source: git/Tst/Long/finvar_l.tst @ 010b3f

spielwiese
Last change on this file since 010b3f was 95fb99, checked in by Hans Schönemann <hannes@…>, 15 years ago
*hannes: syntx fix, activate example R12 git-svn-id: file:///usr/local/Singular/svn/trunk@11820 2c84dea3-7e68-4137-9b89-c4e89433aadc
  • Property mode set to 100644
File size: 15.5 KB
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1// File: finvar_l.tst
2// Long tests for finvar.lib
3
4LIB "tst.lib";
5tst_init();
6LIB "finvar.lib";
7option(redSB);
8
9
10ring R1=0,(u,v,w,x,y,z),(L(255),lp);
11matrix A[6][6];
12A[1,2]=1;
13A[2,3]=1;
14A[3,1]=1;
15A[4,5]=1;
16A[5,6]=1;
17A[6,4]=1;
18matrix B[6][6];
19B[1,2]=1;
20B[2,1]=1;
21B[3,3]=1;
22B[4,5]=1;
23B[5,4]=1;
24B[6,6]=1;
25list L=invariant_ring(A,B,intvec(0,0,1));
26// the following is not unique!
27L;
28tst_status();
29// the following is unique
30groebner(ideal(L[1])+ideal(L[3]));
31tst_status();
32kill R1;
33
34ring R3=2,(w,x,y,z),(L(255),lp);
35matrix A[4][4]=0,1,0,0,-1,0,0,0,0,0,0,-1,0,0,1,0;
36matrix B[4][4]=0,0,1,0,0,0,0,-1,-1,0,0,0,0,1,0,0;
37list L=invariant_ring(A,B,intvec(0,0,1));
38// the following is not unique!
39L;
40tst_status();
41kill R3;
42
43ring R4=11,(x,y),lp;
44matrix A[2][2]=4^3,0,0,4^2;
45number f=4+4^4-4^2-4^3;
46matrix D[2][2]=4^4-4,4^2-4^3,4^2-4^3,4-4^4;
47D=(1/f)*D;
48list L1=invariant_ring(A,D,intvec(0,0,1));
49// the following is not unique!
50L1;
51tst_status();
52// it is a bit faster to work without Molien series:
53list L2=invariant_ring(A,D,intvec(1,0,1));
54// the following is not unique!
55L2;
56tst_status();
57matrix TST4a = groebner(ideal(L1[1])+ideal(L1[3]));
58matrix TST4b = groebner(ideal(L2[1])+ideal(L2[3]));
59// the following is unique
60TST4a;
61TST4a==TST4b;
62tst_status();
63kill R4;
64
65ring R5 = (0),(W1,W2,W3,V1,V2,V3,V4,V5,V6,V7,V8,V9,V10,V11,V12),(L(255),dp(15),C);
66matrix P[1][15] = W1+W2+W3,W1*W2+W1*W3+W2*W3,W1*W2*W3,V7+V10,V7*V10,V3+V6+V8+V9+V11+V12,V8*V9+V3*V11+V6*V12,V6*V8+V3*V9+V11*V12,V3*V8+V6*V9+V6*V11+V9*V11+V3*V12+V8*V12,V3*V6*V11+V3*V8*V11+V8*V9*V11+V3*V6*V12+V6*V9*V12+V8*V9*V12,V3^6+V6^6+V8^6+V9^6+V11^6+V12^6,V1,V2+V4+V5,V2*V4+V2*V5+V4*V5,V2*V4*V5;
67matrix A1[15][15] = 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0;
68matrix A2[15][15] = 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0;
69matrix REY,M = reynolds_molien(A1,A2);
70// the following is unique
71REY;
72M;
73tst_status();
74matrix IS1 = irred_secondary_char0(P,REY,M,1);
75// the following is not unique!
76IS1;
77tst_status();
78matrix IS2 = irred_secondary_no_molien(P,REY,1);
79// the following is not unique!
80IS2;
81tst_status();
82matrix TST5a = groebner(ideal(P)+ideal(IS1));
83matrix TST5b = groebner(ideal(P)+ideal(IS2));
84// the following is unique
85TST5a;
86TST5a==TST5b;
87tst_status();
88kill R5;
89
90ring R6 = (0),(W1,W2,V1,V2,V3,V4,V5,V6,V7,V8,V9,V10,V11),(L(255),dp(13),C);
91matrix A[13][13] = 0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0;
92list L1 = invariant_ring(A,intvec(0,0,1));
93// the following is not unique!
