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[Axiom-developer] CAD test cases
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From: |
daly |
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Subject: |
[Axiom-developer] CAD test cases |
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Date: |
Sun, 7 Sep 2014 22:39:27 -0500 |
Waldek,
Here are some CAD test cases with results.
Tim
========================================================================
\documentclass{article}
\usepackage{axiom}
\setlength{\textwidth}{400pt}
\begin{document}
\title{\$SPAD/src/input cad.input}
\author{Renaud Rioboo}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\begin{chunk}{*}
)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,- 0.78615137748420238],
--R [- 0.61803398933261633,- 0.78615137748420238], [0.,-
0.78615137748420238],
--R [0.61803398933261633,- 0.78615137748420238],
--R [1.6180339884012938,- 0.78615137748420238], [- 2.,0.], [- 1.,0.],
--R [- 0.5,0.], [0.,0.], [0.5,0.], [1.,0.], [2.,0.],
--R [- 1.6180339884012938,0.78615137748420238],
--R [- 0.61803398933261633,0.78615137748420238], [0.,0.78615137748420238],
--R [0.61803398933261633,0.78615137748420238],
--R [1.6180339884012938,0.78615137748420238], [- 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)
\end{chunk}
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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