source: CGBLisp/examples/colored-poly-tests.output@ 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: 20.1 KB
Line 
1Starts dribbling to colored-poly-tests.output (1995/4/30, 18:32:27).
2real time : 0.083 secs
3run time : 0.000 secs
4VALUES--> (NIL)
5
6EVAL> (WARN "Test 1")
7Warning: Test 1
8real time : 0.000 secs
9run time : 0.000 secs
10VALUES--> (NIL)
11
12EVAL> (STRING-GROBNER-SYSTEM "[4*x^2-3*x*y,4*x+5*y]" '(X Y) 'NIL)
13------------------- CASE 1 -------------------
14Condition:
15 Green list: [ ]
16 Red list: [ ]
17 Basis: [ (4) * X + (5) * Y, ( - 10) * Y^2 ]
18real time : 0.117 secs
19run time : 0.033 secs
20VALUES--> NIL
21
22EVAL> (WARN "Test 2 - Enneper")
23Warning: Test 2 - Enneper
24real time : 0.000 secs
25run time : 0.000 secs
26VALUES--> (NIL)
27
28EVAL> (SETF VAL1
29 (STRING-GROBNER-SYSTEM
30 "[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]"
31 '(U V X Y Z) 'NIL :SUPPRESS-VALUE T))
32------------------- CASE 1 -------------------
33Condition:
34 Green list: [ ]
35 Red list: [ ]
36 Basis: [ ( - 3) * U^2 + (3) * V^2 + (1) * Z, (2) * V^3 + (1) * V * Z + (3) * V + ( - 1) * Y, ( - 6) * U * V^2 + (1) * U * Z + ( - 9) * U + (3) * X, (4) * U * V * Z + ( - 3) * U * Y + (3) * V * X, (9) * U * V * Y + ( - 2) * U * Z^2 + (18) * U * Z + ( - 9) * V^2 * X + ( - 6) * X * Z, ( - 27) * U * Y^2 + (8) * U * Z^3 + ( - 72) * U * Z^2 + (36) * V^2 * X * Z + (27) * V * X * Y + (24) * X * Z^2, (34992) * V^2 * X^2 + ( - 34992) * V^2 * Y^2 + ( - 186624) * V^2 * Z + ( - 15552) * V * Y * Z^2 + (46656) * V * Y * Z + (15552) * X^2 * Z + (93312) * X^2 + (19440) * Y^2 * Z + ( - 93312) * Y^2 + ( - 576) * Z^4 + (6912) * Z^3 + (15552) * Z^2 + ( - 279936) * Z, (139968) * U * X + (93312) * V^2 * Z + ( - 139968) * V * Y + (15552) * Z^2 + ( - 139968) * Z, (105815808) * V^2 * Y * Z + (52907904) * V * X^2 + ( - 52907904) * V * Y^2 + (15676416) * V * Z^3 + (141087744) * V * Z^2 + ( - 17635968) * Y * Z^2 + ( - 52907904) * Y * Z, (31104) * V^2 * Z^2 + (93312) * V^2 * Z + ( - 93312) * V * Y * Z + ( - 46656) * X^2 + (46656) * Y^2 + (1728) * Z^3 + ( - 31104) * Z^2 + (139968) * Z, (8817984) * V * X^2 * Z + (26453952) * V * X^2 + (44089920) * V * Y^2 * Z + ( - 26453952) * V * Y^2 + (2612736) * V * Z^4 + (31352832) * V * Z^3 + (70543872) * V * Z^2 + (26453952) * X^2 * Y + ( - 26453952) * Y^3 + ( - 3919104) * Y * Z^3 + ( - 105815808) * Y * Z, ( - 158723712) * V * X^2 * Y + ( - 317447424) * V * Y^3 * Z + (158723712) * V * Y^3 + ( - 23514624) * V * Y * Z^4 + ( - 188116992) * V * Y * Z^3 + ( - 634894848) * V * Y * Z^2 + (26453952) * X^4 + ( - 211631616) * X^2 * Y^2 + (6858432) * X^2 * Z^3 + (88179840) * X^2 * Z^2 + ( - 79361856) * X^2 * Z + (185177664) * Y^4 + (34292160) * Y^2 * Z^3 + ( - 35271936) * Y^2 * Z^2 + (714256704) * Y^2 * Z + ( - 290304) * Z^6 + (2612736) * Z^5 + (23514624) * Z^4 + ( - 211631616) * Z^3, ( - 317447424) * V * Y^3 * Z^2 + ( - 23514624) * V * Y * Z^5 + ( - 211631616) * V * Y * Z^4 + ( - 634894848) * V * Y * Z^3 + ( - 634894848) * V * Y * Z^2 + (26453952) * X^4 * Z + (79361856) * X^4 + ( - 211631616) * X^2 * Y^2 * Z + ( - 158723712) * X^2 * Y^2 + (6858432) * X^2 * Z^4 + (108755136) * X^2 * Z^3 + (185177664) * X^2 * Z^2 + ( - 238085568) * X^2 * Z + (185177664) * Y^4 * Z + (79361856) * Y^4 + (34292160) * Y^2 * Z^4 + ( - 2939328) * Y^2 * Z^3 + (608440896) * Y^2 * Z^2 + (238085568) * Y^2 * Z + ( - 290304) * Z^7 + (1741824) * Z^6 + (31352832) * Z^5 + ( - 141087744) * Z^4 + ( - 634894848) * Z^3, (79361856) * V * X^4 + (2539579392) * V * X^2 + (317447424) * V * Y^4 * Z + ( - 79361856) * V * Y^4 + (23514624) * V * Y^2 * Z^4 + (117573120) * V * Y^2 * Z^3 + ( - 423263232) * V * Y^2 * Z^2 + (5079158784) * V * Y^2 * Z + ( - 2539579392) * V * Y^2 + ( - 6967296) * V * Z^6 + ( - 125411328) * V * Z^5 + ( - 564350976) * V * Z^4 + (752467968) * V * Z^3 + (6772211712) * V * Z^2 + ( - 26453952) * X^4 * Y + (211631616) * X^2 * Y^3 + ( - 6858432) * X^2 * Y * Z^3 + ( - 255721536) * X^2 * Y * Z^2 + ( - 846526464) * X^2 * Y * Z + (2539579392) * X^2 * Y + ( - 185177664) * Y^5 + ( - 34292160) * Y^3 * Z^3 + (44089920) * Y^3 * Z^2 + (211631616) * Y^3 * Z + ( - 2539579392) * Y^3 + (290304) * Y * Z^6 + (10450944) * Y * Z^5 + (7838208) * Y * Z^4 + (188116992) * Y * Z^3 + (3386105856) * Y * Z^2 + ( - 10158317568) * Y * Z, ( - 714256704) * X^6 + (2142770112) * X^4 * Y^2 + ( - 396809280) * X^4 * Z^3 + ( - 4285540224) * X^4 * Z^2 + (2142770112) * X^4 * Z + ( - 2142770112) * X^2 * Y^4 + ( - 2063408256) * X^2 * Y^2 * Z^3 + ( - 4285540224) * X^2 * Y^2 * Z + ( - 47029248) * X^2 * Z^6 + ( - 1269789696) * X^2 * Z^5 + ( - 6348948480) * X^2 * Z^4 + (11428107264) * X^2 * Z^3 + (714256704) * Y^6 + ( - 396809280) * Y^4 * Z^3 + (4285540224) * Y^4 * Z^2 + (2142770112) * Y^4 * Z + (47029248) * Y^2 * Z^6 + ( - 1269789696) * Y^2 * Z^5 + (6348948480) * Y^2 * Z^4 + (11428107264) * Y^2 * Z^3 + (2322432) * Z^9 + ( - 376233984) * Z^7 + (15237476352) * Z^5 ]
37real time : 14.133 secs
38run time : 11.600 secs
39VALUES--> (NIL)
40
41EVAL> (SETF VAL1
42 (GROBNER (MAPCAR #'COLORED-POLY-TO-POLY (CADAR VAL1))))
43real time : 0.000 secs
44run time : 0.000 secs
45VALUES--> (NIL)
46
47EVAL> (SETF VAL2
48 (STRING-GROBNER
49 "[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]"
50 '(U V X Y Z) :SUPPRESS-VALUE T))
51Args:[ U^3 - 3 * U * V^2 - 3 * U + X, - 3 * U^2 * V + V^3 - 3 * V + Y, - 3 * U^2 + 3 * V^2 + Z ]
