source: CGBLisp/tests/tests.lisp@ 1

Last change on this file since 1 was 1, checked in by Marek Rychlik, 15 years ago

First import of a version circa 1997.
File size: 6.1 KB
Line 
1#|
2 SccsId="@(#)tests.lisp, version 1.7 of 5/14/94(11:23:03)
3 *--------------------------------------------------------------------------*
4 | Copyright (C) 1994, Marek Rychlik (e-mail: rychlik@math.arizona.edu) |
5 | Department of Mathematics, University of Arizona, Tucson, AZ 85721 |
6 | |
7 | Everyone is permitted to copy, distribute and modify the code in this |
8 | directory, as long as this copyright note is preserved verbatim. |
9 *--------------------------------------------------------------------------*
10|#
11
12;;(load "grobner-front-end")
13
14(defun run (test)
15 (format t "Test ~a ~:[failed~;succeeded~]...~%" test (time (funcall test))))
16
17(defun test-1 ()
18 (let* ((vars '(x y)))
19 (equalp
20 (mapcar #'(lambda (pred)
21 (let* ((f (poly "4*x^2-3*x*y" vars pred))
22 (g (poly "4*x+5*y" vars pred)))
23 (spoly f g pred)))
24 (list #'lex> #'grlex> #'grevlex>))
25 (list
26 (poly "-32*x*y" vars #'lex>)
27 (poly "-32*x*y" vars #'grlex>)
28 (poly "-32*x*y" vars #'grevlex>)))))
29
30(defun test-2 ()
31 (let* ((vars '(x y z)))
32 (equalp
33 (mapcar #'(lambda (pred)
34 (let* ((f (poly "4*x^5-3*x*y-z^2" vars pred))
35 (g (poly-list "[4*x^3+5*y+z^2,y^2+z]" vars pred)))
36 (normal-form f g pred)))
37 (list #'lex> #'grlex> #'grevlex>))
38 (list
39 (poly "-5*x^2*y-x^2*z^2-3*x*y-z^2" vars #'lex>)
40 (poly "-X^2*Z^2-5*X^2*Y-3*X*Y-Z^2" vars #'grlex>)
41 (poly "-X^2*Z^2-5*X^2*Y-3*X*Y-Z^2" vars #'grevlex>)))))
42
43
44;; Find the equation of the Enneper surface
45(defun test-3 ()
46 (let* ((vars '(u v x y z))
47 (eqns (poly-list
48 "[x-3*u-3*u*v^2+u^3,y-3*v-3*u^2*v+v^3,z-3*u^2+3*v^2]"
49 vars))
50 (ans (poly-list
51 "[X^6 - 3 * X^4 * Y^2 + 5/9 * X^4 * Z^3 + 6 * X^4 * Z^2 - 3 *
52 X^4 * Z + 3 * X^2 * Y^4 + 26/9 * X^2 * Y^2 * Z^3 + 6 * X^2 *
53 Y^2 * Z + 16/243 * X^2 * Z^6 + 16/9 * X^2 * Z^5 + 80/9 * X^2 *
54 Z^4 - 16 * X^2 * Z^3 - Y^6 + 5/9 * Y^4 * Z^3 - 6 * Y^4 * Z^2 -
55 3 * Y^4 * Z - 16/243 * Y^2 * Z^6 + 16/9 * Y^2 * Z^5 - 80/9 *
56 Y^2 * Z^4 - 16 * Y^2 * Z^3 - 64/19683 * Z^9 + 128/243 * Z^7 -
57 64/3 * Z^5]"
58 vars)))
59 (set-coefficient-ring nil) ;char=0
60 (equalp (elimination-ideal eqns 2) ans)))
61
62(defun test-4 ()
63 (let* ((vars '(x y))
64 (id1 (poly-list "[x-y^2,y^2*x]" vars))
65 (id2 (poly-list "[x^2-x*y^2,y^2]" vars))
66 (ans (poly-list "[x^2,y^4,x*y^2]" vars)))
67 (equalp (ideal-intersection id1 id2) ans)))
68
69(defun test-5 ()
70 (let* ((vars '(x y z))
71 (f (poly-list "[x^5+y^4+z^3-1, x^3+y^2+z^2-1]" vars))
72 (ans (poly-list
73 "[ X^2 * Z^4 + X^2 * Z^3 - 2 * X^2 * Z^2 - 1/6 * X * Z^10 - 2/3
74 * X * Z^9 - 1/4 * X * Z^8 + 7/6 * X * Z^7 - 1/12 * X * Z^6 - X
75 * Z^5 + X * Z^4 + 1/2 * Y^10 * Z^2 + 1/3 * Y^10 * Z - 5/12 *
76 Y^10 - 1/6 * Y^8 * Z^4 + 1/3 * Y^8 * Z^3 + 1/4 * Y^8 * Z^2 +
77 1/2 * Y^8 + Y^6 * Z^5 - 5/3 * Y^6 * Z^4 - 17/6 * Y^6 * Z^3 +
78 17/6 * Y^6 * Z^2 + 2/3 * Y^6 * Z - 1/3 * Y^6 - 1/3 * Y^4 * Z^7
