 T CONST)) (|jvmPrivate| (#2# 9 T CONST)) (|jvmFinal| (#2# 12 T CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|\\/| #3=(($ $ $) NIL T ELT)) (= #1#) (|/\\| #3#)) 
(((|JVMFieldAccess|) (|Join| (|SetCategory|) (|Logic|) (CATEGORY |domain| (SIGNATURE |jvmPublic| #1=($) |constant|) (SIGNATURE |jvmPrivate| #1# |constant|) (SIGNATURE |jvmProtected| #1# |constant|) (SIGNATURE |jvmStatic| #1# |constant|) (SIGNATURE |jvmFinal| #1# |constant|) (SIGNATURE |jvmVolatile| #1# |constant|) (SIGNATURE |jvmTransient| #1# |constant|)))) (T |JVMFieldAccess|)) 
((|jvmPublic| #1=(*1 *1) #2=(|isDomain| *1 (|JVMFieldAccess|))) (|jvmPrivate| #1# #2#) (|jvmProtected| #1# #2#) (|jvmStatic| #1# #2#) (|jvmFinal| #1# #2#) (|jvmVolatile| #1# #2#) (|jvmTransient| #1# #2#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (($ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jvmSynchronized| (#2=($) 13 T CONST)) (|jvmStrict| (#2# 16 T CONST)) (|jvmStatic| (#2# 11 T CONST)) (|jvmPublic| (#2# 8 T CONST)) (|jvmProtected| (#2# 10 T CONST)) (|jvmPrivate| (#2# 9 T CONST)) (|jvmNative| (#2# 14 T CONST)) (|jvmFinal| (#2# 12 T CONST)) (|jvmAbstract| (#2# 15 T CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|\\/| #3=(($ $ $) NIL T ELT)) (= #1#) (|/\\| #3#)) 
(((|JVMMethodAccess|) (|Join| (|SetCategory|) (|Logic|) (CATEGORY |domain| (SIGNATURE |jvmPublic| #1=($) |constant|) (SIGNATURE |jvmPrivate| #1# |constant|) (SIGNATURE |jvmProtected| #1# |constant|) (SIGNATURE |jvmStatic| #1# |constant|) (SIGNATURE |jvmFinal| #1# |constant|) (SIGNATURE |jvmSynchronized| #1# |constant|) (SIGNATURE |jvmNative| #1# |constant|) (SIGNATURE |jvmAbstract| #1# |constant|) (SIGNATURE |jvmStrict| #1# |constant|)))) (T |JVMMethodAccess|)) 
((|jvmPublic| #1=(*1 *1) #2=(|isDomain| *1 (|JVMMethodAccess|))) (|jvmPrivate| #1# #2#) (|jvmProtected| #1# #2#) (|jvmStatic| #1# #2#) (|jvmFinal| #1# #2#) (|jvmSynchronized| #1# #2#) (|jvmNative| #1# #2#) (|jvmAbstract| #1# #2#) (|jvmStrict| #1# #2#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 19 T ELT) (($ #2=(|JVMBytecode|)) 12 T ELT) ((#2# $) 11 T ELT) (($ #3=(|Byte|)) NIL T ELT) ((#3# $) 14 T ELT)) (|before?| #1#) (= #1#)) 
(((|JVMOpcode|) (|Join| (|SetCategory|) (|HomotopicTo| (|JVMBytecode|)) (|HomotopicTo| (|Byte|)))) (T |JVMOpcode|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|write!| ((#4=(|Record| (|:| |key| #5=(|String|)) (|:| |entry| |#1|)) $ #4#) 40 T ELT)) (|table| #6=(($ #7=(|List| #4#)) NIL T ELT) #8=(#9=($) NIL T ELT)) (|swap!| (((|Void|) $ #5# #5#) NIL #10=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| (#11=(|#1| $ #5# |#1|) 50 #10# ELT)) (|select!| #12=(($ #13=(|Mapping| #3# #4#) $) NIL #14=(|has| $ (|FiniteAggregate| #4#)) ELT)) (|select| #12#) (|search| (#15=((|Union| |#1| #16="failed") #5# $) 53 T ELT)) (|sample| (#9# NIL T CONST)) (|reopen!| (($ $ #5#) 25 T ELT)) (|removeDuplicates| (#17=($ $) NIL #18=(AND #14# #19=(|has| #4# #20=(|BasicType|))) ELT)) (|remove!| (#15# 54 T ELT) #12# (#21=($ #4# $) NIL #14# ELT)) (|remove| #12# (#21# NIL #18# ELT)) (|reduce| ((#4# #22=(|Mapping| #4# #4# #4#) $) NIL T ELT) ((#4# #22# $ #4#) NIL T ELT) ((#4# #22# $ #4# #4#) NIL #19# ELT)) (|read!| (#23=(#4# $) 39 T ELT)) (|qsetelt!| (#11# NIL #10# ELT)) (|qelt| (#24=(|#1| $ #5#) NIL T ELT)) (|pack!| (#17# 55 T ELT)) (|open| (($ #25=(|FileName|)) 23 T ELT) (($ #25# #5#) 22 T ELT)) (|name| ((#25# $) 41 T ELT)) (|minIndex| #26=(#27=(#5# $) NIL #28=(|has| #5# (|OrderedSet|)) ELT)) (|members| ((#7# $) NIL T ELT)) (|member?| ((#3# #4# $) NIL #19# ELT)) (|maxIndex| #26#) (|map!| #29=(($ (|Mapping| |#1| |#1|) . #30=($)) NIL T ELT) #31=(($ (|Mapping| #4# #4#) . #30#) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL T ELT) #29# #31#) (|latex| (#27# NIL T ELT)) (|keys| (#32=((|List| #5#) $) 46 T ELT)) (|key?| #33=((#3# #5# $) NIL T ELT)) (|iomode| (#27# 42 T ELT)) (|inspect| #34=(#23# NIL T ELT)) (|insert!| (#21# NIL T ELT)) (|indices| (#32# NIL T ELT)) (|index?| #33#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| ((|#1| $) NIL #28# ELT)) (|find| (((|Union| #4# #16#) #13# $) NIL T ELT)) (|fill!| (($ $ |#1|) NIL #10# ELT)) (|extract!| #34#) (|every?| #35=((#3# #13# $) NIL T ELT)) (|eval| (($ $ (|List| #36=(|Equation| |#1|))) NIL #37=(AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| #38=(|SetCategory|))) ELT) (($ $ #36#) NIL #37# ELT) (($ $ |#1| |#1|) NIL #37# ELT) (($ $ #39=(|List| |#1|) #39#) NIL #37# ELT) (($ $ #7# #7#) NIL #40=(AND (|has| #4# (|Evalable| #4#)) (|has| #4# #38#)) ELT) (($ $ #4# #4#) NIL #40# ELT) (($ $ #41=(|Equation| #4#)) NIL #40# ELT) (($ $ (|List| #41#)) NIL #40# ELT)) (|eq?| #1#) (|entry?| ((#3# |#1| $) NIL (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| #20#)) ELT)) (|entries| ((#39# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| (#9# 44 T ELT)) (|elt| (#11# NIL T ELT) (#24# 49 T ELT)) (|dictionary| #6# #8#) (|count| ((#42=(|NonNegativeInteger|) #13# $) NIL T ELT) ((#42# #4# $) NIL #19# ELT)) (|copy| (#17# NIL T ELT)) (|convert| ((#43=(|InputForm|) $) NIL (|has| #4# (|ConvertibleTo| #43#)) ELT)) (|construct| #6#) (|coerce| (((|OutputForm|) $) 21 T ELT)) (|close!| (#17# 26 T ELT)) (|before?| #1#) (|bag| #6#) (|any?| #35#) (= (#2# 20 T ELT)) (|#| ((#42# $) 48 T ELT))) 
(((|KeyedAccessFile| |#1|) (|Join| (|FileCategory| (|FileName|) (|Record| (|:| |key| #1=(|String|)) (|:| |entry| |#1|))) (|TableAggregate| #1# |#1|) (CATEGORY |domain| (SIGNATURE |pack!| ($ $)))) (|SetCategory|)) (T |KeyedAccessFile|)) 
((|pack!| (*1 *1 *1) (AND (|isDomain| *1 (|KeyedAccessFile| *2)) (|ofCategory| *2 (|SetCategory|))))) 
((|keys| (((|List| |#2|) $) 19 T ELT)) (|key?| (((|Boolean|) |#2| $) 12 T ELT)) (|elt| ((|#3| $ |#2|) 20 T ELT) ((|#3| $ |#2| |#3|) 21 T ELT))) 
(((|KeyedDictionary&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |keys| ((|List| |#2|) |#1|)) (SIGNATURE |key?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |elt| (|#3| |#1| |#2| |#3|)) (SIGNATURE |elt| (|#3| |#1| |#2|))) (|KeyedDictionary| |#2| |#3|) #1=(|SetCategory|) #1#) (T |KeyedDictionary&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (OR (|has| |#2| . #2=((|BasicType|))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|swap!| (((|Void|) $ |#1| |#1|) 82 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| ((|#2| $ |#1| |#2|) 70 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|select!| (($ (|Mapping| #3=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #4=($)) 42 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #6=($)) 49 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|search| (((|Union| |#2| "failed") |#1| $) 59 T ELT)) (|sample| (#7=($) 6 T CONST)) (|removeDuplicates| (($ $) 51 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8=((|BasicType|))) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT)) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 44 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Mapping| #3# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #4#) 43 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Union| |#2| "failed") |#1| $) 60 T ELT)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 50 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT) (($ (|Mapping| #5# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #6#) 48 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|qsetelt!| ((|#2| $ |#1| |#2|) 69 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qelt| ((|#2| $ |#1|) 71 T ELT)) (|minIndex| ((|#1| . #9=($)) 79 (|has| |#1| . #10=((|OrderedSet|))) ELT)) (|maxIndex| ((|#1| . #9#) 78 (|has| |#1| . #10#) ELT)) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #11=($)) 39 T ELT) (($ (|Mapping| |#2| |#2|) . #11#) 63 T ELT)) (|map| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #12=($)) 26 T ELT) (($ (|Mapping| |#2| |#2|) . #12#) 64 T ELT)) (|latex| (((|String|) $) 21 (OR (|has| |#2| . #13=((|SetCategory|))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #13#)) ELT)) (|keys| (((|List| |#1|) $) 61 T ELT)) (|key?| (((|Boolean|) |#1| $) 62 T ELT)) (|inspect| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #14=($)) 35 T ELT)) (|insert!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 36 T ELT)) (|indices| (((|List| |#1|) $) 76 T ELT)) (|index?| ((#15=(|Boolean|) |#1| $) 75 T ELT)) (|hash| (((|SingleInteger|) $) 20 (OR (|has| |#2| . #13#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #13#)) ELT)) (|first| ((|#2| $) 80 (|has| |#1| . #10#) ELT)) (|fill!| (($ $ |#2|) 81 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|extract!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #14#) 37 T ELT)) (|eval| (($ $ (|List| (|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|)) . #13#)) ELT) (($ $ (|Equation| (|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|)) . #13#)) ELT) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|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|)) . #13#)) ELT) (($ $ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 22 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #13#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 68 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #13#)) ELT) (($ $ |#2| |#2|) 67 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #13#)) ELT) (($ $ (|Equation| |#2|)) 66 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #13#)) ELT) (($ $ (|List| (|Equation| |#2|))) 65 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #13#)) ELT)) (|eq?| ((#16=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#15# |#2| $) 77 (AND (|has| $ (|FiniteAggregate| |#2|)) (|has| |#2| (|BasicType|))) ELT)) (|entries| (((|List| |#2|) $) 74 T ELT)) (|empty?| ((#16# $) 7 T ELT)) (|empty| (#7# 8 T ELT)) (|elt| ((|#2| $ |#1|) 73 T ELT) ((|#2| $ |#1| |#2|) 72 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 45 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#17=(|InputForm|) $) 52 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| #17#)) ELT)) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 47 T ELT)) (|coerce| ((#18=(|OutputForm|) $) 16 (OR (|has| |#2| . #19=((|CoercibleTo| #18#))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #19#)) ELT)) (|before?| (#1# 19 (OR (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|bag| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 38 T ELT)) (= (#1# 17 (OR (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT))) 
(((|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|))) (|IndexedAggregate| |t#1| |t#2|) (|ShallowlyMutableAggregate| |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| #1=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|BasicType|)) (|has| |#2| (|SetCategory|)) (|has| |#2| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|CoercibleTo| (|OutputForm|))) (|has| |#2| (|SetCategory|)) (|has| |#2| (|CoercibleTo| (|OutputForm|)))) ((|Collection| #1#) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))) ((|Dictionary| #1#) . T) ((|DictionaryOperations| #1#) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| #1#) 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|))) ((|Functorial| #1#) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| #1#) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| |#1| |#2|) . T) ((|InnerEvalable| #1# #1#) 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|))) ((|Join|) . T) ((|SetCategory|) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))) ((|ShallowlyMutableAggregate| #1#) . T) ((|ShallowlyMutableAggregate| |#2|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|symbolIfCan| (((|Union| #4=(|Symbol|) "failed") $) 46 T ELT)) (|setPosition| (((|Void|) $ #5=(|NonNegativeInteger|)) 22 T ELT)) (|position| (#6=(#5# $) 20 T ELT)) (|operator| ((#7=(|BasicOperator|) $) 9 T ELT)) (|min| #8=(($ $ $) NIL T ELT)) (|max| #8#) (|latex| (((|String|) $) NIL T ELT)) (|kernel| (($ #7# #9=(|List| |#1|) #5#) 32 T ELT) (($ #4#) 33 T ELT)) (|is?| ((#3# $ #7#) 15 T ELT) ((#3# $ #4#) 13 T ELT)) (|height| (#6# 17 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| ((#10=(|Pattern| (|Integer|)) $) 99 (|has| |#1| (|ConvertibleTo| #10#)) ELT) ((#11=(|Pattern| (|Float|)) $) 106 (|has| |#1| (|ConvertibleTo| #11#)) ELT) ((#12=(|InputForm|) $) 92 (|has| |#1| (|ConvertibleTo| #12#)) ELT)) (|coerce| (((|OutputForm|) $) 74 T ELT)) (|before?| #1#) (|argument| ((#9# $) 19 T ELT)) (>= #1#) (> #1#) (= (#2# 51 T ELT)) (<= #1#) (< (#2# 53 T ELT))) 
(((|Kernel| |#1|) (|Join| (|CachableSet|) (|OrderedSet|) (|Patternable| |#1|) (CATEGORY |domain| (SIGNATURE |operator| (#1=(|BasicOperator|) $)) (SIGNATURE |argument| (#2=(|List| |#1|) $)) (SIGNATURE |height| (#3=(|NonNegativeInteger|) $)) (SIGNATURE |kernel| ($ #1# #2# #3#)) (SIGNATURE |kernel| ($ #4=(|Symbol|))) (SIGNATURE |symbolIfCan| ((|Union| #4# "failed") $)) (SIGNATURE |is?| (#5=(|Boolean|) $ #1#)) (SIGNATURE |is?| (#5# $ #4#)) (IF (|has| |#1| #6=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #6#) |%noBranch|))) (|SetCategory|)) (T |Kernel|)) 
((|operator| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 #3=(|BasicOperator|)) #4=(|isDomain| *1 (|Kernel| *3)) #5=(|ofCategory| *3 #6=(|SetCategory|)))) (|argument| #1# (AND (|isDomain| *2 (|List| *3)) #4# #5#)) (|height| #1# (AND (|isDomain| *2 #7=(|NonNegativeInteger|)) #4# #5#)) (|kernel| (*1 *1 *2 *3 *4) (AND #2# (|isDomain| *3 (|List| *5)) (|isDomain| *4 #7#) (|ofCategory| *5 #6#) (|isDomain| *1 (|Kernel| *5)))) (|kernel| (*1 *1 *2) (AND #8=(|isDomain| *2 #9=(|Symbol|)) #4# #5#)) (|symbolIfCan| #1# (|partial| AND #8# #4# #5#)) (|is?| #10=(*1 *2 *1 *3) (AND (|isDomain| *3 #3#) #11=(|isDomain| *2 (|Boolean|)) #12=(|isDomain| *1 (|Kernel| *4)) #13=(|ofCategory| *4 #6#))) (|is?| #10# (AND (|isDomain| *3 #9#) #11# #12# #13#))) 
((|constantKernel| ((#1=(|Kernel| |#2|) |#1|) 17 T ELT)) (|constantIfCan| (((|Union| |#1| "failed") #1#) 21 T ELT))) 
(((|KernelFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |constantKernel| (#1=(|Kernel| |#2|) |#1|)) (SIGNATURE |constantIfCan| ((|Union| |#1| "failed") #1#))) #2=(|SetCategory|) #2#) (T |KernelFunctions2|)) 
((|constantIfCan| #1=(*1 *2 *3) (|partial| AND (|isDomain| *3 #2=(|Kernel| *4)) #3=(|ofCategory| *4 #4=(|SetCategory|)) (|ofCategory| *2 #4#) (|isDomain| *1 (|KernelFunctions2| *2 *4)))) (|constantKernel| #1# (AND (|isDomain| *2 #2#) (|isDomain| *1 (|KernelFunctions2| *3 *4)) (|ofCategory| *3 #4#) #3#))) 
((|coerce| ((|#1| $) 6 T ELT))) 
(((|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 T ELT))) 
(((|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| $)))) 
((|kovacic| ((#1=(|Union| (|SparseUnivariatePolynomial| #2=(|Fraction| |#2|)) "failed") #2# #2# #2# (|Mapping| (|Factored| |#2|) |#2|)) 15 T ELT) ((#1# #2# #2# #2#) 16 T ELT))) 
(((|Kovacic| |#1| |#2|) (CATEGORY |package| (SIGNATURE |kovacic| (#1=(|Union| (|SparseUnivariatePolynomial| #2=(|Fraction| |#2|)) "failed") #2# #2# #2#)) (SIGNATURE |kovacic| (#1# #2# #2# #2# (|Mapping| (|Factored| |#2|) |#2|)))) (|Join| (|CharacteristicZero|) (|AlgebraicallyClosedField|) (|RetractableTo| #3=(|Integer|)) (|RetractableTo| (|Fraction| #3#))) (|UnivariatePolynomialCategory| |#1|)) (T |Kovacic|)) 
((|kovacic| (*1 *2 *3 *3 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| (|Factored| *6) *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #1=(|Join| (|CharacteristicZero|) (|AlgebraicallyClosedField|) (|RetractableTo| #2=(|Integer|)) (|RetractableTo| (|Fraction| #2#)))) (|isDomain| *2 (|SparseUnivariatePolynomial| #3=(|Fraction| *6))) (|isDomain| *1 (|Kovacic| *5 *6)) (|isDomain| *3 #3#))) (|kovacic| (*1 *2 *3 *3 *3) (|partial| AND (|ofCategory| *4 #1#) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|SparseUnivariatePolynomial| #4=(|Fraction| *5))) (|isDomain| *1 (|Kovacic| *4 *5)) (|isDomain| *3 #4#)))) 
((|coerce| (($ |#1|) 6 T ELT))) 
(((|CoercibleFrom| |#1|) (|Category|) (|Type|)) (T |CoercibleFrom|)) 
((|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|CoercibleFrom| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE |coerce| ($ |t#1|)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (~ (#4=($ $) NIL T ELT)) (|unknown| (#5=($) 11 T CONST)) (|true| (#5# 13 T CONST)) (|size| (((|NonNegativeInteger|)) 36 T ELT)) (|random| (#5# NIL T ELT)) (|or| (#6=($ $ $) 25 T ELT)) (|not| (#4# 23 T ELT)) (|lookup| ((#7=(|PositiveInteger|) $) 43 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #7#) 42 T ELT)) (|implies| (#6# 26 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|false| (#5# 9 T CONST)) (|equiv| (#6# 27 T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT)) (|case| ((#3# $ (|[\|\|]| |false|)) 20 T ELT) ((#3# $ (|[\|\|]| |unknown|)) 22 T ELT) ((#3# $ (|[\|\|]| |true|)) 18 T ELT)) (|before?| #1#) (|and| (#6# 24 T ELT)) (|\\/| #8=(#6# NIL T ELT)) (= (#2# 16 T ELT)) (|/\\| #8#)) 
(((|KleeneTrivalentLogic|) (|Join| (|PropositionalLogic|) (|Finite|) (CATEGORY |domain| (SIGNATURE |unknown| ($) |constant|) (SIGNATURE |case| (#1=(|Boolean|) $ (|[\|\|]| |false|))) (SIGNATURE |case| (#1# $ (|[\|\|]| |unknown|))) (SIGNATURE |case| (#1# $ (|[\|\|]| |true|)))))) (T |KleeneTrivalentLogic|)) 
((|unknown| (*1 *1) #1=(|isDomain| *1 (|KleeneTrivalentLogic|))) (|case| #2=(*1 *2 *1 *3) (AND (|isDomain| *3 (|[\|\|]| |false|)) #3=(|isDomain| *2 (|Boolean|)) #1#)) (|case| #2# (AND (|isDomain| *3 (|[\|\|]| |unknown|)) #3# #1#)) (|case| #2# (AND (|isDomain| *3 (|[\|\|]| |true|)) #3# #1#))) 
((|convert| (($ |#1|) 6 T ELT))) 
(((|ConvertibleFrom| |#1|) (|Category|) (|Type|)) (T |ConvertibleFrom|)) 
((|convert| (*1 *1 *2) (AND (|ofCategory| *1 (|ConvertibleFrom| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (CATEGORY |domain| (SIGNATURE |convert| ($ |t#1|)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Union| $ "failed") $ $) NIL T ELT)) (|sign| ((#7=(|Integer|) $) NIL #8=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| #9=(#10=($) NIL T CONST)) (|recip| ((#6# $) NIL T ELT)) (|positive?| #11=(#5# NIL #8# ELT)) (|opposite?| #1#) (|one?| #4#) (|numer| ((|#1| $) 13 T ELT)) (|negative?| #11#) (|min| #12=(#13=($ $ $) NIL #8# ELT)) (|max| #12#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#3| $) 15 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #7#) NIL T ELT) (($ |#2|) NIL T ELT)) (|characteristic| ((#14=(|NonNegativeInteger|)) 20 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#15=($ $) NIL #8# ELT)) (|Zero| #9#) (|One| (#10# 12 T CONST)) (>= #16=(#2# NIL #8# ELT)) (> #16#) (= #1#) (<= #16#) (< #16#) (/ (($ $ |#3|) NIL T ELT) (($ |#1| |#3|) 11 T ELT)) (- (#15# NIL T ELT) #17=(#13# NIL T ELT)) (+ #17#) (** (($ $ #18=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #18# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #7# . #19=($)) NIL T ELT) (#13# 17 T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #19#) NIL T ELT))) 
(((|LocalAlgebra| |#1| |#2| |#3|) (|Join| #1=(|Algebra| |#2|) (CATEGORY |domain| (IF (|has| |#1| #2=(|OrderedRing|)) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE / ($ $ |#3|)) (SIGNATURE / ($ |#1| |#3|)) (SIGNATURE |numer| (|#1| $)) (SIGNATURE |denom| (|#3| $)))) #1# (|CommutativeRing|) (|SubsetCategory| (|Monoid|) |#2|)) (T |LocalAlgebra|)) 
((/ (*1 *1 *1 *2) (AND #1=(|ofCategory| *4 #2=(|CommutativeRing|)) #3=(|isDomain| *1 (|LocalAlgebra| *3 *4 *2)) #4=(|ofCategory| *3 #5=(|Algebra| *4)) #6=(|ofCategory| *2 #7=(|SubsetCategory| #8=(|Monoid|) *4)))) (/ (*1 *1 *2 *3) (AND #1# (|isDomain| *1 (|LocalAlgebra| *2 *4 *3)) (|ofCategory| *2 #5#) (|ofCategory| *3 #7#))) (|numer| #9=(*1 *2 *1) (AND (|ofCategory| *3 #2#) (|ofCategory| *2 (|Algebra| *3)) (|isDomain| *1 (|LocalAlgebra| *2 *3 *4)) (|ofCategory| *4 (|SubsetCategory| #8# *3)))) (|denom| #9# (AND #1# #6# #3# #4#))) 
((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) NIL T ELT) (($ |#2|) 10 T ELT))) 
(((|LeftAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|LeftAlgebra| |#2|) (|Ring|)) (T |LeftAlgebra&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 49 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ |#1| . #4#) 50 T ELT))) 
(((|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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|laplace| ((|#2| |#2| #1=(|Symbol|) #1#) 16 T ELT))) 
(((|LaplaceTransform| |#1| |#2|) (CATEGORY |package| (SIGNATURE |laplace| (|#2| |#2| #1=(|Symbol|) #1#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#)) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |LaplaceTransform|)) 
((|laplace| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#))) (|isDomain| *1 (|LaplaceTransform| *4 *2)) (|ofCategory| *2 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4)))))) 
((~= (#1=(#2=(|Boolean|) $ $) 64 T ELT)) (|zero?| (#3=(#2# $) 58 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #6=(#3# NIL T ELT)) (|trailingCoefficient| (#7=(|#1| $) 55 T ELT)) (|subtractIfCan| (#8=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|sizeLess?| (#1# NIL #11=(|has| |#1| (|Field|)) ELT)) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| #12=(|Fraction| |#2|))) #12#) 111 #11# ELT)) (|sample| (#13=($) NIL T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=(#10#)) . #16=($)) NIL #17=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) NIL #19=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| |#1| . #15#) $) 99 T ELT) (((|Union| |#2| . #15#) $) 95 T ELT)) (|retract| (#20=(#14# $) NIL #17# ELT) ((#18# . #21=($)) NIL #19# ELT) (#7# NIL T ELT) ((|#2| . #21#) NIL T ELT)) (|rem| #22=(#23=($ $ $) NIL #11# ELT)) (|reductum| (#5# 27 T ELT)) (|recip| ((#9# $) 88 T ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL #11# ELT)) (|order| (#20# 22 T ELT)) (|opposite?| #26=(#1# NIL T ELT)) (|one?| #6#) (|multiEuclidean| (((|Union| #24# #10#) #24# $) NIL #11# ELT)) (|monomial?| (#3# 40 T ELT)) (|monomial| (($ |#1| #14#) 24 T ELT)) (|leadingCoefficient| (#7# 57 T ELT)) (|lcm| #27=(($ #24#) NIL #11# ELT) #22#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#28=(|SparseUnivariatePolynomial| $) #28# #28#) NIL #11# ELT)) (|gcd| #27# (#23# 101 #11# ELT)) (|extendedEuclidean| (((|Union| (|Record| #29=(|:| |coef1| $) #30=(|:| |coef2| $)) #10#) $ $ $) 116 #11# ELT) (((|Record| #29# #30# #25#) $ $) NIL #11# ELT)) (|exquo| (#8# 93 T ELT)) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL #11# ELT)) (|euclideanSize| ((#31=(|NonNegativeInteger|) $) 115 #11# ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 114 #11# ELT)) (|differentiate| #32=(($ $ #33=(|Mapping| |#2| |#2|) #31#) NIL T ELT) (#34=($ $ #33#) 75 T ELT) #35=(#5# NIL #36=(|has| |#2| (|DifferentialSpace|)) ELT) #37=(#38=($ $ #31#) NIL #36# ELT) #39=(($ $ #40=(|Symbol|)) NIL #41=(|has| |#2| (|PartialDifferentialSpace| #40#)) ELT) #42=(($ $ #43=(|List| #40#)) NIL #41# ELT) #44=(($ $ #40# #31#) NIL #41# ELT) #45=(($ $ #43# (|List| #31#)) NIL #41# ELT)) (|degree| (#20# 38 T ELT)) (|convert| ((#12# $) 47 T ELT)) (|coerce| (((|OutputForm|) $) 69 T ELT) (($ #14#) 35 T ELT) #4# (($ #18#) NIL #19# ELT) (($ |#1|) 34 T ELT) (($ |#2|) 25 T ELT)) (|coefficient| ((|#1| $ #14#) 72 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#31#) 32 T CONST)) (|before?| #26#) (|associates?| #26#) (|annihilate?| #26#) (|Zero| (#13# 9 T CONST)) (|One| (#13# 14 T CONST)) (D #32# (#34# NIL T ELT) #35# #37# #39# #42# #44# #45#) (= (#1# 21 T ELT)) (- (#5# 51 T ELT) (#23# NIL T ELT)) (+ (#23# 90 T ELT)) (** (($ $ #46=(|PositiveInteger|)) NIL T ELT) (#38# NIL T ELT)) (* (($ #46# $) NIL T ELT) (($ #31# $) NIL T ELT) (($ #14# $) 29 T ELT) (#23# 49 T ELT))) 
(((|LaurentPolynomial| |#1| |#2|) (|Join| (|DifferentialExtension| |#2|) #1=(|IntegralDomain|) (|ConvertibleTo| #2=(|Fraction| |#2|)) (|FullyRetractableTo| |#1|) (|RetractableTo| |#2|) (CATEGORY |domain| (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |degree| #3=(#4=(|Integer|) $)) (SIGNATURE |order| #3#) (SIGNATURE |reductum| ($ $)) (SIGNATURE |leadingCoefficient| #5=(|#1| $)) (SIGNATURE |trailingCoefficient| #5#) (SIGNATURE |coefficient| (|#1| $ #4#)) (SIGNATURE |monomial| ($ |#1| #4#)) (IF (|has| |#1| #6=(|CharacteristicZero|)) (ATTRIBUTE #6#) |%noBranch|) (IF (|has| |#1| #7=(|CharacteristicNonZero|)) (ATTRIBUTE #7#) |%noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (ATTRIBUTE (|EuclideanDomain|)) (SIGNATURE |separate| ((|Record| (|:| |polyPart| $) (|:| |fracPart| #2#)) #2#))) |%noBranch|))) #1# (|UnivariatePolynomialCategory| |#1|)) (T |LaurentPolynomial|)) 
((|monomial?| #1=(*1 *2 *1) (AND #2=(|ofCategory| *3 #3=(|IntegralDomain|)) (|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|LaurentPolynomial| *3 *4)) #5=(|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|degree| #1# #6=(AND #2# (|isDomain| *2 #7=(|Integer|)) #4# #5#)) (|order| #1# #6#) (|reductum| (*1 *1 *1) #8=(AND #9=(|ofCategory| *2 #3#) (|isDomain| *1 (|LaurentPolynomial| *2 *3)) (|ofCategory| *3 #10=(|UnivariatePolynomialCategory| *2)))) (|leadingCoefficient| #1# #8#) (|trailingCoefficient| #1# #8#) (|coefficient| (*1 *2 *1 *3) #11=(AND (|isDomain| *3 #7#) #9# (|isDomain| *1 (|LaurentPolynomial| *2 *4)) (|ofCategory| *4 #10#))) (|monomial| (*1 *1 *2 *3) #11#) (|separate| (*1 *2 *3) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *4 #3#) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |polyPart| #12=(|LaurentPolynomial| *4 *5)) (|:| |fracPart| #13=(|Fraction| *5)))) (|isDomain| *1 #12#) (|isDomain| *3 #13#)))) 
((|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) 54 T ELT)) (|normalizeIfCan| ((|#6| |#6|) 48 T ELT))) 
(((|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 #1=(|GcdDomain|)) (|ofCategory| *6 #2=(|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #3=(|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 #1#) (|ofCategory| *4 #2#) (|ofCategory| *5 #3#) (|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))))) 
((|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) #1=(|List| |#3|)) 30 T ELT)) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| #2=(|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| #2# (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) #1# (|List| |#1|) #1#) 68 T ELT))) 
(((|LeadingCoefDetermination| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |polCase| ((|Boolean|) |#3| (|NonNegativeInteger|) #1=(|List| |#3|))) (SIGNATURE |distFact| ((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| #2=(|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| #2# (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) #1# (|List| |#1|) #1#))) (|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 #1=(|List| *3)) (|isDomain| *7 (|List| *8)) (|ofCategory| *8 #2=(|OrderedSet|)) #3=(|ofCategory| *3 (|EuclideanDomain|)) (|ofCategory| *10 (|PolynomialCategory| *3 *9 *8)) (|ofCategory| *9 #4=(|OrderedAbelianMonoidSup|)) (|isDomain| *2 (|Record| (|:| |polfac| (|List| *10)) (|:| |correct| *3) (|:| |corrfact| #5=(|List| (|SparseUnivariatePolynomial| *3))))) (|isDomain| *1 (|LeadingCoefDetermination| *8 *9 *3 *10)) (|isDomain| *4 #5#))) (|polCase| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|isDomain| *5 #1#) #3# (|ofCategory| *6 #2#) (|ofCategory| *7 #4#) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LeadingCoefDetermination| *6 *7 *3 *8)) (|ofCategory| *8 (|PolynomialCategory| *3 *7 *6))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|rhs| (#2=((|SpadAst|) $) 12 T ELT)) (|lhs| (#2# 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|LetAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |lhs| #1=((|SpadAst|) $)) (SIGNATURE |rhs| #1#)))) (T |LetAst|)) 
((|lhs| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|LetAst|)))) (|rhs| #1# #2#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| ((#4=(|List| |#1|) $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|one?| ((#3# $) NIL T ELT)) (|mirror| (#6=($ $) 77 T ELT)) (|log| ((#7=(|LiePolynomial| |#1| |#2|) $) 60 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#6# 81 T ELT)) (|identification| (((|List| (|Equation| |#2|)) $ $) 42 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exp| (($ #7#) 56 T ELT)) (|conjugate| #8=(#9=($ $ $) NIL T ELT)) (|commutator| #8#) (|coerce| (((|OutputForm|) $) 66 T ELT) (((|XDistributedPolynomial| |#1| |#2|) $) NIL T ELT) (((|XPBWPolynomial| |#1| |#2|) $) 74 T ELT)) (|before?| #1#) (|One| (#5# 61 T CONST)) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) #10=(|:| |c| |#2|))) $) 41 T ELT)) (|LyndonBasis| (((|List| #7#) #4#) 73 T ELT)) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) #10#)) $) 46 T ELT)) (= (#2# 62 T ELT)) (/ #8#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ (|Integer|)) NIL T ELT)) (* (#9# 52 T ELT))) 
(((|LieExponentials| |#1| |#2| |#3|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |exp| ($ #1=(|LiePolynomial| |#1| |#2|))) (SIGNATURE |log| (#1# $)) (SIGNATURE |ListOfTerms| ((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) #2=(|:| |c| |#2|))) $)) (SIGNATURE |coerce| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |coerce| ((|XPBWPolynomial| |#1| |#2|) $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |varList| (#3=(|List| |#1|) $)) (SIGNATURE |LyndonBasis| ((|List| #1#) #3#)) (SIGNATURE |LyndonCoordinates| ((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) #2#)) $)) (SIGNATURE |identification| ((|List| (|Equation| |#2|)) $ $)))) (|OrderedSet|) (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|)))) (|PositiveInteger|)) (T |LieExponentials|)) 
((|exp| (*1 *1 *2) (AND #1=(|isDomain| *2 (|LiePolynomial| *3 *4)) #2=(|ofCategory| *3 #3=(|OrderedSet|)) #4=(|ofCategory| *4 #5=(|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) #6=(|isDomain| *1 (|LieExponentials| *3 *4 *5)) #7=(|ofType| *5 #8=(|PositiveInteger|)))) (|log| #9=(*1 *2 *1) (AND #1# #6# #2# #4# #7#)) (|ListOfTerms| #9# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| *3)) #10=(|:| |c| *4)))) #6# #2# #4# #7#)) (|coerce| #9# (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) #6# #2# #4# #7#)) (|coerce| #9# (AND (|isDomain| *2 (|XPBWPolynomial| *3 *4)) #6# #2# #4# #7#)) (|mirror| (*1 *1 *1) (AND (|isDomain| *1 (|LieExponentials| *2 *3 *4)) (|ofCategory| *2 #3#) (|ofCategory| *3 #5#) (|ofType| *4 #8#))) (|varList| #9# (AND (|isDomain| *2 (|List| *3)) #6# #2# #4# #7#)) (|LyndonBasis| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #3#) (|isDomain| *2 (|List| (|LiePolynomial| *4 *5))) (|isDomain| *1 (|LieExponentials| *4 *5 *6)) (|ofCategory| *5 #5#) (|ofType| *6 #8#))) (|LyndonCoordinates| #9# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|LyndonWord| *3)) #10#))) #6# #2# #4# #7#)) (|identification| (*1 *2 *1 *1) (AND (|isDomain| *2 (|List| (|Equation| *4))) #6# #2# #4# #7#))) 
((|zeroSetSplit| (#1=((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| #2=(|OrderedVariableList| |#2|)) #2# #3=(|NewSparseMultivariatePolynomial| |#1| #2#))) #4=(|List| #3#) #5=(|Boolean|)) 103 T ELT) (#6=((|List| (|RegularChain| |#1| |#2|)) #4# #5#) 77 T ELT)) (|zeroDimensional?| ((#5# #4#) 26 T ELT)) (|squareFreeLexTriangular| (#1# 102 T ELT)) (|lexTriangular| (#6# 76 T ELT)) (|groebner| ((#4# #4#) 30 T ELT)) (|fglmIfCan| (((|Union| #4# "failed") #4#) 29 T ELT))) 
(((|LexTriangularPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimensional?| (#1=(|Boolean|) #2=(|List| #3=(|NewSparseMultivariatePolynomial| |#1| #4=(|OrderedVariableList| |#2|))))) (SIGNATURE |fglmIfCan| ((|Union| #2# "failed") #2#)) (SIGNATURE |groebner| (#2# #2#)) (SIGNATURE |lexTriangular| #5=((|List| (|RegularChain| |#1| |#2|)) #2# #1#)) (SIGNATURE |squareFreeLexTriangular| #6=((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| #4#) #4# #3#)) #2# #1#)) (SIGNATURE |zeroSetSplit| #5#) (SIGNATURE |zeroSetSplit| #6#)) (|GcdDomain|) (|List| (|Symbol|))) (T |LexTriangularPackage|)) 
((|zeroSetSplit| #1=(*1 *2 *3 *4) #2=(AND #3=(|isDomain| *3 (|List| #4=(|NewSparseMultivariatePolynomial| *5 #5=(|OrderedVariableList| *6)))) #6=(|isDomain| *4 #7=(|Boolean|)) #8=(|ofCategory| *5 #9=(|GcdDomain|)) #10=(|ofType| *6 #11=(|List| (|Symbol|))) (|isDomain| *2 (|List| (|SquareFreeRegularTriangularSet| *5 (|IndexedExponents| #5#) #5# #4#))) #12=(|isDomain| *1 (|LexTriangularPackage| *5 *6)))) (|zeroSetSplit| #1# #13=(AND #3# #6# #8# #10# (|isDomain| *2 (|List| (|RegularChain| *5 *6))) #12#)) (|squareFreeLexTriangular| #1# #2#) (|lexTriangular| #1# #13#) (|groebner| #14=(*1 *2 *2) (AND #15=(|isDomain| *2 (|List| (|NewSparseMultivariatePolynomial| *3 (|OrderedVariableList| *4)))) #16=(|ofCategory| *3 #9#) #17=(|ofType| *4 #11#) #18=(|isDomain| *1 (|LexTriangularPackage| *3 *4)))) (|fglmIfCan| #14# (|partial| AND #15# #16# #17# #18#)) (|zeroDimensional?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *5)))) (|ofCategory| *4 #9#) (|ofType| *5 #11#) (|isDomain| *2 #7#) (|isDomain| *1 (|LexTriangularPackage| *4 *5))))) 
((|operator| ((#1=(|BasicOperator|) #1#) 88 T ELT)) (|li| (#2=(|#2| |#2|) 28 T ELT)) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) 84 T ELT) ((|#2| |#2| (|Symbol|)) 50 T ELT)) (|erf| (#2# 27 T ELT)) (|dilog| (#2# 29 T ELT)) (|belong?| (((|Boolean|) #1#) 33 T ELT)) (|Si| (#2# 24 T ELT)) (|Ei| (#2# 26 T ELT)) (|Ci| (#2# 25 T ELT))) 
(((|LiouvillianFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) #1=(|BasicOperator|))) (SIGNATURE |operator| (#1# #1#)) (SIGNATURE |Ei| #2=(|#2| |#2|)) (SIGNATURE |Si| #2#) (SIGNATURE |Ci| #2#) (SIGNATURE |li| #2#) (SIGNATURE |erf| #2#) (SIGNATURE |dilog| #2#) (SIGNATURE |integral| (|#2| |#2| (|Symbol|))) (SIGNATURE |integral| (|#2| |#2| (|SegmentBinding| |#2|)))) (|IntegralDomain|) (|Join| (|FunctionSpace| |#1|) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (T |LiouvillianFunction|)) 
((|integral| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 (|SegmentBinding| *2)) #2=(|ofCategory| *2 #3=(|Join| (|FunctionSpace| *4) #4=(|RadicalCategory|) #5=(|TranscendentalFunctionCategory|))) #6=(|ofCategory| *4 #7=(|IntegralDomain|)) #8=(|isDomain| *1 (|LiouvillianFunction| *4 *2)))) (|integral| #1# (AND (|isDomain| *3 (|Symbol|)) #6# #8# #2#)) (|dilog| #9=(*1 *2 *2) #10=(AND #11=(|ofCategory| *3 #7#) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 #12=(|Join| (|FunctionSpace| *3) #4# #5#)))) (|erf| #9# #10#) (|li| #9# #10#) (|Ci| #9# #10#) (|Si| #9# #10#) (|Ei| #9# #10#) (|operator| #9# (AND (|isDomain| *2 #13=(|BasicOperator|)) #11# (|isDomain| *1 (|LiouvillianFunction| *3 *4)) (|ofCategory| *4 #12#))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 #13#) #6# (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LiouvillianFunction| *4 *5)) (|ofCategory| *5 #3#)))) 
((|tanh| (#1=($ $) 38 T ELT)) (|tan| (#2=($ $) 21 T ELT)) (|sinh| (#1# 37 T ELT)) (|sin| (#2# 22 T ELT)) (|sech| (#1# 36 T ELT)) (|sec| (#2# 23 T ELT)) (|pi| (($) 48 T ELT)) (|log| (#3=($ $) 45 T ELT)) (|li| (($ $) 17 T ELT)) (|integral| (($ $ (|SegmentBinding| $)) 7 T ELT) (($ $ (|Symbol|)) 6 T ELT)) (|exp| (#3# 46 T ELT)) (|erf| (($ $) 15 T ELT)) (|dilog| (($ $) 16 T ELT)) (|csch| (#1# 35 T ELT)) (|csc| (#2# 24 T ELT)) (|coth| (#1# 34 T ELT)) (|cot| (#2# 25 T ELT)) (|cosh| (#1# 33 T ELT)) (|cos| (#2# 26 T ELT)) (|atanh| (#4=($ $) 44 T ELT)) (|atan| (#5=($ $) 32 T ELT)) (|asinh| (#4# 43 T ELT)) (|asin| (#5# 31 T ELT)) (|asech| (#4# 42 T ELT)) (|asec| (#5# 30 T ELT)) (|acsch| (#4# 41 T ELT)) (|acsc| (#5# 29 T ELT)) (|acoth| (#4# 40 T ELT)) (|acot| (#5# 28 T ELT)) (|acosh| (#4# 39 T ELT)) (|acos| (#5# 27 T ELT)) (|Si| (($ $) 19 T ELT)) (|Ei| (($ $) 20 T ELT)) (|Ci| (($ $) 18 T ELT)) (** (($ $ $) 47 T ELT))) 
(((|LiouvillianFunctionCategory|) (|Category|)) (T |LiouvillianFunctionCategory|)) 
((|Ei| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|Si| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|Ci| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|li| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|dilog| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|erf| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) 
(|Join| (|PrimitiveFunctionCategory|) (|TranscendentalFunctionCategory|) (CATEGORY |domain| (SIGNATURE |Ei| ($ $)) (SIGNATURE |Si| ($ $)) (SIGNATURE |Ci| ($ $)) (SIGNATURE |li| ($ $)) (SIGNATURE |dilog| ($ $)) (SIGNATURE |erf| ($ $)))) 
(((|ArcHyperbolicFunctionCategory|) . T) ((|ArcTrigonometricFunctionCategory|) . T) ((|ElementaryFunctionCategory|) . T) ((|HyperbolicFunctionCategory|) . T) ((|PrimitiveFunctionCategory|) . T) ((|TranscendentalFunctionCategory|) . T) ((|TrigonometricFunctionCategory|) . T)) 
((|transform| ((#1=(|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) #2=(|DistributedMultivariatePolynomial| |#1| |#2|)) 65 T ELT)) (|totolex| ((#3=(|List| #2#) #4=(|List| #1#)) 90 T ELT)) (|minPol| ((#1# #4# #5=(|OrderedVariableList| |#1|)) 92 T ELT) ((#1# #4# #4# #5#) 91 T ELT)) (|linGenPos| (((|Record| (|:| |gblist| #3#) (|:| |gvlist| #6=(|List| (|Integer|)))) #4#) 136 T ELT)) (|intcompBasis| ((#4# #5# #4# #4#) 105 T ELT)) (|groebgen| (((|Record| (|:| |glbase| #3#) (|:| |glval| #6#)) #3#) 147 T ELT)) (|coord| (((|Vector| |#2|) #1# #4#) 70 T ELT)) (|computeBasis| ((#4# #4#) 47 T ELT)) (|choosemon| ((#2# #2# #3#) 61 T ELT)) (|anticoord| ((#2# (|List| |#2|) #2# #3#) 113 T ELT))) 
(((|LinGroebnerPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |linGenPos| ((|Record| (|:| |gblist| #1=(|List| #2=(|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| #3=(|List| (|Integer|)))) #4=(|List| #5=(|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)))) (SIGNATURE |groebgen| ((|Record| (|:| |glbase| #1#) (|:| |glval| #3#)) #1#)) (SIGNATURE |totolex| (#1# #4#)) (SIGNATURE |minPol| (#5# #4# #4# #6=(|OrderedVariableList| |#1|))) (SIGNATURE |minPol| (#5# #4# #6#)) (SIGNATURE |computeBasis| (#4# #4#)) (SIGNATURE |coord| ((|Vector| |#2|) #5# #4#)) (SIGNATURE |anticoord| (#2# (|List| |#2|) #2# #1#)) (SIGNATURE |intcompBasis| (#4# #6# #4# #4#)) (SIGNATURE |choosemon| (#2# #2# #1#)) (SIGNATURE |transform| (#5# #2#))) (|List| (|Symbol|)) (|GcdDomain|)) (T |LinGroebnerPackage|)) 
((|transform| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|DistributedMultivariatePolynomial| *4 *5)) #3=(|ofType| *4 #4=(|List| (|Symbol|))) #5=(|ofCategory| *5 #6=(|GcdDomain|)) (|isDomain| *2 #7=(|HomogeneousDistributedMultivariatePolynomial| *4 *5)) #8=(|isDomain| *1 (|LinGroebnerPackage| *4 *5)))) (|choosemon| (*1 *2 *2 *3) (AND #9=(|isDomain| *3 #10=(|List| #2#)) (|isDomain| *2 #2#) #3# #5# #8#)) (|intcompBasis| (*1 *2 *3 *2 *2) (AND (|isDomain| *2 #11=(|List| #7#)) (|isDomain| *3 (|OrderedVariableList| *4)) #3# #5# #8#)) (|anticoord| (*1 *2 *3 *2 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| #12=(|DistributedMultivariatePolynomial| *5 *6))) #13=(|ofCategory| *6 #6#) (|isDomain| *2 #12#) #14=(|ofType| *5 #4#) #15=(|isDomain| *1 (|LinGroebnerPackage| *5 *6)))) (|coord| #16=(*1 *2 *3 *4) (AND (|isDomain| *4 #17=(|List| #18=(|HomogeneousDistributedMultivariatePolynomial| *5 *6))) (|isDomain| *3 #18#) #14# #13# (|isDomain| *2 (|Vector| *6)) #15#)) (|computeBasis| (*1 *2 *2) (AND (|isDomain| *2 (|List| (|HomogeneousDistributedMultivariatePolynomial| *3 *4))) (|ofType| *3 #4#) (|ofCategory| *4 #6#) (|isDomain| *1 (|LinGroebnerPackage| *3 *4)))) (|minPol| #16# #19=(AND (|isDomain| *3 #17#) (|isDomain| *4 (|OrderedVariableList| *5)) #14# (|isDomain| *2 #18#) #15# #13#)) (|minPol| (*1 *2 *3 *3 *4) #19#) (|totolex| #1# (AND #20=(|isDomain| *3 #11#) #3# #5# (|isDomain| *2 #10#) #8#)) (|groebgen| #1# (AND #3# #5# (|isDomain| *2 (|Record| (|:| |glbase| #10#) (|:| |glval| #21=(|List| (|Integer|))))) #8# #9#)) (|linGenPos| #1# (AND #20# #3# #5# (|isDomain| *2 (|Record| (|:| |gblist| #10#) (|:| |gvlist| #21#))) #8#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Any|) #6=(|BasicType|)) #7=(|has| #8=(|Record| (|:| |key| #9=(|String|)) (|:| |entry| #5#)) #6#)) ELT)) (|table| #10=(#11=($) NIL T ELT) #12=(($ #13=(|List| #8#)) NIL T ELT)) (|swap!| (((|Void|) $ #9# #9#) NIL #14=(|has| $ (|ShallowlyMutableAggregate| #5#)) ELT)) (|setelt| #15=(#16=(#5# $ #9# #5#) NIL #14# ELT) ((#5# $ #17=(|Symbol|) #5#) 16 T ELT)) (|select!| #18=(($ #19=(|Mapping| #3# #8#) $) NIL #20=(|has| $ (|FiniteAggregate| #8#)) ELT)) (|select| #18#) (|search| #21=(((|Union| #5# #22="failed") #9# $) NIL T ELT)) (|sample| (#11# NIL T CONST)) (|removeDuplicates| (#23=($ $) NIL #24=(AND #20# #7#) ELT)) (|remove!| (#25=($ #8# $) NIL #20# ELT) #18# #21#) (|remove| (#25# NIL #24# ELT) #18#) (|reduce| ((#8# #26=(|Mapping| #8# #8# #8#) $ #8# #8#) NIL #7# ELT) ((#8# #26# $ #8#) NIL T ELT) ((#8# #26# $) NIL T ELT)) (|qsetelt!| #15#) (|qelt| #27=((#5# $ #9#) NIL T ELT)) (|pack!| #28=(#23# NIL T ELT)) (|minIndex| #29=(#30=(#9# $) NIL #31=(|has| #9# (|OrderedSet|)) ELT)) (|members| ((#13# $) NIL T ELT)) (|member?| ((#3# #8# $) NIL #7# ELT)) (|maxIndex| #29#) (|map!| #32=(($ (|Mapping| #8# #8#) . #33=($)) NIL T ELT) #34=(($ (|Mapping| #5# #5#) . #33#) NIL T ELT)) (|map| #32# #34# #32# (($ (|Mapping| #5# #5# #5#) $ $) NIL T ELT)) (|library| (($ (|FileName|)) 8 T ELT)) (|latex| (#30# NIL #35=(OR #36=(|has| #5# #37=(|SetCategory|)) #38=(|has| #8# #37#)) ELT)) (|keys| #39=(((|List| #9#) $) NIL T ELT)) (|key?| #40=((#3# #9# $) NIL T ELT)) (|inspect| #41=((#8# $) NIL T ELT)) (|insert!| (#25# NIL T ELT)) (|indices| #39#) (|index?| #40#) (|hash| (((|SingleInteger|) $) NIL #35# ELT)) (|first| ((#5# $) NIL #31# ELT)) (|find| (((|Union| #8# #22#) #19# $) NIL T ELT)) (|fill!| (($ $ #5#) NIL #14# ELT)) (|extract!| #41#) (|every?| #42=((#3# #19# $) NIL T ELT)) (|eval| #43=(($ $ (|List| #44=(|Equation| #8#))) NIL #45=(AND (|has| #8# (|Evalable| #8#)) #38#) ELT) #46=(($ $ #44#) NIL #45# ELT) #47=(($ $ #8# #8#) NIL #45# ELT) #48=(($ $ #13# #13#) NIL #45# ELT) (($ $ #49=(|List| #5#) #49#) NIL #50=(AND (|has| #5# (|Evalable| #5#)) #36#) ELT) (($ $ #5# #5#) NIL #50# ELT) (($ $ #51=(|Equation| #5#)) NIL #50# ELT) (($ $ (|List| #51#)) NIL #50# ELT) #48# #47# #46# #43#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# #5# $) NIL (AND (|has| $ (|FiniteAggregate| #5#)) #4#) ELT)) (|entries| ((#49# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| #10#) (|elt| #27# (#16# NIL T ELT) ((#5# $ #17#) 14 T ELT)) (|dictionary| #10# #12#) (|count| ((#52=(|NonNegativeInteger|) #8# $) NIL #7# ELT) ((#52# #19# $) NIL T ELT)) (|copy| #28#) (|convert| ((#53=(|InputForm|) $) NIL (|has| #8# (|ConvertibleTo| #53#)) ELT)) (|construct| #12#) (|coerce| ((#54=(|OutputForm|) $) NIL (OR (|has| #8# #55=(|CoercibleTo| #54#)) (|has| #5# #55#)) ELT)) (|before?| #1#) (|bag| #12#) (|any?| #42#) (= #1#) (|#| ((#52# $) NIL T ELT))) 
(((|Library|) (|Join| (|TableAggregate| (|String|) #1=(|Any|)) (|Eltable| #2=(|Symbol|) #1#) (CATEGORY |domain| (SIGNATURE |library| ($ (|FileName|))) (SIGNATURE |pack!| ($ $)) (SIGNATURE |setelt| (#1# $ #2# #1#))))) (T |Library|)) 
((|library| (*1 *1 *2) (AND (|isDomain| *2 (|FileName|)) #1=(|isDomain| *1 (|Library|)))) (|pack!| (*1 *1 *1) #1#) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *2 (|Any|)) (|isDomain| *3 (|Symbol|)) #1#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(OR (AND #7=(|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #8=(|has| |#1| (|IntegralDomain|))) (AND #9=(|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #8#)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#1|))) NIL #9# ELT) ((#10# #12=(|Vector| $)) NIL #7# ELT)) (|someBasis| (#13=(#12#) NIL #7# ELT)) (|sample| (#14=($) NIL T CONST)) (|rightUnits| #15=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #16=((#11#) NIL #9# ELT) #17=(#18=(#11# #12#) NIL #7# ELT)) (|rightTrace| #19=((|#1| $) NIL #7# ELT)) (|rightRegularRepresentation| #20=((#11# $) NIL #9# ELT) #21=((#11# $ #12#) NIL #7# ELT)) (|rightRecip| #22=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #23=(((|SparseUnivariatePolynomial| #24=(|Polynomial| |#1|))) NIL (AND #9# (|has| |#1| (|Field|))) ELT)) (|rightPower| #25=(#26=($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| #28=(#29=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #30=((|#1|) NIL #9# ELT) #31=((|#1| #12#) NIL #7# ELT)) (|rightCharacteristicPolynomial| #32=(#29# NIL #7# ELT)) (|rightAlternative?| #33=((#2#) NIL #7# ELT)) (|represents| #34=(($ #35=(|Vector| |#1|)) NIL #9# ELT) (($ #35# #12#) NIL #7# ELT)) (|recip| #22#) (|rank| ((#27#) NIL #7# ELT)) (|powerAssociative?| #33#) (|plenaryPower| #25#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| #33#) (|leftUnits| #15#) (|leftUnit| #3#) (|leftTraceMatrix| #16# #17#) (|leftTrace| #19#) (|leftRegularRepresentation| #20# #21#) (|leftRecip| #22#) (|leftRankPolynomial| #23#) (|leftPower| #25#) (|leftNorm| #19#) (|leftMinimalPolynomial| #28#) (|leftDiscriminant| #30# #31#) (|leftCharacteristicPolynomial| #32#) (|leftAlternative?| #33#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #33#) (|jordanAdmissible?| #33#) (|jacobiIdentity?| #33#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| #33#) (|elt| ((|#1| $ #36=(|Integer|)) NIL #9# ELT)) (|coordinates| (#18# NIL #9# ELT) #37=((#35# $) NIL #9# ELT) ((#11# #12# #12#) NIL #7# ELT) ((#35# $ #12#) NIL #7# ELT)) (|convert| #34# #37#) (|conditionsForIdempotents| ((#38=(|List| #24#)) NIL #9# ELT) ((#38# #12#) NIL #7# ELT)) (|commutator| #39=(#40=($ $ $) NIL T ELT)) (|commutative?| #33#) (|coerce| (((|OutputForm|) $) NIL T ELT) ((|#2| $) 11 T ELT) (($ |#2|) 12 T ELT)) (|before?| #1#) (|basis| (#13# NIL #9# ELT)) (|associatorDependence| (((|List| #35#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #33#) (|apply| (($ #11# $) NIL #9# ELT)) (|antiCommutator| #39#) (|antiCommutative?| #33#) (|antiAssociative?| #33#) (|alternative?| #33#) (|Zero| (#14# 18 T CONST)) (= #1#) (- (($ $) NIL T ELT) #39#) (+ #39#) (** (#26# 19 T ELT)) (* (($ #27# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #36# . #41=($)) NIL T ELT) (#40# 10 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #41#) NIL T ELT))) 
(((|AssociatedLieAlgebra| |#1| |#2|) (|Join| #1=(|NonAssociativeAlgebra| |#1|) (|CoercibleTo| |#2|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#2|)) (IF (|has| |#2| #2=(|FramedNonAssociativeAlgebra| |#1|)) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |#2| #3=(|FiniteRankNonAssociativeAlgebra| |#1|)) (ATTRIBUTE #3#) |%noBranch|))) (|CommutativeRing|) #1#) (T |AssociatedLieAlgebra|)) 
((|coerce| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|AssociatedLieAlgebra| *3 *2)) (|ofCategory| *2 (|NonAssociativeAlgebra| *3))))) 
((/ (($ $ |#2|) 10 T ELT))) 
(((|LieAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE / (|#1| |#1| |#2|))) (|LieAlgebra| |#2|) (|CommutativeRing|)) (T |LieAlgebra&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|construct| (($ $ $) 40 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 39 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT) (($ $ |#1|) 37 T ELT))) 
(((|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| (ATTRIBUTE |NullSquare|) (ATTRIBUTE |JacobiIdentity|) (SIGNATURE |construct| ($ $ $)) (IF (|has| |t#1| (|Field|)) (SIGNATURE / ($ $ |t#1|)) |%noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|limit| ((#1=(|Union| #2=(|OrderedCompletion| |#2|) #3="failed") |#2| (|Equation| |#2|) (|String|)) 105 T ELT) (((|Union| #2# (|Record| (|:| |leftHandLimit| #1#) (|:| |rightHandLimit| #1#)) #3#) |#2| (|Equation| #2#)) 130 T ELT)) (|complexLimit| (((|Union| #4=(|OnePointCompletion| |#2|) #3#) |#2| (|Equation| #4#)) 135 T ELT))) 
(((|PowerSeriesLimitPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |limit| ((|Union| #1=(|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| #2=(|Union| #1# #3="failed")) (|:| |rightHandLimit| #2#)) #3#) |#2| (|Equation| #1#))) (SIGNATURE |complexLimit| ((|Union| #4=(|OnePointCompletion| |#2|) #3#) |#2| (|Equation| #4#))) (SIGNATURE |limit| (#2# |#2| (|Equation| |#2|) (|String|)))) (|Join| (|GcdDomain|) (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#)) (|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| #1=(|AlgebraicallyClosedField|) #2=(|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) (|ofCategory| *6 #3=(|Join| (|GcdDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#))) (|isDomain| *2 #5=(|OrderedCompletion| *3)) (|isDomain| *1 (|PowerSeriesLimitPackage| *6 *3)))) (|complexLimit| #6=(*1 *2 *3 *4) (|partial| AND (|isDomain| *4 (|Equation| #7=(|OnePointCompletion| *3))) #8=(|ofCategory| *5 #3#) (|isDomain| *2 #7#) #9=(|isDomain| *1 (|PowerSeriesLimitPackage| *5 *3)) #10=(|ofCategory| *3 (|Join| #1# #2# (|FunctionSpace| *5))))) (|limit| #6# (AND (|isDomain| *4 (|Equation| #5#)) #10# #8# (|isDomain| *2 (|Union| #5# (|Record| (|:| |leftHandLimit| #11=(|Union| #5# #12="failed")) (|:| |rightHandLimit| #11#)) #12#)) #9#))) 
((|limit| ((#1=(|Union| #2=(|OrderedCompletion| #3=(|Fraction| #4=(|Polynomial| |#1|))) #5="failed") #3# #6=(|Equation| #3#) (|String|)) 86 T ELT) ((#7=(|Union| #2# (|Record| (|:| |leftHandLimit| #1#) (|:| |rightHandLimit| #1#)) #5#) #3# #6#) 20 T ELT) ((#7# #3# (|Equation| (|OrderedCompletion| #4#))) 35 T ELT)) (|complexLimit| ((#8=(|OnePointCompletion| #3#) #3# #6#) 23 T ELT) ((#8# #3# (|Equation| (|OnePointCompletion| #4#))) 43 T ELT))) 
(((|RationalFunctionLimitPackage| |#1|) (CATEGORY |package| (SIGNATURE |limit| (#1=(|Union| #2=(|OrderedCompletion| #3=(|Fraction| #4=(|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| #5=(|Union| #2# #6="failed")) (|:| |rightHandLimit| #5#)) #6#) #3# (|Equation| (|OrderedCompletion| #4#)))) (SIGNATURE |limit| (#1# #3# #7=(|Equation| #3#))) (SIGNATURE |complexLimit| (#8=(|OnePointCompletion| #3#) #3# (|Equation| (|OnePointCompletion| #4#)))) (SIGNATURE |complexLimit| (#8# #3# #7#)) (SIGNATURE |limit| (#5# #3# #7# (|String|)))) (|GcdDomain|)) (T |RationalFunctionLimitPackage|)) 
((|limit| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Equation| #1=(|Fraction| (|Polynomial| *6)))) (|isDomain| *5 (|String|)) (|isDomain| *3 #1#) (|ofCategory| *6 #2=(|GcdDomain|)) (|isDomain| *2 #3=(|OrderedCompletion| *3)) (|isDomain| *1 (|RationalFunctionLimitPackage| *6)))) (|complexLimit| #4=(*1 *2 *3 *4) (AND #5=(|isDomain| *4 (|Equation| #6=(|Fraction| #7=(|Polynomial| *5)))) #8=(|isDomain| *3 #6#) #9=(|ofCategory| *5 #2#) (|isDomain| *2 (|OnePointCompletion| *3)) #10=(|isDomain| *1 (|RationalFunctionLimitPackage| *5)))) (|complexLimit| #4# (AND (|isDomain| *4 (|Equation| (|OnePointCompletion| #7#))) #9# (|isDomain| *2 (|OnePointCompletion| #6#)) #10# #8#)) (|limit| #4# (AND #5# #8# #9# (|isDomain| *2 (|Union| #3# (|Record| (|:| |leftHandLimit| #11=(|Union| #3# #12="failed")) (|:| |rightHandLimit| #11#)) #12#)) #10#)) (|limit| #4# (AND (|isDomain| *4 (|Equation| (|OrderedCompletion| #7#))) #9# (|isDomain| *2 (|Union| #13=(|OrderedCompletion| #6#) (|Record| (|:| |leftHandLimit| #14=(|Union| #13# #12#)) (|:| |rightHandLimit| #14#)) #12#)) #10# #8#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|random| (#2=($) NIL T ELT)) (|min| #3=(($ $ $) NIL T ELT) #4=(#2# NIL T CONST)) (|max| #3# #4#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) 11 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dual| (($ (|DualBasis| |#1|)) 12 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|OrderedVariableList| |#1|)) 7 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) 
(((|LinearBasis| |#1|) (|Join| (|OrderedFinite|) (|CoercibleFrom| (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |dual| ($ (|DualBasis| |#1|))))) (|List| (|Symbol|))) (T |LinearBasis|)) 
((|dual| (*1 *1 *2) (AND (|isDomain| *2 (|DualBasis| *3)) (|ofType| *3 (|List| (|Symbol|))) (|isDomain| *1 (|LinearBasis| *3))))) 
((|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) #1="failed") #2=(|Vector| |#2|) |#2|) 64 (|not| #3=(|has| |#1| (|Field|))) ELT) ((#4=(|Union| (|Vector| |#1|) #1#) #2# |#2|) 49 #3# ELT)) (|linearlyDependent?| (((|Boolean|) #2#) 33 T ELT)) (|linearDependence| ((#4# #2#) 40 T ELT))) 
(((|LinearDependence| |#1| |#2|) (CATEGORY |package| (SIGNATURE |linearlyDependent?| ((|Boolean|) #1=(|Vector| |#2|))) (SIGNATURE |linearDependence| (#2=(|Union| (|Vector| |#1|) #3="failed") #1#)) (IF (|has| |#1| (|Field|)) (SIGNATURE |solveLinear| (#2# #1# |#2|)) (SIGNATURE |solveLinear| ((|Union| (|Vector| (|Fraction| |#1|)) #3#) #1# |#2|)))) (|IntegralDomain|) (|Join| (|Ring|) (|LinearlyExplicitRingOver| |#1|))) (T |LinearDependence|)) 
((|solveLinear| #1=(*1 *2 *3 *4) (|partial| AND #2=(|isDomain| *3 #3=(|Vector| *4)) #4=(|ofCategory| *4 (|Join| #5=(|Ring|) (|LinearlyExplicitRingOver| *5))) (|not| #6=(|ofCategory| *5 (|Field|))) #7=(|ofCategory| *5 #8=(|IntegralDomain|)) (|isDomain| *2 (|Vector| (|Fraction| *5))) #9=(|isDomain| *1 (|LinearDependence| *5 *4)))) (|solveLinear| #1# (|partial| AND #2# #4# #6# #7# (|isDomain| *2 #10=(|Vector| *5)) #9#)) (|linearDependence| #11=(*1 *2 *3) (|partial| AND #12=(|isDomain| *3 #10#) #13=(|ofCategory| *5 (|Join| #5# (|LinearlyExplicitRingOver| *4))) #14=(|ofCategory| *4 #8#) (|isDomain| *2 #3#) #15=(|isDomain| *1 (|LinearDependence| *4 *5)))) (|linearlyDependent?| #11# (AND #12# #13# #14# (|isDomain| *2 (|Boolean|)) #15#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| #4=(|LinearBasis| |#2|))) $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|reductum| #6=(($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| #4#) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|linearElement| (($ (|List| |#1|)) 25 T ELT)) (|leadingSupport| ((#4# $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 16 T ELT)) (|coordinates| (((|Vector| |#1|) $) 44 T ELT)) (|convert| (($ #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #4#) 11 T ELT)) (|before?| #1#) (|Zero| (#5# 20 T CONST)) (= #1#) (/ #7=(($ $ |#1|) NIL T ELT)) (- #6# (#8=($ $ $) NIL T ELT)) (+ (#8# 17 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #9=($)) NIL T ELT) (($ |#1| . #9#) NIL T ELT) #7#)) 
(((|LinearElement| |#1| |#2|) (|Join| (|VectorSpace| |#1|) (|CoercibleFrom| #1=(|LinearBasis| |#2|)) (|IndexedDirectProductCategory| |#1| #1#) (CATEGORY |domain| (SIGNATURE |linearElement| ($ (|List| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#1|) $)))) (|Field|) (|List| (|Symbol|))) (T |LinearElement|)) 
((|linearElement| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Field|)) #2=(|isDomain| *1 (|LinearElement| *3 *4)) #3=(|ofType| *4 (|List| (|Symbol|))))) (|coordinates| (*1 *2 *1) (AND (|isDomain| *2 (|Vector| *3)) #2# #1# #3#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reducedSystem| (((|Matrix| |#1|) (|Matrix| $)) 36 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 35 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftReducedSystem| (((|Matrix| |#1|) (|Vector| $)) 38 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT))) 
(((|LinearlyExplicitRingOver| |#1|) (|Category|) (|Ring|)) (T |LinearlyExplicitRingOver|)) 
((|leftReducedSystem| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Matrix| *4)))) (|leftReducedSystem| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *4)) (|:| |vec| (|Vector| *4)))))) (|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| (|LeftModule| |t#1|) (CATEGORY |domain| (SIGNATURE |leftReducedSystem| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |leftReducedSystem| ((|Record| (|:| |mat| (|Matrix| |t#1|)) (|:| |vec| (|Vector| |t#1|))) (|Vector| $) $)) (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) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|opposite?| #1#) (|linearForm| (($ (|List| |#1|)) 23 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ (|LinearElement| |#1| |#2|)) 46 T ELT)) (|dimension| (((|CardinalNumber|)) 13 T ELT)) (|coordinates| (((|Vector| |#1|) $) 42 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#3# 18 T CONST)) (= #1#) (/ #4=(($ $ |#1|) NIL T ELT)) (- (($ $) NIL T ELT) (#5=($ $ $) NIL T ELT)) (+ (#5# 14 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #6=($)) NIL T ELT) (($ |#1| . #6#) NIL T ELT) #4#)) 
(((|LinearForm| |#1| |#2|) (|Join| (|VectorSpace| |#1|) (|Eltable| (|LinearElement| |#1| |#2|) |#1|) (CATEGORY |domain| (SIGNATURE |linearForm| ($ (|List| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#1|) $)))) (|Field|) (|List| (|Symbol|))) (T |LinearForm|)) 
((|linearForm| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Field|)) #2=(|isDomain| *1 (|LinearForm| *3 *4)) #3=(|ofType| *4 (|List| (|Symbol|))))) (|coordinates| (*1 *2 *1) (AND (|isDomain| *2 (|Vector| *3)) #2# #1# #3#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (* (($ |#1| $) 17 T ELT) (($ $ |#1|) 20 T ELT))) 
(((|LinearSet| |#1|) (|Category|) (|SemiGroup|)) (T |LinearSet|)) 
NIL 
(|Join| (|LeftLinearSet| |t#1|) (|RightLinearSet| |t#1|)) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| #5=(#6=(|#1| $) NIL T ELT)) (|third| #5#) (|tail| #7=(#8=($ $) NIL T ELT)) (|swap!| (((|Void|) $ #9=(|Integer|) #9#) NIL #10=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|split!| (#11=($ $ #9#) 68 #10# ELT)) (|sorted?| (#12=(#3# $) NIL #13=(|has| |#1| #14=(|OrderedSet|)) ELT) ((#3# #15=(|Mapping| #3# |#1| |#1|) $) NIL T ELT)) (|sort!| (#8# NIL (AND #10# #13#) ELT) (#16=($ #15# $) 65 #10# ELT)) (|sort| (#8# NIL #13# ELT) (#16# NIL T ELT)) (|size?| #17=((#3# $ #18=(|NonNegativeInteger|)) NIL T ELT)) (|setvalue!| #19=(#20=(|#1| $ |#1|) NIL #10# ELT)) (|setrest!| (#21=($ $ $) 26 #10# ELT)) (|setlast!| #19#) (|setfirst!| (#20# 24 #10# ELT)) (|setelt| ((|#1| $ #22="value" |#1|) NIL #10# ELT) ((|#1| $ #23="first" |#1|) 25 #10# ELT) (($ $ #24="rest" $) 27 #10# ELT) ((|#1| $ #25="last" |#1|) NIL #10# ELT) ((|#1| $ #26=(|UniversalSegment| #9#) |#1|) NIL #10# ELT) #27=(#28=(|#1| $ #9# |#1|) NIL #10# ELT)) (|setchildren!| (($ $ #29=(|List| $)) NIL #10# ELT)) (|setUnion| (#21# 74 #30=(|has| |#1| (|SetCategory|)) ELT)) (|setIntersection| (#21# 75 #30# ELT)) (|setDifference| (#21# 79 #30# ELT)) (|select!| #31=(#32=($ #33=(|Mapping| #3# |#1|) $) NIL T ELT)) (|select| #34=(#32# NIL #35=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|second| #5#) (|sample| (#36=($) NIL T CONST)) (|reverse!| (#8# 31 #10# ELT)) (|reverse| (#8# 32 T ELT)) (|rest| (#8# 21 T ELT) (#37=($ $ #18#) 35 T ELT)) (|removeDuplicates!| (#8# 63 #4# ELT)) (|removeDuplicates| (#8# 73 #38=(AND #35# #4#) ELT)) (|remove!| (#39=($ |#1| $) NIL #4# ELT) #31#) (|remove| #34# (#39# NIL #38# ELT)) (|reduce| ((|#1| #40=(|Mapping| |#1| |#1| |#1|) $) NIL T ELT) ((|#1| #40# $ |#1|) NIL T ELT) ((|#1| #40# $ |#1| |#1|) NIL #4# ELT)) (|qsetelt!| #27#) (|qelt| (#41=(|#1| $ #9#) NIL T ELT)) (|possiblyInfinite?| #42=(#12# NIL T ELT)) (|position| ((#9# |#1| $ #9#) NIL #4# ELT) ((#9# |#1| $) NIL #4# ELT) ((#9# #33# $) NIL T ELT)) (|null| (#12# 9 T ELT)) (|nodes| #43=((#29# $) NIL T ELT)) (|node?| #1#) (|nil| (#36# 7 T CONST)) (|new| (($ #18# |#1|) NIL T ELT)) (|more?| #17#) (|minIndex| (#44=(#9# $) 34 #45=(|has| #9# #14#) ELT)) (|min| #46=(#21# NIL #13# ELT)) (|merge!| #46# (#47=($ #15# $ $) 66 T ELT)) (|merge| #46# (#47# NIL T ELT)) (|members| (#48=(#49=(|List| |#1|) $) 30 T ELT)) (|member?| (#50=(#3# |#1| $) 61 #4# ELT)) (|maxIndex| (#44# NIL #45# ELT)) (|max| #46#) (|map!| (#51=($ (|Mapping| |#1| |#1|) $) 92 T ELT)) (|map| (#51# NIL T ELT) (($ #40# $ $) NIL T ELT)) (|list| (($ |#1|) NIL T ELT)) (|less?| #17#) (|leaves| #52=(#48# NIL T ELT)) (|leaf?| #42#) (|latex| (((|String|) $) 59 #30# ELT)) (|last| #5# #53=(#37# NIL T ELT)) (|insert!| #54=(#55=($ $ $ #9#) NIL T ELT) #56=(($ |#1| $ #9#) NIL T ELT)) (|insert| #54# #56#) (|indices| (((|List| #9#) $) NIL T ELT)) (|index?| ((#3# #9# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #30# ELT)) (|first| (#6# 16 T ELT) #53#) (|find| (((|Union| |#1| "failed") #33# $) NIL T ELT)) (|fill!| (#57=($ $ |#1|) NIL #10# ELT)) (|explicitlyFinite?| #42#) (|every?| #58=((#3# #33# $) NIL T ELT)) (|eval| (($ $ (|List| #59=(|Equation| |#1|))) NIL #60=(AND (|has| |#1| (|Evalable| |#1|)) #30#) ELT) (($ $ #59#) NIL #60# ELT) (($ $ |#1| |#1|) NIL #60# ELT) (($ $ #49# #49#) NIL #60# ELT)) (|eq?| (#2# 15 T ELT)) (|entry?| (#50# NIL #38# ELT)) (|entries| #52#) (|empty?| (#12# 20 T ELT)) (|empty| (#36# 19 T ELT)) (|elt| ((|#1| $ #22#) NIL T ELT) ((|#1| $ #23#) 18 T ELT) (($ $ #24#) 23 T ELT) ((|#1| $ #25#) NIL T ELT) #61=(($ $ #26#) NIL T ELT) (#41# 78 T ELT) (#28# NIL T ELT)) (|distance| ((#9# $ $) NIL T ELT)) (|delete!| #61# #62=(#11# NIL T ELT)) (|delete| #61# #62#) (|cyclic?| #42#) (|cycleTail| #7#) (|cycleSplit!| (#8# NIL #10# ELT)) (|cycleLength| (#63=(#18# $) NIL T ELT)) (|cycleEntry| (#8# 40 T ELT)) (|count| ((#18# #33# $) NIL T ELT) ((#18# |#1| $) NIL #4# ELT)) (|copyInto!| (#55# NIL #10# ELT)) (|copy| (#8# 36 T ELT)) (|convert| ((#64=(|InputForm|) $) 87 (|has| |#1| (|ConvertibleTo| #64#)) ELT)) (|construct| (($ #49#) 29 T ELT)) (|cons| (#39# 10 T ELT)) (|concat!| (#21# 62 T ELT) #65=(#57# NIL T ELT)) (|concat| (#21# 72 T ELT) (#39# 14 T ELT) (($ #29#) NIL T ELT) #65#) (|coerce| ((#66=(|OutputForm|) $) 51 (|has| |#1| (|CoercibleTo| #66#)) ELT)) (|children| #43#) (|child?| #1#) (|before?| #1#) (|append| (#21# 11 T ELT)) (|any?| #58#) (>= #67=(#2# NIL #13# ELT)) (> #67#) (= (#2# 55 #4# ELT)) (<= #67#) (< #67#) (|#| (#63# 13 T ELT))) 
(((|List| |#1|) (|Join| (|ListAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |nil| ($) |constant|) (SIGNATURE |null| ((|Boolean|) $)) (SIGNATURE |cons| ($ |#1| $)) (SIGNATURE |append| #1=($ $ $)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |setUnion| #1#) (SIGNATURE |setIntersection| #1#) (SIGNATURE |setDifference| #1#)) |%noBranch|))) (|Type|)) (T |List|)) 
((|nil| (*1 *1) #1=(AND #2=(|isDomain| *1 (|List| *2)) #3=(|ofCategory| *2 #4=(|Type|)))) (|null| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|List| *3)) (|ofCategory| *3 #4#))) (|cons| (*1 *1 *2 *1) #1#) (|append| #5=(*1 *1 *1 *1) #1#) (|setUnion| #5# #6=(AND #2# (|ofCategory| *2 (|SetCategory|)) #3#)) (|setIntersection| #5# #6#) (|setDifference| #5# #6#)) 
((|scan| ((#1=(|List| |#2|) #2=(|Mapping| |#2| |#1| |#2|) #3=(|List| |#1|) |#2|) 16 T ELT)) (|reduce| ((|#2| #2# #3# |#2|) 18 T ELT)) (|map| ((#1# (|Mapping| |#2| |#1|) #3#) 13 T ELT))) 
(((|ListFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |scan| (#1=(|List| |#2|) #2=(|Mapping| |#2| |#1| |#2|) #3=(|List| |#1|) |#2|)) (SIGNATURE |reduce| (|#2| #2# #3# |#2|)) (SIGNATURE |map| (#1# (|Mapping| |#2| |#1|) #3#))) #4=(|Type|) #4#) (T |ListFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) #1=(|isDomain| *4 #2=(|List| *5)) #3=(|ofCategory| *5 #4=(|Type|)) #5=(|ofCategory| *6 #4#) (|isDomain| *2 #6=(|List| *6)) (|isDomain| *1 (|ListFunctions2| *5 *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #1# #3# (|ofCategory| *2 #4#) (|isDomain| *1 (|ListFunctions2| *5 *2)))) (|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) (|isDomain| *4 #6#) #5# #3# (|isDomain| *2 #2#) (|isDomain| *1 (|ListFunctions2| *6 *5))))) 
((|match| ((|#2| #1=(|List| |#1|) #2=(|List| |#2|) |#1| #3=(|Mapping| |#2| |#1|)) 18 T ELT) ((#3# #1# #2# #3#) 19 T ELT) ((|#2| #1# #2# |#1| |#2|) 16 T ELT) ((#3# #1# #2# |#2|) 17 T ELT) ((|#2| #1# #2# |#1|) 10 T ELT) ((#3# #1# #2#) 12 T ELT))) 
(((|ListToMap| |#1| |#2|) (CATEGORY |package| (SIGNATURE |match| (#1=(|Mapping| |#2| |#1|) #2=(|List| |#1|) #3=(|List| |#2|))) (SIGNATURE |match| (|#2| #2# #3# |#1|)) (SIGNATURE |match| (#1# #2# #3# |#2|)) (SIGNATURE |match| (|#2| #2# #3# |#1| |#2|)) (SIGNATURE |match| (#1# #2# #3# #1#)) (SIGNATURE |match| (|#2| #2# #3# |#1| #1#))) (|SetCategory|) (|Type|)) (T |ListToMap|)) 
((|match| (*1 *2 *3 *4 *5 *6) (AND #1=(|isDomain| *3 #2=(|List| *5)) #3=(|isDomain| *4 (|List| *2)) (|isDomain| *6 (|Mapping| *2 *5)) #4=(|ofCategory| *5 #5=(|SetCategory|)) #6=(|ofCategory| *2 #7=(|Type|)) #8=(|isDomain| *1 (|ListToMap| *5 *2)))) (|match| (*1 *2 *3 *4 *2) (AND #9=(|isDomain| *2 (|Mapping| *6 *5)) #1# #10=(|isDomain| *4 #11=(|List| *6)) #4# #12=(|ofCategory| *6 #7#) #13=(|isDomain| *1 (|ListToMap| *5 *6)))) (|match| (*1 *2 *3 *4 *5 *2) #14=(AND #1# #3# #4# #6# #8#)) (|match| #15=(*1 *2 *3 *4 *5) (AND (|isDomain| *3 #11#) (|isDomain| *4 #2#) (|ofCategory| *6 #5#) (|ofCategory| *5 #7#) (|isDomain| *2 (|Mapping| *5 *6)) (|isDomain| *1 (|ListToMap| *6 *5)))) (|match| #15# #14#) (|match| (*1 *2 *3 *4) (AND #1# #10# #4# #12# #9# #13#))) 
((|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) 21 T ELT))) 
(((|ListFunctions3| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)))) #1=(|Type|) #1# #1#) (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 #1=(|Type|)) (|ofCategory| *7 #1#) (|ofCategory| *8 #1#) (|isDomain| *2 (|List| *8)) (|isDomain| *1 (|ListFunctions3| *6 *7 *8))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT) ((|#1| $) 8 T ELT)) (|before?| #1#) (= #1#)) 
(((|Literal| |#1|) (|Join| (|SpadSyntaxCategory|) (|CoercibleTo| |#1|)) (|SetCategory|)) (T |Literal|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (* (($ |#1| $) 17 T ELT))) 
(((|LeftLinearSet| |#1|) (|Category|) (|SemiGroup|)) (T |LeftLinearSet|)) 
((* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|LeftLinearSet| *2)) (|ofCategory| *2 (|SemiGroup|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ |t#1| $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|substitute| (($ |#1| |#1| $) 45 T ELT)) (|select!| (#5=($ #6=(|Mapping| #3# |#1|) $) 61 #7=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| #8=(#5# NIL #7# ELT)) (|sample| (#9=($) NIL T CONST)) (|removeDuplicates!| (#10=($ $) 47 T ELT)) (|removeDuplicates| (#10# NIL #11=(AND #7# #4#) ELT)) (|remove!| (#12=($ |#1| $) 58 #7# ELT) (#5# 60 #7# ELT)) (|remove| (#12# NIL #11# ELT) #8#) (|reduce| ((|#1| #13=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #13# $ |#1|) NIL T ELT) ((|#1| #13# $) NIL T ELT)) (|members| ((#14=(|List| |#1|) $) 9 T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| (#15=($ (|Mapping| |#1| |#1|) $) 41 T ELT)) (|map| (#15# 39 T ELT)) (|latex| (((|String|) $) NIL #16=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#17=(|#1| $) 49 T ELT)) (|insert!| (#12# 30 T ELT) (($ |#1| $ #18=(|NonNegativeInteger|)) 44 T ELT)) (|hash| (((|SingleInteger|) $) NIL #16# ELT)) (|find| (((|Union| |#1| "failed") #6# $) NIL T ELT)) (|extract!| (#17# 52 T ELT)) (|every?| #19=((#3# #6# $) NIL T ELT)) (|eval| (($ $ (|List| #20=(|Equation| |#1|))) NIL #21=(AND (|has| |#1| (|Evalable| |#1|)) #16#) ELT) (($ $ #20#) NIL #21# ELT) (($ $ |#1| |#1|) NIL #21# ELT) (($ $ #14# #14#) NIL #21# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| (#22=(#3# $) 23 T ELT)) (|empty| (#9# 29 T ELT)) (|duplicates?| (#22# 56 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #18#))) $) 69 T ELT)) (|dictionary| (#9# 26 T ELT) (#23=($ #14#) 19 T ELT)) (|count| ((#18# |#1| $) 65 #4# ELT) ((#18# #6# $) NIL T ELT)) (|copy| (#10# 20 T ELT)) (|convert| ((#24=(|InputForm|) $) 36 (|has| |#1| (|ConvertibleTo| #24#)) ELT)) (|construct| (#23# NIL T ELT)) (|coerce| ((#25=(|OutputForm|) $) 14 (|has| |#1| (|CoercibleTo| #25#)) ELT)) (|before?| #1#) (|bag| (#23# 24 T ELT)) (|any?| #19#) (= (#2# 71 #4# ELT)) (|#| ((#18# $) 17 T ELT))) 
(((|ListMultiDictionary| |#1|) (|Join| (|MultiDictionary| |#1|) (|FiniteAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |duplicates?| ((|Boolean|) $)) (SIGNATURE |substitute| ($ |#1| |#1| $)))) (|SetCategory|)) (T |ListMultiDictionary|)) 
((|duplicates?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ListMultiDictionary| *3)) (|ofCategory| *3 #1=(|SetCategory|)))) (|substitute| (*1 *1 *2 *2 *1) (AND (|isDomain| *1 (|ListMultiDictionary| *2)) (|ofCategory| *2 #1#)))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT))) 
(((|LeftModule| |#1|) (|Category|) (|Rng|)) (T |LeftModule|)) 
NIL 
(|Join| (|AbelianGroup|) (|LeftLinearSet| |t#1|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|) $) 17 T ELT)) (|rightMult| (($ $ |#1|) 68 T ELT)) (|reverse!| (#3=($ $) 39 T ELT)) (|reverse| (#3# 37 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 60 T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|plus| (($ |#1| |#2| $) 77 T ELT) (($ $ $) 79 T ELT)) (|outputForm| ((#4=(|OutputForm|) $ #5=(|Mapping| #4# #4# #4#) #5# #6=(|Integer|)) 55 T ELT)) (|nthFactor| ((|#1| $ #6#) 35 T ELT)) (|nthExpon| ((|#2| $ #6#) 34 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 41 T ELT)) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) 46 T ELT)) (|makeUnit| (($) 13 T ELT)) (|makeTerm| (($ |#1| |#2|) 24 T ELT)) (|makeMulti| (($ #7=(|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) 25 T ELT)) (|listOfMonoms| ((#7# $) 14 T ELT)) (|leftMult| (($ |#1| $) 69 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|commutativeEquality| (#2# 74 T ELT)) (|coerce| ((#4# $) 21 T ELT) (($ |#1|) 18 T ELT)) (|before?| #1#) (= (#2# 27 T ELT))) 
(((|ListMonoidOps| |#1| |#2| |#3|) (|Join| #1=(|SetCategory|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| (#2=(|OutputForm|) $ #3=(|Mapping| #2# #2# #2#) #3# #4=(|Integer|))) (SIGNATURE |listOfMonoms| (#5=(|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $)) (SIGNATURE |makeTerm| ($ |#1| |#2|)) (SIGNATURE |makeMulti| ($ #5#)) (SIGNATURE |nthExpon| (|#2| $ #4#)) (SIGNATURE |nthFactor| (|#1| $ #4#)) (SIGNATURE |reverse| #6=($ $)) (SIGNATURE |reverse!| #6#) (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|) $)))) #1# (|AbelianMonoid|) |#2|) (T |ListMonoidOps|)) 
((|outputForm| (*1 *2 *1 *3 *3 *4) (AND (|isDomain| *3 (|Mapping| #1=(|OutputForm|) #1# #1#)) (|isDomain| *4 #2=(|Integer|)) (|isDomain| *2 #1#) (|isDomain| *1 (|ListMonoidOps| *5 *6 *7)) (|ofCategory| *5 #3=(|SetCategory|)) (|ofCategory| *6 #4=(|AbelianMonoid|)) (|ofType| *7 *6))) (|listOfMonoms| #5=(*1 *2 *1) (AND #6=(|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4)))) #7=(|isDomain| *1 (|ListMonoidOps| *3 *4 *5)) #8=(|ofCategory| *3 #3#) #9=(|ofCategory| *4 #4#) #10=(|ofType| *5 *4))) (|makeTerm| (*1 *1 *2 *3) #11=(AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) #12=(|ofCategory| *2 #3#) (|ofCategory| *3 #4#) (|ofType| *4 *3))) (|makeMulti| (*1 *1 *2) (AND #6# #8# #9# #10# #7#)) (|nthExpon| #13=(*1 *2 *1 *3) (AND #14=(|isDomain| *3 #2#) (|ofCategory| *2 #4#) (|isDomain| *1 (|ListMonoidOps| *4 *2 *5)) (|ofCategory| *4 #3#) (|ofType| *5 *2))) (|nthFactor| #13# (AND #14# #12# (|isDomain| *1 (|ListMonoidOps| *2 *4 *5)) #9# #10#)) (|reverse| #15=(*1 *1 *1) #11#) (|reverse!| #15# #11#) (|size| #5# (AND (|isDomain| *2 (|NonNegativeInteger|)) #7# #8# #9# #10#)) (|makeUnit| (*1 *1) #11#) (|rightMult| (*1 *1 *1 *2) #11#) (|leftMult| #16=(*1 *1 *2 *1) #11#) (|plus| (*1 *1 *2 *3 *1) #11#) (|plus| (*1 *1 *1 *1) #11#) (|commutativeEquality| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) #7# #8# #9# #10#)) (|mapExpon| #16# (AND (|isDomain| *2 (|Mapping| *4 *4)) #9# #10# #7# #8#)) (|mapGen| #16# (AND (|isDomain| *2 (|Mapping| *3 *3)) #8# #7# #9# #10#))) 
((|maxIndex| ((#1=(|Integer|) $) 30 T ELT)) (|insert| (($ |#2| $ #1#) 26 T ELT) (($ $ $ #1#) NIL T ELT)) (|indices| (((|List| #1#) $) 12 T ELT)) (|index?| (((|Boolean|) #1# $) 17 T ELT)) (|concat| (($ $ |#2|) 23 T ELT) (($ |#2| $) 24 T ELT) (($ $ $) NIL T ELT) (($ (|List| $)) NIL T ELT))) 
(((|LinearAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |insert| (|#1| |#1| |#1| #1=(|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| #1#)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |maxIndex| (#1# |#1|)) (SIGNATURE |indices| ((|List| #1#) |#1|)) (SIGNATURE |index?| ((|Boolean|) #1# |#1|))) (|LinearAggregate| |#2|) (|Type|)) (T |LinearAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|swap!| (((|Void|) $ #3=(|Integer|) #3#) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #3# |#1|) 47 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #4=(|Boolean|) |#1|) . #5=($)) 69 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#6=($) 6 T CONST)) (|removeDuplicates| (($ $) 71 (AND (|has| |#1| . #7=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 70 (AND (|has| |#1| . #7#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #4# |#1|) . #5#) 68 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|qsetelt!| ((|#1| $ #3# |#1|) 48 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #3#) 46 T ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| ((#3# . #8=($)) 38 (|has| #3# . #9=((|OrderedSet|))) ELT)) (|maxIndex| ((#3# . #8#) 39 (|has| #3# . #9#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 60 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #10=((|SetCategory|))) ELT)) (|insert| (($ |#1| $ (|Integer|)) 57 T ELT) (($ $ $ (|Integer|)) 56 T ELT)) (|indices| (((|List| #3#) $) 41 T ELT)) (|index?| ((#11=(|Boolean|) #3# $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #10#) ELT)) (|first| ((|#1| $) 37 (|has| #3# . #9#) ELT)) (|fill!| (($ $ |#1|) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #10#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #10#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #10#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #10#)) ELT)) (|eq?| ((#12=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#11# |#1| $) 40 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 43 T ELT)) (|empty?| ((#12# $) 7 T ELT)) (|empty| (#6# 8 T ELT)) (|elt| ((|#1| $ #3# |#1|) 45 T ELT) ((|#1| $ #3#) 44 T ELT) (($ $ (|UniversalSegment| (|Integer|))) 66 T ELT)) (|delete| (($ $ (|Integer|)) 59 T ELT) (($ $ (|UniversalSegment| (|Integer|))) 58 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#13=(|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| #13#)) ELT)) (|construct| (($ (|List| |#1|)) 67 T ELT)) (|concat| (($ $ |#1|) 64 T ELT) (($ |#1| $) 63 T ELT) (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|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|)))) (|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|))) (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|IndexedAggregate| (|Integer|) |t#1|) (|Collection| |t#1|) (|Eltable| (|UniversalSegment| (|Integer|)) $) (CATEGORY |domain| (SIGNATURE |new| ($ (|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|) $ $)) (SIGNATURE |delete| ($ $ (|Integer|))) (SIGNATURE |delete| ($ $ (|UniversalSegment| (|Integer|)))) (SIGNATURE |insert| ($ |t#1| $ (|Integer|))) (SIGNATURE |insert| ($ $ $ (|Integer|))) (IF (|has| $ (|ShallowlyMutableAggregate| |t#1|)) (SIGNATURE |setelt| (|t#1| $ (|UniversalSegment| (|Integer|)) |t#1|)) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 15 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sign| ((#5=(|Integer|) $) NIL #6=(|has| |#1| (|OrderedAbelianGroup|)) ELT)) (|sample| (#7=($) NIL T CONST)) (|positive?| #8=(#4# NIL #6# ELT)) (|opposite?| #1#) (|numer| ((|#1| $) 23 T ELT)) (|negative?| #8#) (|min| #9=(#10=($ $ $) NIL #6# ELT)) (|max| #9#) (|latex| (((|String|) $) 48 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#3| $) 24 T ELT)) (|coerce| (((|OutputForm|) $) 43 T ELT)) (|before?| (#2# 22 T ELT)) (|abs| (#11=($ $) NIL #6# ELT)) (|Zero| (#7# 10 T CONST)) (>= #12=(#2# NIL #6# ELT)) (> #12#) (= (#2# 20 T ELT)) (<= #12#) (< (#2# 26 #6# ELT)) (/ (($ $ |#3|) 36 T ELT) (($ |#1| |#3|) 37 T ELT)) (- (#11# 17 T ELT) (#10# NIL T ELT)) (+ (#10# 29 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #5# $) 32 T ELT) (($ |#2| $) 34 T ELT) (($ $ |#2|) NIL T ELT))) 
(((|Localize| |#1| |#2| |#3|) (|Join| #1=(|Module| |#2|) (CATEGORY |domain| (IF (|has| |#1| #2=(|OrderedAbelianGroup|)) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE / ($ $ |#3|)) (SIGNATURE / ($ |#1| |#3|)) (SIGNATURE |numer| (|#1| $)) (SIGNATURE |denom| (|#3| $)))) #1# (|CommutativeRing|) (|SubsetCategory| (|Monoid|) |#2|)) (T |Localize|)) 
((/ (*1 *1 *1 *2) (AND #1=(|ofCategory| *4 #2=(|CommutativeRing|)) #3=(|isDomain| *1 (|Localize| *3 *4 *2)) #4=(|ofCategory| *3 #5=(|Module| *4)) #6=(|ofCategory| *2 #7=(|SubsetCategory| #8=(|Monoid|) *4)))) (/ (*1 *1 *2 *3) (AND #1# (|isDomain| *1 (|Localize| *2 *4 *3)) (|ofCategory| *2 #5#) (|ofCategory| *3 #7#))) (|numer| #9=(*1 *2 *1) (AND (|ofCategory| *3 #2#) (|ofCategory| *2 (|Module| *3)) (|isDomain| *1 (|Localize| *2 *3 *4)) (|ofCategory| *4 (|SubsetCategory| #8# *3)))) (|denom| #9# (AND #1# #6# #3# #4#))) 
((|solve| (((|Union| |#2| #1="failed") |#3| |#2| #2=(|Symbol|) |#2| #3=(|List| |#2|)) 174 T ELT) (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #3#)) #1#) |#3| |#2| #2#) 44 T ELT))) 
(((|ElementaryFunctionLODESolver| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #1=(|List| |#2|))) #2="failed") |#3| |#2| #3=(|Symbol|))) (SIGNATURE |solve| ((|Union| |#2| #2#) |#3| |#2| #3# |#2| #1#))) (|Join| (|EuclideanDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)) (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (T |ElementaryFunctionLODESolver|)) 
((|solve| (*1 *2 *3 *2 *4 *2 *5) (|partial| AND (|isDomain| *4 #1=(|Symbol|)) (|isDomain| *5 (|List| *2)) (|ofCategory| *2 #2=(|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) #3=(|ofCategory| *6 (|Join| (|EuclideanDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#) (|CharacteristicZero|))) (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *2 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)))) (|solve| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 #1#) #3# (|ofCategory| *4 #2#) (|isDomain| *2 (|Record| (|:| |particular| *4) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (#6=($ $ $) 28 #5# ELT)) (|symmetricPower| (#7=($ $ #8=(|NonNegativeInteger|)) 31 #5# ELT)) (|subtractIfCan| (#9=(#10=(|Union| $ #11="failed") $ $) NIL T ELT)) (|sample| (#12=($) NIL T CONST)) (|rightRemainder| #13=(#6# NIL #5# ELT)) (|rightQuotient| #13#) (|rightLcm| #13#) (|rightGcd| #13#) (|rightExtendedGcd| #14=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #15=(#9# NIL #5# ELT)) (|rightDivide| #16=(#17=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #18=(|Integer|) . #19=(#11#)) . #20=($)) NIL #21=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| #22=(|Fraction| #18#) . #19#) . #20#) NIL #23=(|has| |#1| (|RetractableTo| #22#)) ELT) (((|Union| |#1| . #19#) . #20#) NIL T ELT)) (|retract| ((#18# . #24=($)) NIL #21# ELT) ((#22# . #24#) NIL #23# ELT) #25=(#26=(|#1| . #24#) NIL T ELT)) (|reductum| #27=(#4# NIL T ELT)) (|recip| ((#10# $) NIL T ELT)) (|primitivePart| (#4# NIL #28=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #8#) NIL T ELT)) (|monicRightDivide| #29=(#17# NIL #30=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #29#) (|minimumDegree| #31=((#8# $) NIL T ELT)) (|leftRemainder| #13#) (|leftQuotient| #13#) (|leftLcm| #13#) (|leftGcd| #13#) (|leftExtendedGcd| #14#) (|leftExactQuotient| #15#) (|leftDivide| #16#) (|leadingCoefficient| #25#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#10# $ |#1|) NIL #30# ELT)) (|elt| ((|#1| $ |#1|) 24 T ELT)) (|directSum| (#6# 33 #5# ELT)) (|degree| #31#) (|content| (#26# NIL #28# ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #18#) NIL T ELT) (($ #22#) NIL #23# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #8#) NIL T ELT)) (|characteristic| ((#8#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) 23 T ELT)) (|annihilate?| #1#) (|adjoint| #27#) (|Zero| (#12# 21 T CONST)) (|One| (#12# 8 T CONST)) (D (#12# NIL T ELT)) (= #1#) (- #27# #32=(#6# NIL T ELT)) (+ #32#) (** (($ $ #33=(|PositiveInteger|)) NIL T ELT) (#7# NIL T ELT)) (* (($ #33# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #18# . #34=($)) NIL T ELT) #32# (($ $ |#1|) NIL T ELT) (($ |#1| . #34#) NIL T ELT))) 
(((|LinearOrdinaryDifferentialOperator| |#1| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Ring|) (|Mapping| |#1| |#1|)) (T |LinearOrdinaryDifferentialOperator|)) 
NIL 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| #6=(#7=($ $ $) NIL #5# ELT)) (|symmetricPower| (#8=($ $ #9=(|NonNegativeInteger|)) NIL #5# ELT)) (|subtractIfCan| (#10=(#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|sample| #13=(#14=($) NIL T CONST)) (|rightRemainder| #6#) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #15=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #16=(#10# NIL #5# ELT)) (|rightDivide| #17=(#18=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #19=(|Integer|) . #20=(#12#)) . #21=($)) NIL #22=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| #23=(|Fraction| #19#) . #20#) . #21#) NIL #24=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| |#1| . #20#) . #21#) NIL T ELT)) (|retract| ((#19# . #25=($)) NIL #22# ELT) ((#23# . #25#) NIL #24# ELT) #26=(#27=(|#1| . #25#) NIL T ELT)) (|reductum| #28=(#4# NIL T ELT)) (|recip| ((#11# $) NIL T ELT)) (|primitivePart| (#4# NIL #29=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #9#) NIL T ELT)) (|monicRightDivide| #30=(#18# NIL #31=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #30#) (|minimumDegree| #32=((#9# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #15#) (|leftExactQuotient| #16#) (|leftDivide| #17#) (|leadingCoefficient| #26#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#11# $ |#1|) NIL #31# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT)) (|directSum| #6#) (|degree| #32#) (|content| (#27# NIL #29# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) (($ #23#) NIL #24# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #9#) NIL T ELT)) (|characteristic| ((#9#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) NIL T ELT)) (|annihilate?| #1#) (|adjoint| #28#) (|Zero| #13#) (|One| #13#) (D (#14# NIL T ELT)) (= #1#) (- #28# #33=(#7# NIL T ELT)) (+ #33#) (** (($ $ #34=(|PositiveInteger|)) NIL T ELT) (#8# NIL T ELT)) (* (($ #34# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #19# . #35=($)) NIL T ELT) #33# (($ $ |#1|) NIL T ELT) (($ |#1| . #35#) NIL T ELT))) 
(((|LinearOrdinaryDifferentialOperator1| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|DifferentialRing|)) (T |LinearOrdinaryDifferentialOperator1|)) 
NIL 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| #6=(#7=($ $ $) NIL #5# ELT)) (|symmetricPower| (#8=($ $ #9=(|NonNegativeInteger|)) NIL #5# ELT)) (|subtractIfCan| (#10=(#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|sample| #13=(#14=($) NIL T CONST)) (|rightRemainder| #6#) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #15=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #16=(#10# NIL #5# ELT)) (|rightDivide| #17=(#18=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #19=(|Integer|) . #20=(#12#)) . #21=($)) NIL #22=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| #23=(|Fraction| #19#) . #20#) . #21#) NIL #24=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| |#1| . #20#) . #21#) NIL T ELT)) (|retract| ((#19# . #25=($)) NIL #22# ELT) ((#23# . #25#) NIL #24# ELT) #26=(#27=(|#1| . #25#) NIL T ELT)) (|reductum| #28=(#4# NIL T ELT)) (|recip| ((#11# $) NIL T ELT)) (|primitivePart| (#4# NIL #29=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #9#) NIL T ELT)) (|monicRightDivide| #30=(#18# NIL #31=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #30#) (|minimumDegree| #32=((#9# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #15#) (|leftExactQuotient| #16#) (|leftDivide| #17#) (|leadingCoefficient| #26#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#11# $ |#1|) NIL #31# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) ((|#2| $ |#2|) 13 T ELT)) (|directSum| #6#) (|degree| #32#) (|content| (#27# NIL #29# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) (($ #23#) NIL #24# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #9#) NIL T ELT)) (|characteristic| ((#9#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) NIL T ELT)) (|annihilate?| #1#) (|adjoint| #28#) (|Zero| #13#) (|One| #13#) (D (#14# NIL T ELT)) (= #1#) (- #28# #33=(#7# NIL T ELT)) (+ #33#) (** (($ $ #34=(|PositiveInteger|)) NIL T ELT) (#8# NIL T ELT)) (* (($ #34# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #19# . #35=($)) NIL T ELT) #33# (($ $ |#1|) NIL T ELT) (($ |#1| . #35#) NIL T ELT))) 
(((|LinearOrdinaryDifferentialOperator2| |#1| |#2|) (|Join| (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Eltable| |#2| |#2|)) (|DifferentialRing|) (|Join| (|LeftModule| |#1|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $))))) (T |LinearOrdinaryDifferentialOperator2|)) 
NIL 
((|symmetricSquare| (#1=($ $) 29 T ELT)) (|adjoint| (#1# 27 T ELT)) (D (($) 13 T ELT))) 
(((|LinearOrdinaryDifferentialOperatorCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |symmetricSquare| #1=(|#1| |#1|)) (SIGNATURE |adjoint| #1#) (SIGNATURE D (|#1|))) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|Ring|)) (T |LinearOrdinaryDifferentialOperatorCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|symmetricSquare| (($ $) 96 (|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (($ $ $) 98 (|has| |#1| (|Field|)) ELT)) (|symmetricPower| (($ $ (|NonNegativeInteger|)) 97 (|has| |#1| (|Field|)) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (#4=($ $ $) 58 (|has| |#1| . #5=((|Field|))) ELT)) (|rightQuotient| (#4# 59 (|has| |#1| . #5#) ELT)) (|rightLcm| (#4# 61 (|has| |#1| . #5#) ELT)) (|rightGcd| (#4# 56 (|has| |#1| . #5#) ELT)) (|rightExtendedGcd| (#6=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 55 (|has| |#1| . #5#) ELT)) (|rightExactQuotient| (#7=(#8=(|Union| $ "failed") $ $) 57 (|has| |#1| . #5#) ELT)) (|rightDivide| (#9=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 60 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| #10=(|Integer|) . #11=("failed")) . #12=($)) 88 (|has| |#1| . #13=((|RetractableTo| #10#))) ELT) (((|Union| #14=(|Fraction| #10#) . #11#) . #12#) 85 (|has| |#1| . #15=((|RetractableTo| #14#))) ELT) (((|Union| |#1| . #11#) . #12#) 82 T ELT)) (|retract| ((#10# . #16=($)) 87 (|has| |#1| . #13#) ELT) ((#14# . #16#) 84 (|has| |#1| . #15#) ELT) ((|#1| . #16#) 83 T ELT)) (|reductum| (#17=($ $) 77 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (#17# 68 (|has| |#1| . #18=((|GcdDomain|))) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial| (($ |#1| #19=(|NonNegativeInteger|)) 75 T ELT)) (|monicRightDivide| (#9# 70 (|has| |#1| . #20=((|IntegralDomain|))) ELT)) (|monicLeftDivide| (#9# 71 (|has| |#1| . #20#) ELT)) (|minimumDegree| (#21=(#19# $) 79 T ELT)) (|leftRemainder| (#4# 65 (|has| |#1| . #5#) ELT)) (|leftQuotient| (#4# 66 (|has| |#1| . #5#) ELT)) (|leftLcm| (#4# 54 (|has| |#1| . #5#) ELT)) (|leftGcd| (#4# 63 (|has| |#1| . #5#) ELT)) (|leftExtendedGcd| (#6# 62 (|has| |#1| . #5#) ELT)) (|leftExactQuotient| (#7# 64 (|has| |#1| . #5#) ELT)) (|leftDivide| (#9# 67 (|has| |#1| . #5#) ELT)) (|leadingCoefficient| ((|#1| . #22=($)) 78 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| ((#8# $ |#1|) 72 (|has| |#1| . #20#) ELT)) (|elt| ((|#1| $ |#1|) 101 T ELT)) (|directSum| (($ $ $) 95 (|has| |#1| (|Field|)) ELT)) (|degree| (#21# 80 T ELT)) (|content| ((|#1| . #22#) 69 (|has| |#1| . #18#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #14#) 86 (|has| |#1| . #15#) ELT) (($ |#1|) 81 T ELT)) (|coefficients| (((|List| |#1|) $) 74 T ELT)) (|coefficient| ((|#1| $ #19#) 76 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 73 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|adjoint| (($ $) 99 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($) 100 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #23=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #23#) 89 T ELT))) 
(((|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) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Eltable| |#1| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UnivariateSkewPolynomialCategory| |#1|) . T)) 
((|factor1| (#1=(#2=(|List| #3=(|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) #3#) 86 #4=(|has| |#1| (|AlgebraicallyClosedField|)) ELT)) (|factor| (#1# 85 #4# ELT) ((#2# #3# (|Mapping| (|List| |#1|) |#2|)) 19 T ELT))) 
(((|LinearOrdinaryDifferentialOperatorFactorizer| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factor| (#1=(|List| #2=(|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) #2# (|Mapping| (|List| |#1|) |#2|))) (IF (|has| |#1| (|AlgebraicallyClosedField|)) (PROGN (SIGNATURE |factor| #3=(#1# #2#)) (SIGNATURE |factor1| #3#)) |%noBranch|)) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #4=(|Integer|)) (|RetractableTo| (|Fraction| #4#))) (|UnivariatePolynomialCategory| |#1|)) (T |LinearOrdinaryDifferentialOperatorFactorizer|)) 
((|factor1| #1=(*1 *2 *3) #2=(AND (|ofCategory| *4 (|AlgebraicallyClosedField|)) (|ofCategory| *4 #3=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #4=(|Integer|)) (|RetractableTo| (|Fraction| #4#)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| #5=(|LinearOrdinaryDifferentialOperator1| (|Fraction| *5)))) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *4 *5)) (|isDomain| *3 #5#))) (|factor| #1# #2#) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|List| *5) *6)) (|ofCategory| *5 #3#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| #6=(|LinearOrdinaryDifferentialOperator1| (|Fraction| *6)))) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *5 *6)) (|isDomain| *3 #6#)))) 
((|symmetricProduct| (#1=(|#2| |#2| |#2| #2=(|Mapping| |#1| |#1|)) 65 T ELT)) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) #2#) 45 T ELT)) (|directSum| (#1# 67 T ELT))) 
(((|LinearOrdinaryDifferentialOperatorsOps| |#1| |#2|) (CATEGORY |package| (SIGNATURE |symmetricProduct| #1=(|#2| |#2| |#2| #2=(|Mapping| |#1| |#1|))) (SIGNATURE |symmetricPower| (|#2| |#2| (|NonNegativeInteger|) #2#)) (SIGNATURE |directSum| #1#)) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |LinearOrdinaryDifferentialOperatorsOps|)) 
((|directSum| #1=(*1 *2 *2 *2 *3) #2=(AND (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *4 #3=(|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 #3#) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorsOps| *5 *2)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (|symmetricProduct| #1# #2#)) 
((|\\/| (($ $ $) 9 T ELT))) 
(((|Logic&| |#1|) (CATEGORY |package| (SIGNATURE |\\/| (|#1| |#1| |#1|))) (|Logic|)) (T |Logic&|)) 
NIL 
((~ (($ $) 8 T ELT)) (|\\/| (($ $ $) 6 T ELT)) (|/\\| (($ $ $) 7 T ELT))) 
(((|Logic|) (|Category|)) (T |Logic|)) 
((~ (*1 *1 *1) (|ofCategory| *1 (|Logic|))) (|/\\| (*1 *1 *1 *1) (|ofCategory| *1 (|Logic|))) (|\\/| (*1 *1 *1 *1) (|ofCategory| *1 (|Logic|)))) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE ~ ($ $)) (SIGNATURE |/\\| ($ $ $)) (SIGNATURE |\\/| ($ $ $)))) 
(((|Join|) . T) ((|Type|) . T)) 
((|solveLinearPolynomialEquationByFractions| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#1|)) "failed") #1# #2#) 33 T ELT))) 
(((|LinearPolynomialEquationByFractions| |#1|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByFractions| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#1|)) "failed") #1# #2#))) (|PolynomialFactorizationExplicit|)) (T |LinearPolynomialEquationByFractions|)) 
((|solveLinearPolynomialEquationByFractions| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| #1=(|SparseUnivariatePolynomial| *4))) (|isDomain| *3 #1#) (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|LinearPolynomialEquationByFractions| *4))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|varList| ((#5=(|List| |#1|) $) 85 T ELT)) (|trunc| (($ $ #6=(|NonNegativeInteger|)) 95 T ELT)) (|subtractIfCan| ((#7=(|Union| $ #8="failed") $ $) NIL T ELT)) (|sample| (#9=($) NIL T CONST)) (|rquo| (#10=(#11=(|XRecursivePolynomial| |#1| |#2|) #11# $) 50 T ELT)) (|retractIfCan| (((|Union| #12=(|LyndonWord| |#1|) #8#) $) NIL T ELT)) (|retract| #13=((#12# $) NIL T ELT)) (|reductum| (#14=($ $) 94 T ELT)) (|opposite?| #1#) (|numberOfMonomials| (#15=(#6# $) NIL T ELT)) (|monomials| ((#16=(|List| $) $) NIL T ELT)) (|monomial?| #4#) (|monom| (($ #12# |#2|) 70 T ELT)) (|mirror| (#14# 90 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|lquo| (#10# 49 T ELT)) (|leadingTerm| ((#17=(|Record| (|:| |k| #12#) (|:| |c| |#2|)) $) NIL T ELT)) (|leadingMonomial| #13#) (|leadingCoefficient| ((|#2| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| (($ $ |#1| $) 32 T ELT) (($ $ #5# #16#) 34 T ELT)) (|degree| (#15# 92 T ELT)) (|construct| (#18=($ $ $) 20 T ELT) (($ #12# #12#) 79 T ELT) (($ #12# $) 77 T ELT) (($ $ #12#) 78 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) 76 T ELT) ((#19=(|XDistributedPolynomial| |#1| |#2|) $) 60 T ELT) ((#11# $) 43 T ELT) (#20=($ #12#) 27 T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| ((|#2| $ #12#) NIL T ELT)) (|coef| ((|#2| #11# $) 45 T ELT)) (|before?| #1#) (|Zero| (#9# 23 T CONST)) (|ListOfTerms| (((|List| #17#) $) NIL T ELT)) (|LiePolyIfCan| ((#7# #19#) 62 T ELT)) (|LiePoly| (#20# 14 T ELT)) (= (#2# 46 T ELT)) (/ (#21=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- (#14# 68 T ELT) (#18# NIL T ELT)) (+ (#18# 31 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #6# $) NIL T ELT) (($ (|Integer|) . #22=($)) NIL T ELT) (($ |#2| . #22#) 30 T ELT) (#21# NIL T ELT) (($ |#2| #12#) NIL T ELT))) 
(((|LiePolynomial| |#1| |#2|) (|Join| (|FreeLieAlgebra| |#1| |#2|) (|FreeModuleCat| |#2| #1=(|LyndonWord| |#1|)) (CATEGORY |domain| (SIGNATURE |LiePolyIfCan| ((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|))) (SIGNATURE |construct| ($ #1# #1#)) (SIGNATURE |construct| ($ #1# $)) (SIGNATURE |construct| ($ $ #1#)))) (|OrderedSet|) (|CommutativeRing|)) (T |LiePolynomial|)) 
((|LiePolyIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) #1=(|ofCategory| *3 (|OrderedSet|)) #2=(|ofCategory| *4 (|CommutativeRing|)) #3=(|isDomain| *1 (|LiePolynomial| *3 *4)))) (|construct| (*1 *1 *2 *2) #4=(AND (|isDomain| *2 (|LyndonWord| *3)) #1# #3# #2#)) (|construct| (*1 *1 *2 *1) #4#) (|construct| (*1 *1 *1 *2) #4#)) 
((|sorted?| ((#1=(|Boolean|) $) NIL T ELT) ((#1# #2=(|Mapping| #1# |#2| |#2|) $) 59 T ELT)) (|sort!| (#3=($ $) NIL T ELT) (($ #2# $) 12 T ELT)) (|select!| (#4=($ #5=(|Mapping| #1# |#2|) $) 29 T ELT)) (|reverse!| (#3# 65 T ELT)) (|removeDuplicates!| (#3# 74 T ELT)) (|remove!| (($ |#2| $) NIL T ELT) (#4# 43 T ELT)) (|reduce| ((|#2| #6=(|Mapping| |#2| |#2| |#2|) $) 21 T ELT) ((|#2| #6# $ |#2|) 60 T ELT) ((|#2| #6# $ |#2| |#2|) 62 T ELT)) (|position| ((#7=(|Integer|) |#2| $ #7#) 71 T ELT) ((#7# |#2| $) NIL T ELT) ((#7# #5# $) 54 T ELT)) (|new| (($ (|NonNegativeInteger|) |#2|) 63 T ELT)) (|merge!| #8=(($ $ $) NIL T ELT) (#9=($ #2# $ $) 31 T ELT)) (|merge| #8# (#9# 24 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT) (($ #6# $ $) 64 T ELT)) (|list| (($ |#2|) 15 T ELT)) (|insert!| (#10=($ $ $ #7#) 42 T ELT) (($ |#2| $ #7#) 40 T ELT)) (|find| (((|Union| |#2| "failed") #5# $) 53 T ELT)) (|delete!| (($ $ (|UniversalSegment| #7#)) 51 T ELT) (($ $ #7#) 44 T ELT)) (|copyInto!| (#10# 70 T ELT)) (|copy| (#3# 68 T ELT)) (< ((#1# $ $) 76 T ELT))) 
(((|ListAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |list| (|#1| |#2|)) (SIGNATURE |delete!| (|#1| |#1| #1=(|Integer|))) (SIGNATURE |delete!| (|#1| |#1| (|UniversalSegment| #1#))) (SIGNATURE |remove!| #2=(|#1| #3=(|Mapping| #4=(|Boolean|) |#2|) |#1|)) (SIGNATURE |insert!| (|#1| |#2| |#1| #1#)) (SIGNATURE |insert!| #5=(|#1| |#1| |#1| #1#)) (SIGNATURE |merge!| #6=(|#1| #7=(|Mapping| #4# |#2| |#2|) |#1| |#1|)) (SIGNATURE |select!| #2#) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |removeDuplicates!| #8=(|#1| |#1|)) (SIGNATURE |merge!| #9=(|#1| |#1| |#1|)) (SIGNATURE |reduce| (|#2| #10=(|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |find| ((|Union| |#2| "failed") #3# |#1|)) (SIGNATURE |reduce| (|#2| #10# |#1| |#2|)) (SIGNATURE |reduce| (|#2| #10# |#1|)) (SIGNATURE |merge| #6#) (SIGNATURE |sorted?| (#4# #7# |#1|)) (SIGNATURE |position| (#1# #3# |#1|)) (SIGNATURE |position| (#1# |#2| |#1|)) (SIGNATURE |position| (#1# |#2| |#1| #1#)) (SIGNATURE |merge| #9#) (SIGNATURE |sorted?| (#4# |#1|)) (SIGNATURE |copyInto!| #5#) (SIGNATURE |reverse!| #8#) (SIGNATURE |sort!| (|#1| #7# |#1|)) (SIGNATURE |sort!| #8#) (SIGNATURE < (#4# |#1| |#1|)) (SIGNATURE |new| (|#1| (|NonNegativeInteger|) |#2|)) (SIGNATURE |map| (|#1| #10# |#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |copy| #8#)) (|ListAggregate| |#2|) (|Type|)) (T |ListAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|third| ((|#1| . #3=($)) 62 T ELT)) (|tail| (#4=($ $) 64 T ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) 99 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|split!| (($ $ (|Integer|)) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#6=(|Boolean|) $) 155 (|has| |#1| . #7=((|OrderedSet|))) ELT) ((#6# (|Mapping| #6# |#1| |#1|) $) 149 T ELT)) (|sort!| (#8=($ $) 159 (AND (|has| |#1| . #7#) (|has| $ (|ShallowlyMutableAggregate| |#1|))) ELT) (($ (|Mapping| #6# |#1| |#1|) . #9=($)) 158 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sort| (#8# 154 (|has| |#1| . #7#) ELT) (($ (|Mapping| #6# |#1| |#1|) . #9#) 148 T ELT)) (|size?| (#10=(#11=(|Boolean|) $ (|NonNegativeInteger|)) 82 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setrest!| (#12=($ $ $) 53 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #13="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #14="first" |#1|) 54 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ #15="rest" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #16="last" |#1|) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #17=(|UniversalSegment| #5#) |#1|) 115 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #5# |#1|) 88 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #18=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select!| (($ (|Mapping| #19=(|Boolean|) |#1|) . #20=($)) 131 T ELT)) (|select| (($ (|Mapping| #21=(|Boolean|) |#1|) . #22=($)) 103 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|second| ((|#1| . #3#) 63 T ELT)) (|sample| (#23=($) 6 T CONST)) (|reverse!| (#8# 157 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|reverse| (#8# 147 T ELT)) (|rest| (#4# 70 T ELT) (#24=($ $ #25=(|NonNegativeInteger|)) 68 T ELT)) (|removeDuplicates!| (($ $) 133 (|has| |#1| . #26=((|BasicType|))) ELT)) (|removeDuplicates| (($ $) 101 (AND (|has| |#1| . #27=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 132 (|has| |#1| . #26#) ELT) (($ (|Mapping| #19# |#1|) . #20#) 127 T ELT)) (|remove| (($ (|Mapping| #21# |#1|) . #22#) 104 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ |#1| $) 102 (AND (|has| |#1| . #27#) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 140 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 139 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 135 (|has| |#1| . #28=((|BasicType|))) ELT)) (|qsetelt!| ((|#1| $ #5# |#1|) 87 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #5#) 89 T ELT)) (|possiblyInfinite?| (#29=(#11# $) 85 T ELT)) (|position| ((#30=(|Integer|) |#1| $ #30#) 152 (|has| |#1| . #31=((|BasicType|))) ELT) ((#30# |#1| $) 151 (|has| |#1| . #31#) ELT) ((#30# (|Mapping| #6# |#1|) $) 150 T ELT)) (|nodes| (#32=(#18# $) 45 T ELT)) (|node?| (#33=(#34=(|Boolean|) $ $) 37 (|has| |#1| . #35=((|BasicType|))) ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 107 T ELT)) (|more?| (#10# 83 T ELT)) (|minIndex| ((#5# . #36=($)) 97 (|has| #5# . #37=((|OrderedSet|))) ELT)) (|min| (#38=($ $ $) 165 (|has| |#1| . #7#) ELT)) (|merge!| (#39=($ $ $) 134 (|has| |#1| (|OrderedSet|)) ELT) (($ (|Mapping| #19# |#1| |#1|) $ $) 130 T ELT)) (|merge| (($ $ $) 153 (|has| |#1| . #7#) ELT) (($ (|Mapping| #6# |#1| |#1|) $ $) 146 T ELT)) (|members| (((|List| |#1|) $) 141 T ELT)) (|member?| ((#40=(|Boolean|) |#1| $) 136 (|has| |#1| . #28#) ELT)) (|maxIndex| ((#5# . #36#) 96 (|has| #5# . #37#) ELT)) (|max| (#38# 164 (|has| |#1| . #7#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 124 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 110 T ELT)) (|list| (($ |#1|) 123 T ELT)) (|less?| (#10# 84 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (#41=(#34# $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #42=((|SetCategory|))) ELT)) (|last| ((|#1| . #3#) 67 T ELT) (#24# 65 T ELT)) (|insert!| (($ $ $ #43=(|Integer|)) 129 T ELT) (($ |#1| $ #43#) 128 T ELT)) (|insert| (($ $ $ #5#) 114 T ELT) (($ |#1| $ #5#) 113 T ELT)) (|indices| (((|List| #5#) $) 94 T ELT)) (|index?| ((#44=(|Boolean|) #5# $) 93 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #42#) ELT)) (|first| ((|#1| . #3#) 73 T ELT) (#24# 71 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #40# |#1|) $) 138 T ELT)) (|fill!| (($ $ |#1|) 98 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|explicitlyFinite?| (#29# 86 T ELT)) (|every?| ((#40# (|Mapping| #40# |#1|) . #45=($)) 143 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #42#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #42#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #42#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #42#)) ELT)) (|eq?| ((#46=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#44# |#1| $) 95 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 92 T ELT)) (|empty?| ((#46# $) 7 T ELT)) (|empty| (#23# 8 T ELT)) (|elt| ((|#1| $ #13#) 42 T ELT) ((|#1| $ #14#) 72 T ELT) (($ $ #15#) 69 T ELT) ((|#1| $ #16#) 66 T ELT) (($ $ #17#) 106 T ELT) ((|#1| $ #5#) 91 T ELT) ((|#1| $ #5# |#1|) 90 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|delete!| (($ $ (|UniversalSegment| #43#)) 126 T ELT) (($ $ #43#) 125 T ELT)) (|delete| (($ $ #17#) 112 T ELT) (($ $ #5#) 111 T ELT)) (|cyclic?| (#41# 41 T ELT)) (|cycleTail| (#4# 59 T ELT)) (|cycleSplit!| (#4# 56 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|cycleLength| ((#25# $) 60 T ELT)) (|cycleEntry| (#4# 61 T ELT)) (|count| ((#47=(|NonNegativeInteger|) (|Mapping| #40# |#1|) $) 142 T ELT) ((#47# |#1| $) 137 (|has| |#1| . #28#) ELT)) (|copyInto!| (($ $ $ #30#) 156 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#48=(|InputForm|) $) 100 (|has| |#1| (|ConvertibleTo| #48#)) ELT)) (|construct| (($ (|List| |#1|)) 105 T ELT)) (|concat!| (#39# 58 T ELT) (($ $ |#1|) 57 T ELT)) (|concat| (#12# 75 T ELT) (($ |#1| $) 74 T ELT) (($ (|List| $)) 109 T ELT) (($ $ |#1|) 108 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (#32# 46 T ELT)) (|child?| (#33# 38 (|has| |#1| . #35#) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#40# (|Mapping| #40# |#1|) . #45#) 144 T ELT)) (>= (#49=((|Boolean|) $ $) 163 (|has| |#1| . #7#) ELT)) (> (#49# 161 (|has| |#1| . #7#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (<= (#49# 162 (|has| |#1| . #7#) ELT)) (< (#49# 160 (|has| |#1| . #7#) ELT)) (|#| ((#47# $) 145 T ELT))) 
(((|ListAggregate| |#1|) (|Category|) (|Type|)) (T |ListAggregate|)) 
((|list| (*1 *1 *2) (AND (|ofCategory| *1 (|ListAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|StreamAggregate| |t#1|) (|FiniteLinearAggregate| |t#1|) (|ExtensibleLinearAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |list| ($ |t#1|)))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|ExtensibleLinearAggregate| |#1|) . T) ((|FiniteAggregate| |#1|) . T) ((|FiniteLinearAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|ShallowlyMutableAggregate| |#1|) . T) ((|StreamAggregate| |#1|) . T) ((|Type|) . T) ((|UnaryRecursiveAggregate| |#1|) . T)) 
((|solve| (((|List| #1=(|Record| (|:| |particular| #2=(|Union| |#3| "failed")) (|:| |basis| #3=(|List| |#3|)))) |#4| #3#) 66 T ELT) ((#1# |#4| |#3|) 60 T ELT)) (|rank| (((|NonNegativeInteger|) |#4| |#3|) 18 T ELT)) (|particularSolution| ((#2# |#4| |#3|) 21 T ELT)) (|hasSolution?| (((|Boolean|) |#4| |#3|) 14 T ELT))) 
(((|LinearSystemMatrixPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|Record| (|:| |particular| #2=(|Union| |#3| "failed")) (|:| |basis| #3=(|List| |#3|))) |#4| |#3|)) (SIGNATURE |solve| ((|List| #1#) |#4| #3#)) (SIGNATURE |particularSolution| (#2# |#4| |#3|)) (SIGNATURE |hasSolution?| ((|Boolean|) |#4| |#3|)) (SIGNATURE |rank| ((|NonNegativeInteger|) |#4| |#3|))) (|Field|) #4=(|Join| (|FiniteLinearAggregate| |#1|) (|ShallowlyMutableAggregate| |#1|)) #4# (|MatrixCategory| |#1| |#2| |#3|)) (T |LinearSystemMatrixPackage|)) 
((|rank| #1=(*1 *2 *3 *4) (AND #2=(|ofCategory| *5 #3=(|Field|)) #4=(|ofCategory| *6 #5=(|Join| (|FiniteLinearAggregate| *5) (|ShallowlyMutableAggregate| *5))) #6=(|ofCategory| *4 #5#) (|isDomain| *2 (|NonNegativeInteger|)) #7=(|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *4 *3)) #8=(|ofCategory| *3 (|MatrixCategory| *5 *6 *4)))) (|hasSolution?| #1# (AND #2# #4# #6# (|isDomain| *2 (|Boolean|)) #7# #8#)) (|particularSolution| (*1 *2 *3 *2) (|partial| AND (|ofCategory| *4 #3#) (|ofCategory| *5 #9=(|Join| (|FiniteLinearAggregate| *4) (|ShallowlyMutableAggregate| *4))) (|ofCategory| *2 #9#) (|isDomain| *1 (|LinearSystemMatrixPackage| *4 *5 *2 *3)) (|ofCategory| *3 (|MatrixCategory| *4 *5 *2)))) (|solve| #1# (AND #2# #4# (|ofCategory| *7 #5#) (|isDomain| *2 (|List| (|Record| (|:| |particular| (|Union| *7 #10="failed")) (|:| |basis| #11=(|List| *7))))) (|isDomain| *1 (|LinearSystemMatrixPackage| *5 *6 *7 *3)) (|isDomain| *4 #11#) (|ofCategory| *3 (|MatrixCategory| *5 *6 *7)))) (|solve| #1# (AND #2# #4# #6# (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 #10#)) (|:| |basis| (|List| *4)))) #7# #8#))) 
((|solve| ((#1=(|List| #2=(|Record| (|:| |particular| #3=(|Union| #4=(|Vector| |#1|) "failed")) (|:| |basis| #5=(|List| #4#)))) #6=(|List| (|List| |#1|)) #5#) 22 T ELT) ((#1# #7=(|Matrix| |#1|) #5#) 21 T ELT) ((#2# #6# #4#) 18 T ELT) ((#2# #7# #4#) 14 T ELT)) (|rank| (((|NonNegativeInteger|) #7# #4#) 30 T ELT)) (|particularSolution| ((#3# #7# #4#) 24 T ELT)) (|hasSolution?| (((|Boolean|) #7# #4#) 27 T ELT))) 
(((|LinearSystemMatrixPackage1| |#1|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|Record| (|:| |particular| #2=(|Union| #3=(|Vector| |#1|) "failed")) (|:| |basis| #4=(|List| #3#))) #5=(|Matrix| |#1|) #3#)) (SIGNATURE |solve| (#1# #6=(|List| (|List| |#1|)) #3#)) (SIGNATURE |solve| (#7=(|List| #1#) #5# #4#)) (SIGNATURE |solve| (#7# #6# #4#)) (SIGNATURE |particularSolution| (#2# #5# #3#)) (SIGNATURE |hasSolution?| ((|Boolean|) #5# #3#)) (SIGNATURE |rank| ((|NonNegativeInteger|) #5# #3#))) (|Field|)) (T |LinearSystemMatrixPackage1|)) 
((|rank| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Matrix| *5)) #3=(|isDomain| *4 #4=(|Vector| *5)) #5=(|ofCategory| *5 #6=(|Field|)) (|isDomain| *2 (|NonNegativeInteger|)) #7=(|isDomain| *1 (|LinearSystemMatrixPackage1| *5)))) (|hasSolution?| #1# (AND #2# #3# #5# (|isDomain| *2 (|Boolean|)) #7#)) (|particularSolution| (*1 *2 *3 *2) (|partial| AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Matrix| *4)) (|ofCategory| *4 #6#) (|isDomain| *1 (|LinearSystemMatrixPackage1| *4)))) (|solve| #1# (AND #8=(|isDomain| *3 (|List| (|List| *5))) #5# #9=(|isDomain| *2 (|List| #10=(|Record| (|:| |particular| (|Union| #4# "failed")) (|:| |basis| #11=(|List| #4#))))) #7# #12=(|isDomain| *4 #11#))) (|solve| #1# (AND #2# #5# #9# #7# #12#)) (|solve| #1# (AND #8# #5# #13=(|isDomain| *2 #10#) #7# #3#)) (|solve| #1# (AND #2# #5# #13# #7# #3#))) 
((|linSolve| (((|Record| (|:| |particular| (|Union| #1=(|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| #1#))) (|List| |#4|) (|List| |#3|)) 51 T ELT))) 
(((|LinearSystemPolynomialPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |linSolve| ((|Record| (|:| |particular| (|Union| #1=(|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| #1#))) (|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| #1=(|Vector| (|Fraction| *8)) "failed")) (|:| |basis| (|List| #1#)))) (|isDomain| *1 (|LinearSystemPolynomialPackage| *5 *6 *7 *8))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unit| #4=((#5=(|Union| $ #6="failed")) NIL #7=(|has| |#2| (|IntegralDomain|)) ELT)) (|trace| #8=(#9=(|#2| $) NIL T ELT)) (|symmetric?| #3#) (|subtractIfCan| ((#5# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#2|))) NIL T ELT) ((#10# #12=(|Vector| $)) NIL T ELT)) (|square?| #3#) (|someBasis| (#13=(#12#) 41 T ELT)) (|scalarMatrix| #14=(($ |#2|) NIL T ELT)) (|sample| #15=(#16=($) NIL T CONST)) (|rowEchelon| (#17=($ $) NIL (|has| |#2| (|EuclideanDomain|)) ELT)) (|row| #18=((#19=(|DirectProduct| |#1| |#2|) $ #20=(|Integer|)) NIL T ELT)) (|rightUnits| #21=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #6#)) NIL #7# ELT)) (|rightUnit| #4#) (|rightTraceMatrix| #22=((#11#) NIL T ELT) #23=((#11# #12#) NIL T ELT)) (|rightTrace| #8#) (|rightRegularRepresentation| #24=((#11# $) NIL T ELT) #25=((#11# $ #12#) NIL T ELT)) (|rightRecip| #26=(#27=(#5# $) NIL #7# ELT)) (|rightRankPolynomial| #28=(((|SparseUnivariatePolynomial| #29=(|Polynomial| |#2|))) NIL #30=(|has| |#2| (|Field|)) ELT)) (|rightPower| #31=(($ $ #32=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #8#) (|rightMinimalPolynomial| #33=(#34=((|SparseUnivariatePolynomial| |#2|) $) NIL #7# ELT)) (|rightDiscriminant| #35=((|#2|) NIL T ELT) #36=((|#2| #12#) NIL T ELT)) (|rightCharacteristicPolynomial| #37=(#34# NIL T ELT)) (|rightAlternative?| #38=((#2#) NIL T ELT)) (|retractIfCan| (((|Union| #20# . #39=(#6#)) . #40=($)) NIL #41=(|has| |#2| (|RetractableTo| #20#)) ELT) (((|Union| #42=(|Fraction| #20#) . #39#) . #40#) NIL #43=(|has| |#2| (|RetractableTo| #42#)) ELT) ((#44=(|Union| |#2| . #39#) . #40#) NIL T ELT)) (|retract| (#45=(#20# . #46=($)) NIL #41# ELT) ((#42# . #46#) NIL #43# ELT) #8#) (|represents| #47=(($ #48=(|Vector| |#2|)) NIL T ELT) (($ #48# #12#) NIL T ELT)) (|reducedSystem| ((#49=(|Matrix| #20#) . #50=(#51=(|Matrix| $))) NIL #52=(|has| |#2| (|LinearlyExplicitRingOver| #20#)) ELT) ((#53=(|Record| (|:| |mat| #49#) (|:| |vec| (|Vector| #20#))) . #54=(#51# #12#)) NIL #52# ELT) ((#55=(|Record| (|:| |mat| #11#) (|:| |vec| #48#)) . #54#) NIL T ELT) ((#11# . #50#) NIL T ELT)) (|reduce| ((|#2| #56=(|Mapping| |#2| |#2| |#2|) $) NIL T ELT) ((|#2| #56# $ |#2|) NIL T ELT) ((|#2| #56# $ |#2| |#2|) NIL #57=(|has| |#2| (|BasicType|)) ELT)) (|recip| (#27# NIL T ELT)) (|rank| #58=(#59=(#60=(|NonNegativeInteger|) $) NIL #7# ELT) ((#32#) 42 T ELT)) (|qelt| (#61=(|#2| $ #20# #20#) NIL T ELT)) (|powerAssociative?| #38#) (|plenaryPower| #31#) (|opposite?| #1#) (|one?| #3#) (|nullity| #58#) (|nullSpace| (((|List| #19#) $) NIL #7# ELT)) (|nrows| #62=(#59# NIL T ELT)) (|noncommutativeJordanAlgebra?| #38#) (|ncols| #62#) (|minordet| #63=(#9# NIL (|has| |#2| (ATTRIBUTE (|commutative| "*"))) ELT)) (|minRowIndex| #64=(#45# NIL T ELT)) (|minColIndex| #64#) (|members| ((#65=(|List| |#2|) $) NIL T ELT)) (|member?| ((#2# |#2| $) NIL #57# ELT)) (|maxRowIndex| #64#) (|maxColIndex| #64#) (|matrix| (($ #66=(|List| #65#)) NIL T ELT)) (|map| (($ #56# $ $) NIL T ELT) (($ #67=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|listOfLists| ((#66# $) NIL T ELT)) (|lieAlgebra?| #38#) (|lieAdmissible?| #38#) (|leftUnits| #21#) (|leftUnit| #4#) (|leftTraceMatrix| #22# #23#) (|leftTrace| #8#) (|leftRegularRepresentation| #24# #25#) (|leftReducedSystem| ((#49# #12#) NIL #52# ELT) ((#53# . #68=(#12# $)) NIL #52# ELT) ((#55# . #68#) NIL T ELT) #23#) (|leftRecip| #26#) (|leftRankPolynomial| #28#) (|leftPower| #31#) (|leftNorm| #8#) (|leftMinimalPolynomial| #33#) (|leftDiscriminant| #35# #36#) (|leftCharacteristicPolynomial| #37#) (|leftAlternative?| #38#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #38#) (|jordanAdmissible?| #38#) (|jacobiIdentity?| #38#) (|inverse| (#27# NIL #30# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| #38#) (|find| ((#44# #69=(|Mapping| #2# |#2|) $) NIL T ELT)) (|exquo| ((#5# $ |#2|) NIL #7# ELT)) (|every?| #70=((#2# #69# $) NIL T ELT)) (|eval| (($ $ (|List| #71=(|Equation| |#2|))) NIL #72=(AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ELT) (($ $ #71#) NIL #72# ELT) (($ $ |#2| |#2|) NIL #72# ELT) (($ $ #65# #65#) NIL #72# ELT)) (|eq?| #1#) (|empty?| #3#) (|empty| (#16# NIL T ELT)) (|elt| ((|#2| $ #20# #20# |#2|) NIL T ELT) (#61# 27 T ELT) ((|#2| $ #20#) NIL T ELT)) (|differentiate| #73=(($ $ #67# #60#) NIL T ELT) #74=(($ $ #67#) NIL T ELT) #75=(#17# NIL #76=(|has| |#2| (|DifferentialSpace|)) ELT) #77=(#78=($ $ #60#) NIL #76# ELT) #79=(($ $ #80=(|Symbol|)) NIL #81=(|has| |#2| (|PartialDifferentialSpace| #80#)) ELT) #82=(($ $ #83=(|List| #80#)) NIL #81# ELT) #84=(($ $ #80# #60#) NIL #81# ELT) #85=(($ $ #83# (|List| #60#)) NIL #81# ELT)) (|diagonalProduct| #8#) (|diagonalMatrix| (($ #65#) NIL T ELT)) (|diagonal?| #3#) (|diagonal| ((#19# $) NIL T ELT)) (|determinant| #63#) (|count| ((#60# #69# $) NIL T ELT) ((#60# |#2| $) NIL #57# ELT)) (|copy| #86=(#17# NIL T ELT)) (|coordinates| #23# #87=((#48# $) NIL T ELT) ((#11# #12# #12#) NIL T ELT) ((#48# $ #12#) 30 T ELT)) (|convert| #47# #87#) (|conditionsForIdempotents| ((#88=(|List| #29#)) NIL T ELT) ((#88# #12#) NIL T ELT)) (|commutator| #89=(($ $ $) NIL T ELT)) (|commutative?| #38#) (|column| #18#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) (($ #42#) NIL #43# ELT) #14# #24#) (|characteristic| ((#60#) NIL T CONST)) (|before?| #1#) (|basis| (#13# 40 T ELT)) (|associatorDependence| (((|List| #48#)) NIL #7# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #38#) (|apply| (($ #11# $) NIL T ELT)) (|any?| #70#) (|antisymmetric?| #3#) (|antiCommutator| #89#) (|antiCommutative?| #38#) (|antiAssociative?| #38#) (|annihilate?| #1#) (|alternative?| #38#) (|Zero| #15#) (|One| #15#) (D #73# #74# #75# #77# #79# #82# #84# #85#) (= #1#) (/ (#90=($ $ |#2|) NIL #30# ELT)) (- #86# #89#) (+ #89#) (** #31# (#78# NIL T ELT) (($ $ #20#) NIL #30# ELT)) (* (($ #32# $) NIL T ELT) (($ #60# $) NIL T ELT) (($ #20# . #91=($)) NIL T ELT) #89# (#90# NIL T ELT) (($ |#2| . #91#) NIL T ELT) ((#19# $ #19#) NIL T ELT) ((#19# #19# $) NIL T ELT)) (|#| #62#)) 
(((|LieSquareMatrix| |#1| |#2|) (|Join| (|SquareMatrixCategory| |#1| |#2| #1=(|DirectProduct| |#1| |#2|) #1#) (|CoercibleTo| (|Matrix| |#2|)) (|FramedNonAssociativeAlgebra| |#2|)) (|PositiveInteger|) (|CommutativeRing|)) (T |LieSquareMatrix|)) 
NIL 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elements| (((|List| (|SpadAst|)) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|ConstructAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |elements| ((|List| (|SpadAst|)) $))))) (T |ConstructAst|)) 
((|elements| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|ConstructAst|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| ((#4=(|List| |#1|) $) NIL T ELT)) (|right| (#5=($ $) 62 T ELT)) (|retractable?| ((#3# $) NIL T ELT)) (|retractIfCan| (((|Union| |#1| #6="failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|min| #7=(($ $ $) NIL T ELT)) (|max| #7#) (|lyndonIfCan| (((|Union| $ #6#) #8=(|OrderedFreeMonoid| |#1|)) 28 T ELT)) (|lyndon?| ((#3# #8#) 18 T ELT)) (|lyndon| (($ #8#) 29 T ELT)) (|lexico| (#2# 36 T ELT)) (|length| ((#9=(|PositiveInteger|) $) 43 T ELT)) (|left| (#5# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|factor| ((#10=(|List| $) #8#) 20 T ELT)) (|coerce| (((|OutputForm|) $) 51 T ELT) (($ |#1|) 40 T ELT) ((#8# $) 47 T ELT) (((|Magma| |#1|) $) 52 T ELT)) (|before?| #1#) (|LyndonWordsList1| (((|OneDimensionalArray| #10#) #4# #9#) 67 T ELT)) (|LyndonWordsList| ((#10# #4# #9#) 70 T ELT)) (>= #1#) (> #1#) (= (#2# 63 T ELT)) (<= #1#) (< (#2# 46 T ELT))) 
(((|LyndonWord| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |retractable?| (#2=(|Boolean|) $)) (SIGNATURE |left| #3=($ $)) (SIGNATURE |right| #3#) (SIGNATURE |length| (#4=(|PositiveInteger|) $)) (SIGNATURE |lexico| (#2# $ $)) (SIGNATURE |coerce| (#5=(|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |coerce| ((|Magma| |#1|) $)) (SIGNATURE |factor| (#6=(|List| $) #5#)) (SIGNATURE |lyndon?| (#2# #5#)) (SIGNATURE |lyndon| ($ #5#)) (SIGNATURE |lyndonIfCan| ((|Union| $ "failed") #5#)) (SIGNATURE |varList| (#7=(|List| |#1|) $)) (SIGNATURE |LyndonWordsList1| ((|OneDimensionalArray| #6#) #7# #4#)) (SIGNATURE |LyndonWordsList| (#6# #7# #4#)))) #1#) (T |LyndonWord|)) 
((|retractable?| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|LyndonWord| *3)) #5=(|ofCategory| *3 #6=(|OrderedSet|)))) (|left| #7=(*1 *1 *1) #8=(AND (|isDomain| *1 (|LyndonWord| *2)) (|ofCategory| *2 #6#))) (|right| #7# #8#) (|length| #1# (AND (|isDomain| *2 #9=(|PositiveInteger|)) #4# #5#)) (|lexico| (*1 *2 *1 *1) #2#) (|coerce| #1# (AND #10=(|isDomain| *2 (|OrderedFreeMonoid| *3)) #4# #5#)) (|coerce| #1# (AND (|isDomain| *2 (|Magma| *3)) #4# #5#)) (|factor| #11=(*1 *2 *3) (AND #12=(|isDomain| *3 (|OrderedFreeMonoid| *4)) #13=(|ofCategory| *4 #6#) (|isDomain| *2 (|List| #14=(|LyndonWord| *4))) #15=(|isDomain| *1 #14#))) (|lyndon?| #11# (AND #12# #13# #3# #15#)) (|lyndon| #16=(*1 *1 *2) (AND #10# #5# #4#)) (|lyndonIfCan| #16# (|partial| AND #10# #5# #4#)) (|varList| #1# (AND (|isDomain| *2 (|List| *3)) #4# #5#)) (|LyndonWordsList1| #17=(*1 *2 *3 *4) (AND #18=(|isDomain| *3 (|List| *5)) #19=(|isDomain| *4 #9#) #20=(|ofCategory| *5 #6#) (|isDomain| *2 (|OneDimensionalArray| #21=(|List| #22=(|LyndonWord| *5)))) #23=(|isDomain| *1 #22#))) (|LyndonWordsList| #17# (AND #18# #19# #20# (|isDomain| *2 #21#) #23#))) 
((|value| (#1=(|#2| $) 96 T ELT)) (|tail| (#2=($ $) 117 T ELT)) (|size?| (#3=(#4=(|Boolean|) $ #5=(|NonNegativeInteger|)) 35 T ELT)) (|rest| (#2# 105 T ELT) (#6=($ $ #5#) 108 T ELT)) (|possiblyInfinite?| (#7=(#4# $) 118 T ELT)) (|nodes| (#8=((|List| $) $) 92 T ELT)) (|node?| (#9=(#4# $ $) 88 T ELT)) (|more?| (#3# 33 T ELT)) (|minIndex| (#10=(#11=(|Integer|) $) 62 T ELT)) (|maxIndex| (#10# 61 T ELT)) (|less?| (#3# 31 T ELT)) (|leaf?| (#7# 94 T ELT)) (|last| (#1# 109 T ELT) (#6# 113 T ELT)) (|insert| (($ $ $ #11#) 79 T ELT) (($ |#2| $ #11#) 78 T ELT)) (|indices| (((|List| #11#) $) 60 T ELT)) (|index?| ((#4# #11# $) 55 T ELT)) (|first| (#1# NIL T ELT) (#6# 104 T ELT)) (|extend| (#12=($ $ #11#) 121 T ELT)) (|explicitlyFinite?| (#7# 120 T ELT)) (|entries| ((#13=(|List| |#2|) $) 42 T ELT)) (|elt| ((|#2| $ "value") NIL T ELT) ((|#2| $ "first") 103 T ELT) (($ $ "rest") 107 T ELT) ((|#2| $ "last") 116 T ELT) (#14=($ $ (|UniversalSegment| #11#)) 75 T ELT) ((|#2| $ #11#) 53 T ELT) ((|#2| $ #11# |#2|) 54 T ELT)) (|distance| ((#11# $ $) 87 T ELT)) (|delete| (#14# 74 T ELT) (#12# 68 T ELT)) (|cyclic?| (#7# 83 T ELT)) (|cycleTail| (#2# 101 T ELT)) (|cycleLength| ((#5# $) 100 T ELT)) (|cycleEntry| (#2# 99 T ELT)) (|construct| (($ #13#) 49 T ELT)) (|complete| (#2# 122 T ELT)) (|children| (#8# 86 T ELT)) (|child?| (#9# 85 T ELT)) (= (#9# 20 T ELT))) 
(((|LazyStreamAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |complete| #3=(|#1| |#1|)) (SIGNATURE |extend| #4=(|#1| |#1| #5=(|Integer|))) (SIGNATURE |size?| #6=(#2# |#1| #7=(|NonNegativeInteger|))) (SIGNATURE |more?| #6#) (SIGNATURE |less?| #6#) (SIGNATURE |possiblyInfinite?| #8=(#2# |#1|)) (SIGNATURE |explicitlyFinite?| #8#) (SIGNATURE |elt| (|#2| |#1| #5# |#2|)) (SIGNATURE |elt| (|#2| |#1| #5#)) (SIGNATURE |entries| (#9=(|List| |#2|) |#1|)) (SIGNATURE |index?| (#2# #5# |#1|)) (SIGNATURE |indices| ((|List| #5#) |#1|)) (SIGNATURE |maxIndex| #10=(#5# |#1|)) (SIGNATURE |minIndex| #10#) (SIGNATURE |construct| (|#1| #9#)) (SIGNATURE |elt| #11=(|#1| |#1| (|UniversalSegment| #5#))) (SIGNATURE |delete| #4#) (SIGNATURE |delete| #11#) (SIGNATURE |insert| (|#1| |#2| |#1| #5#)) (SIGNATURE |insert| (|#1| |#1| |#1| #5#)) (SIGNATURE |cycleTail| #3#) (SIGNATURE |cycleLength| (#7# |#1|)) (SIGNATURE |cycleEntry| #3#) (SIGNATURE |tail| #3#) (SIGNATURE |last| #12=(|#1| |#1| #7#)) (SIGNATURE |elt| (|#2| |#1| "last")) (SIGNATURE |last| #13=(|#2| |#1|)) (SIGNATURE |rest| #12#) (SIGNATURE |elt| (|#1| |#1| "rest")) (SIGNATURE |rest| #3#) (SIGNATURE |first| #12#) (SIGNATURE |elt| (|#2| |#1| "first")) (SIGNATURE |first| #13#) (SIGNATURE |node?| #1#) (SIGNATURE |child?| #1#) (SIGNATURE |distance| (#5# |#1| |#1|)) (SIGNATURE |cyclic?| #8#) (SIGNATURE |elt| (|#2| |#1| "value")) (SIGNATURE |value| #13#) (SIGNATURE |leaf?| #8#) (SIGNATURE |nodes| #14=((|List| |#1|) |#1|)) (SIGNATURE |children| #14#)) (|LazyStreamAggregate| |#2|) (|Type|)) (T |LazyStreamAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|third| ((|#1| . #3=($)) 62 T ELT)) (|tail| (#4=($ $) 64 T ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) 99 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|split!| (($ $ (|Integer|)) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|size?| (#6=(#7=(|Boolean|) $ (|NonNegativeInteger|)) 82 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setrest!| (#8=($ $ $) 53 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #9="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #10="first" |#1|) 54 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ #11="rest" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #12="last" |#1|) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #13=(|UniversalSegment| #5#) |#1|) 115 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #5# |#1|) 88 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #14=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 103 T ELT)) (|second| ((|#1| . #3#) 63 T ELT)) (|sample| (#15=($) 6 T CONST)) (|rst| (($ $) 123 T ELT)) (|rest| (#4# 70 T ELT) (#16=($ $ #17=(|NonNegativeInteger|)) 68 T ELT)) (|removeDuplicates| (($ $) 101 (AND (|has| |#1| . #18=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 102 (AND (|has| |#1| . #18#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| (|Boolean|) |#1|) $) 104 T ELT)) (|qsetelt!| ((|#1| $ #5# |#1|) 87 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #5#) 89 T ELT)) (|possiblyInfinite?| (#19=(#7# $) 85 T ELT)) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) 122 T ELT)) (|nodes| (#20=(#14# $) 45 T ELT)) (|node?| (#21=(#22=(|Boolean|) $ $) 37 (|has| |#1| . #23=((|BasicType|))) ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 107 T ELT)) (|more?| (#6# 83 T ELT)) (|minIndex| ((#5# . #24=($)) 97 (|has| #5# . #25=((|OrderedSet|))) ELT)) (|maxIndex| ((#5# . #24#) 96 (|has| #5# . #25#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 110 T ELT)) (|less?| (#6# 84 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (#26=(#22# $) 44 T ELT)) (|lazyEvaluate| (($ $) 125 T ELT)) (|lazy?| (((|Boolean|) $) 126 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #27=((|SetCategory|))) ELT)) (|last| ((|#1| . #3#) 67 T ELT) (#16# 65 T ELT)) (|insert| (($ $ $ #5#) 114 T ELT) (($ |#1| $ #5#) 113 T ELT)) (|indices| (((|List| #5#) $) 94 T ELT)) (|index?| ((#28=(|Boolean|) #5# $) 93 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #27#) ELT)) (|frst| ((|#1| $) 124 T ELT)) (|first| ((|#1| . #3#) 73 T ELT) (#16# 71 T ELT)) (|fill!| (($ $ |#1|) 98 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|extend| (($ $ (|Integer|)) 121 T ELT)) (|explicitlyFinite?| (#19# 86 T ELT)) (|explicitlyEmpty?| (((|Boolean|) $) 127 T ELT)) (|explicitEntries?| (((|Boolean|) $) 128 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #27#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #27#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #27#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #27#)) ELT)) (|eq?| ((#29=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#28# |#1| $) 95 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 92 T ELT)) (|empty?| ((#29# $) 7 T ELT)) (|empty| (#15# 8 T ELT)) (|elt| ((|#1| $ #9#) 42 T ELT) ((|#1| $ #10#) 72 T ELT) (($ $ #11#) 69 T ELT) ((|#1| $ #12#) 66 T ELT) (($ $ #13#) 106 T ELT) ((|#1| $ #5#) 91 T ELT) ((|#1| $ #5# |#1|) 90 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|delete| (($ $ #13#) 112 T ELT) (($ $ #5#) 111 T ELT)) (|cyclic?| (#26# 41 T ELT)) (|cycleTail| (#4# 59 T ELT)) (|cycleSplit!| (#4# 56 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|cycleLength| ((#17# $) 60 T ELT)) (|cycleEntry| (#4# 61 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#30=(|InputForm|) $) 100 (|has| |#1| (|ConvertibleTo| #30#)) ELT)) (|construct| (($ (|List| |#1|)) 105 T ELT)) (|concat!| (#8# 58 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ |#1|) 57 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|concat| (#8# 75 T ELT) (($ |#1| $) 74 T ELT) (($ (|List| $)) 109 T ELT) (($ $ |#1|) 108 T ELT)) (|complete| (($ $) 120 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (#20# 46 T ELT)) (|child?| (#21# 38 (|has| |#1| . #23#) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|LazyStreamAggregate| |#1|) (|Category|) (|Type|)) (T |LazyStreamAggregate|)) 
((|remove| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|select| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|explicitEntries?| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|explicitlyEmpty?| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|lazy?| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|lazyEvaluate| (*1 *1 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|frst| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|rst| (*1 *1 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|numberOfComputedEntries| (*1 *2 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|extend| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LazyStreamAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|complete| (*1 *1 *1) (AND (|ofCategory| *1 (|LazyStreamAggregate| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|StreamAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |remove| ($ (|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|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| |#1|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|StreamAggregate| |#1|) . T) ((|Type|) . T) ((|UnaryRecursiveAggregate| |#1|) . T)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|head| (((|HeadAst|) $) 15 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|body| (((|SpadAst|) $) 17 T ELT)) (|before?| #1#) (= #1#)) 
(((|MacroAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |head| ((|HeadAst|) $)) (SIGNATURE |body| ((|SpadAst|) $))))) (T |MacroAst|)) 
((|head| #1=(*1 *2 *1) (AND (|isDomain| *2 (|HeadAst|)) #2=(|isDomain| *1 (|MacroAst|)))) (|body| #1# (AND (|isDomain| *2 (|SpadAst|)) #2#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 15 T ELT)) (|right| (#4=($ $) 19 T ELT)) (|retractable?| ((#3# $) 20 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 23 T ELT)) (|retract| (#5=(|#1| $) 21 T ELT)) (|rest| (#4# 37 T ELT)) (|mirror| (#4# 25 T ELT)) (|min| #6=(#7=($ $ $) NIL T ELT)) (|max| #6#) (|lexico| (#2# 46 T ELT)) (|length| (((|PositiveInteger|) $) 40 T ELT)) (|left| (#4# 18 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#5# 36 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT) (($ |#1|) 24 T ELT) (((|OrderedFreeMonoid| |#1|) $) 28 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= (#2# 13 T ELT)) (<= #1#) (< (#2# 44 T ELT)) (* (#7# 35 T ELT))) 
(((|Magma| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |first| (|#1| $)) (SIGNATURE |left| #2=($ $)) (SIGNATURE |length| ((|PositiveInteger|) $)) (SIGNATURE |lexico| (#3=(|Boolean|) $ $)) (SIGNATURE |mirror| #2#) (SIGNATURE |rest| #2#) (SIGNATURE |retractable?| (#3# $)) (SIGNATURE |right| #2#) (SIGNATURE |varList| ((|List| |#1|) $)))) #1#) (T |Magma|)) 
((* (*1 *1 *1 *1) #1=(AND (|isDomain| *1 (|Magma| *2)) (|ofCategory| *2 #2=(|OrderedSet|)))) (|coerce| #3=(*1 *2 *1) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) #4=(|isDomain| *1 (|Magma| *3)) #5=(|ofCategory| *3 #2#))) (|first| #3# #1#) (|left| #6=(*1 *1 *1) #1#) (|length| #3# (AND (|isDomain| *2 (|PositiveInteger|)) #4# #5#)) (|lexico| (*1 *2 *1 *1) #7=(AND (|isDomain| *2 (|Boolean|)) #4# #5#)) (|mirror| #6# #1#) (|rest| #6# #1#) (|retractable?| #3# #7#) (|right| #6# #1#) (|varList| #3# (AND (|isDomain| *2 (|List| *3)) #4# #5#))) 
((|recur| ((|#1| (|Mapping| |#1| #1=(|NonNegativeInteger|) |#1|) #1# |#1|) 11 T ELT)) (|iter| ((|#1| (|Mapping| |#1| |#1|) #1# |#1|) 9 T ELT))) 
(((|MappingPackageInternalHacks1| |#1|) (CATEGORY |package| (SIGNATURE |iter| (|#1| (|Mapping| |#1| |#1|) #1=(|NonNegativeInteger|) |#1|)) (SIGNATURE |recur| (|#1| (|Mapping| |#1| #1# |#1|) #1# |#1|))) (|SetCategory|)) (T |MappingPackageInternalHacks1|)) 
((|recur| #1=(*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 #2=(|NonNegativeInteger|) *2)) #3=(|isDomain| *4 #2#) #4=(|ofCategory| *2 (|SetCategory|)) #5=(|isDomain| *1 (|MappingPackageInternalHacks1| *2)))) (|iter| #1# (AND (|isDomain| *3 (|Mapping| *2 *2)) #3# #4# #5#))) 
((|arg2| ((|#2| |#1| |#2|) 9 T ELT)) (|arg1| ((|#1| |#1| |#2|) 8 T ELT))) 
(((|MappingPackageInternalHacks2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |arg1| (|#1| |#1| |#2|)) (SIGNATURE |arg2| (|#2| |#1| |#2|))) #1=(|SetCategory|) #1#) (T |MappingPackageInternalHacks2|)) 
((|arg2| (*1 *2 *3 *2) (AND (|isDomain| *1 (|MappingPackageInternalHacks2| *3 *2)) #1=(|ofCategory| *3 #2=(|SetCategory|)) #3=(|ofCategory| *2 #2#))) (|arg1| (*1 *2 *2 *3) (AND (|isDomain| *1 (|MappingPackageInternalHacks2| *2 *3)) #3# #1#))) 
((|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) 11 T ELT))) 
(((|MappingPackageInternalHacks3| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |comp| (|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|))) #1=(|SetCategory|) #1# #1#) (T |MappingPackageInternalHacks3|)) 
((|comp| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *2 *6)) (|isDomain| *4 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 #1#) (|ofCategory| *2 #1#) (|isDomain| *1 (|MappingPackageInternalHacks3| *5 *6 *2))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|target| (#2=(#3=(|TypeAst|) $) 22 T ELT)) (|source| ((#4=(|List| #3#) $) 20 T ELT)) (|mappingAst| (($ #4# #3#) 15 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 30 T ELT) (($ #5=(|Syntax|)) NIL T ELT) ((#5# $) NIL T ELT) (#2# 23 T ELT) (($ (|Signature|)) 11 T ELT)) (|before?| #1#) (= #1#)) 
(((|MappingAst|) (|Join| (|SpadSyntaxCategory|) (|CoercibleTo| #1=(|TypeAst|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Signature|))) (SIGNATURE |mappingAst| ($ #2=(|List| #1#) #1#)) (SIGNATURE |source| (#2# $)) (SIGNATURE |target| (#1# $))))) (T |MappingAst|)) 
((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Signature|)) #1=(|isDomain| *1 (|MappingAst|)))) (|mappingAst| (*1 *1 *2 *3) (AND #2=(|isDomain| *2 (|List| #3=(|TypeAst|))) (|isDomain| *3 #3#) #1#)) (|source| #4=(*1 *2 *1) (AND #2# #1#)) (|target| #4# (AND (|isDomain| *2 #3#) #1#))) 
((|recur| ((#1=(|Mapping| |#1| #2=(|NonNegativeInteger|) |#1|) #1#) 26 T ELT)) (|nullary| (#3=((|Mapping| |#1|) |#1|) 8 T ELT)) (|id| ((|#1| |#1|) 19 T ELT)) (|fixedPoint| ((#4=(|List| |#1|) (|Mapping| #4# #4#) (|Integer|)) 18 T ELT) ((|#1| #5=(|Mapping| |#1| |#1|)) 11 T ELT)) (|coerce| (#3# 9 T ELT)) (** ((#5# #5# #2#) 23 T ELT))) 
(((|MappingPackage1| |#1|) (CATEGORY |package| (SIGNATURE |nullary| #1=((|Mapping| |#1|) |#1|)) (SIGNATURE |coerce| #1#) (SIGNATURE |fixedPoint| (|#1| #2=(|Mapping| |#1| |#1|))) (SIGNATURE |fixedPoint| (#3=(|List| |#1|) (|Mapping| #3# #3#) (|Integer|))) (SIGNATURE |id| (|#1| |#1|)) (SIGNATURE ** (#2# #2# #4=(|NonNegativeInteger|))) (SIGNATURE |recur| (#5=(|Mapping| |#1| #4# |#1|) #5#))) (|SetCategory|)) (T |MappingPackage1|)) 
((|recur| #1=(*1 *2 *2) (AND (|isDomain| *2 (|Mapping| *3 #2=(|NonNegativeInteger|) *3)) #3=(|ofCategory| *3 #4=(|SetCategory|)) #5=(|isDomain| *1 (|MappingPackage1| *3)))) (** (*1 *2 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 #2#) (|ofCategory| *4 #4#) (|isDomain| *1 (|MappingPackage1| *4)))) (|id| #1# (AND #6=(|isDomain| *1 (|MappingPackage1| *2)) #7=(|ofCategory| *2 #4#))) (|fixedPoint| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| #8=(|List| *5) #8#)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 #8#) (|isDomain| *1 (|MappingPackage1| *5)) (|ofCategory| *5 #4#))) (|fixedPoint| #9=(*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *2 *2)) #6# #7#)) (|coerce| #9# #10=(AND (|isDomain| *2 (|Mapping| *3)) #5# #3#)) (|nullary| #9# #10#)) 
((|diag| ((#1=(|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) 16 T ELT)) (|curry| ((#2=(|Mapping| |#2|) #1# |#1|) 13 T ELT)) (|constant| ((#1# #2#) 14 T ELT)) (|const| ((#1# |#2|) 11 T ELT))) 
(((|MappingPackage2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |const| (#1=(|Mapping| |#2| |#1|) |#2|)) (SIGNATURE |curry| (#2=(|Mapping| |#2|) #1# |#1|)) (SIGNATURE |constant| (#1# #2#)) (SIGNATURE |diag| (#1# (|Mapping| |#2| |#1| |#1|)))) #3=(|SetCategory|) #3#) (T |MappingPackage2|)) 
((|diag| #1=(*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 *4 *4)) #2=(|ofCategory| *4 #3=(|SetCategory|)) #4=(|ofCategory| *5 #3#) #5=(|isDomain| *2 #6=(|Mapping| *5 *4)) #7=(|isDomain| *1 (|MappingPackage2| *4 *5)))) (|constant| #1# (AND (|isDomain| *3 #8=(|Mapping| *5)) #4# #5# #7# #2#)) (|curry| (*1 *2 *3 *4) (AND (|isDomain| *3 #6#) #2# #4# (|isDomain| *2 #8#) #7#)) (|const| #1# (AND (|isDomain| *2 (|Mapping| *3 *4)) (|isDomain| *1 (|MappingPackage2| *4 *3)) #2# (|ofCategory| *3 #3#)))) 
((|twist| (((|Mapping| |#3| |#2| |#1|) #1=(|Mapping| |#3| |#1| |#2|)) 17 T ELT)) (|curryRight| ((#2=(|Mapping| |#3| |#1|) #1# |#2|) 11 T ELT)) (|curryLeft| ((#3=(|Mapping| |#3| |#2|) #1# |#1|) 13 T ELT)) (|constantRight| ((#1# #2#) 14 T ELT)) (|constantLeft| ((#1# #3#) 15 T ELT)) (* ((#2# #3# (|Mapping| |#2| |#1|)) 21 T ELT))) 
(((|MappingPackage3| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |curryRight| (#1=(|Mapping| |#3| |#1|) #2=(|Mapping| |#3| |#1| |#2|) |#2|)) (SIGNATURE |curryLeft| (#3=(|Mapping| |#3| |#2|) #2# |#1|)) (SIGNATURE |constantRight| (#2# #1#)) (SIGNATURE |constantLeft| (#2# #3#)) (SIGNATURE |twist| ((|Mapping| |#3| |#2| |#1|) #2#)) (SIGNATURE * (#1# #3# (|Mapping| |#2| |#1|)))) #4=(|SetCategory|) #4# #4#) (T |MappingPackage3|)) 
((* #1=(*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *6)) (|isDomain| *4 #2=(|Mapping| *6 *5)) #3=(|ofCategory| *5 #4=(|SetCategory|)) #5=(|ofCategory| *6 #4#) (|ofCategory| *7 #4#) (|isDomain| *2 (|Mapping| *7 *5)) (|isDomain| *1 (|MappingPackage3| *5 *6 *7)))) (|twist| #6=(*1 *2 *3) (AND #7=(|isDomain| *3 #8=(|Mapping| *6 *4 *5)) #9=(|ofCategory| *4 #4#) #3# #5# (|isDomain| *2 #10=(|Mapping| *6 *5 *4)) #11=(|isDomain| *1 (|MappingPackage3| *4 *5 *6)))) (|constantLeft| #6# (AND (|isDomain| *3 #2#) #3# #5# #12=(|isDomain| *2 #8#) #11# #9#)) (|constantRight| #6# (AND (|isDomain| *3 (|Mapping| *6 *4)) #9# #5# #12# #11# #3#)) (|curryLeft| #1# (AND #7# #9# #3# #5# #13=(|isDomain| *2 #2#) #11#)) (|curryRight| #1# (AND (|isDomain| *3 #10#) #3# #9# #5# #13# (|isDomain| *1 (|MappingPackage3| *5 *4 *6))))) 
((|zero| (($ #1=(|NonNegativeInteger|) #1#) 42 T ELT)) (|vertConcat| (#2=($ $ $) 73 T ELT)) (|transpose| (($ |#3|) 68 T ELT) (#3=($ $) 69 T ELT)) (|symmetric?| (#4=((|Boolean|) $) 36 T ELT)) (|swapRows!| (#5=($ $ #6=(|Integer|) #6#) 84 T ELT)) (|swapColumns!| (#5# 85 T ELT)) (|subMatrix| (($ $ #6# #6# #6# #6#) 90 T ELT)) (|squareTop| (#3# 71 T ELT)) (|square?| (#4# 15 T ELT)) (|setsubMatrix!| (($ $ #6# #6# $) 91 T ELT)) (|setelt| #7=((|#2| $ #6# #6# |#2|) NIL T ELT) (($ $ #8=(|List| #6#) #8# $) 89 T ELT)) (|scalarMatrix| (($ #1# |#2|) 55 T ELT)) (|matrix| (($ #9=(|List| #10=(|List| |#2|))) 51 T ELT) (($ #1# #1# (|Mapping| |#2| #6# #6#)) 53 T ELT)) (|listOfLists| ((#9# $) 80 T ELT)) (|horizConcat| (#2# 72 T ELT)) (|exquo| (((|Union| $ "failed") $ |#2|) 122 T ELT)) (|elt| ((|#2| $ #6# #6#) NIL T ELT) #7# (($ $ #8# #8#) 88 T ELT)) (|diagonalMatrix| (($ #10#) 56 T ELT) (($ (|List| $)) 58 T ELT)) (|diagonal?| (#4# 28 T ELT)) (|coerce| (($ |#4|) 63 T ELT) (((|OutputForm|) $) NIL T ELT)) (|antisymmetric?| (#4# 38 T ELT)) (/ (#11=($ $ |#2|) 124 T ELT)) (- (#2# 95 T ELT) (#3# 98 T ELT)) (+ (#2# 93 T ELT)) (** (($ $ #1#) 111 T ELT) (($ $ #6#) 128 T ELT)) (* (#2# 104 T ELT) (($ |#2| $) 100 T ELT) (#11# 101 T ELT) (($ #6# $) 103 T ELT) ((|#4| $ |#4|) 115 T ELT) ((|#3| |#3| $) 119 T ELT))) 
(((|MatrixCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE ** (|#1| |#1| #1=(|Integer|))) (SIGNATURE / #2=(|#1| |#1| |#2|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#2|)) (SIGNATURE ** (|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE * (|#3| |#3| |#1|)) (SIGNATURE * (|#4| |#1| |#4|)) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE * #2#) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * #4=(|#1| |#1| |#1|)) (SIGNATURE - #5=(|#1| |#1|)) (SIGNATURE - #4#) (SIGNATURE + #4#) (SIGNATURE |setsubMatrix!| (|#1| |#1| #1# #1# |#1|)) (SIGNATURE |subMatrix| (|#1| |#1| #1# #1# #1# #1#)) (SIGNATURE |swapColumns!| #6=(|#1| |#1| #1# #1#)) (SIGNATURE |swapRows!| #6#) (SIGNATURE |setelt| (|#1| |#1| #7=(|List| #1#) #7# |#1|)) (SIGNATURE |elt| (|#1| |#1| #7# #7#)) (SIGNATURE |listOfLists| (#8=(|List| #9=(|List| |#2|)) |#1|)) (SIGNATURE |vertConcat| #4#) (SIGNATURE |horizConcat| #4#) (SIGNATURE |squareTop| #5#) (SIGNATURE |transpose| #5#) (SIGNATURE |transpose| (|#1| |#3|)) (SIGNATURE |coerce| (|#1| |#4|)) (SIGNATURE |diagonalMatrix| (|#1| (|List| |#1|))) (SIGNATURE |diagonalMatrix| (|#1| #9#)) (SIGNATURE |scalarMatrix| (|#1| #3# |#2|)) (SIGNATURE |matrix| (|#1| #3# #3# (|Mapping| |#2| #1# #1#))) (SIGNATURE |matrix| (|#1| #8#)) (SIGNATURE |zero| (|#1| #3# #3#)) (SIGNATURE |antisymmetric?| #10=((|Boolean|) |#1|)) (SIGNATURE |symmetric?| #10#) (SIGNATURE |diagonal?| #10#) (SIGNATURE |square?| #10#) (SIGNATURE |setelt| #11=(|#2| |#1| #1# #1# |#2|)) (SIGNATURE |elt| #11#) (SIGNATURE |elt| (|#2| |#1| #1# #1#))) (|MatrixCategory| |#2| |#3| |#4|) (|Ring|) #12=(|FiniteLinearAggregate| |#2|) #12#) (T |MatrixCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) 108 T ELT)) (|vertConcat| (($ $ $) 97 T ELT)) (|transpose| (($ |#2|) 101 T ELT) (($ $) 100 T ELT)) (|symmetric?| (((|Boolean|) $) 110 T ELT)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) 93 T ELT)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) 92 T ELT)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 91 T ELT)) (|squareTop| (($ $) 99 T ELT)) (|square?| (((|Boolean|) $) 112 T ELT)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) 90 T ELT)) (|setelt| ((|#1| $ #3=(|Integer|) #3# |#1|) 52 T ELT) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) 94 T ELT)) (|setRow!| (($ $ #3# |#2|) 50 T ELT)) (|setColumn!| (($ $ #3# |#3|) 49 T ELT)) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) 105 T ELT)) (|sample| (#4=($) 6 T CONST)) (|rowEchelon| (($ $) 77 (|has| |#1| (|EuclideanDomain|)) ELT)) (|row| ((|#2| $ #3#) 54 T ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 39 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 38 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 34 (|has| |#1| . #5=((|BasicType|))) ELT)) (|rank| (((|NonNegativeInteger|) $) 76 (|has| |#1| (|IntegralDomain|)) ELT)) (|qsetelt!| ((|#1| $ #3# #3# |#1|) 51 T ELT)) (|qelt| ((|#1| . #6=($ #3# #3#)) 56 T ELT)) (|nullity| (((|NonNegativeInteger|) $) 75 (|has| |#1| (|IntegralDomain|)) ELT)) (|nullSpace| (((|List| |#3|) $) 74 (|has| |#1| (|IntegralDomain|)) ELT)) (|nrows| (#7=(#8=(|NonNegativeInteger|) $) 59 T ELT)) (|new| (($ #8# #8# |#1|) 65 T ELT)) (|ncols| (#7# 58 T ELT)) (|minordet| ((|#1| $) 72 (|has| |#1| (ATTRIBUTE (|commutative| #9="*"))) ELT)) (|minRowIndex| (#10=(#3# $) 63 T ELT)) (|minColIndex| (#10# 61 T ELT)) (|members| (((|List| |#1|) $) 40 T ELT)) (|member?| ((#11=(|Boolean|) |#1| $) 35 (|has| |#1| . #5#) ELT)) (|maxRowIndex| (#10# 62 T ELT)) (|maxColIndex| (#10# 60 T ELT)) (|matrix| (($ (|List| (|List| |#1|))) 107 T ELT) (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) 106 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 66 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 48 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) 47 T ELT)) (|listOfLists| (((|List| (|List| |#1|)) $) 96 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #12=((|SetCategory|))) ELT)) (|inverse| (((|Union| $ "failed") $) 71 (|has| |#1| (|Field|)) ELT)) (|horizConcat| (($ $ $) 98 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #12#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #11# |#1|) $) 37 T ELT)) (|fill!| (($ $ |#1|) 64 T ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 79 (|has| |#1| (|IntegralDomain|)) ELT)) (|every?| ((#11# (|Mapping| #11# |#1|) . #13=($)) 42 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #12#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #12#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #12#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #12#)) ELT)) (|eq?| ((#14=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#14# $) 7 T ELT)) (|empty| (#4# 8 T ELT)) (|elt| ((|#1| . #6#) 57 T ELT) ((|#1| $ #3# #3# |#1|) 55 T ELT) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) 95 T ELT)) (|diagonalMatrix| (($ (|List| |#1|)) 104 T ELT) (($ (|List| $)) 103 T ELT)) (|diagonal?| (((|Boolean|) $) 111 T ELT)) (|determinant| ((|#1| $) 73 (|has| |#1| (ATTRIBUTE (|commutative| #9#))) ELT)) (|count| ((#15=(|NonNegativeInteger|) (|Mapping| #11# |#1|) $) 41 T ELT) ((#15# |#1| $) 36 (|has| |#1| . #5#) ELT)) (|copy| (($ $) 9 T ELT)) (|column| ((|#3| $ #3#) 53 T ELT)) (|coerce| (($ |#3|) 102 T ELT) (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#11# (|Mapping| #11# |#1|) . #13#) 43 T ELT)) (|antisymmetric?| (((|Boolean|) $) 109 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (/ (($ $ |#1|) 78 (|has| |#1| (|Field|)) ELT)) (- (($ $ $) 88 T ELT) (($ $) 87 T ELT)) (+ (($ $ $) 89 T ELT)) (** (($ $ (|NonNegativeInteger|)) 80 T ELT) (($ $ (|Integer|)) 70 (|has| |#1| (|Field|)) ELT)) (* (($ $ $) 86 T ELT) (($ |#1| $) 85 T ELT) (($ $ |#1|) 84 T ELT) (($ (|Integer|) $) 83 T ELT) ((|#3| $ |#3|) 82 T ELT) ((|#2| |#2| $) 81 T ELT)) (|#| ((#15# $) 44 T ELT))) 
(((|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 *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|)))) (|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| #1="*"))) (|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| #1#))) (|ofCategory| *2 (|Ring|)))) (|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|))))) 
(|Join| (|TwoDimensionalArrayCategory| |t#1| |t#2| |t#3|) (CATEGORY |domain| (SIGNATURE |square?| ((|Boolean|) $)) (SIGNATURE |diagonal?| ((|Boolean|) $)) (SIGNATURE |symmetric?| ((|Boolean|) $)) (SIGNATURE |antisymmetric?| ((|Boolean|) $)) (SIGNATURE |zero| ($ (|NonNegativeInteger|) (|NonNegativeInteger|))) (SIGNATURE |matrix| ($ (|List| (|List| |t#1|)))) (SIGNATURE |matrix| ($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |t#1| (|Integer|) (|Integer|)))) (SIGNATURE |scalarMatrix| ($ (|NonNegativeInteger|) |t#1|)) (SIGNATURE |diagonalMatrix| ($ (|List| |t#1|))) (SIGNATURE |diagonalMatrix| ($ (|List| $))) (SIGNATURE |coerce| ($ |t#3|)) (SIGNATURE |transpose| ($ |t#2|)) (SIGNATURE |transpose| ($ $)) (SIGNATURE |squareTop| ($ $)) (SIGNATURE |horizConcat| ($ $ $)) (SIGNATURE |vertConcat| ($ $ $)) (SIGNATURE |listOfLists| ((|List| (|List| |t#1|)) $)) (SIGNATURE |elt| ($ $ (|List| (|Integer|)) (|List| (|Integer|)))) (SIGNATURE |setelt| ($ $ (|List| (|Integer|)) (|List| (|Integer|)) $)) (SIGNATURE |swapRows!| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |swapColumns!| ($ $ (|Integer|) (|Integer|))) (SIGNATURE |subMatrix| ($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|))) (SIGNATURE |setsubMatrix!| ($ $ (|Integer|) (|Integer|) $)) (SIGNATURE + ($ $ $)) (SIGNATURE - ($ $ $)) (SIGNATURE - ($ $)) (SIGNATURE * ($ $ $)) (SIGNATURE * ($ |t#1| $)) (SIGNATURE * ($ $ |t#1|)) (SIGNATURE * ($ (|Integer|) $)) (SIGNATURE * (|t#3| $ |t#3|)) (SIGNATURE * (|t#2| |t#2| $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (IF (|has| |t#1| (|IntegralDomain|)) (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#1|)) |%noBranch|) (IF (|has| |t#1| (|Field|)) (SIGNATURE / ($ $ |t#1|)) |%noBranch|) (IF (|has| |t#1| (|EuclideanDomain|)) (SIGNATURE |rowEchelon| ($ $)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |rank| ((|NonNegativeInteger|) $)) (SIGNATURE |nullity| ((|NonNegativeInteger|) $)) (SIGNATURE |nullSpace| ((|List| |t#3|) $))) |%noBranch|) (IF (|has| |t#1| (ATTRIBUTE (|commutative| "*"))) (PROGN (SIGNATURE |determinant| (|t#1| $)) (SIGNATURE |minordet| (|t#1| $))) |%noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |inverse| ((|Union| $ "failed") $)) (SIGNATURE ** ($ $ (|Integer|)))) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|TwoDimensionalArrayCategory| |#1| |#2| |#3|) . T) ((|Type|) . T)) 
((|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) 39 T ELT)) (|map| (((|Union| |#8| #1="failed") (|Mapping| (|Union| |#5| #1#) |#1|) |#4|) 37 T ELT) ((|#8| (|Mapping| |#5| |#1|) |#4|) 31 T ELT))) 
(((|MatrixCategoryFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| (|#8| (|Mapping| |#5| |#1|) |#4|)) (SIGNATURE |map| ((|Union| |#8| #1="failed") (|Mapping| (|Union| |#5| #1#) |#1|) |#4|)) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|))) #2=(|Ring|) #3=(|FiniteLinearAggregate| |#1|) #3# (|MatrixCategory| |#1| |#2| |#3|) #2# #4=(|FiniteLinearAggregate| |#5|) #4# (|MatrixCategory| |#5| |#6| |#7|)) (T |MatrixCategoryFunctions2|)) 
((|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #1=(|ofCategory| *5 #2=(|Ring|)) (|ofCategory| *2 #2#) #3=(|ofCategory| *6 #4=(|FiniteLinearAggregate| *5)) #5=(|ofCategory| *7 #4#) (|ofCategory| *8 #6=(|FiniteLinearAggregate| *2)) (|ofCategory| *9 #6#) (|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *2 *8 *9 *10)) #7=(|ofCategory| *4 (|MatrixCategory| *5 *6 *7)) (|ofCategory| *10 (|MatrixCategory| *2 *8 *9)))) (|map| #8=(*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| (|Union| *8 "failed") *5)) #1# #9=(|ofCategory| *8 #2#) #3# #5# #10=(|ofCategory| *2 (|MatrixCategory| *8 *9 *10)) #11=(|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2)) #7# #12=(|ofCategory| *9 #13=(|FiniteLinearAggregate| *8)) #14=(|ofCategory| *10 #13#))) (|map| #8# (AND (|isDomain| *3 (|Mapping| *8 *5)) #1# #9# #3# #5# #10# #11# #7# #12# #14#))) 
((|rowEchelon| (#1=(|#4| |#4|) 90 #2=(|has| |#1| (|EuclideanDomain|)) ELT)) (|rank| (#3=((|NonNegativeInteger|) |#4|) 92 #4=(|has| |#1| (|IntegralDomain|)) ELT)) (|nullity| (#3# 94 #4# ELT)) (|nullSpace| (((|List| |#3|) |#4|) 101 #4# ELT)) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 124 #2# ELT)) (|minordet| (#5=(|#1| |#4|) 52 T ELT)) (|invertIfCan| (#6=((|Union| |#4| "failed") |#4|) 84 #4# ELT)) (|inverse| (#6# 98 (|has| |#1| (|Field|)) ELT)) (|fractionFreeGauss!| (#1# 76 #4# ELT)) (|elRow2!| (#7=(|#4| |#4| |#1| #8=(|Integer|) #8#) 60 T ELT)) (|elRow1!| ((|#4| |#4| #8# #8#) 55 T ELT)) (|elColumn2!| (#7# 65 T ELT)) (|determinant| (#5# 96 T ELT)) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) 80 #4# ELT))) 
(((|MatrixLinearAlgebraFunctions| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |determinant| #1=(|#1| |#4|)) (SIGNATURE |minordet| #1#) (SIGNATURE |elRow1!| (|#4| |#4| #2=(|Integer|) #2#)) (SIGNATURE |elRow2!| #3=(|#4| |#4| |#1| #2# #2#)) (SIGNATURE |elColumn2!| #3#) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |rank| #4=((|NonNegativeInteger|) |#4|)) (SIGNATURE |nullity| #4#) (SIGNATURE |nullSpace| ((|List| |#3|) |#4|)) (SIGNATURE |fractionFreeGauss!| #5=(|#4| |#4|)) (SIGNATURE |invertIfCan| #6=((|Union| |#4| "failed") |#4|)) (SIGNATURE |adjoint| ((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|))) |%noBranch|) (IF (|has| |#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |rowEchelon| #5#) (SIGNATURE |normalizedDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|))) |%noBranch|) (IF (|has| |#1| (|Field|)) (SIGNATURE |inverse| #6#) |%noBranch|)) (|CommutativeRing|) #7=(|FiniteLinearAggregate| |#1|) #7# (|MatrixCategory| |#1| |#2| |#3|)) (T |MatrixLinearAlgebraFunctions|)) 
((|inverse| #1=(*1 *2 *2) (|partial| AND (|ofCategory| *3 (|Field|)) #2=(|ofCategory| *3 #3=(|CommutativeRing|)) #4=(|ofCategory| *4 #5=(|FiniteLinearAggregate| *3)) #6=(|ofCategory| *5 #5#) #7=(|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *2)) #8=(|ofCategory| *2 #9=(|MatrixCategory| *3 *4 *5)))) (|normalizedDivide| (*1 *2 *3 *3) (AND #10=(|ofCategory| *3 (|EuclideanDomain|)) #2# #4# #6# (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *4 *5 *6)) (|ofCategory| *6 #9#))) (|rowEchelon| #1# (AND #10# #2# #4# #6# #7# #8#)) (|adjoint| #11=(*1 *2 *3) (AND #12=(|ofCategory| *4 #13=(|IntegralDomain|)) #14=(|ofCategory| *4 #3#) #15=(|ofCategory| *5 #16=(|FiniteLinearAggregate| *4)) #17=(|ofCategory| *6 #16#) (|isDomain| *2 (|Record| (|:| |adjMat| *3) (|:| |detMat| *4))) #18=(|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *3)) #19=(|ofCategory| *3 #20=(|MatrixCategory| *4 *5 *6)))) (|invertIfCan| #1# (|partial| AND #21=(|ofCategory| *3 #13#) #2# #4# #6# #7# #8#)) (|fractionFreeGauss!| #1# (AND #21# #2# #4# #6# #7# #8#)) (|nullSpace| #11# (AND #12# #14# #15# #17# (|isDomain| *2 (|List| *6)) #18# #19#)) (|nullity| #11# #22=(AND #12# #14# #15# #17# (|isDomain| *2 (|NonNegativeInteger|)) #18# #19#)) (|rank| #11# #22#) (|elColumn2!| #23=(*1 *2 *2 *3 *4 *4) #24=(AND (|isDomain| *4 #25=(|Integer|)) #2# #6# (|ofCategory| *6 #5#) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *3 *5 *6 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *5 *6)))) (|elRow2!| #23# #24#) (|elRow1!| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 #25#) #14# #15# #17# (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *4 *5 *6 *2)) (|ofCategory| *2 #20#))) (|minordet| #11# #26=(AND (|ofCategory| *4 #27=(|FiniteLinearAggregate| *2)) (|ofCategory| *5 #27#) (|ofCategory| *2 #3#) (|isDomain| *1 (|MatrixLinearAlgebraFunctions| *2 *4 *5 *3)) (|ofCategory| *3 (|MatrixCategory| *2 *4 *5)))) (|determinant| #11# #26#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|zero| (($ #5=(|NonNegativeInteger|) #5#) 63 T ELT)) (|vertConcat| #6=(#7=($ $ $) NIL T ELT)) (|transpose| #8=(#9=($ #10=(|Vector| |#1|)) NIL T ELT) #11=(#12=($ $) NIL T ELT)) (|symmetric?| #13=((#3# $) NIL T ELT)) (|swapRows!| (#14=($ $ #15=(|Integer|) #15#) 21 T ELT)) (|swapColumns!| (#14# NIL T ELT)) (|subMatrix| (($ $ #15# #15# #15# #15#) NIL T ELT)) (|squareTop| #11#) (|square?| #13#) (|setsubMatrix!| (($ $ #15# #15# $) NIL T ELT)) (|setelt| #16=(#17=(|#1| $ #15# #15# |#1|) NIL T ELT) (($ $ #18=(|List| #15#) #18# $) NIL T ELT)) (|setRow!| #19=(($ $ #15# #10#) NIL T ELT)) (|setColumn!| #19#) (|scalarMatrix| (($ #5# |#1|) 37 T ELT)) (|sample| (#20=($) NIL T CONST)) (|rowEchelon| (#12# 46 (|has| |#1| (|EuclideanDomain|)) ELT)) (|row| #21=((#10# $ #15#) NIL T ELT)) (|reduce| ((|#1| #22=(|Mapping| |#1| |#1| |#1|) $) NIL T ELT) ((|#1| #22# $ |#1|) NIL T ELT) ((|#1| #22# $ |#1| |#1|) NIL #4# ELT)) (|rank| (#23=(#5# $) 48 #24=(|has| |#1| (|IntegralDomain|)) ELT)) (|qsetelt!| (#17# 68 T ELT)) (|qelt| #25=((|#1| $ #15# #15#) NIL T ELT)) (|nullity| (#23# 50 #24# ELT)) (|nullSpace| (((|List| #10#) $) 53 #24# ELT)) (|nrows| (#23# 31 T ELT)) (|new| (($ #5# #5# |#1|) 27 T ELT)) (|ncols| (#23# 32 T ELT)) (|minordet| (#26=(|#1| $) 44 #27=(|has| |#1| (ATTRIBUTE (|commutative| "*"))) ELT)) (|minRowIndex| (#28=(#15# $) 9 T ELT)) (|minColIndex| (#28# 10 T ELT)) (|members| ((#29=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|maxRowIndex| (#28# 13 T ELT)) (|maxColIndex| (#28# 64 T ELT)) (|matrix| (($ #30=(|List| #29#)) NIL T ELT) (($ #5# #5# (|Mapping| |#1| #15# #15#)) NIL T ELT)) (|map!| #31=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #31# (($ #22# $ $) NIL T ELT) (($ #22# $ $ |#1|) NIL T ELT)) (|listOfLists| ((#30# $) 75 T ELT)) (|latex| (((|String|) $) NIL #32=(|has| |#1| (|SetCategory|)) ELT)) (|inverse| ((#33=(|Union| $ #34="failed") $) 57 #35=(|has| |#1| (|Field|)) ELT)) (|horizConcat| #6#) (|hash| (((|SingleInteger|) $) NIL #32# ELT)) (|find| (((|Union| |#1| #34#) #36=(|Mapping| #3# |#1|) $) NIL T ELT)) (|fill!| #37=(#38=($ $ |#1|) NIL T ELT)) (|exquo| ((#33# $ |#1|) NIL #24# ELT)) (|every?| #39=((#3# #36# $) NIL T ELT)) (|eval| (($ $ (|List| #40=(|Equation| |#1|))) NIL #41=(AND (|has| |#1| (|Evalable| |#1|)) #32#) ELT) (($ $ #40#) NIL #41# ELT) (($ $ |#1| |#1|) NIL #41# ELT) (($ $ #29# #29#) NIL #41# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| #13#) (|empty| (#20# NIL T ELT)) (|elt| #25# #16# (($ $ #18# #18#) NIL T ELT)) (|diagonalMatrix| (($ #29#) NIL T ELT) (($ (|List| $)) NIL T ELT) (#9# 69 T ELT)) (|diagonal?| #13#) (|determinant| (#26# 42 #27# ELT)) (|count| ((#5# #36# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT)) (|copy| #11#) (|convert| ((#42=(|InputForm|) $) 79 (|has| |#1| (|ConvertibleTo| #42#)) ELT)) (|column| #21#) (|coerce| #8# ((#43=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #43#)) ELT)) (|before?| #1#) (|any?| #39#) (|antisymmetric?| #13#) (= #1#) (/ (#38# NIL #35# ELT)) (- #6# #11#) (+ #6#) (** (($ $ #5#) 38 T ELT) (($ $ #15#) 61 #35# ELT)) (* (#7# 23 T ELT) (($ |#1| $) NIL T ELT) #37# (($ #15# $) NIL T ELT) ((#10# $ #10#) NIL T ELT) ((#10# #10# $) NIL T ELT)) (|#| (#23# NIL T ELT))) 
(((|Matrix| |#1|) (|Join| (|MatrixCategory| |#1| #1=(|Vector| |#1|) #1#) (CATEGORY |domain| (SIGNATURE |diagonalMatrix| ($ #1#)) (IF (|has| |#1| #2=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #2#) |%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 #1=(|Ring|)))) (|diagonalMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 #1#) (|isDomain| *1 (|Matrix| *3))))) 
((|times!| (#1=(#2=(|Matrix| |#1|) #2# #2# #2#) 37 T ELT)) (|rightScalarTimes!| ((#2# #2# #2# |#1|) 32 T ELT)) (|power!| ((#2# #2# #2# #2# #2# #3=(|NonNegativeInteger|)) 43 T ELT)) (|plus!| (#1# 25 T ELT)) (|minus!| (#1# 29 T ELT) (#4=(#2# #2# #2#) 27 T ELT)) (|leftScalarTimes!| ((#2# #2# |#1| #2#) 31 T ELT)) (|copy!| (#4# 23 T ELT)) (** ((#2# #2# #3#) 46 T ELT))) 
(((|StorageEfficientMatrixOperations| |#1|) (CATEGORY |package| (SIGNATURE |copy!| #1=(#2=(|Matrix| |#1|) #2# #2#)) (SIGNATURE |plus!| #3=(#2# #2# #2# #2#)) (SIGNATURE |minus!| #1#) (SIGNATURE |minus!| #3#) (SIGNATURE |leftScalarTimes!| (#2# #2# |#1| #2#)) (SIGNATURE |rightScalarTimes!| (#2# #2# #2# |#1|)) (SIGNATURE |times!| #3#) (SIGNATURE |power!| (#2# #2# #2# #2# #2# #4=(|NonNegativeInteger|))) (SIGNATURE ** (#2# #2# #4#))) (|Ring|)) (T |StorageEfficientMatrixOperations|)) 
((** (*1 *2 *2 *3) #1=(AND (|isDomain| *2 (|Matrix| *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 #2=(|Ring|)) (|isDomain| *1 (|StorageEfficientMatrixOperations| *4)))) (|power!| (*1 *2 *2 *2 *2 *2 *3) #1#) (|times!| #3=(*1 *2 *2 *2 *2) #4=(AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *3 #2#) (|isDomain| *1 (|StorageEfficientMatrixOperations| *3)))) (|rightScalarTimes!| (*1 *2 *2 *2 *3) #4#) (|leftScalarTimes!| (*1 *2 *2 *3 *2) #4#) (|minus!| #3# #4#) (|minus!| #5=(*1 *2 *2 *2) #4#) (|plus!| #3# #4#) (|copy!| #5# #4#)) 
((|retractIfCan| (((|Union| |#1| "failed") $) 18 T ELT)) (|retract| (#1=(|#1| $) NIL T ELT)) (|nothing| (($) 7 T CONST)) (|just| (#2=($ |#1|) 8 T ELT)) (|coerce| (#2# 16 T ELT) (((|OutputForm|) $) 23 T ELT)) (|case| ((#3=(|Boolean|) $ (|[\|\|]| |#1|)) 14 T ELT) ((#3# $ (|[\|\|]| |nothing|)) 11 T ELT)) (|autoCoerce| (#1# 15 T ELT))) 
(((|Maybe| |#1|) (|Join| (|UnionType|) (|RetractableTo| |#1|) #1=(|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |just| ($ |#1|)) (SIGNATURE |case| (#2=(|Boolean|) $ (|[\|\|]| |#1|))) (SIGNATURE |case| (#2# $ (|[\|\|]| |nothing|))) (SIGNATURE |autoCoerce| (|#1| $)) (SIGNATURE |nothing| ($) |constant|))) #1#) (T |Maybe|)) 
((|just| (*1 *1 *2) #1=(AND (|isDomain| *1 (|Maybe| *2)) (|ofCategory| *2 #2=(|CoercibleTo| (|OutputForm|))))) (|case| #3=(*1 *2 *1 *3) (AND (|isDomain| *3 (|[\|\|]| *4)) #4=(|ofCategory| *4 #2#) #5=(|isDomain| *2 (|Boolean|)) #6=(|isDomain| *1 (|Maybe| *4)))) (|case| #3# (AND (|isDomain| *3 (|[\|\|]| |nothing|)) #5# #6# #4#)) (|autoCoerce| (*1 *2 *1) #1#) (|nothing| (*1 *1) #1#)) 
((|splitDenominator| (((|Record| (|:| |num| #1=(|Matrix| |#1|)) (|:| |den| |#1|)) #2=(|Matrix| |#2|)) 20 T ELT)) (|commonDenominator| ((|#1| #2#) 9 T ELT)) (|clearDenominator| ((#1# #2#) 18 T ELT))) 
(((|MatrixCommonDenominator| |#1| |#2|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| #1=(|Matrix| |#2|))) (SIGNATURE |clearDenominator| (#2=(|Matrix| |#1|) #1#)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| #2#) (|:| |den| |#1|)) #1#))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|)) (T |MatrixCommonDenominator|)) 
((|splitDenominator| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 (|Matrix| *5)) #3=(|ofCategory| *5 (|QuotientFieldCategory| *4)) #4=(|ofCategory| *4 #5=(|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |num| #6=(|Matrix| *4)) (|:| |den| *4))) #7=(|isDomain| *1 (|MatrixCommonDenominator| *4 *5)))) (|clearDenominator| #1# (AND #2# #3# #4# (|isDomain| *2 #6#) #7#)) (|commonDenominator| #1# (AND (|isDomain| *3 #6#) (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 #5#) (|isDomain| *1 (|MatrixCommonDenominator| *2 *4))))) 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|select!| (($ (|Mapping| #3=(|Boolean|) |#1|) . #4=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#7=($) 6 T CONST)) (|removeDuplicates!| (($ $) 55 T ELT)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #8=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #3# |#1|) . #4#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #8#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #5# |#1|) . #6#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #9=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #10=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT) (($ |#1| $ (|NonNegativeInteger|)) 56 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #9#) ELT)) (|extract!| ((|#1| . #10#) 37 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT)) (|eq?| ((#11=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#11# $) 7 T ELT)) (|empty| (#7# 8 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) 54 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#12=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #12#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|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|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((|separateFactors| ((#1=(|List| |#1|) #2=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #3=(|Integer|)))) #3#) 66 T ELT)) (|linears| ((|#1| |#1| #3#) 63 T ELT)) (|gcd| ((|#1| |#1| |#1| #3#) 46 T ELT)) (|factor| ((#1# |#1| #3#) 49 T ELT)) (|exptMod| ((|#1| |#1| #3# |#1| #3#) 40 T ELT)) (|ddFact| ((#2# |#1| #3#) 62 T ELT))) 
(((|ModularDistinctDegreeFactorizer| |#1|) (CATEGORY |package| (SIGNATURE |gcd| (|#1| |#1| |#1| #1=(|Integer|))) (SIGNATURE |linears| (|#1| |#1| #1#)) (SIGNATURE |factor| (#2=(|List| |#1|) |#1| #1#)) (SIGNATURE |ddFact| (#3=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #1#))) |#1| #1#)) (SIGNATURE |separateFactors| (#2# #3# #1#)) (SIGNATURE |exptMod| (|#1| |#1| #1# |#1| #1#))) (|UnivariatePolynomialCategory| #1#)) (T |ModularDistinctDegreeFactorizer|)) 
((|exptMod| (*1 *2 *2 *3 *2 *3) #1=(AND (|isDomain| *3 #2=(|Integer|)) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|separateFactors| #3=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| (|:| |factor| *5) (|:| |degree| #2#)))) #4=(|isDomain| *4 #2#) (|ofCategory| *5 #5=(|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *5)))) (|ddFact| #3# (AND #4# (|isDomain| *2 (|List| (|Record| (|:| |factor| *3) (|:| |degree| *4)))) #6=(|isDomain| *1 (|ModularDistinctDegreeFactorizer| *3)) #7=(|ofCategory| *3 #5#))) (|factor| #3# (AND #4# (|isDomain| *2 (|List| *3)) #6# #7#)) (|linears| (*1 *2 *2 *3) #1#) (|gcd| (*1 *2 *2 *2 *3) #1#)) 
((|ptFunc| ((#1=(|Mapping| (|Point| #2=(|DoubleFloat|)) #2# #2#) #3=(|Mapping| #2# #2# #2#) #3# #3# #4=(|Mapping| #2# #2# #2# #2#)) 17 T ELT)) (|meshPar2Var| ((#5=(|ThreeSpace| #2#) #5# #1# #6=(|Segment| #2#) #6# #7=(|List| (|DrawOption|))) 53 T ELT) ((#5# #1# #6# #6# #7#) 55 T ELT) ((#5# #3# #3# #3# #8=(|Union| #4# "undefined") #6# #6# #7#) 57 T ELT)) (|meshPar1Var| ((#5# #9=(|Expression| (|Integer|)) #9# #9# (|Mapping| #2# #2#) #6# #7#) NIL T ELT)) (|meshFun2Var| ((#5# #3# #8# #6# #6# #7#) 58 T ELT))) 
(((|MeshCreationRoutinesForThreeDimensions|) (CATEGORY |package| (SIGNATURE |meshPar2Var| (#1=(|ThreeSpace| #2=(|DoubleFloat|)) #3=(|Mapping| #2# #2# #2#) #3# #3# #4=(|Union| #5=(|Mapping| #2# #2# #2# #2#) "undefined") #6=(|Segment| #2#) #6# #7=(|List| (|DrawOption|)))) (SIGNATURE |meshPar2Var| (#1# #8=(|Mapping| (|Point| #2#) #2# #2#) #6# #6# #7#)) (SIGNATURE |meshPar2Var| (#1# #1# #8# #6# #6# #7#)) (SIGNATURE |meshFun2Var| (#1# #3# #4# #6# #6# #7#)) (SIGNATURE |meshPar1Var| (#1# #9=(|Expression| (|Integer|)) #9# #9# (|Mapping| #2# #2#) #6# #7#)) (SIGNATURE |ptFunc| (#8# #3# #3# #3# #5#)))) (T |MeshCreationRoutinesForThreeDimensions|)) 
