1 | // File: finvar_l.tst |
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2 | // Long tests for finvar.lib |
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3 | |
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4 | LIB "tst.lib"; |
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5 | tst_init(); |
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6 | LIB "finvar.lib"; |
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7 | option(redSB); |
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8 | |
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9 | |
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10 | ring R1=0,(u,v,w,x,y,z),(L(255),lp); |
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11 | matrix A[6][6]; |
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12 | A[1,2]=1; |
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13 | A[2,3]=1; |
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14 | A[3,1]=1; |
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15 | A[4,5]=1; |
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16 | A[5,6]=1; |
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17 | A[6,4]=1; |
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18 | matrix B[6][6]; |
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19 | B[1,2]=1; |
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20 | B[2,1]=1; |
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21 | B[3,3]=1; |
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22 | B[4,5]=1; |
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23 | B[5,4]=1; |
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24 | B[6,6]=1; |
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25 | list L=invariant_ring(A,B,intvec(0,0,1)); |
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26 | // the following is not unique! |
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27 | L; |
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28 | tst_status(); |
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29 | // the following is unique |
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30 | groebner(ideal(L[1])+ideal(L[3])); |
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31 | tst_status(); |
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32 | kill R1; |
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33 | |
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34 | ring R3=2,(w,x,y,z),(L(255),lp); |
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35 | matrix A[4][4]=0,1,0,0,-1,0,0,0,0,0,0,-1,0,0,1,0; |
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36 | matrix B[4][4]=0,0,1,0,0,0,0,-1,-1,0,0,0,0,1,0,0; |
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37 | list L=invariant_ring(A,B,intvec(0,0,1)); |
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38 | // the following is not unique! |
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39 | L; |
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40 | tst_status(); |
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41 | kill R3; |
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42 | |
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43 | ring R4=11,(x,y),lp; |
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44 | matrix A[2][2]=4^3,0,0,4^2; |
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45 | number f=4+4^4-4^2-4^3; |
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46 | matrix D[2][2]=4^4-4,4^2-4^3,4^2-4^3,4-4^4; |
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47 | D=(1/f)*D; |
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48 | list L1=invariant_ring(A,D,intvec(0,0,1)); |
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49 | // the following is not unique! |
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50 | L1; |
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51 | tst_status(); |
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52 | // it is a bit faster to work without Molien series: |
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53 | list L2=invariant_ring(A,D,intvec(1,0,1)); |
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54 | // the following is not unique! |
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55 | L2; |
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56 | tst_status(); |
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57 | matrix TST4a = groebner(ideal(L1[1])+ideal(L1[3])); |
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58 | matrix TST4b = groebner(ideal(L2[1])+ideal(L2[3])); |
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59 | // the following is unique |
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60 | TST4a; |
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61 | TST4a==TST4b; |
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62 | tst_status(); |
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63 | kill R4; |
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64 | |
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65 | ring R5 = (0),(W1,W2,W3,V1,V2,V3,V4,V5,V6,V7,V8,V9,V10,V11,V12),(L(255),dp(15),C); |
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66 | matrix 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; |
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67 | matrix 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; |
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68 | matrix 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; |
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69 | matrix REY,M = reynolds_molien(A1,A2); |
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70 | // the following is unique |
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71 | REY; |
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72 | M; |
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73 | tst_status(); |
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74 | matrix IS1 = irred_secondary_char0(P,REY,M,1); |
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75 | // the following is not unique! |
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76 | IS1; |
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77 | tst_status(); |
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78 | matrix IS2 = irred_secondary_no_molien(P,REY,1); |
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79 | // the following is not unique! |
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80 | IS2; |
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81 | tst_status(); |
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82 | matrix TST5a = groebner(ideal(P)+ideal(IS1)); |
