1 | LIB "tst.lib"; |
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2 | tst_init(); |
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3 | |
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4 | LIB "primdec.lib"; |
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5 | |
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6 | //Singular Trac #636 |
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7 | |
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8 | ring r=integer,(t,a,b,c,d,e,f,g,h,i,j),ws(1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1); |
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9 | ideal inI= |
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10 | 3, |
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11 | gh+2fi+ej, |
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12 | dh+2ci+bj, |
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13 | df+2cg+aj, |
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14 | de+2bg+ai, |
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15 | ce+2bf+ah; |
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16 | lead(std(inI)); |
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17 | kill r; |
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18 | |
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19 | //Github Adi #39 |
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20 | |
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21 | ring rng = (integer),(x,y,z),(ls(3),C); |
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22 | ideal J = -2xz3+x2yz,3z-2xy-3xy2; |
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23 | ideal gJ = std(J); |
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24 | "Zweite:"; |
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25 | ideal ggJ = std(gJ); |
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26 | lead(gJ);lead(ggJ); |
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27 | reduce(J,gJ); |
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28 | kill rng; |
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29 | |
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30 | //Github Adi #32 |
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31 | |
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32 | ring rng = (integer),(x,y,z),dp; |
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33 | ideal I = -25*x^3+104*x*y^3-23*y^2*z-128; |
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34 | ideal J = -118*x*y^3*z+50*x*y^2*z^2-50*x*y*z-49*y,149*x*y^2*z^2-142*y^2-112; |
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35 | ideal gI = std(I); |
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36 | ideal gJ = std(J); |
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37 | reduce (I,gI ); |
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38 | reduce (J,gJ ); |
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39 | kill rng; |
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40 | |
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41 | |
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42 | option(redSB); |
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43 | |
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44 | |
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45 | ring rng = (integer),(x,y,z),(dp(3),C); |
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46 | ideal I = -27*x+25*z,-46*x*z+35*x,21*x-42; |
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47 | ideal gI = std(I); |
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48 | ideal ggI = std(gI); |
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49 | reduce (I,gI ); |
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50 | kill rng; |
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51 | |
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52 | //Github Adi #33 |
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53 | |
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54 | ring rng = (integer),(x,y,z),dp; |
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55 | option(redSB); |
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56 | option(redTail); |
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57 | ideal I = -5*z^2-y*z^2, x^3*y*z-z^2+1, y^2*z^2+5*x^2*y*z; |
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58 | ideal gI = std(I); |
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59 | ideal ggI = std(gI); |
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60 | lead(gI); |
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61 | lead(ggI); |
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62 | reduce(I,gI); |
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63 | kill rng; |
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64 | |
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65 | |
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66 | ring rng = (integer),(x,y,z),(dp(3),C); |
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67 | option(redSB); |
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68 | option(redTail); |
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69 | ideal I = -5*x*z^2-73*y*z^2, 68*x^3*y*z-129*x*z^2+98, 11*y^3*z^2+85*x^2*y*z; |
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70 | ideal gI = std(I); |
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71 | ideal ggI = std(gI); |
