1 | /***************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | *****************************************/ |
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4 | /* $Id: walk.h,v 1.1.1.1 2003-10-06 12:16:04 Singular Exp $ */ |
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5 | /* |
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6 | * ABSTRACT: Declaration of the Groebner walk |
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7 | */ |
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8 | |
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9 | #ifndef WALK_H |
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10 | #define WALK_H |
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11 | |
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12 | #include "structs.h" |
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13 | |
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14 | ////////////////////////////////////////////////////////////////////// |
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15 | ////////////////////////////////////////////////////////////////////// |
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16 | // |
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17 | // IMPORTANT: |
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18 | // The following routines assume that pGetOrder(p) yields the scalar |
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19 | // product of the first row of the order matrix with the exponent |
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20 | // vector of p |
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21 | // Remark: This is true for all degree orderings (like dp) and block |
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22 | // orderings (like a(...),lp) BUT NOT FOR lp!!! |
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23 | // |
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24 | ////////////////////////////////////////////////////////////////////// |
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25 | ////////////////////////////////////////////////////////////////////// |
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26 | |
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27 | |
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28 | |
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29 | ////////////////////////////////////////////////////////////////////// |
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30 | // |
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31 | // walkNextWeight |
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32 | // Returns : weight vector for next step in Groebner walk, if exists |
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33 | // (int) 1, if next weight vector is target_weight |
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34 | // (int) 0, if no next weight vectro exist |
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35 | |
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36 | |
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37 | // assumes that curr_weight is first row of order matrix |
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38 | //intvec* walkNextWeight(intvec* curr_weight, intvec* target_weight, ideal G); |
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39 | |
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40 | //intvec* MwalkNextWeight(intvec* curr_weight, intvec* target_weight, ideal G); |
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41 | // assume curr_weight and target_weight are arrays of length |
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42 | // currRing->N storing current and target weight |
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43 | |
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44 | ////////////////////////////////////////////////////////////////////// |
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45 | // |
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46 | // walkInitials |
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47 | // assume polys of G are ordererd decreasingly w.r.t. curr_weight |
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48 | // returns ideal consisting of leading (w.r.t. curr_weight) monomials |
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49 | //ideal walkInitials(ideal G); |
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50 | |
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51 | //intvec* walkAddIntVec(intvec* v1, intvec* v2); |
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52 | |
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53 | //int MwalkWeightDegree(poly p, intvec* weight_vector); |
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54 | |
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55 | //poly MpolyInitialForm(poly g, intvec* curr_weight); |
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56 | |
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57 | ideal MwalkInitialForm(ideal G, intvec* curr_weight); |
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58 | |
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59 | //poly MOrderedPoly(poly p, intvec* curr_weight); |
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60 | |
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61 | //compute the next weight vector |
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62 | intvec* MwalkNextWeight(intvec* curr_weight,intvec* target_weight, ideal G); |
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63 | //intvec* MwalkNextWeightZ(intvec* curr_weight); |
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64 | //return lead exponent of the polynomial f |
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65 | //intvec* MExpPol(poly f);//11.02 |
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66 | |
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67 | //return the product of two intvecs |
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68 | //intvec* MivMult(intvec* a, intvec* b); //11.02 |
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69 | intvec* Mivdp(int n); |
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70 | intvec* Mivlp(int n); |
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71 | intvec* Mivdp0(int n); |
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72 | //intvec* MivUnit(int n); |
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73 | poly MivSame(intvec* u , intvec* v); |
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74 | poly M3ivSame(intvec* next_weight, intvec* u , intvec* v); |
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75 | /*********************** |
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76 | * create a new ring * |
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77 | ***********************/ |
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78 | //5.12 ring MNextRing(intvec* new_weight_vector); |
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79 | |
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80 | //ring MNextRing(ring startRing, intvec* new_weight_vector); |
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81 | char* MNextRingStringC(ring startRing, intvec* new_weight_vector); |
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82 | |
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83 | // compute an intermediate Groebner basis |
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84 | //ideal MwalkStep(ideal G,intvec* origin_weight, intvec* curr_weight, intvec* weight_order); |
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85 | |
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86 | //ideal MwalkStep(ideal G, intvec* curr_weight, ring NRing); |
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87 | |
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88 | // compute a Groebner basis of an ideal G w.r.t. lexicographic order |
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89 | //ideal Mwalk(ideal G, intvec* curr_weight, intvec* target_weight); |
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90 | |
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91 | //compute the division of two monoms |
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92 | //poly MpDiv(poly a, poly b); |
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93 | |
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94 | //compute the multiplication of two monoms |
