1 | #include <callgfanlib_conversion.h> |
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2 | #include <singularWishlist.h> |
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3 | #include <tropicalDebug.h> |
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4 | #include <containsMonomial.h> |
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5 | #include <tropical.h> |
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6 | #include <initial.h> |
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7 | #include <lift.h> |
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8 | #include <groebnerCone.h> |
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9 | #include <tropicalStrategy.h> |
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10 | #include <tropicalCurves.h> |
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11 | #include <bbcone.h> |
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12 | #include <tropicalVarietyOfPolynomials.h> |
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13 | #include <tropicalVariety.h> |
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14 | #include <tropicalStrategy.h> |
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15 | |
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16 | |
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17 | groebnerCone groebnerStartingCone(const tropicalStrategy& currentStrategy) |
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18 | { |
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19 | groebnerCone sigma(currentStrategy.getStartingIdeal(), currentStrategy.getStartingRing(), currentStrategy); |
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20 | return sigma; |
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21 | } |
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22 | |
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23 | |
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24 | /** |
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25 | * Computes a starting point outside the lineatliy space by traversing the Groebner fan, |
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26 | * checking each cone whether it contains a ray in the tropical variety. |
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27 | * Returns a point in the tropical variety and a maximal Groebner cone containing the point. |
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28 | **/ |
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29 | std::pair<gfan::ZVector,groebnerCone> tropicalStartingPoint(const ideal I, const ring r, const tropicalStrategy& currentStrategy) |
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30 | { |
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31 | // start by computing a maximal Groebner cone and |
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32 | // check whether one of its rays lies in the tropical variety |
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33 | const groebnerCone sigma(I,r,currentStrategy); |
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34 | gfan::ZVector startingPoint = sigma.tropicalPoint(); |
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35 | if (startingPoint.size() > 0) |
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36 | return std::make_pair(startingPoint,sigma); |
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37 | |
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38 | // if not, traverse the groebnerFan and until such a cone is found |
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39 | // and return the maximal cone together with a point in its ray |
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40 | groebnerCones groebnerFan; |
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41 | groebnerCones workingList; |
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42 | workingList.insert(sigma); |
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43 | while (!workingList.empty()) |
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44 | { |
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45 | const groebnerCone sigma = *(workingList.begin()); |
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46 | groebnerCones neighbours = sigma.groebnerNeighbours(); |
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47 | for (groebnerCones::iterator tau = neighbours.begin(); tau!=neighbours.end(); tau++) |
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48 | { |
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49 | if (groebnerFan.count(*tau) == 0) |
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50 | { |
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51 | if (workingList.count(*tau) == 0) |
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52 | { |
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53 | startingPoint = tau->tropicalPoint(); |
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54 | if (startingPoint.size() > 0) |
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55 | return std::make_pair(startingPoint,*tau); |
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56 | } |
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57 | workingList.insert(*tau); |
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58 | } |
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59 | } |
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60 | groebnerFan.insert(sigma); |
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61 | workingList.erase(sigma); |
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62 | } |
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63 | |
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64 | // return some trivial output, if such a cone cannot be found |
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65 | gfan::ZVector emptyVector = gfan::ZVector(0); |
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66 | groebnerCone emptyCone = groebnerCone(); |
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67 | return std::pair<gfan::ZVector,groebnerCone>(emptyVector,emptyCone); |
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68 | } |
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69 | |
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70 | |
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71 | /** |
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72 | * Computes a starting point outside the lineatliy space by traversing the Groebner fan, |
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73 | * checking each cone whether it contains a ray in the tropical variety. |
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74 | * Returns a point in the tropical variety and a maximal Groebner cone containing the point. |
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75 | **/ |
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76 | std::pair<gfan::ZVector,groebnerCone> tropicalStartingDataViaGroebnerFan(const ideal I, const ring r, const tropicalStrategy& currentStrategy) |
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77 | { |
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78 | // start by computing a maximal Groebner cone and |
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79 | // check whether one of its rays lies in the tropical variety |