94L1;
95tst_status();
96list L2 = invariant_ring(A,intvec(1,0,1));
97// the following is not unique!
98L2;
99tst_status();
100matrix TST6a = groebner(ideal(L1[1])+ideal(L1[3]));
101matrix TST6b = groebner(ideal(L2[1])+ideal(L2[3]));
102// the following is unique
103TST6a;
104TST6a==TST6b;
105tst_status();
106kill R6;
107
108ring R7 = (0),(a,b,c,d,e,f),(L(255),dp(6),C);
109matrix A1[6][6] =
1100,0,1,0,0,0,
1111,0,0,0,0,0,
1120,1,0,0,0,0,
1130,0,0,0,1,0,
1140,0,0,0,0,1,
1150,0,0,1,0,0;
116matrix A2[6][6] =
1170,1,0,0,0,0,
1180,0,0,1,0,0,
1190,0,0,0,0,1,
1201,0,0,0,0,0,
1210,0,1,0,0,0,
1220,0,0,0,1,0;
123list L1 = invariant_ring(A1,A2,intvec(0,0,1));
124// the following is not unique!
125L1;
126tst_status();
127list L2 = invariant_ring(A1,A2,intvec(1,0,1));
128// the following is not unique!
129L2;
130tst_status();
131matrix TST7a = groebner(ideal(L1[1])+ideal(L1[3]));
132matrix TST7b = groebner(ideal(L2[1])+ideal(L2[3]));
133// the following is unique
134TST7a;
135TST7a==TST7b;
136tst_status();
137kill R7;
138
139ring R8 = (0),(a,b,c,d,e,f),(L(255),dp(6),C);
140matrix A1[6][6] =
1411,0,0,0,0,0,
1420,0,0,1,0,0,
1430,0,0,0,1,0,
1440,1,0,0,0,0,
1450,0,1,0,0,0,
1460,0,0,0,0,1;
147matrix A2[6][6] =
1480,1,0,0,0,0,
1490,0,0,1,0,0,
1500,0,0,0,0,1,
1511,0,0,0,0,0,
1520,0,1,0,0,0,
1530,0,0,0,1,0;
154list L1 = invariant_ring(A1,A2,intvec(0,0,1));
155// the following is not unique!
156L1;
157tst_status();
158list L2 = invariant_ring(A1,A2,intvec(1,0,1));
159// the following is not unique!
160L2;
161tst_status();
162matrix TST8a = groebner(ideal(L1[1])+ideal(L1[3]));
163matrix TST8b = groebner(ideal(L2[1])+ideal(L2[3]));
164// the following is unique
165TST8a;
166TST8a==TST8b;
167tst_status();
168kill R8;
169
170ring R9 = 0,(x(1..6)),(L(255),dp);
171matrix A1 [6][6]=
1720,0,0,0,0,1,
1730,0,0,0,1,0,
1740,0,0,1,0,0,
1750,0,1,0,0,0,
1760,1,0,0,0,0,
1771,0,0,0,0,0;
178matrix A2[6][6]=
1790,1,0,0,0,0,
1800,0,1,0,0,0,
1811,0,0,0,0,0,
1820,0,0,0,1,0,
1830,0,0,0,0,1,
1840,0,0,1,0,0;
185list L1 = invariant_ring(A1,A2,intvec(0,0,1));
186// the following is not unique!
187L1;
188tst_status();
189list L2 = invariant_ring(A1,A2,intvec(1,0,1));
190// the following is not unique!
191L2;
192tst_status();
193matrix TST9a = groebner(ideal(L1[1])+ideal(L1[3]));
194matrix TST9b = groebner(ideal(L2[1])+ideal(L2[3]));
195// the following is unique
196TST9a;
197TST9a==TST9b;
198tst_status();
199kill R9;
200
201ring R10 = 0,(x(1..8)),(L(255),dp);
202matrix A1 [8][8]=
2030,0,0,0,0,0,0,1,
2040,0,0,0,0,0,1,0,
2050,0,0,0,0,1,0,0,
2060,0,0,0,1,0,0,0,
2070,0,0,1,0,0,0,0,
2080,0,1,0,0,0,0,0,
2090,1,0,0,0,0,0,0,
2101,0,0,0,0,0,0,0;
211matrix A2[8][8]=
2120,1,0,0,0,0,0,0,
2130,0,1,0,0,0,0,0,
2140,0,0,1,0,0,0,0,
2151,0,0,0,0,0,0,0,
2160,0,0,0,0,1,0,0,
2170,0,0,0,0,0,1,0,
2180,0,0,0,0,0,0,1,
2190,0,0,0,1,0,0,0;
220list L = invariant_ring(A1,A2,intvec(0,0,1));
221// the following is not unique!