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83 | matrix TST5b = groebner(ideal(P)+ideal(IS2)); |
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84 | // the following is unique |
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85 | TST5a; |
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86 | TST5a==TST5b; |
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87 | tst_status(); |
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88 | kill R5; |
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89 | |
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90 | ring R6 = (0),(W1,W2,V1,V2,V3,V4,V5,V6,V7,V8,V9,V10,V11),(L(255),dp(13),C); |
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91 | matrix 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; |
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92 | list L1 = invariant_ring(A,intvec(0,0,1)); |
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93 | // the following is not unique! |
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94 | L1; |
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95 | tst_status(); |
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96 | list L2 = invariant_ring(A,intvec(1,0,1)); |
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97 | // the following is not unique! |
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98 | L2; |
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99 | tst_status(); |
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100 | matrix TST6a = groebner(ideal(L1[1])+ideal(L1[3])); |
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101 | matrix TST6b = groebner(ideal(L2[1])+ideal(L2[3])); |
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102 | // the following is unique |
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103 | TST6a; |
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104 | TST6a==TST6b; |
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105 | tst_status(); |
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106 | kill R6; |
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107 | |
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108 | ring R7 = (0),(a,b,c,d,e,f),(L(255),dp(6),C); |
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109 | matrix A1[6][6] = |
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110 | 0,0,1,0,0,0, |
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111 | 1,0,0,0,0,0, |
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112 | 0,1,0,0,0,0, |
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113 | 0,0,0,0,1,0, |
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114 | 0,0,0,0,0,1, |
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115 | 0,0,0,1,0,0; |
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116 | matrix A2[6][6] = |
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117 | 0,1,0,0,0,0, |
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118 | 0,0,0,1,0,0, |
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119 | 0,0,0,0,0,1, |
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120 | 1,0,0,0,0,0, |
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121 | 0,0,1,0,0,0, |
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122 | 0,0,0,0,1,0; |
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123 | list L1 = invariant_ring(A1,A2,intvec(0,0,1)); |
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124 | // the following is not unique! |
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125 | L1; |
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126 | tst_status(); |
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127 | list L2 = invariant_ring(A1,A2,intvec(1,0,1)); |
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128 | // the following is not unique! |
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129 | L2; |
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130 | tst_status(); |
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131 | matrix TST7a = groebner(ideal(L1[1])+ideal(L1[3])); |
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132 | matrix TST7b = groebner(ideal(L2[1])+ideal(L2[3])); |
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133 | // the following is unique |
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134 | TST7a; |
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135 | TST7a==TST7b; |
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136 | tst_status(); |
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137 | kill R7; |
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138 | |
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139 | ring R8 = (0),(a,b,c,d,e,f),(L(255),dp(6),C); |
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140 | matrix A1[6][6] = |
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141 | 1,0,0,0,0,0, |
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142 | 0,0,0,1,0,0, |
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143 | 0,0,0,0,1,0, |
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144 | 0,1,0,0,0,0, |
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145 | 0,0,1,0,0,0, |
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146 | 0,0,0,0,0,1; |
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147 | matrix A2[6][6] = |
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148 | 0,1,0,0,0,0, |
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149 | 0,0,0,1,0,0, |
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150 | 0,0,0,0,0,1, |
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151 | 1,0,0,0,0,0, |
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152 | 0,0,1,0,0,0, |
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153 | 0,0,0,0,1,0; |
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154 | list L1 = invariant_ring(A1,A2,intvec(0,0,1)); |
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155 | // the following is not unique! |
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156 | L1; |
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157 | tst_status(); |
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158 | list L2 = invariant_ring(A1,A2,intvec(1,0,1)); |
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159 | // the following is not unique! |
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160 | L2; |
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161 | tst_status(); |
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162 | matrix TST8a = groebner(ideal(L1[1])+ideal(L1[3])); |
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163 | matrix TST8b = groebner(ideal(L2[1])+ideal(L2[3])); |
