1 | // standard examples for homogeneous ideals |
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2 | |
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3 | //==== elem 30, dim 0, mult 131; |
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4 | //==== Macaulay 1 sec |
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5 | //=== 0.54 sec |
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6 | |
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7 | option(prot); |
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8 | |
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9 | ring b1=32003,(a,b,c,d,e),dp; |
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10 | int n =10; |
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11 | poly s1=a+b+c+d+e; |
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12 | poly s2=de+1cd+1bc+1ae+1ab; |
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13 | poly s3=cde+1bcd+1ade+1abe+1abc; |
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14 | poly s4=bcde+1acde+1abde+1abce+1abcd; |
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15 | poly s5=abcde; |
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16 | ideal i=s1,s2,s3,s4,s5,a^n,b^n,c^n,d^n,e^n; |
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17 | ideal i0=std( i); |
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18 | size(i0); |
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19 | degree (i0); |
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20 | kill n ,b1; |
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21 | |
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22 | //==== 9 9 9 homog |
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23 | //==== elem 83, dim 1, mult 512; |
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24 | //=== Macaulay 0 sec |
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25 | //=== 0.24 sec |
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26 | ring s2=32003,(t,x,y,z),dp; |
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27 | ideal i= |
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28 | 9x8+y7t+5x4y2t2+2xy2z3t2, |
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29 | 9y8+7xy6t+2x5yt2+2x2yz3t2, |
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30 | 9z8+3x2y2z2t2; |
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31 | ideal i0=std( i); |
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32 | size(i0); |
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33 | degree (i0); |
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34 | kill s2; |
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35 | |
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36 | //========= Beipiel Alex1 homog |
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37 | //===== elem 95, dim 3, mult 18 |
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38 | //==== Macaulay 5 sec |
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39 | //=== 3.39 sec |
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40 | |
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41 | ring h1=32003,(w,x,t,y,z),dp; |
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42 | ideal j= |
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43 | 9x8+y7t3z4+5x4y2t2+2xy2z3t2, |
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44 | 9y8+7xy6t+2x5y4t2+2x2yz3t2, |
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45 | 9z8+3x2y3z2t4; |
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46 | ideal i=homog(j,w); |
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47 | ideal i0=std( i); |
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48 | size(i0); |
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49 | degree (i0); |
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50 | kill h1; |
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51 | |
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52 | //========= Beipiel Alex2 homog |
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53 | //=== elem 158, dim 3, mult 52 |
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54 | //==== Macaulay 5 min 0 sec |
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55 | //=== 122.43 sec |
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56 | |
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57 | ring h2=32003,(t,x,y,z,w),dp; |
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58 | ideal j= |
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59 | 2t3x5y2z+x2t5y+2x2y, |
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60 | 2y3z2x+3z2t6x2y+9y2t3z, |
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61 | 2t5z+y3x2t+z2t3y2x5; |
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62 | ideal i=homog(j,w); |
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63 | ideal i0=std( i); |
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64 | size(i0); |
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65 | degree (i0); |
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66 | kill h2; |
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67 | |
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68 | //========= Beipiel Alex3 homog |
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69 | //=== elem 211, dim 3 , mult 7 |
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70 | //==== Macaulay 27 sec |
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71 | //=== 19.43 sec |
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72 | |
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73 | ring h3=32003,(t,x,y,z,w),dp; |
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74 | ideal j= |
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75 | 5t3x8y2z+x2t5y+2x2y+5t, |
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76 | 7y6z2x+6x2y+9y2t3z+4t6x, |
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77 | 4t6z+8y3x5t+2t3y2x3+3x; |
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78 | ideal i=homog(j,w); |
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79 | ideal i0=std( i); |
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80 | size(i0); |
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81 | degree (i0); |
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82 | kill h3; |
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83 | |
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84 | //========= Beipiel Alex4 homog |
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85 | //=== elem 116, dim 3, mult 87 |
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86 | //==== Macaulay 5 sec |
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87 | //=== 4.72 sec |
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88 | |
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89 | //========= Beipiel Alex5 homog |
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90 | //=== elem 52, dim 3, mult 8 |
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91 | //=== Macaulay 17 sec |
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92 | //=== 6.99 sec |
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93 | |
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94 | ring h5=32003,(t,x,y,z,w),dp; |
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95 | ideal j= |
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96 | 4t2z+6z3t+3z2, |
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97 | 5t2z7y3x+5x2z4t3y+3t, |
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98 | 6zt2y+2x+6z2y2t+2y; |