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80 | const groebnerCone sigma(I,r,currentStrategy); |
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81 | gfan::ZVector startingPoint = sigma.tropicalPoint(); |
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82 | if (startingPoint.size() > 0) |
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83 | return std::make_pair(startingPoint,sigma); |
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84 | |
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85 | // if not, traverse the groebnerFan and until such a cone is found |
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86 | // and return the maximal cone together with a point in its ray |
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87 | groebnerCones groebnerFan; |
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88 | groebnerCones workingList; |
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89 | workingList.insert(sigma); |
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90 | while (!workingList.empty()) |
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91 | { |
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92 | const groebnerCone sigma = *(workingList.begin()); |
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93 | groebnerCones neighbours = sigma.groebnerNeighbours(); |
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94 | for (groebnerCones::iterator tau = neighbours.begin(); tau!=neighbours.end(); tau++) |
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95 | { |
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96 | if (groebnerFan.count(*tau) == 0) |
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97 | { |
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98 | if (workingList.count(*tau) == 0) |
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99 | { |
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100 | startingPoint = tau->tropicalPoint(); |
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101 | if (startingPoint.size() > 0) |
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102 | return std::make_pair(startingPoint,*tau); |
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103 | } |
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104 | workingList.insert(*tau); |
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105 | } |
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106 | } |
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107 | groebnerFan.insert(sigma); |
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108 | workingList.erase(sigma); |
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109 | } |
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110 | |
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111 | // return some trivial output, if such a cone cannot be found |
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112 | gfan::ZVector emptyVector = gfan::ZVector(0); |
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113 | groebnerCone emptyCone = groebnerCone(); |
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114 | return std::pair<gfan::ZVector,groebnerCone>(emptyVector,emptyCone); |
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115 | } |
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116 | |
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117 | BOOLEAN positiveTropicalStartingPoint(leftv res, leftv args) |
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118 | { |
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119 | leftv u = args; |
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120 | if ((u!=NULL) && (u->Typ()==IDEAL_CMD)) |
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121 | { |
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122 | ideal I = (ideal) u->Data(); |
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123 | if ((I->m[0]!=NULL) && (idElem(I)==1)) |
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124 | { |
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125 | tropicalStrategy currentStrategy(I,currRing); |
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126 | poly g = I->m[0]; |
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127 | std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,¤tStrategy); |
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128 | for (std::set<gfan::ZCone>::iterator zc=Tg.begin(); zc!=Tg.end(); zc++) |
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129 | { |
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130 | gfan::ZMatrix ray = zc->extremeRays(); |
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131 | for (int i=0; i<ray.getHeight(); i++) |
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132 | { |
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133 | if (ray[i].toVector().isPositive()) |
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134 | { |
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135 | res->rtyp = BIGINTMAT_CMD; |
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136 | res->data = (void*) zVectorToBigintmat(ray[i].toVector()); |
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137 | return FALSE; |
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138 | } |
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139 | } |
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140 | } |
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141 | res->rtyp = BIGINTMAT_CMD; |
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142 | res->data = (void*) zVectorToBigintmat(gfan::ZVector(0)); |
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143 | return FALSE; |
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144 | } |
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145 | WerrorS("positiveTropicalStartingPoint: ideal not principal"); |
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146 | return TRUE; |
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147 | } |
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148 | WerrorS("positiveTropicalStartingPoint: unexpected parameters"); |
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149 | return TRUE; |
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150 | } |
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151 | |
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152 | BOOLEAN nonNegativeTropicalStartingPoint(leftv res, leftv args) |
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153 | { |
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154 | leftv u = args; |
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155 | if ((u!=NULL) && (u->Typ()==IDEAL_CMD)) |
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156 | { |
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157 | ideal I = (ideal) u->Data(); |
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158 | if ((I->m[0]!=NULL) && (idElem(I)==1)) |
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159 | { |
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160 | tropicalStrategy currentStrategy(I,currRing); |
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161 | poly g = I->m[0]; |