222L;
223tst_status();
224matrix REY, M = reynolds_molien(A1,A2);
225matrix IS1 = irred_secondary_char0(L[1],REY,M,1);
226// the following is not unique!
227IS1;
228tst_status();
229matrix IS2 = irred_secondary_no_molien(L[1],REY,1);
230// the following is not unique!
231IS2;
232tst_status();
233matrix TST10a = groebner(ideal(L[1])+ideal(L[3]));
234matrix TST10b = groebner(ideal(L[1])+ideal(IS1));
235matrix TST10c = groebner(ideal(L[1])+ideal(IS2));
236// the following is unique
237TST10a;
238TST10a==TST10b;
239TST10a==TST10c;
240tst_status();
241kill R10;
242
243ring R11 = 0,(x(1..7)),(L(255),dp);
244matrix A1[7][7] =
2450,0,0,0,0,0,1,
2461,0,0,0,0,0,0,
2470,1,0,0,0,0,0,
2480,0,1,0,0,0,0,
2490,0,0,1,0,0,0,
2500,0,0,0,1,0,0,
2510,0,0,0,0,1,0;
252matrix A2[7][7] =
2531,0,0,0,0,0,0,
2540,0,0,0,0,0,1,
2550,0,0,0,0,1,0,
2560,0,0,0,1,0,0,
2570,0,0,1,0,0,0,
2580,0,1,0,0,0,0,
2590,1,0,0,0,0,0;
260list L = invariant_ring(A1,A2,intvec(0,0,1));
261// the following is not unique!
262L;
263tst_status();
264matrix REY,M = reynolds_molien(A1,A2);
265matrix IS1 = irred_secondary_char0(L[1],REY,M,1);
266// the following is not unique!
267IS1;
268tst_status();
269matrix IS2 = irred_secondary_no_molien(L[1],REY,1);
270// the following is not unique!
271IS2;
272tst_status();
273// these are the elementary symmetric polynomials,
274// that can be used as primary invariants in this example:
275matrix P[1][7] =
276x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7),
277x(1)*x(2)+x(1)*x(3)+x(1)*x(4)+x(2)*x(3)+x(2)*x(4)+x(3)*x(4)+x(1)*x(5)+x(2)*x(5)+x(3)*x(5)+x(4)*x(5)+x(1)*x(6)+x(2)*x(6)+x(3)*x(6)+x(4)*x(6)+x(5)*x(6)+x(1)*x(7)+x(2)*x(7)+x(3)*x(7)+x(4)*x(7)+x(5)*x(7)+x(6)*x(7),