((|ptFunc| (*1 *2 *3 *3 *3 *4) (AND #1=(|isDomain| *3 (|Mapping| #2=(|DoubleFloat|) #2# #2#)) (|isDomain| *4 #3=(|Mapping| #2# #2# #2# #2#)) (|isDomain| *2 #4=(|Mapping| (|Point| #2#) #2# #2#)) #5=(|isDomain| *1 (|MeshCreationRoutinesForThreeDimensions|)))) (|meshPar1Var| (*1 *2 *3 *3 *3 *4 *5 *6) (AND (|isDomain| *3 (|Expression| (|Integer|))) (|isDomain| *4 (|Mapping| #2# #2#)) #6=(|isDomain| *5 #7=(|Segment| #2#)) #8=(|isDomain| *6 #9=(|List| (|DrawOption|))) #10=(|isDomain| *2 (|ThreeSpace| #2#)) #5#)) (|meshFun2Var| (*1 *2 *3 *4 *5 *5 *6) #11=(AND #1# (|isDomain| *4 (|Union| #3# "undefined")) #6# #8# #10# #5#)) (|meshPar2Var| (*1 *2 *2 *3 *4 *4 *5) (AND #10# #12=(|isDomain| *3 #4#) #13=(|isDomain| *4 #7#) #14=(|isDomain| *5 #9#) #5#)) (|meshPar2Var| (*1 *2 *3 *4 *4 *5) (AND #12# #13# #14# #10# #5#)) (|meshPar2Var| (*1 *2 *3 *3 *3 *4 *5 *5 *6) #11#)) 
((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#) 87 T ELT) (((|Factored| |#4|) |#4|) 270 T ELT))) 
(((|MultFiniteFactorize| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|)) (SIGNATURE |factor| ((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|FiniteFieldCategory|) (|PolynomialCategory| |#3| |#2| |#1|)) (T |MultFiniteFactorize|)) 
((|factor| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 (|OrderedSet|)) #3=(|ofCategory| *5 (|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *6 (|FiniteFieldCategory|)) (|ofCategory| *7 #5=(|PolynomialCategory| *6 *5 *4)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *7)) (|isDomain| *3 #6#))) (|factor| #1# (AND #2# #3# #4# (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *3)) (|ofCategory| *3 #5#)))) 
((|rowEchelonLocal| ((#1=(|Matrix| |#1|) #1# |#1| |#1|) 85 T ELT)) (|rowEchelon| (#2=(#1# #1# |#1|) 66 T ELT)) (|rowEchLocal| (#2# 86 T ELT)) (|rowEch| ((#1# #1#) 67 T ELT)) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 84 T ELT))) 
(((|ModularHermitianRowReduction| |#1|) (CATEGORY |package| (SIGNATURE |rowEch| (#1=(|Matrix| |#1|) #1#)) (SIGNATURE |rowEchelon| #2=(#1# #1# |#1|)) (SIGNATURE |rowEchLocal| #2#) (SIGNATURE |rowEchelonLocal| (#1# #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))) #1=(|isDomain| *1 (|ModularHermitianRowReduction| *3)) #2=(|ofCategory| *3 (|EuclideanDomain|)))) (|rowEchelonLocal| (*1 *2 *2 *3 *3) #3=(AND (|isDomain| *2 (|Matrix| *3)) #2# #1#)) (|rowEchLocal| #4=(*1 *2 *2 *3) #3#) (|rowEchelon| #4# #3#) (|rowEch| (*1 *2 *2) #3#)) 
((|compiledFunction| ((#1=(|Mapping| |#4| |#2| |#3|) |#1| #2=(|Symbol|) #2#) 19 T ELT)) (|binaryFunction| ((#1# #2#) 12 T ELT))) 
(((|MakeBinaryCompiledFunction| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |binaryFunction| (#1=(|Mapping| |#4| |#2| |#3|) #2=(|Symbol|))) (SIGNATURE |compiledFunction| (#1# |#1| #2# #2#))) (|ConvertibleTo| (|InputForm|)) #3=(|Type|) #3# #3#) (T |MakeBinaryCompiledFunction|)) 
((|compiledFunction| (*1 *2 *3 *4 *4) (AND (|isDomain| *4 #1=(|Symbol|)) #2=(|isDomain| *2 (|Mapping| *7 *5 *6)) (|isDomain| *1 (|MakeBinaryCompiledFunction| *3 *5 *6 *7)) (|ofCategory| *3 #3=(|ConvertibleTo| (|InputForm|))) #4=(|ofCategory| *5 #5=(|Type|)) #6=(|ofCategory| *6 #5#) #7=(|ofCategory| *7 #5#))) (|binaryFunction| (*1 *2 *3) (AND (|isDomain| *3 #1#) #2# (|isDomain| *1 (|MakeBinaryCompiledFunction| *4 *5 *6 *7)) (|ofCategory| *4 #3#) #4# #6# #7#))) 
((|makeFloatFunction| (((|Mapping| #1=(|DoubleFloat|) #1# #1#) |#1| #2=(|Symbol|) #2#) 43 T ELT) (((|Mapping| #1# #1#) |#1| #2#) 48 T ELT))) 
(((|MakeFloatCompiledFunction| |#1|) (CATEGORY |package| (SIGNATURE |makeFloatFunction| ((|Mapping| #1=(|DoubleFloat|) #1#) |#1| #2=(|Symbol|))) (SIGNATURE |makeFloatFunction| ((|Mapping| #1# #1# #1#) |#1| #2# #2#))) (|ConvertibleTo| (|InputForm|))) (T |MakeFloatCompiledFunction|)) 
((|makeFloatFunction| (*1 *2 *3 *4 *4) (AND #1=(|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Mapping| #2=(|DoubleFloat|) #2# #2#)) #3=(|isDomain| *1 (|MakeFloatCompiledFunction| *3)) #4=(|ofCategory| *3 (|ConvertibleTo| (|InputForm|))))) (|makeFloatFunction| (*1 *2 *3 *4) (AND #1# (|isDomain| *2 (|Mapping| #2# #2#)) #3# #4#))) 
((|function| ((#1=(|Symbol|) |#1| #1# (|List| #1#)) 10 T ELT) ((#1# |#1| #1# #1# #1#) 13 T ELT) ((#1# |#1| #1# #1#) 12 T ELT) ((#1# |#1| #1#) 11 T ELT))) 
(((|MakeFunction| |#1|) (CATEGORY |package| (SIGNATURE |function| (#1=(|Symbol|) |#1| #1#)) (SIGNATURE |function| (#1# |#1| #1# #1#)) (SIGNATURE |function| (#1# |#1| #1# #1# #1#)) (SIGNATURE |function| (#1# |#1| #1# (|List| #1#)))) (|ConvertibleTo| (|InputForm|))) (T |MakeFunction|)) 
((|function| (*1 *2 *3 *2 *4) (AND (|isDomain| *4 (|List| #1=(|Symbol|))) #2=(|isDomain| *2 #1#) #3=(|isDomain| *1 (|MakeFunction| *3)) #4=(|ofCategory| *3 (|ConvertibleTo| (|InputForm|))))) (|function| (*1 *2 *3 *2 *2 *2) #5=(AND #2# #3# #4#)) (|function| (*1 *2 *3 *2 *2) #5#) (|function| (*1 *2 *3 *2) #5#)) 
((|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) 9 T ELT))) 
(((|MakeRecord| |#1| |#2|) (CATEGORY |package| (SIGNATURE |makeRecord| ((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|))) #1=(|Type|) #1#) (T |MakeRecord|)) 
((|makeRecord| (*1 *2 *3 *4) (AND (|isDomain| *2 (|Record| (|:| |part1| *3) (|:| |part2| *4))) (|isDomain| *1 (|MakeRecord| *3 *4)) (|ofCategory| *3 #1=(|Type|)) (|ofCategory| *4 #1#)))) 
((|unaryFunction| ((#1=(|Mapping| |#3| |#2|) #2=(|Symbol|)) 11 T ELT)) (|compiledFunction| ((#1# |#1| #2#) 21 T ELT))) 
(((|MakeUnaryCompiledFunction| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |unaryFunction| (#1=(|Mapping| |#3| |#2|) #2=(|Symbol|))) (SIGNATURE |compiledFunction| (#1# |#1| #2#))) (|ConvertibleTo| (|InputForm|)) #3=(|Type|) #3#) (T |MakeUnaryCompiledFunction|)) 
((|compiledFunction| (*1 *2 *3 *4) (AND (|isDomain| *4 #1=(|Symbol|)) #2=(|isDomain| *2 (|Mapping| *6 *5)) (|isDomain| *1 (|MakeUnaryCompiledFunction| *3 *5 *6)) (|ofCategory| *3 #3=(|ConvertibleTo| (|InputForm|))) #4=(|ofCategory| *5 #5=(|Type|)) #6=(|ofCategory| *6 #5#))) (|unaryFunction| (*1 *2 *3) (AND (|isDomain| *3 #1#) #2# (|isDomain| *1 (|MakeUnaryCompiledFunction| *4 *5 *6)) (|ofCategory| *4 #3#) #4# #6#))) 
((|lifting1| ((#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #3# #4=(|List| |#2|) #2# #5=(|List| |#3|) #6=(|List| |#4|) (|List| (|List| (|Record| (|:| |expt| #7=(|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) #8=(|List| #7#) #9=(|Vector| #10=(|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) 92 T ELT)) (|lifting| ((#1# #3# #4# #10# #5# #6# #8# |#3|) 110 T ELT)) (|corrPoly| ((#1# #3# #4# #5# #8# #2# #9# |#3|) 48 T ELT))) 
(((|MultivariateLifting| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |corrPoly| (#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #3# #4=(|List| |#2|) #5=(|List| |#3|) #6=(|List| #7=(|NonNegativeInteger|)) #2# #8=(|Vector| #9=(|List| (|SparseUnivariatePolynomial| |#3|))) |#3|)) (SIGNATURE |lifting| (#1# #3# #4# #9# #5# #10=(|List| |#4|) #6# |#3|)) (SIGNATURE |lifting1| (#1# #3# #4# #2# #5# #10# (|List| (|List| (|Record| (|:| |expt| #7#) (|:| |pcoef| |#4|)))) #6# #8# |#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| #1=(|SparseUnivariatePolynomial| *13))) (|isDomain| *3 #1#) (|isDomain| *4 #2=(|List| *12)) (|isDomain| *5 #3=(|List| *10)) (|isDomain| *6 (|List| *13)) (|isDomain| *7 (|List| (|List| (|Record| (|:| |expt| #4=(|NonNegativeInteger|)) (|:| |pcoef| *13))))) #5=(|isDomain| *8 #6=(|List| #4#)) (|isDomain| *9 (|Vector| (|List| (|SparseUnivariatePolynomial| *10)))) (|ofCategory| *12 #7=(|OrderedSet|)) (|ofCategory| *10 #8=(|EuclideanDomain|)) (|ofCategory| *13 (|PolynomialCategory| *10 *11 *12)) (|ofCategory| *11 #9=(|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 #2#) #5# (|ofCategory| *11 #7#) (|ofCategory| *9 #8#) (|ofCategory| *12 (|PolynomialCategory| *9 *10 *11)) (|ofCategory| *10 #9#) (|isDomain| *2 (|List| #10=(|SparseUnivariatePolynomial| *12))) (|isDomain| *1 (|MultivariateLifting| *10 *11 *9 *12)) (|isDomain| *3 #10#))) (|corrPoly| (*1 *2 *3 *4 *5 *6 *2 *7 *8) (|partial| AND (|isDomain| *2 (|List| #11=(|SparseUnivariatePolynomial| *11))) (|isDomain| *3 #11#) (|isDomain| *4 #3#) (|isDomain| *5 (|List| *8)) (|isDomain| *6 #6#) (|isDomain| *7 (|Vector| (|List| (|SparseUnivariatePolynomial| *8)))) (|ofCategory| *10 #7#) (|ofCategory| *8 #8#) (|ofCategory| *11 (|PolynomialCategory| *8 *9 *10)) (|ofCategory| *9 #9#) (|isDomain| *1 (|MultivariateLifting| *9 *10 *8 *11))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reductum| (($ $) 56 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 54 T ELT)) (|minimumDegree| (((|NonNegativeInteger|) $) 58 T ELT)) (|leadingCoefficient| ((|#1| $) 57 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| (((|NonNegativeInteger|) $) 59 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 53 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 55 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 61 T ELT) (($ |#1| . #4#) 60 T ELT))) 
(((|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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) 23 T ELT))) 
(((|MultipleMap| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| (|#6| (|Mapping| |#4| |#1|) |#3|))) #1=(|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) #1# (|UnivariatePolynomialCategory| |#4|) (|UnivariatePolynomialCategory| (|Fraction| |#5|))) (T |MultipleMap|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *5)) (|ofCategory| *5 #1=(|IntegralDomain|)) (|ofCategory| *7 #1#) (|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))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| ((#2=(|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exprex| (#3=(#2# #4=(|OutputForm|)) 36 T ELT)) (|display| (((|Void|) #2#) 29 T ELT)) (|coerceS| (#3# 26 T ELT)) (|coerceL| (#3# 27 T ELT)) (|coerce| ((#4# $) NIL T ELT) (#3# 25 T ELT)) (|before?| #1#) (= #1#)) 
(((|MathMLFormat|) (|Join| (|SetCategory|) (CATEGORY |package| (SIGNATURE |coerce| #1=(#2=(|String|) (|OutputForm|))) (SIGNATURE |coerceS| #1#) (SIGNATURE |coerceL| #1#) (SIGNATURE |exprex| #1#) (SIGNATURE |display| ((|Void|) #2#))))) (T |MathMLFormat|)) 
((|coerce| #1=(*1 *2 *3) #2=(AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 #3=(|String|)) #4=(|isDomain| *1 (|MathMLFormat|)))) (|coerceS| #1# #2#) (|coerceL| #1# #2#) (|exprex| #1# #2#) (|display| #1# (AND (|isDomain| *3 #3#) (|isDomain| *2 (|Void|)) #4#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| #5=((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #8=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| #9=(($) NIL T CONST)) (|rem| #10=(($ $ $) NIL T ELT)) (|reduce| (($ |#1| |#2|) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|quo| #10#) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) #12=(|:| |generator| $)) #11#) NIL T ELT)) (|prime?| #3#) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #11# #7#) #11# $) NIL T ELT)) (|modulus| ((|#2| $) NIL T ELT)) (|lcm| #10# #13=(($ #11#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#14=(|SparseUnivariatePolynomial| $) #14# #14#) NIL T ELT)) (|gcd| #10# #13#) (|factor| #8#) (|extendedEuclidean| (((|Record| #15=(|:| |coef1| $) #16=(|:| |coef2| $) #12#) $ $) NIL T ELT) (((|Union| (|Record| #15# #16#) #7#) $ $ $) NIL T ELT)) (|exquo| #5#) (|expressIdealMember| (((|Maybe| #11#) #11# $) NIL T ELT)) (|exQuo| #5#) (|euclideanSize| ((#17=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #18=(|Integer|)) NIL T ELT) #4# (($ #19=(|Fraction| #18#)) NIL T ELT) ((|#1| $) NIL T ELT)) (|characteristic| ((#17#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| #9#) (|One| #9#) (= #1#) (/ #10#) (- #4# #10#) (+ #10#) (** (($ $ #20=(|PositiveInteger|)) NIL T ELT) (($ $ #17#) NIL T ELT) (($ $ #18#) NIL T ELT)) (* (($ #20# $) NIL T ELT) (($ #17# $) NIL T ELT) (($ #18# . #21=($)) NIL T ELT) #10# (($ $ #19#) NIL T ELT) (($ #19# . #21#) NIL T ELT))) 
(((|ModularField| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |coerce| (|#1| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| ((|Union| $ #1="failed") $ $)))) (|CommutativeRing|) (|AbelianMonoid|) (|Mapping| |#1| |#1| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2|) (|Mapping| (|Union| |#1| #1#) |#1| |#1| |#2|)) (T |ModularField|)) 
((|modulus| #1=(*1 *2 *1) (AND (|ofCategory| *2 #2=(|AbelianMonoid|)) (|isDomain| *1 (|ModularField| *3 *2 *4 *5 *6)) (|ofCategory| *3 #3=(|CommutativeRing|)) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| #4=(|Union| *2 #5="failed") *2 *2)) (|ofType| *6 (|Mapping| #6=(|Union| *3 #5#) *3 *3 *2)))) (|coerce| #1# (AND #7=(|ofCategory| *2 #3#) #8=(|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6)) #9=(|ofCategory| *3 #2#) #10=(|ofType| *4 (|Mapping| *2 *2 *3)) #11=(|ofType| *5 (|Mapping| #6# *3 *3)) #12=(|ofType| *6 (|Mapping| #4# *2 *2 *3)))) (|reduce| (*1 *1 *2 *3) (AND #8# #7# #9# #10# #11# #12#)) (|exQuo| (*1 *1 *1 *1) (|partial| AND #8# #7# #9# #10# #11# #12#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 37 T ELT)) (|vectorise| ((#5=(|Vector| |#1|) $ #6=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#7=(|List| #8=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #9=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#10=(|SparseUnivariatePolynomial| $) $ #8#) NIL T ELT) #11=((#9# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #12=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #13=(#14=($ $) NIL #12# ELT)) (|unit?| (#4# NIL #12# ELT)) (|totalDegree| #15=(#16=(#6# $) NIL T ELT) ((#6# $ #7#) NIL T ELT)) (|subtractIfCan| (#17=(#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|subResultantGcd| #20=(#21=($ $ $) NIL #12# ELT)) (|squareFreePolynomial| #22=(((|Factored| #10#) #10#) NIL #23=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #24=(#14# NIL #25=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#26=((|Factored| $) $) NIL #25# ELT)) (|solveLinearPolynomialEquation| (((|Union| #27=(|List| #10#) #19#) #27# #10#) NIL #23# ELT)) (|sizeLess?| (#2# NIL #28=(|has| |#1| (|Field|)) ELT)) (|size| (#29=(#6#) 55 #30=(|has| |#1| (|Finite|)) ELT)) (|shiftRight| #31=(#32=($ $ #6#) NIL T ELT)) (|shiftLeft| #31#) (|setPoly| ((|#2| |#2|) 51 T ELT)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #25# ELT)) (|sample| (#33=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #34=(#19#)) . #35=($)) NIL T ELT) (((|Union| #36=(|Fraction| #37=(|Integer|)) . #34#) . #35#) NIL #38=(|has| |#1| (|RetractableTo| #36#)) ELT) (((|Union| #37# . #34#) . #35#) NIL #39=(|has| |#1| (|RetractableTo| #37#)) ELT) #40=(((|Union| #8# . #34#) . #35#) NIL T ELT)) (|retract| #41=(#42=(|#1| . #43=($)) NIL T ELT) ((#36# . #43#) NIL #38# ELT) ((#37# . #43#) NIL #39# ELT) ((#8# . #43#) NIL T ELT)) (|resultant| (($ $ $ #8#) NIL #44=(|has| |#1| (|CommutativeRing|)) ELT) ((|#1| $ $) NIL #44# ELT)) (|rem| #45=(#21# NIL #28# ELT)) (|reductum| (#14# 72 T ELT)) (|reducedSystem| ((#46=(|Matrix| #37#) . #47=(#48=(|Matrix| $))) NIL #49=(|has| |#1| (|LinearlyExplicitRingOver| #37#)) ELT) ((#50=(|Record| (|:| |mat| #46#) (|:| |vec| (|Vector| #37#))) . #51=(#48# #52=(|Vector| $))) NIL #49# ELT) ((#53=(|Record| (|:| |mat| #54=(|Matrix| |#1|)) (|:| |vec| #5#)) . #51#) NIL T ELT) ((#54# . #47#) NIL T ELT)) (|reduce| (#55=($ |#2|) 49 T ELT)) (|recip| ((#18# $) 98 T ELT)) (|random| (#33# 59 #30# ELT)) (|quo| #45#) (|pseudoRemainder| #56=(#21# NIL T ELT)) (|pseudoQuotient| #20#) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) #57=(|:| |quotient| $) #58=(|:| |remainder| $)) $ $) NIL #12# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #59=(|List| $)) #60=(|:| |generator| $)) #59#) NIL #28# ELT)) (|primitivePart| #24# #61=(#62=($ $ #8#) NIL #25# ELT)) (|primitiveMonomials| #63=((#59# $) NIL T ELT)) (|prime?| (#4# NIL #23# ELT)) (|pow| (#64=((|PrimitiveArray| $)) 89 T ELT)) (|pomopo!| (($ $ |#1| #6# $) NIL T ELT)) (|patternMatch| ((#65=(|PatternMatchResult| #66=(|Float|) . #67=($)) $ #68=(|Pattern| #66#) #65#) NIL (AND (|has| #8# #69=(|PatternMatchable| #66#)) (|has| |#1| #69#)) ELT) ((#70=(|PatternMatchResult| #37# . #67#) $ #71=(|Pattern| #37#) #70#) NIL (AND (|has| #8# #72=(|PatternMatchable| #37#)) (|has| |#1| #72#)) ELT)) (|order| ((#6# $ $) NIL #12# ELT)) (|opposite?| #1#) (|one?| #73=(#4# NIL T ELT)) (|numberOfMonomials| #15#) (|nextItem| (#74=((|Maybe| $) $) NIL #75=(|has| |#1| (|StepThrough|)) ELT)) (|multivariate| (($ #9# #8#) NIL T ELT) (($ #10# #8#) NIL T ELT)) (|multiplyExponents| #31#) (|multiEuclidean| ((#76=(|Union| #59# #19#) #59# $) NIL #28# ELT)) (|monomials| #63#) (|monomial?| #73#) (|monomial| (($ |#1| #6#) 86 T ELT) #77=(($ $ #8# #6#) NIL T ELT) #78=(($ $ #7# #79=(|List| #6#)) NIL T ELT)) (|monicDivide| ((#80=(|Record| #57# #58#) $ $ #8#) NIL T ELT) (#81=(#80# $ $) NIL T ELT)) (|modulus| ((|#2|) 52 T ELT)) (|minimumDegree| #15# #82=((#6# $ #8#) NIL T ELT) #83=((#79# $ #7#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #6# #6#) $) NIL T ELT)) (|map| (($ #84=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeSUP| #11#) (|mainVariable| #40#) (|lookup| ((#85=(|PositiveInteger|) $) NIL #30# ELT)) (|lift| ((|#2| $) 48 T ELT)) (|leftReducedSystem| ((#46# . #86=(#52#)) NIL #49# ELT) ((#50# . #87=(#52# $)) NIL #49# ELT) ((#53# . #87#) NIL T ELT) ((#54# . #86#) NIL T ELT)) (|leadingMonomial| #88=(#14# NIL T ELT)) (|leadingCoefficient| (#42# 35 T ELT)) (|lcm| #89=(($ #59#) NIL #25# ELT) #90=(#21# NIL #25# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|karatsubaDivide| ((#80# $ #6#) NIL T ELT)) (|isTimes| #91=((#76# $) NIL T ELT)) (|isPlus| #91#) (|isExpt| (((|Union| (|Record| (|:| |var| #8#) (|:| |exponent| #6#)) #19#) $) NIL T ELT)) (|integrate| (#14# NIL #92=(|has| |#1| (|Algebra| #36#)) ELT)) (|init| (#33# NIL #75# CONST)) (|index| (($ #85#) NIL #30# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #73#) (|ground| #41#) (|gcdPolynomial| ((#10# #10# #10#) NIL #25# ELT)) (|gcd| #89# #90#) (|frobenius| (#14# 88 (|has| |#1| (|FiniteFieldCategory|)) ELT)) (|factorSquareFreePolynomial| #22#) (|factorPolynomial| #22#) (|factor| (#26# NIL #23# ELT)) (|extendedEuclidean| (((|Union| (|Record| #93=(|:| |coef1| $) #94=(|:| |coef2| $)) #19#) $ $ $) NIL #28# ELT) (((|Record| #93# #94# #60#) $ $) NIL #28# ELT)) (|exquo| ((#18# $ |#1|) NIL #12# ELT) (#17# 97 #12# ELT)) (|expressIdealMember| (((|Maybe| #59#) #59# $) NIL #28# ELT)) (|eval| (($ $ (|List| #95=(|Equation| $))) NIL T ELT) (($ $ #95#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #59# #59#) NIL T ELT) (($ $ #8# |#1|) NIL T ELT) (($ $ #7# #96=(|List| |#1|)) NIL T ELT) (($ $ #8# $) NIL T ELT) (($ $ #7# #59#) NIL T ELT)) (|euclideanSize| (#16# NIL #28# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) #56# ((#97=(|Fraction| $) #97# #97#) NIL #12# ELT) ((|#1| #97# |#1|) NIL #28# ELT) ((#97# $ #97#) NIL #12# ELT)) (|divideExponents| ((#18# $ #6#) NIL T ELT)) (|divide| (#81# 99 #28# ELT)) (|discriminant| (#62# NIL #44# ELT) (#42# NIL #44# ELT)) (|differentiate| #78# #77# #98=(($ $ #7#) NIL T ELT) #99=(#62# NIL T ELT) #88# #31# #100=(($ $ #84#) NIL T ELT) #101=(($ $ #84# #6#) NIL T ELT) (($ $ #84# $) NIL T ELT) #102=(($ $ #103=(|Symbol|)) NIL #104=(|has| |#1| (|PartialDifferentialSpace| #103#)) ELT) #105=(($ $ #106=(|List| #103#)) NIL #104# ELT) #107=(($ $ #103# #6#) NIL #104# ELT) #108=(($ $ #106# #79#) NIL #104# ELT)) (|degree| (#16# 39 T ELT) #82# #83#) (|convert| ((#68# . #109=($)) NIL (AND (|has| #8# #110=(|ConvertibleTo| #68#)) (|has| |#1| #110#)) ELT) ((#71# . #109#) NIL (AND (|has| #8# #111=(|ConvertibleTo| #71#)) (|has| |#1| #111#)) ELT) ((#112=(|InputForm|) . #109#) NIL (AND (|has| #8# #113=(|ConvertibleTo| #112#)) (|has| |#1| #113#)) ELT)) (|content| (#42# NIL #25# ELT) #61#) (|conditionP| (((|Union| #52# #19#) #48#) NIL #114=(AND (|has| $ #115=(|CharacteristicNonZero|)) #23#) ELT)) (|computePowers| (#64# 43 T ELT)) (|composite| (#17# NIL #12# ELT) (((|Union| #97# #19#) #97# $) NIL #12# ELT)) (|coerce| (((|OutputForm|) $) 69 T ELT) (($ #37#) NIL T ELT) (($ |#1|) 66 T ELT) (($ #8#) NIL T ELT) (#55# 76 T ELT) (($ #36#) NIL (OR #92# #38#) ELT) #13#) (|coefficients| ((#96# $) NIL T ELT)) (|coefficient| ((|#1| $ #6#) 71 T ELT) #77# #78#) (|charthRoot| (#74# NIL (OR #114# (|has| |#1| #115#)) ELT)) (|characteristic| (#29# NIL T CONST)) (|binomThmExpt| (($ $ $ #6#) NIL #44# ELT)) (|before?| #1#) (|associates?| (#2# NIL #12# ELT)) (|annihilate?| #1#) (|Zero| (#33# 26 T CONST)) (|Vectorise| (#116=(#5# $) 84 T ELT)) (|UnVectorise| (($ #5#) 58 T ELT)) (|One| (#33# 9 T CONST)) (D #78# #77# #98# #99# #88# #31# #100# #101# #102# #105# #107# #108#) (|An| (#116# NIL T ELT)) (= (#2# 77 T ELT)) (/ (#117=($ $ |#1|) NIL #28# ELT)) (- (#14# 80 T ELT) #56#) (+ (#21# 40 T ELT)) (** (($ $ #85#) NIL T ELT) (#32# 93 T ELT)) (* (($ #85# $) NIL T ELT) (($ #6# $) NIL T ELT) (($ #37# $) 65 T ELT) (#21# 83 T ELT) (($ $ #36#) NIL #92# ELT) (($ #36# $) NIL #92# ELT) (($ |#1| $) 63 T ELT) (#117# NIL T ELT))) 
(((|ModMonic| |#1| |#2|) (|Join| #1=(|UnivariatePolynomialCategory| |#1|) (|CoercibleFrom| |#2|) (CATEGORY |domain| (SIGNATURE |setPoly| (|#2| |#2|)) (SIGNATURE |modulus| (|#2|)) (SIGNATURE |reduce| ($ |#2|)) (SIGNATURE |lift| (|#2| $)) (SIGNATURE |Vectorise| #2=(#3=(|Vector| |#1|) $)) (SIGNATURE |UnVectorise| ($ #3#)) (SIGNATURE |An| #2#) (SIGNATURE |pow| #4=((|PrimitiveArray| $))) (SIGNATURE |computePowers| #4#) (IF (|has| |#1| (|FiniteFieldCategory|)) (SIGNATURE |frobenius| ($ $)) |%noBranch|) (IF (|has| |#1| #5=(|Finite|)) (ATTRIBUTE #5#) |%noBranch|))) (|Ring|) #1#) (T |ModMonic|)) 
((|setPoly| (*1 *2 *2) #1=(AND #2=(|ofCategory| *3 #3=(|Ring|)) #4=(|isDomain| *1 (|ModMonic| *3 *2)) #5=(|ofCategory| *2 #6=(|UnivariatePolynomialCategory| *3)))) (|modulus| #7=(*1 *2) #8=(AND #5# #4# #2#)) (|reduce| #9=(*1 *1 *2) #1#) (|lift| #10=(*1 *2 *1) #8#) (|Vectorise| #10# #11=(AND #2# #12=(|isDomain| *2 (|Vector| *3)) #13=(|isDomain| *1 #14=(|ModMonic| *3 *4)) #15=(|ofCategory| *4 #6#))) (|UnVectorise| #9# (AND #12# #2# #13# #15#)) (|An| #10# #11#) (|pow| #7# #16=(AND #2# (|isDomain| *2 (|PrimitiveArray| #14#)) #13# #15#)) (|computePowers| #7# #16#) (|frobenius| (*1 *1 *1) (AND (|ofCategory| *2 (|FiniteFieldCategory|)) (|ofCategory| *2 #3#) (|isDomain| *1 (|ModMonic| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|min| #3=(($ $ $) NIL T ELT)) (|max| #3#) (|latex| (((|String|) $) NIL T ELT)) (|index| ((|#1| $) 13 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exponent| ((|#2| $) 12 T ELT)) (|construct| (($ |#1| |#2|) 16 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #4=(|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) 15 T ELT) ((#4# $) 14 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 11 T ELT))) 
(((|ModuleMonomial| |#1| |#2| |#3|) (|Join| #1=(|OrderedSet|) (|HomotopicTo| #2=(|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) (CATEGORY |domain| (SIGNATURE |exponent| (|#2| $)) (SIGNATURE |index| (|#1| $)) (SIGNATURE |construct| ($ |#1| |#2|)))) #1# (|SetCategory|) (|Mapping| (|Boolean|) #2# #2#)) (T |ModuleMonomial|)) 
((|exponent| #1=(*1 *2 *1) (AND (|ofCategory| *2 #2=(|SetCategory|)) (|isDomain| *1 (|ModuleMonomial| *3 *2 *4)) (|ofCategory| *3 #3=(|OrderedSet|)) (|ofType| *4 (|Mapping| #4=(|Boolean|) #5=(|Record| (|:| |index| *3) (|:| |exponent| *2)) #5#)))) (|index| #1# (AND #6=(|ofCategory| *2 #3#) #7=(|isDomain| *1 (|ModuleMonomial| *2 *3 *4)) #8=(|ofCategory| *3 #2#) #9=(|ofType| *4 (|Mapping| #4# #10=(|Record| (|:| |index| *2) (|:| |exponent| *3)) #10#)))) (|construct| (*1 *1 *2 *3) (AND #7# #6# #8# #9#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) 66 T ELT)) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #7=(#5#)) $) 101 T ELT) (((|Union| #8=(|BasicOperator|) . #7#) $) 107 T ELT)) (|retract| ((|#1| . #9=($)) NIL T ELT) ((#8# . #9#) 39 T ELT)) (|recip| ((#4# $) 102 T ELT)) (|opposite?| #1#) (|opeval| ((|#2| #8# |#2|) 93 T ELT)) (|one?| (#3# NIL T ELT)) (|makeop| (($ |#1| (|FreeGroup| #8#)) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|evaluateInverse| (#10=($ $ (|Mapping| |#2| |#2|)) 65 T ELT)) (|evaluate| (#10# 44 T ELT)) (|elt| ((|#2| $ |#2|) 33 T ELT)) (|conjug| ((|#1| |#1|) 112 #11=(|has| |#1| (|CommutativeRing|)) ELT)) (|coerce| (((|OutputForm|) $) 73 T ELT) (($ #12=(|Integer|)) 18 T ELT) (($ |#1|) 17 T ELT) (($ #8#) 23 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#13=(|NonNegativeInteger|)) 37 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|adjoint| (#14=($ $) 111 #11# ELT) (#15=($ $ $) 115 #11# ELT)) (|Zero| (#6# 21 T CONST)) (|One| (#6# 9 T CONST)) (= #1#) (- (#14# 48 T ELT) (#15# NIL T ELT)) (+ (#15# 83 T ELT)) (** (($ $ #16=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) NIL T ELT) (($ #8# #12#) NIL T ELT) (($ $ #12#) 64 T ELT)) (* (($ #16# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #12# $) 110 T ELT) (#15# 53 T ELT) (($ |#1| $) 108 #11# ELT) (($ $ |#1|) 109 #11# ELT))) 
(((|ModuleOperator| |#1| |#2|) (|Join| #1=(|Ring|) (|RetractableTo| |#1|) (|RetractableTo| #2=(|BasicOperator|)) (|Eltable| |#2| |#2|) (CATEGORY |domain| (IF (|has| |#1| #3=(|CharacteristicZero|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |#1| #4=(|CharacteristicNonZero|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|Algebra| |#1|)) (SIGNATURE |adjoint| ($ $)) (SIGNATURE |adjoint| ($ $ $)) (SIGNATURE |conjug| (|#1| |#1|))) |%noBranch|) (SIGNATURE |evaluate| #5=($ $ (|Mapping| |#2| |#2|))) (SIGNATURE |evaluateInverse| #5#) (SIGNATURE ** ($ #2# #6=(|Integer|))) (SIGNATURE ** ($ $ #6#)) (SIGNATURE |opeval| (|#2| #2# |#2|)) (SIGNATURE |makeop| ($ |#1| (|FreeGroup| #2#))))) #1# (|LeftModule| |#1|)) (T |ModuleOperator|)) 
((|adjoint| (*1 *1 *1) #1=(AND (|ofCategory| *2 (|CommutativeRing|)) #2=(|ofCategory| *2 #3=(|Ring|)) (|isDomain| *1 (|ModuleOperator| *2 *3)) (|ofCategory| *3 #4=(|LeftModule| *2)))) (|adjoint| (*1 *1 *1 *1) #1#) (|conjug| (*1 *2 *2) #1#) (|evaluate| #5=(*1 *1 *1 *2) #6=(AND (|isDomain| *2 (|Mapping| *4 *4)) #7=(|ofCategory| *4 (|LeftModule| *3)) #8=(|ofCategory| *3 #3#) #9=(|isDomain| *1 (|ModuleOperator| *3 *4)))) (|evaluateInverse| #5# #6#) (** #10=(*1 *1 *2 *3) (AND (|isDomain| *2 #11=(|BasicOperator|)) (|isDomain| *3 #12=(|Integer|)) #13=(|ofCategory| *4 #3#) (|isDomain| *1 (|ModuleOperator| *4 *5)) (|ofCategory| *5 #14=(|LeftModule| *4)))) (** #5# (AND (|isDomain| *2 #12#) #8# #9# #7#)) (|opeval| (*1 *2 *3 *2) (AND (|isDomain| *3 #11#) #13# (|isDomain| *1 (|ModuleOperator| *4 *2)) (|ofCategory| *2 #14#))) (|makeop| #10# (AND (|isDomain| *3 (|FreeGroup| #11#)) #2# (|isDomain| *1 (|ModuleOperator| *2 *4)) (|ofCategory| *4 #4#)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 33 T ELT)) (|subtractIfCan| (#5=(#6=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#7=($) NIL T CONST)) (|reduce| (($ |#1| |#2|) 25 T ELT)) (|recip| ((#6# $) 51 T ELT)) (|opposite?| #1#) (|one?| (#4# 35 T ELT)) (|modulus| ((|#2| $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#8=($ $) 52 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exQuo| (#5# 50 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #9=(|Integer|)) 19 T ELT) ((|#1| $) 13 T ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) 28 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#7# 16 T CONST)) (|One| (#7# 30 T CONST)) (= (#2# 41 T ELT)) (- (#8# 46 T ELT) (#11=($ $ $) 40 T ELT)) (+ (#11# 43 T ELT)) (** (($ $ #12=(|PositiveInteger|)) NIL T ELT) (($ $ #10#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #9# $) 21 T ELT) (#11# 20 T ELT))) 
(((|ModularRing| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |modulus| (|#2| $)) (SIGNATURE |coerce| (|#1| $)) (SIGNATURE |reduce| ($ |#1| |#2|)) (SIGNATURE |exQuo| (#1=(|Union| $ #2="failed") $ $)) (SIGNATURE |recip| (#1# $)) (SIGNATURE |inv| ($ $)))) (|CommutativeRing|) (|AbelianMonoid|) (|Mapping| |#1| |#1| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2|) (|Mapping| (|Union| |#1| #2#) |#1| |#1| |#2|)) (T |ModularRing|)) 
((|recip| #1=(*1 *1 *1) #2=(|partial| AND #3=(|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) #4=(|ofCategory| *2 #5=(|CommutativeRing|)) #6=(|ofCategory| *3 #7=(|AbelianMonoid|)) #8=(|ofType| *4 (|Mapping| *2 *2 *3)) #9=(|ofType| *5 (|Mapping| #10=(|Union| *3 #11="failed") *3 *3)) #12=(|ofType| *6 (|Mapping| #13=(|Union| *2 #11#) *2 *2 *3)))) (|modulus| #14=(*1 *2 *1) (AND (|ofCategory| *2 #7#) (|isDomain| *1 (|ModularRing| *3 *2 *4 *5 *6)) (|ofCategory| *3 #5#) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| #13# *2 *2)) (|ofType| *6 (|Mapping| #10# *3 *3 *2)))) (|coerce| #14# (AND #4# #3# #6# #8# #9# #12#)) (|reduce| (*1 *1 *2 *3) #15=(AND #3# #4# #6# #8# #9# #12#)) (|exQuo| (*1 *1 *1 *1) #2#) (|inv| #1# #15#)) 
((* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ |#2|) 9 T ELT))) 
(((|Module&| |#1| |#2|) (CATEGORY |package| (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 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT) (($ $ |#1|) 37 T ELT))) 
(((|Module| |#1|) (|Category|) (|CommutativeRing|)) (T |Module|)) 
NIL 
(|Join| (|BiModule| |t#1| |t#1|) (|LinearSet| |t#1|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|shift| (#4=($ |#1|) 17 T ELT) (#5=($ $ |#1|) 20 T ELT)) (|scale| (#4# 18 T ELT) (#5# 21 T ELT)) (|sample| (#6=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT) (#6# 19 T ELT) (#7=($ $) 22 T ELT)) (|one?| ((#3# $) NIL T ELT)) (|moebius| (($ |#1| |#1| |#1| |#1|) 8 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#7# 16 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| ((|#1| $ |#1|) 24 T ELT) ((#8=(|OnePointCompletion| |#1|) $ #8#) 32 T ELT)) (|conjugate| #9=(#10=($ $ $) NIL T ELT)) (|commutator| #9#) (|coerce| (((|OutputForm|) $) 39 T ELT)) (|before?| #1#) (|One| (#6# 9 T CONST)) (= (#2# 48 T ELT)) (/ #9#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ (|Integer|)) NIL T ELT)) (* (#10# 14 T ELT))) 
(((|MoebiusTransform| |#1|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |moebius| ($ |#1| |#1| |#1| |#1|)) (SIGNATURE |shift| #1=($ |#1|)) (SIGNATURE |scale| #1#) (SIGNATURE |recip| ($)) (SIGNATURE |shift| #2=($ $ |#1|)) (SIGNATURE |scale| #2#) (SIGNATURE |recip| ($ $)) (SIGNATURE |eval| (|#1| $ |#1|)) (SIGNATURE |eval| (#3=(|OnePointCompletion| |#1|) $ #3#)))) (|Field|)) (T |MoebiusTransform|)) 
((|moebius| (*1 *1 *2 *2 *2 *2) #1=(AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 #2=(|Field|)))) (|shift| #3=(*1 *1 *2) #1#) (|scale| #3# #1#) (|recip| (*1 *1) #1#) (|shift| #4=(*1 *1 *1 *2) #1#) (|scale| #4# #1#) (|recip| (*1 *1 *1) #1#) (|eval| #5=(*1 *2 *1 *2) #1#) (|eval| #5# (AND (|isDomain| *2 (|OnePointCompletion| *3)) (|ofCategory| *3 #2#) (|isDomain| *1 (|MoebiusTransform| *3))))) 
((|rightPower| (#1=($ $ (|PositiveInteger|)) 19 T ELT)) (|leftPower| (#1# 20 T ELT)) (** (#1# 10 T ELT))) 
(((|Monad&| |#1|) (CATEGORY |package| (SIGNATURE ** #1=(|#1| |#1| (|PositiveInteger|))) (SIGNATURE |leftPower| #1#) (SIGNATURE |rightPower| #1#)) (|Monad|)) (T |Monad&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|rightPower| (($ $ (|PositiveInteger|)) 19 T ELT)) (|leftPower| (($ $ (|PositiveInteger|)) 18 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT)) (* (($ $ $) 20 T ELT))) 
(((|Monad|) (|Category|)) (T |Monad|)) 
((* (*1 *1 *1 *1) (|ofCategory| *1 (|Monad|))) (|rightPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|)))) (|leftPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |rightPower| ($ $ (|PositiveInteger|))) (SIGNATURE |leftPower| ($ $ (|PositiveInteger|))) (SIGNATURE ** ($ $ (|PositiveInteger|))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|rightPower| #1=(($ $ (|PositiveInteger|)) NIL T ELT) (#2=($ $ (|NonNegativeInteger|)) 18 T ELT)) (|one?| (((|Boolean|) $) 10 T ELT)) (|leftPower| #1# (#2# 19 T ELT)) (** #1# (#2# 16 T ELT))) 
(((|MonadWithUnit&| |#1|) (CATEGORY |package| (SIGNATURE ** #1=(|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |leftPower| #1#) (SIGNATURE |rightPower| #1#) (SIGNATURE |one?| ((|Boolean|) |#1|)) (SIGNATURE ** #2=(|#1| |#1| (|PositiveInteger|))) (SIGNATURE |leftPower| #2#) (SIGNATURE |rightPower| #2#)) (|MonadWithUnit|)) (T |MonadWithUnit&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|rightRecip| (((|Union| $ "failed") $) 22 T ELT)) (|rightPower| (#2=($ $ (|PositiveInteger|)) 19 T ELT) (($ $ (|NonNegativeInteger|)) 27 T ELT)) (|recip| (((|Union| $ "failed") $) 24 T ELT)) (|one?| (((|Boolean|) $) 28 T ELT)) (|leftRecip| (((|Union| $ "failed") $) 23 T ELT)) (|leftPower| (#2# 18 T ELT) (($ $ (|NonNegativeInteger|)) 26 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (($) 29 T CONST)) (= (#1# 8 T ELT)) (** (#2# 17 T ELT) (($ $ (|NonNegativeInteger|)) 25 T ELT)) (* (($ $ $) 20 T ELT))) 
(((|MonadWithUnit|) (|Category|)) (T |MonadWithUnit|)) 
((|One| (*1 *1) (|ofCategory| *1 (|MonadWithUnit|))) (|one?| (*1 *2 *1) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|Boolean|)))) (|rightPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leftPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|NonNegativeInteger|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|MonadWithUnit|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|recip| (*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|))) (|leftRecip| (*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|))) (|rightRecip| (*1 *1 *1) (|partial| |ofCategory| *1 (|MonadWithUnit|)))) 
(|Join| (|Monad|) (CATEGORY |domain| (SIGNATURE |One| ($) |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) ((|Join|) . T) ((|Monad|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|size| ((#1=(|NonNegativeInteger|)) 39 T ELT)) (|retractIfCan| (((|Union| #2=(|Integer|) #3="failed") $) NIL T ELT) (((|Union| #4=(|Fraction| #2#) #3#) $) NIL T ELT) (((|Union| |#2| #3#) $) 26 T ELT)) (|retract| ((#2# $) NIL T ELT) ((#4# $) NIL T ELT) (#5=(|#2| $) 23 T ELT)) (|reduce| (#6=($ |#3|) NIL T ELT) ((#7=(|Union| $ #3#) (|Fraction| |#3|)) 49 T ELT)) (|recip| ((#7# $) 69 T ELT)) (|random| (#8=($) 43 T ELT)) (|norm| (#5# 21 T ELT)) (|generator| (#8# 18 T ELT)) (|differentiate| (($ $ #9=(|Mapping| |#2| |#2|)) 57 T ELT) (($ $ #9# #1#) NIL T ELT) (($ $ #10=(|List| #11=(|Symbol|)) (|List| #1#)) NIL T ELT) (($ $ #11# #1#) NIL T ELT) (($ $ #10#) NIL T ELT) (($ $ #11#) NIL T ELT) (($ $ #1#) NIL T ELT) (($ $) NIL T ELT)) (|derivationCoordinates| (((|Matrix| |#2|) #12=(|Vector| $) #9#) 64 T ELT)) (|convert| ((#13=(|Vector| |#2|) $) NIL T ELT) (($ #13#) NIL T ELT) (#14=(|#3| $) 10 T ELT) (#6# 12 T ELT)) (|characteristicPolynomial| (#14# 36 T ELT)) (|basis| ((#12#) 33 T ELT))) 
(((|MonogenicAlgebra&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #1=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #2=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|List| #2#))) (SIGNATURE |differentiate| (|#1| |#1| #2# #1#)) (SIGNATURE |differentiate| (|#1| |#1| #3# (|List| #1#))) (SIGNATURE |random| #4=(|#1|)) (SIGNATURE |size| (#1#)) (SIGNATURE |differentiate| (|#1| |#1| #5=(|Mapping| |#2| |#2|) #1#)) (SIGNATURE |differentiate| (|#1| |#1| #5#)) (SIGNATURE |derivationCoordinates| ((|Matrix| |#2|) #6=(|Vector| |#1|) #5#)) (SIGNATURE |reduce| (#7=(|Union| |#1| #8="failed") (|Fraction| |#3|))) (SIGNATURE |convert| #9=(|#1| |#3|)) (SIGNATURE |reduce| #9#) (SIGNATURE |generator| #4#) (SIGNATURE |retractIfCan| ((|Union| |#2| #8#) |#1|)) (SIGNATURE |retract| #10=(|#2| |#1|)) (SIGNATURE |retract| (#11=(|Fraction| #12=(|Integer|)) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #11# #8#) |#1|)) (SIGNATURE |retract| (#12# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #12# #8#) |#1|)) (SIGNATURE |convert| #13=(|#3| |#1|)) (SIGNATURE |convert| (|#1| #14=(|Vector| |#2|))) (SIGNATURE |convert| (#14# |#1|)) (SIGNATURE |basis| (#6#)) (SIGNATURE |characteristicPolynomial| #13#) (SIGNATURE |norm| #10#) (SIGNATURE |recip| (#7# |#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))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 114 (|has| |#1| . #3=((|Field|))) ELT)) (|unitCanonical| (($ $) 115 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 117 (|has| |#1| . #3#) ELT)) (|traceMatrix| (((|Matrix| |#1|) #5=(|Vector| $)) 61 T ELT) (((|Matrix| |#1|)) 77 T ELT)) (|trace| ((|#1| . #6=($)) 67 T ELT)) (|tableForDiscreteLogarithm| (((|Table| #7=(|PositiveInteger|) #8=(|NonNegativeInteger|)) #9=(|Integer|)) 167 (|has| |#1| . #10=((|FiniteFieldCategory|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 134 (|has| |#1| . #3#) ELT)) (|squareFree| (#11=((|Factored| $) $) 135 (|has| |#1| . #3#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 125 (|has| |#1| . #3#) ELT)) (|size| (((|NonNegativeInteger|)) 108 (|has| |#1| . #12=((|Finite|))) ELT)) (|sample| (#13=($) 23 T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=("failed")) . #16=($)) 194 (|has| |#1| . #17=((|RetractableTo| #14#))) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) 192 (|has| |#1| . #19=((|RetractableTo| #18#))) ELT) (((|Union| |#1| . #15#) . #16#) 189 T ELT)) (|retract| ((#14# . #20=($)) 193 (|has| |#1| . #17#) ELT) ((#18# . #20#) 191 (|has| |#1| . #19#) ELT) ((|#1| . #20#) 190 T ELT)) (|represents| (($ (|Vector| |#1|) #5#) 63 T ELT) (($ (|Vector| |#1|)) 80 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 173 (|has| |#1| . #10#) ELT)) (|rem| (#21=($ $ $) 129 (|has| |#1| . #3#) ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ #5#) 68 T ELT) (((|Matrix| |#1|) $) 75 T ELT)) (|reducedSystem| (((|Matrix| #22=(|Integer|)) . #23=(#24=(|Matrix| $))) 186 (|has| |#1| . #25=((|LinearlyExplicitRingOver| #22#))) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #26=(#24# #27=(|Vector| $))) 185 (|has| |#1| . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #26#) 184 T ELT) (((|Matrix| |#1|) . #23#) 183 T ELT)) (|reduce| (($ |#2|) 178 T ELT) (((|Union| $ "failed") (|Fraction| |#2|)) 175 (|has| |#1| (|Field|)) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rank| (((|PositiveInteger|)) 69 T ELT)) (|random| (($) 111 (|has| |#1| . #12#) ELT)) (|quo| (#21# 128 (|has| |#1| . #3#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #28=(|List| $)) (|:| |generator| $)) #28#) 123 (|has| |#1| . #3#) ELT)) (|primitiveElement| (#29=($) 169 (|has| |#1| . #10#) ELT)) (|primitive?| (((|Boolean|) $) 170 (|has| |#1| . #10#) ELT)) (|primeFrobenius| (($ $ #30=(|NonNegativeInteger|)) 161 (|has| |#1| . #10#) ELT) (($ $) 160 (|has| |#1| . #10#) ELT)) (|prime?| (((|Boolean|) $) 136 (|has| |#1| . #3#) ELT)) (|order| ((#7# $) 172 (|has| |#1| . #10#) ELT) (((|OnePointCompletion| (|PositiveInteger|)) $) 158 (|has| |#1| . #10#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|norm| ((|#1| . #6#) 66 T ELT)) (|nextItem| (((|Maybe| $) $) 162 (|has| |#1| . #10#) ELT)) (|multiEuclidean| (((|Union| #31=(|List| $) #32="failed") #31# $) 132 (|has| |#1| . #3#) ELT)) (|minimalPolynomial| ((|#2| . #33=($)) 59 (|has| |#1| (|Field|)) ELT)) (|lookup| ((#34=(|PositiveInteger|) $) 110 (|has| |#1| . #12#) ELT)) (|lift| ((|#2| $) 176 T ELT)) (|leftReducedSystem| (((|Matrix| #22#) . #35=(#27#)) 188 (|has| |#1| . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #36=(#27# $)) 187 (|has| |#1| . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #36#) 182 T ELT) (((|Matrix| |#1|) . #35#) 181 T ELT)) (|lcm| (#37=($ (|List| $)) 121 (|has| |#1| . #3#) ELT) (#38=($ $ $) 120 (|has| |#1| . #3#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 137 (|has| |#1| . #3#) ELT)) (|init| (($) 163 (|has| |#1| . #10#) CONST)) (|index| (($ #34#) 109 (|has| |#1| . #12#) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (($) 180 T ELT)) (|gcdPolynomial| ((#39=(|SparseUnivariatePolynomial| $) #39# #39#) 122 (|has| |#1| . #3#) ELT)) (|gcd| (#37# 119 (|has| |#1| . #3#) ELT) (#38# 118 (|has| |#1| . #3#) ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #9#) (|:| |exponent| #9#)))) 166 (|has| |#1| . #10#) ELT)) (|factor| (#11# 133 (|has| |#1| . #3#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $)) #32#) $ $ $) 131 (|has| |#1| . #3#) ELT) (((|Record| #40# #41# (|:| |generator| $)) $ $) 130 (|has| |#1| . #3#) ELT)) (|exquo| (((|Union| $ "failed") $ $) 113 (|has| |#1| . #3#) ELT)) (|expressIdealMember| (((|Maybe| #28#) #28# $) 124 (|has| |#1| . #3#) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 126 (|has| |#1| . #3#) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 127 (|has| |#1| . #3#) ELT)) (|discriminant| ((|#1| #5#) 62 T ELT) ((|#1|) 76 T ELT)) (|discreteLog| ((#8# $) 171 (|has| |#1| . #10#) ELT) (((|Union| #30# "failed") $ $) 159 (|has| |#1| . #10#) ELT)) (|differentiate| (#42=($ $ (|NonNegativeInteger|)) 156 (OR (|and| (|has| |#1| . #43=((|DifferentialSpace|))) (|has| |#1| . #44=((|Field|)))) (|has| |#1| . #10#)) ELT) (($ . #45=($)) 154 (OR (|and| (|has| |#1| . #43#) (|has| |#1| . #44#)) (|has| |#1| . #10#)) ELT) (($ $ (|List| #46=(|Symbol|)) . #47=((|List| #48=(|NonNegativeInteger|)))) 150 (|and| (|has| |#1| . #49=((|PartialDifferentialSpace| (|Symbol|)))) (|has| |#1| . #44#)) ELT) (($ $ #46# . #50=(#48#)) 149 (|and| (|has| |#1| . #49#) (|has| |#1| . #44#)) ELT) (($ $ (|List| #46#)) 148 (|and| (|has| |#1| . #49#) (|has| |#1| . #44#)) ELT) (($ $ #46#) 146 (|and| (|has| |#1| . #49#) (|has| |#1| . #44#)) ELT) (($ $ (|Mapping| |#1| |#1|)) 145 (|has| |#1| . #44#) ELT) (($ $ (|Mapping| |#1| |#1|) . #51=((|NonNegativeInteger|))) 144 (|has| |#1| . #44#) ELT)) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) 174 (|has| |#1| (|Field|)) ELT)) (|definingPolynomial| ((|#2|) 179 T ELT)) (|createPrimitiveElement| (#29# 168 (|has| |#1| . #10#) ELT)) (|coordinates| (((|Vector| |#1|) $ #5#) 65 T ELT) (((|Matrix| |#1|) #5# #5#) 64 T ELT) (((|Vector| |#1|) . #52=($)) 82 T ELT) (((|Matrix| |#1|) #53=(|Vector| $)) 81 T ELT)) (|convert| (((|Vector| |#1|) . #52#) 79 T ELT) (($ (|Vector| |#1|)) 78 T ELT) ((|#2| $) 195 T ELT) (($ |#2|) 177 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 165 (|has| |#1| . #10#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT) (($ $) 112 (|has| |#1| . #3#) ELT) (($ #18#) 107 (OR (|has| |#1| . #3#) (|has| |#1| . #19#)) ELT)) (|charthRoot| (($ $) 164 (|has| |#1| . #10#) ELT) (((|Maybe| $) $) 58 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#2| . #33#) 60 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| ((#53#) 83 T ELT)) (|associates?| ((#4# $ $) 116 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#13# 24 T CONST)) (|One| (($) 45 T CONST)) (D (#42# 157 (OR (|and| (|has| |#1| . #43#) (|has| |#1| . #44#)) (|has| |#1| . #10#)) ELT) (($ . #45#) 155 (OR (|and| (|has| |#1| . #43#) (|has| |#1| . #44#)) (|has| |#1| . #10#)) ELT) (($ $ (|List| #46#) . #47#) 153 (|and| (|has| |#1| . #49#) (|has| |#1| . #44#)) ELT) (($ $ #46# . #50#) 152 (|and| (|has| |#1| . #49#) (|has| |#1| . #44#)) ELT) (($ $ (|List| #46#)) 151 (|and| (|has| |#1| . #49#) (|has| |#1| . #44#)) ELT) (($ $ #46#) 147 (|and| (|has| |#1| . #49#) (|has| |#1| . #44#)) ELT) (($ $ (|Mapping| |#1| |#1|)) 143 (|has| |#1| . #44#) ELT) (($ $ (|Mapping| |#1| |#1|) . #51#) 142 (|has| |#1| . #44#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 141 (|has| |#1| . #3#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #54=(|Integer|)) 138 (|has| |#1| . #3#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #55=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #55#) 53 T ELT) (($ #56=(|Fraction| #54#) . #55#) 140 (|has| |#1| . #3#) ELT) (($ $ #56#) 139 (|has| |#1| . #3#) ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Algebra| |#1|) . T) ((|Algebra| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|BasicType|) . T) ((|BiModule| #1# #1#) 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|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| |#2|) . T) ((|DifferentialDomain| $) OR (|has| |#1| (|FiniteFieldCategory|)) (AND (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|Field|))) (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|)))) ((|DifferentialExtension| |#1|) |has| |#1| (|Field|)) ((|DifferentialRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|)))) ((|DifferentialSpace|) OR (|has| |#1| (|FiniteFieldCategory|)) (AND (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|Field|))) (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|)))) ((|DifferentialSpaceExtension| |#1|) |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| (|FiniteFieldCategory|)) (|has| |#1| (|Finite|))) ((|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|))) ((|Join|) . T) ((|LeftLinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LinearSet| |#1|) . T) ((|LinearSet| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Module| |#1|) . T) ((|Module| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) OR (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialSpace| #3#) OR (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialSpace| (|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) ((|RightLinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|FiniteFieldCategory|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)))) 
((|sample| (($) 11 T CONST)) (|recip| (((|Union| $ "failed") $) 14 T ELT)) (|one?| (((|Boolean|) $) 10 T ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) 20 T ELT))) 
(((|Monoid&| |#1|) (CATEGORY |package| (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |one?| ((|Boolean|) |#1|)) (SIGNATURE |sample| (|#1|) |constant|) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|Monoid|)) (T |Monoid&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|sample| (($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|one?| (((|Boolean|) $) 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (($) 24 T CONST)) (= (#1# 8 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT)) (* (($ $ $) 18 T ELT))) 
(((|Monoid|) (|Category|)) (T |Monoid|)) 
((|One| (*1 *1) (|ofCategory| *1 (|Monoid|))) (|sample| (*1 *1) (|ofCategory| *1 (|Monoid|))) (|one?| (*1 *2 *1) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|Boolean|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|recip| (*1 *1 *1) (|partial| |ofCategory| *1 (|Monoid|)))) 
(|Join| (|SemiGroup|) (CATEGORY |domain| (SIGNATURE |One| ($) |constant|) (SIGNATURE |sample| ($) |constant|) (SIGNATURE |one?| ((|Boolean|) $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE |recip| ((|Union| $ "failed") $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|neutralValue| ((|#1| $) 16 T ELT)) (|monoidOperation| (($ (|Mapping| |#1| |#1| |#1|) |#1|) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ |#1| |#1|) 14 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (((|SemiGroupOperation| |#1|) $) 17 T ELT)) (|before?| #1#) (= #1#)) 
(((|MonoidOperation| |#1|) (|Join| (|MonoidOperatorCategory| |#1|) (|SetCategory|) (|CoercibleTo| (|SemiGroupOperation| |#1|)) (CATEGORY |domain| (SIGNATURE |monoidOperation| ($ (|Mapping| |#1| |#1| |#1|) |#1|)))) (|BasicType|)) (T |MonoidOperation|)) 
((|monoidOperation| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|BasicType|)) (|isDomain| *1 (|MonoidOperation| *3))))) 
((|neutralValue| ((|#1| $) 8 T ELT)) (|elt| ((|#1| $ |#1| |#1|) 6 T ELT))) 
(((|MonoidOperatorCategory| |#1|) (|Category|) (|BasicType|)) (T |MonoidOperatorCategory|)) 
((|neutralValue| (*1 *2 *1) (AND (|ofCategory| *1 (|MonoidOperatorCategory| *2)) (|ofCategory| *2 (|BasicType|))))) 
(|Join| (|SemiGroupOperatorCategory| |t#1|) (CATEGORY |domain| (SIGNATURE |neutralValue| (|t#1| $)) (ATTRIBUTE (|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|)) (SEQ (= (|f| |x| (|neutralValue| |f|)) |x|) (|exit| 1 (= (|f| (|neutralValue| |f|) |x|) |x|)))))))) 
(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|SemiGroupOperatorCategory| |#1|) . T) ((|Type|) . T)) 
((|splitSquarefree| (((|Record| (|:| |normal| #1=(|Factored| |#2|)) (|:| |special| #1#)) |#2| #2=(|Mapping| |#2| |#2|)) 39 T ELT)) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| #2#) 12 T ELT)) (|normalDenom| ((|#2| #3=(|Fraction| |#2|) #2#) 13 T ELT)) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| #3#) (|:| |special| #3#)) #3# #2#) 48 T ELT))) 
(((|MonomialExtensionTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |split| ((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| #1=(|Mapping| |#2| |#2|))) (SIGNATURE |splitSquarefree| ((|Record| (|:| |normal| #2=(|Factored| |#2|)) (|:| |special| #2#)) |#2| #1#)) (SIGNATURE |normalDenom| (|#2| #3=(|Fraction| |#2|) #1#)) (SIGNATURE |decompose| ((|Record| (|:| |poly| |#2|) (|:| |normal| #3#) (|:| |special| #3#)) #3# #1#))) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |MonomialExtensionTools|)) 
((|decompose| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 #2=(|UnivariatePolynomialCategory| *5)) #3=(|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |poly| *6) (|:| |normal| #4=(|Fraction| *6)) (|:| |special| #4#))) (|isDomain| *1 (|MonomialExtensionTools| *5 *6)) (|isDomain| *3 #4#))) (|normalDenom| #1# (AND (|isDomain| *3 (|Fraction| *2)) (|isDomain| *4 (|Mapping| *2 *2)) (|ofCategory| *2 #2#) (|isDomain| *1 (|MonomialExtensionTools| *5 *2)) #3#)) (|splitSquarefree| #1# (AND #5=(|isDomain| *4 (|Mapping| *3 *3)) #6=(|ofCategory| *3 #2#) #3# (|isDomain| *2 (|Record| (|:| |normal| #7=(|Factored| *3)) (|:| |special| #7#))) #8=(|isDomain| *1 (|MonomialExtensionTools| *5 *3)))) (|split| #1# (AND #5# #6# #3# (|isDomain| *2 (|Record| (|:| |normal| *3) (|:| |special| *3))) #8#))) 
((|reshape| ((|#7| (|List| |#5|) |#6|) NIL T ELT)) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) 27 T ELT))) 
(((|MPolyCatFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (CATEGORY |package| (SIGNATURE |map| (|#7| (|Mapping| |#5| |#4|) |#6|)) (SIGNATURE |reshape| (|#7| (|List| |#5|) |#6|))) (|OrderedSet|) #1=(|OrderedAbelianMonoidSup|) #1# #2=(|Ring|) #2# (|PolynomialCategory| |#4| |#2| |#1|) (|PolynomialCategory| |#5| |#3| |#1|)) (T |MPolyCatFunctions2|)) 
((|reshape| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *9)) #2=(|ofCategory| *9 #3=(|Ring|)) #4=(|ofCategory| *5 (|OrderedSet|)) #5=(|ofCategory| *6 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *8 #3#) #8=(|ofCategory| *2 (|PolynomialCategory| *9 *7 *5)) #9=(|isDomain| *1 (|MPolyCatFunctions2| *5 *6 *7 *8 *9 *4 *2)) #10=(|ofCategory| *7 #6#) #11=(|ofCategory| *4 (|PolynomialCategory| *8 *6 *5)))) (|map| #1# (AND (|isDomain| *3 (|Mapping| *9 *8)) #7# #2# #4# #5# #8# #9# #10# #11#))) 
((|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) 28 T ELT))) 
(((|MPolyCatFunctions3| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (CATEGORY |package| (SIGNATURE |map| (|#7| (|Mapping| |#2| |#1|) |#6|))) #1=(|OrderedSet|) #1# #2=(|OrderedAbelianMonoidSup|) #2# (|Ring|) (|PolynomialCategory| |#5| |#3| |#1|) (|PolynomialCategory| |#5| |#4| |#2|)) (T |MPolyCatFunctions3|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|OrderedSet|)) (|ofCategory| *6 #1#) (|ofCategory| *7 #2=(|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|Ring|)) (|ofCategory| *2 (|PolynomialCategory| *9 *8 *6)) (|isDomain| *1 (|MPolyCatFunctions3| *5 *6 *7 *8 *9 *4 *2)) (|ofCategory| *8 #2#) (|ofCategory| *4 (|PolynomialCategory| *9 *7 *5))))) 
((|factor| (((|Factored| |#4|) |#4|) 42 T ELT))) 
(((|MPolyCatPolyFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) (|OrderedAbelianMonoidSup|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#)))) (|EuclideanDomain|) (|PolynomialCategory| (|Polynomial| |#3|) |#1| |#2|)) (T |MPolyCatPolyFactorizer|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#))))) (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MPolyCatPolyFactorizer| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| (|Polynomial| *6) *4 *5))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #8#) #8#) NIL #19=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#12# NIL #21=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #8#) #17#) #23# #8#) NIL #19# ELT)) (|sample| #24=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #25=(#17#)) . #26=($)) NIL T ELT) (((|Union| #27=(|Fraction| #28=(|Integer|)) . #25#) . #26#) NIL #29=(|has| |#2| (|RetractableTo| #27#)) ELT) (((|Union| #28# . #25#) . #26#) NIL #30=(|has| |#2| (|RetractableTo| #28#)) ELT) #31=(((|Union| #7# . #25#) . #26#) NIL T ELT)) (|retract| #32=(#33=(|#2| . #34=($)) NIL T ELT) ((#27# . #34#) NIL #29# ELT) ((#28# . #34#) NIL #30# ELT) ((#7# . #34#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #35=(|has| |#2| (|CommutativeRing|)) ELT)) (|reductum| #36=(#12# NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #28#) . #38=(#39=(|Matrix| $))) NIL #40=(|has| |#2| (|LinearlyExplicitRingOver| #28#)) ELT) ((#41=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #28#))) . #42=(#39# #43=(|Vector| $))) NIL #40# ELT) ((#44=(|Record| (|:| |mat| #45=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #42#) NIL T ELT) ((#45# . #38#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|primitivePart| #20# #46=(#47=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#2| #50=(|IndexedExponents| #7#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#2| #55#)) ELT) ((#56=(|PatternMatchResult| #28# . #53#) $ #57=(|Pattern| #28#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #28#)) (|has| |#2| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#2| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #31#) (|leftReducedSystem| ((#37# . #65=(#43#)) NIL #40# ELT) ((#41# . #66=(#43# $)) NIL #40# ELT) ((#44# . #66#) NIL T ELT) ((#45# . #65#) NIL T ELT)) (|leadingMonomial| #36#) (|leadingCoefficient| #32#) (|lcm| #67=(($ #49#) NIL #21# ELT) #68=(#69=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #17#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #17#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #32#) (|gcdPolynomial| ((#8# #8# #8#) NIL #21# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#16# $ |#2|) NIL #10# ELT) (#15# NIL #10# ELT)) (|eval| (($ $ (|List| #71=(|Equation| $))) NIL T ELT) (($ $ #71#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#2|) NIL T ELT) (($ $ #6# #72=(|List| |#2|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #35# ELT)) (|differentiate| #60# #59# #73=(($ $ #6#) NIL T ELT) #74=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #75=($)) NIL (AND (|has| #7# #76=(|ConvertibleTo| #54#)) (|has| |#2| #76#)) ELT) ((#57# . #75#) NIL (AND (|has| #7# #77=(|ConvertibleTo| #57#)) (|has| |#2| #77#)) ELT) ((#78=(|InputForm|) . #75#) NIL (AND (|has| #7# #79=(|ConvertibleTo| #78#)) (|has| |#2| #79#)) ELT)) (|content| (#33# NIL #21# ELT) #46#) (|conditionP| (((|Union| #43# #17#) #39#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #28#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) #11# (($ #27#) NIL (OR #82=(|has| |#2| (|Algebra| #27#)) #29#) ELT)) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #82# ELT) (($ #27# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) 
(((|MultivariatePolynomial| |#1| |#2|) (|PolynomialCategory| |#2| (|IndexedExponents| #1=(|OrderedVariableList| |#1|)) #1#) (|List| (|Symbol|)) (|Ring|)) (T |MultivariatePolynomial|)) 
NIL 
((|totalfract| (((|Record| (|:| |sup| #1=(|Polynomial| |#3|)) (|:| |inf| #1#)) |#4|) 14 T ELT)) (|pushup| (#2=(|#4| |#4| |#2|) 33 T ELT)) (|pushuconst| ((|#4| (|Fraction| #1#) |#2|) 62 T ELT)) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| #1#) |#2|) 74 T ELT)) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) 49 T ELT)) (|pushdown| (#2# 52 T ELT)) (|factor| (((|Factored| |#4|) |#4|) 40 T ELT))) 
(((|MPolyCatRationalFunctionFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |totalfract| ((|Record| (|:| |sup| #1=(|Polynomial| |#3|)) (|:| |inf| #1#)) |#4|)) (SIGNATURE |pushdown| #2=(|#4| |#4| |#2|)) (SIGNATURE |pushdterm| (|#4| (|SparseUnivariatePolynomial| |#4|) |#2|)) (SIGNATURE |pushup| #2#) (SIGNATURE |pushucoef| (|#4| (|SparseUnivariatePolynomial| #1#) |#2|)) (SIGNATURE |pushuconst| (|#4| #3=(|Fraction| #1#) |#2|)) (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) (|OrderedAbelianMonoidSup|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)))) (|IntegralDomain|) (|PolynomialCategory| #3# |#1| |#2|)) (T |MPolyCatRationalFunctionFactorizer|)) 
((|factor| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *5 #5=(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $))))) #6=(|ofCategory| *6 #7=(|IntegralDomain|)) (|isDomain| *2 (|Factored| *3)) #8=(|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3)) #9=(|ofCategory| *3 (|PolynomialCategory| #10=(|Fraction| #11=(|Polynomial| *6)) *4 *5)))) (|pushuconst| #12=(*1 *2 *3 *4) (AND #6# (|ofCategory| *2 (|PolynomialCategory| *3 *5 *4)) #13=(|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *5 *4 *6 *2)) (|isDomain| *3 #10#) #14=(|ofCategory| *5 #3#) #15=(|ofCategory| *4 #5#))) (|pushucoef| #12# (AND (|isDomain| *3 (|SparseUnivariatePolynomial| #11#)) #6# #16=(|ofCategory| *2 (|PolynomialCategory| #10# *5 *4)) #13# #14# #15#)) (|pushup| #17=(*1 *2 *2 *3) #18=(AND #2# (|ofCategory| *3 #5#) (|ofCategory| *5 #7#) (|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *3 *5 *2)) (|ofCategory| *2 (|PolynomialCategory| (|Fraction| (|Polynomial| *5)) *4 *3)))) (|pushdterm| #12# (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *2)) #16# #13# #14# #15# #6#)) (|pushdown| #17# #18#) (|totalfract| #1# (AND #2# #4# #6# (|isDomain| *2 (|Record| (|:| |sup| #11#) (|:| |inf| #11#))) #8# #9#))) 
((|factor| (((|Factored| |#4|) |#4|) 54 T ELT))) 
(((|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))))) 
((|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) 18 T ELT))) 
(((|MonoidRingFunctions2| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)))) #1=(|Ring|) #1# (|Monoid|)) (T |MonoidRingFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|MonoidRing| *5 *7)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofCategory| *7 (|Monoid|)) (|isDomain| *2 (|MonoidRing| *6 *7)) (|isDomain| *1 (|MonoidRingFunctions2| *5 *6 *7))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 36 T ELT)) (|terms| ((#5=(|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) 37 T ELT)) (|subtractIfCan| ((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|size| (#8=(#9=(|NonNegativeInteger|)) 22 #10=(AND (|has| |#2| #11=(|Finite|)) (|has| |#1| #11#)) ELT)) (|sample| (#12=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #13=(#7#)) $) 76 T ELT) (((|Union| |#1| . #13#) $) 79 T ELT)) (|retract| (#14=(|#2| $) NIL T ELT) (#15=(|#1| $) NIL T ELT)) (|reductum| (#16=($ $) 99 #17=(|has| |#2| (|OrderedSet|)) ELT)) (|recip| ((#6# $) 83 T ELT)) (|random| (#12# 48 #10# ELT)) (|opposite?| #1#) (|one?| #18=(#4# NIL T ELT)) (|numberOfMonomials| ((#9# $) 70 T ELT)) (|monomials| (((|List| $) $) 52 T ELT)) (|monomial?| #18#) (|monomial| (($ |#1| |#2|) 17 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 68 T ELT)) (|lookup| ((#19=(|PositiveInteger|) $) 43 #10# ELT)) (|leadingMonomial| (#14# 98 #17# ELT)) (|leadingCoefficient| (#15# 97 #17# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #19#) 35 #10# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 96 T ELT) (($ #20=(|Integer|)) 59 T ELT) (($ |#2|) 55 T ELT) (($ |#1|) 56 T ELT) (($ #5#) 11 T ELT)) (|coefficients| (((|List| |#1|) $) 54 T ELT)) (|coefficient| ((|#1| $ |#2|) 114 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#12# 12 T CONST)) (|One| (#12# 44 T CONST)) (= (#2# 104 T ELT)) (- (#16# 61 T ELT) (#21=($ $ $) NIL T ELT)) (+ (#21# 33 T ELT)) (** (($ $ #19#) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #19# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #20# $) 66 T ELT) (#21# 117 T ELT) (($ |#1| $) 63 #22=(|has| |#1| (|CommutativeRing|)) ELT) (($ $ |#1|) NIL #22# ELT))) 
(((|MonoidRing| |#1| |#2|) (|Join| #1=(|Ring|) (|RetractableTo| |#2|) (|RetractableTo| |#1|) (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE |monomial| ($ |#1| |#2|)) (SIGNATURE |coefficient| (|#1| $ |#2|)) (SIGNATURE |coerce| ($ #2=(|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))))) (SIGNATURE |terms| (#2# $)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |coefficients| ((|List| |#1|) $)) (SIGNATURE |monomials| ((|List| $) $)) (SIGNATURE |numberOfMonomials| ((|NonNegativeInteger|) $)) (IF (|has| |#1| #3=(|CharacteristicZero|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |#1| #4=(|CharacteristicNonZero|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |%noBranch|) (IF (|has| |#1| #5=(|Finite|)) (IF (|has| |#2| #5#) (ATTRIBUTE #5#) |%noBranch|) |%noBranch|) (IF (|has| |#2| (|OrderedSet|)) (PROGN (SIGNATURE |leadingMonomial| (|#2| $)) (SIGNATURE |leadingCoefficient| (|#1| $)) (SIGNATURE |reductum| ($ $))) |%noBranch|))) #1# (|Monoid|)) (T |MonoidRing|)) 
((|monomial| (*1 *1 *2 *3) (AND #1=(|isDomain| *1 (|MonoidRing| *2 *3)) #2=(|ofCategory| *2 #3=(|Ring|)) #4=(|ofCategory| *3 #5=(|Monoid|)))) (|coefficient| (*1 *2 *1 *3) (AND #2# #1# #4#)) (|coerce| (*1 *1 *2) (AND #6=(|isDomain| *2 (|List| (|Record| (|:| |coef| *3) (|:| |monom| *4)))) #7=(|ofCategory| *3 #3#) #8=(|ofCategory| *4 #5#) #9=(|isDomain| *1 #10=(|MonoidRing| *3 *4)))) (|terms| #11=(*1 *2 *1) (AND #6# #9# #7# #8#)) (|monomial?| #11# (AND (|isDomain| *2 (|Boolean|)) #9# #7# #8#)) (|coefficients| #11# (AND (|isDomain| *2 (|List| *3)) #9# #7# #8#)) (|monomials| #11# (AND (|isDomain| *2 (|List| #10#)) #9# #7# #8#)) (|numberOfMonomials| #11# (AND (|isDomain| *2 (|NonNegativeInteger|)) #9# #7# #8#)) (|leadingMonomial| #11# (AND (|ofCategory| *2 #5#) (|ofCategory| *2 #12=(|OrderedSet|)) (|isDomain| *1 (|MonoidRing| *3 *2)) #7#)) (|leadingCoefficient| #11# (AND #2# #1# #13=(|ofCategory| *3 #12#) #4#)) (|reductum| (*1 *1 *1) (AND #1# #13# #2# #4#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|unique| (#4=(#5=(|List| |#1|) $) 38 T ELT)) (|union| (#6=($ |#1| $) NIL T ELT) #7=(($ $ |#1|) NIL T ELT) (#8=($ $ $) 95 T ELT)) (|symmetricDifference| (#8# 99 T ELT)) (|subset?| (#2# 107 T ELT)) (|set| (#9=($ #5#) 26 T ELT) (#10=($) 17 T ELT)) (|select!| (#11=($ #12=(|Mapping| #3# |#1|) $) 86 #13=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| #14=(#11# NIL #13# ELT)) (|sample| (#10# NIL T CONST)) (|removeDuplicates!| (#15=($ $) 88 T ELT)) (|removeDuplicates| (#15# NIL #16=(AND #13# #17=(|has| |#1| (|BasicType|))) ELT)) (|remove!| (#6# 71 #13# ELT) (#11# 80 #13# ELT) (#18=($ |#1| $ #19=(|Integer|)) 78 T ELT) (#20=($ #12# $ #19#) 81 T ELT)) (|remove| (#6# NIL #16# ELT) #14# (#18# 83 T ELT) (#20# 84 T ELT)) (|reduce| ((|#1| #21=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #17# ELT) ((|#1| #21# $ |#1|) NIL T ELT) ((|#1| #21# $) NIL T ELT)) (|part?| (#2# 106 T ELT)) (|multiset| (#10# 15 T ELT) (($ |#1|) 28 T ELT) (#9# 23 T ELT)) (|members| (#4# 32 T ELT)) (|member?| ((#3# |#1| $) 66 #17# ELT)) (|map!| (#22=($ (|Mapping| |#1| |#1|) $) 91 T ELT)) (|map| (#22# 92 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|intersect| (#8# 97 T ELT)) (|inspect| (#23=(|#1| $) 63 T ELT)) (|insert!| (#6# 64 T ELT) (($ |#1| $ #24=(|NonNegativeInteger|)) 89 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| (((|Union| |#1| "failed") #12# $) NIL T ELT)) (|extract!| (#23# 62 T ELT)) (|every?| #25=((#3# #12# $) NIL T ELT)) (|eval| (($ $ (|List| #26=(|Equation| |#1|))) NIL #27=(AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ELT) (($ $ #26#) NIL #27# ELT) (($ $ |#1| |#1|) NIL #27# ELT) (($ $ #5# #5#) NIL #27# ELT)) (|eq?| #1#) (|empty?| ((#3# $) 57 T ELT)) (|empty| (#10# 14 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #24#))) $) 56 T ELT)) (|difference| #7# (#8# 98 T ELT)) (|dictionary| (#10# 16 T ELT) (#9# 25 T ELT)) (|count| ((#24# |#1| $) 69 #17# ELT) ((#24# #12# $) NIL T ELT)) (|copy| (#15# 82 T ELT)) (|convert| ((#28=(|InputForm|) $) 36 (|has| |#1| (|ConvertibleTo| #28#)) ELT)) (|construct| (#9# 22 T ELT)) (|coerce| (((|OutputForm|) $) 50 T ELT)) (|brace| (#9# 27 T ELT) (#10# 18 T ELT)) (|before?| #1#) (|bag| (#9# 24 T ELT)) (|any?| #25#) (= (#2# 103 T ELT)) (|#| ((#24# $) 68 T ELT))) 
(((|Multiset| |#1|) (|Join| (|MultisetAggregate| |#1|) (|FiniteAggregate| |#1|) (|ShallowlyMutableAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |multiset| ($)) (SIGNATURE |multiset| ($ |#1|)) (SIGNATURE |multiset| ($ #1=(|List| |#1|))) (SIGNATURE |unique| (#1# $)) (SIGNATURE |remove| #2=($ |#1| $ #3=(|Integer|))) (SIGNATURE |remove| #4=($ (|Mapping| (|Boolean|) |#1|) $ #3#)) (SIGNATURE |remove!| #2#) (SIGNATURE |remove!| #4#))) (|SetCategory|)) (T |Multiset|)) 
((|multiset| (*1 *1) #1=(AND #2=(|isDomain| *1 (|Multiset| *2)) #3=(|ofCategory| *2 #4=(|SetCategory|)))) (|multiset| #5=(*1 *1 *2) #1#) (|multiset| #5# (AND #6=(|isDomain| *2 (|List| *3)) #7=(|ofCategory| *3 #4#) #8=(|isDomain| *1 (|Multiset| *3)))) (|unique| (*1 *2 *1) (AND #6# #8# #7#)) (|remove| #9=(*1 *1 *2 *1 *3) #10=(AND #11=(|isDomain| *3 (|Integer|)) #2# #3#)) (|remove| #9# #12=(AND (|isDomain| *2 (|Mapping| (|Boolean|) *4)) #11# (|ofCategory| *4 #4#) (|isDomain| *1 (|Multiset| *4)))) (|remove!| #9# #10#) (|remove!| #9# #12#)) 
((~= (#1=((|Boolean|) $ $) 18 T ELT)) (|union| (($ |#1| $) 71 T ELT) (($ $ |#1|) 70 T ELT) (#2=($ $ $) 69 T ELT)) (|symmetricDifference| (#2# 67 T ELT)) (|subset?| (#3=((|Boolean|) $ $) 68 T ELT)) (|set| (($ (|List| |#1|)) 63 T ELT) (#4=($) 62 T ELT)) (|select!| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #7=(|Boolean|) |#1|) . #8=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#9=($) 6 T CONST)) (|removeDuplicates!| (($ $) 55 T ELT)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #10=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #5# |#1|) . #6#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #10#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #7# |#1|) . #8#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|part?| (#3# 59 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#2# 64 T ELT)) (|inspect| ((|#1| . #11=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT) (($ |#1| $ #12=(|NonNegativeInteger|)) 56 T ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|extract!| ((|#1| . #11#) 37 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #13=((|SetCategory|)))) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #13#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #13#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #13#)) ELT)) (|eq?| ((#14=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#14# $) 7 T ELT)) (|empty| (#9# 8 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #12#))) $) 54 T ELT)) (|difference| (($ $ |#1|) 66 T ELT) (#2# 65 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#15=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #15#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|brace| (($ (|List| |#1|)) 61 T ELT) (#4# 60 T ELT)) (|before?| (#1# 19 T ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (= (#1# 17 T ELT))) 
(((|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|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|MultiDictionary| |#1|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((|systemCommand| (((|Void|) (|String|)) 8 T ELT))) 
(((|MoreSystemCommands|) (CATEGORY |package| (SIGNATURE |systemCommand| ((|Void|) (|String|))))) (T |MoreSystemCommands|)) 
((|systemCommand| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|MoreSystemCommands|))))) 
((|mergeDifference| ((#1=(|List| |#1|) #1# #1#) 15 T ELT))) 
(((|MergeThing| |#1|) (CATEGORY |package| (SIGNATURE |mergeDifference| (#1=(|List| |#1|) #1# #1#))) (|OrderedSet|)) (T |MergeThing|)) 
((|mergeDifference| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|MergeThing| *3))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#2|) $) 160 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 153 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 152 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 150 (|has| |#1| . #3#) ELT)) (|tanh| (#5=($ $) 109 (|has| |#1| . #6=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|tan| (#7=($ $) 92 (|has| |#1| . #6#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sqrt| (($ $) 91 (|has| |#1| . #8=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|sinh| (#5# 108 (|has| |#1| . #6#) ELT)) (|sin| (#7# 93 (|has| |#1| . #6#) ELT)) (|sech| (#5# 107 (|has| |#1| . #6#) ELT)) (|sec| (#7# 94 (|has| |#1| . #6#) ELT)) (|sample| (#9=($) 23 T CONST)) (|reductum| (#10=($ $) 144 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) 122 T ELT) (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) 121 T ELT)) (|pole?| (((|Boolean|) $) 161 T ELT)) (|pi| (($) 119 (|has| |#1| . #6#) ELT)) (|order| (((|NonNegativeInteger|) $ |#2|) 124 T ELT) (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) 123 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #11=(|Integer|)) 90 (|has| |#1| . #8#) ELT)) (|monomial?| (((|Boolean|) $) 142 T ELT)) (|monomial| (($ $ (|List| |#2|) (|List| (|IndexedExponents| |#2|))) 159 T ELT) (($ $ |#2| (|IndexedExponents| |#2|)) 158 T ELT) (($ |#1| (|IndexedExponents| |#2|)) 143 T ELT) (($ $ |#2| (|NonNegativeInteger|)) 126 T ELT) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 125 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 138 T ELT)) (|log| (#12=($ $) 116 (|has| |#1| . #6#) ELT)) (|leadingMonomial| (#10# 140 T ELT)) (|leadingCoefficient| ((|#1| $) 139 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|integrate| (($ $ |#2|) 120 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (($ $ (|NonNegativeInteger|)) 127 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 154 (|has| |#1| . #3#) ELT)) (|exp| (#12# 117 (|has| |#1| . #6#) ELT)) (|eval| (($ $ |#2| $) 135 T ELT) (($ $ (|List| |#2|) (|List| $)) 134 T ELT) (($ $ (|List| (|Equation| $))) 133 T ELT) (($ $ (|Equation| $)) 132 T ELT) (($ $ $ $) 131 T ELT) (($ $ (|List| $) (|List| $)) 130 T ELT)) (|differentiate| (($ $ (|List| |#2|) . #13=((|List| #14=(|NonNegativeInteger|)))) 52 T ELT) (($ $ |#2| . #15=(#14#)) 51 T ELT) (($ $ (|List| |#2|)) 50 T ELT) (($ $ |#2|) 48 T ELT)) (|degree| (((|IndexedExponents| |#2|) $) 141 T ELT)) (|csch| (#5# 106 (|has| |#1| . #6#) ELT)) (|csc| (#7# 95 (|has| |#1| . #6#) ELT)) (|coth| (#5# 105 (|has| |#1| . #6#) ELT)) (|cot| (#7# 96 (|has| |#1| . #6#) ELT)) (|cosh| (#5# 104 (|has| |#1| . #6#) ELT)) (|cos| (#7# 97 (|has| |#1| . #6#) ELT)) (|complete| (($ $) 162 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 157 (|has| |#1| (|CommutativeRing|)) ELT) (($ $) 155 (|has| |#1| . #3#) ELT) (($ #16=(|Fraction| (|Integer|))) 147 (|has| |#1| . #17=((|Algebra| #16#))) ELT)) (|coefficient| ((|#1| $ (|IndexedExponents| |#2|)) 145 T ELT) (($ $ |#2| (|NonNegativeInteger|)) 129 T ELT) (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) 128 T ELT)) (|charthRoot| (((|Maybe| $) $) 156 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|atanh| (#18=($ $) 115 (|has| |#1| . #6#) ELT)) (|atan| (#19=($ $) 103 (|has| |#1| . #6#) ELT)) (|associates?| ((#4# $ $) 151 (|has| |#1| . #3#) ELT)) (|asinh| (#18# 114 (|has| |#1| . #6#) ELT)) (|asin| (#19# 102 (|has| |#1| . #6#) ELT)) (|asech| (#18# 113 (|has| |#1| . #6#) ELT)) (|asec| (#19# 101 (|has| |#1| . #6#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#18# 112 (|has| |#1| . #6#) ELT)) (|acsc| (#19# 100 (|has| |#1| . #6#) ELT)) (|acoth| (#18# 111 (|has| |#1| . #6#) ELT)) (|acot| (#19# 99 (|has| |#1| . #6#) ELT)) (|acosh| (#18# 110 (|has| |#1| . #6#) ELT)) (|acos| (#19# 98 (|has| |#1| . #6#) ELT)) (|Zero| (#9# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|List| |#2|) . #13#) 55 T ELT) (($ $ |#2| . #15#) 54 T ELT) (($ $ (|List| |#2|)) 53 T ELT) (($ $ |#2|) 49 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 146 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ $) 118 (|has| |#1| . #6#) ELT) (($ $ (|Fraction| #11#)) 89 (|has| |#1| . #8#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #20=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #16#) 149 (|has| |#1| . #17#) ELT) (($ #16# . #20#) 148 (|has| |#1| . #17#) ELT) (($ |#1| . #20#) 137 T ELT) (($ $ |#1|) 136 T ELT))) 
(((|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| #1=(|IndexedExponents| |#2|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|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| #2# #2#) |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|)) ((|CoercibleFrom| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|Functorial| |#1|) . T) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|InnerEvalable| |#2| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#2|) . T) ((|PartialDifferentialRing| |#2|) . T) ((|PartialDifferentialSpace| |#2|) . T) ((|PowerSeriesCategory| |#1| #1# |#2|) . T) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T)) 
((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#) 30 T ELT) (((|Factored| |#4|) |#4|) 26 T ELT))) 
(((|MultivariateFactorize| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|)) (SIGNATURE |factor| ((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|PolynomialCategory| |#3| |#2| |#1|)) (T |MultivariateFactorize|)) 
((|factor| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 (|OrderedSet|)) #3=(|ofCategory| *5 (|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *7 #5=(|PolynomialCategory| *6 *5 *4)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|MultivariateFactorize| *4 *5 *6 *7)) (|isDomain| *3 #6#))) (|factor| #1# (AND #2# #3# #4# (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultivariateFactorize| *4 *5 *6 *3)) (|ofCategory| *3 #5#)))) 
((|univcase| ((#1=(|Factored| |#4|) |#4| |#2|) 142 T ELT)) (|squareFreePrim| (#2=(#1# |#4|) NIL T ELT)) (|squareFree| (((|Factored| #3=(|SparseUnivariatePolynomial| |#4|)) #3#) 129 T ELT) (#2# 52 T ELT)) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| #3#) #4=(|:| |exponent| #5=(|Integer|)))))) #3# #6=(|List| |#2|) #7=(|List| #8=(|List| |#3|))) 81 T ELT)) (|normDeriv2| ((#9=(|SparseUnivariatePolynomial| |#3|) #9# #5#) 169 T ELT)) (|myDegree| ((#10=(|List| #11=(|NonNegativeInteger|)) #3# #6# #11#) 75 T ELT)) (|lift| (((|Union| (|List| #3#) "failed") #3# #9# #9# |#4| #6# #10# #8#) 79 T ELT)) (|intChoose| (((|Record| (|:| |upol| #9#) (|:| |Lval| #8#) (|:| |Lfact| #12=(|List| (|Record| (|:| |factor| #9#) #4#))) (|:| |ctpol| |#3|)) #3# #6# #7#) 27 T ELT)) (|consnewpol| (((|Record| (|:| |pol| #3#) (|:| |polval| #9#)) #3# #9# #5#) 72 T ELT)) (|compdegd| ((#5# #12#) 165 T ELT)) (|coefChoose| ((|#4| #5# #1#) 73 T ELT)) (|check| (((|Boolean|) #12# #12#) NIL T ELT))) 
(((|MultivariateSquareFree| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |squareFree| #1=(#2=(|Factored| |#4|) |#4|)) (SIGNATURE |squareFree| ((|Factored| #3=(|SparseUnivariatePolynomial| |#4|)) #3#)) (SIGNATURE |squareFreePrim| #1#) (SIGNATURE |compdegd| (#4=(|Integer|) #5=(|List| (|Record| (|:| |factor| #6=(|SparseUnivariatePolynomial| |#3|)) #7=(|:| |exponent| #4#))))) (SIGNATURE |univcase| (#2# |#4| |#2|)) (SIGNATURE |consnewpol| ((|Record| (|:| |pol| #3#) (|:| |polval| #6#)) #3# #6# #4#)) (SIGNATURE |nsqfree| ((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| #3#) #7#)))) #3# #8=(|List| |#2|) #9=(|List| #10=(|List| |#3|)))) (SIGNATURE |intChoose| ((|Record| (|:| |upol| #6#) (|:| |Lval| #10#) (|:| |Lfact| #5#) (|:| |ctpol| |#3|)) #3# #8# #9#)) (SIGNATURE |coefChoose| (|#4| #4# #2#)) (SIGNATURE |check| ((|Boolean|) #5# #5#)) (SIGNATURE |lift| ((|Union| (|List| #3#) "failed") #3# #6# #6# |#4| #8# #11=(|List| #12=(|NonNegativeInteger|)) #10#)) (SIGNATURE |myDegree| (#11# #3# #8# #12#)) (SIGNATURE |normDeriv2| (#6# #6# #4#))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |MultivariateSquareFree|)) 
((|normDeriv2| (*1 *2 *2 *3) (AND (|isDomain| *2 #1=(|SparseUnivariatePolynomial| *6)) #2=(|isDomain| *3 #3=(|Integer|)) #4=(|ofCategory| *6 #5=(|EuclideanDomain|)) #6=(|ofCategory| *4 #7=(|OrderedAbelianMonoidSup|)) #8=(|ofCategory| *5 #9=(|OrderedSet|)) #10=(|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *7)) #11=(|ofCategory| *7 #12=(|PolynomialCategory| *6 *4 *5)))) (|myDegree| #13=(*1 *2 *3 *4 *5) (AND #14=(|isDomain| *3 #15=(|SparseUnivariatePolynomial| *9)) #16=(|isDomain| *4 (|List| *7)) #17=(|ofCategory| *7 #9#) #18=(|ofCategory| *9 (|PolynomialCategory| *8 *6 *7)) #19=(|ofCategory| *6 #7#) #20=(|ofCategory| *8 #5#) (|isDomain| *2 #21=(|List| #22=(|NonNegativeInteger|))) #23=(|isDomain| *1 (|MultivariateSquareFree| *6 *7 *8 *9)) (|isDomain| *5 #22#))) (|lift| (*1 *2 *3 *4 *4 *5 *6 *7 *8) (|partial| AND (|isDomain| *4 (|SparseUnivariatePolynomial| *11)) (|isDomain| *6 (|List| *10)) (|isDomain| *7 #21#) (|isDomain| *8 (|List| *11)) (|ofCategory| *10 #9#) (|ofCategory| *11 #5#) (|ofCategory| *9 #7#) (|ofCategory| *5 (|PolynomialCategory| *11 *9 *10)) (|isDomain| *2 (|List| #24=(|SparseUnivariatePolynomial| *5))) (|isDomain| *1 (|MultivariateSquareFree| *9 *10 *11 *5)) (|isDomain| *3 #24#))) (|check| (*1 *2 *3 *3) (AND #25=(|isDomain| *3 (|List| (|Record| (|:| |factor| #1#) #26=(|:| |exponent| #3#)))) #4# #6# #8# (|isDomain| *2 (|Boolean|)) #10# #11#)) (|coefChoose| #27=(*1 *2 *3 *4) (AND #2# (|isDomain| *4 (|Factored| *2)) (|ofCategory| *2 (|PolynomialCategory| *7 *5 *6)) (|isDomain| *1 (|MultivariateSquareFree| *5 *6 *7 *2)) #28=(|ofCategory| *5 #7#) (|ofCategory| *6 #9#) (|ofCategory| *7 #5#))) (|intChoose| #13# (AND #14# #16# #29=(|isDomain| *5 (|List| #30=(|List| *8))) #17# #20# #18# #19# (|isDomain| *2 (|Record| (|:| |upol| #31=(|SparseUnivariatePolynomial| *8)) (|:| |Lval| #30#) (|:| |Lfact| (|List| (|Record| (|:| |factor| #31#) #26#))) (|:| |ctpol| *8))) #23#)) (|nsqfree| #13# (AND #16# #29# #17# #20# #19# #18# (|isDomain| *2 (|Record| (|:| |unitPart| *9) (|:| |suPart| (|List| (|Record| (|:| |factor| #15#) #26#))))) #23# #14#)) (|consnewpol| #13# (AND (|isDomain| *5 #3#) #19# #17# #20# #18# (|isDomain| *2 (|Record| (|:| |pol| #15#) (|:| |polval| #31#))) #23# #14# (|isDomain| *4 #31#))) (|univcase| #27# (AND #28# (|ofCategory| *4 #9#) #4# #32=(|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultivariateSquareFree| *5 *4 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4)))) (|compdegd| #33=(*1 *2 *3) (AND #25# #4# #6# #8# (|isDomain| *2 #3#) #10# #11#)) (|squareFreePrim| #33# #34=(AND #6# #8# #4# #32# (|isDomain| *1 (|MultivariateSquareFree| *4 *5 *6 *3)) (|ofCategory| *3 #12#))) (|squareFree| #33# (AND #6# #8# #4# #11# (|isDomain| *2 (|Factored| #35=(|SparseUnivariatePolynomial| *7))) #10# (|isDomain| *3 #35#))) (|squareFree| #33# #34#)) 
((|plenaryPower| (($ $ (|PositiveInteger|)) 17 T ELT))) 
(((|NonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |plenaryPower| (|#1| |#1| (|PositiveInteger|)))) (|NonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |NonAssociativeAlgebra&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 37 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 44 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftPower| (#4# 38 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#5=($ $ $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|antiCommutator| (#5# 33 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 30 T ELT) (($ $ $) 36 T ELT) (($ $ |#1|) 46 T ELT) (($ |#1| . #6#) 45 T ELT))) 
(((|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) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeRng|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|commutator| (#1=($ $ $) 10 T ELT)) (|associator| (($ $ $ $) 9 T ELT)) (|antiCommutator| (#1# 12 T ELT))) 
(((|NonAssociativeRng&| |#1|) (CATEGORY |package| (SIGNATURE |antiCommutator| #1=(|#1| |#1| |#1|)) (SIGNATURE |commutator| #1#) (SIGNATURE |associator| (|#1| |#1| |#1| |#1|))) (|NonAssociativeRng|)) (T |NonAssociativeRng&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 37 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftPower| (#4# 38 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (($ $ $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|antiCommutator| (($ $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 36 T ELT))) 
(((|NonAssociativeRng|) (|Category|)) (T |NonAssociativeRng|)) 
((|associator| (*1 *1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|))) (|commutator| (*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|))) (|antiCommutator| (*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|)))) 
(|Join| (|AbelianGroup|) (|Monad|) (CATEGORY |domain| (SIGNATURE |associator| ($ $ $ $)) (SIGNATURE |commutator| ($ $ $)) (SIGNATURE |antiCommutator| ($ $ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|Monad|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) 10 T ELT))) 
(((|NonAssociativeRing&| |#1|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|NonAssociativeRing|)) (T |NonAssociativeRing&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRecip| (#4=((|Union| $ "failed") $) 49 T ELT)) (|rightPower| (#5=($ $ (|PositiveInteger|)) 37 T ELT) (#6=($ $ (|NonNegativeInteger|)) 44 T ELT)) (|recip| (#4# 47 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 43 T ELT)) (|leftRecip| (#4# 48 T ELT)) (|leftPower| (#5# 38 T ELT) (#6# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#7=($ $ $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 40 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|antiCommutator| (#7# 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 42 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#5# 39 T ELT) (#6# 46 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 36 T ELT))) 
(((|NonAssociativeRing|) (|Category|)) (T |NonAssociativeRing|)) 
((|characteristic| (*1 *2) (AND (|ofCategory| *1 (|NonAssociativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|NonAssociativeRing|))))) 
(|Join| (|NonAssociativeRng|) (|MonadWithUnit|) (CATEGORY |domain| (SIGNATURE |characteristic| ((|NonNegativeInteger|)) |constant|) (SIGNATURE |coerce| ($ (|Integer|))))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|Monad|) . T) ((|MonadWithUnit|) . T) ((|NonAssociativeRng|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|complexEigenvectors| (((|List| (|Record| (|:| |outval| #1=(|Complex| |#1|)) (|:| |outmult| #2=(|Integer|)) (|:| |outvect| (|List| (|Matrix| #1#))))) #3=(|Matrix| #4=(|Complex| (|Fraction| #2#))) |#1|) 33 T ELT)) (|complexEigenvalues| (((|List| #1#) #3# |#1|) 23 T ELT)) (|characteristicPolynomial| ((#5=(|Polynomial| #4#) #3# (|Symbol|)) 20 T ELT) ((#5# #3#) 19 T ELT))) 
(((|NumericComplexEigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (#1=(|Polynomial| #2=(|Complex| (|Fraction| #3=(|Integer|)))) #4=(|Matrix| #2#))) (SIGNATURE |characteristicPolynomial| (#1# #4# (|Symbol|))) (SIGNATURE |complexEigenvalues| ((|List| #5=(|Complex| |#1|)) #4# |#1|)) (SIGNATURE |complexEigenvectors| ((|List| (|Record| (|:| |outval| #5#) (|:| |outmult| #3#) (|:| |outvect| (|List| (|Matrix| #5#))))) #4# |#1|))) (|Join| (|Field|) (|OrderedRing|))) (T |NumericComplexEigenPackage|)) 
((|complexEigenvectors| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Matrix| #3=(|Complex| (|Fraction| #4=(|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |outval| #5=(|Complex| *4)) (|:| |outmult| #4#) (|:| |outvect| (|List| (|Matrix| #5#)))))) #6=(|isDomain| *1 (|NumericComplexEigenPackage| *4)) #7=(|ofCategory| *4 #8=(|Join| (|Field|) (|OrderedRing|))))) (|complexEigenvalues| #1# (AND #2# (|isDomain| *2 (|List| #5#)) #6# #7#)) (|characteristicPolynomial| #1# (AND #2# (|isDomain| *4 (|Symbol|)) #9=(|isDomain| *2 (|Polynomial| #3#)) (|isDomain| *1 (|NumericComplexEigenPackage| *5)) (|ofCategory| *5 #8#))) (|characteristicPolynomial| (*1 *2 *3) (AND #2# #9# #6# #7#))) 
((|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) 27 T ELT))) 
(((|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|))))) 
((|leftRemainder| (#1=(|#1| |#1| |#1|) 28 T ELT)) (|leftQuotient| (#1# 27 T ELT)) (|leftLcm| (#1# 38 T ELT)) (|leftGcd| (#1# 33 T ELT)) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) 31 T ELT)) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 26 T ELT))) 
(((|NonCommutativeOperatorDivision| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |leftQuotient| #1=(|#1| |#1| |#1|)) (SIGNATURE |leftRemainder| #1#) (SIGNATURE |leftExactQuotient| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |leftGcd| #1#) (SIGNATURE |leftLcm| #1#)) (|MonogenicLinearOperator| |#2|) (|Field|)) (T |NonCommutativeOperatorDivision|)) 
((|leftLcm| #1=(*1 *2 *2 *2) #2=(AND #3=(|ofCategory| *3 #4=(|Field|)) #5=(|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3)) #6=(|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|leftGcd| #1# #2#) (|leftExactQuotient| #1# (|partial| AND #3# #5# #6#)) (|leftRemainder| #1# #2#) (|leftQuotient| #1# #2#) (|leftDivide| (*1 *2 *3 *3) (AND (|ofCategory| *4 #4#) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|NonCommutativeOperatorDivision| *3 *4)) (|ofCategory| *3 (|MonogenicLinearOperator| *4))))) 
((|writeUInt8!| (((|Maybe| #1=(|UInt8|)) $ #1#) 27 T ELT)) (|writeInt8!| (((|Maybe| #2=(|Int8|)) $ #2#) 26 T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 28 T ELT)) (|writeByte!| (((|Maybe| #3=(|Byte|)) $ #3#) 25 T ELT)) (|readUInt8!| (((|Maybe| (|UInt8|)) $) 12 T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) 8 T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) 10 T ELT)) (|readInt8!| (((|Maybe| (|Int8|)) $) 13 T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) 9 T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) 11 T ELT)) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 7 T ELT)) (|readByte!| (((|Maybe| (|Byte|)) $) 14 T ELT)) (|isConnected?| (((|Boolean|) $) 32 T ELT)) (|connectTo| (((|Maybe| $) |#1| (|PortNumber|)) 33 T ELT)) (|close!| (($ $) 6 T ELT))) 
(((|NetworkClientSocket| |#1|) (|Category|) (|SetCategory|)) (T |NetworkClientSocket|)) 
((|connectTo| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PortNumber|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|NetworkClientSocket| *3)))) (|isConnected?| (*1 *2 *1) (AND (|ofCategory| *1 (|NetworkClientSocket| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|InputOutputByteConduit|) (CATEGORY |domain| (SIGNATURE |connectTo| ((|Maybe| $) |t#1| (|PortNumber|))) (SIGNATURE |isConnected?| ((|Boolean|) $)))) 
(((|Conduit|) . T) ((|InputByteConduit|) . T) ((|InputOutputByteConduit|) . T) ((|OutputByteConduit|) . T)) 
((|localIntegralBasis| ((#1=(|Record| (|:| |basis| #2=(|Matrix| #3=(|Integer|))) (|:| |basisDen| #3#) (|:| |basisInv| #2#)) #3#) 72 T ELT)) (|integralBasis| ((#1#) 70 T ELT)) (|discriminant| ((#3#) 86 T ELT))) 
(((|NumberFieldIntegralBasis| |#1| |#2|) (CATEGORY |package| (SIGNATURE |discriminant| (#1=(|Integer|))) (SIGNATURE |integralBasis| (#2=(|Record| (|:| |basis| #3=(|Matrix| #1#)) (|:| |basisDen| #1#) (|:| |basisInv| #3#)))) (SIGNATURE |localIntegralBasis| (#2# #1#))) (|UnivariatePolynomialCategory| #1#) (|FramedAlgebra| #1# |#1|)) (T |NumberFieldIntegralBasis|)) 
((|localIntegralBasis| (*1 *2 *3) (AND (|isDomain| *3 #1=(|Integer|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| #2=(|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| #2#))) (|isDomain| *1 (|NumberFieldIntegralBasis| *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|integralBasis| #3=(*1 *2) (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| #1#)) (|isDomain| *2 (|Record| (|:| |basis| #4=(|Matrix| #1#)) (|:| |basisDen| #1#) (|:| |basisInv| #4#))) #5=(|isDomain| *1 (|NumberFieldIntegralBasis| *3 *4)) (|ofCategory| *4 (|FramedAlgebra| #1# *3)))) (|discriminant| #3# (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|isDomain| *2 #1#) #5# (|ofCategory| *4 (|FramedAlgebra| *2 *3))))) 
((|solveInField| (#1=(#2=(|List| (|List| (|Equation| (|Fraction| #3=(|Polynomial| |#1|))))) #4=(|List| #3#)) 19 T ELT) (#5=(#2# #4# (|List| (|Symbol|))) 18 T ELT)) (|solve| (#1# 21 T ELT) (#5# 20 T ELT))) 
(((|NonLinearSolvePackage| |#1|) (CATEGORY |package| (SIGNATURE |solveInField| #1=(#2=(|List| (|List| (|Equation| (|Fraction| #3=(|Polynomial| |#1|))))) #4=(|List| #3#) (|List| (|Symbol|)))) (SIGNATURE |solveInField| #5=(#2# #4#)) (SIGNATURE |solve| #1#) (SIGNATURE |solve| #5#)) (|IntegralDomain|)) (T |NonLinearSolvePackage|)) 
((|solve| #1=(*1 *2 *3) #2=(AND (|isDomain| *3 (|List| #3=(|Polynomial| *4))) (|ofCategory| *4 #4=(|IntegralDomain|)) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| #3#))))) (|isDomain| *1 (|NonLinearSolvePackage| *4)))) (|solve| #5=(*1 *2 *3 *4) #6=(AND (|isDomain| *3 (|List| #7=(|Polynomial| *5))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *5 #4#) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| #7#))))) (|isDomain| *1 (|NonLinearSolvePackage| *5)))) (|solveInField| #1# #2#) (|solveInField| #5# #6#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|sup| (#4=($ $ $) 10 T ELT)) (|subtractIfCan| (#5=(#6=(|Union| $ "failed") $ $) 15 T ELT)) (|shift| (($ $ (|Integer|)) 11 T ELT)) (|sample| #7=(#8=($) NIL T CONST)) (|rem| #9=(#4# NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|random| (($ $) NIL T ELT)) (|quo| #9#) (|positive?| #3#) (|opposite?| #1#) (|one?| #3#) (|min| #9#) (|max| #9#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcd| #9#) (|exquo| (#5# NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#8# 6 T CONST)) (|One| #7#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #9#) (** (($ $ #10=(|NonNegativeInteger|)) NIL T ELT) (($ $ #11=(|PositiveInteger|)) NIL T ELT)) (* (($ #11# $) NIL T ELT) (($ #10# $) NIL T ELT) #9#)) 
(((|NonNegativeInteger|) (|Join| (|OrderedAbelianMonoidSup|) (|Monoid|) (CATEGORY |domain| (SIGNATURE |quo| #1=($ $ $)) (SIGNATURE |rem| #1#) (SIGNATURE |gcd| #1#) (SIGNATURE |divide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |exquo| ((|Union| $ "failed") $ $)) (SIGNATURE |shift| ($ $ (|Integer|))) (SIGNATURE |random| ($ $)) (ATTRIBUTE (|commutative| "*"))))) (T |NonNegativeInteger|)) 
((|quo| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 #3=(|NonNegativeInteger|))) (|rem| #1# #2#) (|gcd| #1# #2#) (|divide| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |quotient| #3#) (|:| |remainder| #3#))) #2#)) (|exquo| #1# (|partial| |isDomain| *1 #3#)) (|shift| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #2#)) (|random| (*1 *1 *1) #2#)) 
((|Integer|) (|%not| (|%ilt| |#1| 0))) 
((|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) 37 T ELT))) 
(((|NonLinearFirstOrderODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solve| ((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)))) (|Join| (|EuclideanDomain|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#) (|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| (|EuclideanDomain|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#) (|CharacteristicZero|))) (|isDomain| *1 (|NonLinearFirstOrderODESolver| *5 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedFunctionSpace| *5) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)))))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 7 T ELT)) (|before?| #1#) (= (#2# 9 T ELT))) 
(((|None|) (|SetCategory|)) (T |None|)) 
NIL 
((|coerce| (((|None|) |#1|) 8 T ELT))) 
(((|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|))))) 
((|norm| ((|#2| |#4|) 35 T ELT))) 
(((|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))))) 
((|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) 57 T ELT)) (|outputArgs| (((|Void|) #1=(|String|) #1# |#4| |#5|) 33 T ELT)) (|normalizedAssociate| ((|#4| |#4| |#5|) 74 T ELT)) (|normalize| (((|List| (|Record| (|:| |val| |#4|) #2=(|:| |tower| |#5|))) |#4| |#5|) 79 T ELT)) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) #2#)) |#4| |#5|) 16 T ELT))) 
(((|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|) #1=(|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |outputArgs| ((|Void|) #2=(|String|) #2# |#4| |#5|)) (SIGNATURE |normInvertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) #1#)) |#4| |#5|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |NormalizationPackage|)) 
((|normInvertible?| #1=(*1 *2 *3 *4) (AND #2=(|ofCategory| *5 #3=(|GcdDomain|)) #4=(|ofCategory| *6 #5=(|OrderedAbelianMonoidSup|)) #6=(|ofCategory| *7 #7=(|OrderedSet|)) #8=(|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|Boolean|)) #9=(|:| |tower| *4)))) #10=(|isDomain| *1 (|NormalizationPackage| *5 *6 *7 *3 *4)) #11=(|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|outputArgs| (*1 *2 *3 *3 *4 *5) (AND (|isDomain| *3 (|String|)) (|ofCategory| *6 #3#) (|ofCategory| *7 #5#) (|ofCategory| *8 #7#) (|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# (AND #2# #4# #6# #8# (|isDomain| *2 (|List| (|Record| (|:| |val| *3) #9#))) #10# #11#)) (|normalizedAssociate| (*1 *2 *2 *3) (AND (|ofCategory| *4 #3#) (|ofCategory| *5 #5#) (|ofCategory| *6 #7#) (|ofCategory| *2 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *1 (|NormalizationPackage| *4 *5 *6 *2 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *2)))) (|recip| #1# (AND #2# #4# #6# #8# (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *3))) #10# #11#))) 
((|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) 53 T ELT)) (|normFactors| (((|List| |#4|) |#4|) 22 T ELT)) (|Frobenius| ((|#4| |#4|) 17 T ELT))) 
(((|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 #1=(|FiniteFieldCategory|)) (|ofCategory| *4 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|NormRetractPackage| *3 *4 *5 *2 *6)) (|ofCategory| *2 #2=(|UnivariatePolynomialCategory| *5)) (|ofType| *6 #3=(|PositiveInteger|)))) (|retractIfCan| #4=(*1 *2 *3) (|partial| AND #5=(|ofCategory| *4 #1#) #6=(|ofCategory| *5 (|FiniteAlgebraicExtensionField| *4)) #7=(|ofCategory| *6 #2#) (|isDomain| *2 (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4))) #8=(|isDomain| *1 (|NormRetractPackage| *4 *5 *6 *3 *7)) #9=(|ofCategory| *3 (|UnivariatePolynomialCategory| *6)) #10=(|ofType| *7 #3#))) (|normFactors| #4# (AND #5# #6# #7# (|isDomain| *2 (|List| *3)) #8# #9# #10#))) 
((|npcoef| (((|Record| (|:| |deter| (|List| #1=(|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| #2=(|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| #3=(|List| |#1|)) (|:| |nlead| #4=(|List| |#5|))) #1# #3# #4#) 72 T ELT)) (|listexp| (((|List| #2#) |#1|) 20 T ELT))) 
(((|NPCoef| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |npcoef| ((|Record| (|:| |deter| (|List| #1=(|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| #2=(|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| #3=(|List| |#1|)) (|:| |nlead| #4=(|List| |#5|))) #1# #3# #4#)) (SIGNATURE |listexp| ((|List| #2#) |#1|))) (|UnivariatePolynomialCategory| |#4|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#4| |#2| |#3|)) (T |NPCoef|)) 
((|listexp| (*1 *2 *3) (AND (|ofCategory| *4 #1=(|OrderedAbelianMonoidSup|)) (|ofCategory| *5 #2=(|OrderedSet|)) (|ofCategory| *6 #3=(|EuclideanDomain|)) (|isDomain| *2 (|List| #4=(|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 #1#) (|ofCategory| *8 #2#) (|ofCategory| *9 #3#) (|ofCategory| *10 (|PolynomialCategory| *9 *7 *8)) (|isDomain| *2 (|Record| (|:| |deter| (|List| #5=(|SparseUnivariatePolynomial| *10))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| #4#) (|:| |pcoef| *10))))) (|:| |nfacts| #6=(|List| *6)) (|:| |nlead| #7=(|List| *10)))) (|isDomain| *1 (|NPCoef| *6 *7 *8 *9 *10)) (|isDomain| *3 #5#) (|isDomain| *4 #6#) (|isDomain| *5 #7#)))) 
((|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| #1=(|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) #2=(|Matrix| #3=(|Fraction| #1#)) |#1|) 31 T ELT)) (|realEigenvalues| (((|List| |#1|) #2# |#1|) 21 T ELT)) (|characteristicPolynomial| ((#4=(|Polynomial| #3#) #2# (|Symbol|)) 18 T ELT) ((#4# #2#) 17 T ELT))) 
(((|NumericRealEigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (#1=(|Polynomial| #2=(|Fraction| #3=(|Integer|))) #4=(|Matrix| #2#))) (SIGNATURE |characteristicPolynomial| (#1# #4# (|Symbol|))) (SIGNATURE |realEigenvalues| ((|List| |#1|) #4# |#1|)) (SIGNATURE |realEigenvectors| ((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| #3#) (|:| |outvect| (|List| (|Matrix| |#1|))))) #4# |#1|))) (|Join| (|Field|) (|OrderedRing|))) (T |NumericRealEigenPackage|)) 
((|realEigenvectors| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Matrix| #3=(|Fraction| #4=(|Integer|)))) (|isDomain| *2 (|List| (|Record| (|:| |outval| *4) (|:| |outmult| #4#) (|:| |outvect| (|List| (|Matrix| *4)))))) #5=(|isDomain| *1 (|NumericRealEigenPackage| *4)) #6=(|ofCategory| *4 #7=(|Join| (|Field|) (|OrderedRing|))))) (|realEigenvalues| #1# (AND #2# (|isDomain| *2 (|List| *4)) #5# #6#)) (|characteristicPolynomial| #1# (AND #2# (|isDomain| *4 (|Symbol|)) #8=(|isDomain| *2 (|Polynomial| #3#)) (|isDomain| *1 (|NumericRealEigenPackage| *5)) (|ofCategory| *5 #7#))) (|characteristicPolynomial| (*1 *2 *3) (AND #2# #8# #5# #6#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 36 T ELT)) (|variables| ((#5=(|List| |#2|) $) NIL T ELT)) (|univariate| ((#6=(|SparseUnivariatePolynomial| $) $ |#2|) NIL T ELT) ((#7=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|totalDegree| #11=(#12=(#13=(|NonNegativeInteger|) $) NIL T ELT) ((#13# $ #5#) NIL T ELT)) (|tail| (#10# 30 T ELT)) (|supRittWu?| #1#) (|subtractIfCan| (#14=(#15=(|Union| $ #16="failed") $ $) NIL T ELT)) (|subResultantGcd| (#17=($ $ $) 110 #8# ELT)) (|subResultantChain| ((#18=(|List| $) $ $) 123 #8# ELT)) (|squareFreePolynomial| #19=(((|Factored| #6#) #6#) NIL #20=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #21=(#10# NIL #22=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#23=((|Factored| $) $) NIL #22# ELT)) (|solveLinearPolynomialEquation| (((|Union| #24=(|List| #6#) #16#) #24# #6#) NIL #20# ELT)) (|sample| (#25=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #26=(#16#)) . #27=($)) NIL T ELT) (((|Union| #28=(|Fraction| #29=(|Integer|)) . #26#) . #27#) NIL #30=(|has| |#1| (|RetractableTo| #28#)) ELT) (((|Union| #29# . #26#) . #27#) NIL #31=(|has| |#1| (|RetractableTo| #29#)) ELT) #32=(((|Union| |#2| . #26#) . #27#) NIL T ELT) ((#15# #33=(|Polynomial| #28#)) NIL #34=(AND #35=(|has| |#1| (|Algebra| #28#)) #36=(|has| |#2| (|ConvertibleTo| (|Symbol|)))) ELT) ((#15# #37=(|Polynomial| #29#)) NIL #38=(OR (AND #39=(|has| |#1| (|Algebra| #29#)) #36# #40=(|not| #35#)) #34#) ELT) ((#15# #41=(|Polynomial| |#1|)) NIL #42=(OR (AND #36# #40# (|not| #39#)) (AND #39# #36# #40# (|not| (|has| |#1| (|IntegerNumberSystem|)))) (AND #35# #36# (|not| (|has| |#1| (|QuotientFieldCategory| #29#))))) ELT) (((|Union| #43=(|SparseMultivariatePolynomial| |#1| |#2|) . #26#) $) 21 T ELT)) (|retract| #44=(#45=(|#1| . #46=($)) NIL T ELT) ((#28# . #46#) NIL #30# ELT) ((#29# . #46#) NIL #31# ELT) (#47=(|#2| . #46#) NIL T ELT) #48=(($ #33#) NIL #34# ELT) #49=(($ #37#) NIL #38# ELT) (#50=($ #41#) NIL #42# ELT) (#51=(#43# . #46#) NIL T ELT)) (|resultant| (#52=($ $ $ |#2|) NIL #53=(|has| |#1| (|CommutativeRing|)) ELT) (#17# 121 #8# ELT)) (|reductum| #54=(#10# NIL T ELT) #55=(#56=($ $ |#2|) NIL T ELT)) (|reducedSystem| ((#57=(|Matrix| #29#) . #58=(#59=(|Matrix| $))) NIL #60=(|has| |#1| (|LinearlyExplicitRingOver| #29#)) ELT) ((#61=(|Record| (|:| |mat| #57#) (|:| |vec| (|Vector| #29#))) . #62=(#59# #63=(|Vector| $))) NIL #60# ELT) ((#64=(|Record| (|:| |mat| #65=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #62#) NIL T ELT) ((#65# . #58#) NIL T ELT)) (|reduced?| #1# #66=((#3# $ #18#) NIL T ELT)) (|recip| ((#15# $) NIL T ELT)) (|quasiMonic?| #67=(#4# NIL T ELT)) (|pseudoDivide| ((#68=(|Record| #69=(|:| |quotient| $) #70=(|:| |remainder| $)) $ $) 81 T ELT)) (|primitivePart!| (#10# 136 #22# ELT)) (|primitivePart| #21# #71=(#56# NIL #22# ELT)) (|primitiveMonomials| #72=(#73=(#18# $) NIL T ELT)) (|prime?| (#4# NIL #20# ELT)) (|primPartElseUnitCanonical!| #9#) (|primPartElseUnitCanonical| #9#) (|prem| (#17# 76 T ELT) #74=(#52# NIL T ELT)) (|pquo| (#17# 79 T ELT) #74#) (|pomopo!| (($ $ |#1| #75=(|IndexedExponents| |#2|) $) NIL T ELT)) (|patternMatch| ((#76=(|PatternMatchResult| #77=(|Float|) . #78=($)) $ #79=(|Pattern| #77#) #76#) NIL (AND (|has| |#1| #80=(|PatternMatchable| #77#)) (|has| |#2| #80#)) ELT) ((#81=(|PatternMatchResult| #29# . #78#) $ #82=(|Pattern| #29#) #81#) NIL (AND (|has| |#1| #83=(|PatternMatchable| #29#)) (|has| |#2| #83#)) ELT)) (|opposite?| #1#) (|one?| (#4# 57 T ELT)) (|numberOfMonomials| #11#) (|normalized?| #1# #66#) (|nextsubResultant2| (($ $ $ $ $) 107 #8# ELT)) (|mvar| (#47# 22 T ELT)) (|multivariate| (($ #7# |#2|) NIL T ELT) (($ #6# |#2|) NIL T ELT)) (|monomials| #72#) (|monomial?| #67#) (|monomial| (($ |#1| #75#) NIL T ELT) (#84=($ $ |#2| #13#) 38 T ELT) #85=(($ $ #5# #86=(|List| #13#)) NIL T ELT)) (|monicModulo| (#17# 63 T ELT)) (|monicDivide| ((#68# $ $ |#2|) NIL T ELT)) (|monic?| #67#) (|minimumDegree| #87=((#75# $) NIL T ELT) (#88=(#13# $ |#2|) NIL T ELT) #89=((#86# $ #5#) NIL T ELT)) (|mdeg| (#12# 23 T ELT)) (|mapExponents| (($ (|Mapping| #75# #75#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mainVariable| #32#) (|mainSquareFreePart| #21#) (|mainPrimitivePart| #21#) (|mainMonomials| #72#) (|mainMonomial| (#10# 39 T ELT)) (|mainContent| #21#) (|mainCoefficients| (#73# 43 T ELT)) (|leftReducedSystem| ((#57# . #90=(#63#)) NIL #60# ELT) ((#61# . #91=(#63# $)) NIL #60# ELT) ((#64# . #91#) NIL T ELT) ((#65# . #90#) NIL T ELT)) (|leastMonomial| (#10# 41 T ELT)) (|leadingMonomial| #54#) (|leadingCoefficient| #44# (#56# 48 T ELT)) (|lcm| #92=(($ #18#) NIL #22# ELT) #93=(#17# NIL #22# ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| #13#)) $ $) 96 T ELT)) (|lazyPseudoDivide| ((#94=(|Record| #95=(|:| |coef| $) #96=(|:| |gap| #13#) #69# #70#) $ $) 78 T ELT) ((#94# $ $ |#2|) NIL T ELT)) (|lazyPremWithDefault| ((#97=(|Record| #95# #96# #70#) $ $) NIL T ELT) ((#97# $ $ |#2|) NIL T ELT)) (|lazyPrem| (#17# 83 T ELT) #74#) (|lazyPquo| (#17# 86 T ELT) #74#) (|latex| (#98=((|String|) $) NIL T ELT)) (|lastSubResultant| (#17# 125 #8# ELT)) (|iteratedInitials| (#73# 32 T ELT)) (|isTimes| #99=(((|Union| #18# #16#) $) NIL T ELT)) (|isPlus| #99#) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| #13#)) #16#) $) NIL T ELT)) (|initiallyReduced?| #1# #66#) (|initiallyReduce| #100=(#17# NIL T ELT)) (|init| (#10# 24 T ELT)) (|infRittWu?| #1#) (|headReduced?| #1# #66#) (|headReduce| #100#) (|head| (#10# 26 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| #101=(|:| |gcd| $) #102=(|:| |coef2| $)) $ $) 116 #8# ELT)) (|halfExtendedSubResultantGcd1| (((|Record| #101# #103=(|:| |coef1| $)) $ $) 113 #8# ELT)) (|ground?| (#4# 56 T ELT)) (|ground| (#45# 58 T ELT)) (|gcdPolynomial| ((#6# #6# #6#) NIL #22# ELT)) (|gcd| ((|#1| |#1| $) 133 #22# ELT) #92# #93#) (|factorSquareFreePolynomial| #19#) (|factorPolynomial| #19#) (|factor| (#23# NIL #20# ELT)) (|extendedSubResultantGcd| (((|Record| #101# #103# #102#) $ $) 119 #8# ELT)) (|exquo| ((#15# $ |#1|) NIL #8# ELT) (#14# 98 #8# ELT)) (|exactQuotient!| (#104=($ $ |#1|) 129 #8# ELT) #105=(#17# NIL #8# ELT)) (|exactQuotient| (#104# 128 #8# ELT) #105#) (|eval| (($ $ (|List| #106=(|Equation| $))) NIL T ELT) (($ $ #106#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #18# #18#) NIL T ELT) (($ $ |#2| |#1|) NIL T ELT) (($ $ #5# #107=(|List| |#1|)) NIL T ELT) (($ $ |#2| $) NIL T ELT) (($ $ #5# #18#) NIL T ELT)) (|discriminant| (#56# NIL #53# ELT)) (|differentiate| #85# #108=(#84# NIL T ELT) #109=(($ $ #5#) NIL T ELT) #55#) (|degree| #87# (#88# 45 T ELT) #89#) (|deepestTail| #54#) (|deepestInitial| (#10# 35 T ELT)) (|convert| ((#79# . #110=($)) NIL (AND (|has| |#1| #111=(|ConvertibleTo| #79#)) (|has| |#2| #111#)) ELT) ((#82# . #110#) NIL (AND (|has| |#1| #112=(|ConvertibleTo| #82#)) (|has| |#2| #112#)) ELT) ((#113=(|InputForm|) . #110#) NIL (AND (|has| |#1| #114=(|ConvertibleTo| #113#)) (|has| |#2| #114#)) ELT) #48# #49# (#50# NIL #36# ELT) (#98# NIL (AND #31# #36#) ELT) #115=((#41# . #110#) NIL #36# ELT)) (|content| (#45# 132 #22# ELT) #71#) (|conditionP| (((|Union| #63# #16#) #59#) NIL #116=(AND (|has| $ #117=(|CharacteristicNonZero|)) #20#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #29#) NIL T ELT) (($ |#1|) NIL T ELT) (($ |#2|) NIL T ELT) #115# (#51# 18 T ELT) (($ #43#) 19 T ELT) (($ #28#) NIL (OR #35# #30#) ELT) #9#) (|coefficients| ((#107# $) NIL T ELT)) (|coefficient| ((|#1| $ #75#) NIL T ELT) (#84# 47 T ELT) #85#) (|charthRoot| (((|Maybe| $) $) NIL (OR #116# (|has| |#1| #117#)) ELT)) (|characteristic| ((#13#) NIL T CONST)) (|binomThmExpt| (#118=($ $ $ #13#) NIL #53# ELT)) (|before?| #1#) (|associates?| (#2# NIL #8# ELT)) (|annihilate?| #1#) (|Zero| (#25# 13 T CONST)) (|RittWuCompare| (((|Union| #3# #16#) $ $) NIL T ELT)) (|One| (#25# 37 T CONST)) (|LazardQuotient2| (($ $ $ $ #13#) 105 #8# ELT)) (|LazardQuotient| (#118# 104 #8# ELT)) (D #85# #108# #109# #55#) (= #1#) (/ (#104# NIL (|has| |#1| (|Field|)) ELT)) (- #54# (#17# 75 T ELT)) (+ (#17# 85 T ELT)) (** (($ $ #119=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) 70 T ELT)) (* (($ #119# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #29# . #120=($)) NIL T ELT) (#17# 62 T ELT) (($ $ #28#) NIL #35# ELT) (($ #28# . #120#) NIL #35# ELT) (($ |#1| . #120#) 61 T ELT) (#104# NIL T ELT))) 
(((|NewSparseMultivariatePolynomial| |#1| |#2|) (|Join| (|RecursivePolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|) (|CoercibleTo| #1=(|SparseMultivariatePolynomial| |#1| |#2|)) (|RetractableTo| #1#)) (|Ring|) (|OrderedSet|)) (T |NewSparseMultivariatePolynomial|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 12 T ELT)) (|vectorise| ((#5=(|Vector| |#1|) $ #6=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#7=(|List| #8=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (#9=($ #10=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#11=(|SparseUnivariatePolynomial| $) $ #8#) NIL T ELT) #12=(#13=(#10# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #15=(#16=($ $) NIL #14# ELT)) (|unit?| (#4# NIL #14# ELT)) (|totalDegree| #17=(#18=(#6# $) NIL T ELT) ((#6# $ #7#) NIL T ELT)) (|subtractIfCan| (#19=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|subResultantsChain| ((#22=(|List| $) $ $) 54 #14# ELT)) (|subResultantGcd| (#23=($ $ $) 50 #14# ELT)) (|squareFreePolynomial| #24=(((|Factored| #11#) #11#) NIL #25=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #26=(#16# NIL #27=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#28=((|Factored| $) $) NIL #27# ELT)) (|solveLinearPolynomialEquation| (((|Union| #29=(|List| #11#) #21#) #29# #11#) NIL #25# ELT)) (|sizeLess?| (#2# NIL #30=(|has| |#1| (|Field|)) ELT)) (|shiftRight| #31=(($ $ #6#) NIL T ELT)) (|shiftLeft| #31#) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #27# ELT)) (|sample| (#32=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #33=(#21#)) . #34=($)) NIL T ELT) (((|Union| #35=(|Fraction| #36=(|Integer|)) . #33#) . #34#) NIL #37=(|has| |#1| (|RetractableTo| #35#)) ELT) (((|Union| #36# . #33#) . #34#) NIL #38=(|has| |#1| (|RetractableTo| #36#)) ELT) #39=(((|Union| #8# . #33#) . #34#) NIL T ELT) (((|Union| #10# . #33#) $) 10 T ELT)) (|retract| #40=(#41=(|#1| . #42=($)) NIL T ELT) ((#35# . #42#) NIL #37# ELT) ((#36# . #42#) NIL #38# ELT) ((#8# . #42#) NIL T ELT) #12#) (|resultant| (($ $ $ #8#) NIL #43=(|has| |#1| (|CommutativeRing|)) ELT) ((|#1| $ $) 58 #43# ELT)) (|rem| #44=(#23# NIL #30# ELT)) (|reductum| #45=(#16# NIL T ELT)) (|reducedSystem| ((#46=(|Matrix| #36#) . #47=(#48=(|Matrix| $))) NIL #49=(|has| |#1| (|LinearlyExplicitRingOver| #36#)) ELT) ((#50=(|Record| (|:| |mat| #46#) (|:| |vec| (|Vector| #36#))) . #51=(#48# #52=(|Vector| $))) NIL #49# ELT) ((#53=(|Record| (|:| |mat| #54=(|Matrix| |#1|)) (|:| |vec| #5#)) . #51#) NIL T ELT) ((#54# . #47#) NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|quo| #44#) (|pseudoRemainder| #55=(#23# NIL T ELT)) (|pseudoQuotient| (#23# 87 #14# ELT)) (|pseudoDivide| (((|Record| #56=(|:| |coef| |#1|) #57=(|:| |quotient| $) #58=(|:| |remainder| $)) $ $) 86 #14# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #22#) #59=(|:| |generator| $)) #22#) NIL #30# ELT)) (|primitivePart| #26# #60=(#61=($ $ #8#) NIL #27# ELT)) (|primitiveMonomials| #62=((#22# $) NIL T ELT)) (|prime?| (#4# NIL #25# ELT)) (|pomopo!| (($ $ |#1| #6# $) NIL T ELT)) (|patternMatch| ((#63=(|PatternMatchResult| #64=(|Float|) . #65=($)) $ #66=(|Pattern| #64#) #63#) NIL (AND (|has| #8# #67=(|PatternMatchable| #64#)) (|has| |#1| #67#)) ELT) ((#68=(|PatternMatchResult| #36# . #65#) $ #69=(|Pattern| #36#) #68#) NIL (AND (|has| #8# #70=(|PatternMatchable| #36#)) (|has| |#1| #70#)) ELT)) (|order| ((#6# $ $) NIL #14# ELT)) (|opposite?| #1#) (|one?| #71=(#4# NIL T ELT)) (|numberOfMonomials| #17#) (|nextItem| (#72=((|Maybe| $) $) NIL #73=(|has| |#1| (|StepThrough|)) ELT)) (|multivariate| (($ #10# #8#) NIL T ELT) (($ #11# #8#) NIL T ELT)) (|multiplyExponents| #31#) (|multiEuclidean| ((#74=(|Union| #22# #21#) #22# $) NIL #30# ELT)) (|monomials| #62#) (|monomial?| #71#) (|monomial| (($ |#1| #6#) NIL T ELT) #75=(($ $ #8# #6#) NIL T ELT) #76=(($ $ #7# #77=(|List| #6#)) NIL T ELT)) (|monicModulo| (#23# 27 T ELT)) (|monicDivide| ((#78=(|Record| #57# #58#) $ $ #8#) NIL T ELT) (#79=(#78# $ $) NIL T ELT)) (|minimumDegree| #17# #80=((#6# $ #8#) NIL T ELT) #81=((#77# $ #7#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #6# #6#) $) NIL T ELT)) (|map| (($ #82=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeSUP| #12#) (|mainVariable| #39#) (|leftReducedSystem| ((#46# . #83=(#52#)) NIL #49# ELT) ((#50# . #84=(#52# $)) NIL #49# ELT) ((#53# . #84#) NIL T ELT) ((#54# . #83#) NIL T ELT)) (|leadingMonomial| #45#) (|leadingCoefficient| #40#) (|lcm| #85=(($ #22#) NIL #27# ELT) #86=(#23# NIL #27# ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| #6#)) $ $) 37 T ELT)) (|lazyPseudoRemainder| (#23# 41 T ELT)) (|lazyPseudoQuotient| (#23# 47 T ELT)) (|lazyPseudoDivide| (((|Record| #56# (|:| |gap| #6#) #57# #58#) $ $) 46 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lastSubResultant| (#23# 56 #14# ELT)) (|karatsubaDivide| ((#78# $ #6#) NIL T ELT)) (|isTimes| #87=((#74# $) NIL T ELT)) (|isPlus| #87#) (|isExpt| (((|Union| (|Record| (|:| |var| #8#) (|:| |exponent| #6#)) #21#) $) NIL T ELT)) (|integrate| (#16# NIL #88=(|has| |#1| (|Algebra| #35#)) ELT)) (|init| (#32# NIL #73# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| #89=(|:| |gcd| $) #90=(|:| |coef2| $)) $ $) 82 #14# ELT)) (|halfExtendedSubResultantGcd1| (((|Record| #89# #91=(|:| |coef1| $)) $ $) 78 #14# ELT)) (|halfExtendedResultant2| (((|Record| #92=(|:| |resultant| |#1|) #90#) $ $) 70 #14# ELT)) (|halfExtendedResultant1| (((|Record| #92# #91#) $ $) 66 #14# ELT)) (|ground?| (#4# 13 T ELT)) (|ground| #40#) (|gcdPolynomial| ((#11# #11# #11#) NIL #27# ELT)) (|gcd| #85# #86#) (|fmecg| (($ $ #6# |#1| $) 26 T ELT)) (|factorSquareFreePolynomial| #24#) (|factorPolynomial| #24#) (|factor| (#28# NIL #25# ELT)) (|extendedSubResultantGcd| (((|Record| #89# #91# #90#) $ $) 74 #14# ELT)) (|extendedResultant| (((|Record| #92# #91# #90#) $ $) 62 #14# ELT)) (|extendedEuclidean| (((|Union| (|Record| #91# #90#) #21#) $ $ $) NIL #30# ELT) (((|Record| #91# #90# #59#) $ $) NIL #30# ELT)) (|exquo| ((#20# $ |#1|) NIL #14# ELT) #93=(#19# NIL #14# ELT)) (|expressIdealMember| (((|Maybe| #22#) #22# $) NIL #30# ELT)) (|eval| (($ $ (|List| #94=(|Equation| $))) NIL T ELT) (($ $ #94#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #22# #22#) NIL T ELT) (($ $ #8# |#1|) NIL T ELT) (($ $ #7# #95=(|List| |#1|)) NIL T ELT) (($ $ #8# $) NIL T ELT) (($ $ #7# #22#) NIL T ELT)) (|euclideanSize| (#18# NIL #30# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) #55# ((#96=(|Fraction| $) #96# #96#) NIL #14# ELT) ((|#1| #96# |#1|) NIL #30# ELT) ((#96# $ #96#) NIL #14# ELT)) (|divideExponents| ((#20# $ #6#) NIL T ELT)) (|divide| (#79# NIL #30# ELT)) (|discriminant| (#61# NIL #43# ELT) (#41# NIL #43# ELT)) (|differentiate| #76# #75# #97=(($ $ #7#) NIL T ELT) #98=(#61# NIL T ELT) #45# #31# #99=(($ $ #82#) NIL T ELT) #100=(($ $ #82# #6#) NIL T ELT) (($ $ #82# $) NIL T ELT) #101=(($ $ #102=(|Symbol|)) NIL #103=(|has| |#1| (|PartialDifferentialSpace| #102#)) ELT) #104=(($ $ #105=(|List| #102#)) NIL #103# ELT) #106=(($ $ #102# #6#) NIL #103# ELT) #107=(($ $ #105# #77#) NIL #103# ELT)) (|degree| #17# #80# #81#) (|convert| ((#66# . #108=($)) NIL (AND (|has| #8# #109=(|ConvertibleTo| #66#)) (|has| |#1| #109#)) ELT) ((#69# . #108#) NIL (AND (|has| #8# #110=(|ConvertibleTo| #69#)) (|has| |#1| #110#)) ELT) ((#111=(|InputForm|) . #108#) NIL (AND (|has| #8# #112=(|ConvertibleTo| #111#)) (|has| |#1| #112#)) ELT)) (|content| (#41# NIL #27# ELT) #60#) (|conditionP| (((|Union| #52# #21#) #48#) NIL #113=(AND (|has| $ #114=(|CharacteristicNonZero|)) #25#) ELT)) (|composite| #93# (((|Union| #96# #21#) #96# $) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #36#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #8#) NIL T ELT) (#13# 7 T ELT) (#9# 8 T ELT) (($ #35#) NIL (OR #88# #37#) ELT) #15#) (|coefficients| ((#95# $) NIL T ELT)) (|coefficient| ((|#1| $ #6#) NIL T ELT) #75# #76#) (|charthRoot| (#72# NIL (OR #113# (|has| |#1| #114#)) ELT)) (|characteristic| ((#6#) NIL T CONST)) (|binomThmExpt| (($ $ $ #6#) NIL #43# ELT)) (|before?| #1#) (|associates?| (#2# NIL #14# ELT)) (|annihilate?| #1#) (|Zero| (#32# 28 T CONST)) (|One| (#32# 32 T CONST)) (D #76# #75# #97# #98# #45# #31# #99# #100# #101# #104# #106# #107#) (= #1#) (/ (#115=($ $ |#1|) NIL #30# ELT)) (- (#16# 40 T ELT) #55#) (+ #55#) (** (($ $ #116=(|PositiveInteger|)) NIL T ELT) #31#) (* (($ #116# $) NIL T ELT) (($ #6# $) NIL T ELT) (($ #36# . #117=($)) NIL T ELT) #55# (($ $ #35#) NIL #88# ELT) (($ #35# . #117#) NIL #88# ELT) (($ |#1| . #117#) 31 T ELT) (#115# NIL T ELT))) 
(((|NewSparseUnivariatePolynomial| |#1|) (|Join| (|UnivariatePolynomialCategory| |#1|) (|CoercibleTo| #1=(|SparseUnivariatePolynomial| |#1|)) (|RetractableTo| #1#) (CATEGORY |domain| (SIGNATURE |fmecg| ($ $ #2=(|NonNegativeInteger|) |#1| $)) (SIGNATURE |monicModulo| #3=($ $ $)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| #2#)) $ $)) (SIGNATURE |lazyPseudoRemainder| #3#) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |gap| #2#) (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPseudoQuotient| #3#) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |subResultantsChain| ((|List| $) $ $)) (SIGNATURE |lastSubResultant| #3#) (SIGNATURE |extendedSubResultantGcd| ((|Record| #4=(|:| |gcd| $) #5=(|:| |coef1| $) #6=(|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd1| ((|Record| #4# #5#) $ $)) (SIGNATURE |halfExtendedSubResultantGcd2| ((|Record| #4# #6#) $ $)) (SIGNATURE |extendedResultant| ((|Record| #7=(|:| |resultant| |#1|) #5# #6#) $ $)) (SIGNATURE |halfExtendedResultant1| ((|Record| #7# #5#) $ $)) (SIGNATURE |halfExtendedResultant2| ((|Record| #7# #6#) $ $))) |%noBranch|))) (|Ring|)) (T |NewSparseUnivariatePolynomial|)) 
((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 #1=(|NonNegativeInteger|)) #2=(|isDomain| *1 #3=(|NewSparseUnivariatePolynomial| *3)) #4=(|ofCategory| *3 #5=(|Ring|)))) (|monicModulo| #6=(*1 *1 *1 *1) #7=(AND #8=(|isDomain| *1 (|NewSparseUnivariatePolynomial| *2)) #9=(|ofCategory| *2 #5#))) (|lazyResidueClass| #10=(*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |polnum| #3#) (|:| |polden| *3) (|:| |power| #1#))) #2# #4#)) (|lazyPseudoRemainder| #6# #7#) (|lazyPseudoDivide| #10# (AND (|isDomain| *2 (|Record| (|:| |coef| *3) (|:| |gap| #1#) (|:| |quotient| #3#) (|:| |remainder| #3#))) #2# #4#)) (|lazyPseudoQuotient| #6# #7#) (|subResultantsChain| #10# (AND (|isDomain| *2 (|List| #3#)) #2# #11=(|ofCategory| *3 #12=(|IntegralDomain|)) #4#)) (|lastSubResultant| #6# (AND #8# (|ofCategory| *2 #12#) #9#)) (|extendedSubResultantGcd| #10# (AND (|isDomain| *2 (|Record| #13=(|:| |gcd| #3#) #14=(|:| |coef1| #3#) #15=(|:| |coef2| #3#))) #2# #11# #4#)) (|halfExtendedSubResultantGcd1| #10# (AND (|isDomain| *2 (|Record| #13# #14#)) #2# #11# #4#)) (|halfExtendedSubResultantGcd2| #10# (AND (|isDomain| *2 (|Record| #13# #15#)) #2# #11# #4#)) (|extendedResultant| #10# (AND (|isDomain| *2 (|Record| #16=(|:| |resultant| *3) #14# #15#)) #2# #11# #4#)) (|halfExtendedResultant1| #10# (AND (|isDomain| *2 (|Record| #16# #14#)) #2# #11# #4#)) (|halfExtendedResultant2| #10# (AND (|isDomain| *2 (|Record| #16# #15#)) #2# #11# #4#))) 
((|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) 13 T ELT))) 
(((|NewSparseUnivariatePolynomialFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)))) #1=(|Ring|) #1#) (T |NewSparseUnivariatePolynomialFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|NewSparseUnivariatePolynomial| *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|NewSparseUnivariatePolynomial| *6)) (|isDomain| *1 (|NewSparseUnivariatePolynomialFunctions2| *5 *6))))) 
((|eulerE| (#1=(|#1| (|NonNegativeInteger|) |#1|) 33 #2=(|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT)) (|cyclotomic| (#1# 23 T ELT)) (|bernoulliB| (#1# 35 #2# ELT))) 
(((|NumberTheoreticPolynomialFunctions| |#1|) (CATEGORY |package| (SIGNATURE |cyclotomic| #1=(|#1| (|NonNegativeInteger|) |#1|)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |bernoulliB| #1#) (SIGNATURE |eulerE| #1#)) |%noBranch|)) (|CommutativeRing|)) (T |NumberTheoreticPolynomialFunctions|)) 
((|eulerE| #1=(*1 *2 *3 *2) #2=(AND #3=(|isDomain| *3 (|NonNegativeInteger|)) #4=(|isDomain| *1 (|NumberTheoreticPolynomialFunctions| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) #5=(|ofCategory| *2 (|CommutativeRing|)))) (|bernoulliB| #1# #2#) (|cyclotomic| #1# (AND #3# #4# #5#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) ((#2=(|List| $) (|List| |#4|) #3=(|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #4=($)) 39 T ELT)) (|trivialIdeal?| (#5=(#6=(|Boolean|) $) 32 T ELT)) (|triangular?| (#5# 23 (|has| |#1| . #7=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#8=(|Boolean|) |#4| . #9=($)) 107 T ELT) (#10=(#8# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #11=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) . #12=(#13=(|:| |tower| $)))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #14=(|Boolean|) |#4|) . #15=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #16=(#17="failed")) $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#5# 28 (|has| |#1| . #7#) ELT)) (|roughSubIdeal?| (#19=(#6# $ $) 30 (|has| |#1| . #7#) ELT)) (|roughEqualIdeals?| (#19# 29 (|has| |#1| . #7#) ELT)) (|roughBase?| (#5# 31 (|has| |#1| . #7#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #20=($)) 24 (|has| |#1| . #7#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #20#) 25 (|has| |#1| . #7#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| ((#21=(|Union| $ #17#) $) 88 T ELT)) (|removeZero| ((|#4| |#4| . #11#) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #22=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #22#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #14# |#4|) . #15#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #7#) ELT)) (|reduced?| ((#8# |#4| $ (|Mapping| #8# |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| . #11#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #23=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| ((#3# |#4| . #24=($)) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| ((#3# |#4| . #24#) 142 T ELT)) (|purelyAlgebraic?| ((#3# |#4| . #24#) 146 T ELT) ((#3# $) 143 T ELT)) (|normalized?| ((#8# |#4| . #9#) 110 T ELT) (#10# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#25=(|Boolean|) |#4| $) 53 (|has| |#4| . #23#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #4#) 38 T ELT)) (|mainVariable?| ((#6# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #2#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) . #12#)) |#4| |#4| $) 136 T ELT)) (|last| (((|Union| |#4| . #16#) . #26=($)) 89 T ELT)) (|invertibleSet| ((#2# |#4| . #27=($)) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #3# #2#) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #13#)) |#4| $) 140 T ELT) ((#3# |#4| . #24#) 139 T ELT)) (|intersect| ((#2# |#4| . #27#) 134 T ELT) ((#2# (|List| |#4|) . #28=($)) 133 T ELT) ((#2# (|List| |#4|) . #29=(#2#)) 132 T ELT) ((#2# |#4| . #30=(#2#)) 131 T ELT)) (|internalAugment| (($ |#4| $) 126 T ELT) (($ (|List| |#4|) $) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#8# |#4| . #9#) 105 T ELT) (#10# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #11#) 96 T ELT)) (|infRittWu?| ((#8# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #7#) ELT)) (|headReduced?| ((#8# |#4| . #9#) 106 T ELT) (#10# 102 T ELT)) (|headReduce| ((|#4| |#4| . #11#) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| . #16#) . #26#) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #25# |#4|) $) 51 T ELT)) (|extendIfCan| ((#21# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) ((#2# |#4| . #27#) 124 T ELT) ((#2# |#4| . #30#) 123 T ELT) ((#2# (|List| |#4|) . #28#) 122 T ELT) ((#2# (|List| |#4|) . #29#) 121 T ELT)) (|every?| ((#25# (|Mapping| #25# |#4|) . #31=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT)) (|eq?| ((#33=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#33# $) 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#34=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#35=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #23#) ELT) ((#35# (|Mapping| #25# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#36=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #36#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #37=($)) 13 T ELT) (((|List| |#4|) . #37#) 43 T ELT)) (|coHeight| (#34# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #38=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #39=(#17#)) (|List| |#4|) (|Mapping| #8# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #38# (|:| |top| (|List| |#4|))) . #39#) (|List| |#4|) (|Mapping| #8# |#4|) (|Mapping| #8# |#4| |#4|)) 114 T ELT)) (|autoReduced?| ((#8# $ (|Mapping| #8# |#4| (|List| |#4|))) 104 T ELT)) (|augment| ((#2# |#4| . #27#) 130 T ELT) ((#2# |#4| . #30#) 129 T ELT) ((#2# (|List| |#4|) . #28#) 128 T ELT) ((#2# (|List| |#4|) . #29#) 127 T ELT)) (|any?| ((#25# (|Mapping| #25# |#4|) . #31#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraicCoefficients?| ((#3# |#4| . #24#) 144 T ELT)) (|algebraic?| ((#8# |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#35# $) 44 T ELT))) 
(((|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|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) 
((|numericIfCan| ((#1=(|Union| #2=(|Float|) #3="failed") #4=(|Expression| |#1|) #5=(|PositiveInteger|)) 60 #6=(AND #7=(|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|))) ELT) ((#1# #4#) 52 #6# ELT) ((#1# #8=(|Fraction| #9=(|Polynomial| |#1|)) #5#) 39 #7# ELT) ((#1# #8#) 35 #7# ELT) ((#1# #9# #5#) 30 #10=(|has| |#1| (|Ring|)) ELT) ((#1# #9#) 24 #10# ELT)) (|numeric| ((#2# #4# #5#) 92 #6# ELT) ((#2# #4#) 87 #6# ELT) ((#2# #8# #5#) 84 #7# ELT) ((#2# #8#) 81 #7# ELT) ((#2# #9# #5#) 80 #10# ELT) ((#2# #9#) 77 #10# ELT) ((#2# |#1| #5#) 73 T ELT) ((#2# |#1|) 22 T ELT)) (|complexNumericIfCan| ((#11=(|Union| #12=(|Complex| #2#) #3#) #13=(|Expression| #14=(|Complex| |#1|)) #5#) 68 #6# ELT) ((#11# #13#) 58 #6# ELT) ((#11# #4# #5#) 61 #6# ELT) ((#11# #4#) 59 #6# ELT) ((#11# #15=(|Fraction| #16=(|Polynomial| #14#)) #5#) 44 #7# ELT) ((#11# #15#) 43 #7# ELT) ((#11# #8# #5#) 38 #7# ELT) ((#11# #8#) 37 #7# ELT) ((#11# #9# #5#) 28 #10# ELT) ((#11# #9#) 26 #10# ELT) ((#11# #16# #5#) 18 #17=(|has| |#1| (|CommutativeRing|)) ELT) ((#11# #16#) 15 #17# ELT)) (|complexNumeric| ((#12# #13# #5#) 95 #6# ELT) ((#12# #13#) 94 #6# ELT) ((#12# #4# #5#) 93 #6# ELT) ((#12# #4#) 91 #6# ELT) ((#12# #15# #5#) 86 #7# ELT) ((#12# #15#) 85 #7# ELT) ((#12# #8# #5#) 83 #7# ELT) ((#12# #8#) 82 #7# ELT) ((#12# #9# #5#) 79 #10# ELT) ((#12# #9#) 78 #10# ELT) ((#12# #16# #5#) 75 #17# ELT) ((#12# #16#) 74 #17# ELT) ((#12# #14# #5#) 17 #17# ELT) ((#12# #14#) 13 #17# ELT) ((#12# |#1| #5#) 27 T ELT) ((#12# |#1|) 25 T ELT))) 
(((|Numeric| |#1|) (CATEGORY |package| (SIGNATURE |numeric| (#1=(|Float|) |#1|)) (SIGNATURE |numeric| (#1# |#1| #2=(|PositiveInteger|))) (SIGNATURE |complexNumeric| (#3=(|Complex| #1#) |#1|)) (SIGNATURE |complexNumeric| (#3# |#1| #2#)) (IF #4=(|has| |#1| (|CommutativeRing|)) (PROGN (SIGNATURE |complexNumeric| (#3# #5=(|Complex| |#1|))) (SIGNATURE |complexNumeric| (#3# #5# #2#)) (SIGNATURE |complexNumeric| (#3# #6=(|Polynomial| #5#))) (SIGNATURE |complexNumeric| (#3# #6# #2#))) |%noBranch|) (IF #7=(|has| |#1| (|Ring|)) (PROGN (SIGNATURE |numeric| (#1# #8=(|Polynomial| |#1|))) (SIGNATURE |numeric| (#1# #8# #2#)) (SIGNATURE |complexNumeric| (#3# #8#)) (SIGNATURE |complexNumeric| (#3# #8# #2#))) |%noBranch|) (IF #9=(|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |numeric| (#1# #10=(|Fraction| #8#))) (SIGNATURE |numeric| (#1# #10# #2#)) (SIGNATURE |complexNumeric| (#3# #10#)) (SIGNATURE |complexNumeric| (#3# #10# #2#)) (SIGNATURE |complexNumeric| (#3# #11=(|Fraction| #6#))) (SIGNATURE |complexNumeric| (#3# #11# #2#)) (IF #12=(|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |numeric| (#1# #13=(|Expression| |#1|))) (SIGNATURE |numeric| (#1# #13# #2#)) (SIGNATURE |complexNumeric| (#3# #13#)) (SIGNATURE |complexNumeric| (#3# #13# #2#)) (SIGNATURE |complexNumeric| (#3# #14=(|Expression| #5#))) (SIGNATURE |complexNumeric| (#3# #14# #2#))) |%noBranch|)) |%noBranch|) (IF #4# (PROGN (SIGNATURE |complexNumericIfCan| (#15=(|Union| #3# #16="failed") #6#)) (SIGNATURE |complexNumericIfCan| (#15# #6# #2#))) |%noBranch|) (IF #7# (PROGN (SIGNATURE |numericIfCan| (#17=(|Union| #1# #16#) #8#)) (SIGNATURE |numericIfCan| (#17# #8# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #8#)) (SIGNATURE |complexNumericIfCan| (#15# #8# #2#))) |%noBranch|) (IF #9# (PROGN (SIGNATURE |numericIfCan| (#17# #10#)) (SIGNATURE |numericIfCan| (#17# #10# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #10#)) (SIGNATURE |complexNumericIfCan| (#15# #10# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #11#)) (SIGNATURE |complexNumericIfCan| (#15# #11# #2#)) (IF #12# (PROGN (SIGNATURE |numericIfCan| (#17# #13#)) (SIGNATURE |numericIfCan| (#17# #13# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #13#)) (SIGNATURE |complexNumericIfCan| (#15# #13# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #14#)) (SIGNATURE |complexNumericIfCan| (#15# #14# #2#))) |%noBranch|)) |%noBranch|)) (|ConvertibleTo| #1#)) (T |Numeric|)) 
((|complexNumericIfCan| #1=(*1 *2 *3 *4) (|partial| AND #2=(|isDomain| *3 (|Expression| #3=(|Complex| *5))) #4=(|isDomain| *4 (|PositiveInteger|)) #5=(|ofCategory| *5 #6=(|IntegralDomain|)) #7=(|ofCategory| *5 #8=(|OrderedSet|)) #9=(|ofCategory| *5 #10=(|ConvertibleTo| #11=(|Float|))) #12=(|isDomain| *2 (|Complex| #11#)) #13=(|isDomain| *1 (|Numeric| *5)))) (|complexNumericIfCan| #14=(*1 *2 *3) (|partial| AND #15=(|isDomain| *3 (|Expression| #16=(|Complex| *4))) #17=(|ofCategory| *4 #6#) #18=(|ofCategory| *4 #8#) #19=(|ofCategory| *4 #10#) #12# #20=(|isDomain| *1 (|Numeric| *4)))) (|complexNumericIfCan| #1# (|partial| AND #21=(|isDomain| *3 (|Expression| *5)) #4# #5# #7# #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #22=(|isDomain| *3 (|Expression| *4)) #17# #18# #19# #12# #20#)) (|numericIfCan| #1# (|partial| AND #21# #4# #5# #7# #23=(|ofCategory| *5 #24=(|ConvertibleTo| *2)) #25=(|isDomain| *2 #11#) #13#)) (|numericIfCan| #14# (|partial| AND #22# #17# #18# #26=(|ofCategory| *4 #24#) #25# #20#)) (|complexNumericIfCan| #1# (|partial| AND #27=(|isDomain| *3 (|Fraction| #28=(|Polynomial| #3#))) #4# #5# #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #29=(|isDomain| *3 (|Fraction| #30=(|Polynomial| #16#))) #17# #19# #12# #20#)) (|complexNumericIfCan| #1# (|partial| AND #31=(|isDomain| *3 (|Fraction| #32=(|Polynomial| *5))) #4# #5# #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #33=(|isDomain| *3 (|Fraction| #34=(|Polynomial| *4))) #17# #19# #12# #20#)) (|numericIfCan| #1# (|partial| AND #31# #4# #5# #23# #25# #13#)) (|numericIfCan| #14# (|partial| AND #33# #17# #26# #25# #20#)) (|complexNumericIfCan| #1# (|partial| AND #35=(|isDomain| *3 #32#) #4# #36=(|ofCategory| *5 #37=(|Ring|)) #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #38=(|isDomain| *3 #34#) #39=(|ofCategory| *4 #37#) #19# #12# #20#)) (|numericIfCan| #1# (|partial| AND #35# #4# #36# #23# #25# #13#)) (|numericIfCan| #14# (|partial| AND #38# #39# #26# #25# #20#)) (|complexNumericIfCan| #1# (|partial| AND #40=(|isDomain| *3 #28#) #4# #41=(|ofCategory| *5 #42=(|CommutativeRing|)) #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #43=(|isDomain| *3 #30#) #44=(|ofCategory| *4 #42#) #19# #12# #20#)) (|complexNumeric| #1# (AND #2# #4# #5# #7# #9# #12# #13#)) (|complexNumeric| #14# (AND #15# #17# #18# #19# #12# #20#)) (|complexNumeric| #1# (AND #21# #4# #5# #7# #9# #12# #13#)) (|complexNumeric| #14# (AND #22# #17# #18# #19# #12# #20#)) (|numeric| #1# (AND #21# #4# #5# #7# #23# #25# #13#)) (|numeric| #14# (AND #22# #17# #18# #26# #25# #20#)) (|complexNumeric| #1# (AND #27# #4# #5# #9# #12# #13#)) (|complexNumeric| #14# (AND #29# #17# #19# #12# #20#)) (|complexNumeric| #1# (AND #31# #4# #5# #9# #12# #13#)) (|complexNumeric| #14# (AND #33# #17# #19# #12# #20#)) (|numeric| #1# (AND #31# #4# #5# #23# #25# #13#)) (|numeric| #14# (AND #33# #17# #26# #25# #20#)) (|complexNumeric| #1# (AND #35# #4# #36# #9# #12# #13#)) (|complexNumeric| #14# (AND #38# #39# #19# #12# #20#)) (|numeric| #1# (AND #35# #4# #36# #23# #25# #13#)) (|numeric| #14# (AND #38# #39# #26# #25# #20#)) (|complexNumeric| #1# (AND #40# #4# #41# #9# #12# #13#)) (|complexNumeric| #14# (AND #43# #44# #19# #12# #20#)) (|complexNumeric| #1# (AND (|isDomain| *3 #3#) #4# #41# #9# #12# #13#)) (|complexNumeric| #14# (AND (|isDomain| *3 #16#) #44# #19# #12# #20#)) (|complexNumeric| #1# (AND #4# #12# #45=(|isDomain| *1 (|Numeric| *3)) #46=(|ofCategory| *3 #10#))) (|complexNumeric| #14# (AND #12# #45# #46#)) (|numeric| #1# (AND #4# #25# #45# #47=(|ofCategory| *3 #24#))) (|numeric| #14# (AND #25# #45# #47#))) 
((|ScanRoman| (#1=(#2=(|PositiveInteger|) #3=(|String|)) 90 T ELT)) (|ScanFloatIgnoreSpacesIfCan| (((|Union| #4=(|Float|) "failed") #3#) 36 T ELT)) (|ScanFloatIgnoreSpaces| ((#4# #3#) 34 T ELT)) (|ScanArabic| (#1# 64 T ELT)) (|FormatRoman| (#5=(#3# #2#) 74 T ELT)) (|FormatArabic| (#5# 63 T ELT))) 
(((|NumberFormats|) (CATEGORY |package| (SIGNATURE |FormatArabic| #1=(#2=(|String|) #3=(|PositiveInteger|))) (SIGNATURE |ScanArabic| #4=(#3# #2#)) (SIGNATURE |FormatRoman| #1#) (SIGNATURE |ScanRoman| #4#) (SIGNATURE |ScanFloatIgnoreSpaces| (#5=(|Float|) #2#)) (SIGNATURE |ScanFloatIgnoreSpacesIfCan| ((|Union| #5# "failed") #2#)))) (T |NumberFormats|)) 
((|ScanFloatIgnoreSpacesIfCan| #1=(*1 *2 *3) (|partial| AND #2=(|isDomain| *3 #3=(|String|)) #4=(|isDomain| *2 (|Float|)) #5=(|isDomain| *1 (|NumberFormats|)))) (|ScanFloatIgnoreSpaces| #1# (AND #2# #4# #5#)) (|ScanRoman| #1# #6=(AND #2# (|isDomain| *2 #7=(|PositiveInteger|)) #5#)) (|FormatRoman| #1# #8=(AND (|isDomain| *3 #7#) (|isDomain| *2 #3#) #5#)) (|ScanArabic| #1# #6#) (|FormatArabic| #1# #8#)) 
((|rk4qc| ((#1=(|Void|) #2=(|Vector| #3=(|Float|)) #4=(|Integer|) #3# #5=(|Record| (|:| |tryValue| #3#) (|:| |did| #3#) (|:| |next| #3#)) #3# #2# #6=(|Mapping| #1# #2# #2# #3#) #2# #2# #2# #2# #2# #2# #2#) 54 T ELT) ((#1# #2# #4# #3# #5# #3# #2# #6#) 51 T ELT)) (|rk4f| ((#1# #2# #4# #3# #3# #4# #6#) 61 T ELT)) (|rk4a| ((#1# #2# #4# #3# #3# #3# #3# #4# #6#) 49 T ELT)) (|rk4| ((#1# #2# #4# #3# #3# #6# #2# #2# #2# #2#) 63 T ELT) ((#1# #2# #4# #3# #3# #6#) 62 T ELT))) 
(((|NumericalOrdinaryDifferentialEquations|) (CATEGORY |package| (SIGNATURE |rk4| (#1=(|Void|) #2=(|Vector| #3=(|Float|)) #4=(|Integer|) #3# #3# #5=(|Mapping| #1# #2# #2# #3#))) (SIGNATURE |rk4| (#1# #2# #4# #3# #3# #5# #2# #2# #2# #2#)) (SIGNATURE |rk4a| (#1# #2# #4# #3# #3# #3# #3# #4# #5#)) (SIGNATURE |rk4qc| (#1# #2# #4# #3# #6=(|Record| (|:| |tryValue| #3#) (|:| |did| #3#) (|:| |next| #3#)) #3# #2# #5#)) (SIGNATURE |rk4qc| (#1# #2# #4# #3# #6# #3# #2# #5# #2# #2# #2# #2# #2# #2# #2#)) (SIGNATURE |rk4f| (#1# #2# #4# #3# #3# #4# #5#)))) (T |NumericalOrdinaryDifferentialEquations|)) 
((|rk4f| (*1 *2 *3 *4 *5 *5 *4 *6) #1=(AND #2=(|isDomain| *4 (|Integer|)) (|isDomain| *6 #3=(|Mapping| #4=(|Void|) #5=(|Vector| *5) #5# #6=(|Float|))) #7=(|isDomain| *3 (|Vector| #6#)) #8=(|isDomain| *5 #6#) #9=(|isDomain| *2 #4#) #10=(|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|)))) (|rk4qc| (*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) #11=(AND #2# (|isDomain| *6 (|Record| (|:| |tryValue| #6#) (|:| |did| #6#) (|:| |next| #6#))) (|isDomain| *7 #3#) #7# #8# #9# #10#)) (|rk4qc| (*1 *2 *3 *4 *5 *6 *5 *3 *7) #11#) (|rk4a| (*1 *2 *3 *4 *5 *5 *5 *5 *4 *6) #1#) (|rk4| (*1 *2 *3 *4 *5 *5 *6 *3 *3 *3 *3) #1#) (|rk4| (*1 *2 *3 *4 *5 *5 *6) #1#)) 
((|trapezoidalo| (#1=(#2=(|Record| (|:| |value| #3=(|Float|)) (|:| |error| #3#) (|:| |totalpts| #4=(|Integer|)) (|:| |success| (|Boolean|))) #5=(|Mapping| #3# #3#) #3# #3# #3# #3# #4# #4#) 65 T ELT)) (|trapezoidal| (#1# 40 T ELT)) (|simpsono| (#1# 64 T ELT)) (|simpson| (#1# 38 T ELT)) (|rombergo| (#1# 63 T ELT)) (|romberg| (#1# 24 T ELT)) (|atrapezoidal| (#6=(#2# #5# #3# #3# #3# #3# #4# #4# #4#) 41 T ELT)) (|asimpson| (#6# 39 T ELT)) (|aromberg| (#6# 37 T ELT))) 
(((|NumericalQuadrature|) (CATEGORY |package| (SIGNATURE |aromberg| #1=(#2=(|Record| (|:| |value| #3=(|Float|)) (|:| |error| #3#) (|:| |totalpts| #4=(|Integer|)) (|:| |success| (|Boolean|))) #5=(|Mapping| #3# #3#) #3# #3# #3# #3# #4# #4# #4#)) (SIGNATURE |asimpson| #1#) (SIGNATURE |atrapezoidal| #1#) (SIGNATURE |romberg| #6=(#2# #5# #3# #3# #3# #3# #4# #4#)) (SIGNATURE |simpson| #6#) (SIGNATURE |trapezoidal| #6#) (SIGNATURE |rombergo| #6#) (SIGNATURE |simpsono| #6#) (SIGNATURE |trapezoidalo| #6#))) (T |NumericalQuadrature|)) 
((|trapezoidalo| #1=(*1 *2 *3 *4 *4 *4 *4 *5 *5) #2=(AND (|isDomain| *3 (|Mapping| #3=(|Float|) #3#)) (|isDomain| *4 #3#) (|isDomain| *2 (|Record| (|:| |value| *4) (|:| |error| *4) (|:| |totalpts| #4=(|Integer|)) (|:| |success| (|Boolean|)))) (|isDomain| *1 (|NumericalQuadrature|)) (|isDomain| *5 #4#))) (|simpsono| #1# #2#) (|rombergo| #1# #2#) (|trapezoidal| #1# #2#) (|simpson| #1# #2#) (|romberg| #1# #2#) (|atrapezoidal| #5=(*1 *2 *3 *4 *4 *4 *4 *5 *5 *5) #2#) (|asimpson| #5# #2#) (|aromberg| #5# #2#)) 
((|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) 69 T ELT))) 
(((|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|))))) 
((|sign| (((|Integer|) $) 17 T ELT)) (|negative?| (((|Boolean|) $) 10 T ELT)) (|abs| (($ $) 19 T ELT))) 
(((|OrderedAbelianGroup&| |#1|) (CATEGORY |package| (SIGNATURE |abs| (|#1| |#1|)) (SIGNATURE |sign| ((|Integer|) |#1|)) (SIGNATURE |negative?| ((|Boolean|) |#1|))) (|OrderedAbelianGroup|)) (T |OrderedAbelianGroup&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 35 T ELT)) (|sign| (((|Integer|) $) 38 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|negative?| (((|Boolean|) $) 39 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|abs| (($ $) 37 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (- (($ $ $) 42 T ELT) (($ $) 41 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ (|Integer|) $) 40 T ELT))) 
(((|OrderedAbelianGroup|) (|Category|)) (T |OrderedAbelianGroup|)) 
((|negative?| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedAbelianGroup|)) (|isDomain| *2 (|Boolean|)))) (|sign| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedAbelianGroup|)) (|isDomain| *2 (|Integer|)))) (|abs| (*1 *1 *1) (|ofCategory| *1 (|OrderedAbelianGroup|)))) 
(|Join| (|OrderedCancellationAbelianMonoid|) (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE |negative?| ((|Boolean|) $)) (SIGNATURE |sign| ((|Integer|) $)) (SIGNATURE |abs| ($ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|positive?| (((|Boolean|) $) 10 T ELT))) 
(((|OrderedAbelianMonoid&| |#1|) (CATEGORY |package| (SIGNATURE |positive?| ((|Boolean|) |#1|))) (|OrderedAbelianMonoid|)) (T |OrderedAbelianMonoid&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT))) 
(((|OrderedAbelianMonoid|) (|Category|)) (T |OrderedAbelianMonoid|)) 
((|positive?| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|OrderedAbelianSemiGroup|) (|AbelianMonoid|) (CATEGORY |domain| (SIGNATURE |positive?| ((|Boolean|) $)))) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|sup| (($ $ $) 36 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 35 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT))) 
(((|OrderedAbelianMonoidSup|) (|Category|)) (T |OrderedAbelianMonoidSup|)) 
((|sup| (*1 *1 *1 *1) (|ofCategory| *1 (|OrderedAbelianMonoidSup|)))) 
(|Join| (|OrderedCancellationAbelianMonoid|) (CATEGORY |domain| (SIGNATURE |sup| ($ $ $)))) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#3=((|Boolean|) $ $) 21 T ELT)) (> (#3# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#3# 20 T ELT)) (< (#3# 18 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT))) 
(((|OrderedAbelianSemiGroup|) (|Category|)) (T |OrderedAbelianSemiGroup|)) 
NIL 
(|Join| (|OrderedSet|) (|AbelianSemiGroup|)) 
(((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|zero?| (#1=(#2=(|Boolean|) $) 42 T ELT)) (|retractIfCan| (((|Union| #3=(|Integer|) #4="failed") $) NIL T ELT) (#5=((|Union| #6=(|Fraction| #3#) #4#) $) NIL T ELT) (((|Union| |#2| #4#) $) 45 T ELT)) (|retract| ((#3# $) NIL T ELT) (#7=(#6# $) NIL T ELT) (#8=(|#2| $) 43 T ELT)) (|rationalIfCan| (#5# 78 T ELT)) (|rational?| (#1# 72 T ELT)) (|rational| (#7# 76 T ELT)) (|norm| (#8# 26 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 23 T ELT)) (|inv| (#9=($ $) 58 T ELT)) (|convert| (((|InputForm|) $) 67 T ELT)) (|conjugate| (#9# 21 T ELT)) (|coerce| (((|OutputForm|) $) 53 T ELT) (($ #3#) 40 T ELT) (($ |#2|) 38 T ELT) (($ #6#) NIL T ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) 10 T CONST)) (|abs| (#8# 71 T ELT)) (= (#11=(#2# $ $) 30 T ELT)) (< (#11# 69 T ELT)) (- (#9# 32 T ELT) #12=(#13=($ $ $) NIL T ELT)) (+ (#13# 31 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #3# $) 36 T ELT) #12# (($ $ |#2|) NIL T ELT) (($ |#2| $) 33 T ELT))) 
(((|OctonionCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE < #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |inv| #3=(|#1| |#1|)) (SIGNATURE |rationalIfCan| #4=((|Union| #5=(|Fraction| #6=(|Integer|)) #7="failed") |#1|)) (SIGNATURE |rational| #8=(#5# |#1|)) (SIGNATURE |rational?| #9=(#2# |#1|)) (SIGNATURE |abs| #10=(|#2| |#1|)) (SIGNATURE |norm| #10#) (SIGNATURE |conjugate| #3#) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #7#) |#1|)) (SIGNATURE |retract| #10#) (SIGNATURE |retract| #8#) (SIGNATURE |retractIfCan| #4#) (SIGNATURE |coerce| (|#1| #5#)) (SIGNATURE |retract| (#6# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #6# #7#) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |characteristic| (#11=(|NonNegativeInteger|)) |constant|) (SIGNATURE |coerce| (|#1| #6#)) (SIGNATURE * #12=(|#1| |#1| |#1|)) (SIGNATURE - #12#) (SIGNATURE - #3#) (SIGNATURE * (|#1| #6# |#1|)) (SIGNATURE * (|#1| #11# |#1|)) (SIGNATURE |zero?| #9#) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE + #12#) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = #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))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|size| (((|NonNegativeInteger|)) 67 (|has| |#1| . #3=((|Finite|))) ELT)) (|sample| (#4=($) 23 T CONST)) (|retractIfCan| (((|Union| #5=(|Integer|) . #6=("failed")) . #7=($)) 109 (|has| |#1| . #8=((|RetractableTo| #5#))) ELT) (((|Union| #9=(|Fraction| #5#) . #6#) . #7#) 106 (|has| |#1| . #10=((|RetractableTo| #9#))) ELT) (((|Union| |#1| . #6#) . #7#) 103 T ELT)) (|retract| ((#5# . #11=($)) 108 (|has| |#1| . #8#) ELT) ((#9# . #11#) 105 (|has| |#1| . #10#) ELT) ((|#1| . #11#) 104 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|real| ((|#1| $) 93 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 80 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (((|Boolean|) $) 82 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational| (((|Fraction| (|Integer|)) $) 81 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|random| (($) 70 (|has| |#1| . #3#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 84 T ELT)) (|norm| ((|#1| $) 85 T ELT)) (|min| (#12=($ $ $) 71 (|has| |#1| . #13=((|OrderedSet|))) ELT)) (|max| (#12# 72 (|has| |#1| . #13#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 95 T ELT)) (|lookup| ((#14=(|PositiveInteger|) $) 69 (|has| |#1| . #3#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 79 (|has| |#1| (|Field|)) ELT)) (|index| (($ #14#) 68 (|has| |#1| . #3#) ELT)) (|imagk| ((|#1| $) 90 T ELT)) (|imagj| ((|#1| $) 91 T ELT)) (|imagi| ((|#1| $) 92 T ELT)) (|imagK| ((|#1| $) 86 T ELT)) (|imagJ| ((|#1| $) 87 T ELT)) (|imagI| ((|#1| $) 88 T ELT)) (|imagE| ((|#1| $) 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 101 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 100 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 99 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 98 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| #15=(|Symbol|)) (|List| |#1|)) 97 (|has| |#1| (|InnerEvalable| #15# |#1|)) ELT) (($ $ #15# |#1|) 96 (|has| |#1| (|InnerEvalable| #15# |#1|)) ELT)) (|elt| (($ $ |#1|) 102 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|convert| (((|InputForm|) $) 77 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT)) (|conjugate| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT) (($ #9#) 107 (|has| |#1| . #10#) ELT)) (|charthRoot| (((|Maybe| $) $) 78 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| ((|#1| $) 83 (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#16=((|Boolean|) $ $) 73 (|has| |#1| . #13#) ELT)) (> (#16# 75 (|has| |#1| . #13#) ELT)) (= (#1# 8 T ELT)) (<= (#16# 74 (|has| |#1| . #13#) ELT)) (< (#16# 76 (|has| |#1| . #13#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #17#) 53 T ELT))) 
(((|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|)) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|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) ((|Functorial| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 35 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT))) 
(((|OrderedCancellationAbelianMonoid|) (|Category|)) (T |OrderedCancellationAbelianMonoid|)) 
NIL 
(|Join| (|OrderedAbelianMonoid|) (|CancellationAbelianMonoid|)) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|size| (#8=(#9=(|NonNegativeInteger|)) NIL #10=(|has| |#1| (|Finite|)) ELT)) (|sample| (#11=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #12=(#7#)) . #13=($)) NIL T ELT) (((|Union| #14=(|Quaternion| |#1|) . #12#) $) 35 T ELT) (((|Union| #15=(|Integer|) . #12#) . #13#) NIL #16=(OR (|has| #14# #17=(|RetractableTo| #15#)) (|has| |#1| #17#)) ELT) (#18=((|Union| #19=(|Fraction| #15#) . #12#) . #13#) NIL #20=(OR (|has| #14# #21=(|RetractableTo| #19#)) (|has| |#1| #21#)) ELT)) (|retract| #22=(#23=(|#1| . #24=($)) NIL T ELT) ((#14# $) 33 T ELT) ((#15# . #24#) NIL #16# ELT) (#25=(#19# . #24#) NIL #20# ELT)) (|recip| ((#6# $) NIL T ELT)) (|real| (#23# 16 T ELT)) (|rationalIfCan| (#18# NIL #26=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#5# NIL #26# ELT)) (|rational| (#25# NIL #26# ELT)) (|random| (#11# NIL #10# ELT)) (|opposite?| #1#) (|one?| #4#) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 28 T ELT) (($ #14# #14#) 29 T ELT)) (|norm| #22#) (|min| #27=(#28=($ $ $) NIL #29=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #27#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|lookup| ((#30=(|PositiveInteger|) $) NIL #10# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#31=($ $) NIL (|has| |#1| (|Field|)) ELT)) (|index| (($ #30#) NIL #10# ELT)) (|imagk| (#23# 22 T ELT)) (|imagj| (#23# 20 T ELT)) (|imagi| (#23# 18 T ELT)) (|imagK| (#23# 26 T ELT)) (|imagJ| (#23# 25 T ELT)) (|imagI| (#23# 24 T ELT)) (|imagE| (#23# 23 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| (($ $ #32=(|List| |#1|) #32#) NIL #33=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #33# ELT) (($ $ #34=(|Equation| |#1|)) NIL #33# ELT) (($ $ (|List| #34#)) NIL #33# ELT) (($ $ (|List| #35=(|Symbol|)) #32#) NIL #36=(|has| |#1| (|InnerEvalable| #35# |#1|)) ELT) (($ $ #35# |#1|) NIL #36# ELT)) (|elt| (#37=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|convert| ((#38=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #38#)) ELT)) (|conjugate| #39=(#31# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #14#) 30 T ELT) (($ #19#) NIL #20# ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#23# NIL (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#11# 8 T CONST)) (|One| (#11# 12 T CONST)) (>= #40=(#2# NIL #29# ELT)) (> #40#) (= #1#) (<= #40#) (< #40#) (- #39# #41=(#28# NIL T ELT)) (+ #41#) (** (($ $ #30#) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #30# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #15# . #42=($)) NIL T ELT) (#28# 40 T ELT) (#37# NIL T ELT) (($ |#1| . #42#) NIL T ELT))) 
(((|Octonion| |#1|) (|Join| (|OctonionCategory| |#1|) (|FullyRetractableTo| #1=(|Quaternion| |#1|)) (CATEGORY |domain| (SIGNATURE |octon| ($ #1# #1#)))) (|CommutativeRing|)) (T |Octonion|)) 
((|octon| (*1 *1 *2 *2) (AND (|isDomain| *2 (|Quaternion| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|Octonion| *3))))) 
((|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) 20 T ELT))) 
(((|OctonionCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) (|OctonionCategory| |#2|) #1=(|CommutativeRing|) (|OctonionCategory| |#4|) #1#) (T |OctonionCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|CommutativeRing|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|OctonionCategory| *6)) (|isDomain| *1 (|OctonionCategoryFunctions2| *4 *5 *2 *6)) (|ofCategory| *4 (|OctonionCategory| *5))))) 
((|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) 19 T ELT))) 
(((|ConstantLODE| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |constDsolve| ((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)))) (|Join| (|EuclideanDomain|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)) (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (T |ConstantLODE|)) 
((|constDsolve| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Symbol|)) (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#) (|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))))) 
((|solve| ((#1=(|Union| |#2| #2="failed") |#2| #3=(|BasicOperator|) #4=(|Equation| |#2|) #5=(|List| |#2|)) 28 T ELT) ((#1# #4# #3# #4# #5#) 29 T ELT) ((#6=(|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #5#)) |#2| #2#) |#2| #3# #7=(|Symbol|)) 17 T ELT) ((#6# #4# #3# #7#) 18 T ELT) ((#8=(|Union| (|Record| (|:| |particular| #9=(|Vector| |#2|)) (|:| |basis| #10=(|List| #9#))) #2#) #5# #11=(|List| #3#) #7#) 24 T ELT) ((#8# (|List| #4#) #11# #7#) 26 T ELT) (((|Union| #10# #2#) #12=(|Matrix| |#2|) #7#) 37 T ELT) ((#8# #12# #9# #7#) 35 T ELT))) 
(((|ElementaryFunctionODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|Union| (|Record| (|:| |particular| #2=(|Vector| |#2|)) (|:| |basis| #3=(|List| #2#))) #4="failed") #5=(|Matrix| |#2|) #2# #6=(|Symbol|))) (SIGNATURE |solve| ((|Union| #3# #4#) #5# #6#)) (SIGNATURE |solve| (#1# (|List| #7=(|Equation| |#2|)) #8=(|List| #9=(|BasicOperator|)) #6#)) (SIGNATURE |solve| (#1# #10=(|List| |#2|) #8# #6#)) (SIGNATURE |solve| (#11=(|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #10#)) |#2| #4#) #7# #9# #6#)) (SIGNATURE |solve| (#11# |#2| #9# #6#)) (SIGNATURE |solve| (#12=(|Union| |#2| #4#) #7# #9# #7# #10#)) (SIGNATURE |solve| (#12# |#2| #9# #7# #10#))) (|Join| (|EuclideanDomain|) (|RetractableTo| #13=(|Integer|)) (|LinearlyExplicitRingOver| #13#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (T |ElementaryFunctionODESolver|)) 
((|solve| (*1 *2 *2 *3 *4 *5) (|partial| AND (|isDomain| *3 #1=(|BasicOperator|)) (|isDomain| *4 #2=(|Equation| *2)) #3=(|isDomain| *5 (|List| *2)) #4=(|ofCategory| *2 #5=(|Join| (|AlgebraicallyClosedFunctionSpace| *6) #6=(|TranscendentalFunctionCategory|) #7=(|PrimitiveFunctionCategory|))) #8=(|ofCategory| *6 #9=(|Join| (|EuclideanDomain|) (|RetractableTo| #10=(|Integer|)) (|LinearlyExplicitRingOver| #10#) (|CharacteristicZero|))) #11=(|isDomain| *1 (|ElementaryFunctionODESolver| *6 *2)))) (|solve| (*1 *2 *3 *4 *3 *5) (|partial| AND (|isDomain| *3 #2#) #12=(|isDomain| *4 #1#) #3# #4# #11# #8#)) (|solve| #13=(*1 *2 *3 *4 *5) (AND #12# #14=(|isDomain| *5 #15=(|Symbol|)) #8# (|isDomain| *2 (|Union| (|Record| (|:| |particular| *3) (|:| |basis| (|List| *3))) *3 #16="failed")) (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *3)) (|ofCategory| *3 #5#))) (|solve| #13# (AND (|isDomain| *3 #17=(|Equation| *7)) #12# #14# #18=(|ofCategory| *7 #5#) #8# (|isDomain| *2 (|Union| (|Record| (|:| |particular| *7) (|:| |basis| #19=(|List| *7))) *7 #16#)) #20=(|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7)))) (|solve| #13# (|partial| AND (|isDomain| *3 #19#) #21=(|isDomain| *4 (|List| #1#)) #14# #18# #8# #22=(|isDomain| *2 (|Record| (|:| |particular| #23=(|Vector| *7)) (|:| |basis| (|List| #23#)))) #20#)) (|solve| #13# (|partial| AND (|isDomain| *3 (|List| #17#)) #21# #14# #18# #8# #22# #20#)) (|solve| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Matrix| *6)) (|isDomain| *4 #15#) (|ofCategory| *6 (|Join| (|AlgebraicallyClosedFunctionSpace| *5) #6# #7#)) (|ofCategory| *5 #9#) (|isDomain| *2 (|List| (|Vector| *6))) (|isDomain| *1 (|ElementaryFunctionODESolver| *5 *6)))) (|solve| #13# (|partial| AND (|isDomain| *3 (|Matrix| *7)) #14# #18# #8# #22# #20# (|isDomain| *4 #23#)))) 
((|int| (#1=(|#2| |#2| #2=(|Symbol|)) 17 T ELT)) (|expint| (#1# 56 T ELT)) (|diff| (((|Mapping| |#2| |#2|) #2#) 11 T ELT))) 
(((|ODEIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |int| #1=(|#2| |#2| #2=(|Symbol|))) (SIGNATURE |expint| #1#) (SIGNATURE |diff| ((|Mapping| |#2| |#2|) #2#))) (|Join| (|EuclideanDomain|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (T |ODEIntegration|)) 
((|diff| (*1 *2 *3) (AND #1=(|isDomain| *3 (|Symbol|)) #2=(|ofCategory| *4 (|Join| (|EuclideanDomain|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#) (|CharacteristicZero|))) (|isDomain| *2 (|Mapping| *5 *5)) (|isDomain| *1 (|ODEIntegration| *4 *5)) (|ofCategory| *5 #4=(|Join| (|AlgebraicallyClosedFunctionSpace| *4) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))))) (|expint| #5=(*1 *2 *2 *3) #6=(AND #1# #2# (|isDomain| *1 (|ODEIntegration| *4 *2)) (|ofCategory| *2 #4#))) (|int| #5# #6#)) 
((|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) 33 T ELT))) 
(((|PureAlgebraicLODE| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |algDsolve| ((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| (|Fraction| #1#))) (|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| #1=(|Integer|)) (|RetractableTo| (|Fraction| #1#)))) (|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))))) 
((|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| #1=(|List| #2=(|Fraction| |#2|)))) |#4| #1#) 53 T ELT)) (|indicialEquations| ((#3=(|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) 62 T ELT) ((#3# |#4|) 61 T ELT) ((#3# |#3| |#2|) 20 T ELT) ((#3# |#3|) 21 T ELT)) (|indicialEquation| ((|#2| |#4| |#1|) 63 T ELT) ((|#2| |#3| |#1|) 28 T ELT)) (|denomLODE| ((|#2| |#3| #1#) 109 T ELT) (((|Union| |#2| "failed") |#3| #2#) 105 T ELT))) 
(((|PrimitiveRatDE| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |denomLODE| ((|Union| |#2| "failed") |#3| #1=(|Fraction| |#2|))) (SIGNATURE |denomLODE| (|#2| |#3| #2=(|List| #1#))) (SIGNATURE |indicialEquations| (#3=(|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|)) (SIGNATURE |indicialEquations| (#3# |#3| |#2|)) (SIGNATURE |indicialEquation| (|#2| |#3| |#1|)) (SIGNATURE |indicialEquations| (#3# |#4|)) (SIGNATURE |indicialEquations| (#3# |#4| |#2|)) (SIGNATURE |indicialEquation| (|#2| |#4| |#1|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |eq| |#3|) (|:| |rh| #2#)) |#4| #2#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| #1#)) (T |PrimitiveRatDE|)) 
((|splitDenominator| #1=(*1 *2 *3 *4) (AND #2=(|ofCategory| *5 #3=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 #4=(|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |eq| *7) (|:| |rh| #5=(|List| #6=(|Fraction| *6))))) (|isDomain| *1 (|PrimitiveRatDE| *5 *6 *7 *3)) (|isDomain| *4 #5#) (|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| *6)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| #6#)))) (|indicialEquation| #1# (AND #7=(|ofCategory| *2 #8=(|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PrimitiveRatDE| *4 *2 *5 *3)) #9=(|ofCategory| *4 #3#) (|ofCategory| *5 #10=(|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *3 #11=(|LinearOrdinaryDifferentialOperatorCategory| #12=(|Fraction| *2))))) (|indicialEquations| #1# (AND #2# #13=(|ofCategory| *4 #4#) #14=(|isDomain| *2 (|List| (|Record| (|:| |center| *4) (|:| |equation| *4)))) (|isDomain| *1 (|PrimitiveRatDE| *5 *4 *6 *3)) #15=(|ofCategory| *6 #16=(|LinearOrdinaryDifferentialOperatorCategory| *4)) (|ofCategory| *3 #17=(|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *4))))) (|indicialEquations| #18=(*1 *2 *3) (AND #9# #19=(|ofCategory| *5 #8#) #20=(|isDomain| *2 (|List| (|Record| (|:| |center| *5) (|:| |equation| *5)))) (|isDomain| *1 (|PrimitiveRatDE| *4 *5 *6 *3)) (|ofCategory| *6 #21=(|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *3 #22=(|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *5))))) (|indicialEquation| #1# (AND #7# (|isDomain| *1 (|PrimitiveRatDE| *4 *2 *3 *5)) #9# #23=(|ofCategory| *3 #10#) (|ofCategory| *5 #11#))) (|indicialEquations| #1# (AND #2# #13# #14# (|isDomain| *1 (|PrimitiveRatDE| *5 *4 *3 *6)) (|ofCategory| *3 #16#) (|ofCategory| *6 #17#))) (|indicialEquations| #18# (AND #9# #19# #20# (|isDomain| *1 (|PrimitiveRatDE| *4 *5 *3 *6)) (|ofCategory| *3 #21#) (|ofCategory| *6 #22#))) (|denomLODE| #1# (AND (|isDomain| *4 (|List| #12#)) #24=(|ofCategory| *2 #4#) #25=(|isDomain| *1 (|PrimitiveRatDE| *5 *2 *3 *6)) #2# #23# (|ofCategory| *6 #11#))) (|denomLODE| #1# (|partial| AND (|isDomain| *4 #12#) #24# #25# #2# #23# #15#))) 
((|singRicDE| (((|List| (|Record| (|:| |frac| #1=(|Fraction| |#2|)) #2=(|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) 156 T ELT)) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) #2#)) |#3| #3=(|Mapping| (|List| |#1|) |#2|)) 52 T ELT)) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) 123 T ELT)) (|denomRicDE| ((|#2| |#3|) 42 T ELT)) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) #2#)) |#3| #3#) 100 T ELT)) (|changeVar| ((|#3| |#3| #1#) 71 T ELT) ((|#3| |#3| |#2|) 97 T ELT))) 
(((|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|) #1=(|:| |eq| |#3|))) |#3| #2=(|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |polyRicDE| ((|List| (|Record| (|:| |poly| |#2|) #1#)) |#3| #2#)) (SIGNATURE |singRicDE| ((|List| (|Record| (|:| |frac| #3=(|Fraction| |#2|)) #1#)) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |changeVar| (|#3| |#3| |#2|)) (SIGNATURE |changeVar| (|#3| |#3| #3#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| #3#)) (T |PrimitiveRatRicDE|)) 
((|changeVar| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 #2=(|Fraction| *5)) #3=(|ofCategory| *4 #4=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) #5=(|ofCategory| *5 #6=(|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *5 *2 *6)) (|ofCategory| *2 #7=(|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *6 #8=(|LinearOrdinaryDifferentialOperatorCategory| *3)))) (|changeVar| #1# (AND #3# (|ofCategory| *3 #6#) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *3 *2 *5)) (|ofCategory| *2 #8#) (|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 #4#) (|isDomain| *2 (|List| (|Record| (|:| |frac| #9=(|Fraction| *7)) #10=(|:| |eq| *3)))) (|isDomain| *1 (|PrimitiveRatRicDE| *6 *7 *3 *8)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *7)) (|ofCategory| *8 (|LinearOrdinaryDifferentialOperatorCategory| #9#)))) (|polyRicDE| #11=(*1 *2 *3 *4) (AND #12=(|isDomain| *4 (|Mapping| (|List| *5) *6)) #13=(|ofCategory| *5 #4#) #14=(|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Record| (|:| |poly| *6) #10#))) #15=(|isDomain| *1 (|PrimitiveRatRicDE| *5 *6 *3 *7)) #16=(|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *6)) #17=(|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *6))))) (|constantCoefficientRicDE| #11# (AND #12# #13# #14# (|isDomain| *2 (|List| (|Record| (|:| |constant| *5) #10#))) #15# #16# #17#)) (|leadingCoefficientRicDE| #18=(*1 *2 *3) (AND #3# #5# (|isDomain| *2 (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| *5)))) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *5 *3 *6)) (|ofCategory| *3 #7#) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| #2#)))) (|denomRicDE| #18# (AND (|ofCategory| *2 #6#) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *2 *3 *5)) #3# (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *2)))))) 
((|ratDsolve| ((#1=(|Record| #2=(|:| |basis| #3=(|List| #4=(|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) #5=(|LinearOrdinaryDifferentialOperator2| |#2| #4#) #3#) 146 T ELT) ((#6=(|Record| (|:| |particular| (|Union| #4# "failed")) #2#) #5# #4#) 145 T ELT) ((#1# #7=(|LinearOrdinaryDifferentialOperator1| #4#) #3#) 140 T ELT) ((#6# #7# #4#) 138 T ELT)) (|indicialEquationAtInfinity| ((|#2| #5#) 86 T ELT) ((|#2| #7#) 89 T ELT))) 
(((|RationalLODE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ratDsolve| (#1=(|Record| (|:| |particular| (|Union| #2=(|Fraction| |#2|) "failed")) #3=(|:| |basis| #4=(|List| #2#))) #5=(|LinearOrdinaryDifferentialOperator1| #2#) #2#)) (SIGNATURE |ratDsolve| (#6=(|Record| #3# (|:| |mat| (|Matrix| |#1|))) #5# #4#)) (SIGNATURE |ratDsolve| (#1# #7=(|LinearOrdinaryDifferentialOperator2| |#2| #2#) #2#)) (SIGNATURE |ratDsolve| (#6# #7# #4#)) (SIGNATURE |indicialEquationAtInfinity| (|#2| #5#)) (SIGNATURE |indicialEquationAtInfinity| (|#2| #7#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #8=(|Integer|)) (|RetractableTo| (|Fraction| #8#))) (|UnivariatePolynomialCategory| |#1|)) (T |RationalLODE|)) 
((|indicialEquationAtInfinity| #1=(*1 *2 *3) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *2 #2=(|Fraction| *2))) #3=(|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) #4=(|isDomain| *1 (|RationalLODE| *4 *2)) #5=(|ofCategory| *4 #6=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #7=(|Integer|)) (|RetractableTo| (|Fraction| #7#)))))) (|indicialEquationAtInfinity| #1# (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| #2#)) #3# #4# #5#)) (|ratDsolve| #8=(*1 *2 *3 *4) (AND #9=(|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 #10=(|Fraction| *6))) #11=(|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) #12=(|ofCategory| *5 #6#) #13=(|isDomain| *2 (|Record| (|:| |basis| #14=(|List| #10#)) (|:| |mat| (|Matrix| *5)))) #15=(|isDomain| *1 (|RationalLODE| *5 *6)) #16=(|isDomain| *4 #14#))) (|ratDsolve| #8# (AND #9# #17=(|isDomain| *4 #10#) #11# #12# #18=(|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) #15#)) (|ratDsolve| #8# (AND #19=(|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| #10#)) #11# #12# #13# #15# #16#)) (|ratDsolve| #8# (AND #19# #17# #11# #12# #18# #15#))) 
((|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) 49 T ELT))) 
(((|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))))) 
((|singRicDE| (((|List| (|Record| (|:| |frac| #1=(|Fraction| |#2|)) #2=(|:| |eq| #3=(|LinearOrdinaryDifferentialOperator2| |#2| #1#)))) #3# #4=(|Mapping| (|Factored| |#2|) |#2|)) 47 T ELT)) (|ricDsolve| ((#5=(|List| #1#) #3# #4#) 163 #6=(|has| |#1| (|AlgebraicallyClosedField|)) ELT) ((#5# #3#) 164 #6# ELT) ((#5# #7=(|LinearOrdinaryDifferentialOperator1| #1#) #4#) 165 #6# ELT) ((#5# #7#) 166 #6# ELT) ((#5# #3# #8=(|Mapping| (|List| |#1|) |#2|) #4#) 38 T ELT) ((#5# #3# #8#) 39 T ELT) ((#5# #7# #8# #4#) 36 T ELT) ((#5# #7# #8#) 37 T ELT)) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) #2#)) #3# #8#) 96 T ELT))) 
