1 | /***************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | *****************************************/ |
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4 | /* $Id$ */ |
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5 | /* |
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6 | * ABSTRACT: Implementation of the Groebner walk |
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7 | */ |
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8 | |
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9 | // define if the Buchberger alg should be used |
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10 | // to compute a reduced GB of a omega-homogenoues ideal |
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11 | // default: we use the hilbert driven algorithm. |
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12 | #define BUCHBERGER_ALG //we use the improved Buchberger alg. |
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13 | |
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14 | //#define UPPER_BOUND //for the original "Tran" algorithm |
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15 | //#define REPRESENTATION_OF_SIGMA //if one perturbs sigma in Tran |
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16 | |
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17 | //#define TEST_OVERFLOW |
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18 | |
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19 | #define CHECK_IDEAL_MWALK //to print intermediate results |
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20 | |
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21 | //#define NEXT_VECTORS_CC |
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22 | //#define PRINT_VECTORS //to print weight vectors |
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23 | |
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24 | #define INVEPS_SMALL_IN_FRACTAL //to choose the small invers of epsilon |
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25 | #define INVEPS_SMALL_IN_MPERTVECTOR //to choose the small invers of epsilon |
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26 | #define INVEPS_SMALL_IN_TRAN //to choose the small invers of epsilon |
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27 | |
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28 | #define FIRST_STEP_FRACTAL // to define the first step of the fractal |
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29 | #define MSTDCC_FRACTAL // apply Buchberger alg to compute a red GB, if tau doesn't stay in the correct cone |
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30 | |
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31 | //#define TIME_TEST // print the used time of each subroutine |
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32 | //#define ENDWALKS //print the size of the last omega-homogenoues Groebner basis |
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33 | |
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34 | /* includes */ |
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35 | |
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36 | #include <kernel/mod2.h> |
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37 | #include <misc/intvec.h> |
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38 | #include <Singular/cntrlc.h> |
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39 | #include <misc/options.h> |
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40 | #include <omalloc/omalloc.h> |
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41 | #include <Singular/ipshell.h> |
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42 | #include <Singular/ipconv.h> |
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43 | #include <coeffs/ffields.h> |
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44 | #include <coeffs/coeffs.h> |
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45 | #include <Singular/subexpr.h> |
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46 | #include <polys/templates/p_Procs.h> |
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47 | |
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48 | #include <polys/monomials/maps.h> |
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49 | |
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50 | /* include Hilbert-function */ |
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51 | #include <kernel/combinatorics/stairc.h> |
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52 | |
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53 | /** kstd2.cc */ |
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54 | #include <kernel/GBEngine/kutil.h> |
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55 | #include <kernel/GBEngine/khstd.h> |
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56 | |
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57 | #include <Singular/walk.h> |
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58 | #include <kernel/polys.h> |
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59 | #include <kernel/ideals.h> |
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60 | #include <Singular/ipid.h> |
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61 | #include <Singular/tok.h> |
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62 | #include <coeffs/numbers.h> |
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63 | #include <Singular/ipid.h> |
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64 | #include <polys/monomials/ring.h> |
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65 | #include <kernel/GBEngine/kstd1.h> |
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66 | #include <polys/matpol.h> |
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67 | #include <polys/weight.h> |
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68 | #include <misc/intvec.h> |
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69 | #include <kernel/GBEngine/syz.h> |
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70 | #include <Singular/lists.h> |
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71 | #include <polys/prCopy.h> |
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72 | #include <polys/monomials/ring.h> |
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73 | //#include <polys/ext_fields/longalg.h> |
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74 | #include <polys/clapsing.h> |
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75 | |
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76 | #include <coeffs/mpr_complex.h> |
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77 | |
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78 | #include <stdio.h> |
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79 | // === Zeit & System (Holger Croeni === |
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80 | #include <time.h> |
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81 | #include <sys/time.h> |
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82 | #include <math.h> |
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83 | #include <sys/stat.h> |
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84 | #include <unistd.h> |
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85 | #include <float.h> |
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86 | #include <misc/mylimits.h> |
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87 | #include <sys/types.h> |
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88 | |
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89 | int nstep; |
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90 | |
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91 | extern BOOLEAN ErrorCheck(); |
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92 | |
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93 | extern BOOLEAN pSetm_error; |
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94 | |
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95 | void Set_Error( BOOLEAN f) { pSetm_error=f; } |
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96 | |
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97 | BOOLEAN Overflow_Error = FALSE; |
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98 | |
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99 | clock_t xtif, xtstd, xtlift, xtred, xtnw; |
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100 | clock_t xftostd, xtextra, xftinput, to; |
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101 | |
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102 | /**************************** |
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103 | * utilities for TSet, LSet * |
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104 | ****************************/ |
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105 | inline static intset initec (int maxnr) |
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106 | { |
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107 | return (intset)omAlloc(maxnr*sizeof(int)); |
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108 | } |
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109 | |
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110 | inline static unsigned long* initsevS (int maxnr) |
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111 | { |
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112 | return (unsigned long*)omAlloc0(maxnr*sizeof(unsigned long)); |
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113 | } |
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114 | inline static int* initS_2_R (int maxnr) |
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115 | { |
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116 | return (int*)omAlloc0(maxnr*sizeof(int)); |
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117 | } |
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118 | |
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119 | /************************************ |
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120 | * construct the set s from F u {P} * |
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121 | ************************************/ |
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122 | // unused |
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123 | /* |
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124 | static void initSSpecialCC (ideal F, ideal Q, ideal P,kStrategy strat) |
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125 | { |
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126 | int i,pos; |
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127 | |
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128 | if (Q!=NULL) i=((IDELEMS(Q)+(setmaxTinc-1))/setmaxTinc)*setmaxTinc; |
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129 | else i=setmaxT; |
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130 | |
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131 | strat->ecartS=initec(i); |
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132 | strat->sevS=initsevS(i); |
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133 | strat->S_2_R=initS_2_R(i); |
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134 | strat->fromQ=NULL; |
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135 | strat->Shdl=idInit(i,F->rank); |
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136 | strat->S=strat->Shdl->m; |
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137 | |
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138 | // - put polys into S - |
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139 | if (Q!=NULL) |
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140 | { |
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141 | strat->fromQ=initec(i); |
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142 | memset(strat->fromQ,0,i*sizeof(int)); |
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143 | for (i=0; i<IDELEMS(Q); i++) |
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144 | { |
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145 | if (Q->m[i]!=NULL) |
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146 | { |
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147 | LObject h; |
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148 | h.p = pCopy(Q->m[i]); |
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149 | //if (TEST_OPT_INTSTRATEGY) |
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150 | //{ |
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151 | // //pContent(h.p); |
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152 | // h.pCleardenom(); // also does a pContent |
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153 | //} |
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154 | //else |
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155 | //{ |
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156 | // h.pNorm(); |
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157 | //} |
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158 | strat->initEcart(&h); |
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159 | if (rHasLocalOrMixedOrdering_currRing()) |
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160 | { |
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161 | deleteHC(&h,strat); |
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162 | } |
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163 | if (h.p!=NULL) |
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164 | { |
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165 | if (strat->sl==-1) |
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166 | pos =0; |
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167 | else |
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168 | { |
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169 | pos = posInS(strat,strat->sl,h.p,h.ecart); |
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170 | } |
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171 | h.sev = pGetShortExpVector(h.p); |
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172 | h.SetpFDeg(); |
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173 | strat->enterS(h,pos,strat, strat->tl+1); |
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174 | enterT(h, strat); |
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175 | strat->fromQ[pos]=1; |
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176 | } |
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177 | } |
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178 | } |
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179 | } |
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180 | //- put polys into S - |
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181 | for (i=0; i<IDELEMS(F); i++) |
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182 | { |
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183 | if (F->m[i]!=NULL) |
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184 | { |
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185 | LObject h; |
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186 | h.p = pCopy(F->m[i]); |
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187 | if (rHasGlobalOrdering(currRing)) |
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188 | { |
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189 | //h.p=redtailBba(h.p,strat->sl,strat); |
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190 | h.p=redtailBba(h.p,strat->sl,strat); |
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191 | } |
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192 | else |
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193 | { |
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194 | deleteHC(&h,strat); |
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195 | } |
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196 | strat->initEcart(&h); |
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197 | if (h.p!=NULL) |
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198 | { |
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199 | if (strat->sl==-1) |
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200 | pos =0; |
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201 | else |
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202 | pos = posInS(strat,strat->sl,h.p,h.ecart); |
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203 | h.sev = pGetShortExpVector(h.p); |
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204 | strat->enterS(h,pos,strat, strat->tl+1); |
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205 | h.length = pLength(h.p); |
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206 | h.SetpFDeg(); |
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207 | enterT(h,strat); |
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208 | } |
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209 | } |
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210 | } |
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211 | #ifdef INITSSPECIAL |
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212 | for (i=0; i<IDELEMS(P); i++) |
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213 | { |
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214 | if (P->m[i]!=NULL) |
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215 | { |
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216 | LObject h; |
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217 | h.p=pCopy(P->m[i]); |
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218 | strat->initEcart(&h); |
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219 | h.length = pLength(h.p); |
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220 | if (TEST_OPT_INTSTRATEGY) |
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221 | { |
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222 | h.pCleardenom(); |
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223 | } |
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224 | else |
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225 | { |
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226 | h.pNorm(); |
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227 | } |
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228 | if(strat->sl>=0) |
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229 | { |
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230 | if (rHasGlobalOrdering(currRing)) |
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231 | { |
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232 | h.p=redBba(h.p,strat->sl,strat); |
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233 | if (h.p!=NULL) |
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234 | h.p=redtailBba(h.p,strat->sl,strat); |
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235 | } |
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236 | else |
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237 | { |
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238 | h.p=redMora(h.p,strat->sl,strat); |
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239 | strat->initEcart(&h); |
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240 | } |
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241 | if(h.p!=NULL) |
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242 | { |
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243 | if (TEST_OPT_INTSTRATEGY) |
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244 | { |
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245 | h.pCleardenom(); |
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246 | } |
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247 | else |
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248 | { |
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249 | h.is_normalized = 0; |
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250 | h.pNorm(); |
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251 | } |
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252 | h.sev = pGetShortExpVector(h.p); |
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253 | h.SetpFDeg(); |
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254 | pos = posInS(strat->S,strat->sl,h.p,h.ecart); |
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255 | enterpairsSpecial(h.p,strat->sl,h.ecart,pos,strat,strat->tl+1); |
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256 | strat->enterS(h,pos,strat, strat->tl+1); |
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257 | enterT(h,strat); |
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258 | } |
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259 | } |
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260 | else |
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261 | { |
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262 | h.sev = pGetShortExpVector(h.p); |
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263 | h.SetpFDeg(); |
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264 | strat->enterS(h,0,strat, strat->tl+1); |
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265 | enterT(h,strat); |
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266 | } |
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267 | } |
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268 | } |
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269 | #endif |
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270 | } |
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271 | */ |
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272 | |
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273 | /***************** |
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274 | *interreduce F * |
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275 | *****************/ |
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276 | static ideal kInterRedCC(ideal F, ideal Q) |
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277 | { |
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278 | int j; |
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279 | kStrategy strat = new skStrategy; |
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280 | /* |
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281 | if (TEST_OPT_PROT) |
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282 | { |
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283 | writeTime("start InterRed:"); |
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284 | mflush(); |
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285 | } |
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286 | strat->syzComp = 0; |
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287 | */ |
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288 | strat->kHEdgeFound = (currRing->ppNoether) != NULL; |
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289 | strat->kNoether=pCopy((currRing->ppNoether)); |
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290 | strat->ak = id_RankFreeModule(F, currRing); |
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291 | initBuchMoraCrit(strat); |
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292 | strat->NotUsedAxis = (BOOLEAN *)omAlloc((currRing->N+1)*sizeof(BOOLEAN)); |
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293 | for(j=currRing->N; j>0; j--) |
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294 | { |
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295 | strat->NotUsedAxis[j] = TRUE; |
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296 | } |
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297 | strat->enterS = enterSBba; |
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298 | strat->posInT = posInT0; |
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299 | strat->initEcart = initEcartNormal; |
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300 | strat->sl = -1; |
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301 | strat->tl = -1; |
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302 | strat->tmax = setmaxT; |
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303 | strat->T = initT(); |
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304 | strat->R = initR(); |
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305 | strat->sevT = initsevT(); |
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306 | if(rHasLocalOrMixedOrdering_currRing()) |
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307 | { |
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308 | strat->honey = TRUE; |
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309 | } |
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310 | |
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311 | //initSCC(F,Q,strat); |
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312 | initS(F,Q,strat); |
