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/usr/share/axiom-20170501/input/cad.input is in axiom-test 20170501-3.

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)set break resume
)spool cad.output
)set message test on
)set message auto off
)clear all
 
--S 1 of 12
Ran := RECLOS(FRAC INT)
--R 
--R
--R   (1)  RealClosure(Fraction(Integer))
--R                                                                 Type: Domain
--E 1

--S 2 of 12
Cad := CAD(Ran)
--R 
--R
--R   (2)
--R   CylindricalAlgebraicDecompositionPackage(RealClosure(Fraction(Integer)))
--R                                                                 Type: Domain
--E 2

--S 3 of 12
p1 : POLY(Ran) := x^2+y^2-1
--R 
--R
--R         2    2
--R   (3)  y  + x  - 1
--R                             Type: Polynomial(RealClosure(Fraction(Integer)))
--E 3

--S 4 of 12
p2 : POLY(Ran) := y-x^2
--R 
--R
--R             2
--R   (4)  y - x
--R                             Type: Polynomial(RealClosure(Fraction(Integer)))
--E 4

--S 5 of 12
lpols : List(POLY(Ran)) := [p1,p2]
--R 
--R
--R          2    2          2
--R   (5)  [y  + x  - 1,y - x ]
--R                       Type: List(Polynomial(RealClosure(Fraction(Integer))))
--E 5

--S 6 of 12
cad := cylindricalDecomposition(lpols)$Cad;
--R 
--R
--R                             Type: List(Cell(RealClosure(Fraction(Integer))))
--E 6

--S 7 of 12
precision(30)
--R 
--R
--R   (7)  68
--R                                                        Type: PositiveInteger
--E 7

--S 8 of 12
ls := [ samplePoint cell for cell in cad]
--R 
--R
--R   (8)
--R                                                      1
--R   [[- 5,- 2], [4,- 2], [5,- 2], [- 2,- 1], [0,- 1], [-,- 1], [1,- 1], [2,- 1],
--R                                                      2
--R       113   7          7        7          7    339   7    49   7    113   7
--R    [- ---,- -], [%A5,- -], [0,- -], [%A6,- -], [---,- -], [--,- -], [---,- -],
--R        64   8          8        8          8    512   8    64   8    128   8
--R          2                 2                    2           2
--R    [- %A1  - 1,%A1], [- %A1 ,%A1], [0,%A1], [%A1 ,%A1], [%A1  + 1,%A1],
--R                         1             1                           2
--R    [- 2,0], [%A7,0], [- -,0], [0,0], [-,0], [%A8,0], [2,0], [- %A2  - 1,%A2],
--R                         2             2
--R          2                    2           2              113 7        7
--R    [- %A2 ,%A2], [0,%A2], [%A2 ,%A2], [%A2  + 1,%A2], [- ---,-], [%A9,-],
--R                                                           64 8        8
--R       7         7    339 7    49 7    113 7                    1
--R    [0,-], [%A10,-], [---,-], [--,-], [---,-], [- 2,1], [0,1], [-,1], [1,1],
--R       8         8    512 8    64 8    128 8                    2
--R    [2,1], [- 5,2], [4,2], [5,2]]
--R                             Type: List(List(RealClosure(Fraction(Integer))))
--E 8