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72 | lead(gI); |
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73 | lead(ggI); |
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74 | reduce(I,gI); |
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75 | kill rng; |
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76 | |
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77 | option(redSB); |
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78 | |
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79 | ring rng = (integer),(x,y,z),(dp(3),C); |
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80 | ideal I = -49*y^2+40*z^2+17,-34*z^2-3,-25*y*z-28*z; |
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81 | ideal gI = std(I); |
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82 | ideal ggI = std(gI); |
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83 | lead(gI); |
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84 | lead(ggI); |
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85 | reduce(I,gI); |
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86 | kill rng; |
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87 | |
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88 | //Github Adi #36 |
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89 | |
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90 | ring rng = (0),(x,y,z),(ls(3),C); |
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91 | ideal I = |
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92 | (68/23)*z-(142/133)*y*z-(64/37)*x*y+(65/71)*x*y*z^2+(1/3)*x^2*y*z,(-2/7)*x*y*z-(61/91)*x*y^2*z; |
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93 | ideal J = (3/53)*x*z+(47/44)*x*y^2*z,(-40/107)*x*z^2+22*x*z^3; |
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94 | ideal gI = std(I); |
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95 | ideal ggI = std(gI); |
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96 | ideal gJ = std(J); |
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97 | ideal ggJ = std(gJ); |
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98 | lead(gI);lead(ggI);lead(gJ);lead(ggJ); |
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99 | reduce (I,gI ); |
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100 | reduce (J,gJ ); |
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101 | kill rng; |
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102 | |
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103 | //Github Adi #37 |
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104 | |
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105 | ring rng = (integer),(x,y,z),dp; |
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106 | ideal i = -5*z^2-y*z^2, x^3*y*z-z^2+1, y^2*z^2+5*x^2*y*z; |
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107 | ideal gI = std(i); |
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108 | ideal ggI = std(gI); |
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109 | lead(gI);lead(ggI); |
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110 | reduce(i,gI); |
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111 | kill rng; |
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112 | |
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113 | //Github Adi #39 |
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114 | //Problem mit ls aber kein problem mit ds,Ds,lp,dp |
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115 | //ls solved: in posinL11Ring one should take the Fdeg instead of pLmCmp |
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116 | |
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117 | option(redSB); |
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118 | |
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119 | |
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120 | ring rng = (integer),(x,y,z),(ls(3),C); |
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121 | ideal I = 1+7*y*z^3,-4*x+2*x*z+14*x^2,-9-10*z^2+8*x*z; |
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122 | ideal J = -14*x*z^3+5*x^2*y*z,15*z-7*x*y+12*x*y*z^2-11*x*y^2; |
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123 | ideal gI = std(I); |
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124 | ideal ggI = std(gI); |
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125 | ideal gJ = std(J); |
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126 | ideal ggJ = std(gJ); |
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127 | reduce (I,gI ); |
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128 | reduce (J,gJ ); |
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129 | idealsEqual(gI,ggI ); |
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130 | idealsEqual(gJ,ggJ ); |
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131 | kill rng; |
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132 | |
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133 | //Github Adi #39 |
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134 | //redtail hat Problemen wenn man im posinL11Ring pLmCmp nimmt statt FDeg |
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135 | |
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136 | |
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137 | ring rng = (integer),(x,y,z),(ls(3),C); |
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138 | option("redTail"); |