(((|RationalRicDE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ricDsolve| (#1=(|List| #2=(|Fraction| |#2|)) #3=(|LinearOrdinaryDifferentialOperator1| #2#) #4=(|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |ricDsolve| (#1# #3# #4# #5=(|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |ricDsolve| (#1# #6=(|LinearOrdinaryDifferentialOperator2| |#2| #2#) #4#)) (SIGNATURE |ricDsolve| (#1# #6# #4# #5#)) (SIGNATURE |singRicDE| ((|List| (|Record| (|:| |frac| #2#) #7=(|:| |eq| #6#))) #6# #5#)) (SIGNATURE |polyRicDE| ((|List| (|Record| (|:| |poly| |#2|) #7#)) #6# #4#)) (IF (|has| |#1| (|AlgebraicallyClosedField|)) (PROGN (SIGNATURE |ricDsolve| (#1# #3#)) (SIGNATURE |ricDsolve| (#1# #3# #5#)) (SIGNATURE |ricDsolve| (#1# #6#)) (SIGNATURE |ricDsolve| (#1# #6# #5#))) |%noBranch|)) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #8=(|Integer|)) (|RetractableTo| (|Fraction| #8#))) (|UnivariatePolynomialCategory| |#1|)) (T |RationalRicDE|)) 
((|ricDsolve| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 #3=(|LinearOrdinaryDifferentialOperator2| *6 #4=(|Fraction| *6))) #5=(|isDomain| *4 (|Mapping| (|Factored| *6) *6)) #6=(|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) #7=(|ofCategory| *5 #8=(|AlgebraicallyClosedField|)) #9=(|ofCategory| *5 #10=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #11=(|Integer|)) (|RetractableTo| (|Fraction| #11#)))) #12=(|isDomain| *2 (|List| #4#)) #13=(|isDomain| *1 (|RationalRicDE| *5 *6)))) (|ricDsolve| #14=(*1 *2 *3) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *5 #15=(|Fraction| *5))) #16=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) #17=(|ofCategory| *4 #8#) #18=(|ofCategory| *4 #10#) #19=(|isDomain| *2 (|List| #15#)) #20=(|isDomain| *1 (|RationalRicDE| *4 *5)))) (|ricDsolve| #1# (AND #21=(|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| #4#)) #5# #6# #7# #9# #12# #13#)) (|ricDsolve| #14# (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| #15#)) #16# #17# #18# #19# #20#)) (|polyRicDE| #1# (AND #22=(|isDomain| *4 (|Mapping| (|List| *5) *6)) #9# #6# (|isDomain| *2 (|List| (|Record| (|:| |poly| *6) #23=(|:| |eq| #3#)))) #13# #2#)) (|singRicDE| #1# (AND #5# #6# #9# (|isDomain| *2 (|List| (|Record| (|:| |frac| #4#) #23#))) #13# #2#)) (|ricDsolve| #24=(*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *7 #25=(|Fraction| *7))) #26=(|isDomain| *4 (|Mapping| (|List| *6) *7)) #27=(|isDomain| *5 (|Mapping| (|Factored| *7) *7)) #28=(|ofCategory| *6 #10#) #29=(|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) #30=(|isDomain| *2 (|List| #25#)) #31=(|isDomain| *1 (|RationalRicDE| *6 *7)))) (|ricDsolve| #1# (AND #2# #22# #9# #6# #12# #13#)) (|ricDsolve| #24# (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| #25#)) #26# #27# #28# #29# #30# #31#)) (|ricDsolve| #1# (AND #21# #22# #9# #6# #12# #13#))) 
((|triangulate| (((|Record| (|:| |mat| #1=(|Matrix| |#2|)) (|:| |vec| #2=(|Vector| |#1|))) #1# #2#) 110 T ELT) (((|Record| (|:| A #3=(|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C #3#) (|:| |g| #2#) (|:| |eq| |#2|) (|:| |rh| |#1|))))) #3# #2#) 15 T ELT)) (|solveInField| (((|Record| (|:| |particular| (|Union| #2# #4="failed")) (|:| |basis| (|List| #2#))) #1# #2# (|Mapping| (|Record| (|:| |particular| (|Union| |#1| #4#)) #5=(|:| |basis| (|List| |#1|))) |#2| |#1|)) 116 T ELT)) (|solve| (((|Union| (|Record| (|:| |particular| #2#) (|:| |basis| #3#)) #4#) #3# #2# (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) #5#) #4#) |#2| |#1|)) 54 T ELT))) 
(((|SystemODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |triangulate| ((|Record| (|:| A #1=(|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C #1#) (|:| |g| #2=(|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) #1# #2#)) (SIGNATURE |triangulate| ((|Record| (|:| |mat| #3=(|Matrix| |#2|)) (|:| |vec| #2#)) #3# #2#)) (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| #2#) (|:| |basis| #1#)) #4="failed") #1# #2# (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) #5=(|:| |basis| (|List| |#1|))) #4#) |#2| |#1|))) (SIGNATURE |solveInField| ((|Record| (|:| |particular| (|Union| #2# #4#)) (|:| |basis| (|List| #2#))) #3# #2# (|Mapping| (|Record| (|:| |particular| (|Union| |#1| #4#)) #5#) |#2| |#1|)))) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |SystemODESolver|)) 
((|solveInField| #1=(*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Matrix| *7)) (|isDomain| *5 (|Mapping| (|Record| (|:| |particular| (|Union| *6 #2="failed")) #3=(|:| |basis| (|List| *6))) *7 *6)) #4=(|ofCategory| *6 #5=(|Field|)) #6=(|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| *6)) (|isDomain| *2 (|Record| (|:| |particular| (|Union| #7=(|Vector| *6) #2#)) (|:| |basis| (|List| #7#)))) #8=(|isDomain| *1 (|SystemODESolver| *6 *7)) #9=(|isDomain| *4 #7#))) (|solve| #1# (|partial| AND (|isDomain| *5 (|Mapping| (|Union| (|Record| (|:| |particular| *6) #3#) #2#) *7 *6)) #4# #6# (|isDomain| *2 (|Record| (|:| |particular| #7#) (|:| |basis| #10=(|Matrix| *6)))) #8# #11=(|isDomain| *3 #10#) #9#)) (|triangulate| #12=(*1 *2 *3 *4) (AND #13=(|ofCategory| *5 #5#) #14=(|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5)) (|isDomain| *2 (|Record| (|:| |mat| #10#) (|:| |vec| #15=(|Vector| *5)))) #16=(|isDomain| *1 (|SystemODESolver| *5 *6)) #11# #17=(|isDomain| *4 #15#))) (|triangulate| #12# (AND #13# (|isDomain| *2 (|Record| (|:| A #18=(|Matrix| *5)) (|:| |eqs| (|List| (|Record| (|:| C #18#) (|:| |g| #15#) (|:| |eq| *6) (|:| |rh| *5)))))) #16# (|isDomain| *3 #18#) #17# #14#))) 
((|wronskianMatrix| ((#1=(|Matrix| |#1|) #2=(|List| |#1|) (|NonNegativeInteger|)) 14 T ELT) ((#1# #2#) 15 T ELT)) (|variationOfParameters| (((|Union| (|Vector| |#1|) #3="failed") |#2| |#1| #2#) 39 T ELT)) (|particularSolution| (((|Union| |#1| #3#) |#2| |#1| #2# (|Mapping| |#1| |#1|)) 46 T ELT))) 
(((|ODETools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |wronskianMatrix| (#1=(|Matrix| |#1|) #2=(|List| |#1|))) (SIGNATURE |wronskianMatrix| (#1# #2# (|NonNegativeInteger|))) (SIGNATURE |variationOfParameters| ((|Union| (|Vector| |#1|) #3="failed") |#2| |#1| #2#)) (SIGNATURE |particularSolution| ((|Union| |#1| #3#) |#2| |#1| #2# (|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 #1=(|Field|)) (|isDomain| *1 (|ODETools| *2 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)))) (|variationOfParameters| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 #2=(|List| *4)) #3=(|ofCategory| *4 #1#) (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|ODETools| *4 *3)) (|ofCategory| *3 #4=(|LinearOrdinaryDifferentialOperatorCategory| *4)))) (|wronskianMatrix| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 #1#) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|ODETools| *5 *6)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (|wronskianMatrix| (*1 *2 *3) (AND (|isDomain| *3 #2#) #3# (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|ODETools| *4 *5)) (|ofCategory| *5 #4#)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) NIL #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) NIL #13=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#14=(|Union| $ #15="failed") $ $) NIL (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#16=(#17=(|NonNegativeInteger|)) NIL #18=(|has| |#2| (|Finite|)) ELT)) (|setelt| #19=(#20=(|#2| $ #10# |#2|) NIL #11# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #22=(#15#)) . #23=($)) NIL #24=(AND (|has| |#2| (|RetractableTo| #10#)) #25=(|has| |#2| (|SetCategory|))) ELT) (((|Union| #26=(|Fraction| #10#) . #22#) . #23#) NIL #27=(AND (|has| |#2| (|RetractableTo| #26#)) #25#) ELT) ((#28=(|Union| |#2| . #22#) . #23#) NIL #25# ELT)) (|retract| (#29=(#10# . #30=($)) NIL #24# ELT) ((#26# . #30#) NIL #27# ELT) (#31=(|#2| . #30#) NIL #25# ELT)) (|reducedSystem| ((#32=(|Matrix| #10#) . #33=(#34=(|Matrix| $))) NIL #35=(AND (|has| |#2| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #10#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#2|)) (|:| |vec| #41=(|Vector| |#2|))) . #37#) NIL #9# ELT) ((#40# . #33#) NIL #9# ELT)) (|reduce| ((|#2| #42=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) NIL #4# ELT) ((|#2| #42# $ |#2|) NIL T ELT) ((|#2| #42# $) NIL T ELT)) (|recip| ((#14# $) NIL #9# ELT)) (|random| (#21# NIL #18# ELT)) (|qsetelt!| #19#) (|qelt| #43=((|#2| $ #10#) NIL T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| #44=(#29# NIL #45=(|has| #10# #46=(|OrderedSet|)) ELT)) (|min| #47=(#12# NIL #48=(|has| |#2| #46#) ELT)) (|members| #49=((#50=(|List| |#2|) $) NIL T ELT)) (|member?| (#51=(#3# |#2| $) NIL #4# ELT)) (|maxIndex| #44#) (|max| #47#) (|map| (($ #52=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #18# ELT)) (|leftReducedSystem| ((#32# . #53=(#38#)) NIL #35# ELT) ((#36# . #54=(#38# $)) NIL #35# ELT) ((#39# . #54#) NIL #9# ELT) ((#40# . #53#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #25# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #18# ELT)) (|hash| (((|SingleInteger|) $) NIL #25# ELT)) (|first| (#31# NIL #45# ELT)) (|find| ((#28# #55=(|Mapping| #3# |#2|) $) NIL T ELT)) (|fill!| (#56=($ $ |#2|) NIL #11# ELT)) (|every?| #57=((#3# #55# $) NIL T ELT)) (|eval| (($ $ (|List| #58=(|Equation| |#2|))) NIL #59=(AND (|has| |#2| (|Evalable| |#2|)) #25#) ELT) (($ $ #58#) NIL #59# ELT) (($ $ |#2| |#2|) NIL #59# ELT) (($ $ #50# #50#) NIL #59# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#51# NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #4#) ELT)) (|entries| #49#) (|empty?| (#5# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#20# NIL T ELT) #43#) (|dot| ((|#2| $ $) NIL #9# ELT)) (|directProduct| (($ #41#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #60=(|has| |#2| (|Field|)) ELT)) (|differentiate| #61=(#62=($ $ #17#) NIL #63=(AND (|has| |#2| (|DifferentialSpace|)) #9#) ELT) #64=(#65=($ $) NIL #63# ELT) #66=(($ $ #67=(|List| #68=(|Symbol|)) (|List| #17#)) NIL #69=(AND (|has| |#2| (|PartialDifferentialSpace| #68#)) #9#) ELT) #70=(($ $ #68# #17#) NIL #69# ELT) #71=(($ $ #67#) NIL #69# ELT) #72=(($ $ #68#) NIL #69# ELT) #73=(($ $ #52#) NIL #9# ELT) #74=(($ $ #52# #17#) NIL #9# ELT)) (|count| ((#17# |#2| $) NIL #4# ELT) ((#17# #55# $) NIL T ELT)) (|copy| (#65# NIL T ELT)) (|coerce| ((#41# . #75=($)) NIL T ELT) (($ #10#) NIL (OR #24# #9#) ELT) (($ #26#) NIL #27# ELT) (($ |#2|) NIL #25# ELT) ((#76=(|OutputForm|) . #75#) NIL (|has| |#2| (|CoercibleTo| #76#)) ELT)) (|characteristic| (#16# NIL #9# CONST)) (|before?| #1#) (|any?| #57#) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#21# NIL #6# CONST)) (|One| (#21# NIL #9# CONST)) (D #61# #64# #66# #70# #71# #72# #73# #74#) (>= #77=(#2# NIL #48# ELT)) (> #77#) (= #1#) (<= #77#) (< (#2# 11 #48# ELT)) (/ (#56# NIL #60# ELT)) (- (#12# NIL #78=(|has| |#2| (|AbelianGroup|)) ELT) (#65# NIL #78# ELT)) (+ (#12# NIL #79=(|has| |#2| (|AbelianSemiGroup|)) ELT)) (** (#62# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# NIL #9# ELT) (#56# NIL #80=(|has| |#2| (|Monoid|)) ELT) (($ |#2| . #81=($)) NIL #80# ELT) (($ #10# . #81#) NIL #78# ELT) (($ #17# $) NIL #6# ELT) (($ #8# $) NIL #79# ELT)) (|#| ((#17# $) NIL T ELT))) 
(((|OrderedDirectProduct| |#1| |#2| |#3|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|OrderedAbelianMonoidSup|) (|Mapping| (|Boolean|) #1=(|Vector| |#2|) #1#)) (T |OrderedDirectProduct|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|weights| ((#6=(|List| #7=(|NonNegativeInteger|)) $) NIL T ELT) ((#6# $ #8=(|Symbol|)) NIL T ELT)) (|weight| #9=((#7# $) NIL T ELT) #10=((#7# $ #8#) NIL T ELT)) (|variables| ((#11=(|List| #12=(|OrderlyDifferentialVariable| #8#)) $) NIL T ELT)) (|univariate| ((#13=(|SparseUnivariatePolynomial| $) $ #12#) NIL T ELT) ((#14=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #15=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #16=(#17=($ $) NIL #15# ELT)) (|unit?| (#5# NIL #15# ELT)) (|totalDegree| #9# ((#7# $ #11#) NIL T ELT)) (|subtractIfCan| (#18=(#19=(|Union| $ #20="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #21=(((|Factored| #13#) #13#) NIL #22=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #23=(#17# NIL #24=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#25=((|Factored| $) $) NIL #24# ELT)) (|solveLinearPolynomialEquation| (((|Union| #26=(|List| #13#) #20#) #26# #13#) NIL #22# ELT)) (|separant| #27=(#17# NIL T ELT)) (|sample| #28=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #29=(#20#)) . #30=($)) NIL T ELT) (((|Union| #31=(|Fraction| #32=(|Integer|)) . #29#) . #30#) NIL #33=(|has| |#1| (|RetractableTo| #31#)) ELT) (((|Union| #32# . #29#) . #30#) NIL #34=(|has| |#1| (|RetractableTo| #32#)) ELT) #35=(((|Union| #12# . #29#) . #30#) NIL T ELT) (((|Union| #8# . #29#) . #30#) NIL T ELT) (((|Union| #36=(|SparseMultivariatePolynomial| |#1| #8#) . #29#) . #30#) NIL T ELT)) (|retract| #37=(#38=(|#1| . #39=($)) NIL T ELT) ((#31# . #39#) NIL #33# ELT) ((#32# . #39#) NIL #34# ELT) #40=((#12# . #39#) NIL T ELT) ((#8# . #39#) NIL T ELT) ((#36# . #39#) NIL T ELT)) (|resultant| (($ $ $ #12#) NIL #41=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #27#) (|reducedSystem| ((#42=(|Matrix| #32#) . #43=(#44=(|Matrix| $))) NIL #45=(|has| |#1| (|LinearlyExplicitRingOver| #32#)) ELT) ((#46=(|Record| (|:| |mat| #42#) (|:| |vec| (|Vector| #32#))) . #47=(#44# #48=(|Vector| $))) NIL #45# ELT) ((#49=(|Record| (|:| |mat| #50=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #47#) NIL T ELT) ((#50# . #43#) NIL T ELT)) (|recip| ((#19# $) NIL T ELT)) (|primitivePart| #23# #51=(#52=($ $ #12#) NIL #24# ELT)) (|primitiveMonomials| #53=((#54=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #22# ELT)) (|pomopo!| (($ $ |#1| #55=(|IndexedExponents| #12#) $) NIL T ELT)) (|patternMatch| ((#56=(|PatternMatchResult| #57=(|Float|) . #58=($)) $ #59=(|Pattern| #57#) #56#) NIL (AND (|has| #12# #60=(|PatternMatchable| #57#)) (|has| |#1| #60#)) ELT) ((#61=(|PatternMatchResult| #32# . #58#) $ #62=(|Pattern| #32#) #61#) NIL (AND (|has| #12# #63=(|PatternMatchable| #32#)) (|has| |#1| #63#)) ELT)) (|order| #10# #9#) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #9#) (|multivariate| (($ #14# #12#) NIL T ELT) (($ #13# #12#) NIL T ELT)) (|monomials| #53#) (|monomial?| #4#) (|monomial| (($ |#1| #55#) NIL T ELT) #64=(($ $ #12# #7#) NIL T ELT) #65=(($ $ #11# #6#) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #12#) NIL T ELT)) (|minimumDegree| #66=((#55# $) NIL T ELT) #67=((#7# $ #12#) NIL T ELT) #68=((#6# $ #11#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #55# #55#) $) NIL T ELT)) (|map| (($ #69=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeVariable| ((#70=(|Mapping| $ #7#) #8#) NIL T ELT) ((#70# $) NIL #71=(|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| #35#) (|leftReducedSystem| ((#42# . #72=(#48#)) NIL #45# ELT) ((#46# . #73=(#48# $)) NIL #45# ELT) ((#49# . #73#) NIL T ELT) ((#50# . #72#) NIL T ELT)) (|leadingMonomial| #27#) (|leadingCoefficient| #37#) (|leader| #40#) (|lcm| #74=(($ #54#) NIL #24# ELT) #75=(#76=($ $ $) NIL #24# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #77=(((|Union| #54# #20#) $) NIL T ELT)) (|isPlus| #77#) (|isExpt| (((|Union| (|Record| (|:| |var| #12#) (|:| |exponent| #7#)) #20#) $) NIL T ELT)) (|initial| #27#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #37#) (|gcdPolynomial| ((#13# #13# #13#) NIL #24# ELT)) (|gcd| #74# #75#) (|factorSquareFreePolynomial| #21#) (|factorPolynomial| #21#) (|factor| (#25# NIL #22# ELT)) (|exquo| ((#19# $ |#1|) NIL #15# ELT) (#18# NIL #15# ELT)) (|eval| (($ $ (|List| #78=(|Equation| $))) NIL T ELT) (($ $ #78#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #54# #54#) NIL T ELT) (($ $ #12# |#1|) NIL T ELT) (($ $ #11# #79=(|List| |#1|)) NIL T ELT) (($ $ #12# $) NIL T ELT) (($ $ #11# #54#) NIL T ELT) (($ $ #8# $) NIL #71# ELT) (($ $ #80=(|List| #8#) #54#) NIL #71# ELT) (($ $ #8# |#1|) NIL #71# ELT) (($ $ #80# #79#) NIL #71# ELT)) (|discriminant| (#52# NIL #41# ELT)) (|differentiate| #65# #64# #81=(($ $ #11#) NIL T ELT) #82=(#52# NIL T ELT) #83=(($ $ #69#) NIL T ELT) #84=(($ $ #69# #7#) NIL T ELT) #85=(($ $ #8#) NIL #86=(|has| |#1| (|PartialDifferentialSpace| #8#)) ELT) #87=(($ $ #80#) NIL #86# ELT) #88=(($ $ #8# #7#) NIL #86# ELT) #89=(($ $ #80# #6#) NIL #86# ELT) #90=(#17# NIL #91=(|has| |#1| (|DifferentialSpace|)) ELT) #92=(#93=($ $ #7#) NIL #91# ELT)) (|differentialVariables| ((#80# $) NIL T ELT)) (|degree| #66# #67# #68# #10#) (|convert| ((#59# . #94=($)) NIL (AND (|has| #12# #95=(|ConvertibleTo| #59#)) (|has| |#1| #95#)) ELT) ((#62# . #94#) NIL (AND (|has| #12# #96=(|ConvertibleTo| #62#)) (|has| |#1| #96#)) ELT) ((#97=(|InputForm|) . #94#) NIL (AND (|has| #12# #98=(|ConvertibleTo| #97#)) (|has| |#1| #98#)) ELT)) (|content| (#38# NIL #24# ELT) #51#) (|conditionP| (((|Union| #48# #20#) #44#) NIL #99=(AND (|has| $ #100=(|CharacteristicNonZero|)) #22#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #32#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #12#) NIL T ELT) (($ #8#) NIL T ELT) (($ #36#) NIL T ELT) (($ #31#) NIL (OR #101=(|has| |#1| (|Algebra| #31#)) #33#) ELT) #16#) (|coefficients| ((#79# $) NIL T ELT)) (|coefficient| ((|#1| $ #55#) NIL T ELT) #64# #65#) (|charthRoot| (((|Maybe| $) $) NIL (OR #99# (|has| |#1| #100#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #41# ELT)) (|before?| #1#) (|associates?| (#2# NIL #15# ELT)) (|annihilate?| #1#) (|Zero| #28#) (|One| #28#) (D #65# #64# #81# #82# #83# #84# #85# #87# #88# #89# #90# #92#) (= #1#) (/ (#102=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #27# #103=(#76# NIL T ELT)) (+ #103#) (** (($ $ #104=(|PositiveInteger|)) NIL T ELT) (#93# NIL T ELT)) (* (($ #104# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #32# . #105=($)) NIL T ELT) #103# (($ $ #31#) NIL #101# ELT) (($ #31# . #105#) NIL #101# ELT) (($ |#1| . #105#) NIL T ELT) (#102# NIL T ELT))) 
(((|OrderlyDifferentialPolynomial| |#1|) (|Join| (|DifferentialPolynomialCategory| |#1| #1=(|Symbol|) #2=(|OrderlyDifferentialVariable| #1#) (|IndexedExponents| #2#)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| #1#))) (|Ring|)) (T |OrderlyDifferentialPolynomial|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #6=(|has| |#2| (|Field|)) ELT)) (|unitCanonical| #7=(#8=($ $) NIL #6# ELT)) (|unit?| #9=(#5# NIL #6# ELT)) (|subtractIfCan| (#10=(#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|squareFreePart| #7#) (|squareFree| #13=(((|Factored| $) $) NIL #6# ELT)) (|sizeLess?| #14=(#2# NIL #6# ELT)) (|sample| #15=(($) NIL T CONST)) (|rem| #16=(#17=($ $ $) NIL #6# ELT)) (|recip| ((#11# $) NIL T ELT)) (|quo| #16#) (|principalIdeal| (((|Record| (|:| |coef| #18=(|List| $)) #19=(|:| |generator| $)) #18#) NIL #6# ELT)) (|prime?| #9#) (|opposite?| #1#) (|one?| #4#) (|multiEuclidean| (((|Union| #18# #12#) #18# $) NIL #6# ELT)) (|lcm| #20=(($ #18#) NIL #6# ELT) #16#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#8# 20 #6# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#21=(|SparseUnivariatePolynomial| $) #21# #21#) NIL #6# ELT)) (|gcd| #20# #16#) (|factor| #13#) (|extendedEuclidean| (((|Union| (|Record| #22=(|:| |coef1| $) #23=(|:| |coef2| $)) #12#) $ $ $) NIL #6# ELT) (((|Record| #22# #23# #19#) $ $) NIL #6# ELT)) (|exquo| (#10# NIL #6# ELT)) (|expressIdealMember| (((|Maybe| #18#) #18# $) NIL #6# ELT)) (|euclideanSize| ((#24=(|NonNegativeInteger|) $) NIL #6# ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #6# ELT)) (|differentiate| (#8# 13 T ELT) #25=(($ $ #24#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #26=(|Integer|)) NIL T ELT) (($ |#2|) 10 T ELT) ((|#2| $) 11 T ELT) (($ #27=(|Fraction| #26#)) NIL #6# ELT) #7#) (|characteristic| ((#24#) NIL T CONST)) (|before?| #1#) (|associates?| #14#) (|annihilate?| #1#) (|Zero| #15#) (|One| #15#) (D #28=(#8# NIL T ELT) #25#) (= #1#) (/ (#17# 15 #6# ELT)) (- #28# #29=(#17# NIL T ELT)) (+ #29#) (** #25# (($ $ #30=(|PositiveInteger|)) NIL T ELT) (($ $ #26#) 18 #6# ELT)) (* (($ #30# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #26# . #31=($)) NIL T ELT) #29# #29# (($ #27# . #31#) NIL #6# ELT) (($ $ #27#) NIL #6# ELT))) 
(((|OrdinaryDifferentialRing| |#1| |#2| |#3|) (|Join| (|BiModule| $ $) (|DifferentialRing|) (|HomotopicTo| |#2|) (CATEGORY |package| (IF (|has| |#2| #1=(|Field|)) (ATTRIBUTE #1#) |%noBranch|))) (|SetCategory|) (|PartialDifferentialRing| |#1|) |#1|) (T |OrdinaryDifferentialRing|)) 
NIL 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|weight| (#2=(#3=(|NonNegativeInteger|) $) NIL T ELT)) (|variable| (#4=(|#1| $) 10 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| (#4# NIL T ELT)) (|order| (#2# 11 T ELT)) (|min| #5=(($ $ $) NIL T ELT)) (|max| #5#) (|makeVariable| (($ |#1| #3#) 9 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|differentiate| #6=(($ $ #3#) NIL T ELT) #7=(($ $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|before?| #1#) (D #6# #7#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) 
(((|OrderlyDifferentialVariable| |#1|) (|DifferentialVariableCategory| |#1|) (|OrderedSet|)) (T |OrderlyDifferentialVariable|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 39 T ELT)) (|size| (#4=(#5=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|rquo| #7=((#8=(|Union| $ #9="failed") $ $) NIL T ELT) (#10=(#8# $ |#1|) 29 T ELT)) (|retractIfCan| (((|Union| |#1| #9#) $) NIL T ELT)) (|retract| (#11=(|#1| $) NIL T ELT)) (|rest| (#12=($ $) 43 T ELT)) (|recip| ((#8# $) NIL T ELT)) (|overlap| (((|Record| #13=(|:| |lm| $) (|:| |mm| $) #14=(|:| |rm| $)) $ $) NIL T ELT)) (|one?| ((#3# $) NIL T ELT)) (|nthFactor| ((|#1| $ #15=(|Integer|)) NIL T ELT)) (|nthExpon| ((#5# $ #15#) NIL T ELT)) (|mirror| (#12# 55 T ELT)) (|min| #16=(($ $ $) NIL T ELT)) (|max| #16#) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapExpon| (($ (|Mapping| #5# #5#) $) NIL T ELT)) (|lquo| #7# (#10# 26 T ELT)) (|lexico| (#2# 52 T ELT)) (|length| (#4# 35 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hcrf| #16#) (|hclf| #16#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#11# 42 T ELT)) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #5#))) $) NIL T ELT)) (|divide| #17=(((|Union| (|Record| #13# #14#) #9#) $ $) NIL T ELT)) (|div| #17#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|before?| #1#) (|One| (#6# 7 T CONST)) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 54 T ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #5#) NIL T ELT) (($ |#1| #5#) NIL T ELT)) (* #16# (($ |#1| $) NIL T ELT) (($ $ |#1|) NIL T ELT))) 
(((|OrderedFreeMonoid| |#1|) (|Join| (|FreeMonoidCategory| |#1|) (|OrderedMonoid|) (CATEGORY |domain| (SIGNATURE |first| (|#1| $)) (SIGNATURE |rest| #1=($ $)) (SIGNATURE |mirror| #1#) (SIGNATURE |lexico| ((|Boolean|) $ $)) (SIGNATURE |lquo| #2=((|Union| $ #3="failed") $ |#1|)) (SIGNATURE |rquo| #2#) (SIGNATURE |div| ((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) #3#) $ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) (|OrderedSet|)) (T |OrderedFreeMonoid|)) 
((|first| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *1 (|OrderedFreeMonoid| *2)) #4=(|ofCategory| *2 #5=(|OrderedSet|)))) (|rest| #6=(*1 *1 *1) #2#) (|mirror| #6# #2#) (|lexico| #7=(*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) #8=(|isDomain| *1 #9=(|OrderedFreeMonoid| *3)) #10=(|ofCategory| *3 #5#))) (|lquo| #11=(*1 *1 *1 *2) #12=(|partial| AND #3# #4#)) (|rquo| #11# #12#) (|div| #7# (|partial| AND (|isDomain| *2 (|Record| (|:| |lm| #9#) (|:| |rm| #9#))) #8# #10#)) (|length| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #8# #10#)) (|varList| #1# (AND (|isDomain| *2 (|List| *3)) #8# #10#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sign| (((|Integer|) $) 69 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|positive?| (((|Boolean|) $) 67 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|negative?| (((|Boolean|) $) 68 T ELT)) (|min| (#5=($ $ $) 61 T ELT)) (|max| (#5# 62 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| (($ $) 70 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#6=((|Boolean|) $ $) 63 T ELT)) (> (#6# 65 T ELT)) (= (#1# 8 T ELT)) (<= (#6# 64 T ELT)) (< (#6# 66 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|OrderedIntegralDomain|) (|Category|)) (T |OrderedIntegralDomain|)) 
NIL 
(|Join| (|IntegralDomain|) (|OrderedRing|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| ((#4=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| #5=(($) NIL T CONST)) (|reductum| #6=(#7=($ $) NIL T ELT)) (|recip| ((#4# $) NIL T ELT)) (|po| ((|#1| $) 10 T ELT)) (|opposite?| #1#) (|op| (($ |#1|) 9 T ELT)) (|one?| #3#) (|monomial| (($ |#2| #8=(|NonNegativeInteger|)) NIL T ELT)) (|minimumDegree| #9=((#8# $) NIL T ELT)) (|leadingCoefficient| ((|#2| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|differentiate| #10=(#7# NIL #11=(|has| |#1| (|DifferentialRing|)) ELT) #12=(#13=($ $ #8#) NIL #11# ELT)) (|degree| #9#) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #14=(|Integer|)) NIL T ELT) (($ |#2|) NIL (|has| |#2| (|CommutativeRing|)) ELT)) (|coefficient| ((|#2| $ #8#) NIL T ELT)) (|characteristic| ((#8#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| #5#) (|One| #5#) (D #10# #12#) (= #1#) (- #6# #15=(#16=($ $ $) NIL T ELT)) (+ #15#) (** (($ $ #17=(|PositiveInteger|)) NIL T ELT) (#13# NIL T ELT)) (* (($ #17# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #18=($)) NIL T ELT) (#16# 12 T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #18#) NIL T ELT))) 
(((|OppositeMonogenicLinearOperator| |#1| |#2|) (|Join| #1=(|MonogenicLinearOperator| |#2|) (CATEGORY |domain| (IF (|has| |#1| #2=(|DifferentialRing|)) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE |op| ($ |#1|)) (SIGNATURE |po| (|#1| $)))) #1# (|Ring|)) (T |OppositeMonogenicLinearOperator|)) 
((|op| (*1 *1 *2) (AND #1=(|ofCategory| *3 (|Ring|)) #2=(|isDomain| *1 (|OppositeMonogenicLinearOperator| *2 *3)) #3=(|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|po| (*1 *2 *1) (AND #3# #2# #1#))) 
((~= (#1=((|Boolean|) $ $) 18 T ELT)) (|union| (($ |#1| $) 71 T ELT) (($ $ |#1|) 70 T ELT) (#2=($ $ $) 69 T ELT)) (|symmetricDifference| (#2# 67 T ELT)) (|subset?| (#3=((|Boolean|) $ $) 68 T ELT)) (|set| (($ (|List| |#1|)) 63 T ELT) (#4=($) 62 T ELT)) (|select!| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #7=(|Boolean|) |#1|) . #8=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#9=($) 6 T CONST)) (|removeDuplicates!| (($ $) 55 T ELT)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #10=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #5# |#1|) . #6#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #10#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #7# |#1|) . #8#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 80 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 79 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 75 (|has| |#1| . #11=((|BasicType|))) ELT)) (|part?| (#3# 59 T ELT)) (|min| ((|#1| $) 74 T ELT)) (|merge!| (#12=($ $ $) 88 T ELT)) (|merge| (#12# 87 T ELT)) (|members| (((|List| |#1|) $) 81 T ELT)) (|member?| ((#13=(|Boolean|) |#1| $) 76 (|has| |#1| . #11#) ELT)) (|max| ((|#1| $) 86 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#2# 64 T ELT)) (|inspect| ((|#1| . #14=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT) (($ |#1| $ #15=(|NonNegativeInteger|)) 56 T ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #13# |#1|) $) 78 T ELT)) (|extract!| ((|#1| . #14#) 37 T ELT)) (|every?| ((#13# (|Mapping| #13# |#1|) . #16=($)) 83 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17=((|SetCategory|)))) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT)) (|eq?| ((#18=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#18# $) 7 T ELT)) (|empty| (#9# 8 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #15#))) $) 54 T ELT)) (|difference| (($ $ |#1|) 66 T ELT) (#2# 65 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|count| ((#19=(|NonNegativeInteger|) (|Mapping| #13# |#1|) $) 82 T ELT) ((#19# |#1| $) 77 (|has| |#1| . #11#) ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#20=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #20#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|brace| (($ (|List| |#1|)) 61 T ELT) (#4# 60 T ELT)) (|before?| (#1# 19 T ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|any?| ((#13# (|Mapping| #13# |#1|) . #16#) 84 T ELT)) (= (#1# 17 T ELT)) (|#| ((#19# $) 85 T ELT))) 
(((|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|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|MultiDictionary| |#1|) . T) ((|MultisetAggregate| |#1|) . T) ((|PriorityQueueAggregate| |#1|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((~= (#1=(#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) NIL #4=(|has| |#1| (|AbelianGroup|)) ELT)) (|subtractIfCan| ((#5=(|Union| $ #6="failed") $ $) NIL #4# ELT)) (|sign| (#7=(#8=(|Integer|) $) NIL #9=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| (#10=($) NIL #4# CONST)) (|retractIfCan| (((|Union| #8# . #11=(#6#)) $) NIL #12=(|has| |#1| (|RetractableTo| #8#)) ELT) (#13=((|Union| #14=(|Fraction| #8#) #6#) $) NIL #15=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| |#1| . #11#) $) 15 T ELT)) (|retract| (#7# NIL #12# ELT) (#16=(#14# $) NIL #15# ELT) ((|#1| $) 9 T ELT)) (|recip| ((#5# $) 42 #9# ELT)) (|rationalIfCan| (#13# 51 #17=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#3# 46 #17# ELT)) (|rational| (#16# 48 #17# ELT)) (|positive?| #18=(#3# NIL #9# ELT)) (|opposite?| (#1# NIL #4# ELT)) (|one?| #18#) (|negative?| #18#) (|min| #19=(#20=($ $ $) NIL #9# ELT)) (|max| #19#) (|latex| (((|String|) $) NIL T ELT)) (|infinity| (#10# 13 T ELT)) (|infinite?| (#3# 12 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|finite?| (#3# 11 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #14#) NIL #15# ELT) (($ |#1|) 8 T ELT) (($ #8#) NIL (OR #9# #12#) ELT)) (|characteristic| ((#21=(|NonNegativeInteger|)) 36 #9# CONST)) (|before?| (#1# 53 T ELT)) (|annihilate?| #22=(#1# NIL #9# ELT)) (|abs| (#23=($ $) NIL #9# ELT)) (|Zero| (#10# 23 #4# CONST)) (|One| (#10# 33 #9# CONST)) (>= #22#) (> #22#) (= (#1# 21 T ELT)) (<= #22#) (< (#1# 45 #9# ELT)) (- (#20# NIL #4# ELT) (#23# 29 #4# ELT)) (+ (#20# 31 #4# ELT)) (** (($ $ #24=(|PositiveInteger|)) NIL #9# ELT) (($ $ #21#) NIL #9# ELT)) (* (#20# 39 #9# ELT) (($ #8# $) 27 #4# ELT) (($ #21# $) NIL #4# ELT) (($ #24# $) NIL #4# ELT))) 
(((|OnePointCompletion| |#1|) (|Join| #1=(|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |infinity| ($)) (SIGNATURE |finite?| #2=((|Boolean|) $)) (SIGNATURE |infinite?| #2#) (IF (|has| |#1| #3=(|AbelianGroup|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |#1| #4=(|OrderedRing|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| #2#) (SIGNATURE |rational| (#5=(|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| #5# "failed") $))) |%noBranch|))) #1#) (T |OnePointCompletion|)) 
((|infinity| (*1 *1) (AND (|isDomain| *1 (|OnePointCompletion| *2)) (|ofCategory| *2 #1=(|SetCategory|)))) (|finite?| #2=(*1 *2 *1) #3=(AND #4=(|isDomain| *2 (|Boolean|)) #5=(|isDomain| *1 (|OnePointCompletion| *3)) #6=(|ofCategory| *3 #1#))) (|infinite?| #2# #3#) (|rational?| #2# (AND #4# #5# #7=(|ofCategory| *3 (|IntegerNumberSystem|)) #6#)) (|rational| #2# (AND #8=(|isDomain| *2 (|Fraction| (|Integer|))) #5# #7# #6#)) (|rationalIfCan| #2# (|partial| AND #8# #5# #7# #6#))) 
((|map| ((#1=(|OnePointCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OnePointCompletion| |#1|) #1#) 12 T ELT) ((#1# #2# #3#) 13 T ELT))) 
(((|OnePointCompletionFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| (#1=(|OnePointCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OnePointCompletion| |#1|))) (SIGNATURE |map| (#1# #2# #3# #1#))) #4=(|SetCategory|) #4#) (T |OnePointCompletionFunctions2|)) 
((|map| (*1 *2 *3 *4 *2) (AND #1=(|isDomain| *2 (|OnePointCompletion| *6)) #2=(|isDomain| *3 (|Mapping| *6 *5)) #3=(|isDomain| *4 (|OnePointCompletion| *5)) #4=(|ofCategory| *5 #5=(|SetCategory|)) #6=(|ofCategory| *6 #5#) #7=(|isDomain| *1 (|OnePointCompletionFunctions2| *5 *6)))) (|map| (*1 *2 *3 *4) (AND #2# #3# #4# #6# #1# #7#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| #6=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #7=(#5#)) . #8=($)) NIL T ELT) (((|Union| #9=(|BasicOperator|) . #7#) . #8#) NIL T ELT)) (|retract| ((|#1| . #10=($)) NIL T ELT) ((#9# . #10#) NIL T ELT)) (|recip| ((#4# $) NIL T ELT)) (|opposite?| #1#) (|opeval| ((|#1| #9# |#1|) NIL T ELT)) (|one?| #3#) (|makeop| (($ |#1| (|FreeGroup| #9#)) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|evaluateInverse| #11=(($ $ (|Mapping| |#1| |#1|)) NIL T ELT)) (|evaluate| #11#) (|elt| ((|#1| $ |#1|) NIL T ELT)) (|conjug| ((|#1| |#1|) NIL #12=(|has| |#1| (|CommutativeRing|)) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #13=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (($ #9#) NIL T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#14=(|NonNegativeInteger|)) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|adjoint| (#15=($ $) NIL #12# ELT) (#16=($ $ $) NIL #12# ELT)) (|Zero| #6#) (|One| #6#) (= #1#) (- (#15# NIL T ELT) #17=(#16# NIL T ELT)) (+ #17#) (** (($ $ #18=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT) (($ #9# #13#) NIL T ELT) (($ $ #13#) NIL T ELT)) (* (($ #18# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #13# . #19=($)) NIL T ELT) #17# (($ |#1| . #19#) NIL #12# ELT) (($ $ |#1|) NIL #12# ELT))) 
(((|Operator| |#1|) (|Join| #1=(|Ring|) (|RetractableTo| |#1|) (|RetractableTo| #2=(|BasicOperator|)) (|Eltable| |#1| |#1|) (CATEGORY |domain| (IF (|has| |#1| #3=(|CharacteristicZero|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |#1| #4=(|CharacteristicNonZero|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|Algebra| |#1|)) (SIGNATURE |adjoint| ($ $)) (SIGNATURE |adjoint| ($ $ $)) (SIGNATURE |conjug| (|#1| |#1|))) |%noBranch|) (SIGNATURE |evaluate| #5=($ $ (|Mapping| |#1| |#1|))) (SIGNATURE |evaluateInverse| #5#) (SIGNATURE ** ($ #2# #6=(|Integer|))) (SIGNATURE ** ($ $ #6#)) (SIGNATURE |opeval| (|#1| #2# |#1|)) (SIGNATURE |makeop| ($ |#1| (|FreeGroup| #2#))))) #1#) (T |Operator|)) 
((|adjoint| (*1 *1 *1) #1=(AND #2=(|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|CommutativeRing|)) #3=(|ofCategory| *2 #4=(|Ring|)))) (|adjoint| (*1 *1 *1 *1) #1#) (|conjug| (*1 *2 *2) #1#) (|evaluate| #5=(*1 *1 *1 *2) #6=(AND (|isDomain| *2 (|Mapping| *3 *3)) #7=(|ofCategory| *3 #4#) #8=(|isDomain| *1 (|Operator| *3)))) (|evaluateInverse| #5# #6#) (** #9=(*1 *1 *2 *3) (AND (|isDomain| *2 #10=(|BasicOperator|)) (|isDomain| *3 #11=(|Integer|)) (|isDomain| *1 (|Operator| *4)) (|ofCategory| *4 #4#))) (** #5# (AND (|isDomain| *2 #11#) #8# #7#)) (|opeval| (*1 *2 *3 *2) (AND (|isDomain| *3 #10#) #2# #3#)) (|makeop| #9# (AND (|isDomain| *3 (|FreeGroup| #10#)) #2# #3#))) 
((|is?| (((|Boolean|) $ |#2|) 14 T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT))) 
(((|OperatorCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |is?| ((|Boolean|) |#1| |#2|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|OperatorCategory| |#2|) (|SetCategory|)) (T |OperatorCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|name| ((|#1| $) 19 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|is?| (((|Boolean|) $ |#1|) 17 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|arity| (((|Arity|) $) 18 T ELT)) (= (#1# 8 T ELT))) 
(((|OperatorCategory| |#1|) (|Category|) (|SetCategory|)) (T |OperatorCategory|)) 
((|name| (*1 *2 *1) (AND (|ofCategory| *1 (|OperatorCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|arity| (*1 *2 *1) (AND (|ofCategory| *1 (|OperatorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Arity|)))) (|is?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OperatorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| (|t#1| $)) (SIGNATURE |arity| ((|Arity|) $)) (SIGNATURE |is?| ((|Boolean|) $ |t#1|)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|getDatabase| (((|Database| (|IndexCard|)) (|String|)) 9 T ELT))) 
(((|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|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|signature| ((#4=(|Signature|) $) 10 T ELT)) (|name| ((#5=(|Identifier|) $) 9 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|is?| ((#3# $ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|construct| (($ #5# #4#) 8 T ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT)) (|before?| #1#) (|arity| (((|Arity|) $) 20 T ELT)) (= (#2# 12 T ELT))) 
(((|OperatorSignature|) (|Join| (|OperatorCategory| #1=(|Identifier|)) (CATEGORY |domain| (SIGNATURE |signature| (#2=(|Signature|) $)) (SIGNATURE |construct| ($ #1# #2#))))) (T |OperatorSignature|)) 
((|signature| (*1 *2 *1) (AND (|isDomain| *2 #1=(|Signature|)) #2=(|isDomain| *1 (|OperatorSignature|)))) (|construct| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 #1#) #2#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) NIL #5=(|has| |#1| (|AbelianGroup|)) ELT)) (|whatInfinity| (#6=((|SingleInteger|) $) 31 T ELT)) (|subtractIfCan| ((#7=(|Union| $ #8="failed") $ $) NIL #5# ELT)) (|sign| (#9=(#10=(|Integer|) $) NIL #11=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| (#12=($) NIL #5# CONST)) (|retractIfCan| (((|Union| #10# . #13=(#8#)) $) NIL #14=(|has| |#1| (|RetractableTo| #10#)) ELT) (#15=((|Union| #16=(|Fraction| #10#) #8#) $) NIL #17=(|has| |#1| (|RetractableTo| #16#)) ELT) (((|Union| |#1| . #13#) $) 18 T ELT)) (|retract| (#9# NIL #14# ELT) (#18=(#16# $) NIL #17# ELT) ((|#1| $) 9 T ELT)) (|recip| ((#7# $) 57 #11# ELT)) (|rationalIfCan| (#15# 65 #19=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#4# 60 #19# ELT)) (|rational| (#18# 63 #19# ELT)) (|positive?| #20=(#4# NIL #11# ELT)) (|plusInfinity| (#12# 14 T ELT)) (|opposite?| (#2# NIL #5# ELT)) (|one?| #20#) (|negative?| #20#) (|minusInfinity| (#12# 16 T ELT)) (|min| #21=(#22=($ $ $) NIL #11# ELT)) (|max| #21#) (|latex| (((|String|) $) NIL T ELT)) (|infinite?| (#4# 12 T ELT)) (|hash| (#6# NIL T ELT)) (|finite?| (#4# 11 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #16#) NIL #17# ELT) (($ |#1|) 8 T ELT) (($ #10#) NIL (OR #11# #14#) ELT)) (|characteristic| ((#23=(|NonNegativeInteger|)) 50 #11# CONST)) (|before?| #1#) (|annihilate?| #24=(#2# NIL #11# ELT)) (|abs| (#25=($ $) NIL #11# ELT)) (|Zero| (#12# 37 #5# CONST)) (|One| (#12# 47 #11# CONST)) (>= #24#) (> #24#) (= (#2# 35 T ELT)) (<= #24#) (< (#2# 59 #11# ELT)) (- (#22# NIL #5# ELT) (#25# 43 #5# ELT)) (+ (#22# 45 #5# ELT)) (** (($ $ #26=(|PositiveInteger|)) NIL #11# ELT) (($ $ #23#) NIL #11# ELT)) (* (#22# 54 #11# ELT) (($ #10# $) 41 #5# ELT) (($ #23# $) NIL #5# ELT) (($ #26# $) NIL #5# ELT))) 
(((|OrderedCompletion| |#1|) (|Join| #1=(|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |plusInfinity| #2=($)) (SIGNATURE |minusInfinity| #2#) (SIGNATURE |finite?| #3=((|Boolean|) $)) (SIGNATURE |infinite?| #3#) (SIGNATURE |whatInfinity| ((|SingleInteger|) $)) (IF (|has| |#1| #4=(|AbelianGroup|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| #5=(|OrderedRing|)) (ATTRIBUTE #5#) |%noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| #3#) (SIGNATURE |rational| (#6=(|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| #6# "failed") $))) |%noBranch|))) #1#) (T |OrderedCompletion|)) 
((|plusInfinity| #1=(*1 *1) #2=(AND (|isDomain| *1 (|OrderedCompletion| *2)) (|ofCategory| *2 #3=(|SetCategory|)))) (|minusInfinity| #1# #2#) (|finite?| #4=(*1 *2 *1) #5=(AND #6=(|isDomain| *2 (|Boolean|)) #7=(|isDomain| *1 (|OrderedCompletion| *3)) #8=(|ofCategory| *3 #3#))) (|infinite?| #4# #5#) (|whatInfinity| #4# (AND (|isDomain| *2 (|SingleInteger|)) #7# #8#)) (|rational?| #4# (AND #6# #7# #9=(|ofCategory| *3 (|IntegerNumberSystem|)) #8#)) (|rational| #4# (AND #10=(|isDomain| *2 (|Fraction| (|Integer|))) #7# #9# #8#)) (|rationalIfCan| #4# (|partial| AND #10# #7# #9# #8#))) 
((|map| ((#1=(|OrderedCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OrderedCompletion| |#1|) #1# #1#) 13 T ELT) ((#1# #2# #3#) 14 T ELT))) 
(((|OrderedCompletionFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| (#1=(|OrderedCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OrderedCompletion| |#1|))) (SIGNATURE |map| (#1# #2# #3# #1# #1#))) #4=(|SetCategory|) #4#) (T |OrderedCompletionFunctions2|)) 
((|map| (*1 *2 *3 *4 *2 *2) (AND #1=(|isDomain| *2 (|OrderedCompletion| *6)) #2=(|isDomain| *3 (|Mapping| *6 *5)) #3=(|isDomain| *4 (|OrderedCompletion| *5)) #4=(|ofCategory| *5 #5=(|SetCategory|)) #6=(|ofCategory| *6 #5#) #7=(|isDomain| *1 (|OrderedCompletionFunctions2| *5 *6)))) (|map| (*1 *2 *3 *4) (AND #2# #3# #4# #6# #1# #7#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|size| (((|NonNegativeInteger|)) 27 T ELT)) (|random| (($) 30 T ELT)) (|min| (#2=($ $ $) 23 T ELT) (($) 26 T CONST)) (|max| (#2# 22 T ELT) (($) 25 T CONST)) (|lookup| ((#3=(|PositiveInteger|) $) 29 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|index| (($ #3#) 28 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#4=((|Boolean|) $ $) 21 T ELT)) (> (#4# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#4# 20 T ELT)) (< (#4# 18 T ELT))) 
(((|OrderedFinite|) (|Category|)) (T |OrderedFinite|)) 
((|min| (*1 *1) (|ofCategory| *1 (|OrderedFinite|))) (|max| (*1 *1) (|ofCategory| *1 (|OrderedFinite|)))) 
(|Join| (|OrderedSet|) (|Finite|) (CATEGORY |domain| (SIGNATURE |min| ($) |constant|) (SIGNATURE |max| ($) |constant|))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Finite|) . T) ((|Join|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|totalLex| (#1=((|Boolean|) #2=(|Vector| |#2|) #2#) 19 T ELT)) (|reverseLex| (#1# 20 T ELT)) (|pureLex| (#1# 16 T ELT))) 
(((|OrderingFunctions| |#1| |#2|) (CATEGORY |package| (SIGNATURE |pureLex| #1=((|Boolean|) #2=(|Vector| |#2|) #2#)) (SIGNATURE |totalLex| #1#) (SIGNATURE |reverseLex| #1#)) (|NonNegativeInteger|) (|OrderedAbelianMonoid|)) (T |OrderingFunctions|)) 
((|reverseLex| #1=(*1 *2 *3 *3) #2=(AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderingFunctions| *4 *5)) (|ofType| *4 (|NonNegativeInteger|)))) (|totalLex| #1# #2#) (|pureLex| #1# #2#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|sample| (#2=($) 29 T CONST)) (|recip| (((|Union| $ "failed") $) 32 T ELT)) (|one?| (((|Boolean|) $) 30 T ELT)) (|min| (#3=($ $ $) 23 T ELT)) (|max| (#3# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#2# 28 T CONST)) (>= (#4=((|Boolean|) $ $) 21 T ELT)) (> (#4# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#4# 20 T ELT)) (< (#4# 18 T ELT)) (** (($ $ (|PositiveInteger|)) 26 T ELT) (($ $ (|NonNegativeInteger|)) 31 T ELT)) (* (($ $ $) 25 T ELT))) 
(((|OrderedMonoid|) (|Category|)) (T |OrderedMonoid|)) 
NIL 
(|Join| (|OrderedSemiGroup|) (|Monoid|)) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monoid|) . T) ((|OrderedSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 35 T ELT)) (|sign| (((|Integer|) $) 38 T ELT)) (|sample| (#3=($) 30 T CONST)) (|recip| (((|Union| $ "failed") $) 55 T ELT)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|one?| (((|Boolean|) $) 53 T ELT)) (|negative?| (((|Boolean|) $) 39 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 56 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 57 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 51 T ELT)) (|abs| (($ $) 37 T ELT)) (|Zero| (#3# 29 T CONST)) (|One| (($) 52 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (- (($ $ $) 42 T ELT) (($ $) 41 T ELT)) (+ (($ $ $) 25 T ELT)) (** (($ $ (|NonNegativeInteger|)) 54 T ELT) (($ $ (|PositiveInteger|)) 49 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ (|Integer|) $) 40 T ELT) (($ $ $) 50 T ELT))) 
(((|OrderedRing|) (|Category|)) (T |OrderedRing|)) 
NIL 
(|Join| (|OrderedAbelianGroup|) (|CharacteristicZero|) (|Monoid|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#3=((|Boolean|) $ $) 21 T ELT)) (> (#3# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#3# 20 T ELT)) (< (#3# 18 T ELT))) 
(((|OrderedSet|) (|Category|)) (T |OrderedSet|)) 
NIL 
(|Join| (|SetCategory|) (|OrderedType|)) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|min| #3=(($ $ $) NIL T ELT)) (|max| #3#) (|coerce| (($ |#1|) 10 T ELT) ((|#1| $) 9 T ELT) ((#4=(|OutputForm|) $) 15 (|has| |#1| (|CoercibleTo| #4#)) ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 12 T ELT))) 
(((|OrderedStructure| |#1| |#2|) (|Join| (|OrderedType|) (|HomotopicTo| |#1|) (CATEGORY |package| (IF (|has| |#1| #1=(|CoercibleTo| (|OutputForm|))) (ATTRIBUTE #1#) |%noBranch|))) (|Type|) (|Mapping| (|Boolean|) |#1| |#1|)) (T |OrderedStructure|)) 
NIL 
((|min| (#1=($ $ $) 16 T ELT)) (|max| (#1# 15 T ELT)) (|before?| (#2=((|Boolean|) $ $) 17 T ELT)) (>= (#2# 12 T ELT)) (> (#2# 9 T ELT)) (= (#2# 14 T ELT)) (<= (#2# 11 T ELT))) 
(((|OrderedType&| |#1|) (CATEGORY |package| (SIGNATURE |min| #1=(|#1| |#1| |#1|)) (SIGNATURE |max| #1#) (SIGNATURE >= #2=((|Boolean|) |#1| |#1|)) (SIGNATURE <= #2#) (SIGNATURE > #2#) (SIGNATURE |before?| #2#) (SIGNATURE = #2#)) (|OrderedType|)) (T |OrderedType&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (($ $ $) 10 T ELT)) (|max| (($ $ $) 11 T ELT)) (|before?| (#1# 6 T ELT)) (>= (((|Boolean|) $ $) 12 T ELT)) (> (((|Boolean|) $ $) 14 T ELT)) (= (#1# 8 T ELT)) (<= (((|Boolean|) $ $) 13 T ELT)) (< (((|Boolean|) $ $) 15 T ELT))) 
(((|OrderedType|) (|Category|)) (T |OrderedType|)) 
((< (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|)))) (> (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|)))) (<= (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|)))) (>= (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|)))) (|max| (*1 *1 *1 *1) (|ofCategory| *1 (|OrderedType|))) (|min| (*1 *1 *1 *1) (|ofCategory| *1 (|OrderedType|)))) 
(|Join| (|BasicType|) (CATEGORY |domain| (SIGNATURE < ((|Boolean|) $ $)) (SIGNATURE > ((|Boolean|) $ $)) (SIGNATURE <= ((|Boolean|) $ $)) (SIGNATURE >= ((|Boolean|) $ $)) (SIGNATURE |max| ($ $ $)) (SIGNATURE |min| ($ $ $)))) 
(((|BasicType|) . T) ((|Join|) . T) ((|Type|) . T)) 
((|rightRemainder| (#1=($ $ $) 49 T ELT)) (|rightQuotient| (#1# 48 T ELT)) (|rightLcm| (#1# 46 T ELT)) (|rightGcd| (#1# 55 T ELT)) (|rightExtendedGcd| (#2=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 50 T ELT)) (|rightExactQuotient| (#3=(#4=(|Union| $ #5="failed") $ $) 53 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) #5#) $) NIL T ELT) (((|Union| #7=(|Fraction| #6#) #5#) $) NIL T ELT) (((|Union| |#2| #5#) $) 29 T ELT)) (|primitivePart| (($ $) 39 T ELT)) (|leftRemainder| (#1# 43 T ELT)) (|leftQuotient| (#1# 42 T ELT)) (|leftLcm| (#1# 51 T ELT)) (|leftGcd| (#1# 57 T ELT)) (|leftExtendedGcd| (#2# 45 T ELT)) (|leftExactQuotient| (#3# 52 T ELT)) (|exquo| ((#4# $ |#2|) 32 T ELT)) (|content| ((|#2| $) 36 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #6#) NIL T ELT) (($ #7#) NIL T ELT) (($ |#2|) 13 T ELT)) (|coefficients| (((|List| |#2|) $) 21 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #6# $) NIL T ELT) (#1# NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) 25 T ELT))) 
(((|UnivariateSkewPolynomialCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftLcm| #1=(|#1| |#1| |#1|)) (SIGNATURE |rightExtendedGcd| #2=((|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|) (|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |rightGcd| #1#) (SIGNATURE |rightExactQuotient| #3=(#4=(|Union| |#1| #5="failed") |#1| |#1|)) (SIGNATURE |rightRemainder| #1#) (SIGNATURE |rightQuotient| #1#) (SIGNATURE |rightLcm| #1#) (SIGNATURE |leftExtendedGcd| #2#) (SIGNATURE |leftGcd| #1#) (SIGNATURE |leftExactQuotient| #3#) (SIGNATURE |leftRemainder| #1#) (SIGNATURE |leftQuotient| #1#) (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |exquo| (#4# |#1| |#2|)) (SIGNATURE |coefficients| ((|List| |#2|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #5#) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #6=(|Fraction| #7=(|Integer|)) #5#) |#1|)) (SIGNATURE |coerce| (|#1| #6#)) (SIGNATURE |retractIfCan| ((|Union| #7# #5#) |#1|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| #7#)) (SIGNATURE * #1#) (SIGNATURE * (|#1| #7# |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|UnivariateSkewPolynomialCategory| |#2|) (|Ring|)) (T |UnivariateSkewPolynomialCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (($ $ $) 58 (|has| |#1| (|Field|)) ELT)) (|rightQuotient| (($ $ $) 59 (|has| |#1| (|Field|)) ELT)) (|rightLcm| (($ $ $) 61 (|has| |#1| (|Field|)) ELT)) (|rightGcd| (($ $ $) 56 (|has| |#1| (|Field|)) ELT)) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 55 (|has| |#1| (|Field|)) ELT)) (|rightExactQuotient| (((|Union| $ "failed") $ $) 57 (|has| |#1| (|Field|)) ELT)) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 60 (|has| |#1| (|Field|)) ELT)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) . #6=($)) 88 (|has| |#1| . #7=((|RetractableTo| #4#))) ELT) (((|Union| #8=(|Fraction| #4#) . #5#) . #6#) 85 (|has| |#1| . #9=((|RetractableTo| #8#))) ELT) (((|Union| |#1| . #5#) . #6#) 82 T ELT)) (|retract| ((#4# . #10=($)) 87 (|has| |#1| . #7#) ELT) ((#8# . #10#) 84 (|has| |#1| . #9#) ELT) ((|#1| . #10#) 83 T ELT)) (|reductum| (($ $) 77 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (($ $) 68 (|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 75 T ELT)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 70 (|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 71 (|has| |#1| (|IntegralDomain|)) ELT)) (|minimumDegree| (((|NonNegativeInteger|) $) 79 T ELT)) (|leftRemainder| (($ $ $) 65 (|has| |#1| (|Field|)) ELT)) (|leftQuotient| (($ $ $) 66 (|has| |#1| (|Field|)) ELT)) (|leftLcm| (($ $ $) 54 (|has| |#1| (|Field|)) ELT)) (|leftGcd| (($ $ $) 63 (|has| |#1| (|Field|)) ELT)) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 62 (|has| |#1| (|Field|)) ELT)) (|leftExactQuotient| (((|Union| $ "failed") $ $) 64 (|has| |#1| (|Field|)) ELT)) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 67 (|has| |#1| (|Field|)) ELT)) (|leadingCoefficient| ((|#1| $) 78 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 72 (|has| |#1| (|IntegralDomain|)) ELT)) (|degree| (((|NonNegativeInteger|) $) 80 T ELT)) (|content| ((|#1| $) 69 (|has| |#1| (|GcdDomain|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #8#) 86 (|has| |#1| . #9#) ELT) (($ |#1|) 81 T ELT)) (|coefficients| (((|List| |#1|) $) 74 T ELT)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 76 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 73 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #11=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #11#) 89 T ELT))) 
(((|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) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FullyRetractableTo| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|times| ((|#2| |#2| |#2| #1=(|Automorphism| |#1|) #2=(|Mapping| |#1| |#1|)) 20 T ELT)) (|rightDivide| (#3=((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| #1#) 46 #4=(|has| |#1| (|Field|)) ELT)) (|monicRightDivide| (#3# 43 #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#3# 42 #5# ELT)) (|leftDivide| (#3# 45 #4# ELT)) (|apply| ((|#1| |#2| |#1| |#1| #1# #2#) 33 T ELT))) 
(((|UnivariateSkewPolynomialCategoryOps| |#1| |#2|) (CATEGORY |package| (SIGNATURE |times| (|#2| |#2| |#2| #1=(|Automorphism| |#1|) #2=(|Mapping| |#1| |#1|))) (SIGNATURE |apply| (|#1| |#2| |#1| |#1| #1# #2#)) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |monicLeftDivide| #3=((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| #1#)) (SIGNATURE |monicRightDivide| #3#)) |%noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |leftDivide| #3#) (SIGNATURE |rightDivide| #3#)) |%noBranch|)) (|Ring|) (|UnivariateSkewPolynomialCategory| |#1|)) (T |UnivariateSkewPolynomialCategoryOps|)) 
((|rightDivide| #1=(*1 *2 *3 *3 *4) #2=(AND #3=(|isDomain| *4 #4=(|Automorphism| *5)) (|ofCategory| *5 (|Field|)) #5=(|ofCategory| *5 #6=(|Ring|)) #7=(|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) #8=(|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3)) #9=(|ofCategory| *3 #10=(|UnivariateSkewPolynomialCategory| *5)))) (|leftDivide| #1# #2#) (|monicRightDivide| #1# #11=(AND #3# (|ofCategory| *5 (|IntegralDomain|)) #5# #7# #8# #9#)) (|monicLeftDivide| #1# #11#) (|apply| (*1 *2 *3 *2 *2 *4 *5) (AND (|isDomain| *4 (|Automorphism| *2)) (|isDomain| *5 (|Mapping| *2 *2)) (|ofCategory| *2 #6#) (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *2 *3)) (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *2)))) (|times| (*1 *2 *2 *2 *3 *4) (AND (|isDomain| *3 #4#) (|isDomain| *4 (|Mapping| *5 *5)) #5# (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *2)) (|ofCategory| *2 #10#)))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (#4=(#5=(|Union| $ #6="failed") $ $) NIL T ELT)) (|sample| #7=(#8=($) NIL T CONST)) (|rightRemainder| #9=(#10=($ $ $) NIL #11=(|has| |#1| (|Field|)) ELT)) (|rightQuotient| #9#) (|rightLcm| #9#) (|rightGcd| #9#) (|rightExtendedGcd| #12=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #11# ELT)) (|rightExactQuotient| #13=(#4# NIL #11# ELT)) (|rightDivide| (#14=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 34 #11# ELT)) (|retractIfCan| (((|Union| #15=(|Integer|) . #16=(#6#)) . #17=($)) NIL #18=(|has| |#1| (|RetractableTo| #15#)) ELT) (((|Union| #19=(|Fraction| #15#) . #16#) . #17#) NIL #20=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| |#1| . #16#) . #17#) NIL T ELT)) (|retract| ((#15# . #21=($)) NIL #18# ELT) ((#19# . #21#) NIL #20# ELT) #22=(#23=(|#1| . #21#) NIL T ELT)) (|reductum| #24=(#25=($ $) NIL T ELT)) (|recip| ((#5# $) NIL T ELT)) (|primitivePart| (#25# NIL #26=(|has| |#1| (|GcdDomain|)) ELT)) (|outputForm| ((#27=(|OutputForm|) $ #27#) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #28=(|NonNegativeInteger|)) NIL T ELT)) (|monicRightDivide| (#14# 30 #29=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#14# 28 #29# ELT)) (|minimumDegree| #30=((#28# $) NIL T ELT)) (|leftRemainder| #9#) (|leftQuotient| #9#) (|leftLcm| #9#) (|leftGcd| #9#) (|leftExtendedGcd| #12#) (|leftExactQuotient| #13#) (|leftDivide| (#14# 32 #11# ELT)) (|leadingCoefficient| #22#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#5# $ |#1|) NIL #29# ELT)) (|degree| #30#) (|content| (#23# NIL #26# ELT)) (|coerce| ((#27# $) NIL T ELT) (($ #15#) NIL T ELT) (($ #19#) NIL #20# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #28#) NIL T ELT)) (|characteristic| ((#28#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) 15 T ELT)) (|annihilate?| #1#) (|Zero| #7#) (|One| (#8# 23 T CONST)) (= #1#) (- #24# #31=(#10# NIL T ELT)) (+ #31#) (** (($ $ #32=(|PositiveInteger|)) 19 T ELT) (($ $ #28#) 24 T ELT)) (* (($ #32# $) NIL T ELT) (($ #28# $) NIL T ELT) (($ #15# . #33=($)) NIL T ELT) (#10# 13 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #33#) NIL T ELT))) 
(((|SparseUnivariateSkewPolynomial| |#1| |#2| |#3|) (|Join| (|UnivariateSkewPolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| (#1=(|OutputForm|) $ #1#)))) (|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))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (#4=(#5=(|Union| $ #6="failed") $ $) NIL T ELT)) (|sample| #7=(#8=($) NIL T CONST)) (|rightRemainder| #9=(#10=($ $ $) NIL #11=(|has| |#2| (|Field|)) ELT)) (|rightQuotient| #9#) (|rightLcm| #9#) (|rightGcd| #9#) (|rightExtendedGcd| #12=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #11# ELT)) (|rightExactQuotient| #13=(#4# NIL #11# ELT)) (|rightDivide| #14=(#15=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #11# ELT)) (|retractIfCan| (((|Union| #16=(|Integer|) . #17=(#6#)) . #18=($)) NIL #19=(|has| |#2| (|RetractableTo| #16#)) ELT) (((|Union| #20=(|Fraction| #16#) . #17#) . #18#) NIL #21=(|has| |#2| (|RetractableTo| #20#)) ELT) (((|Union| |#2| . #17#) . #18#) NIL T ELT)) (|retract| ((#16# . #22=($)) NIL #19# ELT) ((#20# . #22#) NIL #21# ELT) #23=(#24=(|#2| . #22#) NIL T ELT)) (|reductum| #25=(#26=($ $) NIL T ELT)) (|recip| ((#5# $) NIL T ELT)) (|primitivePart| (#26# NIL #27=(|has| |#2| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#2| #28=(|NonNegativeInteger|)) 17 T ELT)) (|monicRightDivide| #29=(#15# NIL #30=(|has| |#2| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #29#) (|minimumDegree| #31=((#28# $) NIL T ELT)) (|leftRemainder| #9#) (|leftQuotient| #9#) (|leftLcm| #9#) (|leftGcd| #9#) (|leftExtendedGcd| #12#) (|leftExactQuotient| #13#) (|leftDivide| #14#) (|leadingCoefficient| #23#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#5# $ |#2|) NIL #30# ELT)) (|degree| #31#) (|content| (#24# NIL #27# ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #16#) NIL T ELT) (($ #20#) NIL #21# ELT) (($ |#2|) NIL T ELT) (($ (|Variable| |#1|)) 19 T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| ((|#2| $ #28#) NIL T ELT)) (|characteristic| ((#28#) NIL T CONST)) (|before?| #1#) (|apply| ((|#2| $ |#2| |#2|) NIL T ELT)) (|annihilate?| #1#) (|Zero| #7#) (|One| (#8# 13 T CONST)) (= #1#) (- #25# #32=(#10# NIL T ELT)) (+ #32#) (** (($ $ #33=(|PositiveInteger|)) NIL T ELT) (($ $ #28#) NIL T ELT)) (* (($ #33# $) NIL T ELT) (($ #28# $) NIL T ELT) (($ #16# . #34=($)) NIL T ELT) #32# (($ $ |#2|) NIL T ELT) (($ |#2| . #34#) NIL T ELT))) 
(((|UnivariateSkewPolynomial| |#1| |#2| |#3| |#4|) (|Join| (|UnivariateSkewPolynomialCategory| |#2|) (|CoercibleFrom| (|Variable| |#1|))) (|Symbol|) (|Ring|) (|Automorphism| |#2|) (|Mapping| |#2| |#2|)) (T |UnivariateSkewPolynomial|)) 
NIL 
((|legendreP| (#1=(|#1| #2=(|NonNegativeInteger|) |#1|) 45 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT)) (|laguerreL| ((|#1| #2# #2# |#1|) 36 T ELT) (#1# 24 T ELT)) (|hermiteH| (#1# 40 T ELT)) (|chebyshevU| (#1# 38 T ELT)) (|chebyshevT| (#1# 37 T ELT))) 
(((|OrthogonalPolynomialFunctions| |#1|) (CATEGORY |package| (SIGNATURE |chebyshevT| #1=(|#1| #2=(|NonNegativeInteger|) |#1|)) (SIGNATURE |chebyshevU| #1#) (SIGNATURE |hermiteH| #1#) (SIGNATURE |laguerreL| #1#) (SIGNATURE |laguerreL| (|#1| #2# #2# |#1|)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |legendreP| #1#) |%noBranch|)) (|CommutativeRing|)) (T |OrthogonalPolynomialFunctions|)) 
((|legendreP| #1=(*1 *2 *3 *2) (AND #2=(|isDomain| *3 (|NonNegativeInteger|)) #3=(|isDomain| *1 (|OrthogonalPolynomialFunctions| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) #4=(|ofCategory| *2 (|CommutativeRing|)))) (|laguerreL| (*1 *2 *3 *3 *2) #5=(AND #2# #3# #4#)) (|laguerreL| #1# #5#) (|hermiteH| #1# #5#) (|chebyshevU| #1# #5#) (|chebyshevT| #1# #5#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#3=((|Boolean|) $ $) 21 T ELT)) (> (#3# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#3# 20 T ELT)) (< (#3# 18 T ELT)) (** (($ $ (|PositiveInteger|)) 26 T ELT)) (* (($ $ $) 25 T ELT))) 
(((|OrderedSemiGroup|) (|Category|)) (T |OrderedSemiGroup|)) 
NIL 
(|Join| (|OrderedSet|) (|SemiGroup|)) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|value| ((#3=(|Integer|) $) 14 T ELT)) (|min| #4=(($ $ $) NIL T ELT)) (|max| #4#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #3#) 13 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= (#2# 10 T ELT)) (<= #1#) (< (#2# 12 T ELT))) 
(((|OrdSetInts|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1=(|Integer|))) (SIGNATURE |value| (#1# $))))) (T |OrdSetInts|)) 
((|coerce| (*1 *1 *2) #1=(AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OrdSetInts|)))) (|value| (*1 *2 *1) #1#)) 
((|outputList| ((#1=(|Void|) (|List| (|Any|))) 23 T ELT)) (|output| ((#1# #2=(|String|) #3=(|OutputForm|)) 13 T ELT) ((#1# #3#) 8 T ELT) ((#1# #2#) 10 T ELT))) 
(((|OutputPackage|) (CATEGORY |package| (SIGNATURE |output| (#1=(|Void|) #2=(|String|))) (SIGNATURE |output| (#1# #3=(|OutputForm|))) (SIGNATURE |output| (#1# #2# #3#)) (SIGNATURE |outputList| (#1# (|List| (|Any|)))))) (T |OutputPackage|)) 
((|outputList| #1=(*1 *2 *3) (AND (|isDomain| *3 (|List| (|Any|))) #2=(|isDomain| *2 (|Void|)) #3=(|isDomain| *1 (|OutputPackage|)))) (|output| (*1 *2 *3 *4) (AND #4=(|isDomain| *3 (|String|)) (|isDomain| *4 #5=(|OutputForm|)) #2# #3#)) (|output| #1# (AND (|isDomain| *3 #5#) #2# #3#)) (|output| #1# (AND #4# #2# #3#))) 
((|writeUInt8!| (((|Maybe| #1=(|UInt8|)) $ #1#) 15 T ELT)) (|writeInt8!| (((|Maybe| #2=(|Int8|)) $ #2#) 12 T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 30 T ELT))) 
(((|OutputByteConduit&| |#1|) (CATEGORY |package| (SIGNATURE |writeBytes!| ((|NonNegativeInteger|) |#1| (|ByteBuffer|))) (SIGNATURE |writeUInt8!| ((|Maybe| #1=(|UInt8|)) |#1| #1#)) (SIGNATURE |writeInt8!| ((|Maybe| #2=(|Int8|)) |#1| #2#))) (|OutputByteConduit|)) (T |OutputByteConduit&|)) 
NIL 
((|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) 8 T ELT)) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) 9 T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 7 T ELT)) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) 10 T ELT)) (|close!| (($ $) 6 T ELT))) 
(((|OutputByteConduit|) (|Category|)) (T |OutputByteConduit|)) 
((|writeByte!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *2 (|Maybe| (|Byte|))) (|isDomain| *3 (|Byte|)))) (|writeInt8!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *2 (|Maybe| (|Int8|))) (|isDomain| *3 (|Int8|)))) (|writeUInt8!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *2 (|Maybe| (|UInt8|))) (|isDomain| *3 (|UInt8|)))) (|writeBytes!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *3 (|ByteBuffer|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|Conduit|) (CATEGORY |domain| (SIGNATURE |writeByte!| ((|Maybe| (|Byte|)) $ (|Byte|))) (SIGNATURE |writeInt8!| ((|Maybe| (|Int8|)) $ (|Int8|))) (SIGNATURE |writeUInt8!| ((|Maybe| (|UInt8|)) $ (|UInt8|))) (SIGNATURE |writeBytes!| ((|NonNegativeInteger|) $ (|ByteBuffer|))))) 
(((|Conduit|) . T)) 
((|writeUInt8!| (((|Maybe| #1=(|UInt8|)) $ #1#) NIL T ELT)) (|writeInt8!| (((|Maybe| #2=(|Int8|)) $ #2#) NIL T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) NIL T ELT)) (|writeByte!| (((|Maybe| #3=(|Byte|)) $ #3#) 22 T ELT)) (|outputBinaryFile| (($ (|FileName|)) 12 T ELT) (($ (|String|)) 14 T ELT)) (|isOpen?| (((|Boolean|) $) 19 T ELT)) (|coerce| (((|OutputForm|) $) 26 T ELT)) (|close!| (($ $) 23 T ELT))) 
(((|OutputBinaryFile|) (|Join| (|OutputByteConduit|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |outputBinaryFile| ($ (|FileName|))) (SIGNATURE |outputBinaryFile| ($ (|String|))) (SIGNATURE |isOpen?| ((|Boolean|) $))))) (T |OutputBinaryFile|)) 
((|outputBinaryFile| #1=(*1 *1 *2) (AND (|isDomain| *2 (|FileName|)) #2=(|isDomain| *1 (|OutputBinaryFile|)))) (|outputBinaryFile| #1# (AND (|isDomain| *2 (|String|)) #2#)) (|isOpen?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) #2#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT) (#4=($ $ $) 85 T ELT)) (|zag| (#4# 125 T ELT)) (|width| (#5=(#6=(|Integer|) $) 31 T ELT) (#7=(#6#) 36 T ELT)) (|vspace| (#8=($ #6#) 53 T ELT)) (|vconcat| (#4# 54 T ELT) (#9=($ #10=(|List| $)) 84 T ELT)) (|supersub| (#11=($ $ #10#) 82 T ELT)) (|superHeight| (#5# 34 T ELT)) (|super| (#4# 73 T ELT)) (|sum| (#12=($ $) 140 T ELT) (#4# 141 T ELT) (#13=($ $ $ $) 142 T ELT)) (|subHeight| (#5# 33 T ELT)) (|sub| (#4# 72 T ELT)) (|string| (#12# 114 T ELT)) (|slash| (#4# 129 T ELT)) (|semicolonSeparate| (#9# 61 T ELT)) (|scripts| (#11# 79 T ELT)) (|rspace| (($ #6# #6#) 55 T ELT)) (|root| (#12# 126 T ELT) (#4# 127 T ELT)) (|right| (#14=($ $ #6#) 43 T ELT) (#12# 46 T ELT)) (|rem| (#4# 97 T ELT)) (|rarrow| (#4# 132 T ELT)) (|quote| (#12# 115 T ELT)) (|quo| (#4# 98 T ELT)) (|prod| (#12# 143 T ELT) (#4# 144 T ELT) (#13# 145 T ELT)) (|print| ((#15=(|Void|) $) 10 T ELT)) (|prime| (#12# 118 T ELT) (#16=($ $ (|NonNegativeInteger|)) 122 T ELT)) (|presuper| (#4# 75 T ELT)) (|presub| (#4# 74 T ELT)) (|prefix| (#11# 110 T ELT)) (|postfix| (#4# 113 T ELT)) (|pile| (#9# 59 T ELT)) (|paren| (#12# 70 T ELT) (#9# 71 T ELT)) (|overlabel| (#4# 123 T ELT)) (|overbar| (#12# 116 T ELT)) (|over| (#4# 128 T ELT)) (|outputForm| (#8# 21 T ELT) (($ (|Symbol|)) 23 T ELT) (#17=($ #18=(|String|)) 30 T ELT) (($ (|DoubleFloat|)) 25 T ELT)) (|or| (#4# 101 T ELT)) (|not| (#12# 102 T ELT)) (|messagePrint| ((#15# #18#) 15 T ELT)) (|message| (#17# 14 T ELT)) (|matrix| (($ (|List| #10#)) 58 T ELT)) (|left| (#14# 42 T ELT) (#12# 45 T ELT)) (|latex| ((#18# $) NIL T ELT)) (|label| (#4# 131 T ELT)) (|int| (#12# 146 T ELT) (#4# 147 T ELT) (#13# 148 T ELT)) (|infix?| ((#3# $) 108 T ELT)) (|infix| (#11# 111 T ELT) (#13# 112 T ELT)) (|hspace| (#8# 39 T ELT)) (|height| (#5# 32 T ELT) (#7# 35 T ELT)) (|hconcat| (#4# 40 T ELT) (#9# 83 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| (#4# 99 T ELT)) (|empty| (($) 13 T ELT)) (|elt| (#11# 109 T ELT)) (|doubleFloatFormat| ((#18# #18#) 8 T ELT)) (|dot| (#12# 117 T ELT) (#16# 121 T ELT)) (|div| (#4# 96 T ELT)) (|differentiate| (#16# 139 T ELT)) (|commaSeparate| (#9# 60 T ELT)) (|coerce| (((|OutputForm|) $) 19 T ELT)) (|center| (#14# 41 T ELT) (#12# 44 T ELT)) (|bracket| (#12# 68 T ELT) (#9# 69 T ELT)) (|brace| (#12# 66 T ELT) (#9# 67 T ELT)) (|box| (#12# 124 T ELT)) (|blankSeparate| (#9# 65 T ELT)) (|binomial| (#4# 105 T ELT)) (|before?| #1#) (|assign| (#4# 130 T ELT)) (|and| (#4# 100 T ELT)) (SEGMENT (#4# 103 T ELT) (#12# 104 T ELT)) (>= (#4# 89 T ELT)) (> (#4# 87 T ELT)) (= (#2# 16 T ELT) (#4# 17 T ELT)) (<= (#4# 88 T ELT)) (< (#4# 86 T ELT)) (/ (#4# 94 T ELT)) (- (#4# 91 T ELT) (#12# 92 T ELT)) (+ (#4# 90 T ELT)) (** (#4# 95 T ELT)) (* (#4# 93 T ELT))) 
(((|OutputForm|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |print| (#1=(|Void|) $)) (SIGNATURE |message| #2=($ #3=(|String|))) (SIGNATURE |messagePrint| (#1# #3#)) (SIGNATURE |outputForm| #4=($ #5=(|Integer|))) (SIGNATURE |outputForm| ($ (|Symbol|))) (SIGNATURE |outputForm| #2#) (SIGNATURE |outputForm| ($ (|DoubleFloat|))) (SIGNATURE |empty| ($)) (SIGNATURE |doubleFloatFormat| (#3# #3#)) (SIGNATURE |width| #6=(#5# $)) (SIGNATURE |height| #6#) (SIGNATURE |width| #7=(#5#)) (SIGNATURE |height| #7#) (SIGNATURE |subHeight| #6#) (SIGNATURE |superHeight| #6#) (SIGNATURE |hspace| #4#) (SIGNATURE |vspace| #4#) (SIGNATURE |rspace| ($ #5# #5#)) (SIGNATURE |left| #8=($ $ #5#)) (SIGNATURE |right| #8#) (SIGNATURE |center| #8#) (SIGNATURE |left| #9=($ $)) (SIGNATURE |right| #9#) (SIGNATURE |center| #9#) (SIGNATURE |hconcat| #10=($ $ $)) (SIGNATURE |vconcat| #10#) (SIGNATURE |hconcat| #11=($ #12=(|List| $))) (SIGNATURE |vconcat| #11#) (SIGNATURE |prefix| #13=($ $ #12#)) (SIGNATURE |infix| #13#) (SIGNATURE |infix| #14=($ $ $ $)) (SIGNATURE |postfix| #10#) (SIGNATURE |infix?| ((|Boolean|) $)) (SIGNATURE |elt| #13#) (SIGNATURE |string| #9#) (SIGNATURE |label| #10#) (SIGNATURE |box| #9#) (SIGNATURE |matrix| ($ (|List| #12#))) (SIGNATURE |zag| #10#) (SIGNATURE |root| #9#) (SIGNATURE |root| #10#) (SIGNATURE |over| #10#) (SIGNATURE |slash| #10#) (SIGNATURE |assign| #10#) (SIGNATURE |rarrow| #10#) (SIGNATURE |differentiate| #15=($ $ (|NonNegativeInteger|))) (SIGNATURE |binomial| #10#) (SIGNATURE |sub| #10#) (SIGNATURE |super| #10#) (SIGNATURE |presub| #10#) (SIGNATURE |presuper| #10#) (SIGNATURE |scripts| #13#) (SIGNATURE |supersub| #13#) (SIGNATURE |quote| #9#) (SIGNATURE |dot| #9#) (SIGNATURE |dot| #15#) (SIGNATURE |prime| #9#) (SIGNATURE |prime| #15#) (SIGNATURE |overbar| #9#) (SIGNATURE |overlabel| #10#) (SIGNATURE |sum| #9#) (SIGNATURE |sum| #10#) (SIGNATURE |sum| #14#) (SIGNATURE |prod| #9#) (SIGNATURE |prod| #10#) (SIGNATURE |prod| #14#) (SIGNATURE |int| #9#) (SIGNATURE |int| #10#) (SIGNATURE |int| #14#) (SIGNATURE |brace| #9#) (SIGNATURE |brace| #11#) (SIGNATURE |bracket| #9#) (SIGNATURE |bracket| #11#) (SIGNATURE |paren| #9#) (SIGNATURE |paren| #11#) (SIGNATURE |pile| #11#) (SIGNATURE |commaSeparate| #11#) (SIGNATURE |semicolonSeparate| #11#) (SIGNATURE |blankSeparate| #11#) (SIGNATURE = #10#) (SIGNATURE ~= #10#) (SIGNATURE < #10#) (SIGNATURE > #10#) (SIGNATURE <= #10#) (SIGNATURE >= #10#) (SIGNATURE + #10#) (SIGNATURE - #10#) (SIGNATURE - #9#) (SIGNATURE * #10#) (SIGNATURE / #10#) (SIGNATURE ** #10#) (SIGNATURE |div| #10#) (SIGNATURE |rem| #10#) (SIGNATURE |quo| #10#) (SIGNATURE |exquo| #10#) (SIGNATURE |and| #10#) (SIGNATURE |or| #10#) (SIGNATURE |not| #9#) (SIGNATURE SEGMENT #10#) (SIGNATURE SEGMENT #9#)))) (T |OutputForm|)) 
((|print| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Void|)) #3=(|isDomain| *1 #4=(|OutputForm|)))) (|message| #5=(*1 *1 *2) #6=(AND (|isDomain| *2 #7=(|String|)) #3#)) (|messagePrint| (*1 *2 *3) (AND (|isDomain| *3 #7#) #2# #3#)) (|outputForm| #5# #8=(AND (|isDomain| *2 (|Integer|)) #3#)) (|outputForm| #5# (AND (|isDomain| *2 (|Symbol|)) #3#)) (|outputForm| #5# #6#) (|outputForm| #5# (AND (|isDomain| *2 (|DoubleFloat|)) #3#)) (|empty| (*1 *1) #3#) (|doubleFloatFormat| (*1 *2 *2) #6#) (|width| #1# #8#) (|height| #1# #8#) (|width| #9=(*1 *2) #8#) (|height| #9# #8#) (|subHeight| #1# #8#) (|superHeight| #1# #8#) (|hspace| #5# #8#) (|vspace| #5# #8#) (|rspace| (*1 *1 *2 *2) #8#) (|left| #10=(*1 *1 *1 *2) #8#) (|right| #10# #8#) (|center| #10# #8#) (|left| #11=(*1 *1 *1) #3#) (|right| #11# #3#) (|center| #11# #3#) (|hconcat| #12=(*1 *1 *1 *1) #3#) (|vconcat| #12# #3#) (|hconcat| #5# #13=(AND (|isDomain| *2 #14=(|List| #4#)) #3#)) (|vconcat| #5# #13#) (|prefix| #10# #13#) (|infix| #10# #13#) (|infix| #15=(*1 *1 *1 *1 *1) #3#) (|postfix| #12# #3#) (|infix?| #1# (AND (|isDomain| *2 (|Boolean|)) #3#)) (|elt| #10# #13#) (|string| #11# #3#) (|label| #12# #3#) (|box| #11# #3#) (|matrix| #5# (AND (|isDomain| *2 (|List| #14#)) #3#)) (|zag| #12# #3#) (|root| #11# #3#) (|root| #12# #3#) (|over| #12# #3#) (|slash| #12# #3#) (|assign| #12# #3#) (|rarrow| #12# #3#) (|differentiate| #10# #16=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3#)) (|binomial| #12# #3#) (|sub| #12# #3#) (|super| #12# #3#) (|presub| #12# #3#) (|presuper| #12# #3#) (|scripts| #10# #13#) (|supersub| #10# #13#) (|quote| #11# #3#) (|dot| #11# #3#) (|dot| #10# #16#) (|prime| #11# #3#) (|prime| #10# #16#) (|overbar| #11# #3#) (|overlabel| #12# #3#) (|sum| #11# #3#) (|sum| #12# #3#) (|sum| #15# #3#) (|prod| #11# #3#) (|prod| #12# #3#) (|prod| #15# #3#) (|int| #11# #3#) (|int| #12# #3#) (|int| #15# #3#) (|brace| #11# #3#) (|brace| #5# #13#) (|bracket| #11# #3#) (|bracket| #5# #13#) (|paren| #11# #3#) (|paren| #5# #13#) (|pile| #5# #13#) (|commaSeparate| #5# #13#) (|semicolonSeparate| #5# #13#) (|blankSeparate| #5# #13#) (= #12# #3#) (~= #12# #3#) (< #12# #3#) (> #12# #3#) (<= #12# #3#) (>= #12# #3#) (+ #12# #3#) (- #12# #3#) (- #11# #3#) (* #12# #3#) (/ #12# #3#) (** #12# #3#) (|div| #12# #3#) (|rem| #12# #3#) (|quo| #12# #3#) (|exquo| #12# #3#) (|and| #12# #3#) (|or| #12# #3#) (|not| #11# #3#) (SEGMENT #12# #3#) (SEGMENT #11# #3#)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|variable| (((|Union| $ "failed") #3=(|Symbol|)) 36 T ELT)) (|size| (((|NonNegativeInteger|)) 32 T ELT)) (|random| (#4=($) NIL T ELT)) (|min| #5=(($ $ $) NIL T ELT) #6=(#4# NIL T CONST)) (|max| #5# #6#) (|lookup| ((#7=(|PositiveInteger|) $) 29 T ELT)) (|latex| (((|String|) $) 43 T ELT)) (|index| (($ #7#) 28 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| ((#3# $) 13 T ELT) (((|InputForm|) $) 19 T ELT) (((|Pattern| (|Float|)) $) 26 T ELT) (((|Pattern| (|Integer|)) $) 22 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= (#2# 40 T ELT)) (<= #1#) (< (#2# 38 T ELT))) 
(((|OrderedVariableList| |#1|) (|Join| (|OrderedFinite|) (|ConvertibleTo| #1=(|Symbol|)) (|ConvertibleTo| (|InputForm|)) (|ConvertibleTo| (|Pattern| (|Float|))) (|ConvertibleTo| (|Pattern| (|Integer|))) (CATEGORY |domain| (SIGNATURE |variable| ((|Union| $ "failed") #1#)))) (|List| #1#)) (T |OrderedVariableList|)) 
((|variable| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|OrderedVariableList| *3)) (|ofType| *3 (|List| *2))))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|name| (((|Identifier|) $) 12 T ELT)) (|members| (((|List| (|FunctionDescriptor|)) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 22 T ELT)) (|before?| #1#) (= (#2# 17 T ELT))) 
(((|OverloadSet|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| ((|Identifier|) $)) (SIGNATURE |members| ((|List| (|FunctionDescriptor|)) $))))) (T |OverloadSet|)) 
((|name| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) #2=(|isDomain| *1 (|OverloadSet|)))) (|members| #1# (AND (|isDomain| *2 (|List| (|FunctionDescriptor|))) #2#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (#4=(#5=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| #6=(($) NIL T CONST)) (|recip| ((#5# $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #7=($)) NIL T ELT) (($ #8=(|Integer|)) NIL T ELT) (($ #9=(|Polynomial| |#1|)) NIL T ELT) ((#9# . #7#) NIL T ELT) (($ |#1|) NIL #10=(|has| |#1| (|CommutativeRing|)) ELT)) (|characteristic| ((#11=(|NonNegativeInteger|)) NIL T CONST)) (|changeWeightLevel| (((|Void|) #11#) NIL T ELT)) (|before?| #1#) (|annihilate?| #1#) (|Zero| #6#) (|One| #6#) (= #1#) (/ (#4# NIL (|has| |#1| (|Field|)) ELT)) (- (($ $) NIL T ELT) #12=(($ $ $) NIL T ELT)) (+ #12#) (** (($ $ #13=(|PositiveInteger|)) NIL T ELT) (($ $ #11#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #11# $) NIL T ELT) (($ #8# . #14=($)) NIL T ELT) #12# (($ |#1| . #14#) NIL #10# ELT) (($ $ |#1|) NIL #10# ELT))) 
(((|OrdinaryWeightedPolynomials| |#1| |#2| |#3| |#4|) (|Join| #1=(|Ring|) (|HomotopicTo| (|Polynomial| |#1|)) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |%noBranch|) (IF (|has| |#1| (|Field|)) (SIGNATURE / ((|Union| $ "failed") $ $)) |%noBranch|) (SIGNATURE |changeWeightLevel| ((|Void|) #2=(|NonNegativeInteger|))))) #1# (|List| (|Symbol|)) (|List| #2#) #2#) (T |OrdinaryWeightedPolynomials|)) 
((/ (*1 *1 *1 *1) (|partial| AND (|isDomain| *1 (|OrdinaryWeightedPolynomials| *2 *3 *4 *5)) (|ofCategory| *2 (|Field|)) (|ofCategory| *2 #1=(|Ring|)) (|ofType| *3 #2=(|List| (|Symbol|))) (|ofType| *4 (|List| #3=(|NonNegativeInteger|))) (|ofType| *5 #3#))) (|changeWeightLevel| (*1 *2 *3) (AND (|isDomain| *3 #3#) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|OrdinaryWeightedPolynomials| *4 *5 *6 *7)) (|ofCategory| *4 #1#) (|ofType| *5 #2#) (|ofType| *6 (|List| *3)) (|ofType| *7 *3)))) 
((|padecf| (((|Union| (|ContinuedFraction| |#3|) #1="failed") #2=(|NonNegativeInteger|) #2# |#2| |#2|) 38 T ELT)) (|pade| (((|Union| (|Fraction| |#3|) #1#) #2# #2# |#2| |#2|) 29 T ELT))) 
(((|PadeApproximants| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |pade| ((|Union| (|Fraction| |#3|) #1="failed") #2=(|NonNegativeInteger|) #2# |#2| |#2|)) (SIGNATURE |padecf| ((|Union| (|ContinuedFraction| |#3|) #1#) #2# #2# |#2| |#2|))) (|Field|) (|UnivariateTaylorSeriesCategory| |#1|) (|UnivariatePolynomialCategory| |#1|)) (T |PadeApproximants|)) 
((|padecf| #1=(*1 *2 *3 *3 *4 *4) (|partial| AND #2=(|isDomain| *3 (|NonNegativeInteger|)) #3=(|ofCategory| *5 (|Field|)) (|isDomain| *2 (|ContinuedFraction| *6)) #4=(|isDomain| *1 (|PadeApproximants| *5 *4 *6)) #5=(|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *5)) #6=(|ofCategory| *6 (|UnivariatePolynomialCategory| *5)))) (|pade| #1# (|partial| AND #2# #3# (|isDomain| *2 (|Fraction| *6)) #4# #5# #6#))) 
((|pade| ((#1=(|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") #2=(|NonNegativeInteger|) #2# #3=(|UnivariateTaylorSeries| |#1| |#2| |#3|)) 30 T ELT) ((#1# #2# #2# #3# #3#) 28 T ELT))) 
(((|PadeApproximantPackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |pade| (#1=(|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") #2=(|NonNegativeInteger|) #2# #3=(|UnivariateTaylorSeries| |#1| |#2| |#3|) #3#)) (SIGNATURE |pade| (#1# #2# #2# #3#))) (|Field|) (|Symbol|) |#1|) (T |PadeApproximantPackage|)) 
((|pade| (*1 *2 *3 *3 *4) #1=(|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) #1#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| #5=((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|sqrt| #8=(($ $ #9=(|Integer|)) NIL T ELT)) (|sizeLess?| #1#) (|sample| #10=(($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| #9#) #9#) NIL T ELT)) (|rem| #11=(($ $ $) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|quotientByP| #4#) (|quo| #11#) (|principalIdeal| (((|Record| (|:| |coef| #12=(|List| $)) #13=(|:| |generator| $)) #12#) NIL T ELT)) (|order| #14=((#15=(|NonNegativeInteger|) $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #12# #7#) #12# $) NIL T ELT)) (|modulus| ((#9#) NIL T ELT)) (|moduloP| ((#9# $) NIL T ELT)) (|lcm| #11# #16=(($ #12#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#17=(|SparseUnivariatePolynomial| $) #17# #17#) NIL T ELT)) (|gcd| #11# #16#) (|extendedEuclidean| (((|Record| #18=(|:| |coef1| $) #19=(|:| |coef2| $) #13#) $ $) NIL T ELT) (((|Union| (|Record| #18# #19#) #7#) $ $ $) NIL T ELT)) (|extend| #8#) (|exquo| #5#) (|expressIdealMember| (((|Maybe| #12#) #12# $) NIL T ELT)) (|euclideanSize| #14#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (((|Stream| #9#) $) NIL T ELT)) (|complete| #4#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #9#) NIL T ELT) #4#) (|characteristic| ((#15#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| ((#9# $ #9#) NIL T ELT)) (|annihilate?| #1#) (|Zero| #10#) (|One| #10#) (= #1#) (- #4# #11#) (+ #11#) (** (($ $ #20=(|PositiveInteger|)) NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #20# $) NIL T ELT) (($ #15# $) NIL T ELT) (($ #9# $) NIL T ELT) #11#)) 
(((|PAdicInteger| |#1|) (|PAdicIntegerCategory| |#1|) (|Integer|)) (T |PAdicInteger|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sqrt| (($ $ (|Integer|)) 78 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#4=($) 23 T CONST)) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 77 T ELT)) (|rem| (#5=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quotientByP| (($ $) 80 T ELT)) (|quo| (#5# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #6=(|List| $)) (|:| |generator| $)) #6#) 66 T ELT)) (|order| (((|NonNegativeInteger|) $) 85 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #7=(|List| $) #8="failed") #7# $) 68 T ELT)) (|modulus| (((|Integer|)) 82 T ELT)) (|moduloP| (((|Integer|) $) 81 T ELT)) (|lcm| (#9=($ $ $) 60 T ELT) (#10=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#11=(|SparseUnivariatePolynomial| $) #11# #11#) 58 T ELT)) (|gcd| (#9# 62 T ELT) (#10# 61 T ELT)) (|extendedEuclidean| (((|Record| #12=(|:| |coef1| $) #13=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #12# #13#) #8#) $ $ $) 69 T ELT)) (|extend| (($ $ (|Integer|)) 84 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #6#) #6# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|digits| (((|Stream| (|Integer|)) $) 86 T ELT)) (|complete| (($ $) 83 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|approximate| (((|Integer|) $ (|Integer|)) 79 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|PAdicInteger| |#1|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #11=((#12=(|Union| $ #13="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #14=(((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) NIL #16=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #18=(|List| #15#) #13#) #18# #15#) NIL #16# ELT)) (|sizeLess?| #1#) (|sign| (#19=(#20=(|Integer|) $) NIL #21=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #22=(#23=($) NIL T CONST)) (|retractIfCan| (((|Union| #7# . #24=(#13#)) . #25=($)) NIL T ELT) (((|Union| #26=(|Symbol|) . #24#) . #25#) NIL #27=(|has| #7# (|RetractableTo| #26#)) ELT) (((|Union| #28=(|Fraction| #20#) . #24#) . #25#) NIL #29=(|has| #7# (|RetractableTo| #20#)) ELT) (((|Union| #20# . #24#) . #25#) NIL #29# ELT)) (|retract| #30=(#6# NIL T ELT) ((#26# . #31=($)) NIL #27# ELT) ((#28# . #31#) NIL #29# ELT) (#19# NIL #29# ELT)) (|removeZeroes| #9# #32=(($ #20# $) NIL T ELT)) (|rem| #33=(#34=($ $ $) NIL T ELT)) (|reducedSystem| ((#35=(|Matrix| #20#) . #36=(#37=(|Matrix| $))) NIL #38=(|has| #7# (|LinearlyExplicitRingOver| #20#)) ELT) ((#39=(|Record| (|:| |mat| #35#) (|:| |vec| (|Vector| #20#))) . #40=(#37# #41=(|Vector| $))) NIL #38# ELT) ((#42=(|Record| (|:| |mat| #43=(|Matrix| #7#)) (|:| |vec| (|Vector| #7#))) . #40#) NIL T ELT) ((#43# . #36#) NIL T ELT)) (|recip| ((#12# $) NIL T ELT)) (|random| (#23# NIL #44=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #33#) (|principalIdeal| (((|Record| (|:| |coef| #45=(|List| $)) #46=(|:| |generator| $)) #45#) NIL T ELT)) (|prime?| #4#) (|positive?| #47=(#5# NIL #21# ELT)) (|patternMatch| ((#48=(|PatternMatchResult| #20# . #49=($)) $ #50=(|Pattern| #20#) #48#) NIL (|has| #7# (|PatternMatchable| #20#)) ELT) ((#51=(|PatternMatchResult| #52=(|Float|) . #49#) $ #53=(|Pattern| #52#) #51#) NIL (|has| #7# (|PatternMatchable| #52#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #30#) (|nextItem| (#54=((|Maybe| $) $) NIL #55=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #47#) (|multiEuclidean| (((|Union| #45# #13#) #45# $) NIL T ELT)) (|min| #56=(#34# NIL #57=(|has| #7# (|OrderedSet|)) ELT)) (|max| #56#) (|map| (($ #58=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| ((#35# . #59=(#41#)) NIL #38# ELT) ((#39# . #60=(#41# $)) NIL #38# ELT) ((#42# . #60#) NIL T ELT) ((#43# . #59#) NIL T ELT)) (|lcm| #33# #61=(($ #45#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#23# NIL #55# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#15# #15# #15#) NIL T ELT)) (|gcd| #33# #61#) (|fractionPart| (#10# NIL #8# ELT)) (|floor| #62=(#6# NIL #44# ELT)) (|factorSquareFreePolynomial| #14#) (|factorPolynomial| #14#) (|factor| #17#) (|extendedEuclidean| (((|Record| #63=(|:| |coef1| $) #64=(|:| |coef2| $) #46#) $ $) NIL T ELT) (((|Union| (|Record| #63# #64#) #13#) $ $ $) NIL T ELT)) (|exquo| #11#) (|expressIdealMember| (((|Maybe| #45#) #45# $) NIL T ELT)) (|eval| (($ $ #65=(|List| #7#) #65#) NIL #66=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #66# ELT) (($ $ #67=(|Equation| #7#)) NIL #66# ELT) (($ $ (|List| #67#)) NIL #66# ELT) (($ $ #68=(|List| #26#) #65#) NIL #69=(|has| #7# (|InnerEvalable| #26# #7#)) ELT) (($ $ #26# #7#) NIL #69# ELT)) (|euclideanSize| ((#70=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#71=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #72=(($ $ #58#) NIL T ELT) #73=(($ $ #58# #70#) NIL T ELT) #74=(($ $ #26#) NIL #75=(|has| #7# (|PartialDifferentialSpace| #26#)) ELT) #76=(($ $ #68#) NIL #75# ELT) #77=(($ $ #26# #70#) NIL #75# ELT) #78=(($ $ #68# (|List| #70#)) NIL #75# ELT) #79=(#10# NIL #80=(|has| #7# (|DifferentialSpace|)) ELT) #81=(#82=($ $ #70#) NIL #80# ELT)) (|denominator| #9#) (|denom| #30#) (|convert| ((#50# . #83=($)) NIL (|has| #7# (|ConvertibleTo| #50#)) ELT) ((#53# . #83#) NIL (|has| #7# (|ConvertibleTo| #53#)) ELT) ((#84=(|InputForm|) . #83#) NIL (|has| #7# (|ConvertibleTo| #84#)) ELT) ((#52# . #83#) NIL #85=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #83#) NIL #85# ELT)) (|continuedFraction| (((|ContinuedFraction| #28#) $) NIL T ELT)) (|conditionP| (((|Union| #41# #13#) #37#) NIL #86=(AND (|has| $ #87=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) #9# (($ #28#) NIL T ELT) (($ #7#) NIL T ELT) (($ #26#) NIL #27# ELT)) (|charthRoot| (#54# NIL (OR #86# (|has| #7# #87#)) ELT)) (|characteristic| ((#70#) NIL T CONST)) (|ceiling| #62#) (|before?| #1#) (|associates?| #1#) (|approximate| ((#28# $ #20#) NIL T ELT)) (|annihilate?| #1#) (|abs| (#10# NIL #21# ELT)) (|Zero| #22#) (|One| #22#) (D #72# #73# #74# #76# #77# #78# #79# #81#) (>= #88=(#2# NIL #57# ELT)) (> #88#) (= #1#) (<= #88#) (< #88#) (/ #33# (($ #7# #7#) NIL T ELT)) (- #9# #33#) (+ #33#) (** (($ $ #89=(|PositiveInteger|)) NIL T ELT) (#82# NIL T ELT) (($ $ #20#) NIL T ELT)) (* (($ #89# $) NIL T ELT) (($ #70# $) NIL T ELT) #32# #33# (($ $ #28#) NIL T ELT) (($ #28# . #90=($)) NIL T ELT) (($ #7# . #90#) NIL T ELT) (#71# NIL T ELT))) 
(((|PAdicRational| |#1|) (|Join| (|QuotientFieldCategory| (|PAdicInteger| |#1|)) (CATEGORY |domain| (SIGNATURE |approximate| (#1=(|Fraction| #2=(|Integer|)) $ #2#)) (SIGNATURE |continuedFraction| ((|ContinuedFraction| #1#) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ #2# $)))) #2#) (T |PAdicRational|)) 
((|approximate| (*1 *2 *1 *3) (AND (|isDomain| *2 #1=(|Fraction| #2=(|Integer|))) (|isDomain| *1 (|PAdicRational| *4)) (|ofType| *4 *3) (|isDomain| *3 #2#))) (|continuedFraction| (*1 *2 *1) (AND (|isDomain| *2 (|ContinuedFraction| #1#)) #3=(|isDomain| *1 (|PAdicRational| *3)) (|ofType| *3 #2#))) (|removeZeroes| (*1 *1 *1) (AND (|isDomain| *1 (|PAdicRational| *2)) (|ofType| *2 #2#))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 #2#) #3# (|ofType| *3 *2)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(|#2| $) NIL #7=(|has| |#2| (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #8=(#9=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #10=((#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #13=(((|Factored| #14=(|SparseUnivariatePolynomial| $)) #14#) NIL #15=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #8#) (|squareFree| #16=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #17=(|List| #14#) #12#) #17# #14#) NIL #15# ELT)) (|sizeLess?| #1#) (|sign| (#18=(#19=(|Integer|) $) NIL #20=(|has| |#2| (|OrderedIntegralDomain|)) ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #22=(#12#)) . #23=($)) NIL T ELT) (((|Union| #24=(|Symbol|) . #22#) . #23#) NIL #25=(|has| |#2| (|RetractableTo| #24#)) ELT) (((|Union| #26=(|Fraction| #19#) . #22#) . #23#) NIL #27=(|has| |#2| (|RetractableTo| #19#)) ELT) (((|Union| #19# . #22#) . #23#) NIL #27# ELT)) (|retract| #28=(#6# NIL T ELT) ((#24# . #29=($)) NIL #25# ELT) ((#26# . #29#) NIL #27# ELT) (#18# NIL #27# ELT)) (|removeZeroes| (#9# 35 T ELT) (#30=($ #19# $) 38 T ELT)) (|rem| #31=(#32=($ $ $) NIL T ELT)) (|reducedSystem| ((#33=(|Matrix| #19#) . #34=(#35=(|Matrix| $))) NIL #36=(|has| |#2| (|LinearlyExplicitRingOver| #19#)) ELT) ((#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #19#))) . #38=(#35# #39=(|Vector| $))) NIL #36# ELT) ((#40=(|Record| (|:| |mat| #41=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #38#) NIL T ELT) ((#41# . #34#) NIL T ELT)) (|recip| ((#11# $) 64 T ELT)) (|random| (#21# NIL #42=(|has| |#2| (|IntegerNumberSystem|)) ELT)) (|quo| #31#) (|principalIdeal| (((|Record| (|:| |coef| #43=(|List| $)) #44=(|:| |generator| $)) #43#) NIL T ELT)) (|prime?| #4#) (|positive?| #45=(#5# NIL #20# ELT)) (|patternMatch| ((#46=(|PatternMatchResult| #19# . #47=($)) $ #48=(|Pattern| #19#) #46#) NIL (|has| |#2| (|PatternMatchable| #19#)) ELT) ((#49=(|PatternMatchResult| #50=(|Float|) . #47#) $ #51=(|Pattern| #50#) #49#) NIL (|has| |#2| (|PatternMatchable| #50#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #8#) (|numer| #28#) (|nextItem| (#52=((|Maybe| $) $) NIL #53=(|has| |#2| (|StepThrough|)) ELT)) (|negative?| #45#) (|multiEuclidean| (((|Union| #43# #12#) #43# $) NIL T ELT)) (|min| #54=(#32# NIL #55=(|has| |#2| (|OrderedSet|)) ELT)) (|max| #54#) (|map| (($ #56=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|leftReducedSystem| ((#33# . #57=(#39#)) NIL #36# ELT) ((#37# . #58=(#39# $)) NIL #36# ELT) ((#40# . #58#) NIL T ELT) ((#41# . #57#) NIL T ELT)) (|lcm| #31# #59=(($ #43#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#9# 60 T ELT)) (|init| (#21# NIL #53# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#14# #14# #14#) NIL T ELT)) (|gcd| #31# #59#) (|fractionPart| (#9# NIL #7# ELT)) (|floor| #60=(#6# NIL #42# ELT)) (|factorSquareFreePolynomial| #13#) (|factorPolynomial| #13#) (|factor| #16#) (|extendedEuclidean| (((|Record| #61=(|:| |coef1| $) #62=(|:| |coef2| $) #44#) $ $) NIL T ELT) (((|Union| (|Record| #61# #62#) #12#) $ $ $) NIL T ELT)) (|exquo| #10#) (|expressIdealMember| (((|Maybe| #43#) #43# $) NIL T ELT)) (|eval| (($ $ #63=(|List| |#2|) #63#) NIL #64=(|has| |#2| (|Evalable| |#2|)) ELT) (($ $ |#2| |#2|) NIL #64# ELT) (($ $ #65=(|Equation| |#2|)) NIL #64# ELT) (($ $ (|List| #65#)) NIL #64# ELT) (($ $ #66=(|List| #24#) #63#) NIL #67=(|has| |#2| (|InnerEvalable| #24# |#2|)) ELT) (($ $ #24# |#2|) NIL #67# ELT)) (|euclideanSize| ((#68=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#69=($ $ |#2|) NIL (|has| |#2| (|Eltable| |#2| |#2|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #70=(($ $ #56#) NIL T ELT) #71=(($ $ #56# #68#) NIL T ELT) #72=(($ $ #24#) NIL #73=(|has| |#2| (|PartialDifferentialSpace| #24#)) ELT) #74=(($ $ #66#) NIL #73# ELT) #75=(($ $ #24# #68#) NIL #73# ELT) #76=(($ $ #66# (|List| #68#)) NIL #73# ELT) #77=(#9# NIL #78=(|has| |#2| (|DifferentialSpace|)) ELT) #79=(#80=($ $ #68#) NIL #78# ELT)) (|denominator| #8#) (|denom| #28#) (|convert| ((#48# . #81=($)) NIL (|has| |#2| (|ConvertibleTo| #48#)) ELT) ((#51# . #81#) NIL (|has| |#2| (|ConvertibleTo| #51#)) ELT) ((#82=(|InputForm|) . #81#) NIL (|has| |#2| (|ConvertibleTo| #82#)) ELT) ((#50# . #81#) NIL #83=(|has| |#2| (|RealConstant|)) ELT) (((|DoubleFloat|) . #81#) NIL #83# ELT)) (|continuedFraction| (((|ContinuedFraction| #26#) $) 78 T ELT)) (|conditionP| (((|Union| #39# #12#) #35#) NIL #84=(AND (|has| $ #85=(|CharacteristicNonZero|)) #15#) ELT)) (|coerce| (((|OutputForm|) $) 105 T ELT) (($ #19#) 20 T ELT) #8# (($ #26#) 25 T ELT) (($ |#2|) 19 T ELT) (($ #24#) NIL #25# ELT)) (|charthRoot| (#52# NIL (OR #84# (|has| |#2| #85#)) ELT)) (|characteristic| ((#68#) NIL T CONST)) (|ceiling| #60#) (|before?| #1#) (|associates?| #1#) (|approximate| ((#26# $ #19#) 71 T ELT)) (|annihilate?| #1#) (|abs| (#9# NIL #20# ELT)) (|Zero| (#21# 15 T CONST)) (|One| (#21# 17 T CONST)) (D #70# #71# #72# #74# #75# #76# #77# #79#) (>= #86=(#2# NIL #55# ELT)) (> #86#) (= (#2# 46 T ELT)) (<= #86#) (< #86#) (/ (#32# 24 T ELT) (($ |#2| |#2|) 65 T ELT)) (- (#9# 50 T ELT) (#32# 52 T ELT)) (+ (#32# 48 T ELT)) (** (($ $ #87=(|PositiveInteger|)) NIL T ELT) (#80# NIL T ELT) (($ $ #19#) 61 T ELT)) (* (($ #87# $) NIL T ELT) (($ #68# $) NIL T ELT) (#30# 53 T ELT) (#32# 55 T ELT) (($ $ #26#) NIL T ELT) (($ #26# $) NIL T ELT) (($ |#2| $) 66 T ELT) (#69# NIL T ELT))) 
(((|PAdicRationalConstructor| |#1| |#2|) (|Join| (|QuotientFieldCategory| |#2|) (CATEGORY |domain| (SIGNATURE |approximate| (#1=(|Fraction| #2=(|Integer|)) $ #2#)) (SIGNATURE |continuedFraction| ((|ContinuedFraction| #1#) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ #2# $)))) #2# (|PAdicIntegerCategory| |#1|)) (T |PAdicRationalConstructor|)) 
((|approximate| (*1 *2 *1 *3) (AND (|ofType| *4 *3) (|isDomain| *2 #1=(|Fraction| #2=(|Integer|))) (|isDomain| *1 (|PAdicRationalConstructor| *4 *5)) (|isDomain| *3 #2#) (|ofCategory| *5 (|PAdicIntegerCategory| *4)))) (|continuedFraction| (*1 *2 *1) (AND (|ofType| *3 #2#) (|isDomain| *2 (|ContinuedFraction| #1#)) #3=(|isDomain| *1 (|PAdicRationalConstructor| *3 *4)) #4=(|ofCategory| *4 (|PAdicIntegerCategory| *3)))) (|removeZeroes| (*1 *1 *1) (AND (|ofType| *2 #2#) (|isDomain| *1 (|PAdicRationalConstructor| *2 *3)) (|ofCategory| *3 (|PAdicIntegerCategory| *2)))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 #2#) (|ofType| *3 *2) #3# #4#))) 
((~= #1=(#2=((|Boolean|) $ $) NIL #3=(AND (|has| |#1| #4=(|SetCategory|)) (|has| |#2| #4#)) ELT)) (|second| ((|#2| $) 12 T ELT)) (|pair| (#5=($ |#1| |#2|) 9 T ELT)) (|latex| (((|String|) $) NIL #3# ELT)) (|hash| (((|SingleInteger|) $) NIL #3# ELT)) (|first| ((|#1| $) 11 T ELT)) (|construct| (#5# 10 T ELT)) (|coerce| ((#6=(|OutputForm|) $) 18 (OR (AND (|has| |#1| #7=(|CoercibleTo| #6#)) (|has| |#2| #7#)) #3#) ELT)) (|before?| #1#) (= (#2# 23 #3# ELT))) 
(((|Pair| |#1| |#2|) (|Join| #1=(|Type|) (CATEGORY |domain| (IF (|has| |#1| #2=(|CoercibleTo| (|OutputForm|))) (IF (|has| |#2| #2#) (ATTRIBUTE #2#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #3=(|SetCategory|)) (IF (|has| |#2| #3#) (ATTRIBUTE #3#) |%noBranch|) |%noBranch|) (SIGNATURE |pair| #4=($ |#1| |#2|)) (SIGNATURE |construct| #4#) (SIGNATURE |first| (|#1| $)) (SIGNATURE |second| (|#2| $)))) #1# #1#) (T |Pair|)) 
((|pair| #1=(*1 *1 *2 *3) #2=(AND #3=(|isDomain| *1 (|Pair| *2 *3)) #4=(|ofCategory| *2 #5=(|Type|)) #6=(|ofCategory| *3 #5#))) (|construct| #1# #2#) (|first| #7=(*1 *2 *1) (AND #4# #3# #6#)) (|second| #7# (AND #4# (|isDomain| *1 (|Pair| *3 *2)) #6#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|shade| (((|Integer|) $) 16 T ELT)) (|pastel| (#2=($ #3=(|Color|)) 13 T ELT)) (|light| (#2# 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hue| ((#3# $) 15 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dim| (#2# 11 T ELT)) (|dark| (#2# 10 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (#2# 17 T ELT)) (|bright| (#2# 12 T ELT)) (|before?| #1#) (= #1#)) 
(((|Palette|) (|Join| (|SetCategory|) (|CoercibleFrom| #1=(|Color|)) (CATEGORY |domain| (SIGNATURE |dark| #2=($ #1#)) (SIGNATURE |dim| #2#) (SIGNATURE |bright| #2#) (SIGNATURE |pastel| #2#) (SIGNATURE |light| #2#) (SIGNATURE |hue| (#1# $)) (SIGNATURE |shade| ((|Integer|) $))))) (T |Palette|)) 
((|dark| #1=(*1 *1 *2) #2=(AND (|isDomain| *2 (|Color|)) #3=(|isDomain| *1 (|Palette|)))) (|dim| #1# #2#) (|bright| #1# #2#) (|pastel| #1# #2#) (|light| #1# #2#) (|hue| #4=(*1 *2 *1) #2#) (|shade| #4# (AND (|isDomain| *2 (|Integer|)) #3#))) 
((|coerce| ((#1=(|Expression| (|Integer|)) (|Fraction| #2=(|Polynomial| (|AlgebraicNumber|)))) 23 T ELT) ((#1# #2#) 18 T ELT))) 
(((|PolynomialAN2Expression|) (CATEGORY |package| (SIGNATURE |coerce| (#1=(|Expression| (|Integer|)) #2=(|Polynomial| (|AlgebraicNumber|)))) (SIGNATURE |coerce| (#1# (|Fraction| #2#))))) (T |PolynomialAN2Expression|)) 
((|coerce| #1=(*1 *2 *3) (AND (|isDomain| *3 (|Fraction| #2=(|Polynomial| (|AlgebraicNumber|)))) #3=(|isDomain| *2 (|Expression| (|Integer|))) #4=(|isDomain| *1 (|PolynomialAN2Expression|)))) (|coerce| #1# (AND (|isDomain| *3 #2#) #3# #4#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|latex| (#4=(#5=(|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #6=(|Syntax|)) NIL T ELT) ((#6# $) NIL T ELT)) (|case| ((#3# $ (|[\|\|]| #7=(|Identifier|))) 9 T ELT) ((#3# $ (|[\|\|]| #5#)) 13 T ELT)) (|before?| #1#) (|autoCoerce| ((#7# $) 10 T ELT) (#4# 14 T ELT)) (= (#2# 15 T ELT))) 
(((|ParameterAst|) (|Join| (|SpadSyntaxCategory|) (|UnionType|) (CATEGORY |domain| (SIGNATURE |case| (#1=(|Boolean|) $ (|[\|\|]| #2=(|Identifier|)))) (SIGNATURE |autoCoerce| (#2# $)) (SIGNATURE |case| (#1# $ (|[\|\|]| #3=(|String|)))) (SIGNATURE |autoCoerce| (#3# $))))) (T |ParameterAst|)) 
((|case| #1=(*1 *2 *1 *3) (AND (|isDomain| *3 (|[\|\|]| #2=(|Identifier|))) #3=(|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|ParameterAst|)))) (|autoCoerce| #5=(*1 *2 *1) (AND (|isDomain| *2 #2#) #4#)) (|case| #1# (AND (|isDomain| *3 (|[\|\|]| #6=(|String|))) #3# #4#)) (|autoCoerce| #5# (AND (|isDomain| *2 #6#) #4#))) 
((|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) 15 T ELT))) 
(((|ParametricPlaneCurveFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)))) #1=(|Type|) #1#) (T |ParametricPlaneCurveFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|ParametricPlaneCurve| *5)) (|ofCategory| *5 #1=(|Type|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|ParametricPlaneCurve| *6)) (|isDomain| *1 (|ParametricPlaneCurveFunctions2| *5 *6))))) 
((|curve| (($ |#1| |#1|) 8 T ELT)) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) 15 T ELT))) 
(((|ParametricPlaneCurve| |#1|) (CATEGORY |domain| (SIGNATURE |curve| ($ |#1| |#1|)) (SIGNATURE |coordinate| (|#1| $ (|NonNegativeInteger|)))) (|Type|)) (T |ParametricPlaneCurve|)) 
((|coordinate| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) #1=(|isDomain| *1 (|ParametricPlaneCurve| *2)) #2=(|ofCategory| *2 (|Type|)))) (|curve| (*1 *1 *2 *2) (AND #1# #2#))) 
((|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) 15 T ELT))) 
(((|ParametricSpaceCurveFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)))) #1=(|Type|) #1#) (T |ParametricSpaceCurveFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|ParametricSpaceCurve| *5)) (|ofCategory| *5 #1=(|Type|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|ParametricSpaceCurve| *6)) (|isDomain| *1 (|ParametricSpaceCurveFunctions2| *5 *6))))) 
((|curve| (($ |#1| |#1| |#1|) 8 T ELT)) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) 15 T ELT))) 
(((|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|)) #1=(|isDomain| *1 (|ParametricSpaceCurve| *2)) #2=(|ofCategory| *2 (|Type|)))) (|curve| (*1 *1 *2 *2 *2) (AND #1# #2#))) 
((|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) 9 T ELT))) 
(((|Parser|) (CATEGORY |package| (SIGNATURE |getSyntaxFormsFromFile| ((|List| (|Syntax|)) (|String|))))) (T |Parser|)) 
((|getSyntaxFormsFromFile| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|List| (|Syntax|))) (|isDomain| *1 (|Parser|))))) 
((|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) 15 T ELT))) 
(((|ParametricSurfaceFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)))) #1=(|Type|) #1#) (T |ParametricSurfaceFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|ParametricSurface| *5)) (|ofCategory| *5 #1=(|Type|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|ParametricSurface| *6)) (|isDomain| *1 (|ParametricSurfaceFunctions2| *5 *6))))) 
((|surface| (($ |#1| |#1| |#1|) 8 T ELT)) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) 15 T ELT))) 
(((|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|)) #1=(|isDomain| *1 (|ParametricSurface| *2)) #2=(|ofCategory| *2 (|Type|)))) (|surface| (*1 *1 *2 *2 *2) (AND #1# #2#))) 
((|shufflein| ((#1=(|Stream| #2=(|List| #3=(|Integer|))) #2# #1#) 41 T ELT)) (|shuffle| (#4=(#1# #2# #2#) 31 T ELT)) (|sequences| ((#1# #2#) 53 T ELT) (#4# 50 T ELT)) (|permutations| ((#1# #3#) 55 T ELT)) (|conjugates| ((#5=(|Stream| #6=(|List| (|PositiveInteger|))) #5#) 22 T ELT)) (|conjugate| ((#6# #6#) 18 T ELT))) 
(((|PartitionsAndPermutations|) (CATEGORY |package| (SIGNATURE |conjugate| (#1=(|List| (|PositiveInteger|)) #1#)) (SIGNATURE |conjugates| (#2=(|Stream| #1#) #2#)) (SIGNATURE |shuffle| #3=(#4=(|Stream| #5=(|List| #6=(|Integer|))) #5# #5#)) (SIGNATURE |shufflein| (#4# #5# #4#)) (SIGNATURE |sequences| #3#) (SIGNATURE |sequences| (#4# #5#)) (SIGNATURE |permutations| (#4# #6#)))) (T |PartitionsAndPermutations|)) 
((|permutations| #1=(*1 *2 *3) (AND #2=(|isDomain| *2 (|Stream| #3=(|List| #4=(|Integer|)))) #5=(|isDomain| *1 (|PartitionsAndPermutations|)) (|isDomain| *3 #4#))) (|sequences| #1# #6=(AND #2# #5# #7=(|isDomain| *3 #3#))) (|sequences| #8=(*1 *2 *3 *3) #6#) (|shufflein| (*1 *2 *3 *2) (AND #2# #7# #5#)) (|shuffle| #8# #6#) (|conjugates| #9=(*1 *2 *2) (AND (|isDomain| *2 (|Stream| #10=(|List| (|PositiveInteger|)))) #5#)) (|conjugate| #9# (AND (|isDomain| *2 #10#) #5#))) 
((|convert| (((|Pattern| (|Float|)) . #1=($)) 9 (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ELT) (((|Pattern| (|Integer|)) . #1#) 8 (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ELT))) 
(((|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|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|new| (#4=($) 14 T ELT)) (|makeResult| (($ #5=(|PatternMatchResult| |#1| |#2|) #6=(|PatternMatchResult| |#1| |#3|)) 28 T ELT)) (|lists| ((#6# $) 16 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|failed?| ((#3# $) 22 T ELT)) (|failed| (#4# 19 T ELT)) (|coerce| (((|OutputForm|) $) 31 T ELT)) (|before?| #1#) (|atoms| ((#5# $) 15 T ELT)) (= (#2# 26 T ELT))) 
(((|PatternMatchListResult| |#1| |#2| |#3|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (SIGNATURE |failed?| ((|Boolean|) $)) (SIGNATURE |failed| #2=($)) (SIGNATURE |new| #2#) (SIGNATURE |makeResult| ($ #3=(|PatternMatchResult| |#1| |#2|) #4=(|PatternMatchResult| |#1| |#3|))) (SIGNATURE |atoms| (#3# $)) (SIGNATURE |lists| (#4# $)))) #1# #1# (|ListAggregate| |#2|)) (T |PatternMatchListResult|)) 
((|failed?| #1=(*1 *2 *1) (AND #2=(|ofCategory| *4 #3=(|SetCategory|)) (|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|PatternMatchListResult| *3 *4 *5)) #5=(|ofCategory| *3 #3#) #6=(|ofCategory| *5 (|ListAggregate| *4)))) (|failed| #7=(*1 *1) #8=(AND #5# (|isDomain| *1 (|PatternMatchListResult| *2 *3 *4)) (|ofCategory| *2 #3#) (|ofCategory| *4 (|ListAggregate| *3)))) (|new| #7# #8#) (|makeResult| (*1 *1 *2 *3) (AND (|isDomain| *2 (|PatternMatchResult| *4 *5)) (|isDomain| *3 (|PatternMatchResult| *4 *6)) #2# (|ofCategory| *5 #3#) (|ofCategory| *6 (|ListAggregate| *5)) (|isDomain| *1 (|PatternMatchListResult| *4 *5 *6)))) (|atoms| #1# (AND #2# (|isDomain| *2 (|PatternMatchResult| *3 *4)) #4# #5# #6#)) (|lists| #1# (AND #2# (|isDomain| *2 (|PatternMatchResult| *3 *5)) #4# #5# #6#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) 17 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|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) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|is?| ((#1=(|Boolean|) #2=(|List| |#2|) |#3|) 23 T ELT) ((#1# |#2| |#3|) 18 T ELT)) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) 45 (AND #3=(|not| #4=(|has| |#2| (|RetractableTo| (|Symbol|)))) (|not| #5=(|has| |#2| (|Ring|)))) ELT) (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) 44 (AND #5# #3#) ELT) (((|List| (|Equation| |#2|)) |#2| |#3|) 36 #4# ELT) (((|PatternMatchListResult| |#1| |#2| #2#) #2# |#3|) 21 T ELT))) 
(((|PatternMatch| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |is?| (#1=(|Boolean|) |#2| |#3|)) (SIGNATURE |is?| (#1# #2=(|List| |#2|) |#3|)) (SIGNATURE |Is| ((|PatternMatchListResult| |#1| |#2| #2#) #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=(*1 *2 *3 *4) (AND #2=(|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|PatternMatchResult| *5 *3)) #3=(|isDomain| *1 (|PatternMatch| *5 *3 *4)) #4=(|not| #5=(|ofCategory| *3 (|RetractableTo| (|Symbol|)))) (|not| #6=(|ofCategory| *3 (|Ring|))) #7=(|ofCategory| *3 #8=(|PatternMatchable| *5)) #9=(|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5))))) (|Is| #1# (AND #2# (|isDomain| *2 (|List| (|Equation| (|Polynomial| *3)))) #3# #6# #4# #7# #9#)) (|Is| #1# (AND #2# (|isDomain| *2 (|List| (|Equation| *3))) #3# #5# #7# #9#)) (|Is| #1# (AND #2# #10=(|ofCategory| *6 #8#) (|isDomain| *2 (|PatternMatchListResult| *5 *6 #11=(|List| *6))) #12=(|isDomain| *1 (|PatternMatch| *5 *6 *4)) #13=(|isDomain| *3 #11#) #9#)) (|is?| #1# (AND #13# #10# #2# #14=(|isDomain| *2 (|Boolean|)) #12# #9#)) (|is?| #1# (AND #2# #14# #3# #7# #9#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|union| (($ $ $) 40 T ELT)) (|satisfy?| (((|Union| #3# #4="failed") $ #5=(|Pattern| |#1|)) 37 T ELT)) (|new| (#6=($) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|insertMatch| (#7=($ #5# |#2| $) 20 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|getMatch| (((|Union| |#2| #4#) #5# $) 51 T ELT)) (|failed?| ((#3# $) 15 T ELT)) (|failed| (#6# 13 T ELT)) (|destruct| ((#8=(|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) 25 T ELT)) (|construct| (($ #8#) 23 T ELT)) (|coerce| (((|OutputForm|) $) 45 T ELT)) (|before?| #1#) (|addMatchRestricted| (($ #5# |#2| $ |#2|) 49 T ELT)) (|addMatch| (#7# 48 T ELT)) (= (#2# 42 T ELT))) 
(((|PatternMatchResult| |#1| |#2|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (SIGNATURE |failed?| (#2=(|Boolean|) $)) (SIGNATURE |failed| #3=($)) (SIGNATURE |new| #3#) (SIGNATURE |union| ($ $ $)) (SIGNATURE |getMatch| ((|Union| |#2| #4="failed") #5=(|Pattern| |#1|) $)) (SIGNATURE |addMatch| #6=($ #5# |#2| $)) (SIGNATURE |insertMatch| #6#) (SIGNATURE |addMatchRestricted| ($ #5# |#2| $ |#2|)) (SIGNATURE |destruct| (#7=(|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $)) (SIGNATURE |construct| ($ #7#)) (SIGNATURE |satisfy?| ((|Union| #2# #4#) $ #5#)))) #1# #1#) (T |PatternMatchResult|)) 
((|failed?| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Boolean|)) #3=(|isDomain| *1 (|PatternMatchResult| *3 *4)) #4=(|ofCategory| *3 #5=(|SetCategory|)) #6=(|ofCategory| *4 #5#))) (|failed| #7=(*1 *1) #8=(AND (|isDomain| *1 (|PatternMatchResult| *2 *3)) #9=(|ofCategory| *2 #5#) #4#)) (|new| #7# #8#) (|union| (*1 *1 *1 *1) #8#) (|getMatch| (*1 *2 *3 *1) (|partial| AND #10=(|isDomain| *3 #11=(|Pattern| *4)) #6# #9# (|isDomain| *1 (|PatternMatchResult| *4 *2)))) (|addMatch| #12=(*1 *1 *2 *3 *1) #13=(AND (|isDomain| *2 #11#) #6# (|isDomain| *1 (|PatternMatchResult| *4 *3)) #4#)) (|insertMatch| #12# #13#) (|addMatchRestricted| (*1 *1 *2 *3 *1 *3) #13#) (|destruct| #1# (AND #14=(|isDomain| *2 (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| *4)))) #3# #4# #6#)) (|construct| (*1 *1 *2) (AND #14# #6# #3# #4#)) (|satisfy?| (*1 *2 *1 *3) (|partial| AND #10# #6# #2# (|isDomain| *1 (|PatternMatchResult| *4 *5)) (|ofCategory| *5 #5#)))) 
((|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) 22 T ELT))) 
(((|PatternMatchResultFunctions2| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)))) #1=(|SetCategory|) #1# #1#) (T |PatternMatchResultFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *6)) (|isDomain| *4 (|PatternMatchResult| *5 *6)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 #1#) (|ofCategory| *7 #1#) (|isDomain| *2 (|PatternMatchResult| *5 *7)) (|isDomain| *1 (|PatternMatchResultFunctions2| *5 *6 *7))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|withPredicates| (#4=($ $ #5=(|List| #6=(|Any|))) 74 T ELT)) (|variables| ((#7=(|List| $) $) 139 T ELT)) (|topPredicate| (((|Record| (|:| |var| #8=(|List| #9=(|Symbol|))) (|:| |pred| #6#)) $) 30 T ELT)) (|symbol?| (#10=(#3# $) 35 T ELT)) (|setTopPredicate| (($ $ #8# #6#) 31 T ELT)) (|setPredicates| (#4# 73 T ELT)) (|retractIfCan| (((|Union| |#1| . #11=(#12="failed")) $) 71 T ELT) (((|Union| #9# . #11#) $) 167 T ELT)) (|retract| ((|#1| $) 68 T ELT) ((#9# $) NIL T ELT)) (|resetBadValues| (#13=($ $) 126 T ELT)) (|quoted?| (#10# 55 T ELT)) (|predicates| (#14=(#5# $) 50 T ELT)) (|patternVariable| (($ #9# #3# #3# #3#) 75 T ELT)) (|optpair| ((#15=(|Union| #7# #12#) #7#) 82 T ELT)) (|optional?| (#10# 58 T ELT)) (|multiple?| (#10# 57 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| (#16=(#15# $) 41 T ELT)) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) #12#) $) 48 T ELT)) (|isPower| (((|Union| (|Record| #17=(|:| |val| $) (|:| |exponent| $)) #12#) $) 97 T ELT)) (|isPlus| (#16# 40 T ELT)) (|isOp| ((#15# $ #18=(|BasicOperator|)) 124 T ELT) (((|Union| (|Record| (|:| |op| #18#) (|:| |arg| #7#)) #12#) $) 107 T ELT)) (|isList| (#16# 42 T ELT)) (|isExpt| (((|Union| (|Record| #17# (|:| |exponent| #19=(|NonNegativeInteger|))) #12#) $) 45 T ELT)) (|inR?| (#10# 34 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|hasTopPredicate?| (#10# 28 T ELT)) (|hasPredicate?| (#10# 52 T ELT)) (|getBadValues| (#14# 130 T ELT)) (|generic?| (#10# 56 T ELT)) (|elt| (($ #18# #7#) 104 T ELT)) (|depth| ((#19# $) 33 T ELT)) (|copy| (#13# 72 T ELT)) (|convert| (($ #7#) 69 T ELT)) (|constant?| (#10# 32 T ELT)) (|coerce| (((|OutputForm|) $) 63 T ELT) (($ |#1|) 23 T ELT) (($ #9#) 76 T ELT)) (|before?| #1#) (|addBadValue| (($ $ #6#) 129 T ELT)) (|Zero| (#20=($) 103 T CONST)) (|One| (#20# 83 T CONST)) (= (#2# 93 T ELT)) (/ (#21=($ $ $) 117 T ELT)) (+ (#21# 121 T ELT)) (** (($ $ #19#) 115 T ELT) (#21# 64 T ELT)) (* (#21# 122 T ELT))) 
(((|Pattern| |#1|) (|Join| #1=(|SetCategory|) (|RetractableTo| |#1|) (|RetractableTo| #2=(|Symbol|)) (CATEGORY |domain| (SIGNATURE |Zero| #3=($) |constant|) (SIGNATURE |One| #3# |constant|) (SIGNATURE |isPlus| #4=(#5=(|Union| #6=(|List| $) #7="failed") $)) (SIGNATURE |isTimes| #4#) (SIGNATURE |isOp| (#5# $ #8=(|BasicOperator|))) (SIGNATURE |isOp| ((|Union| (|Record| (|:| |op| #8#) (|:| |arg| #6#)) #7#) $)) (SIGNATURE |isExpt| ((|Union| (|Record| #9=(|:| |val| $) (|:| |exponent| #10=(|NonNegativeInteger|))) #7#) $)) (SIGNATURE |isQuotient| ((|Union| (|Record| (|:| |num| $) (|:| |den| $)) #7#) $)) (SIGNATURE |isList| #4#) (SIGNATURE |isPower| ((|Union| (|Record| #9# (|:| |exponent| $)) #7#) $)) (SIGNATURE |elt| ($ #8# #6#)) (SIGNATURE + #11=($ $ $)) (SIGNATURE * #11#) (SIGNATURE ** ($ $ #10#)) (SIGNATURE ** #11#) (SIGNATURE / #11#) (SIGNATURE |depth| (#10# $)) (SIGNATURE |convert| ($ #6#)) (SIGNATURE |copy| #12=($ $)) (SIGNATURE |inR?| #13=(#14=(|Boolean|) $)) (SIGNATURE |quoted?| #13#) (SIGNATURE |symbol?| #13#) (SIGNATURE |constant?| #13#) (SIGNATURE |generic?| #13#) (SIGNATURE |multiple?| #13#) (SIGNATURE |optional?| #13#) (SIGNATURE |hasPredicate?| #13#) (SIGNATURE |predicates| #15=(#16=(|List| #17=(|Any|)) $)) (SIGNATURE |setPredicates| #18=($ $ #16#)) (SIGNATURE |withPredicates| #18#) (SIGNATURE |patternVariable| ($ #2# #14# #14# #14#)) (SIGNATURE |setTopPredicate| ($ $ #19=(|List| #2#) #17#)) (SIGNATURE |topPredicate| ((|Record| (|:| |var| #19#) (|:| |pred| #17#)) $)) (SIGNATURE |hasTopPredicate?| #13#) (SIGNATURE |resetBadValues| #12#) (SIGNATURE |addBadValue| ($ $ #17#)) (SIGNATURE |getBadValues| #15#) (SIGNATURE |variables| (#6# $)) (SIGNATURE |optpair| (#5# #6#)))) #1#) (T |Pattern|)) 
((|Zero| #1=(*1 *1) #2=(AND (|isDomain| *1 (|Pattern| *2)) (|ofCategory| *2 #3=(|SetCategory|)))) (|One| #1# #2#) (|isPlus| #4=(*1 *2 *1) #5=(|partial| AND #6=(|isDomain| *2 #7=(|List| #8=(|Pattern| *3))) #9=(|isDomain| *1 #8#) #10=(|ofCategory| *3 #3#))) (|isTimes| #4# #5#) (|isOp| (*1 *2 *1 *3) (|partial| AND (|isDomain| *3 #11=(|BasicOperator|)) (|isDomain| *2 #12=(|List| #13=(|Pattern| *4))) #14=(|isDomain| *1 #13#) #15=(|ofCategory| *4 #3#))) (|isOp| #4# (|partial| AND (|isDomain| *2 (|Record| (|:| |op| #11#) (|:| |arg| #7#))) #9# #10#)) (|isExpt| #4# (|partial| AND (|isDomain| *2 (|Record| #16=(|:| |val| #8#) (|:| |exponent| #17=(|NonNegativeInteger|)))) #9# #10#)) (|isQuotient| #4# (|partial| AND (|isDomain| *2 (|Record| (|:| |num| #8#) (|:| |den| #8#))) #9# #10#)) (|isList| #4# #5#) (|isPower| #4# (|partial| AND (|isDomain| *2 (|Record| #16# (|:| |exponent| #8#))) #9# #10#)) (|elt| (*1 *1 *2 *3) (AND (|isDomain| *2 #11#) (|isDomain| *3 #12#) #14# #15#)) (+ #18=(*1 *1 *1 *1) #2#) (* #18# #2#) (** #19=(*1 *1 *1 *2) #20=(AND (|isDomain| *2 #17#) #9# #10#)) (** #18# #2#) (/ #18# #2#) (|depth| #4# #20#) (|convert| (*1 *1 *2) #21=(AND #6# #9# #10#)) (|copy| #22=(*1 *1 *1) #2#) (|inR?| #4# #23=(AND (|isDomain| *2 #24=(|Boolean|)) #9# #10#)) (|quoted?| #4# #23#) (|symbol?| #4# #23#) (|constant?| #4# #23#) (|generic?| #4# #23#) (|multiple?| #4# #23#) (|optional?| #4# #23#) (|hasPredicate?| #4# #23#) (|predicates| #4# #25=(AND (|isDomain| *2 (|List| #26=(|Any|))) #9# #10#)) (|setPredicates| #19# #25#) (|withPredicates| #19# #25#) (|patternVariable| (*1 *1 *2 *3 *3 *3) (AND (|isDomain| *2 #27=(|Symbol|)) (|isDomain| *3 #24#) #14# #15#)) (|setTopPredicate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 #28=(|List| #27#)) (|isDomain| *3 #26#) #14# #15#)) (|topPredicate| #4# (AND (|isDomain| *2 (|Record| (|:| |var| #28#) (|:| |pred| #26#))) #9# #10#)) (|hasTopPredicate?| #4# #23#) (|resetBadValues| #22# #2#) (|addBadValue| #19# (AND (|isDomain| *2 #26#) #9# #10#)) (|getBadValues| #4# #25#) (|variables| #4# #21#) (|optpair| (*1 *2 *2) #5#)) 
((|suchThat| ((#1=(|Pattern| |#1|) #1# (|List| (|Symbol|)) (|Mapping| #2=(|Boolean|) #3=(|List| |#2|))) 32 T ELT) ((#1# #1# (|List| #4=(|Mapping| #2# |#2|))) 46 T ELT) ((#1# #1# #4#) 35 T ELT)) (|satisfy?| ((#2# #3# #1#) 42 T ELT) ((#2# |#2| #1#) 36 T ELT)) (|predicate| ((#4# #1#) 16 T ELT)) (|badValues| ((#3# #1#) 24 T ELT)) (|addBadValue| ((#1# #1# |#2|) 20 T ELT))) 
(((|PatternFunctions1| |#1| |#2|) (CATEGORY |package| (SIGNATURE |suchThat| (#1=(|Pattern| |#1|) #1# #2=(|Mapping| #3=(|Boolean|) |#2|))) (SIGNATURE |suchThat| (#1# #1# (|List| #2#))) (SIGNATURE |suchThat| (#1# #1# (|List| (|Symbol|)) (|Mapping| #3# #4=(|List| |#2|)))) (SIGNATURE |predicate| (#2# #1#)) (SIGNATURE |satisfy?| (#3# |#2| #1#)) (SIGNATURE |satisfy?| (#3# #4# #1#)) (SIGNATURE |addBadValue| (#1# #1# |#2|)) (SIGNATURE |badValues| (#4# #1#))) (|SetCategory|) (|Type|)) (T |PatternFunctions1|)) 
((|badValues| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|Pattern| *4)) #4=(|ofCategory| *4 #5=(|SetCategory|)) (|isDomain| *2 (|List| *5)) #6=(|isDomain| *1 (|PatternFunctions1| *4 *5)) #7=(|ofCategory| *5 #8=(|Type|)))) (|addBadValue| #9=(*1 *2 *2 *3) (AND #10=(|isDomain| *2 #3#) #4# (|isDomain| *1 (|PatternFunctions1| *4 *3)) #11=(|ofCategory| *3 #8#))) (|satisfy?| #12=(*1 *2 *3 *4) (AND (|isDomain| *3 #13=(|List| *6)) #14=(|isDomain| *4 #15=(|Pattern| *5)) #16=(|ofCategory| *5 #5#) #17=(|ofCategory| *6 #8#) #18=(|isDomain| *2 #19=(|Boolean|)) #20=(|isDomain| *1 (|PatternFunctions1| *5 *6)))) (|satisfy?| #12# (AND #14# #16# #18# (|isDomain| *1 (|PatternFunctions1| *5 *3)) #11#)) (|predicate| #1# (AND #2# #4# (|isDomain| *2 #21=(|Mapping| #19# *5)) #6# #7#)) (|suchThat| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 #15#) (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *4 (|Mapping| #19# #13#)) #16# #17# #20#)) (|suchThat| #9# (AND #10# (|isDomain| *3 (|List| #21#)) #4# #7# #6#)) (|suchThat| #9# (AND #10# (|isDomain| *3 #21#) #4# #7# #6#))) 
((|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) 19 T ELT))) 
(((|PatternFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)))) #1=(|SetCategory|) #1#) (T |PatternFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Pattern| *6)) (|isDomain| *1 (|PatternFunctions2| *5 *6))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 20 T ELT)) (|retractable?| ((#3# $) 49 T ELT)) (|retractIfCan| (((|Union| #4=(|LyndonWord| |#1|) "failed") $) 55 T ELT)) (|retract| (#5=(#4# $) 53 T ELT)) (|rest| (($ $) 24 T ELT)) (|min| #6=(($ $ $) NIL T ELT)) (|max| #6#) (|length| (((|NonNegativeInteger|) $) 60 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#5# 22 T ELT)) (|coerce| (((|OutputForm|) $) 47 T ELT) (($ #4#) 27 T ELT) (((|OrderedFreeMonoid| |#1|) $) 36 T ELT) (($ |#1|) 26 T ELT)) (|before?| #1#) (|One| (($) 11 T CONST)) (|ListOfTerms| (((|List| #4#) $) 28 T ELT)) (>= #1#) (> #1#) (= (#2# 14 T ELT)) (<= #1#) (< (#2# 66 T ELT))) 
(((|PoincareBirkhoffWittLyndonBasis| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| #2=(|LyndonWord| |#1|)) (CATEGORY |domain| (SIGNATURE |One| ($) |constant|) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |first| (#2# $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |ListOfTerms| ((|List| #2#) $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) #1#) (T |PoincareBirkhoffWittLyndonBasis|)) 
((|One| (*1 *1) #1=(AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2)) (|ofCategory| *2 #2=(|OrderedSet|)))) (|coerce| #3=(*1 *2 *1) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) #4=(|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) #5=(|ofCategory| *3 #2#))) (|coerce| (*1 *1 *2) #1#) (|first| #3# (AND (|isDomain| *2 #6=(|LyndonWord| *3)) #4# #5#)) (|length| #3# (AND (|isDomain| *2 (|NonNegativeInteger|)) #4# #5#)) (|ListOfTerms| #3# (AND (|isDomain| *2 (|List| #6#)) #4# #5#)) (|rest| (*1 *1 *1) #1#) (|retractable?| #3# (AND (|isDomain| *2 (|Boolean|)) #4# #5#)) (|varList| #3# (AND (|isDomain| *2 (|List| *3)) #4# #5#))) 
((|compose| ((|#1| |#1| |#1|) 19 T ELT))) 
(((|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))))) 
((D ((|#2| $ |#3|) 10 T ELT))) 
(((|PartialDifferentialDomain&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE D (|#2| |#1| |#3|))) (|PartialDifferentialDomain| |#2| |#3|) #1=(|Type|) #1#) (T |PartialDifferentialDomain&|)) 
NIL 
((|differentiate| ((|#1| $ |#2|) 7 T ELT)) (D ((|#1| $ |#2|) 6 T ELT))) 
(((|PartialDifferentialDomain| |#1| |#2|) (|Category|) (|Type|) (|Type|)) (T |PartialDifferentialDomain|)) 
((|differentiate| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|PartialDifferentialDomain| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|Type|)))) (D (*1 *2 *1 *3) (AND (|ofCategory| *1 (|PartialDifferentialDomain| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |differentiate| (|t#1| $ |t#2|)) (SIGNATURE D (|t#1| $ |t#2|)))) 
(((|Join|) . T) ((|Type|) . T)) 
((|rightFactorCandidate| ((|#1| |#1| #1=(|NonNegativeInteger|)) 26 T ELT)) (|leftFactor| (((|Union| |#1| #2="failed") |#1| |#1|) 23 T ELT)) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) #2#) |#1| #1# #1#) 29 T ELT) (((|List| |#1|) |#1|) 38 T ELT))) 
(((|PolynomialDecomposition| |#1| |#2|) (CATEGORY |package| (SIGNATURE |decompose| ((|List| |#1|) |#1|)) (SIGNATURE |decompose| ((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) #1="failed") |#1| #2=(|NonNegativeInteger|) #2#)) (SIGNATURE |leftFactor| ((|Union| |#1| #1#) |#1| |#1|)) (SIGNATURE |rightFactorCandidate| (|#1| |#1| #2#))) (|UnivariatePolynomialCategory| |#2|) (|Field|)) (T |PolynomialDecomposition|)) 
((|rightFactorCandidate| (*1 *2 *2 *3) (AND (|isDomain| *3 #1=(|NonNegativeInteger|)) #2=(|ofCategory| *4 #3=(|Field|)) (|isDomain| *1 (|PolynomialDecomposition| *2 *4)) (|ofCategory| *2 #4=(|UnivariatePolynomialCategory| *4)))) (|leftFactor| (*1 *2 *2 *2) (|partial| AND (|ofCategory| *3 #3#) (|isDomain| *1 (|PolynomialDecomposition| *2 *3)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|decompose| (*1 *2 *3 *4 *4) (|partial| AND (|isDomain| *4 #1#) (|ofCategory| *5 #3#) (|isDomain| *2 (|Record| (|:| |left| *3) (|:| |right| *3))) (|isDomain| *1 (|PolynomialDecomposition| *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|decompose| (*1 *2 *3) (AND #2# (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialDecomposition| *3 *4)) (|ofCategory| *3 #4#)))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|List| |#2|) . #4=((|List| #5=(|NonNegativeInteger|)))) 45 T ELT) (($ $ |#2| . #6=(#5#)) 44 T ELT) (($ $ (|List| |#2|)) 43 T ELT) (($ $ |#2|) 41 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (($ $ (|List| |#2|) . #4#) 48 T ELT) (($ $ |#2| . #6#) 47 T ELT) (($ $ (|List| |#2|)) 46 T ELT) (($ $ |#2|) 42 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 30 T ELT) (($ |#1| . #7#) 33 T ELT) (($ $ |#1|) 37 T ELT))) 
(((|PartialDifferentialModule| |#1| |#2|) (|Category|) (|Ring|) (|BasicType|)) (T |PartialDifferentialModule|)) 
NIL 
(|Join| (|BiModule| |t#1| |t#1|) (|PartialDifferentialSpace| |t#2|) (CATEGORY |package| (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) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|PartialDifferentialDomain| $ |#2|) . T) ((|PartialDifferentialSpace| |#2|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|List| |#1|) . #4=((|List| #5=(|NonNegativeInteger|)))) 52 T ELT) (($ $ |#1| . #6=(#5#)) 51 T ELT) (($ $ (|List| |#1|)) 50 T ELT) (($ $ |#1|) 48 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|List| |#1|) . #4#) 55 T ELT) (($ $ |#1| . #6#) 54 T ELT) (($ $ (|List| |#1|)) 53 T ELT) (($ $ |#1|) 49 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|PartialDifferentialRing| |#1|) (|Category|) (|BasicType|)) (T |PartialDifferentialRing|)) 
NIL 
(|Join| (|Ring|) (|PartialDifferentialSpace| |t#1|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#1|) . T) ((|PartialDifferentialSpace| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|differentiate| (#1=($ $ |#2|) NIL T ELT) (#2=($ $ #3=(|List| |#2|)) 10 T ELT) (#4=($ $ |#2| #5=(|NonNegativeInteger|)) 12 T ELT) (#6=($ $ #3# (|List| #5#)) 15 T ELT)) (D (#1# 16 T ELT) (#2# 18 T ELT) (#4# 19 T ELT) (#6# 21 T ELT))) 
(((|PartialDifferentialSpace&| |#1| |#2|) (CATEGORY |package| (SIGNATURE D #1=(|#1| |#1| #2=(|List| |#2|) (|List| #3=(|NonNegativeInteger|)))) (SIGNATURE D #4=(|#1| |#1| |#2| #3#)) (SIGNATURE D #5=(|#1| |#1| #2#)) (SIGNATURE |differentiate| #1#) (SIGNATURE |differentiate| #4#) (SIGNATURE |differentiate| #5#) (SIGNATURE D #6=(|#1| |#1| |#2|)) (SIGNATURE |differentiate| #6#)) (|PartialDifferentialSpace| |#2|) (|BasicType|)) (T |PartialDifferentialSpace&|)) 
NIL 
((|differentiate| (($ $ |#1|) 7 T ELT) (($ $ (|List| |#1|)) 15 T ELT) (($ $ |#1| (|NonNegativeInteger|)) 14 T ELT) (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) 13 T ELT)) (D (($ $ |#1|) 6 T ELT) (($ $ (|List| |#1|)) 12 T ELT) (($ $ |#1| (|NonNegativeInteger|)) 11 T ELT) (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) 10 T ELT))) 
(((|PartialDifferentialSpace| |#1|) (|Category|) (|BasicType|)) (T |PartialDifferentialSpace|)) 
((|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PartialDifferentialSpace| *3)) (|ofCategory| *3 (|BasicType|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PartialDifferentialSpace| *2)) (|ofCategory| *2 (|BasicType|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|PartialDifferentialSpace| *4)) (|ofCategory| *4 (|BasicType|)))) (D (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PartialDifferentialSpace| *3)) (|ofCategory| *3 (|BasicType|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PartialDifferentialSpace| *2)) (|ofCategory| *2 (|BasicType|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|PartialDifferentialSpace| *4)) (|ofCategory| *4 (|BasicType|))))) 
(|Join| (|PartialDifferentialDomain| $ |t#1|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $ (|List| |t#1|))) (SIGNATURE |differentiate| ($ $ |t#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| ($ $ (|List| |t#1|) (|List| (|NonNegativeInteger|)))) (SIGNATURE D ($ $ (|List| |t#1|))) (SIGNATURE D ($ $ |t#1| (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|List| |t#1|) (|List| (|NonNegativeInteger|)))))) 
(((|Join|) . T) ((|PartialDifferentialDomain| $ |#1|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 26 T ELT)) (|setvalue!| ((|#1| $ |#1|) NIL #5=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| #6=(#7=($ $ $) NIL #5# ELT)) (|setleft!| #6#) (|setelt| ((|#1| $ #8="value" |#1|) NIL #5# ELT) (($ $ #9="left" $) NIL #5# ELT) (($ $ #10="right" $) NIL #5# ELT)) (|setchildren!| (($ $ #11=(|List| $)) NIL #5# ELT)) (|sample| (#12=($) NIL T CONST)) (|right| (#13=($ $) 25 T ELT)) (|ptree| (($ |#1|) 12 T ELT) (#7# 17 T ELT)) (|nodes| #14=((#11# $) NIL T ELT)) (|node?| #1#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|left| (#13# 23 T ELT)) (|leaves| ((#15=(|List| |#1|) $) NIL T ELT)) (|leaf?| (#16=(#3# $) 20 T ELT)) (|latex| (((|String|) $) NIL #17=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) NIL #17# ELT)) (|eval| (($ $ (|List| #18=(|Equation| |#1|))) NIL #19=(AND (|has| |#1| (|Evalable| |#1|)) #17#) ELT) (($ $ #18#) NIL #19# ELT) (($ $ |#1| |#1|) NIL #19# ELT) (($ $ #15# #15#) NIL #19# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| #20=(#16# NIL T ELT)) (|empty| (#12# NIL T ELT)) (|elt| ((|#1| $ #8#) NIL T ELT) (($ $ #9#) NIL T ELT) (($ $ #10#) NIL T ELT)) (|distance| (((|Integer|) $ $) NIL T ELT)) (|cyclic?| #20#) (|copy| (#13# NIL T ELT)) (|coerce| (((|Tree| |#1|) $) 9 T ELT) ((#21=(|OutputForm|) $) 29 (|has| |#1| (|CoercibleTo| #21#)) ELT)) (|children| #14#) (|child?| #1#) (|before?| #1#) (= (#2# 21 #4# ELT))) 
(((|PendantTree| |#1|) (|Join| (|BinaryRecursiveAggregate| |#1|) (|CoercibleTo| (|Tree| |#1|)) (CATEGORY |domain| (SIGNATURE |ptree| ($ |#1|)) (SIGNATURE |ptree| ($ $ $)))) (|SetCategory|)) (T |PendantTree|)) 
((|ptree| (*1 *1 *2) #1=(AND (|isDomain| *1 (|PendantTree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|ptree| (*1 *1 *1 *1) #1#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|support| (#4=(#5=(|Set| |#1|) $) 61 T ELT)) (|sort| ((#6=(|List| $) #6#) 104 T ELT)) (|sign| ((#7=(|Integer|) $) 84 T ELT)) (|sample| (#8=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|order| (#9=(#10=(|NonNegativeInteger|) $) 81 T ELT)) (|orbit| ((#5# $ |#1|) 71 T ELT)) (|one?| (#11=(#3# $) NIL T ELT)) (|odd?| (#11# 89 T ELT)) (|numberOfCycles| (#9# 85 T ELT)) (|min| #12=(#13=($ $ $) NIL #14=(OR #15=(|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))) ELT)) (|max| #12#) (|listRepresentation| (((|Record| (|:| |preimage| #16=(|List| |#1|)) (|:| |image| #16#)) $) 56 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (($ $) 131 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fixedPoints| (#4# 136 #15# ELT)) (|even?| (#11# 82 T ELT)) (|elt| ((|#1| $ |#1|) 69 T ELT)) (|degree| (#9# 63 T ELT)) (|cycles| (#17=($ (|List| #16#)) 119 T ELT)) (|cyclePartition| (((|Partition|) $) 75 T ELT)) (|cycle| (#18=($ #16#) 32 T ELT)) (|conjugate| #19=(#13# NIL T ELT)) (|commutator| #19#) (|coercePreimagesImages| (#17# 58 T ELT)) (|coerceListOfPairs| (#17# 124 T ELT)) (|coerceImages| (#18# 133 T ELT)) (|coerce| (((|OutputForm|) $) 118 T ELT) (#17# 92 T ELT) (#18# 93 T ELT)) (|before?| #1#) (|One| (#8# 24 T CONST)) (>= #20=(#2# NIL #14# ELT)) (> #20#) (= (#2# 67 T ELT)) (<= #20#) (< (#2# 91 T ELT)) (/ #19#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #10#) NIL T ELT) (($ $ #7#) NIL T ELT)) (* (#13# 33 T ELT))) 
(((|Permutation| |#1|) (|Join| (|PermutationCategory| |#1|) (CATEGORY |domain| (SIGNATURE |listRepresentation| ((|Record| (|:| |preimage| #1=(|List| |#1|)) (|:| |image| #1#)) $)) (SIGNATURE |coercePreimagesImages| #2=($ (|List| #1#))) (SIGNATURE |coerce| #2#) (SIGNATURE |coerce| #3=($ #1#)) (SIGNATURE |coerceListOfPairs| #2#) (SIGNATURE |degree| #4=((|NonNegativeInteger|) $)) (SIGNATURE |cyclePartition| ((|Partition|) $)) (SIGNATURE |order| #4#) (SIGNATURE |numberOfCycles| #4#) (SIGNATURE |sign| ((|Integer|) $)) (SIGNATURE |even?| #5=((|Boolean|) $)) (SIGNATURE |odd?| #5#) (SIGNATURE |sort| (#6=(|List| $) #6#)) (IF #7=(|has| |#1| (|Finite|)) (SIGNATURE |fixedPoints| ((|Set| |#1|) $)) |%noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) #8=(SIGNATURE |coerceImages| #3#) (IF #7# #8# |%noBranch|)))) (|SetCategory|)) (T |Permutation|)) 
((|listRepresentation| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |preimage| #2=(|List| *3)) (|:| |image| #2#))) #3=(|isDomain| *1 #4=(|Permutation| *3)) #5=(|ofCategory| *3 (|SetCategory|)))) (|coercePreimagesImages| #6=(*1 *1 *2) #7=(AND (|isDomain| *2 (|List| #2#)) #5# #3#)) (|coerce| #6# #7#) (|coerce| #6# #8=(AND (|isDomain| *2 #2#) #5# #3#)) (|coerceListOfPairs| #6# #7#) (|degree| #1# #9=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #5#)) (|cyclePartition| #1# (AND (|isDomain| *2 (|Partition|)) #3# #5#)) (|order| #1# #9#) (|numberOfCycles| #1# #9#) (|sign| #1# (AND (|isDomain| *2 (|Integer|)) #3# #5#)) (|even?| #1# #10=(AND (|isDomain| *2 (|Boolean|)) #3# #5#)) (|odd?| #1# #10#) (|sort| (*1 *2 *2) (AND (|isDomain| *2 (|List| #4#)) #3# #5#)) (|fixedPoints| #1# (AND (|isDomain| *2 (|Set| *3)) #3# (|ofCategory| *3 (|Finite|)) #5#)) (|coerceImages| #6# #8#)) 
((|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) 48 T ELT))) 
(((|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))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|support| (((|Set| |#1|) $) 42 T ELT)) (|sample| (#2=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|orbit| (((|Set| |#1|) $ |#1|) 41 T ELT)) (|one?| (((|Boolean|) $) 22 T ELT)) (|min| (#3=($ $ $) 35 (OR (|has| |#1| . #4=((|OrderedSet|))) (|has| |#1| . #5=((|Finite|)))) ELT)) (|max| (#3# 36 (OR (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 30 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|elt| ((|#1| $ |#1|) 45 T ELT)) (|cycles| (($ (|List| (|List| |#1|))) 43 T ELT)) (|cycle| (($ (|List| |#1|)) 44 T ELT)) (|conjugate| (#6=($ $ $) 27 T ELT)) (|commutator| (#6# 26 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#2# 24 T CONST)) (>= (#7=((|Boolean|) $ $) 37 (OR (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (> (#7# 39 (OR (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (= (#1# 8 T ELT)) (<= (#7# 38 (OR (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (< (((|Boolean|) $ $) 40 T ELT)) (/ (#6# 29 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT) (($ $ (|Integer|)) 28 T ELT)) (* (($ $ $) 18 T ELT))) 
(((|PermutationCategory| |#1|) (|Category|) (|SetCategory|)) (T |PermutationCategory|)) 
((|cycle| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|PermutationCategory| *3)))) (|cycles| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|List| *3))) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *1 (|PermutationCategory| *3)))) (|support| (*1 *2 *1) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Set| *3)))) (|orbit| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Set| *3)))) (< (*1 *2 *1 *1) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|Group|) (|Eltable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE |cycle| ($ (|List| |t#1|))) (SIGNATURE |cycles| ($ (|List| (|List| |t#1|)))) (SIGNATURE |support| ((|Set| |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) ((|Eltable| |#1| |#1|) . T) ((|Group|) . T) ((|Join|) . T) ((|Monoid|) . T) ((|OrderedSet|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))) ((|OrderedType|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|wordsForStrongGenerators| (((|List| #4=(|List| #5=(|NonNegativeInteger|))) $) 163 T ELT)) (|wordInStrongGenerators| (#6=(#4# #7=(|Permutation| |#1|) $) 191 T ELT)) (|wordInGenerators| (#6# 192 T ELT)) (|support| ((#8=(|Set| |#1|) $) 155 T ELT)) (|strongGenerators| (#9=(#10=(|List| #7#) $) 152 T ELT)) (|random| ((#7# $ #11=(|Integer|)) 157 T ELT) ((#7# $) 158 T ELT)) (|permutationGroup| (#12=($ #10#) 165 T ELT)) (|order| (#13=(#5# $) 159 T ELT)) (|orbits| ((#14=(|Set| #8#) $) 189 T ELT)) (|orbit| ((#8# $ |#1|) 180 T ELT) ((#14# $ #8#) 201 T ELT) (((|Set| #15=(|List| |#1|)) $ #15#) 204 T ELT)) (|member?| ((#3# #7# $) 140 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|initializeGroupForWordProblem| ((#16=(|Void|) $) 145 T ELT) ((#16# $ #11# #11#) 205 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generators| (#9# 146 T ELT)) (|elt| ((#7# $ #5#) 153 T ELT)) (|degree| (#13# 160 T ELT)) (|coerce| (((|OutputForm|) $) 177 T ELT) (#9# 28 T ELT) (#12# 164 T ELT)) (|before?| #1#) (|base| ((#15# $) 162 T ELT)) (= (#2# 198 T ELT)) (<= (#2# 195 T ELT)) (< (#2# 194 T ELT))) 
(((|PermutationGroup| |#1|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| #2=(#3=(|List| #4=(|Permutation| |#1|)) $)) (SIGNATURE |generators| #2#) (SIGNATURE |elt| (#4# $ #5=(|NonNegativeInteger|))) (SIGNATURE |random| (#4# $ #6=(|Integer|))) (SIGNATURE |random| (#4# $)) (SIGNATURE |order| #7=(#5# $)) (SIGNATURE |degree| #7#) (SIGNATURE |base| (#8=(|List| |#1|) $)) (SIGNATURE |strongGenerators| #2#) (SIGNATURE |wordsForStrongGenerators| ((|List| #9=(|List| #5#)) $)) (SIGNATURE |coerce| #10=($ #3#)) (SIGNATURE |permutationGroup| #10#) (SIGNATURE |orbit| (#11=(|Set| |#1|) $ |#1|)) (SIGNATURE |orbits| (#12=(|Set| #11#) $)) (SIGNATURE |orbit| (#12# $ #11#)) (SIGNATURE |orbit| ((|Set| #8#) $ #8#)) (SIGNATURE |member?| (#13=(|Boolean|) #4# $)) (SIGNATURE |wordInStrongGenerators| #14=(#9# #4# $)) (SIGNATURE |wordInGenerators| #14#) (SIGNATURE |support| (#11# $)) (SIGNATURE < #15=(#13# $ $)) (SIGNATURE <= #15#) (SIGNATURE |initializeGroupForWordProblem| (#16=(|Void|) $)) (SIGNATURE |initializeGroupForWordProblem| (#16# $ #6# #6#)))) #1#) (T |PermutationGroup|)) 
((|coerce| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *2 (|List| #4=(|Permutation| *3))) #5=(|isDomain| *1 (|PermutationGroup| *3)) #6=(|ofCategory| *3 #7=(|SetCategory|)))) (|generators| #1# #2#) (|elt| #8=(*1 *2 *1 *3) (AND (|isDomain| *3 #9=(|NonNegativeInteger|)) #10=(|isDomain| *2 #11=(|Permutation| *4)) #12=(|isDomain| *1 (|PermutationGroup| *4)) #13=(|ofCategory| *4 #7#))) (|random| #8# (AND #14=(|isDomain| *3 (|Integer|)) #10# #12# #13#)) (|random| #1# (AND (|isDomain| *2 #4#) #5# #6#)) (|order| #1# #15=(AND (|isDomain| *2 #9#) #5# #6#)) (|degree| #1# #15#) (|base| #1# (AND (|isDomain| *2 (|List| *3)) #5# #6#)) (|strongGenerators| #1# #2#) (|wordsForStrongGenerators| #1# (AND (|isDomain| *2 (|List| #16=(|List| #9#))) #5# #6#)) (|coerce| #17=(*1 *1 *2) #18=(AND #3# #6# #5#)) (|permutationGroup| #17# #18#) (|orbit| #8# #19=(AND (|isDomain| *2 #20=(|Set| *3)) #5# #6#)) (|orbits| #1# (AND (|isDomain| *2 (|Set| #20#)) #5# #6#)) (|orbit| #8# (AND #13# (|isDomain| *2 (|Set| #21=(|Set| *4))) #12# (|isDomain| *3 #21#))) (|orbit| #8# (AND #13# (|isDomain| *2 (|Set| #22=(|List| *4))) #12# (|isDomain| *3 #22#))) (|member?| #23=(*1 *2 *3 *1) (AND #24=(|isDomain| *3 #11#) #13# #25=(|isDomain| *2 (|Boolean|)) #12#)) (|wordInStrongGenerators| #23# #26=(AND #24# #13# (|isDomain| *2 #16#) #12#)) (|wordInGenerators| #23# #26#) (|support| #1# #19#) (< #27=(*1 *2 *1 *1) #28=(AND #25# #5# #6#)) (<= #27# #28#) (|initializeGroupForWordProblem| #1# (AND #29=(|isDomain| *2 (|Void|)) #5# #6#)) (|initializeGroupForWordProblem| (*1 *2 *1 *3 *3) (AND #14# #29# #12# #13#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| #7=(#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| $ (|Finite|)) ELT) #5#) (|tableForDiscreteLogarithm| (((|Table| #12# #9#) #14=(|Integer|)) NIL T ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| #7#) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| #21=((#16# $) NIL T ELT)) (|retract| #5#) (|represents| (($ #22=(|Vector| $)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL T ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| #21#) (|random| #24=(#20# NIL T ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #3#) (|primeFrobenius| #5# #27=(#28=($ $ #9#) NIL T ELT)) (|prime?| #3#) (|order| #29=((#30=(|OnePointCompletion| #12#) $) NIL T ELT) #31=((#12# $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #32=(#20# NIL #13# ELT)) (|normal?| (#4# NIL #13# ELT)) (|norm| #10# #5#) (|nextItem| #33=(((|Maybe| $) $) NIL T ELT)) (|multiEuclidean| (((|Union| #25# #17#) #25# $) NIL T ELT)) (|minimalPolynomial| ((#34=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT) (#35=(#34# $) NIL T ELT)) (|lookup| #31#) (|linearAssociatedOrder| #36=(#35# NIL #13# ELT)) (|linearAssociatedLog| (((|Union| #34# #17#) $ $) NIL #13# ELT) #36#) (|linearAssociatedExp| (($ $ #34#) NIL #13# ELT)) (|lcm| #23# #37=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| #19#) (|index| (($ #12#) NIL T ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #32#) (|gcdPolynomial| ((#34# #34# #34#) NIL T ELT)) (|gcd| #23# #37#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) NIL T ELT)) (|factor| #18#) (|extensionDegree| ((#12#) NIL T ELT) ((#30#) NIL T ELT)) (|extendedEuclidean| (((|Record| #38=(|:| |coef1| $) #39=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #38# #39#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| #40=((#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (((|Union| #9# #17#) $ $) NIL T ELT) #40#) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #5# #27#) (|degree| #31# #29#) (|definingPolynomial| ((#34#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #32#) (|coordinates| ((#41=(|Matrix| $) #22#) NIL T ELT) ((#22# $) NIL T ELT)) (|convert| ((#14# $) NIL T ELT)) (|conditionP| (((|Union| #22# #17#) #41#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #5# (($ #42=(|Fraction| #14#)) NIL T ELT)) (|charthRoot| #33# #5#) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|basis| ((#22# #12#) NIL T ELT) ((#22#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #19#) (|One| #19#) (|Frobenius| (#28# NIL #13# ELT) (#6# NIL #13# ELT)) (D #5# #27#) (= #1#) (/ #23#) (- #5# #23#) (+ #23#) (** (#11# NIL T ELT) #27# (($ $ #14#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #14# . #43=($)) NIL T ELT) #23# (($ $ #42#) NIL T ELT) (($ #42# . #43#) NIL T ELT))) 
(((|PrimeField| |#1|) (|Join| (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| $) (|ConvertibleTo| (|Integer|))) (|PositiveInteger|)) (T |PrimeField|)) 
NIL 
((|solveLinearPolynomialEquationByRecursion| ((#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #2# #3#) 164 T ELT)) (|randomR| ((|#1|) 101 T ELT)) (|factorSquareFreeByRecursion| (#4=(#5=(|Factored| #3#) #3#) 173 T ELT)) (|factorSFBRlcUnit| ((#5# (|List| |#3|) #3#) 83 T ELT)) (|factorByRecursion| (#4# 183 T ELT)) (|bivariateSLPEBR| ((#1# #2# #3# |#3|) 117 T ELT))) 
(((|PolynomialFactorizationByRecursion| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByRecursion| (#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #2# #3#)) (SIGNATURE |factorByRecursion| #4=(#5=(|Factored| #3#) #3#)) (SIGNATURE |factorSquareFreeByRecursion| #4#) (SIGNATURE |randomR| (|#1|)) (SIGNATURE |bivariateSLPEBR| (#1# #2# #3# |#3|)) (SIGNATURE |factorSFBRlcUnit| (#5# (|List| |#3|) #3#))) (|PolynomialFactorizationExplicit|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |PolynomialFactorizationByRecursion|)) 
((|factorSFBRlcUnit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 #1=(|OrderedSet|)) #2=(|ofCategory| *5 #3=(|PolynomialFactorizationExplicit|)) #4=(|ofCategory| *6 #5=(|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|PolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| *8))) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *5 *6 *7 *8)) (|isDomain| *4 #6#))) (|bivariateSLPEBR| (*1 *2 *2 *3 *4) (|partial| AND #7=(|isDomain| *2 (|List| #8=(|SparseUnivariatePolynomial| *7))) #9=(|isDomain| *3 #8#) (|ofCategory| *7 (|PolynomialCategory| *5 *6 *4)) #2# #4# #10=(|ofCategory| *4 #1#) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *5 *6 *4 *7)))) (|randomR| (*1 *2) (AND (|ofCategory| *3 #5#) #10# (|ofCategory| *2 #3#) (|isDomain| *1 (|PolynomialFactorizationByRecursion| *2 *3 *4 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|factorSquareFreeByRecursion| #11=(*1 *2 *3) #12=(AND #13=(|ofCategory| *4 #3#) #14=(|ofCategory| *5 #5#) #15=(|ofCategory| *6 #1#) #16=(|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Factored| #8#)) #17=(|isDomain| *1 (|PolynomialFactorizationByRecursion| *4 *5 *6 *7)) #9#)) (|factorByRecursion| #11# #12#) (|solveLinearPolynomialEquationByRecursion| (*1 *2 *2 *3) (|partial| AND #7# #9# #16# #13# #14# #15# #17#))) 
((|solveLinearPolynomialEquationByRecursion| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#2|)) "failed") #1# #2#) 39 T ELT)) (|randomR| ((|#1|) 71 T ELT)) (|factorSquareFreeByRecursion| (#3=((|Factored| #2#) #2#) 125 T ELT)) (|factorSFBRlcUnit| (#3# 109 T ELT)) (|factorByRecursion| (#3# 136 T ELT))) 
(((|PolynomialFactorizationByRecursionUnivariate| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByRecursion| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#2|)) "failed") #1# #2#)) (SIGNATURE |factorByRecursion| #3=((|Factored| #2#) #2#)) (SIGNATURE |factorSquareFreeByRecursion| #3#) (SIGNATURE |randomR| (|#1|)) (SIGNATURE |factorSFBRlcUnit| #3#)) (|PolynomialFactorizationExplicit|) (|UnivariatePolynomialCategory| |#1|)) (T |PolynomialFactorizationByRecursionUnivariate|)) 
((|factorSFBRlcUnit| #1=(*1 *2 *3) #2=(AND #3=(|ofCategory| *4 #4=(|PolynomialFactorizationExplicit|)) #5=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| *5))) #7=(|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *4 *5)) #8=(|isDomain| *3 #6#))) (|randomR| (*1 *2) (AND (|ofCategory| *2 #4#) (|isDomain| *1 (|PolynomialFactorizationByRecursionUnivariate| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|factorSquareFreeByRecursion| #1# #2#) (|factorByRecursion| #1# #2#) (|solveLinearPolynomialEquationByRecursion| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| #6#)) #8# #5# #3# #7#))) 
((|solveLinearPolynomialEquation| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| $)) "failed") #1# #2#) 46 T ELT)) (|gcdPolynomial| ((#2# #2# #2#) 18 T ELT)) (|charthRoot| (((|Maybe| $) $) 40 T ELT))) 
(((|PolynomialFactorizationExplicit&| |#1|) (CATEGORY |package| (SIGNATURE |charthRoot| ((|Maybe| |#1|) |#1|)) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#1|)) "failed") #1# #2#)) (SIGNATURE |gcdPolynomial| (#2# #2# #2#))) (|PolynomialFactorizationExplicit|)) (T |PolynomialFactorizationExplicit&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 75 T ELT)) (|squareFreePart| (($ $) 66 T ELT)) (|squareFree| (#4=((|Factored| $) $) 67 T ELT)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 72 T ELT)) (|sample| (#5=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|prime?| (((|Boolean|) $) 68 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (#6=($ $ $) 60 T ELT) (#7=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#8=(|SparseUnivariatePolynomial| $) #8# #8#) 58 T ELT)) (|gcd| (#6# 62 T ELT) (#7# 61 T ELT)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 73 T ELT)) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 74 T ELT)) (|factor| (#4# 65 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 71 (|has| $ (|CharacteristicNonZero|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|charthRoot| (((|Maybe| $) $) 70 (|has| $ (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|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 *2 *1) (AND (|isDomain| *2 (|Maybe| *1)) (|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| ((|Maybe| $) $))) |%noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|torsionIfCan| (((|Union| (|Record| (|:| |order| #1=(|NonNegativeInteger|)) (|:| |function| |#5|)) #2="failed") #3=(|FiniteDivisor| |#2| |#3| |#4| |#5|)) 78 T ELT)) (|torsion?| (((|Boolean|) #3#) 17 T ELT)) (|order| (((|Union| #1# #2#) #3#) 15 T ELT))) 
(((|PointsOfFiniteOrder| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |order| ((|Union| #1=(|NonNegativeInteger|) #2="failed") #3=(|FiniteDivisor| |#2| |#3| |#4| |#5|))) (SIGNATURE |torsion?| ((|Boolean|) #3#)) (SIGNATURE |torsionIfCan| ((|Union| (|Record| (|:| |order| #1#) (|:| |function| |#5|)) #2#) #3#))) (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))) (|FunctionSpace| |#1|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| (|Fraction| |#3|)) (|FunctionFieldCategory| |#2| |#3| |#4|)) (T |PointsOfFiniteOrder|)) 
((|torsionIfCan| #1=(*1 *2 *3) (|partial| AND #2=(|isDomain| *3 (|FiniteDivisor| *5 *6 *7 *8)) #3=(|ofCategory| *5 (|FunctionSpace| *4)) #4=(|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) #5=(|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) #6=(|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7)) #7=(|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |order| #8=(|NonNegativeInteger|)) (|:| |function| *8))) #9=(|isDomain| *1 (|PointsOfFiniteOrder| *4 *5 *6 *7 *8)))) (|torsion?| #1# (AND #2# #3# #4# #5# #6# #7# (|isDomain| *2 (|Boolean|)) #9#)) (|order| #1# (|partial| AND #2# #3# #4# #5# #6# #7# (|isDomain| *2 #8#) #9#))) 
((|torsionIfCan| (((|Union| (|Record| (|:| |order| #1=(|NonNegativeInteger|)) (|:| |function| |#3|)) #2="failed") #3=(|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) 64 T ELT)) (|torsion?| (((|Boolean|) #3#) 16 T ELT)) (|order| (((|Union| #1# #2#) #3#) 14 T ELT))) 
(((|PointsOfFiniteOrderRational| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |order| ((|Union| #1=(|NonNegativeInteger|) #2="failed") #3=(|FiniteDivisor| #4=(|Fraction| (|Integer|)) |#1| |#2| |#3|))) (SIGNATURE |torsion?| ((|Boolean|) #3#)) (SIGNATURE |torsionIfCan| ((|Union| (|Record| (|:| |order| #1#) (|:| |function| |#3|)) #2#) #3#))) (|UnivariatePolynomialCategory| #4#) (|UnivariatePolynomialCategory| (|Fraction| |#1|)) (|FunctionFieldCategory| #4# |#1| |#2|)) (T |PointsOfFiniteOrderRational|)) 
((|torsionIfCan| #1=(*1 *2 *3) (|partial| AND #2=(|isDomain| *3 (|FiniteDivisor| #3=(|Fraction| (|Integer|)) *4 *5 *6)) #4=(|ofCategory| *4 (|UnivariatePolynomialCategory| #3#)) #5=(|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) #6=(|ofCategory| *6 (|FunctionFieldCategory| #3# *4 *5)) (|isDomain| *2 (|Record| (|:| |order| #7=(|NonNegativeInteger|)) (|:| |function| *6))) #8=(|isDomain| *1 (|PointsOfFiniteOrderRational| *4 *5 *6)))) (|torsion?| #1# (AND #2# #4# #5# #6# (|isDomain| *2 (|Boolean|)) #8#)) (|order| #1# (|partial| AND #2# #4# #5# #6# (|isDomain| *2 #7#) #8#))) 
((|polyred| ((|#2| |#2|) 26 T ELT)) (|mix| ((#1=(|Integer|) (|List| #2=(|Record| (|:| |den| #1#) (|:| |gcdnum| #1#)))) 15 T ELT)) (|getGoodPrime| (((|PositiveInteger|) #1#) 38 T ELT)) (|doubleDisc| (#3=(#1# |#2|) 45 T ELT)) (|badNum| (#3# 21 T ELT) ((#2# |#1|) 20 T ELT))) 
(((|PointsOfFiniteOrderTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |getGoodPrime| ((|PositiveInteger|) #1=(|Integer|))) (SIGNATURE |badNum| (#2=(|Record| (|:| |den| #1#) (|:| |gcdnum| #1#)) |#1|)) (SIGNATURE |badNum| #3=(#1# |#2|)) (SIGNATURE |mix| (#1# (|List| #2#))) (SIGNATURE |doubleDisc| #3#) (SIGNATURE |polyred| (|#2| |#2|))) (|UnivariatePolynomialCategory| (|Fraction| #1#)) (|UnivariatePolynomialCategory| (|Fraction| |#1|))) (T |PointsOfFiniteOrderTools|)) 
((|polyred| (*1 *2 *2) (AND #1=(|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| #2=(|Integer|)))) (|isDomain| *1 (|PointsOfFiniteOrderTools| *3 *2)) (|ofCategory| *2 #3=(|UnivariatePolynomialCategory| (|Fraction| *3))))) (|doubleDisc| #4=(*1 *2 *3) #5=(AND #6=(|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) #7=(|isDomain| *2 #2#) (|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *3)) (|ofCategory| *3 #8=(|UnivariatePolynomialCategory| (|Fraction| *4))))) (|mix| #4# (AND (|isDomain| *3 (|List| #9=(|Record| (|:| |den| #2#) (|:| |gcdnum| #2#)))) #6# #7# #10=(|isDomain| *1 (|PointsOfFiniteOrderTools| *4 *5)) #11=(|ofCategory| *5 #8#))) (|badNum| #4# #5#) (|badNum| #4# (AND #1# (|isDomain| *2 #9#) (|isDomain| *1 (|PointsOfFiniteOrderTools| *3 *4)) #12=(|ofCategory| *4 #3#))) (|getGoodPrime| #4# (AND (|isDomain| *3 #2#) #12# (|isDomain| *2 (|PositiveInteger|)) #10# #11#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|wholePart| (#5=(|#1| $) 99 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #6=(#7=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| (#8=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #11=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#12=($) NIL T CONST)) (|rem| #13=(#14=($ $ $) NIL T ELT)) (|recip| ((#9# $) 93 T ELT)) (|quo| #13#) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) NIL T ELT)) (|prime?| #4#) (|partialFraction| (($ |#1| #17=(|Factored| |#1|)) 91 T ELT)) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) 52 T ELT)) (|padicFraction| (#7# 60 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfFractionalTerms| ((#18=(|Integer|) $) 96 T ELT)) (|nthFractionalTerm| (#19=($ $ #18#) 98 T ELT)) (|multiEuclidean| (((|Union| #15# #10#) #15# $) NIL T ELT)) (|lcm| #13# #20=(($ #15#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#21=(|SparseUnivariatePolynomial| $) #21# #21#) NIL T ELT)) (|gcd| #13# #20#) (|firstNumer| (#5# 95 T ELT)) (|firstDenom| ((#17# $) 94 T ELT)) (|factor| #11#) (|extendedEuclidean| (((|Record| #22=(|:| |coef1| $) #23=(|:| |coef2| $) #16#) $ $) NIL T ELT) (((|Union| (|Record| #22# #23#) #10#) $ $ $) NIL T ELT)) (|exquo| (#8# 92 T ELT)) (|expressIdealMember| (((|Maybe| #15#) #15# $) NIL T ELT)) (|euclideanSize| ((#24=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|compactFraction| (#7# 49 T ELT)) (|coerce| (((|OutputForm|) $) 123 T ELT) (($ #18#) 72 T ELT) #6# (($ #25=(|Fraction| #18#)) NIL T ELT) (($ |#1|) 40 T ELT) (((|Fraction| |#1|) $) 77 T ELT) (($ (|Fraction| #17#)) 85 T ELT)) (|characteristic| ((#24#) 70 T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#12# 24 T CONST)) (|One| (#12# 12 T CONST)) (= (#2# 86 T ELT)) (/ #13#) (- (#7# 107 T ELT) #13#) (+ (#14# 48 T ELT)) (** (($ $ #26=(|PositiveInteger|)) NIL T ELT) (($ $ #24#) NIL T ELT) (#19# NIL T ELT)) (* (($ #26# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #18# $) 109 T ELT) (#14# 47 T ELT) (($ $ #25#) NIL T ELT) (($ #25# $) NIL T ELT) (($ |#1| $) 108 T ELT) (($ $ |#1|) NIL T ELT))) 
(((|PartialFraction| |#1|) (|Join| (|Field|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| |#1|) $)) (SIGNATURE |coerce| ($ (|Fraction| #1=(|Factored| |#1|)))) (SIGNATURE |compactFraction| #2=($ $)) (SIGNATURE |firstDenom| (#1# $)) (SIGNATURE |firstNumer| #3=(|#1| $)) (SIGNATURE |nthFractionalTerm| ($ $ #4=(|Integer|))) (SIGNATURE |numberOfFractionalTerms| (#4# $)) (SIGNATURE |padicallyExpand| ((|SparseUnivariatePolynomial| |#1|) |#1| |#1|)) (SIGNATURE |padicFraction| #2#) (SIGNATURE |partialFraction| ($ |#1| #1#)) (SIGNATURE |wholePart| #3#))) (|EuclideanDomain|)) (T |PartialFraction|)) 
((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Fraction| *3)) #2=(|isDomain| *1 (|PartialFraction| *3)) #3=(|ofCategory| *3 #4=(|EuclideanDomain|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| #5=(|Factored| *3))) #3# #2#)) (|compactFraction| #6=(*1 *1 *1) #7=(AND #8=(|isDomain| *1 (|PartialFraction| *2)) #9=(|ofCategory| *2 #4#))) (|firstDenom| #1# (AND (|isDomain| *2 #5#) #2# #3#)) (|firstNumer| #1# #7#) (|nthFractionalTerm| (*1 *1 *1 *2) #10=(AND (|isDomain| *2 (|Integer|)) #2# #3#)) (|numberOfFractionalTerms| #1# #10#) (|padicallyExpand| (*1 *2 *3 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) #2# #3#)) (|padicFraction| #6# #7#) (|partialFraction| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Factored| *2)) #9# #8#)) (|wholePart| #1# #7#)) 
((|partialFraction| ((#1=(|Any|) #2=(|Polynomial| |#1|) (|Factored| #2#) #3=(|Symbol|)) 17 T ELT) ((#1# (|Fraction| #2#) #3#) 18 T ELT))) 
(((|PartialFractionPackage| |#1|) (CATEGORY |package| (SIGNATURE |partialFraction| (#1=(|Any|) (|Fraction| #2=(|Polynomial| |#1|)) #3=(|Symbol|))) (SIGNATURE |partialFraction| (#1# #2# (|Factored| #2#) #3#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (T |PartialFractionPackage|)) 
((|partialFraction| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Factored| #1=(|Polynomial| *6))) (|isDomain| *5 #2=(|Symbol|)) (|isDomain| *3 #1#) (|ofCategory| *6 #3=(|Join| (|EuclideanDomain|) (|CharacteristicZero|))) #4=(|isDomain| *2 (|Any|)) (|isDomain| *1 (|PartialFractionPackage| *6)))) (|partialFraction| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 #2#) (|ofCategory| *5 #3#) #4# (|isDomain| *1 (|PartialFractionPackage| *5))))) 
((|gcdPrimitive| (#1=(|#4| (|List| |#4|)) 148 T ELT) (#2=(#3=(|SparseUnivariatePolynomial| |#4|) #3# #3#) 85 T ELT) (#4=(|#4| |#4| |#4|) 147 T ELT)) (|gcd| ((#3# (|List| #3#)) 141 T ELT) (#2# 61 T ELT) (#1# 70 T ELT) (#4# 108 T ELT))) 
(((|PolynomialGcdPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |gcd| #1=(|#4| |#4| |#4|)) (SIGNATURE |gcd| #2=(|#4| (|List| |#4|))) (SIGNATURE |gcd| #3=(#4=(|SparseUnivariatePolynomial| |#4|) #4# #4#)) (SIGNATURE |gcd| (#4# (|List| #4#))) (SIGNATURE |gcdPrimitive| #1#) (SIGNATURE |gcdPrimitive| #3#) (SIGNATURE |gcdPrimitive| #2#)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |PolynomialGcdPackage|)) 
((|gcdPrimitive| #1=(*1 *2 *3) #2=(AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #3=(|PolynomialCategory| *6 *4 *5)) (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *2)) #4=(|ofCategory| *4 #5=(|OrderedAbelianMonoidSup|)) #6=(|ofCategory| *5 #7=(|OrderedSet|)) #8=(|ofCategory| *6 #9=(|EuclideanDomain|)))) (|gcdPrimitive| #10=(*1 *2 *2 *2) #11=(AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|ofCategory| *6 #12=(|PolynomialCategory| *5 *3 *4)) #13=(|ofCategory| *3 #5#) #14=(|ofCategory| *4 #7#) #15=(|ofCategory| *5 #9#) (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *6)))) (|gcdPrimitive| #10# #16=(AND #13# #14# #15# (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *2)) (|ofCategory| *2 #12#))) (|gcd| #1# (AND (|isDomain| *3 (|List| #17=(|SparseUnivariatePolynomial| *7))) #4# #6# #8# (|isDomain| *2 #17#) (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *7)) (|ofCategory| *7 #3#))) (|gcd| #10# #11#) (|gcd| #1# #2#) (|gcd| #10# #16#)) 
((|youngGroup| ((#1=(|PermutationGroup| #2=(|Integer|)) (|Partition|)) 38 T ELT) (#3=(#1# (|List| #2#)) 34 T ELT)) (|symmetricGroup| (#3# 66 T ELT) (#4=(#1# #5=(|PositiveInteger|)) 67 T ELT)) (|rubiksGroup| (#6=(#1#) 39 T ELT)) (|mathieu24| (#6# 53 T ELT) (#3# 52 T ELT)) (|mathieu23| (#6# 51 T ELT) (#3# 50 T ELT)) (|mathieu22| (#6# 49 T ELT) (#3# 48 T ELT)) (|mathieu12| (#6# 47 T ELT) (#3# 46 T ELT)) (|mathieu11| (#6# 45 T ELT) (#3# 44 T ELT)) (|janko2| (#6# 55 T ELT) (#3# 54 T ELT)) (|dihedralGroup| (#3# 71 T ELT) (#4# 73 T ELT)) (|cyclicGroup| (#3# 68 T ELT) (#4# 69 T ELT)) (|alternatingGroup| (#3# 64 T ELT) (#4# 65 T ELT)) (|abelianGroup| ((#1# (|List| #5#)) 57 T ELT))) 
(((|PermutationGroupExamples|) (CATEGORY |package| (SIGNATURE |symmetricGroup| #1=(#2=(|PermutationGroup| #3=(|Integer|)) #4=(|PositiveInteger|))) (SIGNATURE |symmetricGroup| #5=(#2# (|List| #3#))) (SIGNATURE |alternatingGroup| #1#) (SIGNATURE |alternatingGroup| #5#) (SIGNATURE |abelianGroup| (#2# (|List| #4#))) (SIGNATURE |cyclicGroup| #1#) (SIGNATURE |cyclicGroup| #5#) (SIGNATURE |dihedralGroup| #1#) (SIGNATURE |dihedralGroup| #5#) (SIGNATURE |mathieu11| #5#) (SIGNATURE |mathieu11| #6=(#2#)) (SIGNATURE |mathieu12| #5#) (SIGNATURE |mathieu12| #6#) (SIGNATURE |mathieu22| #5#) (SIGNATURE |mathieu22| #6#) (SIGNATURE |mathieu23| #5#) (SIGNATURE |mathieu23| #6#) (SIGNATURE |mathieu24| #5#) (SIGNATURE |mathieu24| #6#) (SIGNATURE |janko2| #5#) (SIGNATURE |janko2| #6#) (SIGNATURE |rubiksGroup| #6#) (SIGNATURE |youngGroup| #5#) (SIGNATURE |youngGroup| (#2# (|Partition|))))) (T |PermutationGroupExamples|)) 
((|youngGroup| #1=(*1 *2 *3) (AND (|isDomain| *3 (|Partition|)) #2=(|isDomain| *2 (|PermutationGroup| #3=(|Integer|))) #4=(|isDomain| *1 (|PermutationGroupExamples|)))) (|youngGroup| #1# #5=(AND (|isDomain| *3 (|List| #3#)) #2# #4#)) (|rubiksGroup| #6=(*1 *2) #7=(AND #2# #4#)) (|janko2| #6# #7#) (|janko2| #1# #5#) (|mathieu24| #6# #7#) (|mathieu24| #1# #5#) (|mathieu23| #6# #7#) (|mathieu23| #1# #5#) (|mathieu22| #6# #7#) (|mathieu22| #1# #5#) (|mathieu12| #6# #7#) (|mathieu12| #1# #5#) (|mathieu11| #6# #7#) (|mathieu11| #1# #5#) (|dihedralGroup| #1# #5#) (|dihedralGroup| #1# #8=(AND (|isDomain| *3 #9=(|PositiveInteger|)) #2# #4#)) (|cyclicGroup| #1# #5#) (|cyclicGroup| #1# #8#) (|abelianGroup| #1# (AND (|isDomain| *3 (|List| #9#)) #2# #4#)) (|alternatingGroup| #1# #5#) (|alternatingGroup| #1# #8#) (|symmetricGroup| #1# #5#) (|symmetricGroup| #1# #8#)) 
((|totalGroebner| (#1=(#2=(|List| (|Polynomial| |#1|)) #2# (|List| (|Symbol|))) 14 T ELT)) (|lexGroebner| (#1# 13 T ELT))) 
(((|PolyGroebner| |#1|) (CATEGORY |package| (SIGNATURE |lexGroebner| #1=(#2=(|List| (|Polynomial| |#1|)) #2# (|List| (|Symbol|)))) (SIGNATURE |totalGroebner| #1#)) (|GcdDomain|)) (T |PolyGroebner|)) 
((|totalGroebner| #1=(*1 *2 *2 *3) #2=(AND (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *1 (|PolyGroebner| *4)))) (|lexGroebner| #1# #2#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|sample| #3=(($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|one?| ((#2# $) NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT)) (|max| #4#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcd| #4#) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|One| #3#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #4#) (** (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ #5=(|PositiveInteger|)) NIL T ELT)) (* (($ #5# $) NIL T ELT) #4#)) 
(((|PositiveInteger|) (|Join| (|OrderedAbelianSemiGroup|) (|Monoid|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) (ATTRIBUTE (|commutative| "*"))))) (T |PositiveInteger|)) 
((|gcd| (*1 *1 *1 *1) (|isDomain| *1 (|PositiveInteger|)))) 
((|NonNegativeInteger|) (|%ilt| 0 |#1|)) 
((|coerce| (((|Expression| |#1|) (|Pi|)) 16 T ELT))) 
(((|PiCoercions| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|Expression| |#1|) (|Pi|)))) (|IntegralDomain|)) (T |PiCoercions|)) 
((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|Pi|)) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|PiCoercions| *4)) (|ofCategory| *4 (|IntegralDomain|))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 66 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (#5=($ $ $) 60 T ELT) (#6=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 58 T ELT)) (|gcd| (#5# 62 T ELT) (#6# 61 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) 65 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|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 *3 *1) (AND (|ofCategory| *1 (|PrincipalIdealDomain|)) (|isDomain| *2 (|Maybe| (|List| *1))) (|isDomain| *3 (|List| *1))))) 
(|Join| (|GcdDomain|) (CATEGORY |domain| (SIGNATURE |principalIdeal| ((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $))) (SIGNATURE |expressIdealMember| ((|Maybe| (|List| $)) (|List| $) $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|interpolate| (((|SparseUnivariatePolynomial| |#2|) #1=(|List| |#2|) #1#) 17 T ELT) ((#2=(|UnivariatePolynomial| |#1| |#2|) #2# #1# #1#) 13 T ELT))) 
(((|PolynomialInterpolation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |interpolate| (#1=(|UnivariatePolynomial| |#1| |#2|) #1# #2=(|List| |#2|) #2#)) (SIGNATURE |interpolate| ((|SparseUnivariatePolynomial| |#2|) #2# #2#))) (|Symbol|) (|Field|)) (T |PolynomialInterpolation|)) 
((|interpolate| (*1 *2 *3 *3) (AND #1=(|isDomain| *3 (|List| *5)) #2=(|ofCategory| *5 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *5)) #3=(|isDomain| *1 (|PolynomialInterpolation| *4 *5)) #4=(|ofType| *4 (|Symbol|)))) (|interpolate| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *5)) #1# #4# #2# #3#))) 
((|LagrangeInterpolation| ((|#2| #1=(|List| |#1|) #1#) 28 T ELT))) 
(((|PolynomialInterpolationAlgorithms| |#1| |#2|) (CATEGORY |package| (SIGNATURE |LagrangeInterpolation| (|#2| #1=(|List| |#1|) #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))))) 
((|wrregime| ((#1=(|Integer|) #2=(|List| #3=(|Record| (|:| |eqzro| #4=(|List| |#4|)) (|:| |neqzro| #4#) (|:| |wcond| #5=(|List| #6=(|Polynomial| |#1|))) (|:| |bsoln| #7=(|Record| (|:| |partsol| #8=(|Vector| #9=(|Fraction| #6#))) (|:| |basis| (|List| #8#)))))) #10=(|String|)) 175 T ELT)) (|sqfree| ((|#4| |#4|) 194 T ELT)) (|se2rfi| ((#11=(|List| #9#) #12=(|List| (|Symbol|))) 146 T ELT)) (|regime| ((#3# #13=(|Record| (|:| |det| |#4|) #14=(|:| |rows| #15=(|List| #1#)) #16=(|:| |cols| #15#)) #17=(|Matrix| |#4|) #11# #18=(|List| #4#) #19=(|NonNegativeInteger|) #19# #1#) 88 T ELT)) (|redpps| ((#7# #7# #4#) 69 T ELT)) (|redmat| ((#17# #17# #4#) 65 T ELT)) (|rdregime| ((#2# #10#) 187 T ELT)) (|psolve| ((#1# #17# #20=(|PositiveInteger|) #10#) 167 T ELT) ((#1# #17# #12# #20# #10#) 166 T ELT) ((#1# #17# #4# #20# #10#) 165 T ELT) ((#1# #17# #10#) 154 T ELT) ((#1# #17# #12# #10#) 153 T ELT) ((#1# #17# #4# #10#) 152 T ELT) ((#2# #17# #20#) 151 T ELT) ((#2# #17# #12# #20#) 150 T ELT) ((#2# #17# #4# #20#) 149 T ELT) ((#2# #17#) 148 T ELT) ((#2# #17# #12#) 147 T ELT) ((#2# #17# #4#) 143 T ELT)) (|pr2dmp| ((|#4| #6#) 80 T ELT)) (|overset?| ((#21=(|Boolean|) #4# #18#) 191 T ELT)) (|nextSublist| (((|List| #15#) #1# #1#) 161 T ELT)) (|minset| ((#18# #18#) 106 T ELT)) (|minrank| (#22=(#19# #23=(|List| (|Record| #24=(|:| |rank| #19#) (|:| |eqns| #25=(|List| #13#)) (|:| |fgb| #4#)))) 100 T ELT)) (|maxrank| (#22# 99 T ELT)) (|inconsistent?| ((#21# #5#) 19 T ELT) ((#21# #4#) 15 T ELT)) (|hasoln| (((|Record| (|:| |sysok| #21#) (|:| |z0| #4#) (|:| |n0| #4#)) #4# #4#) 84 T ELT)) (|factorset| ((#4# |#4|) 57 T ELT)) (|dmp2rfi| ((#11# #4#) 142 T ELT) ((#26=(|Matrix| #9#) #17#) 66 T ELT) ((#9# |#4|) 139 T ELT)) (|bsolve| (((|Record| (|:| |rgl| #2#) (|:| |rgsz| #1#)) #17# #11# #19# #10# #1#) 112 T ELT)) (|ParCondList| ((#23# #17# #19#) 98 T ELT)) (|ParCond| ((#25# #17# #19#) 121 T ELT)) (|B1solve| ((#7# (|Record| (|:| |mat| #26#) (|:| |vec| #11#) #24# #14# #16#)) 56 T ELT))) 