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313 | |
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314 | /* |
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315 | timetmp=clock();//22.01.02 |
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316 | initSSpecialCC(F,Q,NULL,strat); |
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317 | tininitS=tininitS+clock()-timetmp;//22.01.02 |
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318 | */ |
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319 | if(TEST_OPT_REDSB) |
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320 | { |
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321 | strat->noTailReduction=FALSE; |
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322 | } |
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323 | updateS(TRUE,strat); |
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324 | |
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325 | if(TEST_OPT_REDSB && TEST_OPT_INTSTRATEGY) |
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326 | { |
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327 | completeReduce(strat); |
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328 | } |
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329 | pDelete(&strat->kHEdge); |
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330 | omFreeSize((ADDRESS)strat->T,strat->tmax*sizeof(TObject)); |
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331 | omFreeSize((ADDRESS)strat->ecartS,IDELEMS(strat->Shdl)*sizeof(int)); |
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332 | omFreeSize((ADDRESS)strat->sevS,IDELEMS(strat->Shdl)*sizeof(unsigned long)); |
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333 | omFreeSize((ADDRESS)strat->NotUsedAxis,(currRing->N+1)*sizeof(BOOLEAN)); |
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334 | omfree(strat->sevT); |
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335 | omfree(strat->S_2_R); |
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336 | omfree(strat->R); |
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337 | |
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338 | if(strat->fromQ) |
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339 | { |
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340 | for(j=0; j<IDELEMS(strat->Shdl); j++) |
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341 | { |
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342 | if(strat->fromQ[j]) |
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343 | { |
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344 | pDelete(&strat->Shdl->m[j]); |
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345 | } |
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346 | } |
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347 | omFreeSize((ADDRESS)strat->fromQ,IDELEMS(strat->Shdl)*sizeof(int)); |
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348 | strat->fromQ = NULL; |
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349 | } |
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350 | /* |
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351 | if (TEST_OPT_PROT) |
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352 | { |
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353 | writeTime("end Interred:"); |
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354 | mflush(); |
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355 | } |
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356 | */ |
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357 | ideal shdl=strat->Shdl; |
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358 | idSkipZeroes(shdl); |
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359 | delete(strat); |
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360 | |
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361 | return shdl; |
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362 | } |
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363 | |
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364 | #ifdef TIME_TEST |
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365 | static void TimeString(clock_t tinput, clock_t tostd, clock_t tif,clock_t tstd, |
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366 | clock_t tlf,clock_t tred, clock_t tnw, int step) |
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367 | { |
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368 | double totm = ((double) (clock() - tinput))/1000000; |
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369 | double ostd,mostd, mif, mstd, mlf, mred, mnw, mxif,mxstd,mxlf,mxred,mxnw,tot; |
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370 | // double mextra |
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371 | Print("\n// total time = %.2f sec", totm); |
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372 | Print("\n// tostd = %.2f sec = %.2f", ostd=((double) tostd)/1000000, |
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373 | mostd=((((double) tostd)/1000000)/totm)*100); |
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374 | Print("\n// tif = %.2f sec = %.2f", ((double) tif)/1000000, |
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375 | mif=((((double) tif)/1000000)/totm)*100); |
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376 | Print("\n// std = %.2f sec = %.2f", ((double) tstd)/1000000, |
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377 | mstd=((((double) tstd)/1000000)/totm)*100); |
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378 | Print("\n// lift = %.2f sec = %.2f", ((double) tlf)/1000000, |
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379 | mlf=((((double) tlf)/1000000)/totm)*100); |
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380 | Print("\n// ired = %.2f sec = %.2f", ((double) tred)/1000000, |
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381 | mred=((((double) tred)/1000000)/totm)*100); |
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382 | Print("\n// nextw = %.2f sec = %.2f", ((double) tnw)/1000000, |
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383 | mnw=((((double) tnw)/1000000)/totm)*100); |
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384 | PrintS("\n Time for the last step:"); |
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385 | Print("\n// xinfo = %.2f sec = %.2f", ((double) xtif)/1000000, |
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386 | mxif=((((double) xtif)/1000000)/totm)*100); |
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387 | Print("\n// xstd = %.2f sec = %.2f", ((double) xtstd)/1000000, |
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388 | mxstd=((((double) xtstd)/1000000)/totm)*100); |
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389 | Print("\n// xlift = %.2f sec = %.2f", ((double) xtlift)/1000000, |
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390 | mxlf=((((double) xtlift)/1000000)/totm)*100); |
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391 | Print("\n// xired = %.2f sec = %.2f", ((double) xtred)/1000000, |
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392 | mxred=((((double) xtred)/1000000)/totm)*100); |
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393 | Print("\n// xnextw= %.2f sec = %.2f", ((double) xtnw)/1000000, |
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394 | mxnw=((((double) xtnw)/1000000)/totm)*100); |
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395 | |
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396 | tot=mostd+mif+mstd+mlf+mred+mnw+mxif+mxstd+mxlf+mxred+mxnw; |
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397 | double res = (double) 100 - tot; |
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398 | Print("\n// &%d&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f&%.2f(%.2f)\\ \\", |
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399 | step, ostd, totm, mostd,mif,mstd,mlf,mred,mnw,mxif,mxstd,mxlf,mxred,mxnw,tot,res, |
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400 | ((((double) xtextra)/1000000)/totm)*100); |
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401 | } |
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402 | |
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403 | static void TimeStringFractal(clock_t tinput, clock_t tostd, clock_t tif,clock_t tstd, |
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404 | clock_t textra, clock_t tlf,clock_t tred, clock_t tnw) |
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405 | { |
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406 | |
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407 | double totm = ((double) (clock() - tinput))/1000000; |
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408 | double ostd, mostd, mif, mstd, mextra, mlf, mred, mnw, tot, res; |
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409 | Print("\n// total time = %.2f sec", totm); |
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410 | Print("\n// tostd = %.2f sec = %.2f", ostd=((double) tostd)/1000000, |
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411 | mostd=((((double) tostd)/1000000)/totm)*100); |
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412 | Print("\n// tif = %.2f sec = %.2f", ((double) tif)/1000000, |
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413 | mif=((((double) tif)/1000000)/totm)*100); |
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414 | Print("\n// std = %.2f sec = %.2f", ((double) tstd)/1000000, |
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415 | mstd=((((double) tstd)/1000000)/totm)*100); |
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416 | Print("\n// xstd = %.2f sec = %.2f", ((double) textra)/1000000, |
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417 | mextra=((((double) textra)/1000000)/totm)*100); |
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418 | Print("\n// lift = %.2f sec = %.2f", ((double) tlf)/1000000, |
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419 | mlf=((((double) tlf)/1000000)/totm)*100); |
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420 | Print("\n// ired = %.2f sec = %.2f", ((double) tred)/1000000, |
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421 | mred=((((double) tred)/1000000)/totm)*100); |
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422 | Print("\n// nextw = %.2f sec = %.2f", ((double) tnw)/1000000, |
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423 | mnw=((((double) tnw)/1000000)/totm)*100); |
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424 | tot = mostd+mif+mstd+mextra+mlf+mred+mnw; |
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425 | res = (double) 100.00-tot; |
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426 | Print("\n// &%.2f &%.2f&%.2f &%.2f &%.2f &%.2f &%.2f &%.2f &%.2f&%.2f&%.2f\\ \\ ", |
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427 | ostd,totm,mostd,mif,mstd,mextra,mlf,mred,mnw,tot,res); |
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428 | } |
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429 | #endif |
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430 | |
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431 | #ifdef CHECK_IDEAL_MWALK |
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432 | static void idString(ideal L, const char* st) |
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433 | { |
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434 | int i, nL = IDELEMS(L); |
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435 | |
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436 | Print("\n// ideal %s = ", st); |
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437 | for(i=0; i<nL-1; i++) |
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438 | { |
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439 | Print(" %s, ", pString(L->m[i])); |
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440 | } |
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441 | Print(" %s;", pString(L->m[nL-1])); |
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442 | } |
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443 | #endif |
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444 | /* |
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445 | #if defined(CHECK_IDEAL_MWALK) || defined(ENDWALKS) |
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446 | static void headidString(ideal L, char* st) |
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447 | { |
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448 | int i, nL = IDELEMS(L); |
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449 | |
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450 | Print("\n// ideal %s = ", st); |
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451 | for(i=0; i<nL-1; i++) |
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452 | { |
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453 | Print(" %s, ", pString(pHead(L->m[i]))); |
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454 | } |
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455 | Print(" %s;", pString(pHead(L->m[nL-1]))); |
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456 | } |
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457 | #endif |
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458 | |
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459 | #if defined(CHECK_IDEAL_MWALK) || defined(ENDWALKS) |
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460 | static void idElements(ideal L, char* st) |
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461 | { |
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462 | int i, nL = IDELEMS(L); |
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463 | int *K=(int *)omAlloc(nL*sizeof(int)); |
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464 | |
---|
465 | Print("\n// #monoms of %s = ", st); |
---|
466 | for(i=0; i<nL; i++) |
---|
467 | { |
---|
468 | K[i] = pLength(L->m[i]); |
---|
469 | } |
---|
470 | int j, nsame; |
---|
471 | // int nk=0; |
---|
472 | for(i=0; i<nL; i++) |
---|
473 | { |
---|
474 | if(K[i]!=0) |
---|
475 | { |
---|
476 | nsame = 1; |
---|
477 | for(j=i+1; j<nL; j++) |
---|
478 | { |
---|
479 | if(K[j]==K[i]) |
---|
480 | { |
---|
481 | nsame ++; |
---|
482 | K[j]=0; |
---|
483 | } |
---|
484 | } |
---|
485 | if(nsame == 1) |
---|
486 | { |
---|
487 | Print("%d, ",K[i]); |
---|
488 | } |
---|
489 | else |
---|
490 | { |
---|
491 | Print("%d[%d], ", K[i], nsame); |
---|
492 | } |
---|
493 | } |
---|
494 | } |
---|
495 | omFree(K); |
---|
496 | } |
---|
497 | #endif |
---|
498 | */ |
---|
499 | |
---|
500 | static void ivString(intvec* iv, const char* ch) |
---|
501 | { |
---|
502 | int nV = iv->length()-1; |
---|
503 | Print("\n// intvec %s = ", ch); |
---|
504 | |
---|
505 | for(int i=0; i<nV; i++) |
---|
506 | { |
---|
507 | Print("%d, ", (*iv)[i]); |
---|
508 | } |
---|
509 | Print("%d;", (*iv)[nV]); |
---|
510 | } |
---|
511 | |
---|
512 | #ifdef PRINT_VECTORS |
---|
513 | static void MivString(intvec* iva, intvec* ivb, intvec* ivc) |
---|
514 | { |
---|
515 | int nV = iva->length()-1; |
---|
516 | int i; |
---|
517 | PrintS("\n// ("); |
---|
518 | for(i=0; i<nV; i++) |
---|
519 | { |
---|
520 | Print("%d, ", (*iva)[i]); |
---|
521 | } |
---|
522 | Print("%d) ==> (", (*iva)[nV]); |
---|
523 | for(i=0; i<nV; i++) |
---|
524 | { |
---|
525 | Print("%d, ", (*ivb)[i]); |
---|
526 | } |
---|
527 | Print("%d) := (", (*ivb)[nV]); |
---|
528 | |
---|
529 | for(i=0; i<nV; i++) |
---|
530 | { |
---|
531 | Print("%d, ", (*ivc)[i]); |
---|
532 | } |
---|
533 | Print("%d)", (*ivc)[nV]); |
---|
534 | } |
---|
535 | #endif |
---|
536 | |
---|
537 | /******************************************************************** |
---|
538 | * returns gcd of integers a and b * |
---|
539 | ********************************************************************/ |
---|
540 | static inline long gcd(const long a, const long b) |
---|
541 | { |
---|
542 | long r, p0 = a, p1 = b; |
---|
543 | //assume(p0 >= 0 && p1 >= 0); |
---|
544 | if(p0 < 0) |
---|
545 | { |
---|
546 | p0 = -p0; |
---|
547 | } |
---|
548 | if(p1 < 0) |
---|
549 | { |
---|
550 | p1 = -p1; |
---|
551 | } |
---|
552 | while(p1 != 0) |
---|
553 | { |
---|
554 | r = p0 % p1; |
---|
555 | p0 = p1; |
---|
556 | p1 = r; |
---|
557 | } |
---|
558 | return p0; |
---|
559 | } |
---|
560 | |
---|
561 | /***************************************************************************** |
---|
562 | * compute the gcd of the entries of the vectors curr_weight and diff_weight * |
---|
563 | *****************************************************************************/ |
---|
564 | /* unused: |
---|
565 | static int simplify_gcd(intvec* curr_weight, intvec* diff_weight) |
---|
566 | { |
---|
567 | int j; |
---|
568 | int nRing = currRing->N; |
---|
569 | int gcd_tmp = (*curr_weight)[0]; |
---|
570 | for (j=1; j<nRing; j++) |
---|
571 | { |
---|
572 | gcd_tmp = gcd(gcd_tmp, (*curr_weight)[j]); |
---|
573 | if(gcd_tmp == 1) |
---|
574 | { |
---|
575 | break; |
---|
576 | } |
---|
577 | } |
---|
578 | if(gcd_tmp != 1) |
---|
579 | { |
---|
580 | for (j=0; j<nRing; j++) |
---|
581 | { |
---|
582 | gcd_tmp = gcd(gcd_tmp, (*diff_weight)[j]); |
---|
583 | if(gcd_tmp == 1) |
---|
584 | { |
---|
585 | break; |
---|
586 | } |
---|
587 | } |
---|
588 | } |
---|
589 | return gcd_tmp; |
---|
590 | } |
---|
591 | */ |
---|
592 | |
---|
593 | /********************************************* |
---|
594 | * cancel gcd of integers zaehler and nenner * |
---|
595 | *********************************************/ |
---|
596 | static void cancel(mpz_t zaehler, mpz_t nenner) |
---|
597 | { |
---|
598 | // assume(zaehler >= 0 && nenner > 0); |
---|
599 | mpz_t g; |
---|
600 | mpz_init(g); |
---|
601 | mpz_gcd(g, zaehler, nenner); |
---|
602 | |
---|
603 | mpz_div(zaehler , zaehler, g); |
---|
604 | mpz_div(nenner , nenner, g); |
---|
605 | |
---|
606 | mpz_clear(g); |
---|
607 | } |
---|
608 | |
---|
609 | //unused |
---|
610 | #if 0 |
---|
611 | static int isVectorNeg(intvec* omega) |
---|
612 | { |
---|
613 | int i; |
---|
614 | |
---|
615 | for(i=omega->length(); i>=0; i--) |
---|
616 | { |
---|
617 | if((*omega)[i]<0) |
---|
618 | { |
---|
619 | return 1; |
---|
620 | } |
---|
621 | } |
---|
622 | return 0; |
---|
623 | } |
---|
624 | #endif |
---|
625 | |
---|
626 | /******************************************************************** |
---|
627 | * compute a weight degree of a monomial p w.r.t. a weight_vector * |
---|
628 | ********************************************************************/ |
---|
629 | static inline int MLmWeightedDegree(const poly p, intvec* weight) |
---|
630 | { |
---|
631 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
632 | mpz_t sing_int; |
---|
633 | mpz_init_set_ui(sing_int, 2147483647); |
---|
634 | |
---|
635 | int i, wgrad; |
---|
636 | |
---|
637 | mpz_t zmul; |
---|
638 | mpz_init(zmul); |
---|
639 | mpz_t zvec; |
---|
640 | mpz_init(zvec); |
---|
641 | mpz_t zsum; |
---|
642 | mpz_init(zsum); |
---|
643 | |
---|
644 | for (i=currRing->N; i>0; i--) |
---|
645 | { |
---|
646 | mpz_set_si(zvec, (*weight)[i-1]); |
---|
647 | mpz_mul_ui(zmul, zvec, pGetExp(p, i)); |
---|
648 | mpz_add(zsum, zsum, zmul); |
---|
649 | } |
---|
650 | |
---|
651 | wgrad = mpz_get_ui(zsum); |
---|
652 | |
---|
653 | if(mpz_cmp(zsum, sing_int)>0) |
---|
654 | { |
---|
655 | if(Overflow_Error == FALSE) |
---|
656 | { |
---|
657 | PrintLn(); |
---|
658 | PrintS("\n// ** OVERFLOW in \"MwalkInitialForm\": "); |
---|
659 | mpz_out_str( stdout, 10, zsum); |
---|
660 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
661 | Overflow_Error = TRUE; |
---|
662 | } |
---|
663 | } |
---|
664 | |
---|
665 | mpz_clear(zmul); |
---|
666 | mpz_clear(zvec); |
---|
667 | mpz_clear(zsum); |
---|
668 | mpz_clear(sing_int); |
---|
669 | |
---|
670 | return wgrad; |
---|
671 | } |
---|
672 | |
---|
673 | /******************************************************************** |
---|
674 | * compute a weight degree of a polynomial p w.r.t. a weight_vector * |
---|
675 | ********************************************************************/ |
---|
676 | static inline int MwalkWeightDegree(poly p, intvec* weight_vector) |
---|
677 | { |
---|
678 | assume(weight_vector->length() >= currRing->N); |
---|
679 | int max = 0, maxtemp; |
---|
680 | |
---|
681 | while(p != NULL) |
---|
682 | { |
---|
683 | maxtemp = MLmWeightedDegree(p, weight_vector); |
---|
684 | pIter(p); |
---|
685 | |
---|
686 | if (maxtemp > max) |
---|
687 | { |
---|
688 | max = maxtemp; |
---|
689 | } |
---|
690 | } |
---|
691 | return max; |
---|
692 | } |
---|
693 | |
---|
694 | |
---|
695 | /******************************************************************** |
---|
696 | * compute a weight degree of a monomial p w.r.t. a weight_vector * |
---|
697 | ********************************************************************/ |
---|
698 | static void MLmWeightedDegree_gmp(mpz_t result, const poly p, intvec* weight) |
---|
699 | { |
---|
700 | /* 2147483647 is max. integer representation in SINGULAR */ |
---|
701 | mpz_t sing_int; |
---|
702 | mpz_init_set_ui(sing_int, 2147483647); |
---|
703 | |
---|
704 | int i; |
---|
705 | |
---|
706 | mpz_t zmul; |
---|
707 | mpz_init(zmul); |
---|
708 | mpz_t zvec; |
---|
709 | mpz_init(zvec); |
---|
710 | mpz_t ztmp; |
---|
711 | mpz_init(ztmp); |
---|
712 | |
---|
713 | for (i=currRing->N; i>0; i--) |
---|
714 | { |
---|
715 | mpz_set_si(zvec, (*weight)[i-1]); |
---|
716 | mpz_mul_ui(zmul, zvec, pGetExp(p, i)); |
---|
717 | mpz_add(ztmp, ztmp, zmul); |
---|
718 | } |
---|
719 | mpz_init_set(result, ztmp); |
---|
720 | mpz_clear(ztmp); |
---|
721 | mpz_clear(sing_int); |
---|
722 | mpz_clear(zvec); |
---|
723 | mpz_clear(zmul); |
---|
724 | } |
---|
725 | |
---|
726 | |
---|
727 | /***************************************************************************** |
---|
728 | * return an initial form of the polynom g w.r.t. a weight vector curr_weight * |
---|
729 | *****************************************************************************/ |
---|
730 | static poly MpolyInitialForm(poly g, intvec* curr_weight) |
---|
731 | { |
---|
732 | if(g == NULL) |
---|
733 | { |
---|
734 | return NULL; |
---|
735 | } |
---|
736 | mpz_t max; mpz_init(max); |
---|
737 | mpz_t maxtmp; mpz_init(maxtmp); |
---|
738 | |
---|
739 | poly hg, in_w_g = NULL; |
---|
740 | |
---|
741 | while(g != NULL) |
---|
742 | { |
---|
743 | hg = g; |
---|
744 | pIter(g); |
---|
745 | MLmWeightedDegree_gmp(maxtmp, hg, curr_weight); |
---|
746 | |
---|
747 | if(mpz_cmp(maxtmp, max)>0) |
---|
748 | { |
---|
749 | mpz_set(max, maxtmp); |
---|
750 | if (in_w_g!=NULL) pDelete(&in_w_g); |
---|
751 | in_w_g = pHead(hg); |
---|
752 | } |
---|
753 | else |
---|
754 | { |
---|
755 | if(mpz_cmp(maxtmp, max)==0) |
---|
756 | { |
---|
757 | in_w_g = pAdd(in_w_g, pHead(hg)); |
---|
758 | } |
---|
759 | } |
---|
760 | } |
---|
761 | mpz_clear(maxtmp); |
---|
762 | mpz_clear(max); |
---|
763 | return in_w_g; |
---|
764 | } |
---|
765 | |
---|
766 | /************************************************************************ |
---|
767 | * compute the initial form of an ideal <G> w.r.t. a weight vector iva * |
---|
768 | ************************************************************************/ |
---|
769 | ideal MwalkInitialForm(ideal G, intvec* ivw) |
---|
770 | { |
---|
771 | BOOLEAN nError = Overflow_Error; |
---|
772 | Overflow_Error = FALSE; |
---|
773 | |
---|
774 | int i, nG = IDELEMS(G); |
---|
775 | ideal Gomega = idInit(nG, 1); |
---|
776 | |
---|
777 | for(i=nG-1; i>=0; i--) |
---|
778 | { |
---|
779 | Gomega->m[i] = MpolyInitialForm(G->m[i], ivw); |
---|
780 | } |
---|
781 | if(Overflow_Error == FALSE) |
---|
782 | { |
---|
783 | Overflow_Error = nError; |
---|
784 | } |
---|
785 | return Gomega; |
---|
786 | } |
---|
787 | |
---|
788 | /************************************************************************ |
---|
789 | * test whether the weight vector iv is in the cone of the ideal G * |
---|
790 | * i.e. test whether in(in_w(g)) = in(g) for all g in G * |
---|
791 | ************************************************************************/ |
---|
792 | |
---|
793 | static int test_w_in_ConeCC(ideal G, intvec* iv) |
---|
794 | { |
---|
795 | if(G->m[0] == NULL) |
---|
796 | { |
---|
797 | PrintS("//** the result may be WRONG, i.e. 0!!\n"); |
---|
798 | return 0; |
---|
799 | } |
---|
800 | |
---|
801 | BOOLEAN nError = Overflow_Error; |
---|
802 | Overflow_Error = FALSE; |
---|
803 | |
---|
804 | int i, nG = IDELEMS(G); |
---|
805 | poly mi, gi; |
---|
806 | |
---|
807 | for(i=nG-1; i>=0; i--) |
---|
808 | { |
---|
809 | mi = MpolyInitialForm(G->m[i], iv); |
---|
810 | //Print("\n **// test_w_in_ConeCC: lm(initial)= %s \n",pString(mi)); |
---|
811 | gi = G->m[i]; |
---|
812 | //Print("\n **// test_w_in_ConeCC: lm(ideal)= %s \n",pString(gi)); |
---|