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139 | option(redSB); |
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140 | ideal I = -14*y*z^2+7*x-11*x*y,-15*x*y,-8*y^2*z^2+5*x*y*z,5*y*z^2-15*y^2*z+8*x^2*z^2+3*x^2*y^2; |
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141 | ideal gI = std(I); |
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142 | ideal ggI = std(gI); |
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143 | reduce(I,gI); |
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144 | idealsEqual(gI,ggI ); |
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145 | lead(gI); |
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146 | kill rng; |
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147 | |
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148 | |
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149 | //Github Adi #40 |
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150 | |
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151 | ring rng = (integer),(x,y,z),(ls(3),C); |
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152 | ideal I = -10*x*y*z,12*z^2-8*y-14*x*z+14*x^2*y*z,-7*y^4+4*x^2+9*x^2*y; |
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153 | ideal J = -1+7*y^3*z,-15+14*x+14*x*y*z,15*z+7*x-10*x*z+5*x*y^2; |
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154 | ideal gI = std(I); |
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155 | lead(gI); |
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156 | reduce(I,gI); |
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157 | ideal gJ = std(J); |
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158 | lead(gJ); |
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159 | reduce(J,gJ); |
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160 | kill rng; |
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161 | |
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162 | ring rng = (integer),(x,y,z),(ls(3),C); |
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163 | ideal I = 7*x*z+3*x*z^2-x^2,4*z+6*z^2+2*y; |
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164 | ideal J = 5-5*z^2+3*y^2*z; |
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165 | ideal gI = std(I); |
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166 | lead(gI); |
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167 | reduce(I,gI); |
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168 | ideal gJ = std(J); |
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169 | lead(gJ); |
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170 | reduce(J,gJ); |
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171 | kill rng; |
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172 | |
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173 | //Github Adi #27 |
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174 | |
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175 | ring rng = (integer),(y(1..4),x(1..3)),dp; |
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176 | ideal I = 12*y(3)*y(4)+19*y(1)+6*y(4),2*x(3)*y(4)-2*y(1)+7,2*y(1)*y(3)+y(1)-7*y(3)+6,7*x(3)*y(3)-6*x(3)-6*y(3)-3,y(1)^2+126*y(3)*y(4)+196*y(1)+60*y(4),x(3)*y(1)-3,x(3)*y(3)*y(4)+30*y(3)*y(4)+48*y(1)+15*y(4)+3,48*y(3)*y(4)^2-76*y(1)*y(4)+24*y(4)^2+266*y(4),48*y(3)^2*y(4)+48*y(3)*y(4)+12*y(4),48*y(1)*y(3)*y(4)+24*y(1)*y(4)-168*y(3)*y(4)-84*y(4),48*x(3)*y(3)*y(4)-76*x(3)*y(1)-48*y(1)*y(3)+24*x(3)*y(4)+266*x(3)-24*y(1)+168*y(3)+84,-266*x(3)*y(4)+168*y(3)*y(4)+84*y(4),266*x(3)*y(3)+168*y(3)^2-228*x(3)-60*y(3)-72,336*x(3)*y(3)*y(4)-60*x(3)*y(4)-144*y(3)*y(4)-72*y(4),-266*x(3)^2-168*x(3)*y(3)+144*x(3)+144*y(3)+72,-168*y(3)^2*y(4)+266*y(1)*y(3)+60*y(3)*y(4)-228*y(1)-931*y(3)+72*y(4)+798,-168*y(3)^3-24*y(3)^2+102*y(3)+36,-168*y(1)*y(3)^2+60*y(1)*y(3)+588*y(3)^2+72*y(1)-210*y(3)-252,168*x(3)*y(3)^2+168*x(3)*y(3)-144*y(3)^2+42*x(3)-144*y(3)-36,28*x(3)*y(3)*y(4)-28*y(1)*y(3)+14*x(3)*y(4)-24*y(3)*y(4)+24*y(1)+98*y(3)-12*y(4)-84,-28*x(3)*y(3)^2+10*x(3)*y(3)+12*x(3),-28*x(3)*y(1)*y(3)+24*x(3)*y(1)+98*x(3)*y(3)-84*x(3),28*x(3)^2*y(3)+14*x(3)^2-24*x(3)*y(3)-12*x(3),48*y(1)*y(4)^2-84*y(4)^2,48*y(1)*y(3)*y(4)+24*y(1)*y(4)-84*y(3)*y(4)+72*y(4),72*y(4)^2,48*x(3)*y(1)*y(4)-84*x(3)*y(4)-72*y(4),-48*y(1)^2*y(3)-24*y(1)^2+252*y(1)*y(3)+72*y(3)*y(4)+12*y(1)-294*y(3)+36*y(4)+252,-8*y(1)^2*y(4)+504*y(3)*y(4)^2-756*y(1)*y(4)+252*y(4)^2+2744*y(4),504*y(3)^2*y(4)+492*y(3)*y(4)+120*y(4),504*y(1)*y(3)*y(4)+240*y(1)*y(4)-1764*y(3)*y(4)-840*y(4),-8*x(3)*y(1)^2+504*x(3)*y(3)*y(4)-756*x(3)*y(1)-504*y(1)*y(3)+252*x(3)*y(4)+2744*x(3)-240*y(1)+1764*y(3)+840,168*y(1)*y(3)*y(4)-144*y(1)*y(4)-294*y(3)*y(4)+252*y(4),168*y(1)*y(3)^2-60*y(1)*y(3)-294*y(3)^2-72*y(1)+504*y(3)-216,252*y(3)*y(4)-216*y(4),-168*x(3)*y(1)*y(3)-84*x(3)*y(1)+294*x(3)*y(3)+144*y(1)*y(3)-252*x(3)+72*y(1)-252*y(3)+216,-28*x(3)*y(1)*y(4)-2744*x(3)*y(4)+24*y(1)*y(4)+1764*y(3)*y(4)+840*y(4),28*x(3)*y(1)*y(3)-24*x(3)*y(1)+2744*x(3)*y(3)+1764*y(3)^2-2352*x(3)-672*y(3)-720,3528*x(3)*y(3)*y(4)-672*x(3)*y(4)-1512*y(3)*y(4)-720*y(4),-28*x(3)^2*y(1)-2744*x(3)^2+24*x(3)*y(1)-1764*x(3)*y(3)+1512*x(3)+1512*y(3)+720,28*y(1)^2*y(3)-1764*y(3)^2*y(4)-24*y(1)^2+2646*y(1)*y(3)+630*y(3)*y(4)-2268*y(1)-9604*y(3)+756*y(4)+8232,-1764*y(3)^3-210*y(3)^2+1056*y(3)+360,-1764*y(1)*y(3)^2+672*y(1)*y(3)+6174*y(3)^2+720*y(1)-2352*y(3)-2520,1764*x(3)*y(3)^2+1722*x(3)*y(3)-1512*y(3)^2+420*x(3)-1476*y(3)-360,24*x(3)*y(4)^2+24*y(1)*y(4),24*x(3)*y(3)*