(((|ParametricLinearEquations| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |psolve| (#1=(|List| #2=(|Record| (|:| |eqzro| #3=(|List| |#4|)) (|:| |neqzro| #3#) (|:| |wcond| #4=(|List| #5=(|Polynomial| |#1|))) (|:| |bsoln| #6=(|Record| (|:| |partsol| #7=(|Vector| #8=(|Fraction| #5#))) (|:| |basis| (|List| #7#)))))) #9=(|Matrix| |#4|) #3#)) (SIGNATURE |psolve| (#1# #9# #10=(|List| #11=(|Symbol|)))) (SIGNATURE |psolve| (#1# #9#)) (SIGNATURE |psolve| (#1# #9# #3# #12=(|PositiveInteger|))) (SIGNATURE |psolve| (#1# #9# #10# #12#)) (SIGNATURE |psolve| (#1# #9# #12#)) (SIGNATURE |psolve| (#13=(|Integer|) #9# #3# #14=(|String|))) (SIGNATURE |psolve| (#13# #9# #10# #14#)) (SIGNATURE |psolve| (#13# #9# #14#)) (SIGNATURE |psolve| (#13# #9# #3# #12# #14#)) (SIGNATURE |psolve| (#13# #9# #10# #12# #14#)) (SIGNATURE |psolve| (#13# #9# #12# #14#)) (SIGNATURE |wrregime| (#13# #1# #14#)) (SIGNATURE |rdregime| (#1# #14#)) (SIGNATURE |bsolve| ((|Record| (|:| |rgl| #1#) (|:| |rgsz| #13#)) #9# #15=(|List| #8#) #16=(|NonNegativeInteger|) #14# #13#)) (SIGNATURE |dmp2rfi| (#8# |#4|)) (SIGNATURE |dmp2rfi| (#17=(|Matrix| #8#) #9#)) (SIGNATURE |dmp2rfi| (#15# #3#)) (SIGNATURE |se2rfi| (#15# #10#)) (SIGNATURE |pr2dmp| (|#4| #5#)) (SIGNATURE |hasoln| ((|Record| (|:| |sysok| #18=(|Boolean|)) (|:| |z0| #3#) (|:| |n0| #3#)) #3# #3#)) (SIGNATURE |ParCondList| (#19=(|List| (|Record| #20=(|:| |rank| #16#) (|:| |eqns| #21=(|List| #22=(|Record| (|:| |det| |#4|) #23=(|:| |rows| #24=(|List| #13#)) #25=(|:| |cols| #24#)))) (|:| |fgb| #3#))) #9# #16#)) (SIGNATURE |redpps| (#6# #6# #3#)) (SIGNATURE |B1solve| (#6# (|Record| (|:| |mat| #17#) (|:| |vec| #15#) #20# #23# #25#))) (SIGNATURE |factorset| (#3# |#4|)) (SIGNATURE |maxrank| #26=(#16# #19#)) (SIGNATURE |minrank| #26#) (SIGNATURE |minset| (#27=(|List| #3#) #27#)) (SIGNATURE |nextSublist| ((|List| #24#) #13# #13#)) (SIGNATURE |overset?| (#18# #3# #27#)) (SIGNATURE |ParCond| (#21# #9# #16#)) (SIGNATURE |redmat| (#9# #9# #3#)) (SIGNATURE |regime| (#2# #22# #9# #15# #27# #16# #16# #13#)) (SIGNATURE |sqfree| (|#4| |#4|)) (SIGNATURE |inconsistent?| (#18# #3#)) (SIGNATURE |inconsistent?| (#18# #4#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|Join| (|OrderedSet|) (|ConvertibleTo| #11#)) (|OrderedAbelianMonoidSup|) (|PolynomialCategory| |#1| |#3| |#2|)) (T |ParametricLinearEquations|)) 
((|inconsistent?| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|List| #3=(|Polynomial| *4))) #4=(|ofCategory| *4 #5=(|Join| (|EuclideanDomain|) (|CharacteristicZero|))) #6=(|ofCategory| *5 #7=(|Join| (|OrderedSet|) (|ConvertibleTo| #8=(|Symbol|)))) #9=(|ofCategory| *6 #10=(|OrderedAbelianMonoidSup|)) #11=(|isDomain| *2 #12=(|Boolean|)) #13=(|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *7)) #14=(|ofCategory| *7 #15=(|PolynomialCategory| *4 *6 *5)))) (|inconsistent?| #1# (AND #16=(|isDomain| *3 #17=(|List| *7)) #14# #4# #6# #9# #11# #13#)) (|sqfree| #18=(*1 *2 *2) (AND #19=(|ofCategory| *3 #5#) #20=(|ofCategory| *4 #7#) #21=(|ofCategory| *5 #10#) (|isDomain| *1 (|ParametricLinearEquations| *3 *4 *5 *2)) (|ofCategory| *2 #22=(|PolynomialCategory| *3 *5 *4)))) (|regime| (*1 *2 *3 *4 *5 *6 *7 *7 *8) (AND (|isDomain| *3 (|Record| (|:| |det| *12) #23=(|:| |rows| #24=(|List| #25=(|Integer|))) #26=(|:| |cols| #24#))) (|isDomain| *4 (|Matrix| *12)) (|isDomain| *5 (|List| #27=(|Fraction| #28=(|Polynomial| *9)))) (|isDomain| *6 (|List| #29=(|List| *12))) (|isDomain| *7 #30=(|NonNegativeInteger|)) (|isDomain| *8 #25#) (|ofCategory| *9 #5#) (|ofCategory| *12 (|PolynomialCategory| *9 *11 *10)) (|ofCategory| *10 #7#) (|ofCategory| *11 #10#) (|isDomain| *2 (|Record| (|:| |eqzro| #29#) (|:| |neqzro| #29#) (|:| |wcond| (|List| #28#)) (|:| |bsoln| (|Record| (|:| |partsol| #31=(|Vector| #27#)) (|:| |basis| (|List| #31#)))))) (|isDomain| *1 (|ParametricLinearEquations| *9 *10 *11 *12)))) (|redmat| #32=(*1 *2 *2 *3) (AND (|isDomain| *2 #33=(|Matrix| *7)) #16# #14# #4# #6# #9# #13#)) (|ParCond| #34=(*1 *2 *3 *4) (AND #35=(|isDomain| *3 (|Matrix| *8)) #36=(|isDomain| *4 #30#) #37=(|ofCategory| *8 (|PolynomialCategory| *5 *7 *6)) #38=(|ofCategory| *5 #5#) #39=(|ofCategory| *6 #7#) #40=(|ofCategory| *7 #10#) (|isDomain| *2 #41=(|List| (|Record| (|:| |det| *8) #23# #26#))) #42=(|isDomain| *1 (|ParametricLinearEquations| *5 *6 *7 *8)))) (|overset?| #34# (AND (|isDomain| *4 (|List| #43=(|List| *8))) (|isDomain| *3 #43#) #37# #38# #39# #40# #11# #42#)) (|nextSublist| #44=(*1 *2 *3 *3) (AND #4# #6# #9# (|isDomain| *2 (|List| #24#)) #13# (|isDomain| *3 #25#) #14#)) (|minset| #18# (AND (|isDomain| *2 (|List| (|List| *6))) (|ofCategory| *6 #22#) #19# #20# #21# (|isDomain| *1 (|ParametricLinearEquations| *3 *4 *5 *6)))) (|minrank| #1# #45=(AND (|isDomain| *3 (|List| (|Record| #46=(|:| |rank| #30#) (|:| |eqns| (|List| (|Record| (|:| |det| *7) #23# #26#))) (|:| |fgb| #17#)))) #14# #4# #6# #9# (|isDomain| *2 #30#) #13#)) (|maxrank| #1# #45#) (|factorset| #1# (AND #4# #6# #9# (|isDomain| *2 (|List| *3)) #47=(|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *3)) #48=(|ofCategory| *3 #15#))) (|B1solve| #1# (AND (|isDomain| *3 (|Record| (|:| |mat| #49=(|Matrix| #50=(|Fraction| #3#))) (|:| |vec| #51=(|List| #50#)) #46# #23# #26#)) #4# #6# #9# #52=(|isDomain| *2 #53=(|Record| (|:| |partsol| #54=(|Vector| #50#)) (|:| |basis| (|List| #54#)))) #13# #14#)) (|redpps| #32# (AND #52# #16# #4# #14# #6# #9# #13#)) (|ParCondList| #34# (AND #35# #37# #38# #39# #40# (|isDomain| *2 (|List| (|Record| #46# (|:| |eqns| #41#) (|:| |fgb| #43#)))) #42# #36#)) (|hasoln| #44# (AND #4# #6# #9# #14# (|isDomain| *2 (|Record| (|:| |sysok| #12#) (|:| |z0| #17#) (|:| |n0| #17#))) #13# #16#)) (|pr2dmp| #1# (AND (|isDomain| *3 #3#) #4# (|ofCategory| *2 #15#) (|isDomain| *1 (|ParametricLinearEquations| *4 *5 *6 *2)) #6# #9#)) (|se2rfi| #1# (AND (|isDomain| *3 #55=(|List| #8#)) #4# #6# #9# #56=(|isDomain| *2 #51#) #13# #14#)) (|dmp2rfi| #1# (AND #16# #14# #4# #6# #9# #56# #13#)) (|dmp2rfi| #1# (AND #57=(|isDomain| *3 #33#) #14# #4# #6# #9# (|isDomain| *2 #49#) #13#)) (|dmp2rfi| #1# (AND #4# #6# #9# (|isDomain| *2 #50#) #47# #48#)) (|bsolve| (*1 *2 *3 *4 *5 *6 *7) (AND (|isDomain| *3 (|Matrix| *11)) (|isDomain| *4 (|List| #58=(|Fraction| #59=(|Polynomial| *8)))) (|isDomain| *5 #30#) #60=(|isDomain| *6 #61=(|String|)) (|ofCategory| *8 #5#) (|ofCategory| *11 (|PolynomialCategory| *8 *10 *9)) (|ofCategory| *9 #7#) (|ofCategory| *10 #10#) (|isDomain| *2 (|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| #62=(|List| *11)) (|:| |neqzro| #62#) (|:| |wcond| (|List| #59#)) (|:| |bsoln| (|Record| (|:| |partsol| #63=(|Vector| #58#)) (|:| |basis| (|List| #63#))))))) (|:| |rgsz| #25#))) (|isDomain| *1 (|ParametricLinearEquations| *8 *9 *10 *11)) (|isDomain| *7 #25#))) (|rdregime| #1# (AND (|isDomain| *3 #61#) #4# #6# #9# #64=(|isDomain| *2 (|List| (|Record| (|:| |eqzro| #17#) (|:| |neqzro| #17#) (|:| |wcond| #2#) (|:| |bsoln| #53#)))) #13# #14#)) (|wrregime| #34# (AND (|isDomain| *3 #65=(|List| (|Record| (|:| |eqzro| #43#) (|:| |neqzro| #43#) (|:| |wcond| (|List| #66=(|Polynomial| *5))) (|:| |bsoln| (|Record| (|:| |partsol| #67=(|Vector| (|Fraction| #66#))) (|:| |basis| (|List| #67#))))))) #68=(|isDomain| *4 #61#) #38# #37# #39# #40# #69=(|isDomain| *2 #25#) #42#)) (|psolve| #70=(*1 *2 *3 *4 *5) (AND #71=(|isDomain| *3 (|Matrix| *9)) #72=(|isDomain| *4 #73=(|PositiveInteger|)) #74=(|isDomain| *5 #61#) #75=(|ofCategory| *9 (|PolynomialCategory| *6 *8 *7)) #76=(|ofCategory| *6 #5#) #77=(|ofCategory| *7 #7#) #78=(|ofCategory| *8 #10#) #69# #79=(|isDomain| *1 (|ParametricLinearEquations| *6 *7 *8 *9)))) (|psolve| #80=(*1 *2 *3 *4 *5 *6) (AND #81=(|isDomain| *3 (|Matrix| *10)) #82=(|isDomain| *4 #55#) #83=(|isDomain| *5 #73#) #60# #84=(|ofCategory| *10 (|PolynomialCategory| *7 *9 *8)) #85=(|ofCategory| *7 #5#) #86=(|ofCategory| *8 #7#) #87=(|ofCategory| *9 #10#) #69# #88=(|isDomain| *1 (|ParametricLinearEquations| *7 *8 *9 *10)))) (|psolve| #80# (AND #81# (|isDomain| *4 (|List| *10)) #83# #60# #84# #85# #86# #87# #69# #88#)) (|psolve| #34# (AND #35# #68# #37# #38# #39# #40# #69# #42#)) (|psolve| #70# (AND #71# #82# #74# #75# #76# #77# #78# #69# #79#)) (|psolve| #70# (AND #71# #89=(|isDomain| *4 #90=(|List| *9)) #74# #75# #76# #77# #78# #69# #79#)) (|psolve| #34# (AND #35# #72# #37# #38# #39# #40# #91=(|isDomain| *2 #65#) #42#)) (|psolve| #70# (AND #71# #82# #83# #75# #76# #77# #78# #92=(|isDomain| *2 (|List| (|Record| (|:| |eqzro| #90#) (|:| |neqzro| #90#) (|:| |wcond| (|List| #93=(|Polynomial| *6))) (|:| |bsoln| (|Record| (|:| |partsol| #94=(|Vector| (|Fraction| #93#))) (|:| |basis| (|List| #94#))))))) #79#)) (|psolve| #70# (AND #71# #83# #75# #76# #77# #78# #92# #79# #89#)) (|psolve| #1# (AND #57# #14# #4# #6# #9# #64# #13#)) (|psolve| #34# (AND #35# #82# #37# #38# #39# #40# #91# #42#)) (|psolve| #34# (AND #35# #37# #38# #39# #40# #91# #42# (|isDomain| *4 #43#)))) 
((|zoom| (#1=($ $ #2=(|Segment| #3=(|DoubleFloat|))) 125 T ELT) (($ $ #2# #2#) 126 T ELT)) (|yRange| (#4=(#2# $) 73 T ELT)) (|xRange| (#4# 72 T ELT)) (|tRange| (#4# 74 T ELT)) (|setScreenResolution| (#5=(#6=(|Integer|) #6#) 66 T ELT)) (|setMinPoints| (#5# 61 T ELT)) (|setMaxPoints| (#5# 64 T ELT)) (|setAdaptive| (#7=(#8=(|Boolean|) #8#) 68 T ELT)) (|screenResolution| (#9=(#6#) 65 T ELT)) (|refine| (#1# 129 T ELT) (($ $) 130 T ELT)) (|pointPlot| (($ #10=(|Mapping| #11=(|Point| #3#) #3#) #2#) 148 T ELT) (($ #10# #2# #2# #2#) 149 T ELT)) (|plotPolar| (#12=($ #13=(|Mapping| #3# #3#) #2#) 156 T ELT) (($ #13#) 160 T ELT)) (|plot| (#12# 144 T ELT) (($ #13# #2# #2#) 145 T ELT) (($ #14=(|List| #13#) #2#) 153 T ELT) (($ #14# #2# #2#) 154 T ELT) (($ #13# #13# #2#) 146 T ELT) (($ #13# #13# #2# #2# #2#) 147 T ELT) (#1# 131 T ELT)) (|parametric?| ((#8# $) 69 T ELT)) (|numFunEvals| (#9# 70 T ELT)) (|minPoints| (#9# 59 T ELT)) (|maxPoints| (#9# 62 T ELT)) (|listBranches| (((|List| (|List| #11#)) $) 35 T ELT)) (|debug| (#7# 71 T ELT)) (|coerce| (((|OutputForm|) $) 174 T ELT)) (|adaptive?| ((#8#) 67 T ELT))) 
(((|Plot|) (|Join| (|PlottablePlaneCurveCategory|) (CATEGORY |domain| (SIGNATURE |plot| #1=($ #2=(|Mapping| #3=(|DoubleFloat|) #3#) #4=(|Segment| #3#))) (SIGNATURE |plot| ($ #2# #4# #4#)) (SIGNATURE |plot| ($ #5=(|List| #2#) #4#)) (SIGNATURE |plot| ($ #5# #4# #4#)) (SIGNATURE |plot| ($ #2# #2# #4#)) (SIGNATURE |plot| ($ #2# #2# #4# #4# #4#)) (SIGNATURE |pointPlot| ($ #6=(|Mapping| (|Point| #3#) #3#) #4#)) (SIGNATURE |pointPlot| ($ #6# #4# #4# #4#)) (SIGNATURE |plotPolar| #1#) (SIGNATURE |plotPolar| ($ #2#)) (SIGNATURE |plot| #7=($ $ #4#)) (SIGNATURE |parametric?| (#8=(|Boolean|) $)) (SIGNATURE |zoom| #7#) (SIGNATURE |zoom| ($ $ #4# #4#)) (SIGNATURE |refine| #7#) (SIGNATURE |refine| ($ $)) (SIGNATURE |tRange| (#4# $)) (SIGNATURE |minPoints| #9=(#10=(|Integer|))) (SIGNATURE |setMinPoints| #11=(#10# #10#)) (SIGNATURE |maxPoints| #9#) (SIGNATURE |setMaxPoints| #11#) (SIGNATURE |screenResolution| #9#) (SIGNATURE |setScreenResolution| #11#) (SIGNATURE |adaptive?| (#8#)) (SIGNATURE |setAdaptive| #12=(#8# #8#)) (SIGNATURE |numFunEvals| #9#) (SIGNATURE |debug| #12#)))) (T |Plot|)) 
((|plot| #1=(*1 *1 *2 *3) #2=(AND #3=(|isDomain| *2 #4=(|Mapping| #5=(|DoubleFloat|) #5#)) #6=(|isDomain| *3 #7=(|Segment| #5#)) #8=(|isDomain| *1 (|Plot|)))) (|plot| #9=(*1 *1 *2 *3 *3) #2#) (|plot| #1# #10=(AND (|isDomain| *2 (|List| #4#)) #6# #8#)) (|plot| #9# #10#) (|plot| (*1 *1 *2 *2 *3) #2#) (|plot| (*1 *1 *2 *2 *3 *3 *3) #2#) (|pointPlot| #1# #11=(AND (|isDomain| *2 (|Mapping| (|Point| #5#) #5#)) #6# #8#)) (|pointPlot| (*1 *1 *2 *3 *3 *3) #11#) (|plotPolar| #1# #2#) (|plotPolar| (*1 *1 *2) (AND #3# #8#)) (|plot| #12=(*1 *1 *1 *2) #13=(AND (|isDomain| *2 #7#) #8#)) (|parametric?| #14=(*1 *2 *1) #15=(AND (|isDomain| *2 (|Boolean|)) #8#)) (|zoom| #12# #13#) (|zoom| (*1 *1 *1 *2 *2) #13#) (|refine| #12# #13#) (|refine| (*1 *1 *1) #8#) (|tRange| #14# #13#) (|minPoints| #16=(*1 *2) #17=(AND (|isDomain| *2 (|Integer|)) #8#)) (|setMinPoints| #18=(*1 *2 *2) #17#) (|maxPoints| #16# #17#) (|setMaxPoints| #18# #17#) (|screenResolution| #16# #17#) (|setScreenResolution| #18# #17#) (|adaptive?| #16# #15#) (|setAdaptive| #18# #15#) (|numFunEvals| #16# #17#) (|debug| #18# #15#)) 
((|plotPolar| ((#1=(|Plot|) |#1| #2=(|Symbol|)) 17 T ELT) (#3=(#1# |#1| #2# #4=(|Segment| (|DoubleFloat|))) 21 T ELT)) (|plot| ((#1# |#1| |#1| #2# #4#) 19 T ELT) (#3# 15 T ELT))) 
(((|PlotFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |plot| #1=(#2=(|Plot|) |#1| #3=(|Symbol|) #4=(|Segment| (|DoubleFloat|)))) (SIGNATURE |plot| (#2# |#1| |#1| #3# #4#)) (SIGNATURE |plotPolar| #1#) (SIGNATURE |plotPolar| (#2# |#1| #3#))) (|ConvertibleTo| (|InputForm|))) (T |PlotFunctions1|)) 
((|plotPolar| (*1 *2 *3 *4) (AND #1=(|isDomain| *4 (|Symbol|)) #2=(|isDomain| *2 (|Plot|)) #3=(|isDomain| *1 (|PlotFunctions1| *3)) #4=(|ofCategory| *3 (|ConvertibleTo| (|InputForm|))))) (|plotPolar| #5=(*1 *2 *3 *4 *5) #6=(AND #1# (|isDomain| *5 (|Segment| (|DoubleFloat|))) #2# #3# #4#)) (|plot| (*1 *2 *3 *3 *4 *5) #6#) (|plot| #5# #6#)) 
((|zoom| (($ $ #1=(|Segment| #2=(|DoubleFloat|)) #1# #1#) 123 T ELT)) (|zRange| (#3=(#1# $) 64 T ELT)) (|yRange| (#3# 63 T ELT)) (|xRange| (#3# 62 T ELT)) (|tValues| (((|List| (|List| #2#)) $) 69 T ELT)) (|tRange| (#3# 65 T ELT)) (|setScreenResolution3D| (#4=(#5=(|Integer|) #5#) 57 T ELT)) (|setMinPoints3D| (#4# 52 T ELT)) (|setMaxPoints3D| (#4# 55 T ELT)) (|setAdaptive3D| (#6=(#7=(|Boolean|) #7#) 59 T ELT)) (|screenResolution3D| (#8=(#5#) 56 T ELT)) (|refine| (#9=($ $ #1#) 126 T ELT) (($ $) 127 T ELT)) (|pointPlot| (($ #10=(|Mapping| #11=(|Point| #2#) #2#) #1#) 133 T ELT) (($ #10# #1# #1# #1# #1#) 134 T ELT)) (|plot| (($ #12=(|Mapping| #2# #2#) #12# #12# #12# #1#) 140 T ELT) (($ #12# #12# #12# #12# #1# #1# #1# #1#) 141 T ELT) (#9# 129 T ELT)) (|numFunEvals3D| (#8# 60 T ELT)) (|minPoints3D| (#8# 50 T ELT)) (|maxPoints3D| (#8# 53 T ELT)) (|listBranches| (((|List| (|List| #11#)) $) 157 T ELT)) (|debug3D| (#6# 61 T ELT)) (|coerce| (((|OutputForm|) $) 155 T ELT)) (|adaptive3D?| ((#7#) 58 T ELT))) 
(((|Plot3D|) (|Join| (|PlottableSpaceCurveCategory|) (CATEGORY |domain| (SIGNATURE |pointPlot| ($ #1=(|Mapping| (|Point| #2=(|DoubleFloat|)) #2#) #3=(|Segment| #2#))) (SIGNATURE |pointPlot| ($ #1# #3# #3# #3# #3#)) (SIGNATURE |plot| ($ #4=(|Mapping| #2# #2#) #4# #4# #4# #3#)) (SIGNATURE |plot| ($ #4# #4# #4# #4# #3# #3# #3# #3#)) (SIGNATURE |plot| #5=($ $ #3#)) (SIGNATURE |zoom| ($ $ #3# #3# #3#)) (SIGNATURE |refine| #5#) (SIGNATURE |refine| ($ $)) (SIGNATURE |tRange| (#3# $)) (SIGNATURE |tValues| ((|List| (|List| #2#)) $)) (SIGNATURE |minPoints3D| #6=(#7=(|Integer|))) (SIGNATURE |setMinPoints3D| #8=(#7# #7#)) (SIGNATURE |maxPoints3D| #6#) (SIGNATURE |setMaxPoints3D| #8#) (SIGNATURE |screenResolution3D| #6#) (SIGNATURE |setScreenResolution3D| #8#) (SIGNATURE |adaptive3D?| (#9=(|Boolean|))) (SIGNATURE |setAdaptive3D| #10=(#9# #9#)) (SIGNATURE |numFunEvals3D| #6#) (SIGNATURE |debug3D| #10#)))) (T |Plot3D|)) 
((|pointPlot| (*1 *1 *2 *3) #1=(AND (|isDomain| *2 (|Mapping| (|Point| #2=(|DoubleFloat|)) #2#)) #3=(|isDomain| *3 #4=(|Segment| #2#)) #5=(|isDomain| *1 (|Plot3D|)))) (|pointPlot| (*1 *1 *2 *3 *3 *3 *3) #1#) (|plot| (*1 *1 *2 *2 *2 *2 *3) #6=(AND (|isDomain| *2 (|Mapping| #2# #2#)) #3# #5#)) (|plot| (*1 *1 *2 *2 *2 *2 *3 *3 *3 *3) #6#) (|plot| #7=(*1 *1 *1 *2) #8=(AND (|isDomain| *2 #4#) #5#)) (|zoom| (*1 *1 *1 *2 *2 *2) #8#) (|refine| #7# #8#) (|refine| (*1 *1 *1) #5#) (|tRange| #9=(*1 *2 *1) #8#) (|tValues| #9# (AND (|isDomain| *2 (|List| (|List| #2#))) #5#)) (|minPoints3D| #10=(*1 *2) #11=(AND (|isDomain| *2 (|Integer|)) #5#)) (|setMinPoints3D| #12=(*1 *2 *2) #11#) (|maxPoints3D| #10# #11#) (|setMaxPoints3D| #12# #11#) (|screenResolution3D| #10# #11#) (|setScreenResolution3D| #12# #11#) (|adaptive3D?| #10# #13=(AND (|isDomain| *2 (|Boolean|)) #5#)) (|setAdaptive3D| #12# #13#) (|numFunEvals3D| #10# #11#) (|debug3D| #12# #13#)) 
((|calcRanges| (((|List| (|Segment| #1=(|DoubleFloat|))) (|List| (|List| (|Point| #1#)))) 34 T ELT))) 
(((|PlotTools|) (CATEGORY |package| (SIGNATURE |calcRanges| ((|List| (|Segment| #1=(|DoubleFloat|))) (|List| (|List| (|Point| #1#))))))) (T |PlotTools|)) 
((|calcRanges| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|List| (|Point| #1=(|DoubleFloat|))))) (|isDomain| *2 (|List| (|Segment| #1#))) (|isDomain| *1 (|PlotTools|))))) 
((|optional| (#1=(#2=(|Expression| (|Integer|)) #3=(|Symbol|)) 16 T ELT)) (|multiple| (#1# 14 T ELT)) (|constant| (#1# 12 T ELT)) (|assert| ((#2# #3# (|Identifier|)) 19 T ELT))) 
(((|PatternMatchAssertions|) (CATEGORY |package| (SIGNATURE |assert| (#1=(|Expression| (|Integer|)) #2=(|Symbol|) (|Identifier|))) (SIGNATURE |constant| #3=(#1# #2#)) (SIGNATURE |optional| #3#) (SIGNATURE |multiple| #3#))) (T |PatternMatchAssertions|)) 
((|multiple| #1=(*1 *2 *3) #2=(AND #3=(|isDomain| *3 (|Symbol|)) #4=(|isDomain| *2 (|Expression| (|Integer|))) #5=(|isDomain| *1 (|PatternMatchAssertions|)))) (|optional| #1# #2#) (|constant| #1# #2#) (|assert| (*1 *2 *3 *4) (AND #3# (|isDomain| *4 (|Identifier|)) #4# #5#))) 
((|optional| (#1=(|#2| |#2|) 28 T ELT)) (|multiple| (#1# 29 T ELT)) (|constant| (#1# 27 T ELT)) (|assert| ((|#2| |#2| (|Identifier|)) 26 T ELT))) 
(((|FunctionSpaceAssertions| |#1| |#2|) (CATEGORY |package| (SIGNATURE |assert| (|#2| |#2| (|Identifier|))) (SIGNATURE |constant| #1=(|#2| |#2|)) (SIGNATURE |optional| #1#) (SIGNATURE |multiple| #1#)) (|SetCategory|) (|FunctionSpace| |#1|)) (T |FunctionSpaceAssertions|)) 
((|multiple| #1=(*1 *2 *2) #2=(AND (|ofCategory| *3 #3=(|SetCategory|)) (|isDomain| *1 (|FunctionSpaceAssertions| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)))) (|optional| #1# #2#) (|constant| #1# #2#) (|assert| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Identifier|)) (|ofCategory| *4 #3#) (|isDomain| *1 (|FunctionSpaceAssertions| *4 *2)) (|ofCategory| *2 (|FunctionSpace| *4))))) 
((|patternMatch| ((#1=(|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) #1#) 25 T ELT)) (|fixPredicate| (((|Mapping| #2=(|Boolean|) |#2|) (|Mapping| #2# |#3|)) 13 T ELT))) 
(((|PatternMatchPushDown| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |fixPredicate| ((|Mapping| #1=(|Boolean|) |#2|) (|Mapping| #1# |#3|))) (SIGNATURE |patternMatch| (#2=(|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) #2#))) #3=(|SetCategory|) (|PatternMatchable| |#1|) (|Join| #3# (|RetractableTo| |#2|))) (T |PatternMatchPushDown|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *6)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 (|Join| #1# (|RetractableTo| *3))) (|ofCategory| *3 (|PatternMatchable| *5)) (|isDomain| *1 (|PatternMatchPushDown| *5 *3 *6)))) (|fixPredicate| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| #2=(|Boolean|) *6)) (|ofCategory| *6 (|Join| #1# (|RetractableTo| *5))) (|ofCategory| *5 (|PatternMatchable| *4)) (|ofCategory| *4 #1#) (|isDomain| *2 (|Mapping| #2# *5)) (|isDomain| *1 (|PatternMatchPushDown| *4 *5 *6))))) 
((|patternMatch| ((#1=(|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) #1#) 30 T ELT))) 
(((|PatternMatchFunctionSpace| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| |#1| |#3|) |#3| #2=(|Pattern| |#1|) #1#))) (|SetCategory|) (|Join| (|IntegralDomain|) #3=(|PatternMatchable| |#1|)) (|Join| (|FunctionSpace| |#2|) (|ConvertibleTo| #2#) #3# (|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) #1=(|PatternMatchable| *5) (|RetractableTo| (|Kernel| $)))) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *6 (|Join| (|IntegralDomain|) #1#)) (|isDomain| *1 (|PatternMatchFunctionSpace| *5 *6 *3))))) 
((|patternMatch| ((#1=(|PatternMatchResult| #2=(|Integer|) |#1|) |#1| (|Pattern| #2#) #1#) 13 T ELT))) 
(((|PatternMatchIntegerNumberSystem| |#1|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| #2=(|Integer|) |#1|) |#1| (|Pattern| #2#) #1#))) (|IntegerNumberSystem|)) (T |PatternMatchIntegerNumberSystem|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| #1=(|Integer|) *3)) (|isDomain| *4 (|Pattern| #1#)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *1 (|PatternMatchIntegerNumberSystem| *3))))) 
((|patternMatch| ((#1=(|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) #1#) 57 T ELT))) 
(((|PatternMatchKernel| |#1| |#2|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) #2=(|Pattern| |#1|) #1#))) #3=(|SetCategory|) (|Join| #3# (|RetractableTo| (|Kernel| $)) (|ConvertibleTo| #2#) (|PatternMatchable| |#1|))) (T |PatternMatchKernel|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *6)) (|isDomain| *3 (|Kernel| *6)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 (|Join| #1# (|RetractableTo| (|Kernel| $)) (|ConvertibleTo| *4) (|PatternMatchable| *5))) (|isDomain| *4 (|Pattern| *5)) (|isDomain| *1 (|PatternMatchKernel| *5 *6))))) 
((|patternMatch| ((#1=(|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) #1#) 17 T ELT))) 
(((|PatternMatchListAggregate| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) #1#))) (|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))))) 
((|patternMatch| ((#1=(|PatternMatchResult| |#1| |#5|) |#5| #2=(|Pattern| |#1|) #1#) 17 (|has| |#3| (|PatternMatchable| |#1|)) ELT) ((#1# |#5| #2# #1# (|Mapping| #1# |#3| #2# #1#)) 16 T ELT))) 
(((|PatternMatchPolynomialCategory| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| |#1| |#5|) |#5| #2=(|Pattern| |#1|) #1# (|Mapping| #1# |#3| #2# #1#))) (IF (|has| |#3| #3=(|PatternMatchable| |#1|)) (SIGNATURE |patternMatch| (#1# |#5| #2# #1#)) |%noBranch|)) (|SetCategory|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Join| (|Ring|) #3#) (|Join| (|PolynomialCategory| |#4| |#2| |#3|) (|ConvertibleTo| #2#))) (T |PatternMatchPolynomialCategory|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *3)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *3 (|Join| (|PolynomialCategory| *8 *6 *7) #2=(|ConvertibleTo| *4))) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *7 #3=(|PatternMatchable| *5)) (|ofCategory| *6 #4=(|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #5=(|OrderedSet|)) (|ofCategory| *8 (|Join| #6=(|Ring|) #3#)) (|isDomain| *1 (|PatternMatchPolynomialCategory| *5 *6 *7 *8 *3)))) (|patternMatch| (*1 *2 *3 *4 *2 *5) (AND (|isDomain| *5 (|Mapping| #7=(|PatternMatchResult| *6 *3) *8 #8=(|Pattern| *6) #7#)) (|ofCategory| *8 #5#) (|isDomain| *2 #7#) (|isDomain| *4 #8#) (|ofCategory| *6 #1#) (|ofCategory| *3 (|Join| (|PolynomialCategory| *9 *7 *8) #2#)) (|ofCategory| *7 #4#) (|ofCategory| *9 (|Join| #6# (|PatternMatchable| *6))) (|isDomain| *1 (|PatternMatchPolynomialCategory| *6 *7 *8 *9 *3))))) 
((|suchThat| ((#1=(|Expression| (|Integer|)) #2=(|Symbol|) (|List| #3=(|Mapping| (|Boolean|) |#1|))) 18 T ELT) ((#1# #2# #3#) 15 T ELT))) 
(((|AttachPredicates| |#1|) (CATEGORY |package| (SIGNATURE |suchThat| (#1=(|Expression| (|Integer|)) #2=(|Symbol|) #3=(|Mapping| (|Boolean|) |#1|))) (SIGNATURE |suchThat| (#1# #2# (|List| #3#)))) (|Type|)) (T |AttachPredicates|)) 
((|suchThat| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|List| #3=(|Mapping| (|Boolean|) *5))) #4=(|ofCategory| *5 (|Type|)) #5=(|isDomain| *2 (|Expression| (|Integer|))) #6=(|isDomain| *1 (|AttachPredicates| *5)))) (|suchThat| #1# (AND #2# (|isDomain| *4 #3#) #4# #5# #6#))) 
((|suchThat| ((|#2| |#2| (|List| #1=(|Mapping| (|Boolean|) |#3|))) 12 T ELT) ((|#2| |#2| #1#) 13 T ELT))) 
(((|FunctionSpaceAttachPredicates| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |suchThat| (|#2| |#2| #1=(|Mapping| (|Boolean|) |#3|))) (SIGNATURE |suchThat| (|#2| |#2| (|List| #1#)))) (|SetCategory|) (|FunctionSpace| |#1|) (|Type|)) (T |FunctionSpaceAttachPredicates|)) 
((|suchThat| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 (|List| #2=(|Mapping| (|Boolean|) *5))) #3=(|ofCategory| *5 (|Type|)) #4=(|ofCategory| *4 (|SetCategory|)) #5=(|isDomain| *1 (|FunctionSpaceAttachPredicates| *4 *2 *5)) #6=(|ofCategory| *2 (|FunctionSpace| *4)))) (|suchThat| #1# (AND (|isDomain| *3 #2#) #3# #4# #5# #6#))) 
((|patternMatch| ((#1=(|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) #1#) 25 T ELT))) 
(((|PatternMatchQuotientFieldCategory| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| |#1| |#3|) |#3| #2=(|Pattern| |#1|) #1#))) (|SetCategory|) (|Join| (|IntegralDomain|) (|PatternMatchable| |#1|) (|ConvertibleTo| #2#)) (|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))))) 
((|patternMatch| ((#1=(|PatternMatchResult| |#1| #2=(|Symbol|)) #2# (|Pattern| |#1|) #1#) 18 T ELT))) 
(((|PatternMatchSymbol| |#1|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| |#1| #2=(|Symbol|)) #2# (|Pattern| |#1|) #1#))) (|SetCategory|)) (T |PatternMatchSymbol|)) 
((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 #1=(|Symbol|))) (|isDomain| *3 #1#) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|)) (|isDomain| *1 (|PatternMatchSymbol| *5))))) 
((|patternMatchTimes| ((#1=(|PatternMatchResult| |#1| |#3|) #2=(|List| |#3|) #3=(|List| #4=(|Pattern| |#1|)) #1# #5=(|Mapping| #1# |#3| #4# #1#)) 34 T ELT)) (|patternMatch| ((#1# #2# #3# (|Mapping| |#3| #2#) #1# #5#) 33 T ELT))) 
(((|PatternMatchTools| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| |#1| |#3|) #2=(|List| |#3|) #3=(|List| #4=(|Pattern| |#1|)) (|Mapping| |#3| #2#) #1# #5=(|Mapping| #1# |#3| #4# #1#))) (SIGNATURE |patternMatchTimes| (#1# #2# #3# #1# #5#))) (|SetCategory|) #6=(|Ring|) (|Join| #6# (|ConvertibleTo| #4#) (|RetractableTo| |#2|))) (T |PatternMatchTools|)) 
((|patternMatchTimes| (*1 *2 *3 *4 *2 *5) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|List| #1=(|Pattern| *6))) (|isDomain| *5 (|Mapping| #2=(|PatternMatchResult| *6 *8) *8 #1# #2#)) (|ofCategory| *6 #3=(|SetCategory|)) (|ofCategory| *8 (|Join| #4=(|Ring|) (|ConvertibleTo| #1#) (|RetractableTo| *7))) (|isDomain| *2 #2#) (|ofCategory| *7 #4#) (|isDomain| *1 (|PatternMatchTools| *6 *7 *8)))) (|patternMatch| (*1 *2 *3 *4 *5 *2 *6) (AND (|isDomain| *4 (|List| #5=(|Pattern| *7))) (|isDomain| *5 (|Mapping| *9 #6=(|List| *9))) (|isDomain| *6 (|Mapping| #7=(|PatternMatchResult| *7 *9) *9 #5# #7#)) (|ofCategory| *7 #3#) (|ofCategory| *9 (|Join| #4# (|ConvertibleTo| #5#) (|RetractableTo| *8))) (|isDomain| *2 #7#) (|isDomain| *3 #6#) (|ofCategory| *8 #4#) (|isDomain| *1 (|PatternMatchTools| *7 *8 *9))))) 
((|legendre| (#1=((|SparseUnivariatePolynomial| (|Fraction| #2=(|Integer|))) #2#) 80 T ELT)) (|laguerre| (#3=(#4=(|SparseUnivariatePolynomial| #2#) #2#) 83 T ELT)) (|hermite| (#3# 77 T ELT)) (|fixedDivisor| ((#2# #4#) 73 T ELT)) (|euler| (#1# 66 T ELT)) (|cyclotomic| (#3# 49 T ELT)) (|chebyshevU| (#3# 85 T ELT)) (|chebyshevT| (#3# 84 T ELT)) (|bernoulli| (#1# 68 T ELT))) 
(((|PolynomialNumberTheoryFunctions|) (CATEGORY |package| (SIGNATURE |bernoulli| #1=((|SparseUnivariatePolynomial| (|Fraction| #2=(|Integer|))) #2#)) (SIGNATURE |chebyshevT| #3=(#4=(|SparseUnivariatePolynomial| #2#) #2#)) (SIGNATURE |chebyshevU| #3#) (SIGNATURE |cyclotomic| #3#) (SIGNATURE |euler| #1#) (SIGNATURE |fixedDivisor| (#2# #4#)) (SIGNATURE |hermite| #3#) (SIGNATURE |laguerre| #3#) (SIGNATURE |legendre| #1#))) (T |PolynomialNumberTheoryFunctions|)) 
((|legendre| #1=(*1 *2 *3) #2=(AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Fraction| #3=(|Integer|)))) #4=(|isDomain| *1 (|PolynomialNumberTheoryFunctions|)) #5=(|isDomain| *3 #3#))) (|laguerre| #1# #6=(AND (|isDomain| *2 #7=(|SparseUnivariatePolynomial| #3#)) #4# #5#)) (|hermite| #1# #6#) (|fixedDivisor| #1# (AND (|isDomain| *3 #7#) (|isDomain| *2 #3#) #4#)) (|euler| #1# #2#) (|cyclotomic| #1# #6#) (|chebyshevU| #1# #6#) (|chebyshevT| #1# #6#) (|bernoulli| #1# #2#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|zero| (($ #5=(|NonNegativeInteger|)) NIL (|has| |#1| (|AbelianMonoid|)) ELT)) (|swap!| (((|Void|) $ #6=(|Integer|) #6#) NIL #7=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #8=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#9=(#3# $) NIL #10=(|has| |#1| #11=(|OrderedSet|)) ELT)) (|sort!| (#12=($ #8# $) NIL #7# ELT) (#13=($ $) NIL (AND #7# #10#) ELT)) (|sort| (#12# NIL T ELT) (#13# NIL #10# ELT)) (|setelt| #14=(#15=(|#1| $ #6# |#1|) NIL #7# ELT) ((|#1| $ #16=(|UniversalSegment| #6#) |#1|) NIL #7# ELT)) (|select| #17=(($ #18=(|Mapping| #3# |#1|) $) NIL #19=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#20=($) NIL T CONST)) (|reverse!| (#13# NIL #7# ELT)) (|reverse| #21=(#13# NIL T ELT)) (|removeDuplicates| (#13# NIL #22=(AND #19# #4#) ELT)) (|remove| (#23=($ |#1| $) NIL #22# ELT) #17#) (|reduce| ((|#1| #24=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #24# $ |#1|) NIL T ELT) ((|#1| #24# $) NIL T ELT)) (|qsetelt!| #14#) (|qelt| (#25=(|#1| $ #6#) NIL T ELT)) (|position| ((#6# #18# $) NIL T ELT) ((#6# |#1| $) NIL #4# ELT) ((#6# |#1| $ #6#) NIL #4# ELT)) (|point| (#26=($ #27=(|List| |#1|)) 9 T ELT)) (|outerProduct| (((|Matrix| |#1|) $ $) NIL #28=(|has| |#1| (|Ring|)) ELT)) (|new| (($ #5# |#1|) NIL T ELT)) (|minIndex| #29=((#6# $) NIL #30=(|has| #6# #11#) ELT)) (|min| #31=(#32=($ $ $) NIL #10# ELT)) (|merge| (($ #8# $ $) NIL T ELT) #31#) (|members| #33=((#27# $) NIL T ELT)) (|member?| (#34=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| #29#) (|max| #31#) (|map!| #35=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #35# (($ #24# $ $) NIL T ELT)) (|magnitude| #36=(#37=(|#1| $) NIL (AND (|has| |#1| (|RadicalCategory|)) #28#) ELT)) (|length| #36#) (|latex| (((|String|) $) NIL #38=(|has| |#1| (|SetCategory|)) ELT)) (|insert| (($ |#1| $ #6#) NIL T ELT) (#39=($ $ $ #6#) NIL T ELT)) (|indices| (((|List| #6#) $) NIL T ELT)) (|index?| ((#3# #6# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #38# ELT)) (|first| (#37# NIL #30# ELT)) (|find| (((|Union| |#1| "failed") #18# $) NIL T ELT)) (|fill!| (#40=($ $ |#1|) NIL #7# ELT)) (|extend| (($ $ #27#) 25 T ELT)) (|every?| #41=((#3# #18# $) NIL T ELT)) (|eval| (($ $ (|List| #42=(|Equation| |#1|))) NIL #43=(AND (|has| |#1| (|Evalable| |#1|)) #38#) ELT) (($ $ #42#) NIL #43# ELT) (($ $ |#1| |#1|) NIL #43# ELT) (($ $ #27# #27#) NIL #43# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#34# NIL #22# ELT)) (|entries| #33#) (|empty?| (#9# NIL T ELT)) (|empty| (#20# NIL T ELT)) (|elt| (#15# NIL T ELT) (#25# 18 T ELT) #44=(($ $ #16#) NIL T ELT)) (|dot| ((|#1| $ $) NIL #28# ELT)) (|dimension| (((|PositiveInteger|) $) 13 T ELT)) (|delete| (($ $ #6#) NIL T ELT) #44#) (|cross| (#32# 23 T ELT)) (|count| ((#5# |#1| $) NIL #4# ELT) ((#5# #18# $) NIL T ELT)) (|copyInto!| (#39# NIL #7# ELT)) (|copy| #21#) (|convert| ((#45=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #45#)) ELT) (#26# 14 T ELT)) (|construct| (#26# NIL T ELT)) (|concat| (#40# NIL T ELT) (#23# NIL T ELT) (#32# 24 T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#46=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #46#)) ELT)) (|before?| #1#) (|any?| #41#) (>= #47=(#2# NIL #10# ELT)) (> #47#) (= #1#) (<= #47#) (< #47#) (- (#13# NIL #48=(|has| |#1| (|AbelianGroup|)) ELT) (#32# NIL #48# ELT)) (+ (#32# NIL (|has| |#1| (|AbelianSemiGroup|)) ELT)) (* (($ #6# $) NIL #48# ELT) (#23# NIL #49=(|has| |#1| (|Monoid|)) ELT) (#40# NIL #49# ELT)) (|#| ((#5# $) 11 T ELT))) 
(((|Point| |#1|) (|PointCategory| |#1|) (|Ring|)) (T |Point|)) 
NIL 
((|pToHdmp| ((#1=(|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) #2=(|Polynomial| |#2|)) 22 T ELT)) (|pToDmp| ((#3=(|DistributedMultivariatePolynomial| |#1| |#2|) #2#) 35 T ELT)) (|hdmpToP| ((#2# #1#) 27 T ELT)) (|hdmpToDmp| ((#3# #1#) 57 T ELT)) (|dmpToP| ((#2# #3#) 32 T ELT)) (|dmpToHdmp| ((#1# #3#) 48 T ELT))) 
(((|PolToPol| |#1| |#2|) (CATEGORY |package| (SIGNATURE |dmpToHdmp| (#1=(|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) #2=(|DistributedMultivariatePolynomial| |#1| |#2|))) (SIGNATURE |hdmpToDmp| (#2# #1#)) (SIGNATURE |pToHdmp| (#1# #3=(|Polynomial| |#2|))) (SIGNATURE |hdmpToP| (#3# #1#)) (SIGNATURE |dmpToP| (#3# #2#)) (SIGNATURE |pToDmp| (#2# #3#))) (|List| (|Symbol|)) (|Ring|)) (T |PolToPol|)) 
((|pToDmp| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|Polynomial| *5)) #4=(|ofCategory| *5 (|Ring|)) #5=(|isDomain| *2 #6=(|DistributedMultivariatePolynomial| *4 *5)) #7=(|isDomain| *1 (|PolToPol| *4 *5)) #8=(|ofType| *4 (|List| (|Symbol|))))) (|dmpToP| #1# (AND #9=(|isDomain| *3 #6#) #8# #4# #10=(|isDomain| *2 #3#) #7#)) (|hdmpToP| #1# (AND #11=(|isDomain| *3 #12=(|HomogeneousDistributedMultivariatePolynomial| *4 *5)) #8# #4# #10# #7#)) (|pToHdmp| #1# (AND #2# #4# #13=(|isDomain| *2 #12#) #7# #8#)) (|hdmpToDmp| #1# (AND #11# #8# #4# #5# #7#)) (|dmpToHdmp| #1# (AND #9# #8# #4# #13# #7#))) 
((|sylvesterSequence| ((#1=(|List| |#2|) |#2| |#2|) 10 T ELT)) (|sturmVariationsOf| ((#2=(|NonNegativeInteger|) #3=(|List| |#1|)) 47 #4=(|has| |#1| (|OrderedRing|)) ELT)) (|sturmSequence| ((#1# |#2|) 11 T ELT)) (|lazyVariations| ((#2# #3# #5=(|Integer|) #5#) 45 #4# ELT)) (|boundOfCauchy| ((|#1| |#2|) 37 #4# ELT))) 
(((|RealPolynomialUtilitiesPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sylvesterSequence| (#1=(|List| |#2|) |#2| |#2|)) (SIGNATURE |sturmSequence| (#1# |#2|)) (IF (|has| |#1| (|OrderedRing|)) (PROGN (SIGNATURE |boundOfCauchy| (|#1| |#2|)) (SIGNATURE |sturmVariationsOf| (#2=(|NonNegativeInteger|) #3=(|List| |#1|))) (SIGNATURE |lazyVariations| (#2# #3# #4=(|Integer|) #4#))) |%noBranch|)) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |RealPolynomialUtilitiesPackage|)) 
((|lazyVariations| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| *5)) (|isDomain| *4 (|Integer|)) (|ofCategory| *5 #1=(|OrderedRing|)) (|ofCategory| *5 #2=(|Field|)) #3=(|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *5 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)))) (|sturmVariationsOf| #4=(*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #1#) #5=(|ofCategory| *4 #2#) #3# (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *5)) (|ofCategory| *5 #6=(|UnivariatePolynomialCategory| *4)))) (|boundOfCauchy| #4# (AND (|ofCategory| *2 #2#) (|ofCategory| *2 #1#) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|sturmSequence| #4# #7=(AND #5# (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|RealPolynomialUtilitiesPackage| *4 *3)) (|ofCategory| *3 #6#))) (|sylvesterSequence| (*1 *2 *3 *3) #7#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|Symbol|)) $) 16 T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) 21 T ELT) ((#9=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #8#) #8#) NIL #19=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#12# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #8#) #17#) #23# #8#) NIL #19# ELT)) (|sample| #24=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #25=(#17#)) . #26=($)) 8 T ELT) (((|Union| #27=(|Fraction| #28=(|Integer|)) . #25#) . #26#) NIL #29=(|has| |#1| (|RetractableTo| #27#)) ELT) (((|Union| #28# . #25#) . #26#) NIL #30=(|has| |#1| (|RetractableTo| #28#)) ELT) (#31=((|Union| #7# . #25#) . #26#) NIL T ELT)) (|retract| #32=(#33=(|#1| . #34=($)) NIL T ELT) ((#27# . #34#) NIL #29# ELT) ((#28# . #34#) NIL #30# ELT) ((#7# . #34#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #35=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #36=(#12# NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #28#) . #38=(#39=(|Matrix| $))) NIL #40=(|has| |#1| (|LinearlyExplicitRingOver| #28#)) ELT) ((#41=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #28#))) . #42=(#39# #43=(|Vector| $))) NIL #40# ELT) ((#44=(|Record| (|:| |mat| #45=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #42#) NIL T ELT) ((#45# . #38#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|primitivePart| #20# #46=(#47=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#1| #50=(|IndexedExponents| #7#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#1| #55#)) ELT) ((#56=(|PatternMatchResult| #28# . #53#) $ #57=(|Pattern| #28#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #28#)) (|has| |#1| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#1| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mainVariable| (#31# 19 T ELT)) (|leftReducedSystem| ((#37# . #65=(#43#)) NIL #40# ELT) ((#41# . #66=(#43# $)) NIL #40# ELT) ((#44# . #66#) NIL T ELT) ((#45# . #65#) NIL T ELT)) (|leadingMonomial| #36#) (|leadingCoefficient| #32#) (|lcm| #67=(($ #49#) NIL #21# ELT) #68=(#69=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #17#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #17#) $) NIL T ELT)) (|integrate| (#47# 29 #71=(|has| |#1| (|Algebra| #27#)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #32#) (|gcdPolynomial| ((#8# #8# #8#) NIL #21# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#16# $ |#1|) NIL #10# ELT) (#15# NIL #10# ELT)) (|eval| (($ $ (|List| #72=(|Equation| $))) NIL T ELT) (($ $ #72#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#1|) NIL T ELT) (($ $ #6# #73=(|List| |#1|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #35# ELT)) (|differentiate| #60# #59# #74=(($ $ #6#) NIL T ELT) #75=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #76=($)) NIL (AND (|has| #7# #77=(|ConvertibleTo| #54#)) (|has| |#1| #77#)) ELT) ((#57# . #76#) NIL (AND (|has| #7# #78=(|ConvertibleTo| #57#)) (|has| |#1| #78#)) ELT) ((#79=(|InputForm|) . #76#) NIL (AND (|has| #7# #80=(|ConvertibleTo| #79#)) (|has| |#1| #80#)) ELT)) (|content| (#33# NIL #21# ELT) #46#) (|conditionP| (((|Union| #43# #17#) #39#) NIL #81=(AND (|has| $ #82=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT) (($ #28#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #7#) 27 T ELT) (($ #27#) NIL (OR #71# #29#) ELT) #11#) (|coefficients| ((#73# $) NIL T ELT)) (|coefficient| ((|#1| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #81# (|has| |#1| #82#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #74# #75#) (= #1#) (/ (#83=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #71# ELT) (($ #27# . #86#) NIL #71# ELT) (($ |#1| . #86#) NIL T ELT) (#83# NIL T ELT))) 
(((|Polynomial| |#1|) (|Join| (|PolynomialCategory| |#1| (|IndexedExponents| #1=(|Symbol|)) #1#) (CATEGORY |domain| (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%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|))))) 
((|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) 19 T ELT))) 
(((|PolynomialFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)))) #1=(|Ring|) #1#) (T |PolynomialFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Polynomial| *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Polynomial| *6)) (|isDomain| *1 (|PolynomialFunctions2| *5 *6))))) 
((|univariate| (((|UnivariatePolynomial| |#1| #1=(|Polynomial| |#2|)) #1# (|Variable| |#1|)) 18 T ELT))) 
(((|PolynomialToUnivariatePolynomial| |#1| |#2|) (CATEGORY |package| (SIGNATURE |univariate| ((|UnivariatePolynomial| |#1| #1=(|Polynomial| |#2|)) #1# (|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 #1=(|Polynomial| *6))) (|isDomain| *1 (|PolynomialToUnivariatePolynomial| *5 *6)) (|isDomain| *3 #1#)))) 
((|totalDegree| ((#1=(|NonNegativeInteger|) $) 88 T ELT) ((#1# $ #2=(|List| |#4|)) 93 T ELT)) (|squareFreePart| (#3=($ $) 214 T ELT)) (|squareFree| (#4=((|Factored| $) $) 206 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #5=(|List| #6=(|SparseUnivariatePolynomial| $)) #7="failed") #5# #6#) 141 T ELT)) (|retractIfCan| (((|Union| |#2| #7#) $) NIL T ELT) (((|Union| #8=(|Fraction| #9=(|Integer|)) #7#) $) NIL T ELT) (((|Union| #9# #7#) $) NIL T ELT) (((|Union| |#4| #7#) $) 74 T ELT)) (|retract| #10=((|#2| $) NIL T ELT) ((#8# $) NIL T ELT) ((#9# $) NIL T ELT) ((|#4| $) 73 T ELT)) (|resultant| (($ $ $ |#4|) 95 T ELT)) (|reducedSystem| ((#11=(|Matrix| #9#) #12=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #11#) (|:| |vec| (|Vector| #9#))) #12# #13=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #14=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) #12# #13#) 131 T ELT) ((#14# #12#) 121 T ELT)) (|primitivePart| (#3# 221 T ELT) (#15=($ $ |#4|) 224 T ELT)) (|primitiveMonomials| (#16=(#17=(|List| $) $) 77 T ELT)) (|patternMatch| ((#18=(|PatternMatchResult| #19=(|Float|) $) $ #20=(|Pattern| #19#) #18#) 240 T ELT) ((#21=(|PatternMatchResult| #9# $) $ #22=(|Pattern| #9#) #21#) 233 T ELT)) (|monomials| (#16# 34 T ELT)) (|monomial| (($ |#2| |#3|) NIL T ELT) (#23=($ $ |#4| #1#) NIL T ELT) (#24=($ $ #2# (|List| #1#)) 71 T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) 203 T ELT)) (|isTimes| (#25=((|Union| #17# #7#) $) 52 T ELT)) (|isPlus| (#25# 39 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| #1#)) #7#) $) 57 T ELT)) (|gcdPolynomial| ((#6# #6# #6#) 134 T ELT)) (|factorSquareFreePolynomial| (#26=((|Factored| #6#) #6#) 147 T ELT)) (|factorPolynomial| (#26# 145 T ELT)) (|factor| (#4# 165 T ELT)) (|eval| (($ $ (|List| #27=(|Equation| $))) 24 T ELT) (($ $ #27#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #17# #17#) NIL T ELT) (($ $ |#4| |#2|) NIL T ELT) (($ $ #2# (|List| |#2|)) NIL T ELT) (($ $ |#4| $) NIL T ELT) (($ $ #2# #17#) NIL T ELT)) (|discriminant| (#15# 97 T ELT)) (|convert| ((#20# $) 254 T ELT) ((#22# $) 247 T ELT) (((|InputForm|) $) 262 T ELT)) (|content| #10# (#15# 216 T ELT)) (|conditionP| (((|Union| #13# #7#) #12#) 185 T ELT)) (|coefficient| ((|#2| $ |#3|) NIL T ELT) (#23# 62 T ELT) (#24# 69 T ELT)) (|charthRoot| (((|Maybe| $) $) 195 T ELT)) (|before?| (((|Boolean|) $ $) 227 T ELT))) 
(((|PolynomialCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |gcdPolynomial| (#1=(|SparseUnivariatePolynomial| |#1|) #1# #1#)) (SIGNATURE |squareFree| #2=((|Factored| |#1|) |#1|)) (SIGNATURE |squareFreePart| #3=(|#1| |#1|)) (SIGNATURE |charthRoot| ((|Maybe| |#1|) |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| (#4=(|Pattern| #5=(|Integer|)) |#1|)) (SIGNATURE |convert| (#6=(|Pattern| #7=(|Float|)) |#1|)) (SIGNATURE |patternMatch| (#8=(|PatternMatchResult| #5# |#1|) |#1| #4# #8#)) (SIGNATURE |patternMatch| (#9=(|PatternMatchResult| #7# |#1|) |#1| #6# #9#)) (SIGNATURE |factor| #2#) (SIGNATURE |factorPolynomial| #10=((|Factored| #1#) #1#)) (SIGNATURE |factorSquareFreePolynomial| #10#) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #11=(|List| #1#) #12="failed") #11# #1#)) (SIGNATURE |conditionP| ((|Union| #13=(|Vector| |#1|) #12#) #14=(|Matrix| |#1|))) (SIGNATURE |primitivePart| #15=(|#1| |#1| |#4|)) (SIGNATURE |content| #15#) (SIGNATURE |discriminant| #15#) (SIGNATURE |resultant| (|#1| |#1| |#1| |#4|)) (SIGNATURE |primitiveMonomials| #16=(#17=(|List| |#1|) |#1|)) (SIGNATURE |totalDegree| (#18=(|NonNegativeInteger|) |#1| #19=(|List| |#4|))) (SIGNATURE |totalDegree| (#18# |#1|)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| #18#)) #12#) |#1|)) (SIGNATURE |isTimes| #20=((|Union| #17# #12#) |#1|)) (SIGNATURE |isPlus| #20#) (SIGNATURE |monomial| #21=(|#1| |#1| #19# (|List| #18#))) (SIGNATURE |monomial| #22=(|#1| |#1| |#4| #18#)) (SIGNATURE |monicDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1| |#4|)) (SIGNATURE |monomials| #16#) (SIGNATURE |coefficient| #21#) (SIGNATURE |coefficient| #22#) (SIGNATURE |reducedSystem| (#23=(|Matrix| |#2|) #14#)) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #23#) (|:| |vec| (|Vector| |#2|))) #14# #13#)) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #24=(|Matrix| #5#)) (|:| |vec| (|Vector| #5#))) #14# #13#)) (SIGNATURE |reducedSystem| (#24# #14#)) (SIGNATURE |retractIfCan| ((|Union| |#4| #12#) |#1|)) (SIGNATURE |retract| (|#4| |#1|)) (SIGNATURE |eval| (|#1| |#1| #19# #17#)) (SIGNATURE |eval| (|#1| |#1| |#4| |#1|)) (SIGNATURE |eval| (|#1| |#1| #19# (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| |#4| |#2|)) (SIGNATURE |eval| (|#1| |#1| #17# #17#)) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| (|#1| |#1| #25=(|Equation| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|List| #25#))) (SIGNATURE |monomial| (|#1| |#2| |#3|)) (SIGNATURE |coefficient| (|#2| |#1| |#3|)) (SIGNATURE |retractIfCan| ((|Union| #5# #12#) |#1|)) (SIGNATURE |retract| (#5# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #26=(|Fraction| #5#) #12#) |#1|)) (SIGNATURE |retract| (#26# |#1|)) (SIGNATURE |retract| #27=(|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #12#) |#1|)) (SIGNATURE |content| #27#) (SIGNATURE |primitivePart| #3#) (SIGNATURE |before?| ((|Boolean|) |#1| |#1|))) (|PolynomialCategory| |#2| |#3| |#4|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |PolynomialCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#3|) $) 124 T ELT)) (|univariate| (((|SparseUnivariatePolynomial| $) $ |#3|) 139 T ELT) (((|SparseUnivariatePolynomial| |#1|) $) 138 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 101 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 102 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 104 (|has| |#1| . #3#) ELT)) (|totalDegree| (((|NonNegativeInteger|) $) 126 T ELT) (((|NonNegativeInteger|) $ (|List| |#3|)) 125 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (#5=((|Factored| #6=(|SparseUnivariatePolynomial| $)) #6#) 114 (|has| |#1| . #7=((|PolynomialFactorizationExplicit|))) ELT)) (|squareFreePart| (($ $) 112 (|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#8=((|Factored| $) $) 111 (|has| |#1| (|GcdDomain|)) ELT)) (|solveLinearPolynomialEquation| (((|Union| #9=(|List| #6#) #10="failed") #9# #6#) 117 (|has| |#1| . #7#) ELT)) (|sample| (#11=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| . #12=("failed")) . #13=($)) 182 T ELT) (((|Union| #14=(|Fraction| #15=(|Integer|)) . #12#) . #13#) 179 (|has| |#1| . #16=((|RetractableTo| #14#))) ELT) (((|Union| #15# . #12#) . #13#) 177 (|has| |#1| . #17=((|RetractableTo| #15#))) ELT) (((|Union| |#3| . #12#) . #13#) 154 T ELT)) (|retract| ((|#1| . #18=($)) 181 T ELT) ((#14# . #18#) 180 (|has| |#1| . #16#) ELT) ((#15# . #18#) 178 (|has| |#1| . #17#) ELT) ((|#3| . #18#) 155 T ELT)) (|resultant| (($ $ $ |#3|) 122 (|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| (#19=($ $) 172 T ELT)) (|reducedSystem| (((|Matrix| #20=(|Integer|)) . #21=(#22=(|Matrix| $))) 150 (|has| |#1| . #23=((|LinearlyExplicitRingOver| #20#))) ELT) (((|Record| (|:| |mat| (|Matrix| #20#)) (|:| |vec| (|Vector| #20#))) . #24=(#22# #25=(|Vector| $))) 149 (|has| |#1| . #23#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #24#) 148 T ELT) (((|Matrix| |#1|) . #21#) 147 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (($ $) 194 (|has| |#1| . #26=((|GcdDomain|))) ELT) (($ $ |#3|) 119 (|has| |#1| (|GcdDomain|)) ELT)) (|primitiveMonomials| (((|List| $) $) 123 T ELT)) (|prime?| (((|Boolean|) $) 110 (|has| |#1| . #7#) ELT)) (|pomopo!| (($ $ |#1| |#2| $) 190 T ELT)) (|patternMatch| (((|PatternMatchResult| #27=(|Float|) . #28=($)) $ (|Pattern| #27#) (|PatternMatchResult| #27# . #28#)) 98 (AND (|has| |#3| (|PatternMatchable| (|Float|))) (|has| |#1| (|PatternMatchable| (|Float|)))) ELT) (((|PatternMatchResult| #29=(|Integer|) . #28#) $ (|Pattern| #29#) (|PatternMatchResult| #29# . #28#)) 97 (AND (|has| |#3| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Integer|)))) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numberOfMonomials| ((#30=(|NonNegativeInteger|) $) 187 T ELT)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) |#3|) 131 T ELT) (($ (|SparseUnivariatePolynomial| $) |#3|) 130 T ELT)) (|monomials| (((|List| $) $) 140 T ELT)) (|monomial?| (((|Boolean|) $) 170 T ELT)) (|monomial| (($ |#1| |#2|) 171 T ELT) (($ $ |#3| (|NonNegativeInteger|)) 133 T ELT) (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) 132 T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) 134 T ELT)) (|minimumDegree| ((|#2| $) 188 T ELT) (((|NonNegativeInteger|) $ |#3|) 136 T ELT) (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) 135 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) 189 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 166 T ELT)) (|mainVariable| (((|Union| |#3| "failed") $) 137 T ELT)) (|leftReducedSystem| (((|Matrix| #20#) . #31=(#25#)) 152 (|has| |#1| . #23#) ELT) (((|Record| (|:| |mat| (|Matrix| #20#)) (|:| |vec| (|Vector| #20#))) . #32=(#25# $)) 151 (|has| |#1| . #23#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #32#) 146 T ELT) (((|Matrix| |#1|) . #31#) 145 T ELT)) (|leadingMonomial| (#19# 168 T ELT)) (|leadingCoefficient| ((|#1| $) 167 T ELT)) (|lcm| (#33=($ (|List| $)) 108 (|has| |#1| . #34=((|GcdDomain|))) ELT) (#35=($ $ $) 107 (|has| |#1| . #34#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|isTimes| (((|Union| (|List| $) "failed") $) 128 T ELT)) (|isPlus| (((|Union| (|List| $) "failed") $) 129 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) 127 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|ground?| (((|Boolean|) $) 184 T ELT)) (|ground| ((|#1| . #36=($)) 185 T ELT)) (|gcdPolynomial| ((#37=(|SparseUnivariatePolynomial| $) #37# #37#) 109 (|has| |#1| . #34#) ELT)) (|gcd| (#33# 106 (|has| |#1| . #34#) ELT) (#35# 105 (|has| |#1| . #34#) ELT)) (|factorSquareFreePolynomial| (#5# 116 (|has| |#1| . #7#) ELT)) (|factorPolynomial| (#5# 115 (|has| |#1| . #7#) ELT)) (|factor| (#8# 113 (|has| |#1| . #7#) ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 192 (|has| |#1| (|IntegralDomain|)) ELT) (((|Union| $ "failed") $ $) 100 (|has| |#1| . #3#) ELT)) (|eval| (($ $ (|List| (|Equation| $))) 163 T ELT) (($ $ (|Equation| $)) 162 T ELT) (($ $ $ $) 161 T ELT) (($ $ (|List| $) (|List| $)) 160 T ELT) (($ $ |#3| |#1|) 159 T ELT) (($ $ (|List| |#3|) (|List| |#1|)) 158 T ELT) (($ $ |#3| $) 157 T ELT) (($ $ (|List| |#3|) (|List| $)) 156 T ELT)) (|discriminant| (($ $ |#3|) 121 (|has| |#1| (|CommutativeRing|)) ELT)) (|differentiate| (($ $ (|List| |#3|) . #38=((|List| #39=(|NonNegativeInteger|)))) 52 T ELT) (($ $ |#3| . #40=(#39#)) 51 T ELT) (($ $ (|List| |#3|)) 50 T ELT) (($ $ |#3|) 48 T ELT)) (|degree| ((|#2| $) 169 T ELT) (((|NonNegativeInteger|) $ |#3|) 144 T ELT) (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) 143 T ELT)) (|convert| (((|Pattern| (|Float|)) . #41=($)) 96 (AND (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|))))) ELT) (((|Pattern| (|Integer|)) . #41#) 95 (AND (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|))))) ELT) (((|InputForm|) . #41#) 94 (AND (|has| |#3| (|ConvertibleTo| (|InputForm|))) (|has| |#1| (|ConvertibleTo| (|InputForm|)))) ELT)) (|content| ((|#1| . #36#) 193 (|has| |#1| . #26#) ELT) (($ $ |#3|) 120 (|has| |#1| (|GcdDomain|)) ELT)) (|conditionP| (((|Union| (|Vector| $) #10#) (|Matrix| $)) 118 (|and| #42=(|has| $ (|CharacteristicNonZero|)) (|has| |#1| . #7#)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 183 T ELT) (($ |#3|) 153 T ELT) (($ $) 99 (|has| |#1| . #3#) ELT) (($ #14#) 92 (OR (|has| |#1| . #16#) (|has| |#1| . #43=((|Algebra| #44=(|Fraction| (|Integer|)))))) ELT)) (|coefficients| (((|List| |#1|) $) 186 T ELT)) (|coefficient| ((|#1| $ |#2|) 173 T ELT) (($ $ |#3| (|NonNegativeInteger|)) 142 T ELT) (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) 141 T ELT)) (|charthRoot| (((|Maybe| $) $) 93 (OR (|and| #42# (|has| |#1| . #7#)) (|has| |#1| (|CharacteristicNonZero|))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|binomThmExpt| (($ $ $ #30#) 191 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 103 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#11# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|List| |#3|) . #38#) 55 T ELT) (($ $ |#3| . #40#) 54 T ELT) (($ $ (|List| |#3|)) 53 T ELT) (($ $ |#3|) 49 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 174 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #45=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #44#) 176 (|has| |#1| . #43#) ELT) (($ #44# . #45#) 175 (|has| |#1| . #43#) ELT) (($ |#1| . #45#) 165 T ELT) (($ $ |#1|) 164 T ELT))) 
(((|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| $) $)) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (IF (|has| |t#3| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (IF (|has| |t#3| (|ConvertibleTo| (|Pattern| (|Integer|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Integer|)))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (IF (|has| |t#3| (|ConvertibleTo| (|Pattern| (|Float|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Float|)))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|PatternMatchable| (|Integer|))) (IF (|has| |t#3| (|PatternMatchable| (|Integer|))) (ATTRIBUTE (|PatternMatchable| (|Integer|))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|PatternMatchable| (|Float|))) (IF (|has| |t#3| (|PatternMatchable| (|Float|))) (ATTRIBUTE (|PatternMatchable| (|Float|))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (PROGN (SIGNATURE |resultant| ($ $ $ |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| #1=(|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| #1# #1#) |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|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| |#3|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|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) ((|Functorial| |#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|))) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#3|) . T) ((|PartialDifferentialRing| |#3|) . T) ((|PartialDifferentialSpace| |#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) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) 
((|variables| (((|List| |#2|) |#5|) 40 T ELT)) (|univariate| ((#1=(|SparseUnivariatePolynomial| |#5|) |#5| |#2| #1#) 23 T ELT) ((#2=(|Fraction| #1#) |#5| |#2|) 16 T ELT)) (|multivariate| ((|#5| #2# |#2|) 30 T ELT)) (|mainVariable| (((|Union| |#2| #3="failed") |#5|) 70 T ELT)) (|isTimes| (#4=((|Union| (|List| |#5|) #3#) |#5|) 64 T ELT)) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) #5=(|:| |exponent| (|Integer|))) #3#) |#5|) 53 T ELT)) (|isPlus| (#4# 66 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) #5#) #3#) |#5|) 56 T ELT))) 
(((|PolynomialCategoryQuotientFunctions| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |variables| ((|List| |#2|) |#5|)) (SIGNATURE |mainVariable| ((|Union| |#2| #1="failed") |#5|)) (SIGNATURE |univariate| (#2=(|Fraction| #3=(|SparseUnivariatePolynomial| |#5|)) |#5| |#2|)) (SIGNATURE |multivariate| (|#5| #2# |#2|)) (SIGNATURE |univariate| (#3# |#5| |#2| #3#)) (SIGNATURE |isPlus| #4=((|Union| (|List| |#5|) #1#) |#5|)) (SIGNATURE |isTimes| #4#) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |#2|) #5=(|:| |exponent| (|Integer|))) #1#) |#5|)) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| |#5|) #5#) #1#) |#5|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Ring|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |numer| #6=(|#4| $)) (SIGNATURE |denom| #6#)))) (T |PolynomialCategoryQuotientFunctions|)) 
((|isPower| #1=(*1 *2 *3) (|partial| AND #2=(|ofCategory| *4 #3=(|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *5 #5=(|OrderedSet|)) #6=(|ofCategory| *6 #7=(|Ring|)) #8=(|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Record| (|:| |val| *3) #9=(|:| |exponent| (|Integer|)))) #10=(|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3)) #11=(|ofCategory| *3 #12=(|Join| #13=(|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| #14=(*7 $)) (SIGNATURE |denom| #14#)))))) (|isExpt| #1# (|partial| AND #2# #4# #6# #8# (|isDomain| *2 (|Record| (|:| |var| *5) #9#)) #10# #11#)) (|isTimes| #1# #15=(|partial| AND #2# #4# #6# #8# (|isDomain| *2 (|List| *3)) #10# #11#)) (|isPlus| #1# #15#) (|univariate| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 #16=(|SparseUnivariatePolynomial| *3)) #11# #17=(|ofCategory| *7 (|PolynomialCategory| *6 *5 *4)) #18=(|ofCategory| *5 #3#) #19=(|ofCategory| *4 #5#) #6# #20=(|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *3)))) (|multivariate| #21=(*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|SparseUnivariatePolynomial| *2))) #18# #19# #6# (|ofCategory| *2 #12#) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *2)) #17#)) (|univariate| #21# (AND #18# #19# #6# #17# (|isDomain| *2 (|Fraction| #16#)) #20# #11#)) (|mainVariable| #1# (|partial| AND #2# (|ofCategory| *5 #7#) (|ofCategory| *6 (|PolynomialCategory| *5 *4 *2)) (|ofCategory| *2 #5#) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *2 *5 *6 *3)) (|ofCategory| *3 (|Join| #13# (CATEGORY |domain| (SIGNATURE |coerce| ($ *6)) (SIGNATURE |numer| #22=(*6 $)) (SIGNATURE |denom| #22#)))))) (|variables| #1# (AND #2# #4# #6# #8# (|isDomain| *2 (|List| *5)) #10# #11#))) 
((|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) 24 T ELT))) 
(((|PolynomialCategoryLifting| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |map| (|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Ring|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + #1=($ $ $)) (SIGNATURE * #1#) (SIGNATURE ** ($ $ (|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 + #1=($ $ $)) (SIGNATURE * #1#) (SIGNATURE ** ($ $ (|NonNegativeInteger|)))))) (|isDomain| *1 (|PolynomialCategoryLifting| *6 *7 *8 *5 *2)) (|ofCategory| *5 (|PolynomialCategory| *8 *6 *7))))) 
((|rroot| ((#1=(|Record| #2=(|:| |exponent| #3=(|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| #3#) 48 T ELT)) (|qroot| ((#1# (|Fraction| (|Integer|)) #3#) 43 T ELT)) (|nthr| (((|Record| #2# (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| #3#) 64 T ELT)) (|froot| ((#1# |#5| #3#) 73 (|has| |#3| (|GcdDomain|)) ELT))) 
(((|PolynomialRoots| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |rroot| (#1=(|Record| #2=(|:| |exponent| #3=(|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| #3#)) (SIGNATURE |qroot| (#1# (|Fraction| (|Integer|)) #3#)) (IF (|has| |#3| (|GcdDomain|)) (SIGNATURE |froot| (#1# |#5| #3#)) |%noBranch|) (SIGNATURE |nthr| ((|Record| #2# (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| #3#))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|IntegralDomain|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |numer| #4=(|#4| $)) (SIGNATURE |denom| #4#)))) (T |PolynomialRoots|)) 
((|nthr| #1=(*1 *2 *3 *4) (AND #2=(|ofCategory| *5 (|OrderedAbelianMonoidSup|)) #3=(|ofCategory| *6 (|OrderedSet|)) #4=(|ofCategory| *7 #5=(|IntegralDomain|)) (|ofCategory| *3 #6=(|PolynomialCategory| *7 *5 *6)) (|isDomain| *2 (|Record| #7=(|:| |exponent| #8=(|NonNegativeInteger|)) #9=(|:| |coef| *3) (|:| |radicand| (|List| *3)))) (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *3 *8)) #10=(|isDomain| *4 #8#) (|ofCategory| *8 (|Join| #11=(|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *3)) (SIGNATURE |numer| #12=(*3 $)) (SIGNATURE |denom| #12#)))))) (|froot| #1# (AND (|ofCategory| *7 (|GcdDomain|)) #2# #3# #4# #13=(|ofCategory| *8 #6#) (|isDomain| *2 (|Record| #7# #9# (|:| |radicand| *3))) (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *8 *3)) #10# (|ofCategory| *3 #14=(|Join| #11# (CATEGORY |domain| (SIGNATURE |coerce| ($ *8)) (SIGNATURE |numer| #15=(*8 $)) (SIGNATURE |denom| #15#)))))) (|qroot| #1# (AND (|isDomain| *3 (|Fraction| (|Integer|))) #2# #3# #4# #13# (|isDomain| *2 (|Record| #7# (|:| |coef| *9) (|:| |radicand| *9))) (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *8 *9)) #10# (|ofCategory| *9 #14#))) (|rroot| #1# (AND #2# #3# (|ofCategory| *3 #5#) (|ofCategory| *7 (|PolynomialCategory| *3 *5 *6)) (|isDomain| *2 (|Record| #7# (|:| |coef| *8) (|:| |radicand| *8))) (|isDomain| *1 (|PolynomialRoots| *5 *6 *3 *7 *8)) #10# (|ofCategory| *8 (|Join| #11# (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| #16=(*7 $)) (SIGNATURE |denom| #16#))))))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|port| (($ #3=(|SingleInteger|)) 8 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (#4=(#3# $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 15 T ELT) (#4# 12 T ELT)) (|before?| #1#) (= (#2# 11 T ELT))) 
(((|PortNumber|) (|Join| (|SetCategory|) (|CoercibleTo| #1=(|SingleInteger|)) (CATEGORY |domain| (SIGNATURE |port| ($ #1#))))) (T |PortNumber|)) 
((|port| (*1 *1 *2) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|PortNumber|))))) 
((|yRange| (((|Segment| (|DoubleFloat|)) $) 8 T ELT)) (|xRange| (((|Segment| (|DoubleFloat|)) $) 9 T ELT)) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 6 T ELT))) 
(((|PlottablePlaneCurveCategory|) (|Category|)) (T |PlottablePlaneCurveCategory|)) 
((|listBranches| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))))) (|xRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|))))) (|yRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|)))))) 
(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |listBranches| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |xRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |yRange| ((|Segment| (|DoubleFloat|)) $)))) 
(((|CoercibleTo| (|OutputForm|)) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 80 #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#7=($ $) 81 #6# ELT)) (|unit?| (#5# NIL #6# ELT)) (|subtractIfCan| (#8=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|sample| (#11=($) NIL T CONST)) (|retractIfCan| (((|Union| #12=(|Integer|) . #13=(#10#)) . #14=($)) NIL #15=(|has| |#1| (|RetractableTo| #12#)) ELT) (((|Union| #16=(|Fraction| #12#) . #13#) . #14#) NIL #17=(|has| |#1| (|RetractableTo| #16#)) ELT) (((|Union| |#1| . #13#) $) 35 T ELT)) (|retract| ((#12# . #18=($)) NIL #15# ELT) ((#16# . #18#) NIL #17# ELT) #19=(#20=(|#1| . #18#) NIL T ELT)) (|reductum| (#7# 32 T ELT)) (|recip| ((#9# $) 43 T ELT)) (|primitivePart| (#7# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| |#2| $) 64 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| ((#22=(|NonNegativeInteger|) $) 18 T ELT)) (|monomial?| #4#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|minimumDegree| (#23=(|#2| $) 25 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingMonomial| (#7# 29 T ELT)) (|leadingCoefficient| (#20# 27 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#5# 52 T ELT)) (|ground| #19#) (|fmecg| (($ $ |#2| |#1| $) 90 (AND (|has| |#2| (|CancellationAbelianMonoid|)) #6#) ELT)) (|exquo| (#8# 92 #6# ELT) ((#9# $ |#1|) 87 #6# ELT)) (|degree| (#23# 23 T ELT)) (|content| (#20# NIL #21# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #12#) 47 T ELT) (#7# NIL #6# ELT) (($ |#1|) 42 T ELT) (($ #16#) NIL (OR #24=(|has| |#1| (|Algebra| #16#)) #17#) ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ |#2|) 38 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#22#) 15 T CONST)) (|binomThmExpt| (($ $ $ #22#) 76 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| #1#) (|associates?| (#2# 86 #6# ELT)) (|annihilate?| #1#) (|Zero| (#11# 28 T CONST)) (|One| (#11# 12 T CONST)) (= (#2# 85 T ELT)) (/ (#25=($ $ |#1|) 93 (|has| |#1| (|Field|)) ELT)) (- (#7# NIL T ELT) #26=(#27=($ $ $) NIL T ELT)) (+ #26#) (** (($ $ #28=(|PositiveInteger|)) 71 T ELT) (($ $ #22#) 69 T ELT)) (* (($ #28# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #12# . #29=($)) NIL T ELT) (#27# 68 T ELT) (#25# 66 T ELT) (($ |#1| . #29#) 65 T ELT) (($ #16# . #29#) NIL #24# ELT) (($ $ #16#) NIL #24# ELT))) 
(((|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| #1=(ATTRIBUTE |canonicalUnitNormal|)) #1# |%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|))))) 
((|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) 18 T ELT))) 
(((|PrecomputedAssociatedEquations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |firstUncouplingMatrix| ((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)))) (|IntegralDomain|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |PrecomputedAssociatedEquations|)) 
((|firstUncouplingMatrix| (*1 *2 *3 *4) (|partial| AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|PrecomputedAssociatedEquations| *5 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) NIL #6=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #7=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#8=(#3# $) NIL #9=(|has| |#1| #10=(|OrderedSet|)) ELT)) (|sort!| (#11=($ #7# $) NIL #6# ELT) (#12=($ $) NIL (AND #6# #9#) ELT)) (|sort| (#11# NIL T ELT) (#12# NIL #9# ELT)) (|setelt| (#13=(|#1| $ #5# |#1|) 18 #6# ELT) ((|#1| $ #14=(|UniversalSegment| #5#) |#1|) NIL #6# ELT)) (|select| #15=(($ #16=(|Mapping| #3# |#1|) $) NIL #17=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#18=($) NIL T CONST)) (|reverse!| (#12# NIL #6# ELT)) (|reverse| (#12# NIL T ELT)) (|removeDuplicates| (#12# NIL #19=(AND #17# #4#) ELT)) (|remove| (#20=($ |#1| $) NIL #19# ELT) #15#) (|reduce| ((|#1| #21=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #21# $ |#1|) NIL T ELT) ((|#1| #21# $) NIL T ELT)) (|qsetelt!| (#13# 17 #6# ELT)) (|qelt| (#22=(|#1| $ #5#) 15 T ELT)) (|position| ((#5# #16# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT) ((#5# |#1| $ #5#) NIL #4# ELT)) (|new| (($ #23=(|NonNegativeInteger|) |#1|) 14 T ELT)) (|minIndex| (#24=(#5# $) 10 #25=(|has| #5# #10#) ELT)) (|min| #26=(#27=($ $ $) NIL #9# ELT)) (|merge| (($ #7# $ $) NIL T ELT) #26#) (|members| (#28=(#29=(|List| |#1|) $) 23 T ELT)) (|member?| (#30=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| (#24# 22 #25# ELT)) (|max| #26#) (|map!| #31=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #31# (($ #21# $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #32=(|has| |#1| (|SetCategory|)) ELT)) (|insert| (($ |#1| $ #5#) NIL T ELT) (#33=($ $ $ #5#) NIL T ELT)) (|indices| (((|List| #5#) $) NIL T ELT)) (|index?| ((#3# #5# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #32# ELT)) (|first| ((|#1| $) NIL #25# ELT)) (|find| (((|Union| |#1| "failed") #16# $) NIL T ELT)) (|fill!| (#34=($ $ |#1|) 19 #6# ELT)) (|every?| #35=((#3# #16# $) NIL T ELT)) (|eval| (($ $ (|List| #36=(|Equation| |#1|))) NIL #37=(AND (|has| |#1| (|Evalable| |#1|)) #32#) ELT) (($ $ #36#) NIL #37# ELT) (($ $ |#1| |#1|) NIL #37# ELT) (($ $ #29# #29#) NIL #37# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#30# NIL #19# ELT)) (|entries| (#28# NIL T ELT)) (|empty?| (#8# NIL T ELT)) (|empty| (#18# 11 T ELT)) (|elt| (#13# NIL T ELT) (#22# 16 T ELT) #38=(($ $ #14#) NIL T ELT)) (|delete| (($ $ #5#) NIL T ELT) #38#) (|count| ((#23# |#1| $) NIL #4# ELT) ((#23# #16# $) NIL T ELT)) (|copyInto!| (#33# NIL #6# ELT)) (|copy| (#12# 20 T ELT)) (|convert| ((#39=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #39#)) ELT)) (|construct| (($ #29#) 13 T ELT)) (|concat| (#34# NIL T ELT) (#20# NIL T ELT) (#27# NIL T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#40=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #40#)) ELT)) (|before?| #1#) (|any?| #35#) (>= #41=(#2# NIL #9# ELT)) (> #41#) (= #1#) (<= #41#) (< #41#) (|#| ((#23# $) 8 T ELT))) 
(((|PrimitiveArray| |#1|) (|OneDimensionalArrayAggregate| |#1|) (|Type|)) (T |PrimitiveArray|)) 
NIL 
((|scan| ((#1=(|PrimitiveArray| |#2|) #2=(|Mapping| |#2| |#1| |#2|) #3=(|PrimitiveArray| |#1|) |#2|) 16 T ELT)) (|reduce| ((|#2| #2# #3# |#2|) 18 T ELT)) (|map| ((#1# (|Mapping| |#2| |#1|) #3#) 13 T ELT))) 
(((|PrimitiveArrayFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |scan| (#1=(|PrimitiveArray| |#2|) #2=(|Mapping| |#2| |#1| |#2|) #3=(|PrimitiveArray| |#1|) |#2|)) (SIGNATURE |reduce| (|#2| #2# #3# |#2|)) (SIGNATURE |map| (#1# (|Mapping| |#2| |#1|) #3#))) #4=(|Type|) #4#) (T |PrimitiveArrayFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) #1=(|isDomain| *4 #2=(|PrimitiveArray| *5)) #3=(|ofCategory| *5 #4=(|Type|)) #5=(|ofCategory| *6 #4#) (|isDomain| *2 #6=(|PrimitiveArray| *6)) (|isDomain| *1 (|PrimitiveArrayFunctions2| *5 *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #1# #3# (|ofCategory| *2 #4#) (|isDomain| *1 (|PrimitiveArrayFunctions2| *5 *2)))) (|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) (|isDomain| *4 #6#) #5# #3# (|isDomain| *2 #2#) (|isDomain| *1 (|PrimitiveArrayFunctions2| *6 *5))))) 
((|integral| (($ $ (|SegmentBinding| $)) 7 T ELT) (($ $ (|Symbol|)) 6 T ELT))) 
(((|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| ((#1=(|Record| (|:| |coef| (|List| #2=(|Integer|))) (|:| |poly| (|List| #3=(|SparseUnivariatePolynomial| |#1|))) #4=(|:| |prim| #3#)) #5=(|List| #6=(|Polynomial| |#1|)) #7=(|List| #8=(|Symbol|)) #8#) 26 T ELT) ((#1# #5# #7#) 27 T ELT) (((|Record| (|:| |coef1| #2#) (|:| |coef2| #2#) #4#) #6# #8# #6# #8#) 49 T ELT))) 
(((|PrimitiveElement| |#1|) (CATEGORY |package| (SIGNATURE |primitiveElement| ((|Record| (|:| |coef1| #1=(|Integer|)) (|:| |coef2| #1#) #2=(|:| |prim| #3=(|SparseUnivariatePolynomial| |#1|))) #4=(|Polynomial| |#1|) #5=(|Symbol|) #4# #5#)) (SIGNATURE |primitiveElement| (#6=(|Record| (|:| |coef| (|List| #1#)) (|:| |poly| (|List| #3#)) #2#) #7=(|List| #4#) #8=(|List| #5#))) (SIGNATURE |primitiveElement| (#6# #7# #8# #5#))) (|Join| (|Field|) (|CharacteristicZero|))) (T |PrimitiveElement|)) 
((|primitiveElement| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Polynomial| *6))) #1=(|isDomain| *4 (|List| #2=(|Symbol|))) (|isDomain| *5 #2#) (|ofCategory| *6 #3=(|Join| (|Field|) (|CharacteristicZero|))) (|isDomain| *2 (|Record| #4=(|:| |coef| (|List| #5=(|Integer|))) (|:| |poly| (|List| #6=(|SparseUnivariatePolynomial| *6))) (|:| |prim| #6#))) (|isDomain| *1 (|PrimitiveElement| *6)))) (|primitiveElement| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| #7=(|Polynomial| *5))) #1# #8=(|ofCategory| *5 #3#) (|isDomain| *2 (|Record| #4# (|:| |poly| (|List| #9=(|SparseUnivariatePolynomial| *5))) #10=(|:| |prim| #9#))) #11=(|isDomain| *1 (|PrimitiveElement| *5)))) (|primitiveElement| (*1 *2 *3 *4 *3 *4) (AND (|isDomain| *3 #7#) (|isDomain| *4 #2#) #8# (|isDomain| *2 (|Record| (|:| |coef1| #5#) (|:| |coef2| #5#) #10#)) #11#))) 
((|primes| (((|List| |#1|) |#1| |#1|) 47 T ELT)) (|prime?| (((|Boolean|) |#1|) 44 T ELT)) (|prevPrime| (#1=(|#1| |#1|) 80 T ELT)) (|nextPrime| (#1# 79 T ELT))) 
(((|IntegerPrimesPackage| |#1|) (CATEGORY |package| (SIGNATURE |prime?| ((|Boolean|) |#1|)) (SIGNATURE |nextPrime| #1=(|#1| |#1|)) (SIGNATURE |prevPrime| #1#) (SIGNATURE |primes| ((|List| |#1|) |#1| |#1|))) (|IntegerNumberSystem|)) (T |IntegerPrimesPackage|)) 
((|primes| (*1 *2 *3 *3) (AND (|isDomain| *2 (|List| *3)) #1=(|isDomain| *1 (|IntegerPrimesPackage| *3)) #2=(|ofCategory| *3 #3=(|IntegerNumberSystem|)))) (|prevPrime| #4=(*1 *2 *2) #5=(AND (|isDomain| *1 (|IntegerPrimesPackage| *2)) (|ofCategory| *2 #3#))) (|nextPrime| #4# #5#) (|prime?| (*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) #1# #2#))) 
((|print| (((|Void|) (|OutputForm|)) 9 T ELT))) 
(((|PrintPackage|) (CATEGORY |package| (SIGNATURE |print| ((|Void|) (|OutputForm|))))) (T |PrintPackage|)) 
((|print| (*1 *2 *3) (AND (|isDomain| *3 (|OutputForm|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|PrintPackage|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) NIL #5=(OR #6=(AND (|has| |#1| #7=(|AbelianGroup|)) (|has| |#2| #7#)) #8=(AND (|has| |#1| #9=(|AbelianMonoid|)) (|has| |#2| #9#)) #10=(AND (|has| |#1| #11=(|CancellationAbelianMonoid|)) (|has| |#2| #11#)) #12=(AND (|has| |#1| #13=(|OrderedAbelianMonoidSup|)) (|has| |#2| #13#))) ELT)) (|sup| (#14=($ $ $) 65 #12# ELT)) (|subtractIfCan| ((#15=(|Union| $ "failed") $ $) 52 (OR #6# #10# #12#) ELT)) (|size| ((#16=(|NonNegativeInteger|)) 36 #17=(AND (|has| |#1| #18=(|Finite|)) (|has| |#2| #18#)) ELT)) (|selectsecond| ((|#2| $) 22 T ELT)) (|selectfirst| ((|#1| $) 21 T ELT)) (|sample| (#19=($) NIL (OR #6# #8# #10# #20=(AND (|has| |#1| #21=(|Group|)) (|has| |#2| #21#)) #22=(AND (|has| |#1| #23=(|Monoid|)) (|has| |#2| #23#)) #12#) CONST)) (|recip| ((#15# $) NIL #24=(OR #20# #22#) ELT)) (|random| (#19# NIL #17# ELT)) (|positive?| (#4# NIL #12# ELT)) (|opposite?| (#2# NIL #5# ELT)) (|one?| (#4# NIL #24# ELT)) (|min| #25=(#14# NIL #26=(OR #12# (AND (|has| |#1| #27=(|OrderedSet|)) (|has| |#2| #27#))) ELT)) (|max| #25#) (|makeprod| (($ |#1| |#2|) 20 T ELT)) (|lookup| ((#28=(|PositiveInteger|) $) NIL #17# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#29=($ $) 39 #20# ELT)) (|index| (($ #28#) NIL #17# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|conjugate| #30=(#14# NIL #20# ELT)) (|commutator| #30#) (|coerce| (((|OutputForm|) $) 14 T ELT)) (|before?| #1#) (|Zero| (#19# 42 #5# CONST)) (|One| (#19# 25 #24# CONST)) (>= #31=(#2# NIL #26# ELT)) (> #31#) (= (#2# 19 T ELT)) (<= #31#) (< (#2# 69 #26# ELT)) (/ #30#) (- (#14# 58 #6# ELT) (#29# 55 #6# ELT)) (+ (#14# 45 #5# ELT)) (** (($ $ #32=(|Integer|)) NIL #20# ELT) (($ $ #16#) 32 #24# ELT) (($ $ #28#) NIL #24# ELT)) (* (($ #32# $) 62 #6# ELT) (($ #16# $) 48 #5# ELT) (($ #28# $) NIL #5# ELT) (#14# 28 #24# ELT))) 
(((|Product| |#1| |#2|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (IF (|has| |#1| #2=(|Finite|)) (IF (|has| |#2| #2#) (ATTRIBUTE #2#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #3=(|Monoid|)) (IF (|has| |#2| #3#) (ATTRIBUTE #3#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #4=(|AbelianMonoid|)) (IF (|has| |#2| #4#) (ATTRIBUTE #4#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #5=(|CancellationAbelianMonoid|)) (IF (|has| |#2| #5#) (ATTRIBUTE #5#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #6=(|Group|)) (IF (|has| |#2| #6#) (ATTRIBUTE #6#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #7=(|AbelianGroup|)) (IF (|has| |#2| #7#) (ATTRIBUTE #7#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #8=(|OrderedAbelianMonoidSup|)) (IF (|has| |#2| #8#) (ATTRIBUTE #8#) |%noBranch|) |%noBranch|) (IF (|has| |#1| #9=(|OrderedSet|)) (IF (|has| |#2| #9#) (ATTRIBUTE #9#) |%noBranch|) |%noBranch|) (SIGNATURE |makeprod| ($ |#1| |#2|)) (SIGNATURE |selectfirst| (|#1| $)) (SIGNATURE |selectsecond| (|#2| $)))) #1# #1#) (T |Product|)) 
((|makeprod| (*1 *1 *2 *3) (AND #1=(|isDomain| *1 (|Product| *2 *3)) #2=(|ofCategory| *2 #3=(|SetCategory|)) #4=(|ofCategory| *3 #3#))) (|selectfirst| #5=(*1 *2 *1) (AND #2# #1# #4#)) (|selectsecond| #5# (AND #2# (|isDomain| *1 (|Product| *3 *2)) #4#))) 
((|value| ((#1=(|SExpression|) $) 13 T ELT)) (|property| (($ #2=(|Identifier|) #1#) 15 T ELT)) (|name| ((#2# $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT))) 
(((|Property|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |name| (#1=(|Identifier|) $)) (SIGNATURE |value| (#2=(|SExpression|) $)) (SIGNATURE |property| ($ #1# #2#))))) (T |Property|)) 
((|name| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Identifier|)) #3=(|isDomain| *1 (|Property|)))) (|value| #1# (AND (|isDomain| *2 #4=(|SExpression|)) #3#)) (|property| (*1 *1 *2 *3) (AND #2# (|isDomain| *3 #4#) #3#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (#2=($ $) 29 T ELT)) (|true| (#3=($) 17 T CONST)) (|or| #4=(#5=($ $ $) NIL T ELT)) (|not| (#2# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isOr| (#6=((|Maybe| (|Pair| $ $)) $) 62 T ELT)) (|isNot| (((|Maybe| $) $) 52 T ELT)) (|isImplies| (#6# 63 T ELT)) (|isEquiv| (#6# 64 T ELT)) (|isAtom| (((|Maybe| |#1|) $) 43 T ELT)) (|isAnd| (#6# 61 T ELT)) (|implies| (#5# 38 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|false| (#3# 16 T CONST)) (|equiv| (#5# 39 T ELT)) (|disjunction| (#5# 36 T ELT)) (|conjunction| (#5# 34 T ELT)) (|coerce| (((|OutputForm|) $) 66 T ELT) (($ |#1|) 12 T ELT)) (|before?| #1#) (|and| #4#) (|\\/| (#5# 37 T ELT)) (= #1#) (|/\\| (#5# 35 T ELT))) 
(((|PropositionalFormula| |#1|) (|Join| (|PropositionalLogic|) (|CoercibleFrom| |#1|) (CATEGORY |domain| (SIGNATURE |isAtom| ((|Maybe| |#1|) $)) (SIGNATURE |isNot| ((|Maybe| $) $)) (SIGNATURE |isAnd| #1=((|Maybe| (|Pair| $ $)) $)) (SIGNATURE |isOr| #1#) (SIGNATURE |isImplies| #1#) (SIGNATURE |isEquiv| #1#) (SIGNATURE |conjunction| #2=($ $ $)) (SIGNATURE |disjunction| #2#))) (|SetCategory|)) (T |PropositionalFormula|)) 
((|isAtom| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Maybe| *3)) #2=(|isDomain| *1 #3=(|PropositionalFormula| *3)) #4=(|ofCategory| *3 #5=(|SetCategory|)))) (|isNot| #1# (AND (|isDomain| *2 (|Maybe| #3#)) #2# #4#)) (|isAnd| #1# #6=(AND (|isDomain| *2 (|Maybe| (|Pair| #3# #3#))) #2# #4#)) (|isOr| #1# #6#) (|isImplies| #1# #6#) (|isEquiv| #1# #6#) (|conjunction| #7=(*1 *1 *1 *1) #8=(AND (|isDomain| *1 (|PropositionalFormula| *2)) (|ofCategory| *2 #5#))) (|disjunction| #7# #8#)) 
((|simplify| (#1=(#2=(|PropositionalFormula| |#1|) #2#) 46 T ELT)) (|dual| (#1# 22 T ELT)) (|atoms| (((|Set| |#1|) #2#) 41 T ELT))) 
(((|PropositionalFormulaFunctions1| |#1|) (|Join| (|Type|) (CATEGORY |package| (SIGNATURE |dual| #1=(#2=(|PropositionalFormula| |#1|) #2#)) (SIGNATURE |atoms| ((|Set| |#1|) #2#)) (SIGNATURE |simplify| #1#))) (|SetCategory|)) (T |PropositionalFormulaFunctions1|)) 
((|dual| #1=(*1 *2 *2) #2=(AND (|isDomain| *2 (|PropositionalFormula| *3)) (|ofCategory| *3 #3=(|SetCategory|)) (|isDomain| *1 (|PropositionalFormulaFunctions1| *3)))) (|atoms| (*1 *2 *3) (AND (|isDomain| *3 (|PropositionalFormula| *4)) (|ofCategory| *4 #3#) (|isDomain| *2 (|Set| *4)) (|isDomain| *1 (|PropositionalFormulaFunctions1| *4)))) (|simplify| #1# #2#)) 
((|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) 29 T ELT))) 
(((|PropositionalFormulaFunctions2| |#1| |#2|) (|Join| (|Type|) (CATEGORY |package| (SIGNATURE |map| ((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|))))) #1=(|SetCategory|) #1#) (T |PropositionalFormulaFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|PropositionalFormula| *5)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|PropositionalFormula| *6)) (|isDomain| *1 (|PropositionalFormulaFunctions2| *5 *6))))) 
((~= (#1=((|Boolean|) $ $) 19 T ELT)) (~ (($ $) 8 T ELT)) (|true| (($) 17 T CONST)) (|or| (#2=($ $ $) 9 T ELT)) (|not| (($ $) 11 T ELT)) (|latex| (((|String|) $) 23 T ELT)) (|implies| (($ $ $) 15 T ELT)) (|hash| (((|SingleInteger|) $) 22 T ELT)) (|false| (($) 16 T CONST)) (|equiv| (($ $ $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT)) (|before?| (#1# 20 T ELT)) (|and| (#2# 10 T ELT)) (|\\/| (#3=($ $ $) 6 T ELT)) (= (#1# 18 T ELT)) (|/\\| (#3# 7 T ELT))) 
(((|PropositionalLogic|) (|Category|)) (T |PropositionalLogic|)) 
((|true| (*1 *1) (|ofCategory| *1 (|PropositionalLogic|))) (|false| (*1 *1) (|ofCategory| *1 (|PropositionalLogic|))) (|implies| (*1 *1 *1 *1) (|ofCategory| *1 (|PropositionalLogic|))) (|equiv| (*1 *1 *1 *1) (|ofCategory| *1 (|PropositionalLogic|)))) 
(|Join| (|BooleanLogic|) (|SetCategory|) (CATEGORY |domain| (SIGNATURE |true| ($) |constant|) (SIGNATURE |false| ($) |constant|) (SIGNATURE |implies| ($ $ $)) (SIGNATURE |equiv| ($ $ $)))) 
(((|BasicType|) . T) ((|BooleanLogic|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Logic|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|sample| (#3=($) 6 T CONST)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 54 (|has| |#1| . #4=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 50 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 49 T ELT)) (|merge!| (($ $ $) 41 T ELT)) (|merge| (($ $ $) 42 T ELT)) (|members| (((|List| |#1|) $) 48 T ELT)) (|member?| ((#5=(|Boolean|) |#1| $) 53 (|has| |#1| . #4#) ELT)) (|max| ((|#1| $) 43 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #6=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #7=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #6#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #5# |#1|) $) 51 T ELT)) (|extract!| ((|#1| . #7#) 37 T ELT)) (|every?| ((#5# (|Mapping| #5# |#1|) . #8=($)) 46 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#9=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#9# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|count| ((#10=(|NonNegativeInteger|) |#1| $) 52 (|has| |#1| . #4#) ELT) ((#10# (|Mapping| #5# |#1|) $) 47 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|any?| ((#5# (|Mapping| #5# |#1|) . #8#) 45 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#10# $) 44 T ELT))) 
(((|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|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |max| (|t#1| $)) (SIGNATURE |merge| ($ $ $)) (SIGNATURE |merge!| ($ $ $)))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((|subResultantGcdEuclidean| (((|Record| #1=(|:| |coef1| |#2|) #2=(|:| |coef2| |#2|) #3=(|:| |gcd| |#2|)) |#2| |#2|) 105 T ELT)) (|subResultantGcd| (#4=(|#2| |#2| |#2|) 103 T ELT)) (|semiSubResultantGcdEuclidean2| (((|Record| #2# #3#) |#2| |#2|) 107 T ELT)) (|semiSubResultantGcdEuclidean1| (((|Record| #1# #3#) |#2| |#2|) 109 T ELT)) (|semiResultantReduitEuclidean| (((|Record| #2# #5=(|:| |resultantReduit| |#1|)) |#2| |#2|) 132 #6=(|has| |#1| (|GcdDomain|)) ELT)) (|semiResultantEuclideannaif| (#7=((|Record| #2# #8=(|:| |resultant| |#1|)) |#2| |#2|) 56 T ELT)) (|semiResultantEuclidean2| (#7# 80 T ELT)) (|semiResultantEuclidean1| (((|Record| #1# #8#) |#2| |#2|) 82 T ELT)) (|semiLastSubResultantEuclidean| ((#9=(|Record| #2# #10=(|:| |subResultant| |#2|)) |#2| |#2|) 96 T ELT)) (|semiIndiceSubResultantEuclidean| (#11=(#9# |#2| |#2| #12=(|NonNegativeInteger|)) 89 T ELT)) (|semiDiscriminantEuclidean| (((|Record| #2# #13=(|:| |discriminant| |#1|)) |#2|) 121 T ELT)) (|semiDegreeSubResultantEuclidean| (#11# 92 T ELT)) (|schema| (((|List| #12#) |#2| |#2|) 102 T ELT)) (|resultantnaif| (#14=(|#1| |#2| |#2|) 50 T ELT)) (|resultantReduitEuclidean| (((|Record| #1# #2# #5#) |#2| |#2|) 130 #6# ELT)) (|resultantReduit| (#14# 128 #6# ELT)) (|resultantEuclideannaif| (#15=((|Record| #1# #2# #8#) |#2| |#2|) 54 T ELT)) (|resultantEuclidean| (#15# 79 T ELT)) (|resultant| (#14# 76 T ELT)) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) #16=(|:| |quotient| |#2|) #17=(|:| |remainder| |#2|)) |#2| |#2|) 41 T ELT)) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) 67 T ELT)) (|lastSubResultantEuclidean| ((#18=(|Record| #1# #2# #10#) |#2| |#2|) 94 T ELT)) (|lastSubResultant| (#4# 93 T ELT)) (|indiceSubResultantEuclidean| (#19=(#18# |#2| |#2| #12#) 87 T ELT)) (|indiceSubResultant| (#20=(|#2| |#2| |#2| #12#) 85 T ELT)) (|gcd| (#4# 136 #6# ELT)) (|exquo| ((#21=(|Vector| |#2|) #21# |#1|) 22 T ELT)) (|divide| (((|Record| #16# #17#) |#2| |#2|) 46 T ELT)) (|discriminantEuclidean| (((|Record| #1# #2# #13#) |#2|) 119 T ELT)) (|discriminant| ((|#1| |#2|) 116 T ELT)) (|degreeSubResultantEuclidean| (#19# 91 T ELT)) (|degreeSubResultant| (#20# 90 T ELT)) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) 99 T ELT)) (|Lazard2| ((|#2| |#2| |#1| |#1| #12#) 62 T ELT)) (|Lazard| ((|#1| |#1| |#1| #12#) 61 T ELT)) (* ((#21# |#1| #21#) 17 T ELT))) 
(((|PseudoRemainderSequence| |#1| |#2|) (CATEGORY |package| (SIGNATURE |resultant| #1=(|#1| |#2| |#2|)) (SIGNATURE |resultantEuclidean| #2=((|Record| #3=(|:| |coef1| |#2|) #4=(|:| |coef2| |#2|) #5=(|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantEuclidean2| #6=((|Record| #4# #5#) |#2| |#2|)) (SIGNATURE |semiResultantEuclidean1| ((|Record| #3# #5#) |#2| |#2|)) (SIGNATURE |indiceSubResultant| #7=(|#2| |#2| |#2| #8=(|NonNegativeInteger|))) (SIGNATURE |indiceSubResultantEuclidean| #9=(#10=(|Record| #3# #4# #11=(|:| |subResultant| |#2|)) |#2| |#2| #8#)) (SIGNATURE |semiIndiceSubResultantEuclidean| #12=(#13=(|Record| #4# #11#) |#2| |#2| #8#)) (SIGNATURE |degreeSubResultant| #7#) (SIGNATURE |degreeSubResultantEuclidean| #9#) (SIGNATURE |semiDegreeSubResultantEuclidean| #12#) (SIGNATURE |lastSubResultant| #14=(|#2| |#2| |#2|)) (SIGNATURE |lastSubResultantEuclidean| (#10# |#2| |#2|)) (SIGNATURE |semiLastSubResultantEuclidean| (#13# |#2| |#2|)) (SIGNATURE |subResultantGcd| #14#) (SIGNATURE |subResultantGcdEuclidean| ((|Record| #3# #4# #15=(|:| |gcd| |#2|)) |#2| |#2|)) (SIGNATURE |semiSubResultantGcdEuclidean2| ((|Record| #4# #15#) |#2| |#2|)) (SIGNATURE |semiSubResultantGcdEuclidean1| ((|Record| #3# #15#) |#2| |#2|)) (SIGNATURE |discriminant| (|#1| |#2|)) (SIGNATURE |discriminantEuclidean| ((|Record| #3# #4# #16=(|:| |discriminant| |#1|)) |#2|)) (SIGNATURE |semiDiscriminantEuclidean| ((|Record| #4# #16#) |#2|)) (SIGNATURE |chainSubResultants| ((|List| |#2|) |#2| |#2|)) (SIGNATURE |schema| ((|List| #8#) |#2| |#2|)) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |resultantReduit| #1#) (SIGNATURE |resultantReduitEuclidean| ((|Record| #3# #4# #17=(|:| |resultantReduit| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantReduitEuclidean| ((|Record| #4# #17#) |#2| |#2|)) (SIGNATURE |gcd| #14#)) |%noBranch|) (SIGNATURE * (#18=(|Vector| |#2|) |#1| #18#)) (SIGNATURE |exquo| (#18# #18# |#1|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |#1|) #19=(|:| |quotient| |#2|) #20=(|:| |remainder| |#2|)) |#2| |#2|)) (SIGNATURE |divide| ((|Record| #19# #20#) |#2| |#2|)) (SIGNATURE |Lazard| (|#1| |#1| |#1| #8#)) (SIGNATURE |Lazard2| (|#2| |#2| |#1| |#1| #8#)) (SIGNATURE |nextsousResultant2| (|#2| |#2| |#2| |#2| |#1|)) (SIGNATURE |resultantnaif| #1#) (SIGNATURE |resultantEuclideannaif| #2#) (SIGNATURE |semiResultantEuclideannaif| #6#)) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |PseudoRemainderSequence|)) 
((|semiResultantEuclideannaif| #1=(*1 *2 *3 *3) #2=(AND #3=(|ofCategory| *4 #4=(|IntegralDomain|)) (|isDomain| *2 (|Record| #5=(|:| |coef2| *3) #6=(|:| |resultant| *4))) #7=(|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) #8=(|ofCategory| *3 #9=(|UnivariatePolynomialCategory| *4)))) (|resultantEuclideannaif| #1# #10=(AND #3# (|isDomain| *2 (|Record| #11=(|:| |coef1| *3) #5# #6#)) #7# #8#)) (|resultantnaif| #1# #12=(AND #13=(|ofCategory| *2 #4#) #14=(|isDomain| *1 (|PseudoRemainderSequence| *2 *3)) #15=(|ofCategory| *3 #16=(|UnivariatePolynomialCategory| *2)))) (|nextsousResultant2| (*1 *2 *2 *2 *2 *3) #17=(AND #18=(|ofCategory| *3 #4#) #19=(|isDomain| *1 (|PseudoRemainderSequence| *3 *2)) #20=(|ofCategory| *2 #21=(|UnivariatePolynomialCategory| *3)))) (|Lazard2| (*1 *2 *2 *3 *3 *4) (AND #22=(|isDomain| *4 #23=(|NonNegativeInteger|)) #18# #19# #20#)) (|Lazard| #24=(*1 *2 *2 *2 *3) (AND #25=(|isDomain| *3 #23#) #13# (|isDomain| *1 (|PseudoRemainderSequence| *2 *4)) (|ofCategory| *4 #16#))) (|divide| #1# (AND #3# (|isDomain| *2 (|Record| #26=(|:| |quotient| *3) #27=(|:| |remainder| *3))) #7# #8#)) (|pseudoDivide| #1# (AND #3# (|isDomain| *2 (|Record| (|:| |coef| *4) #26# #27#)) #7# #8#)) (|exquo| (*1 *2 *2 *3) #28=(AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 #21#) #18# (|isDomain| *1 (|PseudoRemainderSequence| *3 *4)))) (* (*1 *2 *3 *2) #28#) (|gcd| #29=(*1 *2 *2 *2) (AND (|ofCategory| *3 #30=(|GcdDomain|)) #18# #19# #20#)) (|semiResultantReduitEuclidean| #1# (AND #31=(|ofCategory| *4 #30#) #3# (|isDomain| *2 (|Record| #5# #32=(|:| |resultantReduit| *4))) #7# #8#)) (|resultantReduitEuclidean| #1# (AND #31# #3# (|isDomain| *2 (|Record| #11# #5# #32#)) #7# #8#)) (|resultantReduit| #1# (AND #13# (|ofCategory| *2 #30#) #14# #15#)) (|schema| #1# (AND #3# (|isDomain| *2 (|List| #23#)) #7# #8#)) (|chainSubResultants| #1# (AND #3# (|isDomain| *2 (|List| *3)) #7# #8#)) (|semiDiscriminantEuclidean| #33=(*1 *2 *3) (AND #3# (|isDomain| *2 (|Record| #5# #34=(|:| |discriminant| *4))) #7# #8#)) (|discriminantEuclidean| #33# (AND #3# (|isDomain| *2 (|Record| #11# #5# #34#)) #7# #8#)) (|discriminant| #33# #12#) (|semiSubResultantGcdEuclidean1| #1# (AND #3# (|isDomain| *2 (|Record| #11# #35=(|:| |gcd| *3))) #7# #8#)) (|semiSubResultantGcdEuclidean2| #1# (AND #3# (|isDomain| *2 (|Record| #5# #35#)) #7# #8#)) (|subResultantGcdEuclidean| #1# (AND #3# (|isDomain| *2 (|Record| #11# #5# #35#)) #7# #8#)) (|subResultantGcd| #29# #17#) (|semiLastSubResultantEuclidean| #1# (AND #3# #36=(|isDomain| *2 (|Record| #5# #37=(|:| |subResultant| *3))) #7# #8#)) (|lastSubResultantEuclidean| #1# (AND #3# #38=(|isDomain| *2 (|Record| #11# #5# #37#)) #7# #8#)) (|lastSubResultant| #29# #17#) (|semiDegreeSubResultantEuclidean| #39=(*1 *2 *3 *3 *4) #40=(AND #22# #41=(|ofCategory| *5 #4#) #36# #42=(|isDomain| *1 (|PseudoRemainderSequence| *5 *3)) #43=(|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|degreeSubResultantEuclidean| #39# #44=(AND #22# #41# #38# #42# #43#)) (|degreeSubResultant| #24# #45=(AND #25# #3# (|isDomain| *1 (|PseudoRemainderSequence| *4 *2)) (|ofCategory| *2 #9#))) (|semiIndiceSubResultantEuclidean| #39# #40#) (|indiceSubResultantEuclidean| #39# #44#) (|indiceSubResultant| #24# #45#) (|semiResultantEuclidean1| #1# (AND #3# (|isDomain| *2 (|Record| #11# #6#)) #7# #8#)) (|semiResultantEuclidean2| #1# #2#) (|resultantEuclidean| #1# #10#) (|resultant| #1# #12#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|target| (((|TypeAst|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|PretendAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |expression| ((|SpadAst|) $)) (SIGNATURE |target| ((|TypeAst|) $))))) (T |PretendAst|)) 
((|expression| #1=(*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) #2=(|isDomain| *1 (|PretendAst|)))) (|target| #1# (AND (|isDomain| *2 (|TypeAst|)) #2#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 40 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 54 T ELT)) (|sample| (#5=($) NIL T CONST)) (|powers| (((|List| (|Pair| #6=(|PositiveInteger|) #6#)) $) 64 T ELT)) (|positive?| (#4# NIL T ELT)) (|pdct| ((#6# $) 91 T ELT)) (|parts| (#7=(#8=(|List| #6#) $) 17 T ELT)) (|partitions| (((|Stream| $) #9=(|NonNegativeInteger|)) 39 T ELT)) (|partition| (($ #8#) 16 T ELT)) (|opposite?| #1#) (|min| #10=(#11=($ $ $) NIL T ELT)) (|max| #10#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|conjugate| (($ $) 67 T ELT)) (|coerce| (((|OutputForm|) $) 87 T ELT) (#7# 11 T ELT)) (|before?| #1#) (|Zero| (#5# 10 T CONST)) (>= #1#) (> #1#) (= (#2# 44 T ELT)) (<= #1#) (< (#2# 42 T ELT)) (+ (#11# 46 T ELT)) (* (($ #6# $) NIL T ELT) (($ #9# $) 49 T ELT)) (|#| ((#9# $) 22 T ELT))) 
(((|Partition|) (|Join| (|OrderedCancellationAbelianMonoid|) (|CoercibleTo| #1=(|List| #2=(|PositiveInteger|))) (CATEGORY |domain| (SIGNATURE |partition| ($ #1#)) (SIGNATURE |parts| (#1# $)) (SIGNATURE |#| (#3=(|NonNegativeInteger|) $)) (SIGNATURE |partitions| ((|Stream| $) #3#)) (SIGNATURE |powers| ((|List| (|Pair| #2# #2#)) $)) (SIGNATURE |pdct| (#2# $)) (SIGNATURE |conjugate| ($ $))))) (T |Partition|)) 
((|partition| (*1 *1 *2) #1=(AND (|isDomain| *2 (|List| #2=(|PositiveInteger|))) #3=(|isDomain| *1 #4=(|Partition|)))) (|parts| #5=(*1 *2 *1) #1#) (|#| #5# (AND (|isDomain| *2 #6=(|NonNegativeInteger|)) #3#)) (|partitions| (*1 *2 *3) (AND (|isDomain| *3 #6#) (|isDomain| *2 (|Stream| #4#)) #3#)) (|powers| #5# (AND (|isDomain| *2 (|List| (|Pair| #2# #2#))) #3#)) (|pdct| #5# (AND (|isDomain| *2 #2#) #3#)) (|conjugate| (*1 *1 *1) #3#)) 
((/ (#1=($ $ |#2|) 31 T ELT)) (- (($ $) 23 T ELT) #2=(($ $ $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #3=(|Integer|) $) 17 T ELT) #2# (#1# 21 T ELT) (($ |#2| $) 20 T ELT) (($ #4=(|Fraction| #3#) $) 27 T ELT) (($ $ #4#) 29 T ELT))) 
(((|PowerSeriesCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE * (|#1| |#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE / #3=(|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * #3#) (SIGNATURE * #4=(|#1| |#1| |#1|)) (SIGNATURE - #4#) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|PowerSeriesCategory| |#2| |#3| |#4|) (|Ring|) (|OrderedAbelianMonoid|) (|OrderedSet|)) (T |PowerSeriesCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#3|) $) 96 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 75 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|reductum| (#6=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| |#2|) 82 T ELT) (($ $ |#3| |#2|) 98 T ELT) (($ $ (|List| |#3|) (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|leadingMonomial| (#6# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #3#) ELT)) (|degree| ((|#2| $) 84 T ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #7=(|Fraction| (|Integer|))) 78 (|has| |#1| . #8=((|Algebra| #7#))) ELT) (($ $) 70 (|has| |#1| . #3#) ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 74 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #9=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #9#) 88 T ELT) (($ #7# . #9#) 77 (|has| |#1| . #8#) ELT) (($ $ #7#) 76 (|has| |#1| . #8#) ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |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|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|zRange| (((|Segment| (|DoubleFloat|)) $) 8 T ELT)) (|yRange| (((|Segment| (|DoubleFloat|)) $) 9 T ELT)) (|xRange| (((|Segment| (|DoubleFloat|)) $) 10 T ELT)) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 6 T ELT))) 
(((|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| (#1=((|List| |#4|) $) 23 T ELT)) (|trivialIdeal?| (#2=(#3=(|Boolean|) $) 55 T ELT)) (|triangular?| (#2# 54 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) 42 T ELT)) (|roughUnitIdeal?| (#2# 56 T ELT)) (|roughSubIdeal?| (#4=(#3# $ $) 62 T ELT)) (|roughEqualIdeals?| (#4# 65 T ELT)) (|roughBase?| (#2# 60 T ELT)) (|rewriteIdealWithRemainder| (#5=(#6=(|List| |#5|) #6# $) 98 T ELT)) (|rewriteIdealWithHeadRemainder| (#5# 95 T ELT)) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) #7=(|:| |den| |#2|)) |#5| $) 88 T ELT)) (|mainVariables| (#1# 27 T ELT)) (|mainVariable?| ((#3# |#4| $) 34 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#5|) #7#) |#5| $) 81 T ELT)) (|collectUpper| (#8=($ $ |#4|) 39 T ELT)) (|collectUnder| (#8# 38 T ELT)) (|collect| (#8# 40 T ELT)) (= (#4# 46 T ELT))) 
(((|PolynomialSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |triangular?| #1=(#2=(|Boolean|) |#1|)) (SIGNATURE |rewriteIdealWithRemainder| #3=(#4=(|List| |#5|) #4# |#1|)) (SIGNATURE |rewriteIdealWithHeadRemainder| #3#) (SIGNATURE |remainder| ((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) #5=(|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |headRemainder| ((|Record| (|:| |num| |#5|) #5#) |#5| |#1|)) (SIGNATURE |roughUnitIdeal?| #1#) (SIGNATURE |roughEqualIdeals?| #6=(#2# |#1| |#1|)) (SIGNATURE |roughSubIdeal?| #6#) (SIGNATURE |roughBase?| #1#) (SIGNATURE |trivialIdeal?| #1#) (SIGNATURE |sort| ((|Record| (|:| |under| |#1|) (|:| |floor| |#1|) (|:| |upper| |#1|)) |#1| |#4|)) (SIGNATURE |collectUpper| #7=(|#1| |#1| |#4|)) (SIGNATURE |collect| #7#) (SIGNATURE |collectUnder| #7#) (SIGNATURE |mainVariable?| (#2# |#4| |#1|)) (SIGNATURE |mainVariables| #8=((|List| |#4|) |#1|)) (SIGNATURE |variables| #8#) (SIGNATURE = #6#)) (|PolynomialSetCategory| |#2| |#3| |#4| |#5|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |PolynomialSetCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|variables| (((|List| |#3|) $) 39 T ELT)) (|trivialIdeal?| (((|Boolean|) $) 32 T ELT)) (|triangular?| (((|Boolean|) $) 23 (|has| |#1| (|IntegralDomain|)) ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #2=(|Boolean|) |#4|) . #3=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|sample| (#4=($) 59 T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 28 (|has| |#1| (|IntegralDomain|)) ELT)) (|roughSubIdeal?| (((|Boolean|) $ $) 30 (|has| |#1| (|IntegralDomain|)) ELT)) (|roughEqualIdeals?| (((|Boolean|) $ $) 29 (|has| |#1| (|IntegralDomain|)) ELT)) (|roughBase?| (((|Boolean|) $) 31 (|has| |#1| (|IntegralDomain|)) ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 24 (|has| |#1| (|IntegralDomain|)) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) 25 (|has| |#1| (|IntegralDomain|)) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #5=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #5#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #2# |#4|) . #3#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| (|IntegralDomain|)) ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #6=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#7=(|Boolean|) |#4| $) 53 (|has| |#4| . #6#) ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) $) 38 T ELT)) (|mainVariable?| (((|Boolean|) |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| (|IntegralDomain|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #7# |#4|) $) 51 T ELT)) (|every?| ((#7# (|Mapping| #7# |#4|) . #8=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9#)) ELT)) (|eq?| ((#10=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#10# $) 58 T ELT)) (|empty| (#4# 57 T ELT)) (|count| ((#11=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #6#) ELT) ((#11# (|Mapping| #7# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#12=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #12#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #13=($)) 13 T ELT) (((|List| |#4|) . #13#) 43 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| ((#7# (|Mapping| #7# |#4|) . #8#) 45 T ELT)) (= (#1# 8 T ELT)) (|#| ((#11# $) 44 T ELT))) 
(((|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|) (|FiniteAggregate| |t#4|) (|CoercibleTo| (|List| |t#4|)) (CATEGORY |domain| (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|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|unprotectedRemoveRedundantFactors| (#1=(#2=(|List| |#4|) |#4| |#4|) 135 T ELT)) (|univariatePolynomialsGcds| ((#2# #2# #3=(|Boolean|)) 123 #4=(|has| |#1| (|GcdDomain|)) ELT) (#5=(#2# #2#) 124 #4# ELT)) (|univariatePolynomials| (#6=(#7=(|Record| (|:| |goodPols| #2#) (|:| |badPols| #2#)) #2#) 44 T ELT)) (|univariate?| (#8=(#3# |#4|) 43 T ELT)) (|squareFreeFactors| ((#2# |#4|) 120 #4# ELT)) (|selectPolynomials| ((#7# #9=(|Mapping| #3# |#4|) #2#) 24 T ELT)) (|selectOrPolynomials| (#10=(#7# (|List| #9#) #2#) 30 T ELT)) (|selectAndPolynomials| (#10# 31 T ELT)) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| #2#)) "failed") #2#) 90 T ELT)) (|rewriteSetByReducingWithParticularGenerators| ((#2# #2# #9# #11=(|Mapping| #3# |#4| |#4|) #12=(|Mapping| |#4| |#4| |#4|)) 103 T ELT)) (|rewriteIdealWithQuasiMonicGenerators| ((#2# #2# #11# #12#) 127 T ELT)) (|removeSquaresIfCan| (#5# 126 T ELT)) (|removeRoughlyRedundantFactorsInPols| ((#2# #2# #2# #3#) 59 T ELT) (#13=(#2# #2# #2#) 61 T ELT)) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| #2#) 60 T ELT)) (|removeRoughlyRedundantFactorsInContents| (#13# 131 #4# ELT)) (|removeRedundantFactorsInPols| (#13# 134 #4# ELT)) (|removeRedundantFactorsInContents| (#13# 133 #4# ELT)) (|removeRedundantFactors| ((#2# #2# #2# (|Mapping| #2# #2#)) 105 T ELT) (#13# 107 T ELT) ((#2# #2# |#4|) 139 T ELT) (#1# 136 T ELT) (#5# 106 T ELT)) (|removeIrreducibleRedundantFactors| (#13# 117 #14=(AND (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|EuclideanDomain|))) ELT)) (|quasiMonicPolynomials| (#6# 52 T ELT)) (|probablyZeroDim?| ((#3# #2#) 79 T ELT)) (|possiblyNewVariety?| ((#3# #2# (|List| #2#)) 67 T ELT)) (|linearPolynomials| (#6# 37 T ELT)) (|linear?| (#8# 36 T ELT)) (|lazyIrreducibleFactors| (#5# 116 #14# ELT)) (|irreducibleFactors| (#5# 115 #14# ELT)) (|interReduce| (#5# 83 T ELT)) (|crushedSet| (#5# 97 T ELT)) (|certainlySubVariety?| ((#3# #2# #2#) 65 T ELT)) (|bivariatePolynomials| (#6# 50 T ELT)) (|bivariate?| (#8# 45 T ELT))) 
(((|PolynomialSetUtilitiesPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |removeRedundantFactors| #1=(#2=(|List| |#4|) #2#)) (SIGNATURE |removeRedundantFactors| #3=(#2# |#4| |#4|)) (SIGNATURE |removeSquaresIfCan| #1#) (SIGNATURE |unprotectedRemoveRedundantFactors| #3#) (SIGNATURE |removeRedundantFactors| (#2# #2# |#4|)) (SIGNATURE |removeRedundantFactors| #4=(#2# #2# #2#)) (SIGNATURE |removeRedundantFactors| (#2# #2# #2# (|Mapping| #2# #2#))) (SIGNATURE |certainlySubVariety?| (#5=(|Boolean|) #2# #2#)) (SIGNATURE |possiblyNewVariety?| (#5# #2# (|List| #2#))) (SIGNATURE |probablyZeroDim?| (#5# #2#)) (SIGNATURE |selectPolynomials| (#6=(|Record| (|:| |goodPols| #2#) (|:| |badPols| #2#)) #7=(|Mapping| #5# |#4|) #2#)) (SIGNATURE |selectOrPolynomials| #8=(#6# (|List| #7#) #2#)) (SIGNATURE |selectAndPolynomials| #8#) (SIGNATURE |quasiMonicPolynomials| #9=(#6# #2#)) (SIGNATURE |univariate?| #10=(#5# |#4|)) (SIGNATURE |univariatePolynomials| #9#) (SIGNATURE |linear?| #10#) (SIGNATURE |linearPolynomials| #9#) (SIGNATURE |bivariate?| #10#) (SIGNATURE |bivariatePolynomials| #9#) (SIGNATURE |removeRoughlyRedundantFactorsInPols| #4#) (SIGNATURE |removeRoughlyRedundantFactorsInPols| (#2# #2# #2# #5#)) (SIGNATURE |removeRoughlyRedundantFactorsInPol| (|#4| |#4| #2#)) (SIGNATURE |interReduce| #1#) (SIGNATURE |roughBasicSet| ((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| #2#)) "failed") #2#)) (SIGNATURE |crushedSet| #1#) (SIGNATURE |rewriteSetByReducingWithParticularGenerators| (#2# #2# #7# #11=(|Mapping| #5# |#4| |#4|) #12=(|Mapping| |#4| |#4| |#4|))) (SIGNATURE |rewriteIdealWithQuasiMonicGenerators| (#2# #2# #11# #12#)) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |squareFreeFactors| (#2# |#4|)) (SIGNATURE |univariatePolynomialsGcds| #1#) (SIGNATURE |univariatePolynomialsGcds| (#2# #2# #5#)) (SIGNATURE |removeRoughlyRedundantFactorsInContents| #4#) (SIGNATURE |removeRedundantFactorsInContents| #4#) (SIGNATURE |removeRedundantFactorsInPols| #4#)) |%noBranch|) (IF (|has| |#1| (|EuclideanDomain|)) (IF (|has| |#1| (|CharacteristicZero|)) (PROGN (SIGNATURE |irreducibleFactors| #1#) (SIGNATURE |lazyIrreducibleFactors| #1#) (SIGNATURE |removeIrreducibleRedundantFactors| #4#)) |%noBranch|) |%noBranch|)) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |PolynomialSetUtilitiesPackage|)) 
((|removeIrreducibleRedundantFactors| #1=(*1 *2 *2 *2) #2=(AND #3=(|isDomain| *2 (|List| *6)) #4=(|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|CharacteristicZero|)) (|ofCategory| *3 (|EuclideanDomain|)) #5=(|ofCategory| *3 #6=(|IntegralDomain|)) #7=(|ofCategory| *4 #8=(|OrderedAbelianMonoidSup|)) #9=(|ofCategory| *5 #10=(|OrderedSet|)) #11=(|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|lazyIrreducibleFactors| #12=(*1 *2 *2) #2#) (|irreducibleFactors| #12# #2#) (|removeRedundantFactorsInPols| #1# #13=(AND #3# #4# (|ofCategory| *3 #14=(|GcdDomain|)) #5# #7# #9# #11#)) (|removeRedundantFactorsInContents| #1# #13#) (|removeRoughlyRedundantFactorsInContents| #1# #13#) (|univariatePolynomialsGcds| #15=(*1 *2 *2 *3) (AND #16=(|isDomain| *2 #17=(|List| *7)) #18=(|isDomain| *3 #19=(|Boolean|)) #20=(|ofCategory| *7 #21=(|RecursivePolynomialCategory| *4 *5 *6)) #22=(|ofCategory| *4 #14#) #23=(|ofCategory| *4 #6#) #24=(|ofCategory| *5 #8#) #25=(|ofCategory| *6 #10#) #26=(|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)))) (|univariatePolynomialsGcds| #12# #13#) (|squareFreeFactors| #27=(*1 *2 *3) (AND #22# #23# #24# #25# #28=(|isDomain| *2 (|List| *3)) #29=(|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *3)) #30=(|ofCategory| *3 #21#))) (|rewriteIdealWithQuasiMonicGenerators| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 #31=(|List| *8)) (|isDomain| *3 (|Mapping| #19# *8 *8)) (|isDomain| *4 (|Mapping| *8 *8 *8)) #32=(|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) #33=(|ofCategory| *5 #6#) #34=(|ofCategory| *6 #8#) #35=(|ofCategory| *7 #10#) #36=(|isDomain| *1 (|PolynomialSetUtilitiesPackage| *5 *6 *7 *8)))) (|rewriteSetByReducingWithParticularGenerators| (*1 *2 *2 *3 *4 *5) (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|Mapping| #19# *9)) (|isDomain| *4 (|Mapping| #19# *9 *9)) (|isDomain| *5 (|Mapping| *9 *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 #6#) (|ofCategory| *7 #8#) (|ofCategory| *8 #10#) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *6 *7 *8 *9)))) (|crushedSet| #12# #37=(AND #3# #4# #5# #7# #9# #11#)) (|roughBasicSet| #27# (|partial| AND #23# #24# #25# #20# (|isDomain| *2 (|Record| (|:| |bas| (|GeneralTriangularSet| *4 *5 *6 *7)) (|:| |top| #17#))) #26# #38=(|isDomain| *3 #17#))) (|interReduce| #12# #37#) (|removeRoughlyRedundantFactorsInPol| #15# (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #21#) #23# #24# #25# (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *2)))) (|removeRoughlyRedundantFactorsInPols| #39=(*1 *2 *2 *2 *3) (AND #16# #18# #20# #23# #24# #25# #26#)) (|removeRoughlyRedundantFactorsInPols| #1# #37#) (|bivariatePolynomials| #27# #40=(AND #23# #24# #25# #20# (|isDomain| *2 (|Record| (|:| |goodPols| #17#) (|:| |badPols| #17#))) #26# #38#)) (|bivariate?| #27# #41=(AND #23# #24# #25# #42=(|isDomain| *2 #19#) #29# #30#)) (|linearPolynomials| #27# #40#) (|linear?| #27# #41#) (|univariatePolynomials| #27# #40#) (|univariate?| #27# #41#) (|quasiMonicPolynomials| #27# #40#) (|selectAndPolynomials| #43=(*1 *2 *3 *4) #44=(AND (|isDomain| *3 (|List| #45=(|Mapping| #19# *8))) #32# #33# #34# #35# #46=(|isDomain| *2 (|Record| (|:| |goodPols| #31#) (|:| |badPols| #31#))) #36# #47=(|isDomain| *4 #31#))) (|selectOrPolynomials| #43# #44#) (|selectPolynomials| #43# (AND (|isDomain| *3 #45#) #32# #33# #34# #35# #46# #36# #47#)) (|probablyZeroDim?| #27# #48=(AND #38# #20# #23# #24# #25# #42# #26#)) (|possiblyNewVariety?| #43# (AND (|isDomain| *4 (|List| #31#)) (|isDomain| *3 #31#) #32# #33# #34# #35# #42# #36#)) (|certainlySubVariety?| #49=(*1 *2 *3 *3) #48#) (|removeRedundantFactors| #39# (AND (|isDomain| *3 (|Mapping| #17# #17#)) #16# #20# #23# #24# #25# #26#)) (|removeRedundantFactors| #1# #37#) (|removeRedundantFactors| #15# (AND #28# #30# #23# #24# #25# #29#)) (|unprotectedRemoveRedundantFactors| #49# #50=(AND #23# #24# #25# #28# #29# #30#)) (|removeSquaresIfCan| #12# #37#) (|removeRedundantFactors| #49# #50#) (|removeRedundantFactors| #12# #37#)) 
((|normalForm| (((|Record| (|:| R #1=(|Matrix| |#1|)) (|:| A #1#) (|:| |Ainv| #1#)) #1# #2=(|Automorphism| |#1|) #3=(|Mapping| |#1| |#1|)) 19 T ELT)) (|companionBlocks| (((|List| (|Record| (|:| C #1#) (|:| |g| #4=(|Vector| |#1|)))) #1# #4#) 45 T ELT)) (|changeBase| ((#1# #1# #1# #2# #3#) 16 T ELT))) 
(((|PseudoLinearNormalForm| |#1|) (CATEGORY |package| (SIGNATURE |normalForm| ((|Record| (|:| R #1=(|Matrix| |#1|)) (|:| A #1#) (|:| |Ainv| #1#)) #1# #2=(|Automorphism| |#1|) #3=(|Mapping| |#1| |#1|))) (SIGNATURE |changeBase| (#1# #1# #1# #2# #3#)) (SIGNATURE |companionBlocks| ((|List| (|Record| (|:| C #1#) (|:| |g| #4=(|Vector| |#1|)))) #1# #4#))) (|Field|)) (T |PseudoLinearNormalForm|)) 
((|companionBlocks| (*1 *2 *3 *4) (AND #1=(|ofCategory| *5 #2=(|Field|)) (|isDomain| *2 (|List| (|Record| (|:| C #3=(|Matrix| *5)) (|:| |g| #4=(|Vector| *5))))) #5=(|isDomain| *1 (|PseudoLinearNormalForm| *5)) (|isDomain| *3 #3#) (|isDomain| *4 #4#))) (|changeBase| (*1 *2 *2 *2 *3 *4) (AND (|isDomain| *2 #3#) (|isDomain| *3 (|Automorphism| *5)) (|isDomain| *4 (|Mapping| *5 *5)) #1# #5#)) (|normalForm| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Automorphism| *6)) (|isDomain| *5 (|Mapping| *6 *6)) (|ofCategory| *6 #2#) (|isDomain| *2 (|Record| (|:| R #6=(|Matrix| *6)) (|:| A #6#) (|:| |Ainv| #6#))) (|isDomain| *1 (|PseudoLinearNormalForm| *6)) (|isDomain| *3 #6#)))) 
((|squareFree| (((|Factored| |#4|) |#4|) 61 T ELT))) 
(((|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))))) 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|zero| (($ (|NonNegativeInteger|)) 123 (|has| |#1| (|AbelianMonoid|)) ELT)) (|swap!| (((|Void|) $ #3=(|Integer|) #3#) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#4=(|Boolean|) (|Mapping| #4# |#1| |#1|) $) 96 T ELT) ((#4# $) 90 (|has| |#1| . #5=((|OrderedSet|))) ELT)) (|sort!| (($ (|Mapping| #4# |#1| |#1|) . #6=($)) 87 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (#7=($ $) 86 (AND (|has| |#1| . #5#) (|has| $ (|ShallowlyMutableAggregate| |#1|))) ELT)) (|sort| (($ (|Mapping| #4# |#1| |#1|) . #6#) 97 T ELT) (#7# 91 (|has| |#1| . #5#) ELT)) (|setelt| ((|#1| $ #3# |#1|) 47 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #8=(|UniversalSegment| #3#) |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #9=(|Boolean|) |#1|) . #10=($)) 69 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#11=($) 6 T CONST)) (|reverse!| (#7# 88 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|reverse| (#7# 98 T ELT)) (|removeDuplicates| (($ $) 71 (AND (|has| |#1| . #12=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 70 (AND (|has| |#1| . #12#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #9# |#1|) . #10#) 68 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 110 (|has| |#1| . #13=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 106 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 105 T ELT)) (|qsetelt!| ((|#1| $ #3# |#1|) 48 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #3#) 46 T ELT)) (|position| ((#14=(|Integer|) (|Mapping| #4# |#1|) $) 95 T ELT) ((#14# |#1| $) 94 (|has| |#1| . #15=((|BasicType|))) ELT) ((#14# |#1| $ #14#) 93 (|has| |#1| . #15#) ELT)) (|point| (($ (|List| |#1|)) 129 T ELT)) (|outerProduct| (((|Matrix| |#1|) $ $) 116 (|has| |#1| . #16=((|Ring|))) ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| ((#3# . #17=($)) 38 (|has| #3# . #18=((|OrderedSet|))) ELT)) (|min| (#19=($ $ $) 80 (|has| |#1| . #5#) ELT)) (|merge| (($ (|Mapping| #4# |#1| |#1|) $ $) 99 T ELT) (($ $ $) 92 (|has| |#1| . #5#) ELT)) (|members| (((|List| |#1|) $) 104 T ELT)) (|member?| ((#20=(|Boolean|) |#1| $) 109 (|has| |#1| . #13#) ELT)) (|maxIndex| ((#3# . #17#) 39 (|has| #3# . #18#) ELT)) (|max| (#19# 81 (|has| |#1| . #5#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 112 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 60 T ELT)) (|magnitude| ((|#1| . #21=($)) 113 (AND (|has| |#1| . #16#) (|has| |#1| . #22=((|RadicalCategory|)))) ELT)) (|length| ((|#1| . #21#) 114 (AND (|has| |#1| . #16#) (|has| |#1| . #22#)) ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #23=((|SetCategory|))) ELT)) (|insert| (($ |#1| $ #3#) 57 T ELT) (($ $ $ #3#) 56 T ELT)) (|indices| (((|List| #3#) $) 41 T ELT)) (|index?| ((#24=(|Boolean|) #3# $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #23#) ELT)) (|first| ((|#1| $) 37 (|has| #3# . #18#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #20# |#1|) $) 107 T ELT)) (|fill!| (($ $ |#1|) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|extend| (($ $ (|List| |#1|)) 127 T ELT)) (|every?| ((#20# (|Mapping| #20# |#1|) . #25=($)) 102 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #23#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #23#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #23#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #23#)) ELT)) (|eq?| ((#26=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#24# |#1| $) 40 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 43 T ELT)) (|empty?| ((#26# $) 7 T ELT)) (|empty| (#11# 8 T ELT)) (|elt| ((|#1| $ #3# |#1|) 45 T ELT) ((|#1| $ #3#) 44 T ELT) (($ $ #8#) 66 T ELT)) (|dot| ((|#1| $ $) 117 (|has| |#1| . #16#) ELT)) (|dimension| (((|PositiveInteger|) $) 128 T ELT)) (|delete| (($ $ #3#) 59 T ELT) (($ $ #8#) 58 T ELT)) (|cross| (($ $ $) 115 T ELT)) (|count| ((#27=(|NonNegativeInteger|) |#1| $) 108 (|has| |#1| . #13#) ELT) ((#27# (|Mapping| #20# |#1|) $) 103 T ELT)) (|copyInto!| (($ $ $ #14#) 89 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#28=(|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| #28#)) ELT) (($ (|List| |#1|)) 130 T ELT)) (|construct| (($ (|List| |#1|)) 67 T ELT)) (|concat| (($ $ |#1|) 64 T ELT) (($ |#1| $) 63 T ELT) (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#20# (|Mapping| #20# |#1|) . #25#) 101 T ELT)) (>= (#29=((|Boolean|) $ $) 82 (|has| |#1| . #5#) ELT)) (> (#29# 84 (|has| |#1| . #5#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (<= (#29# 83 (|has| |#1| . #5#) ELT)) (< (#29# 85 (|has| |#1| . #5#) ELT)) (- (($ $) 122 (|has| |#1| . #30=((|AbelianGroup|))) ELT) (#31=($ $ $) 121 (|has| |#1| . #30#) ELT)) (+ (#31# 124 (|has| |#1| (|AbelianSemiGroup|)) ELT)) (* (($ (|Integer|) $) 120 (|has| |#1| . #30#) ELT) (($ |#1| $) 119 (|has| |#1| . #32=((|Monoid|))) ELT) (($ $ |#1|) 118 (|has| |#1| . #32#) ELT)) (|#| ((#27# $) 100 T ELT))) 
(((|PointCategory| |#1|) (|Category|) (|Ring|)) (T |PointCategory|)) 
((|point| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|PointCategory| *3)))) (|dimension| (*1 *2 *1) (AND (|ofCategory| *1 (|PointCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|PositiveInteger|)))) (|cross| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|PointCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|extend| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PointCategory| *3)) (|ofCategory| *3 (|Ring|))))) 
(|Join| (|VectorCategory| |t#1|) (|ConvertibleFrom| (|List| |t#1|)) (CATEGORY |domain| (SIGNATURE |point| ($ (|List| |t#1|))) (SIGNATURE |dimension| ((|PositiveInteger|) $)) (SIGNATURE |cross| ($ $ $)) (SIGNATURE |extend| ($ $ (|List| |t#1|))))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleFrom| (|List| |#1|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|FiniteLinearAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| |#1|) . T) ((|OneDimensionalArrayAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T) ((|VectorCategory| |#1|) . T)) 
((|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) 17 T ELT))) 
(((|PointFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)))) #1=(|Ring|) #1#) (T |PointFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Point| *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Point| *6)) (|isDomain| *1 (|PointFunctions2| *5 *6))))) 
((|zCoord| (#1=(|#1| (|Point| |#1|)) 14 T ELT)) (|yCoord| (#1# 13 T ELT)) (|xCoord| (#1# 12 T ELT)) (|thetaCoord| (#1# 16 T ELT)) (|shade| (#1# 24 T ELT)) (|rCoord| (#1# 15 T ELT)) (|phiCoord| (#1# 17 T ELT)) (|hue| (#1# 23 T ELT)) (|color| (#1# 22 T ELT))) 
(((|PointPackage| |#1|) (CATEGORY |package| (SIGNATURE |xCoord| #1=(|#1| (|Point| |#1|))) (SIGNATURE |yCoord| #1#) (SIGNATURE |zCoord| #1#) (SIGNATURE |rCoord| #1#) (SIGNATURE |thetaCoord| #1#) (SIGNATURE |phiCoord| #1#) (SIGNATURE |color| #1#) (SIGNATURE |hue| #1#) (SIGNATURE |shade| #1#)) (|Ring|)) (T |PointPackage|)) 
((|shade| #1=(*1 *2 *3) #2=(AND (|isDomain| *3 (|Point| *2)) (|isDomain| *1 (|PointPackage| *2)) (|ofCategory| *2 (|Ring|)))) (|hue| #1# #2#) (|color| #1# #2#) (|phiCoord| #1# #2#) (|thetaCoord| #1# #2#) (|rCoord| #1# #2#) (|zCoord| #1# #2#) (|yCoord| #1# #2#) (|xCoord| #1# #2#)) 
((|tanhIfCan| (((|Union| |#1| "failed") |#1|) 18 T ELT)) (|tanIfCan| (((|Union| |#1| "failed") |#1|) 6 T ELT)) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) 16 T ELT)) (|sinIfCan| (((|Union| |#1| "failed") |#1|) 4 T ELT)) (|sechIfCan| (((|Union| |#1| "failed") |#1|) 20 T ELT)) (|secIfCan| (((|Union| |#1| "failed") |#1|) 8 T ELT)) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) 1 T ELT)) (|logIfCan| (((|Union| |#1| "failed") |#1|) 3 T ELT)) (|expIfCan| (((|Union| |#1| "failed") |#1|) 2 T ELT)) (|cschIfCan| (((|Union| |#1| "failed") |#1|) 21 T ELT)) (|cscIfCan| (((|Union| |#1| "failed") |#1|) 9 T ELT)) (|cothIfCan| (((|Union| |#1| "failed") |#1|) 19 T ELT)) (|cotIfCan| (((|Union| |#1| "failed") |#1|) 7 T ELT)) (|coshIfCan| (((|Union| |#1| "failed") |#1|) 17 T ELT)) (|cosIfCan| (((|Union| |#1| "failed") |#1|) 5 T ELT)) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) 24 T ELT)) (|atanIfCan| (((|Union| |#1| "failed") |#1|) 12 T ELT)) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) 22 T ELT)) (|asinIfCan| (((|Union| |#1| "failed") |#1|) 10 T ELT)) (|asechIfCan| (((|Union| |#1| "failed") |#1|) 26 T ELT)) (|asecIfCan| (((|Union| |#1| "failed") |#1|) 14 T ELT)) (|acschIfCan| (((|Union| |#1| "failed") |#1|) 27 T ELT)) (|acscIfCan| (((|Union| |#1| "failed") |#1|) 15 T ELT)) (|acothIfCan| (((|Union| |#1| "failed") |#1|) 25 T ELT)) (|acotIfCan| (((|Union| |#1| "failed") |#1|) 13 T ELT)) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) 23 T ELT)) (|acosIfCan| (((|Union| |#1| "failed") |#1|) 11 T ELT))) 
(((|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| (#1=(|#4| |#4| (|List| |#3|)) 57 T ELT) (#2=(|#4| |#4| |#3|) 56 T ELT)) (|pushdown| (#1# 24 T ELT) (#2# 20 T ELT)) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) 33 T ELT))) 
(((|PushVariables| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |pushdown| #1=(|#4| |#4| |#3|)) (SIGNATURE |pushdown| #2=(|#4| |#4| (|List| |#3|))) (SIGNATURE |pushup| #1#) (SIGNATURE |pushup| #2#) (SIGNATURE |map| (|#4| (|Mapping| |#4| #3=(|Polynomial| |#1|)) |#4|))) (|Ring|) (|OrderedAbelianMonoidSup|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#4=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #4#)))) (|PolynomialCategory| #3# |#2| |#3|)) (T |PushVariables|)) 
((|map| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Mapping| *2 #1=(|Polynomial| *4))) #2=(|ofCategory| *4 (|Ring|)) #3=(|ofCategory| *2 (|PolynomialCategory| #1# *5 *6)) #4=(|ofCategory| *5 (|OrderedAbelianMonoidSup|)) #5=(|ofCategory| *6 #6=(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#7=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #7#))))) #8=(|isDomain| *1 (|PushVariables| *4 *5 *6 *2)))) (|pushup| #9=(*1 *2 *2 *3) #10=(AND (|isDomain| *3 (|List| *6)) #5# #2# #4# #8# #3#)) (|pushup| #9# #11=(AND #2# #4# (|ofCategory| *3 #6#) (|isDomain| *1 (|PushVariables| *4 *5 *3 *2)) (|ofCategory| *2 (|PolynomialCategory| #1# *5 *3)))) (|pushdown| #9# #10#) (|pushdown| #9# #11#)) 
((|reducedDiscriminant| ((|#2| |#3|) 35 T ELT)) (|localIntegralBasis| ((#1=(|Record| (|:| |basis| #2=(|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| #2#)) |#2|) 79 T ELT)) (|integralBasis| ((#1#) 100 T ELT))) 
(((|PAdicWildFunctionFieldIntegralBasis| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |integralBasis| (#1=(|Record| (|:| |basis| #2=(|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| #2#)))) (SIGNATURE |localIntegralBasis| (#1# |#2|)) (SIGNATURE |reducedDiscriminant| (|#2| |#3|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|MonogenicAlgebra| |#2| |#3|)) (T |PAdicWildFunctionFieldIntegralBasis|)) 
((|reducedDiscriminant| #1=(*1 *2 *3) (AND (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #2=(|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PAdicWildFunctionFieldIntegralBasis| *4 *2 *3 *5)) #3=(|ofCategory| *4 #4=(|FiniteFieldCategory|)) (|ofCategory| *5 (|MonogenicAlgebra| *2 *3)))) (|localIntegralBasis| #1# (AND #3# (|ofCategory| *3 #2#) (|ofCategory| *5 #5=(|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| #6=(|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| #6#))) (|isDomain| *1 (|PAdicWildFunctionFieldIntegralBasis| *4 *3 *5 *6)) (|ofCategory| *6 (|MonogenicAlgebra| *3 *5)))) (|integralBasis| (*1 *2) (AND (|ofCategory| *3 #4#) (|ofCategory| *4 #5#) (|ofCategory| *5 #2#) (|isDomain| *2 (|Record| (|:| |basis| #7=(|Matrix| *4)) (|:| |basisDen| *4) (|:| |basisInv| #7#))) (|isDomain| *1 (|PAdicWildFunctionFieldIntegralBasis| *3 *4 *5 *6)) (|ofCategory| *6 (|MonogenicAlgebra| *4 *5))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|status| ((#3=(|Union| #2# "failed") $) 71 T ELT)) (|simplify| (#4=($ $) 36 (AND (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|EuclideanDomain|))) ELT)) (|setStatus| (($ $ #3#) 72 T ELT)) (|quasiAlgebraicSet| (($ #5=(|List| |#4|) |#4|) 25 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|idealSimplify| (#4# 69 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|empty?| ((#2# $) 70 T ELT)) (|empty| (($) 30 T ELT)) (|definingInequation| ((|#4| $) 74 T ELT)) (|definingEquations| ((#5# $) 73 T ELT)) (|coerce| (((|OutputForm|) $) 68 T ELT)) (|before?| #1#) (= #1#)) 
(((|QuasiAlgebraicSet| |#1| |#2| |#3| |#4|) (|Join| (|SetCategory|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |empty| ($)) (SIGNATURE |quasiAlgebraicSet| ($ #1=(|List| |#4|) |#4|)) (SIGNATURE |status| (#2=(|Union| #3=(|Boolean|) "failed") $)) (SIGNATURE |setStatus| ($ $ #2#)) (SIGNATURE |empty?| (#3# $)) (SIGNATURE |definingEquations| (#1# $)) (SIGNATURE |definingInequation| (|#4| $)) (SIGNATURE |idealSimplify| #4=($ $)) (IF (|has| |#1| (|EuclideanDomain|)) (IF (|has| |#1| (|CharacteristicZero|)) (SIGNATURE |simplify| #4#) |%noBranch|) |%noBranch|))) (|GcdDomain|) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|PolynomialCategory| |#1| |#3| |#2|)) (T |QuasiAlgebraicSet|)) 
((|empty| (*1 *1) #1=(AND #2=(|ofCategory| *2 #3=(|GcdDomain|)) #4=(|ofCategory| *3 #5=(|OrderedSet|)) #6=(|ofCategory| *4 #7=(|OrderedAbelianMonoidSup|)) #8=(|isDomain| *1 (|QuasiAlgebraicSet| *2 *3 *4 *5)) #9=(|ofCategory| *5 (|PolynomialCategory| *2 *4 *3)))) (|quasiAlgebraicSet| (*1 *1 *2 *3) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|PolynomialCategory| *4 *6 *5)) (|ofCategory| *4 #3#) (|ofCategory| *5 #5#) (|ofCategory| *6 #7#) (|isDomain| *1 (|QuasiAlgebraicSet| *4 *5 *6 *3)))) (|status| #10=(*1 *2 *1) (|partial| AND #11=(|ofCategory| *3 #3#) #12=(|ofCategory| *4 #5#) #13=(|ofCategory| *5 #7#) #14=(|isDomain| *2 #15=(|Boolean|)) #16=(|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *6)) #17=(|ofCategory| *6 #18=(|PolynomialCategory| *3 *5 *4)))) (|setStatus| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Union| #15# "failed")) #11# #12# #13# #16# #17#)) (|empty?| #10# (AND #11# #12# #13# #14# #16# #17#)) (|definingEquations| #10# (AND #11# #12# #13# (|isDomain| *2 (|List| *6)) #16# #17#)) (|definingInequation| #10# (AND (|ofCategory| *2 #18#) (|isDomain| *1 (|QuasiAlgebraicSet| *3 *4 *5 *2)) #11# #12# #13#)) (|idealSimplify| #19=(*1 *1 *1) #1#) (|simplify| #19# (AND (|ofCategory| *2 (|CharacteristicZero|)) (|ofCategory| *2 (|EuclideanDomain|)) #2# #4# #6# #8# #9#))) 
((|radicalSimplify| ((#1=(|QuasiAlgebraicSet| #2=(|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| #2#)) #1#) 82 T ELT))) 
(((|QuasiAlgebraicSet2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |radicalSimplify| (#1=(|QuasiAlgebraicSet| #2=(|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| #3=(|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| #2#)) #1#))) (|List| (|Symbol|)) #3#) (T |QuasiAlgebraicSet2|)) 
((|radicalSimplify| (*1 *2 *2) (AND (|isDomain| *2 (|QuasiAlgebraicSet| #1=(|Fraction| (|Integer|)) (|OrderedVariableList| *3) (|DirectProduct| *4 #2=(|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| *3 #1#))) (|ofType| *3 (|List| (|Symbol|))) (|ofType| *4 #2#) (|isDomain| *1 (|QuasiAlgebraicSet2| *3 *4))))) 
((|supDimElseRittWu?| (#1=(#2=(|Boolean|) |#5| |#5|) 44 T ELT)) (|subTriSet?| (#1# 59 T ELT)) (|subQuasiComponent?| ((#2# |#5| #3=(|List| |#5|)) 81 T ELT) (#1# 68 T ELT)) (|subPolSet?| (#4=(#2# #5=(|List| |#4|) #5#) 65 T ELT)) (|subCase?| ((#2# #6=(|Record| (|:| |val| #5#) #7=(|:| |tower| |#5|)) #6#) 70 T ELT)) (|stopTable!| ((#8=(|Void|)) 32 T ELT)) (|startTable!| ((#8# #9=(|String|) #9# #9#) 28 T ELT)) (|removeSuperfluousQuasiComponents| (#10=(#3# #3#) 100 T ELT)) (|removeSuperfluousCases| ((#11=(|List| #6#) #11#) 92 T ELT)) (|prepareDecompose| (((|List| #12=(|Record| (|:| |eq| #5#) #7# (|:| |ineq| #5#))) #5# #3# #2# #2#) 122 T ELT)) (|moreAlgebraic?| (#1# 53 T ELT)) (|internalSubQuasiComponent?| (((|Union| #2# #13="failed") |#5| |#5|) 78 T ELT)) (|internalSubPolSet?| (#4# 64 T ELT)) (|internalInfRittWu?| (#4# 66 T ELT)) (|infRittWu?| (#4# 67 T ELT)) (|branchIfCan| (((|Union| #12# #13#) #5# |#5| #5# #2# #2# #2# #2# #2#) 117 T ELT)) (|algebraicSort| (#10# 49 T ELT))) 
(((|QuasiComponentPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTable!| (#1=(|Void|) #2=(|String|) #2# #2#)) (SIGNATURE |stopTable!| (#1#)) (SIGNATURE |supDimElseRittWu?| #3=(#4=(|Boolean|) |#5| |#5|)) (SIGNATURE |algebraicSort| #5=(#6=(|List| |#5|) #6#)) (SIGNATURE |moreAlgebraic?| #3#) (SIGNATURE |subTriSet?| #3#) (SIGNATURE |subPolSet?| #7=(#4# #8=(|List| |#4|) #8#)) (SIGNATURE |internalSubPolSet?| #7#) (SIGNATURE |internalInfRittWu?| #7#) (SIGNATURE |infRittWu?| #7#) (SIGNATURE |internalSubQuasiComponent?| ((|Union| #4# #9="failed") |#5| |#5|)) (SIGNATURE |subQuasiComponent?| #3#) (SIGNATURE |subQuasiComponent?| (#4# |#5| #6#)) (SIGNATURE |removeSuperfluousQuasiComponents| #5#) (SIGNATURE |subCase?| (#4# #10=(|Record| (|:| |val| #8#) #11=(|:| |tower| |#5|)) #10#)) (SIGNATURE |removeSuperfluousCases| (#12=(|List| #10#) #12#)) (SIGNATURE |prepareDecompose| ((|List| #13=(|Record| (|:| |eq| #8#) #11# (|:| |ineq| #8#))) #8# #6# #4# #4#)) (SIGNATURE |branchIfCan| ((|Union| #13# #9#) #8# |#5| #8# #4# #4# #4# #4# #4#))) (|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 #1=(|isDomain| *5 #2=(|Boolean|)) #3=(|ofCategory| *6 #4=(|GcdDomain|)) #5=(|ofCategory| *7 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *8 #8=(|OrderedSet|)) #9=(|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| #10=(|:| |eq| #11=(|List| *9)) (|:| |tower| *4) #12=(|:| |ineq| #11#))) (|isDomain| *1 (|QuasiComponentPackage| *6 *7 *8 *9 *4)) #13=(|isDomain| *3 #11#) (|ofCategory| *4 #14=(|RegularTriangularSetCategory| *6 *7 *8 *9)))) (|prepareDecompose| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *4 (|List| *10)) #1# (|ofCategory| *10 #14#) #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| #10# (|:| |tower| *10) #12#))) (|isDomain| *1 (|QuasiComponentPackage| *6 *7 *8 *9 *10)) #13#)) (|removeSuperfluousCases| #15=(*1 *2 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *6)) (|:| |tower| *7)))) #16=(|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) #17=(|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) #18=(|ofCategory| *3 #4#) #19=(|ofCategory| *4 #6#) #20=(|ofCategory| *5 #8#) #21=(|isDomain| *1 (|QuasiComponentPackage| *3 *4 *5 *6 *7)))) (|subCase?| #22=(*1 *2 *3 *3) (AND (|isDomain| *3 (|Record| (|:| |val| #23=(|List| *7)) (|:| |tower| *8))) #24=(|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) #25=(|ofCategory| *8 #26=(|RegularTriangularSetCategory| *4 *5 *6 *7)) #27=(|ofCategory| *4 #4#) #28=(|ofCategory| *5 #6#) #29=(|ofCategory| *6 #8#) #30=(|isDomain| *2 #2#) #31=(|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *8)))) (|removeSuperfluousQuasiComponents| #15# #32=(AND (|isDomain| *2 #23#) #17# #18# #19# #20# #16# #21#)) (|subQuasiComponent?| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 #4#) (|ofCategory| *6 #6#) (|ofCategory| *7 #8#) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) #30# (|isDomain| *1 (|QuasiComponentPackage| *5 *6 *7 *8 *3)))) (|subQuasiComponent?| #22# #33=(AND #27# #28# #29# #24# #30# #34=(|isDomain| *1 (|QuasiComponentPackage| *4 *5 *6 *7 *3)) #35=(|ofCategory| *3 #26#))) (|internalSubQuasiComponent?| #22# (|partial| AND #27# #28# #29# #24# #30# #34# #35#)) (|infRittWu?| #22# #36=(AND (|isDomain| *3 #23#) #24# #27# #28# #29# #30# #31# #25#)) (|internalInfRittWu?| #22# #36#) (|internalSubPolSet?| #22# #36#) (|subPolSet?| #22# #36#) (|subTriSet?| #22# #33#) (|moreAlgebraic?| #22# #33#) (|algebraicSort| #15# #32#) (|supDimElseRittWu?| #22# #33#) (|stopTable!| (*1 *2) (AND #18# #19# #20# #16# #37=(|isDomain| *2 (|Void|)) #21# #17#)) (|startTable!| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|String|)) #27# #28# #29# #24# #37# #31# #25#))) 
((|variable| ((#1=(|Symbol|) $) 15 T ELT)) (|value| ((#2=(|String|) $) 16 T ELT)) (|equation| (($ #1# #2#) 14 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT))) 
(((|QueryEquation|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |equation| ($ #1=(|Symbol|) #2=(|String|))) (SIGNATURE |variable| (#1# $)) (SIGNATURE |value| (#2# $))))) (T |QueryEquation|)) 
((|equation| (*1 *1 *2 *3) (AND #1=(|isDomain| *2 (|Symbol|)) (|isDomain| *3 #2=(|String|)) #3=(|isDomain| *1 (|QueryEquation|)))) (|variable| #4=(*1 *2 *1) (AND #1# #3#)) (|value| #4# (AND (|isDomain| *2 #2#) #3#))) 
((|retractIfCan| (((|Union| |#2| #1="failed") $) NIL T ELT) (((|Union| #2=(|Symbol|) #1#) $) 72 T ELT) (((|Union| #3=(|Fraction| #4=(|Integer|)) #1#) $) NIL T ELT) (((|Union| #4# #1#) $) 102 T ELT)) (|retract| ((|#2| $) NIL T ELT) ((#2# $) 67 T ELT) ((#3# $) NIL T ELT) ((#4# $) 99 T ELT)) (|reducedSystem| ((#5=(|Matrix| #4#) #6=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #5#) (|:| |vec| (|Vector| #4#))) #6# #7=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #8=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) #6# #7#) 121 T ELT) ((#8# #6#) 35 T ELT)) (|random| (#9=($) 105 T ELT)) (|patternMatch| ((#10=(|PatternMatchResult| #4# $) $ #11=(|Pattern| #4#) #10#) 82 T ELT) ((#12=(|PatternMatchResult| #13=(|Float|) $) $ #14=(|Pattern| #13#) #12#) 91 T ELT)) (|numerator| (#15=($ $) 10 T ELT)) (|nextItem| (((|Maybe| $) $) 27 T ELT)) (|map| (($ #16=(|Mapping| |#2| |#2|) $) 29 T ELT)) (|init| (#9# 16 T CONST)) (|fractionPart| (#15# 61 T ELT)) (|differentiate| (($ $ #16#) 43 T ELT) (($ $ #16# #17=(|NonNegativeInteger|)) NIL T ELT) (($ $ #2#) NIL T ELT) (($ $ #18=(|List| #2#)) NIL T ELT) (($ $ #2# #17#) NIL T ELT) (($ $ #18# (|List| #17#)) NIL T ELT) #19=(#15# NIL T ELT) (($ $ #17#) NIL T ELT)) (|denominator| (#15# 12 T ELT)) (|convert| ((#11# $) 77 T ELT) ((#14# $) 86 T ELT) (((|InputForm|) $) 47 T ELT) ((#13# $) 51 T ELT) (((|DoubleFloat|) $) 55 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #4#) NIL T ELT) #19# (($ #3#) 97 T ELT) (($ |#2|) NIL T ELT) (($ #2#) 64 T ELT)) (|characteristic| ((#17#) 38 T CONST)) (< (((|Boolean|) $ $) 57 T ELT))) 
(((|QuotientFieldCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE < ((|Boolean|) |#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #1=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #2=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #3=(|List| #4=(|Symbol|)) (|List| #1#))) (SIGNATURE |differentiate| (|#1| |#1| #4# #1#)) (SIGNATURE |differentiate| (|#1| |#1| #3#)) (SIGNATURE |differentiate| (|#1| |#1| #4#)) (SIGNATURE |init| #5=(|#1|) |constant|) (SIGNATURE |nextItem| ((|Maybe| |#1|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #6=(|Integer|) #7="failed") |#1|)) (SIGNATURE |retract| (#6# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #8=(|Fraction| #6#) #7#) |#1|)) (SIGNATURE |retract| (#8# |#1|)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| (#9=(|Float|) |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |coerce| (|#1| #4#)) (SIGNATURE |retractIfCan| ((|Union| #4# #7#) |#1|)) (SIGNATURE |retract| (#4# |#1|)) (SIGNATURE |random| #5#) (SIGNATURE |fractionPart| #2#) (SIGNATURE |denominator| #2#) (SIGNATURE |numerator| #2#) (SIGNATURE |patternMatch| (#10=(|PatternMatchResult| #9# |#1|) |#1| #11=(|Pattern| #9#) #10#)) (SIGNATURE |patternMatch| (#12=(|PatternMatchResult| #6# |#1|) |#1| #13=(|Pattern| #6#) #12#)) (SIGNATURE |convert| (#11# |#1|)) (SIGNATURE |convert| (#13# |#1|)) (SIGNATURE |reducedSystem| (#14=(|Matrix| |#2|) #15=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #14#) (|:| |vec| (|Vector| |#2|))) #15# #16=(|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #17=(|Matrix| #6#)) (|:| |vec| (|Vector| #6#))) #15# #16#)) (SIGNATURE |reducedSystem| (#17# #15#)) (SIGNATURE |differentiate| (|#1| |#1| #18=(|Mapping| |#2| |#2|) #1#)) (SIGNATURE |differentiate| (|#1| |#1| #18#)) (SIGNATURE |map| (|#1| #18# |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #7#) |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| #8#)) (SIGNATURE |coerce| #2#) (SIGNATURE |characteristic| (#1#) |constant|) (SIGNATURE |coerce| (|#1| #6#)) (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))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|wholePart| ((|#1| $) 173 (|has| |#1| (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (#4=((|Factored| #5=(|SparseUnivariatePolynomial| $)) #5#) 164 (|has| |#1| . #6=((|PolynomialFactorizationExplicit|))) ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#7=((|Factored| $) $) 90 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #8=(|List| #5#) #9="failed") #8# #5#) 167 (|has| |#1| . #6#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sign| (((|Integer|) $) 154 (|has| |#1| . #10=((|OrderedIntegralDomain|))) ELT)) (|sample| (#11=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| . #12=("failed")) . #13=($)) 203 T ELT) (((|Union| #14=(|Symbol|) . #12#) . #13#) 162 (|has| |#1| . #15=((|RetractableTo| (|Symbol|)))) ELT) (((|Union| #16=(|Fraction| (|Integer|)) . #12#) . #13#) 145 (|has| |#1| . #17=((|RetractableTo| (|Integer|)))) ELT) (((|Union| #18=(|Integer|) . #12#) . #13#) 143 (|has| |#1| . #19=((|RetractableTo| (|Integer|)))) ELT)) (|retract| ((|#1| . #20=($)) 204 T ELT) ((#14# . #20#) 163 (|has| |#1| . #15#) ELT) ((#16# . #20#) 146 (|has| |#1| . #17#) ELT) ((#18# . #20#) 144 (|has| |#1| . #19#) ELT)) (|rem| (#21=($ $ $) 71 T ELT)) (|reducedSystem| (((|Matrix| #22=(|Integer|)) . #23=(#24=(|Matrix| $))) 188 (|has| |#1| . #25=((|LinearlyExplicitRingOver| #22#))) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #26=(#24# #27=(|Vector| $))) 187 (|has| |#1| . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #26#) 186 T ELT) (((|Matrix| |#1|) . #23#) 185 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|random| (($) 171 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|quo| (#21# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #28=(|List| $)) (|:| |generator| $)) #28#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|positive?| (((|Boolean|) $) 156 (|has| |#1| . #10#) ELT)) (|patternMatch| (((|PatternMatchResult| #29=(|Integer|) . #30=($)) $ (|Pattern| #29#) (|PatternMatchResult| #29# . #30#)) 180 (|has| |#1| (|PatternMatchable| #29#)) ELT) (((|PatternMatchResult| #31=(|Float|) . #30#) $ (|Pattern| #31#) (|PatternMatchResult| #31# . #30#)) 179 (|has| |#1| (|PatternMatchable| #31#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numerator| (($ $) 175 T ELT)) (|numer| ((|#1| $) 177 T ELT)) (|nextItem| (((|Maybe| $) $) 142 (|has| |#1| . #32=((|StepThrough|))) ELT)) (|negative?| (((|Boolean|) $) 155 (|has| |#1| . #10#) ELT)) (|multiEuclidean| (((|Union| #33=(|List| $) #34="failed") #33# $) 68 T ELT)) (|min| (#35=($ $ $) 147 (|has| |#1| . #36=((|OrderedSet|))) ELT)) (|max| (#35# 148 (|has| |#1| . #36#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 195 T ELT)) (|leftReducedSystem| (((|Matrix| #22#) . #37=(#27#)) 190 (|has| |#1| . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #38=(#27# $)) 189 (|has| |#1| . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #38#) 184 T ELT) (((|Matrix| |#1|) . #37#) 183 T ELT)) (|lcm| (#39=($ $ $) 60 T ELT) (#40=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|init| (($) 141 (|has| |#1| . #32#) CONST)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#41=(|SparseUnivariatePolynomial| $) #41# #41#) 58 T ELT)) (|gcd| (#39# 62 T ELT) (#40# 61 T ELT)) (|fractionPart| (($ $) 172 (|has| |#1| (|EuclideanDomain|)) ELT)) (|floor| ((|#1| $) 169 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|factorSquareFreePolynomial| (#4# 166 (|has| |#1| . #6#) ELT)) (|factorPolynomial| (#4# 165 (|has| |#1| . #6#) ELT)) (|factor| (#7# 92 T ELT)) (|extendedEuclidean| (((|Record| #42=(|:| |coef1| $) #43=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #42# #43#) #34#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #28#) #28# $) 65 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 201 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 200 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 199 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 198 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| #44=(|Symbol|)) (|List| |#1|)) 197 (|has| |#1| (|InnerEvalable| #44# |#1|)) ELT) (($ $ #44# |#1|) 196 (|has| |#1| (|InnerEvalable| #44# |#1|)) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|elt| (($ $ |#1|) 202 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|differentiate| (($ $ (|Mapping| |#1| |#1|)) 194 T ELT) (($ $ (|Mapping| |#1| |#1|) . #45=((|NonNegativeInteger|))) 193 T ELT) (($ . #46=($)) 140 (|has| |#1| . #47=((|DifferentialSpace|))) ELT) (#48=($ $ (|NonNegativeInteger|)) 138 (|has| |#1| . #47#) ELT) (($ $ #49=(|Symbol|)) 136 (|has| |#1| . #50=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #49#)) 134 (|has| |#1| . #50#) ELT) (($ $ #49# . #51=(#52=(|NonNegativeInteger|))) 133 (|has| |#1| . #50#) ELT) (($ $ (|List| #49#) . #53=((|List| #52#))) 132 (|has| |#1| . #50#) ELT)) (|denominator| (($ $) 174 T ELT)) (|denom| ((|#1| $) 176 T ELT)) (|convert| ((#54=(|Pattern| (|Integer|)) . #55=($)) 182 (|has| |#1| (|ConvertibleTo| #54#)) ELT) ((#56=(|Pattern| (|Float|)) . #55#) 181 (|has| |#1| (|ConvertibleTo| #56#)) ELT) (((|InputForm|) . #55#) 159 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT) (((|Float|) . #55#) 158 (|has| |#1| . #57=((|RealConstant|))) ELT) (((|DoubleFloat|) . #55#) 157 (|has| |#1| . #57#) ELT)) (|conditionP| (((|Union| (|Vector| $) #9#) (|Matrix| $)) 168 (|and| #58=(|has| $ (|CharacteristicNonZero|)) (|has| |#1| . #6#)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #59=(|Fraction| #60=(|Integer|))) 84 T ELT) (($ |#1|) 207 T ELT) (($ #14#) 161 (|has| |#1| . #15#) ELT)) (|charthRoot| (((|Maybe| $) $) 160 (OR (|has| |#1| (|CharacteristicNonZero|)) (|and| #58# (|has| |#1| . #6#))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|ceiling| ((|#1| $) 170 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| (($ $) 153 (|has| |#1| . #10#) ELT)) (|Zero| (#11# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|Mapping| |#1| |#1|)) 192 T ELT) (($ $ (|Mapping| |#1| |#1|) . #45#) 191 T ELT) (($ . #46#) 139 (|has| |#1| . #47#) ELT) (#48# 137 (|has| |#1| . #47#) ELT) (($ $ #49#) 135 (|has| |#1| . #50#) ELT) (($ $ (|List| #49#)) 131 (|has| |#1| . #50#) ELT) (($ $ #49# . #51#) 130 (|has| |#1| . #50#) ELT) (($ $ (|List| #49#) . #53#) 129 (|has| |#1| . #50#) ELT)) (>= (#61=((|Boolean|) $ $) 149 (|has| |#1| . #36#) ELT)) (> (#61# 151 (|has| |#1| . #36#) ELT)) (= (#1# 8 T ELT)) (<= (#61# 150 (|has| |#1| . #36#) ELT)) (< (#61# 152 (|has| |#1| . #36#) ELT)) (/ (($ $ $) 83 T ELT) (($ |#1| |#1|) 178 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #60#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #62=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #59#) 86 T ELT) (($ #59# . #62#) 85 T ELT) (($ |#1| . #62#) 206 T ELT) (($ $ |#1|) 205 T ELT))) 
(((|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|))))) 
(|Join| (|Field|) (|Algebra| |t#1|) (|RetractableTo| |t#1|) (|FullyEvalableOver| |t#1|) (|DifferentialExtension| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (|Patternable| |t#1|) (|FullyPatternMatchable| |t#1|) (CATEGORY |domain| (SIGNATURE / ($ |t#1| |t#1|)) (SIGNATURE |numer| (|t#1| $)) (SIGNATURE |denom| (|t#1| $)) (SIGNATURE |numerator| ($ $)) (SIGNATURE |denominator| ($ $)) (IF (|has| |t#1| (|StepThrough|)) (ATTRIBUTE (|StepThrough|)) |%noBranch|) (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (PROGN (ATTRIBUTE (|RetractableTo| (|Integer|))) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Integer|))))) |%noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|) (IF (|has| |t#1| (|OrderedIntegralDomain|)) (ATTRIBUTE (|OrderedIntegralDomain|)) |%noBranch|) (IF (|has| |t#1| (|RealConstant|)) (ATTRIBUTE (|RealConstant|)) |%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| (|RetractableTo| (|Symbol|))) (ATTRIBUTE (|RetractableTo| (|Symbol|))) |%noBranch|) (IF (|has| |t#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |wholePart| (|t#1| $)) (SIGNATURE |fractionPart| ($ $))) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |random| ($)) (SIGNATURE |ceiling| (|t#1| $)) (SIGNATURE |floor| (|t#1| $))) |%noBranch|) (IF (|has| |t#1| (|PolynomialFactorizationExplicit|)) (ATTRIBUTE (|PolynomialFactorizationExplicit|)) |%noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| |#1|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) OR (|has| |#1| (|OrderedIntegralDomain|)) (|has| |#1| (|CharacteristicZero|))) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #2=(|Symbol|)) |has| |#1| (|RetractableTo| (|Symbol|))) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|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|)))) ((|DifferentialDomain| $) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#1|) . T) ((|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) ((|Functorial| |#1|) . T) ((|GcdDomain|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| #3=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) . T) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #3#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) . 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|))) ((|OrderedType|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|OrderedIntegralDomain|))) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #4#) OR (|has| |#1| (|PartialDifferentialSpace| (|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| #2#) |has| |#1| (|RetractableTo| (|Symbol|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|StepThrough|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) 14 T ELT))) 
(((|QuotientFieldCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#2| |#1|) |#3|))) #1=(|IntegralDomain|) #1# (|QuotientFieldCategory| |#1|) (|QuotientFieldCategory| |#2|)) (T |QuotientFieldCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|IntegralDomain|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|QuotientFieldCategory| *6)) (|isDomain| *1 (|QuotientFieldCategoryFunctions2| *5 *6 *4 *2)) (|ofCategory| *4 (|QuotientFieldCategory| *5))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| #3=(($) NIL T CONST)) (|quadraticForm| (($ #4=(|SquareMatrix| |#1| |#2|)) 11 T ELT)) (|opposite?| #1#) (|matrix| ((#4# $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) 16 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| #3#) (= #1#) (- (($ $) NIL T ELT) #5=(($ $ $) NIL T ELT)) (+ #5#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT))) 
(((|QuadraticForm| |#1| |#2|) (|Join| (|AbelianGroup|) (|Eltable| (|DirectProduct| |#1| |#2|) |#2|) (CATEGORY |domain| (SIGNATURE |quadraticForm| ($ #1=(|SquareMatrix| |#1| |#2|))) (SIGNATURE |matrix| (#1# $)))) (|PositiveInteger|) (|Field|)) (T |QuadraticForm|)) 
((|quadraticForm| (*1 *1 *2) (AND #1=(|isDomain| *2 (|SquareMatrix| *3 *4)) #2=(|ofType| *3 (|PositiveInteger|)) #3=(|ofCategory| *4 (|Field|)) #4=(|isDomain| *1 (|QuadraticForm| *3 *4)))) (|matrix| (*1 *2 *1) (AND #1# #4# #2# #3#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|QuasiquoteAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |expression| ((|SpadAst|) $))))) (T |QuasiquoteAst|)) 
((|expression| (*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|QuasiquoteAst|))))) 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|sample| (#3=($) 6 T CONST)) (|rotate!| (($ $) 44 T ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 57 (|has| |#1| . #4=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 53 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 52 T ELT)) (|members| (((|List| |#1|) $) 51 T ELT)) (|member?| ((#5=(|Boolean|) |#1| $) 56 (|has| |#1| . #4#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|length| (((|NonNegativeInteger|) $) 43 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #6=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #7=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #6#) ELT)) (|front| ((|#1| $) 42 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #5# |#1|) $) 54 T ELT)) (|extract!| ((|#1| . #7#) 37 T ELT)) (|every?| ((#5# (|Mapping| #5# |#1|) . #8=($)) 49 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#9=(|Boolean|) $ $) 10 T ELT)) (|enqueue!| ((|#1| |#1| $) 46 T ELT)) (|empty?| ((#9# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|dequeue!| ((|#1| $) 45 T ELT)) (|count| ((#10=(|NonNegativeInteger|) |#1| $) 55 (|has| |#1| . #4#) ELT) ((#10# (|Mapping| #5# |#1|) $) 50 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|back| ((|#1| $) 41 T ELT)) (|any?| ((#5# (|Mapping| #5# |#1|) . #8#) 48 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#10# $) 47 T ELT))) 
(((|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|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (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|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|sample| (#8=($) NIL T CONST)) (|retractIfCan| (((|Union| #9=(|Integer|) . #10=(#7#)) . #11=($)) NIL #12=(|has| |#1| (|RetractableTo| #9#)) ELT) (#13=((|Union| #14=(|Fraction| #9#) . #10#) . #11#) NIL #15=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| |#1| . #10#) . #11#) NIL T ELT)) (|retract| ((#9# . #16=($)) NIL #12# ELT) (#17=(#14# . #16#) NIL #15# ELT) #18=(#19=(|#1| . #16#) NIL T ELT)) (|reducedSystem| ((#20=(|Matrix| #9#) . #21=(#22=(|Matrix| $))) NIL #23=(|has| |#1| (|LinearlyExplicitRingOver| #9#)) ELT) ((#24=(|Record| (|:| |mat| #20#) (|:| |vec| (|Vector| #9#))) . #25=(#22# #26=(|Vector| $))) NIL #23# ELT) ((#27=(|Record| (|:| |mat| #28=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #25#) NIL T ELT) ((#28# . #21#) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|real| (#19# 12 T ELT)) (|rationalIfCan| (#13# NIL #29=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#5# NIL #29# ELT)) (|rational| (#17# NIL #29# ELT)) (|quatern| (($ |#1| |#1| |#1| |#1|) 16 T ELT)) (|opposite?| #1#) (|one?| #4#) (|norm| #18#) (|min| #30=(#31=($ $ $) NIL #32=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #30#) (|map| (($ #33=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|leftReducedSystem| ((#20# . #34=(#26#)) NIL #23# ELT) ((#24# . #35=(#26# $)) NIL #23# ELT) ((#27# . #35#) NIL T ELT) ((#28# . #34#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#36=($ $) NIL #37=(|has| |#1| (|Field|)) ELT)) (|imagK| (#19# 15 T ELT)) (|imagJ| (#19# 14 T ELT)) (|imagI| (#19# 13 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| (($ $ #38=(|List| |#1|) #38#) NIL #39=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #39# ELT) (($ $ #40=(|Equation| |#1|)) NIL #39# ELT) (($ $ (|List| #40#)) NIL #39# ELT) (($ $ #41=(|List| #42=(|Symbol|)) #38#) NIL #43=(|has| |#1| (|InnerEvalable| #42# |#1|)) ELT) (($ $ #42# |#1|) NIL #43# ELT)) (|elt| (#44=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|differentiate| #45=(($ $ #33#) NIL T ELT) #46=(($ $ #33# #47=(|NonNegativeInteger|)) NIL T ELT) #48=(#36# NIL #49=(|has| |#1| (|DifferentialSpace|)) ELT) #50=(#51=($ $ #47#) NIL #49# ELT) #52=(($ $ #42#) NIL #53=(|has| |#1| (|PartialDifferentialSpace| #42#)) ELT) #54=(($ $ #41#) NIL #53# ELT) #55=(($ $ #42# #47#) NIL #53# ELT) #56=(($ $ #41# (|List| #47#)) NIL #53# ELT)) (|convert| ((#57=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #57#)) ELT)) (|conjugate| #58=(#36# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #9#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #14#) NIL (OR #37# #15#) ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#47#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#19# NIL (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#8# 8 T CONST)) (|One| (#8# 10 T CONST)) (D #45# #46# #48# #50# #52# #54# #55# #56#) (>= #59=(#2# NIL #32# ELT)) (> #59#) (= #1#) (<= #59#) (< #59#) (- #58# #60=(#31# NIL T ELT)) (+ #60#) (** (($ $ #61=(|PositiveInteger|)) NIL T ELT) (#51# NIL T ELT) (($ $ #9#) NIL #37# ELT)) (* (($ #61# $) NIL T ELT) (($ #47# $) NIL T ELT) (($ #9# . #62=($)) NIL T ELT) (#31# 20 T ELT) (#44# NIL T ELT) (($ |#1| . #62#) NIL T ELT) (($ $ #14#) NIL #37# ELT) (($ #14# . #62#) NIL #37# ELT))) 
(((|Quaternion| |#1|) (|QuaternionCategory| |#1|) (|CommutativeRing|)) (T |Quaternion|)) 
NIL 
((|zero?| (#1=(#2=(|Boolean|) $) 43 T ELT)) (|retractIfCan| (((|Union| #3=(|Integer|) #4="failed") $) NIL T ELT) (#5=((|Union| #6=(|Fraction| #3#) #4#) $) NIL T ELT) (((|Union| |#2| #4#) $) 46 T ELT)) (|retract| ((#3# $) NIL T ELT) (#7=(#6# $) NIL T ELT) (#8=(|#2| $) 44 T ELT)) (|rationalIfCan| (#5# 78 T ELT)) (|rational?| (#1# 72 T ELT)) (|rational| (#7# 76 T ELT)) (|one?| (#1# 42 T ELT)) (|norm| (#8# 22 T ELT)) (|map| (($ #9=(|Mapping| |#2| |#2|) $) 19 T ELT)) (|inv| (#10=($ $) 58 T ELT)) (|differentiate| (($ $ #9#) 35 T ELT) (($ $ #9# #11=(|NonNegativeInteger|)) NIL T ELT) (($ $ #12=(|Symbol|)) NIL T ELT) (($ $ #13=(|List| #12#)) NIL T ELT) (($ $ #12# #11#) NIL T ELT) (($ $ #13# (|List| #11#)) NIL T ELT) (#10# NIL T ELT) (($ $ #11#) NIL T ELT)) (|convert| (((|InputForm|) $) 67 T ELT)) (|conjugate| (#10# 17 T ELT)) (|coerce| (((|OutputForm|) $) 53 T ELT) (($ #3#) 39 T ELT) (($ |#2|) 37 T ELT) (($ #6#) NIL T ELT)) (|characteristic| ((#11#) 10 T CONST)) (|abs| (#8# 71 T ELT)) (= (#14=(#2# $ $) 26 T ELT)) (< (#14# 69 T ELT)) (- (#10# 30 T ELT) (#15=($ $ $) 29 T ELT)) (+ (#15# 27 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #11# $) NIL T ELT) (($ #3# $) 34 T ELT) (#15# NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) 31 T ELT) (($ $ #6#) NIL T ELT) (($ #6# $) NIL T ELT))) 
(((|QuaternionCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #4=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #5=(|List| #6=(|Symbol|)) (|List| #3#))) (SIGNATURE |differentiate| (|#1| |#1| #6# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #5#)) (SIGNATURE |differentiate| (|#1| |#1| #6#)) (SIGNATURE < #7=(#8=(|Boolean|) |#1| |#1|)) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE * (|#1| |#1| #1#)) (SIGNATURE |inv| #4#) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |rationalIfCan| #9=((|Union| #1# #10="failed") |#1|)) (SIGNATURE |rational| #11=(#1# |#1|)) (SIGNATURE |rational?| #12=(#8# |#1|)) (SIGNATURE |abs| #13=(|#2| |#1|)) (SIGNATURE |norm| #13#) (SIGNATURE |conjugate| #4#) (SIGNATURE |map| (|#1| #14=(|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #14# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #14#)) (SIGNATURE |retractIfCan| ((|Union| |#2| #10#) |#1|)) (SIGNATURE |retract| #13#) (SIGNATURE |retract| #11#) (SIGNATURE |retractIfCan| #9#) (SIGNATURE |retract| (#2# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #2# #10#) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |characteristic| (#3#) |constant|) (SIGNATURE |coerce| (|#1| #2#)) (SIGNATURE |one?| #12#) (SIGNATURE * #15=(|#1| |#1| |#1|)) (SIGNATURE - #15#) (SIGNATURE - #4#) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE * (|#1| #3# |#1|)) (SIGNATURE |zero?| #12#) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE + #15#) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = #7#)) (|QuaternionCategory| |#2|) (|CommutativeRing|)) (T |QuaternionCategory&|)) 
((|characteristic| (*1 *2) (AND (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|QuaternionCategory&| *3 *4)) (|ofCategory| *3 (|QuaternionCategory| *4))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) . #6=($)) 143 (|has| |#1| . #7=((|RetractableTo| #4#))) ELT) (((|Union| #8=(|Fraction| #4#) . #5#) . #6#) 141 (|has| |#1| . #9=((|RetractableTo| #8#))) ELT) (((|Union| |#1| . #5#) . #6#) 138 T ELT)) (|retract| ((#4# . #10=($)) 142 (|has| |#1| . #7#) ELT) ((#8# . #10#) 140 (|has| |#1| . #9#) ELT) ((|#1| . #10#) 139 T ELT)) (|reducedSystem| (((|Matrix| #11=(|Integer|)) . #12=(#13=(|Matrix| $))) 123 (|has| |#1| . #14=((|LinearlyExplicitRingOver| #11#))) ELT) (((|Record| (|:| |mat| (|Matrix| #11#)) (|:| |vec| (|Vector| #11#))) . #15=(#13# #16=(|Vector| $))) 122 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #15#) 121 T ELT) (((|Matrix| |#1|) . #12#) 120 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|real| ((|#1| $) 111 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 107 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (((|Boolean|) $) 109 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational| (((|Fraction| (|Integer|)) $) 108 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|quatern| (($ |#1| |#1| |#1| |#1|) 112 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|norm| ((|#1| $) 113 T ELT)) (|min| (#17=($ $ $) 95 (|has| |#1| . #18=((|OrderedSet|))) ELT)) (|max| (#17# 96 (|has| |#1| . #18#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 126 T ELT)) (|leftReducedSystem| (((|Matrix| #11#) . #19=(#16#)) 125 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| #11#)) (|:| |vec| (|Vector| #11#))) . #20=(#16# $)) 124 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #20#) 119 T ELT) (((|Matrix| |#1|) . #19#) 118 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 104 (|has| |#1| . #21=((|Field|))) ELT)) (|imagK| ((|#1| $) 114 T ELT)) (|imagJ| ((|#1| $) 115 T ELT)) (|imagI| ((|#1| $) 116 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 132 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 131 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 130 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 129 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| #22=(|Symbol|)) (|List| |#1|)) 128 (|has| |#1| (|InnerEvalable| #22# |#1|)) ELT) (($ $ #22# |#1|) 127 (|has| |#1| (|InnerEvalable| #22# |#1|)) ELT)) (|elt| (($ $ |#1|) 133 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|differentiate| (($ $ (|Mapping| |#1| |#1|)) 137 T ELT) (($ $ (|Mapping| |#1| |#1|) . #23=((|NonNegativeInteger|))) 136 T ELT) (($ . #24=($)) 94 (|has| |#1| . #25=((|DifferentialSpace|))) ELT) (#26=($ $ (|NonNegativeInteger|)) 92 (|has| |#1| . #25#) ELT) (($ $ #27=(|Symbol|)) 90 (|has| |#1| . #28=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #27#)) 88 (|has| |#1| . #28#) ELT) (($ $ #27# . #29=(#30=(|NonNegativeInteger|))) 87 (|has| |#1| . #28#) ELT) (($ $ (|List| #27#) . #31=((|List| #30#))) 86 (|has| |#1| . #28#) ELT)) (|convert| (((|InputForm|) $) 105 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT)) (|conjugate| (($ $) 117 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT) (($ #8#) 82 (OR (|has| |#1| . #21#) (|has| |#1| . #9#)) ELT)) (|charthRoot| (((|Maybe| $) $) 106 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| ((|#1| $) 110 (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|Mapping| |#1| |#1|)) 135 T ELT) (($ $ (|Mapping| |#1| |#1|) . #23#) 134 T ELT) (($ . #24#) 93 (|has| |#1| . #25#) ELT) (#26# 91 (|has| |#1| . #25#) ELT) (($ $ #27#) 89 (|has| |#1| . #28#) ELT) (($ $ (|List| #27#)) 85 (|has| |#1| . #28#) ELT) (($ $ #27# . #29#) 84 (|has| |#1| . #28#) ELT) (($ $ (|List| #27#) . #31#) 83 (|has| |#1| . #28#) ELT)) (>= (#32=((|Boolean|) $ $) 97 (|has| |#1| . #18#) ELT)) (> (#32# 99 (|has| |#1| . #18#) ELT)) (= (#1# 8 T ELT)) (<= (#32# 98 (|has| |#1| . #18#) ELT)) (< (#32# 100 (|has| |#1| . #18#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #33=(|Integer|)) 103 (|has| |#1| . #21#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #34=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #34#) 53 T ELT) (($ $ #35=(|Fraction| #33#)) 102 (|has| |#1| . #21#) ELT) (($ #35# . #34#) 101 (|has| |#1| . #21#) ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) |has| |#1| (|Field|)) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) |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|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Field|))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DifferentialDomain| $) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#1|) . T) ((|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) ((|Functorial| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Field|)) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Field|)) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Field|)) ((|LinearSet| |#1|) . T) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Field|)) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #3#) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Field|)) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|Field|)) (|has| |#1| (|EntireRing|))) ((|RightModule| #1#) |has| |#1| (|Field|)) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|Field|)) (|has| |#1| (|EntireRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) 16 T ELT))) 
(((|QuaternionCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) (|QuaternionCategory| |#2|) #1=(|CommutativeRing|) (|QuaternionCategory| |#4|) #1#) (T |QuaternionCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|CommutativeRing|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|QuaternionCategory| *6)) (|isDomain| *1 (|QuaternionCategoryFunctions2| *4 *5 *2 *6)) (|ofCategory| *4 (|QuaternionCategory| *5))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|sample| (#5=($) NIL T CONST)) (|rotate!| (#6=($ $) 24 T ELT)) (|reduce| ((|#1| #7=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #7# $ |#1|) NIL T ELT) ((|#1| #7# $) NIL T ELT)) (|queue| (#8=($ #9=(|List| |#1|)) 34 T ELT)) (|members| ((#9# $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| #10=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #10#) (|length| (#11=(#12=(|NonNegativeInteger|) $) 27 T ELT)) (|latex| (((|String|) $) NIL #13=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#14=(|#1| $) 29 T ELT)) (|insert!| (($ |#1| $) 18 T ELT)) (|hash| (((|SingleInteger|) $) NIL #13# ELT)) (|front| (#14# 28 T ELT)) (|find| (((|Union| |#1| "failed") #15=(|Mapping| #3# |#1|) $) NIL T ELT)) (|extract!| (#14# 23 T ELT)) (|every?| #16=((#3# #15# $) NIL T ELT)) (|eval| (($ $ (|List| #17=(|Equation| |#1|))) NIL #18=(AND (|has| |#1| (|Evalable| |#1|)) #13#) ELT) (($ $ #17#) NIL #18# ELT) (($ $ |#1| |#1|) NIL #18# ELT) (($ $ #9# #9#) NIL #18# ELT)) (|eq?| (#2# NIL T ELT)) (|enqueue!| ((|#1| |#1| $) 17 T ELT)) (|empty?| ((#3# $) 19 T ELT)) (|empty| (#5# NIL T ELT)) (|dequeue!| (#14# 22 T ELT)) (|count| ((#12# |#1| $) NIL #4# ELT) ((#12# #15# $) NIL T ELT)) (|copy| (#6# NIL T ELT)) (|coerce| ((#19=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #19#)) ELT)) (|before?| #1#) (|bag| (#8# NIL T ELT)) (|back| (#14# 31 T ELT)) (|any?| #16#) (= #1#) (|#| (#11# NIL T ELT))) 
(((|Queue| |#1|) (|Join| (|QueueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |queue| ($ (|List| |#1|))))) (|SetCategory|)) (T |Queue|)) 
((|queue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Queue| *3))))) 
((|sqrt| (($ $) 12 T ELT)) (|nthRoot| (($ $ (|Integer|)) 13 T ELT))) 
(((|RadicalCategory&| |#1|) (CATEGORY |package| (SIGNATURE |sqrt| (|#1| |#1|)) (SIGNATURE |nthRoot| (|#1| |#1| (|Integer|)))) (|RadicalCategory|)) (T |RadicalCategory&|)) 
NIL 
((|sqrt| (($ $) 6 T ELT)) (|nthRoot| (($ $ (|Integer|)) 7 T ELT)) (** (($ $ (|Fraction| (|Integer|))) 8 T ELT))) 
(((|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|)))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|yCoordinates| (#6=((|Record| (|:| |num| #7=(|Vector| |#2|)) #8=(|:| |den| |#2|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| #10=(|Fraction| |#2|) #11=(|Field|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #9# ELT)) (|unit?| #14=(#5# NIL #9# ELT)) (|traceMatrix| #15=((#16=(|Matrix| #10#) #17=(|Vector| $)) NIL T ELT) (#18=(#16#) NIL T ELT)) (|trace| #19=((#10# $) NIL T ELT)) (|tableForDiscreteLogarithm| (((|Table| #20=(|PositiveInteger|) #21=(|NonNegativeInteger|)) #22=(|Integer|)) NIL #23=(|has| #10# (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#24=(#25=(|Union| $ #26="failed") $ $) NIL T ELT)) (|squareFreePart| #12#) (|squareFree| #27=(((|Factored| $) $) NIL #9# ELT)) (|sizeLess?| #28=(#2# NIL #9# ELT)) (|size| (#29=(#21#) NIL #30=(|has| #10# #31=(|Finite|)) ELT)) (|singularAtInfinity?| #32=(#33=(#3#) NIL T ELT)) (|singular?| (#34=(#3# |#1|) 162 T ELT) (#35=(#3# |#2|) 166 T ELT)) (|sample| #36=(#37=($) NIL T CONST)) (|retractIfCan| (((|Union| #22# . #38=(#26#)) . #39=($)) NIL #40=(|has| #10# (|RetractableTo| #22#)) ELT) (((|Union| #41=(|Fraction| #22#) . #38#) . #39#) NIL #42=(|has| #10# (|RetractableTo| #41#)) ELT) (((|Union| #10# . #38#) . #39#) NIL T ELT)) (|retract| ((#22# . #43=($)) NIL #40# ELT) ((#41# . #43#) NIL #42# ELT) #19#) (|represents| (($ #44=(|Vector| #10#) #17#) NIL T ELT) (#45=($ #44#) 79 T ELT) (#46=($ #7# |#2|) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #23# ELT)) (|rem| #47=(#48=($ $ $) NIL #9# ELT)) (|regularRepresentation| ((#16# $ #17#) NIL T ELT) ((#16# $) NIL T ELT)) (|reducedSystem| ((#49=(|Matrix| #22#) . #50=(#51=(|Matrix| $))) NIL #52=(|has| #10# (|LinearlyExplicitRingOver| #22#)) ELT) ((#53=(|Record| (|:| |mat| #49#) (|:| |vec| (|Vector| #22#))) . #54=(#51# #17#)) NIL #52# ELT) ((#55=(|Record| (|:| |mat| #16#) (|:| |vec| #44#)) . #54#) NIL T ELT) ((#16# . #50#) NIL T ELT)) (|reduceBasisAtInfinity| #56=((#17# #17#) NIL T ELT)) (|reduce| (#57=($ |#3|) 73 T ELT) ((#25# (|Fraction| |#3|)) NIL #9# ELT)) (|recip| ((#25# $) NIL T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| #31#) ELT)) (|rationalPoint?| ((#3# |#1| |#1|) NIL T ELT)) (|rank| ((#20#) NIL T ELT)) (|random| (#37# NIL #30# ELT)) (|ramifiedAtInfinity?| #32#) (|ramified?| (#34# 61 T ELT) (#35# 164 T ELT)) (|quo| #47#) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #9# ELT)) (|primitivePart| #60=(#13# NIL T ELT)) (|primitiveElement| #61=(#37# NIL #23# ELT)) (|primitive?| (#5# NIL #23# ELT)) (|primeFrobenius| (#62=($ $ #21#) NIL #23# ELT) #63=(#13# NIL #23# ELT)) (|prime?| #14#) (|order| (#64=(#20# $) NIL #23# ELT) (((|OnePointCompletion| #20#) $) NIL #23# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfComponents| #65=(#29# NIL T ELT)) (|normalizeAtInfinity| #56#) (|norm| #19#) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #66=(|Symbol|)) NIL (|has| |#1| #11#) ELT)) (|nextItem| (#67=((|Maybe| $) $) NIL #23# ELT)) (|multiEuclidean| (((|Union| #58# #26#) #58# $) NIL #9# ELT)) (|minimalPolynomial| (#68=(|#3| $) NIL #9# ELT)) (|lookup| (#64# NIL #30# ELT)) (|lift| #69=(#68# NIL T ELT)) (|leftReducedSystem| ((#49# #17#) NIL #52# ELT) ((#53# . #70=(#17# $)) NIL #52# ELT) ((#55# . #70#) NIL T ELT) #15#) (|lcm| #71=(($ #58#) NIL #9# ELT) #47#) (|latex| (((|String|) $) NIL T ELT)) (|inverseIntegralMatrixAtInfinity| (#18# 57 T ELT)) (|inverseIntegralMatrix| (#18# 56 T ELT)) (|inv| #12#) (|integralRepresents| (#46# 80 T ELT)) (|integralMatrixAtInfinity| (#18# 55 T ELT)) (|integralMatrix| (#18# 54 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) #8#) #72=(|Mapping| |#2| |#2|)) 95 T ELT)) (|integralCoordinates| (#6# 86 T ELT)) (|integralBasisAtInfinity| (#73=(#17#) 51 T ELT)) (|integralBasis| (#73# 50 T ELT)) (|integralAtInfinity?| #4#) (|integral?| #4# ((#3# $ |#1|) NIL T ELT) ((#3# $ |#2|) NIL T ELT)) (|init| (#37# NIL #23# CONST)) (|index| (($ #20#) NIL #30# ELT)) (|hyperelliptic| (#74=((|Union| |#2| #26#)) 70 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genus| #65#) (|generator| (#37# NIL T ELT)) (|gcdPolynomial| ((#75=(|SparseUnivariatePolynomial| $) #75# #75#) NIL #9# ELT)) (|gcd| #71# #47#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #22#) (|:| |exponent| #22#)))) NIL #23# ELT)) (|factor| #27#) (|extendedEuclidean| (((|Union| (|Record| #76=(|:| |coef1| $) #77=(|:| |coef2| $)) #26#) $ $ $) NIL #9# ELT) (((|Record| #76# #77# #59#) $ $) NIL #9# ELT)) (|exquo| (#24# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #9# ELT)) (|euclideanSize| (#78=(#21# $) NIL #9# ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|elliptic| (#74# 68 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|discriminant| ((#10# #17#) NIL T ELT) ((#10#) 47 T ELT)) (|discreteLog| (#78# NIL #23# ELT) (((|Union| #21# #26#) $ $) NIL #23# ELT)) (|differentiate| #79=(($ $ #80=(|Mapping| #10# #10#)) NIL #9# ELT) #81=(($ $ #80# #21#) NIL #9# ELT) (($ $ #72#) NIL T ELT) #82=(($ $ #83=(|List| #66#) (|List| #21#)) NIL #84=(OR (AND #9# (|has| #10# (|PartialDifferentialRing| #66#))) (AND #9# (|has| #10# (|PartialDifferentialSpace| #66#)))) ELT) #85=(($ $ #66# #21#) NIL #84# ELT) #86=(($ $ #83#) NIL #84# ELT) #87=(($ $ #66#) NIL #84# ELT) #88=(#62# NIL #89=(OR (AND (|has| #10# (|DifferentialRing|)) #9#) (AND (|has| #10# (|DifferentialSpace|)) #9#) #23#) ELT) #90=(#13# NIL #89# ELT)) (|derivationCoordinates| ((#16# #17# #80#) NIL #9# ELT)) (|definingPolynomial| ((|#3|) 58 T ELT)) (|createPrimitiveElement| #61#) (|coordinates| ((#44# $ #17#) NIL T ELT) ((#16# #17# #17#) NIL T ELT) (#91=(#44# $) 81 T ELT) #15#) (|convert| (#91# NIL T ELT) (#45# NIL T ELT) #69# (#57# NIL T ELT)) (|conditionP| (((|Union| #17# #26#) #51#) NIL #23# ELT)) (|complementaryBasis| #56#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #22#) NIL T ELT) (($ #10#) NIL T ELT) (($ #41#) NIL (OR #9# #42#) ELT) #12#) (|charthRoot| #63# (#67# NIL (|has| #10# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| #69#) (|characteristic| (#29# NIL T CONST)) (|branchPointAtInfinity?| (#33# 65 T ELT)) (|branchPoint?| (#34# 167 T ELT) (#35# 168 T ELT)) (|before?| #1#) (|basis| (#73# NIL T ELT)) (|associates?| #28#) (|annihilate?| #1#) (|algSplitSimple| (((|Record| (|:| |num| $) #8# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #72#) NIL T ELT)) (|absolutelyIrreducible?| #32#) (|Zero| #36#) (|One| #36#) (D #79# #81# #82# #85# #86# #87# #88# #90#) (= #1#) (/ #47#) (- #60# #92=(#48# NIL T ELT)) (+ #92#) (** (($ $ #20#) NIL T ELT) (#62# NIL T ELT) (($ $ #22#) NIL #9# ELT)) (* (($ #20# $) NIL T ELT) (($ #21# $) NIL T ELT) (($ #22# . #93=($)) NIL T ELT) #92# (($ $ #10#) NIL T ELT) (($ #10# . #93#) NIL T ELT) (($ #41# . #93#) NIL #9# ELT) (($ $ #41#) NIL #9# ELT))) 