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162 | std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,¤tStrategy); |
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163 | for (std::set<gfan::ZCone>::iterator zc=Tg.begin(); zc!=Tg.end(); zc++) |
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164 | { |
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165 | gfan::ZMatrix ray = zc->extremeRays(); |
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166 | for (int i=0; i<ray.getHeight(); i++) |
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167 | { |
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168 | if (ray[i].toVector().isNonNegative()) |
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169 | { |
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170 | res->rtyp = BIGINTMAT_CMD; |
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171 | res->data = (void*) zVectorToBigintmat(ray[i].toVector()); |
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172 | return FALSE; |
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173 | } |
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174 | } |
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175 | } |
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176 | res->rtyp = BIGINTMAT_CMD; |
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177 | res->data = (void*) zVectorToBigintmat(gfan::ZVector(0)); |
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178 | return FALSE; |
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179 | } |
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180 | WerrorS("nonNegativeTropicalStartingPoint: ideal not principal"); |
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181 | return TRUE; |
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182 | } |
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183 | WerrorS("nonNegativeTropicalStartingPoint: unexpected parameters"); |
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184 | return TRUE; |
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185 | } |
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186 | |
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187 | BOOLEAN negativeTropicalStartingPoint(leftv res, leftv args) |
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188 | { |
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189 | leftv u = args; |
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190 | if ((u!=NULL) && (u->Typ()==IDEAL_CMD)) |
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191 | { |
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192 | ideal I = (ideal) u->Data(); |
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193 | if ((I->m[0]!=NULL) && (idElem(I)==1)) |
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194 | { |
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195 | tropicalStrategy currentStrategy(I,currRing); |
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196 | poly g = I->m[0]; |
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197 | std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,¤tStrategy); |
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198 | for (std::set<gfan::ZCone>::iterator zc=Tg.begin(); zc!=Tg.end(); zc++) |
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199 | { |
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200 | gfan::ZMatrix ray = zc->extremeRays(); |
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201 | for (int i=0; i<ray.getHeight(); i++) |
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202 | { |
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203 | gfan::ZVector negatedRay = gfan::Integer(-1)*ray[i].toVector(); |
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204 | if (negatedRay.isPositive()) |
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205 | { |
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206 | res->rtyp = BIGINTMAT_CMD; |
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207 | res->data = (void*) zVectorToBigintmat(ray[i].toVector()); |
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208 | return FALSE; |
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209 | } |
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210 | } |
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211 | } |
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212 | res->rtyp = BIGINTMAT_CMD; |
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213 | res->data = (void*) zVectorToBigintmat(gfan::ZVector(0)); |
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214 | return FALSE; |
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215 | } |
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216 | WerrorS("negativeTropicalStartingPoint: ideal not principal"); |
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217 | return TRUE; |
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218 | } |
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219 | WerrorS("negativeTropicalStartingPoint: unexpected parameters"); |
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220 | return TRUE; |
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221 | } |
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222 | |
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223 | BOOLEAN nonPositiveTropicalStartingPoint(leftv res, leftv args) |
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224 | { |
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225 | leftv u = args; |
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226 | if ((u!=NULL) && (u->Typ()==IDEAL_CMD)) |
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227 | { |
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228 | ideal I = (ideal) u->Data(); |
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229 | if ((I->m[0]!=NULL) && (idElem(I)==1)) |
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230 | { |
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231 | tropicalStrategy currentStrategy(I,currRing); |
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232 | poly g = I->m[0]; |
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233 | std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,¤tStrategy); |
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234 | for (std::set<gfan::ZCone>::iterator zc=Tg.begin(); zc!=Tg.end(); zc++) |
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235 | { |
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236 | gfan::ZMatrix ray = zc->extremeRays(); |
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237 | for (int i=0; i<ray.getHeight(); i++) |
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238 | { |
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239 | gfan::ZVector negatedRay = gfan::Integer(-1)*ray[i].toVector(); |
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240 | if (negatedRay.isNonNegative()) |
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241 | { |
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242 | res->rtyp = BIGINTMAT_CMD; |
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243 | res->data = (void*) zVectorToBigintmat(ray[i]); |
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244 | return FALSE; |
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245 | } |