y(4)+38*x(3)*y(1)+24*y(1)*y(3)+12*x(3)*y(4)+12*y(1),24*x(3)*y(1)*y(4),24*x(3)^2*y(4),-24*y(1)*y(3)*y(4)+38*y(1)^2-12*y(1)*y(4)-133*y(1),-24*y(1)*y(3)^2-24*y(1)*y(3)-6*y(1),-24*y(1)^2*y(3)-12*y(1)^2+84*y(1)*y(3)+42*y(1),-24*x(3)*y(1)*y(3)-12*x(3)*y(1)+84*x(3)*y(3)+42*x(3),-4*x(3)*y(1)*y(4)-4*y(1)^2+14*x(3)*y(4)+14*y(1),-4*x(3)*y(1)*y(3)-2*x(3)*y(1),-4*x(3)*y(1)^2+14*x(3)*y(1),-4*x(3)^2*y(1)+14*x(3)^2,84*x(3)*y(3)*y(4)+133*x(3)*y(1)-72*x(3)*y(4)-114*y(1),84*x(3)*y(3)^2-30*x(3)*y(3)-36*x(3),-84*x(3)*y(1)*y(3)-42*x(3)*y(1)+72*y(1)*y(3)+36*y(1),-84*x(3)^2*y(3)-42*x(3)^2+72*x(3)*y(3)+36*x(3),-14*x(3)^2*y(4)-14*x(3)*y(1)+12*x(3)*y(4)+12*y(1),14*x(3)^2*y(3)-12*x(3)^2,-14*x(3)^2*y(1)+12*x(3)*y(1),-14*x(3)^3+12*x(3)^2,28*x(3)*y(1)*y(3)-5*x(3)*y(1)-49*x(3)*y(3)-12*y(1)*y(3)+42*x(3)-6*y(1),-24*y(1)^2*y(4)+42*y(1)*y(4),-24*y(1)^2*y(3)-12*y(1)^2+42*y(1)*y(3)-36*y(1),-36*y(1)*y(4),-36*x(3)*y(4),-252*x(3)*y(4)^2-252*y(1)*y(4),-4*x(3)*y(1)^2-252*x(3)*y(3)*y(4)-392*x(3)*y(1)-252*y(1)*y(3)-120*x(3)*y(4)-120*y(1),-252*x(3)*y(1)*y(4),-252*x(3)^2*y(4),-4*y(1)^3+252*y(1)*y(3)*y(4)-378*y(1)^2+126*y(1)*y(4)+1372*y(1),252*y(1)*y(3)^2+246*y(1)*y(3)+60*y(1),252*y(1)^2*y(3)+120*y(1)^2-882*y(1)*y(3)-420*y(1),252*x(3)*y(1)*y(3)+120*x(3)*y(1)-882*x(3)*y(3)-420*x(3),-14*x(3)*y(1)^2-882*x(3)*y(3)*y(4)-1372*x(3)*y(1)+12*y(1)^2+756*x(3)*y(4)+1176*y(1),-882*x(3)*y(3)^2+336*x(3)*y(3)+360*x(3),882*x(3)*y(1)*y(3)+420*x(3)*y(1)-756*y(1)*y(3)-360*y(1),882*x(3)^2*y(3)+420*x(3)^2-756*x(3)*y(3)-360*x(3),-38*x(3)*y(4)^2+24*y(3)*y(4)^2+12*y(4)^2,24*y(3)^2*y(4)+24*y(3)*y(4)+6*y(4),24*x(3)*y(3)*y(4)^2+12*x(3)*y(4)^2,-38*x(3)^2*y(4),-24*y(3)^2*y(4)^2+38*y(1)*y(3)*y(4)-12*y(3)*y(4)^2-133*y(3)*y(4),-24*y(3)^3*y(4)-24*y(3)^2*y(4)-6*y(3)*y(4),-24*y(1)*y(3)^2*y(4)-12*y(1)*y(3)*y(4)+84*y(3)^2*y(4)+42*y(3)*y(4),38*x(3)*y(1)*y(3)+12*x(3)*y(3)*y(4)-133*x(3)*y(3)-12*y(1)*y(3)+6*x(3)*y(4)-6*y(1)+42*y(3)+21,4*x(3)*y(3)*y(4)^2-4*y(1)*y(3)*y(4)+2*x(3)*y(4)^2+120*y(3)*y(4)^2-192*y(1)*y(4)+14*y(3)*y(4)+60*y(4)^2+672*y(4),120*y(3)^2*y(4)+120*y(3)*y(4)+30*y(4),120*y(1)*y(3)*y(4)+60*y(1)*y(4)-420*y(3)*y(4)-210*y(4),4*x(3)^2*y(3)*y(4)-4*x(3)*y(1)*y(3)+2*x(3)^2*y(4)+120*x(3)*y(3)*y(4)-192*x(3)*y(1)+14*x(3)*y(3)-120*y(1)*y(3)+60*x(3)*y(4)+672*x(3)-60*y(1)+420*y(3)+210,114*x(3)*y(4)-72*y(3)*y(4)-36*y(4),-133*x(3)*y(3)^2+114*x(3)*y(3)+42*y(3)^2-15*y(3)-18,-84*x(3)*y(3)^2*y(4)+72*y(3)^2*y(4)-36*x(3)*y(4)+36*y(3)*y(4),133*x(3)^2*y(3)-156*x(3)*y(3)-21*x(3)+36*y(3)+18,-684*x(3)*y(4)+432*y(3)*y(4)+216*y(4),14*x(3)*y(3)^2+660*x(3)*y(3)+420*y(3)^2-576*x(3)-150*y(3)-180,14*x(3)^2*y(3)*y(4)-12*x(3)^2*y(4)+840*x(3)*y(3)*y(4)-150*x(3)*y(4)-360*y(3)*y(4)-180*y(4),-14*x(3)^2*y(3)-672*x(3)^2-408*x(3)*y(3)+366*x(3)+360*y(3)+180,12*x(3)*y(3)*y(4)-432*y(3)^2*y(4)+672*y(1)*y(3)+6*x(3)*y(4)+144*y(3)*y(4)-576*y(1)-2352*y(3)+180*y(4)+2016,-14*x(3)*y(3)^3+5*x(3)*y(3)^2-420*y(3)^3+6*x(3)*y(3)-60*y(3)^2+255*y(3)+90,-14*x(3)*y(1)*y(3)^2+12*x(3)*y(1)*y(3)+49*x(3)*y(3)^2-420*y(1)*y(3)^2-42*x(3)*y(3)+150*y(1)*y(3)+1470*y(3)^2+180*y(1)-525*y(3)-630,14*x(3)^2*y(3)^2+7*x(3)^2*y(3)+408*x(3)*y(3)^2+414*x(3)*y(3)-360*y(3)^2+105*x(3)-360*y(3)-90,-24*y(1)*y(3)*y(4)^2+42*y(3)*y(4)^2,-24*y(1)*y(3)^2*y(4)-12*y(1)*y(3)*y(4)+42*y(3)^2*y(4)-36*y(3)*y(4),-36*y(3)*y(4)^2,12*x(3)*y(1)*y(4)+36*x(3)*y(4)-18*y(4),4*x(3)*y(1)*y(4)^2+392*x(3)*y(4)^2+120*y(1)*y(4)^2-252*y(3)*y(4)^2-336*y(4)^2,120*y(1)*y(3)*y(4)-252*y(3)^2*y(4)+60*y(1)*y(4)-456*y(3)*y(4)+120*y(4),-252*x(3)*y(3)*y(4)^2-120*x(3)*y(4)^2+180*y(4)^2,4*x(3)^2*y(1)*y(4)+392*x(3)^2*y(4)+120*x(3)*y(1)*y(4)-216*x(3)*y(4)-180*y(4),-4*y(1)^2*y(3)*y(4)+252*y(3)^2*y(4)^2-378*y(1)*y(3)*y(4)+126*y(3)*y(4)^2+1372*y(3)*y(4),252*y(3)^3*y(4)+246*y(3)^2*y(4)+60*y(3)*y(4),252*y(1)*y(3)^2*y(4)+120*y(1)*y(3)*y(4)-882*y(3)^2*y(4)-420*y(3)*y(4),-4*x(3)*y(1)^2*y(3)-378*x(3)*y(1)*y(3)-120*y(1)^2*y(3)-120*x(3)*y(3)*y(4)-60*y(1)^2+1372*x(3)*y(3)+756*y(1)*y(3)-60*x(3)*y(4)+180*y(3)*y(4)+90*y(1)-1176*y(3)+90*y(4)+420,-12*x(3)*y(1)*y(4)+432*y(1)*y(3)*y(4)-1176*x(3)*y(4)-360*y(1)*y(4)+1008*y(4),14*x(3)*y(1)*y(3)^2-12*x(3)*y(1)*y(3)+1372*x(3)*y(3)^2+420*y(1)*y(3)^2-1176*x(3)*y(3)-150*y(1)*y(3)-1176*y(3)^2-180*y(1)+1428*y(3)-360,882*x(3)*y(3)^2*y(4)-756*y(3)^2*y(4)+360*x(3)*y(4)+270*y(3)*y(4)-540*y(4),-14*x(3)^2*y(1)*y(3)-1372*x(3)^2*y(3)-408*x(3)*y(1)*y(3)-210*x(3)*y(1)+2352*x(3)*y(3)+360*y(1)*y(3)-420*x(3)+180*y(1)-1008*y(3)+360,-12*x(3)*y(3)*y(4)^2-19*x(3)*y(1)*y(4)+6*y(1)*y(4),-12*x(3)*y(3)^2*y(4)-19*x(3)*y(1)*y(3)-6*x(3)*y(3)*y(4)+6*y(1)*y(3)+3*y(1),6*x(3)*y(1)*y(4),6*x(3)^2*y(4),2*x(3)^2*y(4)^2+2*x(3)*y(1)*y(4)+60*x(3)*y(4)^2+60*y(1)*y(4),2*x(3)*y(1)*y(3)+60*x(3)*y(3)*y(4)+96*x(3)*y(1)+60*y(1)*y(3)+30*x(3)*y(4)+30*y(1),2*x(3)^2*y(1)*y(4)+60*x(3)*y(1)*y(4),2*x(3)^3*y(4)+60*x(3)^2*y(4),-4*x(3)*y(1)*y(3)*y(4)-x(3)*y(1)*y(4)+7*x(3)*y(3)*y(4)-60*y(1)*y(3)*y(4)+96*y(1)^2-30*y(1)*y(4)-336*y(1),-2*x(3)*y(1)*y(3)^2-x(3)*y(1)*y(3)-60*y(1)*y(3)^2-60*y(1)*y(3)-15*y(1),-2*x(3)*y(1)^2*y(3)+7*x(3)*y(1)*y(3)-60*y(1)^2*y(3)-30*y(1)^2+210*y(1)*y(3)+105*y(1),-2*x(3)^2*y(1)*y(3)+7*x(3)^2*y(3)-60*x(3)*y(1)*y(3)-30*x(3)*y(1)+210*x(3)*y(3)+105*x(3),-6*x(3)^2*y(4)+216*x(3)*y(3)*y(4)+336*x(3)*y(1)-180*x(3)*y(4)-288*y(1),7*x(3)^2*y(3)^2-6*x(3)^2*y(3)+210*x(3)*y(3)^2-75*x(3)*y(3)-90*x(3),-7*x(3)^2*y(1)*y(3)-204*x(3)*y(1)*y(3)-105*x(3)*y(1)+180*y(1)*y(3)+90*y(1),-7*x(3)^3*y(3)-204*x(3)^2*y(3)-105*x(3)^2+180*x(3)*y(3)+90*x(3),-2*x(3)*y(1)^2*y(4)-126*x(3)*y(3)*y(4)^2-196*x(3)*y(1)*y(4)-60*y(1)^2*y(4)+168*y(1)*y(4),-2*x(3)*y(1)^2*y(3)-126*x(3)*y(3)^2*y(4)-196*x(3)*y(1)*y(3)-60*y(1)^2*y(3)-60*x(3)*y(3)*y(4)-30*y(1)^2+168*y(1)*y(3)-60*y(1),60*x(3)*y(1)*y(4)-90*y(1)*y(4),60*x(3)^2*y(4)-90*x(3)*y(4); 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177 | ideal J = std(I); |