(((|RadicalFunctionField| |#1| |#2| |#3| |#4| |#5|) (|FunctionFieldCategory| |#1| |#2| |#3|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| #1=(|Fraction| |#2|)) #1# (|NonNegativeInteger|)) (T |RadicalFunctionField|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholeRagits| (#6=(#7=(|List| #8=(|Integer|)) $) 73 T ELT)) (|wholeRadix| (($ #7#) 81 T ELT)) (|wholePart| (#9=(#8# $) 48 #10=(|has| #8# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #11=(#12=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #13=((#14=(|Union| $ #15="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #16=(((|Factored| #17=(|SparseUnivariatePolynomial| $)) #17#) NIL #18=(|has| #8# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #11#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #20=(|List| #17#) #15#) #20# #17#) NIL #18# ELT)) (|sizeLess?| #1#) (|sign| (#9# NIL #21=(|has| #8# (|OrderedIntegralDomain|)) ELT)) (|sample| (#22=($) NIL T CONST)) (|retractIfCan| (#23=((|Union| #8# . #24=(#15#)) $) 60 T ELT) (((|Union| #25=(|Symbol|) . #24#) $) NIL #26=(|has| #8# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #8#) . #24#) $) 57 #28=(|has| #8# (|RetractableTo| #8#)) ELT) (#23# 60 #28# ELT)) (|retract| (#9# NIL T ELT) ((#25# $) NIL #26# ELT) (#29=(#27# $) NIL #28# ELT) (#9# NIL #28# ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|reducedSystem| (#32=(#33=(|Matrix| #8#) #34=(|Matrix| $)) NIL #35=(|has| #8# (|LinearlyExplicitRingOver| #8#)) ELT) (#36=(#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #8#))) #34# #38=(|Vector| $)) NIL #35# ELT) (#36# NIL T ELT) (#32# NIL T ELT)) (|recip| ((#14# $) NIL T ELT)) (|random| (#22# NIL #39=(|has| #8# (|IntegerNumberSystem|)) ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #40=(|List| $)) #41=(|:| |generator| $)) #40#) NIL T ELT)) (|prime?| #4#) (|prefixRagits| (#6# 79 T ELT)) (|positive?| #42=(#5# NIL #21# ELT)) (|patternMatch| ((#43=(|PatternMatchResult| #8# . #44=($)) $ #45=(|Pattern| #8#) #43#) NIL (|has| #8# (|PatternMatchable| #8#)) ELT) ((#46=(|PatternMatchResult| #47=(|Float|) . #44#) $ #48=(|Pattern| #47#) #46#) NIL (|has| #8# (|PatternMatchable| #47#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #11#) (|numer| (#9# 45 T ELT)) (|nextItem| (#49=((|Maybe| $) $) NIL #50=(|has| #8# (|StepThrough|)) ELT)) (|negative?| #42#) (|multiEuclidean| (((|Union| #40# #15#) #40# $) NIL T ELT)) (|min| #51=(#31# NIL #52=(|has| #8# (|OrderedSet|)) ELT)) (|max| #51#) (|map| (($ #53=(|Mapping| #8# #8#) $) NIL T ELT)) (|leftReducedSystem| (#54=(#33# #38#) NIL #35# ELT) (#55=(#37# #38# $) NIL #35# ELT) (#55# NIL T ELT) (#54# NIL T ELT)) (|lcm| #30# #56=(($ #40#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #11#) (|init| (#22# NIL #50# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#17# #17# #17#) NIL T ELT)) (|gcd| #30# #56#) (|fractionPart| (#12# NIL #10# ELT) (#29# 50 T ELT)) (|fractRagits| (((|Stream| #8#) $) 78 T ELT)) (|fractRadix| (($ #7# #7#) 82 T ELT)) (|floor| (#9# 64 #39# ELT)) (|factorSquareFreePolynomial| #16#) (|factorPolynomial| #16#) (|factor| #19#) (|extendedEuclidean| (((|Record| #57=(|:| |coef1| $) #58=(|:| |coef2| $) #41#) $ $) NIL T ELT) (((|Union| (|Record| #57# #58#) #15#) $ $ $) NIL T ELT)) (|exquo| #13#) (|expressIdealMember| (((|Maybe| #40#) #40# $) NIL T ELT)) (|eval| (($ $ #7# #7#) NIL #59=(|has| #8# (|Evalable| #8#)) ELT) (($ $ #8# #8#) NIL #59# ELT) (($ $ #60=(|Equation| #8#)) NIL #59# ELT) (($ $ (|List| #60#)) NIL #59# ELT) (($ $ #61=(|List| #25#) #7#) NIL #62=(|has| #8# (|InnerEvalable| #25# #8#)) ELT) (($ $ #25# #8#) NIL #62# ELT)) (|euclideanSize| ((#63=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#64=($ $ #8#) NIL (|has| #8# (|Eltable| #8# #8#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #65=(($ $ #53#) NIL T ELT) #66=(($ $ #53# #63#) NIL T ELT) #67=(($ $ #25#) NIL #68=(|has| #8# (|PartialDifferentialSpace| #25#)) ELT) #69=(($ $ #61#) NIL #68# ELT) #70=(($ $ #25# #63#) NIL #68# ELT) #71=(($ $ #61# (|List| #63#)) NIL #68# ELT) (#12# 15 #72=(|has| #8# (|DifferentialSpace|)) ELT) #73=(#74=($ $ #63#) NIL #72# ELT)) (|denominator| #11#) (|denom| (#9# 47 T ELT)) (|cycleRagits| (#6# 80 T ELT)) (|convert| ((#45# . #75=($)) NIL (|has| #8# (|ConvertibleTo| #45#)) ELT) ((#48# . #75#) NIL (|has| #8# (|ConvertibleTo| #48#)) ELT) ((#76=(|InputForm|) . #75#) NIL (|has| #8# (|ConvertibleTo| #76#)) ELT) ((#47# . #75#) NIL #77=(|has| #8# (|RealConstant|)) ELT) (((|DoubleFloat|) . #75#) NIL #77# ELT)) (|conditionP| (((|Union| #38# #15#) #34#) NIL #78=(AND (|has| $ #79=(|CharacteristicNonZero|)) #18#) ELT)) (|coerce| (((|OutputForm|) $) 108 T ELT) #80=(($ #8#) 51 T ELT) #11# (($ #27#) 27 T ELT) #80# (($ #25#) NIL #26# ELT) (#29# 25 T ELT)) (|charthRoot| (#49# NIL (OR #78# (|has| #8# #79#)) ELT)) (|characteristic| ((#63#) 13 T CONST)) (|ceiling| (#9# 62 #39# ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#12# NIL #21# ELT)) (|Zero| (#22# 14 T CONST)) (|One| (#22# 17 T CONST)) (D #65# #66# #67# #69# #70# #71# (#12# NIL #72# ELT) #73#) (>= #81=(#2# NIL #52# ELT)) (> #81#) (= (#2# 21 T ELT)) (<= #81#) (< (#2# 40 #52# ELT)) (/ (#31# 36 T ELT) (($ #8# #8#) 38 T ELT)) (- (#12# 23 T ELT) (#31# 30 T ELT)) (+ (#31# 28 T ELT)) (** (($ $ #82=(|PositiveInteger|)) NIL T ELT) (#74# NIL T ELT) #83=(#64# NIL T ELT)) (* (($ #82# $) NIL T ELT) (($ #63# $) NIL T ELT) #84=(($ #8# $) 32 T ELT) (#31# 34 T ELT) (($ $ #27#) NIL T ELT) (($ #27# $) NIL T ELT) #84# #83#)) 
(((|RadixExpansion| |#1|) (|Join| (|QuotientFieldCategory| #1=(|Integer|)) (|CoercibleTo| #2=(|Fraction| #1#)) (CATEGORY |domain| (SIGNATURE |fractionPart| (#2# $)) (SIGNATURE |wholeRagits| #3=(#4=(|List| #1#) $)) (SIGNATURE |fractRagits| ((|Stream| #1#) $)) (SIGNATURE |prefixRagits| #3#) (SIGNATURE |cycleRagits| #3#) (SIGNATURE |wholeRadix| ($ #4#)) (SIGNATURE |fractRadix| ($ #4# #4#)))) #1#) (T |RadixExpansion|)) 
((|fractionPart| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Fraction| #2=(|Integer|))) #3=(|isDomain| *1 (|RadixExpansion| *3)) #4=(|ofType| *3 #2#))) (|wholeRagits| #1# #5=(AND (|isDomain| *2 (|List| #2#)) #3# #4#)) (|fractRagits| #1# (AND (|isDomain| *2 (|Stream| #2#)) #3# #4#)) (|prefixRagits| #1# #5#) (|cycleRagits| #1# #5#) (|wholeRadix| (*1 *1 *2) #5#) (|fractRadix| (*1 *1 *2 *2) #5#)) 
((|radix| (((|Any|) (|Fraction| #1=(|Integer|)) #1#) 9 T ELT))) 
(((|RadixUtilities|) (CATEGORY |package| (SIGNATURE |radix| ((|Any|) (|Fraction| #1=(|Integer|)) #1#)))) (T |RadixUtilities|)) 
((|radix| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| #1=(|Integer|))) (|isDomain| *4 #1#) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|RadixUtilities|))))) 
((|size| (#1=(#2=(|Integer|)) 21 T ELT)) (|seed| (#1# 26 T ELT)) (|reseed| (((|Void|) #2#) 24 T ELT)) (|randnum| ((#2# #2#) 27 T ELT) (#1# 20 T ELT))) 
(((|RandomNumberSource|) (CATEGORY |package| (SIGNATURE |randnum| #1=(#2=(|Integer|))) (SIGNATURE |size| #1#) (SIGNATURE |randnum| (#2# #2#)) (SIGNATURE |reseed| ((|Void|) #2#)) (SIGNATURE |seed| #1#))) (T |RandomNumberSource|)) 
((|seed| #1=(*1 *2) #2=(AND (|isDomain| *2 #3=(|Integer|)) #4=(|isDomain| *1 (|RandomNumberSource|)))) (|reseed| (*1 *2 *3) (AND (|isDomain| *3 #3#) (|isDomain| *2 (|Void|)) #4#)) (|randnum| (*1 *2 *2) #2#) (|size| #1# #2#) (|randnum| #1# #2#)) 
((|factorSquareFree| (#1=((|Factored| |#1|) |#1|) 43 T ELT)) (|factor| (#1# 41 T ELT))) 
(((|RationalFactorize| |#1|) (CATEGORY |package| (SIGNATURE |factor| #1=((|Factored| |#1|) |#1|)) (SIGNATURE |factorSquareFree| #1#)) (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (T |RationalFactorize|)) 
((|factorSquareFree| #1=(*1 *2 *3) #2=(AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|RationalFactorize| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))))) (|factor| #1# #2#)) 
((|rationalIfCan| (((|Union| #1=(|Fraction| (|Integer|)) "failed") |#1|) 15 T ELT)) (|rational?| (((|Boolean|) |#1|) 14 T ELT)) (|rational| ((#1# |#1|) 10 T ELT))) 
(((|RationalRetractions| |#1|) (CATEGORY |package| (SIGNATURE |rational| (#1=(|Fraction| (|Integer|)) |#1|)) (SIGNATURE |rational?| ((|Boolean|) |#1|)) (SIGNATURE |rationalIfCan| ((|Union| #1# "failed") |#1|))) (|RetractableTo| #1#)) (T |RationalRetractions|)) 
((|rationalIfCan| #1=(*1 *2 *3) (|partial| AND #2=(|isDomain| *2 #3=(|Fraction| (|Integer|))) #4=(|isDomain| *1 (|RationalRetractions| *3)) #5=(|ofCategory| *3 (|RetractableTo| *2)))) (|rational?| #1# (AND (|isDomain| *2 (|Boolean|)) #4# (|ofCategory| *3 (|RetractableTo| #3#)))) (|rational| #1# (AND #2# #4# #5#))) 
((|setelt| ((|#2| $ #1="value" |#2|) 12 T ELT)) (|elt| ((|#2| $ #1#) 10 T ELT)) (|child?| (((|Boolean|) $ $) 18 T ELT))) 
(((|RecursiveAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |setelt| (|#2| |#1| #1="value" |#2|)) (SIGNATURE |child?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| #1#))) (|RecursiveAggregate| |#2|) (|Type|)) (T |RecursiveAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ "value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ (|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sample| (#3=($) 6 T CONST)) (|nodes| (((|List| $) $) 45 T ELT)) (|node?| (((|Boolean|) $ $) 37 (|has| |#1| (|BasicType|)) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #4=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #4#) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT)) (|eq?| ((#5=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#5# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|elt| ((|#1| $ "value") 42 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (((|Boolean|) $) 41 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (((|List| $) $) 46 T ELT)) (|child?| (((|Boolean|) $ $) 38 (|has| |#1| (|BasicType|)) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|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 (|BasicType|)) (|isDomain| *2 (|Boolean|)))) (|node?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|BasicType|)) (|isDomain| *2 (|Boolean|)))) (|setchildren!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|ofCategory| *1 (|RecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 "value") (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|RecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setvalue!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|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| (|BasicType|)) (PROGN (SIGNATURE |child?| ((|Boolean|) $ $)) (SIGNATURE |node?| ((|Boolean|) $ $))) |%noBranch|) (IF (|has| $ (|ShallowlyMutableAggregate| |t#1|)) (PROGN (SIGNATURE |setchildren!| ($ $ (|List| $))) (SIGNATURE |setelt| (|t#1| $ "value" |t#1|)) (SIGNATURE |setvalue!| (|t#1| $ |t#1|))) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((|sqrt| (($ $) 9 T ELT) (#1=($ $ #2=(|PositiveInteger|)) 49 T ELT) (($ #3=(|Fraction| #4=(|Integer|))) 13 T ELT) (($ #4#) 15 T ELT)) (|rootOf| ((#5=(|Union| $ "failed") #6=(|SparseUnivariatePolynomial| $) #2# (|OutputForm|)) 24 T ELT) ((#5# #6# #2#) 32 T ELT)) (|nthRoot| (#7=($ $ #4#) 58 T ELT)) (|characteristic| ((#8=(|NonNegativeInteger|)) 18 T CONST)) (|allRootsOf| ((#9=(|List| $) #6#) NIL T ELT) ((#9# (|SparseUnivariatePolynomial| #3#)) 63 T ELT) ((#9# (|SparseUnivariatePolynomial| #4#)) 68 T ELT) ((#9# (|Polynomial| $)) 72 T ELT) ((#9# (|Polynomial| #3#)) 76 T ELT) ((#9# (|Polynomial| #4#)) 80 T ELT)) (** (#1# NIL T ELT) (($ $ #8#) NIL T ELT) (#7# NIL T ELT) (($ $ #3#) 53 T ELT))) 
(((|RealClosedField&| |#1|) (CATEGORY |package| (SIGNATURE |sqrt| (|#1| #1=(|Integer|))) (SIGNATURE |sqrt| (|#1| #2=(|Fraction| #1#))) (SIGNATURE |sqrt| #3=(|#1| |#1| #4=(|PositiveInteger|))) (SIGNATURE |allRootsOf| (#5=(|List| |#1|) (|Polynomial| #1#))) (SIGNATURE |allRootsOf| (#5# (|Polynomial| #2#))) (SIGNATURE |allRootsOf| (#5# (|Polynomial| |#1|))) (SIGNATURE |allRootsOf| (#5# (|SparseUnivariatePolynomial| #1#))) (SIGNATURE |allRootsOf| (#5# (|SparseUnivariatePolynomial| #2#))) (SIGNATURE |allRootsOf| (#5# #6=(|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |rootOf| (#7=(|Union| |#1| "failed") #6# #4#)) (SIGNATURE |rootOf| (#7# #6# #4# (|OutputForm|))) (SIGNATURE ** (|#1| |#1| #2#)) (SIGNATURE |nthRoot| #8=(|#1| |#1| #1#)) (SIGNATURE |sqrt| (|#1| |#1|)) (SIGNATURE ** #8#) (SIGNATURE |characteristic| (#9=(|NonNegativeInteger|)) |constant|) (SIGNATURE ** (|#1| |#1| #9#)) (SIGNATURE ** #3#)) (|RealClosedField|)) (T |RealClosedField&|)) 
((|characteristic| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RealClosedField&| *3)) (|ofCategory| *3 (|RealClosedField|))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 111 T ELT)) (|unitCanonical| (($ $) 112 T ELT)) (|unit?| ((#3=(|Boolean|) $) 114 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 131 T ELT)) (|squareFree| (#4=((|Factored| $) $) 132 T ELT)) (|sqrt| (($ $) 95 T ELT) (($ $ (|PositiveInteger|)) 81 T ELT) (($ (|Fraction| (|Integer|))) 80 T ELT) (($ (|Integer|)) 79 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 122 T ELT)) (|sign| (((|Integer|) $) 148 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) 89 T ELT) (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) 88 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 108 (|has| #9=(|Fraction| (|Integer|)) . #10=((|RetractableTo| #11=(|Integer|)))) ELT) (((|Union| #12=(|Fraction| #6#) . #7#) . #8#) 106 (|has| #9# . #13=((|RetractableTo| (|Fraction| #11#)))) ELT) (((|Union| #9# . #7#) . #8#) 103 T ELT)) (|retract| ((#6# . #14=($)) 107 (|has| #9# . #10#) ELT) ((#12# . #14#) 105 (|has| #9# . #13#) ELT) ((#9# . #14#) 104 T ELT)) (|rename!| (($ $ (|OutputForm|)) 78 T ELT)) (|rename| (($ $ (|OutputForm|)) 77 T ELT)) (|rem| (#15=($ $ $) 126 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#15# 125 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #16=(|List| $)) (|:| |generator| $)) #16#) 120 T ELT)) (|prime?| (((|Boolean|) $) 133 T ELT)) (|positive?| (((|Boolean|) $) 146 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #17=(|Integer|)) 94 T ELT)) (|negative?| (((|Boolean|) $) 147 T ELT)) (|multiEuclidean| (((|Union| #18=(|List| $) #19="failed") #18# $) 129 T ELT)) (|min| (#20=($ $ $) 140 T ELT)) (|max| (#20# 141 T ELT)) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) 90 T ELT)) (|mainForm| (((|Union| (|OutputForm|) "failed") $) 92 T ELT)) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) 91 T ELT)) (|lcm| (#21=($ (|List| $)) 118 T ELT) (#22=($ $ $) 117 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 134 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#23=(|SparseUnivariatePolynomial| $) #23# #23#) 119 T ELT)) (|gcd| (#21# 116 T ELT) (#22# 115 T ELT)) (|factor| (#4# 130 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #24=(|:| |coef1| $) #25=(|:| |coef2| $)) #19#) $ $ $) 128 T ELT) (((|Record| #24# #25# (|:| |generator| $)) $ $) 127 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 110 T ELT)) (|expressIdealMember| (((|Maybe| #16#) #16# $) 121 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 123 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 124 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #26=(|Fraction| #27=(|Integer|))) 138 T ELT) (($ $) 109 T ELT) (($ #9#) 102 T ELT) (($ #28=(|Integer|)) 101 T ELT) (($ #29=(|Fraction| (|Integer|))) 98 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 113 T ELT)) (|approximate| (((|Fraction| (|Integer|)) $ $) 76 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|allRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $)) 87 T ELT) (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) 86 T ELT) (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) 85 T ELT) (((|List| $) (|Polynomial| $)) 84 T ELT) (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) 83 T ELT) (((|List| $) (|Polynomial| (|Integer|))) 82 T ELT)) (|abs| (($ $) 149 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#30=((|Boolean|) $ $) 142 T ELT)) (> (#30# 144 T ELT)) (= (#1# 8 T ELT)) (<= (#30# 143 T ELT)) (< (#30# 145 T ELT)) (/ (($ $ $) 139 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #27#) 135 T ELT) (($ $ (|Fraction| #17#)) 93 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #31=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ #26# . #31#) 137 T ELT) (($ $ #26#) 136 T ELT) (($ #28# . #31#) 100 T ELT) (($ $ #28#) 99 T ELT) (($ #29# . #31#) 97 T ELT) (($ $ #29#) 96 T ELT))) 
(((|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 (|PositiveInteger|)))) (|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| $) (|Polynomial| (|Integer|)))) (SIGNATURE |sqrt| ($ $ (|PositiveInteger|))) (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| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| #2=(|Integer|)) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| #2# #2#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FullyRetractableTo| (|Fraction| (|Integer|))) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| #2#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| #2#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| #2#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) . T) ((|RetractableTo| (|Integer|)) |has| (|Fraction| (|Integer|)) (|RetractableTo| (|Integer|))) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| #2#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| #2#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #1=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2="failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) #1#) #2#) |#2| |#2|)) 67 T ELT))) 
(((|ElementaryRischDE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rischDE| ((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) #1=(|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #2=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) #2#) #3#) |#2| |#2|)))) (|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| #1#) (|LinearlyExplicitRingOver| #1#)) (|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| #1=(|:| |coeff| *4) (|:| |logand| *4))))) #2="failed") *4 (|List| *4))) (|isDomain| *7 (|Mapping| (|Union| (|Record| (|:| |ratpart| *4) #1#) #2#) *4 *4)) (|ofCategory| *4 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedField|) (|FunctionSpace| *8))) (|ofCategory| *8 (|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| *3) (|LinearlyExplicitRingOver| *3))) (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Record| (|:| |ans| *4) (|:| |right| *4) (|:| |sol?| (|Boolean|)))) (|isDomain| *1 (|ElementaryRischDE| *8 *4))))) 
((|rischDEsys| (((|Union| #1=(|List| |#2|) #2="failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #3=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2#) |#2| #1#) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) #3#) #2#) |#2| |#2|)) 55 T ELT))) 
(((|ElementaryRischDESystem| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rischDEsys| ((|Union| #1=(|List| |#2|) #2="failed") #3=(|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #4=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2#) |#2| #1#) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) #4#) #2#) |#2| |#2|)))) (|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| #3#) (|LinearlyExplicitRingOver| #3#)) (|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| #1=(|:| |coeff| *4) (|:| |logand| *4))))) #2="failed") *4 #3=(|List| *4))) (|isDomain| *7 (|Mapping| (|Union| (|Record| (|:| |ratpart| *4) #1#) #2#) *4 *4)) (|ofCategory| *4 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedField|) (|FunctionSpace| *8))) (|ofCategory| *8 (|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| *3) (|LinearlyExplicitRingOver| *3))) (|isDomain| *3 (|Integer|)) (|isDomain| *2 #3#) (|isDomain| *1 (|ElementaryRischDESystem| *8 *4))))) 
((|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) #1=(|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| #2=(|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| #2# #3=(|Mapping| |#2| |#2|)) 39 T ELT)) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| #4=(|Fraction| |#2|)) (|:| |c| #4#) (|:| |t| |#2|)) "failed") #4# #4# #3#) 71 T ELT)) (|baseRDE| (((|Record| (|:| |ans| #4#) #1#) #4# #4#) 76 T ELT))) 
(((|TranscendentalRischDE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monomRDE| ((|Union| (|Record| (|:| |a| |#2|) (|:| |b| #1=(|Fraction| |#2|)) (|:| |c| #1#) (|:| |t| |#2|)) "failed") #1# #1# #2=(|Mapping| |#2| |#2|))) (SIGNATURE |baseRDE| ((|Record| (|:| |ans| #1#) #3=(|:| |nosol| (|Boolean|))) #1# #1#)) (SIGNATURE |polyRDE| ((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) #3#)) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| #4=(|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| #4# #2#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #4#)) (|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| #1=(|Field|) #2=(|CharacteristicZero|) (|RetractableTo| *4))) (|isDomain| *4 #3=(|Integer|)) (|isDomain| *2 (|Union| (|:| |ans| (|Record| (|:| |ans| *3) #4=(|:| |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 #5=(|Join| #1# #2# (|RetractableTo| #3#))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |ans| #6=(|Fraction| *5)) #4#)) (|isDomain| *1 (|TranscendentalRischDE| *4 *5)) (|isDomain| *3 #6#))) (|monomRDE| (*1 *2 *3 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #5#) (|isDomain| *2 (|Record| (|:| |a| *6) (|:| |b| #7=(|Fraction| *6)) (|:| |c| #7#) (|:| |t| *6))) (|isDomain| *1 (|TranscendentalRischDE| *5 *6)) (|isDomain| *3 #7#)))) 
((|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| #1=(|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| #1#) (|:| |c2| #1#) (|:| |t| |#2|)) #2="failed") #1# #1# #1# (|Mapping| |#2| |#2|)) 22 T ELT)) (|baseRDEsys| (((|Union| (|List| #1#) #2#) #1# #1# #1#) 34 T ELT))) 
(((|TranscendentalRischDESystem| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monomRDEsys| ((|Union| (|Record| (|:| |a| |#2|) (|:| |b| #1=(|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| #1#) (|:| |c2| #1#) (|:| |t| |#2|)) #2="failed") #1# #1# #1# (|Mapping| |#2| |#2|))) (SIGNATURE |baseRDEsys| ((|Union| (|List| #1#) #2#) #1# #1# #1#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|))) (|UnivariatePolynomialCategory| |#1|)) (T |TranscendentalRischDESystem|)) 
((|baseRDEsys| (*1 *2 *3 *3 *3) (|partial| AND (|ofCategory| *4 #1=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| #2=(|Fraction| *5))) (|isDomain| *1 (|TranscendentalRischDESystem| *4 *5)) (|isDomain| *3 #2#))) (|monomRDEsys| (*1 *2 *3 *3 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #1#) (|isDomain| *2 (|Record| (|:| |a| *6) (|:| |b| #3=(|Fraction| *6)) (|:| |h| *6) (|:| |c1| #3#) (|:| |c2| #3#) (|:| |t| *6))) (|isDomain| *1 (|TranscendentalRischDESystem| *5 *6)) (|isDomain| *3 #3#)))) 
((|weighted| ((#1=(|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| #2=(|Integer|))))) 34 T ELT)) (|uniform| ((#1# (|Set| |#1|)) 42 T ELT)) (|rdHack1| ((#1# (|Vector| |#1|) (|Vector| #2#) #2#) 31 T ELT))) 
(((|RandomDistributions| |#1|) (CATEGORY |package| (SIGNATURE |uniform| (#1=(|Mapping| |#1|) (|Set| |#1|))) (SIGNATURE |weighted| (#1# (|List| (|Record| (|:| |value| |#1|) (|:| |weight| #2=(|Integer|)))))) (SIGNATURE |rdHack1| (#1# (|Vector| |#1|) (|Vector| #2#) #2#))) (|SetCategory|)) (T |RandomDistributions|)) 
((|rdHack1| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Vector| *6)) (|isDomain| *4 (|Vector| #1=(|Integer|))) (|isDomain| *5 #1#) (|ofCategory| *6 #2=(|SetCategory|)) (|isDomain| *2 (|Mapping| *6)) (|isDomain| *1 (|RandomDistributions| *6)))) (|weighted| #3=(*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |value| *4) (|:| |weight| #1#)))) #4=(|ofCategory| *4 #2#) #5=(|isDomain| *2 (|Mapping| *4)) #6=(|isDomain| *1 (|RandomDistributions| *4)))) (|uniform| #3# (AND (|isDomain| *3 (|Set| *4)) #4# #5# #6#))) 
((|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) 23 T ELT))) 
(((|ReducedDivisor| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |order| ((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)))) #1=(|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) (|Join| (|Finite|) #1#)) (T |ReducedDivisor|)) 
((|order| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|FiniteDivisor| *6 *7 *4 *8)) (|isDomain| *5 (|Mapping| *9 *6)) (|ofCategory| *6 #1=(|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *7))) (|ofCategory| *8 (|FunctionFieldCategory| *6 *7 *4)) (|ofCategory| *9 (|Join| (|Finite|) #1#)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ReducedDivisor| *6 *7 *4 *8 *9))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|operator| (#2=((|SpadAst|) $) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #3=($)) NIL T ELT) (($ #4=(|Syntax|)) NIL T ELT) ((#4# . #3#) NIL T ELT)) (|body| (#2# 12 T ELT)) (|before?| #1#) (= #1#)) 
(((|ReduceAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |operator| #1=((|SpadAst|) $)) (SIGNATURE |body| #1#)))) (T |ReduceAst|)) 
((|operator| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|ReduceAst|)))) (|body| #1# #2#)) 
((|convert| (((|DoubleFloat|) . #1=($)) 6 T ELT) (((|Float|) . #1#) 9 T ELT))) 
(((|RealConstant|) (|Category|)) (T |RealConstant|)) 
NIL 
(|Join| (|ConvertibleTo| (|DoubleFloat|)) (|ConvertibleTo| (|Float|))) 
(((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T)) 
((|refine| (((|Union| #1=(|Record| (|:| |left| #2=(|Fraction| (|Integer|))) (|:| |right| #2#)) "failed") |#1| #1# #1#) 32 T ELT) ((#1# |#1| #1# #2#) 29 T ELT)) (|realZeros| ((#3=(|List| #1#) |#1| #1# #2#) 34 T ELT) ((#3# |#1| #2#) 30 T ELT) ((#3# |#1| #1#) 33 T ELT) ((#3# |#1|) 28 T ELT)) (|midpoints| (((|List| #2#) #3#) 20 T ELT)) (|midpoint| ((#2# #1#) 17 T ELT))) 
(((|RealZeroPackage| |#1|) (CATEGORY |package| (SIGNATURE |realZeros| (#1=(|List| #2=(|Record| (|:| |left| #3=(|Fraction| #4=(|Integer|))) (|:| |right| #3#))) |#1|)) (SIGNATURE |realZeros| (#1# |#1| #2#)) (SIGNATURE |realZeros| (#1# |#1| #3#)) (SIGNATURE |realZeros| (#1# |#1| #2# #3#)) (SIGNATURE |refine| (#2# |#1| #2# #3#)) (SIGNATURE |refine| ((|Union| #2# "failed") |#1| #2# #2#)) (SIGNATURE |midpoint| (#3# #2#)) (SIGNATURE |midpoints| ((|List| #3#) #1#))) (|UnivariatePolynomialCategory| #4#)) (T |RealZeroPackage|)) 
((|midpoints| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|List| #3=(|Record| (|:| |left| #4=(|Fraction| #5=(|Integer|))) (|:| |right| #4#)))) (|isDomain| *2 (|List| #4#)) #6=(|isDomain| *1 (|RealZeroPackage| *4)) #7=(|ofCategory| *4 #8=(|UnivariatePolynomialCategory| #5#)))) (|midpoint| #1# (AND (|isDomain| *3 #3#) (|isDomain| *2 #4#) #6# #7#)) (|refine| (*1 *2 *3 *2 *2) (|partial| AND #9=(|isDomain| *2 #3#) #10=(|isDomain| *1 (|RealZeroPackage| *3)) #11=(|ofCategory| *3 #8#))) (|refine| (*1 *2 *3 *2 *4) (AND #9# #12=(|isDomain| *4 #4#) #10# #11#)) (|realZeros| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 #4#) (|isDomain| *2 (|List| #13=(|Record| (|:| |left| *5) (|:| |right| *5)))) #10# #11# (|isDomain| *4 #13#))) (|realZeros| #14=(*1 *2 *3 *4) (AND #15=(|isDomain| *2 #2#) #10# #11# #12#)) (|realZeros| #14# (AND #15# #10# #11# (|isDomain| *4 #3#))) (|realZeros| #1# (AND #15# #10# #11#))) 
((|refine| (((|Union| #1=(|Record| (|:| |left| #2=(|Fraction| (|Integer|))) (|:| |right| #2#)) "failed") |#1| #1# #1#) 35 T ELT) ((#1# |#1| #1# #2#) 32 T ELT)) (|realZeros| ((#3=(|List| #1#) |#1| #1# #2#) 30 T ELT) ((#3# |#1| #2#) 26 T ELT) ((#3# |#1| #1#) 28 T ELT) ((#3# |#1|) 24 T ELT))) 
(((|RealZeroPackageQ| |#1|) (CATEGORY |package| (SIGNATURE |realZeros| (#1=(|List| #2=(|Record| (|:| |left| #3=(|Fraction| (|Integer|))) (|:| |right| #3#))) |#1|)) (SIGNATURE |realZeros| (#1# |#1| #2#)) (SIGNATURE |realZeros| (#1# |#1| #3#)) (SIGNATURE |realZeros| (#1# |#1| #2# #3#)) (SIGNATURE |refine| (#2# |#1| #2# #3#)) (SIGNATURE |refine| ((|Union| #2# "failed") |#1| #2# #2#))) (|UnivariatePolynomialCategory| #3#)) (T |RealZeroPackageQ|)) 
((|refine| (*1 *2 *3 *2 *2) (|partial| AND #1=(|isDomain| *2 #2=(|Record| (|:| |left| #3=(|Fraction| (|Integer|))) (|:| |right| #3#))) #4=(|isDomain| *1 (|RealZeroPackageQ| *3)) #5=(|ofCategory| *3 (|UnivariatePolynomialCategory| #3#)))) (|refine| (*1 *2 *3 *2 *4) (AND #1# #6=(|isDomain| *4 #3#) #4# #7=(|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|realZeros| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 #3#) (|isDomain| *2 (|List| #8=(|Record| (|:| |left| *5) (|:| |right| *5)))) #4# (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|isDomain| *4 #8#))) (|realZeros| #9=(*1 *2 *3 *4) (AND #6# (|isDomain| *2 (|List| (|Record| (|:| |left| *4) (|:| |right| *4)))) #4# #7#)) (|realZeros| #9# (AND #10=(|isDomain| *2 (|List| #2#)) #4# #5# (|isDomain| *4 #2#))) (|realZeros| (*1 *2 *3) (AND #10# #4# #5#))) 
((|solve| ((#1=(|List| #2=(|Float|)) #3=(|Polynomial| #4=(|Integer|)) #2#) 28 T ELT) ((#1# (|Polynomial| (|Fraction| #4#)) #2#) 27 T ELT)) (|realSolve| (((|List| #1#) (|List| #3#) (|List| (|Symbol|)) #2#) 37 T ELT))) 
(((|RealSolvePackage|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|List| #2=(|Float|)) (|Polynomial| (|Fraction| #3=(|Integer|))) #2#)) (SIGNATURE |solve| (#1# #4=(|Polynomial| #3#) #2#)) (SIGNATURE |realSolve| ((|List| #1#) (|List| #4#) (|List| (|Symbol|)) #2#)))) (T |RealSolvePackage|)) 
((|realSolve| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| #1=(|Polynomial| #2=(|Integer|)))) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| #3=(|List| #4=(|Float|)))) #5=(|isDomain| *1 (|RealSolvePackage|)) (|isDomain| *5 #4#))) (|solve| #6=(*1 *2 *3 *4) (AND (|isDomain| *3 #1#) #7=(|isDomain| *2 #3#) #5# #8=(|isDomain| *4 #4#))) (|solve| #6# (AND (|isDomain| *3 (|Polynomial| (|Fraction| #2#))) #7# #5# #8#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 75 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #7=(#4# NIL T ELT)) (|subtractIfCan| #8=((#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #11=(((|Factored| $) $) NIL T ELT)) (|sqrt| #5# #12=(($ $ #13=(|PositiveInteger|)) NIL T ELT) #14=(($ #15=(|Fraction| #16=(|Integer|))) NIL T ELT) #17=(($ #16#) NIL T ELT)) (|sizeLess?| #1#) (|sign| (#18=(#16# $) 70 T ELT)) (|sample| (#19=($) NIL T CONST)) (|rootOf| ((#9# #20=(|SparseUnivariatePolynomial| $) #13# #21=(|OutputForm|)) NIL T ELT) ((#9# #20# #13#) 55 T ELT)) (|retractIfCan| (#22=((|Union| #15# . #23=(#10#)) . #24=($)) NIL #25=(|has| #15# (|RetractableTo| #15#)) ELT) (#22# NIL T ELT) (((|Union| |#1| . #23#) $) 115 T ELT) (((|Union| #16# . #23#) . #24#) NIL #26=(OR (|has| #15# #27=(|RetractableTo| #16#)) (|has| |#1| #27#)) ELT)) (|retract| (#28=(#15# $) 17 #25# ELT) (#28# 17 T ELT) ((|#1| $) 116 T ELT) (#18# NIL #26# ELT)) (|rename!| (#29=($ $ #21#) 47 T ELT)) (|rename| (#29# 48 T ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|relativeApprox| (#32=(#15# $ $) 21 T ELT)) (|recip| ((#9# $) 88 T ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #33=(|List| $)) #34=(|:| |generator| $)) #33#) NIL T ELT)) (|prime?| #7#) (|positive?| (#4# 66 T ELT)) (|opposite?| #1#) (|one?| #7#) (|nthRoot| #35=(($ $ #16#) NIL T ELT)) (|negative?| (#4# 69 T ELT)) (|multiEuclidean| (((|Union| #33# #10#) #33# $) NIL T ELT)) (|min| #30#) (|max| #30#) (|mainValue| (#36=((|Union| #20# #10#) $) 83 T ELT)) (|mainForm| (((|Union| #21# #10#) $) 82 T ELT)) (|mainDefiningPolynomial| (#36# 80 T ELT)) (|mainCharacterization| (((|Union| #37=(|RightOpenIntervalRootCharacterization| $ #20#) #10#) $) 78 T ELT)) (|lcm| #38=(($ #33#) NIL T ELT) #30#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#6# 89 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#20# #20# #20#) NIL T ELT)) (|gcd| #38# #30#) (|factor| #11#) (|extendedEuclidean| (((|Union| (|Record| #39=(|:| |coef1| $) #40=(|:| |coef2| $)) #10#) $ $ $) NIL T ELT) (((|Record| #39# #40# #34#) $ $) NIL T ELT)) (|exquo| #8#) (|expressIdealMember| (((|Maybe| #33#) #33# $) NIL T ELT)) (|euclideanSize| ((#41=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|coerce| ((#21# $) 87 T ELT) #17# #14# (#6# 63 T ELT) #14# #17# #14# (($ |#1|) 118 T ELT)) (|characteristic| ((#41#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| (#32# 27 T ELT)) (|annihilate?| #1#) (|allRootsOf| ((#33# #20#) 61 T ELT) ((#33# (|SparseUnivariatePolynomial| #15#)) NIL T ELT) ((#33# (|SparseUnivariatePolynomial| #16#)) NIL T ELT) ((#33# (|Polynomial| $)) NIL T ELT) ((#33# (|Polynomial| #15#)) NIL T ELT) ((#33# (|Polynomial| #16#)) NIL T ELT)) (|algebraicOf| (($ #37# #21#) 46 T ELT)) (|abs| (#6# 22 T ELT)) (|Zero| (#19# 32 T CONST)) (|One| (#19# 39 T CONST)) (>= #1#) (> #1#) (= (#2# 76 T ELT)) (<= #1#) (< (#2# 24 T ELT)) (/ (#31# 37 T ELT)) (- (#6# 38 T ELT) (#31# 74 T ELT)) (+ (#31# 111 T ELT)) (** #12# (($ $ #41#) NIL T ELT) #35# #42=(($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #41# $) NIL T ELT) #43=(($ #16# $) 71 T ELT) (#31# 103 T ELT) #44=(($ #15# $) NIL T ELT) #42# #43# #35# #44# #42# (($ |#1| $) 101 T ELT) (($ $ |#1|) NIL T ELT))) 
(((|RealClosure| |#1|) (|Join| (|RealClosedField|) (|FullyRetractableTo| |#1|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |algebraicOf| ($ #1=(|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|))) (SIGNATURE |mainCharacterization| ((|Union| #1# "failed") $)) (SIGNATURE |relativeApprox| ((|Fraction| (|Integer|)) $ $)))) (|Join| (|OrderedRing|) (|Field|) (|RealConstant|))) (T |RealClosure|)) 
((|algebraicOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|RightOpenIntervalRootCharacterization| #1=(|RealClosure| *4) (|SparseUnivariatePolynomial| #1#))) (|isDomain| *3 (|OutputForm|)) (|isDomain| *1 #1#) (|ofCategory| *4 #2=(|Join| (|OrderedRing|) (|Field|) (|RealConstant|))))) (|mainCharacterization| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|RightOpenIntervalRootCharacterization| #3=(|RealClosure| *3) (|SparseUnivariatePolynomial| #3#))) #4=(|isDomain| *1 #3#) #5=(|ofCategory| *3 #2#))) (|relativeApprox| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) #4# #5#))) 
((|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| #1=(|List| |#1|))) |#2| #1#) 32 T ELT) ((|#2| |#2| |#1|) 27 T ELT))) 
(((|ReductionOfOrder| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ReduceOrder| (|#2| |#2| |#1|)) (SIGNATURE |ReduceOrder| ((|Record| (|:| |eq| |#2|) (|:| |op| #1=(|List| |#1|))) |#2| #1#))) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |ReductionOfOrder|)) 
((|ReduceOrder| (*1 *2 *3 *4) (AND (|ofCategory| *5 #1=(|Field|)) (|isDomain| *2 (|Record| (|:| |eq| *3) (|:| |op| #2=(|List| *5)))) (|isDomain| *1 (|ReductionOfOrder| *5 *3)) (|isDomain| *4 #2#) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (|ReduceOrder| (*1 *2 *2 *3) (AND (|ofCategory| *3 #1#) (|isDomain| *1 (|ReductionOfOrder| *3 *2)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *3))))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|setref| ((|#1| $ |#1|) 12 T ELT)) (|ref| (($ |#1|) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|deref| ((|#1| $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 17 T ELT)) (|before?| #1#) (= (#2# 9 T ELT))) 
(((|Reference| |#1|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |ref| ($ |#1|)) (SIGNATURE |deref| (|#1| $)) (SIGNATURE |setref| (|#1| $ |#1|)) (SIGNATURE = ((|Boolean|) $ $)))) (|Type|)) (T |Reference|)) 
((= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Reference| *3)) (|ofCategory| *3 #1=(|Type|)))) (|ref| (*1 *1 *2) #2=(AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 #1#))) (|deref| (*1 *2 *1) #2#) (|setref| (*1 *2 *1 *2) #2#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| |#4|)))) #5#) NIL T ELT)) (|zeroSetSplit| ((#6=(|List| $) #5#) 113 T ELT) ((#6# #5# #3#) 114 T ELT) ((#6# #5# #3# #3#) 112 T ELT) ((#6# #5# #3# #3# #3# #3#) 115 T ELT)) (|variables| #7=(((|List| |#3|) $) NIL T ELT)) (|trivialIdeal?| #8=(#9=(#3# $) NIL T ELT)) (|triangular?| #10=(#9# NIL #11=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #12=(#13=(#3# |#4| $) NIL T ELT) #8#) (|stronglyReduce| #14=(#15=(|#4| |#4| $) NIL T ELT)) (|squareFreePart| ((#16=(|List| (|Record| (|:| |val| |#4|) #17=(|:| |tower| $))) |#4| $) 107 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL T ELT)) (|select| #18=(($ #19=(|Mapping| #3# |#4|) $) NIL #20=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#21=(|Union| |#4| #22="failed") $ |#3|) 62 T ELT)) (|sample| (#23=($) NIL T CONST)) (|roughUnitIdeal?| (#9# 28 #11# ELT)) (|roughSubIdeal?| #24=(#2# NIL #11# ELT)) (|roughEqualIdeals?| #24#) (|roughBase?| #10#) (|rewriteSetWithReduction| ((#5# #5# $ #25=(|Mapping| |#4| |#4| |#4|) #26=(|Mapping| #3# |#4| |#4|)) NIL T ELT)) (|rewriteIdealWithRemainder| #27=((#5# #5# $) NIL #11# ELT)) (|rewriteIdealWithHeadRemainder| #27#) (|retractIfCan| ((#28=(|Union| $ #22#) #5#) NIL T ELT)) (|retract| (#29=($ #5#) NIL T ELT)) (|rest| ((#28# $) 44 T ELT)) (|removeZero| (#15# 65 T ELT)) (|removeDuplicates| (#30=($ $) NIL #31=(AND #20# #32=(|has| |#4| (|BasicType|))) ELT)) (|remove| (#33=($ |#4| $) NIL #31# ELT) #18#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #34=(|:| |den| |#1|)) |#4| $) 80 #11# ELT)) (|reduced?| ((#3# |#4| $ #26#) NIL T ELT)) (|reduceByQuasiMonic| #14#) (|reduce| ((|#4| #25# $ |#4| |#4|) NIL #32# ELT) ((|#4| #25# $ |#4|) NIL T ELT) ((|#4| #25# $) NIL T ELT) ((|#4| |#4| $ #25# #26#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|purelyTranscendental?| #12#) (|purelyAlgebraicLeadingMonomial?| #12#) (|purelyAlgebraic?| #12# #8#) (|preprocess| (((|Record| (|:| |val| #5#) (|:| |towers| #6#)) #5# #3# #3#) 128 T ELT)) (|normalized?| #12# #8#) (|mvar| ((|#3| $) 37 T ELT)) (|members| (#35=(#5# $) 18 T ELT)) (|member?| (#13# 26 #32# ELT)) (|map!| (#36=($ (|Mapping| |#4| |#4|) $) 24 T ELT)) (|map| (#36# 22 T ELT)) (|mainVariables| #7#) (|mainVariable?| (#37=(#3# |#3| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #6#) |#4| |#4| $) NIL T ELT)) (|lastSubResultant| ((#16# |#4| |#4| $) 105 T ELT)) (|last| (#38=(#21# $) 41 T ELT)) (|invertibleSet| (#39=(#6# |#4| $) 88 T ELT)) (|invertibleElseSplit?| (((|Union| #3# #6#) |#4| $) NIL T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #17#)) |#4| $) 98 T ELT) (#13# 60 T ELT)) (|intersect| (#39# 110 T ELT) #40=((#6# #5# $) NIL T ELT) (#41=(#6# #5# #6#) 111 T ELT) #42=((#6# |#4| #6#) NIL T ELT)) (|internalZeroSetSplit| ((#6# #5# #3# #3# #3#) 123 T ELT)) (|internalAugment| (#33# 77 T ELT) (($ #5# $) 78 T ELT) ((#6# |#4| $ #3# #3# #3# #3# #3#) 74 T ELT)) (|initials| (#35# NIL T ELT)) (|initiallyReduced?| #12# #8#) (|initiallyReduce| #14#) (|infRittWu?| #1#) (|headRemainder| (((|Record| (|:| |num| |#4|) #34#) |#4| $) NIL #11# ELT)) (|headReduced?| #12# #8#) (|headReduce| #14#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#38# 39 T ELT)) (|find| ((#21# #19# $) NIL T ELT)) (|extendIfCan| ((#28# $ |#4|) 55 T ELT)) (|extend| (($ $ |#4|) NIL T ELT) (#39# 90 T ELT) #42# #40# (#41# 84 T ELT)) (|every?| #43=((#3# #19# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #44=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) NIL #44# ELT) (($ $ #45=(|Equation| |#4|)) NIL #44# ELT) (($ $ (|List| #45#)) NIL #44# ELT)) (|eq?| #1#) (|empty?| (#9# 17 T ELT)) (|empty| (#23# 14 T ELT)) (|degree| #46=(#47=(#48=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#48# |#4| $) NIL #32# ELT) ((#48# #19# $) NIL T ELT)) (|copy| (#30# 13 T ELT)) (|convert| ((#49=(|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| #49#)) ELT)) (|construct| (#29# 21 T ELT)) (|collectUpper| (#50=($ $ |#3|) 48 T ELT)) (|collectUnder| (#50# 50 T ELT)) (|collectQuasiMonic| (#30# NIL T ELT)) (|collect| (#50# NIL T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT) (#35# 45 T ELT)) (|coHeight| (#47# NIL (|has| |#3| (|Finite|)) ELT)) (|before?| #1#) (|basicSet| ((#51=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #22#) #5# #26#) NIL T ELT) ((#51# #5# #19# #26#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# |#4| #5#)) NIL T ELT)) (|augment| (#39# 87 T ELT) #42# #40# (#41# NIL T ELT)) (|any?| #43#) (|algebraicVariables| #7#) (|algebraicCoefficients?| #12#) (|algebraic?| (#37# 61 T ELT)) (= #1#) (|#| #46#)) 
(((|RegularTriangularSet| |#1| |#2| |#3| |#4|) (|Join| (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |internalAugment| (#1=(|List| $) |#4| $ #2=(|Boolean|) #2# #2# #2# #2#)) (SIGNATURE |zeroSetSplit| (#1# #3=(|List| |#4|) #2# #2#)) (SIGNATURE |zeroSetSplit| (#1# #3# #2# #2# #2# #2#)) (SIGNATURE |internalZeroSetSplit| (#1# #3# #2# #2# #2#)) (SIGNATURE |preprocess| ((|Record| (|:| |val| #3#) (|:| |towers| #1#)) #3# #2# #2#)))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |RegularTriangularSet|)) 
((|internalAugment| (*1 *2 *3 *1 *4 *4 *4 *4 *4) (AND #1=(|isDomain| *4 (|Boolean|)) #2=(|ofCategory| *5 (|GcdDomain|)) #3=(|ofCategory| *6 (|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| #5=(|RegularTriangularSet| *5 *6 *7 *3))) (|isDomain| *1 #5#) (|ofCategory| *3 #6=(|RecursivePolynomialCategory| *5 *6 *7)))) (|zeroSetSplit| #7=(*1 *2 *3 *4 *4) #8=(AND #9=(|isDomain| *3 #10=(|List| *8)) #1# #11=(|ofCategory| *8 #6#) #2# #3# #4# (|isDomain| *2 #12=(|List| #13=(|RegularTriangularSet| *5 *6 *7 *8))) #14=(|isDomain| *1 #13#))) (|zeroSetSplit| (*1 *2 *3 *4 *4 *4 *4) #8#) (|internalZeroSetSplit| (*1 *2 *3 *4 *4 *4) #8#) (|preprocess| #7# (AND #1# #2# #3# #4# #11# (|isDomain| *2 (|Record| (|:| |val| #10#) (|:| |towers| #12#))) #14# #9#))) 
((|radicalEigenvectors| (((|List| (|Record| (|:| |radval| #1=(|Expression| #2=(|Integer|))) (|:| |radmult| #2#) (|:| |radvect| #3=(|List| #4=(|Matrix| #1#))))) #5=(|Matrix| (|Fraction| (|Polynomial| #2#)))) 67 T ELT)) (|radicalEigenvector| ((#3# #1# #5#) 52 T ELT)) (|radicalEigenvalues| (((|List| #1#) #5#) 45 T ELT)) (|orthonormalBasis| ((#3# #5#) 85 T ELT)) (|normalise| ((#4# #4#) 38 T ELT)) (|gramschmidt| ((#3# #3#) 74 T ELT)) (|eigenMatrix| (((|Union| #4# "failed") #5#) 82 T ELT))) 
(((|RadicalEigenPackage|) (CATEGORY |package| (SIGNATURE |radicalEigenvectors| ((|List| (|Record| (|:| |radval| #1=(|Expression| #2=(|Integer|))) (|:| |radmult| #2#) (|:| |radvect| #3=(|List| #4=(|Matrix| #1#))))) #5=(|Matrix| (|Fraction| (|Polynomial| #2#))))) (SIGNATURE |radicalEigenvector| (#3# #1# #5#)) (SIGNATURE |radicalEigenvalues| ((|List| #1#) #5#)) (SIGNATURE |eigenMatrix| ((|Union| #4# "failed") #5#)) (SIGNATURE |normalise| (#4# #4#)) (SIGNATURE |gramschmidt| (#3# #3#)) (SIGNATURE |orthonormalBasis| (#3# #5#)))) (T |RadicalEigenPackage|)) 
((|orthonormalBasis| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|Matrix| (|Fraction| (|Polynomial| #4=(|Integer|))))) #5=(|isDomain| *2 #6=(|List| #7=(|Matrix| #8=(|Expression| #4#)))) #9=(|isDomain| *1 (|RadicalEigenPackage|)))) (|gramschmidt| #10=(*1 *2 *2) (AND #5# #9#)) (|normalise| #10# (AND #11=(|isDomain| *2 #7#) #9#)) (|eigenMatrix| #1# (|partial| AND #2# #11# #9#)) (|radicalEigenvalues| #1# (AND #2# (|isDomain| *2 (|List| #8#)) #9#)) (|radicalEigenvector| (*1 *2 *3 *4) (AND (|isDomain| *4 #3#) #5# #9# (|isDomain| *3 #8#))) (|radicalEigenvectors| #1# (AND #2# (|isDomain| *2 (|List| (|Record| (|:| |radval| #8#) (|:| |radmult| #4#) (|:| |radvect| #6#)))) #9#))) 
((|tensorProduct| ((#1=(|List| #2=(|Matrix| |#1|)) #1#) 69 T ELT) ((#2# #2#) 68 T ELT) ((#1# #1# #1#) 67 T ELT) ((#2# #2# #2#) 64 T ELT)) (|symmetricTensors| (#3=(#1# #1# #4=(|PositiveInteger|)) 62 T ELT) (#5=(#2# #2# #4#) 61 T ELT)) (|permutationRepresentation| ((#6=(|List| #7=(|Matrix| #8=(|Integer|))) (|List| #9=(|List| #8#))) 80 T ELT) ((#6# (|List| #10=(|Permutation| #8#)) #8#) 79 T ELT) ((#7# #9#) 76 T ELT) ((#7# #10# #8#) 74 T ELT)) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) 94 T ELT)) (|antisymmetricTensors| (#3# 48 #11=(|has| |#1| (ATTRIBUTE (|commutative| "*"))) ELT) (#5# 46 #11# ELT))) 
(((|RepresentationPackage1| |#1|) (CATEGORY |package| (IF #1=(|has| |#1| (ATTRIBUTE (|commutative| "*"))) (SIGNATURE |antisymmetricTensors| #2=(#3=(|Matrix| |#1|) #3# #4=(|PositiveInteger|))) |%noBranch|) (IF #1# (SIGNATURE |antisymmetricTensors| #5=(#6=(|List| #3#) #6# #4#)) |%noBranch|) (SIGNATURE |createGenericMatrix| ((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|))) (SIGNATURE |symmetricTensors| #2#) (SIGNATURE |symmetricTensors| #5#) (SIGNATURE |tensorProduct| (#3# #3# #3#)) (SIGNATURE |tensorProduct| (#6# #6# #6#)) (SIGNATURE |tensorProduct| (#3# #3#)) (SIGNATURE |tensorProduct| (#6# #6#)) (SIGNATURE |permutationRepresentation| (#7=(|Matrix| #8=(|Integer|)) #9=(|Permutation| #8#) #8#)) (SIGNATURE |permutationRepresentation| (#7# #10=(|List| #8#))) (SIGNATURE |permutationRepresentation| (#11=(|List| #7#) (|List| #9#) #8#)) (SIGNATURE |permutationRepresentation| (#11# (|List| #10#)))) (|Ring|)) (T |RepresentationPackage1|)) 
((|permutationRepresentation| #1=(*1 *2 *3) (AND (|isDomain| *3 (|List| #2=(|List| #3=(|Integer|)))) (|isDomain| *2 (|List| #4=(|Matrix| #3#))) #5=(|isDomain| *1 (|RepresentationPackage1| *4)) #6=(|ofCategory| *4 #7=(|Ring|)))) (|permutationRepresentation| #8=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| #9=(|Permutation| #3#))) #10=(|isDomain| *4 #3#) #11=(|isDomain| *2 (|List| #12=(|Matrix| *4))) #13=(|isDomain| *1 (|RepresentationPackage1| *5)) #14=(|ofCategory| *5 #7#))) (|permutationRepresentation| #1# (AND (|isDomain| *3 #2#) (|isDomain| *2 #4#) #5# #6#)) (|permutationRepresentation| #8# (AND (|isDomain| *3 #9#) #10# #15=(|isDomain| *2 #12#) #13# #14#)) (|tensorProduct| #16=(*1 *2 *2) #17=(AND (|isDomain| *2 (|List| #18=(|Matrix| *3))) #19=(|ofCategory| *3 #7#) #20=(|isDomain| *1 (|RepresentationPackage1| *3)))) (|tensorProduct| #16# #21=(AND (|isDomain| *2 #18#) #19# #20#)) (|tensorProduct| #22=(*1 *2 *2 *2) #17#) (|tensorProduct| #22# #21#) (|symmetricTensors| #23=(*1 *2 *2 *3) (AND #11# #24=(|isDomain| *3 (|PositiveInteger|)) #6# #5#)) (|symmetricTensors| #23# (AND #15# #24# #6# #5#)) (|createGenericMatrix| #1# (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Matrix| (|Polynomial| *4))) #5# #6#)) (|antisymmetricTensors| #23# (AND #11# #24# #25=(|has| *4 (ATTRIBUTE (|commutative| "*"))) #6# #5#)) (|antisymmetricTensors| #23# (AND #15# #24# #25# #6# #5#))) 
((|standardBasisOfCyclicSubmodule| ((#1=(|Matrix| |#1|) #2=(|List| #1#) #3=(|Vector| |#1|)) 69 #4=(|has| |#1| (|EuclideanDomain|)) ELT)) (|split| ((#5=(|List| #2#) #2# #6=(|Vector| #3#)) 107 #7=(|has| |#1| (|Field|)) ELT) ((#5# #2# #3#) 104 #7# ELT)) (|scanOneDimSubspaces| ((#3# (|List| #3#) #8=(|Integer|)) 113 #9=(AND #7# (|has| |#1| (|Finite|))) ELT)) (|meatAxe| ((#5# #2# (|PositiveInteger|)) 119 #9# ELT) ((#5# #2# #10=(|Boolean|)) 118 #9# ELT) ((#5# #2#) 117 #9# ELT) ((#5# #2# #10# #8# #8#) 116 #9# ELT)) (|isAbsolutelyIrreducible?| ((#10# #2#) 101 #7# ELT) ((#10# #2# #8#) 100 #7# ELT)) (|cyclicSubmodule| ((#6# #2# #3#) 66 #4# ELT)) (|createRandomElement| ((#1# #2# #1#) 46 T ELT)) (|completeEchelonBasis| ((#1# #6#) 39 T ELT)) (|areEquivalent?| ((#1# #2# #2# #8#) 93 #7# ELT) ((#1# #2# #2#) 92 #7# ELT) ((#1# #2# #2# #10# #8#) 91 #7# ELT))) 
(((|RepresentationPackage2| |#1|) (CATEGORY |package| (SIGNATURE |completeEchelonBasis| (#1=(|Matrix| |#1|) #2=(|Vector| #3=(|Vector| |#1|)))) (SIGNATURE |createRandomElement| (#1# #4=(|List| #1#) #1#)) (IF (|has| |#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |cyclicSubmodule| (#2# #4# #3#)) (SIGNATURE |standardBasisOfCyclicSubmodule| (#1# #4# #3#))) |%noBranch|) (IF #5=(|has| |#1| (|Field|)) (PROGN (SIGNATURE |areEquivalent?| (#1# #4# #4# #6=(|Boolean|) #7=(|Integer|))) (SIGNATURE |areEquivalent?| (#1# #4# #4#)) (SIGNATURE |areEquivalent?| (#1# #4# #4# #7#)) (SIGNATURE |isAbsolutelyIrreducible?| (#6# #4# #7#)) (SIGNATURE |isAbsolutelyIrreducible?| (#6# #4#)) (SIGNATURE |split| (#8=(|List| #4#) #4# #3#)) (SIGNATURE |split| (#8# #4# #2#))) |%noBranch|) (IF (|has| |#1| (|Finite|)) (IF #5# (PROGN (SIGNATURE |meatAxe| (#8# #4# #6# #7# #7#)) (SIGNATURE |meatAxe| (#8# #4#)) (SIGNATURE |meatAxe| (#8# #4# #6#)) (SIGNATURE |meatAxe| (#8# #4# (|PositiveInteger|))) (SIGNATURE |scanOneDimSubspaces| (#3# (|List| #3#) #7#))) |%noBranch|) |%noBranch|)) (|Ring|)) (T |RepresentationPackage2|)) 
((|scanOneDimSubspaces| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| #2=(|Vector| *5))) #3=(|isDomain| *4 #4=(|Integer|)) (|isDomain| *2 #2#) #5=(|isDomain| *1 (|RepresentationPackage2| *5)) #6=(|ofCategory| *5 #7=(|Field|)) #8=(|ofCategory| *5 #9=(|Finite|)) #10=(|ofCategory| *5 #11=(|Ring|)))) (|meatAxe| #1# (AND (|isDomain| *4 (|PositiveInteger|)) #6# #8# #10# #12=(|isDomain| *2 (|List| #13=(|List| #14=(|Matrix| *5)))) #5# #15=(|isDomain| *3 #13#))) (|meatAxe| #1# (AND #16=(|isDomain| *4 #17=(|Boolean|)) #6# #8# #10# #12# #5# #15#)) (|meatAxe| #18=(*1 *2 *3) (AND #19=(|ofCategory| *4 #7#) (|ofCategory| *4 #9#) #20=(|ofCategory| *4 #11#) (|isDomain| *2 (|List| #21=(|List| #22=(|Matrix| *4)))) #23=(|isDomain| *1 (|RepresentationPackage2| *4)) #24=(|isDomain| *3 #21#))) (|meatAxe| (*1 *2 *3 *4 *5 *5) (AND #16# #25=(|isDomain| *5 #4#) #26=(|ofCategory| *6 #7#) (|ofCategory| *6 #9#) #27=(|ofCategory| *6 #11#) (|isDomain| *2 (|List| #28=(|List| #29=(|Matrix| *6)))) #30=(|isDomain| *1 (|RepresentationPackage2| *6)) #31=(|isDomain| *3 #28#))) (|split| #1# (AND (|isDomain| *4 #32=(|Vector| #2#)) #6# #10# #12# #5# #15#)) (|split| #1# (AND #33=(|isDomain| *4 #2#) #6# #10# #12# #5# #15#)) (|isAbsolutelyIrreducible?| #18# (AND #24# #19# #20# #34=(|isDomain| *2 #17#) #23#)) (|isAbsolutelyIrreducible?| #1# (AND #15# #3# #6# #10# #34# #5#)) (|areEquivalent?| (*1 *2 *3 *3 *4) (AND #15# #3# #35=(|isDomain| *2 #14#) #5# #6# #10#)) (|areEquivalent?| (*1 *2 *3 *3) (AND #24# #36=(|isDomain| *2 #22#) #23# #19# #20#)) (|areEquivalent?| (*1 *2 *3 *3 *4 *5) (AND #31# #16# #25# (|isDomain| *2 #29#) #30# #26# #27#)) (|standardBasisOfCyclicSubmodule| #1# (AND #15# #33# #37=(|ofCategory| *5 (|EuclideanDomain|)) #10# #35# #5#)) (|cyclicSubmodule| #1# (AND #15# #37# #10# (|isDomain| *2 #32#) #5# #33#)) (|createRandomElement| (*1 *2 *3 *2) (AND #24# #36# #20# #23#)) (|completeEchelonBasis| #18# (AND (|isDomain| *3 (|Vector| (|Vector| *4))) #20# #36# #23#))) 
((|double| ((|#1| (|PositiveInteger|) |#1|) 18 T ELT))) 
(((|RepeatedDoubling| |#1|) (CATEGORY |package| (SIGNATURE |double| (|#1| (|PositiveInteger|) |#1|))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $))))) (T |RepeatedDoubling|)) 
((|double| (*1 *2 *3 *2) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *1 (|RepeatedDoubling| *2)) (|ofCategory| *2 (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $)))))))) 
((|expt| ((|#1| |#1| (|PositiveInteger|)) 18 T ELT))) 
(((|RepeatedSquaring| |#1|) (CATEGORY |package| (SIGNATURE |expt| (|#1| |#1| (|PositiveInteger|)))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $))))) (T |RepeatedSquaring|)) 
((|expt| (*1 *2 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *1 (|RepeatedSquaring| *2)) (|ofCategory| *2 (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)))))))) 
((|coerce| ((|#1| (|Exit|)) 11 T ELT) (((|Void|) |#1|) 9 T ELT))) 
(((|ResolveLatticeCompletion| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|Void|) |#1|)) (SIGNATURE |coerce| (|#1| (|Exit|)))) (|Type|)) (T |ResolveLatticeCompletion|)) 
((|coerce| #1=(*1 *2 *3) (AND (|isDomain| *3 (|Exit|)) (|isDomain| *1 (|ResolveLatticeCompletion| *2)) (|ofCategory| *2 #2=(|Type|)))) (|coerce| #1# (AND (|isDomain| *2 (|Void|)) (|isDomain| *1 (|ResolveLatticeCompletion| *3)) (|ofCategory| *3 #2#)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| ((#5=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|reduce| (#7=($ |#4|) 24 T ELT)) (|recip| ((#5# $) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|lift| ((|#4| $) 26 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 45 T ELT) (($ #8=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (#7# 25 T ELT)) (|characteristic| ((#9=(|NonNegativeInteger|)) 42 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#6# 21 T CONST)) (|One| (#6# 22 T CONST)) (= (#2# 39 T ELT)) (- (($ $) 30 T ELT) (#10=($ $ $) NIL T ELT)) (+ (#10# 28 T ELT)) (** (($ $ #11=(|PositiveInteger|)) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #11# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #8# $) 35 T ELT) (#10# 32 T ELT) (($ |#1| $) 37 T ELT) (($ $ |#1|) NIL T ELT))) 
(((|ResidueRing| |#1| |#2| |#3| |#4| |#5|) (|Join| (|CommutativeRing|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |reduce| #1=($ |#4|)) (SIGNATURE |coerce| #1#) (SIGNATURE |lift| (|#4| $)))) (|Field|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|) (|List| |#4|)) (T |ResidueRing|)) 
((|reduce| #1=(*1 *1 *2) #2=(AND #3=(|ofCategory| *3 (|Field|)) #4=(|ofCategory| *4 (|OrderedAbelianMonoidSup|)) #5=(|ofCategory| *5 (|OrderedSet|)) #6=(|isDomain| *1 (|ResidueRing| *3 *4 *5 *2 *6)) #7=(|ofCategory| *2 (|PolynomialCategory| *3 *4 *5)) #8=(|ofType| *6 (|List| *2)))) (|coerce| #1# #2#) (|lift| (*1 *2 *1) (AND #7# #6# #3# #4# #5# #8#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|ReturnAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |expression| ((|SpadAst|) $))))) (T |ReturnAst|)) 
((|expression| (*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|ReturnAst|))))) 
((|retract| ((|#2| $) 10 T ELT))) 
(((|RetractableTo&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |retract| (|#2| |#1|))) (|RetractableTo| |#2|) (|Type|)) (T |RetractableTo&|)) 
NIL 
((|retractIfCan| (((|Union| |#1| "failed") $) 9 T ELT)) (|retract| ((|#1| $) 8 T ELT)) (|coerce| (($ |#1|) 6 T ELT))) 
(((|RetractableTo| |#1|) (|Category|) (|Type|)) (T |RetractableTo|)) 
((|retractIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|RetractableTo| *2)) (|ofCategory| *2 (|Type|)))) (|retract| (*1 *2 *1) (AND (|ofCategory| *1 (|RetractableTo| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|CoercibleFrom| |t#1|) (CATEGORY |domain| (SIGNATURE |retractIfCan| ((|Union| |t#1| "failed") $)) (SIGNATURE |retract| (|t#1| $)))) 
(((|CoercibleFrom| |#1|) . T)) 
((|solveRetract| (((|List| (|List| (|Equation| (|Fraction| #1=(|Polynomial| |#2|))))) (|List| #1#) (|List| (|Symbol|))) 38 T ELT))) 
(((|RetractSolvePackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solveRetract| ((|List| (|List| (|Equation| (|Fraction| #1=(|Polynomial| |#2|))))) (|List| #1#) (|List| (|Symbol|))))) #2=(|IntegralDomain|) (|Join| #2# (|RetractableTo| |#1|))) (T |RetractSolvePackage|)) 
((|solveRetract| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| #1=(|Polynomial| *6))) (|isDomain| *4 (|List| (|Symbol|))) (|ofCategory| *6 (|Join| #2=(|IntegralDomain|) (|RetractableTo| *5))) (|ofCategory| *5 #2#) (|isDomain| *2 (|List| (|List| (|Equation| (|Fraction| #1#))))) (|isDomain| *1 (|RetractSolvePackage| *5 *6))))) 
((|variables| ((#1=(|List| #2=(|Symbol|)) #3=(|Fraction| (|Polynomial| |#1|))) 17 T ELT)) (|univariate| ((#4=(|Fraction| (|SparseUnivariatePolynomial| #3#)) #3# #2#) 24 T ELT)) (|multivariate| ((#3# #4# #2#) 26 T ELT)) (|mainVariable| (((|Union| #2# "failed") #3#) 20 T ELT)) (|eval| ((#3# #3# (|List| #5=(|Equation| #3#))) 32 T ELT) ((#3# #3# #5#) 33 T ELT) ((#3# #3# #1# (|List| #3#)) 28 T ELT) ((#3# #3# #2# #3#) 29 T ELT)) (|coerce| ((#3# |#1|) 11 T ELT))) 
(((|RationalFunction| |#1|) (CATEGORY |package| (SIGNATURE |variables| (#1=(|List| #2=(|Symbol|)) #3=(|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |mainVariable| ((|Union| #2# "failed") #3#)) (SIGNATURE |univariate| (#4=(|Fraction| (|SparseUnivariatePolynomial| #3#)) #3# #2#)) (SIGNATURE |multivariate| (#3# #4# #2#)) (SIGNATURE |eval| (#3# #3# #2# #3#)) (SIGNATURE |eval| (#3# #3# #1# (|List| #3#))) (SIGNATURE |eval| (#3# #3# #5=(|Equation| #3#))) (SIGNATURE |eval| (#3# #3# (|List| #5#))) (SIGNATURE |coerce| (#3# |#1|))) (|IntegralDomain|)) (T |RationalFunction|)) 
((|coerce| #1=(*1 *2 *3) (AND (|isDomain| *2 (|Fraction| (|Polynomial| *3))) (|isDomain| *1 (|RationalFunction| *3)) (|ofCategory| *3 #2=(|IntegralDomain|)))) (|eval| #3=(*1 *2 *2 *3) (AND (|isDomain| *3 (|List| #4=(|Equation| #5=(|Fraction| (|Polynomial| *4))))) #6=(|isDomain| *2 #5#) #7=(|ofCategory| *4 #2#) #8=(|isDomain| *1 (|RationalFunction| *4)))) (|eval| #3# (AND (|isDomain| *3 #4#) #6# #7# #8#)) (|eval| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 #9=(|List| #10=(|Symbol|))) (|isDomain| *4 (|List| #11=(|Fraction| (|Polynomial| *5)))) #12=(|isDomain| *2 #11#) #13=(|ofCategory| *5 #2#) #14=(|isDomain| *1 (|RationalFunction| *5)))) (|eval| (*1 *2 *2 *3 *2) (AND #6# (|isDomain| *3 #10#) #7# #8#)) (|multivariate| #15=(*1 *2 *3 *4) (AND (|isDomain| *3 #16=(|Fraction| (|SparseUnivariatePolynomial| #11#))) #17=(|isDomain| *4 #10#) #12# #14# #13#)) (|univariate| #15# (AND #17# #13# (|isDomain| *2 #16#) #14# (|isDomain| *3 #11#))) (|mainVariable| #1# (|partial| AND #18=(|isDomain| *3 #5#) #7# (|isDomain| *2 #10#) #8#)) (|variables| #1# (AND #18# #7# (|isDomain| *2 #9#) #8#))) 
((|uniform01| (#1=(#2=(|Float|)) 17 T ELT)) (|uniform| (#3=(#4=(|Mapping| #2#) #2# #2#) 22 T ELT)) (|t| (#5=(#4# #6=(|NonNegativeInteger|)) 48 T ELT)) (|normal01| (#1# 37 T ELT)) (|normal| (#3# 38 T ELT)) (|exponential1| (#1# 29 T ELT)) (|exponential| ((#4# #2#) 30 T ELT)) (|chiSquare1| ((#2# #6#) 43 T ELT)) (|chiSquare| (#5# 44 T ELT)) (F (#7=(#4# #6# #6#) 47 T ELT)) (|Beta| (#7# 45 T ELT))) 
(((|RandomFloatDistributions|) (CATEGORY |package| (SIGNATURE |uniform01| #1=(#2=(|Float|))) (SIGNATURE |normal01| #1#) (SIGNATURE |exponential1| #1#) (SIGNATURE |chiSquare1| (#2# #3=(|NonNegativeInteger|))) (SIGNATURE |uniform| #4=(#5=(|Mapping| #2#) #2# #2#)) (SIGNATURE |normal| #4#) (SIGNATURE |exponential| (#5# #2#)) (SIGNATURE |chiSquare| #6=(#5# #3#)) (SIGNATURE |Beta| #7=(#5# #3# #3#)) (SIGNATURE F #7#) (SIGNATURE |t| #6#))) (T |RandomFloatDistributions|)) 
((|t| #1=(*1 *2 *3) #2=(AND #3=(|isDomain| *3 (|NonNegativeInteger|)) #4=(|isDomain| *2 (|Mapping| #5=(|Float|))) #6=(|isDomain| *1 (|RandomFloatDistributions|)))) (F #7=(*1 *2 *3 *3) #2#) (|Beta| #7# #2#) (|chiSquare| #1# #2#) (|exponential| #1# #8=(AND #4# #6# (|isDomain| *3 #5#))) (|normal| #7# #8#) (|uniform| #7# #8#) (|chiSquare1| #1# (AND #3# #9=(|isDomain| *2 #5#) #6#)) (|exponential1| #10=(*1 *2) #11=(AND #9# #6#)) (|normal01| #10# #11#) (|uniform01| #10# #11#)) 
((|factor| (((|Factored| |#1|) |#1|) 33 T ELT))) 
(((|RationalFunctionFactor| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#1|) |#1|))) (|UnivariatePolynomialCategory| (|Fraction| (|Polynomial| (|Integer|))))) (T |RationalFunctionFactor|)) 
((|factor| (*1 *2 *3) (AND (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|RationalFunctionFactor| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| (|Polynomial| (|Integer|)))))))) 
((|factorFraction| (((|Fraction| (|Factored| #1=(|Polynomial| |#1|))) (|Fraction| #1#)) 14 T ELT))) 
(((|RationalFunctionFactorizer| |#1|) (CATEGORY |package| (SIGNATURE |factorFraction| ((|Fraction| (|Factored| #1=(|Polynomial| |#1|))) (|Fraction| #1#)))) (|EuclideanDomain|)) (T |RationalFunctionFactorizer|)) 
((|factorFraction| (*1 *2 *3) (AND (|isDomain| *3 (|Fraction| #1=(|Polynomial| *4))) (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|Fraction| (|Factored| #1#))) (|isDomain| *1 (|RationalFunctionFactorizer| *4))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|sample| (#3=($) 23 T CONST)) (|red| ((|#1| $) 29 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|green| ((|#1| $) 28 T ELT)) (|componentUpperBound| ((|#1|) 26 T CONST)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|blue| ((|#1| $) 27 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) 
(((|RGBColorModel| |#1|) (|Category|) (|AbelianMonoid|)) (T |RGBColorModel|)) 
((|red| (*1 *2 *1) (AND (|ofCategory| *1 (|RGBColorModel| *2)) (|ofCategory| *2 (|AbelianMonoid|)))) (|green| (*1 *2 *1) (AND (|ofCategory| *1 (|RGBColorModel| *2)) (|ofCategory| *2 (|AbelianMonoid|)))) (|blue| (*1 *2 *1) (AND (|ofCategory| *1 (|RGBColorModel| *2)) (|ofCategory| *2 (|AbelianMonoid|)))) (|componentUpperBound| (*1 *2) (AND (|ofCategory| *1 (|RGBColorModel| *2)) (|ofCategory| *2 (|AbelianMonoid|))))) 
(|Join| (|AbelianMonoid|) (CATEGORY |domain| (SIGNATURE |red| (|t#1| $)) (SIGNATURE |green| (|t#1| $)) (SIGNATURE |blue| (|t#1| $)) (SIGNATURE |componentUpperBound| (|t#1|) |constant|))) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|whitePoint| (($) 31 T CONST)) (|sample| (#3=($) 23 T CONST)) (|red| ((|#1| . #4=($)) 29 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|green| ((|#1| . #4#) 28 T ELT)) (|componentUpperBound| ((|#1|) 26 T CONST)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|blue| ((|#1| . #4#) 27 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) 
(((|RGBColorSpace| |#1|) (|Category|) (|AbelianMonoid|)) (T |RGBColorSpace|)) 
((|whitePoint| (*1 *1) (AND (|ofCategory| *1 (|RGBColorSpace| *2)) (|ofCategory| *2 (|AbelianMonoid|))))) 
(|Join| (|RGBColorModel| |t#1|) (CATEGORY |domain| (SIGNATURE |whitePoint| ($) |constant|))) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|RGBColorModel| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| #6=(|NewSparseMultivariatePolynomial| |#1| #7=(|OrderedVariableList| |#2|)))))) #5#) NIL T ELT)) (|zeroSetSplit| ((#8=(|List| $) #5#) NIL T ELT) ((#8# #5# #3#) NIL T ELT) ((#8# #5# #3# #3#) NIL T ELT)) (|variables| #9=(((|List| #7#) $) NIL T ELT)) (|trivialIdeal?| #10=(#11=(#3# $) NIL T ELT)) (|triangular?| #12=(#11# NIL #13=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #14=(#15=(#3# #6# $) NIL T ELT) #10#) (|stronglyReduce| #16=((#6# #6# $) NIL T ELT)) (|squareFreePart| ((#17=(|List| (|Record| (|:| |val| #6#) #18=(|:| |tower| $))) #6# $) NIL T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ #7#) NIL T ELT)) (|select| #19=(($ #20=(|Mapping| #3# #6#) $) NIL #21=(|has| $ (|FiniteAggregate| #6#)) ELT) ((#22=(|Union| #6# #23="failed") $ #7#) NIL T ELT)) (|sample| (#24=($) NIL T CONST)) (|roughUnitIdeal?| #12#) (|roughSubIdeal?| #25=(#2# NIL #13# ELT)) (|roughEqualIdeals?| #25#) (|roughBase?| #12#) (|rewriteSetWithReduction| ((#5# #5# $ #26=(|Mapping| #6# #6# #6#) #27=(|Mapping| #3# #6# #6#)) NIL T ELT)) (|rewriteIdealWithRemainder| #28=((#5# #5# $) NIL #13# ELT)) (|rewriteIdealWithHeadRemainder| #28#) (|retractIfCan| ((#29=(|Union| $ #23#) #5#) NIL T ELT)) (|retract| #30=(($ #5#) NIL T ELT)) (|rest| ((#29# $) NIL T ELT)) (|removeZero| #16#) (|removeDuplicates| (#31=($ $) NIL #32=(AND #21# #33=(|has| #6# (|BasicType|))) ELT)) (|remove| (#34=($ #6# $) NIL #32# ELT) #19#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| #6#) #35=(|:| |den| |#1|)) #6# $) NIL #13# ELT)) (|reduced?| ((#3# #6# $ #27#) NIL T ELT)) (|reduceByQuasiMonic| #16#) (|reduce| ((#6# #26# $ #6# #6#) NIL #33# ELT) ((#6# #26# $ #6#) NIL T ELT) ((#6# #26# $) NIL T ELT) ((#6# #6# $ #26# #27#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|purelyTranscendental?| #14#) (|purelyAlgebraicLeadingMonomial?| #14#) (|purelyAlgebraic?| #14# #10#) (|normalized?| #14# #10#) (|mvar| ((#7# $) NIL T ELT)) (|members| #36=((#5# $) NIL T ELT)) (|member?| (#15# NIL #33# ELT)) (|map!| #37=(($ (|Mapping| #6# #6#) $) NIL T ELT)) (|map| #37#) (|mainVariables| #9#) (|mainVariable?| #38=((#3# #7# $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lastSubResultantElseSplit| (((|Union| #6# #8#) #6# #6# $) NIL T ELT)) (|lastSubResultant| ((#17# #6# #6# $) NIL T ELT)) (|last| #39=((#22# $) NIL T ELT)) (|invertibleSet| #40=((#8# #6# $) NIL T ELT)) (|invertibleElseSplit?| (((|Union| #3# #8#) #6# $) NIL T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #18#)) #6# $) NIL T ELT) #14#) (|intersect| #40# #41=((#8# #5# $) NIL T ELT) #42=((#8# #5# #8#) NIL T ELT) #43=((#8# #6# #8#) NIL T ELT)) (|internalAugment| (#34# NIL T ELT) (($ #5# $) NIL T ELT)) (|initials| #36#) (|initiallyReduced?| #14# #10#) (|initiallyReduce| #16#) (|infRittWu?| #1#) (|headRemainder| (((|Record| (|:| |num| #6#) #35#) #6# $) NIL #13# ELT)) (|headReduced?| #14# #10#) (|headReduce| #16#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| #39#) (|find| ((#22# #20# $) NIL T ELT)) (|extendIfCan| ((#29# $ #6#) NIL T ELT)) (|extend| (($ $ #6#) NIL T ELT) #40# #43# #41# #42#) (|every?| #44=((#3# #20# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #45=(AND (|has| #6# (|Evalable| #6#)) (|has| #6# (|SetCategory|))) ELT) (($ $ #6# #6#) NIL #45# ELT) (($ $ #46=(|Equation| #6#)) NIL #45# ELT) (($ $ (|List| #46#)) NIL #45# ELT)) (|eq?| #1#) (|empty?| #10#) (|empty| (#24# NIL T ELT)) (|degree| #47=(#48=(#49=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#49# #6# $) NIL #33# ELT) ((#49# #20# $) NIL T ELT)) (|copy| #50=(#31# NIL T ELT)) (|convert| ((#51=(|InputForm|) $) NIL (|has| #6# (|ConvertibleTo| #51#)) ELT)) (|construct| #30#) (|collectUpper| #52=(($ $ #7#) NIL T ELT)) (|collectUnder| #52#) (|collectQuasiMonic| #50#) (|collect| #52#) (|coerce| (((|OutputForm|) $) NIL T ELT) #36#) (|coHeight| (#48# NIL (|has| #7# (|Finite|)) ELT)) (|before?| #1#) (|basicSet| ((#53=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #23#) #5# #27#) NIL T ELT) ((#53# #5# #20# #27#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# #6# #5#)) NIL T ELT)) (|augment| #40# #43# #41# #42#) (|any?| #44#) (|algebraicVariables| #9#) (|algebraicCoefficients?| #14#) (|algebraic?| #38#) (= #1#) (|#| #47#)) 
(((|RegularChain| |#1| |#2|) (|Join| (|RegularTriangularSetCategory| |#1| (|IndexedExponents| #1=(|OrderedVariableList| |#2|)) #1# #2=(|NewSparseMultivariatePolynomial| |#1| #1#)) (CATEGORY |domain| (SIGNATURE |zeroSetSplit| ((|List| $) (|List| #2#) #3=(|Boolean|) #3#)))) (|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| #1=(|RegularChain| *5 *6))) (|isDomain| *1 #1#)))) 
((|uniform| ((#1=(|Mapping| #2=(|Integer|)) (|Segment| #2#)) 32 T ELT)) (|ridHack1| ((#2# #2# #2# #2# #2#) 29 T ELT)) (|poisson| #3=((#1# |RationalNumber|) NIL T ELT)) (|geometric| #3#) (|binomial| ((#1# #2# |RationalNumber|) NIL T ELT))) 
(((|RandomIntegerDistributions|) (CATEGORY |package| (SIGNATURE |uniform| (#1=(|Mapping| #2=(|Integer|)) (|Segment| #2#))) (SIGNATURE |binomial| (#1# #2# |RationalNumber|)) (SIGNATURE |poisson| #3=(#1# |RationalNumber|)) (SIGNATURE |geometric| #3#) (SIGNATURE |ridHack1| (#2# #2# #2# #2# #2#)))) (T |RandomIntegerDistributions|)) 
((|ridHack1| (*1 *2 *2 *2 *2 *2) (AND (|isDomain| *2 #1=(|Integer|)) #2=(|isDomain| *1 (|RandomIntegerDistributions|)))) (|geometric| #3=(*1 *2 *3) #4=(AND (|isDomain| *3 |RationalNumber|) #5=(|isDomain| *2 (|Mapping| #1#)) #2#)) (|poisson| #3# #4#) (|binomial| (*1 *2 *3 *4) (AND (|isDomain| *4 |RationalNumber|) #5# #2# (|isDomain| *3 #1#))) (|uniform| #3# (AND (|isDomain| *3 (|Segment| #1#)) #5# #2#))) 
((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) 10 T ELT))) 
(((|Ring&| |#1|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|Ring|)) (T |Ring&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|Ring|) (|Category|)) (T |Ring|)) 
((|characteristic| (*1 *2) (AND (|ofCategory| *1 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|))))) 
(|Join| (|Rng|) (|SemiRing|) (|LeftModule| $) (|CoercibleFrom| (|Integer|)) (CATEGORY |package| (SIGNATURE |characteristic| ((|NonNegativeInteger|)) |constant|) (ATTRIBUTE |unitsKnown|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|interpolate| (((|Fraction| (|Polynomial| |#2|)) #1=(|List| |#2|) #1# #2=(|NonNegativeInteger|) #2#) 55 T ELT))) 
(((|RationalInterpolation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |interpolate| ((|Fraction| (|Polynomial| |#2|)) #1=(|List| |#2|) #1# #2=(|NonNegativeInteger|) #2#))) (|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|))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (* (($ $ |#1|) 17 T ELT))) 
(((|RightLinearSet| |#1|) (|Category|) (|SemiGroup|)) (T |RightLinearSet|)) 
((* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RightLinearSet| *2)) (|ofCategory| *2 (|SemiGroup|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ |t#1|)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|symmetric?| (#1=((|Boolean|) $) 38 T ELT)) (|square?| (#1# 17 T ELT)) (|nrows| (#2=((|NonNegativeInteger|) $) 13 T ELT)) (|ncols| (#2# 14 T ELT)) (|diagonal?| (#1# 30 T ELT)) (|antisymmetric?| (#1# 40 T ELT))) 
(((|RectangularMatrixCategory&| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |ncols| #1=(#2=(|NonNegativeInteger|) |#1|)) (SIGNATURE |nrows| #1#) (SIGNATURE |antisymmetric?| #3=((|Boolean|) |#1|)) (SIGNATURE |symmetric?| #3#) (SIGNATURE |diagonal?| #3#) (SIGNATURE |square?| #3#)) (|RectangularMatrixCategory| |#2| |#3| |#4| |#5| |#6|) #2# #2# (|Ring|) (|DirectProductCategory| |#3| |#4|) (|DirectProductCategory| |#2| |#4|)) (T |RectangularMatrixCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|symmetric?| (((|Boolean|) $) 63 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|square?| (((|Boolean|) $) 65 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rowEchelon| (($ $) 46 (|has| |#3| (|EuclideanDomain|)) ELT)) (|row| ((|#4| $ (|Integer|)) 51 T ELT)) (|reduce| ((|#3| (|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) 86 (|has| |#3| . #4=((|BasicType|))) ELT) ((|#3| (|Mapping| |#3| |#3| |#3|) $ |#3|) 82 T ELT) ((|#3| (|Mapping| |#3| |#3| |#3|) $) 81 T ELT)) (|rank| (((|NonNegativeInteger|) $) 45 (|has| |#3| (|IntegralDomain|)) ELT)) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) 53 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|nullity| (((|NonNegativeInteger|) $) 44 (|has| |#3| (|IntegralDomain|)) ELT)) (|nullSpace| (((|List| |#5|) $) 43 (|has| |#3| (|IntegralDomain|)) ELT)) (|nrows| (((|NonNegativeInteger|) $) 57 T ELT)) (|ncols| (((|NonNegativeInteger|) $) 56 T ELT)) (|minRowIndex| (((|Integer|) $) 61 T ELT)) (|minColIndex| (((|Integer|) $) 59 T ELT)) (|members| (((|List| |#3|) $) 80 T ELT)) (|member?| ((#5=(|Boolean|) |#3| $) 85 (|has| |#3| . #4#) ELT)) (|maxRowIndex| (((|Integer|) $) 60 T ELT)) (|maxColIndex| (((|Integer|) $) 58 T ELT)) (|matrix| (($ (|List| (|List| |#3|))) 66 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) 71 T ELT) (($ (|Mapping| |#3| |#3| |#3|) $ $) 49 T ELT)) (|listOfLists| (((|List| (|List| |#3|)) $) 55 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#3| "failed") (|Mapping| #5# |#3|) $) 83 T ELT)) (|exquo| (((|Union| $ "failed") $ |#3|) 48 (|has| |#3| (|IntegralDomain|)) ELT)) (|every?| ((#5# (|Mapping| #5# |#3|) . #6=($)) 78 T ELT)) (|eval| (($ $ (|List| |#3|) (|List| |#3|)) 75 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7=((|SetCategory|)))) ELT) (($ $ |#3| |#3|) 74 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT) (($ $ (|Equation| |#3|)) 73 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT) (($ $ (|List| (|Equation| |#3|))) 72 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT)) (|eq?| ((#8=(|Boolean|) $ $) 67 T ELT)) (|empty?| ((#8# $) 70 T ELT)) (|empty| (($) 69 T ELT)) (|elt| ((|#3| $ (|Integer|) (|Integer|)) 54 T ELT) ((|#3| $ (|Integer|) (|Integer|) |#3|) 52 T ELT)) (|diagonal?| (((|Boolean|) $) 64 T ELT)) (|count| ((#9=(|NonNegativeInteger|) |#3| $) 84 (|has| |#3| . #4#) ELT) ((#9# (|Mapping| #5# |#3|) $) 79 T ELT)) (|copy| (($ $) 68 T ELT)) (|column| ((|#5| $ (|Integer|)) 50 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| ((#5# (|Mapping| #5# |#3|) . #6#) 77 T ELT)) (|antisymmetric?| (((|Boolean|) $) 62 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#3|) 47 (|has| |#3| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #10=($)) 30 T ELT) (($ |#3| . #10#) 33 T ELT) (($ $ |#3|) 37 T ELT)) (|#| ((#9# $) 76 T ELT))) 
(((|RectangularMatrixCategory| |#1| |#2| |#3| |#4| |#5|) (|Category|) #1=(|NonNegativeInteger|) #1# (|Ring|) (|DirectProductCategory| |t#2| |t#3|) (|DirectProductCategory| |t#1| |t#3|)) (T |RectangularMatrixCategory|)) 
((|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|) (|FiniteAggregate| |t#3|) (CATEGORY |domain| (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| |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|))) ((|FiniteAggregate| |#3|) . T) ((|Functorial| |#3|) . T) ((|HomogeneousAggregate| |#3|) . T) ((|InnerEvalable| |#3| |#3|) AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#3|) . T) ((|LeftModule| |#3|) . T) ((|LinearSet| |#3|) |has| |#3| (|CommutativeRing|)) ((|Module| |#3|) |has| |#3| (|CommutativeRing|)) ((|RightLinearSet| |#3|) . T) ((|RightModule| |#3|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetric?| #3#) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|square?| #3#) (|sample| (#6=($) NIL T CONST)) (|rowEchelon| (#7=($ $) 46 (|has| |#3| (|EuclideanDomain|)) ELT)) (|row| (((|DirectProduct| |#2| |#3|) $ #8=(|Integer|)) 35 T ELT)) (|reduce| ((|#3| #9=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) NIL #10=(|has| |#3| (|BasicType|)) ELT) ((|#3| #9# $ |#3|) NIL T ELT) ((|#3| #9# $) NIL T ELT)) (|rectangularMatrix| (($ #11=(|Matrix| |#3|)) 44 T ELT)) (|rank| (#12=(#13=(|NonNegativeInteger|) $) 48 #14=(|has| |#3| (|IntegralDomain|)) ELT)) (|qelt| #15=((|#3| $ #8# #8#) NIL T ELT)) (|opposite?| #1#) (|nullity| (#12# 50 #14# ELT)) (|nullSpace| (((|List| #16=(|DirectProduct| |#1| |#3|)) $) 54 #14# ELT)) (|nrows| #17=(#12# NIL T ELT)) (|ncols| #17#) (|minRowIndex| #18=((#8# $) NIL T ELT)) (|minColIndex| #18#) (|members| ((#19=(|List| |#3|) $) NIL T ELT)) (|member?| ((#2# |#3| $) NIL #10# ELT)) (|maxRowIndex| #18#) (|maxColIndex| #18#) (|matrix| (($ #20=(|List| #19#)) 30 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) NIL T ELT) (($ #9# $ $) NIL T ELT)) (|listOfLists| ((#20# $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| (((|Union| |#3| #5#) #21=(|Mapping| #2# |#3|) $) NIL T ELT)) (|exquo| ((#4# $ |#3|) NIL #14# ELT)) (|every?| #22=((#2# #21# $) NIL T ELT)) (|eval| (($ $ #19# #19#) NIL #23=(AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ELT) (($ $ |#3| |#3|) NIL #23# ELT) (($ $ #24=(|Equation| |#3|)) NIL #23# ELT) (($ $ (|List| #24#)) NIL #23# ELT)) (|eq?| #1#) (|empty?| #3#) (|empty| (#6# NIL T ELT)) (|elt| #15# ((|#3| $ #8# #8# |#3|) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 58 #25=(|has| |#3| (|Field|)) ELT)) (|diagonal?| #3#) (|count| ((#13# |#3| $) NIL #10# ELT) ((#13# #21# $) NIL T ELT)) (|copy| #26=(#7# NIL T ELT)) (|convert| ((#27=(|InputForm|) $) 65 (|has| |#3| (|ConvertibleTo| #27#)) ELT)) (|column| ((#16# $ #8#) 39 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) ((#11# $) 41 T ELT)) (|before?| #1#) (|any?| #22#) (|antisymmetric?| #3#) (|Zero| (#6# 15 T CONST)) (= #1#) (/ (#28=($ $ |#3|) NIL #25# ELT)) (- #26# #29=(($ $ $) NIL T ELT)) (+ #29#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #8# . #30=($)) NIL T ELT) (($ |#3| . #30#) NIL T ELT) (#28# NIL T ELT)) (|#| #17#)) 
(((|RectangularMatrix| |#1| |#2| |#3|) (|Join| (|RectangularMatrixCategory| |#1| |#2| |#3| (|DirectProduct| |#2| |#3|) (|DirectProduct| |#1| |#3|)) (|CoercibleTo| #1=(|Matrix| |#3|)) (CATEGORY |domain| (IF (|has| |#3| (|Field|)) (ATTRIBUTE (|VectorSpace| |#3|)) |%noBranch|) (IF (|has| |#3| #2=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE |rectangularMatrix| ($ #1#)))) #3=(|NonNegativeInteger|) #3# (|Ring|)) (T |RectangularMatrix|)) 
((|rectangularMatrix| (*1 *1 *2) (AND (|isDomain| *2 (|Matrix| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *1 (|RectangularMatrix| *3 *4 *5)) (|ofType| *3 #1=(|NonNegativeInteger|)) (|ofType| *4 #1#)))) 
((|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) 36 T ELT)) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) 34 T ELT))) 
(((|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|))) #1=(|NonNegativeInteger|) #1# #2=(|Ring|) (|DirectProductCategory| |#2| |#3|) (|DirectProductCategory| |#1| |#3|) (|RectangularMatrixCategory| |#1| |#2| |#3| |#4| |#5|) #2# (|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)) #1=(|ofCategory| *7 #2=(|Ring|)) (|ofCategory| *2 #2#) #3=(|ofType| *5 #4=(|NonNegativeInteger|)) #5=(|ofType| *6 #4#) #6=(|ofCategory| *8 (|DirectProductCategory| *6 *7)) #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)) #8=(|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)) #1# (|ofCategory| *10 #2#) #3# #5# #6# #7# (|ofCategory| *2 (|RectangularMatrixCategory| *5 *6 *10 *11 *12)) (|isDomain| *1 (|RectangularMatrixCategoryFunctions2| *5 *6 *7 *8 *9 *4 *10 *11 *12 *2)) #8# (|ofCategory| *11 (|DirectProductCategory| *6 *10)) (|ofCategory| *12 (|DirectProductCategory| *5 *10))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ |#1|) 33 T ELT))) 
(((|RightModule| |#1|) (|Category|) (|Rng|)) (T |RightModule|)) 
NIL 
(|Join| (|AbelianGroup|) (|RightLinearSet| |t#1|)) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|RightLinearSet| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|annihilate?| (((|Boolean|) $ $) 10 T ELT))) 
(((|Rng&| |#1|) (CATEGORY |package| (SIGNATURE |annihilate?| ((|Boolean|) |#1| |#1|))) (|Rng|)) (T |Rng&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|Rng|) (|Category|)) (T |Rng|)) 
((|annihilate?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|Rng|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|AbelianGroup|) (|SemiGroup|) (CATEGORY |domain| (SIGNATURE |annihilate?| ((|Boolean|) $ $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=((|Boolean|) $ $) NIL #3=(|has| |#1| (|SetCategory|)) ELT)) (|variable| ((#4=(|Symbol|) $) 11 T ELT)) (|segment| ((|#1| $) 12 T ELT)) (|latex| (((|String|) $) NIL #3# ELT)) (|hash| (((|SingleInteger|) $) NIL #3# ELT)) (|equation| (($ #4# |#1|) 10 T ELT)) (|coerce| (((|OutputForm|) $) 22 #3# ELT)) (|before?| #1#) (= (#2# 17 #3# ELT))) 
(((|RangeBinding| |#1| |#2|) (|Join| #1=(|Type|) (CATEGORY |domain| (SIGNATURE |equation| ($ #2=(|Symbol|) |#1|)) (SIGNATURE |variable| (#2# $)) (SIGNATURE |segment| (|#1| $)) (IF (|has| |#1| #3=(|SetCategory|)) (ATTRIBUTE #3#) |%noBranch|))) (|SegmentCategory| |#2|) #1#) (T |RangeBinding|)) 
((|equation| (*1 *1 *2 *3) (AND #1=(|isDomain| *2 (|Symbol|)) #2=(|ofCategory| *4 #3=(|Type|)) #4=(|isDomain| *1 (|RangeBinding| *3 *4)) #5=(|ofCategory| *3 (|SegmentCategory| *4)))) (|variable| #6=(*1 *2 *1) (AND #2# #1# #4# #5#)) (|segment| #6# (AND (|ofCategory| *2 (|SegmentCategory| *3)) (|isDomain| *1 (|RangeBinding| *2 *3)) (|ofCategory| *3 #3#)))) 
((|truncate| (#1=($ $) 17 T ELT)) (|round| (#1# 25 T ELT)) (|patternMatch| ((#2=(|PatternMatchResult| #3=(|Float|) $) $ #4=(|Pattern| #3#) #2#) 54 T ELT)) (|norm| (#1# 27 T ELT)) (|fractionPart| (#1# 12 T ELT)) (|floor| (#1# 40 T ELT)) (|convert| ((#3# $) NIL T ELT) (((|DoubleFloat|) $) NIL T ELT) ((#4# $) 36 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #5=(($ #6=(|Integer|)) NIL T ELT) (#1# NIL T ELT) #7=(($ (|Fraction| #6#)) 31 T ELT) #5# #7#) (|characteristic| (((|NonNegativeInteger|)) 9 T CONST)) (|ceiling| (#1# 44 T ELT))) 
(((|RealNumberSystem&| |#1|) (CATEGORY |package| (SIGNATURE |round| #1=(|#1| |#1|)) (SIGNATURE |truncate| #1#) (SIGNATURE |fractionPart| #1#) (SIGNATURE |floor| #1#) (SIGNATURE |ceiling| #1#) (SIGNATURE |norm| #1#) (SIGNATURE |patternMatch| (#2=(|PatternMatchResult| #3=(|Float|) |#1|) |#1| #4=(|Pattern| #3#) #2#)) (SIGNATURE |convert| (#4# |#1|)) #5=(SIGNATURE |coerce| (|#1| (|Fraction| #6=(|Integer|)))) #7=(SIGNATURE |coerce| (|#1| #6#)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| (#3# |#1|)) #5# (SIGNATURE |coerce| #1#) (SIGNATURE |characteristic| ((|NonNegativeInteger|)) |constant|) #7# (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|RealNumberSystem|)) (T |RealNumberSystem&|)) 
((|characteristic| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|RealNumberSystem&| *3)) (|ofCategory| *3 (|RealNumberSystem|))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|wholePart| (((|Integer|) $) 108 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|truncate| (($ $) 106 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sqrt| (($ $) 116 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sign| (((|Integer|) $) 133 T ELT)) (|sample| (#5=($) 23 T CONST)) (|round| (($ $) 105 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 121 T ELT) (((|Union| #9=(|Fraction| (|Integer|)) . #7#) . #8#) 118 T ELT)) (|retract| ((#6# . #10=($)) 122 T ELT) ((#9# . #10#) 119 T ELT)) (|rem| (#11=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#11# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #12=(|List| $)) (|:| |generator| $)) #12#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|positive?| (((|Boolean|) $) 131 T ELT)) (|patternMatch| (((|PatternMatchResult| #13=(|Float|) . #14=($)) $ (|Pattern| #13#) (|PatternMatchResult| #13# . #14#)) 112 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #15=(|Integer|)) 115 T ELT)) (|norm| (($ $) 111 T ELT)) (|negative?| (((|Boolean|) $) 132 T ELT)) (|multiEuclidean| (((|Union| #16=(|List| $) #17="failed") #16# $) 68 T ELT)) (|min| (#18=($ $ $) 125 T ELT)) (|max| (#18# 126 T ELT)) (|lcm| (#19=($ $ $) 60 T ELT) (#20=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#21=(|SparseUnivariatePolynomial| $) #21# #21#) 58 T ELT)) (|gcd| (#19# 62 T ELT) (#20# 61 T ELT)) (|fractionPart| (($ $) 107 T ELT)) (|floor| (($ $) 109 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #22=(|:| |coef1| $) #23=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #22# #23#) #17#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #12#) #12# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|convert| (((|Float|) . #24=($)) 124 T ELT) (((|DoubleFloat|) . #24#) 123 T ELT) (((|Pattern| (|Float|)) . #24#) 113 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #25=(|Fraction| #26=(|Integer|))) 84 T ELT) (($ #6#) 120 T ELT) (($ #9#) 117 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|ceiling| (($ $) 110 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| (($ $) 134 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#27=((|Boolean|) $ $) 127 T ELT)) (> (#27# 129 T ELT)) (= (#1# 8 T ELT)) (<= (#27# 128 T ELT)) (< (#27# 130 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #26#) 87 T ELT) (($ $ (|Fraction| #15#)) 114 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #28=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #25#) 86 T ELT) (($ #25# . #28#) 85 T ELT))) 
(((|RealNumberSystem|) (|Category|)) (T |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| #1=(|Integer|)) (|RetractableTo| (|Fraction| #1#)) (|RadicalCategory|) (|ConvertibleTo| (|Pattern| #2=(|Float|))) (|PatternMatchable| #2#) (|CharacteristicZero|) (CATEGORY |domain| (SIGNATURE |norm| #3=($ $)) (SIGNATURE |ceiling| #3#) (SIGNATURE |floor| #3#) (SIGNATURE |wholePart| (#1# $)) (SIGNATURE |fractionPart| #3#) (SIGNATURE |truncate| #3#) (SIGNATURE |round| #3#))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|Pattern| #2=(|Float|))) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PatternMatchable| #2#) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RealConstant|) . T) ((|RetractableTo| (|Fraction| #3=(|Integer|))) . T) ((|RetractableTo| #3#) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# |#2| $) 26 T ELT)) (|size| (#5=(|#1| $) 10 T ELT)) (|sign| (((|Integer|) |#2| $) 119 T ELT)) (|rootOf| (((|Union| $ #6="failed") |#2| (|PositiveInteger|)) 76 T ELT)) (|right| (#5# 31 T ELT)) (|relativeApprox| (#7=(|#1| |#2| $ |#1|) 40 T ELT)) (|refine| (($ $) 28 T ELT)) (|recip| (((|Union| |#2| #6#) |#2| $) 113 T ELT)) (|positive?| #8=(#4# NIL T ELT)) (|negative?| #8#) (|mightHaveRoots| (#4# 27 T ELT)) (|middle| (#5# 120 T ELT)) (|left| (#5# 30 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|definingPolynomial| ((|#2| $) 104 T ELT)) (|coerce| (((|OutputForm|) $) 95 T ELT)) (|before?| #1#) (|approximate| (#7# 41 T ELT)) (|allRootsOf| (((|List| $) |#2|) 78 T ELT)) (= (#2# 99 T ELT))) 
(((|RightOpenIntervalRootCharacterization| |#1| |#2|) (|Join| (|RealRootCharacterizationCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |left| #1=(|#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) #1=(AND (|ofCategory| *2 #2=(|Join| (|OrderedRing|) (|Field|))) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|left| #3=(*1 *2 *1) #1#) (|right| #3# #1#) (|size| #3# #1#) (|middle| #3# #1#) (|refine| (*1 *1 *1) #1#) (|mightHaveRoots| (*1 *2 *3 *1) (AND (|ofCategory| *4 #2#) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #3#) (|symmetricRemainder| #6=(($ $ $) NIL T ELT)) (|subtractIfCan| #7=((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|submod| #10=(($ $ $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #11=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sign| #12=(#13=(#14=(|Integer|) $) NIL T ELT)) (|shift| #6#) (|sample| #15=(#16=($) NIL T CONST)) (|roman| (#17=($ (|Symbol|)) 10 T ELT) (#18=($ #14#) 7 T ELT)) (|retractIfCan| (((|Union| #14# #9#) $) NIL T ELT)) (|retract| #12#) (|rem| #6#) (|reducedSystem| ((#19=(|Record| (|:| |mat| #20=(|Matrix| #14#)) (|:| |vec| (|Vector| #14#))) #21=(|Matrix| $) #22=(|Vector| $)) NIL T ELT) ((#20# #21#) NIL T ELT)) (|recip| ((#8# $) NIL T ELT)) (|rationalIfCan| (((|Union| #23=(|Fraction| #14#) #9#) $) NIL T ELT)) (|rational?| #3#) (|rational| ((#23# $) NIL T ELT)) (|random| #24=(#16# NIL T ELT) #4#) (|quo| #6#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|prime?| #3#) (|powmod| #10#) (|positiveRemainder| #6#) (|positive?| #3#) (|permutation| #6#) (|patternMatch| ((#27=(|PatternMatchResult| #14# $) $ #28=(|Pattern| #14#) #27#) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|odd?| #3#) (|nextItem| (((|Maybe| $) $) NIL T ELT)) (|negative?| #3#) (|multiEuclidean| (((|Union| #25# #9#) #25# $) NIL T ELT)) (|mulmod| #10#) (|min| #6#) (|max| #6#) (|mask| #4#) (|length| #4#) (|leftReducedSystem| ((#19# #22# $) NIL T ELT) ((#20# #22#) NIL T ELT)) (|lcm| #6# #29=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|invmod| #6#) (|init| #15#) (|inc| #4#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#30=(|SparseUnivariatePolynomial| $) #30# #30#) NIL T ELT)) (|gcd| #6# #29#) (|factorial| #4#) (|factor| #11#) (|extendedEuclidean| (((|Union| (|Record| #31=(|:| |coef1| $) #32=(|:| |coef2| $)) #9#) $ $ $) NIL T ELT) (((|Record| #31# #32# #26#) $ $) NIL T ELT)) (|exquo| #7#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|even?| #3#) (|euclideanSize| ((#33=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #4# #34=(($ $ #33#) NIL T ELT)) (|dec| #4#) (|copy| #4#) (|convert| (#13# 16 T ELT) (((|InputForm|) . #35=($)) NIL T ELT) ((#28# . #35#) NIL T ELT) (((|Float|) . #35#) NIL T ELT) (((|DoubleFloat|) . #35#) NIL T ELT) (#17# 9 T ELT)) (|coerce| (((|OutputForm|) $) 23 T ELT) #36=(#18# 6 T ELT) #4# #36#) (|characteristic| ((#33#) NIL T CONST)) (|bit?| #1#) (|binomial| #6#) (|before?| #1#) (|base| #24#) (|associates?| #1#) (|annihilate?| #1#) (|addmod| #10#) (|abs| #4#) (|Zero| #15#) (|One| #15#) (D #4# #34#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (- (#5# 22 T ELT) #6#) (+ #6#) (** (($ $ #37=(|PositiveInteger|)) NIL T ELT) #34#) (* (($ #37# $) NIL T ELT) (($ #33# $) NIL T ELT) #38=(($ #14# $) NIL T ELT) #6# #38#)) 
(((|RomanNumeral|) (|Join| (|IntegerNumberSystem|) (|ConvertibleFrom| #1=(|Symbol|)) (CATEGORY |domain| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|) (SIGNATURE |roman| ($ #1#)) (SIGNATURE |roman| ($ (|Integer|)))))) (T |RomanNumeral|)) 
((|roman| #1=(*1 *1 *2) (AND (|isDomain| *2 (|Symbol|)) #2=(|isDomain| *1 (|RomanNumeral|)))) (|roman| #1# (AND (|isDomain| *2 (|Integer|)) #2#))) 
((|tail| (#1=($ $) 46 T ELT)) (|supRittWu?| (#2=(#3=(|Boolean|) $ $) 82 T ELT)) (|retractIfCan| (((|Union| |#2| #4="failed") $) NIL T ELT) (((|Union| #5=(|Fraction| #6=(|Integer|)) #4#) $) NIL T ELT) (((|Union| #6# #4#) $) NIL T ELT) (((|Union| |#4| #4#) $) NIL T ELT) ((#7=(|Union| $ #4#) #8=(|Polynomial| #5#)) 247 T ELT) ((#7# #9=(|Polynomial| #6#)) 246 T ELT) ((#7# #10=(|Polynomial| |#2|)) 249 T ELT)) (|retract| #11=((|#2| $) NIL T ELT) ((#5# $) NIL T ELT) ((#6# $) NIL T ELT) (#12=(|#4| $) NIL T ELT) (#13=($ #8#) 235 T ELT) (#14=($ #9#) 231 T ELT) (#15=($ #10#) 255 T ELT)) (|reductum| #16=(#1# NIL T ELT) (#17=($ $ |#4|) 44 T ELT)) (|reduced?| (#2# 131 T ELT) (#18=(#3# $ #19=(|List| $)) 135 T ELT)) (|quasiMonic?| (#20=(#3# $) 60 T ELT)) (|pseudoDivide| (((|Record| #21=(|:| |quotient| $) #22=(|:| |remainder| $)) $ $) 125 T ELT)) (|primitivePart!| (#1# 160 T ELT)) (|primPartElseUnitCanonical!| (#1# 156 T ELT)) (|primPartElseUnitCanonical| (#1# 155 T ELT)) (|prem| (#23=($ $ $) 87 T ELT) (#24=($ $ $ |#4|) 92 T ELT)) (|pquo| (#23# 90 T ELT) (#24# 94 T ELT)) (|normalized?| (#2# 143 T ELT) (#18# 144 T ELT)) (|mvar| (#12# 32 T ELT)) (|monicModulo| (#23# 128 T ELT)) (|monic?| (#20# 59 T ELT)) (|mdeg| ((#25=(|NonNegativeInteger|) $) 35 T ELT)) (|mainSquareFreePart| (#1# 174 T ELT)) (|mainPrimitivePart| (#1# 171 T ELT)) (|mainMonomials| (#26=(#19# $) 72 T ELT)) (|mainMonomial| (#1# 62 T ELT)) (|mainContent| (#1# 167 T ELT)) (|mainCoefficients| (#26# 69 T ELT)) (|leastMonomial| (#1# 64 T ELT)) (|leadingCoefficient| #11# (#17# 39 T ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| #25#)) $ $) 130 T ELT)) (|lazyPseudoDivide| ((#27=(|Record| #28=(|:| |coef| $) #29=(|:| |gap| #25#) #21# #22#) $ $) 126 T ELT) ((#27# $ $ |#4|) 127 T ELT)) (|lazyPremWithDefault| ((#30=(|Record| #28# #29# #22#) $ $) 121 T ELT) ((#30# $ $ |#4|) 123 T ELT)) (|lazyPrem| (#23# 97 T ELT) (#24# 106 T ELT)) (|lazyPquo| (#23# 98 T ELT) (#24# 107 T ELT)) (|iteratedInitials| (#26# 54 T ELT)) (|initiallyReduced?| (#2# 140 T ELT) (#18# 141 T ELT)) (|initiallyReduce| (#23# 116 T ELT)) (|init| (#1# 37 T ELT)) (|infRittWu?| (#2# 80 T ELT)) (|headReduced?| (#2# 136 T ELT) (#18# 138 T ELT)) (|headReduce| (#23# 112 T ELT)) (|head| (#1# 41 T ELT)) (|gcd| ((|#2| |#2| $) 164 T ELT) (($ #19#) NIL T ELT) (#23# NIL T ELT)) (|exactQuotient!| (#31=($ $ |#2|) NIL T ELT) (#23# 153 T ELT)) (|exactQuotient| (#31# 148 T ELT) (#23# 151 T ELT)) (|deepestTail| (#1# 49 T ELT)) (|deepestInitial| (#1# 55 T ELT)) (|convert| (((|Pattern| (|Float|)) $) NIL T ELT) (((|Pattern| #6#) $) NIL T ELT) (((|InputForm|) $) NIL T ELT) (#13# 237 T ELT) (#14# 233 T ELT) (#15# 248 T ELT) (((|String|) $) 278 T ELT) (#32=(#10# $) 184 T ELT)) (|coerce| (((|OutputForm|) $) 29 T ELT) (($ #6#) NIL T ELT) (($ |#2|) NIL T ELT) (($ |#4|) NIL T ELT) (#32# 185 T ELT) (($ #5#) NIL T ELT) #16#) (|RittWuCompare| (((|Union| #3# #4#) $ $) 79 T ELT))) 
(((|RecursivePolynomialCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |coerce| #1=(|#1| |#1|)) (SIGNATURE |gcd| #2=(|#1| |#1| |#1|)) (SIGNATURE |gcd| (|#1| #3=(|List| |#1|))) (SIGNATURE |coerce| (|#1| #4=(|Fraction| #5=(|Integer|)))) (SIGNATURE |coerce| #6=(#7=(|Polynomial| |#2|) |#1|)) (SIGNATURE |convert| #6#) (SIGNATURE |convert| ((|String|) |#1|)) (SIGNATURE |mainSquareFreePart| #1#) (SIGNATURE |mainPrimitivePart| #1#) (SIGNATURE |mainContent| #1#) (SIGNATURE |primitivePart!| #1#) (SIGNATURE |gcd| (|#2| |#2| |#1|)) (SIGNATURE |exactQuotient!| #2#) (SIGNATURE |exactQuotient| #2#) (SIGNATURE |exactQuotient!| #8=(|#1| |#1| |#2|)) (SIGNATURE |exactQuotient| #8#) (SIGNATURE |primPartElseUnitCanonical!| #1#) (SIGNATURE |primPartElseUnitCanonical| #1#) (SIGNATURE |convert| #9=(|#1| #7#)) (SIGNATURE |retract| #9#) (SIGNATURE |retractIfCan| (#10=(|Union| |#1| #11="failed") #7#)) (SIGNATURE |convert| #12=(|#1| #13=(|Polynomial| #5#))) (SIGNATURE |retract| #12#) (SIGNATURE |retractIfCan| (#10# #13#)) (SIGNATURE |convert| #14=(|#1| #15=(|Polynomial| #4#))) (SIGNATURE |retract| #14#) (SIGNATURE |retractIfCan| (#10# #15#)) (SIGNATURE |initiallyReduce| #2#) (SIGNATURE |headReduce| #2#) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| |#1|) (|:| |polden| |#1|) (|:| |power| #16=(|NonNegativeInteger|))) |#1| |#1|)) (SIGNATURE |monicModulo| #2#) (SIGNATURE |pseudoDivide| ((|Record| #17=(|:| |quotient| |#1|) #18=(|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |lazyPseudoDivide| (#19=(|Record| #20=(|:| |coef| |#1|) #21=(|:| |gap| #16#) #17# #18#) |#1| |#1| |#4|)) (SIGNATURE |lazyPseudoDivide| (#19# |#1| |#1|)) (SIGNATURE |lazyPremWithDefault| (#22=(|Record| #20# #21# #18#) |#1| |#1| |#4|)) (SIGNATURE |lazyPremWithDefault| (#22# |#1| |#1|)) (SIGNATURE |lazyPquo| #23=(|#1| |#1| |#1| |#4|)) (SIGNATURE |lazyPrem| #23#) (SIGNATURE |lazyPquo| #2#) (SIGNATURE |lazyPrem| #2#) (SIGNATURE |pquo| #23#) (SIGNATURE |prem| #23#) (SIGNATURE |pquo| #2#) (SIGNATURE |prem| #2#) (SIGNATURE |normalized?| #24=(#25=(|Boolean|) |#1| #3#)) (SIGNATURE |normalized?| #26=(#25# |#1| |#1|)) (SIGNATURE |initiallyReduced?| #24#) (SIGNATURE |initiallyReduced?| #26#) (SIGNATURE |headReduced?| #24#) (SIGNATURE |headReduced?| #26#) (SIGNATURE |reduced?| #24#) (SIGNATURE |reduced?| #26#) (SIGNATURE |supRittWu?| #26#) (SIGNATURE |infRittWu?| #26#) (SIGNATURE |RittWuCompare| ((|Union| #25# #11#) |#1| |#1|)) (SIGNATURE |mainMonomials| #27=(#3# |#1|)) (SIGNATURE |mainCoefficients| #27#) (SIGNATURE |leastMonomial| #1#) (SIGNATURE |mainMonomial| #1#) (SIGNATURE |quasiMonic?| #28=(#25# |#1|)) (SIGNATURE |monic?| #28#) (SIGNATURE |reductum| #29=(|#1| |#1| |#4|)) (SIGNATURE |leadingCoefficient| #29#) (SIGNATURE |deepestInitial| #1#) (SIGNATURE |iteratedInitials| #27#) (SIGNATURE |deepestTail| #1#) (SIGNATURE |tail| #1#) (SIGNATURE |head| #1#) (SIGNATURE |init| #1#) (SIGNATURE |mdeg| (#16# |#1|)) (SIGNATURE |mvar| #30=(|#4| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| ((|Pattern| #5#) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |coerce| (|#1| |#4|)) (SIGNATURE |retractIfCan| ((|Union| |#4| #11#) |#1|)) (SIGNATURE |retract| #30#) (SIGNATURE |leadingCoefficient| #31=(|#2| |#1|)) (SIGNATURE |reductum| #1#) (SIGNATURE |retractIfCan| ((|Union| #5# #11#) |#1|)) (SIGNATURE |retract| (#5# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #4# #11#) |#1|)) (SIGNATURE |retract| (#4# |#1|)) (SIGNATURE |retract| #31#) (SIGNATURE |retractIfCan| ((|Union| |#2| #11#) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| #5#)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|RecursivePolynomialCategory| |#2| |#3| |#4|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |RecursivePolynomialCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#3|) $) 124 T ELT)) (|univariate| ((#3=(|SparseUnivariatePolynomial| $) $ |#3|) 139 T ELT) (((|SparseUnivariatePolynomial| |#1|) $) 138 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 101 (|has| |#1| . #4=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 102 (|has| |#1| . #4#) ELT)) (|unit?| ((#5=(|Boolean|) $) 104 (|has| |#1| . #4#) ELT)) (|totalDegree| ((#6=(|NonNegativeInteger|) $) 126 T ELT) ((#6# $ (|List| |#3|)) 125 T ELT)) (|tail| (($ $) 294 T ELT)) (|supRittWu?| (((|Boolean|) $ $) 280 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|subResultantGcd| (($ $ $) 239 (|has| |#1| (|IntegralDomain|)) ELT)) (|subResultantChain| (((|List| $) $ $) 234 (|has| |#1| (|IntegralDomain|)) ELT)) (|squareFreePolynomial| (#7=((|Factored| #8=(|SparseUnivariatePolynomial| $)) #8#) 114 (|has| |#1| . #9=((|PolynomialFactorizationExplicit|))) ELT)) (|squareFreePart| (($ $) 112 (|has| |#1| . #10=((|GcdDomain|))) ELT)) (|squareFree| (#11=((|Factored| $) $) 111 (|has| |#1| . #10#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #12=(|List| #8#) #13="failed") #12# #8#) 117 (|has| |#1| . #9#) ELT)) (|sample| (#14=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| . #15=("failed")) . #16=($)) 182 T ELT) (((|Union| #17=(|Fraction| #18=(|Integer|)) . #15#) . #16#) 179 (|has| |#1| . #19=((|RetractableTo| #17#))) ELT) (((|Union| #18# . #15#) . #16#) 177 (|has| |#1| . #20=((|RetractableTo| #18#))) ELT) (((|Union| |#3| . #15#) . #16#) 154 T ELT) (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) 254 (AND (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) ELT) (((|Union| $ "failed") (|Polynomial| (|Integer|))) 251 (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|))))) ELT) (((|Union| $ "failed") (|Polynomial| |#1|)) 248 (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|))))) ELT)) (|retract| ((|#1| . #21=($)) 181 T ELT) ((#17# . #21#) 180 (|has| |#1| . #19#) ELT) ((#18# . #21#) 178 (|has| |#1| . #20#) ELT) ((|#3| . #21#) 155 T ELT) (($ (|Polynomial| (|Fraction| (|Integer|)))) 253 (AND (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) ELT) (($ (|Polynomial| (|Integer|))) 250 (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|))))) ELT) (($ (|Polynomial| |#1|)) 247 (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|))))) ELT)) (|resultant| (($ $ $ |#3|) 122 (|has| |#1| . #22=((|CommutativeRing|))) ELT) (($ $ $) 235 (|has| |#1| (|IntegralDomain|)) ELT)) (|reductum| (#23=($ $) 172 T ELT) (($ $ |#3|) 289 T ELT)) (|reducedSystem| (((|Matrix| #24=(|Integer|)) . #25=(#26=(|Matrix| $))) 150 (|has| |#1| . #27=((|LinearlyExplicitRingOver| #24#))) ELT) (((|Record| (|:| |mat| (|Matrix| #24#)) (|:| |vec| (|Vector| #24#))) . #28=(#26# #29=(|Vector| $))) 149 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #28#) 148 T ELT) (((|Matrix| |#1|) . #25#) 147 T ELT)) (|reduced?| (((|Boolean|) $ $) 279 T ELT) (((|Boolean|) $ (|List| $)) 278 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quasiMonic?| (((|Boolean|) $) 287 T ELT)) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 259 T ELT)) (|primitivePart!| (($ $) 228 (|has| |#1| (|GcdDomain|)) ELT)) (|primitivePart| (($ $) 194 (|has| |#1| . #30=((|GcdDomain|))) ELT) (($ $ |#3|) 119 (|has| |#1| . #10#) ELT)) (|primitiveMonomials| (#31=(#32=(|List| $) $) 123 T ELT)) (|prime?| (((|Boolean|) $) 110 (|has| |#1| . #9#) ELT)) (|primPartElseUnitCanonical!| (($ $) 244 (|has| |#1| (|IntegralDomain|)) ELT)) (|primPartElseUnitCanonical| (($ $) 245 (|has| |#1| (|IntegralDomain|)) ELT)) (|prem| (($ $ $) 271 T ELT) (($ $ $ |#3|) 269 T ELT)) (|pquo| (($ $ $) 270 T ELT) (($ $ $ |#3|) 268 T ELT)) (|pomopo!| (($ $ |#1| |#2| $) 190 T ELT)) (|patternMatch| (((|PatternMatchResult| #33=(|Float|) . #34=($)) $ (|Pattern| #33#) (|PatternMatchResult| #33# . #34#)) 98 (AND (|has| |#3| #35=(|PatternMatchable| #33#)) (|has| |#1| #35#)) ELT) (((|PatternMatchResult| #36=(|Integer|) . #34#) $ (|Pattern| #36#) (|PatternMatchResult| #36# . #34#)) 97 (AND (|has| |#3| #37=(|PatternMatchable| #36#)) (|has| |#1| #37#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numberOfMonomials| ((#38=(|NonNegativeInteger|) $) 187 T ELT)) (|normalized?| (((|Boolean|) $ $) 273 T ELT) (((|Boolean|) $ (|List| $)) 272 T ELT)) (|nextsubResultant2| (($ $ $ $ $) 230 (|has| |#1| (|IntegralDomain|)) ELT)) (|mvar| ((|#3| $) 298 T ELT)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) |#3|) 131 T ELT) (($ #3# |#3|) 130 T ELT)) (|monomials| (#31# 140 T ELT)) (|monomial?| (((|Boolean|) $) 170 T ELT)) (|monomial| (($ |#1| |#2|) 171 T ELT) (($ $ |#3| . #39=(#6#)) 133 T ELT) (($ $ (|List| |#3|) . #40=(#41=(|List| #6#))) 132 T ELT)) (|monicModulo| (($ $ $) 258 T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) 134 T ELT)) (|monic?| (((|Boolean|) $) 288 T ELT)) (|minimumDegree| ((|#2| $) 188 T ELT) ((#6# $ |#3|) 136 T ELT) ((#41# $ (|List| |#3|)) 135 T ELT)) (|mdeg| (((|NonNegativeInteger|) $) 297 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) 189 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 166 T ELT)) (|mainVariable| (((|Union| |#3| #42="failed") $) 137 T ELT)) (|mainSquareFreePart| (($ $) 225 (|has| |#1| (|GcdDomain|)) ELT)) (|mainPrimitivePart| (($ $) 226 (|has| |#1| (|GcdDomain|)) ELT)) (|mainMonomials| (((|List| $) $) 283 T ELT)) (|mainMonomial| (($ $) 286 T ELT)) (|mainContent| (($ $) 227 (|has| |#1| (|GcdDomain|)) ELT)) (|mainCoefficients| (((|List| $) $) 284 T ELT)) (|leftReducedSystem| (((|Matrix| #24#) . #43=(#29#)) 152 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| #24#)) (|:| |vec| (|Vector| #24#))) . #44=(#29# $)) 151 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #44#) 146 T ELT) (((|Matrix| |#1|) . #43#) 145 T ELT)) (|leastMonomial| (($ $) 285 T ELT)) (|leadingMonomial| (#23# 168 T ELT)) (|leadingCoefficient| ((|#1| $) 167 T ELT) (($ $ |#3|) 290 T ELT)) (|lcm| (#45=($ (|List| $)) 108 (|has| |#1| . #10#) ELT) (#46=($ $ $) 107 (|has| |#1| . #10#) ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) 257 T ELT)) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) 261 T ELT) (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) 260 T ELT)) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) 263 T ELT) (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) 262 T ELT)) (|lazyPrem| (($ $ $) 267 T ELT) (($ $ $ |#3|) 265 T ELT)) (|lazyPquo| (($ $ $) 266 T ELT) (($ $ $ |#3|) 264 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultant| (($ $ $) 233 (|has| |#1| (|IntegralDomain|)) ELT)) (|iteratedInitials| (((|List| $) $) 292 T ELT)) (|isTimes| (#47=((|Union| #32# #42#) $) 128 T ELT)) (|isPlus| (#47# 129 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| #6#)) #42#) $) 127 T ELT)) (|initiallyReduced?| (((|Boolean|) $ $) 275 T ELT) (((|Boolean|) $ (|List| $)) 274 T ELT)) (|initiallyReduce| (($ $ $) 255 T ELT)) (|init| (($ $) 296 T ELT)) (|infRittWu?| (((|Boolean|) $ $) 281 T ELT)) (|headReduced?| (((|Boolean|) $ $) 277 T ELT) (((|Boolean|) $ (|List| $)) 276 T ELT)) (|headReduce| (($ $ $) 256 T ELT)) (|head| (($ $) 295 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) 236 (|has| |#1| (|IntegralDomain|)) ELT)) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) 237 (|has| |#1| (|IntegralDomain|)) ELT)) (|ground?| (((|Boolean|) $) 184 T ELT)) (|ground| ((|#1| . #48=($)) 185 T ELT)) (|gcdPolynomial| ((#49=(|SparseUnivariatePolynomial| $) #49# #49#) 109 (|has| |#1| . #10#) ELT)) (|gcd| ((|#1| |#1| $) 229 (|has| |#1| (|GcdDomain|)) ELT) (#45# 106 (|has| |#1| . #10#) ELT) (#46# 105 (|has| |#1| . #10#) ELT)) (|factorSquareFreePolynomial| (#7# 116 (|has| |#1| . #9#) ELT)) (|factorPolynomial| (#7# 115 (|has| |#1| . #9#) ELT)) (|factor| (#11# 113 (|has| |#1| . #9#) ELT)) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) 238 (|has| |#1| (|IntegralDomain|)) ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 192 (|has| |#1| (|IntegralDomain|)) ELT) (((|Union| $ "failed") $ $) 100 (|has| |#1| . #4#) ELT)) (|exactQuotient!| (($ $ |#1|) 242 (|has| |#1| (|IntegralDomain|)) ELT) (($ $ $) 240 (|has| |#1| (|IntegralDomain|)) ELT)) (|exactQuotient| (($ $ |#1|) 243 (|has| |#1| (|IntegralDomain|)) ELT) (($ $ $) 241 (|has| |#1| (|IntegralDomain|)) ELT)) (|eval| (($ $ (|List| (|Equation| $))) 163 T ELT) (($ $ (|Equation| $)) 162 T ELT) (($ $ $ $) 161 T ELT) (($ $ (|List| $) (|List| $)) 160 T ELT) (($ $ |#3| |#1|) 159 T ELT) (($ $ (|List| |#3|) (|List| |#1|)) 158 T ELT) (($ $ |#3| $) 157 T ELT) (($ $ (|List| |#3|) (|List| $)) 156 T ELT)) (|discriminant| (($ $ |#3|) 121 (|has| |#1| . #22#) ELT)) (|differentiate| (($ $ (|List| |#3|) . #50=((|List| #51=(|NonNegativeInteger|)))) 52 T ELT) (($ $ |#3| . #52=(#51#)) 51 T ELT) (($ $ (|List| |#3|)) 50 T ELT) (($ $ |#3|) 48 T ELT)) (|degree| ((|#2| $) 169 T ELT) ((#6# $ |#3|) 144 T ELT) ((#41# $ (|List| |#3|)) 143 T ELT)) (|deepestTail| (($ $) 293 T ELT)) (|deepestInitial| (($ $) 291 T ELT)) (|convert| ((#53=(|Pattern| #33#) . #54=($)) 96 (AND (|has| |#3| #55=(|ConvertibleTo| #53#)) (|has| |#1| #55#)) ELT) ((#56=(|Pattern| #36#) . #54#) 95 (AND (|has| |#3| #57=(|ConvertibleTo| #56#)) (|has| |#1| #57#)) ELT) ((#58=(|InputForm|) . #54#) 94 (AND (|has| |#3| #59=(|ConvertibleTo| #58#)) (|has| |#1| #59#)) ELT) (($ (|Polynomial| (|Fraction| (|Integer|)))) 252 (AND (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) ELT) (($ (|Polynomial| (|Integer|))) 249 (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|))))) ELT) (($ (|Polynomial| |#1|)) 246 (|has| |#3| (|ConvertibleTo| (|Symbol|))) ELT) (((|String|) . #54#) 224 (AND (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) ELT) (((|Polynomial| |#1|) . #54#) 223 (|has| |#3| (|ConvertibleTo| (|Symbol|))) ELT)) (|content| ((|#1| . #48#) 193 (|has| |#1| . #30#) ELT) (($ $ |#3|) 120 (|has| |#1| . #10#) ELT)) (|conditionP| (((|Union| (|Vector| $) #13#) (|Matrix| $)) 118 (|and| #60=(|has| $ (|CharacteristicNonZero|)) (|has| |#1| . #9#)) ELT)) (|coerce| (((|OutputForm|) . #61=($)) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 183 T ELT) (($ |#3|) 153 T ELT) (((|Polynomial| |#1|) . #61#) 222 (|has| |#3| (|ConvertibleTo| (|Symbol|))) ELT) (($ #62=(|Fraction| (|Integer|))) 92 (OR (|has| |#1| . #19#) (|has| |#1| . #63=((|Algebra| #62#)))) ELT) (($ $) 99 (|has| |#1| . #4#) ELT)) (|coefficients| (((|List| |#1|) $) 186 T ELT)) (|coefficient| ((|#1| $ |#2|) 173 T ELT) (($ $ |#3| . #39#) 142 T ELT) (($ $ (|List| |#3|) . #40#) 141 T ELT)) (|charthRoot| (((|Maybe| $) $) 93 (OR (|and| #60# (|has| |#1| . #9#)) (|has| |#1| (|CharacteristicNonZero|))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|binomThmExpt| (($ $ $ #38#) 191 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#5# $ $) 103 (|has| |#1| . #4#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#14# 24 T CONST)) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) 282 T ELT)) (|One| (($) 45 T CONST)) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) 231 (|has| |#1| (|IntegralDomain|)) ELT)) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) 232 (|has| |#1| (|IntegralDomain|)) ELT)) (D (($ $ (|List| |#3|) . #50#) 55 T ELT) (($ $ |#3| . #52#) 54 T ELT) (($ $ (|List| |#3|)) 53 T ELT) (($ $ |#3|) 49 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 174 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #64=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #62#) 176 (|has| |#1| . #63#) ELT) (($ #62# . #64#) 175 (|has| |#1| . #63#) ELT) (($ |#1| . #64#) 165 T ELT) (($ $ |#1|) 164 T ELT))) 
(((|RecursivePolynomialCategory| |#1| |#2| |#3|) (|Category|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |RecursivePolynomialCategory|)) 
((|mvar| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|mdeg| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|init| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|head| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|tail| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|deepestTail| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|iteratedInitials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|deepestInitial| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|leadingCoefficient| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|reductum| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|monic?| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|quasiMonic?| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|mainMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|leastMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|mainCoefficients| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|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 #1=(|isDomain| *2 (|Polynomial| (|Integer|))) #2=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #3=((|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #1# #2# (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #3#))) (|retract| (*1 *1 *2) (OR (AND #4=(|isDomain| *2 (|Polynomial| (|Integer|))) #5=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #6=((|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #4# #5# (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #6#))) (|convert| (*1 *1 *2) (OR (AND #7=(|isDomain| *2 (|Polynomial| (|Integer|))) #8=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #9=((|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #7# #8# (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #9#))) (|retractIfCan| (*1 *1 *2) (|partial| OR (AND #10=(|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|not| (|ofCategory| *3 (|Algebra| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #11=((|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #10# (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|))) (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #11#) (AND #10# (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|)))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #11#))) (|retract| (*1 *1 *2) (OR (AND #12=(|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|not| (|ofCategory| *3 (|Algebra| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #13=((|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #12# (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|))) (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #13#) (AND #12# (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|)))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #13#))) (|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| #1=(|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| #1# #1#) |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|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| |#3|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|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) ((|Functorial| |#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|))) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#3|) . T) ((|PartialDifferentialRing| |#3|) . T) ((|PartialDifferentialSpace| |#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) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |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) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|iterators| (((|List| #2=(|SpadAst|)) $) 18 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 27 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|body| ((#2# $) 20 T ELT)) (|before?| #1#) (= #1#)) 
(((|RepeatAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |iterators| ((|List| #1=(|SpadAst|)) $)) (SIGNATURE |body| (#1# $))))) (T |RepeatAst|)) 
((|iterators| #1=(*1 *2 *1) (AND (|isDomain| *2 (|List| #2=(|SpadAst|))) #3=(|isDomain| *1 (|RepeatAst|)))) (|body| #1# (AND (|isDomain| *2 #2#) #3#))) 
((|zero?| (#1=((|Boolean|) |#3| $) 15 T ELT)) (|rootOf| (((|Union| $ #2="failed") |#3| (|PositiveInteger|)) 29 T ELT)) (|recip| (((|Union| |#3| #2#) |#3| $) 45 T ELT)) (|positive?| (#1# 19 T ELT)) (|negative?| (#1# 17 T ELT))) 
(((|RealRootCharacterizationCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |rootOf| ((|Union| |#1| #1="failed") |#3| (|PositiveInteger|))) (SIGNATURE |recip| ((|Union| |#3| #1#) |#3| |#1|)) (SIGNATURE |positive?| #2=((|Boolean|) |#3| |#1|)) (SIGNATURE |negative?| #2#) (SIGNATURE |zero?| #2#)) (|RealRootCharacterizationCategory| |#2| |#3|) (|Join| (|OrderedRing|) (|Field|)) (|UnivariatePolynomialCategory| |#2|)) (T |RealRootCharacterizationCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| (((|Boolean|) |#2| $) 25 T ELT)) (|sign| (((|Integer|) |#2| $) 26 T ELT)) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) 19 T ELT)) (|relativeApprox| ((|#1| |#2| $ |#1|) 17 T ELT)) (|recip| (((|Union| |#2| "failed") |#2| $) 22 T ELT)) (|positive?| (((|Boolean|) |#2| $) 23 T ELT)) (|negative?| (((|Boolean|) |#2| $) 24 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|definingPolynomial| ((|#2| $) 21 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|approximate| ((|#1| |#2| $ |#1|) 18 T ELT)) (|allRootsOf| (((|List| $) |#2|) 20 T ELT)) (= (#1# 8 T ELT))) 
(((|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) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|upDateBranches| ((#1=(|List| #2=(|Record| (|:| |val| #3=(|List| |#4|)) (|:| |tower| |#5|))) #3# #4=(|List| |#5|) #1# #5=(|Record| (|:| |done| #4#) (|:| |todo| #1#)) #6=(|NonNegativeInteger|)) 114 T ELT)) (|transcendentalDecompose| (#7=(#5# |#4| |#5|) 64 T ELT) (#8=(#5# |#4| |#5| #6#) 63 T ELT)) (|printInfo| (((|Void|) #1# #6#) 99 T ELT)) (|numberOfVariables| (#9=(#6# #3# #4#) 30 T ELT)) (|internalDecompose| (#7# 66 T ELT) (#8# 65 T ELT) ((#5# |#4| |#5| #6# #10=(|Boolean|)) 67 T ELT)) (|decompose| ((#4# #3# #4# #10# #10# #10# #10# #10#) 86 T ELT) ((#4# #3# #4# #10# #10#) 87 T ELT)) (|convert| (((|String|) #2#) 92 T ELT)) (|algebraicDecompose| ((#5# |#4| |#5| #10#) 62 T ELT)) (|KrullNumber| (#9# 21 T ELT))) 
(((|RegularSetDecompositionPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |KrullNumber| #1=(#2=(|NonNegativeInteger|) #3=(|List| |#4|) #4=(|List| |#5|))) (SIGNATURE |numberOfVariables| #1#) (SIGNATURE |algebraicDecompose| (#5=(|Record| (|:| |done| #4#) (|:| |todo| #6=(|List| #7=(|Record| (|:| |val| #3#) (|:| |tower| |#5|))))) |#4| |#5| #8=(|Boolean|))) (SIGNATURE |transcendentalDecompose| #9=(#5# |#4| |#5| #2#)) (SIGNATURE |transcendentalDecompose| #10=(#5# |#4| |#5|)) (SIGNATURE |internalDecompose| (#5# |#4| |#5| #2# #8#)) (SIGNATURE |internalDecompose| #9#) (SIGNATURE |internalDecompose| #10#) (SIGNATURE |decompose| (#4# #3# #4# #8# #8#)) (SIGNATURE |decompose| (#4# #3# #4# #8# #8# #8# #8# #8#)) (SIGNATURE |upDateBranches| (#6# #3# #4# #6# #5# #2#)) (SIGNATURE |convert| ((|String|) #7#)) (SIGNATURE |printInfo| ((|Void|) #6# #2#))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |RegularSetDecompositionPackage|)) 
((|printInfo| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| #2=(|List| *8)) (|:| |tower| *9)))) (|isDomain| *4 #3=(|NonNegativeInteger|)) #4=(|ofCategory| *8 #5=(|RecursivePolynomialCategory| *5 *6 *7)) #6=(|ofCategory| *9 (|RegularTriangularSetCategory| *5 *6 *7 *8)) #7=(|ofCategory| *5 #8=(|GcdDomain|)) #9=(|ofCategory| *6 #10=(|OrderedAbelianMonoidSup|)) #11=(|ofCategory| *7 #12=(|OrderedSet|)) (|isDomain| *2 (|Void|)) #13=(|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 #8#) (|ofCategory| *5 #10#) (|ofCategory| *6 #12#) (|isDomain| *2 (|String|)) (|isDomain| *1 (|RegularSetDecompositionPackage| *4 *5 *6 *7 *8)))) (|upDateBranches| (*1 *2 *3 *4 *2 *5 *6) (AND (|isDomain| *5 (|Record| (|:| |done| #14=(|List| *11)) (|:| |todo| (|List| (|Record| (|:| |val| *3) #15=(|:| |tower| *11)))))) (|isDomain| *6 #3#) (|isDomain| *2 (|List| (|Record| (|:| |val| #16=(|List| *10)) #15#))) (|isDomain| *3 #16#) (|isDomain| *4 #14#) (|ofCategory| *10 #17=(|RecursivePolynomialCategory| *7 *8 *9)) (|ofCategory| *11 (|RegularTriangularSetCategory| *7 *8 *9 *10)) #18=(|ofCategory| *7 #8#) #19=(|ofCategory| *8 #10#) #20=(|ofCategory| *9 #12#) (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *10 *11)))) (|decompose| (*1 *2 *3 *2 *4 *4 *4 *4 *4) #21=(AND (|isDomain| *2 #22=(|List| *9)) #23=(|isDomain| *3 #2#) (|isDomain| *4 #24=(|Boolean|)) #4# #6# #7# #9# #11# #13#)) (|decompose| (*1 *2 *3 *2 *4 *4) #21#) (|internalDecompose| #1# #25=(AND #7# #9# #11# (|ofCategory| *3 #5#) #26=(|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| #27=(*1 *2 *3 *4 *5) #28=(AND #29=(|isDomain| *5 #3#) #30=(|ofCategory| *6 #8#) #31=(|ofCategory| *7 #10#) #32=(|ofCategory| *8 #12#) #33=(|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) #26# #34=(|isDomain| *1 (|RegularSetDecompositionPackage| *6 *7 *8 *3 *4)) #35=(|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|internalDecompose| (*1 *2 *3 *4 *5 *6) (AND #29# (|isDomain| *6 #24#) #18# #19# #20# (|ofCategory| *3 #17#) #26# (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *7 *8 *9 *3)))) (|transcendentalDecompose| #1# #25#) (|transcendentalDecompose| #27# #28#) (|algebraicDecompose| #27# (AND (|isDomain| *5 #24#) #30# #31# #32# #33# #26# #34# #35#)) (|numberOfVariables| #1# #36=(AND #23# (|isDomain| *4 #22#) #4# #6# #7# #9# #11# (|isDomain| *2 #3#) #13#)) (|KrullNumber| #1# #36#)) 
((|purelyTranscendental?| (#1=(#2=(|Boolean|) |#5| $) 26 T ELT)) (|purelyAlgebraicLeadingMonomial?| (#1# 29 T ELT)) (|purelyAlgebraic?| (#1# 18 T ELT) ((#2# $) 52 T ELT)) (|intersect| #3=((#4=(|List| $) |#5| $) NIL T ELT) (#5=(#4# #6=(|List| |#5|) $) 94 T ELT) (#7=(#4# #6# #4#) 92 T ELT) (#8=(#4# |#5| #4#) 95 T ELT)) (|extend| (($ $ |#5|) NIL T ELT) #3# (#8# 73 T ELT) (#5# 75 T ELT) (#7# 77 T ELT)) (|augment| #3# (#8# 64 T ELT) (#5# 69 T ELT) (#7# 71 T ELT)) (|algebraicCoefficients?| (#1# 32 T ELT))) 
(((|RegularTriangularSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |extend| #1=(#2=(|List| |#1|) #3=(|List| |#5|) #2#)) (SIGNATURE |extend| #4=(#2# #3# |#1|)) (SIGNATURE |extend| #5=(#2# |#5| #2#)) (SIGNATURE |extend| #6=(#2# |#5| |#1|)) (SIGNATURE |augment| #1#) (SIGNATURE |augment| #4#) (SIGNATURE |augment| #5#) (SIGNATURE |augment| #6#) (SIGNATURE |intersect| #5#) (SIGNATURE |intersect| #1#) (SIGNATURE |intersect| #4#) (SIGNATURE |intersect| #6#) (SIGNATURE |purelyAlgebraicLeadingMonomial?| #7=(#8=(|Boolean|) |#5| |#1|)) (SIGNATURE |purelyAlgebraic?| (#8# |#1|)) (SIGNATURE |algebraicCoefficients?| #7#) (SIGNATURE |purelyTranscendental?| #7#) (SIGNATURE |purelyAlgebraic?| #7#) (SIGNATURE |extend| (|#1| |#1| |#5|))) (|RegularTriangularSetCategory| |#2| |#3| |#4| |#5|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |RegularTriangularSetCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) (((|List| $) (|List| |#4|) (|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #2=($)) 39 T ELT)) (|trivialIdeal?| (#3=(#4=(|Boolean|) $) 32 T ELT)) (|triangular?| (#3# 23 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#6=(|Boolean|) |#4| . #7=($)) 107 T ELT) (#8=(#6# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #9=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #10=(|Boolean|) |#4|) . #11=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #12=(#13="failed")) $ |#3|) 85 T ELT)) (|sample| (#14=($) 59 T CONST)) (|roughUnitIdeal?| (#3# 28 (|has| |#1| . #5#) ELT)) (|roughSubIdeal?| (#15=(#4# $ $) 30 (|has| |#1| . #5#) ELT)) (|roughEqualIdeals?| (#15# 29 (|has| |#1| . #5#) ELT)) (|roughBase?| (#3# 31 (|has| |#1| . #5#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #6# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #16=($)) 24 (|has| |#1| . #5#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #16#) 25 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| ((#17=(|Union| $ #13#) $) 88 T ELT)) (|removeZero| ((|#4| |#4| . #9#) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #18=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #18#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #10# |#4|) . #11#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #5#) ELT)) (|reduced?| ((#6# |#4| $ (|Mapping| #6# |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| . #9#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #19=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #6# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| (((|Boolean|) |#4| $) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) 142 T ELT)) (|purelyAlgebraic?| (((|Boolean|) |#4| $) 146 T ELT) (((|Boolean|) $) 143 T ELT)) (|normalized?| ((#6# |#4| . #7#) 110 T ELT) (#8# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#20=(|Boolean|) |#4| $) 53 (|has| |#4| . #19#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #2#) 38 T ELT)) (|mainVariable?| ((#4# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) 136 T ELT)) (|last| (((|Union| |#4| . #12#) . #21=($)) 89 T ELT)) (|invertibleSet| (((|List| $) |#4| $) 138 T ELT)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) 140 T ELT) (((|Boolean|) |#4| $) 139 T ELT)) (|intersect| (((|List| $) |#4| $) 134 T ELT) (((|List| $) (|List| |#4|) $) 133 T ELT) (((|List| $) (|List| |#4|) (|List| $)) 132 T ELT) (((|List| $) |#4| (|List| $)) 131 T ELT)) (|internalAugment| (($ |#4| $) 126 T ELT) (($ (|List| |#4|) $) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#6# |#4| . #7#) 105 T ELT) (#8# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #9#) 96 T ELT)) (|infRittWu?| ((#6# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #5#) ELT)) (|headReduced?| ((#6# |#4| . #7#) 106 T ELT) (#8# 102 T ELT)) (|headReduce| ((|#4| |#4| . #9#) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| . #12#) . #21#) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #20# |#4|) $) 51 T ELT)) (|extendIfCan| ((#17# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) (((|List| $) |#4| $) 124 T ELT) (((|List| $) |#4| (|List| $)) 123 T ELT) (((|List| $) (|List| |#4|) $) 122 T ELT) (((|List| $) (|List| |#4|) (|List| $)) 121 T ELT)) (|every?| ((#20# (|Mapping| #20# |#4|) . #22=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23#)) ELT)) (|eq?| ((#24=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#24# $) 58 T ELT)) (|empty| (#14# 57 T ELT)) (|degree| (#25=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#26=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #19#) ELT) ((#26# (|Mapping| #20# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#27=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #27#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #28=($)) 13 T ELT) (((|List| |#4|) . #28#) 43 T ELT)) (|coHeight| (#25# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #29=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #30=(#13#)) (|List| |#4|) (|Mapping| #6# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #29# (|:| |top| (|List| |#4|))) . #30#) (|List| |#4|) (|Mapping| #6# |#4|) (|Mapping| #6# |#4| |#4|)) 114 T ELT)) (|autoReduced?| ((#6# $ (|Mapping| #6# |#4| (|List| |#4|))) 104 T ELT)) (|augment| (((|List| $) |#4| $) 130 T ELT) (((|List| $) |#4| (|List| $)) 129 T ELT) (((|List| $) (|List| |#4|) $) 128 T ELT) (((|List| $) (|List| |#4|) (|List| $)) 127 T ELT)) (|any?| ((#20# (|Mapping| #20# |#4|) . #22#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) 144 T ELT)) (|algebraic?| ((#6# |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#26# $) 44 T ELT))) 
(((|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|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) 
((|toseSquareFreePart| ((#1=(|List| (|Record| (|:| |val| |#4|) #2=(|:| |tower| |#5|))) |#4| |#5|) 86 T ELT)) (|toseLastSubResultant| (#3=(#1# |#4| |#4| |#5|) 125 T ELT)) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) 74 T ELT)) (|toseInvertible?| (((|List| (|Record| (|:| |val| #4=(|Boolean|)) #2#)) |#4| |#5|) 47 T ELT) ((#4# |#4| |#5|) 55 T ELT)) (|stopTableInvSet!| (#5=(#6=(|Void|)) 36 T ELT)) (|stopTableGcd!| (#5# 25 T ELT)) (|startTableInvSet!| (#7=(#6# #8=(|String|) #8# #8#) 32 T ELT)) (|startTableGcd!| (#7# 21 T ELT)) (|prepareSubResAlgo| ((#9=(|List| (|Record| (|:| |val| (|List| |#4|)) #2#)) |#4| |#4| |#5|) 106 T ELT)) (|internalLastSubResultant| ((#1# #9# |#3| #4#) 117 T ELT) ((#1# |#4| |#4| |#5| #4# #4#) 52 T ELT)) (|integralLastSubResultant| (#3# 112 T ELT))) 
(((|RegularTriangularSetGcdPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTableGcd!| #1=(#2=(|Void|) #3=(|String|) #3# #3#)) (SIGNATURE |stopTableGcd!| #4=(#2#)) (SIGNATURE |startTableInvSet!| #1#) (SIGNATURE |stopTableInvSet!| #4#) (SIGNATURE |prepareSubResAlgo| (#5=(|List| (|Record| (|:| |val| (|List| |#4|)) #6=(|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |internalLastSubResultant| (#7=(|List| (|Record| (|:| |val| |#4|) #6#)) |#4| |#4| |#5| #8=(|Boolean|) #8#)) (SIGNATURE |internalLastSubResultant| (#7# #5# |#3| #8#)) (SIGNATURE |integralLastSubResultant| #9=(#7# |#4| |#4| |#5|)) (SIGNATURE |toseLastSubResultant| #9#) (SIGNATURE |toseInvertible?| (#8# |#4| |#5|)) (SIGNATURE |toseInvertible?| ((|List| (|Record| (|:| |val| #8#) #6#)) |#4| |#5|)) (SIGNATURE |toseInvertibleSet| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |toseSquareFreePart| (#7# |#4| |#5|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |RegularTriangularSetGcdPackage|)) 
((|toseSquareFreePart| #1=(*1 *2 *3 *4) #2=(AND #3=(|ofCategory| *5 #4=(|GcdDomain|)) #5=(|ofCategory| *6 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *7 #8=(|OrderedSet|)) #9=(|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) #10=(|isDomain| *2 (|List| (|Record| (|:| |val| *3) #11=(|:| |tower| *4)))) #12=(|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) #13=(|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|toseInvertibleSet| #1# (AND #3# #5# #7# #9# (|isDomain| *2 (|List| *4)) #12# #13#)) (|toseInvertible?| #1# (AND #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| (|:| |val| #14=(|Boolean|)) #11#))) #12# #13#)) (|toseInvertible?| #1# (AND #3# #5# #7# #9# (|isDomain| *2 #14#) #12# #13#)) (|toseLastSubResultant| #15=(*1 *2 *3 *3 *4) #2#) (|integralLastSubResultant| #15# #2#) (|internalLastSubResultant| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) #16=(|:| |tower| *9)))) #17=(|isDomain| *5 #14#) (|ofCategory| *8 (|RecursivePolynomialCategory| *6 *7 *4)) (|ofCategory| *9 (|RegularTriangularSetCategory| *6 *7 *4 *8)) #18=(|ofCategory| *6 #4#) #19=(|ofCategory| *7 #6#) (|ofCategory| *4 #8#) (|isDomain| *2 (|List| (|Record| (|:| |val| *8) #16#))) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *6 *7 *4 *8 *9)))) (|internalLastSubResultant| (*1 *2 *3 *3 *4 *5 *5) (AND #17# #18# #19# (|ofCategory| *8 #8#) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) #10# (|isDomain| *1 (|RegularTriangularSetGcdPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|prepareSubResAlgo| #15# (AND #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *3)) #11#))) #12# #13#)) (|stopTableInvSet!| #20=(*1 *2) #21=(AND (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) #22=(|isDomain| *2 (|Void|)) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTableInvSet!| #23=(*1 *2 *3 *3 *3) #24=(AND (|isDomain| *3 (|String|)) (|ofCategory| *4 #4#) (|ofCategory| *5 #6#) (|ofCategory| *6 #8#) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) #22# (|isDomain| *1 (|RegularTriangularSetGcdPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|stopTableGcd!| #20# #21#) (|startTableGcd!| #23# #24#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|target| (((|TypeAst|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|RestrictAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |expression| ((|SpadAst|) $)) (SIGNATURE |target| ((|TypeAst|) $))))) (T |RestrictAst|)) 
((|expression| #1=(*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) #2=(|isDomain| *1 (|RestrictAst|)))) (|target| #1# (AND (|isDomain| *2 (|TypeAst|)) #2#))) 
((|eq| (((|Boolean|) $ $) 7 T ELT))) 
(((|RuntimeValue|) (|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |eq| ((|Boolean|) $ $))))) (T |RuntimeValue|)) 
((|eq| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RuntimeValue|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|suchThat| (($ $ #4=(|List| (|Symbol|)) (|Mapping| #3# (|List| |#3|))) 34 T ELT)) (|rule| (($ |#3| |#3|) 23 T ELT) (($ |#3| |#3| #4#) 21 T ELT)) (|rhs| (#5=(|#3| $) 13 T ELT)) (|retractIfCan| (((|Union| #6=(|Equation| |#3|) "failed") $) 60 T ELT)) (|retract| ((#6# $) NIL T ELT)) (|quotedOperators| ((#4# $) 16 T ELT)) (|pattern| (((|Pattern| |#1|) $) 11 T ELT)) (|lhs| (#5# 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#3| $ |#3|) 28 T ELT) ((|#3| $ |#3| (|PositiveInteger|)) 41 T ELT)) (|coerce| (((|OutputForm|) $) 89 T ELT) (($ #6#) 22 T ELT)) (|before?| #1#) (= (#2# 38 T ELT))) 
(((|RewriteRule| |#1| |#2| |#3|) (|Join| #1=(|SetCategory|) (|Eltable| |#3| |#3|) (|RetractableTo| (|Equation| |#3|)) (CATEGORY |domain| (SIGNATURE |rule| ($ |#3| |#3|)) (SIGNATURE |rule| ($ |#3| |#3| #2=(|List| (|Symbol|)))) (SIGNATURE |suchThat| ($ $ #2# (|Mapping| (|Boolean|) (|List| |#3|)))) (SIGNATURE |pattern| (#3=(|Pattern| |#1|) $)) (SIGNATURE |lhs| #4=(|#3| $)) (SIGNATURE |rhs| #4#) (SIGNATURE |elt| (|#3| $ |#3| (|PositiveInteger|))) (SIGNATURE |quotedOperators| (#2# $)))) #1# (|Join| (|Ring|) #5=(|PatternMatchable| |#1|) #6=(|ConvertibleTo| #3#)) (|Join| (|FunctionSpace| |#2|) #5# #6#)) (T |RewriteRule|)) 
((|rule| (*1 *1 *2 *2) (AND #1=(|ofCategory| *3 #2=(|SetCategory|)) #3=(|ofCategory| *4 (|Join| #4=(|Ring|) #5=(|PatternMatchable| *3) #6=(|ConvertibleTo| #7=(|Pattern| *3)))) #8=(|isDomain| *1 (|RewriteRule| *3 *4 *2)) #9=(|ofCategory| *2 #10=(|Join| #11=(|FunctionSpace| *4) #5# #6#)))) (|rule| (*1 *1 *2 *2 *3) (AND (|isDomain| *3 #12=(|List| (|Symbol|))) #13=(|ofCategory| *4 #2#) #14=(|ofCategory| *5 (|Join| #4# #15=(|PatternMatchable| *4) #16=(|ConvertibleTo| (|Pattern| *4)))) #17=(|isDomain| *1 (|RewriteRule| *4 *5 *2)) #18=(|ofCategory| *2 #19=(|Join| (|FunctionSpace| *5) #15# #16#)))) (|suchThat| (*1 *1 *1 *2 *3) (AND #20=(|isDomain| *2 #12#) (|isDomain| *3 (|Mapping| (|Boolean|) (|List| *6))) (|ofCategory| *6 #19#) #13# #14# (|isDomain| *1 (|RewriteRule| *4 *5 *6)))) (|pattern| #21=(*1 *2 *1) (AND #1# (|ofCategory| *4 (|Join| #4# #5# #22=(|ConvertibleTo| *2))) (|isDomain| *2 #7#) #23=(|isDomain| *1 (|RewriteRule| *3 *4 *5)) (|ofCategory| *5 (|Join| #11# #5# #22#)))) (|lhs| #21# #24=(AND #1# #9# #8# #3#)) (|rhs| #21# #24#) (|elt| (*1 *2 *1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) #13# #14# #17# #18#)) (|quotedOperators| #21# (AND #1# #3# #20# #23# (|ofCategory| *5 #10#)))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|name| (((|Symbol|) $) 8 T ELT)) (|latex| (((|String|) $) 17 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT)) (|before?| #1#) (= (#2# 14 T ELT))) 
(((|RuleCalled| |#1|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| (#1=(|Symbol|) $)))) #1#) (T |RuleCalled|)) 
((|name| (*1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|RuleCalled| *3)) (|ofType| *3 *2)))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|ruleset| (($ #3=(|List| (|RewriteRule| |#1| |#2| |#3|))) 15 T ELT)) (|rules| ((#3# $) 22 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#3| $ |#3|) 25 T ELT) ((|#3| $ |#3| (|PositiveInteger|)) 28 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|before?| #1#) (= (#2# 21 T ELT))) 
(((|Ruleset| |#1| |#2| |#3|) (|Join| #1=(|SetCategory|) (|Eltable| |#3| |#3|) (CATEGORY |domain| (SIGNATURE |ruleset| ($ #2=(|List| (|RewriteRule| |#1| |#2| |#3|)))) (SIGNATURE |rules| (#2# $)) (SIGNATURE |elt| (|#3| $ |#3| (|PositiveInteger|))))) #1# (|Join| (|Ring|) #3=(|PatternMatchable| |#1|) #4=(|ConvertibleTo| (|Pattern| |#1|))) (|Join| (|FunctionSpace| |#2|) #3# #4#)) (T |Ruleset|)) 
((|ruleset| (*1 *1 *2) (AND #1=(|isDomain| *2 (|List| (|RewriteRule| *3 *4 *5))) #2=(|ofCategory| *3 #3=(|SetCategory|)) #4=(|ofCategory| *4 (|Join| #5=(|Ring|) #6=(|PatternMatchable| *3) #7=(|ConvertibleTo| (|Pattern| *3)))) #8=(|ofCategory| *5 (|Join| (|FunctionSpace| *4) #6# #7#)) #9=(|isDomain| *1 (|Ruleset| *3 *4 *5)))) (|rules| (*1 *2 *1) (AND #2# #4# #1# #9# #8#)) (|elt| (*1 *2 *1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 #3#) (|ofCategory| *5 (|Join| #5# #10=(|PatternMatchable| *4) #11=(|ConvertibleTo| (|Pattern| *4)))) (|isDomain| *1 (|Ruleset| *4 *5 *2)) (|ofCategory| *2 (|Join| (|FunctionSpace| *5) #10# #11#))))) 
((|rur| ((#1=(|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| #2=(|List| (|Polynomial| |#1|))))) #2# #3=(|Boolean|) #3#) 88 T ELT) ((#1# #2#) 92 T ELT) ((#1# #2# #3#) 90 T ELT))) 
(((|RationalUnivariateRepresentationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rur| (#1=(|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| #2=(|List| (|Polynomial| |#1|))))) #2# #3=(|Boolean|))) (SIGNATURE |rur| (#1# #2#)) (SIGNATURE |rur| (#1# #2# #3# #3#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|List| (|Symbol|))) (T |RationalUnivariateRepresentationPackage|)) 
((|rur| (*1 *2 *3 *4 *4) #1=(AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 #2=(|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5)) (|:| |coordinates| #3=(|List| (|Polynomial| *5)))))) (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *5 *6)) (|isDomain| *3 #3#) (|ofType| *6 #4=(|List| (|Symbol|))))) (|rur| (*1 *2 *3) (AND (|ofCategory| *4 #2#) (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *4)) (|:| |coordinates| #5=(|List| (|Polynomial| *4)))))) (|isDomain| *1 (|RationalUnivariateRepresentationPackage| *4 *5)) (|isDomain| *3 #5#) (|ofType| *5 #4#))) (|rur| (*1 *2 *3 *4) #1#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 132 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|unitCanonical| #6=(#7=($ $) NIL #5# ELT)) (|unit?| #8=(#4# NIL #5# ELT)) (|traceMatrix| #9=(#10=(#11=(|Matrix| |#1|) #12=(|Vector| $)) NIL T ELT) ((#11#) 117 T ELT)) (|trace| (#13=(|#1| $) 121 T ELT)) (|tableForDiscreteLogarithm| (((|Table| #14=(|PositiveInteger|) #15=(|NonNegativeInteger|)) #16=(|Integer|)) NIL #17=(|has| |#1| (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#18=(#19=(|Union| $ #20="failed") $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #21=(((|Factored| $) $) NIL #5# ELT)) (|sizeLess?| #22=(#2# NIL #5# ELT)) (|size| (#23=(#15#) 43 #24=(|has| |#1| (|Finite|)) ELT)) (|sample| (#25=($) NIL T CONST)) (|retractIfCan| (((|Union| #16# . #26=(#20#)) . #27=($)) NIL #28=(|has| |#1| (|RetractableTo| #16#)) ELT) (((|Union| #29=(|Fraction| #16#) . #26#) . #27#) NIL #30=(|has| |#1| (|RetractableTo| #29#)) ELT) (((|Union| |#1| . #26#) . #27#) NIL T ELT)) (|retract| ((#16# . #31=($)) NIL #28# ELT) ((#29# . #31#) NIL #30# ELT) #32=(#13# NIL T ELT)) (|represents| (($ #33=(|Vector| |#1|) #12#) NIL T ELT) (#34=($ #33#) 46 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #17# ELT)) (|rem| #35=(#36=($ $ $) NIL #5# ELT)) (|regularRepresentation| ((#11# $ #12#) NIL T ELT) ((#11# $) NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #16#) #38=(|Matrix| $)) NIL #39=(|has| |#1| (|LinearlyExplicitRingOver| #16#)) ELT) ((#40=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #16#))) #38# #12#) NIL #39# ELT) ((#41=(|Record| (|:| |mat| #11#) (|:| |vec| #33#)) #38# #12#) 109 T ELT) ((#11# #38#) 104 T ELT)) (|reduce| (#42=($ |#2|) 62 T ELT) ((#19# (|Fraction| |#2|)) NIL #5# ELT)) (|recip| ((#19# $) NIL T ELT)) (|rank| ((#14#) 80 T ELT)) (|random| (#25# 47 #24# ELT)) (|quo| #35#) (|principalIdeal| (((|Record| (|:| |coef| #43=(|List| $)) #44=(|:| |generator| $)) #43#) NIL #5# ELT)) (|primitiveElement| #45=(#25# NIL #17# ELT)) (|primitive?| (#4# NIL #17# ELT)) (|primeFrobenius| (#46=($ $ #15#) NIL #17# ELT) #47=(#7# NIL #17# ELT)) (|prime?| #8#) (|order| (#48=(#14# $) NIL #17# ELT) (((|OnePointCompletion| #14#) $) NIL #17# ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|norm| #32#) (|nextItem| (#49=((|Maybe| $) $) NIL #17# ELT)) (|multiEuclidean| (((|Union| #43# #20#) #43# $) NIL #5# ELT)) (|minimalPolynomial| (#50=(|#2| $) 87 #5# ELT)) (|lookup| (#48# 140 #24# ELT)) (|lift| (#50# 59 T ELT)) (|leftReducedSystem| ((#37# #12#) NIL #39# ELT) ((#40# . #51=(#12# $)) NIL #39# ELT) ((#41# . #51#) NIL T ELT) #9#) (|lcm| #52=(($ #43#) NIL #5# ELT) #35#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|init| (#25# NIL #17# CONST)) (|index| (($ #14#) 131 #24# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#25# 123 T ELT)) (|gcdPolynomial| ((#53=(|SparseUnivariatePolynomial| $) #53# #53#) NIL #5# ELT)) (|gcd| #52# #35#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) NIL #17# ELT)) (|factor| #21#) (|extendedEuclidean| (((|Union| (|Record| #54=(|:| |coef1| $) #55=(|:| |coef2| $)) #20#) $ $ $) NIL #5# ELT) (((|Record| #54# #55# #44#) $ $) NIL #5# ELT)) (|exquo| (#18# NIL #5# ELT)) (|expressIdealMember| (((|Maybe| #43#) #43# $) NIL #5# ELT)) (|euclideanSize| (#56=(#15# $) NIL #5# ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|discriminant| ((|#1| #12#) NIL T ELT) ((|#1|) 113 T ELT)) (|discreteLog| (#56# NIL #17# ELT) (((|Union| #15# #20#) $ $) NIL #17# ELT)) (|differentiate| #57=(#46# NIL #58=(OR (AND (|has| |#1| (|DifferentialSpace|)) #5#) #17#) ELT) #59=(#7# NIL #58# ELT) #60=(($ $ #61=(|List| #62=(|Symbol|)) (|List| #15#)) NIL #63=(AND #5# (|has| |#1| (|PartialDifferentialSpace| #62#))) ELT) #64=(($ $ #62# #15#) NIL #63# ELT) #65=(($ $ #61#) NIL #63# ELT) #66=(($ $ #62#) NIL #63# ELT) #67=(($ $ #68=(|Mapping| |#1| |#1|)) NIL #5# ELT) #69=(($ $ #68# #15#) NIL #5# ELT)) (|derivationCoordinates| ((#11# #12# #68#) NIL #5# ELT)) (|definingPolynomial| ((|#2|) 77 T ELT)) (|createPrimitiveElement| #45#) (|coordinates| ((#33# $ #12#) 92 T ELT) ((#11# #12# #12#) NIL T ELT) (#70=(#33# $) 72 T ELT) (#10# 88 T ELT)) (|convert| (#70# NIL T ELT) (#34# NIL T ELT) (#50# NIL T ELT) (#42# NIL T ELT)) (|conditionP| (((|Union| #12# #20#) #38#) NIL #17# ELT)) (|coerce| (((|OutputForm|) $) 58 T ELT) (($ #16#) 53 T ELT) (($ |#1|) 55 T ELT) #6# (($ #29#) NIL (OR #5# #30#) ELT)) (|charthRoot| #47# (#49# NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| (#50# 85 T ELT)) (|characteristic| (#23# 79 T CONST)) (|before?| #1#) (|basis| ((#12#) 84 T ELT)) (|associates?| #22#) (|annihilate?| #1#) (|Zero| (#25# 32 T CONST)) (|One| (#25# 19 T CONST)) (D #57# #59# #60# #64# #65# #66# #67# #69#) (= (#2# 64 T ELT)) (/ #35#) (- (#7# 68 T ELT) (#36# NIL T ELT)) (+ (#36# 66 T ELT)) (** (($ $ #14#) NIL T ELT) (#46# NIL T ELT) (($ $ #16#) NIL #5# ELT)) (* (($ #14# $) NIL T ELT) (($ #15# $) NIL T ELT) (($ #16# $) 51 T ELT) (#36# 70 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| $) 48 T ELT) (($ #29# $) NIL #5# ELT) (($ $ #29#) NIL #5# ELT))) 
(((|SimpleAlgebraicExtension| |#1| |#2| |#3|) (|MonogenicAlgebra| |#1| |#2|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#1|) |#2|) (T |SimpleAlgebraicExtension|)) 
NIL 
((|factor| (((|Factored| |#3|) |#3|) 18 T ELT))) 
(((|SimpleAlgebraicExtensionAlgFactor| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3|))) (|UnivariatePolynomialCategory| #1=(|Fraction| (|Integer|))) (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| #1# |#1|)) (|UnivariatePolynomialCategory| |#2|)) (T |SimpleAlgebraicExtensionAlgFactor|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| #1=(|Fraction| (|Integer|)))) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| #1# *4))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|SimpleAlgebraicExtensionAlgFactor| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
((|factor| (((|Factored| |#3|) |#3|) 19 T ELT))) 
(((|SAERationalFunctionAlgFactor| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3|))) (|UnivariatePolynomialCategory| #1=(|Fraction| (|Polynomial| (|Integer|)))) (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| #1# |#1|)) (|UnivariatePolynomialCategory| |#2|)) (T |SAERationalFunctionAlgFactor|)) 
((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| #1=(|Fraction| (|Polynomial| (|Integer|))))) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|MonogenicAlgebra| #1# *4))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|SAERationalFunctionAlgFactor| *4 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|min| (#3=($ $ $) 16 T ELT)) (|max| (#3# 17 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|create| (($) 6 T ELT)) (|convert| (((|Symbol|) $) 20 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= (#2# 15 T ELT)) (<= #1#) (< (#2# 9 T ELT))) 
(((|SingletonAsOrderedSet|) (|Join| (|OrderedSet|) (|ConvertibleTo| (|Symbol|)) (CATEGORY |domain| (SIGNATURE |create| ($))))) (T |SingletonAsOrderedSet|)) 
((|create| (*1 *1) (|isDomain| *1 (|SingletonAsOrderedSet|)))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) . #2=($)) 13 T ELT) (($ #3=(|Syntax|)) 20 T ELT) ((#3# . #2#) 19 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|SpadSyntaxCategory|) (|Category|)) (T |SpadSyntaxCategory|)) 
NIL 
(|Join| (|AbstractSyntaxCategory|)) 
(((|AbstractSyntaxCategory|) . T) ((|BasicType|) . T) ((|CoercibleFrom| #1=(|Syntax|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) 41 T ELT) ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) 33 T ELT)) (|clearCache| (((|Void|)) 21 T ELT)) (|cache| (((|List| |#1|)) 13 T ELT))) 
(((|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=(*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Integer|) *2 *2)) #2=(|ofCategory| *2 #3=(|CachableSet|)) #4=(|isDomain| *1 (|SortedCache| *2)))) (|enterInCache| #1# (AND (|isDomain| *3 (|Mapping| (|Boolean|) *2)) #2# #4#)) (|cache| #5=(*1 *2) (AND (|isDomain| *2 (|List| *3)) #6=(|isDomain| *1 (|SortedCache| *3)) #7=(|ofCategory| *3 #3#))) (|clearCache| #5# (AND (|isDomain| *2 (|Void|)) #6# #7#))) 
((|pushNewContour| (($ #1=(|Binding|) $) 20 T ELT)) (|findBinding| (((|Maybe| #1#) (|Identifier|) $) 19 T ELT)) (|empty| (#2=($) 7 T ELT)) (|currentScope| (#2# 21 T ELT)) (|currentCategoryFrame| (#2# 22 T ELT)) (|contours| (((|List| (|Contour|)) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT))) 
(((|Scope|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |empty| #1=($)) (SIGNATURE |contours| ((|List| (|Contour|)) $)) (SIGNATURE |findBinding| ((|Maybe| #2=(|Binding|)) (|Identifier|) $)) (SIGNATURE |pushNewContour| ($ #2# $)) (SIGNATURE |currentScope| #1#) (SIGNATURE |currentCategoryFrame| #1#)))) (T |Scope|)) 
((|empty| #1=(*1 *1) #2=(|isDomain| *1 (|Scope|))) (|contours| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|Contour|))) #2#)) (|findBinding| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Identifier|)) (|isDomain| *2 (|Maybe| #3=(|Binding|))) #2#)) (|pushNewContour| (*1 *1 *2 *1) (AND (|isDomain| *2 #3#) #2#)) (|currentScope| #1# #2#) (|currentCategoryFrame| #1# #2#)) 
((|structuralConstants| (((|Vector| #1=(|Matrix| |#1|)) #2=(|List| #1#)) 45 T ELT) (((|Vector| #3=(|Matrix| #4=(|Polynomial| |#1|))) #5=(|List| (|Symbol|)) #3#) 75 T ELT) (((|Vector| #6=(|Matrix| (|Fraction| #4#))) #5# #6#) 92 T ELT)) (|coordinates| (((|Vector| |#1|) #1# #2#) 39 T ELT))) 
(((|StructuralConstantsPackage| |#1|) (CATEGORY |package| (SIGNATURE |structuralConstants| ((|Vector| #1=(|Matrix| (|Fraction| #2=(|Polynomial| |#1|)))) #3=(|List| (|Symbol|)) #1#)) (SIGNATURE |structuralConstants| ((|Vector| #4=(|Matrix| #2#)) #3# #4#)) (SIGNATURE |structuralConstants| ((|Vector| #5=(|Matrix| |#1|)) #6=(|List| #5#))) (SIGNATURE |coordinates| ((|Vector| |#1|) #5# #6#))) (|Field|)) (T |StructuralConstantsPackage|)) 
((|coordinates| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|List| #2=(|Matrix| *5))) (|isDomain| *3 #2#) #3=(|ofCategory| *5 #4=(|Field|)) (|isDomain| *2 (|Vector| *5)) #5=(|isDomain| *1 (|StructuralConstantsPackage| *5)))) (|structuralConstants| (*1 *2 *3) (AND (|isDomain| *3 (|List| #6=(|Matrix| *4))) (|ofCategory| *4 #4#) (|isDomain| *2 (|Vector| #6#)) (|isDomain| *1 (|StructuralConstantsPackage| *4)))) (|structuralConstants| #1# (AND #7=(|isDomain| *3 (|List| (|Symbol|))) #3# (|isDomain| *2 (|Vector| #8=(|Matrix| #9=(|Polynomial| *5)))) #5# (|isDomain| *4 #8#))) (|structuralConstants| #1# (AND #7# #3# (|isDomain| *2 (|Vector| #10=(|Matrix| (|Fraction| #9#)))) #5# (|isDomain| *4 #10#)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|weights| ((#6=(|List| #7=(|NonNegativeInteger|)) $) NIL T ELT) ((#6# $ #8=(|Symbol|)) NIL T ELT)) (|weight| #9=((#7# $) NIL T ELT) #10=((#7# $ #8#) NIL T ELT)) (|variables| ((#11=(|List| #12=(|SequentialDifferentialVariable| #8#)) $) NIL T ELT)) (|univariate| ((#13=(|SparseUnivariatePolynomial| $) $ #12#) NIL T ELT) ((#14=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #15=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #16=(#17=($ $) NIL #15# ELT)) (|unit?| (#5# NIL #15# ELT)) (|totalDegree| #9# ((#7# $ #11#) NIL T ELT)) (|subtractIfCan| (#18=(#19=(|Union| $ #20="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #21=(((|Factored| #13#) #13#) NIL #22=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #23=(#17# NIL #24=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#25=((|Factored| $) $) NIL #24# ELT)) (|solveLinearPolynomialEquation| (((|Union| #26=(|List| #13#) #20#) #26# #13#) NIL #22# ELT)) (|separant| #27=(#17# NIL T ELT)) (|sample| #28=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #29=(#20#)) . #30=($)) NIL T ELT) (((|Union| #31=(|Fraction| #32=(|Integer|)) . #29#) . #30#) NIL #33=(|has| |#1| (|RetractableTo| #31#)) ELT) (((|Union| #32# . #29#) . #30#) NIL #34=(|has| |#1| (|RetractableTo| #32#)) ELT) #35=(((|Union| #12# . #29#) . #30#) NIL T ELT) (((|Union| #8# . #29#) . #30#) NIL T ELT) (((|Union| #36=(|SparseMultivariatePolynomial| |#1| #8#) . #29#) . #30#) NIL T ELT)) (|retract| #37=(#38=(|#1| . #39=($)) NIL T ELT) ((#31# . #39#) NIL #33# ELT) ((#32# . #39#) NIL #34# ELT) #40=((#12# . #39#) NIL T ELT) ((#8# . #39#) NIL T ELT) ((#36# . #39#) NIL T ELT)) (|resultant| (($ $ $ #12#) NIL #41=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #27#) (|reducedSystem| ((#42=(|Matrix| #32#) . #43=(#44=(|Matrix| $))) NIL #45=(|has| |#1| (|LinearlyExplicitRingOver| #32#)) ELT) ((#46=(|Record| (|:| |mat| #42#) (|:| |vec| (|Vector| #32#))) . #47=(#44# #48=(|Vector| $))) NIL #45# ELT) ((#49=(|Record| (|:| |mat| #50=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #47#) NIL T ELT) ((#50# . #43#) NIL T ELT)) (|recip| ((#19# $) NIL T ELT)) (|primitivePart| #23# #51=(#52=($ $ #12#) NIL #24# ELT)) (|primitiveMonomials| #53=((#54=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #22# ELT)) (|pomopo!| (($ $ |#1| #55=(|IndexedExponents| #12#) $) NIL T ELT)) (|patternMatch| ((#56=(|PatternMatchResult| #57=(|Float|) . #58=($)) $ #59=(|Pattern| #57#) #56#) NIL (AND (|has| #12# #60=(|PatternMatchable| #57#)) (|has| |#1| #60#)) ELT) ((#61=(|PatternMatchResult| #32# . #58#) $ #62=(|Pattern| #32#) #61#) NIL (AND (|has| #12# #63=(|PatternMatchable| #32#)) (|has| |#1| #63#)) ELT)) (|order| #10# #9#) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #9#) (|multivariate| (($ #14# #12#) NIL T ELT) (($ #13# #12#) NIL T ELT)) (|monomials| #53#) (|monomial?| #4#) (|monomial| (($ |#1| #55#) NIL T ELT) #64=(($ $ #12# #7#) NIL T ELT) #65=(($ $ #11# #6#) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #12#) NIL T ELT)) (|minimumDegree| #66=((#55# $) NIL T ELT) #67=((#7# $ #12#) NIL T ELT) #68=((#6# $ #11#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #55# #55#) $) NIL T ELT)) (|map| (($ #69=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeVariable| ((#70=(|Mapping| $ #7#) #8#) NIL T ELT) ((#70# $) NIL #71=(|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| #35#) (|leftReducedSystem| ((#42# . #72=(#48#)) NIL #45# ELT) ((#46# . #73=(#48# $)) NIL #45# ELT) ((#49# . #73#) NIL T ELT) ((#50# . #72#) NIL T ELT)) (|leadingMonomial| #27#) (|leadingCoefficient| #37#) (|leader| #40#) (|lcm| #74=(($ #54#) NIL #24# ELT) #75=(#76=($ $ $) NIL #24# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #77=(((|Union| #54# #20#) $) NIL T ELT)) (|isPlus| #77#) (|isExpt| (((|Union| (|Record| (|:| |var| #12#) (|:| |exponent| #7#)) #20#) $) NIL T ELT)) (|initial| #27#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #37#) (|gcdPolynomial| ((#13# #13# #13#) NIL #24# ELT)) (|gcd| #74# #75#) (|factorSquareFreePolynomial| #21#) (|factorPolynomial| #21#) (|factor| (#25# NIL #22# ELT)) (|exquo| ((#19# $ |#1|) NIL #15# ELT) (#18# NIL #15# ELT)) (|eval| (($ $ (|List| #78=(|Equation| $))) NIL T ELT) (($ $ #78#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #54# #54#) NIL T ELT) (($ $ #12# |#1|) NIL T ELT) (($ $ #11# #79=(|List| |#1|)) NIL T ELT) (($ $ #12# $) NIL T ELT) (($ $ #11# #54#) NIL T ELT) (($ $ #8# $) NIL #71# ELT) (($ $ #80=(|List| #8#) #54#) NIL #71# ELT) (($ $ #8# |#1|) NIL #71# ELT) (($ $ #80# #79#) NIL #71# ELT)) (|discriminant| (#52# NIL #41# ELT)) (|differentiate| #65# #64# #81=(($ $ #11#) NIL T ELT) #82=(#52# NIL T ELT) #83=(($ $ #69#) NIL T ELT) #84=(($ $ #69# #7#) NIL T ELT) #85=(($ $ #8#) NIL #86=(|has| |#1| (|PartialDifferentialSpace| #8#)) ELT) #87=(($ $ #80#) NIL #86# ELT) #88=(($ $ #8# #7#) NIL #86# ELT) #89=(($ $ #80# #6#) NIL #86# ELT) #90=(#17# NIL #91=(|has| |#1| (|DifferentialSpace|)) ELT) #92=(#93=($ $ #7#) NIL #91# ELT)) (|differentialVariables| ((#80# $) NIL T ELT)) (|degree| #66# #67# #68# #10#) (|convert| ((#59# . #94=($)) NIL (AND (|has| #12# #95=(|ConvertibleTo| #59#)) (|has| |#1| #95#)) ELT) ((#62# . #94#) NIL (AND (|has| #12# #96=(|ConvertibleTo| #62#)) (|has| |#1| #96#)) ELT) ((#97=(|InputForm|) . #94#) NIL (AND (|has| #12# #98=(|ConvertibleTo| #97#)) (|has| |#1| #98#)) ELT)) (|content| (#38# NIL #24# ELT) #51#) (|conditionP| (((|Union| #48# #20#) #44#) NIL #99=(AND (|has| $ #100=(|CharacteristicNonZero|)) #22#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #32#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #12#) NIL T ELT) (($ #8#) NIL T ELT) (($ #36#) NIL T ELT) (($ #31#) NIL (OR #101=(|has| |#1| (|Algebra| #31#)) #33#) ELT) #16#) (|coefficients| ((#79# $) NIL T ELT)) (|coefficient| ((|#1| $ #55#) NIL T ELT) #64# #65#) (|charthRoot| (((|Maybe| $) $) NIL (OR #99# (|has| |#1| #100#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #41# ELT)) (|before?| #1#) (|associates?| (#2# NIL #15# ELT)) (|annihilate?| #1#) (|Zero| #28#) (|One| #28#) (D #65# #64# #81# #82# #83# #84# #85# #87# #88# #89# #90# #92#) (= #1#) (/ (#102=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #27# #103=(#76# NIL T ELT)) (+ #103#) (** (($ $ #104=(|PositiveInteger|)) NIL T ELT) (#93# NIL T ELT)) (* (($ #104# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #32# . #105=($)) NIL T ELT) #103# (($ $ #31#) NIL #101# ELT) (($ #31# . #105#) NIL #101# ELT) (($ |#1| . #105#) NIL T ELT) (#102# NIL T ELT))) 
(((|SequentialDifferentialPolynomial| |#1|) (|Join| (|DifferentialPolynomialCategory| |#1| #1=(|Symbol|) #2=(|SequentialDifferentialVariable| #1#) (|IndexedExponents| #2#)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| #1#))) (|Ring|)) (T |SequentialDifferentialPolynomial|)) 
NIL 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|weight| (#3=(#4=(|NonNegativeInteger|) $) NIL T ELT)) (|variable| (#5=(|#1| $) 10 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| (#5# NIL T ELT)) (|order| (#3# 11 T ELT)) (|min| #6=(($ $ $) NIL T ELT)) (|max| #6#) (|makeVariable| (($ |#1| #4#) 9 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|differentiate| #7=(($ $ #4#) NIL T ELT) #8=(($ $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|before?| #1#) (D #7# #8#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 16 T ELT))) 
(((|SequentialDifferentialVariable| |#1|) (|DifferentialVariableCategory| |#1|) (|OrderedSet|)) (T |SequentialDifferentialVariable|)) 
NIL 
((~= #1=(#2=((|Boolean|) $ $) NIL #3=(|has| |#1| (|SetCategory|)) ELT)) (|segment| (#4=($ |#1| |#1|) 16 T ELT)) (|map| ((#5=(|List| |#1|) (|Mapping| |#1| |#1|) $) 44 #6=(|has| |#1| (|OrderedRing|)) ELT)) (|low| (#7=(|#1| $) 12 T ELT)) (|lo| (#7# 11 T ELT)) (|latex| (((|String|) $) NIL #3# ELT)) (|incr| ((#8=(|Integer|) $) 15 T ELT)) (|high| (#7# 14 T ELT)) (|hi| (#7# 13 T ELT)) (|hash| (((|SingleInteger|) $) NIL #3# ELT)) (|expand| ((#5# $) 42 #6# ELT) ((#5# (|List| $)) 41 #6# ELT)) (|convert| (($ |#1|) 29 T ELT)) (|coerce| (((|OutputForm|) $) 28 #3# ELT)) (|before?| #1#) (SEGMENT (#4# 10 T ELT)) (BY (($ $ #8#) 17 T ELT)) (= (#2# 22 #3# ELT))) 
(((|Segment| |#1|) (|Join| (|SegmentCategory| |#1|) (CATEGORY |package| (IF (|has| |#1| #1=(|SetCategory|)) (ATTRIBUTE #1#) |%noBranch|) (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|SegmentExpansionCategory| |#1| (|List| |#1|))) |%noBranch|))) (|Type|)) (T |Segment|)) 
NIL 
((|map| (((|List| |#2|) #1=(|Mapping| |#2| |#1|) #2=(|Segment| |#1|)) 27 (|has| |#1| (|OrderedRing|)) ELT) (((|Segment| |#2|) #1# #2#) 14 T ELT))) 
(((|SegmentFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Segment| |#2|) #1=(|Mapping| |#2| |#1|) #2=(|Segment| |#1|))) (IF (|has| |#1| (|OrderedRing|)) (SIGNATURE |map| ((|List| |#2|) #1# #2#)) |%noBranch|)) #3=(|Type|) #3#) (T |SegmentFunctions2|)) 
((|map| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Mapping| *6 *5)) #3=(|isDomain| *4 (|Segment| *5)) (|ofCategory| *5 (|OrderedRing|)) #4=(|ofCategory| *5 #5=(|Type|)) #6=(|ofCategory| *6 #5#) (|isDomain| *2 (|List| *6)) #7=(|isDomain| *1 (|SegmentFunctions2| *5 *6)))) (|map| #1# (AND #2# #3# #4# #6# (|isDomain| *2 (|Segment| *6)) #7#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|bounds| (((|List| (|SpadAst|)) $) 10 T ELT)) (|before?| #1#) (= #1#)) 
(((|SegmentAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |bounds| ((|List| (|SpadAst|)) $))))) (T |SegmentAst|)) 
((|bounds| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|SegmentAst|))))) 
((~= #1=(((|Boolean|) $ $) NIL #2=(|has| #3=(|Segment| |#1|) (|SetCategory|)) ELT)) (|variable| ((#4=(|Symbol|) $) NIL T ELT)) (|segment| ((#3# $) NIL T ELT)) (|latex| (((|String|) $) NIL #2# ELT)) (|hash| (((|SingleInteger|) $) NIL #2# ELT)) (|equation| (($ #4# #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL #2# ELT)) (|before?| #1#) (= #1#)) 
(((|SegmentBinding| |#1|) (|Join| #1=(|Type|) (CATEGORY |domain| (SIGNATURE |equation| ($ #2=(|Symbol|) #3=(|Segment| |#1|))) (SIGNATURE |variable| (#2# $)) (SIGNATURE |segment| (#3# $)) (IF (|has| #3# #4=(|SetCategory|)) (ATTRIBUTE #4#) |%noBranch|))) #1#) (T |SegmentBinding|)) 
((|equation| (*1 *1 *2 *3) (AND #1=(|isDomain| *2 (|Symbol|)) (|isDomain| *3 (|Segment| *4)) (|ofCategory| *4 #2=(|Type|)) (|isDomain| *1 (|SegmentBinding| *4)))) (|variable| #3=(*1 *2 *1) (AND #1# #4=(|isDomain| *1 (|SegmentBinding| *3)) #5=(|ofCategory| *3 #2#))) (|segment| #3# (AND (|isDomain| *2 (|Segment| *3)) #4# #5#))) 
((|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) 19 T ELT))) 
(((|SegmentBindingFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)))) #1=(|Type|) #1#) (T |SegmentBindingFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|SegmentBinding| *5)) (|ofCategory| *5 #1=(|Type|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|SegmentBinding| *6)) (|isDomain| *1 (|SegmentBindingFunctions2| *5 *6))))) 
((|segment| (($ |#1| |#1|) 8 T ELT)) (|low| ((|#1| $) 11 T ELT)) (|lo| ((|#1| $) 13 T ELT)) (|incr| (((|Integer|) $) 9 T ELT)) (|high| ((|#1| $) 10 T ELT)) (|hi| ((|#1| $) 12 T ELT)) (|convert| (($ |#1|) 6 T ELT)) (SEGMENT (($ |#1| |#1|) 15 T ELT)) (BY (($ $ (|Integer|)) 14 T ELT))) 
(((|SegmentCategory| |#1|) (|Category|) (|Type|)) (T |SegmentCategory|)) 
((SEGMENT (*1 *1 *2 *2) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (BY (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|SegmentCategory| *3)) (|ofCategory| *3 (|Type|)))) (|lo| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (|hi| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (|low| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (|high| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (|incr| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Integer|)))) (|segment| (*1 *1 *2 *2) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|))))) 
(|Join| (|ConvertibleFrom| |t#1|) (CATEGORY |domain| (SIGNATURE SEGMENT ($ |t#1| |t#1|)) (SIGNATURE BY ($ $ (|Integer|))) (SIGNATURE |lo| (|t#1| $)) (SIGNATURE |hi| (|t#1| $)) (SIGNATURE |low| (|t#1| $)) (SIGNATURE |high| (|t#1| $)) (SIGNATURE |incr| ((|Integer|) $)) (SIGNATURE |segment| ($ |t#1| |t#1|)))) 
(((|ConvertibleFrom| |#1|) . T)) 
((|segment| (($ |#1| |#1|) 8 T ELT)) (|map| ((|#2| (|Mapping| |#1| |#1|) $) 17 T ELT)) (|low| ((|#1| . #1=($)) 11 T ELT)) (|lo| ((|#1| . #1#) 13 T ELT)) (|incr| ((#2=(|Integer|) $) 9 T ELT)) (|high| ((|#1| . #1#) 10 T ELT)) (|hi| ((|#1| . #1#) 12 T ELT)) (|expand| ((|#2| (|List| $)) 19 T ELT) ((|#2| $) 18 T ELT)) (|convert| (($ |#1|) 6 T ELT)) (SEGMENT (($ |#1| |#1|) 15 T ELT)) (BY (($ $ #2#) 14 T ELT))) 
(((|SegmentExpansionCategory| |#1| |#2|) (|Category|) (|OrderedRing|) (|StreamAggregate| |t#1|)) (T |SegmentExpansionCategory|)) 
((|expand| (*1 *2 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|SegmentExpansionCategory| *4 *2)) (|ofCategory| *4 (|OrderedRing|)) (|ofCategory| *2 (|StreamAggregate| *4)))) (|expand| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentExpansionCategory| *3 *2)) (|ofCategory| *3 (|OrderedRing|)) (|ofCategory| *2 (|StreamAggregate| *3)))) (|map| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *1 (|SegmentExpansionCategory| *4 *2)) (|ofCategory| *4 (|OrderedRing|)) (|ofCategory| *2 (|StreamAggregate| *4))))) 
(|Join| (|SegmentCategory| |t#1|) (CATEGORY |domain| (SIGNATURE |expand| (|t#2| (|List| $))) (SIGNATURE |expand| (|t#2| $)) (SIGNATURE |map| (|t#2| (|Mapping| |t#1| |t#1|) $)))) 
(((|ConvertibleFrom| |#1|) . T) ((|SegmentCategory| |#1|) . T)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|last| ((#2=(|SpadAst|) $) 14 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|body| (((|List| #2#) $) 12 T ELT)) (|before?| #1#) (= #1#)) 
(((|SequenceAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |body| ((|List| #1=(|SpadAst|)) $)) (SIGNATURE |last| (#1# $))))) (T |SequenceAst|)) 
