1 | //Testserie fuer std im Mora-Fall |
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2 | " Testbeispiele Mora "; |
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3 | //timer=1; |
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4 | //test(0); |
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5 | " "; |
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6 | " ============= standard d - =========================="; |
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7 | "elem 19, dim 0, mult 312 "; |
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8 | ";Sing 1.93 (test 3 4 15):4s, (test 3 10 15):6s; Quadra (test4 15): 1 sec"; |
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9 | ring r1 = 32003,(z,y,x),ds; |
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10 | r1; |
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11 | poly s1=1x3y2+21328x5y+10667x2y4+21328x2yz3+10666xy6+10667y9; |
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12 | poly s2=1x2y2z2+3z8; |
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13 | poly s3=5x4y2+4xy5+2x2y2z3+1y7+11x10; |
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14 | ideal i=s1,s2,s3; |
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15 | ideal j=std(i); |
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16 | "dim: "+ string(dim(j)) +", mult: "+ string(mult(j)) +", elem: " |
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17 | + string(size(j)); |
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18 | j; |
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19 | kill r1; |
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20 | " ============= (19,19,4) d - =========================="; |
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21 | "elem 28, dim 0, mult1040 |
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22 | //Sing1/93, (10,15):60s, Quadra (10,15): 22s"; |
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23 | ring r2 = 32003,(x,y,z),ds; |
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24 | r2; |
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25 | int a=19; int b=19; int c=4; int t=1; |
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26 | "a b c t = ",a,b,c,t; |
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27 | poly f=x^a+y^b+z^(3*c)+x^(c+2)*y^(c-1)+x^(c-1)*y^(c-1)*z3+x^(c-2)*y^c*(y2+t*x)^2; |
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28 | f; |
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29 | ideal i=diff(f,x),diff(f,y),diff(f,z); |
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30 | ideal j=std(i); |
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31 | "dim: "+ string(dim(j)) +", mult: "+ string(mult(j)) +", elem: " |
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32 | + string(size(j)); |
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33 | j; |
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34 | kill a,b,c,t,r2; |
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35 | " =========== (a,b,c,d,e,t) min=(9,9,15,5,6) d - ================="; |
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36 | "elem 17, dim 0, mult 154 ? |
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37 | //Sing1/93, (test 10,15):60s, Quadra (test 10,15): 22s"; |
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38 | ring r3 = 32003,(x,y,z),ds; |
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39 | r3; |
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40 | int a=9; int b=9; int c=13; int d=5; int e=5; int t=1; |
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41 | "a b c d e t = ",a,b,c,d,e,t; |
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42 | poly |
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43 | f=x^a+y^b+z^c+x^d*y^(e-5)+x^(d-2)*y^(e-3)+x^(d-3)*y^(e-4)*z^2+x^(d-4)*y^(e-4)*(y^2+t*x)^2; |
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44 | f; |
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45 | ideal i=diff(f,x),diff(f,y),diff(f,z); |
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46 | ideal j=std(i); |
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47 | "dim: "+ string(dim(j)) +", mult: "+ string(mult(j)) +", elem: " |
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48 | + string(size(j)); |
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49 | j; |
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50 | kill a,b,c,e,d,t,r3; |
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51 | " ============= cyclic_roots_5(isol) + =========================="; |
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52 | "deg 131, dim 0, elem 30, Ende im Grad 12 |
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53 | //Macaulay 20 sec (SE/30), Quadra (4 10 15):5 sec"; |
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54 | //Sing1/93:19 sec (test 4 12) (SE/30), 12sec (PowerBook) |
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55 | ring r4 = 32003,(a,b,c,d,e),ds; |
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56 | r4; |
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57 | int n=10; |
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58 | poly s1=a+b+c+d+e; |
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59 | poly s2=de+1cd+1bc+1ae+1ab; |
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60 | poly s3=cde+1bcd+1ade+1abe+1abc; |
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61 | poly s4=bcde+1acde+1abde+1abce+1abcd; |
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62 | poly s5=abcde; |
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63 | ideal i=s1,s2,s3,s4,s5,a^n,b^n,c^n,d^n,e^n; |
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64 | i; |
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65 | ideal j=std(i); |
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66 | "dim: "+ string(dim(j)) +", mult: "+ string(mult(j)) +", elem: " |
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67 | + string(size(j)); |
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68 | j; |
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69 | kill r4,n; |
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70 | " ============= cyclic_roots_6(homog) d- =========================="; |
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71 | "deg 120, dim 1, elem 38, Ende im Grad 14 |
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72 | //Macaulay 17 sec (SE/30), 13 sec (PowerBook) |
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73 | //Sing1/93 10sec (test 4 12) SE/30, 7sec (PowerBook)"; |
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74 | ring r5 = 32003,(a,b,c,d,e,f),ds; |
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75 | r5; |
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76 | poly s1=a+b+c+d+e; |
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77 | poly s2=de+1cd+1bc+1ae+1ab; |
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78 | poly s3=cde+1bcd+1ade+1abe+1abc; |
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79 | poly s4=bcde+1acde+1abde+1abce+1abcd; |
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80 | poly s5=f^5+1abcde; |
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81 | ideal i=s1,s2,s3,s4,s5; |
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82 | ideal j=std(i); |
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83 | "dim: "+ string(dim(j)) +", mult: "+ string(mult(j)) +", elem: " |
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84 | + string(size(j)); |
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85 | j; |
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86 | kill r5; |
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87 | " ============= standardzyx(homog) l1 d3- =========================="; |
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88 | "deg 720, dim 1, elem 109, Ende im Grad 53 |
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89 | //Macaulay 11;48 min (SE/30) |
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90 | //Sing1/93c: 9;58min (test 4 12) (SE/30)"; |
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91 | ring r7 = 32003,(t,z,y,x),(ls(1),ds(3)); |
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92 | r7; |
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93 | poly s1=1x3y2t4+21328x5yt3+10667x2y4t3+21328x2yz3t3+10666xy6t2+10667y9; |