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178 | lead(J); |
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179 | reduce(I,J); |
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180 | kill rng; |
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181 | |
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182 | //Github Adi #20 |
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183 | |
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184 | ring rng = (integer),(xw,xq,xk),(lp(2),lp(1),C); |
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185 | ideal I = -4*xk+10; |
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186 | ideal J = -7*xw+4*xk,-13; |
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187 | ideal IJ = intersect(I,J); |
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188 | ideal stdIstdJ = intersect(std(I),std(J) ); |
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189 | reduce(IJ,stdIstdJ); |
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190 | reduce(stdIstdJ,IJ); |
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191 | kill rng; |
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192 | |
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193 | //Github Adi #42 |
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194 | |
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195 | ring rng = (integer),(x,y,z),(dp(1),dp(2),C); |
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196 | ideal I = 20*x*z+7*y^2; |
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197 | ideal J = 6*x*y+20*z+6,-5*x-16*y-11,8*x*y+2*y^2; |
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198 | ideal gI = std(I); |
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199 | lead(gI); |
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200 | ideal ggI = std(gI); |
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201 | ideal gJ = std(J); |
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202 | lead(gJ); |
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203 | ideal ggJ = std(gJ); |
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204 | std(reduce (I,gI ) ); |
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205 | std(reduce (J,gJ ) ); |
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206 | size(gJ)== size(ggJ ); |
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207 | kill rng; |
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208 | |
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209 | //Github Adi #38 |
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210 | |
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211 | ring rng = (integer),(x(1),x(3),x(4),x(5)),(dp(4),C); |
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212 | ideal Q = x(4)^2-x(3)*x(5), |
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213 | x(3)*x(4)-x(5), |
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214 | x(3)^2-x(4), |
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215 | x(1)^2-121*x(5)^2-11*x(5)-1; |
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216 | Q = std(Q); |
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217 | qring qr = Q; |
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218 | ideal a = x(5)-2; |
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219 | ideal j = 6,x(5)-2,x(4)+2,x(3)-2,x(1)+3; |
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220 | ideal aJJ = quotient(a*j,j); // ? |
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221 | aJJ; |
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222 | std(aJJ); |
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223 | kill rng; |
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224 | |
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225 | //segfaults |
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226 | //ok mit neue posinL11Ring |
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227 | |
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228 | ring rng = (integer),(x(1),x(2),x(3)),(ls(3),C); |
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229 | ideal I = -3*x(1)-10*x(1)*x(3); |
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230 | ideal J = -9*x(2)+9*x(1)*x(2),-3*x(2)*x(3)^2+10*x(1)*x(3)^2+10*x(1)^2*x(2); |
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231 | ideal gI = std(I); |
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232 | ideal ggI = std(gI); |
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233 | ideal gJ = std(J); |
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234 | ideal ggJ = std(gJ); |
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235 | lead(gI); |
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236 | lead(gJ); |
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237 | std(reduce (I,gI ) ); |
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238 | std(reduce (J,gJ ) ); |
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239 | kill rng; |
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240 | |
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241 | //ok now |
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242 | |
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243 | ring rng = (integer),(x(1),x(2)),(ls(2),C); |