813 | if(mi == NULL) |
---|
814 | { |
---|
815 | if(Overflow_Error == FALSE) |
---|
816 | { |
---|
817 | Overflow_Error = nError; |
---|
818 | } |
---|
819 | return 0; |
---|
820 | } |
---|
821 | if(!pLmEqual(mi, gi)) |
---|
822 | { |
---|
823 | pDelete(&mi); |
---|
824 | if(Overflow_Error == FALSE) |
---|
825 | { |
---|
826 | Overflow_Error = nError; |
---|
827 | } |
---|
828 | return 0; |
---|
829 | } |
---|
830 | pDelete(&mi); |
---|
831 | } |
---|
832 | |
---|
833 | if(Overflow_Error == FALSE) |
---|
834 | { |
---|
835 | Overflow_Error = nError; |
---|
836 | } |
---|
837 | return 1; |
---|
838 | } |
---|
839 | |
---|
840 | /*************************************************** |
---|
841 | * compute a least common multiple of two integers * |
---|
842 | ***************************************************/ |
---|
843 | static inline long Mlcm(long &i1, long &i2) |
---|
844 | { |
---|
845 | long temp = gcd(i1, i2); |
---|
846 | return ((i1 / temp)* i2); |
---|
847 | } |
---|
848 | |
---|
849 | |
---|
850 | /*************************************************** |
---|
851 | * return the dot product of two intvecs a and b * |
---|
852 | ***************************************************/ |
---|
853 | static inline long MivDotProduct(intvec* a, intvec* b) |
---|
854 | { |
---|
855 | assume( a->length() == b->length()); |
---|
856 | int i, n = a->length(); |
---|
857 | long result = 0; |
---|
858 | |
---|
859 | for(i=n-1; i>=0; i--) |
---|
860 | { |
---|
861 | result += (*a)[i] * (*b)[i]; |
---|
862 | } |
---|
863 | return result; |
---|
864 | } |
---|
865 | |
---|
866 | /***************************************************** |
---|
867 | * Substract two given intvecs componentwise * |
---|
868 | *****************************************************/ |
---|
869 | static intvec* MivSub(intvec* a, intvec* b) |
---|
870 | { |
---|
871 | assume( a->length() == b->length()); |
---|
872 | int i, n = a->length(); |
---|
873 | intvec* result = new intvec(n); |
---|
874 | |
---|
875 | for(i=n-1; i>=0; i--) |
---|
876 | { |
---|
877 | (*result)[i] = (*a)[i] - (*b)[i]; |
---|
878 | } |
---|
879 | return result; |
---|
880 | } |
---|
881 | |
---|
882 | /***************************************************** |
---|
883 | * return the "intvec" lead exponent of a polynomial * |
---|
884 | *****************************************************/ |
---|
885 | static intvec* MExpPol(poly f) |
---|
886 | { |
---|
887 | int i, nR = currRing->N; |
---|
888 | intvec* result = new intvec(nR); |
---|
889 | |
---|
890 | for(i=nR-1; i>=0; i--) |
---|
891 | { |
---|
892 | (*result)[i] = pGetExp(f,i+1); |
---|
893 | } |
---|
894 | return result; |
---|
895 | } |
---|
896 | |
---|
897 | /***************************************************** |
---|
898 | * Compare two given intvecs and return 1, if they * |
---|
899 | * are the same, otherwise 0 * |
---|
900 | *****************************************************/ |
---|
901 | int MivSame(intvec* u , intvec* v) |
---|
902 | { |
---|
903 | assume(u->length() == v->length()); |
---|
904 | |
---|
905 | int i, niv = u->length(); |
---|
906 | |
---|
907 | for (i=0; i<niv; i++) |
---|
908 | { |
---|
909 | if ((*u)[i] != (*v)[i]) |
---|
910 | { |
---|
911 | return 0; |
---|
912 | } |
---|
913 | } |
---|
914 | return 1; |
---|
915 | } |
---|
916 | |
---|
917 | /****************************************************** |
---|
918 | * Compare 3 given intvecs and return 0, if the first * |
---|
919 | * and the second are the same. Return 1, if the * |
---|
920 | * the second and the third are the same, otherwise 2 * |
---|
921 | ******************************************************/ |
---|
922 | int M3ivSame(intvec* temp, intvec* u , intvec* v) |
---|
923 | { |
---|
924 | assume(temp->length() == u->length() && u->length() == v->length()); |
---|
925 | |
---|
926 | if((MivSame(temp, u)) == 1) |
---|
927 | { |
---|
928 | return 0; |
---|
929 | } |
---|
930 | if((MivSame(temp, v)) == 1) |
---|
931 | { |
---|
932 | return 1; |
---|
933 | } |
---|
934 | return 2; |
---|
935 | } |
---|
936 | |
---|
937 | /***************************************************** |
---|
938 | * compute a Groebner basis of an ideal * |
---|
939 | *****************************************************/ |
---|
940 | static ideal MstdCC(ideal G) |
---|
941 | { |
---|
942 | BITSET save1,save2; |
---|
943 | SI_SAVE_OPT(save1,save2); |
---|
944 | si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB)); |
---|
945 | ideal G1 = kStd(G, NULL, testHomog, NULL); |
---|
946 | SI_RESTORE_OPT(save1,save2); |
---|
947 | |
---|
948 | idSkipZeroes(G1); |
---|
949 | return G1; |
---|
950 | } |
---|
951 | |
---|
952 | /***************************************************** |
---|
953 | * compute a Groebner basis of an homogeneous ideal * |
---|
954 | *****************************************************/ |
---|
955 | static ideal MstdhomCC(ideal G) |
---|
956 | { |
---|
957 | BITSET save1,save2; |
---|
958 | SI_SAVE_OPT(save1,save2); |
---|
959 | si_opt_1|=(Sy_bit(OPT_REDTAIL)|Sy_bit(OPT_REDSB)); |
---|
960 | ideal G1 = kStd(G, NULL, isHomog, NULL); |
---|
961 | SI_RESTORE_OPT(save1,save2); |
---|
962 | |
---|
963 | idSkipZeroes(G1); |
---|
964 | return G1; |
---|
965 | } |
---|
966 | |
---|
967 | |
---|
968 | /***************************************************************************** |
---|
969 | * create a weight matrix order as intvec of an extra weight vector (a(iv),lp)* |
---|
970 | ******************************************************************************/ |
---|
971 | intvec* MivMatrixOrder(intvec* iv) |
---|
972 | { |
---|
973 | int i, nR = iv->length(); |
---|
974 | |
---|
975 | intvec* ivm = new intvec(nR*nR); |
---|
976 | |
---|
977 | for(i=0; i<nR; i++) |
---|
978 | { |
---|
979 | (*ivm)[i] = (*iv)[i]; |
---|
980 | } |
---|
981 | for(i=1; i<nR; i++) |
---|
982 | { |
---|
983 | (*ivm)[i*nR+i-1] = 1; |
---|
984 | } |
---|
985 | return ivm; |
---|
986 | } |
---|
987 | |
---|
988 | /********************************************************************************* |
---|
989 | * create a weight matrix order as intvec of an extra weight vector (a(iv),M(iw)) * |
---|
990 | **********************************************************************************/ |
---|
991 | intvec* MivMatrixOrderRefine(intvec* iv, intvec* iw) |
---|
992 | { |
---|
993 | assume((iv->length())*(iv->length()) == iw->length()); |
---|
994 | int i,j, nR = iv->length(); |
---|
995 | |
---|
996 | intvec* ivm = new intvec(nR*nR); |
---|
997 | |
---|
998 | for(i=0; i<nR; i++) |
---|
999 | { |
---|
1000 | (*ivm)[i] = (*iv)[i]; |
---|
1001 | } |
---|
1002 | for(i=1; i<nR; i++) |
---|
1003 | { |
---|
1004 | for(j=0; j<nR; j++) |
---|
1005 | { |
---|
1006 | (*ivm)[j+i*nR] = (*iw)[j+i*nR]; |
---|
1007 | } |
---|
1008 | } |
---|
1009 | return ivm; |
---|
1010 | } |
---|
1011 | |
---|
1012 | /******************************* |
---|
1013 | * return intvec = (1, ..., 1) * |
---|
1014 | *******************************/ |
---|
1015 | intvec* Mivdp(int nR) |
---|
1016 | { |
---|
1017 | int i; |
---|
1018 | intvec* ivm = new intvec(nR); |
---|
1019 | |
---|
1020 | for(i=nR-1; i>=0; i--) |
---|
1021 | { |
---|
1022 | (*ivm)[i] = 1; |
---|
1023 | } |
---|
1024 | return ivm; |
---|
1025 | } |
---|
1026 | |
---|
1027 | /********************************** |
---|
1028 | * return intvvec = (1,0, ..., 0) * |
---|
1029 | **********************************/ |
---|
1030 | intvec* Mivlp(int nR) |
---|
1031 | { |
---|
1032 | intvec* ivm = new intvec(nR); |
---|
1033 | (*ivm)[0] = 1; |
---|
1034 | |
---|
1035 | return ivm; |
---|
1036 | } |
---|
1037 | |
---|
1038 | //unused |
---|
1039 | /***************************************************************************** |
---|
1040 | * print the max total degree and the max coefficient of G * |
---|
1041 | *****************************************************************************/ |
---|
1042 | /* |
---|
1043 | static void checkComplexity(ideal G, char* cG) |
---|
1044 | { |
---|
1045 | int nV = currRing->N; |
---|
1046 | int nG = IDELEMS(G); |
---|
1047 | intvec* ivUnit = Mivdp(nV); |
---|
1048 | int i, tmpdeg, maxdeg=0; |
---|
1049 | number tmpcoeff , maxcoeff=currRing->cf->nNULL; |
---|
1050 | poly p; |
---|
1051 | for(i=nG-1; i>=0; i--) |
---|
1052 | { |
---|
1053 | tmpdeg = MwalkWeightDegree(G->m[i], ivUnit); |
---|
1054 | if(tmpdeg > maxdeg ) |
---|
1055 | { |
---|
1056 | maxdeg = tmpdeg; |
---|
1057 | } |
---|
1058 | } |
---|
1059 | |
---|
1060 | for(i=nG-1; i>=0; i--) |
---|
1061 | { |
---|
1062 | p = pCopy(G->m[i]); |
---|
1063 | while(p != NULL) |
---|
1064 | { |
---|
1065 | //tmpcoeff = pGetCoeff(pHead(p)); |
---|
1066 | tmpcoeff = pGetCoeff(p); |
---|
1067 | if(nGreater(tmpcoeff,maxcoeff)) |
---|
1068 | { |
---|
1069 | maxcoeff = nCopy(tmpcoeff); |
---|
1070 | } |
---|
1071 | pIter(p); |
---|
1072 | } |
---|
1073 | pDelete(&p); |
---|
1074 | } |
---|
1075 | p = pNSet(maxcoeff); |
---|
1076 | char* pStr = pString(p); |
---|
1077 | delete ivUnit; |
---|
1078 | Print("// max total degree of %s = %d\n",cG, maxdeg); |
---|
1079 | Print("// max coefficient of %s = %s", cG, pStr);//ing(p)); |
---|
1080 | Print(" which consists of %d digits", (int)strlen(pStr)); |
---|
1081 | PrintLn(); |
---|
1082 | } |
---|
1083 | */ |
---|
1084 | |
---|
1085 | /***************************************************************************** |
---|
1086 | * If target_ord = intmat(A1, ..., An) then calculate the perturbation * |
---|
1087 | * vectors * |
---|
1088 | * tau_p_dep = inveps^(p_deg-1)*A1 + inveps^(p_deg-2)*A2 +... + A_p_deg * |
---|
1089 | * where * |
---|
1090 | * inveps > totaldegree(G)*(max(A2)+...+max(A_p_deg)) * |
---|
1091 | * intmat target_ord is an integer order matrix of the monomial ordering of * |
---|
1092 | * basering. * |
---|
1093 | * This programm computes a perturbated vector with a p_deg perturbation * |
---|
1094 | * degree which smaller than the numbers of variables * |
---|
1095 | ******************************************************************************/ |
---|
1096 | intvec* MPertVectors(ideal G, intvec* ivtarget, int pdeg) |
---|
1097 | { |
---|
1098 | // ivtarget is a matrix order of a degree reverse lex. order |
---|
1099 | int nV = currRing->N; |
---|
1100 | //assume(pdeg <= nV && pdeg >= 0); |
---|
1101 | |
---|
1102 | int i, j, nG = IDELEMS(G); |
---|
1103 | intvec* v_null = new intvec(nV); |
---|
1104 | |
---|
1105 | // Check that the perturbed degree is valid |
---|
1106 | if(pdeg > nV || pdeg <= 0) |
---|
1107 | { |
---|
1108 | WerrorS("//** The perturbed degree is wrong!!"); |
---|
1109 | return v_null; |
---|
1110 | } |
---|
1111 | delete v_null; |
---|
1112 | |
---|
1113 | if(pdeg == 1) |
---|
1114 | { |
---|
1115 | return ivtarget; |
---|
1116 | } |
---|
1117 | mpz_t *pert_vector = (mpz_t*)omAlloc(nV*sizeof(mpz_t)); |
---|
1118 | mpz_t *pert_vector1 = (mpz_t*)omAlloc(nV*sizeof(mpz_t)); |
---|
1119 | |
---|
1120 | for(i=0; i<nV; i++) |
---|
1121 | { |
---|
1122 | mpz_init_set_si(pert_vector[i], (*ivtarget)[i]); |
---|
1123 | mpz_init_set_si(pert_vector1[i], (*ivtarget)[i]); |
---|
1124 | } |
---|
1125 | // Calculate max1 = Max(A2)+Max(A3)+...+Max(Apdeg), |
---|
1126 | // where the Ai are the i-te rows of the matrix target_ord. |
---|
1127 | int ntemp, maxAi, maxA=0; |
---|
1128 | for(i=1; i<pdeg; i++) |
---|
1129 | { |
---|
1130 | maxAi = (*ivtarget)[i*nV]; |
---|
1131 | if(maxAi<0) |
---|
1132 | { |
---|
1133 | maxAi = -maxAi; |
---|
1134 | } |
---|
1135 | for(j=i*nV+1; j<(i+1)*nV; j++) |
---|
1136 | { |
---|
1137 | ntemp = (*ivtarget)[j]; |
---|
1138 | if(ntemp < 0) |
---|
1139 | { |
---|
1140 | ntemp = -ntemp; |
---|
1141 | } |
---|
1142 | if(ntemp > maxAi) |
---|
1143 | { |
---|
1144 | maxAi = ntemp; |
---|
1145 | } |
---|
1146 | } |
---|
1147 | maxA += maxAi; |
---|
1148 | } |
---|
1149 | |
---|
1150 | // Calculate inveps = 1/eps, where 1/eps > totaldeg(p)*max1 for all p in G. |
---|
1151 | |
---|
1152 | intvec* ivUnit = Mivdp(nV); |
---|
1153 | |
---|
1154 | mpz_t tot_deg; mpz_init(tot_deg); |
---|
1155 | mpz_t maxdeg; mpz_init(maxdeg); |
---|
1156 | mpz_t inveps; mpz_init(inveps); |
---|
1157 | |
---|
1158 | |
---|
1159 | for(i=nG-1; i>=0; i--) |
---|
1160 | { |
---|
1161 | mpz_set_ui(maxdeg, MwalkWeightDegree(G->m[i], ivUnit)); |
---|
1162 | if (mpz_cmp(maxdeg, tot_deg) > 0 ) |
---|
1163 | { |
---|
1164 | mpz_set(tot_deg, maxdeg); |
---|
1165 | } |
---|
1166 | } |
---|
1167 | |
---|
1168 | delete ivUnit; |
---|
1169 | mpz_mul_ui(inveps, tot_deg, maxA); |
---|
1170 | mpz_add_ui(inveps, inveps, 1); |
---|
1171 | |
---|
1172 | |
---|
1173 | // takes "small" inveps |
---|
1174 | #ifdef INVEPS_SMALL_IN_MPERTVECTOR |
---|
1175 | if(mpz_cmp_ui(inveps, pdeg)>0 && pdeg > 3) |
---|
1176 | { |
---|
1177 | // Print("\n// choose the\"small\" inverse epsilon := %d / %d = ", mpz_get_si(inveps), pdeg); |
---|
1178 | mpz_fdiv_q_ui(inveps, inveps, pdeg); |
---|
1179 | // mpz_out_str(stdout, 10, inveps); |
---|
1180 | } |
---|
1181 | #else |
---|
1182 | // PrintS("\n// the \"big\" inverse epsilon: "); |
---|
1183 | mpz_out_str(stdout, 10, inveps); |
---|
1184 | #endif |
---|
1185 | |
---|
1186 | // pert(A1) = inveps^(pdeg-1)*A1 + inveps^(pdeg-2)*A2+...+A_pdeg, |
---|
1187 | // pert_vector := A1 |
---|
1188 | for( i=1; i < pdeg; i++ ) |
---|
1189 | { |
---|
1190 | for(j=0; j<nV; j++) |
---|
1191 | { |
---|
1192 | mpz_mul(pert_vector[j], pert_vector[j], inveps); |
---|
1193 | if((*ivtarget)[i*nV+j]<0) |
---|
1194 | { |
---|
1195 | mpz_sub_ui(pert_vector[j], pert_vector[j],-(*ivtarget)[i*nV+j]); |
---|
1196 | } |
---|
1197 | else |
---|
1198 | { |
---|
1199 | mpz_add_ui(pert_vector[j], pert_vector[j],(*ivtarget)[i*nV+j]); |
---|
1200 | } |
---|
1201 | } |
---|
1202 | } |
---|
1203 | |
---|
1204 | // 2147483647 is max. integer representation in SINGULAR |
---|
1205 | mpz_t sing_int; |
---|
1206 | mpz_init_set_ui(sing_int, 2147483647); |
---|
1207 | |
---|
1208 | mpz_t check_int; |
---|
1209 | mpz_init_set_ui(check_int, 100000); |
---|
1210 | |
---|
1211 | mpz_t ztemp; |
---|
1212 | mpz_init(ztemp); |
---|
1213 | mpz_set(ztemp, pert_vector[0]); |
---|
1214 | for(i=1; i<nV; i++) |
---|
1215 | { |
---|
1216 | mpz_gcd(ztemp, ztemp, pert_vector[i]); |
---|
1217 | if(mpz_cmp_si(ztemp, 1) == 0) |
---|
1218 | { |
---|
1219 | break; |
---|
1220 | } |
---|
1221 | } |
---|
1222 | if(mpz_cmp_si(ztemp, 1) != 0) |
---|
1223 | { |
---|
1224 | for(i=0; i<nV; i++) |
---|
1225 | { |
---|
1226 | mpz_divexact(pert_vector[i], pert_vector[i], ztemp); |
---|
1227 | } |
---|
1228 | } |
---|
1229 | |
---|
1230 | for(i=0; i<nV; i++) |
---|
1231 | { |
---|
1232 | if(mpz_cmp(pert_vector[i], check_int)>=0) |
---|
1233 | { |
---|
1234 | for(j=0; j<nV; j++) |
---|
1235 | { |
---|
1236 | mpz_fdiv_q_ui(pert_vector1[j], pert_vector[j], 100); |
---|
1237 | } |
---|
1238 | } |
---|
1239 | } |
---|
1240 | |
---|
1241 | intvec* result = new intvec(nV); |
---|
1242 | |
---|
1243 | int ntrue=0; |
---|
1244 | |
---|
1245 | for(i=0; i<nV; i++) |
---|
1246 | { |
---|
1247 | (*result)[i] = mpz_get_si(pert_vector1[i]); |
---|
1248 | if(mpz_cmp(pert_vector1[i], sing_int)>=0) |
---|
1249 | { |
---|
1250 | ntrue++; |
---|
1251 | } |
---|
1252 | } |
---|
1253 | if(ntrue > 0 || test_w_in_ConeCC(G,result)==0) |
---|
1254 | { |
---|
1255 | ntrue=0; |
---|
1256 | for(i=0; i<nV; i++) |
---|
1257 | { |
---|
1258 | (*result)[i] = mpz_get_si(pert_vector[i]); |
---|
1259 | if(mpz_cmp(pert_vector[i], sing_int)>=0) |
---|
1260 | { |
---|
1261 | ntrue++; |
---|
1262 | if(Overflow_Error == FALSE) |
---|
1263 | { |
---|
1264 | Overflow_Error = TRUE; |
---|
1265 | PrintS("\n// ** OVERFLOW in \"MPertvectors\": "); |
---|
1266 | mpz_out_str( stdout, 10, pert_vector[i]); |
---|
1267 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
1268 | Print("\n// So vector[%d] := %d is wrong!!", i+1, (*result)[i]); |
---|
1269 | } |
---|
1270 | } |
---|
1271 | } |
---|
1272 | |
---|
1273 | if(Overflow_Error == TRUE) |
---|
1274 | { |
---|
1275 | ivString(result, "pert_vector"); |
---|
1276 | Print("\n// %d element(s) of it is overflow!!", ntrue); |
---|
1277 | } |
---|
1278 | } |
---|
1279 | |
---|
1280 | mpz_clear(ztemp); |
---|
1281 | mpz_clear(sing_int); |
---|
1282 | mpz_clear(check_int); |
---|
1283 | omFree(pert_vector); |
---|
1284 | omFree(pert_vector1); |
---|
1285 | mpz_clear(tot_deg); |
---|
1286 | mpz_clear(maxdeg); |
---|
1287 | mpz_clear(inveps); |
---|
1288 | |
---|
1289 | rComplete(currRing); |
---|
1290 | for(j=0; j<IDELEMS(G); j++) |
---|
1291 | { |
---|
1292 | poly p=G->m[j]; |
---|
1293 | while(p!=NULL) |
---|
1294 | { |
---|
1295 | p_Setm(p,currRing); pIter(p); |
---|
1296 | } |
---|
1297 | } |
---|
1298 | return result; |
---|
1299 | } |
---|
1300 | |
---|
1301 | /***************************************************************************** |
---|
1302 | * The following procedure returns * |
---|
1303 | * Pert(A1) = 1/eps^(pdeg-1)*A_1 + 1/eps^(pdeg-2)*A_2+...+A_pdeg, * |
---|
1304 | * where the A_i are the i-th rows of the matrix target_ord and * |
---|
1305 | * 1/eps > deg(p)*(max(A_2) + max(A_3)+...+max(A_pdeg)) * |
---|
1306 | *****************************************************************************/ |
---|
1307 | intvec* MPertVectorslp(ideal G, intvec* ivtarget, int pdeg) |
---|
1308 | { |
---|
1309 | // ivtarget is a matrix order of the lex. order |
---|
1310 | int nV = currRing->N; |
---|
1311 | //assume(pdeg <= nV && pdeg >= 0); |
---|
1312 | |
---|
1313 | int i, j, nG = IDELEMS(G); |
---|
1314 | intvec* pert_vector = new intvec(nV); |
---|
1315 | |
---|
1316 | //Checking that the perturbated degree is valid |
---|
1317 | if(pdeg > nV || pdeg <= 0) |
---|
1318 | { |
---|
1319 | WerrorS("//** The perturbed degree is wrong!!"); |
---|
1320 | return pert_vector; |
---|
1321 | } |
---|
1322 | for(i=0; i<nV; i++) |
---|
1323 | { |
---|
1324 | (*pert_vector)[i]=(*ivtarget)[i]; |
---|
1325 | } |
---|
1326 | if(pdeg == 1) |
---|
1327 | { |
---|
1328 | return pert_vector; |
---|
1329 | } |
---|
1330 | // Calculate max1 = Max(A2)+Max(A3)+...+Max(Apdeg), |
---|
1331 | // where the Ai are the i-te rows of the matrix target_ord. |
---|
1332 | int ntemp, maxAi, maxA=0; |
---|
1333 | for(i=1; i<pdeg; i++) |
---|
1334 | { |
---|
1335 | maxAi = (*ivtarget)[i*nV]; |
---|
1336 | for(j=i*nV+1; j<(i+1)*nV; j++) |
---|
1337 | { |
---|
1338 | ntemp = (*ivtarget)[j]; |
---|
1339 | if(ntemp > maxAi) |
---|
1340 | { |
---|
1341 | maxAi = ntemp; |
---|
1342 | } |
---|
1343 | } |
---|
1344 | maxA += maxAi; |
---|
1345 | } |
---|
1346 | |
---|
1347 | // Calculate inveps := 1/eps, where 1/eps > deg(p)*max1 for all p in G. |
---|
1348 | int inveps, tot_deg = 0, maxdeg; |
---|
1349 | |
---|
1350 | intvec* ivUnit = Mivdp(nV);//19.02 |
---|
1351 | for(i=nG-1; i>=0; i--) |
---|
1352 | { |
---|
1353 | // maxdeg = pTotaldegree(G->m[i], currRing); //it's wrong for ex1,2,rose |
---|
1354 | maxdeg = MwalkWeightDegree(G->m[i], ivUnit); |
---|
1355 | if (maxdeg > tot_deg ) |
---|
1356 | { |
---|
1357 | tot_deg = maxdeg; |
---|
1358 | } |
---|
1359 | } |
---|
1360 | delete ivUnit; |
---|
1361 | |
---|
1362 | inveps = (tot_deg * maxA) + 1; |
---|
1363 | |
---|
1364 | #ifdef INVEPS_SMALL_IN_FRACTAL |
---|
1365 | // Print("\n// choose the\"small\" inverse epsilon := %d / %d = ", inveps, pdeg); |
---|
1366 | if(inveps > pdeg && pdeg > 3) |
---|
1367 | { |
---|
1368 | inveps = inveps / pdeg; |
---|
1369 | } |
---|
1370 | // Print(" %d", inveps); |
---|
1371 | #else |
---|
1372 | PrintS("\n// the \"big\" inverse epsilon %d", inveps); |
---|
1373 | #endif |
---|
1374 | |
---|
1375 | // Pert(A1) = inveps^(pdeg-1)*A1 + inveps^(pdeg-2)*A2+...+A_pdeg |
---|
1376 | for ( i=1; i < pdeg; i++ ) |
---|
1377 | { |
---|
1378 | for(j=0; j<nV; j++) |
---|
1379 | { |
---|
1380 | (*pert_vector)[j] = inveps*((*pert_vector)[j]) + (*ivtarget)[i*nV+j]; |
---|
1381 | } |
---|
1382 | } |
---|
1383 | |
---|
1384 | int temp = (*pert_vector)[0]; |
---|
1385 | for(i=1; i<nV; i++) |
---|
1386 | { |
---|
1387 | temp = gcd(temp, (*pert_vector)[i]); |
---|
1388 | if(temp == 1) |
---|
1389 | { |
---|
1390 | break; |
---|
1391 | } |
---|
1392 | } |
---|
1393 | if(temp != 1) |
---|
1394 | { |
---|
1395 | for(i=0; i<nV; i++) |
---|
1396 | { |
---|
1397 | (*pert_vector)[i] = (*pert_vector)[i] / temp; |
---|
1398 | } |
---|
1399 | } |
---|
1400 | |
---|
1401 | intvec* result = pert_vector; |
---|
1402 | delete pert_vector; |
---|
1403 | return result; |
---|
1404 | } |
---|
1405 | |
---|
1406 | /***************************************************************************** |
---|
1407 | * define a lexicographic order matrix as intvec * |
---|
1408 | *****************************************************************************/ |
---|
1409 | intvec* MivMatrixOrderlp(int nV) |
---|
1410 | { |
---|
1411 | int i; |
---|
1412 | intvec* ivM = new intvec(nV*nV); |
---|
1413 | |
---|
1414 | for(i=0; i<nV; i++) |
---|
1415 | { |
---|
1416 | (*ivM)[i*nV + i] = 1; |
---|
1417 | } |
---|
1418 | return(ivM); |
---|
1419 | } |
---|
1420 | |
---|
1421 | |
---|
1422 | /***************************************************************************** |
---|
1423 | * define a reverse lexicographic order (dp) matrix as intvec * |
---|
1424 | *****************************************************************************/ |
---|
1425 | intvec* MivMatrixOrderdp(int nV) |
---|
1426 | { |
---|
1427 | int i; |
---|
1428 | intvec* ivM = new intvec(nV*nV); |
---|
1429 | |
---|
1430 | for(i=0; i<nV; i++) |
---|
1431 | { |
---|
1432 | (*ivM)[i] = 1; |
---|
1433 | } |
---|
1434 | for(i=1; i<nV; i++) |
---|
1435 | { |
---|
1436 | (*ivM)[(i+1)*nV - i] = -1; |
---|
1437 | } |
---|
1438 | return(ivM); |
---|
1439 | } |
---|
1440 | |
---|
1441 | /***************************************************************************** |
---|
1442 | * creates an intvec of the monomial order Wp(ivstart) * |
---|
1443 | *****************************************************************************/ |
---|
1444 | intvec* MivWeightOrderlp(intvec* ivstart) |
---|
1445 | { |
---|
1446 | int i; |
---|
1447 | int nV = ivstart->length(); |
---|
1448 | intvec* ivM = new intvec(nV*nV); |
---|
1449 | |
---|
1450 | for(i=0; i<nV; i++) |
---|
1451 | { |
---|
1452 | (*ivM)[i] = (*ivstart)[i]; |
---|
1453 | } |
---|
1454 | for(i=1; i<nV; i++) |
---|
1455 | { |
---|
1456 | (*ivM)[i*nV + i-1] = 1; |
---|
1457 | } |
---|
1458 | return(ivM); |
---|
1459 | } |
---|
1460 | |
---|
1461 | /***************************************************************************** |
---|
1462 | * creates an intvec of the monomial order dp(ivstart) * |
---|
1463 | *****************************************************************************/ |
---|
1464 | intvec* MivWeightOrderdp(intvec* ivstart) |
---|
1465 | { |
---|
1466 | int i; |
---|
1467 | int nV = ivstart->length(); |
---|
1468 | intvec* ivM = new intvec(nV*nV); |
---|
1469 | |
---|
1470 | for(i=0; i<nV; i++) |
---|
1471 | { |
---|
1472 | (*ivM)[i] = (*ivstart)[i]; |
---|
1473 | } |
---|
1474 | for(i=0; i<nV; i++) |
---|
1475 | { |
---|
1476 | (*ivM)[nV+i] = 1; |
---|
1477 | } |
---|
1478 | for(i=2; i<nV; i++) |
---|
1479 | { |
---|
1480 | (*ivM)[(i+1)*nV - i] = -1; |
---|
1481 | } |
---|
1482 | return(ivM); |
---|
1483 | } |
---|
1484 | |
---|
1485 | //unused |
---|
1486 | /* |
---|
1487 | static intvec* MatrixOrderdp(int nV) |
---|
1488 | { |
---|
1489 | int i; |
---|
1490 | intvec* ivM = new intvec(nV*nV); |
---|
1491 | |
---|
1492 | for(i=0; i<nV; i++) |
---|
1493 | { |
---|
1494 | (*ivM)[i] = 1; |
---|
1495 | } |
---|
1496 | for(i=1; i<nV; i++) |
---|
1497 | { |
---|
1498 | (*ivM)[(i+1)*nV - i] = -1; |
---|
1499 | } |
---|
1500 | return(ivM); |
---|
1501 | } |
---|
1502 | */ |
---|
1503 | |
---|
1504 | intvec* MivUnit(int nV) |
---|
1505 | { |
---|
1506 | int i; |
---|
1507 | intvec* ivM = new intvec(nV); |
---|
1508 | for(i=nV-1; i>=0; i--) |
---|
1509 | { |
---|
1510 | (*ivM)[i] = 1; |
---|
1511 | } |
---|
1512 | return(ivM); |
---|
1513 | } |
---|
1514 | |
---|
1515 | |
---|
1516 | /************************************************************************ |
---|
1517 | * compute a perturbed weight vector of a matrix order w.r.t. an ideal * |
---|
1518 | *************************************************************************/ |
---|
1519 | int Xnlev; |
---|
1520 | intvec* Mfpertvector(ideal G, intvec* ivtarget) |
---|
1521 | { |
---|
1522 | int i, j, nG = IDELEMS(G); |
---|
1523 | int nV = currRing->N; |
---|
1524 | int niv = nV*nV; |
---|
1525 | |
---|
1526 | |
---|
1527 | // Calculate maxA = Max(A2) + Max(A3) + ... + Max(AnV), |
---|
1528 | // where the Ai are the i-te rows of the matrix 'targer_ord'. |
---|
1529 | int ntemp, maxAi, maxA=0; |
---|
1530 | for(i=1; i<nV; i++) |
---|
1531 | { |
---|
1532 | maxAi = (*ivtarget)[i*nV]; |
---|
1533 | if(maxAi<0) |
---|
1534 | { |
---|
1535 | maxAi = -maxAi; |
---|
1536 | } |
---|
1537 | for(j=i*nV+1; j<(i+1)*nV; j++) |
---|
1538 | { |
---|
1539 | ntemp = (*ivtarget)[j]; |
---|
1540 | if(ntemp < 0) |
---|
1541 | { |
---|
1542 | ntemp = -ntemp; |
---|
1543 | } |
---|
1544 | if(ntemp > maxAi) |
---|
1545 | { |
---|
1546 | maxAi = ntemp; |
---|
1547 | } |
---|
1548 | } |
---|
1549 | maxA = maxA + maxAi; |