((|body| #1=(*1 *2 *1) (AND (|isDomain| *2 (|List| #2=(|SpadAst|))) #3=(|isDomain| *1 (|SequenceAst|)))) (|last| #1# (AND (|isDomain| *2 #2#) #3#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|universe| #4=(#5=($) NIL #6=(|has| |#1| (|Finite|)) ELT)) (|union| (#7=($ |#1| $) NIL T ELT) #8=(($ $ |#1|) NIL T ELT) (#9=($ $ $) 84 T ELT)) (|symmetricDifference| (#9# 81 T ELT)) (|subset?| (#2# 83 T ELT)) (|size| ((#10=(|NonNegativeInteger|)) NIL #6# ELT)) (|set| #11=(#12=($ #13=(|List| |#1|)) NIL T ELT) (#5# 14 T ELT)) (|select!| #14=(($ #15=(|Mapping| #3# |#1|) $) NIL #16=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| #14#) (|sample| (#5# NIL T CONST)) (|removeDuplicates| (#17=($ $) NIL #18=(AND #16# #19=(|has| |#1| (|BasicType|))) ELT)) (|remove!| (#7# 75 #16# ELT) #14#) (|remove| (#7# NIL #18# ELT) #14#) (|reduce| ((|#1| #20=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 44 #19# ELT) ((|#1| #20# $ |#1|) 42 T ELT) ((|#1| #20# $) 40 T ELT)) (|random| #4#) (|part?| #1#) (|min| (#21=(|#1| $) 56 #22=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#13# $) 20 T ELT)) (|member?| ((#3# |#1| $) 74 #19# ELT)) (|max| (#21# 54 #22# ELT)) (|map!| (#23=($ (|Mapping| |#1| |#1|) $) 34 T ELT)) (|map| (#23# 35 T ELT)) (|lookup| ((#24=(|PositiveInteger|) $) NIL #6# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|intersect| (#9# 79 T ELT)) (|inspect| (#21# 26 T ELT)) (|insert!| (#7# 70 T ELT)) (|index| (($ #24#) NIL #6# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| (((|Union| |#1| "failed") #15# $) 32 T ELT)) (|extract!| (#21# 28 T ELT)) (|every?| #25=((#3# #15# $) NIL T ELT)) (|eval| (($ $ (|List| #26=(|Equation| |#1|))) NIL #27=(AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ELT) (($ $ #26#) NIL #27# ELT) (($ $ |#1| |#1|) NIL #27# ELT) (($ $ #13# #13#) NIL #27# ELT)) (|eq?| #1#) (|empty?| ((#3# $) 22 T ELT)) (|empty| (#5# 12 T ELT)) (|difference| #8# (#9# 80 T ELT)) (|dictionary| (#5# NIL T ELT) #11#) (|count| ((#10# |#1| $) NIL #19# ELT) ((#10# #15# $) NIL T ELT)) (|copy| (#17# 17 T ELT)) (|convert| ((#28=(|InputForm|) $) 51 (|has| |#1| (|ConvertibleTo| #28#)) ELT)) (|construct| (#12# 63 T ELT)) (|complement| (#17# NIL #6# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|cardinality| (#29=(#10# $) NIL T ELT)) (|brace| #11# (#5# 13 T ELT)) (|before?| #1#) (|bag| #11#) (|any?| #25#) (= (#2# 53 T ELT)) (|#| (#29# 11 T ELT))) 
(((|Set| |#1|) (|FiniteSetAggregate| |#1|) (|SetCategory|)) (T |Set|)) 
NIL 
((|union| #1=(#2=($ $ $) NIL T ELT) (#3=($ $ |#2|) 13 T ELT) (($ |#2| $) 14 T ELT)) (|symmetricDifference| (#2# 10 T ELT)) (|difference| #1# (#3# 15 T ELT))) 
(((|SetAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |union| (|#1| |#2| |#1|)) (SIGNATURE |union| #1=(|#1| |#1| |#2|)) (SIGNATURE |union| #2=(|#1| |#1| |#1|)) (SIGNATURE |symmetricDifference| #2#) (SIGNATURE |difference| #1#) (SIGNATURE |difference| #2#)) (|SetAggregate| |#2|) (|SetCategory|)) (T |SetAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|union| (($ $ $) 23 T ELT) (($ $ |#1|) 22 T ELT) (($ |#1| $) 21 T ELT)) (|symmetricDifference| (($ $ $) 25 T ELT)) (|subset?| (((|Boolean|) $ $) 24 T ELT)) (|set| (($) 30 T ELT) (($ (|List| |#1|)) 29 T ELT)) (|select| (($ (|Mapping| #2=(|Boolean|) |#1|) . #3=($)) 46 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#4=($) 38 T CONST)) (|removeDuplicates| (($ $) 48 (AND (|has| |#1| . #5=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 47 (AND (|has| |#1| . #5#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #2# |#1|) . #3#) 45 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|part?| (((|Boolean|) $ $) 33 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|intersect| (($ $ $) 28 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 43 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6=((|SetCategory|)))) ELT) (($ $ |#1| |#1|) 42 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 41 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| (|Equation| |#1|))) 40 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#7=(|Boolean|) $ $) 34 T ELT)) (|empty?| ((#7# $) 37 T ELT)) (|empty| (#4# 36 T ELT)) (|difference| (($ $ $) 27 T ELT) (($ $ |#1|) 26 T ELT)) (|copy| (($ $) 35 T ELT)) (|convert| ((#8=(|InputForm|) $) 49 (|has| |#1| (|ConvertibleTo| #8#)) ELT)) (|construct| (($ (|List| |#1|)) 44 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|brace| (($) 32 T ELT) (($ (|List| |#1|)) 31 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|SetAggregate| |#1|) (|Category|) (|SetCategory|)) (T |SetAggregate|)) 
((|part?| (*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 |part?| ((|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|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|latex| (((|String|) $) 10 T ELT)) (|hash| (((|SingleInteger|) $) 8 T ELT))) 
(((|SetCategory&| |#1|) (CATEGORY |package| (SIGNATURE |latex| ((|String|) |#1|)) (SIGNATURE |hash| ((|SingleInteger|) |#1|))) (|SetCategory|)) (T |SetCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|SetCategory|) (|Category|)) (T |SetCategory|)) 
((|hash| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|SetCategory|)) (|isDomain| *2 (|SingleInteger|)))) (|latex| #1# (AND #2# (|isDomain| *2 (|String|))))) 
(|Join| (|BasicType|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |hash| ((|SingleInteger|) $)) (SIGNATURE |latex| ((|String|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|size| ((#4=(|NonNegativeInteger|)) 36 T ELT)) (|setOfMinN| (($ #5=(|List| #6=(|PositiveInteger|))) 70 T ELT)) (|replaceKthElement| ((#7=(|Union| $ "failed") $ #6# #6#) 81 T ELT)) (|random| (($) 40 T ELT)) (|member?| ((#3# #6# $) 42 T ELT)) (|lookup| ((#6# $) 64 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #6#) 39 T ELT)) (|incrementKthElement| ((#7# $ #6#) 77 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|enumerate| (((|Vector| $)) 47 T ELT)) (|elements| ((#5# $) 27 T ELT)) (|delta| ((#4# $ #6# #6#) 78 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT)) (|before?| #1#) (= (#2# 24 T ELT))) 
(((|SetOfMIntegersInOneToN| |#1| |#2|) (|Join| (|Finite|) (CATEGORY |domain| (SIGNATURE |incrementKthElement| (#1=(|Union| $ "failed") $ #2=(|PositiveInteger|))) (SIGNATURE |replaceKthElement| (#1# $ #2# #2#)) (SIGNATURE |elements| (#3=(|List| #2#) $)) (SIGNATURE |setOfMinN| ($ #3#)) (SIGNATURE |enumerate| ((|Vector| $))) (SIGNATURE |member?| ((|Boolean|) #2# $)) (SIGNATURE |delta| ((|NonNegativeInteger|) $ #2# #2#)))) #2# #2#) (T |SetOfMIntegersInOneToN|)) 
((|incrementKthElement| (*1 *1 *1 *2) #1=(|partial| AND (|isDomain| *2 #2=(|PositiveInteger|)) #3=(|isDomain| *1 #4=(|SetOfMIntegersInOneToN| *3 *4)) (|ofType| *3 *2) (|ofType| *4 *2))) (|replaceKthElement| (*1 *1 *1 *2 *2) #1#) (|elements| (*1 *2 *1) #5=(AND (|isDomain| *2 (|List| #2#)) #3# #6=(|ofType| *3 #2#) #7=(|ofType| *4 #2#))) (|setOfMinN| (*1 *1 *2) #5#) (|enumerate| (*1 *2) (AND (|isDomain| *2 (|Vector| #4#)) #3# #6# #7#)) (|member?| (*1 *2 *3 *1) (AND #8=(|isDomain| *3 #2#) (|isDomain| *2 (|Boolean|)) #9=(|isDomain| *1 (|SetOfMIntegersInOneToN| *4 *5)) #10=(|ofType| *4 *3) #11=(|ofType| *5 *3))) (|delta| (*1 *2 *1 *3 *3) (AND #8# (|isDomain| *2 (|NonNegativeInteger|)) #9# #10# #11#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|symbol?| #3=((#2# $) NIL T ELT)) (|symbol| ((#4=(|Symbol|) $) NIL T ELT)) (|string?| #3#) (|string| #5=((#6=(|String|) $) NIL T ELT)) (|pair?| #3#) (|null?| #3#) (|list?| #3#) (|latex| #5#) (|integer?| #3#) (|integer| #7=((#8=(|Integer|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|float?| #3#) (|float| ((#9=(|DoubleFloat|) $) NIL T ELT)) (|expr| #10=((#11=(|OutputForm|) $) NIL T ELT)) (|eq| #1#) (|elt| (($ $ #8#) NIL T ELT) (($ $ (|List| #8#)) NIL T ELT)) (|destruct| ((#12=(|List| $) $) NIL T ELT)) (|convert| (($ #6#) NIL T ELT) (($ #4#) NIL T ELT) (($ #8#) NIL T ELT) (($ #9#) NIL T ELT) (($ #11#) NIL T ELT) (($ #12#) NIL T ELT)) (|coerce| #10#) (|cdr| #13=(($ $) NIL T ELT)) (|car| #13#) (|before?| #1#) (|atom?| #3#) (= #1#) (|#| #7#)) 
(((|SExpression|) (|SExpressionCategory| (|String|) (|Symbol|) (|Integer|) (|DoubleFloat|) (|OutputForm|))) (T |SExpression|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|symbol?| (((|Boolean|) $) 36 T ELT)) (|symbol| ((|#2| $) 31 T ELT)) (|string?| (((|Boolean|) $) 37 T ELT)) (|string| ((|#1| $) 32 T ELT)) (|pair?| (((|Boolean|) $) 39 T ELT)) (|null?| (((|Boolean|) $) 41 T ELT)) (|list?| (((|Boolean|) $) 38 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|integer?| (((|Boolean|) $) 35 T ELT)) (|integer| ((|#3| $) 30 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|float?| (((|Boolean|) $) 34 T ELT)) (|float| ((|#4| $) 29 T ELT)) (|expr| ((|#5| $) 28 T ELT)) (|eq| (((|Boolean|) $ $) 42 T ELT)) (|elt| (($ $ (|Integer|)) 44 T ELT) (($ $ (|List| (|Integer|))) 43 T ELT)) (|destruct| (((|List| $) $) 33 T ELT)) (|convert| (($ |#1|) 50 T ELT) (($ |#2|) 49 T ELT) (($ |#3|) 48 T ELT) (($ |#4|) 47 T ELT) (($ |#5|) 46 T ELT) (($ (|List| $)) 45 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|cdr| (($ $) 26 T ELT)) (|car| (($ $) 27 T ELT)) (|before?| (#1# 6 T ELT)) (|atom?| (((|Boolean|) $) 40 T ELT)) (= (#1# 8 T ELT)) (|#| (((|Integer|) $) 25 T ELT))) 
(((|SExpressionCategory| |#1| |#2| |#3| |#4| |#5|) (|Category|) #1=(|SetCategory|) #1# #1# #1# #1#) (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|)))) (|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|))))) 
(|Join| (|SetCategory|) (|ConvertibleFrom| |t#1|) (|ConvertibleFrom| |t#2|) (|ConvertibleFrom| |t#3|) (|ConvertibleFrom| |t#4|) (|ConvertibleFrom| |t#4|) (|ConvertibleFrom| |t#5|) (|ConvertibleFrom| (|List| $)) (|Eltable| (|Integer|) $) (|Eltable| (|List| (|Integer|)) $) (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| $)) (SIGNATURE |car| ($ $)) (SIGNATURE |cdr| ($ $)) (SIGNATURE |#| ((|Integer|) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|ConvertibleFrom| (|List| $)) . T) ((|ConvertibleFrom| |#1|) . T) ((|ConvertibleFrom| |#2|) . T) ((|ConvertibleFrom| |#3|) . T) ((|ConvertibleFrom| |#4|) . T) ((|ConvertibleFrom| |#5|) . T) ((|Eltable| (|Integer|) $) . T) ((|Eltable| (|List| (|Integer|)) $) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|symbol?| (#4=(#3# $) 45 T ELT)) (|symbol| ((|#2| $) 48 T ELT)) (|string?| (#4# 20 T ELT)) (|string| ((|#1| $) 21 T ELT)) (|pair?| (#4# 42 T ELT)) (|null?| (#4# 14 T ELT)) (|list?| (#4# 44 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integer?| (#4# 46 T ELT)) (|integer| ((|#3| $) 50 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|float?| (#4# 47 T ELT)) (|float| ((|#4| $) 49 T ELT)) (|expr| ((|#5| $) 51 T ELT)) (|eq| (#2# 41 T ELT)) (|elt| (($ $ #5=(|Integer|)) 62 T ELT) (($ $ (|List| #5#)) 64 T ELT)) (|destruct| ((#6=(|List| $) $) 27 T ELT)) (|convert| (($ |#1|) 53 T ELT) (($ |#2|) 54 T ELT) (($ |#3|) 55 T ELT) (($ |#4|) 56 T ELT) (($ |#5|) 57 T ELT) (($ #6#) 52 T ELT)) (|coerce| (((|OutputForm|) $) 28 T ELT)) (|cdr| (#7=($ $) 26 T ELT)) (|car| (#7# 58 T ELT)) (|before?| #1#) (|atom?| (#4# 23 T ELT)) (= (#2# 40 T ELT)) (|#| ((#5# $) 60 T ELT))) 
(((|SExpressionOf| |#1| |#2| |#3| |#4| |#5|) (|SExpressionCategory| |#1| |#2| |#3| |#4| |#5|) #1=(|SetCategory|) #1# #1# #1# #1#) (T |SExpressionOf|)) 
NIL 
((|supDimElseRittWu?| (#1=(#2=(|Boolean|) |#5| |#5|) 44 T ELT)) (|subTriSet?| (#1# 59 T ELT)) (|subQuasiComponent?| ((#2# |#5| #3=(|List| |#5|)) 82 T ELT) (#1# 68 T ELT)) (|subPolSet?| (#4=(#2# #5=(|List| |#4|) #5#) 65 T ELT)) (|subCase?| ((#2# #6=(|Record| (|:| |val| #5#) #7=(|:| |tower| |#5|)) #6#) 70 T ELT)) (|stopTable!| ((#8=(|Void|)) 32 T ELT)) (|startTable!| ((#8# #9=(|String|) #9# #9#) 28 T ELT)) (|removeSuperfluousQuasiComponents| (#10=(#3# #3#) 101 T ELT)) (|removeSuperfluousCases| ((#11=(|List| #6#) #11#) 93 T ELT)) (|prepareDecompose| (((|List| #12=(|Record| (|:| |eq| #5#) #7# (|:| |ineq| #5#))) #5# #3# #2# #2#) 123 T ELT)) (|moreAlgebraic?| (#1# 53 T ELT)) (|internalSubQuasiComponent?| (((|Union| #2# #13="failed") |#5| |#5|) 78 T ELT)) (|internalSubPolSet?| (#4# 64 T ELT)) (|internalInfRittWu?| (#4# 66 T ELT)) (|infRittWu?| (#4# 67 T ELT)) (|branchIfCan| (((|Union| #12# #13#) #5# |#5| #5# #2# #2# #2# #2# #2#) 118 T ELT)) (|algebraicSort| (#10# 49 T ELT))) 
(((|SquareFreeQuasiComponentPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTable!| (#1=(|Void|) #2=(|String|) #2# #2#)) (SIGNATURE |stopTable!| (#1#)) (SIGNATURE |supDimElseRittWu?| #3=(#4=(|Boolean|) |#5| |#5|)) (SIGNATURE |algebraicSort| #5=(#6=(|List| |#5|) #6#)) (SIGNATURE |moreAlgebraic?| #3#) (SIGNATURE |subTriSet?| #3#) (SIGNATURE |subPolSet?| #7=(#4# #8=(|List| |#4|) #8#)) (SIGNATURE |internalSubPolSet?| #7#) (SIGNATURE |internalInfRittWu?| #7#) (SIGNATURE |infRittWu?| #7#) (SIGNATURE |internalSubQuasiComponent?| ((|Union| #4# #9="failed") |#5| |#5|)) (SIGNATURE |subQuasiComponent?| #3#) (SIGNATURE |subQuasiComponent?| (#4# |#5| #6#)) (SIGNATURE |removeSuperfluousQuasiComponents| #5#) (SIGNATURE |subCase?| (#4# #10=(|Record| (|:| |val| #8#) #11=(|:| |tower| |#5|)) #10#)) (SIGNATURE |removeSuperfluousCases| (#12=(|List| #10#) #12#)) (SIGNATURE |prepareDecompose| ((|List| #13=(|Record| (|:| |eq| #8#) #11# (|:| |ineq| #8#))) #8# #6# #4# #4#)) (SIGNATURE |branchIfCan| ((|Union| #13# #9#) #8# |#5| #8# #4# #4# #4# #4# #4#))) (|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 #1=(|isDomain| *5 #2=(|Boolean|)) #3=(|ofCategory| *6 #4=(|GcdDomain|)) #5=(|ofCategory| *7 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *8 #8=(|OrderedSet|)) #9=(|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| #10=(|:| |eq| #11=(|List| *9)) (|:| |tower| *4) #12=(|:| |ineq| #11#))) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *6 *7 *8 *9 *4)) #13=(|isDomain| *3 #11#) (|ofCategory| *4 #14=(|RegularTriangularSetCategory| *6 *7 *8 *9)))) (|prepareDecompose| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *4 (|List| *10)) #1# (|ofCategory| *10 #14#) #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| #10# (|:| |tower| *10) #12#))) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *6 *7 *8 *9 *10)) #13#)) (|removeSuperfluousCases| #15=(*1 *2 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *6)) (|:| |tower| *7)))) #16=(|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) #17=(|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) #18=(|ofCategory| *3 #4#) #19=(|ofCategory| *4 #6#) #20=(|ofCategory| *5 #8#) #21=(|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7)))) (|subCase?| #22=(*1 *2 *3 *3) (AND (|isDomain| *3 (|Record| (|:| |val| #23=(|List| *7)) (|:| |tower| *8))) #24=(|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) #25=(|ofCategory| *8 #26=(|RegularTriangularSetCategory| *4 *5 *6 *7)) #27=(|ofCategory| *4 #4#) #28=(|ofCategory| *5 #6#) #29=(|ofCategory| *6 #8#) #30=(|isDomain| *2 #2#) #31=(|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8)))) (|removeSuperfluousQuasiComponents| #15# #32=(AND (|isDomain| *2 #23#) #17# #18# #19# #20# #16# #21#)) (|subQuasiComponent?| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 #4#) (|ofCategory| *6 #6#) (|ofCategory| *7 #8#) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) #30# (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *5 *6 *7 *8 *3)))) (|subQuasiComponent?| #22# #33=(AND #27# #28# #29# #24# #30# #34=(|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3)) #35=(|ofCategory| *3 #26#))) (|internalSubQuasiComponent?| #22# (|partial| AND #27# #28# #29# #24# #30# #34# #35#)) (|infRittWu?| #22# #36=(AND (|isDomain| *3 #23#) #24# #27# #28# #29# #30# #31# #25#)) (|internalInfRittWu?| #22# #36#) (|internalSubPolSet?| #22# #36#) (|subPolSet?| #22# #36#) (|subTriSet?| #22# #33#) (|moreAlgebraic?| #22# #33#) (|algebraicSort| #15# #32#) (|supDimElseRittWu?| #22# #33#) (|stopTable!| (*1 *2) (AND #18# #19# #20# #16# #37=(|isDomain| *2 (|Void|)) #21# #17#)) (|startTable!| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|String|)) #27# #28# #29# #24# #37# #31# #25#))) 
((|stoseSquareFreePart| ((#1=(|List| (|Record| (|:| |val| |#4|) #2=(|:| |tower| |#5|))) |#4| |#5|) 106 T ELT)) (|stosePrepareSubResAlgo| ((#3=(|List| (|Record| (|:| |val| (|List| |#4|)) #2#)) |#4| |#4| |#5|) 79 T ELT)) (|stoseLastSubResultant| (#4=(#1# |#4| |#4| |#5|) 100 T ELT)) (|stoseInvertibleSetsqfreg| (#5=((|List| |#5|) |#4| |#5|) 122 T ELT)) (|stoseInvertibleSetreg| (#5# 129 T ELT)) (|stoseInvertibleSet| (#5# 130 T ELT)) (|stoseInvertible?sqfreg| (#6=((|List| (|Record| (|:| |val| #7=(|Boolean|)) #2#)) |#4| |#5|) 107 T ELT)) (|stoseInvertible?reg| (#6# 128 T ELT)) (|stoseInvertible?| (#6# 47 T ELT) ((#7# |#4| |#5|) 55 T ELT)) (|stoseInternalLastSubResultant| ((#1# #3# |#3| #7#) 91 T ELT) ((#1# |#4| |#4| |#5| #7# #7#) 52 T ELT)) (|stoseIntegralLastSubResultant| (#4# 86 T ELT)) (|stopTableInvSet!| (#8=(#9=(|Void|)) 36 T ELT)) (|stopTableGcd!| (#8# 25 T ELT)) (|startTableInvSet!| (#10=(#9# #11=(|String|) #11# #11#) 32 T ELT)) (|startTableGcd!| (#10# 21 T ELT))) 
(((|SquareFreeRegularTriangularSetGcdPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTableGcd!| #1=(#2=(|Void|) #3=(|String|) #3# #3#)) (SIGNATURE |stopTableGcd!| #4=(#2#)) (SIGNATURE |startTableInvSet!| #1#) (SIGNATURE |stopTableInvSet!| #4#) (SIGNATURE |stosePrepareSubResAlgo| (#5=(|List| (|Record| (|:| |val| (|List| |#4|)) #6=(|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |stoseInternalLastSubResultant| (#7=(|List| (|Record| (|:| |val| |#4|) #6#)) |#4| |#4| |#5| #8=(|Boolean|) #8#)) (SIGNATURE |stoseInternalLastSubResultant| (#7# #5# |#3| #8#)) (SIGNATURE |stoseIntegralLastSubResultant| #9=(#7# |#4| |#4| |#5|)) (SIGNATURE |stoseLastSubResultant| #9#) (SIGNATURE |stoseInvertible?| (#8# |#4| |#5|)) (SIGNATURE |stoseInvertible?sqfreg| #10=((|List| (|Record| (|:| |val| #8#) #6#)) |#4| |#5|)) (SIGNATURE |stoseInvertibleSetsqfreg| #11=((|List| |#5|) |#4| |#5|)) (SIGNATURE |stoseInvertible?reg| #10#) (SIGNATURE |stoseInvertibleSetreg| #11#) (SIGNATURE |stoseInvertible?| #10#) (SIGNATURE |stoseInvertibleSet| #11#) (SIGNATURE |stoseSquareFreePart| (#7# |#4| |#5|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |SquareFreeRegularTriangularSetGcdPackage|)) 
((|stoseSquareFreePart| #1=(*1 *2 *3 *4) #2=(AND #3=(|ofCategory| *5 #4=(|GcdDomain|)) #5=(|ofCategory| *6 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *7 #8=(|OrderedSet|)) #9=(|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) #10=(|isDomain| *2 (|List| (|Record| (|:| |val| *3) #11=(|:| |tower| *4)))) #12=(|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) #13=(|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInvertibleSet| #1# #14=(AND #3# #5# #7# #9# (|isDomain| *2 (|List| *4)) #12# #13#)) (|stoseInvertible?| #1# #15=(AND #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| (|:| |val| #16=(|Boolean|)) #11#))) #12# #13#)) (|stoseInvertibleSetreg| #1# #14#) (|stoseInvertible?reg| #1# #15#) (|stoseInvertibleSetsqfreg| #1# #14#) (|stoseInvertible?sqfreg| #1# #15#) (|stoseInvertible?| #1# (AND #3# #5# #7# #9# (|isDomain| *2 #16#) #12# #13#)) (|stoseLastSubResultant| #17=(*1 *2 *3 *3 *4) #2#) (|stoseIntegralLastSubResultant| #17# #2#) (|stoseInternalLastSubResultant| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) #18=(|:| |tower| *9)))) #19=(|isDomain| *5 #16#) (|ofCategory| *8 (|RecursivePolynomialCategory| *6 *7 *4)) (|ofCategory| *9 (|RegularTriangularSetCategory| *6 *7 *4 *8)) #20=(|ofCategory| *6 #4#) #21=(|ofCategory| *7 #6#) (|ofCategory| *4 #8#) (|isDomain| *2 (|List| (|Record| (|:| |val| *8) #18#))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *6 *7 *4 *8 *9)))) (|stoseInternalLastSubResultant| (*1 *2 *3 *3 *4 *5 *5) (AND #19# #20# #21# (|ofCategory| *8 #8#) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) #10# (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|stosePrepareSubResAlgo| #17# (AND #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *3)) #11#))) #12# #13#)) (|stopTableInvSet!| #22=(*1 *2) #23=(AND (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) #24=(|isDomain| *2 (|Void|)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTableInvSet!| #25=(*1 *2 *3 *3 *3) #26=(AND (|isDomain| *3 (|String|)) (|ofCategory| *4 #4#) (|ofCategory| *5 #6#) (|ofCategory| *6 #8#) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) #24# (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|stopTableGcd!| #22# #23#) (|startTableGcd!| #25# #26#)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) ((#2=(|List| $) (|List| |#4|) #3=(|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #4=($)) 39 T ELT)) (|trivialIdeal?| (#5=(#6=(|Boolean|) $) 32 T ELT)) (|triangular?| (#5# 23 (|has| |#1| . #7=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#8=(|Boolean|) |#4| . #9=($)) 107 T ELT) (#10=(#8# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #11=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) . #12=(#13=(|:| |tower| $)))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #14=(|Boolean|) |#4|) . #15=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #16=(#17="failed")) $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#5# 28 (|has| |#1| . #7#) ELT)) (|roughSubIdeal?| (#19=(#6# $ $) 30 (|has| |#1| . #7#) ELT)) (|roughEqualIdeals?| (#19# 29 (|has| |#1| . #7#) ELT)) (|roughBase?| (#5# 31 (|has| |#1| . #7#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #20=($)) 24 (|has| |#1| . #7#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #20#) 25 (|has| |#1| . #7#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| ((#21=(|Union| $ #17#) $) 88 T ELT)) (|removeZero| ((|#4| |#4| . #11#) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #22=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #22#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #14# |#4|) . #15#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #7#) ELT)) (|reduced?| ((#8# |#4| $ (|Mapping| #8# |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| . #11#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #23=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| ((#3# |#4| . #24=($)) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| ((#3# |#4| . #24#) 142 T ELT)) (|purelyAlgebraic?| ((#3# |#4| . #24#) 146 T ELT) ((#3# $) 143 T ELT)) (|normalized?| ((#8# |#4| . #9#) 110 T ELT) (#10# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#25=(|Boolean|) |#4| $) 53 (|has| |#4| . #23#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #4#) 38 T ELT)) (|mainVariable?| ((#6# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #2#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) . #12#)) |#4| |#4| $) 136 T ELT)) (|last| (((|Union| |#4| . #16#) . #26=($)) 89 T ELT)) (|invertibleSet| ((#2# |#4| . #27=($)) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #3# #2#) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #13#)) |#4| $) 140 T ELT) ((#3# |#4| . #24#) 139 T ELT)) (|intersect| ((#2# |#4| . #27#) 134 T ELT) ((#2# (|List| |#4|) . #28=($)) 133 T ELT) ((#2# (|List| |#4|) . #29=(#2#)) 132 T ELT) ((#2# |#4| . #30=(#2#)) 131 T ELT)) (|internalAugment| (($ |#4| $) 126 T ELT) (($ (|List| |#4|) $) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#8# |#4| . #9#) 105 T ELT) (#10# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #11#) 96 T ELT)) (|infRittWu?| ((#8# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #7#) ELT)) (|headReduced?| ((#8# |#4| . #9#) 106 T ELT) (#10# 102 T ELT)) (|headReduce| ((|#4| |#4| . #11#) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| . #16#) . #26#) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #25# |#4|) $) 51 T ELT)) (|extendIfCan| ((#21# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) ((#2# |#4| . #27#) 124 T ELT) ((#2# |#4| . #30#) 123 T ELT) ((#2# (|List| |#4|) . #28#) 122 T ELT) ((#2# (|List| |#4|) . #29#) 121 T ELT)) (|every?| ((#25# (|Mapping| #25# |#4|) . #31=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT)) (|eq?| ((#33=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#33# $) 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#34=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#35=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #23#) ELT) ((#35# (|Mapping| #25# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#36=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #36#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #37=($)) 13 T ELT) (((|List| |#4|) . #37#) 43 T ELT)) (|coHeight| (#34# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #38=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #39=(#17#)) (|List| |#4|) (|Mapping| #8# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #38# (|:| |top| (|List| |#4|))) . #39#) (|List| |#4|) (|Mapping| #8# |#4|) (|Mapping| #8# |#4| |#4|)) 114 T ELT)) (|autoReduced?| ((#8# $ (|Mapping| #8# |#4| (|List| |#4|))) 104 T ELT)) (|augment| ((#2# |#4| . #27#) 130 T ELT) ((#2# |#4| . #30#) 129 T ELT) ((#2# (|List| |#4|) . #28#) 128 T ELT) ((#2# (|List| |#4|) . #29#) 127 T ELT)) (|any?| ((#25# (|Mapping| #25# |#4|) . #31#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraicCoefficients?| ((#3# |#4| . #24#) 144 T ELT)) (|algebraic?| ((#8# |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#35# $) 44 T ELT))) 
(((|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|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) 
((|unrankImproperPartitions1| (#1=(#2=(|List| #3=(|Integer|)) #3# #3# #3#) 40 T ELT)) (|unrankImproperPartitions0| (#1# 30 T ELT)) (|subSet| (#1# 35 T ELT)) (|numberOfImproperPartitions| ((#3# #3# #3#) 22 T ELT)) (|nextPartition| ((#4=(|Vector| #3#) #2# #4# #3#) 78 T ELT) ((#4# #4# #4# #3#) 73 T ELT)) (|nextLatticePermutation| ((#2# #5=(|List| (|PositiveInteger|)) #2# (|Boolean|)) 56 T ELT)) (|nextColeman| ((#6=(|Matrix| #3#) #2# #2# #6#) 77 T ELT)) (|makeYoungTableau| ((#6# #5# #2#) 61 T ELT)) (|listYoungTableaus| (((|List| #6#) #5#) 66 T ELT)) (|inverseColeman| ((#2# #2# #2# #6#) 81 T ELT)) (|coleman| ((#6# #2# #2# #2#) 91 T ELT))) 
(((|SymmetricGroupCombinatoricFunctions|) (CATEGORY |package| (SIGNATURE |coleman| (#1=(|Matrix| #2=(|Integer|)) #3=(|List| #2#) #3# #3#)) (SIGNATURE |inverseColeman| (#3# #3# #3# #1#)) (SIGNATURE |listYoungTableaus| ((|List| #1#) #4=(|List| (|PositiveInteger|)))) (SIGNATURE |makeYoungTableau| (#1# #4# #3#)) (SIGNATURE |nextColeman| (#1# #3# #3# #1#)) (SIGNATURE |nextLatticePermutation| (#3# #4# #3# (|Boolean|))) (SIGNATURE |nextPartition| (#5=(|Vector| #2#) #5# #5# #2#)) (SIGNATURE |nextPartition| (#5# #3# #5# #2#)) (SIGNATURE |numberOfImproperPartitions| (#2# #2# #2#)) (SIGNATURE |subSet| #6=(#3# #2# #2# #2#)) (SIGNATURE |unrankImproperPartitions0| #6#) (SIGNATURE |unrankImproperPartitions1| #6#))) (T |SymmetricGroupCombinatoricFunctions|)) 
((|unrankImproperPartitions1| #1=(*1 *2 *3 *3 *3) #2=(AND #3=(|isDomain| *2 #4=(|List| #5=(|Integer|))) #6=(|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)) #7=(|isDomain| *3 #5#))) (|unrankImproperPartitions0| #1# #2#) (|subSet| #1# #2#) (|numberOfImproperPartitions| (*1 *2 *2 *2) (AND (|isDomain| *2 #5#) #6#)) (|nextPartition| #8=(*1 *2 *3 *2 *4) (AND #9=(|isDomain| *2 (|Vector| #5#)) #10=(|isDomain| *3 #4#) (|isDomain| *4 #5#) #6#)) (|nextPartition| #11=(*1 *2 *2 *2 *3) (AND #9# #7# #6#)) (|nextLatticePermutation| #8# (AND #3# #12=(|isDomain| *3 (|List| (|PositiveInteger|))) (|isDomain| *4 (|Boolean|)) #6#)) (|nextColeman| (*1 *2 *3 *3 *2) (AND #13=(|isDomain| *2 #14=(|Matrix| #5#)) #10# #6#)) (|makeYoungTableau| (*1 *2 *3 *4) (AND #12# (|isDomain| *4 #4#) #13# #6#)) (|listYoungTableaus| (*1 *2 *3) (AND #12# (|isDomain| *2 (|List| #14#)) #6#)) (|inverseColeman| #11# (AND #3# (|isDomain| *3 #14#) #6#)) (|coleman| #1# (AND #10# #13# #6#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|semiGroupOperation| (($ (|Mapping| |#1| |#1| |#1|)) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|SemiGroupOperation| |#1|) (|Join| (|SemiGroupOperatorCategory| |#1|) (|SetCategory|) (CATEGORY |domain| (SIGNATURE |semiGroupOperation| ($ (|Mapping| |#1| |#1| |#1|))))) (|BasicType|)) (T |SemiGroupOperation|)) 
((|semiGroupOperation| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|BasicType|)) (|isDomain| *1 (|SemiGroupOperation| *3))))) 
((|elt| ((|#1| $ |#1| |#1|) 6 T ELT))) 
(((|SemiGroupOperatorCategory| |#1|) (|Category|) (|BasicType|)) (T |SemiGroupOperatorCategory|)) 
NIL 
(|Join| (|BinaryOperatorCategory| |t#1|) (CATEGORY |domain| (ATTRIBUTE (|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|) (|:| |y| |t#1|) (|:| |z| |t#1|)) (= (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|)))))))) 
(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . T)) 
((** (($ $ (|PositiveInteger|)) 10 T ELT))) 
(((|SemiGroup&| |#1|) (CATEGORY |package| (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|SemiGroup|)) (T |SemiGroup&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT)) (* (($ $ $) 18 T ELT))) 
(((|SemiGroup|) (|Category|)) (T |SemiGroup|)) 
((* (*1 *1 *1 *1) (|ofCategory| *1 (|SemiGroup|))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|SemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|PositiveInteger|))))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#3| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#3| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) NIL #9=(|has| |#3| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#3|)) ELT)) (|sup| (#12=($ $ $) NIL #13=(|has| |#3| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#14=(|Union| $ #15="failed") $ $) NIL (|has| |#3| (|CancellationAbelianMonoid|)) ELT)) (|size| (#16=(#17=(|NonNegativeInteger|)) NIL #18=(|has| |#3| (|Finite|)) ELT)) (|setelt| #19=(#20=(|#3| $ #10# |#3|) NIL #11# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #22=(#15#)) . #23=($)) NIL #24=(AND (|has| |#3| (|RetractableTo| #10#)) #25=(|has| |#3| (|SetCategory|))) ELT) (((|Union| #26=(|Fraction| #10#) . #22#) . #23#) NIL #27=(AND (|has| |#3| (|RetractableTo| #26#)) #25#) ELT) ((#28=(|Union| |#3| . #22#) . #23#) NIL #25# ELT)) (|retract| (#29=(#10# . #30=($)) NIL #24# ELT) ((#26# . #30#) NIL #27# ELT) (#31=(|#3| . #30#) NIL #25# ELT)) (|reducedSystem| ((#32=(|Matrix| #10#) . #33=(#34=(|Matrix| $))) NIL #35=(AND (|has| |#3| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #10#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#3|)) (|:| |vec| #41=(|Vector| |#3|))) . #37#) NIL #9# ELT) ((#40# . #33#) NIL #9# ELT)) (|reduce| ((|#3| #42=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) NIL #4# ELT) ((|#3| #42# $ |#3|) NIL T ELT) ((|#3| #42# $) NIL T ELT)) (|recip| ((#14# $) NIL #9# ELT)) (|random| (#21# NIL #18# ELT)) (|qsetelt!| #19#) (|qelt| (#43=(|#3| $ #10#) 12 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| #44=(#29# NIL #45=(|has| #10# #46=(|OrderedSet|)) ELT)) (|min| #47=(#12# NIL #48=(|has| |#3| #46#) ELT)) (|members| #49=((#50=(|List| |#3|) $) NIL T ELT)) (|member?| (#51=(#3# |#3| $) NIL #4# ELT)) (|maxIndex| #44#) (|max| #47#) (|map| (($ #52=(|Mapping| |#3| |#3|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #18# ELT)) (|leftReducedSystem| ((#32# . #53=(#38#)) NIL #35# ELT) ((#36# . #54=(#38# $)) NIL #35# ELT) ((#39# . #54#) NIL #9# ELT) ((#40# . #53#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #25# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #18# ELT)) (|hash| (((|SingleInteger|) $) NIL #25# ELT)) (|first| (#31# NIL #45# ELT)) (|find| ((#28# #55=(|Mapping| #3# |#3|) $) NIL T ELT)) (|fill!| (#56=($ $ |#3|) NIL #11# ELT)) (|every?| #57=((#3# #55# $) NIL T ELT)) (|eval| (($ $ (|List| #58=(|Equation| |#3|))) NIL #59=(AND (|has| |#3| (|Evalable| |#3|)) #25#) ELT) (($ $ #58#) NIL #59# ELT) (($ $ |#3| |#3|) NIL #59# ELT) (($ $ #50# #50#) NIL #59# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#51# NIL (AND (|has| $ (|FiniteAggregate| |#3|)) #4#) ELT)) (|entries| #49#) (|empty?| (#5# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#20# NIL T ELT) (#43# NIL T ELT)) (|dot| ((|#3| $ $) NIL #9# ELT)) (|directProduct| (($ #41#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #60=(|has| |#3| (|Field|)) ELT)) (|differentiate| #61=(#62=($ $ #17#) NIL #63=(AND (|has| |#3| (|DifferentialSpace|)) #9#) ELT) #64=(#65=($ $) NIL #63# ELT) #66=(($ $ #67=(|List| #68=(|Symbol|)) (|List| #17#)) NIL #69=(AND (|has| |#3| (|PartialDifferentialSpace| #68#)) #9#) ELT) #70=(($ $ #68# #17#) NIL #69# ELT) #71=(($ $ #67#) NIL #69# ELT) #72=(($ $ #68#) NIL #69# ELT) #73=(($ $ #52#) NIL #9# ELT) #74=(($ $ #52# #17#) NIL #9# ELT)) (|count| ((#17# |#3| $) NIL #4# ELT) ((#17# #55# $) NIL T ELT)) (|copy| (#65# NIL T ELT)) (|coerce| ((#41# . #75=($)) NIL T ELT) (($ #10#) NIL (OR #24# #9#) ELT) (($ #26#) NIL #27# ELT) (($ |#3|) NIL #25# ELT) ((#76=(|OutputForm|) . #75#) NIL (|has| |#3| (|CoercibleTo| #76#)) ELT)) (|characteristic| (#16# NIL #9# CONST)) (|before?| #1#) (|any?| #57#) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#21# NIL #6# CONST)) (|One| (#21# NIL #9# CONST)) (D #61# #64# #66# #70# #71# #72# #73# #74#) (>= #77=(#2# NIL #48# ELT)) (> #77#) (= #1#) (<= #77#) (< (#2# 24 #48# ELT)) (/ (#56# NIL #60# ELT)) (- (#12# NIL #78=(|has| |#3| (|AbelianGroup|)) ELT) (#65# NIL #78# ELT)) (+ (#12# NIL #79=(|has| |#3| (|AbelianSemiGroup|)) ELT)) (** (#62# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# NIL #9# ELT) (#56# NIL #80=(|has| |#3| (|Monoid|)) ELT) (($ |#3| . #81=($)) NIL #80# ELT) (($ #10# . #81#) NIL #78# ELT) (($ #17# $) NIL #6# ELT) (($ #8# $) NIL #79# ELT)) (|#| ((#17# $) NIL T ELT))) 
(((|SplitHomogeneousDirectProduct| |#1| |#2| |#3|) (|DirectProductCategory| |#1| |#3|) #1=(|NonNegativeInteger|) #1# (|OrderedAbelianMonoidSup|)) (T |SplitHomogeneousDirectProduct|)) 
NIL 
((|subresultantSequence| (#1=((|List| #2=(|UnivariatePolynomial| |#2| |#1|)) #2# #2#) 50 T ELT)) (|countRealRootsMultiple| (#3=(#4=(|Integer|) #2#) 95 #5=(|has| |#1| (|GcdDomain|)) ELT)) (|countRealRoots| (#3# 79 T ELT)) (|SturmHabichtSequence| (#1# 58 T ELT)) (|SturmHabichtMultiple| (#6=(#4# #2# #2#) 81 #5# ELT)) (|SturmHabichtCoefficients| (((|List| |#1|) #2# #2#) 61 T ELT)) (|SturmHabicht| (#6# 78 T ELT))) 
(((|SturmHabichtPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |subresultantSequence| #1=((|List| #2=(|UnivariatePolynomial| |#2| |#1|)) #2# #2#)) (SIGNATURE |SturmHabichtSequence| #1#) (SIGNATURE |SturmHabichtCoefficients| ((|List| |#1|) #2# #2#)) (SIGNATURE |SturmHabicht| #3=(#4=(|Integer|) #2# #2#)) (SIGNATURE |countRealRoots| #5=(#4# #2#)) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |SturmHabichtMultiple| #3#) (SIGNATURE |countRealRootsMultiple| #5#)) |%noBranch|)) (|OrderedIntegralDomain|) (|Symbol|)) (T |SturmHabichtPackage|)) 
((|countRealRootsMultiple| #1=(*1 *2 *3) #2=(AND #3=(|isDomain| *3 #4=(|UnivariatePolynomial| *5 *4)) (|ofCategory| *4 (|GcdDomain|)) #5=(|ofCategory| *4 (|OrderedIntegralDomain|)) #6=(|ofType| *5 (|Symbol|)) #7=(|isDomain| *2 (|Integer|)) #8=(|isDomain| *1 (|SturmHabichtPackage| *4 *5)))) (|SturmHabichtMultiple| #9=(*1 *2 *3 *3) #2#) (|countRealRoots| #1# #10=(AND #3# #5# #6# #7# #8#)) (|SturmHabicht| #9# #10#) (|SturmHabichtCoefficients| #9# (AND #3# #5# #6# (|isDomain| *2 (|List| *4)) #8#)) (|SturmHabichtSequence| #9# #11=(AND #5# #6# (|isDomain| *2 (|List| #4#)) #8# #3#)) (|subresultantSequence| #9# #11#)) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|target| ((#3=(|Syntax|) $) 12 T ELT)) (|source| ((#4=(|List| #3#) $) 14 T ELT)) (|signature| (($ #4# #3#) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 29 T ELT)) (|before?| #1#) (= (#2# 17 T ELT))) 
(((|Signature|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |signature| ($ #1=(|List| #2=(|Syntax|)) #2#)) (SIGNATURE |target| (#2# $)) (SIGNATURE |source| (#1# $))))) (T |Signature|)) 
((|signature| (*1 *1 *2 *3) (AND #1=(|isDomain| *2 (|List| #2=(|Syntax|))) (|isDomain| *3 #2#) #3=(|isDomain| *1 (|Signature|)))) (|target| #4=(*1 *2 *1) (AND (|isDomain| *2 #2#) #3#)) (|source| #4# (AND #1# #3#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|signatureAst| (($ #2=(|Identifier|) #3=(|Signature|)) 14 T ELT)) (|signature| ((#3# $) 20 T ELT)) (|name| ((#2# $) 17 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 27 T ELT) (($ #4=(|Syntax|)) NIL T ELT) ((#4# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|SignatureAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |signatureAst| ($ #1=(|Identifier|) #2=(|Signature|))) (SIGNATURE |name| (#1# $)) (SIGNATURE |signature| (#2# $))))) (T |SignatureAst|)) 
((|signatureAst| (*1 *1 *2 *3) (AND #1=(|isDomain| *2 (|Identifier|)) (|isDomain| *3 #2=(|Signature|)) #3=(|isDomain| *1 (|SignatureAst|)))) (|name| #4=(*1 *2 *1) (AND #1# #3#)) (|signature| #4# (AND (|isDomain| *2 #2#) #3#))) 
((|sign| ((#1=(|Union| (|Integer|) "failed") |#2| #2=(|Symbol|) |#2| (|String|)) 19 T ELT) ((#1# |#2| #2# (|OrderedCompletion| |#2|)) 17 T ELT) ((#1# |#2|) 60 T ELT))) 
(((|ElementaryFunctionSign| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sign| (#1=(|Union| #2=(|Integer|) "failed") |#2|)) (SIGNATURE |sign| (#1# |#2| #3=(|Symbol|) (|OrderedCompletion| |#2|))) (SIGNATURE |sign| (#1# |#2| #3# |#2| (|String|)))) (|Join| (|IntegralDomain|) (|RetractableTo| #2#) (|LinearlyExplicitRingOver| #2#) (|GcdDomain|)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |ElementaryFunctionSign|)) 
((|sign| (*1 *2 *3 *4 *3 *5) (|partial| AND #1=(|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|String|)) #2=(|ofCategory| *6 #3=(|Join| (|IntegralDomain|) (|RetractableTo| *2) (|LinearlyExplicitRingOver| *2) (|GcdDomain|))) #4=(|isDomain| *2 (|Integer|)) #5=(|isDomain| *1 (|ElementaryFunctionSign| *6 *3)) #6=(|ofCategory| *3 (|Join| #7=(|AlgebraicallyClosedField|) #8=(|TranscendentalFunctionCategory|) (|FunctionSpace| *6))))) (|sign| (*1 *2 *3 *4 *5) (|partial| AND #1# (|isDomain| *5 (|OrderedCompletion| *3)) #6# #2# #4# #5#)) (|sign| (*1 *2 *3) (|partial| AND (|ofCategory| *4 #3#) #4# (|isDomain| *1 (|ElementaryFunctionSign| *4 *3)) (|ofCategory| *3 (|Join| #7# #8# (|FunctionSpace| *4)))))) 
((|sign| ((#1=(|Union| (|Integer|) "failed") #2=(|Fraction| (|Polynomial| |#1|)) #3=(|Symbol|) #2# (|String|)) 38 T ELT) ((#1# #2# #3# (|OrderedCompletion| #2#)) 33 T ELT) ((#1# #2#) 14 T ELT))) 
(((|RationalFunctionSign| |#1|) (CATEGORY |package| (SIGNATURE |sign| (#1=(|Union| (|Integer|) "failed") #2=(|Fraction| (|Polynomial| |#1|)))) (SIGNATURE |sign| (#1# #2# #3=(|Symbol|) (|OrderedCompletion| #2#))) (SIGNATURE |sign| (#1# #2# #3# #2# (|String|)))) (|GcdDomain|)) (T |RationalFunctionSign|)) 
((|sign| (*1 *2 *3 *4 *3 *5) (|partial| AND #1=(|isDomain| *3 #2=(|Fraction| (|Polynomial| *6))) #3=(|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|String|)) #4=(|ofCategory| *6 #5=(|GcdDomain|)) #6=(|isDomain| *2 (|Integer|)) #7=(|isDomain| *1 (|RationalFunctionSign| *6)))) (|sign| (*1 *2 *3 *4 *5) (|partial| AND #3# (|isDomain| *5 (|OrderedCompletion| #2#)) #1# #4# #6# #7#)) (|sign| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Fraction| (|Polynomial| *4))) (|ofCategory| *4 #5#) #6# (|isDomain| *1 (|RationalFunctionSign| *4))))) 
((|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) 12 T ELT))) 
(((|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|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (~ (#4=($ $) 22 T ELT)) (|zero?| (#5=(#3# $) 49 T ELT)) (|xor| (#6=($ $ $) 28 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 75 T ELT)) (|unitCanonical| #7=(#4# NIL T ELT)) (|unit?| #8=(#5# NIL T ELT)) (|symmetricRemainder| #9=(#6# NIL T ELT)) (|subtractIfCan| #10=((#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|submod| (#13=($ $ $ $) 59 T ELT)) (|squareFreePart| #7#) (|squareFree| #14=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#15=(#16=(|NonNegativeInteger|)) 61 T ELT)) (|sign| #17=(#18=(#19=(|Integer|) $) NIL T ELT)) (|shift| (#6# 56 T ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #19# #12#) $) NIL T ELT)) (|retract| #17#) (|rem| (#6# 42 T ELT)) (|reducedSystem| ((#22=(|Record| (|:| |mat| #23=(|Matrix| #19#)) (|:| |vec| (|Vector| #19#))) #24=(|Matrix| $) #25=(|Vector| $)) 70 T ELT) ((#23# #24#) 8 T ELT)) (|recip| ((#11# $) NIL T ELT)) (|rationalIfCan| (((|Union| #26=(|Fraction| #19#) #12#) $) NIL T ELT)) (|rational?| #8#) (|rational| ((#26# $) NIL T ELT)) (|random| (#21# 73 T ELT) (#4# 72 T ELT)) (|quo| (#6# 41 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #27=(|List| $)) #28=(|:| |generator| $)) #27#) NIL T ELT)) (|prime?| #8#) (|powmod| (#13# NIL T ELT)) (|positiveRemainder| (#6# 71 T ELT)) (|positive?| (#5# 76 T ELT)) (|permutation| #9#) (|patternMatch| ((#29=(|PatternMatchResult| #19# $) $ #30=(|Pattern| #19#) #29#) NIL T ELT)) (|or| (#6# 27 T ELT)) (|opposite?| #1#) (|one?| (#5# 50 T ELT)) (|odd?| (#5# 47 T ELT)) (|not| (#4# 23 T ELT)) (|nextItem| (((|Maybe| $) $) NIL T ELT)) (|negative?| (#5# 60 T ELT)) (|multiEuclidean| (((|Union| #27# #12#) #27# $) NIL T ELT)) (|mulmod| (#13# 57 T ELT)) (|min| (#6# 52 T ELT) (#21# 19 T CONST)) (|max| (#6# 51 T ELT) (#21# 18 T CONST)) (|mask| #7#) (|lookup| ((#31=(|PositiveInteger|) $) 66 T ELT)) (|length| (#4# 55 T ELT)) (|leftReducedSystem| ((#22# #25# $) NIL T ELT) ((#23# #25#) NIL T ELT)) (|lcm| #9# #32=(($ #27#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|invmod| #9#) (|init| #20#) (|index| (($ #31#) 65 T ELT)) (|inc| (#4# 33 T ELT)) (|hash| (((|SingleInteger|) $) 54 T ELT)) (|gcdPolynomial| ((#33=(|SparseUnivariatePolynomial| $) #33# #33#) NIL T ELT)) (|gcd| (#6# 45 T ELT) #32#) (|factorial| #7#) (|factor| #14#) (|extendedEuclidean| (((|Union| (|Record| #34=(|:| |coef1| $) #35=(|:| |coef2| $)) #12#) $ $ $) NIL T ELT) (((|Record| #34# #35# #28#) $ $) NIL T ELT)) (|exquo| #10#) (|expressIdealMember| (((|Maybe| #27#) #27# $) NIL T ELT)) (|even?| (#5# 48 T ELT)) (|euclideanSize| ((#16# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 44 T ELT)) (|differentiate| #7# #36=(#37=($ $ #16#) NIL T ELT)) (|dec| (#4# 34 T ELT)) (|copy| #7#) (|convert| (#18# 12 T ELT) (((|InputForm|) . #38=($)) NIL T ELT) ((#30# . #38#) NIL T ELT) (((|Float|) . #38#) NIL T ELT) (((|DoubleFloat|) . #38#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT) #39=(($ #19#) 13 T ELT) #7# #39#) (|characteristic| (#15# NIL T CONST)) (|bit?| #1#) (|binomial| #9#) (|before?| #1#) (|base| (#21# 17 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|and| (#6# 26 T ELT)) (|addmod| (#13# 58 T ELT)) (|abs| (#4# 46 T ELT)) (|\\/| (#6# 25 T ELT)) (|Zero| (#21# 15 T CONST)) (|One| (#21# 16 T CONST)) (D #7# #36#) (>= (#2# 32 T ELT)) (> (#2# 30 T ELT)) (= (#2# 21 T ELT)) (<= (#2# 31 T ELT)) (< (#2# 29 T ELT)) (|/\\| (#6# 24 T ELT)) (- (#4# 35 T ELT) (#6# 37 T ELT)) (+ (#6# 36 T ELT)) (** (($ $ #31#) NIL T ELT) (#37# 40 T ELT)) (* (($ #31# $) NIL T ELT) (($ #16# $) NIL T ELT) #40=(($ #19# $) 14 T ELT) (#6# 38 T ELT) #40#)) 
(((|SingleInteger|) (|Join| (|IntegerNumberSystem|) (|OrderedFinite|) (|BooleanLogic|) (CATEGORY |domain| (ATTRIBUTE |canonical|) (ATTRIBUTE |canonicalsClosed|) (ATTRIBUTE |noetherian|) (SIGNATURE |xor| ($ $ $))))) (T |SingleInteger|)) 
((|xor| (*1 *1 *1 *1) (|isDomain| *1 (|SingleInteger|)))) 
((|Integer|) (|%ismall?| |#1|)) 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|top| ((|#1| $) 42 T ELT)) (|sample| (#3=($) 6 T CONST)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 55 (|has| |#1| . #4=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 51 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 50 T ELT)) (|push!| ((|#1| |#1| $) 44 T ELT)) (|pop!| ((|#1| $) 43 T ELT)) (|members| (((|List| |#1|) $) 49 T ELT)) (|member?| ((#5=(|Boolean|) |#1| $) 54 (|has| |#1| . #4#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #6=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #7=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #6#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #5# |#1|) $) 52 T ELT)) (|extract!| ((|#1| . #7#) 37 T ELT)) (|every?| ((#5# (|Mapping| #5# |#1|) . #8=($)) 47 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#9=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#9# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|depth| (((|NonNegativeInteger|) $) 41 T ELT)) (|count| ((#10=(|NonNegativeInteger|) |#1| $) 53 (|has| |#1| . #4#) ELT) ((#10# (|Mapping| #5# |#1|) $) 48 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|any?| ((#5# (|Mapping| #5# |#1|) . #8#) 46 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#10# $) 45 T ELT))) 
(((|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|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |push!| (|t#1| |t#1| $)) (SIGNATURE |pop!| (|t#1| $)) (SIGNATURE |top| (|t#1| $)) (SIGNATURE |depth| ((|NonNegativeInteger|) $)))) 
(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) 
((|sample| (#1=($) 6 T CONST)) (|map!| (($ (|Mapping| |#1| |#1|) $) 12 T ELT)) (|eq?| ((#2=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#1# 8 T ELT)) (|copy| (($ $) 9 T ELT))) 
(((|ShallowlyMutableAggregate| |#1|) (|Category|) (|Type|)) (T |ShallowlyMutableAggregate|)) 
((|map!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|ofCategory| *3 (|Type|))))) 
(|Join| (|Aggregate|) (CATEGORY |domain| (SIGNATURE |map!| ($ (|Mapping| |t#1| |t#1|) $)))) 
(((|Aggregate|) . T) ((|Join|) . T) ((|Type|) . T)) 
((|trace| (#1=(|#3| $) 87 T ELT)) (|retractIfCan| (((|Union| #2=(|Integer|) #3="failed") $) NIL T ELT) (((|Union| #4=(|Fraction| #2#) #3#) $) NIL T ELT) (((|Union| |#3| #3#) $) 50 T ELT)) (|retract| ((#2# $) NIL T ELT) ((#4# $) NIL T ELT) (#1# 47 T ELT)) (|reducedSystem| ((#5=(|Matrix| #2#) #6=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #5#) (|:| |vec| (|Vector| #2#))) #6# #7=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #8=(|Matrix| |#3|)) (|:| |vec| (|Vector| |#3|))) #6# #7#) 84 T ELT) ((#8# #6#) 76 T ELT)) (|differentiate| (($ $ #9=(|Mapping| |#3| |#3|) #10=(|NonNegativeInteger|)) NIL T ELT) (($ $ #9#) 28 T ELT) (($ $) NIL T ELT) (#11=($ $ #10#) NIL T ELT) (($ $ #12=(|Symbol|)) NIL T ELT) (($ $ #13=(|List| #12#)) NIL T ELT) (($ $ #12# #10#) NIL T ELT) (($ $ #13# (|List| #10#)) NIL T ELT)) (|diagonalProduct| (#1# 89 T ELT)) (|diagonal| ((|#4| $) 43 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #2#) NIL T ELT) (($ #4#) NIL T ELT) (($ |#3|) 25 T ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (#11# 24 T ELT) (($ $ #2#) 95 T ELT))) 
(((|SquareMatrixCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |differentiate| (|#1| |#1| #1=(|List| #2=(|Symbol|)) (|List| #3=(|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| #2# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #1#)) (SIGNATURE |differentiate| (|#1| |#1| #2#)) (SIGNATURE |differentiate| #4=(|#1| |#1| #3#)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE ** (|#1| |#1| #5=(|Integer|))) (SIGNATURE |diagonalProduct| #6=(|#3| |#1|)) (SIGNATURE |trace| #6#) (SIGNATURE |diagonal| (|#4| |#1|)) (SIGNATURE |reducedSystem| (#7=(|Matrix| |#3|) #8=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #7#) (|:| |vec| (|Vector| |#3|))) #8# #9=(|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #10=(|Matrix| #5#)) (|:| |vec| (|Vector| #5#))) #8# #9#)) (SIGNATURE |reducedSystem| (#10# #8#)) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |retractIfCan| ((|Union| |#3| #11="failed") |#1|)) (SIGNATURE |retract| #6#) (SIGNATURE |retract| (#12=(|Fraction| #5#) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #12# #11#) |#1|)) (SIGNATURE |coerce| (|#1| #12#)) (SIGNATURE |retract| (#5# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #5# #11#) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #13=(|Mapping| |#3| |#3|))) (SIGNATURE |differentiate| (|#1| |#1| #13# #3#)) (SIGNATURE |coerce| (|#1| #5#)) (SIGNATURE ** #4#) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|SquareMatrixCategory| |#2| |#3| |#4| |#5|) #3# (|Ring|) #14=(|DirectProductCategory| |#2| |#3|) #14#) (T |SquareMatrixCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|trace| ((|#2| $) 91 T ELT)) (|symmetric?| (#3=((|Boolean|) $) 134 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|square?| (#3# 132 T ELT)) (|scalarMatrix| (($ |#2|) 94 T ELT)) (|sample| (#4=($) 23 T CONST)) (|rowEchelon| (($ $) 151 (|has| |#2| (|EuclideanDomain|)) ELT)) (|row| ((|#3| $ #5=(|Integer|)) 146 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 110 (|has| |#2| . #9=((|RetractableTo| #6#))) ELT) (((|Union| #10=(|Fraction| #6#) . #7#) . #8#) 107 (|has| |#2| . #11=((|RetractableTo| #10#))) ELT) (((|Union| |#2| . #7#) . #8#) 104 T ELT)) (|retract| ((#6# . #12=($)) 109 (|has| |#2| . #9#) ELT) ((#10# . #12#) 106 (|has| |#2| . #11#) ELT) ((|#2| . #12#) 105 T ELT)) (|reducedSystem| (((|Matrix| #13=(|Integer|)) . #14=(#15=(|Matrix| $))) 100 (|has| |#2| . #16=((|LinearlyExplicitRingOver| #13#))) ELT) (((|Record| (|:| |mat| (|Matrix| #13#)) (|:| |vec| (|Vector| #13#))) . #17=(#15# #18=(|Vector| $))) 99 (|has| |#2| . #16#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #17#) 98 T ELT) (((|Matrix| |#2|) . #14#) 97 T ELT)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $) 116 T ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 115 T ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 111 (|has| |#2| . #19=((|BasicType|))) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rank| (#20=((|NonNegativeInteger|) $) 152 (|has| |#2| . #21=((|IntegralDomain|))) ELT)) (|qelt| ((|#2| . #22=($ #5# #5#)) 144 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nullity| (#20# 153 (|has| |#2| . #21#) ELT)) (|nullSpace| (((|List| |#4|) $) 154 (|has| |#2| . #21#) ELT)) (|nrows| (#20# 140 T ELT)) (|ncols| (#20# 141 T ELT)) (|minordet| ((|#2| $) 86 (|has| |#2| (ATTRIBUTE (|commutative| #23="*"))) ELT)) (|minRowIndex| (#24=(#5# $) 136 T ELT)) (|minColIndex| (#24# 138 T ELT)) (|members| (((|List| |#2|) $) 117 T ELT)) (|member?| ((#25=(|Boolean|) |#2| $) 112 (|has| |#2| . #19#) ELT)) (|maxRowIndex| (#24# 137 T ELT)) (|maxColIndex| (#24# 139 T ELT)) (|matrix| (($ (|List| (|List| |#2|))) 131 T ELT)) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) 148 T ELT) (($ (|Mapping| |#2| |#2|) $) 126 T ELT)) (|listOfLists| (((|List| (|List| |#2|)) $) 142 T ELT)) (|leftReducedSystem| (((|Matrix| #13#) . #26=(#18#)) 102 (|has| |#2| . #16#) ELT) (((|Record| (|:| |mat| (|Matrix| #13#)) (|:| |vec| (|Vector| #13#))) . #27=(#18# $)) 101 (|has| |#2| . #16#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #27#) 96 T ELT) (((|Matrix| |#2|) . #26#) 95 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inverse| (((|Union| $ "failed") $) 85 (|has| |#2| (|Field|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#2| "failed") (|Mapping| #25# |#2|) $) 114 T ELT)) (|exquo| (((|Union| $ "failed") $ |#2|) 149 (|has| |#2| . #21#) ELT)) (|every?| ((#25# (|Mapping| #25# |#2|) . #28=($)) 119 T ELT)) (|eval| (($ $ (|List| (|Equation| |#2|))) 125 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29=((|SetCategory|)))) ELT) (($ $ (|Equation| |#2|)) 124 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29#)) ELT) (($ $ |#2| |#2|) 123 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 122 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #29#)) ELT)) (|eq?| ((#30=(|Boolean|) $ $) 130 T ELT)) (|empty?| ((#30# $) 127 T ELT)) (|empty| (($) 128 T ELT)) (|elt| ((|#2| $ #5# #5# |#2|) 145 T ELT) ((|#2| . #22#) 143 T ELT)) (|differentiate| (($ $ (|Mapping| |#2| |#2|) . #31=((|NonNegativeInteger|))) 65 T ELT) (($ $ (|Mapping| |#2| |#2|)) 64 T ELT) (($ . #32=($)) 55 (|has| |#2| . #33=((|DifferentialSpace|))) ELT) (#34=($ $ (|NonNegativeInteger|)) 53 (|has| |#2| . #33#) ELT) (($ $ #35=(|Symbol|)) 63 (|has| |#2| . #36=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #35#)) 61 (|has| |#2| . #36#) ELT) (($ $ #35# . #37=(#38=(|NonNegativeInteger|))) 60 (|has| |#2| . #36#) ELT) (($ $ (|List| #35#) . #39=((|List| #38#))) 59 (|has| |#2| . #36#) ELT)) (|diagonalProduct| ((|#2| $) 90 T ELT)) (|diagonalMatrix| (($ (|List| |#2|)) 93 T ELT)) (|diagonal?| (#3# 133 T ELT)) (|diagonal| ((|#3| $) 92 T ELT)) (|determinant| ((|#2| $) 87 (|has| |#2| (ATTRIBUTE (|commutative| #23#))) ELT)) (|count| ((#40=(|NonNegativeInteger|) (|Mapping| #25# |#2|) $) 118 T ELT) ((#40# |#2| $) 113 (|has| |#2| . #19#) ELT)) (|copy| (($ $) 129 T ELT)) (|column| ((|#4| $ #5#) 147 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #10#) 108 (|has| |#2| . #11#) ELT) (($ |#2|) 103 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|any?| ((#25# (|Mapping| #25# |#2|) . #28#) 120 T ELT)) (|antisymmetric?| (#3# 135 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|Mapping| |#2| |#2|) . #31#) 67 T ELT) (($ $ (|Mapping| |#2| |#2|)) 66 T ELT) (($ . #32#) 54 (|has| |#2| . #33#) ELT) (#34# 52 (|has| |#2| . #33#) ELT) (($ $ #35#) 62 (|has| |#2| . #36#) ELT) (($ $ (|List| #35#)) 58 (|has| |#2| . #36#) ELT) (($ $ #35# . #37#) 57 (|has| |#2| . #36#) ELT) (($ $ (|List| #35#) . #39#) 56 (|has| |#2| . #36#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#2|) 150 (|has| |#2| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ (|Integer|)) 84 (|has| |#2| (|Field|)) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #41=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#2|) 156 T ELT) (($ |#2| . #41#) 155 T ELT) ((|#4| $ |#4|) 89 T ELT) ((|#3| |#3| $) 88 T ELT)) (|#| ((#40# $) 121 T ELT))) 
(((|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| #1="*"))) (|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| #1#))) (|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|))))) 
(|Join| (|DifferentialExtension| |t#2|) (|BiModule| |t#2| |t#2|) (|RectangularMatrixCategory| |t#1| |t#1| |t#2| |t#3| |t#4|) (|FullyRetractableTo| |t#2|) (|FullyLinearlyExplicitRingOver| |t#2|) (CATEGORY |domain| (IF (|has| |t#2| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#2|)) |%noBranch|) (SIGNATURE |scalarMatrix| ($ |t#2|)) (SIGNATURE |diagonalMatrix| ($ (|List| |t#2|))) (SIGNATURE |diagonal| (|t#3| $)) (SIGNATURE |trace| (|t#2| $)) (SIGNATURE |diagonalProduct| (|t#2| $)) (SIGNATURE * (|t#4| $ |t#4|)) (SIGNATURE * (|t#3| |t#3| $)) (IF (|has| |t#2| (ATTRIBUTE (|commutative| "*"))) (PROGN (ATTRIBUTE (|Algebra| |t#2|)) (SIGNATURE |determinant| (|t#2| $)) (SIGNATURE |minordet| (|t#2| $))) |%noBranch|) (IF (|has| |t#2| (|Field|)) (PROGN (SIGNATURE |inverse| ((|Union| $ "failed") $)) (SIGNATURE ** ($ $ (|Integer|)))) |%noBranch|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Aggregate|) . T) ((|Algebra| |#2|) |has| |#2| (ATTRIBUTE (|commutative| #1="*"))) ((|BasicType|) . T) ((|BiModule| |#2| |#2|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #2=(|Fraction| (|Integer|))) |has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#2|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) OR (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|DifferentialRing|))) ((|DifferentialExtension| |#2|) . T) ((|DifferentialRing|) |has| |#2| (|DifferentialRing|)) ((|DifferentialSpace|) OR (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|FiniteAggregate| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#2|) . T) ((|FullyRetractableTo| |#2|) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#2|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #3=(|Integer|)) |has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#2|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#2|) OR (|has| |#2| (|CommutativeRing|)) (|has| |#2| (ATTRIBUTE (|commutative| #1#)))) ((|LinearlyExplicitRingOver| #3#) |has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#2|) . T) ((|Module| |#2|) OR (|has| |#2| (|CommutativeRing|)) (|has| |#2| (ATTRIBUTE (|commutative| #1#)))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#2| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #4#) OR (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) ((|RectangularMatrixCategory| |#1| |#1| |#2| |#3| |#4|) . T) ((|RetractableTo| #2#) |has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#2| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|smith| (#1=(|#4| |#4|) 81 T ELT)) (|hermite| (#1# 76 T ELT)) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) 91 T ELT)) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) 80 T ELT)) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) 78 T ELT))) 
(((|SmithNormalForm| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |hermite| #1=(|#4| |#4|)) (SIGNATURE |completeHermite| ((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|)) (SIGNATURE |smith| #1#) (SIGNATURE |completeSmith| ((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|)) (SIGNATURE |diophantineSystem| ((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|))) (|EuclideanDomain|) #2=(|FiniteLinearAggregate| |#1|) #2# (|MatrixCategory| |#1| |#2| |#3|)) (T |SmithNormalForm|)) 
((|diophantineSystem| (*1 *2 *3 *4) (AND (|ofCategory| *5 #1=(|EuclideanDomain|)) (|ofCategory| *6 #2=(|FiniteLinearAggregate| *5)) (|ofCategory| *4 #2#) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|SmithNormalForm| *5 *6 *4 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *4)))) (|completeSmith| #3=(*1 *2 *3) (AND #4=(|ofCategory| *4 #1#) #5=(|ofCategory| *5 #6=(|FiniteLinearAggregate| *4)) #7=(|ofCategory| *6 #6#) (|isDomain| *2 (|Record| (|:| |Smith| *3) (|:| |leftEqMat| *3) (|:| |rightEqMat| *3))) #8=(|isDomain| *1 (|SmithNormalForm| *4 *5 *6 *3)) #9=(|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|smith| #10=(*1 *2 *2) #11=(AND (|ofCategory| *3 #1#) (|ofCategory| *4 #12=(|FiniteLinearAggregate| *3)) (|ofCategory| *5 #12#) (|isDomain| *1 (|SmithNormalForm| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|completeHermite| #3# (AND #4# #5# #7# (|isDomain| *2 (|Record| (|:| |Hermite| *3) (|:| |eqMat| *3))) #8# #9#)) (|hermite| #10# #11#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 18 T ELT)) (|variables| ((#5=(|List| |#2|) $) 174 T ELT)) (|univariate| ((#6=(|SparseUnivariatePolynomial| $) $ |#2|) 60 T ELT) ((#7=(|SparseUnivariatePolynomial| |#1|) $) 49 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 116 #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#9=($ $) 118 #8# ELT)) (|unit?| (#4# 120 #8# ELT)) (|totalDegree| (#10=(#11=(|NonNegativeInteger|) $) NIL T ELT) ((#11# $ #5#) 214 T ELT)) (|subtractIfCan| (#12=(#13=(|Union| $ #14="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #15=(((|Factored| #6#) #6#) NIL #16=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #17=(#9# NIL #18=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#19=((|Factored| $) $) NIL #18# ELT)) (|solveLinearPolynomialEquation| (((|Union| #20=(|List| #6#) #14#) #20# #6#) NIL #16# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #22=(#14#)) $) 167 T ELT) (((|Union| #23=(|Fraction| #24=(|Integer|)) . #22#) . #25=($)) NIL #26=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| #24# . #22#) . #25#) NIL #27=(|has| |#1| (|RetractableTo| #24#)) ELT) (#28=((|Union| |#2| . #22#) . #25#) NIL T ELT)) (|retract| (#29=(|#1| $) 165 T ELT) ((#23# . #30=($)) NIL #26# ELT) ((#24# . #30#) NIL #27# ELT) ((|#2| . #30#) NIL T ELT)) (|resultant| (($ $ $ |#2|) NIL #31=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| (#9# 218 T ELT)) (|reducedSystem| ((#32=(|Matrix| #24#) . #33=(#34=(|Matrix| $))) NIL #35=(|has| |#1| (|LinearlyExplicitRingOver| #24#)) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #24#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #37#) NIL T ELT) ((#40# . #33#) NIL T ELT)) (|recip| ((#13# $) 90 T ELT)) (|primitivePart| #17# (#41=($ $ |#2|) NIL #18# ELT)) (|primitiveMonomials| #42=((#43=(|List| $) $) NIL T ELT)) (|prime?| (#4# NIL #16# ELT)) (|pomopo!| (($ $ |#1| #44=(|IndexedExponents| |#2|) $) NIL T ELT)) (|patternMatch| ((#45=(|PatternMatchResult| #46=(|Float|) . #47=($)) $ #48=(|Pattern| #46#) #45#) NIL (AND (|has| |#1| #49=(|PatternMatchable| #46#)) (|has| |#2| #49#)) ELT) ((#50=(|PatternMatchResult| #24# . #47#) $ #51=(|Pattern| #24#) #50#) NIL (AND (|has| |#1| #52=(|PatternMatchable| #24#)) (|has| |#2| #52#)) ELT)) (|opposite?| #1#) (|one?| (#4# 20 T ELT)) (|numberOfMonomials| (#10# 30 T ELT)) (|multivariate| (($ #7# |#2|) 54 T ELT) (($ #6# |#2|) 71 T ELT)) (|monomials| #42#) (|monomial?| (#4# 38 T ELT)) (|monomial| (($ |#1| #44#) 78 T ELT) (#53=($ $ |#2| #11#) 58 T ELT) #54=(($ $ #5# #55=(|List| #11#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#2|) NIL T ELT)) (|minimumDegree| (#56=(#44# $) 205 T ELT) (#57=(#11# $ |#2|) 206 T ELT) (#58=(#55# $ #5#) 207 T ELT)) (|mapExponents| (($ (|Mapping| #44# #44#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 128 T ELT)) (|mainVariable| (#28# 177 T ELT)) (|leftReducedSystem| ((#32# . #59=(#38#)) NIL #35# ELT) ((#36# . #60=(#38# $)) NIL #35# ELT) ((#39# . #60#) NIL T ELT) ((#40# . #59#) NIL T ELT)) (|leadingMonomial| (#9# 217 T ELT)) (|leadingCoefficient| (#29# 43 T ELT)) (|lcm| (#61=($ #43#) NIL #18# ELT) (#62=($ $ $) NIL #18# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #63=(((|Union| #43# #14#) $) NIL T ELT)) (|isPlus| #63#) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| #11#)) #14#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#4# 39 T ELT)) (|ground| (#29# NIL T ELT)) (|gcdPolynomial| ((#6# #6# #6#) 148 #18# ELT)) (|gcd| (#61# 153 #18# ELT) (#62# 138 #18# ELT)) (|factorSquareFreePolynomial| #15#) (|factorPolynomial| #15#) (|factor| (#19# NIL #16# ELT)) (|exquo| ((#13# $ |#1|) NIL #8# ELT) (#12# 126 #8# ELT)) (|eval| (($ $ (|List| #64=(|Equation| $))) NIL T ELT) (($ $ #64#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #43# #43#) NIL T ELT) (($ $ |#2| |#1|) 180 T ELT) (($ $ #5# #65=(|List| |#1|)) 195 T ELT) (($ $ |#2| $) 179 T ELT) (($ $ #5# #43#) 194 T ELT)) (|discriminant| (#41# NIL #31# ELT)) (|differentiate| #54# #66=(#53# NIL T ELT) #67=(($ $ #5#) NIL T ELT) (#41# 216 T ELT)) (|degree| (#56# 201 T ELT) (#57# 196 T ELT) (#58# 199 T ELT)) (|convert| ((#48# . #68=($)) NIL (AND (|has| |#1| #69=(|ConvertibleTo| #48#)) (|has| |#2| #69#)) ELT) ((#51# . #68#) NIL (AND (|has| |#1| #70=(|ConvertibleTo| #51#)) (|has| |#2| #70#)) ELT) ((#71=(|InputForm|) . #68#) NIL (AND (|has| |#1| #72=(|ConvertibleTo| #71#)) (|has| |#2| #72#)) ELT)) (|content| (#29# 134 #18# ELT) (#41# 137 #18# ELT)) (|conditionP| (((|Union| #38# #14#) #34#) NIL #73=(AND (|has| $ #74=(|CharacteristicNonZero|)) #16#) ELT)) (|coerce| (((|OutputForm|) $) 159 T ELT) (($ #24#) 84 T ELT) (($ |#1|) 85 T ELT) (($ |#2|) 33 T ELT) (#9# NIL #8# ELT) (($ #23#) NIL (OR #75=(|has| |#1| (|Algebra| #23#)) #26#) ELT)) (|coefficients| ((#65# $) 162 T ELT)) (|coefficient| ((|#1| $ #44#) 80 T ELT) #66# #54#) (|charthRoot| (((|Maybe| $) $) NIL (OR #73# (|has| |#1| #74#)) ELT)) (|characteristic| ((#11#) 87 T CONST)) (|binomThmExpt| (($ $ $ #11#) NIL #31# ELT)) (|before?| #1#) (|associates?| (#2# 123 #8# ELT)) (|annihilate?| #1#) (|Zero| (#21# 12 T CONST)) (|One| (#21# 14 T CONST)) (D #54# #66# #67# (#41# NIL T ELT)) (= (#2# 106 T ELT)) (/ (#76=($ $ |#1|) 132 (|has| |#1| (|Field|)) ELT)) (- (#9# 93 T ELT) (#62# 104 T ELT)) (+ (#62# 55 T ELT)) (** (($ $ #77=(|PositiveInteger|)) 110 T ELT) (($ $ #11#) 109 T ELT)) (* (($ #77# $) NIL T ELT) (($ #11# $) NIL T ELT) (($ #24# $) 96 T ELT) (#62# 72 T ELT) (($ $ #23#) NIL #75# ELT) (($ #23# $) NIL #75# ELT) (($ |#1| $) 99 T ELT) (#76# NIL T ELT))) 
(((|SparseMultivariatePolynomial| |#1| |#2|) (|PolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|) (|Ring|) (|OrderedSet|)) (T |SparseMultivariatePolynomial|)) 
NIL 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #7=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #8=(#9=($ $) NIL #7# ELT)) (|unit?| (#5# NIL #7# ELT)) (|tanh| (#9# 149 #10=(|has| |#1| (|Algebra| #11=(|Fraction| #12=(|Integer|)))) ELT)) (|tan| (#9# 125 #10# ELT)) (|subtractIfCan| (#13=(#14=(|Union| $ "failed") $ $) NIL T ELT)) (|sqrt| (#9# NIL #10# ELT)) (|sinh| (#9# 145 #10# ELT)) (|sin| (#9# 121 #10# ELT)) (|sech| (#9# 153 #10# ELT)) (|sec| (#9# 129 #10# ELT)) (|sample| (#15=($) NIL T CONST)) (|reductum| #16=(#9# NIL T ELT)) (|recip| ((#14# $) NIL T ELT)) (|polynomial| ((#17=(|Polynomial| |#1|) $ #18=(|NonNegativeInteger|)) NIL T ELT) ((#17# $ #18# #18#) NIL T ELT)) (|pole?| #4#) (|pi| (#15# NIL #10# ELT)) (|order| ((#18# $ |#2|) NIL T ELT) ((#18# $ |#2| #18#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (($ $ #12#) NIL #10# ELT)) (|monomial?| #4#) (|monomial| (($ $ #6# (|List| #19=(|IndexedExponents| |#2|))) NIL T ELT) (($ $ |#2| #19#) NIL T ELT) (($ |#1| #19#) NIL T ELT) (#20=($ $ |#2| #18#) 63 T ELT) #21=(($ $ #6# (|List| #18#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| (#9# 119 #10# ELT)) (|leadingMonomial| #16#) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#22=($ $ |#2|) NIL #10# ELT) (($ $ |#2| |#1|) 171 #10# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) 170 #10# ELT)) (|extend| (#23=($ $ #18#) 17 T ELT)) (|exquo| (#13# NIL #7# ELT)) (|exp| (#9# 117 #10# ELT)) (|eval| (($ $ |#2| $) 104 T ELT) (($ $ #6# #24=(|List| $)) 99 T ELT) (($ $ (|List| #25=(|Equation| $))) NIL T ELT) (($ $ #25#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #24# #24#) NIL T ELT)) (|differentiate| #21# #26=(#20# NIL T ELT) #27=(($ $ #6#) NIL T ELT) (#22# 106 T ELT)) (|degree| ((#19# $) NIL T ELT)) (|csubst| (((|Mapping| #28=(|Stream| |#3|) |#3|) #6# (|List| #28#)) 87 T ELT)) (|csch| (#9# 155 #10# ELT)) (|csc| (#9# 131 #10# ELT)) (|coth| (#9# 151 #10# ELT)) (|cot| (#9# 127 #10# ELT)) (|cosh| (#9# 147 #10# ELT)) (|cos| (#9# 123 #10# ELT)) (|complete| (#9# 19 T ELT)) (|coerce| (((|OutputForm|) $) 194 T ELT) (($ #12#) NIL T ELT) (($ |#1|) 45 (|has| |#1| (|CommutativeRing|)) ELT) #8# (($ #11#) NIL #10# ELT) (($ |#2|) 70 T ELT) (($ |#3|) 68 T ELT)) (|coefficient| ((|#1| $ #19#) NIL T ELT) #26# #21# ((|#3| $ #18#) 43 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#18#) NIL T CONST)) (|before?| #1#) (|atanh| (#9# 161 #10# ELT)) (|atan| (#9# 137 #10# ELT)) (|associates?| (#2# NIL #7# ELT)) (|asinh| (#9# 157 #10# ELT)) (|asin| (#9# 133 #10# ELT)) (|asech| (#9# 165 #10# ELT)) (|asec| (#9# 141 #10# ELT)) (|annihilate?| #1#) (|acsch| (#9# 167 #10# ELT)) (|acsc| (#9# 143 #10# ELT)) (|acoth| (#9# 163 #10# ELT)) (|acot| (#9# 139 #10# ELT)) (|acosh| (#9# 159 #10# ELT)) (|acos| (#9# 135 #10# ELT)) (|Zero| (#15# 52 T CONST)) (|One| (#15# 62 T CONST)) (D #21# #26# #27# (#22# NIL T ELT)) (= #1#) (/ (#29=($ $ |#1|) 196 (|has| |#1| (|Field|)) ELT)) (- #16# (#30=($ $ $) NIL T ELT)) (+ (#30# 66 T ELT)) (** (($ $ #31=(|PositiveInteger|)) NIL T ELT) (#23# 77 T ELT) (#30# NIL #10# ELT) (#32=($ $ #11#) 109 #10# ELT)) (* (($ #31# $) NIL T ELT) (($ #18# $) NIL T ELT) (($ #12# $) NIL T ELT) (#30# 65 T ELT) (#32# 114 #10# ELT) (($ #11# $) 112 #10# ELT) (($ |#1| $) 48 T ELT) (#29# 49 T ELT) (($ |#3| $) 47 T ELT))) 
(((|SparseMultivariateTaylorSeries| |#1| |#2| |#3|) (|Join| (|MultivariateTaylorSeriesCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |coefficient| (|#3| $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |coerce| ($ |#3|)) (SIGNATURE * ($ |#3| $)) (SIGNATURE |csubst| ((|Mapping| #1=(|Stream| |#3|) |#3|) (|List| |#2|) (|List| #1#))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ |#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)) #1=(|ofCategory| *4 #2=(|Ring|)) (|ofCategory| *5 #3=(|OrderedSet|)))) (|coerce| #4=(*1 *1 *2) (AND #5=(|ofCategory| *3 #2#) #6=(|ofCategory| *2 #3#) #7=(|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *2 *4)) #8=(|ofCategory| *4 (|PolynomialCategory| *3 (|IndexedExponents| *2) *2)))) (|coerce| #4# #9=(AND #5# (|ofCategory| *4 #3#) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *4 *2)) (|ofCategory| *2 (|PolynomialCategory| *3 (|IndexedExponents| *4) *4)))) (* (*1 *1 *2 *1) #9#) (|csubst| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| #10=(|Stream| *7))) (|ofCategory| *6 #3#) (|ofCategory| *7 (|PolynomialCategory| *5 (|IndexedExponents| *6) *6)) (|ofCategory| *5 #2#) (|isDomain| *2 (|Mapping| #10# *7)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *5 *6 *7)))) (|integrate| (*1 *1 *1 *2 *3) (AND (|ofCategory| *3 #11=(|Algebra| (|Fraction| (|Integer|)))) #5# #6# #7# #8#)) (|fintegrate| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Mapping| #12=(|SparseMultivariateTaylorSeries| *4 *3 *5))) (|ofCategory| *4 #11#) #1# (|ofCategory| *3 #3#) (|isDomain| *1 #12#) (|ofCategory| *5 (|PolynomialCategory| *4 (|IndexedExponents| *3) *3))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) ((#2=(|List| $) (|List| |#4|) #3=(|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #4=($)) 39 T ELT)) (|trivialIdeal?| (#5=(#6=(|Boolean|) $) 32 T ELT)) (|triangular?| (#5# 23 (|has| |#1| . #7=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#8=(|Boolean|) |#4| . #9=($)) 107 T ELT) (#10=(#8# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #11=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) . #12=(#13=(|:| |tower| $)))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #14=(|Boolean|) |#4|) . #15=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #16=(#17="failed")) $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#5# 28 (|has| |#1| . #7#) ELT)) (|roughSubIdeal?| (#19=(#6# $ $) 30 (|has| |#1| . #7#) ELT)) (|roughEqualIdeals?| (#19# 29 (|has| |#1| . #7#) ELT)) (|roughBase?| (#5# 31 (|has| |#1| . #7#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #20=($)) 24 (|has| |#1| . #7#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #20#) 25 (|has| |#1| . #7#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| ((#21=(|Union| $ #17#) $) 88 T ELT)) (|removeZero| ((|#4| |#4| . #11#) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #22=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #22#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #14# |#4|) . #15#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #7#) ELT)) (|reduced?| ((#8# |#4| $ (|Mapping| #8# |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| . #11#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #23=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| ((#3# |#4| . #24=($)) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| ((#3# |#4| . #24#) 142 T ELT)) (|purelyAlgebraic?| ((#3# |#4| . #24#) 146 T ELT) ((#3# $) 143 T ELT)) (|normalized?| ((#8# |#4| . #9#) 110 T ELT) (#10# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#25=(|Boolean|) |#4| $) 53 (|has| |#4| . #23#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #4#) 38 T ELT)) (|mainVariable?| ((#6# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #2#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) . #12#)) |#4| |#4| $) 136 T ELT)) (|last| (((|Union| |#4| . #16#) . #26=($)) 89 T ELT)) (|invertibleSet| ((#2# |#4| . #27=($)) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #3# #2#) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #13#)) |#4| $) 140 T ELT) ((#3# |#4| . #24#) 139 T ELT)) (|intersect| ((#2# |#4| . #27#) 134 T ELT) ((#2# (|List| |#4|) . #28=($)) 133 T ELT) ((#2# (|List| |#4|) . #29=(#2#)) 132 T ELT) ((#2# |#4| . #30=(#2#)) 131 T ELT)) (|internalAugment| (($ |#4| $) 126 T ELT) (($ (|List| |#4|) $) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#8# |#4| . #9#) 105 T ELT) (#10# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #11#) 96 T ELT)) (|infRittWu?| ((#8# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #7#) ELT)) (|headReduced?| ((#8# |#4| . #9#) 106 T ELT) (#10# 102 T ELT)) (|headReduce| ((|#4| |#4| . #11#) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| . #16#) . #26#) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #25# |#4|) $) 51 T ELT)) (|extendIfCan| ((#21# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) ((#2# |#4| . #27#) 124 T ELT) ((#2# |#4| . #30#) 123 T ELT) ((#2# (|List| |#4|) . #28#) 122 T ELT) ((#2# (|List| |#4|) . #29#) 121 T ELT)) (|every?| ((#25# (|Mapping| #25# |#4|) . #31=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT)) (|eq?| ((#33=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#33# $) 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#34=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#35=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #23#) ELT) ((#35# (|Mapping| #25# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#36=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #36#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #37=($)) 13 T ELT) (((|List| |#4|) . #37#) 43 T ELT)) (|coHeight| (#34# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #38=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #39=(#17#)) (|List| |#4|) (|Mapping| #8# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #38# (|:| |top| (|List| |#4|))) . #39#) (|List| |#4|) (|Mapping| #8# |#4|) (|Mapping| #8# |#4| |#4|)) 114 T ELT)) (|autoReduced?| ((#8# $ (|Mapping| #8# |#4| (|List| |#4|))) 104 T ELT)) (|augment| ((#2# |#4| . #27#) 130 T ELT) ((#2# |#4| . #30#) 129 T ELT) ((#2# (|List| |#4|) . #28#) 128 T ELT) ((#2# (|List| |#4|) . #29#) 127 T ELT)) (|any?| ((#25# (|Mapping| #25# |#4|) . #31#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraicCoefficients?| ((#3# |#4| . #24#) 144 T ELT)) (|algebraic?| ((#8# |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#35# $) 44 T ELT))) 
(((|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|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|NormalizedTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) 
((|solve| (#1=(#2=(|List| |#2|) |#1|) 15 T ELT)) (|quartic| ((#2# |#2| |#2| |#2| |#2| |#2|) 47 T ELT) (#1# 61 T ELT)) (|quadratic| ((#2# |#2| |#2| |#2|) 45 T ELT) (#1# 59 T ELT)) (|particularSolution| ((|#2| |#1|) 54 T ELT)) (|mapSolve| (((|Record| (|:| |solns| #2#) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) 20 T ELT)) (|linear| ((#2# |#2| |#2|) 42 T ELT) (#1# 58 T ELT)) (|cubic| ((#2# |#2| |#2| |#2| |#2|) 46 T ELT) (#1# 60 T ELT)) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) 53 T ELT)) (|aQuadratic| ((|#2| |#2| |#2| |#2|) 51 T ELT)) (|aLinear| ((|#2| |#2| |#2|) 50 T ELT)) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) 52 T ELT))) 
(((|PolynomialSolveByFormulas| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solve| #1=(#2=(|List| |#2|) |#1|)) (SIGNATURE |particularSolution| (|#2| |#1|)) (SIGNATURE |mapSolve| ((|Record| (|:| |solns| #2#) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |linear| #1#) (SIGNATURE |quadratic| #1#) (SIGNATURE |cubic| #1#) (SIGNATURE |quartic| #1#) (SIGNATURE |linear| (#2# |#2| |#2|)) (SIGNATURE |quadratic| (#2# |#2| |#2| |#2|)) (SIGNATURE |cubic| (#2# |#2| |#2| |#2| |#2|)) (SIGNATURE |quartic| (#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) #1=(AND (|ofCategory| *2 #2=(|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|aCubic| (*1 *2 *2 *2 *2 *2) #1#) (|aQuadratic| (*1 *2 *2 *2 *2) #1#) (|aLinear| (*1 *2 *2 *2) #1#) (|quartic| (*1 *2 *3 *3 *3 *3 *3) #3=(AND (|ofCategory| *3 #2#) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|cubic| (*1 *2 *3 *3 *3 *3) #3#) (|quadratic| (*1 *2 *3 *3 *3) #3#) (|linear| (*1 *2 *3 *3) #3#) (|quartic| #4=(*1 *2 *3) #5=(AND (|ofCategory| *4 #2#) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|cubic| #4# #5#) (|quadratic| #4# #5#) (|linear| #4# #5#) (|mapSolve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 #2#) (|isDomain| *2 (|Record| (|:| |solns| (|List| *5)) (|:| |maps| (|List| (|Record| (|:| |arg| *5) (|:| |res| *5)))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|particularSolution| #4# #1#) (|solve| #4# #5#)) 
((|radicalSolve| ((#1=(|List| #2=(|List| (|Equation| #3=(|Expression| |#1|)))) #4=(|List| #5=(|Equation| #6=(|Fraction| (|Polynomial| |#1|))))) 119 T ELT) ((#1# #4# #7=(|List| #8=(|Symbol|))) 118 T ELT) ((#1# #9=(|List| #6#)) 116 T ELT) ((#1# #9# #7#) 113 T ELT) ((#2# #5#) 97 T ELT) ((#2# #5# #8#) 98 T ELT) ((#2# #6#) 92 T ELT) ((#2# #6# #8#) 82 T ELT)) (|radicalRoots| (((|List| #10=(|List| #3#)) #9# #7#) 111 T ELT) ((#10# #6# #8#) 54 T ELT)) (|contractSolve| ((#11=(|SuchThat| #10# #2#) #6# #8#) 123 T ELT) ((#11# #5# #8#) 122 T ELT))) 
(((|RadicalSolvePackage| |#1|) (CATEGORY |package| (SIGNATURE |radicalSolve| (#1=(|List| (|Equation| #2=(|Expression| |#1|))) #3=(|Fraction| (|Polynomial| |#1|)) #4=(|Symbol|))) (SIGNATURE |radicalSolve| (#1# #3#)) (SIGNATURE |radicalSolve| (#1# #5=(|Equation| #3#) #4#)) (SIGNATURE |radicalSolve| (#1# #5#)) (SIGNATURE |radicalSolve| (#6=(|List| #1#) #7=(|List| #3#) #8=(|List| #4#))) (SIGNATURE |radicalSolve| (#6# #7#)) (SIGNATURE |radicalSolve| (#6# #9=(|List| #5#) #8#)) (SIGNATURE |radicalSolve| (#6# #9#)) (SIGNATURE |radicalRoots| (#10=(|List| #2#) #3# #4#)) (SIGNATURE |radicalRoots| ((|List| #10#) #7# #8#)) (SIGNATURE |contractSolve| (#11=(|SuchThat| #10# #1#) #5# #4#)) (SIGNATURE |contractSolve| (#11# #3# #4#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (T |RadicalSolvePackage|)) 
((|contractSolve| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 #3=(|Fraction| (|Polynomial| *5))) #4=(|isDomain| *4 #5=(|Symbol|)) #6=(|ofCategory| *5 #7=(|Join| (|EuclideanDomain|) (|CharacteristicZero|))) #8=(|isDomain| *2 (|SuchThat| #9=(|List| #10=(|Expression| *5)) #11=(|List| (|Equation| #10#)))) #12=(|isDomain| *1 (|RadicalSolvePackage| *5)))) (|contractSolve| #1# (AND #13=(|isDomain| *3 #14=(|Equation| #3#)) #4# #6# #8# #12#)) (|radicalRoots| #1# (AND #15=(|isDomain| *3 (|List| #3#)) #16=(|isDomain| *4 (|List| #5#)) #6# (|isDomain| *2 (|List| #9#)) #12#)) (|radicalRoots| #1# (AND #2# #4# #6# (|isDomain| *2 #9#) #12#)) (|radicalSolve| #17=(*1 *2 *3) (AND (|isDomain| *3 (|List| #18=(|Equation| #19=(|Fraction| (|Polynomial| *4))))) #20=(|ofCategory| *4 #7#) #21=(|isDomain| *2 (|List| #22=(|List| (|Equation| (|Expression| *4))))) #23=(|isDomain| *1 (|RadicalSolvePackage| *4)))) (|radicalSolve| #1# (AND (|isDomain| *3 (|List| #14#)) #16# #6# #24=(|isDomain| *2 (|List| #11#)) #12#)) (|radicalSolve| #17# (AND (|isDomain| *3 (|List| #19#)) #20# #21# #23#)) (|radicalSolve| #1# (AND #15# #16# #6# #24# #12#)) (|radicalSolve| #17# (AND (|isDomain| *3 #18#) #20# #25=(|isDomain| *2 #22#) #23#)) (|radicalSolve| #1# (AND #13# #4# #6# #26=(|isDomain| *2 #11#) #12#)) (|radicalSolve| #17# (AND (|isDomain| *3 #19#) #20# #25# #23#)) (|radicalSolve| #1# (AND #2# #4# #6# #26# #12#))) 
((|unvectorise| ((#1=(|Fraction| (|SparseUnivariatePolynomial| #2=(|Expression| |#1|))) (|Vector| #2#) #1# (|Integer|)) 36 T ELT)) (|decomposeFunc| ((#1# #1# #1# #1#) 48 T ELT))) 
(((|TransSolvePackageService| |#1|) (CATEGORY |package| (SIGNATURE |decomposeFunc| (#1=(|Fraction| (|SparseUnivariatePolynomial| #2=(|Expression| |#1|))) #1# #1# #1#)) (SIGNATURE |unvectorise| (#1# (|Vector| #2#) #1# (|Integer|)))) (|IntegralDomain|)) (T |TransSolvePackageService|)) 
((|unvectorise| (*1 *2 *3 *2 *4) (AND (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| #1=(|Expression| *5)))) (|isDomain| *3 (|Vector| #1#)) (|isDomain| *4 (|Integer|)) (|ofCategory| *5 #2=(|IntegralDomain|)) (|isDomain| *1 (|TransSolvePackageService| *5)))) (|decomposeFunc| (*1 *2 *2 *2 *2) (AND (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| (|Expression| *3)))) (|ofCategory| *3 #2#) (|isDomain| *1 (|TransSolvePackageService| *3))))) 
((|solve| (((|List| #1=(|List| #2=(|Equation| #3=(|Expression| |#1|)))) #1# (|List| #4=(|Symbol|))) 244 T ELT) ((#1# #3# #4#) 23 T ELT) ((#1# #2# #4#) 29 T ELT) ((#1# #2#) 28 T ELT) ((#1# #3#) 24 T ELT))) 
(((|TransSolvePackage| |#1|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|List| #2=(|Equation| #3=(|Expression| |#1|))) #3#)) (SIGNATURE |solve| (#1# #2#)) (SIGNATURE |solve| (#1# #2# #4=(|Symbol|))) (SIGNATURE |solve| (#1# #3# #4#)) (SIGNATURE |solve| ((|List| #1#) #1# (|List| #4#)))) (|Join| (|EuclideanDomain|) (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#) (|CharacteristicZero|))) (T |TransSolvePackage|)) 
((|solve| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|List| #2=(|Symbol|))) #3=(|ofCategory| *5 #4=(|Join| (|EuclideanDomain|) (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#) (|CharacteristicZero|))) (|isDomain| *2 (|List| #6=(|List| #7=(|Equation| #8=(|Expression| *5))))) #9=(|isDomain| *1 (|TransSolvePackage| *5)) (|isDomain| *3 #6#))) (|solve| #1# (AND #10=(|isDomain| *4 #2#) #3# #11=(|isDomain| *2 #6#) #9# (|isDomain| *3 #8#))) (|solve| #1# (AND #10# #3# #11# #9# (|isDomain| *3 #7#))) (|solve| #12=(*1 *2 *3) (AND #13=(|ofCategory| *4 #4#) #14=(|isDomain| *2 (|List| #15=(|Equation| #16=(|Expression| *4)))) #17=(|isDomain| *1 (|TransSolvePackage| *4)) (|isDomain| *3 #15#))) (|solve| #12# (AND #13# #14# #17# (|isDomain| *3 #16#)))) 
((|insertionSort!| (#1=(|#2| |#2|) 28 #2=(|has| |#1| (|OrderedSet|)) ELT) (#3=(|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) 25 T ELT)) (|bubbleSort!| (#1# 27 #2# ELT) (#3# 22 T ELT))) 
(((|SortPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |bubbleSort!| #1=(|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|))) (SIGNATURE |insertionSort!| #1#) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |bubbleSort!| #2=(|#2| |#2|)) (SIGNATURE |insertionSort!| #2#)) |%noBranch|)) (|Type|) (|Join| (|IndexedAggregate| (|Integer|) |#1|) (|FiniteAggregate| |#1|) (|ShallowlyMutableAggregate| |#1|))) (T |SortPackage|)) 
((|insertionSort!| #1=(*1 *2 *2) #2=(AND (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 #3=(|Type|)) (|isDomain| *1 (|SortPackage| *3 *2)) (|ofCategory| *2 (|Join| (|IndexedAggregate| #4=(|Integer|) *3) (|FiniteAggregate| *3) (|ShallowlyMutableAggregate| *3))))) (|bubbleSort!| #1# #2#) (|insertionSort!| #5=(*1 *2 *2 *3) #6=(AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 #3#) (|isDomain| *1 (|SortPackage| *4 *2)) (|ofCategory| *2 (|Join| (|IndexedAggregate| #4# *4) (|FiniteAggregate| *4) (|ShallowlyMutableAggregate| *4))))) (|bubbleSort!| #5# #6#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|subspace| ((#3=(|SubSpace| 3 |#1|) $) 141 T ELT)) (|polygon?| (#4=(#2# $) 101 T ELT)) (|polygon| (#5=($ $ #6=(|List| #7=(|Point| |#1|))) 44 T ELT) (#8=($ $ #9=(|List| #10=(|List| |#1|))) 104 T ELT) (#11=($ #6#) 103 T ELT) (#12=(#6# $) 102 T ELT)) (|point?| (#4# 72 T ELT)) (|point| (($ $ #7#) 76 T ELT) (($ $ #10#) 81 T ELT) (($ $ #13=(|NonNegativeInteger|)) 83 T ELT) (($ #7#) 77 T ELT) ((#7# $) 75 T ELT)) (|objects| (((|Record| (|:| |points| #13#) (|:| |curves| #13#) (|:| |polygons| #13#) (|:| |constructs| #13#)) $) 139 T ELT)) (|numberOfComposites| (#14=(#13# $) 53 T ELT)) (|numberOfComponents| (#14# 52 T ELT)) (|modifyPointData| (($ $ #13# #7#) 67 T ELT)) (|mesh?| (#4# 111 T ELT)) (|mesh| (($ $ #15=(|List| #6#) #16=(|List| #17=(|SubSpaceComponentProperty|)) #17#) 118 T ELT) (($ $ #18=(|List| #9#) #16# #17#) 120 T ELT) (($ $ #15# #2# #2#) 115 T ELT) (($ $ #18# #2# #2#) 127 T ELT) (($ #15#) 116 T ELT) (($ #15# #2# #2#) 117 T ELT) ((#15# $) 114 T ELT)) (|merge| (#19=($ #20=(|List| $)) 56 T ELT) (($ $ $) 57 T ELT)) (|lprop| ((#16# $) 133 T ELT)) (|lp| (#12# 130 T ELT)) (|llprop| (((|List| #16#) $) 132 T ELT)) (|lllp| (((|List| #15#) $) NIL T ELT)) (|lllip| (((|List| (|List| (|List| #13#))) $) 131 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|enterPointData| ((#13# $ #6#) 65 T ELT)) (|curve?| (#4# 84 T ELT)) (|curve| (#5# 86 T ELT) (#8# 92 T ELT) (#11# 87 T ELT) (#12# 85 T ELT)) (|create3Space| (($) 48 T ELT) (($ #3#) 49 T ELT)) (|copy| (#21=($ $) 63 T ELT)) (|composites| (#22=(#20# $) 62 T ELT)) (|composite| (#19# 59 T ELT)) (|components| (#22# 61 T ELT)) (|coerce| (((|OutputForm|) $) 146 T ELT)) (|closedCurve?| (#4# 94 T ELT)) (|closedCurve| (#5# 96 T ELT) (#8# 99 T ELT) (#11# 97 T ELT) (#12# 95 T ELT)) (|check| (#21# 140 T ELT)) (|before?| #1#) (= #1#)) 
(((|ThreeSpace| |#1|) (|ThreeSpaceCategory| |#1|) (|Ring|)) (T |ThreeSpace|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|subspace| (((|SubSpace| 3 |#1|) $) 17 T ELT)) (|polygon?| (((|Boolean|) $) 33 T ELT)) (|polygon| (($ $ (|List| (|Point| |#1|))) 37 T ELT) (($ $ (|List| (|List| |#1|))) 36 T ELT) (($ (|List| (|Point| |#1|))) 35 T ELT) (((|List| (|Point| |#1|)) $) 34 T ELT)) (|point?| (((|Boolean|) $) 48 T ELT)) (|point| (($ $ (|Point| |#1|)) 53 T ELT) (($ $ (|List| |#1|)) 52 T ELT) (($ $ (|NonNegativeInteger|)) 51 T ELT) (($ (|Point| |#1|)) 50 T ELT) (((|Point| |#1|) $) 49 T ELT)) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) 19 T ELT)) (|numberOfComposites| (((|NonNegativeInteger|) $) 62 T ELT)) (|numberOfComponents| (((|NonNegativeInteger|) $) 63 T ELT)) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) 54 T ELT)) (|mesh?| (((|Boolean|) $) 25 T ELT)) (|mesh| (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) 32 T ELT) (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) 31 T ELT) (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) 30 T ELT) (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) 29 T ELT) (($ (|List| (|List| (|Point| |#1|)))) 28 T ELT) (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) 27 T ELT) (((|List| (|List| (|Point| |#1|))) $) 26 T ELT)) (|merge| (($ (|List| $)) 61 T ELT) (($ $ $) 60 T ELT)) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) 20 T ELT)) (|lp| (((|List| (|Point| |#1|)) $) 24 T ELT)) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) 21 T ELT)) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) 22 T ELT)) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) 23 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) 55 T ELT)) (|curve?| (((|Boolean|) $) 43 T ELT)) (|curve| (($ $ (|List| (|Point| |#1|))) 47 T ELT) (($ $ (|List| (|List| |#1|))) 46 T ELT) (($ (|List| (|Point| |#1|))) 45 T ELT) (((|List| (|Point| |#1|)) $) 44 T ELT)) (|create3Space| (($) 65 T ELT) (($ (|SubSpace| 3 |#1|)) 64 T ELT)) (|copy| (($ $) 56 T ELT)) (|composites| (((|List| $) $) 57 T ELT)) (|composite| (($ (|List| $)) 59 T ELT)) (|components| (((|List| $) $) 58 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|closedCurve?| (((|Boolean|) $) 38 T ELT)) (|closedCurve| (($ $ (|List| (|Point| |#1|))) 42 T ELT) (($ $ (|List| (|List| |#1|))) 41 T ELT) (($ (|List| (|Point| |#1|))) 40 T ELT) (((|List| (|Point| |#1|)) $) 39 T ELT)) (|check| (($ $) 18 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|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) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|latex| (#3=(#4=(|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 185 T ELT) (($ #5=(|Syntax|)) NIL T ELT) ((#5# $) 7 T ELT)) (|case| ((#2# $ (|[\|\|]| #6=(|ImportAst|))) 19 T ELT) ((#2# $ (|[\|\|]| #7=(|DefinitionAst|))) 23 T ELT) ((#2# $ (|[\|\|]| #8=(|MacroAst|))) 27 T ELT) ((#2# $ (|[\|\|]| #9=(|WhereAst|))) 31 T ELT) ((#2# $ (|[\|\|]| #10=(|CategoryAst|))) 35 T ELT) ((#2# $ (|[\|\|]| #11=(|JoinAst|))) 39 T ELT) ((#2# $ (|[\|\|]| #12=(|CapsuleAst|))) 43 T ELT) ((#2# $ (|[\|\|]| #13=(|SignatureAst|))) 47 T ELT) ((#2# $ (|[\|\|]| #14=(|AttributeAst|))) 51 T ELT) ((#2# $ (|[\|\|]| #15=(|MappingAst|))) 55 T ELT) ((#2# $ (|[\|\|]| #16=(|IfAst|))) 59 T ELT) ((#2# $ (|[\|\|]| #17=(|RepeatAst|))) 63 T ELT) ((#2# $ (|[\|\|]| #18=(|WhileAst|))) 67 T ELT) ((#2# $ (|[\|\|]| #19=(|InAst|))) 71 T ELT) ((#2# $ (|[\|\|]| #20=(|StepAst|))) 75 T ELT) ((#2# $ (|[\|\|]| #21=(|CollectAst|))) 79 T ELT) ((#2# $ (|[\|\|]| #22=(|ConstructAst|))) 83 T ELT) ((#2# $ (|[\|\|]| #23=(|ExitAst|))) 87 T ELT) ((#2# $ (|[\|\|]| #24=(|ReturnAst|))) 91 T ELT) ((#2# $ (|[\|\|]| #25=(|CoerceAst|))) 95 T ELT) ((#2# $ (|[\|\|]| #26=(|PretendAst|))) 99 T ELT) ((#2# $ (|[\|\|]| #27=(|RestrictAst|))) 103 T ELT) ((#2# $ (|[\|\|]| #28=(|SegmentAst|))) 107 T ELT) ((#2# $ (|[\|\|]| #29=(|SequenceAst|))) 111 T ELT) ((#2# $ (|[\|\|]| #30=(|LetAst|))) 116 T ELT) ((#2# $ (|[\|\|]| #31=(|SuchThatAst|))) 120 T ELT) ((#2# $ (|[\|\|]| #32=(|ColonAst|))) 124 T ELT) ((#2# $ (|[\|\|]| #33=(|CaseAst|))) 128 T ELT) ((#2# $ (|[\|\|]| #34=(|HasAst|))) 132 T ELT) ((#2# $ (|[\|\|]| #35=(|IsAst|))) 136 T ELT) ((#2# $ (|[\|\|]| #36=(|Identifier|))) 140 T ELT) ((#2# $ (|[\|\|]| #4#)) 144 T ELT) ((#2# $ (|[\|\|]| #37=(|Integer|))) 148 T ELT)) (|before?| #1#) (|autoCoerce| ((#6# $) 20 T ELT) ((#7# $) 24 T ELT) ((#8# $) 28 T ELT) ((#9# $) 32 T ELT) ((#10# $) 36 T ELT) ((#11# $) 40 T ELT) ((#12# $) 44 T ELT) ((#13# $) 48 T ELT) ((#14# $) 52 T ELT) ((#15# $) 56 T ELT) ((#16# $) 60 T ELT) ((#17# $) 64 T ELT) ((#18# $) 68 T ELT) ((#19# $) 72 T ELT) ((#20# $) 76 T ELT) ((#21# $) 80 T ELT) ((#22# $) 84 T ELT) ((#23# $) 88 T ELT) ((#24# $) 92 T ELT) ((#25# $) 96 T ELT) ((#26# $) 100 T ELT) ((#27# $) 104 T ELT) ((#28# $) 108 T ELT) ((#29# $) 112 T ELT) ((#30# $) 117 T ELT) ((#31# $) 121 T ELT) ((#32# $) 125 T ELT) ((#33# $) 129 T ELT) ((#34# $) 133 T ELT) ((#35# $) 137 T ELT) ((#36# $) 141 T ELT) (#3# 145 T ELT) ((#37# $) 149 T ELT)) (= #1#)) 
(((|SpadAst|) (|SpadAstExports|)) (T |SpadAst|)) 
NIL 
((|parse| (((|List| (|Syntax|)) (|String|)) 9 T ELT))) 
(((|SpadParser|) (CATEGORY |package| (SIGNATURE |parse| ((|List| (|Syntax|)) (|String|))))) (T |SpadParser|)) 
((|parse| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|List| (|Syntax|))) (|isDomain| *1 (|SpadParser|))))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) . #2=($)) 13 T ELT) (($ #3=(|Syntax|)) 20 T ELT) ((#3# . #2#) 19 T ELT)) (|case| (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) 88 T ELT) (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) 86 T ELT) (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) 84 T ELT) (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) 82 T ELT) (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) 80 T ELT) (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) 78 T ELT) (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) 76 T ELT) (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) 74 T ELT) (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) 72 T ELT) (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) 70 T ELT) (((|Boolean|) $ (|[\|\|]| (|IfAst|))) 68 T ELT) (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) 66 T ELT) (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) 64 T ELT) (((|Boolean|) $ (|[\|\|]| (|InAst|))) 62 T ELT) (((|Boolean|) $ (|[\|\|]| (|StepAst|))) 60 T ELT) (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) 58 T ELT) (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) 56 T ELT) (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) 54 T ELT) (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) 52 T ELT) (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) 50 T ELT) (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) 48 T ELT) (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) 46 T ELT) (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) 44 T ELT) (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) 42 T ELT) (((|Boolean|) $ (|[\|\|]| (|LetAst|))) 40 T ELT) (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) 38 T ELT) (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) 36 T ELT) (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) 34 T ELT) (((|Boolean|) $ (|[\|\|]| (|HasAst|))) 32 T ELT) (((|Boolean|) $ (|[\|\|]| (|IsAst|))) 30 T ELT) (((|Boolean|) $ (|[\|\|]| (|Identifier|))) 28 T ELT) (((|Boolean|) $ (|[\|\|]| (|String|))) 26 T ELT) (((|Boolean|) $ (|[\|\|]| (|Integer|))) 24 T ELT)) (|before?| (#1# 6 T ELT)) (|autoCoerce| (((|ImportAst|) $) 87 T ELT) (((|DefinitionAst|) $) 85 T ELT) (((|MacroAst|) $) 83 T ELT) (((|WhereAst|) $) 81 T ELT) (((|CategoryAst|) $) 79 T ELT) (((|JoinAst|) $) 77 T ELT) (((|CapsuleAst|) $) 75 T ELT) (((|SignatureAst|) $) 73 T ELT) (((|AttributeAst|) $) 71 T ELT) (((|MappingAst|) $) 69 T ELT) (((|IfAst|) $) 67 T ELT) (((|RepeatAst|) $) 65 T ELT) (((|WhileAst|) $) 63 T ELT) (((|InAst|) $) 61 T ELT) (((|StepAst|) $) 59 T ELT) (((|CollectAst|) $) 57 T ELT) (((|ConstructAst|) $) 55 T ELT) (((|ExitAst|) $) 53 T ELT) (((|ReturnAst|) $) 51 T ELT) (((|CoerceAst|) $) 49 T ELT) (((|PretendAst|) $) 47 T ELT) (((|RestrictAst|) $) 45 T ELT) (((|SegmentAst|) $) 43 T ELT) (((|SequenceAst|) $) 41 T ELT) (((|LetAst|) $) 39 T ELT) (((|SuchThatAst|) $) 37 T ELT) (((|ColonAst|) $) 35 T ELT) (((|CaseAst|) $) 33 T ELT) (((|HasAst|) $) 31 T ELT) (((|IsAst|) $) 29 T ELT) (((|Identifier|) $) 27 T ELT) (((|String|) $) 25 T ELT) (((|Integer|) $) 23 T ELT)) (= (#1# 8 T ELT))) 
(((|SpadAstExports|) (|Category|)) (T |SpadAstExports|)) 
((|case| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *3 (|[\|\|]| (|ImportAst|))) (|isDomain| *2 (|Boolean|)))) (|autoCoerce| (*1 *2 *1) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|ImportAst|)))) (|case| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *3 (|[\|\|]| (|DefinitionAst|))) (|isDomain| *2 (|Boolean|)))) (|autoCoerce| (*1 *2 *1) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|DefinitionAst|)))) (|case| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *3 (|[\|\|]| (|MacroAst|))) (|isDomain| *2 (|Boolean|)))) (|autoCoerce| (*1 *2 *1) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|MacroAst|)))) (|case| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *3 (|[\|\|]| (|WhereAst|))) (|isDomain| *2 (|Boolean|)))) (|autoCoerce| (*1 *2 *1) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|WhereAst|)))) (|case| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *3 (|[\|\|]| (|CategoryAst|))) (|isDomain| *2 (|Boolean|)))) (|autoCoerce| (*1 *2 *1) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|CategoryAst|)))) (|case| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *3 (|[\|\|]| (|JoinAst|))) (|isDomain| *2 (|Boolean|)))) (|autoCoerce| (*1 *2 *1) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|JoinAst|)))) (|case| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *3 (|[\|\|]| (|CapsuleAst|))) (|isDomain| *2 (|Boolean|)))) (|autoCoerce| (*1 *2 *1) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|CapsuleAst|)))) (|case| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *3 (|[\|\|]| (|SignatureAst|))) (|isDomain| *2 (|Boolean|)))) (|autoCoerce| (*1 *2 *1) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *2 (|SignatureAst|)))) (|case| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|SpadAstExports|)) (|isDomain| *3 (|[\|\|]| 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(((|SplittingNode| |#1| |#2|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (SIGNATURE |empty| ($)) (SIGNATURE |empty?| #2=(#3=(|Boolean|) $)) (SIGNATURE |value| (|#1| $)) (SIGNATURE |condition| (|#2| $)) (SIGNATURE |status| #2#) (SIGNATURE |construct| ($ |#1| |#2| #3#)) (SIGNATURE |construct| ($ |#1| |#2|)) (SIGNATURE |construct| ($ #4=(|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) (SIGNATURE |construct| (#5=(|List| $) (|List| #4#))) (SIGNATURE |construct| (#5# |#1| (|List| |#2|))) (SIGNATURE |copy| #6=($ $)) (SIGNATURE |setValue!| ($ $ |#1|)) (SIGNATURE |setCondition!| ($ $ |#2|)) (SIGNATURE |setStatus!| ($ $ #3#)) (SIGNATURE |setEmpty!| #6#) (SIGNATURE |infLex?| (#3# $ $ (|Mapping| #3# |#1| |#1|) #7=(|Mapping| #3# |#2| |#2|))) (SIGNATURE |subNode?| (#3# $ $ #7#)))) #8=(|Join| #1# (|Aggregate|)) #8#) (T |SplittingNode|)) 
((|empty| (*1 *1) #1=(AND #2=(|isDomain| *1 (|SplittingNode| *2 *3)) #3=(|ofCategory| *2 #4=(|Join| (|SetCategory|) (|Aggregate|))) #5=(|ofCategory| *3 #4#))) (|empty?| #6=(*1 *2 *1) #7=(AND #8=(|isDomain| *2 #9=(|Boolean|)) #10=(|isDomain| *1 (|SplittingNode| *3 *4)) #5# #11=(|ofCategory| *4 #4#))) (|value| #6# (AND #3# #2# #5#)) (|condition| #6# (AND #3# #12=(|isDomain| *1 (|SplittingNode| *3 *2)) #5#)) (|status| #6# #7#) (|construct| (*1 *1 *2 *3 *4) (AND (|isDomain| *4 #9#) #2# #3# #5#)) (|construct| (*1 *1 *2 *3) #1#) (|construct| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |val| *3) (|:| |tower| *4))) #5# #11# #10#)) (|construct| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| *4) (|:| |tower| *5)))) #11# #13=(|ofCategory| *5 #4#) (|isDomain| *2 (|List| #14=(|SplittingNode| *4 *5))) #15=(|isDomain| *1 #14#))) (|construct| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *5)) #13# (|isDomain| *2 (|List| #16=(|SplittingNode| *3 *5))) (|isDomain| *1 #16#) #5#)) (|copy| #17=(*1 *1 *1) #1#) (|setValue!| #18=(*1 *1 *1 *2) #1#) (|setCondition!| #18# (AND #12# #5# #3#)) (|setStatus!| #18# #7#) (|setEmpty!| #17# #1#) (|infLex?| (*1 *2 *1 *1 *3 *4) (AND #19=(|isDomain| *3 (|Mapping| #9# *5 *5)) (|isDomain| *4 (|Mapping| #9# *6 *6)) #13# (|ofCategory| *6 #4#) #8# (|isDomain| *1 (|SplittingNode| *5 *6)))) (|subNode?| (*1 *2 *1 *1 *3) (AND #19# #13# #8# #15# #11#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| #5=(|SplittingNode| |#1| |#2|) (|BasicType|)) ELT)) (|value| ((#5# $) 27 T ELT)) (|updateStatus!| (#6=($ $) 91 T ELT)) (|subNodeOf?| ((#3# #5# $ #7=(|Mapping| #3# |#2| |#2|)) 100 T ELT)) (|splitNodeOf!| (($ $ $ #8=(|List| #5#)) 108 T ELT) (($ $ $ #8# #7#) 109 T ELT)) (|setvalue!| ((#5# $ #5#) 46 #9=(|has| $ (|ShallowlyMutableAggregate| #5#)) ELT)) (|setelt| ((#5# $ #10="value" #5#) NIL #9# ELT)) (|setchildren!| (($ $ #11=(|List| $)) 44 #9# ELT)) (|sample| (#12=($) NIL T CONST)) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) 95 T ELT)) (|remove!| (#13=($ #5# $) 42 T ELT)) (|remove| (#13# 34 T ELT)) (|reduce| ((#5# #14=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #14# $ #5#) NIL T ELT) ((#5# #14# $) NIL T ELT)) (|nodes| (#15=(#11# $) 54 T ELT)) (|nodeOf?| (#16=(#3# #5# $) 97 T ELT)) (|node?| #1#) (|members| (#17=(#8# $) 58 T ELT)) (|member?| (#16# NIL #4# ELT)) (|map!| (#18=($ (|Mapping| #5# #5#) $) 50 T ELT)) (|map| (#18# 49 T ELT)) (|leaves| (#17# 56 T ELT)) (|leaf?| (#19=(#3# $) 45 T ELT)) (|latex| (((|String|) $) NIL #20=(|has| #5# (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) NIL #20# ELT)) (|find| (((|Union| #5# #21="failed") #22=(|Mapping| #3# #5#) $) NIL T ELT)) (|extractSplittingLeaf| (((|Union| $ #21#) $) 89 T ELT)) (|every?| #23=((#3# #22# $) NIL T ELT)) (|eval| (($ $ (|List| #24=(|Equation| #5#))) NIL #25=(AND (|has| #5# (|Evalable| #5#)) #20#) ELT) (($ $ #24#) NIL #25# ELT) (($ $ #5# #5#) NIL #25# ELT) (($ $ #8# #8#) NIL #25# ELT)) (|eq?| (#2# 53 T ELT)) (|empty?| (#19# 24 T ELT)) (|empty| (#12# 26 T ELT)) (|elt| ((#5# $ #10#) NIL T ELT)) (|distance| (((|Integer|) $ $) NIL T ELT)) (|cyclic?| (#19# 47 T ELT)) (|count| ((#26=(|NonNegativeInteger|) #5# $) NIL #4# ELT) ((#26# #22# $) NIL T ELT)) (|copy| (#6# 52 T ELT)) (|construct| (($ #5#) 10 T ELT) (($ |#1| |#2| #11#) 13 T ELT) (($ |#1| |#2| #8#) 15 T ELT) (($ |#1| |#2| |#1| #27=(|List| |#2|)) 18 T ELT)) (|conditions| ((#27# $) 96 T ELT)) (|coerce| ((#28=(|OutputForm|) $) 87 (|has| #5# (|CoercibleTo| #28#)) ELT)) (|children| (#15# 31 T ELT)) (|child?| #1#) (|before?| #1#) (|any?| #23#) (= (#2# 70 #4# ELT)) (|#| ((#26# $) 64 T ELT))) 
(((|SplittingTree| |#1| |#2|) (|Join| (|RecursiveAggregate| #1=(|SplittingNode| |#1| |#2|)) (|FiniteAggregate| #1#) (|ShallowlyMutableAggregate| #1#) (CATEGORY |domain| (SIGNATURE |extractSplittingLeaf| ((|Union| $ "failed") $)) (SIGNATURE |updateStatus!| ($ $)) (SIGNATURE |construct| ($ #1#)) (SIGNATURE |construct| ($ |#1| |#2| (|List| $))) (SIGNATURE |construct| ($ |#1| |#2| #2=(|List| #1#))) (SIGNATURE |construct| ($ |#1| |#2| |#1| #3=(|List| |#2|))) (SIGNATURE |conditions| (#3# $)) (SIGNATURE |result| ((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $)) (SIGNATURE |nodeOf?| (#4=(|Boolean|) #1# $)) (SIGNATURE |subNodeOf?| (#4# #1# $ #5=(|Mapping| #4# |#2| |#2|))) (SIGNATURE |remove| #6=($ #1# $)) (SIGNATURE |remove!| #6#) (SIGNATURE |splitNodeOf!| ($ $ $ #2#)) (SIGNATURE |splitNodeOf!| ($ $ $ #2# #5#)))) #7=(|Join| (|SetCategory|) (|Aggregate|)) #7#) (T |SplittingTree|)) 
((|extractSplittingLeaf| #1=(*1 *1 *1) (|partial| AND #2=(|isDomain| *1 #3=(|SplittingTree| *2 *3)) #4=(|ofCategory| *2 #5=(|Join| (|SetCategory|) (|Aggregate|))) #6=(|ofCategory| *3 #5#))) (|updateStatus!| #1# (AND #2# #4# #6#)) (|construct| (*1 *1 *2) #7=(AND (|isDomain| *2 #8=(|SplittingNode| *3 *4)) #6# #9=(|ofCategory| *4 #5#) #10=(|isDomain| *1 (|SplittingTree| *3 *4)))) (|construct| #11=(*1 *1 *2 *3 *4) (AND (|isDomain| *4 (|List| #3#)) #2# #4# #6#)) (|construct| #11# (AND (|isDomain| *4 (|List| (|SplittingNode| *2 *3))) #4# #6# #2#)) (|construct| (*1 *1 *2 *3 *2 *4) (AND (|isDomain| *4 (|List| *3)) #6# #2# #4#)) (|conditions| #12=(*1 *2 *1) (AND (|isDomain| *2 (|List| *4)) #10# #6# #9#)) (|result| #12# (AND (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) #10# #6# #9#)) (|nodeOf?| (*1 *2 *3 *1) (AND (|isDomain| *3 #13=(|SplittingNode| *4 *5)) #9# #14=(|ofCategory| *5 #5#) #15=(|isDomain| *2 #16=(|Boolean|)) #17=(|isDomain| *1 (|SplittingTree| *4 *5)))) (|subNodeOf?| (*1 *2 *3 *1 *4) (AND (|isDomain| *3 (|SplittingNode| *5 *6)) (|isDomain| *4 (|Mapping| #16# *6 *6)) #14# (|ofCategory| *6 #5#) #15# (|isDomain| *1 (|SplittingTree| *5 *6)))) (|remove| #18=(*1 *1 *2 *1) #7#) (|remove!| #18# #7#) (|splitNodeOf!| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|List| #8#)) #6# #9# #10#)) (|splitNodeOf!| (*1 *1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| #13#)) (|isDomain| *3 (|Mapping| #16# *5 *5)) #9# #14# #17#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|transpose| #4=(#5=($ $) NIL T ELT)) (|trace| #6=(#7=(|#2| $) NIL T ELT)) (|symmetric?| #3#) (|subtractIfCan| ((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|squareMatrix| (($ #10=(|Matrix| |#2|)) 53 T ELT)) (|square?| #3#) (|scalarMatrix| (#11=($ |#2|) 14 T ELT)) (|sample| (#12=($) NIL T CONST)) (|rowEchelon| (#5# 66 (|has| |#2| (|EuclideanDomain|)) ELT)) (|row| (#13=(#14=(|DirectProduct| |#1| |#2|) $ #15=(|Integer|)) 40 T ELT)) (|retractIfCan| (((|Union| #15# . #16=(#9#)) . #17=($)) NIL #18=(|has| |#2| (|RetractableTo| #15#)) ELT) (((|Union| #19=(|Fraction| #15#) . #16#) . #17#) NIL #20=(|has| |#2| (|RetractableTo| #19#)) ELT) ((#21=(|Union| |#2| . #16#) . #17#) NIL T ELT)) (|retract| (#22=(#15# . #23=($)) NIL #18# ELT) ((#19# . #23#) NIL #20# ELT) #6#) (|reducedSystem| ((#24=(|Matrix| #15#) . #25=(#26=(|Matrix| $))) NIL #27=(|has| |#2| (|LinearlyExplicitRingOver| #15#)) ELT) ((#28=(|Record| (|:| |mat| #24#) (|:| |vec| (|Vector| #15#))) . #29=(#26# #30=(|Vector| $))) NIL #27# ELT) ((#31=(|Record| (|:| |mat| #10#) (|:| |vec| (|Vector| |#2|))) . #29#) NIL T ELT) ((#10# . #25#) NIL T ELT)) (|reduce| ((|#2| #32=(|Mapping| |#2| |#2| |#2|) $) NIL T ELT) ((|#2| #32# $ |#2|) NIL T ELT) ((|#2| #32# $ |#2| |#2|) NIL #33=(|has| |#2| (|BasicType|)) ELT)) (|recip| (#34=(#8# $) 80 T ELT)) (|rank| (#35=(#36=(|NonNegativeInteger|) $) 68 #37=(|has| |#2| (|IntegralDomain|)) ELT)) (|qelt| #38=((|#2| $ #15# #15#) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|nullity| (#35# 70 #37# ELT)) (|nullSpace| (((|List| #14#) $) 74 #37# ELT)) (|nrows| #39=(#35# NIL T ELT)) (|new| (#11# 23 T ELT)) (|ncols| #39#) (|minordet| (#7# 64 #40=(|has| |#2| (ATTRIBUTE (|commutative| "*"))) ELT)) (|minRowIndex| #41=(#22# NIL T ELT)) (|minColIndex| #41#) (|members| ((#42=(|List| |#2|) $) NIL T ELT)) (|member?| ((#2# |#2| $) NIL #33# ELT)) (|maxRowIndex| #41#) (|maxColIndex| #41#) (|matrix| (($ #43=(|List| #42#)) 35 T ELT)) (|map| (($ #32# $ $) NIL T ELT) (($ #44=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|listOfLists| ((#43# $) NIL T ELT)) (|leftReducedSystem| ((#24# . #45=(#30#)) NIL #27# ELT) ((#28# . #46=(#30# $)) NIL #27# ELT) ((#31# . #46#) NIL T ELT) ((#10# . #45#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inverse| (#34# 77 #47=(|has| |#2| (|Field|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| ((#21# #48=(|Mapping| #2# |#2|) $) NIL T ELT)) (|exquo| ((#8# $ |#2|) NIL #37# ELT)) (|every?| #49=((#2# #48# $) NIL T ELT)) (|eval| (($ $ (|List| #50=(|Equation| |#2|))) NIL #51=(AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ELT) (($ $ #50#) NIL #51# ELT) (($ $ |#2| |#2|) NIL #51# ELT) (($ $ #42# #42#) NIL #51# ELT)) (|eq?| #1#) (|empty?| #3#) (|empty| (#12# NIL T ELT)) (|elt| ((|#2| $ #15# #15# |#2|) NIL T ELT) #38#) (|differentiate| #52=(($ $ #44# #36#) NIL T ELT) #53=(($ $ #44#) NIL T ELT) #54=(#5# NIL #55=(|has| |#2| (|DifferentialSpace|)) ELT) #56=(#57=($ $ #36#) NIL #55# ELT) #58=(($ $ #59=(|Symbol|)) NIL #60=(|has| |#2| (|PartialDifferentialSpace| #59#)) ELT) #61=(($ $ #62=(|List| #59#)) NIL #60# ELT) #63=(($ $ #59# #36#) NIL #60# ELT) #64=(($ $ #62# (|List| #36#)) NIL #60# ELT)) (|diagonalProduct| #6#) (|diagonalMatrix| (($ #42#) 48 T ELT)) (|diagonal?| #3#) (|diagonal| ((#14# $) NIL T ELT)) (|determinant| (#7# 62 #40# ELT)) (|count| ((#36# #48# $) NIL T ELT) ((#36# |#2| $) NIL #33# ELT)) (|copy| #4#) (|convert| ((#65=(|InputForm|) $) 87 (|has| |#2| (|ConvertibleTo| #65#)) ELT)) (|column| (#13# 42 T ELT)) (|coerce| (((|OutputForm|) $) 45 T ELT) (($ #15#) NIL T ELT) (($ #19#) NIL #20# ELT) (#11# NIL T ELT) ((#10# $) 50 T ELT)) (|characteristic| ((#36#) 21 T CONST)) (|before?| #1#) (|any?| #49#) (|antisymmetric?| #3#) (|annihilate?| #1#) (|Zero| (#12# 15 T CONST)) (|One| (#12# 19 T CONST)) (D #52# #53# #54# #56# #58# #61# #63# #64#) (= #1#) (/ (#66=($ $ |#2|) NIL #47# ELT)) (- #4# #67=(($ $ $) NIL T ELT)) (+ #67#) (** (($ $ #68=(|PositiveInteger|)) NIL T ELT) (#57# 60 T ELT) (($ $ #15#) 79 #47# ELT)) (* (($ #68# $) NIL T ELT) (($ #36# $) NIL T ELT) (($ #15# . #69=($)) NIL T ELT) #67# (#66# NIL T ELT) (($ |#2| . #69#) NIL T ELT) ((#14# $ #14#) 56 T ELT) ((#14# #14# $) 58 T ELT)) (|#| #39#)) 
(((|SquareMatrix| |#1| |#2|) (|Join| (|SquareMatrixCategory| |#1| |#2| #1=(|DirectProduct| |#1| |#2|) #1#) (|CoercibleTo| #2=(|Matrix| |#2|)) (CATEGORY |domain| (SIGNATURE |new| ($ |#2|)) (SIGNATURE |transpose| ($ $)) (SIGNATURE |squareMatrix| ($ #2#)) (IF #3=(|has| |#2| (ATTRIBUTE (|commutative| "*"))) (ATTRIBUTE |central|) |%noBranch|) (IF #3# (IF (|has| |#2| #4=(ATTRIBUTE |unitsKnown|)) #4# |%noBranch|) |%noBranch|) (IF (|has| |#2| #5=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #5#) |%noBranch|))) (|NonNegativeInteger|) (|Ring|)) (T |SquareMatrix|)) 
((|new| #1=(*1 *1 *2) (AND (|isDomain| *1 (|SquareMatrix| *3 *2)) #2=(|ofType| *3 #3=(|NonNegativeInteger|)) (|ofCategory| *2 #4=(|Ring|)))) (|transpose| (*1 *1 *1) (AND (|isDomain| *1 (|SquareMatrix| *2 *3)) (|ofType| *2 #3#) (|ofCategory| *3 #4#))) (|squareMatrix| #1# (AND (|isDomain| *2 (|Matrix| *4)) (|ofCategory| *4 #4#) (|isDomain| *1 (|SquareMatrix| *3 *4)) #2#))) 
((|upperCase| (#1=($ $) 19 T ELT)) (|trim| (($ $ #2=(|Character|)) 10 T ELT) (($ $ (|CharacterClass|)) 14 T ELT)) (|prefix?| (((|Boolean|) $ $) 24 T ELT)) (|lowerCase| (#1# 17 T ELT)) (|elt| ((#2# $ #3=(|Integer|) #2#) NIL T ELT) ((#2# $ #3#) NIL T ELT) (($ $ (|UniversalSegment| #3#)) NIL T ELT) (($ $ $) 31 T ELT)) (|coerce| (($ #2#) 29 T ELT) (((|OutputForm|) $) NIL T ELT))) 
(((|StringAggregate&| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |elt| (|#1| |#1| |#1|)) (SIGNATURE |trim| (|#1| |#1| (|CharacterClass|))) (SIGNATURE |trim| (|#1| |#1| #1=(|Character|))) (SIGNATURE |coerce| (|#1| #1#)) (SIGNATURE |prefix?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |upperCase| #2=(|#1| |#1|)) (SIGNATURE |lowerCase| #2#) (SIGNATURE |elt| (|#1| |#1| (|UniversalSegment| #3=(|Integer|)))) (SIGNATURE |elt| (#1# |#1| #3#)) (SIGNATURE |elt| (#1# |#1| #3# #1#))) (|StringAggregate|)) (T |StringAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| #2=(|Character|) . #3=((|BasicType|))) ELT)) (|upperCase!| (($ $) 131 T ELT)) (|upperCase| (($ $) 132 T ELT)) (|trim| (($ $ (|Character|)) 119 T ELT) (($ $ (|CharacterClass|)) 118 T ELT)) (|swap!| (((|Void|) $ #4=(|Integer|) #4#) 35 (|has| $ (|ShallowlyMutableAggregate| #2#)) ELT)) (|suffix?| (((|Boolean|) $ $) 129 T ELT)) (|substring?| (((|Boolean|) $ $ (|Integer|)) 128 T ELT)) (|split| (((|List| $) $ (|Character|)) 121 T ELT) (((|List| $) $ (|CharacterClass|)) 120 T ELT)) (|sorted?| ((#5=(|Boolean|) (|Mapping| #5# #2# #2#) $) 96 T ELT) ((#5# $) 90 (|has| #2# . #6=((|OrderedSet|))) ELT)) (|sort!| (($ (|Mapping| #5# #2# #2#) . #7=($)) 87 (|has| $ (|ShallowlyMutableAggregate| #2#)) ELT) (#8=($ $) 86 (AND (|has| #2# . #6#) (|has| $ (|ShallowlyMutableAggregate| #2#))) ELT)) (|sort| (($ (|Mapping| #5# #2# #2#) . #7#) 97 T ELT) (#8# 91 (|has| #2# . #6#) ELT)) (|setelt| ((#2# $ #4# #2#) 47 (|has| $ (|ShallowlyMutableAggregate| #2#)) ELT) ((#2# $ #9=(|UniversalSegment| #4#) #2#) 55 (|has| $ (|ShallowlyMutableAggregate| #2#)) ELT)) (|select| (($ (|Mapping| #10=(|Boolean|) #2#) . #11=($)) 69 (|has| $ (|FiniteAggregate| #2#)) ELT)) (|sample| (#12=($) 6 T CONST)) (|rightTrim| (($ $ (|Character|)) 115 T ELT) (($ $ (|CharacterClass|)) 114 T ELT)) (|reverse!| (#8# 88 (|has| $ (|ShallowlyMutableAggregate| #2#)) ELT)) (|reverse| (#8# 98 T ELT)) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) 125 T ELT)) (|removeDuplicates| (($ $) 71 (AND (|has| #2# . #13=((|BasicType|))) (|has| $ (|FiniteAggregate| #2#))) ELT)) (|remove| (($ #2# $) 70 (AND (|has| #2# . #13#) (|has| $ (|FiniteAggregate| #2#))) ELT) (($ (|Mapping| #10# #2#) . #11#) 68 (|has| $ (|FiniteAggregate| #2#)) ELT)) (|reduce| ((#2# (|Mapping| #2# #2# #2#) $ #2# #2#) 110 (|has| #2# . #14=((|BasicType|))) ELT) ((#2# (|Mapping| #2# #2# #2#) $ #2#) 106 T ELT) ((#2# (|Mapping| #2# #2# #2#) $) 105 T ELT)) (|qsetelt!| ((#2# $ #4# #2#) 48 (|has| $ (|ShallowlyMutableAggregate| #2#)) ELT)) (|qelt| ((#2# $ #4#) 46 T ELT)) (|prefix?| (((|Boolean|) $ $) 130 T ELT)) (|position| ((#15=(|Integer|) (|Mapping| #5# #2#) $) 95 T ELT) ((#15# #2# $) 94 (|has| #2# . #16=((|BasicType|))) ELT) ((#15# #2# $ #15#) 93 (|has| #2# . #16#) ELT) (((|Integer|) $ $ (|Integer|)) 124 T ELT) (((|Integer|) (|CharacterClass|) $ (|Integer|)) 123 T ELT)) (|new| (($ (|NonNegativeInteger|) #2#) 65 T ELT)) (|minIndex| ((#4# . #17=($)) 38 (|has| #4# . #18=((|OrderedSet|))) ELT)) (|min| (#19=($ $ $) 80 (|has| #2# . #6#) ELT)) (|merge| (($ (|Mapping| #5# #2# #2#) $ $) 99 T ELT) (($ $ $) 92 (|has| #2# . #6#) ELT)) (|members| (((|List| #2#) $) 104 T ELT)) (|member?| ((#20=(|Boolean|) #2# $) 109 (|has| #2# . #14#) ELT)) (|maxIndex| ((#4# . #17#) 39 (|has| #4# . #18#) ELT)) (|max| (#19# 81 (|has| #2# . #6#) ELT)) (|match?| (((|Boolean|) $ $ (|Character|)) 126 T ELT)) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) 127 T ELT)) (|map!| (($ (|Mapping| #2# #2#) $) 112 T ELT)) (|map| (($ (|Mapping| #2# #2#) $) 26 T ELT) (($ (|Mapping| #2# #2# #2#) $ $) 60 T ELT)) (|lowerCase!| (($ $) 133 T ELT)) (|lowerCase| (($ $) 134 T ELT)) (|leftTrim| (($ $ (|Character|)) 117 T ELT) (($ $ (|CharacterClass|)) 116 T ELT)) (|latex| (((|String|) $) 21 (|has| #2# . #21=((|SetCategory|))) ELT)) (|insert| (($ #2# $ #4#) 57 T ELT) (($ $ $ #4#) 56 T ELT)) (|indices| (((|List| #4#) $) 41 T ELT)) (|index?| ((#22=(|Boolean|) #4# $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| #2# . #21#) ELT)) (|first| ((#2# $) 37 (|has| #4# . #18#) ELT)) (|find| (((|Union| #2# "failed") (|Mapping| #20# #2#) $) 107 T ELT)) (|fill!| (($ $ #2#) 36 (|has| $ (|ShallowlyMutableAggregate| #2#)) ELT)) (|every?| ((#20# (|Mapping| #20# #2#) . #23=($)) 102 T ELT)) (|eval| (($ $ (|List| (|Equation| #2#))) 25 (AND (|has| #2# (|Evalable| #2#)) (|has| #2# . #21#)) ELT) (($ $ (|Equation| #2#)) 24 (AND (|has| #2# (|Evalable| #2#)) (|has| #2# . #21#)) ELT) (($ $ #2# #2#) 23 (AND (|has| #2# (|Evalable| #2#)) (|has| #2# . #21#)) ELT) 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(|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| #2# . #3#) ELT)) (|any?| ((#20# (|Mapping| #20# #2#) . #23#) 101 T ELT)) (>= (#27=((|Boolean|) $ $) 82 (|has| #2# . #6#) ELT)) (> (#27# 84 (|has| #2# . #6#) ELT)) (= (#1# 17 (|has| #2# . #3#) ELT)) (<= (#27# 83 (|has| #2# . #6#) ELT)) (< (#27# 85 (|has| #2# . #6#) ELT)) (|#| ((#25# $) 100 T ELT))) 
(((|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|)))) 
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(((|Aggregate|) . T) ((|BasicType|) OR (|has| (|Character|) (|SetCategory|)) (|has| (|Character|) (|OrderedSet|)) (|has| (|Character|) (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| (|Character|) (|SetCategory|)) (|has| (|Character|) (|OrderedSet|)) (|has| (|Character|) (|CoercibleTo| (|OutputForm|)))) ((|Collection| #1=(|Character|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Character|) (|ConvertibleTo| (|InputForm|))) ((|Eltable| #2=(|Integer|) #1#) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #2# #1#) . T) ((|Evalable| #1#) AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|))) ((|FiniteAggregate| #1#) . T) ((|FiniteLinearAggregate| #1#) . T) ((|Functorial| #1#) . T) ((|HomogeneousAggregate| #1#) . T) ((|IndexedAggregate| #2# #1#) . T) ((|InnerEvalable| #1# #1#) AND (|has| (|Character|) (|Evalable| (|Character|))) (|has| (|Character|) (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| #1#) . T) ((|OneDimensionalArrayAggregate| #1#) . T) ((|OrderedSet|) |has| (|Character|) (|OrderedSet|)) ((|OrderedType|) |has| (|Character|) (|OrderedSet|)) ((|SetCategory|) OR (|has| (|Character|) (|SetCategory|)) (|has| (|Character|) (|OrderedSet|))) ((|ShallowlyMutableAggregate| #1#) . T) ((|Type|) . T)) 
((|upDateBranches| ((#1=(|List| #2=(|Record| (|:| |val| #3=(|List| |#4|)) (|:| |tower| |#5|))) #3# #4=(|List| |#5|) #1# #5=(|Record| (|:| |done| #4#) (|:| |todo| #1#)) #6=(|NonNegativeInteger|)) 112 T ELT)) (|transcendentalDecompose| (#7=(#5# |#4| |#5|) 62 T ELT) (#8=(#5# |#4| |#5| #6#) 61 T ELT)) (|printInfo| (((|Void|) #1# #6#) 97 T ELT)) (|numberOfVariables| (#9=(#6# #3# #4#) 30 T ELT)) (|internalDecompose| (#7# 64 T ELT) (#8# 63 T ELT) ((#5# |#4| |#5| #6# #10=(|Boolean|)) 65 T ELT)) (|decompose| ((#4# #3# #4# #10# #10# #10# #10# #10#) 84 T ELT) ((#4# #3# #4# #10# #10#) 85 T ELT)) (|convert| (((|String|) #2#) 90 T ELT)) (|algebraicDecompose| (#7# 60 T ELT)) (|KrullNumber| (#9# 21 T ELT))) 
(((|SquareFreeRegularSetDecompositionPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |KrullNumber| #1=(#2=(|NonNegativeInteger|) #3=(|List| |#4|) #4=(|List| |#5|))) (SIGNATURE |numberOfVariables| #1#) (SIGNATURE |algebraicDecompose| #5=(#6=(|Record| (|:| |done| #4#) (|:| |todo| #7=(|List| #8=(|Record| (|:| |val| #3#) (|:| |tower| |#5|))))) |#4| |#5|)) (SIGNATURE |transcendentalDecompose| #9=(#6# |#4| |#5| #2#)) (SIGNATURE |transcendentalDecompose| #5#) (SIGNATURE |internalDecompose| (#6# |#4| |#5| #2# #10=(|Boolean|))) (SIGNATURE |internalDecompose| #9#) (SIGNATURE |internalDecompose| #5#) (SIGNATURE |decompose| (#4# #3# #4# #10# #10#)) (SIGNATURE |decompose| (#4# #3# #4# #10# #10# #10# #10# #10#)) (SIGNATURE |upDateBranches| (#7# #3# #4# #7# #6# #2#)) (SIGNATURE |convert| ((|String|) #8#)) (SIGNATURE |printInfo| ((|Void|) #7# #2#))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |SquareFreeRegularSetDecompositionPackage|)) 
((|printInfo| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| #2=(|List| *8)) (|:| |tower| *9)))) (|isDomain| *4 #3=(|NonNegativeInteger|)) #4=(|ofCategory| *8 #5=(|RecursivePolynomialCategory| *5 *6 *7)) #6=(|ofCategory| *9 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)) #7=(|ofCategory| *5 #8=(|GcdDomain|)) #9=(|ofCategory| *6 #10=(|OrderedAbelianMonoidSup|)) #11=(|ofCategory| *7 #12=(|OrderedSet|)) (|isDomain| *2 (|Void|)) #13=(|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 #8#) (|ofCategory| *5 #10#) (|ofCategory| *6 #12#) (|isDomain| *2 (|String|)) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *4 *5 *6 *7 *8)))) (|upDateBranches| (*1 *2 *3 *4 *2 *5 *6) (AND (|isDomain| *5 (|Record| (|:| |done| #14=(|List| *11)) (|:| |todo| (|List| (|Record| (|:| |val| *3) #15=(|:| |tower| *11)))))) (|isDomain| *6 #3#) (|isDomain| *2 (|List| (|Record| (|:| |val| #16=(|List| *10)) #15#))) (|isDomain| *3 #16#) (|isDomain| *4 #14#) (|ofCategory| *10 #17=(|RecursivePolynomialCategory| *7 *8 *9)) (|ofCategory| *11 (|SquareFreeRegularTriangularSetCategory| *7 *8 *9 *10)) #18=(|ofCategory| *7 #8#) #19=(|ofCategory| *8 #10#) #20=(|ofCategory| *9 #12#) (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *7 *8 *9 *10 *11)))) (|decompose| (*1 *2 *3 *2 *4 *4 *4 *4 *4) #21=(AND (|isDomain| *2 #22=(|List| *9)) #23=(|isDomain| *3 #2#) (|isDomain| *4 #24=(|Boolean|)) #4# #6# #7# #9# #11# #13#)) (|decompose| (*1 *2 *3 *2 *4 *4) #21#) (|internalDecompose| #1# #25=(AND #7# #9# #11# (|ofCategory| *3 #5#) #26=(|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| #27=(*1 *2 *3 *4 *5) #28=(AND #29=(|isDomain| *5 #3#) (|ofCategory| *6 #8#) (|ofCategory| *7 #10#) (|ofCategory| *8 #12#) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) #26# (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|SquareFreeRegularTriangularSetCategory| *6 *7 *8 *3)))) (|internalDecompose| (*1 *2 *3 *4 *5 *6) (AND #29# (|isDomain| *6 #24#) #18# #19# #20# (|ofCategory| *3 #17#) #26# (|isDomain| *1 (|SquareFreeRegularSetDecompositionPackage| *7 *8 *9 *3 *4)) (|ofCategory| *4 (|SquareFreeRegularTriangularSetCategory| *7 *8 *9 *3)))) (|transcendentalDecompose| #1# #25#) (|transcendentalDecompose| #27# #28#) (|algebraicDecompose| #1# #25#) (|numberOfVariables| #1# #30=(AND #23# (|isDomain| *4 #22#) #4# #6# #7# #9# #11# (|isDomain| *2 #3#) #13#)) (|KrullNumber| #1# #30#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| |#4|)))) #5#) NIL T ELT)) (|zeroSetSplit| ((#6=(|List| $) #5#) 117 T ELT) ((#6# #5# #3#) 118 T ELT) ((#6# #5# #3# #3#) 116 T ELT) ((#6# #5# #3# #3# #3# #3#) 119 T ELT)) (|variables| #7=(((|List| |#3|) $) NIL T ELT)) (|trivialIdeal?| #8=(#9=(#3# $) NIL T ELT)) (|triangular?| #10=(#9# NIL #11=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #12=(#13=(#3# |#4| $) NIL T ELT) #8#) (|stronglyReduce| #14=(#15=(|#4| |#4| $) NIL T ELT)) (|squareFreePart| ((#16=(|List| (|Record| (|:| |val| |#4|) #17=(|:| |tower| $))) |#4| $) 90 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL T ELT)) (|select| #18=(($ #19=(|Mapping| #3# |#4|) $) NIL #20=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#21=(|Union| |#4| #22="failed") $ |#3|) 69 T ELT)) (|sample| (#23=($) NIL T CONST)) (|roughUnitIdeal?| (#9# 28 #11# ELT)) (|roughSubIdeal?| #24=(#2# NIL #11# ELT)) (|roughEqualIdeals?| #24#) (|roughBase?| #10#) (|rewriteSetWithReduction| ((#5# #5# $ #25=(|Mapping| |#4| |#4| |#4|) #26=(|Mapping| #3# |#4| |#4|)) NIL T ELT)) (|rewriteIdealWithRemainder| #27=((#5# #5# $) NIL #11# ELT)) (|rewriteIdealWithHeadRemainder| #27#) (|retractIfCan| ((#28=(|Union| $ #22#) #5#) NIL T ELT)) (|retract| (#29=($ #5#) NIL T ELT)) (|rest| ((#28# $) 44 T ELT)) (|removeZero| (#15# 72 T ELT)) (|removeDuplicates| (#30=($ $) NIL #31=(AND #20# #32=(|has| |#4| (|BasicType|))) ELT)) (|remove| (#33=($ |#4| $) NIL #31# ELT) #18#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #34=(|:| |den| |#1|)) |#4| $) 84 #11# ELT)) (|reduced?| ((#3# |#4| $ #26#) NIL T ELT)) (|reduceByQuasiMonic| #14#) (|reduce| ((|#4| #25# $ |#4| |#4|) NIL #32# ELT) ((|#4| #25# $ |#4|) NIL T ELT) ((|#4| #25# $) NIL T ELT) ((|#4| |#4| $ #25# #26#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|purelyTranscendental?| #12#) (|purelyAlgebraicLeadingMonomial?| #12#) (|purelyAlgebraic?| #12# #8#) (|preprocess| (((|Record| (|:| |val| #5#) (|:| |towers| #6#)) #5# #3# #3#) 132 T ELT)) (|normalized?| #12# #8#) (|mvar| ((|#3| $) 37 T ELT)) (|members| (#35=(#5# $) 18 T ELT)) (|member?| (#13# 26 #32# ELT)) (|map!| (#36=($ (|Mapping| |#4| |#4|) $) 24 T ELT)) (|map| (#36# 22 T ELT)) (|mainVariables| #7#) (|mainVariable?| (#37=(#3# |#3| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #6#) |#4| |#4| $) NIL T ELT)) (|lastSubResultant| ((#16# |#4| |#4| $) 110 T ELT)) (|last| (#38=(#21# $) 41 T ELT)) (|invertibleSet| (#39=(#6# |#4| $) 95 T ELT)) (|invertibleElseSplit?| (((|Union| #3# #6#) |#4| $) NIL T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #17#)) |#4| $) 105 T ELT) (#13# 61 T ELT)) (|intersect| (#39# 114 T ELT) #40=((#6# #5# $) NIL T ELT) (#41=(#6# #5# #6#) 115 T ELT) #42=((#6# |#4| #6#) NIL T ELT)) (|internalZeroSetSplit| ((#6# #5# #3# #3# #3#) 127 T ELT)) (|internalAugment| (#33# 81 T ELT) (($ #5# $) 82 T ELT) ((#6# |#4| $ #3# #3# #3# #3# #3#) 80 T ELT)) (|initials| (#35# NIL T ELT)) (|initiallyReduced?| #12# #8#) (|initiallyReduce| #14#) (|infRittWu?| #1#) (|headRemainder| (((|Record| (|:| |num| |#4|) #34#) |#4| $) NIL #11# ELT)) (|headReduced?| #12# #8#) (|headReduce| #14#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#38# 39 T ELT)) (|find| ((#21# #19# $) NIL T ELT)) (|extendIfCan| ((#28# $ |#4|) 55 T ELT)) (|extend| (($ $ |#4|) NIL T ELT) (#39# 97 T ELT) #42# #40# (#41# 92 T ELT)) (|every?| #43=((#3# #19# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #44=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) NIL #44# ELT) (($ $ #45=(|Equation| |#4|)) NIL #44# ELT) (($ $ (|List| #45#)) NIL #44# ELT)) (|eq?| #1#) (|empty?| (#9# 17 T ELT)) (|empty| (#23# 14 T ELT)) (|degree| #46=(#47=(#48=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#48# |#4| $) NIL #32# ELT) ((#48# #19# $) NIL T ELT)) (|copy| (#30# 13 T ELT)) (|convert| ((#49=(|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| #49#)) ELT)) (|construct| (#29# 21 T ELT)) (|collectUpper| (#50=($ $ |#3|) 48 T ELT)) (|collectUnder| (#50# 50 T ELT)) (|collectQuasiMonic| (#30# NIL T ELT)) (|collect| (#50# NIL T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT) (#35# 45 T ELT)) (|coHeight| (#47# NIL (|has| |#3| (|Finite|)) ELT)) (|before?| #1#) (|basicSet| ((#51=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #22#) #5# #26#) NIL T ELT) ((#51# #5# #19# #26#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# |#4| #5#)) NIL T ELT)) (|augment| (#39# 62 T ELT) #42# #40# (#41# NIL T ELT)) (|any?| #43#) (|algebraicVariables| #7#) (|algebraicCoefficients?| #12#) (|algebraic?| (#37# 68 T ELT)) (= #1#) (|#| #46#)) 
(((|SquareFreeRegularTriangularSet| |#1| |#2| |#3| |#4|) (|Join| (|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |internalAugment| (#1=(|List| $) |#4| $ #2=(|Boolean|) #2# #2# #2# #2#)) (SIGNATURE |zeroSetSplit| (#1# #3=(|List| |#4|) #2# #2#)) (SIGNATURE |zeroSetSplit| (#1# #3# #2# #2# #2# #2#)) (SIGNATURE |internalZeroSetSplit| (#1# #3# #2# #2# #2#)) (SIGNATURE |preprocess| ((|Record| (|:| |val| #3#) (|:| |towers| #1#)) #3# #2# #2#)))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |SquareFreeRegularTriangularSet|)) 
((|internalAugment| (*1 *2 *3 *1 *4 *4 *4 *4 *4) (AND #1=(|isDomain| *4 (|Boolean|)) #2=(|ofCategory| *5 (|GcdDomain|)) #3=(|ofCategory| *6 (|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| #5=(|SquareFreeRegularTriangularSet| *5 *6 *7 *3))) (|isDomain| *1 #5#) (|ofCategory| *3 #6=(|RecursivePolynomialCategory| *5 *6 *7)))) (|zeroSetSplit| #7=(*1 *2 *3 *4 *4) #8=(AND #9=(|isDomain| *3 #10=(|List| *8)) #1# #11=(|ofCategory| *8 #6#) #2# #3# #4# (|isDomain| *2 #12=(|List| #13=(|SquareFreeRegularTriangularSet| *5 *6 *7 *8))) #14=(|isDomain| *1 #13#))) (|zeroSetSplit| (*1 *2 *3 *4 *4 *4 *4) #8#) (|internalZeroSetSplit| (*1 *2 *3 *4 *4 *4) #8#) (|preprocess| #7# (AND #1# #2# #3# #4# #11# (|isDomain| *2 (|Record| (|:| |val| #10#) (|:| |towers| #12#))) #14# #9#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 32 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 30 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 29 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|NonNegativeInteger|)) 31 T ELT) (($ $ (|PositiveInteger|)) 28 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ $ $) 27 T ELT))) 
(((|SemiRing|) (|Category|)) (T |SemiRing|)) 
NIL 
(|Join| (|AbelianMonoid|) (|Monoid|)) 
(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monoid|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|top| (#5=(|#1| $) 38 T ELT)) (|stack| (#6=($ #7=(|List| |#1|)) 46 T ELT)) (|sample| (#8=($) NIL T CONST)) (|reduce| ((|#1| #9=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #9# $ |#1|) NIL T ELT) ((|#1| #9# $) NIL T ELT)) (|push!| ((|#1| |#1| $) 41 T ELT)) (|pop!| (#5# 36 T ELT)) (|members| ((#7# $) 19 T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| (#10=($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|map| (#10# 23 T ELT)) (|latex| (((|String|) $) NIL #11=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#5# 39 T ELT)) (|insert!| (($ |#1| $) 42 T ELT)) (|hash| (((|SingleInteger|) $) NIL #11# ELT)) (|find| (((|Union| |#1| "failed") #12=(|Mapping| #3# |#1|) $) NIL T ELT)) (|extract!| (#5# 37 T ELT)) (|every?| #13=((#3# #12# $) NIL T ELT)) (|eval| (($ $ (|List| #14=(|Equation| |#1|))) NIL #15=(AND (|has| |#1| (|Evalable| |#1|)) #11#) ELT) (($ $ #14#) NIL #15# ELT) (($ $ |#1| |#1|) NIL #15# ELT) (($ $ #7# #7#) NIL #15# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| ((#3# $) 33 T ELT)) (|empty| (#8# 44 T ELT)) (|depth| (#16=(#17=(|NonNegativeInteger|) $) 31 T ELT)) (|count| ((#17# |#1| $) NIL #4# ELT) ((#17# #12# $) NIL T ELT)) (|copy| (($ $) 28 T ELT)) (|coerce| ((#18=(|OutputForm|) $) 15 (|has| |#1| (|CoercibleTo| #18#)) ELT)) (|before?| #1#) (|bag| (#6# NIL T ELT)) (|any?| #13#) (= (#2# 18 #4# ELT)) (|#| (#16# 32 T ELT))) 
(((|Stack| |#1|) (|Join| (|StackAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |stack| ($ (|List| |#1|))))) (|Type|)) (T |Stack|)) 
((|stack| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Stack| *3))))) 
((|setelt| ((|#2| $ #1="value" |#2|) NIL T ELT) ((|#2| $ #2="first" |#2|) NIL T ELT) (($ $ #3="rest" $) NIL T ELT) ((|#2| $ #4="last" |#2|) NIL T ELT) ((|#2| $ #5=(|UniversalSegment| #6=(|Integer|)) |#2|) 51 T ELT) (#7=(|#2| $ #6# |#2|) 48 T ELT)) (|possiblyInfinite?| (#8=((|Boolean|) $) 12 T ELT)) (|first| ((|#2| $) NIL T ELT) (($ $ (|NonNegativeInteger|)) 17 T ELT)) (|fill!| (#9=($ $ |#2|) 47 T ELT)) (|explicitlyFinite?| (#8# 11 T ELT)) (|elt| ((|#2| $ #1#) NIL T ELT) ((|#2| $ #2#) NIL T ELT) (($ $ #3#) NIL T ELT) ((|#2| $ #4#) NIL T ELT) (($ $ #5#) 36 T ELT) ((|#2| $ #6#) 25 T ELT) (#7# NIL T ELT)) (|concat!| (#10=($ $ $) 54 T ELT) #11=(#9# NIL T ELT)) (|concat| (#10# 38 T ELT) (($ |#2| $) NIL T ELT) (($ (|List| $)) 45 T ELT) #11#)) 
(((|StreamAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |possiblyInfinite?| #1=((|Boolean|) |#1|)) (SIGNATURE |explicitlyFinite?| #1#) (SIGNATURE |setelt| #2=(|#2| |#1| #3=(|Integer|) |#2|)) (SIGNATURE |elt| #2#) (SIGNATURE |elt| (|#2| |#1| #3#)) (SIGNATURE |fill!| #4=(|#1| |#1| |#2|)) (SIGNATURE |elt| (|#1| |#1| #5=(|UniversalSegment| #3#))) (SIGNATURE |concat| #4#) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |setelt| (|#2| |#1| #5# |#2|)) (SIGNATURE |setelt| (|#2| |#1| #6="last" |#2|)) (SIGNATURE |setelt| (|#1| |#1| #7="rest" |#1|)) (SIGNATURE |setelt| (|#2| |#1| #8="first" |#2|)) (SIGNATURE |concat!| #4#) (SIGNATURE |concat!| #9=(|#1| |#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| #6#)) (SIGNATURE |elt| (|#1| |#1| #7#)) (SIGNATURE |first| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |elt| (|#2| |#1| #8#)) (SIGNATURE |first| (|#2| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| #9#) (SIGNATURE |setelt| (|#2| |#1| #10="value" |#2|)) (SIGNATURE |elt| (|#2| |#1| #10#))) (|StreamAggregate| |#2|) (|Type|)) (T |StreamAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|third| ((|#1| . #3=($)) 62 T ELT)) (|tail| (#4=($ $) 64 T ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) 99 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|split!| (($ $ (|Integer|)) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) 82 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setrest!| (#6=($ $ $) 53 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #7="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #8="first" |#1|) 54 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ #9="rest" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #10="last" |#1|) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #11=(|UniversalSegment| #5#) |#1|) 115 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #5# |#1|) 88 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #12=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #13=(|Boolean|) |#1|) . #14=($)) 103 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|second| ((|#1| . #3#) 63 T ELT)) (|sample| (#15=($) 6 T CONST)) (|rest| (#4# 70 T ELT) (#16=($ $ #17=(|NonNegativeInteger|)) 68 T ELT)) (|removeDuplicates| (($ $) 101 (AND (|has| |#1| . #18=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ (|Mapping| #13# |#1|) . #14#) 104 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ |#1| $) 102 (AND (|has| |#1| . #18#) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|qsetelt!| ((|#1| $ #5# |#1|) 87 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #5#) 89 T ELT)) (|possiblyInfinite?| (((|Boolean|) $) 85 T ELT)) (|nodes| (#19=(#12# $) 45 T ELT)) (|node?| (#20=(#21=(|Boolean|) $ $) 37 (|has| |#1| . #22=((|BasicType|))) ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 107 T ELT)) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) 83 T ELT)) (|minIndex| ((#5# . #23=($)) 97 (|has| #5# . #24=((|OrderedSet|))) ELT)) (|maxIndex| ((#5# . #23#) 96 (|has| #5# . #24#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 110 T ELT)) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) 84 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (#25=(#21# $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #26=((|SetCategory|))) ELT)) (|last| ((|#1| . #3#) 67 T ELT) (#16# 65 T ELT)) (|insert| (($ $ $ #5#) 114 T ELT) (($ |#1| $ #5#) 113 T ELT)) (|indices| (((|List| #5#) $) 94 T ELT)) (|index?| ((#27=(|Boolean|) #5# $) 93 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #26#) ELT)) (|first| ((|#1| . #3#) 73 T ELT) (#16# 71 T ELT)) (|fill!| (($ $ |#1|) 98 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|explicitlyFinite?| (((|Boolean|) $) 86 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #26#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #26#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #26#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #26#)) ELT)) (|eq?| ((#28=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#27# |#1| $) 95 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 92 T ELT)) (|empty?| ((#28# $) 7 T ELT)) (|empty| (#15# 8 T ELT)) (|elt| ((|#1| $ #7#) 42 T ELT) ((|#1| $ #8#) 72 T ELT) (($ $ #9#) 69 T ELT) ((|#1| $ #10#) 66 T ELT) (($ $ #11#) 106 T ELT) ((|#1| $ #5#) 91 T ELT) ((|#1| $ #5# |#1|) 90 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|delete| (($ $ #11#) 112 T ELT) (($ $ #5#) 111 T ELT)) (|cyclic?| (#25# 41 T ELT)) (|cycleTail| (#4# 59 T ELT)) (|cycleSplit!| (#4# 56 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|cycleLength| ((#17# $) 60 T ELT)) (|cycleEntry| (#4# 61 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#29=(|InputForm|) $) 100 (|has| |#1| (|ConvertibleTo| #29#)) ELT)) (|construct| (($ (|List| |#1|)) 105 T ELT)) (|concat!| (#6# 58 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ |#1|) 57 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|concat| (#6# 75 T ELT) (($ |#1| $) 74 T ELT) (($ (|List| $)) 109 T ELT) (($ $ |#1|) 108 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (#19# 46 T ELT)) (|child?| (#20# 38 (|has| |#1| . #22#) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|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|)))) (|less?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|StreamAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|more?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|StreamAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|size?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|StreamAggregate| *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|))))) 
(|Join| (|UnaryRecursiveAggregate| |t#1|) (|LinearAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |explicitlyFinite?| ((|Boolean|) $)) (SIGNATURE |possiblyInfinite?| ((|Boolean|) $)) (SIGNATURE |less?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |more?| ((|Boolean|) $ (|NonNegativeInteger|))) (SIGNATURE |size?| ((|Boolean|) $ (|NonNegativeInteger|))))) 
(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| |#1|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T) ((|UnaryRecursiveAggregate| |#1|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #6=(|BasicType|)) #7=(|has| |#2| #6#)) ELT)) (|table| #8=(#9=($) NIL T ELT) #10=(($ #11=(|List| #5#)) NIL T ELT)) (|swap!| (((|Void|) $ |#1| |#1|) NIL #12=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| #13=(#14=(|#2| $ |#1| |#2|) NIL #12# ELT)) (|select!| #15=(($ #16=(|Mapping| #3# #5#) $) NIL #17=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|select| #15#) (|search| #18=(((|Union| |#2| #19="failed") |#1| $) NIL T ELT)) (|sample| (#9# NIL T CONST)) (|removeDuplicates| (#20=($ $) NIL #21=(AND #17# #4#) ELT)) (|remove!| (#22=($ #5# $) NIL #17# ELT) #15# #18#) (|remove| (#22# NIL #21# ELT) #15#) (|reduce| ((#5# #23=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #23# $ #5#) NIL T ELT) ((#5# #23# $) NIL T ELT)) (|qsetelt!| #13#) (|qelt| #24=((|#2| $ |#1|) NIL T ELT)) (|minIndex| #25=((|#1| $) NIL #26=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#11# $) NIL T ELT)) (|member?| ((#3# #5# $) NIL #4# ELT)) (|maxIndex| #25#) (|map!| #27=(($ (|Mapping| #5# #5#) . #28=($)) NIL T ELT) #29=(($ (|Mapping| |#2| |#2|) . #28#) NIL T ELT)) (|map| #27# #29# #27# (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #30=(OR #31=(|has| #5# #32=(|SetCategory|)) #33=(|has| |#2| #32#)) ELT)) (|keys| #34=(((|List| |#1|) $) NIL T ELT)) (|key?| #35=((#3# |#1| $) NIL T ELT)) (|inspect| #36=((#5# $) NIL T ELT)) (|insert!| (#22# NIL T ELT)) (|indices| #34#) (|index?| #35#) (|hash| (((|SingleInteger|) $) NIL #30# ELT)) (|first| ((|#2| $) NIL #26# ELT)) (|find| (((|Union| #5# #19#) #16# $) NIL T ELT)) (|fill!| (($ $ |#2|) NIL #12# ELT)) (|extract!| #36#) (|every?| #37=((#3# #16# $) NIL T ELT)) (|eval| #38=(($ $ (|List| #39=(|Equation| #5#))) NIL #40=(AND (|has| #5# (|Evalable| #5#)) #31#) ELT) #41=(($ $ #39#) NIL #40# ELT) #42=(($ $ #5# #5#) NIL #40# ELT) #43=(($ $ #11# #11#) NIL #40# ELT) (($ $ #44=(|List| |#2|) #44#) NIL #45=(AND (|has| |#2| (|Evalable| |#2|)) #33#) ELT) (($ $ |#2| |#2|) NIL #45# ELT) (($ $ #46=(|Equation| |#2|)) NIL #45# ELT) (($ $ (|List| #46#)) NIL #45# ELT) #43# #42# #41# #38#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#2| $) NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #7#) ELT)) (|entries| ((#44# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| #8#) (|elt| #24# (#14# NIL T ELT)) (|dictionary| #8# #10#) (|count| ((#47=(|NonNegativeInteger|) #5# $) NIL #4# ELT) ((#47# #16# $) NIL T ELT)) (|copy| (#20# NIL T ELT)) (|convert| ((#48=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #48#)) ELT)) (|construct| #10#) (|coerce| ((#49=(|OutputForm|) $) NIL (OR (|has| #5# #50=(|CoercibleTo| #49#)) (|has| |#2| #50#)) ELT)) (|before?| #1#) (|bag| #10#) (|any?| #37#) (= #1#) (|#| ((#47# $) NIL T ELT))) 
(((|SparseTable| |#1| |#2| |#3|) (|TableAggregate| |#1| |#2|) #1=(|SetCategory|) #1# |#2|) (T |SparseTable|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|nextItem| (((|Maybe| $) $) 17 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|init| (($) 18 T CONST)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) 
(((|StepThrough|) (|Category|)) (T |StepThrough|)) 
((|init| (*1 *1) (|ofCategory| *1 (|StepThrough|))) (|nextItem| (*1 *2 *1) (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|StepThrough|))))) 
(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |init| ($) |constant|) (SIGNATURE |nextItem| ((|Maybe| $) $)))) 
(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|upperBound| (((|Maybe| #2=(|SpadAst|)) $) 28 T ELT)) (|step| (#3=(#2# $) 16 T ELT)) (|lowerBound| (#3# 18 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|iterationVar| (((|Identifier|) $) 14 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 38 T ELT) (($ #4=(|Syntax|)) NIL T ELT) ((#4# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|StepAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |iterationVar| ((|Identifier|) $)) (SIGNATURE |lowerBound| #1=(#2=(|SpadAst|) $)) (SIGNATURE |upperBound| ((|Maybe| #2#) $)) (SIGNATURE |step| #1#)))) (T |StepAst|)) 
((|iterationVar| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Identifier|)) #2=(|isDomain| *1 (|StepAst|)))) (|lowerBound| #1# #3=(AND (|isDomain| *2 #4=(|SpadAst|)) #2#)) (|upperBound| #1# (AND (|isDomain| *2 (|Maybe| #4#)) #2#)) (|step| #1# #3#)) 
((|oddInfiniteProduct| (#1=(#2=(|Stream| |#1|) #2#) 17 T ELT)) (|infiniteProduct| (#1# 13 T ELT)) (|generalInfiniteProduct| ((#2# #2# #3=(|Integer|) #3#) 20 T ELT)) (|evenInfiniteProduct| (#1# 15 T ELT))) 
(((|StreamInfiniteProduct| |#1|) (CATEGORY |package| (SIGNATURE |infiniteProduct| #1=(#2=(|Stream| |#1|) #2#)) (SIGNATURE |evenInfiniteProduct| #1#) (SIGNATURE |oddInfiniteProduct| #1#) (SIGNATURE |generalInfiniteProduct| (#2# #2# #3=(|Integer|) #3#))) (|Join| (|IntegralDomain|) (|CharacteristicZero|))) (T |StreamInfiniteProduct|)) 
((|generalInfiniteProduct| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|Stream| *4)) (|isDomain| *3 (|Integer|)) (|ofCategory| *4 #1=(|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *1 (|StreamInfiniteProduct| *4)))) (|oddInfiniteProduct| #2=(*1 *2 *2) #3=(AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 #1#) (|isDomain| *1 (|StreamInfiniteProduct| *3)))) (|evenInfiniteProduct| #2# #3#) (|infiniteProduct| #2# #3#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| #5=(#6=(|#1| $) NIL T ELT)) (|third| #5#) (|tail| (#7=($ $) 60 T ELT)) (|swap!| ((#8=(|Void|) $ #9=(|Integer|) #9#) 93 #10=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|split!| (#11=($ $ #9#) 122 #10# ELT)) (|size?| #12=((#3# $ #13=(|NonNegativeInteger|)) NIL T ELT)) (|showAllElements| (#14=(#15=(|OutputForm|) $) 46 #16=(|has| |#1| (|SetCategory|)) ELT)) (|showAll?| ((#3#) 49 #16# ELT)) (|setvalue!| (#17=(|#1| $ |#1|) NIL #10# ELT)) (|setrest!| (#18=($ $ $) 109 #10# ELT) (($ $ #9# $) 135 T ELT)) (|setlast!| (#17# 119 #10# ELT)) (|setfirst!| (#17# 114 #10# ELT)) (|setelt| ((|#1| $ #19="value" |#1|) NIL #10# ELT) ((|#1| $ #20="first" |#1|) 116 #10# ELT) (($ $ #21="rest" $) 118 #10# ELT) ((|#1| $ #22="last" |#1|) 121 #10# ELT) ((|#1| $ #23=(|UniversalSegment| #9#) |#1|) 106 #10# ELT) (#24=(|#1| $ #9# |#1|) 72 #10# ELT)) (|setchildren!| (($ $ #25=(|List| $)) NIL #10# ELT)) (|select| (#26=($ (|Mapping| #3# |#1|) $) 75 T ELT)) (|second| #5#) (|sample| (#27=($) NIL T CONST)) (|rst| (#7# 11 T ELT)) (|rest| (#7# 35 T ELT) (#28=($ $ #13#) 105 T ELT)) (|repeating?| ((#3# #29=(|List| |#1|) $) 128 #16# ELT)) (|repeating| (#30=($ #29#) 124 T ELT)) (|removeDuplicates| (#7# NIL #31=(AND (|has| $ (|FiniteAggregate| |#1|)) #4#) ELT)) (|remove| (#32=($ |#1| $) NIL #31# ELT) (#26# 74 T ELT)) (|qsetelt!| (#24# NIL #10# ELT)) (|qelt| (#33=(|#1| $ #9#) NIL T ELT)) (|possiblyInfinite?| #34=(#35=(#3# $) NIL T ELT)) (|output| ((#8# #9# $) 133 #16# ELT)) (|numberOfComputedEntries| (#36=(#13# $) 131 T ELT)) (|nodes| #37=((#25# $) NIL T ELT)) (|node?| #1#) (|new| (($ #13# |#1|) NIL T ELT)) (|more?| #12#) (|minIndex| #38=((#9# $) NIL (|has| #9# (|OrderedSet|)) ELT)) (|maxIndex| #38#) (|map!| (#39=($ #40=(|Mapping| |#1| |#1|) $) 89 T ELT)) (|map| (#39# 80 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 84 T ELT)) (|less?| #12#) (|leaves| #41=((#29# $) NIL T ELT)) (|leaf?| #34#) (|lazyEvaluate| (#7# 107 T ELT)) (|lazy?| (#35# 10 T ELT)) (|latex| (((|String|) $) NIL #16# ELT)) (|last| #5# (#28# NIL T ELT)) (|insert| (($ $ $ #9#) NIL T ELT) (($ |#1| $ #9#) NIL T ELT)) (|indices| (((|List| #9#) $) NIL T ELT)) (|index?| ((#3# #9# $) 90 T ELT)) (|hash| (((|SingleInteger|) $) NIL #16# ELT)) (|generate| (($ (|Mapping| |#1|)) 137 T ELT) (($ #40# |#1|) 138 T ELT)) (|frst| (#6# 7 T ELT)) (|first| (#6# 34 T ELT) (#28# 58 T ELT)) (|findCycle| (((|Record| (|:| |cycle?| #3#) (|:| |prefix| #13#) (|:| |period| #13#)) #13# $) 29 T ELT)) (|filterWhile| (#26# 139 T ELT)) (|filterUntil| (#26# 140 T ELT)) (|fill!| (#42=($ $ |#1|) 85 #10# ELT)) (|extend| (#11# 40 T ELT)) (|explicitlyFinite?| (#35# 88 T ELT)) (|explicitlyEmpty?| (#35# 9 T ELT)) (|explicitEntries?| (#35# 130 T ELT)) (|eval| (($ $ (|List| #43=(|Equation| |#1|))) NIL #44=(AND (|has| |#1| (|Evalable| |#1|)) #16#) ELT) (($ $ #43#) NIL #44# ELT) (($ $ |#1| |#1|) NIL #44# ELT) (($ $ #29# #29#) NIL #44# ELT)) (|eq?| (#2# 25 T ELT)) (|entry?| ((#3# |#1| $) NIL #31# ELT)) (|entries| #41#) (|empty?| (#35# 14 T ELT)) (|empty| (#27# 53 T ELT)) (|elt| ((|#1| $ #19#) NIL T ELT) ((|#1| $ #20#) NIL T ELT) (($ $ #21#) NIL T ELT) ((|#1| $ #22#) NIL T ELT) #45=(($ $ #23#) NIL T ELT) (#33# 70 T ELT) (#24# NIL T ELT)) (|distance| ((#9# $ $) 57 T ELT)) (|delete| #45# (#11# NIL T ELT)) (|delay| (($ (|Mapping| $)) 56 T ELT)) (|cyclic?| (#35# 86 T ELT)) (|cycleTail| (#7# 87 T ELT)) (|cycleSplit!| (#7# 110 #10# ELT)) (|cycleLength| (#36# NIL T ELT)) (|cycleEntry| (#7# NIL T ELT)) (|copy| (#7# 52 T ELT)) (|convert| ((#46=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #46#)) ELT)) (|construct| (#30# 68 T ELT)) (|cons| (#32# 108 T ELT)) (|concat!| (#18# 112 #10# ELT) (#42# 113 #10# ELT)) (|concat| (#18# 95 T ELT) (#32# 54 T ELT) (($ #25#) 100 T ELT) (#42# 94 T ELT)) (|complete| (#7# 59 T ELT)) (|coerce| (#30# 123 T ELT) (#14# 50 (|has| |#1| (|CoercibleTo| #15#)) ELT)) (|children| #37#) (|child?| #1#) (|before?| #1#) (= (#2# 126 #4# ELT))) 
(((|Stream| |#1|) (|Join| (|LazyStreamAggregate| |#1|) (|CoercibleFrom| #1=(|List| |#1|)) (|ShallowlyMutableAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |repeating| ($ #1#)) (IF #2=(|has| |#1| (|SetCategory|)) (SIGNATURE |repeating?| (#3=(|Boolean|) #1# $)) |%noBranch|) (SIGNATURE |findCycle| ((|Record| (|:| |cycle?| #3#) (|:| |prefix| #4=(|NonNegativeInteger|)) (|:| |period| #4#)) #4# $)) (SIGNATURE |delay| ($ (|Mapping| $))) (SIGNATURE |cons| ($ |#1| $)) (IF #2# (PROGN (SIGNATURE |output| ((|Void|) #5=(|Integer|) $)) (SIGNATURE |showAllElements| ((|OutputForm|) $)) (SIGNATURE |showAll?| (#3#))) |%noBranch|) (SIGNATURE |setrest!| ($ $ #5# $)) (SIGNATURE |generate| ($ (|Mapping| |#1|))) (SIGNATURE |generate| ($ (|Mapping| |#1| |#1|) |#1|)) (SIGNATURE |filterWhile| #6=($ (|Mapping| #3# |#1|) $)) (SIGNATURE |filterUntil| #6#))) (|Type|)) (T |Stream|)) 
((|repeating| #1=(*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #2=(|ofCategory| *3 #3=(|Type|)) #4=(|isDomain| *1 #5=(|Stream| *3)))) (|repeating?| #6=(*1 *2 *3 *1) (AND (|isDomain| *3 (|List| *4)) #7=(|ofCategory| *4 #8=(|SetCategory|)) #9=(|ofCategory| *4 #3#) #10=(|isDomain| *2 #11=(|Boolean|)) #12=(|isDomain| *1 (|Stream| *4)))) (|findCycle| #6# (AND (|isDomain| *2 (|Record| (|:| |cycle?| #11#) (|:| |prefix| #13=(|NonNegativeInteger|)) (|:| |period| #13#))) #12# #9# (|isDomain| *3 #13#))) (|delay| #1# (AND (|isDomain| *2 (|Mapping| #5#)) #4# #2#)) (|cons| #14=(*1 *1 *2 *1) (AND (|isDomain| *1 (|Stream| *2)) (|ofCategory| *2 #3#))) (|output| #6# (AND (|isDomain| *3 #15=(|Integer|)) (|isDomain| *2 (|Void|)) #12# #7# #9#)) (|showAllElements| (*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) #4# #16=(|ofCategory| *3 #8#) #2#)) (|showAll?| (*1 *2) (AND #10# #4# #16# #2#)) (|setrest!| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 #15#) #4# #2#)) (|generate| #1# (AND (|isDomain| *2 (|Mapping| *3)) #2# #4#)) (|generate| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3 *3)) #2# #4#)) (|filterWhile| #14# #17=(AND (|isDomain| *2 (|Mapping| #11# *3)) #2# #4#)) (|filterUntil| #14# #17#)) 
((|concat| ((#1=(|Stream| |#1|) (|Stream| #1#)) 15 T ELT))) 
(((|StreamFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |concat| (#1=(|Stream| |#1|) (|Stream| #1#)))) (|Type|)) (T |StreamFunctions1|)) 
((|concat| (*1 *2 *3) (AND (|isDomain| *3 (|Stream| #1=(|Stream| *4))) (|isDomain| *2 #1#) (|isDomain| *1 (|StreamFunctions1| *4)) (|ofCategory| *4 (|Type|))))) 
((|scan| ((#1=(|Stream| |#2|) |#2| #2=(|Mapping| |#2| |#1| |#2|) #3=(|Stream| |#1|)) 25 T ELT)) (|reduce| ((|#2| |#2| #2# #3#) 26 T ELT)) (|map| ((#1# (|Mapping| |#2| |#1|) #3#) 16 T ELT))) 
(((|StreamFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| (#1=(|Stream| |#2|) (|Mapping| |#2| |#1|) #2=(|Stream| |#1|))) (SIGNATURE |scan| (#1# |#2| #3=(|Mapping| |#2| |#1| |#2|) #2#)) (SIGNATURE |reduce| (|#2| |#2| #3# #2#))) #4=(|Type|) #4#) (T |StreamFunctions2|)) 
((|reduce| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #1=(|isDomain| *4 (|Stream| *5)) #2=(|ofCategory| *5 #3=(|Type|)) (|ofCategory| *2 #3#) (|isDomain| *1 (|StreamFunctions2| *5 *2)))) (|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Mapping| *3 *6 *3)) (|isDomain| *5 #4=(|Stream| *6)) #5=(|ofCategory| *6 #3#) (|ofCategory| *3 #3#) (|isDomain| *2 (|Stream| *3)) (|isDomain| *1 (|StreamFunctions2| *6 *3)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) #1# #2# #5# (|isDomain| *2 #4#) (|isDomain| *1 (|StreamFunctions2| *5 *6))))) 
((|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) 21 T ELT))) 
(((|StreamFunctions3| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |map| ((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)))) #1=(|Type|) #1# #1#) (T |StreamFunctions3|)) 
((|map| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *8 *6 *7)) (|isDomain| *4 (|Stream| *6)) (|isDomain| *5 (|Stream| *7)) (|ofCategory| *6 #1=(|Type|)) (|ofCategory| *7 #1#) (|ofCategory| *8 #1#) (|isDomain| *2 (|Stream| *8)) (|isDomain| *1 (|StreamFunctions3| *6 *7 *8))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| #5=(|Character|) (|BasicType|)) ELT)) (|upperCase!| (#6=($ $) 42 T ELT)) (|upperCase| #7=(#6# NIL T ELT)) (|trim| #8=(#9=($ $ #5#) NIL T ELT) (#10=($ $ #11=(|CharacterClass|)) NIL T ELT)) (|swap!| (((|Void|) $ #12=(|Integer|) #12#) NIL #13=(|has| $ (|ShallowlyMutableAggregate| #5#)) ELT)) (|suffix?| (#2# 67 T ELT)) (|substring?| ((#3# $ $ #12#) 62 T ELT)) (|string| (($ #12#) 7 T ELT) (($ (|DoubleFloat|)) 9 T ELT) (($ (|Identifier|)) 11 T ELT)) (|split| ((#14=(|List| $) $ #5#) 76 T ELT) ((#14# $ #11#) 77 T ELT)) (|sorted?| ((#3# #15=(|Mapping| #3# #5# #5#) $) NIL T ELT) (#16=(#3# $) NIL #17=(|has| #5# #18=(|OrderedSet|)) ELT)) (|sort!| (#19=($ #15# $) NIL #13# ELT) (#6# NIL (AND #13# #17#) ELT)) (|sort| (#19# NIL T ELT) (#6# NIL #17# ELT)) (|setelt| (#20=(#5# $ #12# #5#) 59 #13# ELT) ((#5# $ #21=(|UniversalSegment| #12#) #5#) NIL #13# ELT)) (|select| #22=(($ #23=(|Mapping| #3# #5#) $) NIL #24=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|sample| (#25=($) NIL T CONST)) (|rightTrim| (#9# 80 T ELT) (#10# 81 T ELT)) (|reverse!| (#6# NIL #13# ELT)) (|reverse| #7#) (|replace| (($ $ #21# $) 57 T ELT)) (|removeDuplicates| (#6# NIL #26=(AND #24# #4#) ELT)) (|remove| (#27=($ #5# $) NIL #26# ELT) #22#) (|reduce| ((#5# #28=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #28# $ #5#) NIL T ELT) ((#5# #28# $) NIL T ELT)) (|qsetelt!| (#20# NIL #13# ELT)) (|qelt| (#29=(#5# $ #12#) NIL T ELT)) (|prefix?| (#2# 91 T ELT)) (|position| ((#12# #23# $) NIL T ELT) ((#12# #5# $) NIL #4# ELT) ((#12# #5# $ #12#) 64 #4# ELT) ((#12# $ $ #12#) 63 T ELT) ((#12# #11# $ #12#) 66 T ELT)) (|new| (($ #30=(|NonNegativeInteger|) #5#) 14 T ELT)) (|minIndex| (#31=(#12# $) 36 #32=(|has| #12# #18#) ELT)) (|min| #33=(#34=($ $ $) NIL #17# ELT)) (|merge| (($ #15# $ $) NIL T ELT) #33#) (|members| #35=((#36=(|List| #5#) $) NIL T ELT)) (|member?| (#37=(#3# #5# $) NIL #4# ELT)) (|maxIndex| (#31# 50 #32# ELT)) (|max| #33#) (|match?| ((#3# $ $ #5#) 92 T ELT)) (|match| ((#30# $ $ #5#) 88 T ELT)) (|map!| (#38=($ (|Mapping| #5# #5#) $) 41 T ELT)) (|map| (#38# NIL T ELT) (($ #28# $ $) NIL T ELT)) (|lowerCase!| (#6# 45 T ELT)) (|lowerCase| #7#) (|leftTrim| (#9# 78 T ELT) (#10# 79 T ELT)) (|latex| (((|String|) $) 46 #39=(|has| #5# (|SetCategory|)) ELT)) (|insert| (($ #5# $ #12#) NIL T ELT) (#40=($ $ $ #12#) 31 T ELT)) (|indices| (((|List| #12#) $) NIL T ELT)) (|index?| ((#3# #12# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) 87 #39# ELT)) (|first| ((#5# $) NIL #32# ELT)) (|find| (((|Union| #5# "failed") #23# $) NIL T ELT)) (|fill!| (#9# NIL #13# ELT)) (|every?| #41=((#3# #23# $) NIL T ELT)) (|eval| (($ $ (|List| #42=(|Equation| #5#))) NIL #43=(AND (|has| #5# (|Evalable| #5#)) #39#) ELT) (($ $ #42#) NIL #43# ELT) (($ $ #5# #5#) NIL #43# ELT) (($ $ #36# #36#) NIL #43# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#37# NIL #26# ELT)) (|entries| #35#) (|empty?| (#16# 19 T ELT)) (|empty| (#25# 16 T ELT)) (|elt| (#20# NIL T ELT) (#29# 69 T ELT) (#44=($ $ #21#) 29 T ELT) (#34# NIL T ELT)) (|delete| (($ $ #12#) NIL T ELT) (#44# NIL T ELT)) (|count| ((#30# #5# $) NIL #4# ELT) ((#30# #23# $) NIL T ELT)) (|copyInto!| (#40# 83 #13# ELT)) (|copy| (#6# 24 T ELT)) (|convert| ((#45=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #45#)) ELT)) (|construct| (($ #36#) NIL T ELT)) (|concat| #8# (#27# NIL T ELT) (#34# 23 T ELT) (($ #14#) 84 T ELT)) (|coerce| (($ #5#) NIL T ELT) ((#46=(|OutputForm|) $) 35 (|has| #5# (|CoercibleTo| #46#)) ELT)) (|before?| #1#) (|any?| #41#) (>= #47=(#2# NIL #17# ELT)) (> #47#) (= (#2# 21 #4# ELT)) (<= #47#) (< (#2# 22 #17# ELT)) (|#| ((#30# $) 20 T ELT))) 
(((|String|) (|Join| (|StringAggregate|) (CATEGORY |domain| (SIGNATURE |string| ($ (|Integer|))) (SIGNATURE |string| ($ (|DoubleFloat|))) (SIGNATURE |string| ($ (|Identifier|)))))) (T |String|)) 
((|string| #1=(*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #2=(|isDomain| *1 (|String|)))) (|string| #1# (AND (|isDomain| *2 (|DoubleFloat|)) #2#)) (|string| #1# (AND (|isDomain| *2 (|Identifier|)) #2#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| #6=(|String|)) (|:| |entry| |#1|)) #7=(|BasicType|)) #8=(|has| |#1| #7#)) ELT)) (|table| #9=(#10=($) NIL T ELT) #11=(($ #12=(|List| #5#)) NIL T ELT)) (|swap!| (((|Void|) $ #6# #6#) NIL #13=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| #14=(#15=(|#1| $ #6# |#1|) NIL #13# ELT)) (|select!| #16=(($ #17=(|Mapping| #3# #5#) $) NIL #18=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|select| #16#) (|search| #19=(((|Union| |#1| #20="failed") #6# $) NIL T ELT)) (|sample| (#10# NIL T CONST)) (|removeDuplicates| (#21=($ $) NIL #22=(AND #18# #4#) ELT)) (|remove!| (#23=($ #5# $) NIL #18# ELT) #16# #19#) (|remove| (#23# NIL #22# ELT) #16#) (|reduce| ((#5# #24=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #24# $ #5#) NIL T ELT) ((#5# #24# $) NIL T ELT)) (|qsetelt!| #14#) (|qelt| #25=((|#1| $ #6#) NIL T ELT)) (|minIndex| #26=(#27=(#6# $) NIL #28=(|has| #6# (|OrderedSet|)) ELT)) (|members| ((#12# $) NIL T ELT)) (|member?| ((#3# #5# $) NIL #4# ELT)) (|maxIndex| #26#) (|map!| #29=(($ (|Mapping| #5# #5#) . #30=($)) NIL T ELT) #31=(($ (|Mapping| |#1| |#1|) . #30#) NIL T ELT)) (|map| #29# #31# #29# (($ (|Mapping| |#1| |#1| |#1|) $ $) NIL T ELT)) (|latex| (#27# NIL #32=(OR #33=(|has| #5# #34=(|SetCategory|)) #35=(|has| |#1| #34#)) ELT)) (|keys| #36=(((|List| #6#) $) NIL T ELT)) (|key?| #37=((#3# #6# $) NIL T ELT)) (|inspect| #38=((#5# $) NIL T ELT)) (|insert!| (#23# NIL T ELT)) (|indices| #36#) (|index?| #37#) (|hash| (((|SingleInteger|) $) NIL #32# ELT)) (|first| ((|#1| $) NIL #28# ELT)) (|find| (((|Union| #5# #20#) #17# $) NIL T ELT)) (|fill!| (($ $ |#1|) NIL #13# ELT)) (|extract!| #38#) (|every?| #39=((#3# #17# $) NIL T ELT)) (|eval| #40=(($ $ (|List| #41=(|Equation| #5#))) NIL #42=(AND (|has| #5# (|Evalable| #5#)) #33#) ELT) #43=(($ $ #41#) NIL #42# ELT) #44=(($ $ #5# #5#) NIL #42# ELT) #45=(($ $ #12# #12#) NIL #42# ELT) (($ $ #46=(|List| |#1|) #46#) NIL #47=(AND (|has| |#1| (|Evalable| |#1|)) #35#) ELT) (($ $ |#1| |#1|) NIL #47# ELT) (($ $ #48=(|Equation| |#1|)) NIL #47# ELT) (($ $ (|List| #48#)) NIL #47# ELT) #45# #44# #43# #40#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#1| $) NIL (AND (|has| $ (|FiniteAggregate| |#1|)) #8#) ELT)) (|entries| ((#46# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| #9#) (|elt| #25# (#15# NIL T ELT)) (|dictionary| #9# #11#) (|count| ((#49=(|NonNegativeInteger|) #5# $) NIL #4# ELT) ((#49# #17# $) NIL T ELT)) (|copy| (#21# NIL T ELT)) (|convert| ((#50=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #50#)) ELT)) (|construct| #11#) (|coerce| ((#51=(|OutputForm|) $) NIL (OR (|has| #5# #52=(|CoercibleTo| #51#)) (|has| |#1| #52#)) ELT)) (|before?| #1#) (|bag| #11#) (|any?| #39#) (= #1#) (|#| ((#49# $) NIL T ELT))) 
(((|StringTable| |#1|) (|TableAggregate| (|String|) |#1|) (|SetCategory|)) (T |StringTable|)) 
NIL 
((|revert| (#1=(#2=(|Stream| |#1|) #2#) 83 T ELT)) (|recip| ((#3=(|Union| #2# "failed") #2#) 39 T ELT)) (|powern| ((#2# #4=(|Fraction| #5=(|Integer|)) #2#) 131 #6=(|has| |#1| (|Algebra| #4#)) ELT)) (|power| (#7=(#2# |#1| #2#) 135 #8=(|has| |#1| (|Field|)) ELT)) (|oddlambert| (#1# 97 T ELT)) (|oddintegers| (#9=((|Stream| #5#) #5#) 63 T ELT)) (|nlde| (#10=(#2# (|Stream| #2#)) 116 #6# ELT)) (|multisect| (#11=(#2# #5# #5# #2#) 103 T ELT)) (|monom| ((#2# |#1| #5#) 51 T ELT)) (|mapmult| (#12=(#2# #2# #2#) 66 T ELT)) (|mapdiv| (#12# 133 #8# ELT)) (|lazyIntegrate| ((#2# |#1| #13=(|Mapping| #2#)) 115 #6# ELT)) (|lazyGintegrate| ((#2# #14=(|Mapping| |#1| #5#) |#1| #13#) 134 #8# ELT)) (|lambert| (#1# 96 T ELT)) (|lagrange| (#1# 82 T ELT)) (|invmultisect| (#11# 104 T ELT)) (|integrate| (#7# 113 #6# ELT)) (|integers| (#9# 62 T ELT)) (|int| (#15=(#2# |#1|) 65 T ELT)) (|generalLambert| ((#2# #2# #5# #5#) 100 T ELT)) (|gderiv| ((#2# #14# #2#) 72 T ELT)) (|exquo| ((#3# #2# #2#) 37 T ELT)) (|evenlambert| (#1# 98 T ELT)) (|eval| (#16=(#2# #2# |#1|) 77 T ELT)) (|deriv| (#1# 68 T ELT)) (|compose| (#12# 78 T ELT)) (|coerce| (#15# 73 T ELT)) (|addiag| (#10# 88 T ELT)) (/ (#12# 38 T ELT)) (- (#1# 21 T ELT) (#12# 23 T ELT)) (+ (#12# 17 T ELT)) (* (#16# 29 T ELT) (#7# 26 T ELT) (#12# 27 T ELT))) 
(((|StreamTaylorSeriesOperations| |#1|) (CATEGORY |package| (SIGNATURE + #1=(#2=(|Stream| |#1|) #2# #2#)) (SIGNATURE - #1#) (SIGNATURE - #3=(#2# #2#)) (SIGNATURE * #1#) (SIGNATURE * #4=(#2# |#1| #2#)) (SIGNATURE * #5=(#2# #2# |#1|)) (SIGNATURE |exquo| (#6=(|Union| #2# "failed") #2# #2#)) (SIGNATURE / #1#) (SIGNATURE |recip| (#6# #2#)) (SIGNATURE |monom| (#2# |#1| #7=(|Integer|))) (SIGNATURE |integers| #8=((|Stream| #7#) #7#)) (SIGNATURE |oddintegers| #8#) (SIGNATURE |int| #9=(#2# |#1|)) (SIGNATURE |mapmult| #1#) (SIGNATURE |deriv| #3#) (SIGNATURE |gderiv| (#2# #10=(|Mapping| |#1| #7#) #2#)) (SIGNATURE |coerce| #9#) (SIGNATURE |eval| #5#) (SIGNATURE |compose| #1#) (SIGNATURE |lagrange| #3#) (SIGNATURE |revert| #3#) (SIGNATURE |addiag| #11=(#2# (|Stream| #2#))) (SIGNATURE |lambert| #3#) (SIGNATURE |oddlambert| #3#) (SIGNATURE |evenlambert| #3#) (SIGNATURE |generalLambert| (#2# #2# #7# #7#)) (SIGNATURE |multisect| #12=(#2# #7# #7# #2#)) (SIGNATURE |invmultisect| #12#) (IF (|has| |#1| (|Algebra| #13=(|Fraction| #7#))) (PROGN (SIGNATURE |integrate| #4#) (SIGNATURE |lazyIntegrate| (#2# |#1| #14=(|Mapping| #2#))) (SIGNATURE |nlde| #11#) (SIGNATURE |powern| (#2# #13# #2#))) |%noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |mapdiv| #1#) (SIGNATURE |lazyGintegrate| (#2# #10# |#1| #14#)) (SIGNATURE |power| #4#)) |%noBranch|)) (|Ring|)) (T |StreamTaylorSeriesOperations|)) 
((|power| #1=(*1 *2 *3 *2) #2=(AND #3=(|isDomain| *2 #4=(|Stream| *3)) (|ofCategory| *3 #5=(|Field|)) #6=(|ofCategory| *3 #7=(|Ring|)) #8=(|isDomain| *1 (|StreamTaylorSeriesOperations| *3)))) (|lazyGintegrate| (*1 *2 *3 *4 *5) (AND #9=(|isDomain| *3 (|Mapping| *4 #10=(|Integer|))) (|isDomain| *5 (|Mapping| #11=(|Stream| *4))) (|ofCategory| *4 #5#) #12=(|ofCategory| *4 #7#) #13=(|isDomain| *2 #11#) #14=(|isDomain| *1 (|StreamTaylorSeriesOperations| *4)))) (|mapdiv| #15=(*1 *2 *2 *2) #2#) (|powern| #1# (AND #13# (|ofCategory| *4 (|Algebra| *3)) #12# (|isDomain| *3 #16=(|Fraction| #10#)) #14#)) (|nlde| #17=(*1 *2 *3) (AND #18=(|isDomain| *3 (|Stream| #11#)) #13# #14# (|ofCategory| *4 #19=(|Algebra| #16#)) #12#)) (|lazyIntegrate| #20=(*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| #4#)) #3# #8# #21=(|ofCategory| *3 #19#) #6#)) (|integrate| #1# (AND #3# #21# #6# #8#)) (|invmultisect| #22=(*1 *2 *3 *3 *2) #23=(AND #13# #24=(|isDomain| *3 #10#) #12# #14#)) (|multisect| #22# #23#) (|generalLambert| (*1 *2 *2 *3 *3) #23#) (|evenlambert| #25=(*1 *2 *2) #26=(AND #3# #6# #8#)) (|oddlambert| #25# #26#) (|lambert| #25# #26#) (|addiag| #17# (AND #18# #13# #14# #12#)) (|revert| #25# #26#) (|lagrange| #25# #26#) (|compose| #15# #26#) (|eval| #27=(*1 *2 *2 *3) #26#) (|coerce| #17# #28=(AND #3# #8# #6#)) (|gderiv| #1# (AND #13# #9# #12# #14#)) (|deriv| #25# #26#) (|mapmult| #15# #26#) (|int| #17# #28#) (|oddintegers| #17# #29=(AND (|isDomain| *2 (|Stream| #10#)) #14# #12# #24#)) (|integers| #17# #29#) (|monom| #20# (AND (|isDomain| *4 #10#) #3# #8# #6#)) (|recip| #25# #30=(|partial| AND #3# #6# #8#)) (/ #15# #26#) (|exquo| #15# #30#) (* #27# #26#) (* #1# #26#) (* #15# #26#) (- #25# #26#) (- #15# #26#) (+ #15# #26#)) 
((|tanh| (#1=(#2=(|Stream| |#1|) #2#) 102 T ELT)) (|tan| (#1# 59 T ELT)) (|sinhcosh| (((|Record| (|:| |sinh| #2#) (|:| |cosh| #2#)) #2#) 98 T ELT)) (|sinh| (#1# 99 T ELT)) (|sincos| (((|Record| (|:| |sin| #2#) (|:| |cos| #2#)) #2#) 54 T ELT)) (|sin| (#1# 55 T ELT)) (|sech| (#1# 104 T ELT)) (|sec| (#1# 66 T ELT)) (|log| (#1# 40 T ELT)) (|exp| (#1# 37 T ELT)) (|csch| (#1# 105 T ELT)) (|csc| (#1# 67 T ELT)) (|coth| (#1# 103 T ELT)) (|cot| (#1# 62 T ELT)) (|cosh| (#1# 100 T ELT)) (|cos| (#1# 56 T ELT)) (|atanh| (#1# 113 T ELT)) (|atan| (#1# 88 T ELT)) (|asinh| (#1# 107 T ELT)) (|asin| (#1# 84 T ELT)) (|asech| (#1# 117 T ELT)) (|asec| (#1# 92 T ELT)) (|acsch| (#1# 119 T ELT)) (|acsc| (#1# 94 T ELT)) (|acoth| (#1# 115 T ELT)) (|acot| (#1# 90 T ELT)) (|acosh| (#1# 109 T ELT)) (|acos| (#1# 86 T ELT)) (** ((#2# #2# #2#) 41 T ELT))) 
(((|StreamTranscendentalFunctions| |#1|) (CATEGORY |package| (SIGNATURE |exp| #1=(#2=(|Stream| |#1|) #2#)) (SIGNATURE |log| #1#) (SIGNATURE ** (#2# #2# #2#)) (SIGNATURE |sincos| ((|Record| (|:| |sin| #2#) (|:| |cos| #2#)) #2#)) (SIGNATURE |sin| #1#) (SIGNATURE |cos| #1#) (SIGNATURE |tan| #1#) (SIGNATURE |cot| #1#) (SIGNATURE |sec| #1#) (SIGNATURE |csc| #1#) (SIGNATURE |asin| #1#) (SIGNATURE |acos| #1#) (SIGNATURE |atan| #1#) (SIGNATURE |acot| #1#) (SIGNATURE |asec| #1#) (SIGNATURE |acsc| #1#) (SIGNATURE |sinhcosh| ((|Record| (|:| |sinh| #2#) (|:| |cosh| #2#)) #2#)) (SIGNATURE |sinh| #1#) (SIGNATURE |cosh| #1#) (SIGNATURE |tanh| #1#) (SIGNATURE |coth| #1#) (SIGNATURE |sech| #1#) (SIGNATURE |csch| #1#) (SIGNATURE |asinh| #1#) (SIGNATURE |acosh| #1#) (SIGNATURE |atanh| #1#) (SIGNATURE |acoth| #1#) (SIGNATURE |asech| #1#) (SIGNATURE |acsch| #1#)) (|Algebra| (|Fraction| (|Integer|)))) (T |StreamTranscendentalFunctions|)) 
((|acsch| #1=(*1 *2 *2) #2=(AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 #3=(|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctions| *3)))) (|asech| #1# #2#) (|acoth| #1# #2#) (|atanh| #1# #2#) (|acosh| #1# #2#) (|asinh| #1# #2#) (|csch| #1# #2#) (|sech| #1# #2#) (|coth| #1# #2#) (|tanh| #1# #2#) (|cosh| #1# #2#) (|sinh| #1# #2#) (|sinhcosh| #4=(*1 *2 *3) (AND #5=(|ofCategory| *4 #3#) (|isDomain| *2 (|Record| (|:| |sinh| #6=(|Stream| *4)) (|:| |cosh| #6#))) #7=(|isDomain| *1 (|StreamTranscendentalFunctions| *4)) #8=(|isDomain| *3 #6#))) (|acsc| #1# #2#) (|asec| #1# #2#) (|acot| #1# #2#) (|atan| #1# #2#) (|acos| #1# #2#) (|asin| #1# #2#) (|csc| #1# #2#) (|sec| #1# #2#) (|cot| #1# #2#) (|tan| #1# #2#) (|cos| #1# #2#) (|sin| #1# #2#) (|sincos| #4# (AND #5# (|isDomain| *2 (|Record| (|:| |sin| #6#) (|:| |cos| #6#))) #7# #8#)) (** (*1 *2 *2 *2) #2#) (|log| #1# #2#) (|exp| #1# #2#)) 
((|tanh| (#1=(#2=(|Stream| |#1|) #2#) 60 T ELT)) (|tan| (#1# 42 T ELT)) (|sinh| (#1# 56 T ELT)) (|sin| (#1# 38 T ELT)) (|sech| (#1# 63 T ELT)) (|sec| (#1# 45 T ELT)) (|log| (#1# 34 T ELT)) (|exp| (#1# 29 T ELT)) (|csch| (#1# 64 T ELT)) (|csc| (#1# 46 T ELT)) (|coth| (#1# 61 T ELT)) (|cot| (#1# 43 T ELT)) (|cosh| (#1# 58 T ELT)) (|cos| (#1# 40 T ELT)) (|atanh| (#1# 68 T ELT)) (|atan| (#1# 50 T ELT)) (|asinh| (#1# 66 T ELT)) (|asin| (#1# 48 T ELT)) (|asech| (#1# 71 T ELT)) (|asec| (#1# 53 T ELT)) (|acsch| (#1# 72 T ELT)) (|acsc| (#1# 54 T ELT)) (|acoth| (#1# 70 T ELT)) (|acot| (#1# 52 T ELT)) (|acosh| (#1# 69 T ELT)) (|acos| (#1# 51 T ELT)) (** ((#2# #2# #2#) 36 T ELT))) 
(((|StreamTranscendentalFunctionsNonCommutative| |#1|) (CATEGORY |package| (SIGNATURE |exp| #1=(#2=(|Stream| |#1|) #2#)) (SIGNATURE |log| #1#) (SIGNATURE ** (#2# #2# #2#)) (SIGNATURE |sin| #1#) (SIGNATURE |cos| #1#) (SIGNATURE |tan| #1#) (SIGNATURE |cot| #1#) (SIGNATURE |sec| #1#) (SIGNATURE |csc| #1#) (SIGNATURE |asin| #1#) (SIGNATURE |acos| #1#) (SIGNATURE |atan| #1#) (SIGNATURE |acot| #1#) (SIGNATURE |asec| #1#) (SIGNATURE |acsc| #1#) (SIGNATURE |sinh| #1#) (SIGNATURE |cosh| #1#) (SIGNATURE |tanh| #1#) (SIGNATURE |coth| #1#) (SIGNATURE |sech| #1#) (SIGNATURE |csch| #1#) (SIGNATURE |asinh| #1#) (SIGNATURE |acosh| #1#) (SIGNATURE |atanh| #1#) (SIGNATURE |acoth| #1#) (SIGNATURE |asech| #1#) (SIGNATURE |acsch| #1#)) (|Algebra| (|Fraction| (|Integer|)))) (T |StreamTranscendentalFunctionsNonCommutative|)) 