52[ 54 * V^2 * Y * Z + 27 * V * X^2 - 27 * V * Y^2 + 8 * V * Z^3 + 72 * V * Z^2 - 9 * Y * Z^2 - 27 * Y * Z, 9 * U * X + 6 * V^2 * Z - 9 * V * Y + Z^2 - 9 * Z, 243 * V^2 * X^2 - 243 * V^2 * Y^2 - 1296 * V^2 * Z - 108 * V * Y * Z^2 + 324 * V * Y * Z + 108 * X^2 * Z + 648 * X^2 + 135 * Y^2 * Z - 648 * Y^2 - 4 * Z^4 + 48 * Z^3 + 108 * Z^2 - 1944 * Z, 2 * V^3 + V * Z + 3 * V - Y, 6 * U * V^2 - U * Z + 9 * U - 3 * X, 3 * U^2 - 3 * V^2 - Z, 4 * U * V * Z - 3 * U * Y + 3 * V * X, 9 * U * V * Y - 2 * U * Z^2 + 18 * U * Z - 9 * V^2 * X - 6 * X * Z, 27 * U * Y^2 - 8 * U * Z^3 + 72 * U * Z^2 - 36 * V^2 * X * Z - 27 * V * X * Y - 24 * X * Z^2, 18 * V^2 * Z^2 + 54 * V^2 * Z - 54 * V * Y * Z - 27 * X^2 + 27 * Y^2 + Z^3 - 18 * Z^2 + 81 * Z, 27 * V * X^2 * Z + 81 * V * X^2 + 135 * V * Y^2 * Z - 81 * V * Y^2 + 8 * V * Z^4 + 96 * V * Z^3 + 216 * V * Z^2 + 81 * X^2 * Y - 81 * Y^3 - 12 * Y * Z^3 - 324 * Y * Z, 4374 * V * X^2 * Y + 8748 * V * Y^3 * Z - 4374 * V * Y^3 + 648 * V * Y * Z^4 + 5184 * V * Y * Z^3 + 17496 * V * Y * Z^2 - 729 * X^4 + 5832 * X^2 * Y^2 - 189 * X^2 * Z^3 - 2430 * X^2 * Z^2 + 2187 * X^2 * Z - 5103 * Y^4 - 945 * Y^2 * Z^3 + 972 * Y^2 * Z^2 - 19683 * Y^2 * Z + 8 * Z^6 - 72 * Z^5 - 648 * Z^4 + 5832 * Z^3, 8748 * V * Y^3 * Z^2 + 648 * V * Y * Z^5 + 5832 * V * Y * Z^4 + 17496 * V * Y * Z^3 + 17496 * V * Y * Z^2 - 729 * X^4 * Z - 2187 * X^4 + 5832 * X^2 * Y^2 * Z + 4374 * X^2 * Y^2 - 189 * X^2 * Z^4 - 2997 * X^2 * Z^3 - 5103 * X^2 * Z^2 + 6561 * X^2 * Z - 5103 * Y^4 * Z - 2187 * Y^4 - 945 * Y^2 * Z^4 + 81 * Y^2 * Z^3 - 16767 * Y^2 * Z^2 - 6561 * Y^2 * Z + 8 * Z^7 - 48 * Z^6 - 864 * Z^5 + 3888 * Z^4 + 17496 * Z^3, 2187 * V * X^4 + 69984 * V * X^2 + 8748 * V * Y^4 * Z - 2187 * V * Y^4 + 648 * V * Y^2 * Z^4 + 3240 * V * Y^2 * Z^3 - 11664 * V * Y^2 * Z^2 + 139968 * V * Y^2 * Z - 69984 * V * Y^2 - 192 * V * Z^6 - 3456 * V * Z^5 - 15552 * V * Z^4 + 20736 * V * Z^3 + 186624 * V * Z^2 - 729 * X^4 * Y + 5832 * X^2 * Y^3 - 189 * X^2 * Y * Z^3 - 7047 * X^2 * Y * Z^2 - 23328 * X^2 * Y * Z + 69984 * X^2 * Y - 5103 * Y^5 - 945 * Y^3 * Z^3 + 1215 * Y^3 * Z^2 + 5832 * Y^3 * Z - 69984 * Y^3 + 8 * Y * Z^6 + 288 * Y * Z^5 + 216 * Y * Z^4 + 5184 * Y * Z^3 + 93312 * Y * Z^2 - 279936 * Y * Z, 19683 * X^6 - 59049 * X^4 * Y^2 + 10935 * X^4 * Z^3 + 118098 * X^4 * Z^2 - 59049 * X^4 * Z + 59049 * X^2 * Y^4 + 56862 * X^2 * Y^2 * Z^3 + 118098 * X^2 * Y^2 * Z + 1296 * X^2 * Z^6 + 34992 * X^2 * Z^5 + 174960 * X^2 * Z^4 - 314928 * X^2 * Z^3 - 19683 * Y^6 + 10935 * Y^4 * Z^3 - 118098 * Y^4 * Z^2 - 59049 * Y^4 * Z - 1296 * Y^2 * Z^6 + 34992 * Y^2 * Z^5 - 174960 * Y^2 * Z^4 - 314928 * Y^2 * Z^3 - 64 * Z^9 + 10368 * Z^7 - 419904 * Z^5 ]
53real time : 7.733 secs
54run time : 6.900 secs
55VALUES--> (NIL)
56
57EVAL> (GROBNER-EQUAL VAL1 VAL2)