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246 | } |
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247 | } |
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248 | res->rtyp = BIGINTMAT_CMD; |
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249 | res->data = (void*) zVectorToBigintmat(gfan::ZVector(0)); |
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250 | return FALSE; |
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251 | } |
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252 | WerrorS("nonPositiveTropicalStartingPoint: ideal not principal"); |
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253 | return TRUE; |
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254 | } |
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255 | WerrorS("nonPositiveTropicalStartingPoint: unexpected parameters"); |
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256 | return TRUE; |
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257 | } |
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258 | |
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259 | BOOLEAN tropicalStartingPoint(leftv res, leftv args) |
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260 | { |
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261 | leftv u = args; |
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262 | if ((u!=NULL) && (u->Typ()==IDEAL_CMD)) |
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263 | { |
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264 | ideal I = (ideal) u->Data(); |
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265 | tropicalStrategy currentStrategy(I,currRing); |
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266 | if ((I->m[0]!=NULL) && (idElem(I)==1)) |
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267 | { |
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268 | poly g = I->m[0]; |
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269 | std::set<gfan::ZCone> Tg = tropicalVariety(g,currRing,¤tStrategy); |
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270 | if (Tg.empty()) |
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271 | { |
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272 | res->rtyp = BIGINTMAT_CMD; |
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273 | res->data = (void*) zVectorToBigintmat(gfan::ZVector(0)); |
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274 | return FALSE; |
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275 | } |
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276 | gfan::ZCone C = *(Tg.begin()); |
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277 | gfan::ZMatrix rays = C.extremeRays(); |
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278 | if (rays.getHeight()==0) |
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279 | { |
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280 | gfan::ZMatrix lin = C.generatorsOfLinealitySpace(); |
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281 | res->rtyp = BIGINTMAT_CMD; |
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282 | res->data = (void*) zVectorToBigintmat(lin[0]); |
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283 | return FALSE; |
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284 | } |
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285 | res->rtyp = BIGINTMAT_CMD; |
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286 | res->data = (void*) zVectorToBigintmat(rays[0]); |
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287 | return FALSE; |
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288 | } |
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289 | gfan::ZCone C0 = currentStrategy.getHomogeneitySpace(); |
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290 | if (C0.dimension()==currentStrategy.getExpectedDimension()) |
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291 | { |
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292 | gfan::ZMatrix lin = C0.generatorsOfLinealitySpace(); |
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293 | res->rtyp = BIGINTMAT_CMD; |
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294 | res->data = (void*) zVectorToBigintmat(lin[0]); |
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295 | return FALSE; |
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296 | } |
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297 | std::pair<gfan::ZVector,groebnerCone> startingData = tropicalStartingDataViaGroebnerFan(I,currRing,currentStrategy); |
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298 | gfan::ZVector startingPoint = startingData.first; |
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299 | res->rtyp = BIGINTMAT_CMD; |
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300 | res->data = (void*) zVectorToBigintmat(startingPoint); |
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301 | return FALSE; |
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302 | } |
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303 | WerrorS("tropicalStartingPoint: unexpected parameters"); |
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304 | return TRUE; |
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305 | } |
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306 | |
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307 | /*** |
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308 | * returs the lineality space of the Groebner fan |
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309 | **/ |
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310 | static gfan::ZCone linealitySpaceOfGroebnerFan(const ideal I, const ring r) |
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311 | { |
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312 | int n = rVar(r); |
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313 | gfan::ZMatrix equations = gfan::ZMatrix(0,n); |
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314 | int* expv = (int*) omAlloc((n+1)*sizeof(int)); |
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315 | int k = IDELEMS(I); |
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316 | for (int i=0; i<k; i++) |
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317 | { |
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318 | poly g = I->m[i]; |
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319 | if (g) |
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320 | { |
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321 | p_GetExpV(g,expv,r); |
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322 | gfan::ZVector leadexp = intStar2ZVector(n,expv); |
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323 | for (pIter(g); g; pIter(g)) |
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324 | { |
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325 | p_GetExpV(g,expv,r); |
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326 | equations.appendRow(leadexp-intStar2ZVector(n,expv)); |
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327 | } |
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328 | } |
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329 | } |
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330 | omFreeSize(expv,(n+1)*sizeof(int)); |