---|
1550 | } |
---|
1551 | intvec* ivUnit = Mivdp(nV); |
---|
1552 | |
---|
1553 | // Calculate inveps = 1/eps, where 1/eps > deg(p)*maxA for all p in G. |
---|
1554 | mpz_t tot_deg; mpz_init(tot_deg); |
---|
1555 | mpz_t maxdeg; mpz_init(maxdeg); |
---|
1556 | mpz_t inveps; mpz_init(inveps); |
---|
1557 | |
---|
1558 | |
---|
1559 | for(i=nG-1; i>=0; i--) |
---|
1560 | { |
---|
1561 | mpz_set_ui(maxdeg, MwalkWeightDegree(G->m[i], ivUnit)); |
---|
1562 | if (mpz_cmp(maxdeg, tot_deg) > 0 ) |
---|
1563 | { |
---|
1564 | mpz_set(tot_deg, maxdeg); |
---|
1565 | } |
---|
1566 | } |
---|
1567 | |
---|
1568 | delete ivUnit; |
---|
1569 | //inveps = (tot_deg * maxA) + 1; |
---|
1570 | mpz_mul_ui(inveps, tot_deg, maxA); |
---|
1571 | mpz_add_ui(inveps, inveps, 1); |
---|
1572 | |
---|
1573 | // takes "small" inveps |
---|
1574 | #ifdef INVEPS_SMALL_IN_FRACTAL |
---|
1575 | if(mpz_cmp_ui(inveps, nV)>0 && nV > 3) |
---|
1576 | { |
---|
1577 | mpz_cdiv_q_ui(inveps, inveps, nV); |
---|
1578 | } |
---|
1579 | // choose the small inverse epsilon |
---|
1580 | #endif |
---|
1581 | |
---|
1582 | // PrintLn(); mpz_out_str(stdout, 10, inveps); |
---|
1583 | |
---|
1584 | // Calculate the perturbed target orders: |
---|
1585 | mpz_t *ivtemp=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
1586 | mpz_t *pert_vector=(mpz_t *)omAlloc(niv*sizeof(mpz_t)); |
---|
1587 | |
---|
1588 | for(i=0; i < nV; i++) |
---|
1589 | { |
---|
1590 | mpz_init_set_si(ivtemp[i], (*ivtarget)[i]); |
---|
1591 | mpz_init_set_si(pert_vector[i], (*ivtarget)[i]); |
---|
1592 | } |
---|
1593 | |
---|
1594 | mpz_t ztmp; mpz_init(ztmp); |
---|
1595 | // BOOLEAN isneg = FALSE; |
---|
1596 | |
---|
1597 | for(i=1; i<nV; i++) |
---|
1598 | { |
---|
1599 | for(j=0; j<nV; j++) |
---|
1600 | { |
---|
1601 | mpz_mul(ztmp, inveps, ivtemp[j]); |
---|
1602 | if((*ivtarget)[i*nV+j]<0) |
---|
1603 | { |
---|
1604 | mpz_sub_ui(ivtemp[j], ztmp, -(*ivtarget)[i*nV+j]); |
---|
1605 | } |
---|
1606 | else |
---|
1607 | { |
---|
1608 | mpz_add_ui(ivtemp[j], ztmp,(*ivtarget)[i*nV+j]); |
---|
1609 | } |
---|
1610 | } |
---|
1611 | |
---|
1612 | for(j=0; j<nV; j++) |
---|
1613 | { |
---|
1614 | mpz_init_set(pert_vector[i*nV+j],ivtemp[j]); |
---|
1615 | } |
---|
1616 | } |
---|
1617 | |
---|
1618 | // 2147483647 is max. integer representation in SINGULAR |
---|
1619 | mpz_t sing_int; |
---|
1620 | mpz_init_set_ui(sing_int, 2147483647); |
---|
1621 | |
---|
1622 | intvec* result = new intvec(niv); |
---|
1623 | intvec* result1 = new intvec(niv); |
---|
1624 | BOOLEAN nflow = FALSE; |
---|
1625 | |
---|
1626 | // computes gcd |
---|
1627 | mpz_set(ztmp, pert_vector[0]); |
---|
1628 | for(i=0; i<niv; i++) |
---|
1629 | { |
---|
1630 | mpz_gcd(ztmp, ztmp, pert_vector[i]); |
---|
1631 | if(mpz_cmp_si(ztmp, 1)==0) |
---|
1632 | { |
---|
1633 | break; |
---|
1634 | } |
---|
1635 | } |
---|
1636 | |
---|
1637 | for(i=0; i<niv; i++) |
---|
1638 | { |
---|
1639 | mpz_divexact(pert_vector[i], pert_vector[i], ztmp); |
---|
1640 | (* result)[i] = mpz_get_si(pert_vector[i]); |
---|
1641 | } |
---|
1642 | |
---|
1643 | CHECK_OVERFLOW: |
---|
1644 | |
---|
1645 | for(i=0; i<niv; i++) |
---|
1646 | { |
---|
1647 | if(mpz_cmp(pert_vector[i], sing_int)>0) |
---|
1648 | { |
---|
1649 | if(nflow == FALSE) |
---|
1650 | { |
---|
1651 | Xnlev = i / nV; |
---|
1652 | nflow = TRUE; |
---|
1653 | Overflow_Error = TRUE; |
---|
1654 | Print("\n// Xlev = %d and the %d-th element is", Xnlev, i+1); |
---|
1655 | PrintS("\n// ** OVERFLOW in \"Mfpertvector\": "); |
---|
1656 | mpz_out_str( stdout, 10, pert_vector[i]); |
---|
1657 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
1658 | Print("\n// So vector[%d] := %d is wrong!!", i+1, (*result)[i]); |
---|
1659 | } |
---|
1660 | } |
---|
1661 | } |
---|
1662 | if(Overflow_Error == TRUE) |
---|
1663 | { |
---|
1664 | ivString(result, "new_vector"); |
---|
1665 | } |
---|
1666 | omFree(pert_vector); |
---|
1667 | omFree(ivtemp); |
---|
1668 | mpz_clear(ztmp); |
---|
1669 | mpz_clear(tot_deg); |
---|
1670 | mpz_clear(maxdeg); |
---|
1671 | mpz_clear(inveps); |
---|
1672 | mpz_clear(sing_int); |
---|
1673 | |
---|
1674 | rComplete(currRing); |
---|
1675 | for(j=0; j<IDELEMS(G); j++) |
---|
1676 | { |
---|
1677 | poly p=G->m[j]; |
---|
1678 | while(p!=NULL) |
---|
1679 | { |
---|
1680 | p_Setm(p,currRing); |
---|
1681 | pIter(p); |
---|
1682 | } |
---|
1683 | } |
---|
1684 | return result; |
---|
1685 | } |
---|
1686 | |
---|
1687 | /**************************************************************** |
---|
1688 | * Multiplication of two ideals element by element * |
---|
1689 | * i.e. Let be A := (a_i) and B := (b_i), return C := (a_i*b_i) * |
---|
1690 | * destroy A, keeps B * |
---|
1691 | ****************************************************************/ |
---|
1692 | static ideal MidMult(ideal A, ideal B) |
---|
1693 | { |
---|
1694 | int mA = IDELEMS(A), mB = IDELEMS(B); |
---|
1695 | |
---|
1696 | if(A==NULL || B==NULL) |
---|
1697 | { |
---|
1698 | return NULL; |
---|
1699 | } |
---|
1700 | if(mB < mA) |
---|
1701 | { |
---|
1702 | mA = mB; |
---|
1703 | } |
---|
1704 | ideal result = idInit(mA, 1); |
---|
1705 | |
---|
1706 | int i, k=0; |
---|
1707 | for(i=0; i<mA; i++) |
---|
1708 | { |
---|
1709 | result->m[k] = pMult(A->m[i], pCopy(B->m[i])); |
---|
1710 | A->m[i]=NULL; |
---|
1711 | if (result->m[k]!=NULL) |
---|
1712 | { |
---|
1713 | k++; |
---|
1714 | } |
---|
1715 | } |
---|
1716 | |
---|
1717 | idDelete(&A); |
---|
1718 | idSkipZeroes(result); |
---|
1719 | return result; |
---|
1720 | } |
---|
1721 | |
---|
1722 | /********************************************************************* |
---|
1723 | * G is a red. Groebner basis w.r.t. <_1 * |
---|
1724 | * Gomega is an initial form ideal of <G> w.r.t. a weight vector w * |
---|
1725 | * M is a subideal of <Gomega> and M selft is a red. Groebner basis * |
---|
1726 | * of the ideal <Gomega> w.r.t. <_w * |
---|
1727 | * Let m_i = h1.gw1 + ... + hs.gws for each m_i in M; gwi in Gomega * |
---|
1728 | * return F with n(F) = n(M) and f_i = h1.g1 + ... + hs.gs for each i* |
---|
1729 | ********************************************************************/ |
---|
1730 | static ideal MLifttwoIdeal(ideal Gw, ideal M, ideal G) |
---|
1731 | { |
---|
1732 | ideal Mtmp = idLift(Gw, M, NULL, FALSE, TRUE, TRUE, NULL); |
---|
1733 | |
---|
1734 | // If Gw is a GB, then isSB = TRUE, otherwise FALSE |
---|
1735 | // So, it is better, if one tests whether Gw is a GB |
---|
1736 | // in ideals.cc: |
---|
1737 | // idLift (ideal mod, ideal submod,ideal * rest, BOOLEAN goodShape, |
---|
1738 | // BOOLEAN isSB,BOOLEAN divide,matrix * unit) |
---|
1739 | |
---|
1740 | // Let be Mtmp = {m1,...,ms}, where mi=sum hij.in_gj, for all i=1,...,s |
---|
1741 | // We compute F = {f1,...,fs}, where fi=sum hij.gj |
---|
1742 | int i, j, nM = IDELEMS(Mtmp); |
---|
1743 | ideal idpol, idLG; |
---|
1744 | ideal F = idInit(nM, 1); |
---|
1745 | |
---|
1746 | for(i=0; i<nM; i++) |
---|
1747 | { |
---|
1748 | idpol = idVec2Ideal(Mtmp->m[i]); |
---|
1749 | idLG = MidMult(idpol, G); |
---|
1750 | idpol = NULL; |
---|
1751 | F->m[i] = NULL; |
---|
1752 | for(j=IDELEMS(idLG)-1; j>=0; j--) |
---|
1753 | { |
---|
1754 | F->m[i] = pAdd(F->m[i], idLG->m[j]); |
---|
1755 | idLG->m[j]=NULL; |
---|
1756 | } |
---|
1757 | idDelete(&idLG); |
---|
1758 | } |
---|
1759 | idDelete(&Mtmp); |
---|
1760 | return F; |
---|
1761 | } |
---|
1762 | |
---|
1763 | //unused |
---|
1764 | /* |
---|
1765 | static void checkidealCC(ideal G, char* Ch) |
---|
1766 | { |
---|
1767 | int i,nmon=0,ntmp; |
---|
1768 | int nG = IDELEMS(G); |
---|
1769 | int n = nG-1; |
---|
1770 | Print("\n//** Ideal %s besteht aus %d Polynomen mit ", Ch, nG); |
---|
1771 | |
---|
1772 | for(i=0; i<nG; i++) |
---|
1773 | { |
---|
1774 | ntmp = pLength(G->m[i]); |
---|
1775 | nmon += ntmp; |
---|
1776 | |
---|
1777 | if(i != n) |
---|
1778 | { |
---|
1779 | Print("%d, ", ntmp); |
---|
1780 | } |
---|
1781 | else |
---|
1782 | { |
---|
1783 | Print(" bzw. %d ", ntmp); |
---|
1784 | } |
---|
1785 | } |
---|
1786 | PrintS(" Monomen.\n"); |
---|
1787 | Print("//** %s besitzt %d Monome.", Ch, nmon); |
---|
1788 | PrintLn(); |
---|
1789 | } |
---|
1790 | */ |
---|
1791 | |
---|
1792 | //unused |
---|
1793 | /* |
---|
1794 | static void HeadidString(ideal L, char* st) |
---|
1795 | { |
---|
1796 | int i, nL = IDELEMS(L)-1; |
---|
1797 | |
---|
1798 | Print("// The head terms of the ideal %s = ", st); |
---|
1799 | for(i=0; i<nL; i++) |
---|
1800 | { |
---|
1801 | Print(" %s, ", pString(pHead(L->m[i]))); |
---|
1802 | } |
---|
1803 | Print(" %s;\n", pString(pHead(L->m[nL]))); |
---|
1804 | } |
---|
1805 | |
---|
1806 | */ |
---|
1807 | static inline int MivComp(intvec* iva, intvec* ivb) |
---|
1808 | { |
---|
1809 | assume(iva->length() == ivb->length()); |
---|
1810 | int i; |
---|
1811 | for(i=iva->length()-1; i>=0; i--) |
---|
1812 | { |
---|
1813 | if((*iva)[i] - (*ivb)[i] != 0) |
---|
1814 | { |
---|
1815 | return 0; |
---|
1816 | } |
---|
1817 | } |
---|
1818 | return 1; |
---|
1819 | } |
---|
1820 | |
---|
1821 | /********************************************** |
---|
1822 | * Look for the smallest absolut value in vec * |
---|
1823 | **********************************************/ |
---|
1824 | static int MivAbsMax(intvec* vec) |
---|
1825 | { |
---|
1826 | int i,k; |
---|
1827 | if((*vec)[0] < 0) |
---|
1828 | { |
---|
1829 | k = -(*vec)[0]; |
---|
1830 | } |
---|
1831 | else |
---|
1832 | { |
---|
1833 | k = (*vec)[0]; |
---|
1834 | } |
---|
1835 | for(i=1; i < (vec->length()); i++) |
---|
1836 | { |
---|
1837 | if((*vec)[i] < 0) |
---|
1838 | { |
---|
1839 | if(-(*vec)[i] > k) |
---|
1840 | { |
---|
1841 | k = -(*vec)[i]; |
---|
1842 | } |
---|
1843 | } |
---|
1844 | else |
---|
1845 | { |
---|
1846 | if((*vec)[i] > k) |
---|
1847 | { |
---|
1848 | k = (*vec)[i]; |
---|
1849 | } |
---|
1850 | } |
---|
1851 | } |
---|
1852 | return k; |
---|
1853 | } |
---|
1854 | |
---|
1855 | |
---|
1856 | /************************************************************** |
---|
1857 | * Look for the position of the smallest absolut value in vec * |
---|
1858 | **************************************************************/ |
---|
1859 | static int MivAbsMaxArg(intvec* vec) |
---|
1860 | { |
---|
1861 | int k = MivAbsMax(vec); |
---|
1862 | int i=0; |
---|
1863 | while(1) |
---|
1864 | { |
---|
1865 | if((*vec)[i] == k || (*vec)[i] == -k) |
---|
1866 | { |
---|
1867 | break; |
---|
1868 | } |
---|
1869 | i++; |
---|
1870 | } |
---|
1871 | return i; |
---|
1872 | } |
---|
1873 | |
---|
1874 | |
---|
1875 | /********************************************************************** |
---|
1876 | * Compute a next weight vector between curr_weight and target_weight * |
---|
1877 | * with respect to an ideal <G>. * |
---|
1878 | **********************************************************************/ |
---|
1879 | /* |
---|
1880 | static intvec* MwalkNextWeightCC(intvec* curr_weight, intvec* target_weight, |
---|
1881 | ideal G) |
---|
1882 | { |
---|
1883 | BOOLEAN nError = Overflow_Error; |
---|
1884 | Overflow_Error = FALSE; |
---|
1885 | |
---|
1886 | assume(currRing != NULL && curr_weight != NULL && |
---|
1887 | target_weight != NULL && G != NULL); |
---|
1888 | |
---|
1889 | int nRing = currRing->N; |
---|
1890 | int checkRed, j, nG = IDELEMS(G); |
---|
1891 | intvec* ivtemp; |
---|
1892 | |
---|
1893 | mpz_t t_zaehler, t_nenner; |
---|
1894 | mpz_init(t_zaehler); |
---|
1895 | mpz_init(t_nenner); |
---|
1896 | |
---|
1897 | mpz_t s_zaehler, s_nenner, temp, MwWd; |
---|
1898 | mpz_init(s_zaehler); |
---|
1899 | mpz_init(s_nenner); |
---|
1900 | mpz_init(temp); |
---|
1901 | mpz_init(MwWd); |
---|
1902 | |
---|
1903 | mpz_t sing_int; |
---|
1904 | mpz_init(sing_int); |
---|
1905 | mpz_set_si(sing_int, 2147483647); |
---|
1906 | |
---|
1907 | mpz_t sing_int_half; |
---|
1908 | mpz_init(sing_int_half); |
---|
1909 | mpz_set_si(sing_int_half, 3*(1073741824/2)); |
---|
1910 | |
---|
1911 | mpz_t deg_w0_p1, deg_d0_p1; |
---|
1912 | mpz_init(deg_w0_p1); |
---|
1913 | mpz_init(deg_d0_p1); |
---|
1914 | |
---|
1915 | mpz_t sztn, sntz; |
---|
1916 | mpz_init(sztn); |
---|
1917 | mpz_init(sntz); |
---|
1918 | |
---|
1919 | mpz_t t_null; |
---|
1920 | mpz_init(t_null); |
---|
1921 | |
---|
1922 | mpz_t ggt; |
---|
1923 | mpz_init(ggt); |
---|
1924 | |
---|
1925 | mpz_t dcw; |
---|
1926 | mpz_init(dcw); |
---|
1927 | |
---|
1928 | int gcd_tmp; |
---|
1929 | intvec* diff_weight = MivSub(target_weight, curr_weight); |
---|
1930 | |
---|
1931 | intvec* diff_weight1 = MivSub(target_weight, curr_weight); |
---|
1932 | poly g; |
---|
1933 | |
---|
1934 | for (j=0; j<nG; j++) |
---|
1935 | { |
---|
1936 | g = G->m[j]; |
---|
1937 | if (g != NULL) |
---|
1938 | { |
---|
1939 | ivtemp = MExpPol(g); |
---|
1940 | mpz_set_si(deg_w0_p1, MivDotProduct(ivtemp, curr_weight)); |
---|
1941 | mpz_set_si(deg_d0_p1, MivDotProduct(ivtemp, diff_weight)); |
---|
1942 | delete ivtemp; |
---|
1943 | |
---|
1944 | pIter(g); |
---|
1945 | while (g != NULL) |
---|
1946 | { |
---|
1947 | ivtemp = MExpPol(g); |
---|
1948 | mpz_set_si(MwWd, MivDotProduct(ivtemp, curr_weight)); |
---|
1949 | mpz_sub(s_zaehler, deg_w0_p1, MwWd); |
---|
1950 | if(mpz_cmp(s_zaehler, t_null) != 0) |
---|
1951 | { |
---|
1952 | mpz_set_si(MwWd, MivDotProduct(ivtemp, diff_weight)); |
---|
1953 | mpz_sub(s_nenner, MwWd, deg_d0_p1); |
---|
1954 | // check for 0 < s <= 1 |
---|
1955 | if( (mpz_cmp(s_zaehler,t_null) > 0 && |
---|
1956 | mpz_cmp(s_nenner, s_zaehler)>=0) || |
---|
1957 | (mpz_cmp(s_zaehler, t_null) < 0 && |
---|
1958 | mpz_cmp(s_nenner, s_zaehler)<=0)) |
---|
1959 | { |
---|
1960 | // make both positive |
---|
1961 | if (mpz_cmp(s_zaehler, t_null) < 0) |
---|
1962 | { |
---|
1963 | mpz_neg(s_zaehler, s_zaehler); |
---|
1964 | mpz_neg(s_nenner, s_nenner); |
---|
1965 | } |
---|
1966 | |
---|
1967 | //compute a simple fraction of s |
---|
1968 | cancel(s_zaehler, s_nenner); |
---|
1969 | |
---|
1970 | if(mpz_cmp(t_nenner, t_null) != 0) |
---|
1971 | { |
---|
1972 | mpz_mul(sztn, s_zaehler, t_nenner); |
---|
1973 | mpz_mul(sntz, s_nenner, t_zaehler); |
---|
1974 | |
---|
1975 | if(mpz_cmp(sztn,sntz) < 0) |
---|
1976 | { |
---|
1977 | mpz_add(t_nenner, t_null, s_nenner); |
---|
1978 | mpz_add(t_zaehler,t_null, s_zaehler); |
---|
1979 | } |
---|
1980 | } |
---|
1981 | else |
---|
1982 | { |
---|
1983 | mpz_add(t_nenner, t_null, s_nenner); |
---|
1984 | mpz_add(t_zaehler,t_null, s_zaehler); |
---|
1985 | } |
---|
1986 | } |
---|
1987 | } |
---|
1988 | pIter(g); |
---|
1989 | delete ivtemp; |
---|
1990 | } |
---|
1991 | } |
---|
1992 | } |
---|
1993 | //Print("\n// Alloc Size = %d \n", nRing*sizeof(mpz_t)); |
---|
1994 | mpz_t *vec=(mpz_t*)omAlloc(nRing*sizeof(mpz_t)); |
---|
1995 | |
---|
1996 | |
---|
1997 | // there is no 0<t<1 and define the next weight vector that is equal |
---|
1998 | // to the current weight vector |
---|
1999 | if(mpz_cmp(t_nenner, t_null) == 0) |
---|
2000 | { |
---|
2001 | #ifndef SING_NDEBUG |
---|
2002 | Print("\n//MwalkNextWeightCC: t_nenner=0\n"); |
---|
2003 | #endif |
---|
2004 | delete diff_weight; |
---|
2005 | diff_weight = ivCopy(curr_weight);//take memory |
---|
2006 | goto FINISH; |
---|
2007 | } |
---|
2008 | |
---|
2009 | // define the target vector as the next weight vector, if t = 1 |
---|
2010 | if(mpz_cmp_si(t_nenner, 1)==0 && mpz_cmp_si(t_zaehler,1)==0) |
---|
2011 | { |
---|
2012 | delete diff_weight; |
---|
2013 | diff_weight = ivCopy(target_weight); //this takes memory |
---|
2014 | goto FINISH; |
---|
2015 | } |
---|
2016 | |
---|
2017 | checkRed = 0; |
---|
2018 | |
---|
2019 | SIMPLIFY_GCD: |
---|
2020 | |
---|
2021 | // simplify the vectors curr_weight and diff_weight (C-int) |
---|
2022 | gcd_tmp = (*curr_weight)[0]; |
---|
2023 | |
---|
2024 | for (j=1; j<nRing; j++) |
---|
2025 | { |
---|
2026 | gcd_tmp = gcd(gcd_tmp, (*curr_weight)[j]); |
---|
2027 | if(gcd_tmp == 1) |
---|
2028 | { |
---|
2029 | break; |
---|
2030 | } |
---|
2031 | } |
---|
2032 | if(gcd_tmp != 1) |
---|
2033 | { |
---|
2034 | for (j=0; j<nRing; j++) |
---|
2035 | { |
---|
2036 | gcd_tmp = gcd(gcd_tmp, (*diff_weight)[j]); |
---|
2037 | if(gcd_tmp == 1) |
---|
2038 | { |
---|
2039 | break; |
---|
2040 | } |
---|
2041 | } |
---|
2042 | } |
---|
2043 | if(gcd_tmp != 1) |
---|
2044 | { |
---|
2045 | for (j=0; j<nRing; j++) |
---|
2046 | { |
---|
2047 | (*curr_weight)[j] = (*curr_weight)[j]/gcd_tmp; |
---|
2048 | (*diff_weight)[j] = (*diff_weight)[j]/gcd_tmp; |
---|
2049 | } |
---|
2050 | } |
---|
2051 | if(checkRed > 0) |
---|
2052 | { |
---|
2053 | for (j=0; j<nRing; j++) |
---|
2054 | { |
---|
2055 | mpz_set_si(vec[j], (*diff_weight)[j]); |
---|
2056 | } |
---|
2057 | goto TEST_OVERFLOW; |
---|
2058 | } |
---|
2059 | |
---|
2060 | #ifdef NEXT_VECTORS_CC |
---|
2061 | Print("\n// gcd of the weight vectors (current and target) = %d", gcd_tmp); |
---|
2062 | ivString(curr_weight, "new cw"); |
---|
2063 | ivString(diff_weight, "new dw"); |
---|
2064 | |
---|
2065 | PrintS("\n// t_zaehler: "); mpz_out_str( stdout, 10, t_zaehler); |
---|
2066 | PrintS(", t_nenner: "); mpz_out_str( stdout, 10, t_nenner); |
---|
2067 | #endif |
---|
2068 | |
---|
2069 | // construct a new weight vector and check whether vec[j] is overflow, |
---|
2070 | // i.e. vec[j] > 2^31. |
---|
2071 | // If vec[j] doesn't overflow, define a weight vector. Otherwise, |
---|
2072 | // report that overflow appears. In the second case, test whether the |
---|
2073 | // the correctness of the new vector plays an important role |
---|
2074 | |
---|
2075 | for (j=0; j<nRing; j++) |
---|
2076 | { |
---|
2077 | mpz_set_si(dcw, (*curr_weight)[j]); |
---|
2078 | mpz_mul(s_nenner, t_nenner, dcw); |
---|
2079 | |
---|
2080 | if( (*diff_weight)[j]>0) |
---|
2081 | { |
---|
2082 | mpz_mul_ui(s_zaehler, t_zaehler, (*diff_weight)[j]); |
---|
2083 | } |
---|
2084 | else |
---|
2085 | { |
---|
2086 | mpz_mul_ui(s_zaehler, t_zaehler, -(*diff_weight)[j]); |
---|
2087 | mpz_neg(s_zaehler, s_zaehler); |
---|
2088 | } |
---|
2089 | mpz_add(sntz, s_nenner, s_zaehler); |
---|
2090 | mpz_init_set(vec[j], sntz); |
---|
2091 | |
---|
2092 | #ifdef NEXT_VECTORS_CC |
---|
2093 | Print("\n// j = %d ==> ", j); |
---|
2094 | PrintS("("); |
---|
2095 | mpz_out_str( stdout, 10, t_nenner); |
---|
2096 | Print(" * %d)", (*curr_weight)[j]); |
---|
2097 | Print(" + ("); mpz_out_str( stdout, 10, t_zaehler); |
---|
2098 | Print(" * %d) = ", (*diff_weight)[j]); |
---|
2099 | mpz_out_str( stdout, 10, s_nenner); |
---|
2100 | PrintS(" + "); |
---|
2101 | mpz_out_str( stdout, 10, s_zaehler); |
---|
2102 | PrintS(" = "); mpz_out_str( stdout, 10, sntz); |
---|
2103 | Print(" ==> vector[%d]: ", j); mpz_out_str(stdout, 10, vec[j]); |
---|
2104 | #endif |
---|
2105 | |
---|
2106 | if(j==0) |
---|
2107 | { |
---|
2108 | mpz_set(ggt, sntz); |
---|
2109 | } |
---|
2110 | else |
---|
2111 | { |
---|
2112 | if(mpz_cmp_si(ggt,1) != 0) |
---|
2113 | { |
---|
2114 | mpz_gcd(ggt, ggt, sntz); |
---|
2115 | } |
---|
2116 | } |
---|
2117 | } |
---|
2118 | // reduce the vector with the gcd |
---|
2119 | if(mpz_cmp_si(ggt,1) != 0) |
---|
2120 | { |
---|
2121 | for (j=0; j<nRing; j++) |
---|
2122 | { |
---|
2123 | mpz_divexact(vec[j], vec[j], ggt); |
---|
2124 | } |
---|
2125 | } |
---|
2126 | #ifdef NEXT_VECTORS_CC |
---|
2127 | PrintS("\n// gcd of elements of the vector: "); |
---|
2128 | mpz_out_str( stdout, 10, ggt); |
---|
2129 | #endif |
---|
2130 | |
---|
2131 | for(j=0; j<nRing; j++) |
---|
2132 | { |
---|
2133 | if(mpz_cmp(vec[j], sing_int_half) >= 0) |
---|
2134 | { |
---|
2135 | goto REDUCTION; |
---|
2136 | } |
---|
2137 | } |
---|
2138 | checkRed = 1; |
---|
2139 | for (j=0; j<nRing; j++) |
---|
2140 | { |
---|
2141 | (*diff_weight)[j] = mpz_get_si(vec[j]); |
---|
2142 | } |
---|
2143 | goto SIMPLIFY_GCD; |
---|
2144 | |
---|
2145 | REDUCTION: |
---|
2146 | checkRed = 1; |
---|
2147 | for (j=0; j<nRing; j++) |
---|
2148 | { |
---|
2149 | (*diff_weight1)[j] = mpz_get_si(vec[j]); |
---|
2150 | } |
---|
2151 | while(test_w_in_ConeCC(G,diff_weight1)) |
---|
2152 | { |
---|
2153 | for(j=0; j<nRing; j++) |
---|
2154 | { |
---|
2155 | (*diff_weight)[j] = (*diff_weight1)[j]; |
---|
2156 | mpz_set_si(vec[j], (*diff_weight)[j]); |
---|
2157 | } |
---|
2158 | for(j=0; j<nRing; j++) |
---|
2159 | { |
---|
2160 | (*diff_weight1)[j] = floor(0.1*(*diff_weight)[j] + 0.5); |
---|
2161 | } |
---|
2162 | } |
---|
2163 | if(MivAbsMax(diff_weight)>10000) |
---|
2164 | { |
---|
2165 | for(j=0; j<nRing; j++) |
---|
2166 | { |
---|
2167 | (*diff_weight1)[j] = (*diff_weight)[j]; |
---|
2168 | } |
---|
2169 | j = 0; |
---|
2170 | while(test_w_in_ConeCC(G,diff_weight1)) |
---|
2171 | { |
---|
2172 | (*diff_weight)[j] = (*diff_weight1)[j]; |
---|
2173 | mpz_set_si(vec[j], (*diff_weight)[j]); |
---|
2174 | j = MivAbsMaxArg(diff_weight1); |
---|
2175 | (*diff_weight1)[j] = floor(0.1*(*diff_weight1)[j] + 0.5); |
---|
2176 | } |
---|
2177 | goto SIMPLIFY_GCD; |
---|
2178 | } |
---|
2179 | |
---|
2180 | TEST_OVERFLOW: |
---|
2181 | |
---|
2182 | for (j=0; j<nRing; j++) |
---|
2183 | { |
---|
2184 | if(mpz_cmp(vec[j], sing_int)>=0) |
---|
2185 | { |
---|
2186 | if(Overflow_Error == FALSE) |
---|
2187 | { |
---|
2188 | Overflow_Error = TRUE; |
---|
2189 | PrintS("\n// ** OVERFLOW in \"MwalkNextWeightCC\": "); |
---|
2190 | mpz_out_str( stdout, 10, vec[j]); |
---|
2191 | PrintS(" is greater than 2147483647 (max. integer representation)\n"); |
---|
2192 | //Print("// So vector[%d] := %d is wrong!!\n",j+1, vec[j]);// vec[j] is mpz_t |
---|
2193 | } |
---|
2194 | } |
---|
2195 | } |
---|
2196 | |
---|
2197 | FINISH: |
---|
2198 | delete diff_weight1; |
---|
2199 | mpz_clear(t_zaehler); |
---|
2200 | mpz_clear(t_nenner); |
---|
2201 | mpz_clear(s_zaehler); |
---|
2202 | mpz_clear(s_nenner); |
---|
2203 | mpz_clear(sntz); |
---|
2204 | mpz_clear(sztn); |
---|
2205 | mpz_clear(temp); |
---|
2206 | mpz_clear(MwWd); |
---|
2207 | mpz_clear(deg_w0_p1); |
---|
2208 | mpz_clear(deg_d0_p1); |
---|
2209 | mpz_clear(ggt); |
---|
2210 | omFree(vec); |
---|
2211 | mpz_clear(sing_int_half); |
---|
2212 | mpz_clear(sing_int); |
---|
2213 | mpz_clear(dcw); |
---|
2214 | mpz_clear(t_null); |
---|
2215 | |
---|
2216 | if(Overflow_Error == FALSE) |
---|
2217 | { |
---|
2218 | Overflow_Error = nError; |
---|
2219 | } |
---|
2220 | rComplete(currRing); |
---|
2221 | for(j=0; j<IDELEMS(G); j++) |
---|
2222 | { |
---|
2223 | poly p=G->m[j]; |
---|
2224 | while(p!=NULL) |
---|
2225 | { |
---|
2226 | p_Setm(p,currRing); |
---|
2227 | pIter(p); |
---|
2228 | } |
---|
2229 | } |
---|
2230 | return diff_weight; |
---|
2231 | } |
---|
2232 | */ |
---|
2233 | /********************************************************************** |
---|
2234 | * Compute a next weight vector between curr_weight and target_weight * |
---|
2235 | * with respect to an ideal <G>. * |
---|
2236 | **********************************************************************/ |
---|
2237 | static intvec* MwalkNextWeightCC(intvec* curr_weight, intvec* target_weight, |
---|
2238 | ideal G) |
---|
2239 | { |
---|
2240 | BOOLEAN nError = Overflow_Error; |
---|
2241 | Overflow_Error = FALSE; |
---|
2242 | |
---|
2243 | assume(currRing != NULL && curr_weight != NULL && |
---|
2244 | target_weight != NULL && G != NULL); |
---|
2245 | |
---|
2246 | int nRing = currRing->N; |
---|
2247 | int j, nG = IDELEMS(G); |
---|
2248 | intvec* ivtemp; |
---|
2249 | |
---|
2250 | mpz_t t_zaehler, t_nenner; |
---|
2251 | mpz_init(t_zaehler); |
---|
2252 | mpz_init(t_nenner); |
---|
2253 | |
---|
2254 | mpz_t s_zaehler, s_nenner, temp, MwWd; |
---|
2255 | mpz_init(s_zaehler); |
---|
2256 | mpz_init(s_nenner); |
---|
2257 | mpz_init(temp); |
---|
2258 | mpz_init(MwWd); |
---|
2259 | |
---|
2260 | mpz_t sing_int; |
---|
2261 | mpz_init(sing_int); |
---|
2262 | mpz_set_si(sing_int, 2147483647); |
---|
2263 | |
---|
2264 | mpz_t sing_int_half; |
---|
2265 | mpz_init(sing_int_half); |
---|
2266 | mpz_set_si(sing_int_half, 3*(1073741824/2)); |
---|
2267 | |
---|
2268 | mpz_t deg_w0_p1, deg_d0_p1; |
---|
2269 | mpz_init(deg_w0_p1); |
---|
2270 | mpz_init(deg_d0_p1); |
---|
2271 | |
---|
2272 | mpz_t sztn, sntz; |
---|
2273 | mpz_init(sztn); |
---|
2274 | mpz_init(sntz); |
---|
2275 | |
---|
2276 | mpz_t t_null; |
---|
2277 | mpz_init(t_null); |
---|
2278 | |
---|
2279 | mpz_t ggt; |
---|
2280 | mpz_init(ggt); |
---|
2281 | |
---|
2282 | mpz_t dcw; |
---|
2283 | mpz_init(dcw); |
---|
2284 | |
---|
2285 | int gcd_tmp; |
---|
2286 | //intvec* diff_weight = MivSub(target_weight, curr_weight); |
---|
2287 | |
---|
2288 | intvec* diff_weight1 = new intvec(nRing); //MivSub(target_weight, curr_weight); |
---|
2289 | poly g; |
---|
2290 | |
---|
2291 | // reduce the size of the entries of the current weight vector |
---|
2292 | if(TEST_OPT_REDSB) |
---|
2293 | { |
---|
2294 | for (j=0; j<nRing; j++) |
---|
2295 | { |
---|
2296 | (*diff_weight1)[j] = (*curr_weight)[j]; |
---|
2297 | } |
---|
2298 | while(MivAbsMax(diff_weight1)>10000 && test_w_in_ConeCC(G,diff_weight1)==1) |
---|
2299 | { |
---|
2300 | for(j=0; j<nRing; j++) |
---|