278x(1)*x(2)*x(3)+x(1)*x(2)*x(4)+x(1)*x(3)*x(4)+x(2)*x(3)*x(4)+x(1)*x(2)*x(5)+x(1)*x(3)*x(5)+x(1)*x(4)*x(5)+x(2)*x(3)*x(5)+x(2)*x(4)*x(5)+x(3)*x(4)*x(5)+x(1)*x(2)*x(6)+x(1)*x(3)*x(6)+x(1)*x(4)*x(6)+x(1)*x(5)*x(6)+x(2)*x(3)*x(6)+x(2)*x(4)*x(6)+x(2)*x(5)*x(6)+x(3)*x(4)*x(6)+x(3)*x(5)*x(6)+x(4)*x(5)*x(6)+x(1)*x(2)*x(7)+x(1)*x(3)*x(7)+x(1)*x(4)*x(7)+x(1)*x(5)*x(7)+x(1)*x(6)*x(7)+x(2)*x(3)*x(7)+x(2)*x(4)*x(7)+x(2)*x(5)*x(7)+x(2)*x(6)*x(7)+x(3)*x(4)*x(7)+x(3)*x(5)*x(7)+x(3)*x(6)*x(7)+x(4)*x(5)*x(7)+x(4)*x(6)*x(7)+x(5)*x(6)*x(7),
279x(1)*x(2)*x(3)*x(4)+x(1)*x(2)*x(3)*x(5)+x(1)*x(2)*x(4)*x(5)+x(1)*x(3)*x(4)*x(5)+x(2)*x(3)*x(4)*x(5)+x(1)*x(2)*x(3)*x(6)+x(1)*x(2)*x(4)*x(6)+x(1)*x(2)*x(5)*x(6)+x(1)*x(3)*x(4)*x(6)+x(1)*x(3)*x(5)*x(6)+x(1)*x(4)*x(5)*x(6)+x(2)*x(3)*x(4)*x(6)+x(2)*x(3)*x(5)*x(6)+x(2)*x(4)*x(5)*x(6)+x(3)*x(4)*x(5)*x(6)+x(1)*x(2)*x(3)*x(7)+x(1)*x(2)*x(4)*x(7)+x(1)*x(2)*x(5)*x(7)+x(1)*x(2)*x(6)*x(7)+x(1)*x(3)*x(4)*x(7)+x(1)*x(3)*x(5)*x(7)+x(1)*x(3)*x(6)*x(7)+x(1)*x(4)*x(5)*x(7)+x(1)*x(4)*x(6)*x(7)+x(1)*x(5)*x(6)*x(7)+x(2)*x(3)*x(4)*x(7)+x(2)*x(3)*x(5)*x(7)+x(2)*x(3)*x(6)*x(7)+x(2)*x(4)*x(5)*x(7)+x(2)*x(4)*x(6)*x(7)+x(2)*x(5)*x(6)*x(7)+x(3)*x(4)*x(5)*x(7)+x(3)*x(4)*x(6)*x(7)+x(3)*x(5)*x(6)*x(7)+x(4)*x(5)*x(6)*x(7),
280x(1)*x(2)*x(3)*x(4)*x(5)+x(1)*x(2)*x(3)*x(4)*x(6)+x(1)*x(2)*x(3)*x(5)*x(6)+x(1)*x(2)*x(4)*x(5)*x(6)+x(1)*x(3)*x(4)*x(5)*x(6)+x(2)*x(3)*x(4)*x(5)*x(6)+x(1)*x(2)*x(3)*x(4)*x(7)+x(1)*x(2)*x(3)*x(5)*x(7)+x(1)*x(2)*x(3)*x(6)*x(7)+x(1)*x(2)*x(4)*x(5)*x(7)+x(1)*x(2)*x(4)*x(6)*x(7)+x(1)*x(2)*x(5)*x(6)*x(7)+x(1)*x(3)*x(4)*x(5)*x(7)+x(1)*x(3)*x(4)*x(6)*x(7)+x(1)*x(3)*x(5)*x(6)*x(7)+x(1)*x(4)*x(5)*x(6)*x(7)+x(2)*x(3)*x(4)*x(5)*x(7)+x(2)*x(3)*x(4)*x(6)*x(7)+x(2)*x(3)*x(5)*x(6)*x(7)+x(2)*x(4)*x(5)*x(6)*x(7)+x(3)*x(4)*x(5)*x(6)*x(7),
281x(1)*x(2)*x(3)*x(4)*x(5)*x(6)+x(1)*x(2)*x(3)*x(4)*x(5)*x(7)+x(1)*x(2)*x(3)*x(4)*x(6)*x(7)+x(1)*x(2)*x(3)*x(5)*x(6)*x(7)+x(1)*x(2)*x(4)*x(5)*x(6)*x(7)+x(1)*x(3)*x(4)*x(5)*x(6)*x(7)+x(2)*x(3)*x(4)*x(5)*x(6)*x(7),
282x(1)*x(2)*x(3)*x(4)*x(5)*x(6)*x(7);
283matrix IS3 = irred_secondary_char0(P,REY,M,1);
284// the following is not unique!
285IS3;
286tst_status();
287matrix IS4 = irred_secondary_no_molien(P,REY,1);
288// the following is not unique!