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331 | return gfan::ZCone(gfan::ZMatrix(0,n),equations); |
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332 | } |
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333 | |
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334 | /*** |
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335 | * Computes a starting cone in the tropical variety. |
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336 | **/ |
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337 | groebnerCone tropicalStartingCone(const tropicalStrategy& currentStrategy) |
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338 | { |
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339 | ring r = currentStrategy.getStartingRing(); |
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340 | ideal I = currentStrategy.getStartingIdeal(); |
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341 | currentStrategy.reduce(I,r); |
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342 | if (currentStrategy.isValuationTrivial()) |
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343 | { |
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344 | // copy the data, so that it be deleted when passed to the loop |
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345 | // s <- r |
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346 | // inI <- I |
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347 | ring s = rCopy(r); |
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348 | int k = IDELEMS(I); ideal inI = idInit(k); |
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349 | nMapFunc identityMap = n_SetMap(r->cf,s->cf); |
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350 | for (int i=0; i<k; i++) |
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351 | { |
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352 | if(I->m[i]!=NULL) |
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353 | { |
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354 | inI->m[i] = p_PermPoly(I->m[i],NULL,r,s,identityMap,NULL,0); |
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355 | } |
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356 | } |
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357 | |
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358 | // repeatedly computes a point in the tropical variety outside the lineality space, |
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359 | // take the initial ideal with respect to it |
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360 | // and check whether the dimension of its homogeneity space |
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361 | // equals the dimension of the tropical variety |
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362 | gfan::ZCone zc = linealitySpaceOfGroebnerFan(inI,s); |
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363 | gfan::ZVector startingPoint; groebnerCone ambientMaximalCone; |
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364 | if (zc.dimension()>=currentStrategy.getExpectedDimension()) |
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365 | { |
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366 | // check whether the lineality space is contained in the tropical variety |
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367 | // i.e. whether the ideal does not contain a monomial |
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368 | poly mon = checkForMonomialViaSuddenSaturation(I,r); |
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369 | if (mon) |
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370 | { |
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371 | groebnerCone emptyCone = groebnerCone(); |
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372 | p_Delete(&mon,r); |
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373 | id_Delete(&inI,s); |
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374 | return emptyCone; |
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375 | } |
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376 | groebnerCone startingCone(inI,inI,s,currentStrategy); |
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377 | id_Delete(&inI,s); |
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378 | return startingCone; |
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379 | } |
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380 | while (zc.dimension()<currentStrategy.getExpectedDimension()) |
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381 | { |
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382 | // compute a point in the tropical variety outside the lineality space |
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383 | std::pair<gfan::ZVector,groebnerCone> startingData = tropicalStartingDataViaGroebnerFan(inI,s,currentStrategy); |
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384 | startingPoint = startingData.first; |
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385 | ambientMaximalCone = groebnerCone(startingData.second); |
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386 | |
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387 | id_Delete(&inI,s); rDelete(s); |
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388 | inI = ambientMaximalCone.getPolynomialIdeal(); |
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389 | s = ambientMaximalCone.getPolynomialRing(); |
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390 | |
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391 | // compute the initial ideal with respect to the weight |
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392 | inI = initial(inI,s,startingPoint); |
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393 | zc = linealitySpaceOfGroebnerFan(inI,s); |
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394 | } |
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395 | |
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396 | // once the dimension of the homogeneity space equals that of the tropical variety |
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397 | // we know that we have an initial ideal with respect to a weight |
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398 | // in the relative interior of a maximal cone in the tropical variety |
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399 | // from this we can read of the inequalities and equations |
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400 | |
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401 | // but before doing so, we must lift the generating set of inI |
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402 | // to a generating set of I |
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403 | ideal J = lift(I,r,inI,s); // todo: use computeLift from tropicalStrategy |
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404 | groebnerCone startingCone(J,inI,s,currentStrategy); |
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405 | id_Delete(&inI,s); |
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406 | id_Delete(&J,s); |
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407 | |