2301 | { |
---|
2302 | (*curr_weight)[j] = (*diff_weight1)[j]; |
---|
2303 | } |
---|
2304 | for(j=0; j<nRing; j++) |
---|
2305 | { |
---|
2306 | (*diff_weight1)[j] = floor(0.1*(*diff_weight1)[j] + 0.5); |
---|
2307 | } |
---|
2308 | } |
---|
2309 | |
---|
2310 | if(MivAbsMax(curr_weight)>100000) |
---|
2311 | { |
---|
2312 | for(j=0; j<nRing; j++) |
---|
2313 | { |
---|
2314 | (*diff_weight1)[j] = (*curr_weight)[j]; |
---|
2315 | } |
---|
2316 | j = 0; |
---|
2317 | while(test_w_in_ConeCC(G,diff_weight1)==1 && MivAbsMax(diff_weight1)>1000) |
---|
2318 | { |
---|
2319 | (*curr_weight)[j] = (*diff_weight1)[j]; |
---|
2320 | j = MivAbsMaxArg(diff_weight1); |
---|
2321 | (*diff_weight1)[j] = floor(0.1*(*diff_weight1)[j] + 0.5); |
---|
2322 | } |
---|
2323 | } |
---|
2324 | |
---|
2325 | } |
---|
2326 | intvec* diff_weight = MivSub(target_weight, curr_weight); |
---|
2327 | |
---|
2328 | // compute a suitable next weight vector |
---|
2329 | for (j=0; j<nG; j++) |
---|
2330 | { |
---|
2331 | g = G->m[j]; |
---|
2332 | if (g != NULL) |
---|
2333 | { |
---|
2334 | ivtemp = MExpPol(g); |
---|
2335 | mpz_set_si(deg_w0_p1, MivDotProduct(ivtemp, curr_weight)); |
---|
2336 | mpz_set_si(deg_d0_p1, MivDotProduct(ivtemp, diff_weight)); |
---|
2337 | delete ivtemp; |
---|
2338 | |
---|
2339 | pIter(g); |
---|
2340 | while (g != NULL) |
---|
2341 | { |
---|
2342 | ivtemp = MExpPol(g); |
---|
2343 | mpz_set_si(MwWd, MivDotProduct(ivtemp, curr_weight)); |
---|
2344 | mpz_sub(s_zaehler, deg_w0_p1, MwWd); |
---|
2345 | if(mpz_cmp(s_zaehler, t_null) != 0) |
---|
2346 | { |
---|
2347 | mpz_set_si(MwWd, MivDotProduct(ivtemp, diff_weight)); |
---|
2348 | mpz_sub(s_nenner, MwWd, deg_d0_p1); |
---|
2349 | // check for 0 < s <= 1 |
---|
2350 | if( (mpz_cmp(s_zaehler,t_null) > 0 && |
---|
2351 | mpz_cmp(s_nenner, s_zaehler)>=0) || |
---|
2352 | (mpz_cmp(s_zaehler, t_null) < 0 && |
---|
2353 | mpz_cmp(s_nenner, s_zaehler)<=0)) |
---|
2354 | { |
---|
2355 | // make both positive |
---|
2356 | if (mpz_cmp(s_zaehler, t_null) < 0) |
---|
2357 | { |
---|
2358 | mpz_neg(s_zaehler, s_zaehler); |
---|
2359 | mpz_neg(s_nenner, s_nenner); |
---|
2360 | } |
---|
2361 | |
---|
2362 | //compute a simple fraction of s |
---|
2363 | cancel(s_zaehler, s_nenner); |
---|
2364 | |
---|
2365 | if(mpz_cmp(t_nenner, t_null) != 0) |
---|
2366 | { |
---|
2367 | mpz_mul(sztn, s_zaehler, t_nenner); |
---|
2368 | mpz_mul(sntz, s_nenner, t_zaehler); |
---|
2369 | |
---|
2370 | if(mpz_cmp(sztn,sntz) < 0) |
---|
2371 | { |
---|
2372 | mpz_add(t_nenner, t_null, s_nenner); |
---|
2373 | mpz_add(t_zaehler,t_null, s_zaehler); |
---|
2374 | } |
---|
2375 | } |
---|
2376 | else |
---|
2377 | { |
---|
2378 | mpz_add(t_nenner, t_null, s_nenner); |
---|
2379 | mpz_add(t_zaehler,t_null, s_zaehler); |
---|
2380 | } |
---|
2381 | } |
---|
2382 | } |
---|
2383 | pIter(g); |
---|
2384 | delete ivtemp; |
---|
2385 | } |
---|
2386 | } |
---|
2387 | } |
---|
2388 | //Print("\n// Alloc Size = %d \n", nRing*sizeof(mpz_t)); |
---|
2389 | mpz_t *vec=(mpz_t*)omAlloc(nRing*sizeof(mpz_t)); |
---|
2390 | |
---|
2391 | |
---|
2392 | // there is no 0<t<1 and define the next weight vector that is equal |
---|
2393 | // to the current weight vector |
---|
2394 | if(mpz_cmp(t_nenner, t_null) == 0) |
---|
2395 | { |
---|
2396 | #ifndef SING_NDEBUG |
---|
2397 | Print("\n//MwalkNextWeightCC: t_nenner=0\n"); |
---|
2398 | #endif |
---|
2399 | delete diff_weight; |
---|
2400 | diff_weight = ivCopy(curr_weight);//take memory |
---|
2401 | goto FINISH; |
---|
2402 | } |
---|
2403 | |
---|
2404 | // define the target vector as the next weight vector, if t = 1 |
---|
2405 | if(mpz_cmp_si(t_nenner, 1)==0 && mpz_cmp_si(t_zaehler,1)==0) |
---|
2406 | { |
---|
2407 | delete diff_weight; |
---|
2408 | diff_weight = ivCopy(target_weight); //this takes memory |
---|
2409 | goto FINISH; |
---|
2410 | } |
---|
2411 | |
---|
2412 | SIMPLIFY_GCD: |
---|
2413 | |
---|
2414 | // simplify the vectors curr_weight and diff_weight (C-int) |
---|
2415 | gcd_tmp = (*curr_weight)[0]; |
---|
2416 | |
---|
2417 | for (j=1; j<nRing; j++) |
---|
2418 | { |
---|
2419 | gcd_tmp = gcd(gcd_tmp, (*curr_weight)[j]); |
---|
2420 | if(gcd_tmp == 1) |
---|
2421 | { |
---|
2422 | break; |
---|
2423 | } |
---|
2424 | } |
---|
2425 | if(gcd_tmp != 1) |
---|
2426 | { |
---|
2427 | for (j=0; j<nRing; j++) |
---|
2428 | { |
---|
2429 | gcd_tmp = gcd(gcd_tmp, (*diff_weight)[j]); |
---|
2430 | if(gcd_tmp == 1) |
---|
2431 | { |
---|
2432 | break; |
---|
2433 | } |
---|
2434 | } |
---|
2435 | } |
---|
2436 | if(gcd_tmp != 1) |
---|
2437 | { |
---|
2438 | for (j=0; j<nRing; j++) |
---|
2439 | { |
---|
2440 | (*curr_weight)[j] = (*curr_weight)[j]/gcd_tmp; |
---|
2441 | (*diff_weight)[j] = (*diff_weight)[j]/gcd_tmp; |
---|
2442 | } |
---|
2443 | } |
---|
2444 | |
---|
2445 | #ifdef NEXT_VECTORS_CC |
---|
2446 | Print("\n// gcd of the weight vectors (current and target) = %d", gcd_tmp); |
---|
2447 | ivString(curr_weight, "new cw"); |
---|
2448 | ivString(diff_weight, "new dw"); |
---|
2449 | |
---|
2450 | PrintS("\n// t_zaehler: "); mpz_out_str( stdout, 10, t_zaehler); |
---|
2451 | PrintS(", t_nenner: "); mpz_out_str( stdout, 10, t_nenner); |
---|
2452 | #endif |
---|
2453 | |
---|
2454 | // construct a new weight vector and check whether vec[j] is overflow, i.e. vec[j] > 2^31. |
---|
2455 | // If vec[j] doesn't overflow, define a weight vector. Otherwise, report that overflow |
---|
2456 | // appears. In the second case, test whether the the correctness of the new vector plays |
---|
2457 | // an important role |
---|
2458 | |
---|
2459 | for (j=0; j<nRing; j++) |
---|
2460 | { |
---|
2461 | mpz_set_si(dcw, (*curr_weight)[j]); |
---|
2462 | mpz_mul(s_nenner, t_nenner, dcw); |
---|
2463 | |
---|
2464 | if( (*diff_weight)[j]>0) |
---|
2465 | { |
---|
2466 | mpz_mul_ui(s_zaehler, t_zaehler, (*diff_weight)[j]); |
---|
2467 | } |
---|
2468 | else |
---|
2469 | { |
---|
2470 | mpz_mul_ui(s_zaehler, t_zaehler, -(*diff_weight)[j]); |
---|
2471 | mpz_neg(s_zaehler, s_zaehler); |
---|
2472 | } |
---|
2473 | mpz_add(sntz, s_nenner, s_zaehler); |
---|
2474 | mpz_init_set(vec[j], sntz); |
---|
2475 | |
---|
2476 | #ifdef NEXT_VECTORS_CC |
---|
2477 | Print("\n// j = %d ==> ", j); |
---|
2478 | PrintS("("); |
---|
2479 | mpz_out_str( stdout, 10, t_nenner); |
---|
2480 | Print(" * %d)", (*curr_weight)[j]); |
---|
2481 | Print(" + ("); mpz_out_str( stdout, 10, t_zaehler); |
---|
2482 | Print(" * %d) = ", (*diff_weight)[j]); |
---|
2483 | mpz_out_str( stdout, 10, s_nenner); |
---|
2484 | PrintS(" + "); |
---|
2485 | mpz_out_str( stdout, 10, s_zaehler); |
---|
2486 | PrintS(" = "); mpz_out_str( stdout, 10, sntz); |
---|
2487 | Print(" ==> vector[%d]: ", j); mpz_out_str(stdout, 10, vec[j]); |
---|
2488 | #endif |
---|
2489 | |
---|
2490 | if(j==0) |
---|
2491 | { |
---|
2492 | mpz_set(ggt, sntz); |
---|
2493 | } |
---|
2494 | else |
---|
2495 | { |
---|
2496 | if(mpz_cmp_si(ggt,1) != 0) |
---|
2497 | { |
---|
2498 | mpz_gcd(ggt, ggt, sntz); |
---|
2499 | } |
---|
2500 | } |
---|
2501 | } |
---|
2502 | // reduce the vector with the gcd |
---|
2503 | if(mpz_cmp_si(ggt,1) != 0) |
---|
2504 | { |
---|
2505 | for (j=0; j<nRing; j++) |
---|
2506 | { |
---|
2507 | mpz_divexact(vec[j], vec[j], ggt); |
---|
2508 | } |
---|
2509 | } |
---|
2510 | #ifdef NEXT_VECTORS_CC |
---|
2511 | PrintS("\n// gcd of elements of the vector: "); |
---|
2512 | mpz_out_str( stdout, 10, ggt); |
---|
2513 | #endif |
---|
2514 | |
---|
2515 | for (j=0; j<nRing; j++) |
---|
2516 | { |
---|
2517 | (*diff_weight)[j] = mpz_get_si(vec[j]); |
---|
2518 | } |
---|
2519 | |
---|
2520 | TEST_OVERFLOW: |
---|
2521 | |
---|
2522 | for (j=0; j<nRing; j++) |
---|
2523 | { |
---|
2524 | if(mpz_cmp(vec[j], sing_int)>=0) |
---|
2525 | { |
---|
2526 | if(Overflow_Error == FALSE) |
---|
2527 | { |
---|
2528 | Overflow_Error = TRUE; |
---|
2529 | PrintS("\n// ** OVERFLOW in \"MwalkNextWeightCC\": "); |
---|
2530 | mpz_out_str( stdout, 10, vec[j]); |
---|
2531 | PrintS(" is greater than 2147483647 (max. integer representation)\n"); |
---|
2532 | //Print("// So vector[%d] := %d is wrong!!\n",j+1, vec[j]);// vec[j] is mpz_t |
---|
2533 | } |
---|
2534 | } |
---|
2535 | } |
---|
2536 | |
---|
2537 | FINISH: |
---|
2538 | delete diff_weight1; |
---|
2539 | mpz_clear(t_zaehler); |
---|
2540 | mpz_clear(t_nenner); |
---|
2541 | mpz_clear(s_zaehler); |
---|
2542 | mpz_clear(s_nenner); |
---|
2543 | mpz_clear(sntz); |
---|
2544 | mpz_clear(sztn); |
---|
2545 | mpz_clear(temp); |
---|
2546 | mpz_clear(MwWd); |
---|
2547 | mpz_clear(deg_w0_p1); |
---|
2548 | mpz_clear(deg_d0_p1); |
---|
2549 | mpz_clear(ggt); |
---|
2550 | omFree(vec); |
---|
2551 | mpz_clear(sing_int_half); |
---|
2552 | mpz_clear(sing_int); |
---|
2553 | mpz_clear(dcw); |
---|
2554 | mpz_clear(t_null); |
---|
2555 | |
---|
2556 | if(Overflow_Error == FALSE) |
---|
2557 | { |
---|
2558 | Overflow_Error = nError; |
---|
2559 | } |
---|
2560 | rComplete(currRing); |
---|
2561 | for(j=0; j<IDELEMS(G); j++) |
---|
2562 | { |
---|
2563 | poly p=G->m[j]; |
---|
2564 | while(p!=NULL) |
---|
2565 | { |
---|
2566 | p_Setm(p,currRing); |
---|
2567 | pIter(p); |
---|
2568 | } |
---|
2569 | } |
---|
2570 | return diff_weight; |
---|
2571 | } |
---|
2572 | |
---|
2573 | |
---|
2574 | /********************************************************************** |
---|
2575 | * Compute an intermediate weight vector from iva to ivb w.r.t. * |
---|
2576 | * the reduced Groebner basis G. * |
---|
2577 | * Return NULL, if it is equal to iva or iva = avb. * |
---|
2578 | **********************************************************************/ |
---|
2579 | intvec* MkInterRedNextWeight(intvec* iva, intvec* ivb, ideal G) |
---|
2580 | { |
---|
2581 | intvec* tmp = new intvec(iva->length()); |
---|
2582 | intvec* result; |
---|
2583 | |
---|
2584 | if(G == NULL) |
---|
2585 | { |
---|
2586 | return tmp; |
---|
2587 | } |
---|
2588 | if(MivComp(iva, ivb) == 1) |
---|
2589 | { |
---|
2590 | return tmp; |
---|
2591 | } |
---|
2592 | result = MwalkNextWeightCC(iva, ivb, G); |
---|
2593 | |
---|
2594 | if(MivComp(result, iva) == 1) |
---|
2595 | { |
---|
2596 | delete result; |
---|
2597 | return tmp; |
---|
2598 | } |
---|
2599 | |
---|
2600 | delete tmp; |
---|
2601 | return result; |
---|
2602 | } |
---|
2603 | |
---|
2604 | /******************************************************************** |
---|
2605 | * define and execute a new ring which order is (a(vb),a(va),lp,C) * |
---|
2606 | * ******************************************************************/ |
---|
2607 | /*static ring VMrHomogeneous(intvec* va, intvec* vb) |
---|
2608 | { |
---|
2609 | |
---|
2610 | if ((currRing->ppNoether)!=NULL) |
---|
2611 | { |
---|
2612 | pDelete(&(currRing->ppNoether)); |
---|
2613 | } |
---|
2614 | if (((sLastPrinted.rtyp>BEGIN_RING) && (sLastPrinted.rtyp<END_RING)) || |
---|
2615 | ((sLastPrinted.rtyp==LIST_CMD)&&(lRingDependend((lists)sLastPrinted.data)))) |
---|
2616 | { |
---|
2617 | sLastPrinted.CleanUp(); |
---|
2618 | } |
---|
2619 | |
---|
2620 | ring r = (ring) omAlloc0Bin(sip_sring_bin); |
---|
2621 | int i, nv = currRing->N; |
---|
2622 | |
---|
2623 | r->cf = currRing->cf; |
---|
2624 | r->N = currRing->N; |
---|
2625 | int nb = 4; |
---|
2626 | |
---|
2627 | |
---|
2628 | //names |
---|
2629 | char* Q; // In order to avoid the corrupted memory, do not change. |
---|
2630 | r->names = (char **) omAlloc0(nv * sizeof(char_ptr)); |
---|
2631 | for(i=0; i<nv; i++) |
---|
2632 | { |
---|
2633 | Q = currRing->names[i]; |
---|
2634 | r->names[i] = omStrDup(Q); |
---|
2635 | } |
---|
2636 | |
---|
2637 | //weights: entries for 3 blocks: NULL Made:??? |
---|
2638 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2639 | r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
2640 | r->wvhdl[1] = (int*) omAlloc((nv)*sizeof(int)); |
---|
2641 | |
---|
2642 | for(i=0; i<nv; i++) |
---|
2643 | { |
---|
2644 | r->wvhdl[1][i] = (*vb)[i]; |
---|
2645 | r->wvhdl[0][i] = (*va)[i]; |
---|
2646 | } |
---|
2647 | r->wvhdl[0][nv] = (*va)[nv]; |
---|
2648 | |
---|
2649 | // order: (1..1),a,lp,C |
---|
2650 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2651 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2652 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2653 | |
---|
2654 | // ringorder a for the first block: var 1..nv |
---|
2655 | r->order[0] = ringorder_a; |
---|
2656 | r->block0[0] = 1; |
---|
2657 | r->block1[0] = nv; |
---|
2658 | |
---|
2659 | // ringorder a for the second block: var 2..nv |
---|
2660 | r->order[1] = ringorder_a; |
---|
2661 | r->block0[1] = 1; |
---|
2662 | r->block1[1] = nv; |
---|
2663 | |
---|
2664 | // ringorder lp for the third block: var 2..nv |
---|
2665 | r->order[2] = ringorder_lp; |
---|
2666 | r->block0[2] = 1; |
---|
2667 | r->block1[2] = nv; |
---|
2668 | |
---|
2669 | // ringorder C for the 4th block |
---|
2670 | // it is very important within "idLift", |
---|
2671 | // especially, by ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
2672 | // therefore, nb must be (nBlocks(currRing) + 1) |
---|
2673 | r->order[3] = ringorder_C; |
---|
2674 | |
---|
2675 | // polynomial ring |
---|
2676 | r->OrdSgn = 1; |
---|
2677 | |
---|
2678 | // complete ring intializations |
---|
2679 | |
---|
2680 | rComplete(r); |
---|
2681 | return r; |
---|
2682 | //rChangeCurrRing(r); |
---|
2683 | } |
---|
2684 | */ |
---|
2685 | |
---|
2686 | /************************************************************** |
---|
2687 | * define and execute a new ring which order is (a(va),lp,C) * |
---|
2688 | * ************************************************************/ |
---|
2689 | static ring VMrDefault(intvec* va) |
---|
2690 | { |
---|
2691 | |
---|
2692 | ring r = rCopy0(currRing,FALSE,FALSE); |
---|
2693 | int i, nv = currRing->N; |
---|
2694 | |
---|
2695 | int nb = 4; |
---|
2696 | |
---|
2697 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2698 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2699 | r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
2700 | for(i=0; i<nv; i++) |
---|
2701 | r->wvhdl[0][i] = (*va)[i]; |
---|
2702 | |
---|
2703 | /* order: a,lp,C,0 */ |
---|
2704 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2705 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2706 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2707 | |
---|
2708 | // ringorder a for the first block: var 1..nv |
---|
2709 | r->order[0] = ringorder_a; |
---|
2710 | r->block0[0] = 1; |
---|
2711 | r->block1[0] = nv; |
---|
2712 | |
---|
2713 | // ringorder lp for the second block: var 1..nv |
---|
2714 | r->order[1] = ringorder_lp; |
---|
2715 | r->block0[1] = 1; |
---|
2716 | r->block1[1] = nv; |
---|
2717 | |
---|
2718 | // ringorder C for the third block |
---|
2719 | // it is very important within "idLift", |
---|
2720 | // especially, by ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
2721 | // therefore, nb must be (nBlocks(currRing) + 1) |
---|
2722 | r->order[2] = ringorder_C; |
---|
2723 | |
---|
2724 | // the last block: everything is 0 |
---|
2725 | r->order[3] = 0; |
---|
2726 | |
---|
2727 | // polynomial ring |
---|
2728 | r->OrdSgn = 1; |
---|
2729 | |
---|
2730 | // complete ring intializations |
---|
2731 | |
---|
2732 | rComplete(r); |
---|
2733 | return r; |
---|
2734 | //rChangeCurrRing(r); |
---|
2735 | } |
---|
2736 | |
---|
2737 | /**************************************************************** |
---|
2738 | * define and execute a new ring with ordering (a(va),Wp(vb),C) * |
---|
2739 | * **************************************************************/ |
---|
2740 | static ring VMrRefine(intvec* va, intvec* vb) |
---|
2741 | { |
---|
2742 | |
---|
2743 | ring r = rCopy0(currRing,FALSE,FALSE); |
---|
2744 | int i, nv = currRing->N; |
---|
2745 | |
---|
2746 | int nb = 5; |
---|
2747 | |
---|
2748 | //weights: entries for 3 blocks: NULL Made:??? |
---|
2749 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2750 | r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
2751 | r->wvhdl[1] = (int*) omAlloc(nv*sizeof(int)); |
---|
2752 | |
---|
2753 | for(i=0; i<nv; i++) |
---|
2754 | { |
---|
2755 | r->wvhdl[0][i] = (*vb)[i]; |
---|
2756 | r->wvhdl[1][i] = (*va)[i]; |
---|
2757 | } |
---|
2758 | |
---|
2759 | // order: (1..1),a,lp,C |
---|
2760 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2761 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2762 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2763 | |
---|
2764 | // ringorder a for the first block: var 1..nv |
---|
2765 | r->order[0] = ringorder_a; |
---|
2766 | r->block0[0] = 1; |
---|
2767 | r->block1[0] = nv; |
---|
2768 | |
---|
2769 | // ringorder Wp for the second block: var 1..nv |
---|
2770 | r->order[1] = ringorder_a; |
---|
2771 | r->block0[1] = 1; |
---|
2772 | r->block1[1] = nv; |
---|
2773 | |
---|
2774 | // ringorder lp for the third block: var 1..nv |
---|
2775 | r->order[2] = ringorder_lp; |
---|
2776 | r->block0[2] = 1; |
---|
2777 | r->block1[2] = nv; |
---|
2778 | |
---|
2779 | // ringorder C for the 4th block |
---|
2780 | // it is very important within "idLift", |
---|
2781 | // especially, by ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
2782 | // therefore, nb must be (nBlocks(currRing) + 1) |
---|
2783 | r->order[3] = ringorder_C; |
---|
2784 | |
---|
2785 | // the last block: everything is 0 |
---|
2786 | r->order[4] = 0; |
---|
2787 | |
---|
2788 | // complete ring intializations |
---|
2789 | |
---|
2790 | rComplete(r); |
---|
2791 | |
---|
2792 | //rChangeCurrRing(r); |
---|
2793 | return r; |
---|
2794 | } |
---|
2795 | |
---|
2796 | /***************************************************** |
---|
2797 | * define and execute a new ring with ordering (M,C) * |
---|
2798 | *****************************************************/ |
---|
2799 | static ring VMatrDefault(intvec* va) |
---|
2800 | { |
---|
2801 | |
---|
2802 | ring r = rCopy0(currRing,FALSE,FALSE); |
---|
2803 | int i, nv = currRing->N; |
---|
2804 | |
---|
2805 | int nb = 4; |
---|
2806 | |
---|
2807 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2808 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2809 | r->wvhdl[0] = (int*) omAlloc(nv*nv*sizeof(int)); |
---|
2810 | r->wvhdl[1] =NULL; // (int*) omAlloc(nv*sizeof(int)); |
---|
2811 | r->wvhdl[2]=NULL; |
---|
2812 | r->wvhdl[3]=NULL; |
---|
2813 | for(i=0; i<nv*nv; i++) |
---|
2814 | r->wvhdl[0][i] = (*va)[i]; |
---|
2815 | |
---|
2816 | /* order: a,lp,C,0 */ |
---|
2817 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2818 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2819 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2820 | |
---|
2821 | // ringorder a for the first block: var 1..nv |
---|
2822 | r->order[0] = ringorder_M; |
---|
2823 | r->block0[0] = 1; |
---|
2824 | r->block1[0] = nv; |
---|
2825 | |
---|
2826 | // ringorder C for the second block |
---|
2827 | r->order[1] = ringorder_C; |
---|
2828 | r->block0[1] = 1; |
---|
2829 | r->block1[1] = nv; |
---|
2830 | |
---|
2831 | // ringorder C for the third block: var 1..nv |
---|
2832 | r->order[2] = ringorder_C; |
---|
2833 | r->block0[2] = 1; |
---|
2834 | r->block1[2] = nv; |
---|
2835 | |
---|
2836 | // the last block: everything is 0 |
---|
2837 | r->order[3] = 0; |
---|
2838 | |
---|
2839 | // complete ring intializations |
---|
2840 | |
---|
2841 | rComplete(r); |
---|
2842 | |
---|
2843 | //rChangeCurrRing(r); |
---|
2844 | return r; |
---|
2845 | } |
---|
2846 | |
---|
2847 | /*********************************************************** |
---|
2848 | * define and execute a new ring with ordering (a(vb),M,C) * |
---|
2849 | ***********************************************************/ |
---|
2850 | static ring VMatrRefine(intvec* va, intvec* vb) |
---|
2851 | { |
---|
2852 | |
---|
2853 | ring r = rCopy0(currRing,FALSE,FALSE); |
---|
2854 | int i, nv = currRing->N; |
---|
2855 | int nvs = nv*nv; |
---|
2856 | |
---|
2857 | int nb = 4; |
---|
2858 | |
---|
2859 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2860 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2861 | r->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
2862 | r->wvhdl[1] = (int*) omAlloc(nvs*sizeof(int)); |
---|
2863 | r->wvhdl[2]=NULL; |
---|
2864 | r->wvhdl[3]=NULL; |
---|
2865 | for(i=0; i<nvs; i++) |
---|
2866 | { |
---|
2867 | r->wvhdl[1][i] = (*va)[i]; |
---|
2868 | } |
---|
2869 | for(i=0; i<nv; i++) |
---|
2870 | { |
---|
2871 | r->wvhdl[0][i] = (*vb)[i]; |
---|
2872 | } |
---|
2873 | /* order: a,lp,C,0 */ |
---|
2874 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2875 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2876 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2877 | |
---|
2878 | // ringorder a for the first block: var 1..nv |
---|
2879 | r->order[0] = ringorder_a; |
---|
2880 | r->block0[0] = 1; |
---|
2881 | r->block1[0] = nv; |
---|
2882 | |
---|
2883 | // ringorder M for the second block: var 1..nv |
---|
2884 | r->order[1] = ringorder_M; |
---|
2885 | r->block0[1] = 1; |
---|
2886 | r->block1[1] = nv; |
---|
2887 | |
---|
2888 | // ringorder C for the third block: var 1..nv |
---|
2889 | r->order[2] = ringorder_C; |
---|
2890 | r->block0[2] = 1; |
---|
2891 | r->block1[2] = nv; |
---|
2892 | |
---|
2893 | // the last block: everything is 0 |
---|
2894 | r->order[3] = 0; |
---|
2895 | |
---|
2896 | // complete ring intializations |
---|
2897 | |
---|
2898 | rComplete(r); |
---|
2899 | |
---|
2900 | //rChangeCurrRing(r); |
---|
2901 | return r; |
---|
2902 | } |
---|
2903 | |
---|
2904 | /********************************************************************** |
---|
2905 | * define and execute a new ring which order is a lexicographic order * |
---|
2906 | ***********************************************************************/ |
---|
2907 | static void VMrDefaultlp(void) |
---|
2908 | { |
---|
2909 | ring r = rCopy0(currRing,FALSE,FALSE); |
---|
2910 | int i, nv = currRing->N; |
---|
2911 | |
---|
2912 | int nb = rBlocks(currRing) + 1; |
---|
2913 | |
---|
2914 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2915 | |
---|
2916 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2917 | |
---|
2918 | /* order: lp,C,0 */ |
---|
2919 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2920 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2921 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2922 | |
---|
2923 | /* ringorder lp for the first block: var 1..nv */ |
---|
2924 | r->order[0] = ringorder_lp; |
---|
2925 | r->block0[0] = 1; |
---|
2926 | r->block1[0] = nv; |
---|
2927 | |
---|
2928 | /* ringorder C for the second block */ |
---|
2929 | r->order[1] = ringorder_C; |
---|
2930 | |
---|
2931 | /* the last block: everything is 0 */ |
---|
2932 | r->order[2] = 0; |
---|
2933 | |
---|
2934 | /*polynomial ring*/ |
---|
2935 | r->OrdSgn = 1; |
---|
2936 | |
---|
2937 | /* complete ring intializations */ |
---|
2938 | |
---|
2939 | rComplete(r); |
---|
2940 | |
---|
2941 | rChangeCurrRing(r); |
---|
2942 | } |
---|
2943 | |
---|
2944 | /*************************************************** |
---|
2945 | * define a ring with parameters und change to it * |
---|
2946 | * DefRingPar and DefRingParlp corrupt still memory * |
---|
2947 | ****************************************************/ |
---|
2948 | static void DefRingPar(intvec* va) |
---|
2949 | { |
---|
2950 | int i, nv = currRing->N; |
---|
2951 | int nb = rBlocks(currRing) + 1; |
---|
2952 | |
---|
2953 | ring res=rCopy0(currRing,FALSE,FALSE); |
---|
2954 | |
---|
2955 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
2956 | res->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
2957 | res->wvhdl[0] = (int*) omAlloc(nv*sizeof(int)); |
---|
2958 | for(i=0; i<nv; i++) |
---|
2959 | res->wvhdl[0][i] = (*va)[i]; |
---|
2960 | |
---|
2961 | /* order: a,lp,C,0 */ |
---|
2962 | |
---|
2963 | res->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
2964 | res->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2965 | res->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
2966 | |
---|
2967 | // ringorder a for the first block: var 1..nv |
---|
2968 | res->order[0] = ringorder_a; |
---|
2969 | res->block0[0] = 1; |
---|
2970 | res->block1[0] = nv; |
---|
2971 | |
---|
2972 | // ringorder lp for the second block: var 1..nv |
---|
2973 | res->order[1] = ringorder_lp; |
---|
2974 | res->block0[1] = 1; |
---|
2975 | res->block1[1] = nv; |
---|
2976 | |
---|
2977 | // ringorder C for the third block |
---|
2978 | // it is very important within "idLift", |
---|
2979 | // especially, by ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
2980 | // therefore, nb must be (nBlocks(currRing) + 1) |
---|
2981 | res->order[2] = ringorder_C; |
---|
2982 | |
---|
2983 | // the last block: everything is 0 |
---|
2984 | res->order[3] = 0; |
---|
2985 | |
---|
2986 | // polynomial ring |
---|
2987 | res->OrdSgn = 1; |
---|
2988 | |
---|
2989 | |
---|
2990 | // complete ring intializations |
---|
2991 | rComplete(res); |
---|
2992 | |
---|
2993 | // execute the created ring |
---|
2994 | rChangeCurrRing(res); |
---|
2995 | } |