58real time : 0.000 secs
59run time : 0.000 secs
60VALUES--> (T)
61
62EVAL> (WARN " Test 3 - staple")
63Warning: Test 3 - staple
64real time : 0.000 secs
65run time : 0.000 secs
66VALUES--> (NIL)
67
68EVAL> (STRING-GROBNER-SYSTEM "[x+y,x+u*y]" '(X Y) '(U))
69------------------- CASE 1 -------------------
70Condition:
71 Green list: [ ]
72 Red list: [ U - 1 ]
73 Basis: [ (U - 1) * X, ( - U + 1) * Y ]
74------------------- CASE 2 -------------------
75Condition:
76 Green list: [ U - 1 ]
77 Red list: [ ]
78 Basis: [ (1) * X + (1) * Y ]
79real time : 0.200 secs
80run time : 0.150 secs
81VALUES--> NIL
82
83EVAL> (WARN " Test 4 - staple")
84Warning: Test 4 - staple
85real time : 0.000 secs
86run time : 0.000 secs
87VALUES--> (NIL)
88
89EVAL> (STRING-GROBNER-SYSTEM "[x+y,u*x+y]" '(X Y) '(U))
90------------------- CASE 1 -------------------
91Condition:
92 Green list: [ U ]
93 Red list: [ ]
94 Basis: [ (1) * X, (1) * Y ]
95------------------- CASE 2 -------------------
96Condition:
97 Green list: [ ]
98 Red list: [ U, U - 1 ]
99 Basis: [ (U^2 - U) * X, (U - 1) * Y ]
100------------------- CASE 3 -------------------
101Condition:
102 Green list: [ U - 1 ]
103 Red list: [ U ]
104 Basis: [ (1) * X + (1) * Y ]
105real time : 0.150 secs
106run time : 0.100 secs
107VALUES--> NIL
108
109EVAL> (WARN "Test 5 - a small robot example")
110Warning: Test 5 - a small robot example
111real time : 0.000 secs
112run time : 0.000 secs
113VALUES--> (NIL)
114
115EVAL> (STRING-GROBNER-SYSTEM
116 "[a-l3*c1*c2+l3*s1*s2-l2*c1, b-l3*c1*s2-l3*c2*s1-l2*s1, c1^2+s1^2-1, c2^2+s2^2-1]"
117 '(C2 S2 C1 S1) '(A B L2 L3) :COVER '(("[]" "[l2,l3]")))
118------------------- CASE 1 -------------------
119Condition:
120 Green list: [ ]
121 Red list: [ L3, A^2 + B^2, L2, A ]
122 Basis: [ ( - 2 * A * L2 * L3) * S2 + ( - 2 * A^2 * L2 - 2 * B^2 * L2) * S1 + (A^2 * B + B^3 + B * L2^2 - B * L3^2), ( - 2 * L2 * L3) * C2 + (A^2 + B^2 - L2^2 - L3^2), ( - 2 * A * L2) * C1 + ( - 2 * B * L2) * S1 + (A^2 + B^2 + L2^2 - L3^2), (4 * A^2 * L2^2 + 4 * B^2 * L2^2) * S1^2 + ( - 4 * A^2 * B * L2 - 4 * B^3 * L2 - 4 * B * L2^3 + 4 * B * L2 * L3^2) * S1 + (A^4 + 2 * A^2 * B^2 - 2 * A^2 * L2^2 - 2 * A^2 * L3^2 + B^4 + 2 * B^2 * L2^2 - 2 * B^2 * L3^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4) ]
123------------------- CASE 2 -------------------
124Condition:
125 Green list: [ A^2 + B^2 ]
126 Red list: [ L3, A^2 * B + B^3 + B * L2^2 - B * L3^2, L2, A ]
127 Basis: [ (4 * A * B * L2^3 * L3 - 4 * A * B * L2 * L3^3) * S2 + ( - 2 * B^2 * L2^4 + 4 * B^2 * L2^2 * L3^2 - 2 * B^2 * L3^4), ( - 2 * L2 * L3) * C2 + ( - L2^2 - L3^2), (4 * A * L2^3 - 4 * A * L2 * L3^2) * C1 + (4 * B^2 * L2^2 - L2^4 + 2 * L2^2 * L3^2 - L3^4), ( - 4 * B * L2^3 + 4 * B * L2 * L3^2) * S1 + (4 * B^2 * L2^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4) ]