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94 | poly s2=1x2y2z2t2+3z8; |
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95 | poly s3=5x4y2t4+4xy5t4+2x2y2z3t3+1y7t3+11x10; |
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96 | ideal i=s1,s2,s3; |
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97 | i; |
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98 | ideal j=std(i); |
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99 | "dim: "+ string(dim(j)) +", mult: "+ string(mult(j)) +", elem: " |
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100 | + string(size(j)); |
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101 | j; |
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102 | kill r7; |
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103 | "================= NF w:1 1 1 - =================="; |
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104 | //elem 5, dim 1, mult 4, Quadra (4 10 15):2 sec |
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105 | //Sing1;93, (10,15):0s,##elem2##, (3,10,15):16s (Powerbook) |
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106 | ring r10=32003,(x,y,z),(ws(1,1,1)); |
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107 | poly s1=x2-y2; |
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108 | poly s2=y3; |
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109 | poly s3=y2-zyx; |
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110 | poly s4=xy2z; |
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111 | ideal i=s1,s3,s4; |
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112 | ideal j=std(i); |
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113 | //size(j); |
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114 | degree (j); |
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115 | reduce(s2,j); |
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116 | kill r10; |
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117 | "==================== parametric curves l - =================="; |
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118 | //Zeit: (l,test 0) H7 0/59, W 26/53 |
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119 | ring a1=32003,(x,y,z,t),ls; |
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120 | ideal i= |
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121 | x31-x6-x-y, |
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122 | x8-z, |
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123 | x10-t; |
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124 | ideal j=std (i); |
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125 | //size(j); |
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126 | degree (j); |
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127 | j; |
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128 | kill a1; |
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129 | "==================== standard char0 ============================="; |
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130 | // H7 l, char 0, test0,11,1: 61/31 ohne vollst; Reduktion |
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131 | ring r= |
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132 | 0,(x,y),ls; |
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133 | poly f=x5+y11+xy9+x3y9; |
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134 | ideal i=jacob(f); |
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135 | ideal j=std( i); |
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136 | j; |
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137 | degree (j); |
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138 | //size(j); |
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139 | kill r; |
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140 | "=============== integer-programming2 l1 d8 - ================="; |
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141 | //elem 26, dim 6, mult 4191 |
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142 | //Sing 1;93 (4 15):2s, (3 4 15):2s (SE/30) |
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143 | ring a3=32003,(t,a,b,c,d,e,x,y,z),(ls(1),ds(8)); |
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144 | ideal i= |
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145 | -y82a+x32z23, |
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146 | x45-y13z21b, |
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147 | y33z12-z41c, |
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148 | -y33z12d+x22, |
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149 | x5y17z22e, |
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150 | xyzt; |
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151 | i; |
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152 | ideal j=std (i); |
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153 | j; |
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154 | degree (j); |
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155 | //size(j); |
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156 | kill a3; |
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157 | "================ entartet d- ================="; |
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158 | ring r=32003,(x,y,z),ds; |
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159 | int s=1; |
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160 | int t=1; |
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161 | int u=1; |
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162 | poly f=(xyz+s*xy+t*yz+u*xz)*(x+y+z)^2 +x12+y12+z12; |
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163 | ideal i=jacob(f); |
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164 | ideal j=std(i); |
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165 | degree(j); |
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166 | j; |
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167 | kill r; |
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168 | "==================== omega2 d - =================="; |
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169 | ring M=32003,(x,y,z),ds; |
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170 | int o=167; |
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171 | int m=167; |
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172 | poly f1=xy+z^(o-1); |
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173 | poly f2=xz+y^(m-1)+yz2; |
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174 | poly fx=diff(f1,x); |
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175 | poly fy=diff(f1,y); |
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176 | poly fz=diff(f1,z); |
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177 | poly gx=diff(f2,x); |
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178 | poly gy=diff(f2,y); |
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179 | poly gz=diff(f2,z); |
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180 | module i= |
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181 | [f1,0,0], |
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182 | [0,f1,0], |
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183 | [0,0,f1], |
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184 | [f2,0,0], |
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185 | [0,f2,0], |
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186 | [0,0,f2], |
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187 | [fy,fz,0], |
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188 | [fx,0,-fz], |
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189 | [0,fx,fy], |
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190 | [gy,gz,0], |
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191 | [gx,0,-gz], |
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192 | [0,gx,gy]; |
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193 | module j=std (i); |
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194 | j; |
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195 | //size(j) |
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196 | "dimension of omega 2 ="; |
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197 | degree(j); |
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198 | LIB "tst.lib";tst_status(1);$ |
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