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408 | // assume(checkContainmentInTropicalVariety(startingCone)); |
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409 | return startingCone; |
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410 | } |
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411 | else |
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412 | { |
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413 | // copy the data, so that it be deleted when passed to the loop |
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414 | // s <- r |
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415 | // inJ <- I |
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416 | ring s = rCopy(r); |
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417 | int k = IDELEMS(I); ideal inJ = idInit(k); |
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418 | nMapFunc identityMap = n_SetMap(r->cf,s->cf); |
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419 | for (int i=0; i<k; i++) |
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420 | { |
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421 | if(I->m[i]!=NULL) |
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422 | { |
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423 | inJ->m[i] = p_PermPoly(I->m[i],NULL,r,s,identityMap,NULL,0); |
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424 | } |
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425 | } |
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426 | |
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427 | // and check whether the dimension of its homogeneity space |
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428 | // equals the dimension of the tropical variety |
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429 | gfan::ZCone zc = linealitySpaceOfGroebnerFan(inJ,s); |
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430 | if (zc.dimension()>=currentStrategy.getExpectedDimension()) |
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431 | { // this shouldn't happen as trivial cases should be caught beforehand |
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432 | // this is the case that the tropical variety consists soely out of the lineality space |
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433 | poly mon = checkForMonomialViaSuddenSaturation(I,r); |
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434 | if (mon) |
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435 | { |
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436 | groebnerCone emptyCone = groebnerCone(); |
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437 | p_Delete(&mon,r); |
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438 | return emptyCone; |
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439 | } |
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440 | groebnerCone startingCone(I,inJ,s,currentStrategy); |
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441 | id_Delete(&inJ,s); |
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442 | rDelete(s); |
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443 | return startingCone; |
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444 | } |
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445 | |
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446 | // compute a point in the tropical variety outside the lineality space |
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447 | // compute the initial ideal with respect to the weight |
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448 | std::pair<gfan::ZVector,groebnerCone> startingData = tropicalStartingDataViaGroebnerFan(inJ,s,currentStrategy); |
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449 | gfan::ZVector startingPoint = startingData.first; |
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450 | groebnerCone ambientMaximalCone = groebnerCone(startingData.second); |
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451 | id_Delete(&inJ,s); rDelete(s); |
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452 | inJ = ambientMaximalCone.getPolynomialIdeal(); |
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453 | s = ambientMaximalCone.getPolynomialRing(); |
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454 | inJ = initial(inJ,s,startingPoint); |
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455 | ideal inI = initial(I,r,startingPoint); |
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456 | zc = linealitySpaceOfGroebnerFan(inJ,s); |
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457 | |
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458 | // and check whether the dimension of its homogeneity space |
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459 | // equals the dimension of the tropical variety |
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460 | if (zc.dimension()==currentStrategy.getExpectedDimension()) |
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461 | { // this case shouldn't happen as trivial cases should be caught beforehand |
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462 | // this is the case that the tropical variety has a one-codimensional lineality space |
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463 | ideal J = lift(I,r,inJ,s); // todo: use computeLift from tropicalStrategy |
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464 | groebnerCone startingCone(J,inJ,s,currentStrategy); |
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465 | id_Delete(&inJ,s); |
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466 | id_Delete(&J,s); |
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467 | return startingCone; |
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468 | } |
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469 | |
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470 | // from this point on, inJ contains the uniformizing parameter, |
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471 | // hence it contains a monomial if and only if its residue over the residue field does. |
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472 | // so we will switch to the residue field |
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473 | ring rShortcut = rCopy0(r); |
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474 | nKillChar(rShortcut->cf); |
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475 | rShortcut->cf = nCopyCoeff((currentStrategy.getShortcutRing())->cf); |
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476 | rComplete(rShortcut); |
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477 | rTest(rShortcut); |
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478 | k = IDELEMS(inJ); |
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479 | ideal inJShortcut = idInit(k); |
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480 | nMapFunc takingResidues = n_SetMap(s->cf,rShortcut->cf); |
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481 | for (int i=0; i<k; i++) |
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482 | { |
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483 | if(inJ->m[i]!=NULL) |
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484 | { |