128------------------- CASE 3 -------------------
129Condition:
130 Green list: [ A^2 + B^2, L2^2 - L3^2 ]
131 Red list: [ L3, A, L2, A^4 + 2 * A^2 * B^2 - 2 * A^2 * L2^2 - 2 * A^2 * L3^2 + B^4 + 2 * B^2 * L2^2 - 2 * B^2 * L3^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4 ]
132 Basis: [ (4 * B^2 * L3^2) ]
133------------------- CASE 4 -------------------
134Condition:
135 Green list: [ A ]
136 Red list: [ L3, B, L2 ]
137 Basis: [ (4 * B^2 * L2^2) * C1^2 + (B^4 - 2 * B^2 * L2^2 - 2 * B^2 * L3^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4), (2 * B * L2 * L3) * S2 + ( - 2 * B^2 * L2) * C1, ( - 2 * L2 * L3) * C2 + (B^2 - L2^2 - L3^2), ( - 2 * B * L2) * S1 + (B^2 + L2^2 - L3^2) ]
138------------------- CASE 5 -------------------
139Condition:
140 Green list: [ A, B ]
141 Red list: [ L3, L2, A^2 + B^2 + L2^2 - L3^2 ]
142 Basis: [ (L2^2 - L3^2) ]
143------------------- CASE 6 -------------------
144Condition:
145 Green list: [ A, B, L2^2 - L3^2 ]
146 Red list: [ L3, L2 ]
147 Basis: [ (1) * C1^2 + (1) * S1^2 + ( - 1), (L3) * S2, (L3) * C2 + (L2) ]
148real time : 6.750 secs
149run time : 5.900 secs
150VALUES--> NIL
151
152EVAL> (WARN "Test 6 - Circle of Apollonius")
153Warning: Test 6 - Circle of Apollonius
154real time : 0.000 secs
155run time : 0.000 secs
156VALUES--> (NIL)
157
158EVAL> (STRING-GROBNER-SYSTEM
159 "[2*x1-u1,2*x2-u2,2*x3-u1,2*x4-u2,x5*u1-x6*u2,x5*u2+x6*u1-u1*u2,x1^2-2*x1*x7+x7^2+x8^2-x7^2-x8^2+2*x8*x2-x2^2,x1^2-2*x1*x7+x7^2+x6^2-2*x6*x8+x8^2-x3^2+2*x3*x7-x7^2-x4^2+2*x4*x8-x8^2,1-s*x5^2+2*s*x5*x7-s*x7^2-s*x6^2+2*s*x6*x8-s*x8^2+s*x1^2-2*s*x1*x7+s*x7^2+s*x8^2]"
160 '(S X1 X2 X3 X4 X5 X6 X7 X8) '(U1 U2))
161------------------- CASE 1 -------------------
162Condition:
163 Green list: [ U2, U1 ]
164 Red list: [ ]
165 Basis: [ (2) * X1, (2) * X2, (2) * X3, (2) * X4, ( - 4) * X6^2 + (8) * X6 * X8, (4) * S * X5^2 + ( - 8) * S * X5 * X7 + ( - 4) ]
166------------------- CASE 2 -------------------
167Condition:
168 Green list: [ U2 ]
169 Red list: [ U1 ]
170 Basis: [ ( - 4 * U1^3) ]
171------------------- CASE 3 -------------------
172Condition:
173 Green list: [ U1 ]
174 Red list: [ U2 ]
175 Basis: [ (4 * U2^2) ]
176------------------- CASE 4 -------------------
177Condition:
178 Green list: [ ]
179 Red list: [ U1, U2, U1^2 - U2^2, U1^2 + U2^2 ]
180 Basis: [ (2) * X1 + ( - U1), (2) * X2 + ( - U2), (2) * X3 + ( - U1), (2) * X4 + ( - U2), (U1^2 * U2 + U2^3) * X5 + ( - U1 * U2^3), ( - U1^2 - U2^2) * X6 + (U1^2 * U2), ( - 4 * U1^5 + 4 * U1 * U2^4) * X7 + (U1^6 + 2 * U1^4 * U2^2 - 3 * U1^2 * U2^4), ( - 4 * U1^4 * U2 + 4 * U2^5) * X8 + (3 * U1^4 * U2^2 - 2 * U1^2 * U2^4 - U2^6), (2 * U1^6 * U2^2 - 2 * U1^4 * U2^4) * S + (4 * U1^6 - 4 * U1^2 * U2^4) ]