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244 | ideal I = -41*x(1)-10*x(1)^3*x(2),-22*x(2)^2-12*x(1)^3; |
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245 | ideal J = 14,35*x(1)*x(2)+12*x(1)*x(2)^3; |
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246 | ideal gI = std(I); |
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247 | ideal ggI = std(gI); |
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248 | ideal gJ = std(J); |
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249 | lead(gI); |
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250 | lead(gJ); |
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251 | std(reduce (I,gI ) ); |
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252 | std(reduce (J,gJ ) ); |
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253 | kill rng; |
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254 | |
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255 | //ok now |
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256 | |
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257 | ring rng = (integer),(x(1),x(2)),(ls(2),C); |
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258 | ideal I = -22-24*x(1)^3,4*x(1)*x(2)^2-19*x(1)^2*x(2); |
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259 | ideal J = 16*x(1)*x(2),12-31*x(1)-43*x(1)*x(2); |
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260 | ideal gI = std(I); |
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261 | ideal ggI = std(gI); |
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262 | ideal gJ = std(J); |
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263 | lead(gI); |
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264 | lead(gJ); |
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265 | std(reduce (I,gI ) ); |
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266 | std(reduce (J,gJ ) ); |
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267 | kill rng; |
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268 | |
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269 | |
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270 | //in the new posinL11Ring works smooth, in the other one takes forever |
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271 | |
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272 | ring rng = (integer),(x(1),x(2)),(ls(2),C); |
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273 | ideal I = -11*x(2),3*x(2)^2+8*x(1)*x(2)+3*x(1)*x(2)^2+12*x(1)^3,8*x(1)*x(2)^2-15*x(1)^3; |
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274 | ideal J = -2*x(1)-11*x(1)^2+10*x(1)^2*x(2),-13*x(1)*x(2)-10*x(1)^3; |
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275 | ideal gI = std(I); |
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276 | ideal ggI = std(gI); |
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277 | ideal gJ = std(J); |
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278 | lead(gI); |
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279 | lead(gJ); |
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280 | std(reduce (I,gI ) ); |
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281 | std(reduce (J,gJ ) ); |
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282 | kill rng; |
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283 | |
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284 | //ok now |
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285 | |
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286 | ring rng = (integer),(x(1),x(2)),(ls(2),C); |
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287 | ideal I = -10,15*x(1)*x(2)+8*x(1)*x(2)^2; |
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288 | ideal J = 2*x(1)^2*x(2),-3+2*x(1)*x(2); |
---|
289 | ideal gI = std(I); |
---|
290 | ideal gJ = std(J); |
---|
291 | lead(gI); |
---|
292 | lead(gJ); |
---|
293 | std(reduce (I,gI ) ); |
---|
294 | std(reduce (J,gJ ) ); |
---|
295 | kill rng; |
---|
296 | |
---|
297 | //ok now |
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298 | |
---|
299 | ring rng = (integer),(x(1)),(ls(1),C); |
---|
300 | ideal I = -12+2*x(1)^2; |
---|
301 | ideal J = -6*x(1)^2+11*x(1)^4,-15; |
---|
302 | ideal gI = std(I); |
---|
303 | ideal gJ = std(J); |
---|
304 | lead(gI); |
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305 | lead(gJ); |
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306 | std(reduce (I,gI ) ); |
---|
307 | std(reduce (J,gJ ) ); |
---|
308 | kill rng; |
---|
309 | |
---|
310 | //Github Adi #47 |
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311 | |
---|
312 | ring R = integer,x,dp; |
---|
313 | reduce(x,std(2*x)); |
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314 | |
---|
315 | ring S = integer,x,ls; |
---|
316 | reduce(x,std(2*x)); |
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317 | kill R,S; |
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318 | |
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319 | //Github Adi #46 |
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320 | |
---|
321 | ring rng = integer,x,ds; |
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322 | ideal J = -7, -3-15*x^2, -6+18*x-x^2; |
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323 | ideal gJ = std(J); |
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324 | reduce(J,gJ); |
---|
325 | kill rng; |
