1 | // Test File for 'zeroset.lib" |
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2 | // |
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3 | // Implementation by : Thomas Bayer |
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4 | // Curretn Adress: |
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5 | // Institut fuer Informatik, Technische Universitaet Muenchen |
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6 | // www: http://wwwmayr.informatik.tu-muenchen.de/personen/bayert/ |
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7 | // email : bayert@in.tum.de |
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8 | // |
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9 | // Last change 10.12.2000 |
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10 | // |
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11 | // written in the frame of the diploma thesis (advisor: Prof. Gert-Martin Greuel) |
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12 | // "Computations of moduli spaces of semiquasihomogenous singularities and an |
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13 | // implementation in Singular" |
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14 | // Arbeitsgruppe Algebraische Geometrie, Fachbereich Mathematik, |
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15 | // Universitaet Kaiserslautern |
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16 | /////////////////////////////////////////////////////////////////////////////// |
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17 | |
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18 | LIB "tst.lib"; |
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19 | LIB "zeroset.lib"; |
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20 | |
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21 | tst_init(); |
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22 | tst_ignore("CVS ID $Id: zeroset1.tst,v 1.2 2009-04-14 10:29:45 Singular Exp $"); |
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23 | |
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24 | |
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25 | |
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26 | proc TestzerosetLIB(S) |
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27 | // plug in the elements from the zero-set in the generators of the ideal |
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28 | // result should be 0,0,...,0. |
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29 | { |
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30 | |
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31 | setring S; |
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32 | map F; |
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33 | |
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34 | print(" #Points = " + string(vdim(std(id))) + "; #Solutions = " + string(size(theZeroset))); |
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35 | print(" minpoly = " + string(minpoly)); |
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36 | print(" ideal = " + string(id)); |
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37 | |
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38 | |
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39 | for(int i = 1; i <= size(theZeroset); i++) { |
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40 | F = theZeroset[i]; |
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41 | print(string(theZeroset[i]) + " --> " + string(F(id))); |
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42 | } |
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43 | } |
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44 | |
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45 | // example 1 |
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46 | |
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47 | ring R = 0,(x,y,z), lp; |
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48 | ideal I = x2-1,y3-1,z-2x; |
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49 | |
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50 | def S = zeroSet(I);TestzerosetLIB(S); |
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51 | setring S; |
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52 | minpoly; |
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53 | id; |
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54 | theZeroset; |
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55 | |
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56 | kill R; |
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57 | kill S; |
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58 | //tst_status(); |
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59 | |
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60 | // example 2 |
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61 | |
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62 | ring R = 0,(x,y,z), lp; |
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63 | ideal I = x3-1,3y-x,z4-1; |
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64 | |
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65 | def S = zeroSet(I);TestzerosetLIB(S); |
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66 | setring S; |
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67 | minpoly; |
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68 | id; |
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69 | theZeroset; |
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70 | |
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71 | kill R; |
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72 | kill S; |
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73 | //tst_status(); |
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74 | |
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75 | // example 3 |
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76 | |
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77 | ring R = 0, (x(1..5)), lp; |
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78 | ideal I = x(1)^2+1,x(2)^4-1,x(3)-x(4),x(4)^2+1,x(5)-x(4); |
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79 | |
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80 | def S = zeroSet(I);TestzerosetLIB(S); |
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81 | setring S; |
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82 | minpoly; |
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83 | id; |
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84 | theZeroset; |
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85 | |
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86 | kill R; |
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87 | kill S; |
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88 | //tst_status(); |
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89 | |
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90 | // example 4 |
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91 | |
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92 | ring R = (0,a),(x,y), lp; |
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93 | minpoly = a2+1; |
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94 | ideal I = x2-a,y-2x; |
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95 | |
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96 | def S = zeroSet(I);TestzerosetLIB(S); |
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97 | setring S; |
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98 | minpoly; |
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99 | id; |
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100 | theZeroset; |
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101 | |
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102 | kill R; |
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103 | kill S; |
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104 | //tst_status(); |
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105 | |
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106 | // example 5 |
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107 | |
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108 | ring R = (0,a),(x,y,z), lp; |
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109 | minpoly = a2+a+1; |
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110 | ideal I = x3-1,a*y^2-x,z^2-a*y; |
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111 | |
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112 | def S = zeroSet(I);TestzerosetLIB(S); |
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113 | setring S; |
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114 | minpoly; |
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115 | id; |
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116 | theZeroset; |
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117 | |
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118 | kill R; |
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119 | kill S; |
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120 | //tst_status(); |
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121 | |
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122 | // example 6 |
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123 | |
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124 | ring R = (0,a),(x,y,z), lp; |
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125 | minpoly = a2+1; |
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126 | ideal I = x2-2,a*y^2-2*x,z^2 - a; // 2 |
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127 | |
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128 | def S = zeroSet(I);TestzerosetLIB(S); |
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129 | setring S; |
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130 | minpoly; |
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131 | id; |
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132 | theZeroset; |
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133 | |
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134 | kill R; |
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135 | kill S; |
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136 | //tst_status(); |
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137 | |
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138 | // example 7 |
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139 | |
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140 | ring R = (0,a),(x(1..5)), lp; |
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141 | minpoly = a2+a+1; |
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142 | ideal I = x(1)^2 - 2,x(2) -a*x(1), x(3)^2 + 1, x(4)^2 + a, a*x(5) - x(1); |
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143 | |
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144 | def S = zeroSet(I);TestzerosetLIB(S); |
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145 | setring S; |
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146 | minpoly; |
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147 | id; |
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148 | theZeroset; |
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149 | |
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150 | kill S; |
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151 | |
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152 | setring R; |
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153 | def S = zeroSet(I, 1);TestzerosetLIB(S); |
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154 | setring S; |
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155 | minpoly; |
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156 | id; |
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157 | theZeroset; |
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158 | |
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159 | kill R; |
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160 | kill S; |
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161 | |
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162 | //tst_status(); |
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163 | |
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164 | // example 8 |
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165 | |
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166 | ring R = (0,a),(s(1..4)), lp; |
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167 | minpoly = a2+1; |
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168 | ideal I = s(3)*s(4),s(2)*s(4),s(1)*s(3),s(1)*s(2),s(3)^8+s(4)^8-1,s(2)^8+s(4)^8-1,s(1)^8-s(4)^8,s(4)^9-s(4),s(1)*s(4)^8-s(1); |
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169 | |
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170 | def S = zeroSet(I);TestzerosetLIB(S); |
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171 | setring S; |
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172 | minpoly; |
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173 | id; |
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174 | theZeroset; |
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175 | |
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176 | kill S; |
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177 | |
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178 | setring R; |
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179 | def S = zeroSet(I, 1);TestzerosetLIB(S); |
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180 | setring S; |
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181 | minpoly; |
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182 | id; |
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183 | theZeroset; |
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184 | |
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185 | kill S; |
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186 | |
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187 | tst_status(1); $ |
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