289IS4;
290tst_status();
291matrix TST11a = groebner(ideal(L[1])+ideal(L[3]));
292matrix TST11b = groebner(ideal(L[1])+ideal(IS1));
293matrix TST11c = groebner(ideal(L[1])+ideal(IS2));
294matrix TST11d = groebner(ideal(P)+ideal(IS3));
295matrix TST11e = groebner(ideal(P)+ideal(IS4));
296// the following is unique
297TST11a;
298TST11a==TST11b;
299TST11a==TST11c;
300TST11a==TST11d;
301TST11a==TST11e;
302tst_status();
303kill R11;
304
305ring R12 = 0,(W1,W2,W3,V5,V3,V12,V11,V14,V9,V6,V4,V7,V2,V8,V10,V1,V13,V15),(L(255),dp,C);
306matrix P[1][18] = W1+W2+W3,W1*W2+W1*W3+W2*W3,W1*W2*W3,V5+V9+V8,V5*V9+V5*V8+V9*V8,V5*V9*V8,V1+V13+V15,V1*V13+V1*V15+V13*V15,V1*V13*V15,V12+V11+V6,V12*V11+V12*V6+V11*V6,V12*V11*V6,V3+V14+V4+V7+V2+V10,V3*V7+V14*V2+V4*V10,V14*V4+V7*V2+V3*V10,V3*V4+V14*V7+V3*V2+V4*V2+V14*V10+V7*V10,V3*V14*V7+V3*V4*V7+V3*V14*V2+V4*V7*V10+V14*V2*V10+V4*V2*V10,V3^6+V14^6+V4^6+V7^6+V2^6+V10^6;
307matrix A1[18][18] = 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1;
308matrix A2[18][18] = 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0;
309matrix REY,M = reynolds_molien(A1,A2);
310kill A1,A2;
311matrix IS1 = irred_secondary_char0(P,REY,M,1);
312// the following is not unique!
313IS1;
314tst_status();
315matrix IS2 = irred_secondary_no_molien(P,REY,1);
316kill REY;
317// the following is not unique!
318IS2;
319tst_status();
320matrix TST12a = groebner(ideal(P)+ideal(IS1));
321matrix TST12b = groebner(ideal(P)+ideal(IS2));
322// the following is unique
323TST12a;
324TST12a==TST12b;
325tst_status();
326kill R12;
327
328ring R13 = (0),(W1,W2,W3,V1,V2,V3,V4,V5,V6,V7,V8,V9,V10,V11,V12,V13,V14,V15,V16,V17,V18,V19),(L(255),dp(22),C);
329matrix P[1][22] = W1+W2+W3,W1*W2+W1*W3+W2*W3,W1*W2*W3,V6,V1,V2+V13+V18,V2*V13+V2*V18+V13*V18,V2*V13*V18,V3+V4+V7+V8+V10+V12,V7*V8+V3*V10+V4*V12,V4*V7+V3*V8+V10*V12,V3*V7+V4*V8+V4*V10+V8*V10+V3*V12+V7*V12,V3*V4*V10+V3*V7*V10+V7*V8*V10+V3*V4*V12+V4*V8*V12+V7*V8*V12,V3^6+V4^6+V7^6+V8^6+V10^6+V12^6,V11+V15,V11*V15,V5+V9+V14+V16+V17+V19,V5*V16+V9*V17+V14*V19,V9*V14+V16*V17+V5*V19,V5*V14+V9*V16+V5*V17+V14*V17+V9*V19+V16*V19,V5*V9*V16+V5*V14*V16+V5*V9*V17+V14*V16*V19+V9*V17*V19+V14*V17*V19,V5^6+V9^6+V14^6+V16^6+V17^6+V19^6;
330matrix A1[22][22] = 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0;
331matrix A2[22][22] = 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0;
332matrix REY,M = reynolds_molien(A1,A2);
333kill A1,A2;
334matrix IS1 = irred_secondary_char0(P,REY,M,1);
335// the following is not unique!
336IS1;
337tst_status();
338matrix IS2 = irred_secondary_no_molien(P,REY,1);
339// the following is not unique!
340IS2;
341kill REY;
342tst_status();
343matrix TST13a = groebner(ideal(P)+ideal(IS1));
344matrix TST13b = groebner(ideal(P)+ideal(IS2));
345// the following is unique
346TST13a;
347TST13a==TST13b;
348tst_status();
349
350ring R14 = 0,(x(1..9)),dp;
351matrix Gperm =
352   invariant_algebra_perm(list(list(list(1,2,3,4,5,6,7,8,9))));
353tst_status();
354list L = group_reynolds(GetGroup(list(list(list(1,2,3,4,5,6,7,8,9)))));
355matrix Grey  =
356   invariant_algebra_reynolds(L[1]);
357tst_status();
358// the following is not unique!
359Gperm;
360Grey;
361// the following is unique!
362matrix Tst14a = groebner(ideal(Gperm));
363matrix Tst14b = groebner(ideal(Grey));
364Tst14a;
365Tst14a==Tst14b;
366
367
368tst_status(1);$
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