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164 | // the following is unique |
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165 | TST8a; |
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166 | TST8a==TST8b; |
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167 | tst_status(); |
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168 | kill R8; |
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169 | |
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170 | ring R9 = 0,(x(1..6)),(L(255),dp); |
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171 | matrix A1 [6][6]= |
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172 | 0,0,0,0,0,1, |
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173 | 0,0,0,0,1,0, |
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174 | 0,0,0,1,0,0, |
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175 | 0,0,1,0,0,0, |
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176 | 0,1,0,0,0,0, |
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177 | 1,0,0,0,0,0; |
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178 | matrix A2[6][6]= |
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179 | 0,1,0,0,0,0, |
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180 | 0,0,1,0,0,0, |
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181 | 1,0,0,0,0,0, |
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182 | 0,0,0,0,1,0, |
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183 | 0,0,0,0,0,1, |
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184 | 0,0,0,1,0,0; |
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185 | list L1 = invariant_ring(A1,A2,intvec(0,0,1)); |
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186 | // the following is not unique! |
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187 | L1; |
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188 | tst_status(); |
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189 | list L2 = invariant_ring(A1,A2,intvec(1,0,1)); |
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190 | // the following is not unique! |
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191 | L2; |
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192 | tst_status(); |
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193 | matrix TST9a = groebner(ideal(L1[1])+ideal(L1[3])); |
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194 | matrix TST9b = groebner(ideal(L2[1])+ideal(L2[3])); |
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195 | // the following is unique |
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196 | TST9a; |
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197 | TST9a==TST9b; |
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198 | tst_status(); |
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199 | kill R9; |
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200 | |
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201 | ring R10 = 0,(x(1..8)),(L(255),dp); |
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202 | matrix A1 [8][8]= |
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203 | 0,0,0,0,0,0,0,1, |
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204 | 0,0,0,0,0,0,1,0, |
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205 | 0,0,0,0,0,1,0,0, |
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206 | 0,0,0,0,1,0,0,0, |
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207 | 0,0,0,1,0,0,0,0, |
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208 | 0,0,1,0,0,0,0,0, |
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209 | 0,1,0,0,0,0,0,0, |
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210 | 1,0,0,0,0,0,0,0; |
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211 | matrix A2[8][8]= |
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212 | 0,1,0,0,0,0,0,0, |
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213 | 0,0,1,0,0,0,0,0, |
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214 | 0,0,0,1,0,0,0,0, |
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215 | 1,0,0,0,0,0,0,0, |
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216 | 0,0,0,0,0,1,0,0, |
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217 | 0,0,0,0,0,0,1,0, |
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218 | 0,0,0,0,0,0,0,1, |
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219 | 0,0,0,0,1,0,0,0; |
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220 | list L = invariant_ring(A1,A2,intvec(0,0,1)); |
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221 | // the following is not unique! |
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222 | L; |
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223 | tst_status(); |
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224 | matrix REY, M = reynolds_molien(A1,A2); |
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225 | matrix IS1 = irred_secondary_char0(L[1],REY,M,1); |
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226 | // the following is not unique! |
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227 | IS1; |
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228 | tst_status(); |
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229 | matrix IS2 = irred_secondary_no_molien(L[1],REY,1); |
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230 | // the following is not unique! |
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231 | IS2; |
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232 | tst_status(); |
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233 | matrix TST10a = groebner(ideal(L[1])+ideal(L[3])); |
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234 | matrix TST10b = groebner(ideal(L[1])+ideal(IS1)); |
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235 | matrix TST10c = groebner(ideal(L[1])+ideal(IS2)); |
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236 | // the following is unique |
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237 | TST10a; |
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238 | TST10a==TST10b; |
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239 | TST10a==TST10c; |
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240 | tst_status(); |
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241 | kill R10; |
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242 | |
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243 | ring R11 = 0,(x(1..7)),(L(255),dp); |
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244 | matrix A1[7][7] = |
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245 | 0,0,0,0,0,0,1, |