((|acsch| #1=(*1 *2 *2) #2=(AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|isDomain| *1 (|StreamTranscendentalFunctionsNonCommutative| *3)))) (|asech| #1# #2#) (|acoth| #1# #2#) (|atanh| #1# #2#) (|acosh| #1# #2#) (|asinh| #1# #2#) (|csch| #1# #2#) (|sech| #1# #2#) (|coth| #1# #2#) (|tanh| #1# #2#) (|cosh| #1# #2#) (|sinh| #1# #2#) (|acsc| #1# #2#) (|asec| #1# #2#) (|acot| #1# #2#) (|atan| #1# #2#) (|acos| #1# #2#) (|asin| #1# #2#) (|csc| #1# #2#) (|sec| #1# #2#) (|cot| #1# #2#) (|tan| #1# #2#) (|cos| #1# #2#) (|sin| #1# #2#) (** (*1 *2 *2 *2) #2#) (|log| #1# #2#) (|exp| #1# #2#)) 
((|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) 51 T ELT)) (|primitivePart| ((|#2| |#2| |#1|) 19 (|has| |#1| (|EuclideanDomain|)) ELT))) 
(((|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 #1=(|IntegralDomain|)) (|isDomain| *1 (|SubResultantPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|subresultantVector| (*1 *2 *3 *3) (AND (|ofCategory| *4 #1#) (|isDomain| *2 (|PrimitiveArray| *3)) (|isDomain| *1 (|SubResultantPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|traverse| (($ $ #4=(|List| #5=(|NonNegativeInteger|))) 79 T ELT)) (|subspace| (#6=($) 33 T ELT)) (|shallowCopy| (#7=($ $) 51 T ELT)) (|separate| (#8=(#9=(|List| $) $) 60 T ELT)) (|root?| (#10=(#3# $) 19 T ELT)) (|pointData| (((|List| #11=(|Point| |#2|)) $) 86 T ELT)) (|parent| (#7# 80 T ELT)) (|numberOfChildren| (#12=(#5# $) 47 T ELT)) (|new| (#6# 32 T ELT)) (|modifyPoint| (#13=($ $ #4# #11#) 72 T ELT) (#14=($ $ #4# #5#) 73 T ELT) (($ $ #5# #11#) 75 T ELT)) (|merge| (($ $ $) 57 T ELT) (($ #9#) 59 T ELT)) (|level| (#12# 87 T ELT)) (|leaf?| (#10# 15 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|internal?| (#10# 22 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|extractProperty| ((#15=(|SubSpaceComponentProperty|) $) 85 T ELT)) (|extractPoint| ((#11# $) 81 T ELT)) (|extractIndex| (#12# 82 T ELT)) (|extractClosed| (#10# 84 T ELT)) (|defineProperty| (($ $ #4# #15#) 78 T ELT)) (|deepCopy| (#7# 52 T ELT)) (|coerce| (((|OutputForm|) $) 99 T ELT)) (|closeComponent| (($ $ #4# #3#) 77 T ELT)) (|children| (#8# 11 T ELT)) (|child| (($ $ #5#) 46 T ELT)) (|birth| (#7# 43 T ELT)) (|before?| #1#) (|addPointLast| (($ $ $ #11# #5#) 68 T ELT)) (|addPoint2| (($ $ #11#) 67 T ELT)) (|addPoint| (#13# 66 T ELT) (#14# 70 T ELT) ((#5# $ #11#) 71 T ELT)) (= (#2# 92 T ELT))) 
(((|SubSpace| |#1| |#2|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |leaf?| #1=(#2=(|Boolean|) $)) (SIGNATURE |root?| #1#) (SIGNATURE |internal?| #1#) (SIGNATURE |new| #3=($)) (SIGNATURE |subspace| #3#) (SIGNATURE |birth| #4=($ $)) (SIGNATURE |child| ($ $ #5=(|NonNegativeInteger|))) (SIGNATURE |children| #6=(#7=(|List| $) $)) (SIGNATURE |numberOfChildren| #8=(#5# $)) (SIGNATURE |shallowCopy| #4#) (SIGNATURE |deepCopy| #4#) (SIGNATURE |merge| ($ $ $)) (SIGNATURE |merge| ($ #7#)) (SIGNATURE |separate| #6#) (SIGNATURE |addPoint| #9=($ $ #10=(|List| #5#) #11=(|Point| |#2|))) (SIGNATURE |addPoint2| ($ $ #11#)) (SIGNATURE |addPointLast| ($ $ $ #11# #5#)) (SIGNATURE |modifyPoint| #9#) (SIGNATURE |addPoint| #12=($ $ #10# #5#)) (SIGNATURE |modifyPoint| #12#) (SIGNATURE |addPoint| (#5# $ #11#)) (SIGNATURE |modifyPoint| ($ $ #5# #11#)) (SIGNATURE |closeComponent| ($ $ #10# #2#)) (SIGNATURE |defineProperty| ($ $ #10# #13=(|SubSpaceComponentProperty|))) (SIGNATURE |traverse| ($ $ #10#)) (SIGNATURE |extractPoint| (#11# $)) (SIGNATURE |extractIndex| #8#) (SIGNATURE |extractClosed| #1#) (SIGNATURE |extractProperty| (#13# $)) (SIGNATURE |level| #8#) (SIGNATURE |parent| #4#) (SIGNATURE |pointData| ((|List| #11#) $)))) (|PositiveInteger|) (|Ring|)) (T |SubSpace|)) 
((|leaf?| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 #3=(|Boolean|)) #4=(|isDomain| *1 #5=(|SubSpace| *3 *4)) #6=(|ofType| *3 #7=(|PositiveInteger|)) #8=(|ofCategory| *4 #9=(|Ring|)))) (|root?| #1# #2#) (|internal?| #1# #2#) (|new| #10=(*1 *1) #11=(AND (|isDomain| *1 (|SubSpace| *2 *3)) (|ofType| *2 #7#) (|ofCategory| *3 #9#))) (|subspace| #10# #11#) (|birth| #12=(*1 *1 *1) #11#) (|child| #13=(*1 *1 *1 *2) #14=(AND #15=(|isDomain| *2 #16=(|NonNegativeInteger|)) #4# #6# #8#)) (|children| #1# #17=(AND (|isDomain| *2 (|List| #5#)) #4# #6# #8#)) (|numberOfChildren| #1# #14#) (|shallowCopy| #12# #11#) (|deepCopy| #12# #11#) (|merge| (*1 *1 *1 *1) #11#) (|merge| (*1 *1 *2) #17#) (|separate| #1# #17#) (|addPoint| #18=(*1 *1 *1 *2 *3) #19=(AND #20=(|isDomain| *2 (|List| #16#)) #21=(|isDomain| *3 #22=(|Point| *5)) #23=(|ofCategory| *5 #9#) #24=(|isDomain| *1 (|SubSpace| *4 *5)) #25=(|ofType| *4 #7#))) (|addPoint2| #13# (AND #26=(|isDomain| *2 #27=(|Point| *4)) #8# #4# #6#)) (|addPointLast| (*1 *1 *1 *1 *2 *3) (AND (|isDomain| *2 #22#) #28=(|isDomain| *3 #16#) #23# #24# #25#)) (|modifyPoint| #18# #19#) (|addPoint| #18# #29=(AND #20# #28# #24# #25# #23#)) (|modifyPoint| #18# #29#) (|addPoint| (*1 *2 *1 *3) (AND #21# #23# #15# #24# #25#)) (|modifyPoint| #18# (AND #15# #21# #23# #24# #25#)) (|closeComponent| #18# (AND #20# (|isDomain| *3 #3#) #24# #25# #23#)) (|defineProperty| #18# (AND #20# (|isDomain| *3 #30=(|SubSpaceComponentProperty|)) #24# #25# #23#)) (|traverse| #13# (AND #20# #4# #6# #8#)) (|extractPoint| #1# (AND #26# #4# #6# #8#)) (|extractIndex| #1# #14#) (|extractClosed| #1# #2#) (|extractProperty| #1# (AND (|isDomain| *2 #30#) #4# #6# #8#)) (|level| #1# #14#) (|parent| #12# #11#) (|pointData| #1# (AND (|isDomain| *2 (|List| #27#)) #4# #6# #8#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|rhs| ((|#2| $) 11 T ELT)) (|lhs| ((|#1| $) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|construct| (($ |#1| |#2|) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|before?| #1#) (= #1#)) 
(((|SuchThat| |#1| |#2|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (SIGNATURE |construct| ($ |#1| |#2|)) (SIGNATURE |lhs| (|#1| $)) (SIGNATURE |rhs| (|#2| $)))) #1# #1#) (T |SuchThat|)) 
((|construct| (*1 *1 *2 *3) (AND #1=(|isDomain| *1 (|SuchThat| *2 *3)) #2=(|ofCategory| *2 #3=(|SetCategory|)) #4=(|ofCategory| *3 #3#))) (|lhs| #5=(*1 *2 *1) (AND #2# #1# #4#)) (|rhs| #5# (AND #2# (|isDomain| *1 (|SuchThat| *3 *2)) #4#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|predicate| (((|SpadAst|) $) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|SuchThatAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |predicate| ((|SpadAst|) $))))) (T |SuchThatAst|)) 
((|predicate| (*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|SuchThatAst|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) $) NIL #8=(AND (|has| #7# (|EuclideanDomain|)) #9=(|has| |#1| (|Field|))) ELT)) (|variables| ((#10=(|List| #11=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| (#12=(#13=(|Symbol|) $) 11 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(OR #15=(AND #16=(|has| #7# (|PolynomialFactorizationExplicit|)) #9#) #17=(AND (|has| #7# (|OrderedIntegralDomain|)) #9#) #18=(|has| |#1| (|IntegralDomain|))) ELT)) (|unitCanonical| #19=(#20=($ $) NIL #14# ELT)) (|unit?| (#5# NIL #14# ELT)) (|truncate| (#21=($ $ #22=(|Integer|)) NIL T ELT) (($ $ #22# #22#) 75 T ELT)) (|terms| ((#23=(|Stream| (|Record| (|:| |k| #22#) (|:| |c| |#1|))) $) NIL T ELT)) (|taylorRep| (#6# 42 T ELT)) (|taylorIfCan| (#24=((|Union| #7# #25="failed") $) 32 T ELT)) (|taylor| (#6# 33 T ELT)) (|tanh| (#20# 116 #26=(|has| |#1| (|Algebra| #27=(|Fraction| #22#))) ELT)) (|tan| (#20# 92 #26# ELT)) (|subtractIfCan| (#28=(#29=(|Union| $ #25#) $ $) NIL T ELT)) (|squareFreePolynomial| #30=(((|Factored| #31=(|SparseUnivariatePolynomial| $)) #31#) NIL #15# ELT)) (|squareFreePart| #32=(#20# NIL #9# ELT)) (|squareFree| #33=(((|Factored| $) $) NIL #9# ELT)) (|sqrt| (#20# NIL #26# ELT)) (|solveLinearPolynomialEquation| (((|Union| #34=(|List| #31#) #25#) #34# #31#) NIL #15# ELT)) (|sizeLess?| (#2# NIL #9# ELT)) (|sinh| (#20# 112 #26# ELT)) (|sin| (#20# 88 #26# ELT)) (|sign| (#35=(#22# $) NIL #17# ELT)) (|series| (($ #23#) NIL T ELT)) (|sech| (#20# 120 #26# ELT)) (|sec| (#20# 96 #26# ELT)) (|sample| (#36=($) NIL T CONST)) (|retractIfCan| (#24# 34 T ELT) (((|Union| #13# . #37=(#25#)) . #38=($)) NIL #39=(AND (|has| #7# (|RetractableTo| #13#)) #9#) ELT) (((|Union| #27# . #37#) . #38#) NIL #40=(AND (|has| #7# (|RetractableTo| #22#)) #9#) ELT) (((|Union| #22# . #37#) . #38#) NIL #40# ELT)) (|retract| (#6# 140 T ELT) (#12# NIL #39# ELT) ((#27# $) NIL #40# ELT) (#35# NIL #40# ELT)) (|removeZeroes| (#20# 37 T ELT) (#41=($ #22# $) 38 T ELT)) (|rem| #42=(#43=($ $ $) NIL #9# ELT)) (|reductum| #44=(#20# NIL T ELT)) (|reducedSystem| ((#45=(|Matrix| #7#) . #46=(#47=(|Matrix| $))) NIL #9# ELT) ((#48=(|Record| (|:| |mat| #45#) (|:| |vec| (|Vector| #7#))) . #49=(#47# #50=(|Vector| $))) NIL #9# ELT) ((#51=(|Record| (|:| |mat| #52=(|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #49#) NIL #53=(AND (|has| #7# (|LinearlyExplicitRingOver| #22#)) #9#) ELT) ((#52# . #46#) NIL #53# ELT)) (|recip| ((#29# $) 54 T ELT)) (|rationalFunction| ((#54=(|Fraction| (|Polynomial| |#1|)) $ #22#) 74 #18# ELT) ((#54# $ #22# #22#) 76 #18# ELT)) (|random| (#36# NIL #55=(AND (|has| #7# (|IntegerNumberSystem|)) #9#) ELT)) (|quo| #42#) (|principalIdeal| (((|Record| (|:| |coef| #56=(|List| $)) #57=(|:| |generator| $)) #56#) NIL #9# ELT)) (|prime?| (#5# NIL #9# ELT)) (|positive?| #58=(#5# NIL #17# ELT)) (|pole?| (#5# 28 T ELT)) (|pi| (#36# NIL #26# ELT)) (|patternMatch| ((#59=(|PatternMatchResult| #60=(|Float|) . #61=($)) $ #62=(|Pattern| #60#) #59#) NIL (AND (|has| #7# (|PatternMatchable| #60#)) #9#) ELT) ((#63=(|PatternMatchResult| #22# . #61#) $ #64=(|Pattern| #22#) #63#) NIL (AND (|has| #7# (|PatternMatchable| #22#)) #9#) ELT)) (|order| (#35# NIL T ELT) ((#22# $ #22#) 26 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #32#) (|numer| (#6# 44 #9# ELT)) (|nthRoot| (#21# NIL #26# ELT)) (|nextItem| (#65=((|Maybe| $) $) NIL #66=(AND (|has| #7# (|StepThrough|)) #9#) ELT)) (|negative?| #58#) (|multiplyExponents| #67=(($ $ #68=(|PositiveInteger|)) NIL T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #22#) $) NIL T ELT)) (|multiEuclidean| (((|Union| #56# #25#) #56# $) NIL #9# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #22#) 19 T ELT) (($ $ #11# #22#) NIL T ELT) (($ $ #10# (|List| #22#)) NIL T ELT)) (|min| #69=(#43# NIL #70=(OR #17# (AND (|has| #7# (|OrderedSet|)) #9#)) ELT)) (|max| #69#) (|map| (($ (|Mapping| |#1| |#1|) . #71=($)) NIL T ELT) (($ #72=(|Mapping| #7# #7#) . #71#) NIL #9# ELT)) (|log| (#20# 81 #26# ELT)) (|leftReducedSystem| ((#45# . #73=(#50#)) NIL #9# ELT) ((#48# . #74=(#50# $)) NIL #9# ELT) ((#51# . #74#) NIL #53# ELT) ((#52# . #73#) NIL #53# ELT)) (|leadingMonomial| #44#) (|leadingCoefficient| (#75=(|#1| $) NIL T ELT)) (|lcm| #76=(($ #56#) NIL #9# ELT) #42#) (|laurent| (($ #22# #7#) 36 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #32#) (|integrate| (#20# 79 #26# ELT) (#77=($ $ #13#) NIL (OR (AND #26# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #22#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #26# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #13#))) (|has| |#1| (SIGNATURE |variables| (#78=(|List| #13#) |#1|))))) ELT) (#79=($ $ #80=(|Variable| |#2|)) 80 #26# ELT)) (|init| (#36# NIL #66# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#31# #31# #31#) NIL #9# ELT)) (|gcd| #76# #42#) (|fractionPart| (#20# NIL #8# ELT)) (|floor| #81=(#6# NIL #55# ELT)) (|factorSquareFreePolynomial| #30#) (|factorPolynomial| #30#) (|factor| #33#) (|extendedEuclidean| (((|Union| (|Record| #82=(|:| |coef1| $) #83=(|:| |coef2| $)) #25#) $ $ $) NIL #9# ELT) (((|Record| #82# #83# #57#) $ $) NIL #9# ELT)) (|extend| (#21# 158 T ELT)) (|exquo| (#28# 55 #14# ELT)) (|expressIdealMember| (((|Maybe| #56#) #56# $) NIL #9# ELT)) (|exp| (#20# 82 #26# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) NIL #84=(|has| |#1| (SIGNATURE ** (|#1| |#1| #22#))) ELT) (($ $ #13# #7#) NIL #85=(AND (|has| #7# (|InnerEvalable| #13# #7#)) #9#) ELT) (($ $ #78# #86=(|List| #7#)) NIL #85# ELT) (($ $ (|List| #87=(|Equation| #7#))) NIL #88=(AND (|has| #7# (|Evalable| #7#)) #9#) ELT) (($ $ #87#) NIL #88# ELT) (($ $ #7# #7#) NIL #88# ELT) (($ $ #86# #86#) NIL #88# ELT)) (|euclideanSize| ((#89=(|NonNegativeInteger|) $) NIL #9# ELT)) (|elt| (#90=(|#1| $ #22#) NIL T ELT) (#43# 61 (|has| #22# (|SemiGroup|)) ELT) (#91=($ $ #7#) NIL (AND (|has| #7# (|Eltable| #7# #7#)) #9#) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|differentiate| #92=(($ $ #72# #89#) NIL #9# ELT) #93=(($ $ #72#) NIL #9# ELT) (#79# 57 T ELT) (#20# 56 #94=(OR (AND (|has| #7# (|DifferentialRing|)) #9#) (AND (|has| #7# (|DifferentialSpace|)) #9#) #95=(|has| |#1| (SIGNATURE * (|#1| #22# |#1|)))) ELT) #96=(#97=($ $ #89#) NIL #94# ELT) #98=(#77# NIL #99=(OR (AND (|has| #7# #100=(|PartialDifferentialRing| #13#)) #9#) (AND (|has| #7# (|PartialDifferentialSpace| #13#)) #9#) (AND (|has| |#1| #100#) #95#)) ELT) #101=(($ $ #78#) NIL #99# ELT) #102=(($ $ #13# #89#) NIL #99# ELT) #103=(($ $ #78# (|List| #89#)) NIL #99# ELT)) (|denominator| #32#) (|denom| (#6# 46 #9# ELT)) (|degree| (#35# 43 T ELT)) (|csch| (#20# 122 #26# ELT)) (|csc| (#20# 98 #26# ELT)) (|coth| (#20# 118 #26# ELT)) (|cot| (#20# 94 #26# ELT)) (|cosh| (#20# 114 #26# ELT)) (|cos| (#20# 90 #26# ELT)) (|convert| ((#104=(|InputForm|) . #105=($)) NIL (AND (|has| #7# (|ConvertibleTo| #104#)) #9#) ELT) ((#60# . #105#) NIL #106=(AND (|has| #7# (|RealConstant|)) #9#) ELT) (((|DoubleFloat|) . #105#) NIL #106# ELT) ((#62# . #105#) NIL (AND (|has| #7# (|ConvertibleTo| #62#)) #9#) ELT) ((#64# . #105#) NIL (AND (|has| #7# (|ConvertibleTo| #64#)) #9#) ELT)) (|conditionP| (((|Union| #50# #25#) #47#) NIL #107=(AND (|has| $ #108=(|CharacteristicNonZero|)) #16# #9#) ELT)) (|complete| #44#) (|coerce| (((|OutputForm|) $) 162 T ELT) (($ #22#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #7#) 30 T ELT) (($ #80#) 25 T ELT) (($ #13#) NIL #39# ELT) #19# (($ #27#) NIL (OR #40# #26#) ELT)) (|coefficient| (#90# 77 T ELT)) (|charthRoot| (#65# NIL (OR #107# (AND (|has| #7# #108#) #9#) (|has| |#1| #108#)) ELT)) (|characteristic| ((#89#) NIL T CONST)) (|center| (#75# 12 T ELT)) (|ceiling| #81#) (|before?| #1#) (|atanh| (#20# 128 #26# ELT)) (|atan| (#20# 104 #26# ELT)) (|associates?| (#2# NIL #14# ELT)) (|asinh| (#20# 124 #26# ELT)) (|asin| (#20# 100 #26# ELT)) (|asech| (#20# 132 #26# ELT)) (|asec| (#20# 108 #26# ELT)) (|approximate| (#90# NIL (AND #84# (|has| |#1| (SIGNATURE |coerce| (|#1| #13#)))) ELT)) (|annihilate?| #1#) (|acsch| (#20# 134 #26# ELT)) (|acsc| (#20# 110 #26# ELT)) (|acoth| (#20# 130 #26# ELT)) (|acot| (#20# 106 #26# ELT)) (|acosh| (#20# 126 #26# ELT)) (|acos| (#20# 102 #26# ELT)) (|abs| (#20# NIL #17# ELT)) (|Zero| (#36# 21 T CONST)) (|One| (#36# 16 T CONST)) (D #92# #93# (#79# NIL T ELT) (#20# NIL #94# ELT) #96# #98# #101# #102# #103#) (>= #109=(#2# NIL #70# ELT)) (> #109#) (= #1#) (<= #109#) (< #109#) (/ (#110=($ $ |#1|) NIL #9# ELT) (#43# 49 #9# ELT) (($ #7# #7#) 50 #9# ELT)) (- #44# (#43# NIL T ELT)) (+ (#43# 23 T ELT)) (** #67# (#97# 60 T ELT) (#21# NIL #9# ELT) (#43# 83 #26# ELT) (#111=($ $ #27#) 137 #26# ELT)) (* (($ #68# $) NIL T ELT) (($ #89# $) NIL T ELT) (#41# NIL T ELT) (#43# 35 T ELT) (#110# NIL T ELT) (($ |#1| . #112=($)) NIL T ELT) (#91# 48 #9# ELT) (($ #7# $) 47 #9# ELT) (($ #27# . #112#) NIL #26# ELT) (#111# NIL #26# ELT))) 
(((|SparseUnivariateLaurentSeries| |#1| |#2| |#3|) (|Join| (|UnivariateLaurentSeriesConstructorCategory| |#1| (|SparseUnivariateTaylorSeries| |#1| |#2| |#3|)) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1#)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |SparseUnivariateLaurentSeries|)) 
((|coerce| (*1 *1 *2) (AND #1=(|isDomain| *2 (|Variable| *4)) #2=(|ofType| *4 (|Symbol|)) #3=(|isDomain| *1 (|SparseUnivariateLaurentSeries| *3 *4 *5)) #4=(|ofCategory| *3 (|Ring|)) #5=(|ofType| *5 *3))) (|integrate| (*1 *1 *1 *2) (AND #1# #2# #3# (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) #4# #5#))) 
((|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) 26 T ELT) ((|#2| |#2| (|Symbol|)) 28 T ELT))) 
(((|FunctionSpaceSum| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sum| (|#2| |#2| (|Symbol|))) (SIGNATURE |sum| (|#2| |#2| (|SegmentBinding| |#2|)))) (|Join| (|IntegralDomain|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#)) (|Join| (|FunctionSpace| |#1|) (|CombinatorialOpsCategory|) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) (T |FunctionSpaceSum|)) 
((|sum| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 (|SegmentBinding| *2)) #2=(|ofCategory| *2 (|Join| (|FunctionSpace| *4) (|CombinatorialOpsCategory|) (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|))) #3=(|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#))) #5=(|isDomain| *1 (|FunctionSpaceSum| *4 *2)))) (|sum| #1# (AND (|isDomain| *3 (|Symbol|)) #3# #5# #2#))) 
((|sum| ((#1=(|Union| #2=(|Fraction| #3=(|Polynomial| |#1|)) (|Expression| |#1|)) #2# (|SegmentBinding| #2#)) 31 T ELT) ((#2# #3# (|SegmentBinding| #3#)) 44 T ELT) ((#1# #2# #4=(|Symbol|)) 33 T ELT) ((#2# #3# #4#) 36 T ELT))) 
(((|RationalFunctionSum| |#1|) (CATEGORY |package| (SIGNATURE |sum| (#1=(|Fraction| #2=(|Polynomial| |#1|)) #2# #3=(|Symbol|))) (SIGNATURE |sum| (#4=(|Union| #1# (|Expression| |#1|)) #1# #3#)) (SIGNATURE |sum| (#1# #2# (|SegmentBinding| #2#))) (SIGNATURE |sum| (#4# #1# (|SegmentBinding| #1#)))) (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (T |RationalFunctionSum|)) 
((|sum| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|SegmentBinding| #2=(|Fraction| #3=(|Polynomial| *5)))) #4=(|isDomain| *3 #2#) #5=(|ofCategory| *5 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Union| *3 #6=(|Expression| *5))) #7=(|isDomain| *1 (|RationalFunctionSum| *5)))) (|sum| #1# (AND (|isDomain| *4 (|SegmentBinding| #3#)) #8=(|isDomain| *3 #3#) #5# (|isDomain| *2 (|Fraction| *3)) #7#)) (|sum| #1# (AND #9=(|isDomain| *4 (|Symbol|)) #5# (|isDomain| *2 (|Union| #2# #6#)) #7# #4#)) (|sum| #1# (AND #9# #5# (|isDomain| *2 #2#) #7# #8#))) 
((~= (#1=(#2=(|Boolean|) $ $) 172 T ELT)) (|zero?| (#3=(#2# $) 44 T ELT)) (|vectorise| ((#4=(|Vector| |#1|) $ #5=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #8=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#9=(|SparseUnivariatePolynomial| $) $ #7#) 83 T ELT) (#10=(#8# $) 72 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #11=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#12=($ $) 166 #11# ELT)) (|unit?| (#3# NIL #11# ELT)) (|totalDegree| #13=(#14=(#5# $) NIL T ELT) ((#5# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|subResultantGcd| (#18=($ $ $) 160 #11# ELT)) (|squareFreePolynomial| (#19=((|Factored| #9#) #9#) 97 #20=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| (#12# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #9#) #17#) #23# #9#) 117 #20# ELT)) (|sizeLess?| (#1# NIL #24=(|has| |#1| (|Field|)) ELT)) (|shiftRight| (#25=($ $ #5#) 62 T ELT)) (|shiftLeft| (#25# 64 T ELT)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #21# ELT)) (|sample| (#26=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #27=(#17#)) . #28=($)) NIL T ELT) (((|Union| #29=(|Fraction| #30=(|Integer|)) . #27#) . #28#) NIL #31=(|has| |#1| (|RetractableTo| #29#)) ELT) (((|Union| #30# . #27#) . #28#) NIL #32=(|has| |#1| (|RetractableTo| #30#)) ELT) #33=(((|Union| #7# . #27#) . #28#) NIL T ELT)) (|retract| #34=(#35=(|#1| . #36=($)) NIL T ELT) ((#29# . #36#) NIL #31# ELT) ((#30# . #36#) NIL #32# ELT) ((#7# . #36#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #37=(|has| |#1| (|CommutativeRing|)) ELT) ((|#1| $ $) 162 #37# ELT)) (|rem| #38=(#18# NIL #24# ELT)) (|reductum| (#12# 81 T ELT)) (|reducedSystem| ((#39=(|Matrix| #30#) . #40=(#41=(|Matrix| $))) NIL #42=(|has| |#1| (|LinearlyExplicitRingOver| #30#)) ELT) ((#43=(|Record| (|:| |mat| #39#) (|:| |vec| (|Vector| #30#))) . #44=(#41# #45=(|Vector| $))) NIL #42# ELT) ((#46=(|Record| (|:| |mat| #47=(|Matrix| |#1|)) (|:| |vec| #4#)) . #44#) NIL T ELT) ((#47# . #40#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|quo| #38#) (|pseudoRemainder| (#18# 133 T ELT)) (|pseudoQuotient| (#18# NIL #11# ELT)) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) #48=(|:| |quotient| $) #49=(|:| |remainder| $)) $ $) NIL #11# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #50=(|List| $)) #51=(|:| |generator| $)) #50#) NIL #24# ELT)) (|primitivePart| (#12# 167 #21# ELT) #52=(#53=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #54=((#50# $) NIL T ELT)) (|prime?| (#3# NIL #20# ELT)) (|pomopo!| (($ $ |#1| #5# $) 70 T ELT)) (|patternMatch| ((#55=(|PatternMatchResult| #56=(|Float|) . #57=($)) $ #58=(|Pattern| #56#) #55#) NIL (AND (|has| #7# #59=(|PatternMatchable| #56#)) (|has| |#1| #59#)) ELT) ((#60=(|PatternMatchResult| #30# . #57#) $ #61=(|Pattern| #30#) #60#) NIL (AND (|has| #7# #62=(|PatternMatchable| #30#)) (|has| |#1| #62#)) ELT)) (|outputForm| ((#63=(|OutputForm|) $ #63#) 150 T ELT)) (|order| ((#5# $ $) NIL #11# ELT)) (|opposite?| #64=(#1# NIL T ELT)) (|one?| (#3# 49 T ELT)) (|numberOfMonomials| #13#) (|nextItem| (#65=((|Maybe| $) $) NIL #66=(|has| |#1| (|StepThrough|)) ELT)) (|multivariate| (($ #8# #7#) 74 T ELT) (($ #9# #7#) 91 T ELT)) (|multiplyExponents| (#25# 52 T ELT)) (|multiEuclidean| ((#67=(|Union| #50# #17#) #50# $) NIL #24# ELT)) (|monomials| #54#) (|monomial?| (#3# NIL T ELT)) (|monomial| (($ |#1| #5#) 89 T ELT) #68=(($ $ #7# #5#) NIL T ELT) #69=(($ $ #6# #70=(|List| #5#)) NIL T ELT)) (|monicDivide| ((#71=(|Record| #48# #49#) $ $ #7#) NIL T ELT) (#72=(#71# $ $) 155 T ELT)) (|minimumDegree| #13# #73=((#5# $ #7#) NIL T ELT) #74=((#70# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #5# #5#) $) NIL T ELT)) (|map| (($ #75=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeSUP| (#10# NIL T ELT)) (|mainVariable| #33#) (|leftReducedSystem| ((#39# . #76=(#45#)) NIL #42# ELT) ((#43# . #77=(#45# $)) NIL #42# ELT) ((#46# . #77#) NIL T ELT) ((#47# . #76#) NIL T ELT)) (|leadingMonomial| #78=(#12# NIL T ELT)) (|leadingCoefficient| (#35# 77 T ELT)) (|lcm| #79=(($ #50#) NIL #21# ELT) (#18# NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|karatsubaDivide| ((#71# $ #5#) 61 T ELT)) (|isTimes| #80=((#67# $) NIL T ELT)) (|isPlus| #80#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #5#)) #17#) $) NIL T ELT)) (|integrate| (#12# NIL #81=(|has| |#1| (|Algebra| #29#)) ELT)) (|init| (#26# NIL #66# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#3# 51 T ELT)) (|ground| #34#) (|gcdPolynomial| ((#9# #9# #9#) 105 #21# ELT)) (|gcd| #79# (#18# 169 #21# ELT)) (|fmecg| (($ $ #5# |#1| $) 125 T ELT)) (|factorSquareFreePolynomial| (#19# 103 #20# ELT)) (|factorPolynomial| (#19# 102 #20# ELT)) (|factor| (#22# 110 #20# ELT)) (|extendedEuclidean| (((|Union| (|Record| #82=(|:| |coef1| $) #83=(|:| |coef2| $)) #17#) $ $ $) NIL #24# ELT) (((|Record| #82# #83# #51#) $ $) NIL #24# ELT)) (|exquo| ((#16# $ |#1|) 165 #11# ELT) (#15# 126 #11# ELT)) (|expressIdealMember| (((|Maybe| #50#) #50# $) NIL #24# ELT)) (|eval| (($ $ (|List| #84=(|Equation| $))) NIL T ELT) (($ $ #84#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #50# #50#) NIL T ELT) (($ $ #7# |#1|) NIL T ELT) (($ $ #6# #85=(|List| |#1|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #50#) NIL T ELT)) (|euclideanSize| (#14# NIL #24# ELT)) (|elt| ((|#1| $ |#1|) 152 T ELT) (#18# 153 T ELT) ((#86=(|Fraction| $) #86# #86#) NIL #11# ELT) ((|#1| #86# |#1|) NIL #24# ELT) ((#86# $ #86#) NIL #11# ELT)) (|divideExponents| ((#16# $ #5#) 55 T ELT)) (|divide| (#72# 173 #24# ELT)) (|discriminant| (#53# NIL #37# ELT) (#35# 158 #37# ELT)) (|differentiate| #69# #68# #87=(($ $ #6#) NIL T ELT) #88=(#53# NIL T ELT) #78# #89=(#25# NIL T ELT) #90=(($ $ #75#) NIL T ELT) #91=(($ $ #75# #5#) NIL T ELT) (($ $ #75# $) NIL T ELT) #92=(($ $ #93=(|Symbol|)) NIL #94=(|has| |#1| (|PartialDifferentialSpace| #93#)) ELT) #95=(($ $ #96=(|List| #93#)) NIL #94# ELT) #97=(($ $ #93# #5#) NIL #94# ELT) #98=(($ $ #96# #70#) NIL #94# ELT)) (|degree| (#14# 79 T ELT) #73# #74#) (|convert| ((#58# . #99=($)) NIL (AND (|has| #7# #100=(|ConvertibleTo| #58#)) (|has| |#1| #100#)) ELT) ((#61# . #99#) NIL (AND (|has| #7# #101=(|ConvertibleTo| #61#)) (|has| |#1| #101#)) ELT) ((#102=(|InputForm|) . #99#) NIL (AND (|has| #7# #103=(|ConvertibleTo| #102#)) (|has| |#1| #103#)) ELT)) (|content| (#35# 164 #21# ELT) #52#) (|conditionP| (((|Union| #45# #17#) #41#) NIL #104=(AND (|has| $ #105=(|CharacteristicNonZero|)) #20#) ELT)) (|composite| (#15# NIL #11# ELT) (((|Union| #86# #17#) #86# $) NIL #11# ELT)) (|coerce| ((#63# $) 151 T ELT) (($ #30#) NIL T ELT) (($ |#1|) 78 T ELT) (($ #7#) NIL T ELT) (($ #29#) NIL (OR #81# #31#) ELT) (#12# NIL #11# ELT)) (|coefficients| ((#85# $) NIL T ELT)) (|coefficient| ((|#1| $ #5#) NIL T ELT) #68# #69#) (|charthRoot| (#65# NIL (OR #104# (|has| |#1| #105#)) ELT)) (|characteristic| ((#5#) NIL T CONST)) (|binomThmExpt| (($ $ $ #5#) 42 #37# ELT)) (|before?| #64#) (|associates?| (#1# NIL #11# ELT)) (|annihilate?| #64#) (|Zero| (#26# 18 T CONST)) (|One| (#26# 20 T CONST)) (D #69# #68# #87# #88# #78# #89# #90# #91# #92# #95# #97# #98#) (= (#1# 122 T ELT)) (/ (#106=($ $ |#1|) 174 #24# ELT)) (- #78# (#18# NIL T ELT)) (+ (#18# 92 T ELT)) (** (($ $ #107=(|PositiveInteger|)) 14 T ELT) (#25# 12 T ELT)) (* (($ #107# $) NIL T ELT) (($ #5# $) NIL T ELT) (($ #30# . #108=($)) NIL T ELT) (#18# 40 T ELT) (($ $ #29#) NIL #81# ELT) (($ #29# . #108#) NIL #81# ELT) (($ |#1| . #108#) 131 T ELT) (#106# NIL T ELT))) 
(((|SparseUnivariatePolynomial| |#1|) (|Join| (|UnivariatePolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| (#1=(|OutputForm|) $ #1#)) (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#1| $)))) (|Ring|)) (T |SparseUnivariatePolynomial|)) 
((|outputForm| (*1 *2 *1 *2) (AND (|isDomain| *2 (|OutputForm|)) #1=(|isDomain| *1 (|SparseUnivariatePolynomial| *3)) #2=(|ofCategory| *3 (|Ring|)))) (|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) #1# #2#))) 
((|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) 13 T ELT))) 
(((|SparseUnivariatePolynomialFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)))) #1=(|Ring|) #1#) (T |SparseUnivariatePolynomialFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|SparseUnivariatePolynomial| *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|isDomain| *1 (|SparseUnivariatePolynomialFunctions2| *5 *6))))) 
((|squareFree| (#1=((|Factored| #2=(|SparseUnivariatePolynomial| (|Fraction| |#4|))) #2#) 51 T ELT)) (|factor| (#1# 52 T ELT))) 
(((|SupFractionFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| #1=((|Factored| #2=(|SparseUnivariatePolynomial| (|Fraction| |#4|))) #2#)) (SIGNATURE |squareFree| #1#)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|GcdDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |SupFractionFactorizer|)) 
((|squareFree| #1=(*1 *2 *3) #2=(AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Factored| #3=(|SparseUnivariatePolynomial| (|Fraction| *7)))) (|isDomain| *1 (|SupFractionFactorizer| *4 *5 *6 *7)) (|isDomain| *3 #3#))) (|factor| #1# #2#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 11 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| (#19=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|squareFreePart| #22=(#11# NIL #23=(|has| |#1| (|Field|)) ELT)) (|squareFree| #24=(((|Factored| $) $) NIL #23# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #23# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #25=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| (#26=($) NIL T CONST)) (|retractIfCan| (#27=((|Union| #28=(|SparseUnivariateLaurentSeries| |#1| |#2| |#3|) . #29=(#21#)) $) 33 T ELT) (((|Union| #30=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) . #29#) $) 36 T ELT)) (|retract| #31=(#32=(#28# . #33=($)) NIL T ELT) ((#30# . #33#) NIL T ELT)) (|rem| #34=(#35=($ $ $) NIL #23# ELT)) (|reductum| #36=(#11# NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|rationalPower| (#37=(#14# $) 59 T ELT)) (|quo| #34#) (|puiseux| (($ #14# #28#) NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #38=(|List| $)) #39=(|:| |generator| $)) #38#) NIL #23# ELT)) (|prime?| (#5# NIL #23# ELT)) (|pole?| #4#) (|pi| (#26# NIL #18# ELT)) (|order| #40=(#37# NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#41=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #42=(($ $ #43=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #38# #21#) #38# $) NIL #23# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) 20 T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #17#) (|leadingMonomial| #36#) (|leadingCoefficient| (#44=(|#1| $) NIL T ELT)) (|lcm| #45=(($ #38#) NIL #23# ELT) #34#) (|laurentRep| (#32# 41 T ELT)) (|laurentIfCan| (#27# NIL T ELT)) (|laurent| #31#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #22#) (|integrate| (#11# 39 #18# ELT) (#46=($ $ #8#) NIL (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#47=(|List| #8#) |#1|))))) ELT) (#48=($ $ #49=(|Variable| |#2|)) 40 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#50=(|SparseUnivariatePolynomial| $) #50# #50#) NIL #23# ELT)) (|gcd| #45# #34#) (|factor| #24#) (|extendedEuclidean| (((|Union| (|Record| #51=(|:| |coef1| $) #52=(|:| |coef2| $)) #21#) $ $ $) NIL #23# ELT) (((|Record| #51# #52# #39#) $ $) NIL #23# ELT)) (|extend| #12#) (|exquo| (#19# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #38#) #38# $) NIL #23# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #53=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#25# $) NIL #23# ELT)) (|elt| #54=(#55=(|#1| $ #14#) NIL T ELT) (#35# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #23# ELT)) (|differentiate| #56=(#46# NIL #57=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #58=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #59=(($ $ #47#) NIL #57# ELT) #60=(($ $ #8# #25#) NIL #57# ELT) #61=(($ $ #47# (|List| #25#)) NIL #57# ELT) (#11# 37 #58# ELT) #62=(#63=($ $ #25#) NIL #58# ELT) (#48# 38 T ELT)) (|degree| #40#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #36#) (|coerce| (((|OutputForm|) $) 62 T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #28#) 30 T ELT) (($ #30#) 31 T ELT) (($ #49#) 26 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #54#) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#25#) NIL T CONST)) (|center| (#44# 12 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#55# NIL (AND #53# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| (#26# 22 T CONST)) (|One| (#26# 16 T CONST)) (D #56# #59# #60# #61# (#11# NIL #58# ELT) #62# (#48# NIL T ELT)) (= #1#) (/ (#64=($ $ |#1|) NIL #23# ELT) #34#) (- #36# #65=(#35# NIL T ELT)) (+ (#35# 24 T ELT)) (** #42# (#63# NIL T ELT) (#41# NIL #23# ELT) (#35# NIL #18# ELT) #66=(#13# NIL #18# ELT)) (* (($ #43# $) NIL T ELT) (($ #25# $) NIL T ELT) (($ #15# . #67=($)) NIL T ELT) #65# (#64# NIL T ELT) (($ |#1| . #67#) NIL T ELT) (($ #14# . #67#) NIL #18# ELT) #66#)) 
(((|SparseUnivariatePuiseuxSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesConstructorCategory| |#1| (|SparseUnivariateLaurentSeries| |#1| |#2| |#3|)) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (|RetractableTo| (|SparseUnivariateTaylorSeries| |#1| |#2| |#3|)) (|CoercibleFrom| #1#) (CATEGORY |domain| (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |SparseUnivariatePuiseuxSeries|)) 
((|integrate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|SparseUnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 129 T ELT)) (|variables| ((#5=(|List| #6=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#7=(|Symbol|) $) 119 T ELT)) (|univariatePolynomial| ((#8=(|UnivariatePolynomial| |#2| |#1|) $ #9=(|NonNegativeInteger|)) 69 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#4# NIL #10# ELT)) (|truncate| (#13=($ $ #9#) 85 T ELT) (($ $ #9# #9#) 82 T ELT)) (|terms| ((#14=(|Stream| (|Record| (|:| |k| #9#) (|:| |c| |#1|))) $) 105 T ELT)) (|tanh| (#12# 173 #15=(|has| |#1| (|Algebra| #16=(|Fraction| #17=(|Integer|)))) ELT)) (|tan| (#12# 149 #15# ELT)) (|subtractIfCan| (#18=(#19=(|Union| $ "failed") $ $) NIL T ELT)) (|sqrt| (#12# NIL #15# ELT)) (|sinh| (#12# 169 #15# ELT)) (|sin| (#12# 145 #15# ELT)) (|series| (($ #14#) 118 T ELT) (($ #20=(|Stream| |#1|)) 113 T ELT)) (|sech| (#12# 177 #15# ELT)) (|sec| (#12# 153 #15# ELT)) (|sample| (#21=($) NIL T CONST)) (|reductum| #22=(#12# NIL T ELT)) (|recip| ((#19# $) 25 T ELT)) (|quoByVar| (#12# 28 T ELT)) (|polynomial| ((#23=(|Polynomial| |#1|) $ #9#) 81 T ELT) ((#23# $ #9# #9#) 83 T ELT)) (|pole?| (#4# 124 T ELT)) (|pi| (#21# NIL #15# ELT)) (|order| (#24=(#9# $) 126 T ELT) ((#9# $ #9#) 128 T ELT)) (|opposite?| #1#) (|one?| #25=(#4# NIL T ELT)) (|nthRoot| (($ $ #17#) NIL #15# ELT)) (|multiplyExponents| #26=(($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #17#) $) NIL T ELT)) (|monomial?| #25#) (|monomial| (($ |#1| #9#) 13 T ELT) (($ $ #6# #9#) NIL T ELT) (($ $ #5# #28=(|List| #9#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| (#12# 135 #15# ELT)) (|leadingMonomial| #22#) (|leadingCoefficient| (#29=(|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#12# 133 #15# ELT) (#30=($ $ #7#) NIL (OR (AND #15# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #17#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #15# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |variables| (#31=(|List| #7#) |#1|))))) ELT) (#32=($ $ #33=(|Variable| |#2|)) 134 #15# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|extend| (#13# 15 T ELT)) (|exquo| (#18# 26 #10# ELT)) (|exp| (#12# 137 #15# ELT)) (|eval| ((#20# $ |#1|) NIL #34=(|has| |#1| (SIGNATURE ** (|#1| |#1| #9#))) ELT)) (|elt| (#35=(|#1| $ #9#) 122 T ELT) (#36=($ $ $) 132 (|has| #9# (|SemiGroup|)) ELT)) (|differentiate| #37=(#30# NIL #38=(AND (|has| |#1| (|PartialDifferentialRing| #7#)) #39=(|has| |#1| (SIGNATURE * (|#1| #9# |#1|)))) ELT) #40=(($ $ #31#) NIL #38# ELT) #41=(($ $ #7# #9#) NIL #38# ELT) #42=(($ $ #31# #28#) NIL #38# ELT) (#12# 29 #39# ELT) #43=(#13# NIL #39# ELT) (#32# 31 T ELT)) (|degree| (#24# NIL T ELT)) (|csch| (#12# 179 #15# ELT)) (|csc| (#12# 155 #15# ELT)) (|coth| (#12# 175 #15# ELT)) (|cot| (#12# 151 #15# ELT)) (|cosh| (#12# 171 #15# ELT)) (|cos| (#12# 147 #15# ELT)) (|complete| #22#) (|coerce| (((|OutputForm|) $) 206 T ELT) (($ #17#) NIL T ELT) (($ #16#) NIL #15# ELT) #11# (($ |#1|) 130 (|has| |#1| (|CommutativeRing|)) ELT) (($ #8#) 55 T ELT) (($ #33#) 36 T ELT)) (|coefficients| ((#20# $) 101 T ELT)) (|coefficient| (#35# 121 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#9#) NIL T CONST)) (|center| (#29# 58 T ELT)) (|before?| #1#) (|atanh| (#12# 185 #15# ELT)) (|atan| (#12# 161 #15# ELT)) (|associates?| (#2# NIL #10# ELT)) (|asinh| (#12# 181 #15# ELT)) (|asin| (#12# 157 #15# ELT)) (|asech| (#12# 189 #15# ELT)) (|asec| (#12# 165 #15# ELT)) (|approximate| (#35# NIL (AND #34# (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| #1#) (|acsch| (#12# 191 #15# ELT)) (|acsc| (#12# 167 #15# ELT)) (|acoth| (#12# 187 #15# ELT)) (|acot| (#12# 163 #15# ELT)) (|acosh| (#12# 183 #15# ELT)) (|acos| (#12# 159 #15# ELT)) (|Zero| (#21# 17 T CONST)) (|One| (#21# 20 T CONST)) (D #37# #40# #41# #42# (#12# NIL #39# ELT) #43# (#32# NIL T ELT)) (= #1#) (/ (#44=($ $ |#1|) NIL #45=(|has| |#1| (|Field|)) ELT)) (- #22# (#36# 198 T ELT)) (+ (#36# 35 T ELT)) (** #26# (#13# NIL T ELT) (#44# 203 #45# ELT) (#36# 138 #15# ELT) (#46=($ $ #16#) 141 #15# ELT)) (* (($ #27# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #17# . #47=($)) NIL T ELT) (#36# 136 T ELT) (#44# NIL T ELT) (($ |#1| . #47#) NIL T ELT) (($ #16# . #47#) NIL #15# ELT) (#46# NIL #15# ELT))) 
(((|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) (|Join| (|UnivariateTaylorSeriesCategory| |#1|) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #2=(|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |univariatePolynomial| (#2# $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ #1#)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |SparseUnivariateTaylorSeries|)) 
((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *3)) #2=(|ofCategory| *3 #3=(|Ring|)) #4=(|ofType| *4 #5=(|Symbol|)) #6=(|ofType| *5 *3) #7=(|isDomain| *1 (|SparseUnivariateTaylorSeries| *3 *4 *5)))) (|univariatePolynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|UnivariatePolynomial| *5 *4)) (|isDomain| *1 (|SparseUnivariateTaylorSeries| *4 *5 *6)) (|ofCategory| *4 #3#) (|ofType| *5 #5#) (|ofType| *6 *4))) (|coerce| #1# (AND #8=(|isDomain| *2 (|Variable| *4)) #4# #7# #2# #6#)) (|integrate| (*1 *1 *1 *2) (AND #8# #4# #7# (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) #2# #6#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|superscript| (#4=($ $ #5=(|List| #6=(|OutputForm|))) 48 T ELT)) (|subscript| (#4# 46 T ELT)) (|string| (#7=(#8=(|String|) $) 88 T ELT)) (|scripts| ((#9=(|Record| (|:| |sub| #5#) (|:| |sup| #5#) (|:| |presup| #5#) (|:| |presub| #5#) (|:| |args| #5#)) $) 95 T ELT)) (|scripted?| ((#3# $) 86 T ELT)) (|script| (($ $ (|List| #5#)) 45 T ELT) (($ $ #9#) 85 T ELT)) (|sample| (#10=($) 151 T CONST)) (|retractIfCan| (((|Union| #11=(|Identifier|) "failed") $) 155 T ELT)) (|retract| ((#11# $) NIL T ELT)) (|resetNew| (((|Void|)) 123 T ELT)) (|patternMatch| ((#12=(|PatternMatchResult| #13=(|Integer|) . #14=($)) $ #15=(|Pattern| #13#) #12#) 55 T ELT) ((#16=(|PatternMatchResult| #17=(|Float|) . #14#) $ #18=(|Pattern| #17#) #16#) 62 T ELT)) (|new| (#10# 109 T ELT) (#19=($ $) 118 T ELT)) (|name| (#19# 87 T ELT)) (|min| #20=(($ $ $) NIL T ELT)) (|max| #20#) (|list| (((|List| $) $) 124 T ELT)) (|latex| (#7# 101 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| (#4# 47 T ELT)) (|convert| (((|InputForm|) $) 33 T ELT) (((|Symbol|) $) 34 T ELT) ((#15# $) 66 T ELT) ((#18# $) 64 T ELT)) (|coerce| ((#6# $) 41 T ELT) (($ #8#) 35 T ELT) (($ #11#) 153 T ELT)) (|before?| #1#) (|argscript| (#4# 49 T ELT)) (>= #1#) (> #1#) (= (#2# 37 T ELT)) (<= #1#) (< (#2# 38 T ELT))) 
((#1=(|Symbol|) (|Join| (|OrderedSet|) (|ConvertibleTo| (|InputForm|)) (|ConvertibleTo| #1#) (|CoercibleFrom| #2=(|String|)) (|RetractableTo| (|Identifier|)) (|ConvertibleTo| (|Pattern| #3=(|Integer|))) (|ConvertibleTo| (|Pattern| #4=(|Float|))) (|PatternMatchable| #3#) (|PatternMatchable| #4#) (CATEGORY |domain| (SIGNATURE |new| #5=($)) (SIGNATURE |new| #6=($ $)) (SIGNATURE |resetNew| ((|Void|))) (SIGNATURE |name| #6#) (SIGNATURE |scripted?| ((|Boolean|) $)) (SIGNATURE |scripts| (#7=(|Record| (|:| |sub| #8=(|List| (|OutputForm|))) (|:| |sup| #8#) (|:| |presup| #8#) (|:| |presub| #8#) (|:| |args| #8#)) $)) (SIGNATURE |script| ($ $ (|List| #8#))) (SIGNATURE |script| ($ $ #7#)) (SIGNATURE |subscript| #9=($ $ #8#)) (SIGNATURE |superscript| #9#) (SIGNATURE |argscript| #9#) (SIGNATURE |elt| #9#) (SIGNATURE |string| (#2# $)) (SIGNATURE |list| ((|List| $) $)) (SIGNATURE |sample| #5# |constant|)))) (T |Symbol|)) 
((|new| #1=(*1 *1) #2=(|isDomain| *1 #3=(|Symbol|))) (|new| #4=(*1 *1 *1) #2#) (|resetNew| (*1 *2) (AND (|isDomain| *2 (|Void|)) #2#)) (|name| #4# #2#) (|scripted?| #5=(*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) #2#)) (|scripts| #5# #6=(AND (|isDomain| *2 (|Record| (|:| |sub| #7=(|List| (|OutputForm|))) (|:| |sup| #7#) (|:| |presup| #7#) (|:| |presub| #7#) (|:| |args| #7#))) #2#)) (|script| #8=(*1 *1 *1 *2) (AND (|isDomain| *2 (|List| #7#)) #2#)) (|script| #8# #6#) (|subscript| #8# #9=(AND (|isDomain| *2 #7#) #2#)) (|superscript| #8# #9#) (|argscript| #8# #9#) (|elt| #8# #9#) (|string| #5# (AND (|isDomain| *2 (|String|)) #2#)) (|list| #5# (AND (|isDomain| *2 (|List| #3#)) #2#)) (|sample| #1# #2#)) 
((|symFunc| ((#1=(|Vector| |#1|) |#1| (|PositiveInteger|)) 18 T ELT) ((#1# (|List| |#1|)) 25 T ELT))) 
(((|SymmetricFunctions| |#1|) (CATEGORY |package| (SIGNATURE |symFunc| (#1=(|Vector| |#1|) (|List| |#1|))) (SIGNATURE |symFunc| (#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 #1=(|Ring|)))) (|symFunc| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #1#) (|isDomain| *2 (|Vector| *4)) (|isDomain| *1 (|SymmetricFunctions| *4))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #7=(#8=($ $) NIL #6# ELT)) (|unit?| (#5# NIL #6# ELT)) (|subtractIfCan| (#9=(#10=(|Union| $ #11="failed") $ $) NIL T ELT)) (|sample| #12=(#13=($) NIL T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=(#11#)) . #16=($)) NIL #17=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) NIL #19=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| |#1| . #15#) . #16#) NIL T ELT)) (|retract| ((#14# . #20=($)) NIL #17# ELT) ((#18# . #20#) NIL #19# ELT) #21=(#22=(|#1| . #20#) NIL T ELT)) (|reductum| #23=(#8# NIL T ELT)) (|recip| ((#10# $) NIL T ELT)) (|primitivePart| (#8# NIL #24=(|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| #25=(|Partition|) $) NIL T ELT)) (|opposite?| #1#) (|one?| (#5# 18 T ELT)) (|numberOfMonomials| ((#26=(|NonNegativeInteger|) $) NIL T ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #25#) NIL T ELT)) (|minimumDegree| #27=((#25# $) NIL T ELT)) (|mapExponents| (($ (|Mapping| #25# #25#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingMonomial| #23#) (|leadingCoefficient| #21#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #21#) (|fmecg| (($ $ #25# |#1| $) NIL (AND (|has| #25# (|CancellationAbelianMonoid|)) #6#) ELT)) (|exquo| (#9# NIL #6# ELT) ((#10# $ |#1|) NIL #6# ELT)) (|degree| #27#) (|content| (#22# NIL #24# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #7# (($ |#1|) NIL T ELT) (($ #18#) NIL (OR #28=(|has| |#1| (|Algebra| #18#)) #19#) ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #25#) NIL T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#26#) NIL T CONST)) (|binomThmExpt| (($ $ $ #26#) NIL (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| #1#) (|associates?| (#2# NIL #6# ELT)) (|annihilate?| #1#) (|Zero| (#13# 13 T CONST)) (|One| #12#) (= #1#) (/ (#29=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #23# (#30=($ $ $) NIL T ELT)) (+ (#30# 22 T ELT)) (** (($ $ #31=(|PositiveInteger|)) NIL T ELT) (($ $ #26#) NIL T ELT)) (* (($ #31# $) NIL T ELT) (($ #26# $) NIL T ELT) (($ #14# . #32=($)) NIL T ELT) (#30# 23 T ELT) (#29# NIL T ELT) (($ |#1| . #32#) 17 T ELT) (($ #18# . #32#) NIL #28# ELT) (($ $ #18#) NIL #28# ELT))) 
(((|SymmetricPolynomial| |#1|) (|Join| (|FiniteAbelianMonoidRing| |#1| #1=(|Partition|)) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (IF (|has| #1# (|CancellationAbelianMonoid|)) (SIGNATURE |fmecg| ($ $ #1# |#1| $)) |%noBranch|) |%noBranch|) (IF (|has| |#1| #2=(ATTRIBUTE |canonicalUnitNormal|)) #2# |%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|))))) 
((|symbolTableOf| (((|SymbolTable|) #1=(|Symbol|) $) 26 T ELT)) (|showTheSymbolTable| (#2=($) 30 T ELT)) (|returnTypeOf| ((#3=(|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) #1# $) 23 T ELT)) (|returnType!| ((#4=(|Void|) #1# #3# $) 42 T ELT) ((#4# #1# #3#) 43 T ELT) ((#4# #3#) 44 T ELT)) (|printTypes| (#5=(#4# #1#) 59 T ELT)) (|printHeader| ((#4# #1# $) 56 T ELT) (#5# 57 T ELT) (#6=(#4#) 58 T ELT)) (|newSubProgram| (#5# 38 T ELT)) (|endSubProgram| (#7=(#1#) 37 T ELT)) (|empty| (#2# 35 T ELT)) (|declare!| ((#8=(|FortranType|) #1# #8# #1# $) 46 T ELT) ((#8# #9=(|List| #1#) #8# #1# $) 50 T ELT) ((#8# #1# #8#) 47 T ELT) ((#8# #1# #8# #1#) 51 T ELT)) (|currentSubProgram| (#7# 36 T ELT)) (|coerce| (((|OutputForm|) $) 29 T ELT)) (|clearTheSymbolTable| (#6# 31 T ELT) (#5# 34 T ELT)) (|argumentListOf| ((#9# #1# $) 25 T ELT)) (|argumentList!| ((#4# #1# #9# $) 39 T ELT) ((#4# #1# #9#) 40 T ELT) ((#4# #9#) 41 T ELT))) 
(((|TheSymbolTable|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |showTheSymbolTable| #1=($)) (SIGNATURE |clearTheSymbolTable| #2=(#3=(|Void|))) (SIGNATURE |clearTheSymbolTable| #4=(#3# #5=(|Symbol|))) (SIGNATURE |declare!| (#6=(|FortranType|) #5# #6# #5# $)) (SIGNATURE |declare!| (#6# #7=(|List| #5#) #6# #5# $)) (SIGNATURE |declare!| (#6# #5# #6#)) (SIGNATURE |declare!| (#6# #5# #6# #5#)) (SIGNATURE |newSubProgram| #4#) (SIGNATURE |currentSubProgram| #8=(#5#)) (SIGNATURE |endSubProgram| #8#) (SIGNATURE |argumentList!| (#3# #5# #7# $)) (SIGNATURE |argumentList!| (#3# #5# #7#)) (SIGNATURE |argumentList!| (#3# #7#)) (SIGNATURE |returnType!| (#3# #5# #9=(|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $)) (SIGNATURE |returnType!| (#3# #5# #9#)) (SIGNATURE |returnType!| (#3# #9#)) (SIGNATURE |printHeader| (#3# #5# $)) (SIGNATURE |printHeader| #4#) (SIGNATURE |printHeader| #2#) (SIGNATURE |printTypes| #4#) (SIGNATURE |empty| #1#) (SIGNATURE |returnTypeOf| (#9# #5# $)) (SIGNATURE |argumentListOf| (#7# #5# $)) (SIGNATURE |symbolTableOf| ((|SymbolTable|) #5# $))))) (T |TheSymbolTable|)) 
((|showTheSymbolTable| #1=(*1 *1) #2=(|isDomain| *1 (|TheSymbolTable|))) (|clearTheSymbolTable| #3=(*1 *2) #4=(AND #5=(|isDomain| *2 (|Void|)) #2#)) (|clearTheSymbolTable| #6=(*1 *2 *3) #7=(AND #8=(|isDomain| *3 #9=(|Symbol|)) #5# #2#)) (|declare!| (*1 *2 *3 *2 *3 *1) #10=(AND #11=(|isDomain| *2 (|FortranType|)) #8# #2#)) (|declare!| (*1 *2 *3 *2 *4 *1) (AND #11# #12=(|isDomain| *3 #13=(|List| #9#)) (|isDomain| *4 #9#) #2#)) (|declare!| (*1 *2 *3 *2) #10#) (|declare!| (*1 *2 *3 *2 *3) #10#) (|newSubProgram| #6# #7#) (|currentSubProgram| #3# #14=(AND (|isDomain| *2 #9#) #2#)) (|endSubProgram| #3# #14#) (|argumentList!| #15=(*1 *2 *3 *4 *1) #16=(AND (|isDomain| *4 #13#) #8# #5# #2#)) (|argumentList!| #17=(*1 *2 *3 *4) #16#) (|argumentList!| #6# (AND #12# #5# #2#)) (|returnType!| #15# #18=(AND #8# (|isDomain| *4 #19=(|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) #5# #2#)) (|returnType!| #17# #18#) (|returnType!| #6# (AND (|isDomain| *3 #19#) #5# #2#)) (|printHeader| #20=(*1 *2 *3 *1) #7#) (|printHeader| #6# #7#) (|printHeader| #3# #4#) (|printTypes| #6# #7#) (|empty| #1# #2#) (|returnTypeOf| #20# (AND #8# (|isDomain| *2 #19#) #2#)) (|argumentListOf| #20# (AND (|isDomain| *2 #13#) #2# #8#)) (|symbolTableOf| #20# (AND #8# (|isDomain| *2 (|SymbolTable|)) #2#))) 
((|typeLists| (((|List| #1=(|List| (|Union| (|:| |name| #2=(|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S #2#) (|:| P (|Polynomial| (|Integer|))))))))) $) 66 T ELT)) (|typeList| ((#1# (|FortranScalarType|) $) 47 T ELT)) (|symbolTable| (($ (|List| (|Record| (|:| |key| #2#) (|:| |entry| #3=(|FortranType|))))) 17 T ELT)) (|printTypes| (((|Void|) $) 73 T ELT)) (|parametersOf| (#4=(#5=(|List| #2#) $) 22 T ELT)) (|newTypeLists| (((|SExpression|) $) 60 T ELT)) (|fortranTypeOf| ((#3# #2# $) 27 T ELT)) (|externalList| (#4# 30 T ELT)) (|empty| (($) 19 T ELT)) (|declare!| ((#3# #5# #3# $) 25 T ELT) ((#3# #2# #3# $) 24 T ELT)) (|coerce| (((|OutputForm|) $) 12 T ELT) (((|Table| #2# #3#) $) 13 T ELT))) 
(((|SymbolTable|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |coerce| ((|Table| #1=(|Symbol|) #2=(|FortranType|)) $)) (SIGNATURE |empty| ($)) (SIGNATURE |declare!| (#2# #3=(|List| #1#) #2# $)) (SIGNATURE |declare!| (#2# #1# #2# $)) (SIGNATURE |fortranTypeOf| (#2# #1# $)) (SIGNATURE |parametersOf| #4=(#3# $)) (SIGNATURE |typeList| (#5=(|List| (|Union| (|:| |name| #1#) (|:| |bounds| (|List| (|Union| (|:| S #1#) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $)) (SIGNATURE |externalList| #4#) (SIGNATURE |typeLists| ((|List| #5#) $)) (SIGNATURE |newTypeLists| ((|SExpression|) $)) (SIGNATURE |printTypes| ((|Void|) $)) (SIGNATURE |symbolTable| ($ (|List| (|Record| (|:| |key| #1#) (|:| |entry| #2#)))))))) (T |SymbolTable|)) 
((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Table| #2=(|Symbol|) #3=(|FortranType|))) #4=(|isDomain| *1 (|SymbolTable|)))) (|empty| (*1 *1) #4#) (|declare!| #5=(*1 *2 *3 *2 *1) (AND #6=(|isDomain| *2 #3#) (|isDomain| *3 #7=(|List| #2#)) #4#)) (|declare!| #5# (AND #6# #8=(|isDomain| *3 #2#) #4#)) (|fortranTypeOf| #9=(*1 *2 *3 *1) (AND #8# #6# #4#)) (|parametersOf| #1# #10=(AND (|isDomain| *2 #7#) #4#)) (|typeList| #9# (AND (|isDomain| *3 (|FortranScalarType|)) (|isDomain| *2 #11=(|List| (|Union| (|:| |name| #2#) (|:| |bounds| (|List| (|Union| (|:| S #2#) (|:| P (|Polynomial| (|Integer|))))))))) #4#)) (|externalList| #1# #10#) (|typeLists| #1# (AND (|isDomain| *2 (|List| #11#)) #4#)) (|newTypeLists| #1# (AND (|isDomain| *2 (|SExpression|)) #4#)) (|printTypes| #1# (AND (|isDomain| *2 (|Void|)) #4#)) (|symbolTable| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| #2#) (|:| |entry| #3#)))) #4#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) $) 29 T ELT) (((|Union| #6=(|DoubleFloat|) . #5#) $) 35 T ELT) (((|Union| #7=(|Identifier|) . #5#) $) 43 T ELT) (((|Union| #8=(|String|) . #5#) $) 47 T ELT)) (|retract| (#9=(#4# $) 30 T ELT) (#10=(#6# $) 36 T ELT) (#11=(#7# $) 40 T ELT) (#12=(#8# $) 48 T ELT)) (|nil?| (#13=(#3# $) 53 T ELT)) (|latex| (#12# NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|getOperator| (((|Union| #4# #6# #7# #8# $) $) 56 T ELT)) (|getOperands| ((#14=(|List| $) $) 58 T ELT)) (|convert| ((#15=(|SExpression|) $) 24 T ELT) (($ #15#) 25 T ELT)) (|compound?| (#13# 57 T ELT)) (|coerce| (((|OutputForm|) $) 23 T ELT) (($ #4#) 26 T ELT) (($ #6#) 32 T ELT) (($ #7#) 38 T ELT) (($ #8#) 44 T ELT) (((|InputForm|) $) 60 T ELT) (#9# 31 T ELT) (#10# 37 T ELT) (#11# 41 T ELT) (#12# 49 T ELT)) (|case| ((#3# $ (|[\|\|]| #4#)) 10 T ELT) ((#3# $ (|[\|\|]| #6#)) 13 T ELT) ((#3# $ (|[\|\|]| #7#)) 19 T ELT) ((#3# $ (|[\|\|]| #8#)) 16 T ELT)) (|buildSyntax| (($ #7# #14#) 51 T ELT) (($ $ #14#) 52 T ELT)) (|before?| #1#) (|autoCoerce| (#9# 27 T ELT) (#10# 33 T ELT) (#11# 39 T ELT) (#12# 45 T ELT)) (= (#2# 7 T ELT))) 
(((|Syntax|) (|Join| (|UnionType|) (|SetCategory|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| #2=(|DoubleFloat|)) (|RetractableTo| #3=(|Identifier|)) (|RetractableTo| #4=(|String|)) (|CoercibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |convert| (#5=(|SExpression|) $)) (SIGNATURE |convert| ($ #5#)) (SIGNATURE |coerce| #6=(#1# $)) (SIGNATURE |autoCoerce| #6#) (SIGNATURE |coerce| #7=(#2# $)) (SIGNATURE |autoCoerce| #7#) (SIGNATURE |coerce| #8=(#3# $)) (SIGNATURE |autoCoerce| #8#) (SIGNATURE |coerce| #9=(#4# $)) (SIGNATURE |autoCoerce| #9#) (SIGNATURE |buildSyntax| ($ #3# #10=(|List| $))) (SIGNATURE |buildSyntax| ($ $ #10#)) (SIGNATURE |nil?| #11=(#12=(|Boolean|) $)) (SIGNATURE |getOperator| ((|Union| #1# #2# #3# #4# $) $)) (SIGNATURE |getOperands| (#10# $)) (SIGNATURE |compound?| #11#) (SIGNATURE |case| (#12# $ (|[\|\|]| #1#))) (SIGNATURE |case| (#12# $ (|[\|\|]| #2#))) (SIGNATURE |case| (#12# $ (|[\|\|]| #3#))) (SIGNATURE |case| (#12# $ (|[\|\|]| #4#)))))) (T |Syntax|)) 
((|convert| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SExpression|)) #3=(|isDomain| *1 #4=(|Syntax|)))) (|convert| (*1 *1 *2) #2#) (|coerce| #1# #5=(AND (|isDomain| *2 #6=(|Integer|)) #3#)) (|autoCoerce| #1# #5#) (|coerce| #1# #7=(AND (|isDomain| *2 #8=(|DoubleFloat|)) #3#)) (|autoCoerce| #1# #7#) (|coerce| #1# #9=(AND #10=(|isDomain| *2 #11=(|Identifier|)) #3#)) (|autoCoerce| #1# #9#) (|coerce| #1# #12=(AND (|isDomain| *2 #13=(|String|)) #3#)) (|autoCoerce| #1# #12#) (|buildSyntax| (*1 *1 *2 *3) (AND #10# (|isDomain| *3 #14=(|List| #4#)) #3#)) (|buildSyntax| (*1 *1 *1 *2) #15=(AND (|isDomain| *2 #14#) #3#)) (|nil?| #1# #16=(AND #17=(|isDomain| *2 (|Boolean|)) #3#)) (|getOperator| #1# (AND (|isDomain| *2 (|Union| #6# #8# #11# #13# #4#)) #3#)) (|getOperands| #1# #15#) (|compound?| #1# #16#) (|case| #18=(*1 *2 *1 *3) (AND (|isDomain| *3 (|[\|\|]| #6#)) #17# #3#)) (|case| #18# (AND (|isDomain| *3 (|[\|\|]| #8#)) #17# #3#)) (|case| #18# (AND (|isDomain| *3 (|[\|\|]| #11#)) #17# #3#)) (|case| #18# (AND (|isDomain| *3 (|[\|\|]| #13#)) #17# #3#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) 21 T ELT)) (|sample| (#2=($) 10 T CONST)) (|random| (#2# 25 T ELT)) (|min| #3=(($ $ $) NIL T ELT) (#2# 18 T CONST)) (|max| #3# (#2# 19 T CONST)) (|lookup| ((#4=(|PositiveInteger|) $) 23 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #4#) 22 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#)) 
(((|SystemInteger| |#1|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |sample| ($) |constant|))) (|PositiveInteger|)) (T |SystemInteger|)) 
((|sample| (*1 *1) (AND (|isDomain| *1 (|SystemInteger| *2)) (|ofType| *2 (|PositiveInteger|))))) 
((|Integer|) (|%not| (|%ilt| @1 (|%ilength| |#1|)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (($ $) 24 T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| (#2=($) 18 T CONST)) (|random| (#2# NIL T ELT)) (|min| #3=(#4=($ $ $) NIL T ELT) (#2# 11 T CONST)) (|max| #3# (#2# 17 T CONST)) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|bitior| (#4# 20 T ELT)) (|bitand| (#4# 19 T ELT)) (|before?| #1#) (|\\/| (#4# 22 T ELT)) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (|/\\| (#4# 21 T ELT))) 
(((|SystemNonNegativeInteger| |#1|) (|Join| (|OrderedFinite|) (|Logic|) (CATEGORY |domain| (SIGNATURE |bitand| #1=($ $ $)) (SIGNATURE |bitior| #1#) (SIGNATURE |sample| ($) |constant|))) (|PositiveInteger|)) (T |SystemNonNegativeInteger|)) 
((|bitand| #1=(*1 *1 *1 *1) #2=(AND (|isDomain| *1 (|SystemNonNegativeInteger| *2)) (|ofType| *2 (|PositiveInteger|)))) (|bitior| #1# #2#) (|sample| (*1 *1) #2#)) 
((|NonNegativeInteger|) (|%not| (|%ilt| @1 (|%ilength| |#1|)))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 9 T ELT)) (|before?| #1#) (= (#2# 7 T ELT))) 
(((|SystemPointer|) (|SetCategory|)) (T |SystemPointer|)) 
NIL 
((|triangularSystems| (((|List| (|List| #1=(|Polynomial| |#1|))) #2=(|List| #3=(|Fraction| #1#)) #4=(|List| #5=(|Symbol|))) 69 T ELT)) (|solve| ((#6=(|List| #7=(|Equation| #3#)) #7#) 81 T ELT) ((#6# #3#) 77 T ELT) ((#6# #7# #5#) 82 T ELT) ((#6# #3# #5#) 76 T ELT) ((#8=(|List| #6#) #6#) 108 T ELT) ((#8# #2#) 107 T ELT) ((#8# #6# #4#) 109 T ELT) ((#8# #2# #4#) 106 T ELT))) 
(((|SystemSolvePackage| |#1|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|List| #2=(|List| #3=(|Equation| #4=(|Fraction| #5=(|Polynomial| |#1|))))) #6=(|List| #4#) #7=(|List| #8=(|Symbol|)))) (SIGNATURE |solve| (#1# #2# #7#)) (SIGNATURE |solve| (#1# #6#)) (SIGNATURE |solve| (#1# #2#)) (SIGNATURE |solve| (#2# #4# #8#)) (SIGNATURE |solve| (#2# #3# #8#)) (SIGNATURE |solve| (#2# #4#)) (SIGNATURE |solve| (#2# #3#)) (SIGNATURE |triangularSystems| ((|List| (|List| #5#)) #6# #7#))) (|IntegralDomain|)) (T |SystemSolvePackage|)) 
((|triangularSystems| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|List| #3=(|Fraction| #4=(|Polynomial| *5)))) #5=(|isDomain| *4 (|List| #6=(|Symbol|))) #7=(|ofCategory| *5 #8=(|IntegralDomain|)) (|isDomain| *2 (|List| (|List| #4#))) #9=(|isDomain| *1 (|SystemSolvePackage| *5)))) (|solve| #10=(*1 *2 *3) (AND #11=(|ofCategory| *4 #8#) #12=(|isDomain| *2 #13=(|List| #14=(|Equation| #15=(|Fraction| (|Polynomial| *4))))) #16=(|isDomain| *1 (|SystemSolvePackage| *4)) (|isDomain| *3 #14#))) (|solve| #10# (AND #11# #12# #16# (|isDomain| *3 #15#))) (|solve| #1# (AND #17=(|isDomain| *4 #6#) #7# #18=(|isDomain| *2 #19=(|List| #20=(|Equation| #3#))) #9# (|isDomain| *3 #20#))) (|solve| #1# (AND #17# #7# #18# #9# (|isDomain| *3 #3#))) (|solve| #10# (AND #11# #21=(|isDomain| *2 (|List| #13#)) #16# (|isDomain| *3 #13#))) (|solve| #10# (AND (|isDomain| *3 (|List| #15#)) #11# #21# #16#)) (|solve| #1# (AND #5# #7# #22=(|isDomain| *2 (|List| #19#)) #9# (|isDomain| *3 #19#))) (|solve| #1# (AND #2# #5# #7# #22# #9#))) 
((|rootDirectory| (#1=(#2=(|String|)) 7 T ELT)) (|nativeModuleExtension| (#1# 11 T CONST)) (|loadNativeModule| (((|Void|) #2#) 13 T ELT)) (|hostPlatform| (#1# 8 T CONST)) (|hostByteOrder| (((|ByteOrder|)) 10 T CONST))) 
(((|System|) (|Join| (|Type|) (CATEGORY |package| (SIGNATURE |rootDirectory| #1=(#2=(|String|))) (SIGNATURE |hostPlatform| #1# |constant|) (SIGNATURE |hostByteOrder| ((|ByteOrder|)) |constant|) (SIGNATURE |nativeModuleExtension| #1# |constant|) (SIGNATURE |loadNativeModule| ((|Void|) #2#))))) (T |System|)) 
((|rootDirectory| #1=(*1 *2) #2=(AND (|isDomain| *2 #3=(|String|)) #4=(|isDomain| *1 (|System|)))) (|hostPlatform| #1# #2#) (|hostByteOrder| #1# (AND (|isDomain| *2 (|ByteOrder|)) #4#)) (|nativeModuleExtension| #1# #2#) (|loadNativeModule| (*1 *2 *3) (AND (|isDomain| *3 #3#) (|isDomain| *2 (|Void|)) #4#))) 
((|untab| ((#1=(|List| #2=(|List| |#1|)) #1# #3=(|List| #1#)) 56 T ELT)) (|tab1| ((#3# #1#) 38 T ELT)) (|tab| ((#4=(|Tableau| #2#) #2#) 49 T ELT)) (|slex| ((#1# #2#) 45 T ELT)) (|mr| ((#5=(|Record| (|:| |f1| #2#) (|:| |f2| #3#) (|:| |f3| #1#) (|:| |f4| #3#)) #3#) 53 T ELT)) (|maxrow| ((#5# #2# #3# #1# #3# #3# #3#) 52 T ELT)) (|lex| ((#1# #1#) 43 T ELT)) (|inverse| ((#2# #2#) 46 T ELT)) (|bumptab1| ((#3# #2# #3#) 32 T ELT)) (|bumptab| ((#3# #6=(|Mapping| #7=(|Boolean|) |#1| |#1|) #2# #3#) 29 T ELT)) (|bumprow| (((|Record| (|:| |fs| #7#) (|:| |sd| #2#) (|:| |td| #1#)) #6# #2# #1#) 24 T ELT)) (|bat1| ((#1# #3#) 58 T ELT)) (|bat| ((#1# #4#) 60 T ELT))) 
(((|TableauxBumpers| |#1|) (CATEGORY |package| (SIGNATURE |bumprow| ((|Record| (|:| |fs| #1=(|Boolean|)) (|:| |sd| #2=(|List| |#1|)) (|:| |td| #3=(|List| #2#))) #4=(|Mapping| #1# |#1| |#1|) #2# #3#)) (SIGNATURE |bumptab| (#5=(|List| #3#) #4# #2# #5#)) (SIGNATURE |bumptab1| (#5# #2# #5#)) (SIGNATURE |untab| (#3# #3# #5#)) (SIGNATURE |bat1| (#3# #5#)) (SIGNATURE |bat| (#3# #6=(|Tableau| #2#))) (SIGNATURE |tab1| (#5# #3#)) (SIGNATURE |tab| (#6# #2#)) (SIGNATURE |lex| (#3# #3#)) (SIGNATURE |slex| (#3# #2#)) (SIGNATURE |inverse| (#2# #2#)) (SIGNATURE |maxrow| (#7=(|Record| (|:| |f1| #2#) (|:| |f2| #5#) (|:| |f3| #3#) (|:| |f4| #5#)) #2# #5# #3# #5# #5# #5#)) (SIGNATURE |mr| (#7# #5#))) (|OrderedSet|)) (T |TableauxBumpers|)) 
((|mr| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |f1| #4=(|List| *4)) (|:| |f2| #5=(|List| #6=(|List| #4#))) (|:| |f3| #6#) (|:| |f4| #5#))) #7=(|isDomain| *1 (|TableauxBumpers| *4)) #8=(|isDomain| *3 #5#))) (|maxrow| (*1 *2 *3 *4 *5 *4 *4 *4) (AND #9=(|ofCategory| *6 #3#) (|isDomain| *3 #10=(|List| *6)) (|isDomain| *5 #11=(|List| *3)) (|isDomain| *2 (|Record| (|:| |f1| *3) (|:| |f2| #12=(|List| *5)) (|:| |f3| *5) (|:| |f4| #12#))) #13=(|isDomain| *1 (|TableauxBumpers| *6)) #14=(|isDomain| *4 #12#))) (|inverse| #15=(*1 *2 *2) (AND (|isDomain| *2 #11#) #16=(|ofCategory| *3 #3#) #17=(|isDomain| *1 (|TableauxBumpers| *3)))) (|slex| #1# (AND #2# #18=(|isDomain| *2 #6#) #7# #19=(|isDomain| *3 #4#))) (|lex| #15# (AND (|isDomain| *2 (|List| #11#)) #16# #17#)) (|tab| #1# (AND #2# (|isDomain| *2 #20=(|Tableau| #4#)) #7# #19#)) (|tab1| #1# (AND #2# #21=(|isDomain| *2 #5#) #7# (|isDomain| *3 #6#))) (|bat| #1# (AND (|isDomain| *3 #20#) #2# #18# #7#)) (|bat1| #1# (AND #8# #18# #7# #2#)) (|untab| (*1 *2 *2 *3) (AND #8# #18# #2# #7#)) (|bumptab1| (*1 *2 *3 *2) (AND #21# #19# #2# #7#)) (|bumptab| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|List| (|List| #12#))) (|isDomain| *3 (|Mapping| #22=(|Boolean|) *5 *5)) #14# (|ofCategory| *5 #3#) (|isDomain| *1 (|TableauxBumpers| *5)))) (|bumprow| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| #22# *6 *6)) #9# (|isDomain| *4 #10#) (|isDomain| *2 (|Record| (|:| |fs| #22#) (|:| |sd| *4) (|:| |td| #4#))) #13# (|isDomain| *5 #4#)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #6=(|BasicType|)) #7=(|has| |#2| #6#)) ELT)) (|table| #8=(#9=($) NIL T ELT) #10=(($ #11=(|List| #5#)) NIL T ELT)) (|swap!| (((|Void|) $ |#1| |#1|) NIL #12=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| #13=(#14=(|#2| $ |#1| |#2|) NIL #12# ELT)) (|select!| #15=(($ #16=(|Mapping| #3# #5#) $) NIL #17=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|select| #15#) (|search| #18=(((|Union| |#2| #19="failed") |#1| $) NIL T ELT)) (|sample| (#9# NIL T CONST)) (|removeDuplicates| (#20=($ $) NIL #21=(AND #17# #4#) ELT)) (|remove!| (#22=($ #5# $) NIL #17# ELT) #15# #18#) (|remove| (#22# NIL #21# ELT) #15#) (|reduce| ((#5# #23=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) ((#5# #23# $ #5#) NIL T ELT) ((#5# #23# $) NIL T ELT)) (|qsetelt!| #13#) (|qelt| #24=((|#2| $ |#1|) NIL T ELT)) (|minIndex| #25=((|#1| $) NIL #26=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#11# $) NIL T ELT)) (|member?| ((#3# #5# $) NIL #4# ELT)) (|maxIndex| #25#) (|map!| #27=(($ (|Mapping| #5# #5#) . #28=($)) NIL T ELT) #29=(($ (|Mapping| |#2| |#2|) . #28#) NIL T ELT)) (|map| #27# #29# #27# (($ (|Mapping| |#2| |#2| |#2|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #30=(OR #31=(|has| #5# #32=(|SetCategory|)) #33=(|has| |#2| #32#)) ELT)) (|keys| #34=(((|List| |#1|) $) NIL T ELT)) (|key?| #35=((#3# |#1| $) NIL T ELT)) (|inspect| #36=((#5# $) NIL T ELT)) (|insert!| (#22# NIL T ELT)) (|indices| #34#) (|index?| #35#) (|hash| (((|SingleInteger|) $) NIL #30# ELT)) (|first| ((|#2| $) NIL #26# ELT)) (|find| (((|Union| #5# #19#) #16# $) NIL T ELT)) (|fill!| (($ $ |#2|) NIL #12# ELT)) (|extract!| #36#) (|every?| #37=((#3# #16# $) NIL T ELT)) (|eval| #38=(($ $ (|List| #39=(|Equation| #5#))) NIL #40=(AND (|has| #5# (|Evalable| #5#)) #31#) ELT) #41=(($ $ #39#) NIL #40# ELT) #42=(($ $ #5# #5#) NIL #40# ELT) #43=(($ $ #11# #11#) NIL #40# ELT) (($ $ #44=(|List| |#2|) #44#) NIL #45=(AND (|has| |#2| (|Evalable| |#2|)) #33#) ELT) (($ $ |#2| |#2|) NIL #45# ELT) (($ $ #46=(|Equation| |#2|)) NIL #45# ELT) (($ $ (|List| #46#)) NIL #45# ELT) #43# #42# #41# #38#) (|eq?| (#2# NIL T ELT)) (|entry?| ((#3# |#2| $) NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #7#) ELT)) (|entries| ((#44# $) NIL T ELT)) (|empty?| ((#3# $) NIL T ELT)) (|empty| #8#) (|elt| #24# (#14# NIL T ELT)) (|dictionary| #8# #10#) (|count| ((#47=(|NonNegativeInteger|) #5# $) NIL #4# ELT) ((#47# #16# $) NIL T ELT)) (|copy| (#20# NIL T ELT)) (|convert| ((#48=(|InputForm|) $) NIL (|has| #5# (|ConvertibleTo| #48#)) ELT)) (|construct| #10#) (|coerce| ((#49=(|OutputForm|) $) NIL (OR (|has| #5# #50=(|CoercibleTo| #49#)) (|has| |#2| #50#)) ELT)) (|before?| #1#) (|bag| #10#) (|any?| #37#) (= #1#) (|#| ((#47# $) NIL T ELT))) 
(((|Table| |#1| |#2|) (|TableAggregate| |#1| |#2|) #1=(|SetCategory|) #1#) (T |Table|)) 
NIL 
((|tableau| (($ #1=(|List| (|List| |#1|))) 10 T ELT)) (|listOfLists| ((#1# $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT))) 
(((|Tableau| |#1|) (CATEGORY |domain| (SIGNATURE |tableau| ($ #1=(|List| (|List| |#1|)))) (SIGNATURE |listOfLists| (#1# $)) (SIGNATURE |coerce| ((|OutputForm|) $))) (|SetCategory|)) (T |Tableau|)) 
((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) #2=(|isDomain| *1 (|Tableau| *3)) #3=(|ofCategory| *3 (|SetCategory|)))) (|listOfLists| #1# (AND #4=(|isDomain| *2 (|List| (|List| *3))) #2# #3#)) (|tableau| (*1 *1 *2) (AND #4# #3# #2#))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|operator| (($ |#1| #3=(|Arity|)) 11 T ELT)) (|name| ((|#1| $) 13 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|is?| ((#2# $ |#1|) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|arity| ((#3# $) 15 T ELT)) (= #1#)) 
(((|TermAlgebraOperator| |#1|) (|Join| (|OperatorCategory| |#1|) (CATEGORY |domain| (SIGNATURE |operator| ($ |#1| (|Arity|))))) (|SetCategory|)) (T |TermAlgebraOperator|)) 
((|operator| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Arity|)) (|isDomain| *1 (|TermAlgebraOperator| *2)) (|ofCategory| *2 (|SetCategory|))))) 
((|tanSum| ((|#1| (|List| |#1|)) 46 T ELT)) (|tanNa| ((|#1| |#1| (|Integer|)) 24 T ELT)) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) 20 T ELT))) 
(((|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|)) #1=(|isDomain| *1 (|TangentExpansions| *2)) #2=(|ofCategory| *2 #3=(|Field|)))) (|tanAn| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|isDomain| *1 (|TangentExpansions| *3)) (|ofCategory| *3 #3#))) (|tanSum| (*1 *2 *3) (AND (|isDomain| *3 (|List| *2)) #1# #2#))) 
((|table| (($) 10 T ELT) (($ #1=(|List| #2=(|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) 14 T ELT)) (|remove!| (#3=($ #2# $) 63 T ELT) (($ #4=(|Mapping| #5=(|Boolean|) #2#) $) NIL T ELT) (((|Union| |#3| #6="failed") |#2| $) NIL T ELT)) (|members| ((#1# $) 35 T ELT)) (|map!| (#7=($ (|Mapping| #2# #2#) $) 53 T ELT) (#8=($ (|Mapping| |#3| |#3|) $) 29 T ELT)) (|map| #9=(#7# 49 T ELT) (#8# NIL T ELT) #9# (($ (|Mapping| |#3| |#3| |#3|) $ $) 34 T ELT)) (|inspect| (#10=(#2# $) 56 T ELT)) (|insert!| (#3# 16 T ELT)) (|indices| (((|List| |#2|) $) 19 T ELT)) (|index?| ((#5# |#2| $) 61 T ELT)) (|find| (((|Union| #2# #6#) #4# $) 60 T ELT)) (|extract!| (#10# 65 T ELT)) (|entries| (((|List| |#3|) $) 37 T ELT)) (|coerce| (((|OutputForm|) $) 27 T ELT)) (= ((#5# $ $) 47 T ELT))) 
(((|TableAggregate&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE = (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#3| |#3| |#3|) |#1| |#1|)) (SIGNATURE |table| (|#1| #2=(|List| #3=(|Record| (|:| |key| |#2|) (|:| |entry| |#3|))))) (SIGNATURE |table| (|#1|)) #4=(SIGNATURE |map| #5=(|#1| (|Mapping| #3# #3#) |#1|)) (SIGNATURE |members| (#2# |#1|)) (SIGNATURE |find| ((|Union| #3# #6="failed") #7=(|Mapping| #1# #3#) |#1|)) (SIGNATURE |remove!| ((|Union| |#3| #6#) |#2| |#1|)) (SIGNATURE |map!| #8=(|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |map| #8#) (SIGNATURE |entries| ((|List| |#3|) |#1|)) (SIGNATURE |index?| (#1# |#2| |#1|)) (SIGNATURE |indices| ((|List| |#2|) |#1|)) (SIGNATURE |remove!| (|#1| #7# |#1|)) (SIGNATURE |remove!| #9=(|#1| #3# |#1|)) (SIGNATURE |inspect| #10=(#3# |#1|)) (SIGNATURE |insert!| #9#) (SIGNATURE |extract!| #10#) (SIGNATURE |map!| #5#) #4#) (|TableAggregate| |#2| |#3|) #11=(|SetCategory|) #11#) (T |TableAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2=((|BasicType|))) (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|table| (($) 95 T ELT) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 94 T ELT)) (|swap!| (((|Void|) $ |#1| |#1|) 82 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| ((|#2| $ |#1| |#2|) 70 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|select!| (($ (|Mapping| #3=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #4=($)) 42 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #6=($)) 49 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|search| (((|Union| |#2| . #7=("failed")) |#1| . #8=($)) 59 T ELT)) (|sample| (#9=($) 6 T CONST)) (|removeDuplicates| (($ $) 51 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #10=((|BasicType|))) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT)) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 44 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Mapping| #3# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #4#) 43 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Union| |#2| . #7#) |#1| . #8#) 60 T ELT)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 50 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #10#) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT) (($ (|Mapping| #5# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #6#) 48 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|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|))) 111 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #11=((|BasicType|))) ELT) (((|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|))) 107 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 106 T ELT)) (|qsetelt!| ((|#2| $ |#1| |#2|) 69 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qelt| ((|#2| $ |#1|) 71 T ELT)) (|minIndex| ((|#1| . #12=($)) 79 (|has| |#1| . #13=((|OrderedSet|))) ELT)) (|members| (((|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 105 T ELT)) (|member?| ((#14=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 110 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #11#) ELT)) (|maxIndex| ((|#1| . #12#) 78 (|has| |#1| . #13#) ELT)) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #15=($)) 39 T ELT) (($ (|Mapping| |#2| |#2|) . #15#) 63 T ELT)) (|map| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #16=($)) 26 T ELT) (($ (|Mapping| |#2| |#2|) . #16#) 64 T ELT) (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #16#) 96 T ELT) (($ (|Mapping| |#2| |#2| |#2|) $ $) 93 T ELT)) (|latex| (((|String|) $) 21 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17=((|SetCategory|))) (|has| |#2| . #17#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17#)) ELT)) (|keys| (((|List| |#1|) $) 61 T ELT)) (|key?| (((|Boolean|) |#1| $) 62 T ELT)) (|inspect| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #18=($)) 35 T ELT)) (|insert!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 36 T ELT)) (|indices| (((|List| |#1|) $) 76 T ELT)) (|index?| ((#19=(|Boolean|) |#1| $) 75 T ELT)) (|hash| (((|SingleInteger|) $) 20 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17#) (|has| |#2| . #17#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17#)) ELT)) (|first| ((|#2| $) 80 (|has| |#1| . #13#) ELT)) (|find| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") (|Mapping| #14# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 108 T ELT)) (|fill!| (($ $ |#2|) 81 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|extract!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #18#) 37 T ELT)) (|every?| ((#14# (|Mapping| #14# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #20=($)) 103 T ELT)) (|eval| (($ $ (|List| (|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|)) . #17#)) ELT) (($ $ (|Equation| (|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|)) . #17#)) ELT) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|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|)) . #17#)) ELT) (($ $ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 22 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 68 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #17#)) ELT) (($ $ |#2| |#2|) 67 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #17#)) ELT) (($ $ (|Equation| |#2|)) 66 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #17#)) ELT) (($ $ (|List| (|Equation| |#2|))) 65 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #17#)) ELT) (($ $ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 100 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17#)) ELT) (($ $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 99 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17#)) ELT) (($ $ (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 98 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17#)) ELT) (($ $ (|List| (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) 97 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17#)) ELT)) (|eq?| ((#21=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#19# |#2| $) 77 (AND (|has| $ (|FiniteAggregate| |#2|)) (|has| |#2| (|BasicType|))) ELT)) (|entries| (((|List| |#2|) $) 74 T ELT)) (|empty?| ((#21# $) 7 T ELT)) (|empty| (#9# 8 T ELT)) (|elt| ((|#2| $ |#1|) 73 T ELT) ((|#2| $ |#1| |#2|) 72 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 45 T ELT)) (|count| ((#22=(|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 109 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #11#) ELT) ((#22# (|Mapping| #14# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 104 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#23=(|InputForm|) $) 52 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| #23#)) ELT)) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #24=((|CoercibleTo| (|OutputForm|)))) (|has| |#2| . #24#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #24#)) ELT)) (|before?| (#1# 19 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#) (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|bag| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 38 T ELT)) (|any?| ((#14# (|Mapping| #14# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #20#) 102 T ELT)) (= (#1# 17 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#) (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|#| ((#22# $) 101 T ELT))) 
(((|TableAggregate| |#1| |#2|) (|Category|) (|SetCategory|) (|SetCategory|)) (T |TableAggregate|)) 
((|table| (*1 *1) (AND (|ofCategory| *1 (|TableAggregate| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|table| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| *3) (|:| |entry| *4)))) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *1 (|TableAggregate| *3 *4)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *4 *4 *4)) (|ofCategory| *1 (|TableAggregate| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) 
(|Join| (|KeyedDictionary| |t#1| |t#2|) (|FiniteAggregate| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))) (CATEGORY |domain| (SIGNATURE |table| ($)) (SIGNATURE |table| ($ (|List| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))))) (SIGNATURE |map| ($ (|Mapping| |t#2| |t#2| |t#2|) $ $)))) 
(((|Aggregate|) . T) ((|BagAggregate| #1=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|BasicType|)) (|has| |#2| (|SetCategory|)) (|has| |#2| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|CoercibleTo| (|OutputForm|))) (|has| |#2| (|SetCategory|)) (|has| |#2| (|CoercibleTo| (|OutputForm|)))) ((|Collection| #1#) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))) ((|Dictionary| #1#) . T) ((|DictionaryOperations| #1#) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| #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|))) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|FiniteAggregate| #2#) . T) ((|Functorial| #2#) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| #2#) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| |#1| |#2|) . T) ((|InnerEvalable| #2# #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|))) ((|Join|) . T) ((|KeyedDictionary| |#1| |#2|) . T) ((|SetCategory|) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))) ((|ShallowlyMutableAggregate| #1#) . T) ((|ShallowlyMutableAggregate| |#2|) . T) ((|Type|) . T)) 
((|usingTable?| (#1=((|Boolean|)) 29 T ELT)) (|startStats!| ((#2=(|Void|) #3=(|String|)) 31 T ELT)) (|printingInfo?| (#1# 41 T ELT)) (|printStats!| (#4=(#2#) 39 T ELT)) (|printInfo!| ((#2# #3# #3#) 30 T ELT)) (|makingStats?| (#1# 42 T ELT)) (|insert!| ((#2# |#1| |#2|) 53 T ELT)) (|initTable!| (#4# 26 T ELT)) (|extractIfCan| (((|Union| |#2| "failed") |#1|) 51 T ELT)) (|clearTable!| (#4# 40 T ELT))) 
(((|TabulatedComputationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |initTable!| #1=(#2=(|Void|))) (SIGNATURE |printInfo!| (#2# #3=(|String|) #3#)) (SIGNATURE |startStats!| (#2# #3#)) (SIGNATURE |printStats!| #1#) (SIGNATURE |clearTable!| #1#) (SIGNATURE |usingTable?| #4=((|Boolean|))) (SIGNATURE |printingInfo?| #4#) (SIGNATURE |makingStats?| #4#) (SIGNATURE |extractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |insert!| (#2# |#1| |#2|))) #5=(|SetCategory|) #5#) (T |TabulatedComputationPackage|)) 
((|insert!| (*1 *2 *3 *4) #1=(AND #2=(|isDomain| *2 (|Void|)) #3=(|isDomain| *1 (|TabulatedComputationPackage| *3 *4)) #4=(|ofCategory| *3 #5=(|SetCategory|)) #6=(|ofCategory| *4 #5#))) (|extractIfCan| #7=(*1 *2 *3) (|partial| AND (|ofCategory| *2 #5#) (|isDomain| *1 (|TabulatedComputationPackage| *3 *2)) #4#)) (|makingStats?| #8=(*1 *2) #9=(AND (|isDomain| *2 (|Boolean|)) #3# #4# #6#)) (|printingInfo?| #8# #9#) (|usingTable?| #8# #9#) (|clearTable!| #8# #1#) (|printStats!| #8# #1#) (|startStats!| #7# #10=(AND (|isDomain| *3 (|String|)) #2# (|isDomain| *1 (|TabulatedComputationPackage| *4 *5)) #6# (|ofCategory| *5 #5#))) (|printInfo!| (*1 *2 *3 *3) #10#) (|initTable!| #8# #1#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|tex| (#2=(#3=(|List| #4=(|String|)) $) 37 T ELT)) (|setTex!| (#5=(#3# $ #3#) 40 T ELT)) (|setPrologue!| (#5# 39 T ELT)) (|setEpilogue!| (#5# 41 T ELT)) (|prologue| (#2# 36 T ELT)) (|new| (($) 26 T ELT)) (|latex| ((#4# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|epilogue| (#2# 38 T ELT)) (|display| ((#6=(|Void|) $ #7=(|Integer|)) 33 T ELT) ((#6# $) 34 T ELT)) (|convert| (($ #8=(|OutputForm|) #7#) 31 T ELT) (($ #8# #7# #8#) NIL T ELT)) (|coerce| ((#8# $) 47 T ELT) (($ #8#) 30 T ELT)) (|before?| #1#) (= #1#)) 
(((|TexFormat|) (|Join| (|SetCategory|) (|CoercibleFrom| #1=(|OutputForm|)) (CATEGORY |domain| (SIGNATURE |convert| ($ #1# #2=(|Integer|))) (SIGNATURE |convert| ($ #1# #2# #1#)) (SIGNATURE |display| (#3=(|Void|) $ #2#)) (SIGNATURE |display| (#3# $)) (SIGNATURE |epilogue| #4=(#5=(|List| (|String|)) $)) (SIGNATURE |tex| #4#) (SIGNATURE |new| ($)) (SIGNATURE |prologue| #4#) (SIGNATURE |setEpilogue!| #6=(#5# $ #5#)) (SIGNATURE |setTex!| #6#) (SIGNATURE |setPrologue!| #6#)))) (T |TexFormat|)) 
((|convert| (*1 *1 *2 *3) #1=(AND (|isDomain| *2 (|OutputForm|)) #2=(|isDomain| *3 (|Integer|)) #3=(|isDomain| *1 (|TexFormat|)))) (|convert| (*1 *1 *2 *3 *2) #1#) (|display| (*1 *2 *1 *3) (AND #2# #4=(|isDomain| *2 (|Void|)) #3#)) (|display| #5=(*1 *2 *1) (AND #4# #3#)) (|epilogue| #5# #6=(AND (|isDomain| *2 (|List| (|String|))) #3#)) (|tex| #5# #6#) (|new| (*1 *1) #3#) (|prologue| #5# #6#) (|setEpilogue!| #7=(*1 *2 *1 *2) #6#) (|setTex!| #7# #6#) (|setPrologue!| #7# #6#)) 
((|coerce| (((|TexFormat|) |#1|) 11 T ELT))) 
(((|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|))))) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|writeLine!| (#3=(#4=(|String|) $ #4#) 21 T ELT) (#5=(#4# $) 20 T ELT)) (|write!| (#3# 19 T ELT)) (|reopen!| (($ $ #4#) NIL T ELT)) (|readLineIfCan!| (#6=((|Union| #4# "failed") $) 11 T ELT)) (|readLine!| (#5# 8 T ELT)) (|readIfCan!| (#6# 12 T ELT)) (|read!| (#5# 9 T ELT)) (|open| (($ #7=(|FileName|)) NIL T ELT) (($ #7# #4#) NIL T ELT)) (|name| ((#7# $) NIL T ELT)) (|latex| #8=(#5# NIL T ELT)) (|iomode| #8#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|endOfFile?| ((#2# $) 25 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|close!| (($ $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|TextFile|) (|Join| (|FileCategory| (|FileName|) #1=(|String|)) (CATEGORY |domain| (SIGNATURE |writeLine!| (#1# $ #1#)) (SIGNATURE |writeLine!| #2=(#1# $)) (SIGNATURE |readLine!| #2#) (SIGNATURE |readLineIfCan!| #3=((|Union| #1# "failed") $)) (SIGNATURE |readIfCan!| #3#) (SIGNATURE |endOfFile?| ((|Boolean|) $))))) (T |TextFile|)) 
((|writeLine!| (*1 *2 *1 *2) #1=(AND #2=(|isDomain| *2 (|String|)) #3=(|isDomain| *1 (|TextFile|)))) (|writeLine!| #4=(*1 *2 *1) #1#) (|readLine!| #4# #1#) (|readLineIfCan!| #4# #5=(|partial| AND #2# #3#)) (|readIfCan!| #4# #5#) (|endOfFile?| #4# (AND (|isDomain| *2 (|Boolean|)) #3#))) 
((|sign| (#1=((|Union| #2=(|Integer|) "failed") |#1|) 19 T ELT)) (|nonQsign| (#1# 14 T ELT)) (|direction| ((#2# (|String|)) 33 T ELT))) 
(((|ToolsForSign| |#1|) (CATEGORY |package| (SIGNATURE |sign| #1=((|Union| #2=(|Integer|) "failed") |#1|)) (SIGNATURE |nonQsign| #1#) (SIGNATURE |direction| (#2# (|String|)))) (|Ring|)) (T |ToolsForSign|)) 
((|direction| #1=(*1 *2 *3) (AND (|isDomain| *3 (|String|)) #2=(|isDomain| *2 (|Integer|)) (|isDomain| *1 (|ToolsForSign| *4)) (|ofCategory| *4 #3=(|Ring|)))) (|nonQsign| #1# #4=(|partial| AND #2# (|isDomain| *1 (|ToolsForSign| *3)) (|ofCategory| *3 #3#))) (|sign| #1# #4#)) 
((|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) 9 T ELT))) 
(((|TopLevelThreeSpace|) (CATEGORY |package| (SIGNATURE |createThreeSpace| ((|ThreeSpace| (|DoubleFloat|)))))) (T |TopLevelThreeSpace|)) 
((|createThreeSpace| (*1 *2) (AND (|isDomain| *2 (|ThreeSpace| (|DoubleFloat|))) (|isDomain| *1 (|TopLevelThreeSpace|))))) 
((|pi| (($) 12 T ELT)) (|atanh| (#1=($ $) 36 T ELT)) (|asinh| (#1# 34 T ELT)) (|asin| (#1# 26 T ELT)) (|asech| (#1# 18 T ELT)) (|acsch| (#1# 16 T ELT)) (|acoth| (#1# 20 T ELT)) (|acot| (#1# 31 T ELT)) (|acosh| (#1# 35 T ELT)) (|acos| (#1# 30 T ELT))) 
(((|TranscendentalFunctionCategory&| |#1|) (CATEGORY |package| (SIGNATURE |pi| (|#1|)) (SIGNATURE |atanh| #1=(|#1| |#1|)) (SIGNATURE |asinh| #1#) (SIGNATURE |asech| #1#) (SIGNATURE |acsch| #1#) (SIGNATURE |acoth| #1#) (SIGNATURE |acosh| #1#) (SIGNATURE |asin| #1#) (SIGNATURE |acot| #1#) (SIGNATURE |acos| #1#)) (|TranscendentalFunctionCategory|)) (T |TranscendentalFunctionCategory&|)) 
NIL 
((|tanh| (#1=($ $) 26 T ELT)) (|tan| (#2=($ $) 11 T ELT)) (|sinh| (#1# 27 T ELT)) (|sin| (#2# 10 T ELT)) (|sech| (#1# 28 T ELT)) (|sec| (#2# 9 T ELT)) (|pi| (($) 16 T ELT)) (|log| (#3=($ $) 19 T ELT)) (|exp| (#3# 18 T ELT)) (|csch| (#1# 29 T ELT)) (|csc| (#2# 8 T ELT)) (|coth| (#1# 30 T ELT)) (|cot| (#2# 7 T ELT)) (|cosh| (#1# 31 T ELT)) (|cos| (#2# 6 T ELT)) (|atanh| (#4=($ $) 20 T ELT)) (|atan| (#5=($ $) 32 T ELT)) (|asinh| (#4# 21 T ELT)) (|asin| (#5# 33 T ELT)) (|asech| (#4# 22 T ELT)) (|asec| (#5# 34 T ELT)) (|acsch| (#4# 23 T ELT)) (|acsc| (#5# 35 T ELT)) (|acoth| (#4# 24 T ELT)) (|acot| (#5# 36 T ELT)) (|acosh| (#4# 25 T ELT)) (|acos| (#5# 37 T ELT)) (** (($ $ $) 17 T ELT))) 
(((|TranscendentalFunctionCategory|) (|Category|)) (T |TranscendentalFunctionCategory|)) 
((|pi| (*1 *1) (|ofCategory| *1 (|TranscendentalFunctionCategory|)))) 
(|Join| (|TrigonometricFunctionCategory|) (|ArcTrigonometricFunctionCategory|) (|HyperbolicFunctionCategory|) (|ArcHyperbolicFunctionCategory|) (|ElementaryFunctionCategory|) (CATEGORY |domain| (SIGNATURE |pi| ($)))) 
(((|ArcHyperbolicFunctionCategory|) . T) ((|ArcTrigonometricFunctionCategory|) . T) ((|ElementaryFunctionCategory|) . T) ((|HyperbolicFunctionCategory|) . T) ((|TrigonometricFunctionCategory|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 19 T ELT)) (|tree| (($ |#1| #5=(|List| $)) 28 T ELT) (($ #6=(|List| |#1|)) 35 T ELT) (($ |#1|) 30 T ELT)) (|setvalue!| ((|#1| $ |#1|) 14 #7=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #8="value" |#1|) NIL #7# ELT)) (|setchildren!| (($ $ #5#) 13 #7# ELT)) (|sample| (#9=($) NIL T CONST)) (|reduce| ((|#1| #10=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #10# $ |#1|) NIL T ELT) ((|#1| #10# $) NIL T ELT)) (|nodes| (#11=(#5# $) 59 T ELT)) (|node?| (#2# 50 #4# ELT)) (|members| (#12=(#6# $) 70 T ELT)) (|member?| ((#3# |#1| $) 69 #4# ELT)) (|map!| (#13=($ (|Mapping| |#1| |#1|) $) 29 T ELT)) (|map| (#13# 27 T ELT)) (|leaves| (#12# 55 T ELT)) (|leaf?| (#14=(#3# $) 53 T ELT)) (|latex| (((|String|) $) NIL #15=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) NIL #15# ELT)) (|find| (((|Union| |#1| "failed") #16=(|Mapping| #3# |#1|) $) NIL T ELT)) (|every?| (#17=(#3# #16# $) 67 T ELT)) (|eval| (($ $ (|List| #18=(|Equation| |#1|))) NIL #19=(AND (|has| |#1| (|Evalable| |#1|)) #15#) ELT) (($ $ #18#) NIL #19# ELT) (($ $ |#1| |#1|) NIL #19# ELT) (($ $ #6# #6#) NIL #19# ELT)) (|eq?| (#2# 101 T ELT)) (|empty?| (#14# 9 T ELT)) (|empty| (#9# 10 T ELT)) (|elt| ((|#1| $ #8#) NIL T ELT)) (|distance| (((|Integer|) $ $) 48 T ELT)) (|cyclicParents| (#11# 83 T ELT)) (|cyclicEqual?| (#2# 104 T ELT)) (|cyclicEntries| (#11# 99 T ELT)) (|cyclicCopy| (#20=($ $) 100 T ELT)) (|cyclic?| (#14# 76 T ELT)) (|count| ((#21=(|NonNegativeInteger|) |#1| $) 17 #4# ELT) ((#21# #16# $) 25 T ELT)) (|copy| (#20# 82 T ELT)) (|coerce| ((#22=(|OutputForm|) $) 85 (|has| |#1| (|CoercibleTo| #22#)) ELT)) (|children| (#11# 12 T ELT)) (|child?| (#2# 39 #4# ELT)) (|before?| #1#) (|any?| (#17# 66 T ELT)) (= (#2# 37 #4# ELT)) (|#| ((#21# $) 80 T ELT))) 
(((|Tree| |#1|) (|Join| (|RecursiveAggregate| |#1|) (|FiniteAggregate| |#1|) (|ShallowlyMutableAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |tree| ($ |#1| #1=(|List| $))) (SIGNATURE |tree| ($ (|List| |#1|))) (SIGNATURE |tree| ($ |#1|)) (SIGNATURE |cyclic?| (#2=(|Boolean|) $)) (SIGNATURE |cyclicCopy| ($ $)) (SIGNATURE |cyclicEntries| #3=(#1# $)) (SIGNATURE |cyclicEqual?| (#2# $ $)) (SIGNATURE |cyclicParents| #3#))) (|SetCategory|)) (T |Tree|)) 
((|cyclic?| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|Boolean|)) #3=(|isDomain| *1 #4=(|Tree| *3)) #5=(|ofCategory| *3 #6=(|SetCategory|)))) (|tree| (*1 *1 *2 *3) (AND (|isDomain| *3 (|List| #7=(|Tree| *2))) #8=(|isDomain| *1 #7#) #9=(|ofCategory| *2 #6#))) (|tree| #10=(*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #5# #3#)) (|tree| #10# #11=(AND #8# #9#)) (|cyclicCopy| (*1 *1 *1) #11#) (|cyclicEntries| #1# #12=(AND (|isDomain| *2 (|List| #4#)) #3# #5#)) (|cyclicEqual?| (*1 *2 *1 *1) #2#) (|cyclicParents| #1# #12#)) 
((|tan| (#1=($ $) 15 T ELT)) (|sec| (#1# 12 T ELT)) (|csc| (#1# 10 T ELT)) (|cot| (#1# 17 T ELT))) 
(((|TrigonometricFunctionCategory&| |#1|) (CATEGORY |package| (SIGNATURE |cot| #1=(|#1| |#1|)) (SIGNATURE |csc| #1#) (SIGNATURE |sec| #1#) (SIGNATURE |tan| #1#)) (|TrigonometricFunctionCategory|)) (T |TrigonometricFunctionCategory&|)) 
NIL 
((|tan| (($ $) 11 T ELT)) (|sin| (($ $) 10 T ELT)) (|sec| (($ $) 9 T ELT)) (|csc| (($ $) 8 T ELT)) (|cot| (($ $) 7 T ELT)) (|cos| (($ $) 6 T ELT))) 
(((|TrigonometricFunctionCategory|) (|Category|)) (T |TrigonometricFunctionCategory|)) 
((|tan| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|sin| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|sec| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|csc| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|cot| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|cos| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|)))) 
(|Join| (CATEGORY |domain| (SIGNATURE |cos| ($ $)) (SIGNATURE |cot| ($ $)) (SIGNATURE |csc| ($ $)) (SIGNATURE |sec| ($ $)) (SIGNATURE |sin| ($ $)) (SIGNATURE |tan| ($ $)))) 
((|trigs| (#1=(|#2| |#2|) 95 T ELT)) (|real?| (((|Boolean|) |#2|) 29 T ELT)) (|real| (#1# 33 T ELT)) (|imag| (#1# 35 T ELT)) (|complexNormalize| (#2=(|#2| |#2| (|Symbol|)) 89 T ELT) (#1# 90 T ELT)) (|complexForm| (((|Complex| |#2|) |#2|) 31 T ELT)) (|complexElementary| (#2# 91 T ELT) (#1# 92 T ELT))) 
(((|TrigonometricManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |complexNormalize| #1=(|#2| |#2|)) (SIGNATURE |complexNormalize| #2=(|#2| |#2| (|Symbol|))) (SIGNATURE |complexElementary| #1#) (SIGNATURE |complexElementary| #2#) (SIGNATURE |trigs| #1#) (SIGNATURE |real| #1#) (SIGNATURE |imag| #1#) (SIGNATURE |real?| ((|Boolean|) |#2|)) (SIGNATURE |complexForm| ((|Complex| |#2|) |#2|))) (|Join| (|GcdDomain|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |TrigonometricManipulations|)) 
((|complexForm| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|Join| (|GcdDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#))) (|isDomain| *2 (|Complex| *3)) #5=(|isDomain| *1 (|TrigonometricManipulations| *4 *3)) #6=(|ofCategory| *3 #7=(|Join| #8=(|AlgebraicallyClosedField|) #9=(|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|real?| #1# (AND #2# (|isDomain| *2 (|Boolean|)) #5# #6#)) (|imag| #10=(*1 *2 *2) #11=(AND (|ofCategory| *3 #3#) (|isDomain| *1 (|TrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| #8# #9# (|FunctionSpace| *3))))) (|real| #10# #11#) (|trigs| #10# #11#) (|complexElementary| #12=(*1 *2 *2 *3) #13=(AND (|isDomain| *3 (|Symbol|)) #2# (|isDomain| *1 (|TrigonometricManipulations| *4 *2)) (|ofCategory| *2 #7#))) (|complexElementary| #10# #11#) (|complexNormalize| #12# #13#) (|complexNormalize| #10# #11#)) 
((|UpTriBddDenomInv| (#1=(|#4| |#4| |#1|) 31 T ELT)) (|LowTriBddDenomInv| (#1# 32 T ELT))) 
(((|TriangularMatrixOperations| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |UpTriBddDenomInv| #1=(|#4| |#4| |#1|)) (SIGNATURE |LowTriBddDenomInv| #1#)) (|IntegralDomain|) #2=(|FiniteLinearAggregate| |#1|) #2# (|MatrixCategory| |#1| |#2| |#3|)) (T |TriangularMatrixOperations|)) 
((|LowTriBddDenomInv| #1=(*1 *2 *2 *3) #2=(AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 #3=(|FiniteLinearAggregate| *3)) (|ofCategory| *5 #3#) (|isDomain| *1 (|TriangularMatrixOperations| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|UpTriBddDenomInv| #1# #2#)) 
((|tanh2trigh| (#1=(|#2| |#2|) 148 T ELT)) (|tanh2coth| (#1# 145 T ELT)) (|tan2trig| (#1# 136 T ELT)) (|tan2cot| (#1# 133 T ELT)) (|sinh2csch| (#1# 141 T ELT)) (|sin2csc| (#1# 129 T ELT)) (|simplifyLog| (#1# 44 T ELT)) (|simplifyExp| (#1# 105 T ELT)) (|simplify| (#1# 88 T ELT)) (|sech2cosh| (#1# 143 T ELT)) (|sec2cos| (#1# 131 T ELT)) (|removeSinhSq| (#1# 153 T ELT)) (|removeSinSq| (#1# 151 T ELT)) (|removeCoshSq| (#1# 152 T ELT)) (|removeCosSq| (#1# 150 T ELT)) (|htrigs| (#1# 163 T ELT)) (|expandTrigProducts| (#1# 30 (AND (|has| |#2| #2=(|ConvertibleTo| (|Pattern| |#1|))) (|has| |#2| #3=(|PatternMatchable| |#1|)) (|has| |#1| #2#) (|has| |#1| #3#)) ELT)) (|expandPower| (#1# 89 T ELT)) (|expandLog| (#1# 154 T ELT)) (|expand| (#1# 155 T ELT)) (|csch2sinh| (#1# 142 T ELT)) (|csc2sin| (#1# 130 T ELT)) (|coth2trigh| (#1# 149 T ELT)) (|coth2tanh| (#1# 147 T ELT)) (|cot2trig| (#1# 137 T ELT)) (|cot2tan| (#1# 135 T ELT)) (|cosh2sech| (#1# 139 T ELT)) (|cos2sec| (#1# 127 T ELT))) 
(((|TranscendentalManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |expand| #1=(|#2| |#2|)) (SIGNATURE |simplify| #1#) (SIGNATURE |htrigs| #1#) (SIGNATURE |simplifyExp| #1#) (SIGNATURE |simplifyLog| #1#) (SIGNATURE |expandPower| #1#) (SIGNATURE |expandLog| #1#) (SIGNATURE |cos2sec| #1#) (SIGNATURE |cosh2sech| #1#) (SIGNATURE |cot2trig| #1#) (SIGNATURE |coth2trigh| #1#) (SIGNATURE |csc2sin| #1#) (SIGNATURE |csch2sinh| #1#) (SIGNATURE |sec2cos| #1#) (SIGNATURE |sech2cosh| #1#) (SIGNATURE |sin2csc| #1#) (SIGNATURE |sinh2csch| #1#) (SIGNATURE |tan2trig| #1#) (SIGNATURE |tanh2trigh| #1#) (SIGNATURE |tan2cot| #1#) (SIGNATURE |tanh2coth| #1#) (SIGNATURE |cot2tan| #1#) (SIGNATURE |coth2tanh| #1#) (SIGNATURE |removeCosSq| #1#) (SIGNATURE |removeSinSq| #1#) (SIGNATURE |removeCoshSq| #1#) (SIGNATURE |removeSinhSq| #1#) (IF (|has| |#1| #2=(|PatternMatchable| |#1|)) (IF (|has| |#1| #3=(|ConvertibleTo| (|Pattern| |#1|))) (IF (|has| |#2| #3#) (IF (|has| |#2| #2#) (SIGNATURE |expandTrigProducts| #1#) |%noBranch|) |%noBranch|) |%noBranch|) |%noBranch|)) (|GcdDomain|) (|Join| (|FunctionSpace| |#1|) (|TranscendentalFunctionCategory|))) (T |TranscendentalManipulations|)) 
((|expandTrigProducts| #1=(*1 *2 *2) (AND (|ofCategory| *3 #2=(|ConvertibleTo| (|Pattern| *3))) (|ofCategory| *3 #3=(|PatternMatchable| *3)) #4=(|ofCategory| *3 (|GcdDomain|)) #5=(|isDomain| *1 (|TranscendentalManipulations| *3 *2)) (|ofCategory| *2 #2#) (|ofCategory| *2 #3#) #6=(|ofCategory| *2 (|Join| (|FunctionSpace| *3) (|TranscendentalFunctionCategory|))))) (|removeSinhSq| #1# #7=(AND #4# #5# #6#)) (|removeCoshSq| #1# #7#) (|removeSinSq| #1# #7#) (|removeCosSq| #1# #7#) (|coth2tanh| #1# #7#) (|cot2tan| #1# #7#) (|tanh2coth| #1# #7#) (|tan2cot| #1# #7#) (|tanh2trigh| #1# #7#) (|tan2trig| #1# #7#) (|sinh2csch| #1# #7#) (|sin2csc| #1# #7#) (|sech2cosh| #1# #7#) (|sec2cos| #1# #7#) (|csch2sinh| #1# #7#) (|csc2sin| #1# #7#) (|coth2trigh| #1# #7#) (|cot2trig| #1# #7#) (|cosh2sech| #1# #7#) (|cos2sec| #1# #7#) (|expandLog| #1# #7#) (|expandPower| #1# #7#) (|simplifyLog| #1# #7#) (|simplifyExp| #1# #7#) (|htrigs| #1# #7#) (|simplify| #1# #7#) (|expand| #1# #7#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|Symbol|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#5# NIL #8# ELT)) (|tanh| #11=(#10# NIL #12=(|has| |#1| (|Algebra| #13=(|Fraction| #14=(|Integer|)))) ELT)) (|tan| #11#) (|subtractIfCan| (#15=(#16=(|Union| $ "failed") $ $) NIL T ELT)) (|sqrt| #11#) (|sinh| #11#) (|sin| #11#) (|sech| #11#) (|sec| #11#) (|sample| #17=(#18=($) NIL T CONST)) (|reductum| #19=(#10# NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|polynomial| (#20=(#21=(|Polynomial| |#1|) $ #22=(|NonNegativeInteger|)) 18 T ELT) ((#21# $ #22# #22#) NIL T ELT)) (|pole?| #4#) (|pi| (#18# NIL #12# ELT)) (|order| ((#22# $ #7#) NIL T ELT) ((#22# $ #7# #22#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (($ $ #14#) NIL #12# ELT)) (|monomial?| #4#) (|monomial| (($ $ #6# (|List| #23=(|IndexedExponents| #7#))) NIL T ELT) (($ $ #7# #23#) NIL T ELT) (($ |#1| #23#) NIL T ELT) #24=(($ $ #7# #22#) NIL T ELT) #25=(($ $ #6# (|List| #22#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #11#) (|leadingMonomial| #19#) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#26=($ $ #7#) NIL #12# ELT) (($ $ #7# |#1|) NIL #12# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fintegrate| (($ (|Mapping| $) #7# |#1|) NIL #12# ELT)) (|extend| #27=(($ $ #22#) NIL T ELT)) (|exquo| (#15# NIL #8# ELT)) (|exp| #11#) (|eval| (($ $ #7# $) NIL T ELT) (($ $ #6# #28=(|List| $)) NIL T ELT) (($ $ (|List| #29=(|Equation| $))) NIL T ELT) (($ $ #29#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #28# #28#) NIL T ELT)) (|differentiate| #25# #24# #30=(($ $ #6#) NIL T ELT) #31=(#26# NIL T ELT)) (|degree| ((#23# $) NIL T ELT)) (|csch| #11#) (|csc| #11#) (|coth| #11#) (|cot| #11#) (|cosh| #11#) (|cos| #11#) (|complete| #19#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) #9# (($ #13#) NIL #12# ELT) (($ #7#) NIL T ELT) (($ #21#) NIL T ELT)) (|coefficient| ((|#1| $ #23#) NIL T ELT) #24# #25# (#20# NIL T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#22#) NIL T CONST)) (|before?| #1#) (|atanh| #11#) (|atan| #11#) (|associates?| (#2# NIL #8# ELT)) (|asinh| #11#) (|asin| #11#) (|asech| #11#) (|asec| #11#) (|annihilate?| #1#) (|acsch| #11#) (|acsc| #11#) (|acoth| #11#) (|acot| #11#) (|acosh| #11#) (|acos| #11#) (|Zero| #17#) (|One| #17#) (D #25# #24# #30# #31#) (= #1#) (/ (#32=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #19# #33=(#34=($ $ $) NIL T ELT)) (+ #33#) (** (($ $ #35=(|PositiveInteger|)) NIL T ELT) #27# (#34# NIL #12# ELT) #36=(($ $ #13#) NIL #12# ELT)) (* (($ #35# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #14# . #37=($)) NIL T ELT) #33# #36# (($ #13# . #37#) NIL #12# ELT) (($ |#1| . #37#) NIL T ELT) (#32# NIL T ELT))) 
(((|TaylorSeries| |#1|) (|Join| (|MultivariateTaylorSeriesCategory| |#1| #1=(|Symbol|)) (CATEGORY |domain| (SIGNATURE |coefficient| (#2=(|Polynomial| |#1|) $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ #1#)) (SIGNATURE |coerce| ($ #2#)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ #1# |#1|)) (SIGNATURE |fintegrate| ($ (|Mapping| $) #1# |#1|))) |%noBranch|))) (|Ring|)) (T |TaylorSeries|)) 
((|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Polynomial| *4)) #1=(|isDomain| *1 #2=(|TaylorSeries| *4)) #3=(|ofCategory| *4 #4=(|Ring|)))) (|coerce| #5=(*1 *1 *2) (AND #6=(|isDomain| *2 #7=(|Symbol|)) #8=(|isDomain| *1 (|TaylorSeries| *3)) #9=(|ofCategory| *3 #4#))) (|coerce| #5# (AND (|isDomain| *2 (|Polynomial| *3)) #9# #8#)) (|integrate| (*1 *1 *1 *2 *3) (AND #6# #8# (|ofCategory| *3 #10=(|Algebra| (|Fraction| (|Integer|)))) #9#)) (|fintegrate| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Mapping| #2#)) (|isDomain| *3 #7#) #1# (|ofCategory| *4 #10#) #3#))) 
((|stronglyReduced?| (#1=(#2=(|Boolean|) |#5| $) 68 T ELT) (#3=(#2# $) 109 T ELT)) (|stronglyReduce| (#4=(|#5| |#5| $) 83 T ELT)) (|select| (($ #5=(|Mapping| #2# |#5|) $) NIL T ELT) ((#6=(|Union| |#5| #7="failed") $ |#4|) 126 T ELT)) (|rewriteSetWithReduction| ((#8=(|List| |#5|) #8# $ #9=(|Mapping| |#5| |#5| |#5|) #10=(|Mapping| #2# |#5| |#5|)) 81 T ELT)) (|retractIfCan| ((#11=(|Union| $ #7#) #8#) 134 T ELT)) (|rest| ((#11# $) 119 T ELT)) (|removeZero| (#4# 101 T ELT)) (|reduced?| ((#2# |#5| $ #10#) 36 T ELT)) (|reduceByQuasiMonic| (#4# 105 T ELT)) (|reduce| ((|#5| #9# $ |#5| |#5|) NIL T ELT) ((|#5| #9# $ |#5|) NIL T ELT) ((|#5| #9# $) NIL T ELT) ((|#5| |#5| $ #9# #10#) 77 T ELT)) (|quasiComponent| (((|Record| (|:| |close| #8#) (|:| |open| #8#)) $) 63 T ELT)) (|normalized?| (#1# 66 T ELT) (#3# 110 T ELT)) (|mvar| ((|#4| $) 115 T ELT)) (|last| (#12=(#6# $) 117 T ELT)) (|initials| (#13=(#8# $) 55 T ELT)) (|initiallyReduced?| (#1# 75 T ELT) (#3# 114 T ELT)) (|initiallyReduce| (#4# 89 T ELT)) (|infRittWu?| (#14=(#2# $ $) 29 T ELT)) (|headReduced?| (#1# 71 T ELT) (#3# 112 T ELT)) (|headReduce| (#4# 86 T ELT)) (|first| (#12# 116 T ELT)) (|extend| (($ $ |#5|) 135 T ELT)) (|degree| (#15=((|NonNegativeInteger|) $) 60 T ELT)) (|construct| (($ #8#) 132 T ELT)) (|collectUpper| (#16=($ $ |#4|) 130 T ELT)) (|collectUnder| (#16# 128 T ELT)) (|collectQuasiMonic| (($ $) 127 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (#13# 120 T ELT)) (|coHeight| (#15# 139 T ELT)) (|basicSet| ((#17=(|Union| (|Record| (|:| |bas| $) (|:| |top| #8#)) #7#) #8# #10#) 49 T ELT) ((#17# #8# #5# #10#) 51 T ELT)) (|autoReduced?| ((#2# $ (|Mapping| #2# |#5| #8#)) 107 T ELT)) (|algebraicVariables| (((|List| |#4|) $) 122 T ELT)) (|algebraic?| ((#2# |#4| $) 125 T ELT)) (= (#14# 20 T ELT))) 
(((|TriangularSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |coHeight| #1=((|NonNegativeInteger|) |#1|)) (SIGNATURE |extend| (|#1| |#1| |#5|)) (SIGNATURE |select| (#2=(|Union| |#5| #3="failed") |#1| |#4|)) (SIGNATURE |algebraic?| (#4=(|Boolean|) |#4| |#1|)) (SIGNATURE |algebraicVariables| ((|List| |#4|) |#1|)) (SIGNATURE |rest| (#5=(|Union| |#1| #3#) |#1|)) (SIGNATURE |last| #6=(#2# |#1|)) (SIGNATURE |first| #6#) (SIGNATURE |reduceByQuasiMonic| #7=(|#5| |#5| |#1|)) (SIGNATURE |collectQuasiMonic| (|#1| |#1|)) (SIGNATURE |removeZero| #7#) (SIGNATURE |initiallyReduce| #7#) (SIGNATURE |headReduce| #7#) (SIGNATURE |stronglyReduce| #7#) (SIGNATURE |rewriteSetWithReduction| (#8=(|List| |#5|) #8# |#1| #9=(|Mapping| |#5| |#5| |#5|) #10=(|Mapping| #4# |#5| |#5|))) (SIGNATURE |reduce| (|#5| |#5| |#1| #9# #10#)) (SIGNATURE |initiallyReduced?| #11=(#4# |#1|)) (SIGNATURE |headReduced?| #11#) (SIGNATURE |stronglyReduced?| #11#) (SIGNATURE |autoReduced?| (#4# |#1| (|Mapping| #4# |#5| #8#))) (SIGNATURE |initiallyReduced?| #12=(#4# |#5| |#1|)) (SIGNATURE |headReduced?| #12#) (SIGNATURE |stronglyReduced?| #12#) (SIGNATURE |reduced?| (#4# |#5| |#1| #10#)) (SIGNATURE |normalized?| #11#) (SIGNATURE |normalized?| #12#) (SIGNATURE |quasiComponent| ((|Record| (|:| |close| #8#) (|:| |open| #8#)) |#1|)) (SIGNATURE |degree| #1#) (SIGNATURE |initials| #13=(#8# |#1|)) (SIGNATURE |basicSet| (#14=(|Union| (|Record| (|:| |bas| |#1|) (|:| |top| #8#)) #3#) #8# #15=(|Mapping| #4# |#5|) #10#)) (SIGNATURE |basicSet| (#14# #8# #10#)) (SIGNATURE |infRittWu?| #16=(#4# |#1| |#1|)) (SIGNATURE |collectUpper| #17=(|#1| |#1| |#4|)) (SIGNATURE |collectUnder| #17#) (SIGNATURE |mvar| (|#4| |#1|)) (SIGNATURE |retractIfCan| (#5# #8#)) (SIGNATURE |coerce| #13#) (SIGNATURE |reduce| (|#5| #9# |#1|)) (SIGNATURE |reduce| (|#5| #9# |#1| |#5|)) (SIGNATURE |reduce| (|#5| #9# |#1| |#5| |#5|)) (SIGNATURE |construct| (|#1| #8#)) (SIGNATURE |select| (|#1| #15# |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = #16#)) (|TriangularSetCategory| |#2| |#3| |#4| |#5|) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |TriangularSetCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT)) (|variables| (((|List| |#3|) . #2=($)) 39 T ELT)) (|trivialIdeal?| (#3=(#4=(|Boolean|) $) 32 T ELT)) (|triangular?| (#3# 23 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|stronglyReduced?| (((|Boolean|) |#4| $) 107 T ELT) (((|Boolean|) $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| $) 98 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #6=(|Boolean|) |#4|) . #7=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| "failed") $ |#3|) 85 T ELT)) (|sample| (#8=($) 59 T CONST)) (|roughUnitIdeal?| (#3# 28 (|has| |#1| . #5#) ELT)) (|roughSubIdeal?| (#9=(#4# $ $) 30 (|has| |#1| . #5#) ELT)) (|roughEqualIdeals?| (#9# 29 (|has| |#1| . #5#) ELT)) (|roughBase?| (#3# 31 (|has| |#1| . #5#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #10=($)) 24 (|has| |#1| . #5#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #10#) 25 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| (((|Union| $ "failed") $) 88 T ELT)) (|removeZero| ((|#4| |#4| $) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #11=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #11#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #6# |#4|) . #7#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #5#) ELT)) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| $) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #12=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|normalized?| (((|Boolean|) |#4| $) 110 T ELT) (((|Boolean|) $) 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#13=(|Boolean|) |#4| $) 53 (|has| |#4| . #12#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #2#) 38 T ELT)) (|mainVariable?| ((#4# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|last| (((|Union| |#4| "failed") $) 89 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| (((|Boolean|) |#4| $) 105 T ELT) (((|Boolean|) $) 101 T ELT)) (|initiallyReduce| ((|#4| |#4| $) 96 T ELT)) (|infRittWu?| (((|Boolean|) $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #5#) ELT)) (|headReduced?| (((|Boolean|) |#4| $) 106 T ELT) (((|Boolean|) $) 102 T ELT)) (|headReduce| ((|#4| |#4| $) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| "failed") $) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #13# |#4|) $) 51 T ELT)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT)) (|every?| ((#13# (|Mapping| #13# |#4|) . #14=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15#)) ELT)) (|eq?| ((#16=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#16# $) 58 T ELT)) (|empty| (#8# 57 T ELT)) (|degree| (((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#17=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #12#) ELT) ((#17# (|Mapping| #13# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#18=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #18#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #19=($)) 13 T ELT) (((|List| |#4|) . #19#) 43 T ELT)) (|coHeight| (((|NonNegativeInteger|) $) 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 115 T ELT) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 114 T ELT)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) 104 T ELT)) (|any?| ((#13# (|Mapping| #13# |#4|) . #14#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraic?| (((|Boolean|) |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#17# $) 44 T ELT))) 
(((|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|) (|ShallowlyMutableAggregate| |t#4|) (CATEGORY |domain| (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|) $)) |%noBranch|))) 
(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|Type|) . T)) 
((|tube| (($ |#1| #1=(|List| (|List| (|Point| (|DoubleFloat|)))) #2=(|Boolean|)) 19 T ELT)) (|setClosed| ((#2# $ #2#) 18 T ELT)) (|open?| (#3=(#2# $) 17 T ELT)) (|listLoops| ((#1# $) 13 T ELT)) (|getCurve| ((|#1| $) 8 T ELT)) (|closed?| (#3# 15 T ELT))) 
(((|TubePlot| |#1|) (CATEGORY |domain| (SIGNATURE |getCurve| (|#1| $)) (SIGNATURE |listLoops| (#1=(|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |closed?| #2=(#3=(|Boolean|) $)) (SIGNATURE |open?| #2#) (SIGNATURE |setClosed| (#3# $ #3#)) (SIGNATURE |tube| ($ |#1| #1# #3#))) (|PlottableSpaceCurveCategory|)) (T |TubePlot|)) 
((|tube| (*1 *1 *2 *3 *4) (AND (|isDomain| *3 #1=(|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *4 #2=(|Boolean|)) #3=(|isDomain| *1 (|TubePlot| *2)) #4=(|ofCategory| *2 #5=(|PlottableSpaceCurveCategory|)))) (|setClosed| (*1 *2 *1 *2) #6=(AND (|isDomain| *2 #2#) #7=(|isDomain| *1 (|TubePlot| *3)) #8=(|ofCategory| *3 #5#))) (|open?| #9=(*1 *2 *1) #6#) (|closed?| #9# #6#) (|listLoops| #9# (AND (|isDomain| *2 #1#) #7# #8#)) (|getCurve| #9# (AND #3# #4#))) 
((|unitVector| ((#1=(|Point| #2=(|DoubleFloat|)) #1#) 31 T ELT)) (|point| ((#1# #2# #2# #2# #2#) 10 T ELT)) (|loopPoints| (((|List| #1#) #1# #1# #1# #2# #3=(|List| (|List| #2#))) 57 T ELT)) (|dot| ((#2# #1# #1#) 27 T ELT)) (|cross| (#4=(#1# #1# #1#) 28 T ELT)) (|cosSinInfo| ((#3# (|Integer|)) 45 T ELT)) (- (#4# 26 T ELT)) (+ (#4# 24 T ELT)) (* ((#1# #2# #1#) 22 T ELT))) 
(((|TubePlotTools|) (CATEGORY |package| (SIGNATURE |point| (#1=(|Point| #2=(|DoubleFloat|)) #2# #2# #2# #2#)) (SIGNATURE * (#1# #2# #1#)) (SIGNATURE + #3=(#1# #1# #1#)) (SIGNATURE - #3#) (SIGNATURE |dot| (#2# #1# #1#)) (SIGNATURE |cross| #3#) (SIGNATURE |unitVector| (#1# #1#)) (SIGNATURE |cosSinInfo| (#4=(|List| (|List| #2#)) (|Integer|))) (SIGNATURE |loopPoints| ((|List| #1#) #1# #1# #1# #2# #4#)))) (T |TubePlotTools|)) 
((|loopPoints| (*1 *2 *3 *3 *3 *4 *5) (AND (|isDomain| *5 #1=(|List| (|List| #2=(|DoubleFloat|)))) (|isDomain| *4 #2#) (|isDomain| *2 (|List| #3=(|Point| *4))) #4=(|isDomain| *1 (|TubePlotTools|)) (|isDomain| *3 #3#))) (|cosSinInfo| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 #1#) #4#)) (|unitVector| (*1 *2 *2) #5=(AND #6=(|isDomain| *2 #7=(|Point| #2#)) #4#)) (|cross| #8=(*1 *2 *2 *2) #5#) (|dot| (*1 *2 *3 *3) (AND (|isDomain| *3 #7#) (|isDomain| *2 #2#) #4#)) (- #8# #5#) (+ #8# #5#) (* (*1 *2 *3 *2) (AND #6# #9=(|isDomain| *3 #2#) #4#)) (|point| (*1 *2 *3 *3 *3 *3) (AND #6# #4# #9#))) 
((~= #1=(#2=((|Boolean|) $ $) NIL #3=(|has| |#1| (|SetCategory|)) ELT)) (|select| ((|#1| $ #4=(|NonNegativeInteger|)) 18 T ELT)) (|length| ((#4# $) 13 T ELT)) (|latex| (((|String|) $) NIL #3# ELT)) (|hash| (((|SingleInteger|) $) NIL #3# ELT)) (|coerce| ((#5=(|PrimitiveArray| |#1|) $) 12 T ELT) (($ #5#) 11 T ELT) ((#6=(|OutputForm|) $) 29 (|has| |#1| (|CoercibleTo| #6#)) ELT)) (|before?| #1#) (= (#2# 22 #3# ELT))) 
(((|Tuple| |#1|) (|Join| (|HomotopicTo| (|PrimitiveArray| |#1|)) (CATEGORY |domain| (SIGNATURE |select| (|#1| $ #1=(|NonNegativeInteger|))) (SIGNATURE |length| (#1# $)) (IF (|has| |#1| #2=(|CoercibleTo| (|OutputForm|))) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |#1| #3=(|SetCategory|)) (ATTRIBUTE #3#) |%noBranch|))) (|Type|)) (T |Tuple|)) 
((|select| (*1 *2 *1 *3) (AND (|isDomain| *3 #1=(|NonNegativeInteger|)) (|isDomain| *1 (|Tuple| *2)) (|ofCategory| *2 #2=(|Type|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 #1#) (|isDomain| *1 (|Tuple| *3)) (|ofCategory| *3 #2#)))) 
((|twoFactor| ((#1=(|Factored| #2=(|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) #2# (|Integer|)) 92 T ELT)) (|generalTwoFactor| (#3=(#1# #2#) 84 T ELT)) (|generalSqFr| (#3# 68 T ELT))) 
(((|TwoFactorize| |#1|) (CATEGORY |package| (SIGNATURE |generalTwoFactor| #1=(#2=(|Factored| #3=(|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) #3#)) (SIGNATURE |generalSqFr| #1#) (SIGNATURE |twoFactor| (#2# #3# (|Integer|)))) (|FiniteFieldCategory|)) (T |TwoFactorize|)) 
((|twoFactor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *5 #1=(|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| #2=(|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *5)))) (|isDomain| *1 (|TwoFactorize| *5)) (|isDomain| *3 #2#))) (|generalSqFr| #3=(*1 *2 *3) #4=(AND (|ofCategory| *4 #1#) (|isDomain| *2 (|Factored| #5=(|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))) (|isDomain| *1 (|TwoFactorize| *4)) (|isDomain| *3 #5#))) (|generalTwoFactor| #3# #4#)) 
NIL 
(((|Type|) (|Category|)) (T |Type|)) 
NIL 
(|Join|) 
(((|Join|) . T)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 9 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|TypeAst|) (|SpadSyntaxCategory|)) (T |TypeAst|)) 
NIL 
((|userOrdered?| ((#1=(|Boolean|)) 18 T ELT)) (|setOrder| ((#2=(|Void|) #3=(|List| |#1|) #3#) 22 T ELT) ((#2# #3#) 23 T ELT)) (|more?| ((#1# |#1| |#1|) 37 #4=(|has| |#1| (|OrderedSet|)) ELT)) (|less?| ((#1# |#1| |#1| #5=(|Mapping| #1# |#1| |#1|)) 29 T ELT) (((|Union| #1# "failed") |#1| |#1|) 27 T ELT)) (|largest| ((|#1| #3#) 38 #4# ELT) ((|#1| #3# #5#) 32 T ELT)) (|getOrder| (((|Record| (|:| |low| #3#) (|:| |high| #3#))) 20 T ELT))) 
(((|UserDefinedPartialOrdering| |#1|) (CATEGORY |package| (SIGNATURE |setOrder| (#1=(|Void|) #2=(|List| |#1|))) (SIGNATURE |setOrder| (#1# #2# #2#)) (SIGNATURE |getOrder| ((|Record| (|:| |low| #2#) (|:| |high| #2#)))) (SIGNATURE |less?| ((|Union| #3=(|Boolean|) "failed") |#1| |#1|)) (SIGNATURE |less?| (#3# |#1| |#1| #4=(|Mapping| #3# |#1| |#1|))) (SIGNATURE |largest| (|#1| #2# #4#)) (SIGNATURE |userOrdered?| (#3#)) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |largest| (|#1| #2#)) (SIGNATURE |more?| (#3# |#1| |#1|))) |%noBranch|)) (|SetCategory|)) (T |UserDefinedPartialOrdering|)) 
((|more?| #1=(*1 *2 *3 *3) (AND #2=(|isDomain| *2 #3=(|Boolean|)) #4=(|isDomain| *1 (|UserDefinedPartialOrdering| *3)) (|ofCategory| *3 #5=(|OrderedSet|)) #6=(|ofCategory| *3 #7=(|SetCategory|)))) (|largest| #8=(*1 *2 *3) (AND #9=(|isDomain| *3 (|List| *2)) #10=(|ofCategory| *2 #7#) (|ofCategory| *2 #5#) #11=(|isDomain| *1 (|UserDefinedPartialOrdering| *2)))) (|userOrdered?| #12=(*1 *2) (AND #2# #4# #6#)) (|largest| (*1 *2 *3 *4) (AND #9# (|isDomain| *4 (|Mapping| #3# *2 *2)) #11# #10#)) (|less?| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|Mapping| #3# *3 *3)) #6# #2# #4#)) (|less?| #1# (|partial| AND #2# #4# #6#)) (|getOrder| #12# (AND (|isDomain| *2 (|Record| (|:| |low| #13=(|List| *3)) (|:| |high| #13#))) #4# #6#)) (|setOrder| #1# #14=(AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #7#) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|UserDefinedPartialOrdering| *4)))) (|setOrder| #8# #14#)) 
((|setVariableOrder| ((#1=(|Void|) #2=(|List| (|Symbol|)) #2#) 14 T ELT) ((#1# #2#) 12 T ELT)) (|resetVariableOrder| ((#1#) 16 T ELT)) (|getVariableOrder| (((|Record| (|:| |high| #2#) (|:| |low| #2#))) 20 T ELT))) 
(((|UserDefinedVariableOrdering|) (CATEGORY |package| (SIGNATURE |setVariableOrder| (#1=(|Void|) #2=(|List| (|Symbol|)))) (SIGNATURE |setVariableOrder| (#1# #2# #2#)) (SIGNATURE |getVariableOrder| ((|Record| (|:| |high| #2#) (|:| |low| #2#)))) (SIGNATURE |resetVariableOrder| (#1#)))) (T |UserDefinedVariableOrdering|)) 
((|resetVariableOrder| #1=(*1 *2) (AND #2=(|isDomain| *2 (|Void|)) #3=(|isDomain| *1 (|UserDefinedVariableOrdering|)))) (|getVariableOrder| #1# (AND (|isDomain| *2 (|Record| (|:| |high| #4=(|List| (|Symbol|))) (|:| |low| #4#))) #3#)) (|setVariableOrder| (*1 *2 *3 *3) #5=(AND (|isDomain| *3 #4#) #2# #3#)) (|setVariableOrder| (*1 *2 *3) #5#)) 
((|squareFreePart| (($ $) 17 T ELT)) (|prime?| (((|Boolean|) $) 27 T ELT))) 
(((|UniqueFactorizationDomain&| |#1|) (CATEGORY |package| (SIGNATURE |squareFreePart| (|#1| |#1|)) (SIGNATURE |prime?| ((|Boolean|) |#1|))) (|UniqueFactorizationDomain|)) (T |UniqueFactorizationDomain&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 66 T ELT)) (|squareFree| (((|Factored| $) $) 67 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|prime?| (((|Boolean|) $) 68 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (#5=($ $ $) 60 T ELT) (#6=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 58 T ELT)) (|gcd| (#5# 62 T ELT) (#6# 61 T ELT)) (|factor| (((|Factored| $) $) 65 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) 
(((|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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (($ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|bitior| #4#) (|bitand| #4#) (|before?| #1#) (|\\/| #4#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (|/\\| #4#)) 
(((|UInt16|) (|Join| (|OrderedFinite|) (|Logic|) (CATEGORY |domain| (SIGNATURE |bitand| #1=($ $ $)) (SIGNATURE |bitior| #1#) (SIGNATURE |sample| ($) |constant|)))) (T |UInt16|)) 
((|bitand| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|UInt16|))) (|bitior| #1# #2#) (|sample| (*1 *1) #2#)) 
((|NonNegativeInteger|) (|%not| (|%ilt| 16 (|%ilength| |#1|)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (($ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|bitior| #4#) (|bitand| #4#) (|before?| #1#) (|\\/| #4#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (|/\\| #4#)) 
(((|UInt32|) (|Join| (|OrderedFinite|) (|Logic|) (CATEGORY |domain| (SIGNATURE |bitand| #1=($ $ $)) (SIGNATURE |bitior| #1#) (SIGNATURE |sample| ($) |constant|)))) (T |UInt32|)) 
((|bitand| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|UInt32|))) (|bitior| #1# #2#) (|sample| (*1 *1) #2#)) 
((|NonNegativeInteger|) (|%not| (|%ilt| 32 (|%ilength| |#1|)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (($ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|bitior| #4#) (|bitand| #4#) (|before?| #1#) (|\\/| #4#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (|/\\| #4#)) 
(((|UInt64|) (|Join| (|OrderedFinite|) (|Logic|) (CATEGORY |domain| (SIGNATURE |bitand| #1=($ $ $)) (SIGNATURE |bitior| #1#) (SIGNATURE |sample| ($) |constant|)))) (T |UInt64|)) 
((|bitand| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|UInt64|))) (|bitior| #1# #2#) (|sample| (*1 *1) #2#)) 
((|NonNegativeInteger|) (|%not| (|%ilt| 64 (|%ilength| |#1|)))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (($ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|bitior| #4#) (|bitand| #4#) (|before?| #1#) (|\\/| #4#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (|/\\| #4#)) 
(((|UInt8|) (|Join| (|OrderedFinite|) (|Logic|) (CATEGORY |domain| (SIGNATURE |bitand| #1=($ $ $)) (SIGNATURE |bitior| #1#) (SIGNATURE |sample| ($) |constant|)))) (T |UInt8|)) 
((|bitand| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|UInt8|))) (|bitior| #1# #2#) (|sample| (*1 *1) #2#)) 
((|NonNegativeInteger|) (|%not| (|%ilt| 8 (|%ilength| |#1|)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|UnivariateTaylorSeries| |#1| |#2| |#3|) $) NIL #8=(AND (|has| #7# (|EuclideanDomain|)) #9=(|has| |#1| (|Field|))) ELT)) (|variables| ((#10=(|List| #11=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| (#12=(#13=(|Symbol|) $) 10 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(OR #15=(AND (|has| #7# (|OrderedIntegralDomain|)) #9#) #16=(AND #17=(|has| #7# (|PolynomialFactorizationExplicit|)) #9#) #18=(|has| |#1| (|IntegralDomain|))) ELT)) (|unitCanonical| #19=(#20=($ $) NIL #14# ELT)) (|unit?| (#5# NIL #14# ELT)) (|truncate| #21=(#22=($ $ #23=(|Integer|)) NIL T ELT) (($ $ #23# #23#) NIL T ELT)) (|terms| ((#24=(|Stream| (|Record| (|:| |k| #23#) (|:| |c| |#1|))) $) NIL T ELT)) (|taylorRep| #25=(#6# NIL T ELT)) (|taylorIfCan| #26=(((|Union| #7# #27="failed") $) NIL T ELT)) (|taylor| #25#) (|tanh| #28=(#20# NIL #29=(|has| |#1| (|Algebra| #30=(|Fraction| #23#))) ELT)) (|tan| #28#) (|subtractIfCan| (#31=(#32=(|Union| $ #27#) $ $) NIL T ELT)) (|squareFreePolynomial| #33=(((|Factored| #34=(|SparseUnivariatePolynomial| $)) #34#) NIL #16# ELT)) (|squareFreePart| #35=(#20# NIL #9# ELT)) (|squareFree| #36=(((|Factored| $) $) NIL #9# ELT)) (|sqrt| #28#) (|solveLinearPolynomialEquation| (((|Union| #37=(|List| #34#) #27#) #37# #34#) NIL #16# ELT)) (|sizeLess?| (#2# NIL #9# ELT)) (|sinh| #28#) (|sin| #28#) (|sign| (#38=(#23# $) NIL #15# ELT)) (|series| (($ #24#) NIL T ELT)) (|sech| #28#) (|sec| #28#) (|sample| (#39=($) NIL T CONST)) (|retractIfCan| #26# (((|Union| #13# . #40=(#27#)) . #41=($)) NIL #42=(AND (|has| #7# (|RetractableTo| #13#)) #9#) ELT) (((|Union| #30# . #40#) . #41#) NIL #43=(AND (|has| #7# (|RetractableTo| #23#)) #9#) ELT) (((|Union| #23# . #40#) . #41#) NIL #43# ELT)) (|retract| #25# (#12# NIL #42# ELT) ((#30# $) NIL #43# ELT) (#38# NIL #43# ELT)) (|removeZeroes| #44=(#20# NIL T ELT) #45=(($ #23# $) NIL T ELT)) (|rem| #46=(#47=($ $ $) NIL #9# ELT)) (|reductum| #44#) (|reducedSystem| ((#48=(|Matrix| #7#) . #49=(#50=(|Matrix| $))) NIL #9# ELT) ((#51=(|Record| (|:| |mat| #48#) (|:| |vec| (|Vector| #7#))) . #52=(#50# #53=(|Vector| $))) NIL #9# ELT) ((#54=(|Record| (|:| |mat| #55=(|Matrix| #23#)) (|:| |vec| (|Vector| #23#))) . #52#) NIL #56=(AND (|has| #7# (|LinearlyExplicitRingOver| #23#)) #9#) ELT) ((#55# . #49#) NIL #56# ELT)) (|recip| ((#32# $) NIL T ELT)) (|rationalFunction| ((#57=(|Fraction| (|Polynomial| |#1|)) $ #23#) NIL #18# ELT) ((#57# $ #23# #23#) NIL #18# ELT)) (|random| (#39# NIL #58=(AND (|has| #7# (|IntegerNumberSystem|)) #9#) ELT)) (|quo| #46#) (|principalIdeal| (((|Record| (|:| |coef| #59=(|List| $)) #60=(|:| |generator| $)) #59#) NIL #9# ELT)) (|prime?| (#5# NIL #9# ELT)) (|positive?| #61=(#5# NIL #15# ELT)) (|pole?| #4#) (|pi| (#39# NIL #29# ELT)) (|patternMatch| ((#62=(|PatternMatchResult| #63=(|Float|) . #64=($)) $ #65=(|Pattern| #63#) #62#) NIL (AND (|has| #7# (|PatternMatchable| #63#)) #9#) ELT) ((#66=(|PatternMatchResult| #23# . #64#) $ #67=(|Pattern| #23#) #66#) NIL (AND (|has| #7# (|PatternMatchable| #23#)) #9#) ELT)) (|order| #68=(#38# NIL T ELT) ((#23# $ #23#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #35#) (|numer| #69=(#6# NIL #9# ELT)) (|nthRoot| (#22# NIL #29# ELT)) (|nextItem| (#70=((|Maybe| $) $) NIL #71=(AND (|has| #7# (|StepThrough|)) #9#) ELT)) (|negative?| #61#) (|multiplyExponents| #72=(($ $ #73=(|PositiveInteger|)) NIL T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #23#) $) NIL T ELT)) (|multiEuclidean| (((|Union| #59# #27#) #59# $) NIL #9# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #23#) 18 T ELT) (($ $ #11# #23#) NIL T ELT) (($ $ #10# (|List| #23#)) NIL T ELT)) (|min| #74=(#47# NIL #75=(OR #15# (AND (|has| #7# (|OrderedSet|)) #9#)) ELT)) (|max| #74#) (|map| (($ (|Mapping| |#1| |#1|) . #76=($)) NIL T ELT) (($ #77=(|Mapping| #7# #7#) . #76#) NIL #9# ELT)) (|log| #28#) (|leftReducedSystem| ((#48# . #78=(#53#)) NIL #9# ELT) ((#51# . #79=(#53# $)) NIL #9# ELT) ((#54# . #79#) NIL #56# ELT) ((#55# . #78#) NIL #56# ELT)) (|leadingMonomial| #44#) (|leadingCoefficient| (#80=(|#1| $) NIL T ELT)) (|lcm| #81=(($ #59#) NIL #9# ELT) #46#) (|laurent| (($ #23# #7#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #35#) (|integrate| (#20# 27 #29# ELT) (#82=($ $ #13#) NIL (OR (AND #29# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #23#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #29# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #13#))) (|has| |#1| (SIGNATURE |variables| (#83=(|List| #13#) |#1|))))) ELT) (#84=($ $ #85=(|Variable| |#2|)) 28 #29# ELT)) (|init| (#39# NIL #71# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#34# #34# #34#) NIL #9# ELT)) (|gcd| #81# #46#) (|fractionPart| (#20# NIL #8# ELT)) (|floor| #86=(#6# NIL #58# ELT)) (|factorSquareFreePolynomial| #33#) (|factorPolynomial| #33#) (|factor| #36#) (|extendedEuclidean| (((|Union| (|Record| #87=(|:| |coef1| $) #88=(|:| |coef2| $)) #27#) $ $ $) NIL #9# ELT) (((|Record| #87# #88# #60#) $ $) NIL #9# ELT)) (|extend| #21#) (|exquo| (#31# NIL #14# ELT)) (|expressIdealMember| (((|Maybe| #59#) #59# $) NIL #9# ELT)) (|exp| #28#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #89=(|has| |#1| (SIGNATURE ** (|#1| |#1| #23#))) ELT) (($ $ #13# #7#) NIL #90=(AND (|has| #7# (|InnerEvalable| #13# #7#)) #9#) ELT) (($ $ #83# #91=(|List| #7#)) NIL #90# ELT) (($ $ (|List| #92=(|Equation| #7#))) NIL #93=(AND (|has| #7# (|Evalable| #7#)) #9#) ELT) (($ $ #92#) NIL #93# ELT) (($ $ #7# #7#) NIL #93# ELT) (($ $ #91# #91#) NIL #93# ELT)) (|euclideanSize| ((#94=(|NonNegativeInteger|) $) NIL #9# ELT)) (|elt| #95=(#96=(|#1| $ #23#) NIL T ELT) (#47# NIL (|has| #23# (|SemiGroup|)) ELT) (#97=($ $ #7#) NIL (AND (|has| #7# (|Eltable| #7# #7#)) #9#) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|differentiate| #98=(($ $ #77# #94#) NIL #9# ELT) #99=(($ $ #77#) NIL #9# ELT) (#84# 26 T ELT) (#20# 25 #100=(OR (AND (|has| #7# (|DifferentialRing|)) #9#) (AND (|has| #7# (|DifferentialSpace|)) #9#) #101=(|has| |#1| (SIGNATURE * (|#1| #23# |#1|)))) ELT) #102=(#103=($ $ #94#) NIL #100# ELT) #104=(#82# NIL #105=(OR (AND (|has| #7# #106=(|PartialDifferentialRing| #13#)) #9#) (AND (|has| #7# (|PartialDifferentialSpace| #13#)) #9#) (AND (|has| |#1| #106#) #101#)) ELT) #107=(($ $ #83#) NIL #105# ELT) #108=(($ $ #13# #94#) NIL #105# ELT) #109=(($ $ #83# (|List| #94#)) NIL #105# ELT)) (|denominator| #35#) (|denom| #69#) (|degree| #68#) (|csch| #28#) (|csc| #28#) (|coth| #28#) (|cot| #28#) (|cosh| #28#) (|cos| #28#) (|convert| ((#110=(|InputForm|) . #111=($)) NIL (AND (|has| #7# (|ConvertibleTo| #110#)) #9#) ELT) ((#63# . #111#) NIL #112=(AND (|has| #7# (|RealConstant|)) #9#) ELT) (((|DoubleFloat|) . #111#) NIL #112# ELT) ((#65# . #111#) NIL (AND (|has| #7# (|ConvertibleTo| #65#)) #9#) ELT) ((#67# . #111#) NIL (AND (|has| #7# (|ConvertibleTo| #67#)) #9#) ELT)) (|conditionP| (((|Union| #53# #27#) #50#) NIL #113=(AND (|has| $ #114=(|CharacteristicNonZero|)) #17# #9#) ELT)) (|complete| #44#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #23#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #7#) NIL T ELT) (($ #85#) 24 T ELT) (($ #13#) NIL #42# ELT) #19# (($ #30#) NIL (OR #43# #29#) ELT)) (|coefficient| #95#) (|charthRoot| (#70# NIL (OR #113# (AND (|has| #7# #114#) #9#) (|has| |#1| #114#)) ELT)) (|characteristic| ((#94#) NIL T CONST)) (|center| (#80# 11 T ELT)) (|ceiling| #86#) (|before?| #1#) (|atanh| #28#) (|atan| #28#) (|associates?| (#2# NIL #14# ELT)) (|asinh| #28#) (|asin| #28#) (|asech| #28#) (|asec| #28#) (|approximate| (#96# NIL (AND #89# (|has| |#1| (SIGNATURE |coerce| (|#1| #13#)))) ELT)) (|annihilate?| #1#) (|acsch| #28#) (|acsc| #28#) (|acoth| #28#) (|acot| #28#) (|acosh| #28#) (|acos| #28#) (|abs| (#20# NIL #15# ELT)) (|Zero| (#39# 20 T CONST)) (|One| (#39# 15 T CONST)) (D #98# #99# (#84# NIL T ELT) (#20# NIL #100# ELT) #102# #104# #107# #108# #109#) (>= #115=(#2# NIL #75# ELT)) (> #115#) (= #1#) (<= #115#) (< #115#) (/ (#116=($ $ |#1|) NIL #9# ELT) #46# (($ #7# #7#) NIL #9# ELT)) (- #44# #117=(#47# NIL T ELT)) (+ (#47# 22 T ELT)) (** #72# (#103# NIL T ELT) (#22# NIL #9# ELT) (#47# NIL #29# ELT) #118=(($ $ #30#) NIL #29# ELT)) (* (($ #73# $) NIL T ELT) (($ #94# $) NIL T ELT) #45# #117# (#116# NIL T ELT) (($ |#1| . #119=($)) NIL T ELT) (#97# NIL #9# ELT) (($ #7# . #119#) NIL #9# ELT) (($ #30# . #119#) NIL #29# ELT) #118#)) 
(((|UnivariateLaurentSeries| |#1| |#2| |#3|) (|Join| (|UnivariateLaurentSeriesConstructorCategory| |#1| (|UnivariateTaylorSeries| |#1| |#2| |#3|)) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1#)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |UnivariateLaurentSeries|)) 
((|coerce| (*1 *1 *2) (AND #1=(|isDomain| *2 (|Variable| *4)) #2=(|ofType| *4 (|Symbol|)) #3=(|isDomain| *1 (|UnivariateLaurentSeries| *3 *4 *5)) #4=(|ofCategory| *3 (|Ring|)) #5=(|ofType| *5 *3))) (|integrate| (*1 *1 *1 *2) (AND #1# #2# #3# (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) #4# #5#))) 
((|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) 23 T ELT))) 
(((|UnivariateLaurentSeriesFunctions2| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| ((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)))) #1=(|Ring|) #1# #2=(|Symbol|) #2# |#1| |#2|) (T |UnivariateLaurentSeriesFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|UnivariateLaurentSeries| *5 *7 *9)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofType| *7 #2=(|Symbol|)) (|ofType| *9 *5) (|ofType| *10 *6) (|isDomain| *2 (|UnivariateLaurentSeries| *6 *8 *10)) (|isDomain| *1 (|UnivariateLaurentSeriesFunctions2| *5 *6 *7 *8 *9 *10)) (|ofType| *8 #2#)))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| ((#4=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 75 (|has| |#1| . #5#) ELT)) (|truncate| (($ $ #7=(|Integer|)) 125 T ELT) (($ $ #7# #7#) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| #7#) (|:| |c| |#1|))) $) 131 T ELT)) (|tanh| (#8=($ $) 164 (|has| |#1| . #9=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|tan| (#10=($ $) 147 (|has| |#1| . #9#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 191 (|has| |#1| . #11=((|Field|))) ELT)) (|squareFree| (#12=((|Factored| $) $) 192 (|has| |#1| . #11#) ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #13=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|sizeLess?| (((|Boolean|) $ $) 182 (|has| |#1| . #11#) ELT)) (|sinh| (#8# 163 (|has| |#1| . #9#) ELT)) (|sin| (#10# 148 (|has| |#1| . #9#) ELT)) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) 202 T ELT)) (|sech| (#8# 162 (|has| |#1| . #9#) ELT)) (|sec| (#10# 149 (|has| |#1| . #9#) ELT)) (|sample| (#14=($) 23 T CONST)) (|rem| (#15=($ $ $) 186 (|has| |#1| . #11#) ELT)) (|reductum| (#16=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) 200 (|has| |#1| (|IntegralDomain|)) ELT) (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) 199 (|has| |#1| (|IntegralDomain|)) ELT)) (|quo| (#15# 185 (|has| |#1| . #11#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #17=(|List| $)) (|:| |generator| $)) #17#) 180 (|has| |#1| . #11#) ELT)) (|prime?| (((|Boolean|) $) 193 (|has| |#1| . #11#) ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|pi| (($) 174 (|has| |#1| . #9#) ELT)) (|order| ((#7# $) 127 T ELT) ((#7# $ #7#) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #18=(|Integer|)) 145 (|has| |#1| . #13#) ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) 201 T ELT)) (|multiEuclidean| (((|Union| #19=(|List| $) #20="failed") #19# $) 189 (|has| |#1| . #11#) ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| #7#) 82 T ELT) (($ $ #3# #7#) 98 T ELT) (($ $ (|List| #3#) (|List| #7#)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|log| (#21=($ $) 171 (|has| |#1| . #9#) ELT)) (|leadingMonomial| (#16# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|lcm| (#22=($ (|List| $)) 178 (|has| |#1| . #11#) ELT) (#23=($ $ $) 177 (|has| |#1| . #11#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 194 (|has| |#1| . #11#) ELT)) (|integrate| (($ $) 198 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT) (($ $ (|Symbol|)) 197 (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|)))))) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#24=(|SparseUnivariatePolynomial| $) #24# #24#) 179 (|has| |#1| . #11#) ELT)) (|gcd| (#22# 176 (|has| |#1| . #11#) ELT) (#23# 175 (|has| |#1| . #11#) ELT)) (|factor| (#12# 190 (|has| |#1| . #11#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #25=(|:| |coef1| $) #26=(|:| |coef2| $)) #20#) $ $ $) 188 (|has| |#1| . #11#) ELT) (((|Record| #25# #26# (|:| |generator| $)) $ $) 187 (|has| |#1| . #11#) ELT)) (|extend| (($ $ #7#) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #5#) ELT)) (|expressIdealMember| (((|Maybe| #17#) #17# $) 181 (|has| |#1| . #11#) ELT)) (|exp| (#21# 172 (|has| |#1| . #9#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 183 (|has| |#1| . #11#) ELT)) (|elt| ((|#1| $ #7#) 132 T ELT) (($ $ $) 108 (|has| #7# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 184 (|has| |#1| . #11#) ELT)) (|differentiate| (($ $ #4#) 120 (AND (|has| |#1| . #27=((|PartialDifferentialRing| #4#))) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#)) 118 (AND (|has| |#1| . #27#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #4# . #28=(#29=(|NonNegativeInteger|))) 117 (AND (|has| |#1| . #27#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#) . #30=((|List| #29#))) 116 (AND (|has| |#1| . #27#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #31=($)) 112 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#32=($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (|degree| ((#7# $) 84 T ELT)) (|csch| (#8# 161 (|has| |#1| . #9#) ELT)) (|csc| (#10# 150 (|has| |#1| . #9#) ELT)) (|coth| (#8# 160 (|has| |#1| . #9#) ELT)) (|cot| (#10# 151 (|has| |#1| . #9#) ELT)) (|cosh| (#8# 159 (|has| |#1| . #9#) ELT)) (|cos| (#10# 152 (|has| |#1| . #9#) ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT) (($ #33=(|Fraction| #34=(|Integer|))) 78 (|has| |#1| . #35=((|Algebra| (|Fraction| (|Integer|))))) ELT) (($ $) 70 (|has| |#1| . #5#) ELT)) (|coefficient| ((|#1| $ #7#) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|before?| (#1# 6 T ELT)) (|atanh| (#36=($ $) 170 (|has| |#1| . #9#) ELT)) (|atan| (#37=($ $) 158 (|has| |#1| . #9#) ELT)) (|associates?| ((#6# $ $) 74 (|has| |#1| . #5#) ELT)) (|asinh| (#36# 169 (|has| |#1| . #9#) ELT)) (|asin| (#37# 157 (|has| |#1| . #9#) ELT)) (|asech| (#36# 168 (|has| |#1| . #9#) ELT)) (|asec| (#37# 156 (|has| |#1| . #9#) ELT)) (|approximate| ((|#1| $ #7#) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |coerce| (|#1| #4#)))) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#36# 167 (|has| |#1| . #9#) ELT)) (|acsc| (#37# 155 (|has| |#1| . #9#) ELT)) (|acoth| (#36# 166 (|has| |#1| . #9#) ELT)) (|acot| (#37# 154 (|has| |#1| . #9#) ELT)) (|acosh| (#36# 165 (|has| |#1| . #9#) ELT)) (|acos| (#37# 153 (|has| |#1| . #9#) ELT)) (|Zero| (#14# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ #4#) 119 (AND (|has| |#1| . #27#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#)) 115 (AND (|has| |#1| . #27#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #4# . #28#) 114 (AND (|has| |#1| . #27#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#) . #30#) 113 (AND (|has| |#1| . #27#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #31#) 111 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#32# 109 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT) (($ $ $) 196 (|has| |#1| . #11#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #34#) 195 (|has| |#1| . #11#) ELT) (($ $ $) 173 (|has| |#1| . #9#) ELT) (($ $ (|Fraction| #18#)) 144 (|has| |#1| . #13#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #38=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #38#) 88 T ELT) (($ #33# . #38#) 77 (|has| |#1| . #35#) ELT) (($ $ #33#) 76 (|has| |#1| . #35#) ELT))) 
(((|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 #1=(|isDomain| *2 (|Symbol|)) #2=(|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3)) #3=(|ofCategory| *3 (|Ring|)) (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|ofCategory| *3 (|PrimitiveFunctionCategory|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))) (AND #1# #2# #3# (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| #1=(|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|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| #2# #2#) 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|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) |has| (|Integer|) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Module| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) 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) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) 
((|zero?| (((|Boolean|) $) 12 T ELT)) (|retractIfCan| (((|Union| |#3| #1="failed") $) 17 T ELT) (((|Union| #2=(|Symbol|) #1#) $) NIL T ELT) (((|Union| #3=(|Fraction| #4=(|Integer|)) #1#) $) NIL T ELT) (((|Union| #4# #1#) $) NIL T ELT)) (|retract| ((|#3| $) 14 T ELT) ((#2# $) NIL T ELT) ((#3# $) NIL T ELT) ((#4# $) NIL T ELT))) 
(((|UnivariateLaurentSeriesConstructorCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |retractIfCan| ((|Union| #1=(|Integer|) #2="failed") |#1|)) (SIGNATURE |retract| (#1# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #3=(|Fraction| #1#) #2#) |#1|)) (SIGNATURE |retract| (#3# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #4=(|Symbol|) #2#) |#1|)) (SIGNATURE |retract| (#4# |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#3| #2#) |#1|)) (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|))) (|UnivariateLaurentSeriesConstructorCategory| |#2| |#3|) (|Ring|) (|UnivariateTaylorSeriesCategory| |#2|)) (T |UnivariateLaurentSeriesConstructorCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|wholePart| ((|#2| . #3=($)) 267 (|and| (|has| |#2| . #4=((|EuclideanDomain|))) (|has| |#1| . #5=((|Field|)))) ELT)) (|variables| (((|List| #6=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| ((#7=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #8=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #8#) ELT)) (|unit?| ((#9=(|Boolean|) $) 75 (|has| |#1| . #8#) ELT)) (|truncate| (($ $ #10=(|Integer|)) 125 T ELT) (($ $ #10# #10#) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| #10#) (|:| |c| |#1|))) $) 131 T ELT)) (|taylorRep| ((|#2| $) 303 T ELT)) (|taylorIfCan| (((|Union| |#2| "failed") $) 299 T ELT)) (|taylor| ((|#2| $) 300 T ELT)) (|tanh| (#11=($ $) 164 (|has| |#1| . #12=((|Algebra| (|Fraction| #10#)))) ELT)) (|tan| (#13=($ $) 147 (|has| |#1| . #12#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (#14=((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) 276 (|and| (|has| |#2| . #16=((|PolynomialFactorizationExplicit|))) (|has| |#1| . #5#)) ELT)) (|squareFreePart| (($ $) 191 (|has| |#1| . #17=((|Field|))) ELT)) (|squareFree| (#18=((|Factored| $) $) 192 (|has| |#1| . #17#) ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #12#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #19=(|List| #15#) #20="failed") #19# #15#) 273 (|and| (|has| |#2| . #16#) (|has| |#1| . #5#)) ELT)) (|sizeLess?| (((|Boolean|) $ $) 182 (|has| |#1| . #17#) ELT)) (|sinh| (#11# 163 (|has| |#1| . #12#) ELT)) (|sin| (#13# 148 (|has| |#1| . #12#) ELT)) (|sign| (((|Integer|) $) 285 (|and| (|has| |#2| . #21=((|OrderedIntegralDomain|))) (|has| |#1| . #5#)) ELT)) (|series| (($ (|Stream| (|Record| (|:| |k| #10#) (|:| |c| |#1|)))) 202 T ELT)) (|sech| (#11# 162 (|has| |#1| . #12#) ELT)) (|sec| (#13# 149 (|has| |#1| . #12#) ELT)) (|sample| (#22=($) 23 T CONST)) (|retractIfCan| (((|Union| |#2| . #23=("failed")) . #24=($)) 306 T ELT) (((|Union| #25=(|Integer|) . #23#) . #24#) 296 (|and| (|has| |#2| . #26=((|RetractableTo| #25#))) (|has| |#1| . #5#)) ELT) (((|Union| #27=(|Fraction| #25#) . #23#) . #24#) 294 (|and| (|has| |#2| . #26#) (|has| |#1| . #5#)) ELT) (((|Union| #28=(|Symbol|) . #23#) . #24#) 278 (|and| (|has| |#2| . #29=((|RetractableTo| #28#))) (|has| |#1| . #5#)) ELT)) (|retract| ((|#2| . #30=($)) 307 T ELT) ((#25# . #30#) 295 (|and| (|has| |#2| . #26#) (|has| |#1| . #5#)) ELT) ((#27# . #30#) 293 (|and| (|has| |#2| . #26#) (|has| |#1| . #5#)) ELT) ((#28# . #30#) 277 (|and| (|has| |#2| . #29#) (|has| |#1| . #5#)) ELT)) (|removeZeroes| (($ $) 302 T ELT) (($ (|Integer|) $) 301 T ELT)) (|rem| (#31=($ $ $) 186 (|has| |#1| . #17#) ELT)) (|reductum| (#32=($ $) 81 T ELT)) (|reducedSystem| (((|Matrix| |#2|) . #33=(#34=(|Matrix| $))) 255 (|has| |#1| . #5#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #35=(#34# #36=(|Vector| $))) 254 (|has| |#1| . #5#) ELT) (((|Record| (|:| |mat| (|Matrix| #37=(|Integer|))) (|:| |vec| (|Vector| #37#))) . #35#) 253 (|and| (|has| |#2| . #38=((|LinearlyExplicitRingOver| #37#))) (|has| |#1| . #5#)) ELT) (((|Matrix| #37#) . #33#) 252 (|and| (|has| |#2| . #38#) (|has| |#1| . #5#)) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ #10#) 200 (|has| |#1| . #39=((|IntegralDomain|))) ELT) (((|Fraction| (|Polynomial| |#1|)) $ #10# #10#) 199 (|has| |#1| . #39#) ELT)) (|random| (($) 269 (|and| (|has| |#2| . #40=((|IntegerNumberSystem|))) (|has| |#1| . #5#)) ELT)) (|quo| (#31# 185 (|has| |#1| . #17#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) (|:| |generator| $)) #41#) 180 (|has| |#1| . #17#) ELT)) (|prime?| (((|Boolean|) $) 193 (|has| |#1| . #17#) ELT)) (|positive?| (((|Boolean|) $) 283 (|and| (|has| |#2| . #21#) (|has| |#1| . #5#)) ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|pi| (($) 174 (|has| |#1| . #12#) ELT)) (|patternMatch| (((|PatternMatchResult| #42=(|Float|) . #43=($)) $ (|Pattern| #42#) (|PatternMatchResult| #42# . #43#)) 261 (|and| (|has| |#2| (|PatternMatchable| #42#)) (|has| |#1| . #5#)) ELT) (((|PatternMatchResult| #44=(|Integer|) . #43#) $ (|Pattern| #44#) (|PatternMatchResult| #44# . #43#)) 260 (|and| (|has| |#2| (|PatternMatchable| #44#)) (|has| |#1| . #5#)) ELT)) (|order| ((#10# $) 127 T ELT) ((#10# $ #10#) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numerator| (#45=($ $) 265 (|has| |#1| . #5#) ELT)) (|numer| ((|#2| . #3#) 263 (|has| |#1| . #5#) ELT)) (|nthRoot| (($ $ #46=(|Integer|)) 145 (|has| |#1| . #12#) ELT)) (|nextItem| (((|Maybe| $) $) 297 (|and| (|has| |#2| . #47=((|StepThrough|))) (|has| |#1| . #5#)) ELT)) (|negative?| (((|Boolean|) $) 284 (|and| (|has| |#2| . #21#) (|has| |#1| . #5#)) ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #10#) $) 201 T ELT)) (|multiEuclidean| (((|Union| #48=(|List| $) #49="failed") #48# $) 189 (|has| |#1| . #17#) ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| #10#) 82 T ELT) (($ $ #6# #10#) 98 T ELT) (($ $ (|List| #6#) (|List| #10#)) 97 T ELT)) (|min| (#50=($ $ $) 292 (|and| (|has| |#2| . #51=((|OrderedSet|))) (|has| |#1| . #5#)) ELT)) (|max| (#50# 291 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (|map| (($ (|Mapping| |#1| |#1|) . #52=($)) 87 T ELT) (($ (|Mapping| |#2| |#2|) . #52#) 245 (|has| |#1| . #5#) ELT)) (|log| (#53=($ $) 171 (|has| |#1| . #12#) ELT)) (|leftReducedSystem| (((|Matrix| |#2|) . #54=(#36#)) 257 (|has| |#1| . #5#) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #55=(#36# $)) 256 (|has| |#1| . #5#) ELT) (((|Record| (|:| |mat| (|Matrix| #37#)) (|:| |vec| (|Vector| #37#))) . #55#) 251 (|and| (|has| |#2| . #38#) (|has| |#1| . #5#)) ELT) (((|Matrix| #37#) . #54#) 250 (|and| (|has| |#2| . #38#) (|has| |#1| . #5#)) ELT)) (|leadingMonomial| (#32# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|lcm| (#56=($ (|List| $)) 178 (|has| |#1| . #17#) ELT) (#57=($ $ $) 177 (|has| |#1| . #17#) ELT)) (|laurent| (($ (|Integer|) |#2|) 304 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 194 (|has| |#1| . #17#) ELT)) (|integrate| (($ $) 198 (|has| |#1| . #12#) ELT) (($ $ #58=(|Symbol|)) 197 (OR (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #10#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)) (|has| |#1| . #12#)) (AND (|has| |#1| (SIGNATURE |variables| ((|List| #58#) |#1|))) (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #58#))) (|has| |#1| . #12#))) ELT)) (|init| (($) 298 (|and| (|has| |#2| . #47#) (|has| |#1| . #5#)) CONST)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#59=(|SparseUnivariatePolynomial| $) #59# #59#) 179 (|has| |#1| . #17#) ELT)) (|gcd| (#56# 176 (|has| |#1| . #17#) ELT) (#57# 175 (|has| |#1| . #17#) ELT)) (|fractionPart| (#45# 268 (|and| (|has| |#2| . #4#) (|has| |#1| . #5#)) ELT)) (|floor| ((|#2| . #3#) 271 (|and| (|has| |#2| . #40#) (|has| |#1| . #5#)) ELT)) (|factorSquareFreePolynomial| (#14# 274 (|and| (|has| |#2| . #16#) (|has| |#1| . #5#)) ELT)) (|factorPolynomial| (#14# 275 (|and| (|has| |#2| . #16#) (|has| |#1| . #5#)) ELT)) (|factor| (#18# 190 (|has| |#1| . #17#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #60=(|:| |coef1| $) #61=(|:| |coef2| $)) #49#) $ $ $) 188 (|has| |#1| . #17#) ELT) (((|Record| #60# #61# (|:| |generator| $)) $ $) 187 (|has| |#1| . #17#) ELT)) (|extend| (($ $ #10#) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #8#) ELT)) (|expressIdealMember| (((|Maybe| #41#) #41# $) 181 (|has| |#1| . #17#) ELT)) (|exp| (#53# 172 (|has| |#1| . #12#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| #10#))) ELT) (($ $ #62=(|Symbol|) |#2|) 244 (|and| (|has| |#2| (|InnerEvalable| #62# |#2|)) (|has| |#1| . #5#)) ELT) (($ $ (|List| #62#) (|List| |#2|)) 243 (|and| (|has| |#2| (|InnerEvalable| #62# |#2|)) (|has| |#1| . #5#)) ELT) (($ $ (|List| (|Equation| |#2|))) 242 (|and| (|has| |#2| (|Evalable| |#2|)) (|has| |#1| . #5#)) ELT) (($ $ (|Equation| |#2|)) 241 (|and| (|has| |#2| (|Evalable| |#2|)) (|has| |#1| . #5#)) ELT) (($ $ |#2| |#2|) 240 (|and| (|has| |#2| (|Evalable| |#2|)) (|has| |#1| . #5#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 239 (|and| (|has| |#2| (|Evalable| |#2|)) (|has| |#1| . #5#)) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 183 (|has| |#1| . #17#) ELT)) (|elt| ((|#1| $ #10#) 132 T ELT) (($ $ $) 108 (|has| #10# (|SemiGroup|)) ELT) (($ $ |#2|) 238 (|and| (|has| |#2| (|Eltable| |#2| |#2|)) (|has| |#1| . #5#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 184 (|has| |#1| . #17#) ELT)) (|differentiate| (($ $ (|Mapping| |#2| |#2|) . #63=((|NonNegativeInteger|))) 247 (|has| |#1| . #5#) ELT) (($ $ (|Mapping| |#2| |#2|)) 246 (|has| |#1| . #5#) ELT) (($ . #64=($)) 112 (OR (|and| (|has| |#2| . #65=((|DifferentialSpace|))) (|has| |#1| . #5#)) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (#66=($ $ (|NonNegativeInteger|)) 110 (OR (|and| (|has| |#2| . #65#) (|has| |#1| . #5#)) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (($ $ #7#) 120 (OR (|and| (|has| |#2| . #67=((|PartialDifferentialSpace| (|Symbol|)))) (|has| |#1| . #5#)) (AND (|has| |#1| . #68=((|PartialDifferentialRing| #7#))) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#)) 118 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ #7# . #69=(#70=(|NonNegativeInteger|))) 117 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#) . #71=((|List| #70#))) 116 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT)) (|denominator| (#45# 266 (|has| |#1| . #5#) ELT)) (|denom| ((|#2| . #3#) 264 (|has| |#1| . #5#) ELT)) (|degree| ((#10# $) 84 T ELT)) (|csch| (#11# 161 (|has| |#1| . #12#) ELT)) (|csc| (#13# 150 (|has| |#1| . #12#) ELT)) (|coth| (#11# 160 (|has| |#1| . #12#) ELT)) (|cot| (#13# 151 (|has| |#1| . #12#) ELT)) (|cosh| (#11# 159 (|has| |#1| . #12#) ELT)) (|cos| (#13# 152 (|has| |#1| . #12#) ELT)) (|convert| (((|DoubleFloat|) . #72=($)) 282 (|and| (|has| |#2| . #73=((|RealConstant|))) (|has| |#1| . #5#)) ELT) (((|Float|) . #72#) 281 (|and| (|has| |#2| . #73#) (|has| |#1| . #5#)) ELT) ((#74=(|InputForm|) . #72#) 280 (|and| (|has| |#2| (|ConvertibleTo| #74#)) (|has| |#1| . #5#)) ELT) ((#75=(|Pattern| (|Float|)) . #72#) 259 (|and| (|has| |#2| (|ConvertibleTo| #75#)) (|has| |#1| . #5#)) ELT) ((#76=(|Pattern| (|Integer|)) . #72#) 258 (|and| (|has| |#2| (|ConvertibleTo| #76#)) (|has| |#1| . #5#)) ELT)) (|conditionP| (((|Union| (|Vector| $) #20#) (|Matrix| $)) 272 (|and| (|and| #77=(|has| $ (|CharacteristicNonZero|)) (|has| |#2| . #16#)) (|has| |#1| . #5#)) ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#2|) 305 T ELT) (($ #28#) 279 (|and| (|has| |#2| . #29#) (|has| |#1| . #5#)) ELT) (($ #78=(|Fraction| #79=(|Integer|))) 78 (|has| |#1| . #80=((|Algebra| (|Fraction| (|Integer|))))) ELT) (($ $) 70 (|has| |#1| . #8#) ELT)) (|coefficient| ((|#1| $ #10#) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (OR (|and| (OR (|has| |#2| (|CharacteristicNonZero|)) (|and| #77# (|has| |#2| . #16#))) (|has| |#1| . #5#)) (|has| |#1| (|CharacteristicNonZero|))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|ceiling| ((|#2| . #3#) 270 (|and| (|has| |#2| . #40#) (|has| |#1| . #5#)) ELT)) (|before?| (#1# 6 T ELT)) (|atanh| (#81=($ $) 170 (|has| |#1| . #12#) ELT)) (|atan| (#82=($ $) 158 (|has| |#1| . #12#) ELT)) (|associates?| ((#9# $ $) 74 (|has| |#1| . #8#) ELT)) (|asinh| (#81# 169 (|has| |#1| . #12#) ELT)) (|asin| (#82# 157 (|has| |#1| . #12#) ELT)) (|asech| (#81# 168 (|has| |#1| . #12#) ELT)) (|asec| (#82# 156 (|has| |#1| . #12#) ELT)) (|approximate| ((|#1| $ #10#) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| #10#))) (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#81# 167 (|has| |#1| . #12#) ELT)) (|acsc| (#82# 155 (|has| |#1| . #12#) ELT)) (|acoth| (#81# 166 (|has| |#1| . #12#) ELT)) (|acot| (#82# 154 (|has| |#1| . #12#) ELT)) (|acosh| (#81# 165 (|has| |#1| . #12#) ELT)) (|acos| (#82# 153 (|has| |#1| . #12#) ELT)) (|abs| (($ $) 286 (|and| (|has| |#2| . #21#) (|has| |#1| . #5#)) ELT)) (|Zero| (#22# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|Mapping| |#2| |#2|) . #63#) 249 (|has| |#1| . #5#) ELT) (($ $ (|Mapping| |#2| |#2|)) 248 (|has| |#1| . #5#) ELT) (($ . #64#) 111 (OR (|and| (|has| |#2| . #65#) (|has| |#1| . #5#)) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (#66# 109 (OR (|and| (|has| |#2| . #65#) (|has| |#1| . #5#)) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (($ $ #7#) 119 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#)) 115 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ #7# . #69#) 114 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#) . #71#) 113 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT)) (>= (#83=((|Boolean|) $ $) 290 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (> (#83# 288 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (= (#1# 8 T ELT)) (<= (#83# 289 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (< (#83# 287 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT) (($ $ $) 196 (|has| |#1| . #17#) ELT) (($ |#2| |#2|) 262 (|has| |#1| . #5#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #79#) 195 (|has| |#1| . #17#) ELT) (($ $ $) 173 (|has| |#1| . #12#) ELT) (($ $ (|Fraction| #46#)) 144 (|has| |#1| . #12#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #84=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #84#) 88 T ELT) (($ $ |#2|) 237 (|has| |#1| . #5#) ELT) (($ |#2| . #84#) 236 (|has| |#1| . #5#) ELT) (($ #78# . #84#) 77 (|has| |#1| . #80#) ELT) (($ $ #78#) 76 (|has| |#1| . #80#) ELT))) 
(((|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|)))) (|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|) (|CoercibleFrom| |t#2|) (CATEGORY |domain| (SIGNATURE |laurent| ($ (|Integer|) |t#2|)) (SIGNATURE |degree| ((|Integer|) $)) (SIGNATURE |taylorRep| (|t#2| $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)) (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| #1=(|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|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| #2# #2#) 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| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|CharacteristicZero|))) (|has| |#1| (|CharacteristicZero|))) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #3=(|Symbol|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Symbol|)))) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|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|))))) ((|DifferentialDomain| $) OR (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialSpace|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|)))) ((|DifferentialExtension| |#2|) |has| |#1| (|Field|)) ((|DifferentialRing|) OR (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|)))) ((|DifferentialSpace|) OR (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialSpace|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|)))) ((|DifferentialSpaceExtension| |#2|) |has| |#1| (|Field|)) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|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|)) ((|Functorial| |#1|) . T) ((|Functorial| |#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|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| |#2|) |has| |#1| (|Field|)) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| #4=(|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| |#2|) |has| |#1| (|Field|)) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| |#2|) |has| |#1| (|Field|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|LinearlyExplicitRingOver| #4#) AND (|has| |#1| (|Field|)) (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) ((|LinearlyExplicitRingOver| |#2|) |has| |#1| (|Field|)) ((|Module| #2#) 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|)))) ((|OrderedType|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedSet|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|)))) ((|PartialDifferentialDomain| $ #5=(|Symbol|)) OR (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialRing| (|Symbol|)) OR (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialSpace| #5#) OR (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|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| #1# (|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| #3#) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Symbol|)))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| |#2|) |has| |#1| (|Field|)) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) 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) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) AND (|has| |#1| (|Field|)) (|has| |#2| (|StepThrough|))) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariateLaurentSeriesCategory| |#1|) . T) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 83 T ELT)) (|wholePart| (#5=(|#2| $) NIL #6=(AND #7=(|has| |#1| (|Field|)) (|has| |#2| (|EuclideanDomain|))) ELT)) (|variables| ((#8=(|List| #9=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| (#10=(#11=(|Symbol|) $) 102 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #12=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #13=(#14=($ $) NIL #12# ELT)) (|unit?| (#4# NIL #12# ELT)) (|truncate| (#15=($ $ #16=(|Integer|)) 111 T ELT) (($ $ #16# #16#) 114 T ELT)) (|terms| ((#17=(|Stream| (|Record| (|:| |k| #16#) (|:| |c| |#1|))) $) 51 T ELT)) (|taylorRep| (#5# 11 T ELT)) (|taylorIfCan| (#18=((|Union| |#2| #19="failed") $) 35 T ELT)) (|taylor| (#5# 36 T ELT)) (|tanh| (#14# 208 #20=(|has| |#1| (|Algebra| #21=(|Fraction| #16#))) ELT)) (|tan| (#14# 184 #20# ELT)) (|subtractIfCan| (#22=(#23=(|Union| $ #19#) $ $) NIL T ELT)) (|squareFreePolynomial| #24=(((|Factored| #25=(|SparseUnivariatePolynomial| $)) #25#) NIL #26=(AND #7# #27=(|has| |#2| (|PolynomialFactorizationExplicit|))) ELT)) (|squareFreePart| #28=(#14# NIL #7# ELT)) (|squareFree| #29=(((|Factored| $) $) NIL #7# ELT)) (|sqrt| (#14# NIL #20# ELT)) (|solveLinearPolynomialEquation| (((|Union| #30=(|List| #25#) #19#) #30# #25#) NIL #26# ELT)) (|sizeLess?| (#2# NIL #7# ELT)) (|sinh| (#14# 204 #20# ELT)) (|sin| (#14# 180 #20# ELT)) (|sign| (#31=(#16# $) NIL #32=(AND #7# (|has| |#2| (|OrderedIntegralDomain|))) ELT)) (|series| (($ #17#) 59 T ELT)) (|sech| (#14# 212 #20# ELT)) (|sec| (#14# 188 #20# ELT)) (|sample| (#33=($) NIL T CONST)) (|retractIfCan| (#18# 159 T ELT) (((|Union| #16# . #34=(#19#)) . #35=($)) NIL #36=(AND #7# (|has| |#2| (|RetractableTo| #16#))) ELT) (((|Union| #21# . #34#) . #35#) NIL #36# ELT) (((|Union| #11# . #34#) . #35#) NIL #37=(AND #7# (|has| |#2| (|RetractableTo| #11#))) ELT)) (|retract| (#5# 158 T ELT) (#31# NIL #36# ELT) ((#21# $) NIL #36# ELT) (#10# NIL #37# ELT)) (|removeZeroes| (#14# 65 T ELT) (#38=($ #16# $) 28 T ELT)) (|rem| #39=(#40=($ $ $) NIL #7# ELT)) (|reductum| #41=(#14# NIL T ELT)) (|reducedSystem| ((#42=(|Matrix| |#2|) . #43=(#44=(|Matrix| $))) NIL #7# ELT) ((#45=(|Record| (|:| |mat| #42#) (|:| |vec| (|Vector| |#2|))) . #46=(#44# #47=(|Vector| $))) NIL #7# ELT) ((#48=(|Record| (|:| |mat| #49=(|Matrix| #16#)) (|:| |vec| (|Vector| #16#))) . #46#) NIL #50=(AND #7# (|has| |#2| (|LinearlyExplicitRingOver| #16#))) ELT) ((#49# . #43#) NIL #50# ELT)) (|recip| ((#23# $) 90 T ELT)) (|rationalFunction| ((#51=(|Fraction| (|Polynomial| |#1|)) $ #16#) 126 #12# ELT) ((#51# $ #16# #16#) 128 #12# ELT)) (|random| (#33# NIL #52=(AND #7# (|has| |#2| (|IntegerNumberSystem|))) ELT)) (|quo| #39#) (|principalIdeal| (((|Record| (|:| |coef| #53=(|List| $)) #54=(|:| |generator| $)) #53#) NIL #7# ELT)) (|prime?| (#4# NIL #7# ELT)) (|positive?| #55=(#4# NIL #32# ELT)) (|pole?| (#4# 76 T ELT)) (|pi| (#33# NIL #20# ELT)) (|patternMatch| ((#56=(|PatternMatchResult| #57=(|Float|) . #58=($)) $ #59=(|Pattern| #57#) #56#) NIL (AND #7# (|has| |#2| (|PatternMatchable| #57#))) ELT) ((#60=(|PatternMatchResult| #16# . #58#) $ #61=(|Pattern| #16#) #60#) NIL (AND #7# (|has| |#2| (|PatternMatchable| #16#))) ELT)) (|order| (#31# 107 T ELT) ((#16# $ #16#) 109 T ELT)) (|opposite?| #1#) (|one?| #62=(#4# NIL T ELT)) (|numerator| #28#) (|numer| (#5# 167 #7# ELT)) (|nthRoot| (#15# NIL #20# ELT)) (|nextItem| (#63=((|Maybe| $) $) NIL #64=(AND #7# (|has| |#2| (|StepThrough|))) ELT)) (|negative?| #55#) (|multiplyExponents| (#65=($ $ #66=(|PositiveInteger|)) 150 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #16#) $) 146 T ELT)) (|multiEuclidean| (((|Union| #53# #19#) #53# $) NIL #7# ELT)) (|monomial?| #62#) (|monomial| (($ |#1| #16#) 20 T ELT) (($ $ #9# #16#) NIL T ELT) (($ $ #8# (|List| #16#)) NIL T ELT)) (|min| #67=(#40# NIL #68=(AND #7# (|has| |#2| (|OrderedSet|))) ELT)) (|max| #67#) (|map| (($ (|Mapping| |#1| |#1|) $) 143 T ELT) (($ #69=(|Mapping| |#2| |#2|) $) NIL #7# ELT)) (|log| (#14# 178 #20# ELT)) (|leftReducedSystem| ((#42# . #70=(#47#)) NIL #7# ELT) ((#45# . #71=(#47# $)) NIL #7# ELT) ((#48# . #71#) NIL #50# ELT) ((#49# . #70#) NIL #50# ELT)) (|leadingMonomial| #41#) (|leadingCoefficient| (#72=(|#1| $) NIL T ELT)) (|lcm| #73=(($ #53#) NIL #7# ELT) #39#) (|laurent| (($ #16# |#2|) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#14# 161 #7# ELT)) (|integrate| (#14# 230 #20# ELT) (#74=($ $ #11#) 235 (OR (AND #20# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #16#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #20# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #11#))) (|has| |#1| (SIGNATURE |variables| (#75=(|List| #11#) |#1|))))) ELT)) (|init| (#33# NIL #64# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#25# #25# #25#) NIL #7# ELT)) (|gcd| #73# #39#) (|fractionPart| (#14# NIL #6# ELT)) (|floor| #76=(#5# NIL #52# ELT)) (|factorSquareFreePolynomial| #24#) (|factorPolynomial| #24#) (|factor| #29#) (|extendedEuclidean| (((|Union| (|Record| #77=(|:| |coef1| $) #78=(|:| |coef2| $)) #19#) $ $ $) NIL #7# ELT) (((|Record| #77# #78# #54#) $ $) NIL #7# ELT)) (|extend| (#15# 140 T ELT)) (|exquo| (#22# 130 #12# ELT)) (|expressIdealMember| (((|Maybe| #53#) #53# $) NIL #7# ELT)) (|exp| (#14# 176 #20# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 99 #79=(|has| |#1| (SIGNATURE ** (|#1| |#1| #16#))) ELT) (($ $ #11# |#2|) NIL #80=(AND #7# (|has| |#2| (|InnerEvalable| #11# |#2|))) ELT) (($ $ #75# #81=(|List| |#2|)) NIL #80# ELT) (($ $ (|List| #82=(|Equation| |#2|))) NIL #83=(AND #7# (|has| |#2| (|Evalable| |#2|))) ELT) (($ $ #82#) NIL #83# ELT) (($ $ |#2| |#2|) NIL #83# ELT) (($ $ #81# #81#) NIL #83# ELT)) (|euclideanSize| ((#84=(|NonNegativeInteger|) $) NIL #7# ELT)) (|elt| (#85=(|#1| $ #16#) 105 T ELT) (#40# 92 (|has| #16# (|SemiGroup|)) ELT) (#86=($ $ |#2|) NIL (AND #7# (|has| |#2| (|Eltable| |#2| |#2|))) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #7# ELT)) (|differentiate| #87=(($ $ #69# #84#) NIL #7# ELT) #88=(($ $ #69#) NIL #7# ELT) (#14# 151 #89=(OR (AND #7# (|has| |#2| (|DifferentialSpace|))) #90=(|has| |#1| (SIGNATURE * (|#1| #16# |#1|)))) ELT) #91=(#92=($ $ #84#) NIL #89# ELT) (#74# 155 #93=(OR (AND (|has| |#1| (|PartialDifferentialRing| #11#)) #90#) (AND #7# (|has| |#2| (|PartialDifferentialSpace| #11#)))) ELT) #94=(($ $ #75#) NIL #93# ELT) #95=(($ $ #11# #84#) NIL #93# ELT) #96=(($ $ #75# (|List| #84#)) NIL #93# ELT)) (|denominator| #28#) (|denom| (#5# 168 #7# ELT)) (|degree| (#31# 12 T ELT)) (|csch| (#14# 214 #20# ELT)) (|csc| (#14# 190 #20# ELT)) (|coth| (#14# 210 #20# ELT)) (|cot| (#14# 186 #20# ELT)) (|cosh| (#14# 206 #20# ELT)) (|cos| (#14# 182 #20# ELT)) (|convert| (((|DoubleFloat|) . #97=($)) NIL #98=(AND #7# (|has| |#2| (|RealConstant|))) ELT) ((#57# . #97#) NIL #98# ELT) ((#99=(|InputForm|) . #97#) NIL (AND #7# (|has| |#2| (|ConvertibleTo| #99#))) ELT) ((#59# . #97#) NIL (AND #7# (|has| |#2| (|ConvertibleTo| #59#))) ELT) ((#61# . #97#) NIL (AND #7# (|has| |#2| (|ConvertibleTo| #61#))) ELT)) (|conditionP| (((|Union| #47# #19#) #44#) NIL #100=(AND (|has| $ #101=(|CharacteristicNonZero|)) #7# #27#) ELT)) (|complete| (#14# 138 T ELT)) (|coerce| (((|OutputForm|) $) 268 T ELT) (($ #16#) 24 T ELT) (($ |#1|) 22 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#2|) 21 T ELT) (($ #11#) NIL #37# ELT) (($ #21#) 171 #20# ELT) #13#) (|coefficient| (#85# 87 T ELT)) (|charthRoot| (#63# NIL (OR #100# (|has| |#1| #101#) (AND #7# (|has| |#2| #101#))) ELT)) (|characteristic| ((#84#) 157 T CONST)) (|center| (#72# 104 T ELT)) (|ceiling| #76#) (|before?| #1#) (|atanh| (#14# 220 #20# ELT)) (|atan| (#14# 196 #20# ELT)) (|associates?| (#2# NIL #12# ELT)) (|asinh| (#14# 216 #20# ELT)) (|asin| (#14# 192 #20# ELT)) (|asech| (#14# 224 #20# ELT)) (|asec| (#14# 200 #20# ELT)) (|approximate| (#85# 136 (AND #79# (|has| |#1| (SIGNATURE |coerce| (|#1| #11#)))) ELT)) (|annihilate?| #1#) (|acsch| (#14# 226 #20# ELT)) (|acsc| (#14# 202 #20# ELT)) (|acoth| (#14# 222 #20# ELT)) (|acot| (#14# 198 #20# ELT)) (|acosh| (#14# 218 #20# ELT)) (|acos| (#14# 194 #20# ELT)) (|abs| (#14# NIL #32# ELT)) (|Zero| (#33# 13 T CONST)) (|One| (#33# 18 T CONST)) (D #87# #88# (#14# NIL #89# ELT) #91# (#74# NIL #93# ELT) #94# #95# #96#) (>= #102=(#2# NIL #68# ELT)) (> #102#) (= (#2# 74 T ELT)) (<= #102#) (< #102#) (/ (#103=($ $ |#1|) NIL #7# ELT) (#40# 165 #7# ELT) (($ |#2| |#2|) 166 #7# ELT)) (- (#14# 229 T ELT) (#40# 80 T ELT)) (+ (#40# 78 T ELT)) (** (#65# NIL T ELT) (#92# 86 T ELT) (#15# 162 #7# ELT) (#40# NIL #20# ELT) (#104=($ $ #21#) 174 #20# ELT)) (* (($ #66# $) NIL T ELT) (($ #84# $) NIL T ELT) (#38# NIL T ELT) (#40# 81 T ELT) (#103# NIL T ELT) (($ |#1| . #105=($)) 154 T ELT) (#86# 164 #7# ELT) (($ |#2| $) 163 #7# ELT) (($ #21# . #105#) NIL #20# ELT) (#104# NIL #20# ELT))) 
(((|UnivariateLaurentSeriesConstructor| |#1| |#2|) (|UnivariateLaurentSeriesConstructorCategory| |#1| |#2|) (|Ring|) (|UnivariateTaylorSeriesCategory| |#1|)) (T |UnivariateLaurentSeriesConstructor|)) 
NIL 
((|henselFact| (((|Record| (|:| |contp| #1=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #1#))))) |#1| (|Boolean|)) 13 T ELT)) (|factorSquareFree| (#2=((|Factored| |#1|) |#1|) 26 T ELT)) (|factor| (#2# 24 T ELT))) 
(((|UnivariateFactorize| |#1|) (CATEGORY |package| (SIGNATURE |factor| #1=((|Factored| |#1|) |#1|)) (SIGNATURE |factorSquareFree| #1#) (SIGNATURE |henselFact| ((|Record| (|:| |contp| #2=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #2#))))) |#1| (|Boolean|)))) (|UnivariatePolynomialCategory| #2#)) (T |UnivariateFactorize|)) 
((|henselFact| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|isDomain| *2 (|Record| (|:| |contp| #1=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| *3) (|:| |pow| #1#)))))) #2=(|isDomain| *1 (|UnivariateFactorize| *3)) #3=(|ofCategory| *3 (|UnivariatePolynomialCategory| #1#)))) (|factorSquareFree| #4=(*1 *2 *3) #5=(AND (|isDomain| *2 (|Factored| *3)) #2# #3#)) (|factor| #4# #5#)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|SetCategory|)) ELT)) (|segment| (#5=($ |#1| |#1|) 11 T ELT) (#6=($ |#1|) 10 T ELT)) (|map| ((#7=(|Stream| |#1|) (|Mapping| |#1| |#1|) $) 44 #8=(|has| |#1| (|OrderedRing|)) ELT)) (|low| (#9=(|#1| $) 15 T ELT)) (|lo| (#9# 12 T ELT)) (|latex| (((|String|) $) NIL #4# ELT)) (|incr| ((#10=(|Integer|) $) 19 T ELT)) (|high| (#9# 18 T ELT)) (|hi| (#9# 13 T ELT)) (|hash| (((|SingleInteger|) $) NIL #4# ELT)) (|hasHi| ((#3# $) 17 T ELT)) (|expand| ((#7# $) 41 #8# ELT) ((#7# (|List| $)) 40 #8# ELT)) (|convert| (#6# 26 T ELT)) (|coerce| (($ (|Segment| |#1|)) 25 T ELT) (((|OutputForm|) $) 37 #4# ELT)) (|before?| #1#) (SEGMENT (#5# 21 T ELT) (#6# 20 T ELT)) (BY (($ $ #10#) 14 T ELT)) (= (#2# 30 #4# ELT))) 
(((|UniversalSegment| |#1|) (|Join| (|SegmentCategory| |#1|) (CATEGORY |domain| (SIGNATURE SEGMENT #1=($ |#1|)) (SIGNATURE |segment| #1#) (SIGNATURE |coerce| ($ (|Segment| |#1|))) (SIGNATURE |hasHi| ((|Boolean|) $)) (IF (|has| |#1| #2=(|SetCategory|)) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |#1| (|OrderedRing|)) (ATTRIBUTE (|SegmentExpansionCategory| |#1| (|Stream| |#1|))) |%noBranch|))) (|Type|)) (T |UniversalSegment|)) 
((SEGMENT #1=(*1 *1 *2) #2=(AND (|isDomain| *1 (|UniversalSegment| *2)) (|ofCategory| *2 #3=(|Type|)))) (|segment| #1# #2#) (|coerce| #1# (AND (|isDomain| *2 (|Segment| *3)) #4=(|ofCategory| *3 #3#) #5=(|isDomain| *1 (|UniversalSegment| *3)))) (|hasHi| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) #5# #4#))) 
((|map| (((|Stream| |#2|) #1=(|Mapping| |#2| |#1|) #2=(|UniversalSegment| |#1|)) 23 (|has| |#1| (|OrderedRing|)) ELT) (((|UniversalSegment| |#2|) #1# #2#) 17 T ELT))) 
(((|UniversalSegmentFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|UniversalSegment| |#2|) #1=(|Mapping| |#2| |#1|) #2=(|UniversalSegment| |#1|))) (IF (|has| |#1| (|OrderedRing|)) (SIGNATURE |map| ((|Stream| |#2|) #1# #2#)) |%noBranch|)) #3=(|Type|) #3#) (T |UniversalSegmentFunctions2|)) 