---|
2996 | |
---|
2997 | static void DefRingParlp(void) |
---|
2998 | { |
---|
2999 | int i, nv = currRing->N; |
---|
3000 | |
---|
3001 | ring r=rCopy0(currRing,FALSE,FALSE); |
---|
3002 | |
---|
3003 | int nb = rBlocks(currRing) + 1; |
---|
3004 | |
---|
3005 | /*weights: entries for 3 blocks: NULL Made:???*/ |
---|
3006 | |
---|
3007 | r->wvhdl = (int **)omAlloc0(nb * sizeof(int_ptr)); |
---|
3008 | |
---|
3009 | /* order: lp,C,0 */ |
---|
3010 | r->order = (int *) omAlloc(nb * sizeof(int *)); |
---|
3011 | r->block0 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
3012 | r->block1 = (int *)omAlloc0(nb * sizeof(int *)); |
---|
3013 | |
---|
3014 | /* ringorder lp for the first block: var 1..nv */ |
---|
3015 | r->order[0] = ringorder_lp; |
---|
3016 | r->block0[0] = 1; |
---|
3017 | r->block1[0] = nv; |
---|
3018 | |
---|
3019 | /* ringorder C for the second block */ |
---|
3020 | r->order[1] = ringorder_C; |
---|
3021 | |
---|
3022 | /* the last block: everything is 0 */ |
---|
3023 | r->order[2] = 0; |
---|
3024 | |
---|
3025 | /*polynomial ring*/ |
---|
3026 | r->OrdSgn = 1; |
---|
3027 | |
---|
3028 | |
---|
3029 | // if (rParameter(currRing)!=NULL) |
---|
3030 | // { |
---|
3031 | // r->cf->extRing->qideal->m[0]=p_Copy(currRing->cf->extRing->qideal->m[0], currRing->cf->extRing); |
---|
3032 | // int l=rPar(currRing); |
---|
3033 | // r->cf->extRing->names=(char **)omAlloc(l*sizeof(char_ptr)); |
---|
3034 | // |
---|
3035 | // for(i=l-1;i>=0;i--) |
---|
3036 | // { |
---|
3037 | // rParameter(r)[i]=omStrDup(rParameter(currRing)[i]); |
---|
3038 | // } |
---|
3039 | // } |
---|
3040 | |
---|
3041 | // complete ring intializations |
---|
3042 | |
---|
3043 | rComplete(r); |
---|
3044 | |
---|
3045 | // execute the created ring |
---|
3046 | rChangeCurrRing(r); |
---|
3047 | } |
---|
3048 | |
---|
3049 | /************************************************************* |
---|
3050 | * check whether one or more components of a vector are zero * |
---|
3051 | *************************************************************/ |
---|
3052 | /* unused: |
---|
3053 | static int isNolVector(intvec* hilb) |
---|
3054 | { |
---|
3055 | int i; |
---|
3056 | for(i=hilb->length()-1; i>=0; i--) |
---|
3057 | { |
---|
3058 | if((* hilb)[i]==0) |
---|
3059 | { |
---|
3060 | return 1; |
---|
3061 | } |
---|
3062 | } |
---|
3063 | return 0; |
---|
3064 | } |
---|
3065 | */ |
---|
3066 | |
---|
3067 | /************************************************************* |
---|
3068 | * check whether one or more components of a vector are <= 0 * |
---|
3069 | *************************************************************/ |
---|
3070 | static int isNegNolVector(intvec* hilb) |
---|
3071 | { |
---|
3072 | int i; |
---|
3073 | for(i=hilb->length()-1; i>=0; i--) |
---|
3074 | { |
---|
3075 | if((* hilb)[i]<=0) |
---|
3076 | { |
---|
3077 | return 1; |
---|
3078 | } |
---|
3079 | } |
---|
3080 | return 0; |
---|
3081 | } |
---|
3082 | |
---|
3083 | /************************************************************************** |
---|
3084 | * Gomega is the initial ideal of G w. r. t. the current weight vector * |
---|
3085 | * curr_weight. Check whether curr_weight lies on a border of the Groebner * |
---|
3086 | * cone, i. e. check whether a monomial is divisible by a leading monomial * |
---|
3087 | ***************************************************************************/ |
---|
3088 | static ideal middleOfCone(ideal G, ideal Gomega) |
---|
3089 | { |
---|
3090 | BOOLEAN middle = FALSE; |
---|
3091 | int i,j,N = IDELEMS(Gomega); |
---|
3092 | poly p,lm,factor1,factor2; |
---|
3093 | |
---|
3094 | ideal Go = idCopy(G); |
---|
3095 | |
---|
3096 | // check whether leading monomials of G and Gomega coincide |
---|
3097 | // and return NULL if not |
---|
3098 | for(i=0; i<N; i++) |
---|
3099 | { |
---|
3100 | if(!pIsConstant(pSub(pCopy(Gomega->m[i]),pCopy(pHead(G->m[i]))))) |
---|
3101 | { |
---|
3102 | idDelete(&Go); |
---|
3103 | return NULL; |
---|
3104 | } |
---|
3105 | } |
---|
3106 | for(i=0; i<N; i++) |
---|
3107 | { |
---|
3108 | for(j=0; j<N; j++) |
---|
3109 | { |
---|
3110 | if(i!=j) |
---|
3111 | { |
---|
3112 | p = pCopy(Gomega->m[i]); |
---|
3113 | lm = pCopy(Gomega->m[j]); |
---|
3114 | pIter(p); |
---|
3115 | while(p!=NULL) |
---|
3116 | { |
---|
3117 | if(pDivisibleBy(lm,p)) |
---|
3118 | { |
---|
3119 | if(middle == FALSE) |
---|
3120 | { |
---|
3121 | middle = TRUE; |
---|
3122 | } |
---|
3123 | factor1 = singclap_pdivide(pHead(p),lm,currRing); |
---|
3124 | factor2 = pMult(pCopy(factor1),pCopy(Go->m[j])); |
---|
3125 | pDelete(&factor1); |
---|
3126 | Go->m[i] = pAdd((Go->m[i]),pNeg(pCopy(factor2))); |
---|
3127 | pDelete(&factor2); |
---|
3128 | } |
---|
3129 | pIter(p); |
---|
3130 | } |
---|
3131 | pDelete(&lm); |
---|
3132 | pDelete(&p); |
---|
3133 | } |
---|
3134 | } |
---|
3135 | } |
---|
3136 | |
---|
3137 | if(middle == TRUE) |
---|
3138 | { |
---|
3139 | return Go; |
---|
3140 | } |
---|
3141 | idDelete(&Go); |
---|
3142 | return NULL; |
---|
3143 | } |
---|
3144 | |
---|
3145 | /****************************** Februar 2002 **************************** |
---|
3146 | * G is a Groebner basis w.r.t. (a(curr_weight),lp) and * |
---|
3147 | * we compute a GB of <G> w.r.t. the lex. order by the perturbation walk * |
---|
3148 | * its perturbation degree is tp_deg * |
---|
3149 | * We call the following subfunction LastGB, if * |
---|
3150 | * the computed intermediate weight vector or * |
---|
3151 | * if the perturbed target weight vector does NOT lie n the correct cone * |
---|
3152 | **************************************************************************/ |
---|
3153 | |
---|
3154 | static ideal LastGB(ideal G, intvec* curr_weight,int tp_deg) |
---|
3155 | { |
---|
3156 | BOOLEAN nError = Overflow_Error; |
---|
3157 | Overflow_Error = FALSE; |
---|
3158 | |
---|
3159 | int i, nV = currRing->N; |
---|
3160 | int nwalk=0, endwalks=0, nnwinC=1; |
---|
3161 | int nlast = 0; |
---|
3162 | ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG; |
---|
3163 | ring newRing, oldRing, TargetRing; |
---|
3164 | intvec* iv_M_lp; |
---|
3165 | intvec* target_weight; |
---|
3166 | intvec* iv_lp = Mivlp(nV); //define (1,0,...,0) |
---|
3167 | intvec* pert_target_vector; |
---|
3168 | intvec* ivNull = new intvec(nV); |
---|
3169 | intvec* extra_curr_weight = new intvec(nV); |
---|
3170 | intvec* next_weight; |
---|
3171 | |
---|
3172 | #ifndef BUCHBERGER_ALG |
---|
3173 | intvec* hilb_func; |
---|
3174 | #endif |
---|
3175 | |
---|
3176 | // to avoid (1,0,...,0) as the target vector |
---|
3177 | intvec* last_omega = new intvec(nV); |
---|
3178 | for(i=nV-1; i>0; i--) |
---|
3179 | { |
---|
3180 | (*last_omega)[i] = 1; |
---|
3181 | } |
---|
3182 | (*last_omega)[0] = 10000; |
---|
3183 | |
---|
3184 | ring EXXRing = currRing; |
---|
3185 | |
---|
3186 | // compute a pertubed weight vector of the target weight vector |
---|
3187 | if(tp_deg > 1 && tp_deg <= nV) |
---|
3188 | { |
---|
3189 | //..25.03.03 VMrDefaultlp();// VMrDefault(target_weight); |
---|
3190 | if (rParameter (currRing) != NULL) |
---|
3191 | { |
---|
3192 | DefRingParlp(); |
---|
3193 | } |
---|
3194 | else |
---|
3195 | { |
---|
3196 | VMrDefaultlp(); |
---|
3197 | } |
---|
3198 | TargetRing = currRing; |
---|
3199 | ssG = idrMoveR(G,EXXRing,currRing); |
---|
3200 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
3201 | //target_weight = MPertVectorslp(ssG, iv_M_lp, tp_deg); |
---|
3202 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
3203 | delete iv_M_lp; |
---|
3204 | pert_target_vector = target_weight; |
---|
3205 | |
---|
3206 | rChangeCurrRing(EXXRing); |
---|
3207 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
3208 | } |
---|
3209 | else |
---|
3210 | { |
---|
3211 | target_weight = Mivlp(nV); |
---|
3212 | } |
---|
3213 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
3214 | |
---|
3215 | while(1) |
---|
3216 | { |
---|
3217 | nwalk++; |
---|
3218 | nstep++; |
---|
3219 | to=clock(); |
---|
3220 | // compute a next weight vector |
---|
3221 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
3222 | xtnw=xtnw+clock()-to; |
---|
3223 | |
---|
3224 | #ifdef PRINT_VECTORS |
---|
3225 | MivString(curr_weight, target_weight, next_weight); |
---|
3226 | #endif |
---|
3227 | |
---|
3228 | if(Overflow_Error == TRUE) |
---|
3229 | { |
---|
3230 | newRing = currRing; |
---|
3231 | nnwinC = 0; |
---|
3232 | if(tp_deg == 1) |
---|
3233 | { |
---|
3234 | nlast = 1; |
---|
3235 | } |
---|
3236 | delete next_weight; |
---|
3237 | |
---|
3238 | //idElements(G, "G"); |
---|
3239 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
3240 | |
---|
3241 | break; |
---|
3242 | } |
---|
3243 | |
---|
3244 | if(MivComp(next_weight, ivNull) == 1) |
---|
3245 | { |
---|
3246 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
3247 | newRing = currRing; |
---|
3248 | delete next_weight; |
---|
3249 | break; |
---|
3250 | } |
---|
3251 | |
---|
3252 | if(MivComp(next_weight, target_weight) == 1) |
---|
3253 | endwalks = 1; |
---|
3254 | |
---|
3255 | for(i=nV-1; i>=0; i--) |
---|
3256 | { |
---|
3257 | (*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
3258 | } |
---|
3259 | /* 06.11.01 NOT Changed */ |
---|
3260 | for(i=nV-1; i>=0; i--) |
---|
3261 | { |
---|
3262 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
3263 | } |
---|
3264 | oldRing = currRing; |
---|
3265 | to=clock(); |
---|
3266 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
3267 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
3268 | xtif=xtif+clock()-to; |
---|
3269 | |
---|
3270 | #ifdef ENDWALKS |
---|
3271 | if(endwalks == 1) |
---|
3272 | { |
---|
3273 | Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
3274 | /* |
---|
3275 | idElements(Gomega, "Gw"); |
---|
3276 | headidString(Gomega, "Gw"); |
---|
3277 | */ |
---|
3278 | } |
---|
3279 | #endif |
---|
3280 | |
---|
3281 | #ifndef BUCHBERGER_ALG |
---|
3282 | if(isNolVector(curr_weight) == 0) |
---|
3283 | { |
---|
3284 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
3285 | } |
---|
3286 | else |
---|
3287 | { |
---|
3288 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
3289 | } |
---|
3290 | #endif // BUCHBERGER_ALG |
---|
3291 | |
---|
3292 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
3293 | //..25.03.03 VMrDefault(curr_weight); |
---|
3294 | if (rParameter (currRing) != NULL) |
---|
3295 | { |
---|
3296 | DefRingPar(curr_weight); |
---|
3297 | } |
---|
3298 | else |
---|
3299 | { |
---|
3300 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
3301 | } |
---|
3302 | newRing = currRing; |
---|
3303 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
3304 | |
---|
3305 | to=clock(); |
---|
3306 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
3307 | #ifdef BUCHBERGER_ALG |
---|
3308 | M = MstdhomCC(Gomega1); |
---|
3309 | #else |
---|
3310 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
3311 | delete hilb_func; |
---|
3312 | #endif // BUCHBERGER_ALG |
---|
3313 | xtstd=xtstd+clock()-to; |
---|
3314 | /* change the ring to oldRing */ |
---|
3315 | rChangeCurrRing(oldRing); |
---|
3316 | M1 = idrMoveR(M, newRing,currRing); |
---|
3317 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
3318 | |
---|
3319 | to=clock(); |
---|
3320 | /* compute a reduced Groebner basis of <G> w.r.t. "newRing" */ |
---|
3321 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
3322 | xtlift=xtlift+clock()-to; |
---|
3323 | |
---|
3324 | idDelete(&M1); |
---|
3325 | idDelete(&G); |
---|
3326 | |
---|
3327 | /* change the ring to newRing */ |
---|
3328 | rChangeCurrRing(newRing); |
---|
3329 | F1 = idrMoveR(F, oldRing,currRing); |
---|
3330 | |
---|
3331 | to=clock(); |
---|
3332 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
3333 | G = kInterRedCC(F1, NULL); |
---|
3334 | xtred=xtred+clock()-to; |
---|
3335 | idDelete(&F1); |
---|
3336 | |
---|
3337 | if(endwalks == 1) |
---|
3338 | { |
---|
3339 | //Print("\n// ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
3340 | break; |
---|
3341 | } |
---|
3342 | |
---|
3343 | delete next_weight; |
---|
3344 | }//while |
---|
3345 | |
---|
3346 | delete ivNull; |
---|
3347 | |
---|
3348 | if(tp_deg != 1) |
---|
3349 | { |
---|
3350 | //..25.03.03 VMrDefaultlp();//define and execute the ring "lp" |
---|
3351 | if (rParameter (currRing) != NULL) |
---|
3352 | { |
---|
3353 | DefRingParlp(); |
---|
3354 | } |
---|
3355 | else |
---|
3356 | { |
---|
3357 | VMrDefaultlp(); |
---|
3358 | } |
---|
3359 | F1 = idrMoveR(G, newRing,currRing); |
---|
3360 | |
---|
3361 | if(nnwinC == 0 || test_w_in_ConeCC(F1, pert_target_vector) != 1) |
---|
3362 | { |
---|
3363 | oldRing = currRing; |
---|
3364 | rChangeCurrRing(newRing); |
---|
3365 | G = idrMoveR(F1, oldRing,currRing); |
---|
3366 | Print("\n// takes %d steps and calls the recursion of level %d:", |
---|
3367 | nwalk, tp_deg-1); |
---|
3368 | |
---|
3369 | F1 = LastGB(G,curr_weight, tp_deg-1); |
---|
3370 | } |
---|
3371 | |
---|
3372 | TargetRing = currRing; |
---|
3373 | rChangeCurrRing(EXXRing); |
---|
3374 | result = idrMoveR(F1, TargetRing,currRing); |
---|
3375 | } |
---|
3376 | else |
---|
3377 | { |
---|
3378 | if(nlast == 1) |
---|
3379 | { |
---|
3380 | //OMEGA_OVERFLOW_LASTGB: |
---|
3381 | /* |
---|
3382 | if(MivSame(curr_weight, iv_lp) == 1) |
---|
3383 | if (rParameter(currRing) != NULL) |
---|
3384 | DefRingParlp(); |
---|
3385 | else |
---|
3386 | VMrDefaultlp(); |
---|
3387 | else |
---|
3388 | if (rParameter(currRing) != NULL) |
---|
3389 | DefRingPar(curr_weight); |
---|
3390 | else |
---|
3391 | VMrDefault(curr_weight); |
---|
3392 | */ |
---|
3393 | |
---|
3394 | //..25.03.03 VMrDefaultlp();//define and execute the ring "lp" |
---|
3395 | if (rParameter (currRing) != NULL) |
---|
3396 | { |
---|
3397 | DefRingParlp(); |
---|
3398 | } |
---|
3399 | else |
---|
3400 | { |
---|
3401 | VMrDefaultlp(); |
---|
3402 | } |
---|
3403 | |
---|
3404 | F1 = idrMoveR(G, newRing,currRing); |
---|
3405 | //Print("\n// Apply \"std\" in ring r%d_%d = %s;\n", tp_deg, nwalk, rString(currRing)); |
---|
3406 | |
---|
3407 | G = MstdCC(F1); |
---|
3408 | idDelete(&F1); |
---|
3409 | newRing = currRing; |
---|
3410 | } |
---|
3411 | |
---|
3412 | rChangeCurrRing(EXXRing); |
---|
3413 | result = idrMoveR(G, newRing,currRing); |
---|
3414 | } |
---|
3415 | delete target_weight; |
---|
3416 | delete last_omega; |
---|
3417 | delete iv_lp; |
---|
3418 | |
---|
3419 | if(Overflow_Error == FALSE) |
---|
3420 | { |
---|
3421 | Overflow_Error = nError; |
---|
3422 | } |
---|
3423 | return(result); |
---|
3424 | } |
---|
3425 | |
---|
3426 | /********************************************************** |
---|
3427 | * check whether a polynomial of G has least 4 monomials * |
---|
3428 | **********************************************************/ |
---|
3429 | static int lengthpoly(ideal G) |
---|
3430 | { |
---|
3431 | int i; |
---|
3432 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
3433 | { |
---|
3434 | if((G->m[i]!=NULL) /* len >=0 */ |
---|
3435 | && (G->m[i]->next!=NULL) /* len >=1 */ |
---|
3436 | && (G->m[i]->next->next!=NULL) /* len >=2 */ |
---|
3437 | && (G->m[i]->next->next->next!=NULL) /* len >=3 */ |
---|
3438 | && (G->m[i]->next->next->next->next!=NULL) /* len >=4*/ ) |
---|
3439 | { |
---|
3440 | return 1; |
---|
3441 | } |
---|
3442 | } |
---|
3443 | return 0; |
---|
3444 | } |
---|
3445 | |
---|
3446 | /***************************************** |
---|
3447 | * return maximal polynomial length of G * |
---|
3448 | *****************************************/ |
---|
3449 | static int maxlengthpoly(ideal G) |
---|
3450 | { |
---|
3451 | int i,k,length=0; |
---|
3452 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
3453 | { |
---|
3454 | k = pLength(G->m[i]); |
---|
3455 | if(k>length) |
---|
3456 | { |
---|
3457 | length = k; |
---|
3458 | } |
---|
3459 | } |
---|
3460 | return length; |
---|
3461 | } |
---|
3462 | |
---|
3463 | /********************************************************* |
---|
3464 | * check whether a polynomial of G has least 2 monomials * |
---|
3465 | **********************************************************/ |
---|
3466 | static int islengthpoly2(ideal G) |
---|
3467 | { |
---|
3468 | int i; |
---|
3469 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
3470 | { |
---|
3471 | if((G->m[i]!=NULL) /* len >=0 */ |
---|
3472 | && (G->m[i]->next!=NULL) /* len >=1 */ |
---|
3473 | && (G->m[i]->next->next!=NULL)) /* len >=2 */ |
---|
3474 | { |
---|
3475 | return 1; |
---|
3476 | } |
---|
3477 | } |
---|
3478 | return 0; |
---|
3479 | } |
---|
3480 | |
---|
3481 | |
---|
3482 | |
---|
3483 | /* Implementation of the improved Groebner walk algorithm which is written |
---|
3484 | by Quoc-Nam Tran (2000). |
---|
3485 | One perturbs the original target weight vector, only if |
---|
3486 | the next intermediate weight vector is equal to the current target weight |
---|
3487 | vector. This must be repeated until the wanted reduced Groebner basis |
---|
3488 | to reach. |
---|
3489 | If the numbers of variables is big enough, the representation of the origin |
---|
3490 | weight vector may be very big. Therefore, it is possible the intermediate |
---|
3491 | weight vector doesn't stay in the correct Groebner cone. |
---|
3492 | In this case we have just a reduced Groebner basis of the given ideal |
---|
3493 | with respect to another monomial order. Then we have to compute |
---|
3494 | a wanted reduced Groebner basis of it with respect to the given order. |
---|
3495 | At the following subroutine we use the improved Buchberger algorithm or |
---|
3496 | the changed perturbation walk algorithm with a decrased degree. |
---|
3497 | */ |
---|
3498 | |
---|
3499 | /*************************************** |
---|
3500 | * return the initial term of an ideal * |
---|
3501 | ***************************************/ |
---|
3502 | static ideal idHeadCC(ideal h) |
---|
3503 | { |
---|
3504 | int i, nH =IDELEMS(h); |
---|
3505 | |
---|
3506 | ideal m = idInit(nH,h->rank); |
---|
3507 | |
---|
3508 | for (i=nH-1;i>=0; i--) |
---|
3509 | { |
---|
3510 | if (h->m[i]!=NULL) |
---|
3511 | { |
---|
3512 | m->m[i]=pHead(h->m[i]); |
---|
3513 | } |
---|
3514 | } |
---|
3515 | return m; |
---|
3516 | } |
---|
3517 | |
---|
3518 | /********************************************** |
---|
3519 | * check whether two head-ideals are the same * |
---|
3520 | **********************************************/ |
---|
3521 | static inline int test_G_GB_walk(ideal H0, ideal H1) |
---|
3522 | { |
---|
3523 | int i, nG = IDELEMS(H0); |
---|
3524 | |
---|
3525 | if(nG != IDELEMS(H1)) |
---|
3526 | { |
---|
3527 | return 0; |
---|
3528 | } |
---|
3529 | for(i=nG-1; i>=0; i--) |
---|
3530 | { |
---|
3531 | /* |
---|
3532 | poly t; |
---|
3533 | if((t=pSub(pCopy(H0->m[i]), pCopy(H1->m[i]))) != NULL) |
---|
3534 | { |
---|
3535 | pDelete(&t); |
---|
3536 | return 0; |
---|
3537 | } |
---|
3538 | pDelete(&t); |
---|
3539 | */ |
---|
3540 | if(!pEqualPolys(H0->m[i],H1->m[i])) |
---|
3541 | { |
---|
3542 | return 0; |
---|
3543 | } |
---|
3544 | } |
---|
3545 | return 1; |
---|
3546 | } |
---|
3547 | |
---|
3548 | //unused |
---|
3549 | /***************************************************** |
---|
3550 | * find the maximal total degree of polynomials in G * |
---|
3551 | *****************************************************/ |
---|
3552 | /* |
---|
3553 | static int Trandegreebound(ideal G) |
---|
3554 | { |
---|
3555 | int i, nG = IDELEMS(G); |
---|
3556 | // int np=1; |
---|
3557 | int nV = currRing->N; |
---|
3558 | int degtmp, result = 0; |
---|
3559 | intvec* ivUnit = Mivdp(nV); |
---|
3560 | |
---|
3561 | for(i=nG-1; i>=0; i--) |
---|
3562 | { |
---|
3563 | // find the maximal total degree of the polynomial G[i] |
---|
3564 | degtmp = MwalkWeightDegree(G->m[i], ivUnit); |
---|
3565 | if(degtmp > result) |
---|
3566 | { |
---|
3567 | result = degtmp; |
---|
3568 | } |
---|
3569 | } |
---|
3570 | delete ivUnit; |
---|
3571 | return result; |
---|
3572 | } |
---|
3573 | */ |
---|
3574 | |
---|
3575 | //unused |
---|
3576 | /************************************************************************ |
---|
3577 | * perturb the weight vector iva w.r.t. the ideal G. * |
---|
3578 | * the monomial order of the current ring is the w_1 weight lex. order * |
---|
3579 | * define w := d^(n-1)w_1+ d^(n-2)w_2, ...+ dw_(n-1)+ w_n * |
---|
3580 | * where d := 1 + max{totdeg(g):g in G}*m, or * |
---|
3581 | * d := (2*maxdeg*maxdeg + (nV+1)*maxdeg)*m; * |
---|
3582 | ************************************************************************/ |
---|
3583 | #if 0 |
---|
3584 | static intvec* TranPertVector(ideal G, intvec* iva) |
---|
3585 | { |
---|
3586 | BOOLEAN nError = Overflow_Error; |
---|
3587 | Overflow_Error = FALSE; |
---|
3588 | |
---|
3589 | int i, j; |
---|
3590 | // int nG = IDELEMS(G); |
---|
3591 | int nV = currRing->N; |
---|
3592 | |
---|
3593 | // define the sequence which expresses the current monomial ordering |
---|
3594 | // w_1 = iva; w_2 = (1,0,..,0); w_n = (0,...,0,1,0) |
---|
3595 | intvec* ivMat = MivMatrixOrder(iva); |
---|
3596 | |
---|
3597 | int mtmp, m=(*iva)[0]; |
---|
3598 | |
---|
3599 | for(i=ivMat->length(); i>=0; i--) |
---|
3600 | { |
---|
3601 | mtmp = (*ivMat)[i]; |
---|
3602 | if(mtmp <0) |
---|
3603 | { |
---|
3604 | mtmp = -mtmp; |
---|
3605 | } |
---|
3606 | if(mtmp > m) |
---|
3607 | { |
---|
3608 | m = mtmp; |
---|
3609 | } |
---|
3610 | } |
---|
3611 | |
---|
3612 | // define the maximal total degree of polynomials of G |
---|
3613 | mpz_t ndeg; |
---|
3614 | mpz_init(ndeg); |
---|
3615 | |
---|
3616 | // 12 Juli 03 |
---|
3617 | #ifndef UPPER_BOUND |
---|
3618 | mpz_set_si(ndeg, Trandegreebound(G)+1); |
---|
3619 | #else |
---|
3620 | mpz_t ztmp; |
---|
3621 | mpz_init(ztmp); |
---|
3622 | |
---|
3623 | mpz_t maxdeg; |
---|
3624 | mpz_init_set_si(maxdeg, Trandegreebound(G)); |
---|
3625 | |
---|
3626 | //ndeg = (2*maxdeg*maxdeg + (nV+1)*maxdeg)*m;//Kalkbrenner (1999) |
---|
3627 | mpz_pow_ui(ztmp, maxdeg, 2); |
---|
3628 | mpz_mul_ui(ztmp, ztmp, 2); |
---|
3629 | mpz_mul_ui(maxdeg, maxdeg, nV+1); |
---|
3630 | mpz_add(ndeg, ztmp, maxdeg); |
---|
3631 | mpz_mul_ui(ndeg, ndeg, m); |
---|
3632 | |
---|
3633 | mpz_clear(ztmp); |
---|
3634 | |
---|
3635 | //PrintS("\n// with the new upper degree bound (2d^2+(n+1)d)*m "); |
---|
3636 | //Print("\n// where d = %d, n = %d and bound = %d", maxdeg, nV, ndeg); |
---|
3637 | #endif //UPPER_BOUND |
---|
3638 | |
---|
3639 | #ifdef INVEPS_SMALL_IN_TRAN |
---|
3640 | if(mpz_cmp_ui(ndeg, nV)>0 && nV > 3) |
---|
3641 | { |
---|
3642 | mpz_cdiv_q_ui(ndeg, ndeg, nV); |
---|
3643 | } |
---|
3644 | //PrintS("\n// choose the \"small\" inverse epsilon:"); |
---|
3645 | //mpz_out_str(stdout, 10, ndeg); |
---|
3646 | #endif |
---|
3647 | mpz_t deg_tmp; |
---|
3648 | mpz_init_set(deg_tmp, ndeg); |
---|
3649 | |
---|
3650 | mpz_t *ivres=( mpz_t *) omAlloc(nV*sizeof(mpz_t)); |
---|
3651 | mpz_init_set_si(ivres[nV-1],1); |
---|
3652 | |
---|
3653 | for(i=nV-2; i>=0; i--) |
---|
3654 | { |
---|
3655 | mpz_init_set(ivres[i], deg_tmp); |
---|
3656 | mpz_mul(deg_tmp, deg_tmp, ndeg); |
---|
3657 | } |
---|
3658 | |
---|
3659 | mpz_t *ivtmp=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
3660 | for(i=0; i<nV; i++) |
---|
3661 | { |
---|
3662 | mpz_init(ivtmp[i]); |
---|
3663 | } |
---|
3664 | mpz_t sing_int; |
---|
3665 | mpz_init_set_ui(sing_int, 2147483647); |
---|
3666 | |
---|
3667 | intvec* repr_vector = new intvec(nV); |
---|
3668 | |
---|
3669 | // define ivtmp := ndeg^(n-1).w_1 + ndeg^(n-2).w_2 + ... + w_n |
---|
3670 | for(i=0; i<nV; i++) |
---|
3671 | { |
---|
3672 | for(j=0; j<nV; j++) |
---|
3673 | { |
---|
3674 | if( (*ivMat)[i*nV+j] >= 0 ) |
---|
3675 | { |
---|
3676 | mpz_mul_ui(ivres[i], ivres[i], (*ivMat)[i*nV+j]); |
---|
3677 | } |
---|
3678 | else |
---|
3679 | { |
---|
3680 | mpz_mul_ui(ivres[i], ivres[i], -(*ivMat)[i*nV+j]); |
---|
3681 | mpz_neg(ivres[i], ivres[i]); |
---|
3682 | } |
---|
3683 | mpz_add(ivtmp[j], ivtmp[j], ivres[i]); |
---|
3684 | } |
---|
3685 | } |
---|
3686 | delete ivMat; |
---|
3687 | |
---|
3688 | int ntrue=0; |
---|
3689 | for(i=0; i<nV; i++) |
---|
3690 | { |
---|
3691 | (*repr_vector)[i] = mpz_get_si(ivtmp[i]); |
---|
3692 | if(mpz_cmp(ivtmp[i], sing_int)>=0) |
---|
3693 | { |
---|
3694 | ntrue++; |
---|
3695 | if(Overflow_Error == FALSE) |
---|
3696 | { |
---|
3697 | Overflow_Error = TRUE; |
---|
3698 | |
---|
3699 | PrintS("\n// ** OVERFLOW in \"Repr.Vector\": "); |
---|
3700 | mpz_out_str( stdout, 10, ivtmp[i]); |
---|
3701 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
3702 | Print("\n// So vector[%d] := %d is wrong!!\n",i+1,(*repr_vector)[i]); |
---|
3703 | } |
---|
3704 | } |
---|
3705 | } |
---|
3706 | if(Overflow_Error == TRUE) |
---|
3707 | { |
---|
3708 | ivString(repr_vector, "repvector"); |
---|
3709 | Print("\n// %d element(s) of it are overflow!!", ntrue); |
---|
3710 | } |
---|
3711 | |
---|
3712 | if(Overflow_Error == FALSE) |
---|
3713 | Overflow_Error=nError; |
---|
3714 | |
---|
3715 | omFree(ivres); |
---|
3716 | omFree(ivtmp); |
---|
3717 | |
---|