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326 | |
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327 | //Github Adi #49 |
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328 | |
---|
329 | ring rng = (integer),(x,y,z),(dp(3),C); |
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330 | ideal Q = x,yz2+5; |
---|
331 | qring QR = std(Q); |
---|
332 | poly a = z; |
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333 | std(a); |
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334 | ideal J = 5,z,x; |
---|
335 | ideal aJJ = quotient( a*J, J ); |
---|
336 | aJJ; |
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337 | kill rng; |
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338 | kill QR; |
---|
339 | |
---|
340 | //Github Adi #50 |
---|
341 | |
---|
342 | ring rng = (integer),(x(1)),(lp(1),C); |
---|
343 | ideal I = 4*x(1)^3+35*x(1)^2+24*x(1),45*x(1),35; |
---|
344 | ideal J = 18*x(1)^3+43*x(1)^2,-7*x(1)-10,-12*x(1)^2-20*x(1)+13; |
---|
345 | ideal I_J = intersect(I,J); |
---|
346 | size(I_J); |
---|
347 | kill rng; |
---|
348 | |
---|
349 | //Github Adi #21 |
---|
350 | |
---|
351 | ring r = integer,(a,d,g,h,i,j),ws(-1,-1,-1,-1,-1,-1); |
---|
352 | ideal inI= gh+2i, dh+j, d+2g+aj, d+2g+ai; |
---|
353 | ideal g= std(inI); |
---|
354 | reduce(inI,g); |
---|
355 | /// |
---|
356 | ring rng = (integer),(x,y,z),(ws(-1,-1,-1),C); |
---|
357 | ideal I = 6yz-6,6xy-6yz-8y; |
---|
358 | ideal gI =std(I); |
---|
359 | reduce(I,gI); |
---|
360 | kill rng; |
---|
361 | /// |
---|
362 | ring rng = (integer),(x,y,z),(ws(-1,-1,-1),C); |
---|
363 | ideal I = -10x+15y,4y-7; |
---|
364 | ideal gI =std(I); |
---|
365 | reduce(I,gI); |
---|
366 | kill rng; |
---|
367 | /// |
---|
368 | ring rng = (integer),(x,y,z),(ws(-1,-1,-1),C); |
---|
369 | ideal I = 9x-14y,15z-2; |
---|
370 | ideal gI =std(I); |
---|
371 | reduce(I,gI); |
---|
372 | kill rng; |
---|
373 | /// |
---|
374 | ring rng = (integer),(x,y),(ws(-1,-1),C); |
---|
375 | ideal I = 8x+7,-6x-13y; |
---|
376 | ideal gI =std(I); |
---|
377 | reduce(I,gI); |
---|
378 | kill rng; |
---|
379 | kill r; |
---|
380 | |
---|
381 | // Singular bug #648 |
---|
382 | |
---|
383 | ring r=integer,(t,x(1..4)),ws(1,-1,-11,-3,-19); |
---|
384 | ideal inJ = |
---|
385 | 3, |
---|
386 | t*x(3)*x(4)+2*t*x(1)*x(2), |
---|
387 | t*x(1)*x(2)^2+2*t^3*x(1)*x(2)*x(3), |
---|
388 | x(1)^2*x(2)*x(3)*x(4)+2*t^2*x(1)^3*x(2)*x(3); |
---|
389 | ideal J = |
---|
390 | x(1)^2*x(2)*x(3)*x(4)-t*x(1)^2*x(2)^3+5*t*x(1)^2*x(2)*x(3)*x(4)+16*t^3*x(1)*x(2)*x(3)^2*x(4)-2*x(1)^3*x(2)^2-1536*x(1)^3*x(3)*x(4)+32*t^2*x(1)^2*x(3)^2*x(4), |
---|
391 | t*x(1)*x(2)^2+2*x(1)^2*x(2)+2*t^3*x(1)*x(2)*x(3)-192*x(1)^3+4*t^2*x(1)^2*x(3), |
---|
392 | t*x(3)*x(4)-3*t^2*x(3)*x(4)-t*x(1)*x(2)-2*x(1)^2, |
---|
393 | 3-t; |
---|
394 | reduce(inJ,J); |
---|
395 | kill r; |
---|
396 | |
---|
397 | //Github Adi #48 |
---|
398 | |
---|
399 | ring rng = integer,x,ds; |
---|
400 | ideal I = -8*x+2*x^2, -16+9*x^2-x^3; |
---|
401 | ideal gI = std(I); |
---|
402 | lead(gI); |
---|
403 | lead(std(gI)); |
---|
404 | reduce(I,gI); |
---|
405 | kill rng; |
---|
406 | |
---|
407 | //Github Adi #43 |
---|
408 | |
---|
409 | ring rng = integer,(x),lp; |
---|
410 | short = 0 ; |
---|
411 | ideal J = -10*x^2-9*x,-8*x^2-4; |
---|
412 | ideal gJ = std(J); |
---|
413 | ideal ggJ = std(gJ); |
---|
414 | reduce (J,gJ ); |
---|
415 | kill rng; |
---|
416 | |
---|
417 | ring rng = integer,x,lp; |
---|
418 | option(noredSB) ; |
---|
419 | option(noredTail) ; |
---|
420 | ideal I = -8*x^3+7*x^2-7*x, 8*x^2+10*x-2; |
---|
421 | ideal gI = std(I); |
---|
422 | ideal ggI = std(gI); |
---|
423 | reduce (I,gI ); // <>0 !! |
---|
424 | lead(gI); |
---|
425 | lead(ggI); |
---|
426 | kill rng; |
---|
427 | |
---|
428 | ring rng = integer,x,lp; |
---|
429 | short = 0 ; |
---|
430 | ideal I = 8*x^3-4,-10*x^3+9*x; |
---|
431 | ideal gI = std(I); |
---|
432 | ideal ggI = std(gI); |
---|
433 | reduce (I,gI ); |
---|
434 | size(gI)== size(ggI) ; |
---|
435 | lead(gI); |
---|
436 | lead(ggI); |
---|
437 | kill rng; |
---|
438 | |
---|
439 | //Github Adi #25 |
---|
440 | |
---|
441 | ring r = integer,(a,d,g,h,i,j),ws(-1,-1,-1,-1,-1,-1); |
---|
442 | ideal inI= gh+2i, dh+j, d+2g+aj, d+2g+ai; |
---|
443 | ideal g= std(inI); |
---|
444 | lead(g); |
---|
445 | reduce(inI,g); |
---|
446 | kill r; |
---|
447 | |
---|
448 | ring rng = (integer),(x,y,z),(ws(-1,-1,-1),C); |
---|
449 | ideal I = 6yz-6,6xy-6yz-8y; |
---|
450 | ideal gI =std(I); |
---|
451 | lead(I);lead(gI); |
---|
452 | reduce(I,gI); |
---|
453 | kill rng; |
---|
454 | |
---|
455 | // Yue's Bug |
---|
456 | |
---|
457 | ring r = 0,(t,x(1..4)),ws(1,-1,-1,-1,-1); |
---|
458 | ideal I = |
---|
459 | 2*x(1)^2+3*x(1)*x(2)+24*x(3)*x(4), |
---|
460 | 8*x(1)^3+x(2)*x(3)*x(4)+18*x(3)^2*x(4); |
---|
461 | I = std(I); |
---|
462 | ring s = integer,(t,x(1..4)),ws(1,-1,-1,-1,-1); |
---|
463 | ideal I = fetch(r,I); |
---|
464 | ideal J = I,2-t; |
---|
465 | ideal J2 = std(J); |
---|
466 | lead(J2); |
---|
467 | reduce(J,J2); |
---|
468 | lead(std(J2)); |
---|
469 | kill r; |
---|
470 | |
---|
471 | // Infinite reduction small example |
---|
472 | |
---|
473 | ring r = integer,(t,x,y),(dp(1),ds); |
---|
474 | ideal i = 6+y+x2,4+x; |
---|
475 | ideal gi = std(i); |
---|
476 | lead(gi); |
---|
477 | reduce(i,gi); |
---|
478 | kill r; |
---|
479 | |
---|
480 | // Intersect with the elimination takes for ever. With the module is immediate |
---|
481 | |
---|
482 | ring rng = integer,(x),dp; |