((|map| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Mapping| *6 *5)) #3=(|isDomain| *4 (|UniversalSegment| *5)) (|ofCategory| *5 (|OrderedRing|)) #4=(|ofCategory| *5 #5=(|Type|)) #6=(|ofCategory| *6 #5#) (|isDomain| *2 (|Stream| *6)) #7=(|isDomain| *1 (|UniversalSegmentFunctions2| *5 *6)))) (|map| #1# (AND #2# #3# #4# #6# (|isDomain| *2 (|UniversalSegment| *6)) #7#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|vectorise| ((#6=(|Vector| |#2|) $ #7=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#8=(|List| #9=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #10=(|SparseUnivariatePolynomial| |#2|)) NIL T ELT)) (|univariate| ((#11=(|SparseUnivariatePolynomial| $) $ #9#) NIL T ELT) #12=((#10# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #13=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #14=(#15=($ $) NIL #13# ELT)) (|unit?| (#5# NIL #13# ELT)) (|totalDegree| #16=(#17=(#7# $) NIL T ELT) ((#7# $ #8#) NIL T ELT)) (|subtractIfCan| (#18=(#19=(|Union| $ #20="failed") $ $) NIL T ELT)) (|subResultantGcd| #21=(#22=($ $ $) NIL #13# ELT)) (|squareFreePolynomial| #23=(((|Factored| #11#) #11#) NIL #24=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #25=(#15# NIL #26=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#27=((|Factored| $) $) NIL #26# ELT)) (|solveLinearPolynomialEquation| (((|Union| #28=(|List| #11#) #20#) #28# #11#) NIL #24# ELT)) (|sizeLess?| (#2# NIL #29=(|has| |#2| (|Field|)) ELT)) (|shiftRight| #30=(($ $ #7#) NIL T ELT)) (|shiftLeft| #30#) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #26# ELT)) (|sample| #31=(#32=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #33=(#20#)) . #34=($)) NIL T ELT) (((|Union| #35=(|Fraction| #36=(|Integer|)) . #33#) . #34#) NIL #37=(|has| |#2| (|RetractableTo| #35#)) ELT) (((|Union| #36# . #33#) . #34#) NIL #38=(|has| |#2| (|RetractableTo| #36#)) ELT) #39=(((|Union| #9# . #33#) . #34#) NIL T ELT)) (|retract| #40=(#41=(|#2| . #42=($)) NIL T ELT) ((#35# . #42#) NIL #37# ELT) ((#36# . #42#) NIL #38# ELT) ((#9# . #42#) NIL T ELT)) (|resultant| (($ $ $ #9#) NIL #43=(|has| |#2| (|CommutativeRing|)) ELT) ((|#2| $ $) NIL #43# ELT)) (|rem| #44=(#22# NIL #29# ELT)) (|reductum| #45=(#15# NIL T ELT)) (|reducedSystem| ((#46=(|Matrix| #36#) . #47=(#48=(|Matrix| $))) NIL #49=(|has| |#2| (|LinearlyExplicitRingOver| #36#)) ELT) ((#50=(|Record| (|:| |mat| #46#) (|:| |vec| (|Vector| #36#))) . #51=(#48# #52=(|Vector| $))) NIL #49# ELT) ((#53=(|Record| (|:| |mat| #54=(|Matrix| |#2|)) (|:| |vec| #6#)) . #51#) NIL T ELT) ((#54# . #47#) NIL T ELT)) (|recip| ((#19# $) NIL T ELT)) (|quo| #44#) (|pseudoRemainder| #55=(#22# NIL T ELT)) (|pseudoQuotient| #21#) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) #56=(|:| |quotient| $) #57=(|:| |remainder| $)) $ $) NIL #13# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #29# ELT)) (|primitivePart| #25# #60=(#61=($ $ #9#) NIL #26# ELT)) (|primitiveMonomials| #62=((#58# $) NIL T ELT)) (|prime?| (#5# NIL #24# ELT)) (|pomopo!| (($ $ |#2| #7# $) NIL T ELT)) (|patternMatch| ((#63=(|PatternMatchResult| #64=(|Float|) . #65=($)) $ #66=(|Pattern| #64#) #63#) NIL (AND (|has| #9# #67=(|PatternMatchable| #64#)) (|has| |#2| #67#)) ELT) ((#68=(|PatternMatchResult| #36# . #65#) $ #69=(|Pattern| #36#) #68#) NIL (AND (|has| #9# #70=(|PatternMatchable| #36#)) (|has| |#2| #70#)) ELT)) (|order| ((#7# $ $) NIL #13# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #16#) (|nextItem| (#71=((|Maybe| $) $) NIL #72=(|has| |#2| (|StepThrough|)) ELT)) (|multivariate| (($ #10# #9#) NIL T ELT) (($ #11# #9#) NIL T ELT)) (|multiplyExponents| #30#) (|multiEuclidean| ((#73=(|Union| #58# #20#) #58# $) NIL #29# ELT)) (|monomials| #62#) (|monomial?| #4#) (|monomial| (($ |#2| #7#) 18 T ELT) #74=(($ $ #9# #7#) NIL T ELT) #75=(($ $ #8# #76=(|List| #7#)) NIL T ELT)) (|monicDivide| ((#77=(|Record| #56# #57#) $ $ #9#) NIL T ELT) (#78=(#77# $ $) NIL T ELT)) (|minimumDegree| #16# #79=((#7# $ #9#) NIL T ELT) #80=((#76# $ #8#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #7# #7#) $) NIL T ELT)) (|map| (($ #81=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|makeSUP| #12#) (|mainVariable| #39#) (|leftReducedSystem| ((#46# . #82=(#52#)) NIL #49# ELT) ((#50# . #83=(#52# $)) NIL #49# ELT) ((#53# . #83#) NIL T ELT) ((#54# . #82#) NIL T ELT)) (|leadingMonomial| #45#) (|leadingCoefficient| #40#) (|lcm| #84=(($ #58#) NIL #26# ELT) #85=(#22# NIL #26# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|karatsubaDivide| ((#77# $ #7#) NIL T ELT)) (|isTimes| #86=((#73# $) NIL T ELT)) (|isPlus| #86#) (|isExpt| (((|Union| (|Record| (|:| |var| #9#) (|:| |exponent| #7#)) #20#) $) NIL T ELT)) (|integrate| (#15# NIL #87=(|has| |#2| (|Algebra| #35#)) ELT)) (|init| (#32# NIL #72# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #40#) (|gcdPolynomial| ((#11# #11# #11#) NIL #26# ELT)) (|gcd| #84# #85#) (|fmecg| (($ $ #7# |#2| $) NIL T ELT)) (|factorSquareFreePolynomial| #23#) (|factorPolynomial| #23#) (|factor| (#27# NIL #24# ELT)) (|extendedEuclidean| (((|Union| (|Record| #88=(|:| |coef1| $) #89=(|:| |coef2| $)) #20#) $ $ $) NIL #29# ELT) (((|Record| #88# #89# #59#) $ $) NIL #29# ELT)) (|exquo| ((#19# $ |#2|) NIL #13# ELT) #90=(#18# NIL #13# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #29# ELT)) (|eval| (($ $ (|List| #91=(|Equation| $))) NIL T ELT) (($ $ #91#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #58# #58#) NIL T ELT) (($ $ #9# |#2|) NIL T ELT) (($ $ #8# #92=(|List| |#2|)) NIL T ELT) (($ $ #9# $) NIL T ELT) (($ $ #8# #58#) NIL T ELT)) (|euclideanSize| (#17# NIL #29# ELT)) (|elt| ((|#2| $ |#2|) NIL T ELT) #55# ((#93=(|Fraction| $) #93# #93#) NIL #13# ELT) ((|#2| #93# |#2|) NIL #29# ELT) ((#93# $ #93#) NIL #13# ELT)) (|divideExponents| ((#19# $ #7#) NIL T ELT)) (|divide| (#78# NIL #29# ELT)) (|discriminant| (#61# NIL #43# ELT) (#41# NIL #43# ELT)) (|differentiate| #75# #74# #94=(($ $ #8#) NIL T ELT) #95=(#61# NIL T ELT) #45# #30# #96=(($ $ #81#) NIL T ELT) #97=(($ $ #81# #7#) NIL T ELT) (($ $ #81# $) NIL T ELT) #98=(($ $ #99=(|Symbol|)) NIL #100=(|has| |#2| (|PartialDifferentialSpace| #99#)) ELT) #101=(($ $ #102=(|List| #99#)) NIL #100# ELT) #103=(($ $ #99# #7#) NIL #100# ELT) #104=(($ $ #102# #76#) NIL #100# ELT)) (|degree| #16# #79# #80#) (|convert| ((#66# . #105=($)) NIL (AND (|has| #9# #106=(|ConvertibleTo| #66#)) (|has| |#2| #106#)) ELT) ((#69# . #105#) NIL (AND (|has| #9# #107=(|ConvertibleTo| #69#)) (|has| |#2| #107#)) ELT) ((#108=(|InputForm|) . #105#) NIL (AND (|has| #9# #109=(|ConvertibleTo| #108#)) (|has| |#2| #109#)) ELT)) (|content| (#41# NIL #26# ELT) #60#) (|conditionP| (((|Union| #52# #20#) #48#) NIL #110=(AND (|has| $ #111=(|CharacteristicNonZero|)) #24#) ELT)) (|composite| #90# (((|Union| #93# #20#) #93# $) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #36#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #9#) NIL T ELT) (($ (|Variable| |#1|)) 20 T ELT) (($ #35#) NIL (OR #87# #37#) ELT) #14#) (|coefficients| ((#92# $) NIL T ELT)) (|coefficient| ((|#2| $ #7#) NIL T ELT) #74# #75#) (|charthRoot| (#71# NIL (OR #110# (|has| |#2| #111#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #43# ELT)) (|before?| #1#) (|associates?| (#2# NIL #13# ELT)) (|annihilate?| #1#) (|Zero| #31#) (|One| (#32# 14 T CONST)) (D #75# #74# #94# #95# #45# #30# #96# #97# #98# #101# #103# #104#) (= #1#) (/ (#112=($ $ |#2|) NIL #29# ELT)) (- #45# #55#) (+ #55#) (** (($ $ #113=(|PositiveInteger|)) NIL T ELT) #30#) (* (($ #113# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #36# . #114=($)) NIL T ELT) #55# (($ $ #35#) NIL #87# ELT) (($ #35# . #114#) NIL #87# ELT) (($ |#2| . #114#) NIL T ELT) (#112# NIL T ELT))) 
(((|UnivariatePolynomial| |#1| |#2|) (|Join| (|UnivariatePolynomialCategory| |#2|) (|CoercibleFrom| (|Variable| |#1|)) (CATEGORY |domain| (SIGNATURE |fmecg| ($ $ (|NonNegativeInteger|) |#2| $)))) (|Symbol|) (|Ring|)) (T |UnivariatePolynomial|)) 
((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|UnivariatePolynomial| *4 *3)) (|ofType| *4 (|Symbol|)) (|ofCategory| *3 (|Ring|))))) 
((|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) 15 T ELT))) 
(((|UnivariatePolynomialFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| ((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)))) #1=(|Symbol|) #2=(|Ring|) #1# #2#) (T |UnivariatePolynomialFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *8 *6)) (|isDomain| *4 (|UnivariatePolynomial| *5 *6)) (|ofType| *5 #1=(|Symbol|)) (|ofCategory| *6 #2=(|Ring|)) (|ofCategory| *8 #2#) (|isDomain| *2 (|UnivariatePolynomial| *7 *8)) (|isDomain| *1 (|UnivariatePolynomialFunctions2| *5 *6 *7 *8)) (|ofType| *7 #1#)))) 
((|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) 21 T ELT)) (|commonDenominator| ((|#1| |#3|) 13 T ELT)) (|clearDenominator| ((|#3| |#3|) 19 T ELT))) 
(((|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=(*1 *2 *3) (AND (|ofCategory| *4 #2=(|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 #2#) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *3 *4 *2)) (|ofCategory| *2 #3=(|UnivariatePolynomialCategory| *4)))) (|commonDenominator| #1# (AND (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 #2#) (|isDomain| *1 (|UnivariatePolynomialCommonDenominator| *2 *4 *3)) (|ofCategory| *3 #3#)))) 
((|rightFactorIfCan| ((#1=(|Union| |#2| #2="failed") |#2| #3=(|NonNegativeInteger|) |#1|) 35 T ELT)) (|monicRightFactorIfCan| ((#1# |#2| #3#) 36 T ELT)) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) #2#) |#2|) 50 T ELT)) (|monicCompleteDecompose| (((|List| |#2|) |#2|) 52 T ELT)) (|leftFactorIfCan| ((#1# |#2| |#2|) 46 T ELT))) 
(((|UnivariatePolynomialDecompositionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monicRightFactorIfCan| (#1=(|Union| |#2| #2="failed") |#2| #3=(|NonNegativeInteger|))) (SIGNATURE |rightFactorIfCan| (#1# |#2| #3# |#1|)) (SIGNATURE |leftFactorIfCan| (#1# |#2| |#2|)) (SIGNATURE |monicDecomposeIfCan| ((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) #2#) |#2|)) (SIGNATURE |monicCompleteDecompose| ((|List| |#2|) |#2|))) (|Join| (|IntegralDomain|) (|CharacteristicZero|)) (|UnivariatePolynomialCategory| |#1|)) (T |UnivariatePolynomialDecompositionPackage|)) 
((|monicCompleteDecompose| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|Join| (|IntegralDomain|) (|CharacteristicZero|))) (|isDomain| *2 (|List| *3)) #4=(|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *3)) #5=(|ofCategory| *3 #6=(|UnivariatePolynomialCategory| *4)))) (|monicDecomposeIfCan| #1# (|partial| AND #2# (|isDomain| *2 (|Record| (|:| |left| *3) (|:| |right| *3))) #4# #5#)) (|leftFactorIfCan| (*1 *2 *2 *2) (|partial| AND (|ofCategory| *3 #3#) (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|rightFactorIfCan| (*1 *2 *2 *3 *4) #7=(|partial| AND (|isDomain| *3 (|NonNegativeInteger|)) #2# (|isDomain| *1 (|UnivariatePolynomialDecompositionPackage| *4 *2)) (|ofCategory| *2 #6#))) (|monicRightFactorIfCan| (*1 *2 *2 *3) #7#)) 
((|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) 30 T ELT))) 
(((|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))))) 
((|noKaratsuba| (#1=(|#2| |#2| |#2|) 22 T ELT)) (|karatsubaOnce| (#1# 36 T ELT)) (|karatsuba| ((|#2| |#2| |#2| #2=(|NonNegativeInteger|) #2#) 44 T ELT))) 
(((|UnivariatePolynomialMultiplicationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |noKaratsuba| #1=(|#2| |#2| |#2|)) (SIGNATURE |karatsubaOnce| #1#) (SIGNATURE |karatsuba| (|#2| |#2| |#2| #2=(|NonNegativeInteger|) #2#))) (|Ring|) (|UnivariatePolynomialCategory| |#1|)) (T |UnivariatePolynomialMultiplicationPackage|)) 
((|karatsuba| (*1 *2 *2 *2 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 #1=(|Ring|)) (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)))) (|karatsubaOnce| #2=(*1 *2 *2 *2) #3=(AND (|ofCategory| *3 #1#) (|isDomain| *1 (|UnivariatePolynomialMultiplicationPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|noKaratsuba| #2# #3#)) 
((|vectorise| (((|Vector| |#2|) $ #1=(|NonNegativeInteger|)) 129 T ELT)) (|variables| ((#2=(|List| #3=(|SingletonAsOrderedSet|)) $) 16 T ELT)) (|unmakeSUP| (($ #4=(|SparseUnivariatePolynomial| |#2|)) 80 T ELT)) (|totalDegree| #5=(#6=(#1# $) NIL T ELT) ((#1# $ #2#) 21 T ELT)) (|squareFreePolynomial| (#7=((|Factored| #8=(|SparseUnivariatePolynomial| $)) #8#) 217 T ELT)) (|squareFreePart| (#9=($ $) 207 T ELT)) (|squareFree| (#10=((|Factored| $) $) 205 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #11=(|List| #8#) #12="failed") #11# #8#) 95 T ELT)) (|shiftRight| (#13=($ $ #1#) 84 T ELT)) (|shiftLeft| (#13# 86 T ELT)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) 157 T ELT)) (|retractIfCan| (((|Union| |#2| #12#) $) 132 T ELT) (((|Union| #14=(|Fraction| #15=(|Integer|)) #12#) $) NIL T ELT) (((|Union| #15# #12#) $) NIL T ELT) (#16=((|Union| #3# #12#) $) NIL T ELT)) (|retract| (#17=(|#2| $) 130 T ELT) ((#14# $) NIL T ELT) ((#15# $) NIL T ELT) ((#3# $) NIL T ELT)) (|pseudoQuotient| (#18=($ $ $) 182 T ELT)) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) #19=(|:| |quotient| $) #20=(|:| |remainder| $)) $ $) 185 T ELT)) (|order| ((#1# $ $) 202 T ELT)) (|nextItem| (((|Maybe| $) $) 149 T ELT)) (|monomial| (($ |#2| #1#) NIL T ELT) (#21=($ $ #3# #1#) 59 T ELT) #22=(($ $ #2# #23=(|List| #1#)) NIL T ELT)) (|minimumDegree| #5# (#24=(#1# $ #3#) 54 T ELT) (#25=(#23# $ #2#) 55 T ELT)) (|makeSUP| ((#4# $) 72 T ELT)) (|mainVariable| (#16# 52 T ELT)) (|karatsubaDivide| ((#26=(|Record| #19# #20#) $ #1#) 83 T ELT)) (|integrate| (#9# 232 T ELT)) (|init| (($) 134 T CONST)) (|gcdPolynomial| ((#8# #8# #8#) 214 T ELT)) (|factorSquareFreePolynomial| (#7# 101 T ELT)) (|factorPolynomial| (#7# 99 T ELT)) (|factor| (#10# 120 T ELT)) (|eval| (($ $ (|List| #27=(|Equation| $))) 51 T ELT) (($ $ #27#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #28=(|List| $) #28#) NIL T ELT) (($ $ #3# |#2|) 39 T ELT) (($ $ #2# (|List| |#2|)) 36 T ELT) (($ $ #3# $) 32 T ELT) (($ $ #2# #28#) 30 T ELT)) (|euclideanSize| (#6# 220 T ELT)) (|elt| ((|#2| $ |#2|) NIL T ELT) (#18# NIL T ELT) ((#29=(|Fraction| $) #29# #29#) 176 T ELT) ((|#2| #29# |#2|) 219 T ELT) ((#29# $ #29#) 201 T ELT)) (|divide| ((#26# $ $) 225 T ELT)) (|differentiate| #22# (#21# NIL T ELT) (($ $ #2#) NIL T ELT) (#30=($ $ #3#) 169 T ELT) (#9# 167 T ELT) (#13# NIL T ELT) (($ $ #31=(|Mapping| |#2| |#2|)) 166 T ELT) (($ $ #31# #1#) NIL T ELT) (($ $ #31# $) 161 T ELT) (($ $ #32=(|Symbol|)) NIL T ELT) (($ $ #33=(|List| #32#)) NIL T ELT) (($ $ #32# #1#) NIL T ELT) (($ $ #33# #23#) NIL T ELT)) (|degree| #5# (#24# 17 T ELT) (#25# 23 T ELT)) (|content| (#17# NIL T ELT) (#30# 151 T ELT)) (|composite| (((|Union| $ #12#) $ $) 193 T ELT) (((|Union| #29# #12#) #29# $) 189 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #3#) 64 T ELT) (($ #14#) NIL T ELT) (#9# NIL T ELT))) 
(((|UnivariatePolynomialCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| #1=(|#1| |#1|)) (SIGNATURE |gcdPolynomial| (#2=(|SparseUnivariatePolynomial| |#1|) #2# #2#)) (SIGNATURE |differentiate| (|#1| |#1| #3=(|List| #4=(|Symbol|)) #5=(|List| #6=(|NonNegativeInteger|)))) (SIGNATURE |differentiate| (|#1| |#1| #4# #6#)) (SIGNATURE |differentiate| (|#1| |#1| #3#)) (SIGNATURE |differentiate| (|#1| |#1| #4#)) (SIGNATURE |squareFree| #7=((|Factored| |#1|) |#1|)) (SIGNATURE |squareFreePart| #1#) (SIGNATURE |coerce| (|#1| #8=(|Fraction| #9=(|Integer|)))) (SIGNATURE |init| (|#1|) |constant|) (SIGNATURE |nextItem| ((|Maybe| |#1|) |#1|)) (SIGNATURE |elt| (#10=(|Fraction| |#1|) |#1| #10#)) (SIGNATURE |euclideanSize| #11=(#6# |#1|)) (SIGNATURE |divide| (#12=(|Record| #13=(|:| |quotient| |#1|) #14=(|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |integrate| #1#) (SIGNATURE |elt| (|#2| #10# |#2|)) (SIGNATURE |separate| ((|Record| (|:| |primePart| |#1|) (|:| |commonPart| |#1|)) |#1| |#1|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |#2|) #13# #14#) |#1| |#1|)) (SIGNATURE |pseudoQuotient| #15=(|#1| |#1| |#1|)) (SIGNATURE |composite| ((|Union| #10# #16="failed") #10# |#1|)) (SIGNATURE |composite| ((|Union| |#1| #16#) |#1| |#1|)) (SIGNATURE |order| (#6# |#1| |#1|)) (SIGNATURE |elt| (#10# #10# #10#)) (SIGNATURE |differentiate| (|#1| |#1| #17=(|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |shiftLeft| #18=(|#1| |#1| #6#)) (SIGNATURE |shiftRight| #18#) (SIGNATURE |karatsubaDivide| (#12# |#1| #6#)) (SIGNATURE |unmakeSUP| (|#1| #19=(|SparseUnivariatePolynomial| |#2|))) (SIGNATURE |makeSUP| (#19# |#1|)) (SIGNATURE |vectorise| ((|Vector| |#2|) |#1| #6#)) (SIGNATURE |differentiate| (|#1| |#1| #17# #6#)) (SIGNATURE |differentiate| (|#1| |#1| #17#)) (SIGNATURE |differentiate| #18#) (SIGNATURE |differentiate| #1#) (SIGNATURE |elt| #15#) (SIGNATURE |elt| (|#2| |#1| |#2|)) (SIGNATURE |factor| #7#) (SIGNATURE |squareFreePolynomial| #20=((|Factored| #2#) #2#)) (SIGNATURE |factorPolynomial| #20#) (SIGNATURE |factorSquareFreePolynomial| #20#) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #21=(|List| #2#) #16#) #21# #2#)) (SIGNATURE |content| #22=(|#1| |#1| #23=(|SingletonAsOrderedSet|))) (SIGNATURE |variables| (#24=(|List| #23#) |#1|)) (SIGNATURE |totalDegree| (#6# |#1| #24#)) (SIGNATURE |totalDegree| #11#) (SIGNATURE |monomial| #25=(|#1| |#1| #24# #5#)) (SIGNATURE |monomial| #26=(|#1| |#1| #23# #6#)) (SIGNATURE |minimumDegree| #27=(#5# |#1| #24#)) (SIGNATURE |minimumDegree| #28=(#6# |#1| #23#)) (SIGNATURE |mainVariable| #29=((|Union| #23# #16#) |#1|)) (SIGNATURE |degree| #27#) (SIGNATURE |degree| #28#) (SIGNATURE |coerce| (|#1| #23#)) (SIGNATURE |retractIfCan| #29#) (SIGNATURE |retract| (#23# |#1|)) (SIGNATURE |eval| (|#1| |#1| #24# #30=(|List| |#1|))) (SIGNATURE |eval| (|#1| |#1| #23# |#1|)) (SIGNATURE |eval| (|#1| |#1| #24# (|List| |#2|))) (SIGNATURE |eval| (|#1| |#1| #23# |#2|)) (SIGNATURE |eval| (|#1| |#1| #30# #30#)) (SIGNATURE |eval| (|#1| |#1| |#1| |#1|)) (SIGNATURE |eval| (|#1| |#1| #31=(|Equation| |#1|))) (SIGNATURE |eval| (|#1| |#1| (|List| #31#))) (SIGNATURE |degree| #11#) (SIGNATURE |monomial| (|#1| |#2| #6#)) (SIGNATURE |retractIfCan| ((|Union| #9# #16#) |#1|)) (SIGNATURE |retract| (#9# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #8# #16#) |#1|)) (SIGNATURE |retract| (#8# |#1|)) (SIGNATURE |retract| #32=(|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #16#) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |minimumDegree| #11#) (SIGNATURE |content| #32#) (SIGNATURE |differentiate| #22#) (SIGNATURE |differentiate| (|#1| |#1| #24#)) (SIGNATURE |differentiate| #26#) (SIGNATURE |differentiate| #25#) (SIGNATURE |coerce| (|#1| #9#)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|UnivariatePolynomialCategory| |#2|) (|Ring|)) (T |UnivariatePolynomialCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) 272 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 124 T ELT)) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) 270 T ELT)) (|univariate| ((#4=(|SparseUnivariatePolynomial| $) $ #3#) 139 T ELT) (((|SparseUnivariatePolynomial| |#1|) $) 138 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 101 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 102 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 104 (|has| |#1| . #5#) ELT)) (|totalDegree| ((#7=(|NonNegativeInteger|) $) 126 T ELT) ((#7# $ (|List| #3#)) 125 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|subResultantGcd| (($ $ $) 257 (|has| |#1| (|IntegralDomain|)) ELT)) (|squareFreePolynomial| (#8=((|Factored| #9=(|SparseUnivariatePolynomial| $)) #9#) 114 (|has| |#1| . #10=((|PolynomialFactorizationExplicit|))) ELT)) (|squareFreePart| (($ $) 112 (|has| |#1| . #11=((|GcdDomain|))) ELT)) (|squareFree| (#12=((|Factored| $) $) 111 (|has| |#1| . #11#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #13=(|List| #9#) #14="failed") #13# #9#) 117 (|has| |#1| . #10#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 242 (|has| |#1| . #15=((|Field|))) ELT)) (|shiftRight| (($ $ (|NonNegativeInteger|)) 265 T ELT)) (|shiftLeft| (($ $ (|NonNegativeInteger|)) 264 T ELT)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) 252 (|has| |#1| (|GcdDomain|)) ELT)) (|sample| (#16=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| . #17=("failed")) . #18=($)) 182 T ELT) (((|Union| #19=(|Fraction| #20=(|Integer|)) . #17#) . #18#) 179 (|has| |#1| . #21=((|RetractableTo| #19#))) ELT) (((|Union| #20# . #17#) . #18#) 177 (|has| |#1| . #22=((|RetractableTo| #20#))) ELT) (((|Union| #3# . #17#) . #18#) 154 T ELT)) (|retract| ((|#1| . #23=($)) 181 T ELT) ((#19# . #23#) 180 (|has| |#1| . #21#) ELT) ((#20# . #23#) 178 (|has| |#1| . #22#) ELT) ((#3# . #23#) 155 T ELT)) (|resultant| (($ $ $ #3#) 122 (|has| |#1| . #24=((|CommutativeRing|))) ELT) ((|#1| $ $) 260 (|has| |#1| (|CommutativeRing|)) ELT)) (|rem| (#25=($ $ $) 246 (|has| |#1| . #15#) ELT)) (|reductum| (#26=($ $) 172 T ELT)) (|reducedSystem| (((|Matrix| #27=(|Integer|)) . #28=(#29=(|Matrix| $))) 150 (|has| |#1| . #30=((|LinearlyExplicitRingOver| #27#))) ELT) (((|Record| (|:| |mat| (|Matrix| #27#)) (|:| |vec| (|Vector| #27#))) . #31=(#29# #32=(|Vector| $))) 149 (|has| |#1| . #30#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #31#) 148 T ELT) (((|Matrix| |#1|) . #28#) 147 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#25# 245 (|has| |#1| . #15#) ELT)) (|pseudoRemainder| (($ $ $) 263 T ELT)) (|pseudoQuotient| (($ $ $) 254 (|has| |#1| (|IntegralDomain|)) ELT)) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) 253 (|has| |#1| (|IntegralDomain|)) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #33=(|List| $)) (|:| |generator| $)) #33#) 240 (|has| |#1| . #15#) ELT)) (|primitivePart| (($ $) 194 (|has| |#1| . #34=((|GcdDomain|))) ELT) (($ $ #3#) 119 (|has| |#1| . #11#) ELT)) (|primitiveMonomials| (#35=(#36=(|List| $) $) 123 T ELT)) (|prime?| (((|Boolean|) $) 110 (|has| |#1| . #10#) ELT)) (|pomopo!| (($ $ |#1| #37=(|NonNegativeInteger|) $) 190 T ELT)) (|patternMatch| (((|PatternMatchResult| #38=(|Float|) . #39=($)) $ (|Pattern| #38#) (|PatternMatchResult| #38# . #39#)) 98 (AND (|has| #3# #40=(|PatternMatchable| #38#)) (|has| |#1| #40#)) ELT) (((|PatternMatchResult| #41=(|Integer|) . #39#) $ (|Pattern| #41#) (|PatternMatchResult| #41# . #39#)) 97 (AND (|has| #3# #42=(|PatternMatchable| #41#)) (|has| |#1| #42#)) ELT)) (|order| (((|NonNegativeInteger|) $ $) 258 (|has| |#1| (|IntegralDomain|)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|numberOfMonomials| ((#43=(|NonNegativeInteger|) $) 187 T ELT)) (|nextItem| (((|Maybe| $) $) 238 (|has| |#1| . #44=((|StepThrough|))) ELT)) (|multivariate| (($ (|SparseUnivariatePolynomial| |#1|) #3#) 131 T ELT) (($ #4# #3#) 130 T ELT)) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) 269 T ELT)) (|multiEuclidean| (((|Union| #45=(|List| $) #46="failed") #45# $) 249 (|has| |#1| . #15#) ELT)) (|monomials| (#35# 140 T ELT)) (|monomial?| (((|Boolean|) $) 170 T ELT)) (|monomial| (($ |#1| #37#) 171 T ELT) (($ $ #3# . #47=(#7#)) 133 T ELT) (($ $ (|List| #3#) . #48=(#49=(|List| #7#))) 132 T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #3#) 134 T ELT) (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 267 T ELT)) (|minimumDegree| ((#37# $) 188 T ELT) ((#7# $ #3#) 136 T ELT) ((#49# $ (|List| #3#)) 135 T ELT)) (|mapExponents| (($ (|Mapping| #37# #37#) $) 189 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 166 T ELT)) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) 271 T ELT)) (|mainVariable| (((|Union| #3# #50="failed") $) 137 T ELT)) (|leftReducedSystem| (((|Matrix| #27#) . #51=(#32#)) 152 (|has| |#1| . #30#) ELT) (((|Record| (|:| |mat| (|Matrix| #27#)) (|:| |vec| (|Vector| #27#))) . #52=(#32# $)) 151 (|has| |#1| . #30#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #52#) 146 T ELT) (((|Matrix| |#1|) . #51#) 145 T ELT)) (|leadingMonomial| (#26# 168 T ELT)) (|leadingCoefficient| ((|#1| $) 167 T ELT)) (|lcm| (#53=($ (|List| $)) 108 (|has| |#1| . #11#) ELT) (#54=($ $ $) 107 (|has| |#1| . #11#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) 266 T ELT)) (|isTimes| (#55=((|Union| #36# #50#) $) 128 T ELT)) (|isPlus| (#55# 129 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| #3#) (|:| |exponent| #7#)) #50#) $) 127 T ELT)) (|integrate| (($ $) 250 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT)) (|init| (($) 237 (|has| |#1| . #44#) CONST)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|ground?| (((|Boolean|) $) 184 T ELT)) (|ground| ((|#1| . #56=($)) 185 T ELT)) (|gcdPolynomial| ((#57=(|SparseUnivariatePolynomial| $) #57# #57#) 109 (|has| |#1| . #11#) ELT)) (|gcd| (#53# 106 (|has| |#1| . #11#) ELT) (#54# 105 (|has| |#1| . #11#) ELT)) (|factorSquareFreePolynomial| (#8# 116 (|has| |#1| . #10#) ELT)) (|factorPolynomial| (#8# 115 (|has| |#1| . #10#) ELT)) (|factor| (#12# 113 (|has| |#1| . #10#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #58=(|:| |coef1| $) #59=(|:| |coef2| $)) #46#) $ $ $) 248 (|has| |#1| . #15#) ELT) (((|Record| #58# #59# (|:| |generator| $)) $ $) 247 (|has| |#1| . #15#) ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 192 (|has| |#1| (|IntegralDomain|)) ELT) (((|Union| $ "failed") $ $) 100 (|has| |#1| . #5#) ELT)) (|expressIdealMember| (((|Maybe| #33#) #33# $) 241 (|has| |#1| . #15#) ELT)) (|eval| (($ $ (|List| (|Equation| $))) 163 T ELT) (($ $ (|Equation| $)) 162 T ELT) (($ $ $ $) 161 T ELT) (($ $ (|List| $) (|List| $)) 160 T ELT) (($ $ #3# |#1|) 159 T ELT) (($ $ (|List| #3#) (|List| |#1|)) 158 T ELT) (($ $ #3# $) 157 T ELT) (($ $ (|List| #3#) (|List| $)) 156 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 243 (|has| |#1| . #15#) ELT)) (|elt| ((|#1| $ |#1|) 282 T ELT) (($ $ $) 281 T ELT) (((|Fraction| $) (|Fraction| $) (|Fraction| $)) 259 (|has| |#1| (|IntegralDomain|)) ELT) ((|#1| (|Fraction| $) |#1|) 251 (|has| |#1| (|Field|)) ELT) (((|Fraction| $) $ (|Fraction| $)) 239 (|has| |#1| (|IntegralDomain|)) ELT)) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) 268 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 244 (|has| |#1| . #15#) ELT)) (|discriminant| (($ $ #3#) 121 (|has| |#1| . #24#) ELT) ((|#1| $) 261 (|has| |#1| (|CommutativeRing|)) ELT)) (|differentiate| (($ $ (|List| #3#) . #60=((|List| #61=(|NonNegativeInteger|)))) 52 T ELT) (($ $ #3# . #62=(#61#)) 51 T ELT) (($ $ (|List| #3#)) 50 T ELT) (($ $ #3#) 48 T ELT) (($ . #63=($)) 280 T ELT) (#64=($ $ (|NonNegativeInteger|)) 278 T ELT) (($ $ (|Mapping| |#1| |#1|)) 276 T ELT) (($ $ (|Mapping| |#1| |#1|) . #65=((|NonNegativeInteger|))) 275 T ELT) (($ $ (|Mapping| |#1| |#1|) $) 262 T ELT) (($ $ #66=(|Symbol|)) 236 (|has| |#1| . #67=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #66#)) 234 (|has| |#1| . #67#) ELT) (($ $ #66# . #62#) 233 (|has| |#1| . #67#) ELT) (($ $ (|List| #66#) . #60#) 232 (|has| |#1| . #67#) ELT)) (|degree| ((#37# $) 169 T ELT) ((#7# $ #3#) 144 T ELT) ((#49# $ (|List| #3#)) 143 T ELT)) (|convert| ((#68=(|Pattern| #38#) . #69=($)) 96 (AND (|has| #3# #70=(|ConvertibleTo| #68#)) (|has| |#1| #70#)) ELT) ((#71=(|Pattern| #41#) . #69#) 95 (AND (|has| #3# #72=(|ConvertibleTo| #71#)) (|has| |#1| #72#)) ELT) ((#73=(|InputForm|) . #69#) 94 (AND (|has| #3# #74=(|ConvertibleTo| #73#)) (|has| |#1| #74#)) ELT)) (|content| ((|#1| . #56#) 193 (|has| |#1| . #34#) ELT) (($ $ #3#) 120 (|has| |#1| . #11#) ELT)) (|conditionP| (((|Union| (|Vector| $) #14#) (|Matrix| $)) 118 (|and| #75=(|has| $ (|CharacteristicNonZero|)) (|has| |#1| . #10#)) ELT)) (|composite| (((|Union| $ "failed") $ $) 256 (|has| |#1| (|IntegralDomain|)) ELT) (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) 255 (|has| |#1| (|IntegralDomain|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 183 T ELT) (($ #3#) 153 T ELT) (($ #76=(|Fraction| (|Integer|))) 92 (OR (|has| |#1| . #21#) (|has| |#1| . #77=((|Algebra| #76#)))) ELT) (($ $) 99 (|has| |#1| . #5#) ELT)) (|coefficients| (((|List| |#1|) $) 186 T ELT)) (|coefficient| ((|#1| $ #37#) 173 T ELT) (($ $ #3# . #47#) 142 T ELT) (($ $ (|List| #3#) . #48#) 141 T ELT)) (|charthRoot| (((|Maybe| $) $) 93 (OR (|and| #75# (|has| |#1| . #10#)) (|has| |#1| (|CharacteristicNonZero|))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|binomThmExpt| (($ $ $ #43#) 191 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#6# $ $) 103 (|has| |#1| . #5#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#16# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|List| #3#) . #60#) 55 T ELT) (($ $ #3# . #62#) 54 T ELT) (($ $ (|List| #3#)) 53 T ELT) (($ $ #3#) 49 T ELT) (($ . #63#) 279 T ELT) (#64# 277 T ELT) (($ $ (|Mapping| |#1| |#1|)) 274 T ELT) (($ $ (|Mapping| |#1| |#1|) . #65#) 273 T ELT) (($ $ #66#) 235 (|has| |#1| . #67#) ELT) (($ $ (|List| #66#)) 231 (|has| |#1| . #67#) ELT) (($ $ #66# . #62#) 230 (|has| |#1| . #67#) ELT) (($ $ (|List| #66#) . #60#) 229 (|has| |#1| . #67#) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 174 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #78=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #76#) 176 (|has| |#1| . #77#) ELT) (($ #76# . #78#) 175 (|has| |#1| . #77#) ELT) (($ |#1| . #78#) 165 T ELT) (($ $ |#1|) 164 T ELT))) 
(((|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)))) (|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 |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| #1=(|NonNegativeInteger|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|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| #2# #2#) |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|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #3=(|SingletonAsOrderedSet|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|DifferentialDomain| $) . T) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|DifferentialSpaceExtension| |#1|) . 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| #1#) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|InnerEvalable| #3# |#1|) . T) ((|InnerEvalable| #3# $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #4=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|LinearlyExplicitRingOver| #4#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #2#) |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) ((|PartialDifferentialDomain| $ #3#) . T) ((|PartialDifferentialDomain| $ #5=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| #3#) . T) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #3#) . T) ((|PartialDifferentialSpace| #5#) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Integer|)))) ((|PolynomialCategory| |#1| #1# #3#) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #3#) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) |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) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|StepThrough|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) 
((|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 22 T ELT))) 
(((|UnivariatePolynomialCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|))) #1=(|Ring|) (|UnivariatePolynomialCategory| |#1|) #1# (|UnivariatePolynomialCategory| |#3|)) (T |UnivariatePolynomialCategoryFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|UnivariatePolynomialCategory| *6)) (|isDomain| *1 (|UnivariatePolynomialCategoryFunctions2| *5 *4 *6 *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *5))))) 
((|variables| ((#1=(|List| #2=(|SingletonAsOrderedSet|)) $) 34 T ELT)) (|reductum| (#3=($ $) 31 T ELT)) (|monomial| (($ |#2| |#3|) NIL T ELT) (($ $ #2# |#3|) 28 T ELT) (($ $ #1# (|List| |#3|)) 27 T ELT)) (|leadingMonomial| (#3# 14 T ELT)) (|leadingCoefficient| ((|#2| $) 12 T ELT)) (|degree| ((|#3| $) 10 T ELT))) 
(((|UnivariatePowerSeriesCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |variables| (#1=(|List| #2=(|SingletonAsOrderedSet|)) |#1|)) (SIGNATURE |monomial| (|#1| |#1| #1# (|List| |#3|))) (SIGNATURE |monomial| (|#1| |#1| #2# |#3|)) (SIGNATURE |reductum| #3=(|#1| |#1|)) (SIGNATURE |monomial| (|#1| |#2| |#3|)) (SIGNATURE |degree| (|#3| |#1|)) (SIGNATURE |leadingMonomial| #3#) (SIGNATURE |leadingCoefficient| (|#2| |#1|))) (|UnivariatePowerSeriesCategory| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |UnivariatePowerSeriesCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| (((|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #4=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #4#) ELT)) (|unit?| ((#5=(|Boolean|) $) 75 (|has| |#1| . #4#) ELT)) (|truncate| (($ $ |#2|) 125 T ELT) (($ $ |#2| |#2|) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 131 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#6=($) 23 T CONST)) (|reductum| (#7=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|order| ((|#2| $) 127 T ELT) ((|#2| $ |#2|) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| |#2|) 82 T ELT) (($ $ #3# |#2|) 98 T ELT) (($ $ (|List| #3#) (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|leadingMonomial| (#7# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (($ $ |#2|) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #4#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) ELT)) (|elt| ((|#1| $ |#2|) 132 T ELT) (($ $ $) 108 (|has| |#2| (|SemiGroup|)) ELT)) (|differentiate| (($ $ #8=(|Symbol|)) 120 (AND (|has| |#1| . #9=((|PartialDifferentialRing| (|Symbol|)))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#)) 118 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ #8# . #10=(#11=(|NonNegativeInteger|))) 117 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#) . #12=((|List| #11#))) 116 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ . #13=($)) 112 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT) (#14=($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT)) (|degree| ((|#2| $) 84 T ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #15=(|Fraction| (|Integer|))) 78 (|has| |#1| . #16=((|Algebra| #15#))) ELT) (($ $) 70 (|has| |#1| . #4#) ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#5# $ $) 74 (|has| |#1| . #4#) ELT)) (|approximate| ((|#1| $ |#2|) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#6# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ #8#) 119 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#)) 115 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ #8# . #10#) 114 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#) . #12#) 113 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ . #13#) 111 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT) (#14# 109 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #17#) 88 T ELT) (($ #15# . #17#) 77 (|has| |#1| . #16#) ELT) (($ $ #15#) 76 (|has| |#1| . #16#) ELT))) 
(((|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)))))) (|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|)) (|Eltable| |t#2| |t#1|) (CATEGORY |domain| (SIGNATURE |terms| ((|Stream| (|Record| (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (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| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |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|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|Eltable| |#2| |#1|) . T) ((|Eltable| $ $) |has| |#2| (|SemiGroup|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #2=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ((|PartialDifferentialRing| #2#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ((|PartialDifferentialSpace| #2#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ((|PowerSeriesCategory| |#1| |#2| (|SingletonAsOrderedSet|)) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|squareFreePart| ((|#2| |#2|) 12 T ELT)) (|squareFree| (((|Factored| |#2|) |#2|) 14 T ELT)) (|BumInSepFFE| ((#1=(|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) #1#) 30 T ELT))) 
(((|UnivariatePolynomialSquareFree| |#1| |#2|) (CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#2|) |#2|)) (SIGNATURE |squareFreePart| (|#2| |#2|)) (SIGNATURE |BumInSepFFE| (#1=(|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) #1#))) #2=(|IntegralDomain|) (|Join| (|UnivariatePolynomialCategory| |#1|) #2# (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) (T |UnivariatePolynomialSquareFree|)) 
((|BumInSepFFE| #1=(*1 *2 *2) (AND (|isDomain| *2 (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (|Integer|)))) (|ofCategory| *4 #2=(|Join| (|UnivariatePolynomialCategory| *3) #3=(|IntegralDomain|) #4=(CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) #5=(|ofCategory| *3 #3#) (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *4)))) (|squareFreePart| #1# (AND #5# (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *2)) (|ofCategory| *2 #2#))) (|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 #3#) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|UnivariatePolynomialSquareFree| *4 *3)) (|ofCategory| *3 (|Join| (|UnivariatePolynomialCategory| *4) #3# #4#))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 11 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| (#19=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|squareFreePart| #22=(#11# NIL #23=(|has| |#1| (|Field|)) ELT)) (|squareFree| #24=(((|Factored| $) $) NIL #23# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #23# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #25=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| (#26=($) NIL T CONST)) (|retractIfCan| (#27=((|Union| #28=(|UnivariateLaurentSeries| |#1| |#2| |#3|) . #29=(#21#)) $) 19 T ELT) (((|Union| #30=(|UnivariateTaylorSeries| |#1| |#2| |#3|) . #29#) $) 22 T ELT)) (|retract| #31=(#32=(#28# . #33=($)) NIL T ELT) ((#30# . #33#) NIL T ELT)) (|rem| #34=(#35=($ $ $) NIL #23# ELT)) (|reductum| #36=(#11# NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|rationalPower| (#37=(#14# $) 68 T ELT)) (|quo| #34#) (|puiseux| (($ #14# #28#) NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #38=(|List| $)) #39=(|:| |generator| $)) #38#) NIL #23# ELT)) (|prime?| (#5# NIL #23# ELT)) (|pole?| #4#) (|pi| (#26# NIL #18# ELT)) (|order| #40=(#37# NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#41=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #42=(($ $ #43=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #38# #21#) #38# $) NIL #23# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) 30 T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #17#) (|leadingMonomial| #36#) (|leadingCoefficient| (#44=(|#1| $) NIL T ELT)) (|lcm| #45=(($ #38#) NIL #23# ELT) #34#) (|laurentRep| (#32# 71 T ELT)) (|laurentIfCan| (#27# NIL T ELT)) (|laurent| #31#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #22#) (|integrate| (#11# 39 #18# ELT) (#46=($ $ #8#) NIL (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#47=(|List| #8#) |#1|))))) ELT) (#48=($ $ #49=(|Variable| |#2|)) 40 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#50=(|SparseUnivariatePolynomial| $) #50# #50#) NIL #23# ELT)) (|gcd| #45# #34#) (|factor| #24#) (|extendedEuclidean| (((|Union| (|Record| #51=(|:| |coef1| $) #52=(|:| |coef2| $)) #21#) $ $ $) NIL #23# ELT) (((|Record| #51# #52# #39#) $ $) NIL #23# ELT)) (|extend| #12#) (|exquo| (#19# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #38#) #38# $) NIL #23# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #53=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#25# $) NIL #23# ELT)) (|elt| #54=(#55=(|#1| $ #14#) NIL T ELT) (#35# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #23# ELT)) (|differentiate| #56=(#46# NIL #57=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #58=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #59=(($ $ #47#) NIL #57# ELT) #60=(($ $ #8# #25#) NIL #57# ELT) #61=(($ $ #47# (|List| #25#)) NIL #57# ELT) (#11# 37 #58# ELT) #62=(#63=($ $ #25#) NIL #58# ELT) (#48# 38 T ELT)) (|degree| #40#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #36#) (|coerce| (((|OutputForm|) $) 107 T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #28#) 16 T ELT) (($ #30#) 17 T ELT) (($ #49#) 36 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #54#) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#25#) NIL T CONST)) (|center| (#44# 12 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#55# 73 (AND #53# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| (#26# 32 T CONST)) (|One| (#26# 26 T CONST)) (D #56# #59# #60# #61# (#11# NIL #58# ELT) #62# (#48# NIL T ELT)) (= #1#) (/ (#64=($ $ |#1|) NIL #23# ELT) #34#) (- #36# #65=(#35# NIL T ELT)) (+ (#35# 34 T ELT)) (** #42# (#63# NIL T ELT) (#41# NIL #23# ELT) (#35# NIL #18# ELT) #66=(#13# NIL #18# ELT)) (* (($ #43# $) NIL T ELT) (($ #25# $) NIL T ELT) (($ #15# . #67=($)) NIL T ELT) #65# (#64# NIL T ELT) (($ |#1| . #67#) NIL T ELT) (($ #14# . #67#) NIL #18# ELT) #66#)) 
(((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesConstructorCategory| |#1| (|UnivariateLaurentSeries| |#1| |#2| |#3|)) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (|RetractableTo| (|UnivariateTaylorSeries| |#1| |#2| |#3|)) (|CoercibleFrom| #1#) (CATEGORY |domain| (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |UnivariatePuiseuxSeries|)) 
((|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)))) 
((|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) 24 T ELT))) 
(((|UnivariatePuiseuxSeriesFunctions2| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| ((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)))) #1=(|Ring|) #1# #2=(|Symbol|) #2# |#1| |#2|) (T |UnivariatePuiseuxSeriesFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|UnivariatePuiseuxSeries| *5 *7 *9)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofType| *7 #2=(|Symbol|)) (|ofType| *9 *5) (|ofType| *10 *6) (|isDomain| *2 (|UnivariatePuiseuxSeries| *6 *8 *10)) (|isDomain| *1 (|UnivariatePuiseuxSeriesFunctions2| *5 *6 *7 *8 *9 *10)) (|ofType| *8 #2#)))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| ((#4=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 75 (|has| |#1| . #5#) ELT)) (|truncate| (($ $ #7=(|Fraction| (|Integer|))) 125 T ELT) (($ $ #7# #7#) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| #7#) (|:| |c| |#1|))) $) 131 T ELT)) (|tanh| (#8=($ $) 164 (|has| |#1| . #9=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|tan| (#10=($ $) 147 (|has| |#1| . #9#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 191 (|has| |#1| . #11=((|Field|))) ELT)) (|squareFree| (#12=((|Factored| $) $) 192 (|has| |#1| . #11#) ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #13=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|sizeLess?| (((|Boolean|) $ $) 182 (|has| |#1| . #11#) ELT)) (|sinh| (#8# 163 (|has| |#1| . #9#) ELT)) (|sin| (#10# 148 (|has| |#1| . #9#) ELT)) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) 200 T ELT)) (|sech| (#8# 162 (|has| |#1| . #9#) ELT)) (|sec| (#10# 149 (|has| |#1| . #9#) ELT)) (|sample| (#14=($) 23 T CONST)) (|rem| (#15=($ $ $) 186 (|has| |#1| . #11#) ELT)) (|reductum| (#16=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#15# 185 (|has| |#1| . #11#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #17=(|List| $)) (|:| |generator| $)) #17#) 180 (|has| |#1| . #11#) ELT)) (|prime?| (((|Boolean|) $) 193 (|has| |#1| . #11#) ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|pi| (($) 174 (|has| |#1| . #9#) ELT)) (|order| ((#7# $) 127 T ELT) ((#7# $ #7#) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #18=(|Integer|)) 145 (|has| |#1| . #13#) ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT) (($ $ (|Fraction| (|Integer|))) 199 T ELT)) (|multiEuclidean| (((|Union| #19=(|List| $) #20="failed") #19# $) 189 (|has| |#1| . #11#) ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| #7#) 82 T ELT) (($ $ #3# #7#) 98 T ELT) (($ $ (|List| #3#) (|List| #7#)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|log| (#21=($ $) 171 (|has| |#1| . #9#) ELT)) (|leadingMonomial| (#16# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|lcm| (#22=($ (|List| $)) 178 (|has| |#1| . #11#) ELT) (#23=($ $ $) 177 (|has| |#1| . #11#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 194 (|has| |#1| . #11#) ELT)) (|integrate| (($ $) 198 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT) (($ $ (|Symbol|)) 197 (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|)))))) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#24=(|SparseUnivariatePolynomial| $) #24# #24#) 179 (|has| |#1| . #11#) ELT)) (|gcd| (#22# 176 (|has| |#1| . #11#) ELT) (#23# 175 (|has| |#1| . #11#) ELT)) (|factor| (#12# 190 (|has| |#1| . #11#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #25=(|:| |coef1| $) #26=(|:| |coef2| $)) #20#) $ $ $) 188 (|has| |#1| . #11#) ELT) (((|Record| #25# #26# (|:| |generator| $)) $ $) 187 (|has| |#1| . #11#) ELT)) (|extend| (($ $ #7#) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #5#) ELT)) (|expressIdealMember| (((|Maybe| #17#) #17# $) 181 (|has| |#1| . #11#) ELT)) (|exp| (#21# 172 (|has| |#1| . #9#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 183 (|has| |#1| . #11#) ELT)) (|elt| ((|#1| $ #7#) 132 T ELT) (($ $ $) 108 (|has| #7# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 184 (|has| |#1| . #11#) ELT)) (|differentiate| (($ $ #27=(|Symbol|)) 120 (AND (|has| |#1| . #28=((|PartialDifferentialRing| #4#))) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #27#)) 118 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #27# . #29=(#30=(|NonNegativeInteger|))) 117 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #27#) . #31=((|List| #30#))) 116 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #32=($)) 112 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#33=($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (|degree| ((#7# $) 84 T ELT)) (|csch| (#8# 161 (|has| |#1| . #9#) ELT)) (|csc| (#10# 150 (|has| |#1| . #9#) ELT)) (|coth| (#8# 160 (|has| |#1| . #9#) ELT)) (|cot| (#10# 151 (|has| |#1| . #9#) ELT)) (|cosh| (#8# 159 (|has| |#1| . #9#) ELT)) (|cos| (#10# 152 (|has| |#1| . #9#) ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT) (($ #34=(|Fraction| #35=(|Integer|))) 78 (|has| |#1| . #36=((|Algebra| (|Fraction| (|Integer|))))) ELT) (($ $) 70 (|has| |#1| . #5#) ELT)) (|coefficient| ((|#1| $ #7#) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|before?| (#1# 6 T ELT)) (|atanh| (#37=($ $) 170 (|has| |#1| . #9#) ELT)) (|atan| (#38=($ $) 158 (|has| |#1| . #9#) ELT)) (|associates?| ((#6# $ $) 74 (|has| |#1| . #5#) ELT)) (|asinh| (#37# 169 (|has| |#1| . #9#) ELT)) (|asin| (#38# 157 (|has| |#1| . #9#) ELT)) (|asech| (#37# 168 (|has| |#1| . #9#) ELT)) (|asec| (#38# 156 (|has| |#1| . #9#) ELT)) (|approximate| ((|#1| $ #7#) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |coerce| (|#1| #4#)))) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#37# 167 (|has| |#1| . #9#) ELT)) (|acsc| (#38# 155 (|has| |#1| . #9#) ELT)) (|acoth| (#37# 166 (|has| |#1| . #9#) ELT)) (|acot| (#38# 154 (|has| |#1| . #9#) ELT)) (|acosh| (#37# 165 (|has| |#1| . #9#) ELT)) (|acos| (#38# 153 (|has| |#1| . #9#) ELT)) (|Zero| (#14# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ #27#) 119 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #27#)) 115 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #27# . #29#) 114 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #27#) . #31#) 113 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #32#) 111 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#33# 109 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT) (($ $ $) 196 (|has| |#1| . #11#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #35#) 195 (|has| |#1| . #11#) ELT) (($ $ $) 173 (|has| |#1| . #9#) ELT) (($ $ (|Fraction| #18#)) 144 (|has| |#1| . #13#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #39=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #39#) 88 T ELT) (($ #34# . #39#) 77 (|has| |#1| . #36#) ELT) (($ $ #34#) 76 (|has| |#1| . #36#) ELT))) 
(((|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 #1=(|isDomain| *2 (|Symbol|)) #2=(|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *3)) #3=(|ofCategory| *3 (|Ring|)) (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|ofCategory| *3 (|PrimitiveFunctionCategory|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))) (AND #1# #2# #3# (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| #1=(|Fraction| (|Integer|))) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|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| #2# #2#) 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|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) |has| (|Fraction| (|Integer|)) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Module| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) 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) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) 
((|zero?| (((|Boolean|) $) 12 T ELT)) (|retractIfCan| (((|Union| |#3| "failed") $) 17 T ELT)) (|retract| ((|#3| $) 14 T ELT))) 
(((|UnivariatePuiseuxSeriesConstructorCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |retractIfCan| ((|Union| |#3| "failed") |#1|)) (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|))) (|UnivariatePuiseuxSeriesConstructorCategory| |#2| |#3|) (|Ring|) (|UnivariateLaurentSeriesCategory| |#2|)) (T |UnivariatePuiseuxSeriesConstructorCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| ((#4=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 75 (|has| |#1| . #5#) ELT)) (|truncate| (($ $ #7=(|Fraction| #8=(|Integer|))) 125 T ELT) (($ $ #7# #7#) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| #7#) (|:| |c| |#1|))) $) 131 T ELT)) (|tanh| (#9=($ $) 164 (|has| |#1| . #10=((|Algebra| #7#))) ELT)) (|tan| (#11=($ $) 147 (|has| |#1| . #10#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 191 (|has| |#1| . #12=((|Field|))) ELT)) (|squareFree| (#13=((|Factored| $) $) 192 (|has| |#1| . #12#) ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #10#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 182 (|has| |#1| . #12#) ELT)) (|sinh| (#9# 163 (|has| |#1| . #10#) ELT)) (|sin| (#11# 148 (|has| |#1| . #10#) ELT)) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| #7#) (|:| |c| |#1|)))) 200 T ELT)) (|sech| (#9# 162 (|has| |#1| . #10#) ELT)) (|sec| (#11# 149 (|has| |#1| . #10#) ELT)) (|sample| (#14=($) 23 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 213 T ELT)) (|retract| ((|#2| $) 214 T ELT)) (|rem| (#15=($ $ $) 186 (|has| |#1| . #12#) ELT)) (|reductum| (#16=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rationalPower| (((|Fraction| (|Integer|)) $) 210 T ELT)) (|quo| (#15# 185 (|has| |#1| . #12#) ELT)) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) 211 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #17=(|List| $)) (|:| |generator| $)) #17#) 180 (|has| |#1| . #12#) ELT)) (|prime?| (((|Boolean|) $) 193 (|has| |#1| . #12#) ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|pi| (($) 174 (|has| |#1| . #10#) ELT)) (|order| ((#7# $) 127 T ELT) ((#7# $ #7#) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #18=(|Integer|)) 145 (|has| |#1| . #10#) ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT) (($ $ #7#) 199 T ELT)) (|multiEuclidean| (((|Union| #19=(|List| $) #20="failed") #19# $) 189 (|has| |#1| . #12#) ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| #7#) 82 T ELT) (($ $ #3# #7#) 98 T ELT) (($ $ (|List| #3#) (|List| #7#)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|log| (#21=($ $) 171 (|has| |#1| . #10#) ELT)) (|leadingMonomial| (#16# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|lcm| (#22=($ (|List| $)) 178 (|has| |#1| . #12#) ELT) (#23=($ $ $) 177 (|has| |#1| . #12#) ELT)) (|laurentRep| ((|#2| $) 209 T ELT)) (|laurentIfCan| (((|Union| |#2| "failed") $) 207 T ELT)) (|laurent| ((|#2| $) 208 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 194 (|has| |#1| . #12#) ELT)) (|integrate| (($ $) 198 (|has| |#1| . #10#) ELT) (($ $ #24=(|Symbol|)) 197 (OR (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #8#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)) (|has| |#1| . #10#)) (AND (|has| |#1| (SIGNATURE |variables| ((|List| #24#) |#1|))) (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #24#))) (|has| |#1| . #10#))) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#25=(|SparseUnivariatePolynomial| $) #25# #25#) 179 (|has| |#1| . #12#) ELT)) (|gcd| (#22# 176 (|has| |#1| . #12#) ELT) (#23# 175 (|has| |#1| . #12#) ELT)) (|factor| (#13# 190 (|has| |#1| . #12#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #26=(|:| |coef1| $) #27=(|:| |coef2| $)) #20#) $ $ $) 188 (|has| |#1| . #12#) ELT) (((|Record| #26# #27# (|:| |generator| $)) $ $) 187 (|has| |#1| . #12#) ELT)) (|extend| (($ $ #7#) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #5#) ELT)) (|expressIdealMember| (((|Maybe| #17#) #17# $) 181 (|has| |#1| . #12#) ELT)) (|exp| (#21# 172 (|has| |#1| . #10#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 183 (|has| |#1| . #12#) ELT)) (|elt| ((|#1| $ #7#) 132 T ELT) (($ $ $) 108 (|has| #7# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 184 (|has| |#1| . #12#) ELT)) (|differentiate| (($ $ #4#) 120 (AND (|has| |#1| . #28=((|PartialDifferentialRing| #4#))) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#)) 118 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #4# . #29=(#30=(|NonNegativeInteger|))) 117 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#) . #31=((|List| #30#))) 116 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #32=($)) 112 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#33=($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (|degree| ((#7# $) 84 T ELT)) (|csch| (#9# 161 (|has| |#1| . #10#) ELT)) (|csc| (#11# 150 (|has| |#1| . #10#) ELT)) (|coth| (#9# 160 (|has| |#1| . #10#) ELT)) (|cot| (#11# 151 (|has| |#1| . #10#) ELT)) (|cosh| (#9# 159 (|has| |#1| . #10#) ELT)) (|cos| (#11# 152 (|has| |#1| . #10#) ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#2|) 212 T ELT) (($ #34=(|Fraction| #35=(|Integer|))) 78 (|has| |#1| . #36=((|Algebra| (|Fraction| (|Integer|))))) ELT) (($ $) 70 (|has| |#1| . #5#) ELT)) (|coefficient| ((|#1| $ #7#) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|before?| (#1# 6 T ELT)) (|atanh| (#37=($ $) 170 (|has| |#1| . #10#) ELT)) (|atan| (#38=($ $) 158 (|has| |#1| . #10#) ELT)) (|associates?| ((#6# $ $) 74 (|has| |#1| . #5#) ELT)) (|asinh| (#37# 169 (|has| |#1| . #10#) ELT)) (|asin| (#38# 157 (|has| |#1| . #10#) ELT)) (|asech| (#37# 168 (|has| |#1| . #10#) ELT)) (|asec| (#38# 156 (|has| |#1| . #10#) ELT)) (|approximate| ((|#1| $ #7#) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |coerce| (|#1| #4#)))) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#37# 167 (|has| |#1| . #10#) ELT)) (|acsc| (#38# 155 (|has| |#1| . #10#) ELT)) (|acoth| (#37# 166 (|has| |#1| . #10#) ELT)) (|acot| (#38# 154 (|has| |#1| . #10#) ELT)) (|acosh| (#37# 165 (|has| |#1| . #10#) ELT)) (|acos| (#38# 153 (|has| |#1| . #10#) ELT)) (|Zero| (#14# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ #4#) 119 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#)) 115 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #4# . #29#) 114 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#) . #31#) 113 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #32#) 111 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#33# 109 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT) (($ $ $) 196 (|has| |#1| . #12#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #35#) 195 (|has| |#1| . #12#) ELT) (($ $ $) 173 (|has| |#1| . #10#) ELT) (($ $ (|Fraction| #18#)) 144 (|has| |#1| . #10#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #39=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #39#) 88 T ELT) (($ #34# . #39#) 77 (|has| |#1| . #36#) ELT) (($ $ #34#) 76 (|has| |#1| . #36#) ELT))) 
(((|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|))))) (|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|) (|CoercibleFrom| |t#2|) (CATEGORY |domain| (SIGNATURE |puiseux| ($ (|Fraction| (|Integer|)) |t#2|)) (SIGNATURE |rationalPower| ((|Fraction| (|Integer|)) $)) (SIGNATURE |laurentRep| (|t#2| $)) (SIGNATURE |degree| ((|Fraction| (|Integer|)) $)) (SIGNATURE |laurent| (|t#2| $)) (SIGNATURE |laurentIfCan| ((|Union| |t#2| "failed") $)))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Fraction| (|Integer|))) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|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| #2# #2#) 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|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) |has| (|Fraction| (|Integer|)) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Module| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) 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) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T) ((|UnivariatePuiseuxSeriesCategory| |#1|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 104 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| (#12=($ $ #13=(|Fraction| #14=(|Integer|))) 116 T ELT) (($ $ #13# #13#) 118 T ELT)) (|terms| ((#15=(|Stream| (|Record| (|:| |k| #13#) (|:| |c| |#1|))) $) 54 T ELT)) (|tanh| (#11# 192 #16=(|has| |#1| (|Algebra| #13#)) ELT)) (|tan| (#11# 168 #16# ELT)) (|subtractIfCan| (#17=(#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePart| (#11# NIL #20=(|has| |#1| (|Field|)) ELT)) (|squareFree| #21=(((|Factored| $) $) NIL #20# ELT)) (|sqrt| (#11# NIL #16# ELT)) (|sizeLess?| (#2# NIL #20# ELT)) (|sinh| (#11# 188 #16# ELT)) (|sin| (#11# 164 #16# ELT)) (|series| (($ #22=(|NonNegativeInteger|) #15#) 65 T ELT)) (|sech| (#11# 196 #16# ELT)) (|sec| (#11# 172 #16# ELT)) (|sample| (#23=($) NIL T CONST)) (|retractIfCan| (#24=((|Union| |#2| #19#) $) NIL T ELT)) (|retract| (#25=(|#2| $) NIL T ELT)) (|rem| #26=(#27=($ $ $) NIL #20# ELT)) (|reductum| #28=(#11# NIL T ELT)) (|recip| ((#18# $) 85 T ELT)) (|rationalPower| (#29=(#13# $) 13 T ELT)) (|quo| #26#) (|puiseux| (($ #13# |#2|) 11 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #30=(|List| $)) #31=(|:| |generator| $)) #30#) NIL #20# ELT)) (|prime?| (#5# NIL #20# ELT)) (|pole?| (#5# 74 T ELT)) (|pi| (#23# NIL #16# ELT)) (|order| (#29# 113 T ELT) ((#13# $ #13#) 114 T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#32=($ $ #14#) NIL #16# ELT)) (|multiplyExponents| (#33=($ $ #34=(|PositiveInteger|)) 130 T ELT) (#12# 128 T ELT)) (|multiEuclidean| (((|Union| #30# #19#) #30# $) NIL #20# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #13#) 33 T ELT) (($ $ #7# #13#) NIL T ELT) (($ $ #6# (|List| #13#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 125 T ELT)) (|log| (#11# 162 #16# ELT)) (|leadingMonomial| #28#) (|leadingCoefficient| (#35=(|#1| $) NIL T ELT)) (|lcm| #36=(($ #30#) NIL #20# ELT) #26#) (|laurentRep| (#25# 12 T ELT)) (|laurentIfCan| (#24# 44 T ELT)) (|laurent| (#25# 45 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#11# 101 #20# ELT)) (|integrate| (#11# 146 #16# ELT) (#37=($ $ #8#) 151 (OR (AND #16# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #14#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #16# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#38=(|List| #8#) |#1|))))) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#39=(|SparseUnivariatePolynomial| $) #39# #39#) NIL #20# ELT)) (|gcd| #36# #26#) (|factor| #21#) (|extendedEuclidean| (((|Union| (|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $)) #19#) $ $ $) NIL #20# ELT) (((|Record| #40# #41# #31#) $ $) NIL #20# ELT)) (|extend| (#12# 122 T ELT)) (|exquo| (#17# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #30#) #30# $) NIL #20# ELT)) (|exp| (#11# 160 #16# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 98 #42=(|has| |#1| (SIGNATURE ** (|#1| |#1| #13#))) ELT)) (|euclideanSize| ((#22# $) NIL #20# ELT)) (|elt| (#43=(|#1| $ #13#) 108 T ELT) (#27# 94 (|has| #13# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #20# ELT)) (|differentiate| (#37# 138 #44=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #45=(|has| |#1| (SIGNATURE * (|#1| #13# |#1|)))) ELT) #46=(($ $ #38#) NIL #44# ELT) #47=(($ $ #8# #22#) NIL #44# ELT) #48=(($ $ #38# (|List| #22#)) NIL #44# ELT) (#11# 134 #45# ELT) #49=(#50=($ $ #22#) NIL #45# ELT)) (|degree| (#29# 16 T ELT)) (|csch| (#11# 198 #16# ELT)) (|csc| (#11# 174 #16# ELT)) (|coth| (#11# 194 #16# ELT)) (|cot| (#11# 170 #16# ELT)) (|cosh| (#11# 190 #16# ELT)) (|cos| (#11# 166 #16# ELT)) (|complete| (#11# 120 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) 37 T ELT) (($ |#1|) 27 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#2|) 34 T ELT) (($ #13#) 139 #16# ELT) #10#) (|coefficient| (#43# 107 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#22#) 127 T CONST)) (|center| (#35# 106 T ELT)) (|before?| #1#) (|atanh| (#11# 204 #16# ELT)) (|atan| (#11# 180 #16# ELT)) (|associates?| (#2# NIL #9# ELT)) (|asinh| (#11# 200 #16# ELT)) (|asin| (#11# 176 #16# ELT)) (|asech| (#11# 208 #16# ELT)) (|asec| (#11# 184 #16# ELT)) (|approximate| (#43# NIL (AND #42# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| (#11# 210 #16# ELT)) (|acsc| (#11# 186 #16# ELT)) (|acoth| (#11# 206 #16# ELT)) (|acot| (#11# 182 #16# ELT)) (|acosh| (#11# 202 #16# ELT)) (|acos| (#11# 178 #16# ELT)) (|Zero| (#23# 21 T CONST)) (|One| (#23# 17 T CONST)) (D (#37# NIL #44# ELT) #46# #47# #48# (#11# NIL #45# ELT) #49#) (= (#2# 72 T ELT)) (/ (#51=($ $ |#1|) NIL #20# ELT) (#27# 100 #20# ELT)) (- (#11# 142 T ELT) (#27# 78 T ELT)) (+ (#27# 76 T ELT)) (** (#33# NIL T ELT) (#50# 82 T ELT) (#32# 157 #20# ELT) (#27# NIL #16# ELT) (#12# 158 #16# ELT)) (* (($ #34# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #14# . #52=($)) NIL T ELT) (#27# 80 T ELT) (#51# NIL T ELT) (($ |#1| . #52#) 137 T ELT) (($ #13# . #52#) NIL #16# ELT) (#12# NIL #16# ELT))) 
(((|UnivariatePuiseuxSeriesConstructor| |#1| |#2|) (|UnivariatePuiseuxSeriesConstructorCategory| |#1| |#2|) (|Ring|) (|UnivariateLaurentSeriesCategory| |#1|)) (T |UnivariatePuiseuxSeriesConstructor|)) 
NIL 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) 37 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #6=(#3# NIL T ELT)) (|subtractIfCan| #7=((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|sample| #10=(($) NIL T CONST)) (|retractIfCan| (((|Union| #11=(|Integer|) . #12=(#9#)) . #13=($)) NIL #14=(|has| #15=(|UnivariatePuiseuxSeries| |#2| |#3| |#4|) (|RetractableTo| #11#)) ELT) (((|Union| #16=(|Fraction| #11#) . #12#) . #13#) NIL #17=(|has| #15# (|RetractableTo| #16#)) ELT) (((|Union| #15# . #12#) $) 22 T ELT)) (|retract| ((#11# . #18=($)) NIL #14# ELT) ((#16# . #18#) NIL #17# ELT) #19=(#20=(#15# . #18#) NIL T ELT)) (|reductum| (#5# 41 T ELT)) (|recip| ((#8# $) 27 T ELT)) (|primitivePart| (#5# NIL #21=(|has| #15# (|GcdDomain|)) ELT)) (|pomopo!| (($ $ #15# #22=(|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|) $) NIL T ELT)) (|opposite?| #1#) (|one?| #6#) (|numberOfMonomials| ((#23=(|NonNegativeInteger|) $) 11 T ELT)) (|monomial?| #6#) (|monomial| (($ #15# #22#) 25 T ELT)) (|minimumDegree| (#24=(#22# $) NIL T ELT)) (|mapExponents| (($ (|Mapping| #22# #22#) $) NIL T ELT)) (|map| (($ (|Mapping| #15# #15#) $) NIL T ELT)) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) #9#) $) 91 T ELT)) (|leadingMonomial| #4#) (|leadingCoefficient| (#20# 20 T ELT)) (|latex| ((#25=(|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #6#) (|ground| #19#) (|exquo| ((#8# $ #15#) NIL (|has| #15# (|IntegralDomain|)) ELT) #7#) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| #15#) (|:| |%expon| #22#) (|:| |%expTerms| (|List| (|Record| (|:| |k| #16#) (|:| |c| |#2|)))))) (|:| |%type| #25#)) #9#) $) 74 T ELT)) (|degree| (#24# 17 T ELT)) (|content| (#20# NIL #21# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #11#) NIL T ELT) (($ #15#) NIL T ELT) #4# (($ #16#) NIL (OR #17# #26=(|has| #15# (|Algebra| #16#))) ELT)) (|coefficients| (((|List| #15#) $) NIL T ELT)) (|coefficient| ((#15# $ #22#) NIL T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| #15# (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#23#) NIL T CONST)) (|binomThmExpt| (($ $ $ #23#) NIL (|has| #15# (|CommutativeRing|)) ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| #10#) (|One| #10#) (= #1#) (/ (#27=($ $ #15#) NIL (|has| #15# (|Field|)) ELT)) (- #4# #28=(($ $ $) NIL T ELT)) (+ #28#) (** (($ $ #29=(|PositiveInteger|)) NIL T ELT) (($ $ #23#) NIL T ELT)) (* (($ #29# $) NIL T ELT) (($ #23# $) NIL T ELT) (($ #11# . #30=($)) NIL T ELT) #28# (#27# NIL T ELT) (($ #15# . #30#) NIL T ELT) (($ #16# . #30#) NIL #26# ELT) (($ $ #16#) NIL #26# ELT))) 
(((|UnivariatePuiseuxSeriesWithExponentialSingularity| |#1| |#2| |#3| |#4|) (|Join| (|FiniteAbelianMonoidRing| #1=(|UnivariatePuiseuxSeries| |#2| |#3| |#4|) #2=(|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |limitPlus| ((|Union| (|OrderedCompletion| |#2|) #3="failed") $)) (SIGNATURE |dominantTerm| ((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| #1#) (|:| |%expon| #2#) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| #4=(|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) #3#) $)))) (|Join| (|RetractableTo| #4#) (|LinearlyExplicitRingOver| #4#) (|GcdDomain|)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|)) (|Symbol|) |#2|) (T |UnivariatePuiseuxSeriesWithExponentialSingularity|)) 
((|limitPlus| #1=(*1 *2 *1) (|partial| AND #2=(|ofCategory| *3 (|Join| (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#) (|GcdDomain|))) (|isDomain| *2 (|OrderedCompletion| *4)) #4=(|isDomain| *1 (|UnivariatePuiseuxSeriesWithExponentialSingularity| *3 *4 *5 *6)) #5=(|ofCategory| *4 (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| *3))) #6=(|ofType| *5 (|Symbol|)) #7=(|ofType| *6 *4))) (|dominantTerm| #1# (|partial| AND #2# (|isDomain| *2 (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| *4 *5 *6)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| *4 *5 *6)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| #3#)) (|:| |c| *4)))))) (|:| |%type| (|String|)))) #4# #5# #6# #7#))) 
((|value| (#1=(|#2| $) 34 T ELT)) (|third| (#1# 18 T ELT)) (|tail| (#2=($ $) 43 T ELT)) (|split!| (($ $ (|Integer|)) 78 T ELT)) (|setvalue!| (#3=(|#2| $ |#2|) 75 T ELT)) (|setlast!| (#3# 71 T ELT)) (|setelt| ((|#2| $ #4="value" |#2|) NIL T ELT) ((|#2| $ #5="first" |#2|) 64 T ELT) (($ $ #6="rest" $) 68 T ELT) ((|#2| $ #7="last" |#2|) 66 T ELT)) (|setchildren!| (($ $ #8=(|List| $)) 74 T ELT)) (|second| (#1# 17 T ELT)) (|rest| (#2# NIL T ELT) (#9=($ $ #10=(|NonNegativeInteger|)) 51 T ELT)) (|nodes| (#11=(#8# $) 31 T ELT)) (|node?| (#12=(#13=(|Boolean|) $ $) 62 T ELT)) (|leaf?| (#14=(#13# $) 33 T ELT)) (|last| (#1# 25 T ELT) (#9# 57 T ELT)) (|elt| ((|#2| $ #4#) NIL T ELT) ((|#2| $ #5#) 10 T ELT) (($ $ #6#) 16 T ELT) ((|#2| $ #7#) 13 T ELT)) (|cyclic?| (#14# 23 T ELT)) (|cycleTail| (#2# 46 T ELT)) (|cycleSplit!| (#2# 79 T ELT)) (|cycleLength| ((#10# $) 50 T ELT)) (|cycleEntry| (#2# 49 T ELT)) (|concat| (($ $ $) 70 T ELT) (($ |#2| $) NIL T ELT)) (|children| (#11# 32 T ELT)) (= (#12# 60 T ELT))) 
(((|UnaryRecursiveAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |split!| (|#1| |#1| (|Integer|))) (SIGNATURE |setelt| (|#2| |#1| #3="last" |#2|)) (SIGNATURE |setlast!| #4=(|#2| |#1| |#2|)) (SIGNATURE |setelt| (|#1| |#1| #5="rest" |#1|)) (SIGNATURE |setelt| (|#2| |#1| #6="first" |#2|)) (SIGNATURE |cycleSplit!| #7=(|#1| |#1|)) (SIGNATURE |cycleTail| #7#) (SIGNATURE |cycleLength| (#8=(|NonNegativeInteger|) |#1|)) (SIGNATURE |cycleEntry| #7#) (SIGNATURE |third| #9=(|#2| |#1|)) (SIGNATURE |second| #9#) (SIGNATURE |tail| #7#) (SIGNATURE |last| #10=(|#1| |#1| #8#)) (SIGNATURE |elt| (|#2| |#1| #3#)) (SIGNATURE |last| #9#) (SIGNATURE |rest| #10#) (SIGNATURE |elt| (|#1| |#1| #5#)) (SIGNATURE |rest| #7#) (SIGNATURE |elt| (|#2| |#1| #6#)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |setvalue!| #4#) (SIGNATURE |setelt| (|#2| |#1| #11="value" |#2|)) (SIGNATURE |setchildren!| (|#1| |#1| #12=(|List| |#1|))) (SIGNATURE |node?| #1#) (SIGNATURE |cyclic?| #13=(#2# |#1|)) (SIGNATURE |elt| (|#2| |#1| #11#)) (SIGNATURE |value| #9#) (SIGNATURE |leaf?| #13#) (SIGNATURE |nodes| #14=(#12# |#1|)) (SIGNATURE |children| #14#)) (|UnaryRecursiveAggregate| |#2|) (|Type|)) (T |UnaryRecursiveAggregate&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|third| ((|#1| $) 62 T ELT)) (|tail| (($ $) 64 T ELT)) (|split!| (($ $ (|Integer|)) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setrest!| (($ $ $) 53 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #3="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ "first" |#1|) 54 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ "rest" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ "last" |#1|) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #4=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|second| ((|#1| $) 63 T ELT)) (|sample| (#5=($) 6 T CONST)) (|rest| (($ $) 70 T ELT) (($ $ (|NonNegativeInteger|)) 68 T ELT)) (|nodes| (#6=(#4# $) 45 T ELT)) (|node?| (#7=(#8=(|Boolean|) $ $) 37 (|has| |#1| . #9=((|BasicType|))) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (#10=(#8# $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #11=((|SetCategory|))) ELT)) (|last| ((|#1| $) 67 T ELT) (($ $ (|NonNegativeInteger|)) 65 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #11#) ELT)) (|first| ((|#1| $) 73 T ELT) (($ $ (|NonNegativeInteger|)) 71 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT)) (|eq?| ((#12=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#12# $) 7 T ELT)) (|empty| (#5# 8 T ELT)) (|elt| ((|#1| $ #3#) 42 T ELT) ((|#1| $ "first") 72 T ELT) (($ $ "rest") 69 T ELT) ((|#1| $ "last") 66 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (#10# 41 T ELT)) (|cycleTail| (($ $) 59 T ELT)) (|cycleSplit!| (($ $) 56 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|cycleLength| (((|NonNegativeInteger|) $) 60 T ELT)) (|cycleEntry| (($ $) 61 T ELT)) (|copy| (($ $) 9 T ELT)) (|concat!| (($ $ $) 58 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ |#1|) 57 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|concat| (($ $ $) 75 T ELT) (($ |#1| $) 74 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (#6# 46 T ELT)) (|child?| (#7# 38 (|has| |#1| . #9#) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) 
(((|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 (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|cycleSplit!| (*1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setfirst!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 "first") (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setrest!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 "rest") (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setlast!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 "last") (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|UnaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|split!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|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| $ (|ShallowlyMutableAggregate| |t#1|)) (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|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 87 T ELT)) (|univariatePolynomial| ((#9=(|UnivariatePolynomial| |#2| |#1|) $ #10=(|NonNegativeInteger|)) 70 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #11=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #11# ELT)) (|unit?| (#5# 139 #11# ELT)) (|truncate| (#14=($ $ #10#) 125 T ELT) (($ $ #10# #10#) 127 T ELT)) (|terms| ((#15=(|Stream| (|Record| (|:| |k| #10#) (|:| |c| |#1|))) $) 42 T ELT)) (|tanh| #16=(#13# NIL #17=(|has| |#1| (|Algebra| #18=(|Fraction| #19=(|Integer|)))) ELT)) (|tan| #16#) (|subtractIfCan| (#20=(#21=(|Union| $ "failed") $ $) NIL T ELT)) (|sqrt| #16#) (|sinh| #16#) (|sin| #16#) (|series| (($ #15#) 49 T ELT) (($ #22=(|Stream| |#1|)) NIL T ELT)) (|sech| #16#) (|sec| #16#) (|sample| (#23=($) NIL T CONST)) (|revert| (#13# 131 T ELT)) (|reductum| #24=(#13# NIL T ELT)) (|recip| ((#21# $) NIL T ELT)) (|quoByVar| (#13# 137 T ELT)) (|polynomial| ((#25=(|Polynomial| |#1|) $ #10#) 60 T ELT) ((#25# $ #10# #10#) 62 T ELT)) (|pole?| #4#) (|pi| (#23# NIL #17# ELT)) (|order| #26=((#10# $) NIL T ELT) ((#10# $ #10#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|oddlambert| (#13# 115 T ELT)) (|nthRoot| (($ $ #19#) NIL #17# ELT)) (|multisect| (#27=($ #19# #19# $) 133 T ELT)) (|multiplyExponents| (#28=($ $ #29=(|PositiveInteger|)) 136 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #19#) $) 109 T ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #10#) 16 T ELT) (($ $ #7# #10#) NIL T ELT) (($ $ #6# #30=(|List| #10#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 96 T ELT)) (|log| #16#) (|leadingMonomial| #24#) (|leadingCoefficient| (#31=(|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lambert| (#13# 113 T ELT)) (|lagrange| (#13# 111 T ELT)) (|invmultisect| (#27# 135 T ELT)) (|integrate| (#13# 147 #17# ELT) (#32=($ $ #8#) 153 (OR (AND #17# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #19#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #17# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#33=(|List| #8#) |#1|))))) ELT) (#34=($ $ #35=(|Variable| |#2|)) 148 #17# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generalLambert| (($ $ #19# #19#) 119 T ELT)) (|extend| (#14# 121 T ELT)) (|exquo| (#20# NIL #11# ELT)) (|exp| #16#) (|evenlambert| (#13# 117 T ELT)) (|eval| ((#22# $ |#1|) 98 #36=(|has| |#1| (SIGNATURE ** (|#1| |#1| #10#))) ELT)) (|elt| (#37=(|#1| $ #10#) 93 T ELT) (#38=($ $ $) 129 (|has| #10# (|SemiGroup|)) ELT)) (|differentiate| (#32# 106 #39=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #40=(|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) #41=(($ $ #33#) NIL #39# ELT) #42=(($ $ #8# #10#) NIL #39# ELT) #43=(($ $ #33# #30#) NIL #39# ELT) (#13# 100 #40# ELT) #44=(#14# NIL #40# ELT) (#34# 101 T ELT)) (|degree| #26#) (|csch| #16#) (|csc| #16#) (|coth| #16#) (|cot| #16#) (|cosh| #16#) (|cos| #16#) (|complete| (#13# 123 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) 26 T ELT) (($ #18#) 145 #17# ELT) #12# (($ |#1|) 25 (|has| |#1| (|CommutativeRing|)) ELT) (($ #9#) 78 T ELT) (($ #35#) 22 T ELT)) (|coefficients| ((#22# $) NIL T ELT)) (|coefficient| (#37# 92 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#10#) NIL T CONST)) (|center| (#31# 88 T ELT)) (|before?| #1#) (|atanh| #16#) (|atan| #16#) (|associates?| (#2# NIL #11# ELT)) (|asinh| #16#) (|asin| #16#) (|asech| #16#) (|asec| #16#) (|approximate| (#37# 86 (AND #36# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #16#) (|acsc| #16#) (|acoth| #16#) (|acot| #16#) (|acosh| #16#) (|acos| #16#) (|Zero| (#23# 18 T CONST)) (|One| (#23# 13 T CONST)) (D (#32# NIL #39# ELT) #41# #42# #43# (#13# NIL #40# ELT) #44# (#34# NIL T ELT)) (= #1#) (/ (#45=($ $ |#1|) NIL #46=(|has| |#1| (|Field|)) ELT)) (- #24# (#38# 105 T ELT)) (+ (#38# 20 T ELT)) (** (#28# NIL T ELT) (#14# NIL T ELT) (#45# 142 #46# ELT) (#38# NIL #17# ELT) #47=(($ $ #18#) NIL #17# ELT)) (* (($ #29# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #19# . #48=($)) NIL T ELT) (#38# NIL T ELT) (#45# NIL T ELT) (($ |#1| . #48#) 104 T ELT) (($ #18# . #48#) NIL #17# ELT) #47#)) 
(((|UnivariateTaylorSeries| |#1| |#2| |#3|) (|Join| (|UnivariateTaylorSeriesCategory| |#1|) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #2=(|UnivariatePolynomial| |#2| |#1|))) (SIGNATURE |univariatePolynomial| (#2# $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ #1#)) (SIGNATURE |lagrange| #3=($ $)) (SIGNATURE |lambert| #3#) (SIGNATURE |oddlambert| #3#) (SIGNATURE |evenlambert| #3#) (SIGNATURE |generalLambert| ($ $ #4=(|Integer|) #4#)) (SIGNATURE |revert| #3#) (SIGNATURE |multisect| #5=($ #4# #4# $)) (SIGNATURE |invmultisect| #5#) (IF (|has| |#1| (|Algebra| (|Fraction| #4#))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |UnivariateTaylorSeries|)) 
((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *3)) #2=(|ofCategory| *3 #3=(|Ring|)) #4=(|ofType| *4 #5=(|Symbol|)) #6=(|ofType| *5 *3) #7=(|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 #3#) (|ofType| *5 #5#) (|ofType| *6 *4))) (|coerce| #1# (AND #8=(|isDomain| *2 (|Variable| *4)) #4# #7# #2# #6#)) (|lagrange| #9=(*1 *1 *1) #10=(AND (|isDomain| *1 (|UnivariateTaylorSeries| *2 *3 *4)) (|ofCategory| *2 #3#) (|ofType| *3 #5#) (|ofType| *4 *2))) (|lambert| #9# #10#) (|oddlambert| #9# #10#) (|evenlambert| #9# #10#) (|generalLambert| (*1 *1 *1 *2 *2) #11=(AND (|isDomain| *2 #12=(|Integer|)) #7# #2# #4# #6#)) (|revert| #9# #10#) (|multisect| #13=(*1 *1 *2 *2 *1) #11#) (|invmultisect| #13# #11#) (|integrate| (*1 *1 *1 *2) (AND #8# #4# #7# (|ofCategory| *3 (|Algebra| (|Fraction| #12#))) #2# #6#))) 
((|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) 17 T ELT))) 
(((|UnivariateTaylorSeriesFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#2| |#1|) |#3|))) #1=(|Ring|) #1# (|UnivariateTaylorSeriesCategory| |#1|) (|UnivariateTaylorSeriesCategory| |#2|)) (T |UnivariateTaylorSeriesFunctions2|)) 
((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *6)) (|isDomain| *1 (|UnivariateTaylorSeriesFunctions2| *5 *6 *4 *2)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *5))))) 
((|zero?| (((|Boolean|) $) 17 T ELT)) (|tanh| (#1=($ $) 105 T ELT)) (|tan| (#1# 81 T ELT)) (|sinh| (#1# 101 T ELT)) (|sin| (#1# 77 T ELT)) (|sech| (#1# 109 T ELT)) (|sec| (#1# 85 T ELT)) (|log| (#1# 75 T ELT)) (|exp| (#1# 73 T ELT)) (|csch| (#1# 111 T ELT)) (|csc| (#1# 87 T ELT)) (|coth| (#1# 107 T ELT)) (|cot| (#1# 83 T ELT)) (|cosh| (#1# 103 T ELT)) (|cos| (#1# 79 T ELT)) (|coerce| (((|OutputForm|) $) 61 T ELT) (($ #2=(|Integer|)) NIL T ELT) (($ #3=(|Fraction| #2#)) NIL T ELT) (#1# NIL T ELT) (($ |#2|) NIL T ELT)) (|atanh| (#1# 117 T ELT)) (|atan| (#1# 93 T ELT)) (|asinh| (#1# 113 T ELT)) (|asin| (#1# 89 T ELT)) (|asech| (#1# 121 T ELT)) (|asec| (#1# 97 T ELT)) (|acsch| (#1# 123 T ELT)) (|acsc| (#1# 99 T ELT)) (|acoth| (#1# 119 T ELT)) (|acot| (#1# 95 T ELT)) (|acosh| (#1# 115 T ELT)) (|acos| (#1# 91 T ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ |#2|) 65 T ELT) (($ $ $) 68 T ELT) (($ $ #3#) 71 T ELT))) 
(((|UnivariateTaylorSeriesCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE ** (|#1| |#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE |tan| #3=(|#1| |#1|)) (SIGNATURE |sin| #3#) (SIGNATURE |sec| #3#) (SIGNATURE |csc| #3#) (SIGNATURE |cot| #3#) (SIGNATURE |cos| #3#) (SIGNATURE |acos| #3#) (SIGNATURE |acot| #3#) (SIGNATURE |acsc| #3#) (SIGNATURE |asec| #3#) (SIGNATURE |asin| #3#) (SIGNATURE |atan| #3#) (SIGNATURE |cosh| #3#) (SIGNATURE |coth| #3#) (SIGNATURE |csch| #3#) (SIGNATURE |sech| #3#) (SIGNATURE |sinh| #3#) (SIGNATURE |tanh| #3#) (SIGNATURE |acosh| #3#) (SIGNATURE |acoth| #3#) (SIGNATURE |acsch| #3#) (SIGNATURE |asech| #3#) (SIGNATURE |asinh| #3#) (SIGNATURE |atanh| #3#) (SIGNATURE |log| #3#) (SIGNATURE |exp| #3#) (SIGNATURE ** (|#1| |#1| |#1|)) (SIGNATURE ** (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| #3#) (SIGNATURE |coerce| (|#1| #1#)) (SIGNATURE |coerce| (|#1| #2#)) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|))) (SIGNATURE |zero?| ((|Boolean|) |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|UnivariateTaylorSeriesCategory| |#2|) (|Ring|)) (T |UnivariateTaylorSeriesCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| ((#4=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 72 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 75 (|has| |#1| . #5#) ELT)) (|truncate| (($ $ #7=(|NonNegativeInteger|)) 125 T ELT) (($ $ #7# #7#) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| #7#) (|:| |c| |#1|))) $) 131 T ELT)) (|tanh| (#8=($ $) 164 (|has| |#1| . #9=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|tan| (#10=($ $) 147 (|has| |#1| . #9#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #11=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|sinh| (#8# 163 (|has| |#1| . #9#) ELT)) (|sin| (#10# 148 (|has| |#1| . #9#) ELT)) (|series| (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) 184 T ELT) (($ (|Stream| |#1|)) 182 T ELT)) (|sech| (#8# 162 (|has| |#1| . #9#) ELT)) (|sec| (#10# 149 (|has| |#1| . #9#) ELT)) (|sample| (#12=($) 23 T CONST)) (|reductum| (#13=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quoByVar| (($ $) 181 T ELT)) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) 179 T ELT) (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) 178 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|pi| (($) 174 (|has| |#1| . #9#) ELT)) (|order| ((#7# $) 127 T ELT) ((#7# $ #7#) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #14=(|Integer|)) 145 (|has| |#1| . #11#) ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) 180 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| #7#) 82 T ELT) (($ $ #3# #7#) 98 T ELT) (($ $ (|List| #3#) (|List| #7#)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|log| (#15=($ $) 171 (|has| |#1| . #9#) ELT)) (|leadingMonomial| (#13# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|integrate| (($ $) 176 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT) (($ $ (|Symbol|)) 175 (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|)))))) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (($ $ #7#) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #5#) ELT)) (|exp| (#15# 172 (|has| |#1| . #9#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) ELT)) (|elt| ((|#1| $ #7#) 132 T ELT) (($ $ $) 108 (|has| #7# (|SemiGroup|)) ELT)) (|differentiate| (($ $ #4#) 120 (AND (|has| |#1| . #16=((|PartialDifferentialRing| #4#))) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#)) 118 (AND (|has| |#1| . #16#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #4# . #17=(#18=(|NonNegativeInteger|))) 117 (AND (|has| |#1| . #16#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#) . #19=((|List| #18#))) 116 (AND (|has| |#1| . #16#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #20=($)) 112 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#21=($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (|degree| ((#7# $) 84 T ELT)) (|csch| (#8# 161 (|has| |#1| . #9#) ELT)) (|csc| (#10# 150 (|has| |#1| . #9#) ELT)) (|coth| (#8# 160 (|has| |#1| . #9#) ELT)) (|cot| (#10# 151 (|has| |#1| . #9#) ELT)) (|cosh| (#8# 159 (|has| |#1| . #9#) ELT)) (|cos| (#10# 152 (|has| |#1| . #9#) ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #22=(|Fraction| (|Integer|))) 78 (|has| |#1| . #23=((|Algebra| #22#))) ELT) (($ $) 70 (|has| |#1| . #5#) ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficients| (((|Stream| |#1|) $) 183 T ELT)) (|coefficient| ((|#1| $ #7#) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|before?| (#1# 6 T ELT)) (|atanh| (#24=($ $) 170 (|has| |#1| . #9#) ELT)) (|atan| (#25=($ $) 158 (|has| |#1| . #9#) ELT)) (|associates?| ((#6# $ $) 74 (|has| |#1| . #5#) ELT)) (|asinh| (#24# 169 (|has| |#1| . #9#) ELT)) (|asin| (#25# 157 (|has| |#1| . #9#) ELT)) (|asech| (#24# 168 (|has| |#1| . #9#) ELT)) (|asec| (#25# 156 (|has| |#1| . #9#) ELT)) (|approximate| ((|#1| $ #7#) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |coerce| (|#1| #4#)))) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|acsch| (#24# 167 (|has| |#1| . #9#) ELT)) (|acsc| (#25# 155 (|has| |#1| . #9#) ELT)) (|acoth| (#24# 166 (|has| |#1| . #9#) ELT)) (|acot| (#25# 154 (|has| |#1| . #9#) ELT)) (|acosh| (#24# 165 (|has| |#1| . #9#) ELT)) (|acos| (#25# 153 (|has| |#1| . #9#) ELT)) (|Zero| (#12# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ #4#) 119 (AND (|has| |#1| . #16#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#)) 115 (AND (|has| |#1| . #16#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #4# . #17#) 114 (AND (|has| |#1| . #16#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#) . #19#) 113 (AND (|has| |#1| . #16#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #20#) 111 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#21# 109 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ |#1|) 177 (|has| |#1| (|Field|)) ELT) (($ $ $) 173 (|has| |#1| . #9#) ELT) (($ $ (|Fraction| #14#)) 144 (|has| |#1| . #11#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #26=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #26#) 88 T ELT) (($ #22# . #26#) 77 (|has| |#1| . #23#) ELT) (($ $ #22#) 76 (|has| |#1| . #23#) ELT))) 
(((|UnivariateTaylorSeriesCategory| |#1|) (|Category|) (|Ring|)) (T |UnivariateTaylorSeriesCategory|)) 
((|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| *3)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Stream| *3)))) (|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)))) (|quoByVar| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|multiplyCoefficients| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 (|Integer|))) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|polynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Polynomial| *4)))) (|polynomial| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Polynomial| *4)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|integrate| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))))) (|integrate| (*1 *1 *1 *2) (OR (AND #1=(|isDomain| *2 (|Symbol|)) #2=(|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)) #3=(|ofCategory| *3 (|Ring|)) (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|ofCategory| *3 (|PrimitiveFunctionCategory|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))) (AND #1# #2# #3# (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3))) (|has| *3 (SIGNATURE |integrate| (*3 *3 *2))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))))) 
(|Join| (|UnivariatePowerSeriesCategory| |t#1| (|NonNegativeInteger|)) (CATEGORY |domain| (SIGNATURE |series| ($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |t#1|))))) (SIGNATURE |coefficients| ((|Stream| |t#1|) $)) (SIGNATURE |series| ($ (|Stream| |t#1|))) (SIGNATURE |quoByVar| ($ $)) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |t#1| (|Integer|)) $)) (SIGNATURE |polynomial| ((|Polynomial| |t#1|) $ (|NonNegativeInteger|))) (SIGNATURE |polynomial| ((|Polynomial| |t#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|))) (IF (|has| |t#1| (|Field|)) (SIGNATURE ** ($ $ |t#1|)) |%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|))) 
(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|NonNegativeInteger|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|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| #2# #2#) |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|)) ((|CoercibleFrom| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) |has| (|NonNegativeInteger|) (|SemiGroup|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) 
((|stFuncN| (((|Mapping| #1=(|Stream| |#1|) (|List| #1#)) #2=(|Mapping| |#2| #3=(|List| |#2|))) 24 T ELT)) (|stFunc2| (((|Mapping| #1# #1# #1#) #4=(|Mapping| |#2| |#2| |#2|)) 16 T ELT)) (|stFunc1| (((|Mapping| #1# #1#) #5=(|Mapping| |#2| |#2|)) 13 T ELT)) (|ode2| ((|#2| #4# |#1| |#1|) 48 T ELT)) (|ode1| ((|#2| #5# |#1|) 46 T ELT)) (|ode| ((|#2| #2# #6=(|List| |#1|)) 60 T ELT)) (|mpsode| ((#3# #6# (|List| #2#)) 66 T ELT)) (|fixedPointExquo| ((|#2| |#2| |#2|) 43 T ELT))) 
(((|UnivariateTaylorSeriesODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |stFunc1| ((|Mapping| #1=(|Stream| |#1|) #1#) #2=(|Mapping| |#2| |#2|))) (SIGNATURE |stFunc2| ((|Mapping| #1# #1# #1#) #3=(|Mapping| |#2| |#2| |#2|))) (SIGNATURE |stFuncN| ((|Mapping| #1# (|List| #1#)) #4=(|Mapping| |#2| #5=(|List| |#2|)))) (SIGNATURE |fixedPointExquo| (|#2| |#2| |#2|)) (SIGNATURE |ode1| (|#2| #2# |#1|)) (SIGNATURE |ode2| (|#2| #3# |#1| |#1|)) (SIGNATURE |ode| (|#2| #4# #6=(|List| |#1|))) (SIGNATURE |mpsode| (#5# #6# (|List| #4#)))) (|Algebra| (|Fraction| (|Integer|))) (|UnivariateTaylorSeriesCategory| |#1|)) (T |UnivariateTaylorSeriesODESolver|)) 
((|mpsode| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 #2=(|List| *5)) (|isDomain| *4 (|List| (|Mapping| *6 #3=(|List| *6)))) #4=(|ofCategory| *5 #5=(|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *6 #6=(|UnivariateTaylorSeriesCategory| *5)) (|isDomain| *2 #3#) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *5 *6)))) (|ode| #1# (AND (|isDomain| *3 (|Mapping| *2 (|List| *2))) (|isDomain| *4 #2#) #4# (|ofCategory| *2 #6#) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *5 *2)))) (|ode2| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) #7=(|ofCategory| *2 #8=(|UnivariateTaylorSeriesCategory| *4)) #9=(|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *4 *2)) #10=(|ofCategory| *4 #5#))) (|ode1| #1# (AND (|isDomain| *3 (|Mapping| *2 *2)) #7# #9# #10#)) (|fixedPointExquo| (*1 *2 *2 *2) (AND (|ofCategory| *3 #5#) (|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *3 *2)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|stFuncN| #11=(*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 #2#)) #12=(|ofCategory| *5 #8#) #10# (|isDomain| *2 (|Mapping| #13=(|Stream| *4) (|List| #13#))) #14=(|isDomain| *1 (|UnivariateTaylorSeriesODESolver| *4 *5)))) (|stFunc2| #11# (AND (|isDomain| *3 (|Mapping| *5 *5 *5)) #12# #10# (|isDomain| *2 (|Mapping| #13# #13# #13#)) #14#)) (|stFunc1| #11# (AND (|isDomain| *3 (|Mapping| *5 *5)) #12# #10# (|isDomain| *2 (|Mapping| #13# #13#)) #14#))) 
((UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) 31 T ELT)) (UP2UTS ((|#4| |#2|) 26 T ELT)) (RF2UTS ((|#4| (|Fraction| |#2|)) 49 (|has| |#1| (|IntegralDomain|)) ELT)) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) 43 T ELT))) 
(((|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=(*1 *2 *3) (AND (|isDomain| *3 (|Fraction| *5)) #2=(|ofCategory| *5 #3=(|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|IntegralDomain|)) #4=(|ofCategory| *4 #5=(|Ring|)) #6=(|ofCategory| *2 #7=(|UnivariateTaylorSeriesCategory| *4)) (|isDomain| *1 (|UTSodetools| *4 *5 *6 *2)) (|ofCategory| *6 #8=(|LinearOrdinaryDifferentialOperatorCategory| *5)))) (LODO2FUN #1# (AND #4# #2# (|isDomain| *2 (|Mapping| *6 (|List| *6))) (|isDomain| *1 (|UTSodetools| *4 *5 *3 *6)) (|ofCategory| *3 #8#) (|ofCategory| *6 #7#))) (UTS2UP (*1 *2 *3 *4) (AND (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 #5#) (|ofCategory| *2 (|UnivariatePolynomialCategory| *5)) (|isDomain| *1 (|UTSodetools| *5 *2 *6 *3)) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *5)))) (UP2UTS #1# (AND #4# (|ofCategory| *3 #3#) #6# (|isDomain| *1 (|UTSodetools| *4 *3 *5 *2)) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| *3))))) 
NIL 
(((|UnionType|) (|Category|)) (T |UnionType|)) 
NIL 
(|Join| (CATEGORY |package| (ATTRIBUTE |nil|))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|variable| ((#3=(|Symbol|)) 12 T ELT)) (|latex| (((|String|) $) 18 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT) ((#3# $) 8 T ELT)) (|before?| #1#) (= (#2# 15 T ELT))) 
(((|Variable| |#1|) (|Join| (|SetCategory|) (|CoercibleTo| #1=(|Symbol|)) (CATEGORY |domain| (SIGNATURE |coerce| (#1# $)) (SIGNATURE |variable| (#1#)))) #1#) (T |Variable|)) 
((|coerce| (*1 *2 *1) #1=(AND (|isDomain| *2 (|Symbol|)) (|isDomain| *1 (|Variable| *3)) (|ofType| *3 *2))) (|variable| (*1 *2) #1#)) 
((|zero| (($ (|NonNegativeInteger|)) 19 T ELT)) (|outerProduct| (((|Matrix| |#2|) $ $) 41 T ELT)) (|magnitude| (#1=(|#2| $) 51 T ELT)) (|length| (#1# 50 T ELT)) (|dot| ((|#2| $ $) 36 T ELT)) (|cross| (#2=($ $ $) 47 T ELT)) (- (($ $) 23 T ELT) (#2# 29 T ELT)) (+ (#2# 15 T ELT)) (* (($ (|Integer|) $) 26 T ELT) (($ |#2| $) 32 T ELT) (($ $ |#2|) 31 T ELT))) 
(((|VectorCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |magnitude| #1=(|#2| |#1|)) (SIGNATURE |length| #1#) (SIGNATURE |cross| #2=(|#1| |#1| |#1|)) (SIGNATURE |outerProduct| ((|Matrix| |#2|) |#1| |#1|)) (SIGNATURE |dot| (|#2| |#1| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE - #2#) (SIGNATURE - (|#1| |#1|)) (SIGNATURE |zero| (|#1| (|NonNegativeInteger|))) (SIGNATURE + #2#)) (|VectorCategory| |#2|) (|Type|)) (T |VectorCategory&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|zero| (($ (|NonNegativeInteger|)) 123 (|has| |#1| (|AbelianMonoid|)) ELT)) (|swap!| (((|Void|) $ #3=(|Integer|) #3#) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#4=(|Boolean|) (|Mapping| #4# |#1| |#1|) $) 96 T ELT) ((#4# $) 90 (|has| |#1| . #5=((|OrderedSet|))) ELT)) (|sort!| (($ (|Mapping| #4# |#1| |#1|) . #6=($)) 87 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (#7=($ $) 86 (AND (|has| |#1| . #5#) (|has| $ (|ShallowlyMutableAggregate| |#1|))) ELT)) (|sort| (($ (|Mapping| #4# |#1| |#1|) . #6#) 97 T ELT) (#7# 91 (|has| |#1| . #5#) ELT)) (|setelt| ((|#1| $ #3# |#1|) 47 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #8=(|UniversalSegment| #3#) |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #9=(|Boolean|) |#1|) . #10=($)) 69 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#11=($) 6 T CONST)) (|reverse!| (#7# 88 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|reverse| (#7# 98 T ELT)) (|removeDuplicates| (($ $) 71 (AND (|has| |#1| . #12=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 70 (AND (|has| |#1| . #12#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #9# |#1|) . #10#) 68 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 110 (|has| |#1| . #13=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 106 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 105 T ELT)) (|qsetelt!| ((|#1| $ #3# |#1|) 48 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #3#) 46 T ELT)) (|position| ((#14=(|Integer|) (|Mapping| #4# |#1|) $) 95 T ELT) ((#14# |#1| $) 94 (|has| |#1| . #15=((|BasicType|))) ELT) ((#14# |#1| $ #14#) 93 (|has| |#1| . #15#) ELT)) (|outerProduct| (((|Matrix| |#1|) $ $) 116 (|has| |#1| (|Ring|)) ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| ((#3# . #16=($)) 38 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((|#1| $) 37 (|has| #3# . #17#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #19# |#1|) $) 107 T ELT)) (|fill!| (($ $ |#1|) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|every?| ((#19# (|Mapping| #19# |#1|) . #22=($)) 102 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #20#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #20#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #20#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #20#)) ELT)) (|eq?| ((#23=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#21# |#1| $) 40 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 43 T ELT)) (|empty?| ((#23# $) 7 T ELT)) (|empty| (#11# 8 T ELT)) (|elt| ((|#1| $ #3# |#1|) 45 T ELT) ((|#1| $ #3#) 44 T ELT) (($ $ #8#) 66 T ELT)) (|dot| ((|#1| $ $) 117 (|has| |#1| (|Ring|)) ELT)) 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(((|VectorCategory| |#1|) (|Category|) (|Type|)) (T |VectorCategory|)) 
((+ (*1 *1 *1 *1) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|AbelianSemiGroup|)))) (|zero| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|VectorCategory| *3)) (|ofCategory| *3 (|AbelianMonoid|)) (|ofCategory| *3 (|Type|)))) (- (*1 *1 *1) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|AbelianGroup|)))) (- (*1 *1 *1 *1) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|AbelianGroup|)))) (* (*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|VectorCategory| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|AbelianGroup|)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Monoid|)))) (* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Monoid|)))) (|dot| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Ring|)))) (|outerProduct| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|VectorCategory| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Matrix| *3)))) (|cross| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Ring|)))) (|length| (*1 *2 *1) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|RadicalCategory|)) (|ofCategory| *2 (|Ring|)))) (|magnitude| (*1 *2 *1) (AND (|ofCategory| *1 (|VectorCategory| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|RadicalCategory|)) (|ofCategory| *2 (|Ring|))))) 
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(((|Vector| |#1|) (|Join| (|VectorCategory| |#1|) (CATEGORY |domain| (SIGNATURE |vector| ($ (|List| |#1|))))) (|Type|)) (T |Vector|)) 
((|vector| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Vector| *3))))) 
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(((|VectorFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |scan| (#1=(|Vector| |#2|) #2=(|Mapping| |#2| |#1| |#2|) #3=(|Vector| |#1|) |#2|)) (SIGNATURE |reduce| (|#2| #2# #3# |#2|)) (SIGNATURE |map| (#1# (|Mapping| |#2| |#1|) #3#)) (SIGNATURE |map| ((|Union| #1# #4="failed") (|Mapping| (|Union| |#2| #4#) |#1|) #3#))) #5=(|Type|) #5#) (T |VectorFunctions2|)) 
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((|graphCurves| ((#1=(|GraphImage|) #2=(|List| (|List| (|Point| (|DoubleFloat|)))) #3=(|List| (|DrawOption|))) 22 T ELT) ((#1# #2#) 21 T ELT) ((#1# #2# #4=(|Palette|) #4# #5=(|PositiveInteger|) #3#) 20 T ELT)) (|drawCurves| ((#6=(|TwoDimensionalViewport|) #2# #3#) 30 T ELT) ((#6# #2# #4# #4# #5# #3#) 29 T ELT)) (|coerce| ((#6# #1#) 46 T ELT))) 
(((|ViewportPackage|) (CATEGORY |package| (SIGNATURE |graphCurves| (#1=(|GraphImage|) #2=(|List| (|List| (|Point| (|DoubleFloat|)))) #3=(|Palette|) #3# #4=(|PositiveInteger|) #5=(|List| (|DrawOption|)))) (SIGNATURE |graphCurves| (#1# #2#)) (SIGNATURE |graphCurves| (#1# #2# #5#)) (SIGNATURE |drawCurves| (#6=(|TwoDimensionalViewport|) #2# #3# #3# #4# #5#)) (SIGNATURE |drawCurves| (#6# #2# #5#)) (SIGNATURE |coerce| (#6# #1#)))) (T |ViewportPackage|)) 
((|coerce| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|GraphImage|)) #3=(|isDomain| *2 (|TwoDimensionalViewport|)) #4=(|isDomain| *1 (|ViewportPackage|)))) (|drawCurves| #5=(*1 *2 *3 *4) (AND #6=(|isDomain| *3 (|List| (|List| (|Point| (|DoubleFloat|))))) #7=(|isDomain| *4 #8=(|List| (|DrawOption|))) #3# #4#)) (|drawCurves| #9=(*1 *2 *3 *4 *4 *5 *6) (AND #6# #10=(|isDomain| *4 (|Palette|)) #11=(|isDomain| *5 (|PositiveInteger|)) #12=(|isDomain| *6 #8#) #3# #4#)) (|graphCurves| #5# (AND #6# #7# #13=(|isDomain| *2 #2#) #4#)) (|graphCurves| #1# (AND #6# #13# #4#)) (|graphCurves| #9# (AND #6# #10# #11# #12# #13# #4#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|write| ((#2=(|String|) $ #2#) 107 T ELT) ((#2# $ #2# #2#) 105 T ELT) ((#2# $ #2# (|List| #2#)) 104 T ELT)) (|viewport2D| (($) 69 T ELT)) (|update| (#3=(#4=(|Void|) $ #5=(|GraphImage|) #6=(|PositiveInteger|)) 54 T ELT)) (|units| (#7=(#4# $ #6# #2#) 89 T ELT) (#8=(#4# $ #6# #9=(|Palette|)) 90 T ELT)) (|translate| (#10=(#4# $ #6# #11=(|Float|) #11#) 57 T ELT)) (|title| (#12=(#4# $ #2#) 84 T ELT)) (|show| (#7# 94 T ELT)) (|scale| (#10# 58 T ELT)) (|resize| ((#4# $ #6# #6#) 55 T ELT)) (|reset| (#13=(#4# $) 85 T ELT)) (|region| (#7# 93 T ELT)) (|putGraph| (#3# 41 T ELT)) (|points| (#7# 92 T ELT)) (|options| ((#14=(|List| (|DrawOption|)) $) 29 T ELT) (($ $ #14#) 30 T ELT)) (|move| ((#4# $ #15=(|NonNegativeInteger|) #15#) 52 T ELT)) (|makeViewport2D| (($ $) 70 T ELT) (($ #5# #14#) 71 T ELT)) (|latex| ((#2# $) NIL T ELT)) (|key| ((#16=(|Integer|) $) 48 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|graphs| (((|Vector| (|Union| #5# "undefined")) $) 47 T ELT)) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| #17=(|DoubleFloat|)) (|:| |scaleY| #17#) (|:| |deltaX| #17#) (|:| |deltaY| #17#) (|:| |points| #16#) (|:| |connect| #16#) (|:| |spline| #16#) (|:| |axes| #16#) (|:| |axesColor| #9#) (|:| |units| #16#) (|:| |unitsColor| #9#) (|:| |showing| #16#))) $) 46 T ELT)) (|graphState| ((#4# $ #6# #17# #17# #17# #17# #16# #16# #16# #16# #9# #16# #9# #16#) 83 T ELT)) (|getPickedPoints| (((|List| (|Point| #17#)) $) NIL T ELT)) (|getGraph| ((#5# $ #6#) 43 T ELT)) (|dimensions| ((#4# $ #15# #15# #6# #6#) 50 T ELT)) (|controlPanel| (#12# 95 T ELT)) (|connect| (#7# 91 T ELT)) (|coerce| (((|OutputForm|) $) 102 T ELT)) (|close| (#13# 96 T ELT)) (|before?| #1#) (|axes| (#7# 87 T ELT) (#8# 88 T ELT)) (= #1#)) 
(((|TwoDimensionalViewport|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |getPickedPoints| ((|List| (|Point| #1=(|DoubleFloat|))) $)) (SIGNATURE |viewport2D| ($)) (SIGNATURE |makeViewport2D| ($ $)) (SIGNATURE |options| (#2=(|List| (|DrawOption|)) $)) (SIGNATURE |options| ($ $ #2#)) (SIGNATURE |makeViewport2D| ($ #3=(|GraphImage|) #2#)) (SIGNATURE |graphState| (#4=(|Void|) $ #5=(|PositiveInteger|) #1# #1# #1# #1# #6=(|Integer|) #6# #6# #6# #7=(|Palette|) #6# #7# #6#)) (SIGNATURE |graphStates| ((|Vector| (|Record| (|:| |scaleX| #1#) (|:| |scaleY| #1#) (|:| |deltaX| #1#) (|:| |deltaY| #1#) (|:| |points| #6#) (|:| |connect| #6#) (|:| |spline| #6#) (|:| |axes| #6#) (|:| |axesColor| #7#) (|:| |units| #6#) (|:| |unitsColor| #7#) (|:| |showing| #6#))) $)) (SIGNATURE |graphs| ((|Vector| (|Union| #3# "undefined")) $)) (SIGNATURE |title| #8=(#4# $ #9=(|String|))) (SIGNATURE |putGraph| #10=(#4# $ #3# #5#)) (SIGNATURE |getGraph| (#3# $ #5#)) (SIGNATURE |axes| #11=(#4# $ #5# #9#)) (SIGNATURE |axes| #12=(#4# $ #5# #7#)) (SIGNATURE |units| #11#) (SIGNATURE |units| #12#) (SIGNATURE |points| #11#) (SIGNATURE |region| #11#) (SIGNATURE |connect| #11#) (SIGNATURE |controlPanel| #8#) (SIGNATURE |close| #13=(#4# $)) (SIGNATURE |dimensions| (#4# $ #14=(|NonNegativeInteger|) #14# #5# #5#)) (SIGNATURE |scale| #15=(#4# $ #5# #16=(|Float|) #16#)) (SIGNATURE |translate| #15#) (SIGNATURE |show| #11#) (SIGNATURE |move| (#4# $ #14# #14#)) (SIGNATURE |update| #10#) (SIGNATURE |resize| (#4# $ #5# #5#)) (SIGNATURE |write| (#9# $ #9#)) (SIGNATURE |write| (#9# $ #9# #9#)) (SIGNATURE |write| (#9# $ #9# (|List| #9#))) (SIGNATURE |reset| #13#) (SIGNATURE |key| (#6# $)) (SIGNATURE |coerce| ((|OutputForm|) $))))) (T |TwoDimensionalViewport|)) 
((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|OutputForm|)) #2=(|isDomain| *1 (|TwoDimensionalViewport|)))) (|getPickedPoints| #1# (AND (|isDomain| *2 (|List| (|Point| #3=(|DoubleFloat|)))) #2#)) (|viewport2D| (*1 *1) #2#) (|makeViewport2D| (*1 *1 *1) #2#) (|options| #1# #4=(AND (|isDomain| *2 #5=(|List| (|DrawOption|))) #2#)) (|options| (*1 *1 *1 *2) #4#) (|makeViewport2D| (*1 *1 *2 *3) (AND #6=(|isDomain| *2 #7=(|GraphImage|)) (|isDomain| *3 #5#) #2#)) (|graphState| (*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) (AND #8=(|isDomain| *3 #9=(|PositiveInteger|)) (|isDomain| *4 #3#) (|isDomain| *5 #10=(|Integer|)) (|isDomain| *6 #11=(|Palette|)) #12=(|isDomain| *2 (|Void|)) #2#)) (|graphStates| #1# (AND (|isDomain| *2 (|Vector| (|Record| (|:| |scaleX| #3#) (|:| |scaleY| #3#) (|:| |deltaX| #3#) (|:| |deltaY| #3#) (|:| |points| #10#) (|:| |connect| #10#) (|:| |spline| #10#) (|:| |axes| #10#) (|:| |axesColor| #11#) (|:| |units| #10#) (|:| |unitsColor| #11#) (|:| |showing| #10#)))) #2#)) (|graphs| #1# (AND (|isDomain| *2 (|Vector| (|Union| #7# "undefined"))) #2#)) (|title| #13=(*1 *2 *1 *3) #14=(AND (|isDomain| *3 #15=(|String|)) #12# #2#)) (|putGraph| #16=(*1 *2 *1 *3 *4) #17=(AND (|isDomain| *3 #7#) #18=(|isDomain| *4 #9#) #12# #2#)) (|getGraph| #13# (AND #8# #6# #2#)) (|axes| #16# #19=(AND #8# (|isDomain| *4 #15#) #12# #2#)) (|axes| #16# #20=(AND #8# (|isDomain| *4 #11#) #12# #2#)) (|units| #16# #19#) (|units| #16# #20#) (|points| #16# #19#) (|region| #16# #19#) (|connect| #16# #19#) (|controlPanel| #13# #14#) (|close| #1# #21=(AND #12# #2#)) (|dimensions| (*1 *2 *1 *3 *3 *4 *4) (AND #22=(|isDomain| *3 (|NonNegativeInteger|)) #18# #12# #2#)) (|scale| #23=(*1 *2 *1 *3 *4 *4) #24=(AND #8# (|isDomain| *4 (|Float|)) #12# #2#)) (|translate| #23# #24#) (|show| #16# #19#) (|move| #25=(*1 *2 *1 *3 *3) (AND #22# #12# #2#)) (|update| #16# #17#) (|resize| #25# (AND #8# #12# #2#)) (|write| (*1 *2 *1 *2) #26=(AND #27=(|isDomain| *2 #15#) #2#)) (|write| (*1 *2 *1 *2 *2) #26#) (|write| (*1 *2 *1 *2 *3) (AND (|isDomain| *3 (|List| #15#)) #27# #2#)) (|reset| #1# #21#) (|key| #1# (AND (|isDomain| *2 #10#) #2#))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|zoom| (#2=(#3=(|Void|) $ #4=(|Float|)) 168 T ELT) (#5=(#3# $ #4# #4# #4#) 169 T ELT)) (|write| ((#6=(|String|) $ #6#) 177 T ELT) ((#6# $ #6# #6#) 175 T ELT) ((#6# $ #6# (|List| #6#)) 174 T ELT)) (|viewport3D| (($) 67 T ELT)) (|viewpoint| ((#3# $ #4# #4# #4# #4# #4#) 140 T ELT) ((#7=(|Record| (|:| |theta| #8=(|DoubleFloat|)) (|:| |phi| #8#) (|:| |scale| #8#) (|:| |scaleX| #8#) (|:| |scaleY| #8#) (|:| |scaleZ| #8#) (|:| |deltaX| #8#) (|:| |deltaY| #8#)) $) 138 T ELT) ((#3# $ #7#) 139 T ELT) ((#3# $ #9=(|Integer|) #9# #4# #4# #4#) 143 T ELT) (#10=(#3# $ #4# #4#) 144 T ELT) (#5# 151 T ELT)) (|viewZoomDefault| (#11=(#4#) 121 T ELT) (#12=(#4# #4#) 122 T ELT)) (|viewThetaDefault| (#11# 116 T ELT) (#12# 118 T ELT)) (|viewPhiDefault| (#11# 119 T ELT) (#12# 120 T ELT)) (|viewDeltaYDefault| (#11# 125 T ELT) (#12# 126 T ELT)) (|viewDeltaXDefault| (#11# 123 T ELT) (#12# 124 T ELT)) (|translate| (#10# 170 T ELT)) (|title| (#13=(#3# $ #6#) 152 T ELT)) (|subspace| ((#14=(|ThreeSpace| #8#) $) 68 T ELT) (($ $ #14#) 69 T ELT)) (|showRegion| (#13# 186 T ELT)) (|showClipRegion| (#13# 187 T ELT)) (|rotate| (#10# 150 T ELT) ((#3# $ #9# #9#) 167 T ELT)) (|resize| ((#3# $ #15=(|PositiveInteger|) #15#) 159 T ELT)) (|reset| (#16=(#3# $) 136 T ELT)) (|perspective| (#13# 185 T ELT)) (|outlineRender| (#13# 133 T ELT)) (|options| ((#17=(|List| (|DrawOption|)) $) 70 T ELT) (($ $ #17#) 71 T ELT)) (|move| ((#3# $ #18=(|NonNegativeInteger|) #18#) 158 T ELT)) (|modifyPointData| ((#3# $ #18# (|Point| #8#)) 192 T ELT)) (|makeViewport3D| (($ $) 73 T ELT) (($ #14# #6#) 74 T ELT) (($ #14# #17#) 75 T ELT)) (|lighting| (#5# 130 T ELT)) (|latex| ((#6# $) NIL T ELT)) (|key| ((#9# $) 127 T ELT)) (|intensity| (#2# 172 T ELT)) (|hitherPlane| (#2# 190 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eyeDistance| (#2# 189 T ELT)) (|drawStyle| (#13# 135 T ELT)) (|dimensions| ((#3# $ #18# #18# #15# #15#) 157 T ELT)) (|diagonals| (#13# 132 T ELT)) (|controlPanel| (#13# 134 T ELT)) (|colorDef| ((#3# $ #19=(|Color|) #19#) 156 T ELT)) (|coerce| (((|OutputForm|) $) 165 T ELT)) (|close| (#16# 137 T ELT)) (|clipSurface| (#13# 188 T ELT)) (|before?| #1#) (|axes| (#13# 131 T ELT)) (= #1#)) 
(((|ThreeDimensionalViewport|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |viewThetaDefault| #1=(#2=(|Float|))) (SIGNATURE |viewThetaDefault| #3=(#2# #2#)) (SIGNATURE |viewPhiDefault| #1#) (SIGNATURE |viewPhiDefault| #3#) (SIGNATURE |viewZoomDefault| #1#) (SIGNATURE |viewZoomDefault| #3#) (SIGNATURE |viewDeltaXDefault| #1#) (SIGNATURE |viewDeltaXDefault| #3#) (SIGNATURE |viewDeltaYDefault| #1#) (SIGNATURE |viewDeltaYDefault| #3#) (SIGNATURE |viewport3D| ($)) (SIGNATURE |makeViewport3D| ($ $)) (SIGNATURE |makeViewport3D| ($ #4=(|ThreeSpace| #5=(|DoubleFloat|)) #6=(|String|))) (SIGNATURE |makeViewport3D| ($ #4# #7=(|List| (|DrawOption|)))) (SIGNATURE |subspace| (#4# $)) (SIGNATURE |subspace| ($ $ #4#)) (SIGNATURE |modifyPointData| (#8=(|Void|) $ #9=(|NonNegativeInteger|) (|Point| #5#))) (SIGNATURE |options| (#7# $)) (SIGNATURE |options| ($ $ #7#)) (SIGNATURE |move| (#8# $ #9# #9#)) (SIGNATURE |resize| (#8# $ #10=(|PositiveInteger|) #10#)) (SIGNATURE |title| #11=(#8# $ #6#)) (SIGNATURE |dimensions| (#8# $ #9# #9# #10# #10#)) (SIGNATURE |viewpoint| (#8# $ #2# #2# #2# #2# #2#)) (SIGNATURE |viewpoint| (#12=(|Record| (|:| |theta| #5#) (|:| |phi| #5#) (|:| |scale| #5#) (|:| |scaleX| #5#) (|:| |scaleY| #5#) (|:| |scaleZ| #5#) (|:| |deltaX| #5#) (|:| |deltaY| #5#)) $)) (SIGNATURE |viewpoint| (#8# $ #12#)) (SIGNATURE |viewpoint| (#8# $ #13=(|Integer|) #13# #2# #2# #2#)) (SIGNATURE |viewpoint| #14=(#8# $ #2# #2#)) (SIGNATURE |viewpoint| #15=(#8# $ #2# #2# #2#)) (SIGNATURE |controlPanel| #11#) (SIGNATURE |axes| #11#) (SIGNATURE |diagonals| #11#) (SIGNATURE |outlineRender| #11#) (SIGNATURE |drawStyle| #11#) (SIGNATURE |rotate| #14#) (SIGNATURE |rotate| (#8# $ #13# #13#)) (SIGNATURE |zoom| #16=(#8# $ #2#)) (SIGNATURE |zoom| #15#) (SIGNATURE |translate| #14#) (SIGNATURE |perspective| #11#) (SIGNATURE |eyeDistance| #16#) (SIGNATURE |hitherPlane| #16#) (SIGNATURE |showRegion| #11#) (SIGNATURE |showClipRegion| #11#) (SIGNATURE |clipSurface| #11#) (SIGNATURE |lighting| #15#) (SIGNATURE |intensity| #16#) (SIGNATURE |reset| #17=(#8# $)) (SIGNATURE |colorDef| (#8# $ #18=(|Color|) #18#)) (SIGNATURE |write| (#6# $ #6#)) (SIGNATURE |write| (#6# $ #6# #6#)) (SIGNATURE |write| (#6# $ #6# (|List| #6#))) (SIGNATURE |close| #17#) (SIGNATURE |key| (#13# $))))) (T |ThreeDimensionalViewport|)) 
((|viewThetaDefault| #1=(*1 *2) #2=(AND (|isDomain| *2 #3=(|Float|)) #4=(|isDomain| *1 (|ThreeDimensionalViewport|)))) (|viewThetaDefault| #5=(*1 *2 *2) #2#) (|viewPhiDefault| #1# #2#) (|viewPhiDefault| #5# #2#) (|viewZoomDefault| #1# #2#) (|viewZoomDefault| #5# #2#) (|viewDeltaXDefault| #1# #2#) (|viewDeltaXDefault| #5# #2#) (|viewDeltaYDefault| #1# #2#) (|viewDeltaYDefault| #5# #2#) (|viewport3D| (*1 *1) #4#) (|makeViewport3D| (*1 *1 *1) #4#) (|makeViewport3D| #6=(*1 *1 *2 *3) (AND #7=(|isDomain| *2 (|ThreeSpace| #8=(|DoubleFloat|))) #9=(|isDomain| *3 #10=(|String|)) #4#)) (|makeViewport3D| #6# (AND #7# (|isDomain| *3 #11=(|List| (|DrawOption|))) #4#)) (|subspace| #12=(*1 *2 *1) #13=(AND #7# #4#)) (|subspace| #14=(*1 *1 *1 *2) #13#) (|modifyPointData| (*1 *2 *1 *3 *4) (AND #15=(|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Point| #8#)) #16=(|isDomain| *2 (|Void|)) #4#)) (|options| #12# #17=(AND (|isDomain| *2 #11#) #4#)) (|options| #14# #17#) (|move| #18=(*1 *2 *1 *3 *3) (AND #15# #16# #4#)) (|resize| #18# (AND (|isDomain| *3 #19=(|PositiveInteger|)) #16# #4#)) (|title| #20=(*1 *2 *1 *3) #21=(AND #9# #16# #4#)) (|dimensions| (*1 *2 *1 *3 *3 *4 *4) (AND #15# (|isDomain| *4 #19#) #16# #4#)) (|viewpoint| (*1 *2 *1 *3 *3 *3 *3 *3) #22=(AND (|isDomain| *3 #3#) #16# #4#)) (|viewpoint| #12# (AND (|isDomain| *2 #23=(|Record| (|:| |theta| #8#) (|:| |phi| #8#) (|:| |scale| #8#) (|:| |scaleX| #8#) (|:| |scaleY| #8#) (|:| |scaleZ| #8#) (|:| |deltaX| #8#) (|:| |deltaY| #8#))) #4#)) (|viewpoint| #20# (AND (|isDomain| *3 #23#) #16# #4#)) (|viewpoint| (*1 *2 *1 *3 *3 *4 *4 *4) (AND #24=(|isDomain| *3 #25=(|Integer|)) (|isDomain| *4 #3#) #16# #4#)) (|viewpoint| #18# #22#) (|viewpoint| #26=(*1 *2 *1 *3 *3 *3) #22#) (|controlPanel| #20# #21#) (|axes| #20# #21#) (|diagonals| #20# #21#) (|outlineRender| #20# #21#) (|drawStyle| #20# #21#) (|rotate| #18# #22#) (|rotate| #18# (AND #24# #16# #4#)) (|zoom| #20# #22#) (|zoom| #26# #22#) (|translate| #18# #22#) (|perspective| #20# #21#) (|eyeDistance| #20# #22#) (|hitherPlane| #20# #22#) (|showRegion| #20# #21#) (|showClipRegion| #20# #21#) (|clipSurface| #20# #21#) (|lighting| #26# #22#) (|intensity| #20# #22#) (|reset| #12# #27=(AND #16# #4#)) (|colorDef| #18# (AND (|isDomain| *3 (|Color|)) #16# #4#)) (|write| (*1 *2 *1 *2) #28=(AND #29=(|isDomain| *2 #10#) #4#)) (|write| (*1 *2 *1 *2 *2) #28#) (|write| (*1 *2 *1 *2 *3) (AND (|isDomain| *3 (|List| #10#)) #29# #4#)) (|close| #12# #27#) (|key| #12# (AND (|isDomain| *2 #25#) #4#))) 
((|viewWriteDefault| ((#1=(|List| (|String|)) #1#) 103 T ELT) (#2=(#1#) 96 T ELT)) (|viewWriteAvailable| (#2# 94 T ELT)) (|viewSizeDefault| ((#3=(|List| #4=(|PositiveInteger|)) #3#) 69 T ELT) ((#3#) 64 T ELT)) (|viewPosDefault| ((#5=(|List| (|NonNegativeInteger|)) #5#) 61 T ELT) ((#5#) 55 T ELT)) (|viewDefaults| (((|Void|)) 71 T ELT)) (|var2StepsDefault| (#6=(#4# #4#) 87 T ELT) (#7=(#4#) 86 T ELT)) (|var1StepsDefault| (#6# 85 T ELT) (#7# 84 T ELT)) (|unitsColorDefault| (#8=(#9=(|Palette|) #9#) 81 T ELT) (#10=(#9#) 80 T ELT)) (|tubeRadiusDefault| ((#11=(|DoubleFloat|)) 91 T ELT) ((#11# (|Float|)) 93 T ELT)) (|tubePointsDefault| (#7# 88 T ELT) (#6# 89 T ELT)) (|pointSizeDefault| (#6# 83 T ELT) (#7# 82 T ELT)) (|pointColorDefault| (#8# 75 T ELT) (#10# 73 T ELT)) (|lineColorDefault| (#8# 77 T ELT) (#10# 76 T ELT)) (|axesColorDefault| (#8# 79 T ELT) (#10# 78 T ELT))) 
(((|ViewDefaultsPackage|) (CATEGORY |package| (SIGNATURE |pointColorDefault| #1=(#2=(|Palette|))) (SIGNATURE |pointColorDefault| #3=(#2# #2#)) (SIGNATURE |lineColorDefault| #1#) (SIGNATURE |lineColorDefault| #3#) (SIGNATURE |axesColorDefault| #1#) (SIGNATURE |axesColorDefault| #3#) (SIGNATURE |unitsColorDefault| #1#) (SIGNATURE |unitsColorDefault| #3#) (SIGNATURE |pointSizeDefault| #4=(#5=(|PositiveInteger|))) (SIGNATURE |pointSizeDefault| #6=(#5# #5#)) (SIGNATURE |viewPosDefault| (#7=(|List| (|NonNegativeInteger|)))) (SIGNATURE |viewPosDefault| (#7# #7#)) (SIGNATURE |viewSizeDefault| (#8=(|List| #5#))) (SIGNATURE |viewSizeDefault| (#8# #8#)) (SIGNATURE |viewDefaults| ((|Void|))) (SIGNATURE |viewWriteDefault| #9=(#10=(|List| (|String|)))) (SIGNATURE |viewWriteDefault| (#10# #10#)) (SIGNATURE |viewWriteAvailable| #9#) (SIGNATURE |var1StepsDefault| #4#) (SIGNATURE |var2StepsDefault| #4#) (SIGNATURE |var1StepsDefault| #6#) (SIGNATURE |var2StepsDefault| #6#) (SIGNATURE |tubePointsDefault| #6#) (SIGNATURE |tubePointsDefault| #4#) (SIGNATURE |tubeRadiusDefault| (#11=(|DoubleFloat|) (|Float|))) (SIGNATURE |tubeRadiusDefault| (#11#)))) (T |ViewDefaultsPackage|)) 
((|tubeRadiusDefault| #1=(*1 *2) (AND #2=(|isDomain| *2 (|DoubleFloat|)) #3=(|isDomain| *1 (|ViewDefaultsPackage|)))) (|tubeRadiusDefault| (*1 *2 *3) (AND (|isDomain| *3 (|Float|)) #2# #3#)) (|tubePointsDefault| #1# #4=(AND (|isDomain| *2 #5=(|PositiveInteger|)) #3#)) (|tubePointsDefault| #6=(*1 *2 *2) #4#) (|var2StepsDefault| #6# #4#) (|var1StepsDefault| #6# #4#) (|var2StepsDefault| #1# #4#) (|var1StepsDefault| #1# #4#) (|viewWriteAvailable| #1# #7=(AND (|isDomain| *2 (|List| (|String|))) #3#)) (|viewWriteDefault| #6# #7#) (|viewWriteDefault| #1# #7#) (|viewDefaults| #1# (AND (|isDomain| *2 (|Void|)) #3#)) (|viewSizeDefault| #6# #8=(AND (|isDomain| *2 (|List| #5#)) #3#)) (|viewSizeDefault| #1# #8#) (|viewPosDefault| #6# #9=(AND (|isDomain| *2 (|List| (|NonNegativeInteger|))) #3#)) (|viewPosDefault| #1# #9#) (|pointSizeDefault| #6# #4#) (|pointSizeDefault| #1# #4#) (|unitsColorDefault| #6# #10=(AND (|isDomain| *2 (|Palette|)) #3#)) (|unitsColorDefault| #1# #10#) (|axesColorDefault| #6# #10#) (|axesColorDefault| #1# #10#) (|lineColorDefault| #6# #10#) (|lineColorDefault| #1# #10#) (|pointColorDefault| #6# #10#) (|pointColorDefault| #1# #10#)) 
((|void| (($) 6 T ELT)) (|coerce| (((|OutputForm|) $) 9 T ELT))) 
(((|Void|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |void| ($))))) (T |Void|)) 
((|void| (*1 *1) (|isDomain| *1 (|Void|)))) 
((/ (($ $ |#2|) 10 T ELT))) 
(((|VectorSpace&| |#1| |#2|) (CATEGORY |package| (SIGNATURE / (|#1| |#1| |#2|))) (|VectorSpace| |#2|) (|Field|)) (T |VectorSpace&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|dimension| (((|CardinalNumber|)) 39 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 40 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ |#1| . #4#) 33 T ELT) (($ $ |#1|) 37 T ELT))) 
(((|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) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((|weierstrass| (((|List| #1=(|TaylorSeries| |#1|)) #2=(|Symbol|) #1#) 83 T ELT)) (|sts2stst| (((|Stream| #3=(|Stream| #4=(|Polynomial| |#1|))) #2# #3#) 63 T ELT)) (|qqq| (((|Mapping| #5=(|Stream| #1#) #5#) #6=(|NonNegativeInteger|) #1# #5#) 74 T ELT)) (|crest| (#7=((|Mapping| #3# #3#) #6#) 65 T ELT)) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| #4#) #4#) #2#) 32 T ELT)) (|cfirst| (#7# 64 T ELT))) 
(((|WeierstrassPreparation| |#1|) (CATEGORY |package| (SIGNATURE |crest| #1=((|Mapping| #2=(|Stream| #3=(|Polynomial| |#1|)) #2#) #4=(|NonNegativeInteger|))) (SIGNATURE |cfirst| #1#) (SIGNATURE |sts2stst| ((|Stream| #2#) #5=(|Symbol|) #2#)) (SIGNATURE |clikeUniv| ((|Mapping| (|SparseUnivariatePolynomial| #3#) #3#) #5#)) (SIGNATURE |weierstrass| ((|List| #6=(|TaylorSeries| |#1|)) #5# #6#)) (SIGNATURE |qqq| ((|Mapping| #7=(|Stream| #6#) #7#) #4# #6# #7#))) (|Field|)) (T |WeierstrassPreparation|)) 
((|qqq| (*1 *2 *3 *4 *5) (AND #1=(|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *6 #2=(|Field|)) (|isDomain| *4 (|TaylorSeries| *6)) (|isDomain| *2 (|Mapping| #3=(|Stream| *4) #3#)) (|isDomain| *1 (|WeierstrassPreparation| *6)) (|isDomain| *5 #3#))) (|weierstrass| #4=(*1 *2 *3 *4) (AND #5=(|isDomain| *3 (|Symbol|)) #6=(|ofCategory| *5 #2#) (|isDomain| *2 (|List| #7=(|TaylorSeries| *5))) #8=(|isDomain| *1 (|WeierstrassPreparation| *5)) (|isDomain| *4 #7#))) (|clikeUniv| #9=(*1 *2 *3) (AND #5# (|isDomain| *2 (|Mapping| (|SparseUnivariatePolynomial| #10=(|Polynomial| *4)) #10#)) #11=(|isDomain| *1 (|WeierstrassPreparation| *4)) #12=(|ofCategory| *4 #2#))) (|sts2stst| #4# (AND #5# #6# (|isDomain| *2 (|Stream| #13=(|Stream| (|Polynomial| *5)))) #8# (|isDomain| *4 #13#))) (|cfirst| #9# #14=(AND #1# (|isDomain| *2 (|Mapping| #15=(|Stream| #10#) #15#)) #11# #12#)) (|crest| #9# #14#)) 
((|localIntegralBasis| ((#1=(|Record| (|:| |basis| #2=(|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| #2#)) |#2|) 80 T ELT)) (|integralBasis| ((#1#) 79 T ELT))) 
(((|WildFunctionFieldIntegralBasis| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |integralBasis| (#1=(|Record| (|:| |basis| #2=(|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| #2#)))) (SIGNATURE |localIntegralBasis| (#1# |#2|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|FramedAlgebra| |#2| |#3|)) (T |WildFunctionFieldIntegralBasis|)) 
((|localIntegralBasis| (*1 *2 *3) (AND (|ofCategory| *4 #1=(|FiniteFieldCategory|)) (|ofCategory| *3 #2=(|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 #3=(|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| #4=(|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| #4#))) (|isDomain| *1 (|WildFunctionFieldIntegralBasis| *4 *3 *5 *6)) (|ofCategory| *6 (|FramedAlgebra| *3 *5)))) (|integralBasis| (*1 *2) (AND (|ofCategory| *3 #1#) (|ofCategory| *4 #3#) (|ofCategory| *5 #2#) (|isDomain| *2 (|Record| (|:| |basis| #5=(|Matrix| *4)) (|:| |basisDen| *4) (|:| |basisInv| #5#))) (|isDomain| *1 (|WildFunctionFieldIntegralBasis| *3 *4 *5 *6)) (|ofCategory| *6 (|FramedAlgebra| *4 *5))))) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|qualifier| (#2=((|SpadAst|) $) 12 T ELT)) (|mainExpression| (#2# 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|WhereAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |mainExpression| #1=((|SpadAst|) $)) (SIGNATURE |qualifier| #1#)))) (T |WhereAst|)) 
((|mainExpression| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|WhereAst|)))) (|qualifier| #1# #2#)) 
((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|condition| (((|SpadAst|) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) 
(((|WhileAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |condition| ((|SpadAst|) $))))) (T |WhileAst|)) 
((|condition| (*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|WhileAst|))))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 59 T ELT)) (|subtractIfCan| (#5=(#6=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#7=($) NIL T CONST)) (|recip| ((#6# $) NIL T ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 82 T ELT) (($ #8=(|Integer|)) NIL T ELT) (($ |#4|) 66 T ELT) ((|#4| $) 71 T ELT) (($ |#1|) NIL #9=(|has| |#1| (|CommutativeRing|)) ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) NIL T CONST)) (|changeWeightLevel| (((|Void|) #10#) 16 T ELT)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#7# 36 T CONST)) (|One| (#7# 85 T CONST)) (= (#2# 88 T ELT)) (/ (#5# NIL (|has| |#1| (|Field|)) ELT)) (- (($ $) 90 T ELT) (#11=($ $ $) NIL T ELT)) (+ (#11# 64 T ELT)) (** (($ $ #12=(|PositiveInteger|)) NIL T ELT) (($ $ #10#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #8# . #13=($)) NIL T ELT) (#11# 92 T ELT) (($ |#1| . #13#) NIL #9# ELT) (($ $ |#1|) NIL #9# ELT))) 
(((|WeightedPolynomials| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (|Join| #1=(|Ring|) (|HomotopicTo| |#4|) (CATEGORY |domain| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |#1|)) |%noBranch|) (IF (|has| |#1| (|Field|)) (SIGNATURE / ((|Union| $ "failed") $ $)) |%noBranch|) (SIGNATURE |changeWeightLevel| ((|Void|) #2=(|NonNegativeInteger|))))) #1# (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|PolynomialCategory| |#1| |#3| |#2|) (|List| |#2|) (|List| #2#) #2#) (T |WeightedPolynomials|)) 
((/ (*1 *1 *1 *1) (|partial| AND (|ofCategory| *2 (|Field|)) (|ofCategory| *2 #1=(|Ring|)) (|ofCategory| *3 #2=(|OrderedSet|)) (|ofCategory| *4 #3=(|OrderedAbelianMonoidSup|)) (|ofType| *6 #4=(|List| *3)) (|isDomain| *1 (|WeightedPolynomials| *2 *3 *4 *5 *6 *7 *8)) (|ofCategory| *5 (|PolynomialCategory| *2 *4 *3)) (|ofType| *7 (|List| #5=(|NonNegativeInteger|))) (|ofType| *8 #5#))) (|changeWeightLevel| (*1 *2 *3) (AND (|isDomain| *3 #5#) (|ofCategory| *4 #1#) (|ofCategory| *5 #2#) (|ofCategory| *6 #3#) (|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 #4#) (|ofType| *10 *3)))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| |#4|)))) #5#) NIL T ELT)) (|zeroSetSplit| (#6=(#7=(|List| $) #5#) 95 T ELT)) (|variables| #8=(((|List| |#3|) $) NIL T ELT)) (|trivialIdeal?| #9=(#10=(#3# $) NIL T ELT)) (|triangular?| #11=(#10# NIL #12=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #13=(#14=(#3# |#4| $) NIL T ELT) #9#) (|stronglyReduce| #15=(#16=(|#4| |#4| $) NIL T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL T ELT)) (|select| #17=(($ #18=(|Mapping| #3# |#4|) $) NIL #19=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#20=(|Union| |#4| #21="failed") $ |#3|) NIL T ELT)) (|sample| (#22=($) NIL T CONST)) (|roughUnitIdeal?| #11#) (|roughSubIdeal?| #23=(#2# NIL #12# ELT)) (|roughEqualIdeals?| #23#) (|roughBase?| #11#) (|rewriteSetWithReduction| ((#5# #5# $ #24=(|Mapping| |#4| |#4| |#4|) #25=(|Mapping| #3# |#4| |#4|)) 31 T ELT)) (|rewriteIdealWithRemainder| (#26=(#5# #5# $) 28 #12# ELT)) (|rewriteIdealWithHeadRemainder| (#26# NIL #12# ELT)) (|retractIfCan| (#27=(#28=(|Union| $ #21#) #5#) NIL T ELT)) (|retract| #29=(($ #5#) NIL T ELT)) (|rest| ((#28# $) 77 T ELT)) (|removeZero| (#16# 82 T ELT)) (|removeDuplicates| (#30=($ $) NIL #31=(AND #19# #32=(|has| |#4| (|BasicType|))) ELT)) (|remove| (($ |#4| $) NIL #31# ELT) #17#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #33=(|:| |den| |#1|)) |#4| $) NIL #12# ELT)) (|reduced?| ((#3# |#4| $ #25#) NIL T ELT)) (|reduceByQuasiMonic| #15#) (|reduce| ((|#4| #24# $ |#4| |#4|) NIL #32# ELT) ((|#4| #24# $ |#4|) NIL T ELT) ((|#4| #24# $) NIL T ELT) ((|#4| |#4| $ #24# #25#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|normalized?| #13# #9#) (|mvar| ((|#3| $) 83 T ELT)) (|members| (#34=(#5# $) 32 T ELT)) (|member?| (#14# NIL #32# ELT)) (|medialSet| (#35=(#28# #5# #25# #24#) 35 T ELT) (#27# 38 T ELT)) (|map!| #36=(($ (|Mapping| |#4| |#4|) $) NIL T ELT)) (|map| #36#) (|mainVariables| #8#) (|mainVariable?| #37=((#3# |#3| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|last| (#38=(#20# $) NIL T ELT)) (|initials| (#34# 53 T ELT)) (|initiallyReduced?| #13# #9#) (|initiallyReduce| (#16# 81 T ELT)) (|infRittWu?| (#2# 92 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) #33#) |#4| $) NIL #12# ELT)) (|headReduced?| #13# #9#) (|headReduce| #15#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#38# 76 T ELT)) (|find| ((#20# #18# $) NIL T ELT)) (|extendIfCan| ((#28# $ |#4|) NIL T ELT)) (|extend| (($ $ |#4|) NIL T ELT)) (|every?| #39=((#3# #18# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #40=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) NIL #40# ELT) (($ $ #41=(|Equation| |#4|)) NIL #40# ELT) (($ $ (|List| #41#)) NIL #40# ELT)) (|eq?| #1#) (|empty?| (#10# 74 T ELT)) (|empty| (#22# 45 T ELT)) (|degree| #42=(#43=(#44=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#44# |#4| $) NIL #32# ELT) ((#44# #18# $) NIL T ELT)) (|copy| #45=(#30# NIL T ELT)) (|convert| ((#46=(|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| #46#)) ELT)) (|construct| #29#) (|collectUpper| #47=(($ $ |#3|) NIL T ELT)) (|collectUnder| #47#) (|collectQuasiMonic| #45#) (|collect| #47#) (|coerce| (((|OutputForm|) $) NIL T ELT) (#34# 62 T ELT)) (|coHeight| (#43# NIL (|has| |#3| (|Finite|)) ELT)) (|characteristicSet| (#35# 43 T ELT) (#27# 44 T ELT)) (|characteristicSerie| ((#7# #5# #25# #24#) 72 T ELT) (#6# 73 T ELT)) (|before?| #1#) (|basicSet| ((#48=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #21#) #5# #25#) 27 T ELT) ((#48# #5# #18# #25#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# |#4| #5#)) NIL T ELT)) (|any?| #39#) (|algebraicVariables| #8#) (|algebraic?| #37#) (= #1#) (|#| #42#)) 
(((|WuWenTsunTriangularSet| |#1| |#2| |#3| |#4|) (|Join| (|TriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |medialSet| #1=(#2=(|Union| $ "failed") #3=(|List| |#4|) #4=(|Mapping| (|Boolean|) |#4| |#4|) #5=(|Mapping| |#4| |#4| |#4|))) (SIGNATURE |medialSet| #6=(#2# #3#)) (SIGNATURE |characteristicSet| #1#) (SIGNATURE |characteristicSet| #6#) (SIGNATURE |characteristicSerie| (#7=(|List| $) #3# #4# #5#)) (SIGNATURE |characteristicSerie| (#7# #3#)))) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |WuWenTsunTriangularSet|)) 
((|medialSet| #1=(*1 *1 *2 *3 *4) #2=(|partial| AND (|isDomain| *2 (|List| *8)) (|isDomain| *3 (|Mapping| #3=(|Boolean|) *8 *8)) (|isDomain| *4 (|Mapping| *8 *8 *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 #4=(|IntegralDomain|)) (|ofCategory| *6 #5=(|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #6=(|OrderedSet|)) (|isDomain| *1 (|WuWenTsunTriangularSet| *5 *6 *7 *8)))) (|medialSet| #7=(*1 *1 *2) #8=(|partial| AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 #4#) (|ofCategory| *4 #5#) (|ofCategory| *5 #6#) (|isDomain| *1 (|WuWenTsunTriangularSet| *3 *4 *5 *6)))) (|characteristicSet| #1# #2#) (|characteristicSet| #7# #8#) (|characteristicSerie| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| *9)) (|isDomain| *4 (|Mapping| #3# *9 *9)) (|isDomain| *5 (|Mapping| *9 *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 #4#) (|ofCategory| *7 #5#) (|ofCategory| *8 #6#) (|isDomain| *2 (|List| #9=(|WuWenTsunTriangularSet| *6 *7 *8 *9))) (|isDomain| *1 #9#))) (|characteristicSerie| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 #4#) (|ofCategory| *5 #5#) (|ofCategory| *6 #6#) (|isDomain| *2 (|List| #10=(|WuWenTsunTriangularSet| *4 *5 *6 *7))) (|isDomain| *1 #10#)))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 53 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #4#) 54 T ELT))) 
(((|XAlgebra| |#1|) (|Category|) (|Ring|)) (T |XAlgebra|)) 
NIL 
(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (|CoercibleFrom| |t#1|) (CATEGORY |package| (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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) 
((~= (#1=(#2=(|Boolean|) $ $) 69 T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|varList| (((|List| |#1|) $) 54 T ELT)) (|trunc| (#5=($ $ #6=(|NonNegativeInteger|)) 47 T ELT)) (|subtractIfCan| ((#7=(|Union| $ #8="failed") $ $) NIL T ELT)) (|sh| (#5# 25 #9=(|has| |#2| (|CommutativeRing|)) ELT) (#10=($ $ $) 26 #9# ELT)) (|sample| (#11=($) NIL T CONST)) (|rquo| (#10# 72 T ELT) (#12=($ $ #13=(|OrderedFreeMonoid| |#1|)) 58 T ELT) (#14=($ $ |#1|) 62 T ELT)) (|retractIfCan| (((|Union| #13# #8#) $) NIL T ELT)) (|retract| #15=(#16=(#13# $) NIL T ELT)) (|reductum| (#17=($ $) 40 T ELT)) (|recip| ((#7# $) NIL T ELT)) (|quasiRegular?| #3#) (|quasiRegular| #18=(#17# NIL T ELT)) (|opposite?| #19=(#1# NIL T ELT)) (|one?| #3#) (|numberOfMonomials| (#20=(#6# $) NIL T ELT)) (|monomials| (((|List| $) $) NIL T ELT)) (|monomial?| #3#) (|monom| (($ #13# |#2|) 39 T ELT)) (|mirror| (#17# 41 T ELT)) (|mindegTerm| (#21=(#22=(|Record| (|:| |k| #13#) (|:| |c| |#2|)) $) 13 T ELT)) (|mindeg| #15#) (|maxdeg| (#16# 42 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|lquo| (#10# 71 T ELT) (#12# 60 T ELT) (#14# 64 T ELT)) (|leadingTerm| (#21# NIL T ELT)) (|leadingMonomial| (#16# 36 T ELT)) (|leadingCoefficient| (#23=(|#2| $) 38 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|degree| (#20# 44 T ELT)) (|constant?| (#4# 48 T ELT)) (|constant| (#23# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #13#) 31 T ELT) (($ |#1|) 32 T ELT) (($ |#2|) NIL T ELT) (($ #24=(|Integer|)) NIL T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| #25=((|#2| $ #13#) NIL T ELT)) (|coef| ((|#2| $ $) 78 T ELT) #25#) (|characteristic| ((#6#) NIL T CONST)) (|before?| #19#) (|annihilate?| #19#) (|Zero| (#11# 14 T CONST)) (|One| (#11# 20 T CONST)) (|ListOfTerms| (((|List| #22#) $) NIL T ELT)) (= (#1# 45 T ELT)) (- #26=(#10# NIL T ELT) #18#) (+ (#10# 29 T ELT)) (** (#5# NIL T ELT) (($ $ #27=(|PositiveInteger|)) NIL T ELT)) (* (($ $ |#2|) 70 T ELT) (($ |#2| . #28=($)) 28 T ELT) (($ #24# . #28#) NIL T ELT) (($ #6# $) NIL T ELT) (($ #27# $) NIL T ELT) (($ |#2| #13#) NIL T ELT) (($ |#1| $) 34 T ELT) #26#)) 
(((|XDistributedPolynomial| |#1| |#2|) (|Join| (|FreeModuleCat| |#2| (|OrderedFreeMonoid| |#1|)) (|XPolynomialsCat| |#1| |#2|)) (|OrderedSet|) (|Ring|)) (T |XDistributedPolynomial|)) 
NIL 
((|log| (#1=(|#3| |#3| #2=(|NonNegativeInteger|)) 28 T ELT)) (|exp| (#1# 34 T ELT)) (|Hausdorff| ((|#3| |#3| |#3| #2#) 35 T ELT))) 
(((|XExponentialPackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |exp| #1=(|#3| |#3| #2=(|NonNegativeInteger|))) (SIGNATURE |log| #1#) (SIGNATURE |Hausdorff| (|#3| |#3| |#3| #2#))) (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|)))) (|OrderedSet|) (|XPolynomialsCat| |#2| |#1|)) (T |XExponentialPackage|)) 
((|Hausdorff| (*1 *2 *2 *2 *3) #1=(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| #2=(*1 *2 *2 *3) #1#) (|exp| #2# #1#)) 
((|transcendent?| (#1=((|Boolean|) $) 15 T ELT)) (|algebraic?| (#1# 14 T ELT)) (|Frobenius| (($ $) 19 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT))) 
(((|ExtensionField&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |Frobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |Frobenius| (|#1| |#1|)) (SIGNATURE |transcendent?| #1=((|Boolean|) |#1|)) (SIGNATURE |algebraic?| #1#)) (|ExtensionField| |#2|) (|Field|)) (T |ExtensionField&|)) 
NIL 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|transcendent?| (((|Boolean|) $) 114 T ELT)) (|transcendenceDegree| (((|NonNegativeInteger|)) 110 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 121 T ELT)) (|retract| ((|#1| $) 122 T ELT)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|primeFrobenius| (($ $ #8=(|NonNegativeInteger|)) 107 (OR (|has| |#1| . #9=((|CharacteristicNonZero|))) (|has| |#1| . #10=((|Finite|)))) ELT) (($ $) 106 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 104 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #11=(|List| $) #12="failed") #11# $) 68 T ELT)) (|lcm| (#13=($ $ $) 60 T ELT) (#14=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|inGroundField?| (((|Boolean|) $) 113 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#15=(|SparseUnivariatePolynomial| $) #15# #15#) 58 T ELT)) (|gcd| (#13# 62 T ELT) (#14# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) 111 T ELT)) (|extendedEuclidean| (((|Record| #16=(|:| |coef1| $) #17=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #16# #17#) #12#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| (((|Union| #8# "failed") $ $) 105 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|dimension| (((|CardinalNumber|)) 119 T ELT)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) 112 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #18=(|Fraction| #19=(|Integer|))) 84 T ELT) (($ |#1|) 120 T ELT)) (|charthRoot| (((|Maybe| $) $) 103 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|algebraic?| (((|Boolean|) $) 115 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (|Frobenius| (($ $) 109 (|has| |#1| (|Finite|)) ELT) (($ $ (|NonNegativeInteger|)) 108 (|has| |#1| (|Finite|)) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT) (($ $ |#1|) 118 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #19#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #20=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #18#) 86 T ELT) (($ #18# . #20#) 85 T ELT) (($ $ |#1|) 117 T ELT) (($ |#1| . #20#) 116 T ELT))) 
(((|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| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|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) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| |#1|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T) ((|VectorSpace| |#1|) . T)) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|varList| (((|List| |#1|) $) 56 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sh| (($ $ $) 58 (|has| |#2| (|CommutativeRing|)) ELT) (($ $ (|NonNegativeInteger|)) 57 (|has| |#2| (|CommutativeRing|)) ELT)) (|sample| (#3=($) 23 T CONST)) (|rquo| (($ $ |#1|) 69 T ELT) (($ $ (|OrderedFreeMonoid| |#1|)) 68 T ELT) (($ $ $) 67 T ELT)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) 79 T ELT)) (|retract| (((|OrderedFreeMonoid| |#1|) $) 80 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quasiRegular?| (((|Boolean|) $) 60 T ELT)) (|quasiRegular| (($ $) 59 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial?| (((|Boolean|) $) 65 T ELT)) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) 66 T ELT)) (|mirror| (($ $) 64 T ELT)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) 75 T ELT)) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) 76 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 81 T ELT)) (|lquo| (($ $ |#1|) 72 T ELT) (($ $ (|OrderedFreeMonoid| |#1|)) 71 T ELT) (($ $ $) 70 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|constant?| (((|Boolean|) $) 62 T ELT)) (|constant| ((|#2| $) 61 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#2|) 84 T ELT) (($ (|OrderedFreeMonoid| |#1|)) 78 T ELT) (($ |#1|) 63 T ELT)) (|coef| ((|#2| $ (|OrderedFreeMonoid| |#1|)) 74 T ELT) ((|#2| $ $) 73 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ |#2| . #4#) 83 T ELT) (($ $ |#2|) 82 T ELT) (($ |#1| $) 77 T ELT))) 
(((|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|)))) (|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|) (|Functorial| |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 |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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #1=(|OrderedFreeMonoid| |#1|)) . T) ((|CoercibleFrom| |#2|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Functorial| |#2|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#2|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#2|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#2|) |has| |#2| (|CommutativeRing|)) ((|Module| |#2|) |has| |#2| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|XAlgebra| |#2|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|varList| (((|List| |#1|) $) 99 T ELT)) (|trunc| (#6=($ $ #7=(|NonNegativeInteger|)) 103 T ELT)) (|subtractIfCan| ((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|sh| (#10=($ $ $) NIL #11=(|has| |#2| (|CommutativeRing|)) ELT) (#6# NIL #11# ELT)) (|sample| (#12=($) NIL T CONST)) (|rquo| #13=(($ $ |#1|) NIL T ELT) #14=(($ $ #15=(|OrderedFreeMonoid| |#1|)) NIL T ELT) #16=(#10# NIL T ELT)) (|retractIfCan| (((|Union| #15# . #17=(#9#)) . #18=($)) NIL T ELT) (((|Union| #19=(|PoincareBirkhoffWittLyndonBasis| |#1|) . #17#) . #18#) NIL T ELT)) (|retract| #20=((#15# . #21=($)) NIL T ELT) (#22=(#19# . #21#) NIL T ELT)) (|reductum| (#23=($ $) 102 T ELT)) (|recip| ((#8# $) NIL T ELT)) (|quasiRegular?| (#5# 90 T ELT)) (|quasiRegular| (#23# 93 T ELT)) (|product| (($ $ $ #7#) 104 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| (#24=(#7# $) NIL T ELT)) (|monomials| (((|List| $) $) NIL T ELT)) (|monomial?| #4#) (|monom| (($ #15# |#2|) NIL T ELT) (($ #19# |#2|) 28 T ELT)) (|mirror| (#23# 120 T ELT)) (|mindegTerm| (((|Record| (|:| |k| #15#) #25=(|:| |c| |#2|)) $) NIL T ELT)) (|mindeg| #20#) (|maxdeg| #20#) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|lquo| #13# #14# #16#) (|log| (#6# 113 #26=(|has| |#2| (|Module| (|Fraction| #27=(|Integer|)))) ELT)) (|leadingTerm| ((#28=(|Record| (|:| |k| #19#) #25#) $) NIL T ELT)) (|leadingMonomial| (#22# 84 T ELT)) (|leadingCoefficient| (#29=(|#2| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exp| (#6# 110 #26# ELT)) (|degree| (#24# 100 T ELT)) (|constant?| (#5# 85 T ELT)) (|constant| (#29# 88 T ELT)) (|coerce| (((|OutputForm|) $) 70 T ELT) (($ #27#) NIL T ELT) (($ |#2|) 59 T ELT) (($ #15#) NIL T ELT) (($ |#1|) 72 T ELT) (($ #19#) NIL T ELT) (($ #30=(|LiePolynomial| |#1| |#2|)) 47 T ELT) (((|XDistributedPolynomial| |#1| |#2|) $) 77 T ELT) (((|XRecursivePolynomial| |#1| |#2|) $) 82 T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| ((|#2| $ #19#) NIL T ELT)) (|coef| ((|#2| $ #15#) NIL T ELT) ((|#2| $ $) NIL T ELT)) (|characteristic| ((#7#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#12# 21 T CONST)) (|One| (#12# 27 T CONST)) (|ListOfTerms| (((|List| #28#) $) NIL T ELT)) (|LiePolyIfCan| (((|Union| #30# #9#) $) 119 T ELT)) (= (#2# 78 T ELT)) (- (#23# 112 T ELT) (#10# 111 T ELT)) (+ (#10# 20 T ELT)) (** (($ $ #31=(|PositiveInteger|)) NIL T ELT) (#6# NIL T ELT)) (* (($ #31# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #27# . #32=($)) NIL T ELT) (#10# 48 T ELT) (($ |#2| . #32#) 19 T ELT) (($ $ |#2|) NIL T ELT) (($ |#1| $) NIL T ELT) (($ |#2| #19#) NIL T ELT))) 
(((|XPBWPolynomial| |#1| |#2|) (|Join| (|XPolynomialsCat| |#1| |#2|) (|FreeModuleCat| |#2| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1=(|LiePolynomial| |#1| |#2|))) (SIGNATURE |coerce| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |coerce| ((|XRecursivePolynomial| |#1| |#2|) $)) (SIGNATURE |LiePolyIfCan| ((|Union| #1# "failed") $)) (SIGNATURE |product| ($ $ $ #2=(|NonNegativeInteger|))) (IF (|has| |#2| (|Module| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |exp| #3=($ $ #2#)) (SIGNATURE |log| #3#)) |%noBranch|))) (|OrderedSet|) (|CommutativeRing|)) (T |XPBWPolynomial|)) 
((|coerce| (*1 *1 *2) (AND #1=(|isDomain| *2 (|LiePolynomial| *3 *4)) #2=(|ofCategory| *3 (|OrderedSet|)) #3=(|ofCategory| *4 (|CommutativeRing|)) #4=(|isDomain| *1 (|XPBWPolynomial| *3 *4)))) (|coerce| #5=(*1 *2 *1) (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) #4# #2# #3#)) (|coerce| #5# (AND (|isDomain| *2 (|XRecursivePolynomial| *3 *4)) #4# #2# #3#)) (|LiePolyIfCan| #5# (|partial| AND #1# #4# #2# #3#)) (|product| (*1 *1 *1 *1 *2) (AND #6=(|isDomain| *2 (|NonNegativeInteger|)) #4# #2# #3#)) (|exp| #7=(*1 *1 *1 *2) #8=(AND #6# #4# (|ofCategory| *4 (|Module| (|Fraction| (|Integer|)))) #2# #3#)) (|log| #7# #8#)) 
((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|varList| (((|List| #4=(|Symbol|)) $) NIL T ELT)) (|unexpand| (($ #5=(|XDistributedPolynomial| #4# |#1|)) NIL T ELT)) (|trunc| #6=(#7=($ $ #8=(|NonNegativeInteger|)) NIL T ELT)) (|subtractIfCan| ((#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|sh| (#11=($ $ $) NIL #12=(|has| |#1| (|CommutativeRing|)) ELT) (#7# NIL #12# ELT)) (|sample| #13=(($) NIL T CONST)) (|rquo| #14=(($ $ #4#) NIL T ELT) #15=(($ $ #16=(|OrderedFreeMonoid| #4#)) NIL T ELT) #17=(#11# NIL T ELT)) (|retractIfCan| (((|Union| #16# #10#) $) NIL T ELT)) (|retract| #18=((#16# $) NIL T ELT)) (|recip| ((#9# $) NIL T ELT)) (|quasiRegular?| #3#) (|quasiRegular| #19=(($ $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial?| #3#) (|monom| (($ #16# |#1|) NIL T ELT)) (|mirror| #19#) (|mindegTerm| (((|Record| (|:| |k| #16#) (|:| |c| |#1|)) $) NIL T ELT)) (|mindeg| #18#) (|maxdeg| #18#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|lquo| #14# #15# #17#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expand| ((#5# $) NIL T ELT)) (|degree| ((#8# $) NIL T ELT)) (|constant?| #3#) (|constant| ((|#1| $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (($ #16#) NIL T ELT) (($ #4#) NIL T ELT)) (|coef| ((|#1| $ #16#) NIL T ELT) ((|#1| $ $) NIL T ELT)) (|characteristic| ((#8#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| #13#) (|RemainderList| (((|List| (|Record| (|:| |k| #4#) (|:| |c| $))) $) NIL T ELT)) (|One| #13#) (= #1#) (- #19# #17#) (+ #17#) (** (($ $ #21=(|PositiveInteger|)) NIL T ELT) #6#) (* (($ #21# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #20# . #22=($)) NIL T ELT) #17# (($ |#1| . #22#) NIL T ELT) (($ $ |#1|) NIL T ELT) (($ #4# $) NIL T ELT))) 
(((|XPolynomial| |#1|) (|Join| (|XPolynomialsCat| #1=(|Symbol|) |#1|) (CATEGORY |domain| (SIGNATURE |expand| (#2=(|XDistributedPolynomial| #1# |#1|) $)) (SIGNATURE |unexpand| ($ #2#)) (SIGNATURE |RemainderList| ((|List| (|Record| (|:| |k| #1#) (|:| |c| $))) $)))) (|Ring|)) (T |XPolynomial|)) 
((|expand| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|XDistributedPolynomial| #3=(|Symbol|) *3)) #4=(|isDomain| *1 #5=(|XPolynomial| *3)) #6=(|ofCategory| *3 (|Ring|)))) (|unexpand| (*1 *1 *2) (AND #2# #6# #4#)) (|RemainderList| #1# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| #3#) (|:| |c| #5#)))) #4# #6#))) 
((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|varList| (((|List| |#1|) $) 56 T ELT)) (|trunc| (($ $ (|NonNegativeInteger|)) 90 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sh| (#3=($ $ $) 58 (|has| |#2| . #4=((|CommutativeRing|))) ELT) (($ $ (|NonNegativeInteger|)) 57 (|has| |#2| . #4#) ELT)) (|sample| (#5=($) 23 T CONST)) (|rquo| (($ $ |#1|) 69 T ELT) (($ $ (|OrderedFreeMonoid| |#1|)) 68 T ELT) (#3# 67 T ELT)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) 79 T ELT)) (|retract| (((|OrderedFreeMonoid| |#1|) $) 80 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quasiRegular?| (#6=((|Boolean|) $) 60 T ELT)) (|quasiRegular| (#7=($ $) 59 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial?| (#6# 65 T ELT)) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) 66 T ELT)) (|mirror| (#7# 64 T ELT)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) 75 T ELT)) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) 76 T ELT)) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) 92 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 81 T ELT)) (|lquo| (($ $ |#1|) 72 T ELT) (($ $ (|OrderedFreeMonoid| |#1|)) 71 T ELT) (#3# 70 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| (((|NonNegativeInteger|) $) 91 T ELT)) (|constant?| (#6# 62 T ELT)) (|constant| ((|#2| $) 61 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#2|) 84 T ELT) (($ (|OrderedFreeMonoid| |#1|)) 78 T ELT) (($ |#1|) 63 T ELT)) (|coef| ((|#2| $ (|OrderedFreeMonoid| |#1|)) 74 T ELT) ((|#2| $ $) 73 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #8=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ |#2| . #8#) 83 T ELT) (($ $ |#2|) 82 T ELT) (($ |#1| $) 77 T ELT))) 
(((|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) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #1=(|OrderedFreeMonoid| |#1|)) . T) ((|CoercibleFrom| |#2|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Functorial| |#2|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#2|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#2|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#2|) |has| |#2| (|CommutativeRing|)) ((|Module| |#2|) |has| |#2| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|XAlgebra| |#2|) . T) ((|XFreeAlgebra| |#1| |#2|) . T)) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|sample| (#8=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| #7#) $) NIL T ELT)) (|retract| #9=(#10=(|#2| $) NIL T ELT)) (|reductum| #11=(#12=($ $) NIL T ELT)) (|recip| ((#6# $) 43 T ELT)) (|quasiRegular?| (#5# 37 T ELT)) (|quasiRegular| (#12# 38 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| (#13=(#14=(|NonNegativeInteger|) $) NIL T ELT)) (|monomials| (((|List| $) $) NIL T ELT)) (|monomial?| #4#) (|monom| (($ |#2| |#1|) NIL T ELT)) (|mindeg| (#10# 25 T ELT)) (|maxdeg| (#10# 23 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingTerm| ((#15=(|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) NIL T ELT)) (|leadingMonomial| #9#) (|leadingCoefficient| (#16=(|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|constant?| (#5# 33 T ELT)) (|constant| (#16# 34 T ELT)) (|coerce| (((|OutputForm|) $) 66 T ELT) (($ #17=(|Integer|)) 47 T ELT) (($ |#1|) 42 T ELT) (($ |#2|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| (#18=(|#1| $ |#2|) NIL T ELT)) (|coef| (#18# 29 T ELT)) (|characteristic| ((#14#) 14 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#8# 30 T CONST)) (|One| (#8# 11 T CONST)) (|ListOfTerms| (((|List| #15#) $) NIL T ELT)) (= (#2# 31 T ELT)) (/ (#19=($ $ |#1|) 68 (|has| |#1| (|Field|)) ELT)) (- #11# (#20=($ $ $) NIL T ELT)) (+ (#20# 51 T ELT)) (** (($ $ #21=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) 53 T ELT)) (* (($ #21# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #17# . #22=($)) NIL T ELT) (#20# 52 T ELT) (($ |#1| . #22#) 48 T ELT) (#19# NIL T ELT) (($ |#1| |#2|) NIL T ELT)) (|#| (#13# 18 T ELT))) 
(((|XPolynomialRing| |#1| |#2|) (|Join| #1=(|Ring|) (|XAlgebra| |#1|) (|FreeModuleCat| |#1| |#2|) (|CoercibleFrom| |#2|) (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE * #2=($ $ |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) $)) (SIGNATURE |maxdeg| #3=(|#2| $)) (SIGNATURE |mindeg| #3#) (SIGNATURE |reductum| #4=($ $)) (SIGNATURE |coef| (|#1| $ |#2|)) (SIGNATURE |constant?| #5=((|Boolean|) $)) (SIGNATURE |constant| (|#1| $)) (SIGNATURE |quasiRegular?| #5#) (SIGNATURE |quasiRegular| #4#) (IF (|has| |#1| (|Field|)) (SIGNATURE / #2#) |%noBranch|) (IF (|has| |#1| #6=(ATTRIBUTE |noZeroDivisors|)) #6# |%noBranch|) (IF (|has| |#1| #7=(ATTRIBUTE |unitsKnown|)) #7# |%noBranch|) (IF (|has| |#1| #8=(ATTRIBUTE |canonicalUnitNormal|)) #8# |%noBranch|))) #1# (|OrderedMonoid|)) (T |XPolynomialRing|)) 
((* #1=(*1 *1 *1 *2) #2=(AND #3=(|isDomain| *1 (|XPolynomialRing| *2 *3)) #4=(|ofCategory| *2 #5=(|Ring|)) #6=(|ofCategory| *3 #7=(|OrderedMonoid|)))) (|reductum| #8=(*1 *1 *1) #2#) (|#| #9=(*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) #10=(|isDomain| *1 (|XPolynomialRing| *3 *4)) #11=(|ofCategory| *3 #5#) #12=(|ofCategory| *4 #7#))) (|maxdeg| #9# #13=(AND (|ofCategory| *2 #7#) (|isDomain| *1 (|XPolynomialRing| *3 *2)) #11#)) (|mindeg| #9# #13#) (|coef| (*1 *2 *1 *3) #14=(AND #4# #3# #6#)) (|constant?| #9# #15=(AND (|isDomain| *2 (|Boolean|)) #10# #11# #12#)) (|constant| #9# #14#) (|quasiRegular?| #9# #15#) (|quasiRegular| #8# #2#) (/ #1# (AND #3# (|ofCategory| *2 (|Field|)) #4# #6#))) 
((~= (#1=(#2=(|Boolean|) $ $) 27 T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|varList| (((|List| |#1|) $) 132 T ELT)) (|unexpand| (($ #5=(|XDistributedPolynomial| |#1| |#2|)) 50 T ELT)) (|trunc| (#6=($ $ #7=(|NonNegativeInteger|)) 38 T ELT)) (|subtractIfCan| ((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|sh| (#10=($ $ $) 54 #11=(|has| |#2| (|CommutativeRing|)) ELT) (#6# 52 #11# ELT)) (|sample| (#12=($) NIL T CONST)) (|rquo| (#13=($ $ |#1|) 114 T ELT) (#14=($ $ #15=(|OrderedFreeMonoid| |#1|)) 115 T ELT) (#10# 26 T ELT)) (|retractIfCan| (((|Union| #15# #9#) $) NIL T ELT)) (|retract| (#16=(#15# $) NIL T ELT)) (|recip| ((#8# $) 122 T ELT)) (|quasiRegular?| (#4# 117 T ELT)) (|quasiRegular| (#17=($ $) 118 T ELT)) (|opposite?| #18=(#1# NIL T ELT)) (|one?| #3#) (|monomial?| #3#) (|monom| (($ #15# |#2|) 20 T ELT)) (|mirror| (#17# NIL T ELT)) (|mindegTerm| (((|Record| (|:| |k| #15#) (|:| |c| |#2|)) $) NIL T ELT)) (|mindeg| (#16# 123 T ELT)) (|maxdeg| (#16# 126 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 131 T ELT)) (|lquo| (#13# 112 T ELT) (#14# 113 T ELT) (#10# 62 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expand| ((#5# $) 94 T ELT)) (|degree| ((#7# $) 129 T ELT)) (|constant?| (#4# 81 T ELT)) (|constant| ((|#2| $) 32 T ELT)) (|coerce| (((|OutputForm|) $) 73 T ELT) (($ #19=(|Integer|)) 87 T ELT) (($ |#2|) 85 T ELT) (($ #15#) 18 T ELT) (($ |#1|) 84 T ELT)) (|coef| ((|#2| $ #15#) 116 T ELT) ((|#2| $ $) 28 T ELT)) (|characteristic| ((#7#) 120 T CONST)) (|before?| #18#) (|annihilate?| #18#) (|Zero| (#12# 15 T CONST)) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) 59 T ELT)) (|One| (#12# 33 T CONST)) (= (#1# 14 T ELT)) (- (#17# 98 T ELT) (#10# 101 T ELT)) (+ (#10# 61 T ELT)) (** (($ $ #20=(|PositiveInteger|)) NIL T ELT) (#6# 55 T ELT)) (* (($ #20# $) NIL T ELT) (($ #7# $) 53 T ELT) (($ #19# $) 106 T ELT) (#10# 22 T ELT) (($ |#2| $) 19 T ELT) (($ $ |#2|) 21 T ELT) (($ |#1| $) 92 T ELT))) 
(((|XRecursivePolynomial| |#1| |#2|) (|Join| (|XPolynomialsCat| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |expand| (#1=(|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |unexpand| ($ #1#)) (SIGNATURE |RemainderList| ((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $)))) (|OrderedSet|) (|Ring|)) (T |XRecursivePolynomial|)) 
((|expand| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|XDistributedPolynomial| *3 *4)) #3=(|isDomain| *1 #4=(|XRecursivePolynomial| *3 *4)) #5=(|ofCategory| *3 (|OrderedSet|)) #6=(|ofCategory| *4 (|Ring|)))) (|unexpand| (*1 *1 *2) (AND #2# #5# #6# #3#)) (|RemainderList| #1# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| *3) (|:| |c| #4#)))) #3# #5# #6#))) 
((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|youngDiagram| (($ (|List| (|PositiveInteger|))) 11 T ELT)) (|shape| (#3=(#4=(|Partition|) $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT) (($ #4#) 14 T ELT) (#3# 13 T ELT)) (|before?| #1#) (= (#2# 17 T ELT))) 
(((|YoungDiagram|) (|Join| (|SetCategory|) (|HomotopicTo| #1=(|Partition|)) (CATEGORY |domain| (SIGNATURE |youngDiagram| ($ (|List| (|PositiveInteger|)))) (SIGNATURE |shape| (#1# $))))) (T |YoungDiagram|)) 
((|youngDiagram| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|PositiveInteger|))) #1=(|isDomain| *1 (|YoungDiagram|)))) (|shape| (*1 *2 *1) (AND (|isDomain| *2 (|Partition|)) #1#))) 
((Y ((#1=(|List| #2=(|Stream| |#1|)) (|Mapping| #1# #1#) (|Integer|)) 16 T ELT) ((#2# (|Mapping| #2# #2#)) 13 T ELT))) 
(((|ParadoxicalCombinatorsForStreams| |#1|) (CATEGORY |package| (SIGNATURE Y (#1=(|Stream| |#1|) (|Mapping| #1# #1#))) (SIGNATURE Y (#2=(|List| #1#) (|Mapping| #2# #2#) (|Integer|)))) (|Type|)) (T |ParadoxicalCombinatorsForStreams|)) 
((Y (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| #1=(|List| (|Stream| *5)) #1#)) (|isDomain| *4 (|Integer|)) (|isDomain| *2 #1#) (|isDomain| *1 (|ParadoxicalCombinatorsForStreams| *5)) (|ofCategory| *5 #2=(|Type|)))) (Y (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| #3=(|Stream| *4) #3#)) (|isDomain| *2 #3#) (|isDomain| *1 (|ParadoxicalCombinatorsForStreams| *4)) (|ofCategory| *4 #2#)))) 
((|univariateSolve| ((#1=(|List| (|Record| (|:| |complexRoots| #2=(|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| #3=(|List| #4=(|Polynomial| |#1|))))) #3#) 174 T ELT) ((#1# #3# #5=(|Boolean|)) 173 T ELT) ((#1# #3# #5# #5#) 172 T ELT) ((#1# #3# #5# #5# #5#) 171 T ELT) ((#1# #6=(|RegularChain| |#1| |#2|)) 156 T ELT)) (|triangSolve| ((#7=(|List| #6#) #3#) 85 T ELT) ((#7# #3# #5#) 84 T ELT) ((#7# #3# #5# #5#) 83 T ELT)) (|squareFree| (((|List| #8=(|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| #9=(|OrderedVariableList| |#3|)) #9# #10=(|NewSparseMultivariatePolynomial| |#1| #9#))) #6#) 73 T ELT)) (|realSolve| (#11=(#12=(|List| (|List| #13=(|RealClosure| (|Fraction| |#1|)))) #3#) 140 T ELT) (#14=(#12# #3# #5#) 139 T ELT) (#15=(#12# #3# #5# #5#) 138 T ELT) ((#12# #3# #5# #5# #5#) 137 T ELT) (#16=(#12# #6#) 132 T ELT)) (|positiveSolve| (#11# 145 T ELT) (#14# 144 T ELT) (#15# 143 T ELT) (#16# 142 T ELT)) (|convert| (((|List| #10#) #8#) 111 T ELT) (((|SparseUnivariatePolynomial| #13#) #2#) 102 T ELT) ((#17=(|Polynomial| #13#) #10#) 109 T ELT) ((#17# #4#) 107 T ELT) ((#10# (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) 33 T ELT))) 
(((|ZeroDimensionalSolvePackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |triangSolve| (#1=(|List| #2=(|RegularChain| |#1| |#2|)) #3=(|List| #4=(|Polynomial| |#1|)) #5=(|Boolean|) #5#)) (SIGNATURE |triangSolve| (#1# #3# #5#)) (SIGNATURE |triangSolve| (#1# #3#)) (SIGNATURE |univariateSolve| (#6=(|List| (|Record| (|:| |complexRoots| #7=(|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| #3#))) #2#)) (SIGNATURE |univariateSolve| (#6# #3# #5# #5# #5#)) (SIGNATURE |univariateSolve| (#6# #3# #5# #5#)) (SIGNATURE |univariateSolve| (#6# #3# #5#)) (SIGNATURE |univariateSolve| (#6# #3#)) (SIGNATURE |realSolve| #8=(#9=(|List| (|List| #10=(|RealClosure| (|Fraction| |#1|)))) #2#)) (SIGNATURE |realSolve| (#9# #3# #5# #5# #5#)) (SIGNATURE |realSolve| #11=(#9# #3# #5# #5#)) (SIGNATURE |realSolve| #12=(#9# #3# #5#)) (SIGNATURE |realSolve| #13=(#9# #3#)) (SIGNATURE |positiveSolve| #8#) (SIGNATURE |positiveSolve| #11#) (SIGNATURE |positiveSolve| #12#) (SIGNATURE |positiveSolve| #13#) (SIGNATURE |squareFree| ((|List| #14=(|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| #15=(|OrderedVariableList| |#3|)) #15# #16=(|NewSparseMultivariatePolynomial| |#1| #15#))) #2#)) (SIGNATURE |convert| (#16# (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (SIGNATURE |convert| (#17=(|Polynomial| #10#) #4#)) (SIGNATURE |convert| (#17# #16#)) (SIGNATURE |convert| ((|SparseUnivariatePolynomial| #10#) #7#)) (SIGNATURE |convert| ((|List| #16#) #14#))) (|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|)) #18=(|List| (|Symbol|)) #18#) (T |ZeroDimensionalSolvePackage|)) 
((|convert| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|SquareFreeRegularTriangularSet| *4 (|IndexedExponents| #3=(|OrderedVariableList| *6)) #3# #4=(|NewSparseMultivariatePolynomial| *4 #3#))) #5=(|ofCategory| *4 #6=(|Join| (|OrderedRing|) (|EuclideanDomain|) (|CharacteristicZero|) (|RealConstant|))) #7=(|ofType| *6 #8=(|List| (|Symbol|))) (|isDomain| *2 (|List| #4#)) #9=(|isDomain| *1 (|ZeroDimensionalSolvePackage| *4 *5 *6)) #10=(|ofType| *5 #8#))) (|convert| #1# (AND (|isDomain| *3 #11=(|SparseUnivariatePolynomial| *4)) #5# (|isDomain| *2 (|SparseUnivariatePolynomial| #12=(|RealClosure| (|Fraction| *4)))) #9# #10# #7#)) (|convert| #1# (AND (|isDomain| *3 #4#) #5# #7# #13=(|isDomain| *2 (|Polynomial| #12#)) #9# #10#)) (|convert| #1# (AND (|isDomain| *3 #14=(|Polynomial| *4)) #5# #13# #9# #10# #7#)) (|convert| #1# (AND (|isDomain| *3 (|NewSparseMultivariatePolynomial| *4 (|OrderedVariableList| *5))) #5# #10# (|isDomain| *2 #4#) #9# #7#)) (|squareFree| #1# (AND #15=(|isDomain| *3 #16=(|RegularChain| *4 *5)) #5# #10# (|isDomain| *2 (|List| #2#)) #9# #7#)) (|positiveSolve| #1# #17=(AND #18=(|isDomain| *3 #19=(|List| #14#)) #5# #20=(|isDomain| *2 (|List| (|List| #12#))) #9# #10# #7#)) (|positiveSolve| #21=(*1 *2 *3 *4) #22=(AND #23=(|isDomain| *3 #24=(|List| (|Polynomial| *5))) #25=(|isDomain| *4 (|Boolean|)) #26=(|ofCategory| *5 #6#) (|isDomain| *2 (|List| (|List| (|RealClosure| (|Fraction| *5))))) #27=(|isDomain| *1 (|ZeroDimensionalSolvePackage| *5 *6 *7)) #7# #28=(|ofType| *7 #8#))) (|positiveSolve| #29=(*1 *2 *3 *4 *4) #22#) (|positiveSolve| #1# #30=(AND #15# #5# #10# #20# #9# #7#)) (|realSolve| #1# #17#) (|realSolve| #21# #22#) (|realSolve| #29# #22#) (|realSolve| #31=(*1 *2 *3 *4 *4 *4) #22#) (|realSolve| #1# #30#) (|univariateSolve| #1# (AND #5# #32=(|isDomain| *2 (|List| (|Record| (|:| |complexRoots| #11#) (|:| |coordinates| #19#)))) #9# #18# #10# #7#)) (|univariateSolve| #21# #33=(AND #25# #26# (|isDomain| *2 (|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| *5)) (|:| |coordinates| #24#)))) #27# #23# #7# #28#)) (|univariateSolve| #29# #33#) (|univariateSolve| #31# #33#) (|univariateSolve| #1# (AND #15# #5# #10# #32# #9# #7#)) (|triangSolve| #1# (AND #18# #5# (|isDomain| *2 (|List| #16#)) #9# #10# #7#)) (|triangSolve| #21# #34=(AND #23# #25# #26# (|isDomain| *2 (|List| (|RegularChain| *5 *6))) #27# #7# #28#)) (|triangSolve| #29# #34#)) 
((|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| #1=(|Integer|))) #2="failed") #3=(|Vector| |#1|) |#1|) 21 T ELT)) (|linearlyDependentOverZ?| (((|Boolean|) #3#) 12 T ELT)) (|linearDependenceOverZ| (((|Union| (|Vector| #1#) #2#) #3#) 16 T ELT))) 
(((|IntegerLinearDependence| |#1|) (CATEGORY |package| (SIGNATURE |linearlyDependentOverZ?| ((|Boolean|) #1=(|Vector| |#1|))) (SIGNATURE |linearDependenceOverZ| ((|Union| (|Vector| #2=(|Integer|)) #3="failed") #1#)) (SIGNATURE |solveLinearlyOverQ| ((|Union| (|Vector| (|Fraction| #2#)) #3#) #1# |#1|))) (|Join| (|Ring|) (|LinearlyExplicitRingOver| #2#))) (T |IntegerLinearDependence|)) 
((|solveLinearlyOverQ| (*1 *2 *3 *4) (|partial| AND #1=(|isDomain| *3 (|Vector| *4)) #2=(|ofCategory| *4 (|Join| (|Ring|) (|LinearlyExplicitRingOver| #3=(|Integer|)))) (|isDomain| *2 (|Vector| (|Fraction| #3#))) #4=(|isDomain| *1 (|IntegerLinearDependence| *4)))) (|linearDependenceOverZ| #5=(*1 *2 *3) (|partial| AND #1# #2# (|isDomain| *2 (|Vector| #3#)) #4#)) (|linearlyDependentOverZ?| #5# (AND #1# #2# (|isDomain| *2 (|Boolean|)) #4#))) 
((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 12 T ELT)) (|subtractIfCan| ((#5=(|Union| $ "failed") $ $) NIL T ELT)) (|size| (#6=(#7=(|NonNegativeInteger|)) 9 T ELT)) (|sample| (#8=($) NIL T CONST)) (|recip| ((#5# $) 57 T ELT)) (|random| (#8# 46 T ELT)) (|opposite?| #1#) (|one?| (#4# 38 T ELT)) (|nextItem| (((|Maybe| $) $) 36 T ELT)) (|lookup| ((#9=(|PositiveInteger|) $) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|init| (#8# 26 T CONST)) (|index| (($ #9#) 47 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| ((#10=(|Integer|) $) 16 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT) (($ #10#) 18 T ELT)) (|characteristic| (#6# 10 T CONST)) (|before?| (#2# 59 T ELT)) (|annihilate?| #1#) (|Zero| (#8# 23 T CONST)) (|One| (#8# 25 T CONST)) (= (#2# 31 T ELT)) (- (($ $) 50 T ELT) (#11=($ $ $) 44 T ELT)) (+ (#11# 29 T ELT)) (** (($ $ #9#) NIL T ELT) (($ $ #7#) 52 T ELT)) (* (($ #9# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #10# $) 41 T ELT) (#11# 40 T ELT))) 
(((|IntegerMod| |#1|) (|Join| (|CommutativeRing|) (|Finite|) (|ConvertibleTo| (|Integer|)) (|StepThrough|)) (|PositiveInteger|)) (T |IntegerMod|)) 
NIL 
NIL 
NIL 
NIL 
NIL 
NIL 
NIL 
NIL 
NIL 
NIL 
NIL 
NIL 
NIL 
((|Union| 2994614 2994619 2994624 NIL NIL NIL (NIL) |domain| NIL NIL NIL) (|Record| 2994599 2994604 2994609 NIL NIL NIL (NIL) |domain| NIL NIL NIL) (|Mapping| 2994584 2994589 2994594 NIL NIL NIL (NIL) |domain| NIL NIL NIL) (|Enumeration| 2994569 2994574 2994579 NIL NIL NIL (NIL) |domain| NIL NIL NIL) (|IntegerMod| 2993419 2994416 2994564 "ZMOD" NIL ZMOD (NIL NIL) |domain| NIL NIL NIL) (|IntegerLinearDependence| 2992336 2992589 2992976 "ZLINDEP" NIL ZLINDEP (NIL T) |package| NIL NIL NIL) (|ZeroDimensionalSolvePackage| 2987126 2988309 2989937 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) |package| NIL NIL NIL) (|ParadoxicalCombinatorsForStreams| 2986384 2986504 2986739 "YSTREAM" NIL YSTREAM (NIL T) |package| NIL NIL NIL) (|YoungDiagram| 2985658 2985998 2986205 "YDIAGRAM" NIL YDIAGRAM (NIL) |domain| NIL NIL NIL) (|XRecursivePolynomial| 2983002 2984979 2985304 "XRPOLY" NIL XRPOLY (NIL T T) |domain| NIL NIL NIL) (|XPolynomialRing| 2979727 2981499 2982297 "XPR" NIL XPR (NIL T T) |domain| NIL NIL 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2584133 "SUP2" NIL SUP2 (NIL T T) |package| NIL NIL NIL) (|SparseUnivariatePolynomial| 2575586 2583273 2583530 "SUP" NIL SUP (NIL T) |domain| NIL NIL NIL) (|RationalFunctionSum| 2574404 2574631 2575014 "SUMRF" NIL SUMRF (NIL T) |package| NIL NIL NIL) (|FunctionSpaceSum| 2573484 2573576 2573970 "SUMFS" NIL SUMFS (NIL T T) |package| NIL NIL NIL) (|SparseUnivariateLaurentSeries| 2563738 2572742 2573169 "SULS" NIL SULS (NIL T NIL NIL) |domain| NIL NIL NIL) (|SuchThatAst| 2563236 2563513 2563644 "SUCHTAST" NIL SUCHTAST (NIL) |domain| NIL NIL NIL) (|SuchThat| 2562524 2562804 2562995 "SUCH" NIL SUCH (NIL T T) |domain| NIL NIL NIL) (|SubSpace| 2558154 2559475 2560753 "SUBSPACE" NIL SUBSPACE (NIL NIL T) |domain| NIL NIL NIL) (|SubResultantPackage| 2557275 2557425 2557732 "SUBRESP" NIL SUBRESP (NIL T T) |package| NIL NIL NIL) (|StreamTranscendentalFunctionsNonCommutative| 2555148 2555827 2556642 "STTFNC" NIL STTFNC (NIL T) |package| NIL NIL NIL) (|StreamTranscendentalFunctions| 2552456 2553292 2554223 "STTF" NIL STTF (NIL T) |package| NIL NIL NIL) (|StreamTaylorSeriesOperations| 2548046 2549338 2550731 "STTAYLOR" NIL STTAYLOR (NIL T) |package| NIL NIL NIL) (|StringTable| 2545178 2547946 2548041 "STRTBL" NIL STRTBL (NIL T) |domain| NIL NIL NIL) (|String| 2541158 2544777 2544973 "STRING" NIL STRING (NIL) |domain| NIL NIL NIL) (|StreamFunctions3| 2540578 2540677 2540877 "STREAM3" NIL STREAM3 (NIL T T T) |package| NIL NIL NIL) (|StreamFunctions2| 2539542 2539733 2540014 "STREAM2" NIL STREAM2 (NIL T T) |package| NIL NIL NIL) (|StreamFunctions1| 2539178 2539239 2539380 "STREAM1" NIL STREAM1 (NIL T) |package| NIL NIL NIL) (|Stream| 2533147 2537129 2537994 "STREAM" NIL STREAM (NIL T) |domain| NIL NIL NIL) (|StreamInfiniteProduct| 2532175 2532381 2532716 "STINPROD" NIL STINPROD (NIL T) |package| NIL NIL NIL) (|StepAst| 2531293 2531692 2531934 "STEPAST" NIL STEPAST (NIL) |domain| NIL NIL NIL) (|StepThrough| 2530595 2530863 2530915 "STEP" 2531062 STEP (NIL) |category| NIL 2531181 NIL) 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open-axiom-databases 1.5.0~svn3056+ds-1 / usr / lib / open-axiom / algebra / interp.daase