--S 9 of 12
lf := [ [relativeApprox(coord,2^(-precision()))::Float for coord in point] for point in ls]
--R 
--R
--R   (9)
--R   [[- 5.0,- 2.0], [4.0,- 2.0], [5.0,- 2.0], [- 2.0,- 1.0], [0.0,- 1.0],
--R    [0.5,- 1.0], [1.0,- 1.0], [2.0,- 1.0], [- 1.765625,- 0.875],
--R    [- 0.48412292,- 0.875], [0.0,- 0.875], [0.48412292,- 0.875],
--R    [0.66210938,- 0.875], [0.765625,- 0.875], [0.8828125,- 0.875],
--R    [- 1.618034,- 0.78615138], [- 0.61803399,- 0.78615138], [0.0,- 0.78615138],
--R    [0.61803399,- 0.78615138], [1.618034,- 0.78615138], [- 2.0,0.0],
--R    [- 1.0,0.0], [- 0.5,0.0], [0.0,0.0], [0.5,0.0], [1.0,0.0], [2.0,0.0],
--R    [- 1.618034,0.78615138], [- 0.61803399,0.78615138], [0.0,0.78615138],
--R    [0.61803399,0.78615138], [1.618034,0.78615138], [- 1.765625,0.875],
--R    [- 0.48412292,0.875], [0.0,0.875], [0.48412292,0.875], [0.66210938,0.875],
--R    [0.765625,0.875], [0.8828125,0.875], [- 2.0,1.0], [0.0,1.0], [0.5,1.0],
--R    [1.0,1.0], [2.0,1.0], [- 5.0,2.0], [4.0,2.0], [5.0,2.0]]
--R                                                      Type: List(List(Float))
--E 9

--S 10 of 12
lp := [ point(term::List(DoubleFloat))$Point(DoubleFloat) for term in lf ]
--R 
--R
--R   (10)
--R   [[- 5.,- 2.], [4.,- 2.], [5.,- 2.], [- 2.,- 1.], [0.,- 1.], [0.5,- 1.],
--R    [1.,- 1.], [2.,- 1.], [- 1.765625,- 0.875],
--R    [- 0.48412291845306754,- 0.875], [0.,- 0.875],
--R    [0.48412291845306754,- 0.875], [0.662109375,- 0.875], [0.765625,- 0.875],
--R    [0.8828125,- 0.875], [- 1.6180339884012938,- 0.7861513774842024],
--R    [- 0.6180339893326163,- 0.7861513774842024], [0.,- 0.7861513774842024],
--R    [0.6180339893326163,- 0.7861513774842024],
--R    [1.6180339884012938,- 0.7861513774842024], [- 2.,0.], [- 1.,0.],
--R    [- 0.5,0.], [0.,0.], [0.5,0.], [1.,0.], [2.,0.],
--R    [- 1.6180339884012938,0.7861513774842024],
--R    [- 0.6180339893326163,0.7861513774842024], [0.,0.7861513774842024],
--R    [0.6180339893326163,0.7861513774842024],
--R    [1.6180339884012938,0.7861513774842024], [- 1.765625,0.875],
--R    [- 0.48412291845306754,0.875], [0.,0.875], [0.48412291845306754,0.875],
--R    [0.662109375,0.875], [0.765625,0.875], [0.8828125,0.875], [- 2.,1.],
--R    [0.,1.], [0.5,1.], [1.,1.], [2.,1.], [- 5.,2.], [4.,2.], [5.,2.]]
--R                                               Type: List(Point(DoubleFloat))
--E 10

--S 11 of 12
[ sign(eval(p1,variables(p1),samplePoint(cell))::Ran) for cell in cad ]
--R 
--R
--R   (11)
--R   [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, - 1, 0, 1, 1, 1, 1, 0, - 1, 0, 1, 1, 0, - 1,
--R    - 1, - 1, 0, 1, 1, 0, - 1, 0, 1, 1, 0, - 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1,
--R    1, 1]
--R                                                          Type: List(Integer)
--E 11

--S 12 of 12
[ sign(eval(p2,variables(p2),samplePoint(cell))::Ran) for cell in cad ]
--R 
--R
--R   (12)
--R   [- 1, 0, 1, - 1, - 1, - 1, 0, 1, - 1, - 1, - 1, - 1, - 1, 0, 1, - 1, - 1,
--R    - 1, 0, 1, - 1, - 1, - 1, 0, 1, 1, 1, - 1, - 1, - 1, 0, 1, - 1, - 1, - 1,
--R    - 1, - 1, 0, 1, - 1, - 1, - 1, 0, 1, - 1, 0, 1]
--R                                                          Type: List(Integer)
--E 12

)spool 
)lisp (bye)