3718 | mpz_clear(sing_int); |
---|
3719 | mpz_clear(deg_tmp); |
---|
3720 | mpz_clear(ndeg); |
---|
3721 | |
---|
3722 | return repr_vector; |
---|
3723 | } |
---|
3724 | #endif |
---|
3725 | |
---|
3726 | //unused |
---|
3727 | #if 0 |
---|
3728 | static intvec* TranPertVector_lp(ideal G) |
---|
3729 | { |
---|
3730 | BOOLEAN nError = Overflow_Error; |
---|
3731 | Overflow_Error = FALSE; |
---|
3732 | // int j, nG = IDELEMS(G); |
---|
3733 | int i; |
---|
3734 | int nV = currRing->N; |
---|
3735 | |
---|
3736 | // define the maximal total degree of polynomials of G |
---|
3737 | mpz_t ndeg; |
---|
3738 | mpz_init(ndeg); |
---|
3739 | |
---|
3740 | // 12 Juli 03 |
---|
3741 | #ifndef UPPER_BOUND |
---|
3742 | mpz_set_si(ndeg, Trandegreebound(G)+1); |
---|
3743 | #else |
---|
3744 | mpz_t ztmp; |
---|
3745 | mpz_init(ztmp); |
---|
3746 | |
---|
3747 | mpz_t maxdeg; |
---|
3748 | mpz_init_set_si(maxdeg, Trandegreebound(G)); |
---|
3749 | |
---|
3750 | //ndeg = (2*maxdeg*maxdeg + (nV+1)*maxdeg);//Kalkbrenner (1999) |
---|
3751 | mpz_pow_ui(ztmp, maxdeg, 2); |
---|
3752 | mpz_mul_ui(ztmp, ztmp, 2); |
---|
3753 | mpz_mul_ui(maxdeg, maxdeg, nV+1); |
---|
3754 | mpz_add(ndeg, ztmp, maxdeg); |
---|
3755 | // PrintS("\n// with the new upper degree bound (2d^2+(n+1)d)*m "); |
---|
3756 | // Print("\n// where d = %d, n = %d and bound = %d", |
---|
3757 | // mpz_get_si(maxdeg), nV, mpz_get_si(ndeg)); |
---|
3758 | |
---|
3759 | mpz_clear(ztmp); |
---|
3760 | |
---|
3761 | #endif |
---|
3762 | |
---|
3763 | #ifdef INVEPS_SMALL_IN_TRAN |
---|
3764 | if(mpz_cmp_ui(ndeg, nV)>0 && nV > 3) |
---|
3765 | mpz_cdiv_q_ui(ndeg, ndeg, nV); |
---|
3766 | |
---|
3767 | //PrintS("\n// choose the \"small\" inverse epsilon:"); |
---|
3768 | // mpz_out_str(stdout, 10, ndeg); |
---|
3769 | #endif |
---|
3770 | |
---|
3771 | mpz_t deg_tmp; |
---|
3772 | mpz_init_set(deg_tmp, ndeg); |
---|
3773 | |
---|
3774 | mpz_t *ivres=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
3775 | mpz_init_set_si(ivres[nV-1], 1); |
---|
3776 | |
---|
3777 | for(i=nV-2; i>=0; i--) |
---|
3778 | { |
---|
3779 | mpz_init_set(ivres[i], deg_tmp); |
---|
3780 | mpz_mul(deg_tmp, deg_tmp, ndeg); |
---|
3781 | } |
---|
3782 | |
---|
3783 | mpz_t sing_int; |
---|
3784 | mpz_init_set_ui(sing_int, 2147483647); |
---|
3785 | |
---|
3786 | intvec* repr_vector = new intvec(nV); |
---|
3787 | int ntrue=0; |
---|
3788 | for(i=0; i<nV; i++) |
---|
3789 | { |
---|
3790 | (*repr_vector)[i] = mpz_get_si(ivres[i]); |
---|
3791 | |
---|
3792 | if(mpz_cmp(ivres[i], sing_int)>=0) |
---|
3793 | { |
---|
3794 | ntrue++; |
---|
3795 | if(Overflow_Error == FALSE) |
---|
3796 | { |
---|
3797 | Overflow_Error = TRUE; |
---|
3798 | PrintS("\n// ** OVERFLOW in \"Repr.Vector\": "); |
---|
3799 | mpz_out_str( stdout, 10, ivres[i]); |
---|
3800 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
3801 | Print("\n// So vector[%d] := %d is wrong!!\n",i+1,(*repr_vector)[i]); |
---|
3802 | } |
---|
3803 | } |
---|
3804 | } |
---|
3805 | if(Overflow_Error == TRUE) |
---|
3806 | { |
---|
3807 | ivString(repr_vector, "repvector"); |
---|
3808 | Print("\n// %d element(s) of it are overflow!!", ntrue); |
---|
3809 | } |
---|
3810 | if(Overflow_Error == FALSE) |
---|
3811 | Overflow_Error = nError; |
---|
3812 | |
---|
3813 | omFree(ivres); |
---|
3814 | |
---|
3815 | mpz_clear(ndeg); |
---|
3816 | mpz_clear(sing_int); |
---|
3817 | |
---|
3818 | return repr_vector; |
---|
3819 | } |
---|
3820 | #endif |
---|
3821 | |
---|
3822 | //unused |
---|
3823 | #if 0 |
---|
3824 | static intvec* RepresentationMatrix_Dp(ideal G, intvec* M) |
---|
3825 | { |
---|
3826 | BOOLEAN nError = Overflow_Error; |
---|
3827 | Overflow_Error = FALSE; |
---|
3828 | |
---|
3829 | int i, j; |
---|
3830 | int nV = currRing->N; |
---|
3831 | |
---|
3832 | intvec* ivUnit = Mivdp(nV); |
---|
3833 | int degtmp, maxdeg = 0; |
---|
3834 | |
---|
3835 | for(i=IDELEMS(G)-1; i>=0; i--) |
---|
3836 | { |
---|
3837 | // find the maximal total degree of the polynomial G[i] |
---|
3838 | degtmp = MwalkWeightDegree(G->m[i], ivUnit); |
---|
3839 | if(degtmp > maxdeg) |
---|
3840 | maxdeg = degtmp; |
---|
3841 | } |
---|
3842 | |
---|
3843 | mpz_t ztmp; |
---|
3844 | mpz_init_set_si(ztmp, maxdeg); |
---|
3845 | mpz_t *ivres=(mpz_t *)omAlloc(nV*sizeof(mpz_t)); |
---|
3846 | mpz_init_set_si(ivres[nV-1], 1); // (*ivres)[nV-1] = 1; |
---|
3847 | |
---|
3848 | for(i=nV-2; i>=0; i--) |
---|
3849 | { |
---|
3850 | mpz_init_set(ivres[i], ztmp); //(*ivres)[i] = ztmp; |
---|
3851 | mpz_mul_ui(ztmp, ztmp, maxdeg); //ztmp *=maxdeg; |
---|
3852 | } |
---|
3853 | |
---|
3854 | mpz_t *ivtmp=(mpz_t*)omAlloc(nV*sizeof(mpz_t)); |
---|
3855 | for(i=0; i<nV; i++) |
---|
3856 | mpz_init(ivtmp[i]); |
---|
3857 | |
---|
3858 | // define ivtmp := ndeg^(n-1).w_1 + ndeg^(n-2).w_2 + ... + w_n |
---|
3859 | for(i=0; i<nV; i++) |
---|
3860 | for(j=0; j<nV; j++) |
---|
3861 | { |
---|
3862 | if((*M)[i*nV+j] < 0) |
---|
3863 | { |
---|
3864 | mpz_mul_ui(ztmp, ivres[i], -(*M)[i*nV+j]); |
---|
3865 | mpz_neg(ztmp, ztmp); |
---|
3866 | } |
---|
3867 | else |
---|
3868 | mpz_mul_ui(ztmp, ivres[i], (*M)[i*nV+j]); |
---|
3869 | |
---|
3870 | mpz_add(ivtmp[j], ivtmp[j], ztmp); |
---|
3871 | } |
---|
3872 | delete ivres; |
---|
3873 | mpz_t sing_int; |
---|
3874 | mpz_init_set_ui(sing_int, 2147483647); |
---|
3875 | |
---|
3876 | int ntrue=0; |
---|
3877 | intvec* repvector = new intvec(nV); |
---|
3878 | for(i=0; i<nV; i++) |
---|
3879 | { |
---|
3880 | (*repvector)[i] = mpz_get_si(ivtmp[i]); |
---|
3881 | if(mpz_cmp(ivtmp[i], sing_int)>0) |
---|
3882 | { |
---|
3883 | ntrue++; |
---|
3884 | if(Overflow_Error == FALSE) |
---|
3885 | { |
---|
3886 | Overflow_Error = TRUE; |
---|
3887 | PrintS("\n// ** OVERFLOW in \"Repr.Matrix\": "); |
---|
3888 | mpz_out_str( stdout, 10, ivtmp[i]); |
---|
3889 | PrintS(" is greater than 2147483647 (max. integer representation)"); |
---|
3890 | Print("\n// So vector[%d] := %d is wrong!!\n",i+1,(*repvector)[i]); |
---|
3891 | } |
---|
3892 | } |
---|
3893 | } |
---|
3894 | if(Overflow_Error == TRUE) |
---|
3895 | { |
---|
3896 | ivString(repvector, "repvector"); |
---|
3897 | Print("\n// %d element(s) of it are overflow!!", ntrue); |
---|
3898 | } |
---|
3899 | |
---|
3900 | if(Overflow_Error == FALSE) |
---|
3901 | Overflow_Error = nError; |
---|
3902 | |
---|
3903 | mpz_clear(sing_int); |
---|
3904 | mpz_clear(ztmp); |
---|
3905 | omFree(ivtmp); |
---|
3906 | omFree(ivres); |
---|
3907 | return repvector; |
---|
3908 | } |
---|
3909 | #endif |
---|
3910 | |
---|
3911 | /***************************************************************************** |
---|
3912 | * The following subroutine is the implementation of our first improved * |
---|
3913 | * Groebner walk algorithm, i.e. the first altervative algorithm. * |
---|
3914 | * First we use the Grobner walk algorithm and then we call the changed * |
---|
3915 | * perturbation walk algorithm with decreased degree, if an intermediate * |
---|
3916 | * weight vector is equal to the current target weight vector. * |
---|
3917 | * This call will be only repeated until we get the wanted reduced Groebner * |
---|
3918 | * basis or n times, where n is the numbers of variables. * |
---|
3919 | *****************************************************************************/ |
---|
3920 | |
---|
3921 | // npwinc = 0, if curr_weight doesn't stay in the correct Groebner cone |
---|
3922 | static ideal Rec_LastGB(ideal G, intvec* curr_weight, |
---|
3923 | intvec* orig_target_weight, int tp_deg, int npwinc) |
---|
3924 | { |
---|
3925 | BOOLEAN nError = Overflow_Error; |
---|
3926 | Overflow_Error = FALSE; |
---|
3927 | // BOOLEAN nOverflow_Error = FALSE; |
---|
3928 | |
---|
3929 | clock_t tproc=0; |
---|
3930 | clock_t tinput = clock(); |
---|
3931 | |
---|
3932 | int i, nV = currRing->N; |
---|
3933 | int nwalk=0, endwalks=0, nnwinC=1; |
---|
3934 | int nlast = 0; |
---|
3935 | ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG; |
---|
3936 | ring newRing, oldRing, TargetRing; |
---|
3937 | intvec* iv_M_lp; |
---|
3938 | intvec* target_weight; |
---|
3939 | intvec* ivNull = new intvec(nV); //define (0,...,0) |
---|
3940 | ring EXXRing = currRing; |
---|
3941 | //int NEG=0; //19 juni 03 |
---|
3942 | intvec* next_weight; |
---|
3943 | #ifndef BUCHBERGER_ALG |
---|
3944 | //08 Juli 03 |
---|
3945 | intvec* hilb_func; |
---|
3946 | #endif |
---|
3947 | // to avoid (1,0,...,0) as the target vector |
---|
3948 | intvec* last_omega = new intvec(nV); |
---|
3949 | for(i=nV-1; i>0; i--) |
---|
3950 | (*last_omega)[i] = 1; |
---|
3951 | (*last_omega)[0] = 10000; |
---|
3952 | |
---|
3953 | BOOLEAN isGB = FALSE; |
---|
3954 | |
---|
3955 | // compute a pertubed weight vector of the target weight vector |
---|
3956 | if(tp_deg > 1 && tp_deg <= nV) |
---|
3957 | { |
---|
3958 | ideal H0 = idHeadCC(G); |
---|
3959 | |
---|
3960 | if (rParameter (currRing) != NULL) |
---|
3961 | { |
---|
3962 | DefRingParlp(); |
---|
3963 | } |
---|
3964 | else |
---|
3965 | { |
---|
3966 | VMrDefaultlp(); |
---|
3967 | } |
---|
3968 | TargetRing = currRing; |
---|
3969 | ssG = idrMoveR(G,EXXRing,currRing); |
---|
3970 | |
---|
3971 | ideal H0_tmp = idrMoveR(H0,EXXRing,currRing); |
---|
3972 | ideal H1 = idHeadCC(ssG); |
---|
3973 | |
---|
3974 | // Apply Lemma 2.2 in Collart et. al (1997) to check whether cone(k-1) is equal to cone(k) |
---|
3975 | if(test_G_GB_walk(H0_tmp,H1)==1) |
---|
3976 | { |
---|
3977 | idDelete(&H0_tmp); |
---|
3978 | idDelete(&H1); |
---|
3979 | G = ssG; |
---|
3980 | ssG = NULL; |
---|
3981 | newRing = currRing; |
---|
3982 | delete ivNull; |
---|
3983 | |
---|
3984 | if(npwinc != 0) |
---|
3985 | { |
---|
3986 | goto LastGB_Finish; |
---|
3987 | } |
---|
3988 | else |
---|
3989 | { |
---|
3990 | isGB = TRUE; |
---|
3991 | goto KSTD_Finish; |
---|
3992 | } |
---|
3993 | } |
---|
3994 | idDelete(&H0_tmp); |
---|
3995 | idDelete(&H1); |
---|
3996 | |
---|
3997 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
3998 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
3999 | delete iv_M_lp; |
---|
4000 | //PrintS("\n// Input is not GB!!"); |
---|
4001 | rChangeCurrRing(EXXRing); |
---|
4002 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
4003 | |
---|
4004 | if(Overflow_Error == TRUE) |
---|
4005 | { |
---|
4006 | //nOverflow_Error = Overflow_Error; |
---|
4007 | //NEG = 1; |
---|
4008 | newRing = currRing; |
---|
4009 | goto JUNI_STD; |
---|
4010 | } |
---|
4011 | } |
---|
4012 | |
---|
4013 | while(1) |
---|
4014 | { |
---|
4015 | nwalk ++; |
---|
4016 | nstep++; |
---|
4017 | |
---|
4018 | if(nwalk==1) |
---|
4019 | { |
---|
4020 | goto FIRST_STEP; |
---|
4021 | } |
---|
4022 | to=clock(); |
---|
4023 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
4024 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
4025 | xtif=xtif+clock()-to; |
---|
4026 | |
---|
4027 | #ifndef BUCHBERGER_ALG |
---|
4028 | if(isNolVector(curr_weight) == 0) |
---|
4029 | { |
---|
4030 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
4031 | } |
---|
4032 | else |
---|
4033 | { |
---|
4034 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
4035 | } |
---|
4036 | #endif // BUCHBERGER_ALG |
---|
4037 | |
---|
4038 | oldRing = currRing; |
---|
4039 | |
---|
4040 | // defiNe a new ring that its ordering is "(a(curr_weight),lp) |
---|
4041 | if (rParameter(currRing) != NULL) |
---|
4042 | { |
---|
4043 | DefRingPar(curr_weight); |
---|
4044 | } |
---|
4045 | else |
---|
4046 | { |
---|
4047 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
4048 | } |
---|
4049 | newRing = currRing; |
---|
4050 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
4051 | to=clock(); |
---|
4052 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
4053 | #ifdef BUCHBERGER_ALG |
---|
4054 | M = MstdhomCC(Gomega1); |
---|
4055 | #else |
---|
4056 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
4057 | delete hilb_func; |
---|
4058 | #endif // BUCHBERGER_ALG |
---|
4059 | xtstd=xtstd+clock()-to; |
---|
4060 | // change the ring to oldRing |
---|
4061 | rChangeCurrRing(oldRing); |
---|
4062 | M1 = idrMoveR(M, newRing,currRing); |
---|
4063 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
4064 | |
---|
4065 | to=clock(); |
---|
4066 | // compute a reduced Groebner basis of <G> w.r.t. "newRing" by the lifting process |
---|
4067 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
4068 | xtlift=xtlift+clock()-to; |
---|
4069 | idDelete(&M1); |
---|
4070 | idDelete(&Gomega2); |
---|
4071 | idDelete(&G); |
---|
4072 | |
---|
4073 | // change the ring to newRing |
---|
4074 | rChangeCurrRing(newRing); |
---|
4075 | F1 = idrMoveR(F, oldRing,currRing); |
---|
4076 | |
---|
4077 | to=clock(); |
---|
4078 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
4079 | G = kInterRedCC(F1, NULL); |
---|
4080 | xtred=xtred+clock()-to; |
---|
4081 | idDelete(&F1); |
---|
4082 | |
---|
4083 | if(endwalks == 1) |
---|
4084 | { |
---|
4085 | break; |
---|
4086 | } |
---|
4087 | FIRST_STEP: |
---|
4088 | to=clock(); |
---|
4089 | Overflow_Error = FALSE; |
---|
4090 | // compute a next weight vector |
---|
4091 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
4092 | xtnw=xtnw+clock()-to; |
---|
4093 | #ifdef PRINT_VECTORS |
---|
4094 | MivString(curr_weight, target_weight, next_weight); |
---|
4095 | #endif |
---|
4096 | if(Overflow_Error == TRUE) |
---|
4097 | { |
---|
4098 | //PrintS("\n// ** The next vector does NOT stay in Cone!!\n"); |
---|
4099 | #ifdef TEST_OVERFLOW |
---|
4100 | goto LastGB_Finish; |
---|
4101 | #endif |
---|
4102 | |
---|
4103 | nnwinC = 0; |
---|
4104 | if(tp_deg == nV) |
---|
4105 | { |
---|
4106 | nlast = 1; |
---|
4107 | } |
---|
4108 | delete next_weight; |
---|
4109 | break; |
---|
4110 | } |
---|
4111 | |
---|
4112 | if(MivComp(next_weight, ivNull) == 1) |
---|
4113 | { |
---|
4114 | //newRing = currRing; |
---|
4115 | delete next_weight; |
---|
4116 | break; |
---|
4117 | } |
---|
4118 | |
---|
4119 | if(MivComp(next_weight, target_weight) == 1) |
---|
4120 | { |
---|
4121 | if(tp_deg == nV) |
---|
4122 | { |
---|
4123 | endwalks = 1; |
---|
4124 | } |
---|
4125 | else |
---|
4126 | { |
---|
4127 | // REC_LAST_GB_ALT2: |
---|
4128 | //nOverflow_Error = Overflow_Error; |
---|
4129 | tproc=tproc+clock()-tinput; |
---|
4130 | |
---|
4131 | /*Print("\n// takes %d steps and calls \"Rec_LastGB\" (%d):", |
---|
4132 | nwalk, tp_deg+1); |
---|
4133 | */ |
---|
4134 | G = Rec_LastGB(G,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
4135 | newRing = currRing; |
---|
4136 | delete next_weight; |
---|
4137 | break; |
---|
4138 | } |
---|
4139 | } |
---|
4140 | |
---|
4141 | for(i=nV-1; i>=0; i--) |
---|
4142 | { |
---|
4143 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
4144 | } |
---|
4145 | delete next_weight; |
---|
4146 | }//while |
---|
4147 | |
---|
4148 | delete ivNull; |
---|
4149 | |
---|
4150 | if(tp_deg != nV) |
---|
4151 | { |
---|
4152 | newRing = currRing; |
---|
4153 | |
---|
4154 | if (rParameter(currRing) != NULL) |
---|
4155 | { |
---|
4156 | DefRingParlp(); |
---|
4157 | } |
---|
4158 | else |
---|
4159 | { |
---|
4160 | VMrDefaultlp(); |
---|
4161 | } |
---|
4162 | F1 = idrMoveR(G, newRing,currRing); |
---|
4163 | |
---|
4164 | if(nnwinC == 0 || test_w_in_ConeCC(F1, target_weight) != 1 ) |
---|
4165 | { |
---|
4166 | // nOverflow_Error = Overflow_Error; |
---|
4167 | //Print("\n// takes %d steps and calls \"Rec_LastGB (%d):", tp_deg+1); |
---|
4168 | tproc=tproc+clock()-tinput; |
---|
4169 | F1 = Rec_LastGB(F1,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
4170 | } |
---|
4171 | delete target_weight; |
---|
4172 | |
---|
4173 | TargetRing = currRing; |
---|
4174 | rChangeCurrRing(EXXRing); |
---|
4175 | result = idrMoveR(F1, TargetRing,currRing); |
---|
4176 | } |
---|
4177 | else |
---|
4178 | { |
---|
4179 | if(nlast == 1) |
---|
4180 | { |
---|
4181 | JUNI_STD: |
---|
4182 | |
---|
4183 | newRing = currRing; |
---|
4184 | if (rParameter(currRing) != NULL) |
---|
4185 | { |
---|
4186 | DefRingParlp(); |
---|
4187 | } |
---|
4188 | else |
---|
4189 | { |
---|
4190 | VMrDefaultlp(); |
---|
4191 | } |
---|
4192 | KSTD_Finish: |
---|
4193 | if(isGB == FALSE) |
---|
4194 | { |
---|
4195 | F1 = idrMoveR(G, newRing,currRing); |
---|
4196 | } |
---|
4197 | else |
---|
4198 | { |
---|
4199 | F1 = G; |
---|
4200 | } |
---|
4201 | to=clock(); |
---|
4202 | // Print("\n// apply the Buchberger's alg in ring = %s",rString(currRing)); |
---|
4203 | // idElements(F1, "F1"); |
---|
4204 | G = MstdCC(F1); |
---|
4205 | xtextra=xtextra+clock()-to; |
---|
4206 | |
---|
4207 | |
---|
4208 | idDelete(&F1); |
---|
4209 | newRing = currRing; |
---|
4210 | } |
---|
4211 | |
---|
4212 | LastGB_Finish: |
---|
4213 | rChangeCurrRing(EXXRing); |
---|
4214 | result = idrMoveR(G, newRing,currRing); |
---|
4215 | } |
---|
4216 | |
---|
4217 | if(Overflow_Error == FALSE) |
---|
4218 | { |
---|
4219 | Overflow_Error=nError; |
---|
4220 | } |
---|
4221 | #ifdef TIME_TEST |
---|
4222 | //Print("\n// \"Rec_LastGB\" (%d) took %d steps and %.2f sec.Overflow_Error (%d)", tp_deg, nwalk, ((double) tproc)/1000000, nOverflow_Error); |
---|
4223 | #endif |
---|
4224 | return(result); |
---|
4225 | } |
---|
4226 | |
---|
4227 | /* The following subroutine is the implementation of our second improved |
---|
4228 | Groebner walk algorithm, i.e. the second altervative algorithm. |
---|
4229 | First we use the Grobner walk algorithm and then we call the changed |
---|
4230 | perturbation walk algorithm with increased degree, if an intermediate |
---|
4231 | weight vector is equal to the current target weight vector. |
---|
4232 | This call will be only repeated until we get the wanted reduced Groebner |
---|
4233 | basis or n times, where n is the numbers of variables. |
---|
4234 | */ |
---|
4235 | |
---|
4236 | /****************************** |
---|
4237 | * walk + recursive LastGB * |
---|
4238 | ******************************/ |
---|
4239 | ideal MAltwalk2(ideal Go, intvec* curr_weight, intvec* target_weight) |
---|
4240 | { |
---|
4241 | Set_Error(FALSE); |
---|
4242 | Overflow_Error = FALSE; |
---|
4243 | //BOOLEAN nOverflow_Error = FALSE; |
---|
4244 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
4245 | #ifdef TIME_TEST |
---|
4246 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
4247 | xftinput = clock(); |
---|
4248 | clock_t tostd, tproc; |
---|
4249 | #endif |
---|
4250 | nstep = 0; |
---|
4251 | int i, nV = currRing->N; |
---|
4252 | int nwalk=0, endwalks=0; |
---|
4253 | // int nhilb = 1; |
---|
4254 | ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G; |
---|
4255 | //ideal G1; |
---|
4256 | //ring endRing; |
---|
4257 | ring newRing, oldRing; |
---|
4258 | intvec* ivNull = new intvec(nV); |
---|
4259 | intvec* next_weight; |
---|
4260 | //intvec* extra_curr_weight = new intvec(nV); |
---|
4261 | //intvec* hilb_func; |
---|
4262 | intvec* exivlp = Mivlp(nV); |
---|
4263 | ring XXRing = currRing; |
---|
4264 | |
---|
4265 | //Print("\n// ring r_input = %s;", rString(currRing)); |
---|
4266 | #ifdef TIME_TEST |
---|
4267 | to = clock(); |
---|
4268 | #endif |
---|
4269 | /* compute the reduced Groebner basis of the given ideal w.r.t. |
---|
4270 | a "fast" monomial order, e.g. degree reverse lex. order (dp) */ |
---|
4271 | G = MstdCC(Go); |
---|
4272 | #ifdef TIME_TEST |
---|
4273 | tostd=clock()-to; |
---|
4274 | |
---|
4275 | Print("\n// Computation of the first std took = %.2f sec", |
---|
4276 | ((double) tostd)/1000000); |
---|
4277 | #endif |
---|
4278 | if(currRing->order[0] == ringorder_a) |
---|
4279 | { |
---|
4280 | goto NEXT_VECTOR; |
---|
4281 | } |
---|
4282 | while(1) |
---|
4283 | { |
---|
4284 | nwalk ++; |
---|
4285 | nstep ++; |
---|
4286 | #ifdef TIME_TEST |
---|
4287 | to = clock(); |
---|
4288 | #endif |
---|
4289 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
4290 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
4291 | #ifdef TIME_TEST |
---|
4292 | xtif=xtif+clock()-to; |
---|
4293 | #endif |
---|
4294 | /* |
---|
4295 | if(Overflow_Error == TRUE) |
---|
4296 | { |
---|
4297 | for(i=nV-1; i>=0; i--) |
---|
4298 | (*curr_weight)[i] = (*extra_curr_weight)[i]; |
---|
4299 | delete extra_curr_weight; |
---|
4300 | goto LAST_GB_ALT2; |
---|
4301 | } |
---|
4302 | */ |
---|
4303 | oldRing = currRing; |
---|
4304 | |
---|
4305 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
4306 | if (rParameter(currRing) != NULL) |
---|
4307 | { |
---|
4308 | DefRingPar(curr_weight); |
---|
4309 | } |
---|
4310 | else |
---|
4311 | { |
---|
4312 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
4313 | } |
---|
4314 | newRing = currRing; |
---|
4315 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
4316 | #ifdef TIME_TEST |
---|
4317 | to = clock(); |
---|
4318 | #endif |
---|
4319 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
4320 | M = MstdhomCC(Gomega1); |
---|
4321 | #ifdef TIME_TEST |
---|
4322 | xtstd=xtstd+clock()-to; |
---|
4323 | #endif |
---|
4324 | /* change the ring to oldRing */ |
---|
4325 | rChangeCurrRing(oldRing); |
---|
4326 | M1 = idrMoveR(M, newRing,currRing); |
---|
4327 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
4328 | #ifdef TIME_TEST |
---|
4329 | to = clock(); |
---|
4330 | #endif |
---|
4331 | /* compute the reduced Groebner basis of <G> w.r.t. "newRing" |
---|
4332 | by the liftig process */ |
---|
4333 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
4334 | #ifdef TIME_TEST |
---|
4335 | xtlift=xtlift+clock()-to; |
---|
4336 | #endif |
---|
4337 | idDelete(&M1); |
---|
4338 | idDelete(&Gomega2); |
---|
4339 | idDelete(&G); |
---|
4340 | |
---|
4341 | /* change the ring to newRing */ |
---|
4342 | rChangeCurrRing(newRing); |
---|
4343 | F1 = idrMoveR(F, oldRing,currRing); |
---|
4344 | #ifdef TIME_TEST |
---|
4345 | to = clock(); |
---|
4346 | #endif |
---|
4347 | /* reduce the Groebner basis <G> w.r.t. newRing */ |
---|
4348 | G = kInterRedCC(F1, NULL); |
---|
4349 | #ifdef TIME_TEST |
---|
4350 | xtred=xtred+clock()-to; |
---|
4351 | #endif |
---|
4352 | idDelete(&F1); |
---|
4353 | |
---|
4354 | if(endwalks == 1) |
---|
4355 | break; |
---|
4356 | |
---|
4357 | NEXT_VECTOR: |
---|
4358 | #ifdef TIME_TEST |
---|
4359 | to = clock(); |
---|
4360 | #endif |
---|
4361 | /* compute a next weight vector */ |
---|
4362 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
4363 | #ifdef TIME_TEST |
---|
4364 | xtnw=xtnw+clock()-to; |
---|
4365 | #endif |
---|
4366 | #ifdef PRINT_VECTORS |
---|
4367 | MivString(curr_weight, target_weight, next_weight); |
---|
4368 | #endif |
---|
4369 | |
---|
4370 | if(Overflow_Error == TRUE) |
---|
4371 | { |
---|
4372 | /* |
---|
4373 | ivString(next_weight, "omega"); |
---|
4374 | PrintS("\n// ** The weight vector does NOT stay in Cone!!\n"); |
---|
4375 | */ |
---|
4376 | #ifdef TEST_OVERFLOW |
---|
4377 | goto TEST_OVERFLOW_OI; |
---|
4378 | #endif |
---|
4379 | |
---|
4380 | newRing = currRing; |
---|
4381 | if (rParameter(currRing) != NULL) |
---|
4382 | { |
---|
4383 | DefRingPar(target_weight); |
---|
4384 | } |
---|
4385 | else |
---|
4386 | { |
---|
4387 | rChangeCurrRing(VMrDefault(target_weight)); // Aenderung |
---|
4388 | } |
---|
4389 | F1 = idrMoveR(G, newRing,currRing); |
---|
4390 | G = MstdCC(F1); |
---|
4391 | idDelete(&F1); |
---|
4392 | newRing = currRing; |
---|
4393 | break; |
---|
4394 | } |
---|
4395 | |
---|
4396 | if(MivComp(next_weight, ivNull) == 1) |
---|
4397 | { |
---|
4398 | newRing = currRing; |
---|
4399 | delete next_weight; |
---|
4400 | break; |
---|
4401 | } |
---|
4402 | |
---|
4403 | if(MivComp(next_weight, target_weight) == 1) |
---|
4404 | { |
---|
4405 | if(MivSame(target_weight, exivlp)==1) |
---|
4406 | { |
---|
4407 | // LAST_GB_ALT2: |
---|
4408 | //nOverflow_Error = Overflow_Error; |
---|
4409 | #ifdef TIME_TEST |
---|
4410 | tproc = clock()-xftinput; |
---|
4411 | #endif |
---|
4412 | //Print("\n// takes %d steps and calls the recursion of level 2:", nwalk); |
---|
4413 | /* call the changed perturbation walk algorithm with degree 2 */ |
---|
4414 | G = Rec_LastGB(G, curr_weight, target_weight, 2,1); |
---|
4415 | newRing = currRing; |
---|
4416 | delete next_weight; |
---|
4417 | break; |
---|
4418 | } |
---|
4419 | endwalks = 1; |
---|
4420 | } |
---|
4421 | |
---|
4422 | for(i=nV-1; i>=0; i--) |
---|
4423 | { |
---|
4424 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
4425 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
4426 | } |
---|
4427 | delete next_weight; |
---|
4428 | } |
---|
4429 | #ifdef TEST_OVERFLOW |
---|
4430 | TEST_OVERFLOW_OI: |
---|
4431 | #endif |
---|
4432 | rChangeCurrRing(XXRing); |
---|
4433 | G = idrMoveR(G, newRing,currRing); |
---|
4434 | delete ivNull; |
---|
4435 | delete exivlp; |
---|
4436 | |
---|
4437 | #ifdef TIME_TEST |
---|
4438 | /*Print("\n// \"Main procedure\" took %d steps dnd %.2f sec. Overflow_Error (%d)", |
---|
4439 | nwalk, ((double) tproc)/1000000, nOverflow_Error); |
---|
4440 | */ |
---|
4441 | TimeStringFractal(xftinput, tostd, xtif, xtstd, xtextra,xtlift, xtred,xtnw); |
---|
4442 | |
---|
4443 | //Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