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485 | inJShortcut->m[i] = p_PermPoly(inJ->m[i],NULL,s,rShortcut,takingResidues,NULL,0); |
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486 | } |
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487 | } |
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488 | idSkipZeroes(inJShortcut); |
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489 | id_Delete(&inJ,s); |
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490 | |
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491 | // we are interested in a maximal cone of the tropical variety of inJShortcut |
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492 | // this basically equivalent to the case without valuation (or constant coefficient case) |
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493 | // except that our ideal is still only homogeneous in the later variables, |
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494 | // hence we set the optional parameter completelyHomogeneous as 'false' |
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495 | tropicalStrategy shortcutStrategy(inJShortcut,rShortcut,false); |
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496 | groebnerCone startingConeShortcut = tropicalStartingCone(shortcutStrategy); |
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497 | id_Delete(&inJShortcut,rShortcut); rDelete(rShortcut); |
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498 | |
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499 | // now we need to obtain the initial of the residue of inJ |
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500 | // with respect to a weight in the tropical cone, |
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501 | // and obtain the initial of inJ with respect to the same weight |
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502 | ring sShortcut = startingConeShortcut.getPolynomialRing(); |
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503 | inJShortcut = startingConeShortcut.getPolynomialIdeal(); |
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504 | gfan::ZCone zd = startingConeShortcut.getPolyhedralCone(); |
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505 | gfan::ZVector interiorPoint = startingConeShortcut.getInteriorPoint(); |
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506 | inJShortcut = initial(inJShortcut,sShortcut,interiorPoint); |
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507 | inI = initial(inI,r,interiorPoint); |
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508 | |
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509 | s = rCopy0(sShortcut); // s will be a ring over the valuation ring |
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510 | nKillChar(s->cf); // with the same ordering as sShortcut |
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511 | s->cf = nCopyCoeff(r->cf); |
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512 | rComplete(s); |
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513 | rTest(s); |
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514 | |
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515 | k = IDELEMS(inJShortcut); // inJ will be overwritten with initial of inJ |
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516 | inJ = idInit(k+1); |
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517 | inJ->m[0] = p_One(s); // with respect to that weight |
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518 | identityMap = n_SetMap(r->cf,s->cf); // first element will obviously be p |
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519 | p_SetCoeff(inJ->m[0],identityMap(currentStrategy.getUniformizingParameter(),r->cf,s->cf),s); |
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520 | nMapFunc findingRepresentatives = n_SetMap(sShortcut->cf,s->cf); |
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521 | for (int i=0; i<k; i++) // and then come the rest |
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522 | { |
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523 | if(inJShortcut->m[i]!=NULL) |
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524 | { |
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525 | inJ->m[i+1] = p_PermPoly(inJShortcut->m[i],NULL,sShortcut,s,findingRepresentatives,NULL,0); |
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526 | } |
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527 | } |
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528 | |
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529 | ideal J = currentStrategy.computeLift(inJ,s,inI,I,r); |
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530 | // currentStrategy.reduce(J,s); |
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531 | groebnerCone startingCone(J,inJ,s,currentStrategy); |
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532 | id_Delete(&inJ,s); |
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533 | id_Delete(&J,s); |
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534 | rDelete(s); |
---|
535 | id_Delete(&inI,r); |
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536 | |
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537 | // assume(checkContainmentInTropicalVariety(startingCone)); |
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538 | return startingCone; |
---|
539 | } |
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540 | } |
---|
541 | |
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542 | BOOLEAN tropicalStartingCone(leftv res, leftv args) |
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543 | { |
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544 | leftv u = args; |
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545 | if ((u != NULL) && (u->Typ() == IDEAL_CMD)) |
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546 | { |
---|
547 | ideal I = (ideal) u->CopyD(); |
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548 | leftv v = u->next; |
---|
549 | if ((v != NULL) && (v->Typ() == NUMBER_CMD)) |
---|
550 | { |
---|
551 | number p = (number) v->Data(); |
---|
552 | leftv w = v->next; |
---|
553 | if (w==NULL) |
---|
554 | { |
---|
555 | tropicalStrategy currentStrategy(I,p,currRing); |
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556 | groebnerCone sigma = tropicalStartingCone(currentStrategy); |
---|
557 | gfan::ZCone* startingCone = new gfan::ZCone(sigma.getPolyhedralCone()); |
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558 | res->rtyp = coneID; |
---|
559 | res->data = (char*) startingCone; |
---|
560 | return FALSE; |
---|
561 | } |
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562 | } |
---|
563 | else |
---|
564 | { |
---|
565 | if (v==NULL) |
---|
566 | { |
---|
567 | tropicalStrategy currentStrategy(I,currRing); |
---|
568 | groebnerCone sigma = tropicalStartingCone(currentStrategy); |
---|
569 | res->rtyp = coneID; |
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570 | res->data = (char*) new gfan::ZCone(sigma.getPolyhedralCone()); |
---|
571 | return FALSE; |
---|
572 | } |
---|
573 | } |
---|
574 | } |
---|
575 | WerrorS("tropicalStartingCone: unexpected parameters"); |
---|
576 | return TRUE; |
---|
577 | } |
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