79 - 7/2 * Y^4 * Z^6 - 3 * Y^4 * Z^5 + 131/12 * Y^4 * Z^4 + 23/4 *
80 Y^4 * Z^3 - 13 * Y^4 * Z^2 - 8/3 * Y^4 * Z + 29/6 * Y^4 - 17/6
81 * Y^2 * Z^8 - 4 * Y^2 * Z^7 + 119/12 * Y^2 * Z^6 + 17/2 * Y^2 *
82 Z^5 - 16 * Y^2 * Z^4 - 14/3 * Y^2 * Z^3 + 12 * Y^2 * Z^2 + 5/3
83 * Y^2 * Z - 55/12 * Y^2 - 7/6 * Z^10 - 7/6 * Z^9 + 55/12 * Z^8
84 + 21/4 * Z^7 - 31/4 * Z^6 - 15/2 * Z^5 + 83/12 * Z^4 + 41/12 *
85 Z^3 - 31/12 * Z^2, X * Y^2 * Z - X * Y^2 - 1/8 * X * Z^10 -
86 7/24 * X * Z^9 + 1/2 * X * Z^8 + 7/8 * X * Z^7 - 23/24 * X *
87 Z^6 + 1/2 * X * Z^4 - 1/2 * X * Z^3 - X * Z + X + 3/8 * Y^10 *
88 Z^2 - 3/8 * Y^10 * Z - 7/24 * Y^10 - 1/8 * Y^8 * Z^4 + 11/24 *
89 Y^8 * Z^3 - 3/8 * Y^8 * Z^2 + 1/4 * Y^8 * Z - 1/4 * Y^8 + 3/4 *
90 Y^6 * Z^5 - 5/2 * Y^6 * Z^4 + 5/6 * Y^6 * Z^3 + 31/12 * Y^6 *
91 Z^2 - Y^6 * Z - 1/3 * Y^6 - 1/4 * Y^4 * Z^7 - 53/24 * Y^4 * Z^6
92 + 11/6 * Y^4 * Z^5 + 113/12 * Y^4 * Z^4 - 55/8 * Y^4 * Z^3 -
93 29/4 * Y^4 * Z^2 + 15/4 * Y^4 * Z + 19/12 * Y^4 - 17/8 * Y^2 *
94 Z^8 + 13/24 * Y^2 * Z^7 + 239/24 * Y^2 * Z^6 - 59/12 * Y^2 *
95 Z^5 - 151/12 * Y^2 * Z^4 + 85/12 * Y^2 * Z^3 + 43/8 * Y^2 * Z^2
96 - 29/8 * Y^2 * Z + 7/24 * Y^2 - 7/8 * Z^10 + 7/12 * Z^9 + 31/8
97 * Z^8 - 11/12 * Z^7 - 103/12 * Z^6 + 17/6 * Z^5 + 127/24 * Z^4
98 - 3/2 * Z^3 - 17/24 * Z^2 + Z - 1, X * Z^11 + 4 * X * Z^10 + X
99 * Z^9 - 10 * X * Z^8 - 4 * X * Z^7 + 8 * X * Z^6 - 3 * Y^10 *
100 Z^3 - 2 * Y^10 * Z^2 + 4 * Y^10 * Z + 4 * Y^10 + Y^8 * Z^5 - 2
101 * Y^8 * Z^4 - 2 * Y^8 * Z^3 - 6 * Y^6 * Z^6 + 10 * Y^6 * Z^5 +
102 20 * Y^6 * Z^4 - 16 * Y^6 * Z^3 - 24 * Y^6 * Z^2 + 8 * Y^6 * Z
103 + 8 * Y^6 + 2 * Y^4 * Z^8 + 21 * Y^4 * Z^7 + 17 * Y^4 * Z^6 -
104 78 * Y^4 * Z^5 - 64 * Y^4 * Z^4 + 90 * Y^4 * Z^3 + 76 * Y^4 *
105 Z^2 - 32 * Y^4 * Z - 32 * Y^4 + 17 * Y^2 * Z^9 + 24 * Y^2 * Z^8
106 - 68 * Y^2 * Z^7 - 80 * Y^2 * Z^6 + 106 * Y^2 * Z^5 + 108 * Y^2
107 * Z^4 - 77 * Y^2 * Z^3 - 70 * Y^2 * Z^2 + 20 * Y^2 * Z + 20 *
108 Y^2 + 7 * Z^11 + 7 * Z^10 - 31 * Z^9 - 42 * Z^8 + 55 * Z^7 + 77
109 * Z^6 - 39 * Z^5 - 62 * Z^4 + 8 * Z^3 + 20 * Z^2, Y^12 - Y^10 +
110 3 * Y^8 * Z^3 - 5 * Y^8 * Z^2 + 2 * Y^8 - 10 * Y^6 * Z^4 + 20 *
111 Y^6 * Z^2 - 10 * Y^6 - 7 * Y^4 * Z^6 + 30 * Y^4 * Z^4 - 6 * Y^4
112 * Z^3 - 30 * Y^4 * Z^2 + 13 * Y^4 - 5 * Y^2 * Z^8 + 20 * Y^2 *
113 Z^6 - 30 * Y^2 * Z^4 + 20 * Y^2 * Z^2 - 5 * Y^2 - Z^10 + Z^9 +
114 5 * Z^8 - 13 * Z^6 + 10 * Z^4 + 3 * Z^3 - 5 * Z^2, X * Y^4 + X
115 * Z^3 - X + Y^4 + 2 * Y^2 * Z^2 - 2 * Y^2 + Z^4 - 2 * Z^2 + 1,
116 X^2 * Y^2 + X^2 * Z^2 - X^2 - Y^4 - Z^3 + 1, X^3 + Y^2 + Z^2 -
117 1 ]" vars)))
118 (equalp (grobner f :reduce t) ans)))
119
120(defun test-6 ()
121 (let* ((vars '(x y z))
122 (f (poly-list "[x^5+y^4+z^3-1,x^3+y^3+z^2-1]" vars))
123 (ans (poly-list "[x]" vars))) ;unknown yet
124 (equalp (grobner f :reduce t) ans)))
125
126;;----------------------------------------------------------------
127
128(defun run-short-tests ()
129 (dolist (test '(test-1 test-2 test-4))
130 (run test)))
131
132(defun run-long-tests ()
133 (dolist (test '(test-3 test-5))
134 (run test)))
135
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