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99 | ideal i=homog(j,w); |
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100 | ideal i0=std( i); |
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101 | size(i0); |
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102 | degree (i0); |
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103 | kill h5; |
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104 | |
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105 | //========= Beipiel Alex6 homog |
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106 | //=== elem 49, dim 3, mult 5 |
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107 | //=== Macaulay 27 sec |
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108 | //=== 18.14 sec |
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109 | |
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110 | ring h6=32003,(t,x,y,z,w),dp; |
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111 | ideal j= |
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112 | 4t2z+6z3t+3z2tx+3z, |
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113 | 5t7yx+5x2z4t3y+3t, |
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114 | 6zt2y+2x+6z2y2t+2y; |
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115 | ideal i=homog(j,w); |
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116 | ideal i0=std( i); |
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117 | size(i0); |
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118 | degree (i0); |
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119 | kill h6; |
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120 | |
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121 | //==== Beispiel Behnke |
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122 | //==== elem 149, dim 1, mult 120 |
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123 | //==== Macaulay 5 sec |
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124 | //=== 3.82 sec |
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125 | |
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126 | ring be=32003,(a,b,c,d,e),dp; |
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127 | ideal i= |
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128 | a5-b5, |
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129 | b5-c5, |
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130 | c5-d5, |
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131 | d5-e5, |
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132 | a4b+b4c+c4d+d4e+e4a; |
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133 | test(15); |
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134 | ideal i0=std( i); |
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135 | size(i0); |
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136 | degree (i0); |
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137 | test(-15); |
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138 | kill be; |
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139 | |
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140 | //==== elem 82, dim 3, mult 3 |
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141 | //==== Macaulay 1 min 11 sec |
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142 | //=== 17.50 sec |
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143 | |
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144 | ring rh1=32003,(w,t,x,y,z),dp; |
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145 | ideal j= |
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146 | 5t3x2z+2t2y3x5, |
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147 | 7y+4x2y+y2x+2zt, |
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148 | 3tz+3yz2+2yz4; |
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149 | ideal i=homog(j,w); |
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150 | ideal i0=std( i); |
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151 | size(i0); |
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152 | degree (i0); |
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153 | kill rh1; |
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154 | |
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155 | //==== elem 68, dim 1, mutl 720 |
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156 | //==== Macaulay 3 sec |
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157 | //=== 1.27 sec |
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158 | |
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159 | ring rh2=32003,(w,x,y,z),dp; |
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160 | poly p1 = 1x3y2+21328x5y+10667x2y4+21328x2yz3+10666xy6+10667y9; |
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161 | poly p2 = 1x2y2z2+3z8; |
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162 | poly p3 = 5x4y2+4xy5+2x2y2z3+1y7+11x10; |
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163 | ideal j= p1,p2,p3; |
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164 | ideal i=homog(j,w); |
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165 | ideal i0=std( i); |
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166 | size(i0); |
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167 | degree (i0); |
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168 | kill rh2; |
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169 | |
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170 | //==== elem 75, dim 1, mult 720 |
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171 | //==== Macaulay 3 sec |
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172 | //=== 1.53 sec |
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173 | |
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174 | ring rh3=32003,(w,x,y,z),dp; |
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175 | int a =11; |
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176 | int b =10; |
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177 | int c =3; |
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178 | int t =1; |
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179 | |
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180 | 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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181 | ideal j= jacob(f); |
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182 | ideal i=homog(j,w); |
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183 | ideal i0=std( i); |
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184 | size(i0); |
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185 | degree (i0); |
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186 | kill rh3; |
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187 | |
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188 | //=== elem 41, dim 1, mult 125 |
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189 | //==== Macaulay 4 sec |
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190 | //=== 1.60 sec |
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191 | |
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192 | ring rh4=32003,(w,x,y,z),dp; |
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193 | int a=6; |
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194 | poly f =xyz*(x+y+z)^2 +(x+y+z)^3 +x^a+y^a+z^a; |
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195 | ideal j= jacob(f); |