181------------------- CASE 5 -------------------
182Condition:
183 Green list: [ U1^2 - U2^2 ]
184 Red list: [ U1, U1^2 + U2^2, U2 ]
185 Basis: [ (2) * X1 + ( - U1), (2) * X2 + ( - U2), (2) * X3 + ( - U1), (2) * X4 + ( - U2), (2 * U2^3) * X5 + ( - U1 * U2^3), ( - 2 * U2^2) * X6 + (U2^3), (4 * U1) * X7 + ( - 4 * U2) * X8, ( - 8 * U2^5) * S * X8 + (2 * U2^6) * S + ( - 8 * U2^4) ]
186------------------- CASE 6 -------------------
187Condition:
188 Green list: [ U1^2 + U2^2 ]
189 Red list: [ U1, U2 ]
190 Basis: [ ( - U2^3) ]
191real time : 5.400 secs
192run time : 4.633 secs
193VALUES--> NIL
194
195EVAL> (WARN "Test 7")
196Warning: Test 7
197real time : 0.000 secs
198run time : 0.000 secs
199VALUES--> (NIL)
200
201EVAL> (SETF FL
202 (PARSE-STRING-TO-SORTED-ALIST
203 "[a^2*x^2*y+b*x^2*y+a^3*b*x*y+a^3*c*x*y,c^2*a*x^2+c^2*b*x^2+b*y+4]"
204 '(X Y A B C)))
205real time : 0.100 secs
206run time : 0.050 secs
207VALUES--> (((((2 1 2 0 0) . 1) ((2 1 0 1 0) . 1) ((1 1 3 1 0) . 1)
208 ((1 1 3 0 1) . 1))
209 (((2 0 1 0 2) . 1) ((2 0 0 1 2) . 1) ((0 1 0 1 0) . 1)
210 ((0 0 0 0 0) . 4))))
211
212EVAL> (SETF CFL (MAKE-COLORED-POLY-LIST FL 2))
213real time : 0.000 secs
214run time : 0.000 secs
215VALUES--> (((((2 1) (((2 0 0) . 1) ((0 1 0) . 1)) . :WHITE)
216 ((1 1) (((3 1 0) . 1) ((3 0 1) . 1)) . :WHITE))
217 (((2 0) (((1 0 2) . 1) ((0 1 2) . 1)) . :WHITE)
218 ((0 1) (((0 1 0) . 1)) . :WHITE)
219 ((0 0) (((0 0 0) . 4)) . :WHITE))))
220
221EVAL> (COND-SYSTEM-PRINT (DETERMINE CFL) '(X Y) '(A B C))
222------------------- CASE 1 -------------------
223Condition:
224 Green list: [ ]
225 Red list: [ A * C^2 + B * C^2, A^2 + B ]
226 Basis: [ (A^2 + B) * X^2 * Y + (A^3 * B + A^3 * C) * X * Y, (A * C^2 + B * C^2) * X^2 + (B) * Y + (4) ]
227------------------- CASE 2 -------------------
228Condition:
229 Green list: [ A^2 + B ]
230 Red list: [ A * C^2 + B * C^2, A^3 * B + A^3 * C ]
231 Basis: [ (A^3 * B + A^3 * C) * X * Y, (A * C^2 + B * C^2) * X^2 + (B) * Y + (4) ]
232------------------- CASE 3 -------------------
233Condition:
234 Green list: [ A^2 - C, B + C ]
235 Red list: [ A * C^2 + B * C^2 ]
236 Basis: [ (A * C^2 + B * C^2) * X^2 + (B) * Y + (4) ]
237------------------- CASE 4 -------------------
238Condition:
239 Green list: [ A * C^2 + B * C^2 ]
240 Red list: [ B, A^2 + B ]
241 Basis: [ (A^2 + B) * X^2 * Y + (A^3 * B + A^3 * C) * X * Y, (B) * Y + (4) ]
242------------------- CASE 5 -------------------
243Condition:
244 Green list: [ A * C^2 - C^2, A^2 + B, B * C^2 + C^2 ]
245 Red list: [ B, A^3 * B + A^3 * C ]