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246 | 1,0,0,0,0,0,0, |
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247 | 0,1,0,0,0,0,0, |
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248 | 0,0,1,0,0,0,0, |
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249 | 0,0,0,1,0,0,0, |
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250 | 0,0,0,0,1,0,0, |
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251 | 0,0,0,0,0,1,0; |
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252 | matrix A2[7][7] = |
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253 | 1,0,0,0,0,0,0, |
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254 | 0,0,0,0,0,0,1, |
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255 | 0,0,0,0,0,1,0, |
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256 | 0,0,0,0,1,0,0, |
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257 | 0,0,0,1,0,0,0, |
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258 | 0,0,1,0,0,0,0, |
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259 | 0,1,0,0,0,0,0; |
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260 | list L = invariant_ring(A1,A2,intvec(0,0,1)); |
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261 | // the following is not unique! |
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262 | L; |
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263 | tst_status(); |
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264 | matrix REY,M = reynolds_molien(A1,A2); |
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265 | matrix IS1 = irred_secondary_char0(L[1],REY,M,1); |
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266 | // the following is not unique! |
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267 | IS1; |
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268 | tst_status(); |
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269 | matrix IS2 = irred_secondary_no_molien(L[1],REY,1); |
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270 | // the following is not unique! |
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271 | IS2; |
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272 | tst_status(); |
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273 | // these are the elementary symmetric polynomials, |
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274 | // that can be used as primary invariants in this example: |
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275 | matrix P[1][7] = |
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276 | x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7), |
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277 | x(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), |
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278 | x(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), |
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279 | x(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), |
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280 | x(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), |
---|
281 | x(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), |
---|
282 | x(1)*x(2)*x(3)*x(4)*x(5)*x(6)*x(7); |
---|
283 | matrix IS3 = irred_secondary_char0(P,REY,M,1); |
---|
284 | // the following is not unique! |
---|
285 | IS3; |
---|
286 | tst_status(); |
---|
287 | matrix IS4 = irred_secondary_no_molien(P,REY,1); |
---|
288 | // the following is not unique! |
---|
289 | IS4; |
---|
290 | tst_status(); |
---|
291 | matrix TST11a = groebner(ideal(L[1])+ideal(L[3])); |
---|
292 | matrix TST11b = groebner(ideal(L[1])+ideal(IS1)); |
---|
293 | matrix TST11c = groebner(ideal(L[1])+ideal(IS2)); |
---|
294 | matrix TST11d = groebner(ideal(P)+ideal(IS3)); |
---|
295 | matrix TST11e = groebner(ideal(P)+ideal(IS4)); |
---|
296 | // the following is unique |
---|
297 | TST11a; |
---|
298 | TST11a==TST11b; |
---|
299 | TST11a==TST11c; |
---|
300 | TST11a==TST11d; |
---|
301 | TST11a==TST11e; |
---|
302 | tst_status(); |
---|
303 | kill R11; |
---|
304 | |
---|
305 | ring R12 = 0,(W1,W2,W3,V5,V3,V12,V11,V14,V9,V6,V4,V7,V2,V8,V10,V1,V13,V15),(L(255),dp,C); |
---|
306 | matrix 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; |
---|
307 | matrix 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; |
---|
308 | matrix 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; |
---|
309 | matrix REY,M = reynolds_molien(A1,A2); |
---|
310 | kill A1,A2; |
---|
311 | matrix IS1 = irred_secondary_char0(P,REY,M,1); |
---|
312 | // the following is not unique! |
---|
313 | IS1; |
---|
314 | tst_status(); |
---|
315 | matrix IS2 = irred_secondary_no_molien(P,REY,1); |
---|
316 | kill REY; |
---|
317 | // the following is not unique! |
---|
318 | IS2; |
---|
319 | tst_status(); |
---|
320 | matrix TST12a = groebner(ideal(P)+ideal(IS1)); |
---|
321 | matrix TST12b = groebner(ideal(P)+ideal(IS2)); |
---|
322 | // the following is unique |
---|
323 | TST12a; |
---|
324 | TST12a==TST12b; |
---|
325 | tst_status(); |
---|
326 | kill R12; |
---|
327 | |
---|
328 | ring 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); |
---|
329 | matrix 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; |
---|
330 | matrix 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; |
---|
331 | matrix 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; |
---|
332 | matrix REY,M = reynolds_molien(A1,A2); |
---|
333 | kill A1,A2; |
---|
334 | matrix IS1 = irred_secondary_char0(P,REY,M,1); |
---|
335 | // the following is not unique! |
---|
336 | IS1; |
---|
337 | tst_status(); |
---|
338 | matrix IS2 = irred_secondary_no_molien(P,REY,1); |
---|
339 | // the following is not unique! |
---|
340 | IS2; |
---|
341 | kill REY; |
---|
342 | tst_status(); |
---|
343 | matrix TST13a = groebner(ideal(P)+ideal(IS1)); |
---|
344 | matrix TST13b = groebner(ideal(P)+ideal(IS2)); |
---|
345 | // the following is unique |
---|
346 | TST13a; |
---|
347 | TST13a==TST13b; |
---|
348 | tst_status(); |
---|
349 | |
---|
350 | ring R14 = 0,(x(1..9)),dp; |
---|
351 | matrix Gperm = |
---|
352 | invariant_algebra_perm(list(list(list(1,2,3,4,5,6,7,8,9)))); |
---|
353 | tst_status(); |
---|
354 | list L = group_reynolds(GetGroup(list(list(list(1,2,3,4,5,6,7,8,9))))); |
---|
355 | matrix Grey = |
---|
356 | invariant_algebra_reynolds(L[1]); |
---|
357 | tst_status(); |
---|
358 | // the following is not unique! |
---|
359 | Gperm; |
---|
360 | Grey; |
---|
361 | // the following is unique! |
---|
362 | matrix Tst14a = groebner(ideal(Gperm)); |
---|
363 | matrix Tst14b = groebner(ideal(Grey)); |
---|
364 | Tst14a; |
---|
365 | Tst14a==Tst14b; |
---|
366 | |
---|
367 | |
---|
368 | tst_status(1);$ |
---|