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196 | ideal i=homog(j,w); |
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197 | ideal i0=std( i); |
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198 | size(i0); |
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199 | degree (i0); |
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200 | kill rh4; |
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201 | |
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202 | //=== elem 44, dim 1, mult 216 |
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203 | //==== Macaulay 4 sec |
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204 | //=== 1.69 sec |
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205 | |
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206 | ring rh5=32003,(w,x,y,z),dp; |
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207 | int a =7; |
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208 | poly f=xyz*(x+y+z)^2 +(x+y+z)^3 +x^a+y^a+z^a; |
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209 | ideal j= jacob(f); |
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210 | ideal i=homog(j,w); |
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211 | ideal i0=std( i); |
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212 | size(i0); |
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213 | degree (i0); |
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214 | kill rh5; |
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215 | |
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216 | //=== elem 117, dim 1, mult 107 |
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217 | //==== Macaulay 3 sec |
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218 | //=== 2.85 sec |
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219 | |
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220 | ring rh6=32003,(w,x,y,z),dp; |
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221 | int a= 6; |
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222 | int b= 8; |
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223 | int c =10; |
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224 | int alpha=5; |
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225 | int beta= 5; |
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226 | int t=0; |
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227 | poly f= x^a+y^b+z^c+x^alpha*y^(beta-5)+x^(alpha-2)*y^(beta-3)+x^(alpha-3)*y^(beta-4)*z^2+x^(alpha-4)*y^(beta-4)*(y^2+t*x)^2; |
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228 | ideal j= jacob(f); |
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229 | j=j,(f); |
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230 | ideal i=homog(j,w); |
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231 | ideal i0=std( i); |
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232 | size(i0); |
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233 | degree (i0); |
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234 | kill a, b, c, alpha ,beta, t, rh6; |
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235 | |
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236 | //=== elem 66, dim 1, mult 315 |
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237 | //==== Macaulay 4 sec |
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238 | //=== 1.79 sec |
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239 | |
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240 | ring rh7=32003,(u,x,y,z),dp; |
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241 | int a= 6; |
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242 | int b= 8; |
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243 | int c =10; |
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244 | int alpha=5; |
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245 | int beta= 5; |
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246 | int t=0; |
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247 | poly f =x^a+y^b+z^c+x^alpha*y^(beta-5)+x^(alpha-2)*y^(beta-3)+x^(alpha-3)*y^(beta-4)*z^2+x^(alpha-4)*y^(beta-4)*(y^2+t*x)^2; |
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248 | ideal j =jacob(f); |
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249 | ideal i=homog(j,u); |
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250 | ideal i0=std( i); |
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251 | size(i0); |
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252 | degree (i0); |
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253 | kill a, b, c, alpha ,beta, t, rh7; |
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254 | |
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255 | //=== elem 169, dim 1, mult 251 |
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256 | //==== Macaulay 6 sec |
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257 | //=== 3.65 |
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258 | |
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259 | ring rh9=32003,(w,x,y,z),dp; |
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260 | int a =11; |
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261 | int b =10; |
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262 | int c =3; |
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263 | int t =1; |
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264 | |
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265 | 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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266 | ideal j= jacob(f); |
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267 | j=j,(f); |
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268 | ideal i=homog(j,w); |
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269 | ideal i0=std( i); |
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270 | size(i0); |
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271 | degree (i0); |
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272 | kill b,c,t,a,rh9; |
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273 | |
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274 | //=== elem 75, dim 1, mult 44 |
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275 | //==== Macaulay 2 sec |
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276 | //=== 1.71 sec |
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277 | |
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278 | ring rh10=32003,(w,x,y,z),dp; |
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279 | int a =6; |
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280 | poly f =xyz*(x+y+z)^2 +(x+y+z)^3 +x^a+y^a+z^a; |
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281 | ideal j= jacob(f); |
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282 | j=j,(f); |
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283 | ideal i=homog(j,w); |
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284 | ideal i0=std( i); |
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285 | size(i0); |
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286 | degree (i0); |
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287 | |
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288 | kill a,rh10; |
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289 | |
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290 | //=== elem 61, dim 1, mult 67 |
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291 | //==== Macaulay 1 sec |