246 Basis: [ (A^3 * B + A^3 * C) * X * Y, (B) * Y + (4) ]
247------------------- CASE 6 -------------------
248Condition:
249 Green list: [ B + 1, C - 1, A - 1 ]
250 Red list: [ B ]
251 Basis: [ (B) * Y + (4) ]
252------------------- CASE 7 -------------------
253Condition:
254 Green list: [ B, C^2 ]
255 Red list: [ 4, A^2 + B ]
256 Basis: [ (A^2 + B) * X^2 * Y + (A^3 * B + A^3 * C) * X * Y, (4) ]
257------------------- CASE 8 -------------------
258Condition:
259 Green list: [ A^2, A * C^2, B ]
260 Red list: [ 4 ]
261 Basis: [ (4) ]
262real time : 1.033 secs
263run time : 0.733 secs
264VALUES--> NIL
265
266EVAL> (WARN "Test 8")
267Warning: Test 8
268real time : 0.000 secs
269run time : 0.000 secs
270VALUES--> (NIL)
271
272EVAL> (SETF FL (PARSE-STRING-TO-SORTED-ALIST "[a^2*x+5*a]" '(X A)))
273real time : 0.017 secs
274run time : 0.033 secs
275VALUES--> (((((1 2) . 1) ((0 1) . 5))))
276
277EVAL> (SETF CFL (MAKE-COLORED-POLY-LIST FL 1))
278real time : 0.000 secs
279run time : 0.000 secs
280VALUES--> (((((1) (((2) . 1)) . :WHITE) ((0) (((1) . 5)) . :WHITE))))
281
282EVAL> (COND-SYSTEM-PRINT (DETERMINE CFL) '(X) '(A))
283------------------- CASE 1 -------------------
284Condition:
285 Green list: [ ]
286 Red list: [ A^2 ]
287 Basis: [ (A^2) * X + (5 * A) ]
288------------------- CASE 2 -------------------
289Condition:
290 Green list: [ A^2 ]
291 Red list: [ ]
292 Basis: [ ]
293real time : 0.033 secs
294run time : 0.017 secs
295VALUES--> NIL
296
297EVAL> (WARN "Test 9 - the discriminant of a quadratic polynomial")
298Warning: Test 9 - the discriminant of a quadratic polynomial
299real time : 0.000 secs
300run time : 0.000 secs
301VALUES--> (NIL)
302
303EVAL> (STRING-GROBNER-SYSTEM "[a*x^2+b*x+c,2*a*x+b]" '(X) '(A B C)
304 :COVER (LIST (LIST "[]" "[a]")))
305------------------- CASE 1 -------------------
306Condition:
307 Green list: [ ]
308 Red list: [ A, 4 * A * C - B^2 ]
309 Basis: [ (4 * A * C - B^2) ]
310------------------- CASE 2 -------------------
311Condition:
312 Green list: [ 4 * A * C - B^2 ]
313 Red list: [ A ]
314 Basis: [ (2 * A) * X + (B) ]
315real time : 0.183 secs
316run time : 0.133 secs
317VALUES--> NIL
318
319EVAL> (WARN "Test 10 - the discriminant of a cubic polynomial")
320Warning: Test 10 - the discriminant of a cubic polynomial
321real time : 0.000 secs
322run time : 0.000 secs
323VALUES--> (NIL)
324
325EVAL> (STRING-GROBNER-SYSTEM "[x^3+p*x+q,3*x^2+p]" '(X) '(P Q) :COVER
326 (LIST (LIST "[]" "[]")))
327------------------- CASE 1 -------------------
328Condition:
329 Green list: [ ]
330 Red list: [ P, 4 * P^3 + 27 * Q^2 ]
331 Basis: [ ( - 4 * P^3 - 27 * Q^2) ]
332------------------- CASE 2 -------------------
333Condition:
334 Green list: [ 4 * P^3 + 27 * Q^2 ]
335 Red list: [ P ]
336 Basis: [ (2 * P) * X + (3 * Q) ]
337------------------- CASE 3 -------------------
338Condition:
339 Green list: [ P ]
340 Red list: [ Q ]
341 Basis: [ (3 * Q) ]
342------------------- CASE 4 -------------------
343Condition:
344 Green list: [ P, Q ]
345 Red list: [ ]
346 Basis: [ (3) * X^2 ]
347real time : 0.317 secs
348run time : 0.250 secs
349VALUES--> NIL
350
351EVAL> (WARN "Test 11 - the discriminant of a quartic polynomial")
352Warning: Test 11 - the discriminant of a quartic polynomial
353real time : 0.000 secs
354run time : 0.000 secs
355VALUES--> (NIL)
356
357EVAL> (STRING-GROBNER-SYSTEM "[x^4+p*x^2+q*x+r,4*x^3+2*p*x+q]" '(X)
358 '(P Q R) :COVER (LIST (LIST "[]" "[]")))
359------------------- CASE 1 -------------------
360Condition:
361 Green list: [ ]
362 Red list: [ 16 * P^4 * R - 4 * P^3 * Q^2 - 128 * P^2 * R^2 + 144 * P * Q^2 * R - 27 * Q^4 + 256 * R^3, P, 2 * P^3 - 8 * P * R + 9 * Q^2 ]
363 Basis: [ (16 * P^6 * R - 4 * P^5 * Q^2 - 128 * P^4 * R^2 + 144 * P^3 * Q^2 * R - 27 * P^2 * Q^4 + 256 * P^2 * R^3) ]
364------------------- CASE 2 -------------------
365Condition:
366 Green list: [ 16 * P^4 * R - 4 * P^3 * Q^2 - 128 * P^2 * R^2 + 144 * P * Q^2 * R - 27 * Q^4 + 256 * R^3 ]
367 Red list: [ P, 2 * P^3 - 8 * P * R + 9 * Q^2 ]
368 Basis: [ ( - 2 * P^3 + 8 * P * R - 9 * Q^2) * X + ( - P^2 * Q - 12 * Q * R) ]
369------------------- CASE 3 -------------------
370Condition:
371 Green list: [ 2 * P^3 - 8 * P * R + 9 * Q^2 ]
372 Red list: [ P, P^2 * Q + 12 * Q * R ]
373 Basis: [ ( - P^2 * Q - 12 * Q * R) ]
374------------------- CASE 4 -------------------
375Condition:
376 Green list: [ 2 * P^3 - 8 * P * R + 9 * Q^2, P^2 * Q + 12 * Q * R, 32 * P * Q * R - 9 * Q^3, 3 * P * Q^3 + 128 * Q * R^2, 27 * Q^5 + 4096 * Q * R^3, 8 * P^2 * R - 3 * P * Q^2 - 32 * R^2 ]
377 Red list: [ P ]
378 Basis: [ (2 * P) * X^2 + (3 * Q) * X + (4 * R) ]
379------------------- CASE 5 -------------------
380Condition:
381 Green list: [ P ]
382 Red list: [ Q, 72 * P * Q^2 * R - 27 * Q^4 + 256 * R^3 ]
383 Basis: [ (27 * Q^4 - 256 * R^3) ]
384------------------- CASE 6 -------------------
385Condition:
386 Green list: [ P, 27 * Q^4 - 256 * R^3 ]
387 Red list: [ Q ]
388 Basis: [ (3 * Q) * X + (4 * R) ]
389------------------- CASE 7 -------------------
390Condition:
391 Green list: [ P, Q ]
392 Red list: [ R ]
393 Basis: [ (4 * R) ]
394------------------- CASE 8 -------------------
395Condition:
396 Green list: [ P, Q, R ]
397 Red list: [ ]
398 Basis: [ (4) * X^3 ]
399real time : 2.600 secs
400run time : 2.133 secs
401VALUES--> NIL
402
403EVAL> (DRIBBLE)
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