---|
483 | ideal I = -3*x^2-8; |
---|
484 | ideal J = 9,5*x^2+8; |
---|
485 | option(intersectSyz); |
---|
486 | ideal I_J = intersect(I,J); |
---|
487 | lead(I_J); |
---|
488 | kill rng; |
---|
489 | |
---|
490 | // Github Adi #61 |
---|
491 | |
---|
492 | ring rng = integer,x,lp; |
---|
493 | ideal QQQ = 42*x^2; |
---|
494 | qring QR = QQQ; |
---|
495 | ideal I = 41,-36*x1; |
---|
496 | module syzI = syz (I); |
---|
497 | print(syzI); |
---|
498 | kill rng,QR; |
---|
499 | |
---|
500 | // Github Adi #60 |
---|
501 | |
---|
502 | ring rng = integer,x,dp; |
---|
503 | ideal QQQ = 4*x; |
---|
504 | qring QR = QQQ; |
---|
505 | ideal I = 13; |
---|
506 | ideal J = -7; |
---|
507 | ideal gJ = std(J); |
---|
508 | ideal I_J = intersect(I,J); |
---|
509 | ideal IGJ = I+gJ; |
---|
510 | intersect(I_J, IGJ) ; |
---|
511 | kill rng,QR; |
---|
512 | |
---|
513 | // Github Adi #59 |
---|
514 | |
---|
515 | ring rng = integer,(x,y),lp; |
---|
516 | ideal I = -2*y^2+11,14*x^2+5*y; |
---|
517 | ideal J = x^2-3*x,9*x*y+2*y^2; |
---|
518 | ideal I_J = intersect(I,J); |
---|
519 | lead(I_J); |
---|
520 | reduce(I_J,std(I)); |
---|
521 | reduce(I_J,std(J)); |
---|
522 | kill rng; |
---|
523 | |
---|
524 | // Github Adi #58 |
---|
525 | |
---|
526 | ring rng = (integer),(x(1)),(lp(1),C); |
---|
527 | short = 0 ; |
---|
528 | ideal QQQ = 4*x(1); |
---|
529 | qring QR = QQQ; |
---|
530 | ideal I = 13; |
---|
531 | ideal J = -7; |
---|
532 | ideal gI = std(I); |
---|
533 | ideal gJ = std(J); |
---|
534 | ideal I_J = intersect(I,J); |
---|
535 | intersect(I_J, I+gJ); |
---|
536 | kill rng; |
---|
537 | |
---|
538 | // Github Adi #56 |
---|
539 | |
---|
540 | ring rng = (integer),(x,y),(ls(2),C); |
---|
541 | ideal I = -8-y^2+13*x^2*y,-12+2*x-9*x^2*y; |
---|
542 | ideal gI = std(I); |
---|
543 | lead(gI); |
---|
544 | reduce(I,gI); |
---|
545 | kill rng; |
---|
546 | |
---|
547 | ring rng = (integer),(x,y,z),(dp(3),C); |
---|
548 | ideal I = -10*y^2*z^2-7*x*y-2*x+2, 7*x*y^3+11, 15*x*y^2*z-8*y*z-11; |
---|
549 | ideal gI = std(I); |
---|
550 | reduce(I,gI); |
---|
551 | I = 8*y^2*z+3*x*z, -3*x^2*z-9*y^2*z+3, 5*x*z^2-9*y*z+2*z; |
---|
552 | gI = std(I); |
---|
553 | reduce(I,gI); |
---|
554 | kill rng; |
---|
555 | |
---|
556 | // Github Adi #51 |
---|
557 | |
---|
558 | ring rng = (integer),(x(1),x(2)),(ls(1),ls(1),C); |
---|
559 | ideal I = -36+26*x(1)-29*x(1)^3,26+6*x(2)-13*x(1); |
---|
560 | ideal J = 44+28*x(1)*x(2); |
---|
561 | ideal gI = std(I); |
---|
562 | ideal gJ = std(J); |
---|
563 | lead(gI); |
---|
564 | lead(gJ); |
---|
565 | std(gI); |
---|
566 | reduce(I,gI); |
---|
567 | reduce(J,gJ); |
---|
568 | kill rng; |
---|
569 | |
---|
570 | ring rng = (integer),(x,y,z),(Ds(1),Ds(2),C); |
---|
571 | option(redSB); |
---|
572 | ideal J = -3+4*z-x,-2*z+y^2-3*z^3; |
---|
573 | ideal gJ = std(J); |
---|
574 | lead(gJ); |
---|
575 | reduce (J,gJ ) ; |
---|
576 | kill rng; |
---|
577 | |
---|
578 | ring rng = (integer),(x(1),x(2),x(3)),(is(2),is(1),C); |
---|
579 | ideal I = 2*x(3)+15*x(3)^3+x(1),-15+13*x(3)+6*x(1); |
---|
580 | ideal gI = std(I); |
---|
581 | lead(gI); |
---|
582 | reduce (I,gI ); |
---|
583 | kill rng; |
---|
584 | |
---|
585 | // Singular Trac: #719 |
---|
586 | |
---|
587 | ring r = integer,(t,x(1..5)),ws(1,-1,-1,-1,-1,-1); |
---|
588 | poly h = 3*t*x(2)*x(4)-21*t*x(1)*x(5)-12*t^2*x(1)*x(2)-2*t^2*x(1)*x(3)-6*t^2*x(1)*x(4); |
---|
589 | ideal G = |
---|
590 | x(2)+6*x(4)+7*x(5)+4*t*x(2), |
---|
591 | x(2)+8*x(3)+7*x(5)+t*x(2), |
---|
592 | t*x(1)+3*t*x(2)+t^2*x(1), |
---|
593 | t*x(4)+21*t*x(5)+12*t^2*x(2)+2*t^2*x(3)+7*t^2*x(4), |
---|
594 | 2-t; |
---|
595 | ideal Gstd = std(G); |
---|
596 | lead(Gstd); |
---|
597 | reduce(h,Gstd); |
---|
598 | reduce(G,Gstd); |
---|
599 | kill r; |
---|
600 | |
---|
601 | // Memory leak |
---|
602 | |
---|
603 | ring r=integer,t,ds; |
---|
604 | ideal I = 2,3-t; |
---|
605 | int i; |
---|
606 | bigint m=memory(0); |
---|
607 | for(i=1; i<100; i++) |
---|
608 | { |
---|
609 | ideal II = std(I); |
---|
610 | II = reduce(I,II); |
---|
611 | kill II; |
---|
612 | } |
---|
613 | m-memory(0); // should be 0 |
---|
614 | |
---|
615 | // Singular Trac: #747 |
---|
616 | |
---|
617 | ring rng = (integer),(x,y),(Ds(2),C); |
---|
618 | intvec op = 67108864,16787537; |
---|
619 | ideal I = 6-x^2*y, -2-3*x+2*y; |
---|
620 | ideal gI = std(I); |
---|
621 | lead(gI); |
---|
622 | lead(std(gI)); |
---|
623 | reduce(I,gI); |
---|
624 | kill rng; |
---|
625 | |
---|
626 | // Github Adi: #29 |
---|
627 | |
---|
628 | ring rng = (integer),(x,y,z),lp; |
---|
629 | option(redSB); |
---|
630 | option(redTail); |
---|
631 | ideal I = -4*z+10; |
---|
632 | ideal J = -7*x+4*z,-13; |
---|
633 | ideal gI = std(I); |
---|
634 | ideal gJ = std(J); |
---|
635 | ideal IJ = intersect(I,J) ; |
---|
636 | ideal gIJ = intersect( gI,gJ ); // falsch! |
---|
637 | ASSUME(0, idealsEqual(IJ , gIJ ) ) ; |
---|
638 | lead(gI); |
---|
639 | lead(gJ); |
---|
640 | lead(IJ); |
---|
641 | lead(gIJ); |
---|
642 | attrib(gI,"isSB",0); |
---|
643 | attrib(gJ,"isSB",0); |
---|
644 | ideal ngIJ = intersect(gI,gJ ); // wrong |
---|
645 | kill rng; |
---|
646 | |
---|
647 | // Janko's Beispiel |
---|
648 | |
---|
649 | ring r =integer,(z,x,y),lp; |
---|
650 | poly f = z7x5 + z2xy9 + zy11 + x3y9; |
---|
651 | ideal ii = diff(f,x),diff(f,y),diff(f,z); |
---|
652 | ideal I = std(ii); |
---|
653 | lead(I); |
---|
654 | kill r; |
---|
655 | |
---|
656 | tst_status(1);$; |
---|
657 | |
---|