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292 | //=== 0.78 sec |
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293 | |
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294 | ring rh11=32003,(w,x,y,z),dp; |
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295 | int a =7; |
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296 | poly f =xyz*(x+y+z)^2 +(x+y+z)^3 +x^a+y^a+z^a; |
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297 | ideal j= jacob(f); |
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298 | j=j,(f); |
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299 | ideal i=homog(j,w); |
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300 | ideal i0=std( i); |
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301 | size(i0); |
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302 | degree (i0); |
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303 | kill a,rh11; |
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304 | |
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305 | //=== elem 83, dim 2, mult 26400 |
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306 | //==== Macaulay 1 sec |
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307 | //=== 0.46 sec |
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308 | |
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309 | ring rh12=32003,(t,x,y,z,w),dp; |
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310 | ideal j=x2-z10-z20,xy3-z10-z30,y6-xy3w40; |
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311 | ideal i=homog(j,w); |
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312 | ideal i0=std( i); |
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313 | size(i0); |
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314 | degree (i0); |
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315 | kill rh12; |
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316 | |
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317 | //=== elem 23, dim 1, mult 380 |
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318 | //==== Macaulay 4 sec |
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319 | //=== 1.81 sec |
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320 | |
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321 | ring rh13=32003,(w,x,y),dp; |
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322 | poly f=(x+y)^20 +y21+(x+y)^10 +x9y9+x3y15+x2y11+x4y4+(x+y)^17; |
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323 | ideal j= jacob(f); |
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324 | ideal i=homog(j,w); |
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325 | ideal i0=std( i); |
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326 | size(i0); |
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327 | degree (i0); |
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328 | kill rh13; |
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329 | |
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330 | //=== elem 254, dim 1, mult 56 |
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331 | //==== Macaulay 44 sec |
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332 | //=== 23.08 sec |
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333 | |
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334 | ring rh14=32003,(w,x,y),dp; |
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335 | poly f=(x+y)^20 +y21+(x+y)^10 +x9y9+x3y15+x2y11+x4y4+(x+y)^17; |
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336 | ideal j= jacob(f); |
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337 | j=j,(f); |
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338 | ideal i=homog(j,w); |
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339 | ideal i0=std( i); |
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340 | size(i0); |
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341 | degree (i0); |
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342 | kill rh14; |
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343 | |
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344 | //=== elem 143, dim 1, mult 194 |
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345 | //==== Macaulay 11 sec |
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346 | //=== 2.05 sec |
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347 | |
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348 | ring rh17=32003,(w,x,y,z),dp; |
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349 | ideal j= |
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350 | 1x3+1y4+2xz3+1z5+32000x4y2+2z6+3z7, |
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351 | 1xz3+32001x4y2+1z6+2z7, |
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352 | 9x3z2+18x2z5+31998z7+12x4y2z2+42x2z6+40x3y2z4+7z9+24x3y2z5, |
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353 | 31999y3z3+31991x6y+32x3y5+32001x4yz3, |
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354 | 12xy3z2+6x5yz2+24y3z5+20x4yz4+56y3z6+12x4yz5; |
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355 | ideal i=homog(j,w); |
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356 | ideal i0=std( i); |
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357 | size(i0); |
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358 | degree (i0); |
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359 | kill rh17; |
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360 | |
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361 | //=== elem 22, dim 2, mult 416 |
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362 | //==== Macaulay 4 sec |
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363 | //=== 0.77 sec |
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364 | |
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365 | ring rh18=32003,(w,t,x,y,z),dp; |
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366 | ideal j= |
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367 | 4t2z+6z3t+3z3+tz, |
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368 | 5t2z7y3x+5x2z4t3y+3t7, |
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369 | 6zt2y+2x8+6z2y2t+2y5; |
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370 | ideal i=homog(j,w); |
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371 | ideal i0=std( i); |
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372 | size(i0); |
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373 | degree (i0); |
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374 | kill rh18; |
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375 | |
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376 | //===== elem 111,dim 1, mult 3564 |
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377 | //==== Macaulay 15 sec |
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378 | //=== 9.11 sec |
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379 | |
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380 | ring rh19=32003,(w,x,y,z),dp; |
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381 | int a =19; |
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382 | int b =19; |
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383 | int c =4; |
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384 | int t =1; |
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385 | |
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386 | 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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387 | ideal j= jacob(f); |