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95 | //poly MpMult(poly a, poly b); |
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96 | |
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97 | //compare a intvec to intvec NULL |
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98 | //int Mivcomp(intvec* op); |
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99 | |
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100 | //define a monomial which exponent is intvec iv |
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101 | poly MPolVar(intvec* iv); |
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102 | |
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103 | |
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104 | //int* MExpSub(int* i1, int*i2); |
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105 | |
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106 | //int* Mleadexp(poly f); |
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107 | |
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108 | //compute the multiplikation of two ideals by "elementweise" |
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109 | ideal MidMultLift(ideal A, ideal B); |
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110 | |
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111 | //poly maIMap(ring r, poly h); |
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112 | |
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113 | //compute a Groebner basis of an ideal G |
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114 | ideal Mstd(ideal G); |
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115 | ideal Mstdhom(ideal G); |
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116 | //compute a reduced Groebner basis of a Groebner basis G |
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117 | ideal MkInterRed(ideal G); |
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118 | ideal MidMinBase(ideal G); |
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119 | /********** Perturbation Walk ******************/ |
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120 | /***************************************************************************** |
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121 | * compute an ordering matrix of the basering ordering. * |
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122 | * if the basering ordering is a block order, then its weight vector must be * |
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123 | * entered as the input this programm, otherwise the input is arbitrary * |
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124 | * integer weight vector which its size is the numbers of variables. * |
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125 | ******************************************************************************/ |
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126 | |
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127 | intvec* MivMatrixOrder(intvec* iv); |
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128 | intvec* MivMatrixOrderdp(int iv); |
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129 | intvec* MPertVectors(ideal G, intvec* ivtarget, int pdeg); |
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130 | intvec* MPertVectorslp(ideal G, intvec* ivtarget, int pdeg); |
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131 | //ideal pwalk(ideal G, intvec* delta, intvec* teta, int op_deg, int tp_deg); |
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132 | |
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133 | /**** Fractal Walk *****/ |
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134 | intvec* MivMatrixOrderlp(int nV); |
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135 | |
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136 | intvec* Mfpertvector(ideal G, intvec* iv); |
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137 | intvec* MivUnit(int nV); |
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138 | /* |
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139 | //ideal MFractalWalkR(ideal G, int nlev, intvec* sigma, intvec* tau, int step); |
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140 | ideal MFractalWalkR(ideal G, int nlev, intvec* tau, int step); |
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141 | ideal MFractalWalk(ideal I, intvec* ivstart); |
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142 | poly Mpsimple(poly p); |
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143 | poly Mpofid(ideal H); |
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144 | |
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145 | intvec* MivMatrixOrderlp(int n); |
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146 | */ |
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147 | intvec* MivWeightOrderlp(intvec* ivstart); |
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148 | intvec* MivWeightOrderdp(intvec* ivstart); |
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149 | //ideal Mimap(ring oldRing, ideal G); |
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150 | |
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151 | ideal MidLift(ideal Gomega, ideal M); |
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152 | ideal MLiftLmalG(ideal L, ideal G); |
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153 | ideal MLiftLmalGNew(ideal Gomega, ideal M, ideal G); |
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154 | ideal MLiftLmalGMin(ideal L, ideal G); |
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155 | //intvec* MwalkNextWeight(intvec* curr_weight,intvec* target_weight, ideal G); |
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156 | intvec* Mfivpert(ideal G, intvec* target, int p_deg); |
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157 | |
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158 | |
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159 | //int MpSame(poly a, poly b); |
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160 | //char* MidString(ideal G); |
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161 | |
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162 | |
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163 | //intvec* MwalkNextWeightZ(intvec* iv); |
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164 | //intvec* MNextWeightList(intvec* curr_weight, intvec* target_weight, ideal G); |
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165 | |
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166 | ideal MNWstdhomRed(ideal G, intvec* iv); |
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167 | poly MMinPoly(poly p, ideal G); |
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168 | ideal MMinIdeal(ideal G); |
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169 | ideal MadeLift4(ideal M, ideal pHGw, ideal Gw, ideal G); |
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170 | ideal MadeLift(ideal M, ideal Gw, ideal G); |
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171 | //poly MadepDivId(poly f, ideal Gw, ideal G); |
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172 | ideal MpHeadIdeal(ideal G); |
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173 | void* test_w_in_Cone(ideal G, intvec* iv); |
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174 | void* checkideal(ideal G); |
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175 | matrix MaMidLift(ideal Gomega, ideal M); |
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176 | |
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177 | //ideal MNormalForm(poly f, ideal G); |
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178 | //poly MpolyConversion(poly f, ideal GW, ideal G); |
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179 | ideal MidealConversion(ideal M, ideal GW, ideal G); |
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180 | //poly MCheckpRedId(poly f, ideal G); |
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181 | poly MpReduceId(poly f, ideal G); |
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182 | //poly MpMinimId(poly f, ideal M); |
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183 | ideal MidMinimId(ideal M); |
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184 | |
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185 | |
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186 | #endif //WALK_H |
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