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388 | ideal i=homog(j,w); |
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389 | ideal i0=std( i); |
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390 | size(i0); |
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391 | degree (i0); |
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392 | kill b,c,t,a,rh19; |
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393 | |
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394 | //==== elem 278,dim 1, mult 8602 |
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395 | //==== Macaulay 6 min 9 sec |
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396 | //=== 239.13 sec (3 min 59.13 sec) |
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397 | |
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398 | ring rh20=32003,(w,x,y,z),dp; |
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399 | int a =24; |
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400 | int b =23; |
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401 | int c =6; |
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402 | int t =1; |
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403 | |
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404 | 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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405 | ideal j= jacob(f); |
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406 | ideal i=homog(j,w); |
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407 | ideal i0=std( i); |
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408 | size(i0); |
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409 | degree (i0); |
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410 | kill b,c,t,a,rh20; |
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411 | |
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412 | //=== elem 103, dim 1, mult 729 |
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413 | //=== Macaulay 4 min 33 sec |
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414 | //=== 144.50 sec (2 min 24.50 sec) |
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415 | |
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416 | ring testh1=32003,(w,x,y,z),dp; |
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417 | int a =10; |
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418 | poly f=(xyz+xy+yz+xz)*(x+y+z)^2 +x^a+y^a+z^a; |
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419 | ideal j= jacob(f); |
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420 | ideal i=homog(j,w); |
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421 | ideal i0=std( i); |
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422 | size(i0); |
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423 | degree (i0); |
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424 | kill a,testh1; |
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425 | |
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426 | //==== elem 443, dim 2, mult 392 |
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427 | //==== Macaulay 29 min 17 sec |
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428 | //=== 1019.78 sec (16 min 59.78 sec) |
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429 | |
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430 | ring testh2=32003,(a,b,c,d,e,f,g,h),dp; |
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431 | ideal i= |
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432 | a+b+c+d+e+f+g, |
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433 | ab+bc+cd+de+ef+fg+ga, |
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434 | abc+bcd+cde+d*ef+efg+fga+gab, |
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435 | abcd+bcde+cdef+defg+efga+fgab+gabc, |
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436 | abcde+bcdef+cdefg+defga+efgab+fgabc+gabcd, |
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437 | abcdef+bcdefg+cdefga+defgab+efgabc+fgabcd+gabcde, |
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438 | abcdefg+h^7; |
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439 | ideal i0=std(i); |
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440 | size(i0); |
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441 | degree (i0); |
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442 | kill testh2; |
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443 | |
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444 | //=== elem 767, dim 2 mult 86 |
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445 | //== Macaulay 42 min 0 sec |
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446 | //=== 1616.59 sec (26 min 56.59 sec) |
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447 | |
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448 | ring rh15=32003,(w,x,y,z),dp; |
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449 | poly p1= x2y *(47x5y7z3+28xy5z8+63+91x5y3z7); |
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450 | poly p2= xyz *(57y6+21x2yz9+51y2z2+15x2z4); |
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451 | poly p3= xy4z *(74y+32x6z7+53x5y2z+17x2y3z); |
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452 | poly p4= y3z *(21x2z6+32x10y6z5+23x5y5z7+27y2); |
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453 | poly p5= xz *(36y2z2+81x9y10+19x2y5z4+79x4z6); |
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454 | ideal j= p1,p2,p3,p4,p5; |
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455 | ideal i=homog(j,w); |
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456 | ideal i0=std( i); |
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457 | size(i0); |
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458 | degree (i0); |
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459 | kill rh15; |
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460 | |
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461 | //=== elem ,dim 0, mult 90 |
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462 | //=== Macaulay 3 sec |
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463 | //=== 2.21 |
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464 | |
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465 | ring testh4 = 31991,(u,v,w,x,y,z),dp; |
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466 | |
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467 | ideal i = xy+y2+uz-wz-xz+yz, x2-y2+uz-wz-xz+z2, wy, wx-uz+yz, w2-y2+uz-z2, vz-yz-z2, |
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468 | vy-y2-wz+xz+yz+z2, vx-y2+uz+yz-z2, vw-y2+uz+yz-z2, v2+y2+uz-xz-yz-z2, uy+y2+yz, |
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469 | ux-y2+wz-xz-z2, uw-y2+uz+yz-z2, uv-y2-xz+yz, u2+yz; |
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470 | |
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471 | ideal i3 = i^2; |
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472 | ideal j = std(i3); |
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473 | size(j); |
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474 | degree(j); |
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475 | |
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476 | kill testh4; |
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477 | LIB "tst.lib";tst_status(1);$ |
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