4444 | //Print("\n// Overflow_Error? (%d)", nOverflow_Error); |
---|
4445 | //Print("\n// Awalk2 took %d steps!!", nstep); |
---|
4446 | #endif |
---|
4447 | |
---|
4448 | return(G); |
---|
4449 | } |
---|
4450 | |
---|
4451 | |
---|
4452 | /************************************** |
---|
4453 | * perturb the matrix order of "lex" * |
---|
4454 | **************************************/ |
---|
4455 | static intvec* NewVectorlp(ideal I) |
---|
4456 | { |
---|
4457 | int nV = currRing->N; |
---|
4458 | intvec* iv_wlp = MivMatrixOrderlp(nV); |
---|
4459 | intvec* result = Mfpertvector(I, iv_wlp); |
---|
4460 | delete iv_wlp; |
---|
4461 | return result; |
---|
4462 | } |
---|
4463 | |
---|
4464 | int ngleich; |
---|
4465 | intvec* Xsigma; |
---|
4466 | intvec* Xtau; |
---|
4467 | int xn; |
---|
4468 | intvec* Xivinput; |
---|
4469 | intvec* Xivlp; |
---|
4470 | |
---|
4471 | |
---|
4472 | /******************************** |
---|
4473 | * compute a next weight vector * |
---|
4474 | ********************************/ |
---|
4475 | static intvec* MWalkRandomNextWeight(ideal G, intvec* orig_M, intvec* target_weight, |
---|
4476 | int weight_rad, int pert_deg) |
---|
4477 | { |
---|
4478 | assume(currRing != NULL && orig_M != NULL && |
---|
4479 | target_weight != NULL && G->m[0] != NULL); |
---|
4480 | |
---|
4481 | //BOOLEAN nError = Overflow_Error; |
---|
4482 | Overflow_Error = FALSE; |
---|
4483 | |
---|
4484 | BOOLEAN found_random_weight = FALSE; |
---|
4485 | int i,nV = currRing->N; |
---|
4486 | intvec* curr_weight = new intvec(nV); |
---|
4487 | |
---|
4488 | for(i=0; i<nV; i++) |
---|
4489 | { |
---|
4490 | (*curr_weight)[i] = (*orig_M)[i]; |
---|
4491 | } |
---|
4492 | |
---|
4493 | int k=0,weight_norm; |
---|
4494 | intvec* next_weight; |
---|
4495 | intvec* next_weight1 = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
4496 | intvec* next_weight2 = new intvec(nV); |
---|
4497 | intvec* next_weight22 = new intvec(nV); |
---|
4498 | intvec* result = new intvec(nV); |
---|
4499 | intvec* curr_weight1; |
---|
4500 | ideal G_test, G_test1, G_test2; |
---|
4501 | |
---|
4502 | //try to find a random next weight vector "next_weight2" |
---|
4503 | if(weight_rad > 0) |
---|
4504 | { |
---|
4505 | while(k<10) |
---|
4506 | { |
---|
4507 | weight_norm = 0; |
---|
4508 | while(weight_norm == 0) |
---|
4509 | { |
---|
4510 | for(i=0; i<nV; i++) |
---|
4511 | { |
---|
4512 | (*next_weight2)[i] = rand() % 60000 - 30000; |
---|
4513 | weight_norm = weight_norm + (*next_weight2)[i]*(*next_weight2)[i]; |
---|
4514 | } |
---|
4515 | weight_norm = 1 + floor(sqrt(weight_norm)); |
---|
4516 | } |
---|
4517 | for(i=0; i<nV; i++) |
---|
4518 | { |
---|
4519 | if((*next_weight2)[i] < 0) |
---|
4520 | { |
---|
4521 | (*next_weight2)[i] = 1 + (*curr_weight)[i] + floor(weight_rad*(*next_weight2)[i]/weight_norm); |
---|
4522 | } |
---|
4523 | else |
---|
4524 | { |
---|
4525 | (*next_weight2)[i] = (*curr_weight)[i] + floor(weight_rad*(*next_weight2)[i]/weight_norm); |
---|
4526 | } |
---|
4527 | } |
---|
4528 | if(test_w_in_ConeCC(G,next_weight2) == 1) |
---|
4529 | { |
---|
4530 | if(maxlengthpoly(MwalkInitialForm(G,next_weight2))<2) |
---|
4531 | { |
---|
4532 | next_weight2 = MkInterRedNextWeight(next_weight2,target_weight,G); |
---|
4533 | } |
---|
4534 | G_test2 = MwalkInitialForm(G, next_weight2); |
---|
4535 | found_random_weight = TRUE; |
---|
4536 | break; |
---|
4537 | } |
---|
4538 | k++; |
---|
4539 | } |
---|
4540 | } |
---|
4541 | |
---|
4542 | // compute "perturbed" next weight vector |
---|
4543 | if(pert_deg > 1) |
---|
4544 | { |
---|
4545 | curr_weight1 = MPertVectors(G,orig_M,pert_deg); |
---|
4546 | next_weight = MkInterRedNextWeight(curr_weight1,target_weight,G); |
---|
4547 | delete curr_weight1; |
---|
4548 | } |
---|
4549 | else |
---|
4550 | { |
---|
4551 | next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
4552 | } |
---|
4553 | if(MivSame(curr_weight,next_weight)==1 || Overflow_Error == TRUE) |
---|
4554 | { |
---|
4555 | Overflow_Error = FALSE; |
---|
4556 | delete next_weight; |
---|
4557 | next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
4558 | } |
---|
4559 | G_test=MwalkInitialForm(G,next_weight); |
---|
4560 | G_test1=MwalkInitialForm(G,next_weight1); |
---|
4561 | |
---|
4562 | // compare next weights |
---|
4563 | if(Overflow_Error == FALSE) |
---|
4564 | { |
---|
4565 | if(found_random_weight == TRUE) |
---|
4566 | { |
---|
4567 | // random next weight vector found |
---|
4568 | if(G_test1->m[0] != NULL && maxlengthpoly(G_test1) < maxlengthpoly(G_test)) |
---|
4569 | { |
---|
4570 | if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test1)) |
---|
4571 | { |
---|
4572 | for(i=0; i<nV; i++) |
---|
4573 | { |
---|
4574 | (*result)[i] = (*next_weight2)[i]; |
---|
4575 | } |
---|
4576 | } |
---|
4577 | else |
---|
4578 | { |
---|
4579 | for(i=0; i<nV; i++) |
---|
4580 | { |
---|
4581 | (*result)[i] = (*next_weight1)[i]; |
---|
4582 | } |
---|
4583 | } |
---|
4584 | } |
---|
4585 | else |
---|
4586 | { |
---|
4587 | if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test)) |
---|
4588 | { |
---|
4589 | for(i=0; i<nV; i++) |
---|
4590 | { |
---|
4591 | (*result)[i] = (*next_weight2)[i]; |
---|
4592 | } |
---|
4593 | } |
---|
4594 | else |
---|
4595 | { |
---|
4596 | for(i=0; i<nV; i++) |
---|
4597 | { |
---|
4598 | (*result)[i] = (*next_weight)[i]; |
---|
4599 | } |
---|
4600 | } |
---|
4601 | } |
---|
4602 | } |
---|
4603 | else |
---|
4604 | { |
---|
4605 | // no random next weight vector found |
---|
4606 | if(G_test1->m[0] != NULL && maxlengthpoly(G_test1) < maxlengthpoly(G_test)) |
---|
4607 | { |
---|
4608 | for(i=0; i<nV; i++) |
---|
4609 | { |
---|
4610 | (*result)[i] = (*next_weight1)[i]; |
---|
4611 | } |
---|
4612 | } |
---|
4613 | else |
---|
4614 | { |
---|
4615 | for(i=0; i<nV; i++) |
---|
4616 | { |
---|
4617 | (*result)[i] = (*next_weight)[i]; |
---|
4618 | } |
---|
4619 | } |
---|
4620 | } |
---|
4621 | } |
---|
4622 | else |
---|
4623 | { |
---|
4624 | Overflow_Error = FALSE; |
---|
4625 | if(found_random_weight == TRUE) |
---|
4626 | { |
---|
4627 | if(G_test2->m[0] != NULL && maxlengthpoly(G_test2) < maxlengthpoly(G_test)) |
---|
4628 | { |
---|
4629 | for(i=1; i<nV; i++) |
---|
4630 | { |
---|
4631 | (*result)[i] = (*next_weight2)[i]; |
---|
4632 | } |
---|
4633 | } |
---|
4634 | else |
---|
4635 | { |
---|
4636 | for(i=0; i<nV; i++) |
---|
4637 | { |
---|
4638 | (*result)[i] = (*next_weight)[i]; |
---|
4639 | } |
---|
4640 | } |
---|
4641 | } |
---|
4642 | else |
---|
4643 | { |
---|
4644 | for(i=0; i<nV; i++) |
---|
4645 | { |
---|
4646 | (*result)[i] = (*next_weight)[i]; |
---|
4647 | } |
---|
4648 | } |
---|
4649 | } |
---|
4650 | |
---|
4651 | delete next_weight; |
---|
4652 | delete next_weight2; |
---|
4653 | idDelete(&G_test); |
---|
4654 | idDelete(&G_test1); |
---|
4655 | if(found_random_weight == TRUE) |
---|
4656 | { |
---|
4657 | idDelete(&G_test2); |
---|
4658 | } |
---|
4659 | if(test_w_in_ConeCC(G, result) == 1 && MivSame(curr_weight,result)==0) |
---|
4660 | { |
---|
4661 | delete curr_weight; |
---|
4662 | delete next_weight1; |
---|
4663 | return result; |
---|
4664 | } |
---|
4665 | else |
---|
4666 | { |
---|
4667 | delete curr_weight; |
---|
4668 | delete result; |
---|
4669 | return next_weight1; |
---|
4670 | } |
---|
4671 | } |
---|
4672 | |
---|
4673 | |
---|
4674 | /*************************************************************************** |
---|
4675 | * The procedur REC_GB_Mwalk computes a GB for <G> w.r.t. the weight order * |
---|
4676 | * otw, where G is a reduced GB w.r.t. the weight order cw. * |
---|
4677 | * The new procedure Mwalk calls REC_GB. * |
---|
4678 | ***************************************************************************/ |
---|
4679 | static ideal REC_GB_Mwalk(ideal G, intvec* curr_weight, intvec* orig_target_weight, |
---|
4680 | int tp_deg, int npwinc) |
---|
4681 | { |
---|
4682 | BOOLEAN nError = Overflow_Error; |
---|
4683 | Overflow_Error = FALSE; |
---|
4684 | |
---|
4685 | int i, nV = currRing->N; |
---|
4686 | int nwalk=0, endwalks=0, nnwinC=1, nlast = 0; |
---|
4687 | ideal Gomega, M, F, Gomega1, Gomega2, M1,F1,result,ssG; |
---|
4688 | ring newRing, oldRing, TargetRing; |
---|
4689 | intvec* target_weight; |
---|
4690 | intvec* ivNull = new intvec(nV); |
---|
4691 | #ifndef BUCHBERGER_ALG |
---|
4692 | intvec* hilb_func; |
---|
4693 | // to avoid (1,0,...,0) as the target vector |
---|
4694 | intvec* last_omega = new intvec(nV); |
---|
4695 | for(i=nV-1; i>0; i--) |
---|
4696 | { |
---|
4697 | (*last_omega)[i] = 1; |
---|
4698 | } |
---|
4699 | (*last_omega)[0] = 10000; |
---|
4700 | #endif |
---|
4701 | BOOLEAN isGB = FALSE; |
---|
4702 | |
---|
4703 | ring EXXRing = currRing; |
---|
4704 | |
---|
4705 | // compute a pertubed weight vector of the target weight vector |
---|
4706 | if(tp_deg > 1 && tp_deg <= nV) |
---|
4707 | { |
---|
4708 | ideal H0 = idHeadCC(G); |
---|
4709 | if (rParameter(currRing) != NULL) |
---|
4710 | { |
---|
4711 | DefRingPar(orig_target_weight); |
---|
4712 | } |
---|
4713 | else |
---|
4714 | { |
---|
4715 | rChangeCurrRing(VMrDefault(orig_target_weight)); |
---|
4716 | } |
---|
4717 | TargetRing = currRing; |
---|
4718 | ssG = idrMoveR(G,EXXRing,currRing); |
---|
4719 | |
---|
4720 | ideal H0_tmp = idrMoveR(H0,EXXRing,currRing); |
---|
4721 | ideal H1 = idHeadCC(ssG); |
---|
4722 | id_Delete(&H0,EXXRing); |
---|
4723 | |
---|
4724 | if(test_G_GB_walk(H0_tmp,H1)==1) |
---|
4725 | { |
---|
4726 | //Print("\n//REC_GB_Mwalk: input in %d-th recursive is a GB!\n",tp_deg); |
---|
4727 | idDelete(&H0_tmp); |
---|
4728 | idDelete(&H1); |
---|
4729 | G = ssG; |
---|
4730 | ssG = NULL; |
---|
4731 | newRing = currRing; |
---|
4732 | delete ivNull; |
---|
4733 | if(npwinc == 0) |
---|
4734 | { |
---|
4735 | isGB = TRUE; |
---|
4736 | goto KSTD_Finish; |
---|
4737 | } |
---|
4738 | else |
---|
4739 | { |
---|
4740 | goto LastGB_Finish; |
---|
4741 | } |
---|
4742 | } |
---|
4743 | idDelete(&H0_tmp); |
---|
4744 | idDelete(&H1); |
---|
4745 | |
---|
4746 | target_weight = MPertVectors(ssG, MivMatrixOrder(orig_target_weight), tp_deg); |
---|
4747 | |
---|
4748 | rChangeCurrRing(EXXRing); |
---|
4749 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
4750 | } |
---|
4751 | |
---|
4752 | while(1) |
---|
4753 | { |
---|
4754 | nwalk ++; |
---|
4755 | nstep++; |
---|
4756 | if(nwalk == 1) |
---|
4757 | { |
---|
4758 | goto NEXT_STEP; |
---|
4759 | } |
---|
4760 | //Print("\n//REC_GB_Mwalk: Entering the %d-th step in the %d-th recursive:\n",nwalk,tp_deg); |
---|
4761 | to = clock(); |
---|
4762 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
4763 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
4764 | xtif = xtif + clock()-to; |
---|
4765 | |
---|
4766 | #ifndef BUCHBERGER_ALG |
---|
4767 | if(isNolVector(curr_weight) == 0) |
---|
4768 | { |
---|
4769 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
4770 | } |
---|
4771 | else |
---|
4772 | { |
---|
4773 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
4774 | } |
---|
4775 | #endif |
---|
4776 | |
---|
4777 | oldRing = currRing; |
---|
4778 | |
---|
4779 | // define a new ring with ordering "(a(curr_weight),lp) |
---|
4780 | if (rParameter(currRing) != NULL) |
---|
4781 | { |
---|
4782 | DefRingPar(curr_weight); |
---|
4783 | } |
---|
4784 | else |
---|
4785 | { |
---|
4786 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
4787 | } |
---|
4788 | newRing = currRing; |
---|
4789 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
4790 | |
---|
4791 | to = clock(); |
---|
4792 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
4793 | #ifdef BUCHBERGER_ALG |
---|
4794 | M = MstdhomCC(Gomega1); |
---|
4795 | #else |
---|
4796 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
4797 | delete hilb_func; |
---|
4798 | #endif |
---|
4799 | xtstd = xtstd + clock() - to; |
---|
4800 | |
---|
4801 | // change the ring to oldRing |
---|
4802 | rChangeCurrRing(oldRing); |
---|
4803 | |
---|
4804 | M1 = idrMoveR(M, newRing,currRing); |
---|
4805 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
4806 | |
---|
4807 | to = clock(); |
---|
4808 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
4809 | xtlift = xtlift + clock() -to; |
---|
4810 | |
---|
4811 | idDelete(&M1); |
---|
4812 | idDelete(&Gomega2); |
---|
4813 | idDelete(&G); |
---|
4814 | |
---|
4815 | |
---|
4816 | // change the ring to newRing |
---|
4817 | rChangeCurrRing(newRing); |
---|
4818 | F1 = idrMoveR(F, oldRing,currRing); |
---|
4819 | |
---|
4820 | to = clock(); |
---|
4821 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
4822 | G = kInterRedCC(F1, NULL); |
---|
4823 | xtred = xtred + clock() -to; |
---|
4824 | |
---|
4825 | idDelete(&F1); |
---|
4826 | |
---|
4827 | if(endwalks == 1) |
---|
4828 | { |
---|
4829 | break; |
---|
4830 | } |
---|
4831 | NEXT_STEP: |
---|
4832 | to = clock(); |
---|
4833 | // compute a next weight vector |
---|
4834 | intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
4835 | |
---|
4836 | |
---|
4837 | xtnw = xtnw + clock() - to; |
---|
4838 | |
---|
4839 | #ifdef PRINT_VECTORS |
---|
4840 | MivString(curr_weight, target_weight, next_weight); |
---|
4841 | #endif |
---|
4842 | |
---|
4843 | if(Overflow_Error == TRUE) |
---|
4844 | { |
---|
4845 | //PrintS("\n//REC_GB_Mwalk: The computed vector does NOT stay in the correct cone!!\n"); |
---|
4846 | nnwinC = 0; |
---|
4847 | if(tp_deg == nV) |
---|
4848 | { |
---|
4849 | nlast = 1; |
---|
4850 | } |
---|
4851 | delete next_weight; |
---|
4852 | break; |
---|
4853 | } |
---|
4854 | if(MivComp(next_weight, ivNull) == 1) |
---|
4855 | { |
---|
4856 | newRing = currRing; |
---|
4857 | delete next_weight; |
---|
4858 | break; |
---|
4859 | } |
---|
4860 | |
---|
4861 | if(MivComp(next_weight, target_weight) == 1) |
---|
4862 | { |
---|
4863 | if(tp_deg == nV) |
---|
4864 | { |
---|
4865 | endwalks = 1; |
---|
4866 | } |
---|
4867 | else |
---|
4868 | { |
---|
4869 | G = REC_GB_Mwalk(G,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
4870 | newRing = currRing; |
---|
4871 | delete next_weight; |
---|
4872 | break; |
---|
4873 | } |
---|
4874 | } |
---|
4875 | |
---|
4876 | for(i=nV-1; i>=0; i--) |
---|
4877 | { |
---|
4878 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
4879 | } |
---|
4880 | delete next_weight; |
---|
4881 | } |
---|
4882 | |
---|
4883 | delete ivNull; |
---|
4884 | |
---|
4885 | if(tp_deg != nV) |
---|
4886 | { |
---|
4887 | newRing = currRing; |
---|
4888 | |
---|
4889 | if (rParameter(currRing) != NULL) |
---|
4890 | { |
---|
4891 | DefRingPar(orig_target_weight); |
---|
4892 | } |
---|
4893 | else |
---|
4894 | { |
---|
4895 | rChangeCurrRing(VMrDefault(orig_target_weight)); |
---|
4896 | } |
---|
4897 | F1 = idrMoveR(G, newRing,currRing); |
---|
4898 | |
---|
4899 | if(nnwinC == 0) |
---|
4900 | { |
---|
4901 | F1 = REC_GB_Mwalk(F1,curr_weight, orig_target_weight, tp_deg+1,nnwinC); |
---|
4902 | } |
---|
4903 | else |
---|
4904 | { |
---|
4905 | if(test_w_in_ConeCC(F1, target_weight) != 1) |
---|
4906 | { |
---|
4907 | F1 = REC_GB_Mwalk(F1,curr_weight, orig_target_weight,tp_deg+1,nnwinC); |
---|
4908 | } |
---|
4909 | } |
---|
4910 | delete target_weight; |
---|
4911 | |
---|
4912 | TargetRing = currRing; |
---|
4913 | rChangeCurrRing(EXXRing); |
---|
4914 | result = idrMoveR(F1, TargetRing,currRing); |
---|
4915 | } |
---|
4916 | else |
---|
4917 | { |
---|
4918 | if(nlast == 1) |
---|
4919 | { |
---|
4920 | if (rParameter(currRing) != NULL) |
---|
4921 | { |
---|
4922 | DefRingPar(orig_target_weight); |
---|
4923 | } |
---|
4924 | else |
---|
4925 | { |
---|
4926 | rChangeCurrRing(VMrDefault(orig_target_weight)); |
---|
4927 | } |
---|
4928 | KSTD_Finish: |
---|
4929 | if(isGB == FALSE) |
---|
4930 | { |
---|
4931 | F1 = idrMoveR(G, newRing,currRing); |
---|
4932 | } |
---|
4933 | else |
---|
4934 | { |
---|
4935 | F1 = G; |
---|
4936 | } |
---|
4937 | to=clock(); |
---|
4938 | // apply Buchberger alg to compute a red. GB of F1 |
---|
4939 | G = MstdCC(F1); |
---|
4940 | xtextra=clock()-to; |
---|
4941 | idDelete(&F1); |
---|
4942 | newRing = currRing; |
---|
4943 | } |
---|
4944 | |
---|
4945 | LastGB_Finish: |
---|
4946 | rChangeCurrRing(EXXRing); |
---|
4947 | result = idrMoveR(G, newRing,currRing); |
---|
4948 | } |
---|
4949 | |
---|
4950 | if(Overflow_Error == FALSE) |
---|
4951 | { |
---|
4952 | Overflow_Error = nError; |
---|
4953 | } |
---|
4954 | #ifndef BUCHBERGER_ALG |
---|
4955 | delete last_omega; |
---|
4956 | #endif |
---|
4957 | return(result); |
---|
4958 | } |
---|
4959 | |
---|
4960 | |
---|
4961 | // THE NEW GROEBNER WALK ALGORITHM |
---|
4962 | // Groebnerwalk with a recursive "second" alternative GW, called REC_GB_Mwalk that only computes the last reduced GB |
---|
4963 | ideal MwalkAlt(ideal Go, intvec* curr_weight, intvec* target_weight) |
---|
4964 | { |
---|
4965 | Set_Error(FALSE); |
---|
4966 | Overflow_Error = FALSE; |
---|
4967 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
4968 | |
---|
4969 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
4970 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
4971 | tinput = clock(); |
---|
4972 | clock_t tim; |
---|
4973 | nstep=0; |
---|
4974 | int i; |
---|
4975 | int nV = currRing->N; |
---|
4976 | int nwalk=0; |
---|
4977 | int endwalks=0; |
---|
4978 | |
---|
4979 | ideal Gomega, M, F, Gomega1, Gomega2, M1, F1, G; |
---|
4980 | |
---|
4981 | ring newRing, oldRing; |
---|
4982 | intvec* ivNull = new intvec(nV); |
---|
4983 | intvec* exivlp = Mivlp(nV); |
---|
4984 | #ifndef BUCHBERGER_ALG |
---|
4985 | intvec* hilb_func; |
---|
4986 | #endif |
---|
4987 | intvec* tmp_weight = new intvec(nV); |
---|
4988 | for(i=nV-1; i>=0; i--) |
---|
4989 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
4990 | |
---|
4991 | // to avoid (1,0,...,0) as the target vector |
---|
4992 | intvec* last_omega = new intvec(nV); |
---|
4993 | for(i=nV-1; i>0; i--) |
---|
4994 | (*last_omega)[i] = 1; |
---|
4995 | (*last_omega)[0] = 10000; |
---|
4996 | |
---|
4997 | ring XXRing = currRing; |
---|
4998 | |
---|
4999 | to = clock(); |
---|
5000 | // the monomial ordering of this current ring would be "dp" |
---|
5001 | G = MstdCC(Go); |
---|
5002 | tostd = clock()-to; |
---|
5003 | |
---|
5004 | if(currRing->order[0] == ringorder_a) |
---|
5005 | goto NEXT_VECTOR; |
---|
5006 | |
---|
5007 | while(1) |
---|
5008 | { |
---|
5009 | nwalk ++; |
---|
5010 | nstep ++; |
---|
5011 | to = clock(); |
---|
5012 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
5013 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
5014 | tif = tif + clock()-to; |
---|
5015 | oldRing = currRing; |
---|
5016 | |
---|
5017 | if(endwalks == 1) |
---|
5018 | { |
---|
5019 | /* compute a reduced Groebner basis of Gomega w.r.t. >>_cw by |
---|
5020 | the recursive changed perturbation walk alg. */ |
---|
5021 | tim = clock(); |
---|
5022 | #ifdef CHECK_IDEAL_MWALK |
---|
5023 | Print("\n// **** Groebnerwalk took %d steps and ", nwalk); |
---|
5024 | PrintS("\n// **** call the rec. Pert. Walk to compute a red GB of:"); |
---|
5025 | idString(Gomega, "Gomega"); |
---|
5026 | #endif |
---|
5027 | |
---|
5028 | if(MivSame(exivlp, target_weight)==1) |
---|
5029 | M = REC_GB_Mwalk(idCopy(Gomega), tmp_weight, curr_weight, 2,1); |
---|
5030 | else |
---|
5031 | goto NORMAL_GW; |
---|
5032 | #ifdef TIME_TEST |
---|
5033 | Print("\n// time for the last std(Gw) = %.2f sec", |
---|
5034 | ((double) (clock()-tim)/1000000)); |
---|
5035 | #endif |
---|
5036 | /* |
---|
5037 | #ifdef CHECK_IDEAL_MWALK |
---|
5038 | idElements(Gomega, "G_omega"); |
---|
5039 | headidString(Gomega, "Gw"); |
---|
5040 | idElements(M, "M"); |
---|
5041 | //headidString(M, "M"); |
---|
5042 | #endif |
---|
5043 | */ |
---|
5044 | to = clock(); |
---|
5045 | F = MLifttwoIdeal(Gomega, M, G); |
---|
5046 | xtlift = xtlift + clock() - to; |
---|
5047 | |
---|
5048 | idDelete(&Gomega); |
---|
5049 | idDelete(&M); |
---|
5050 | idDelete(&G); |
---|
5051 | |
---|
5052 | oldRing = currRing; |
---|
5053 | |
---|
5054 | // create a new ring newRing |
---|
5055 | if (rParameter(currRing) != NULL) |
---|
5056 | { |
---|
5057 | DefRingPar(curr_weight); |
---|
5058 | } |
---|
5059 | else |
---|
5060 | { |
---|
5061 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
5062 | } |
---|
5063 | newRing = currRing; |
---|
5064 | F1 = idrMoveR(F, oldRing,currRing); |
---|
5065 | } |
---|
5066 | else |
---|
5067 | { |
---|
5068 | NORMAL_GW: |
---|
5069 | #ifndef BUCHBERGER_ALG |
---|
5070 | if(isNolVector(curr_weight) == 0) |
---|
5071 | { |
---|
5072 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
5073 | } |
---|
5074 | else |
---|
5075 | { |
---|
5076 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
5077 | } |
---|
5078 | #endif // BUCHBERGER_ALG |
---|
5079 | |
---|
5080 | // define a new ring that its ordering is "(a(curr_weight),lp) |
---|
5081 | if (rParameter(currRing) != NULL) |
---|
5082 | { |
---|
5083 | DefRingPar(curr_weight); |
---|
5084 | } |
---|
5085 | else |
---|
5086 | { |
---|
5087 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
5088 | } |
---|
5089 | newRing = currRing; |
---|
5090 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
5091 | |
---|
5092 | to = clock(); |
---|
5093 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
5094 | #ifdef BUCHBERGER_ALG |
---|
5095 | M = MstdhomCC(Gomega1); |
---|
5096 | #else |
---|
5097 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
5098 | delete hilb_func; |
---|
5099 | #endif |
---|
5100 | tstd = tstd + clock() - to; |
---|
5101 | |
---|
5102 | // change the ring to oldRing |
---|
5103 | rChangeCurrRing(oldRing); |
---|
5104 | M1 = idrMoveR(M, newRing,currRing); |
---|
5105 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
5106 | |
---|
5107 | to = clock(); |
---|
5108 | // compute a representation of the generators of submod (M) with respect |
---|
5109 | // to those of mod (Gomega). |
---|
5110 | // Gomega is a reduced Groebner basis w.r.t. the current ring. |
---|
5111 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
5112 | tlift = tlift + clock() - to; |
---|
5113 | |
---|
5114 | idDelete(&M1); |
---|
5115 | idDelete(&Gomega2); |
---|
5116 | idDelete(&G); |
---|
5117 | |
---|
5118 | // change the ring to newRing |
---|
5119 | rChangeCurrRing(newRing); |
---|
5120 | F1 = idrMoveR(F, oldRing,currRing); |
---|
5121 | } |
---|
5122 | |
---|
5123 | to = clock(); |
---|
5124 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
5125 | G = kInterRedCC(F1, NULL); |
---|
5126 | if(endwalks != 1) |
---|
5127 | { |
---|
5128 | tred = tred + clock() - to; |
---|
5129 | } |
---|
5130 | else |
---|
5131 | { |
---|
5132 | xtred = xtred + clock() - to; |
---|
5133 | } |
---|
5134 | idDelete(&F1); |
---|
5135 | if(endwalks == 1) |
---|
5136 | { |
---|
5137 | break; |
---|
5138 | } |
---|
5139 | NEXT_VECTOR: |
---|
5140 | to = clock(); |
---|
5141 | // compute a next weight vector |
---|
5142 | intvec* next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
5143 | tnw = tnw + clock() - to; |
---|
5144 | #ifdef PRINT_VECTORS |
---|
5145 | MivString(curr_weight, target_weight, next_weight); |
---|
5146 | #endif |
---|
5147 | |
---|
5148 | //if(test_w_in_ConeCC(G, next_weight) != 1) |
---|
5149 | if(Overflow_Error == TRUE) |
---|
5150 | { |
---|
5151 | newRing = currRing; |
---|
5152 | PrintS("\n// ** The computed vector does NOT stay in Cone!!\n"); |
---|
5153 | |
---|
5154 | if (rParameter(currRing) != NULL) |
---|
5155 | { |
---|
5156 | DefRingPar(target_weight); |
---|
5157 | } |
---|
5158 | else |
---|
5159 | { |
---|
5160 | rChangeCurrRing(VMrDefault(target_weight)); |
---|
5161 | } |
---|
5162 | F1 = idrMoveR(G, newRing,currRing); |
---|
5163 | G = MstdCC(F1); |
---|
5164 | idDelete(&F1); |
---|
5165 | |
---|
5166 | newRing = currRing; |
---|
5167 | break; |
---|
5168 | } |
---|
5169 | |
---|
5170 | if(MivComp(next_weight, ivNull) == 1) |
---|
5171 | { |
---|
5172 | newRing = currRing; |
---|
5173 | delete next_weight; |
---|
5174 | break; |
---|
5175 | } |
---|
5176 | if(MivComp(next_weight, target_weight) == 1) |
---|
5177 | { |
---|
5178 | endwalks = 1; |
---|
5179 | } |
---|
5180 | for(i=nV-1; i>=0; i--) |
---|
5181 | { |
---|
5182 | (*tmp_weight)[i] = (*curr_weight)[i]; |
---|
5183 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
5184 | } |
---|
5185 | delete next_weight; |
---|
5186 | } |
---|
5187 | rChangeCurrRing(XXRing); |
---|
5188 | G = idrMoveR(G, newRing,currRing); |
---|
5189 | |
---|
5190 | delete tmp_weight; |
---|
5191 | delete ivNull; |
---|
5192 | delete exivlp; |
---|
5193 | |
---|
5194 | #ifdef TIME_TEST |
---|
5195 | TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep); |
---|
5196 | |
---|
5197 | //Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
5198 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
5199 | #endif |
---|
5200 | return(G); |
---|
5201 | } |
---|
5202 | |
---|
5203 | /******************************* |
---|
5204 | * THE GROEBNER WALK ALGORITHM * |
---|
5205 | *******************************/ |
---|
5206 | ideal Mwalk(ideal Go, intvec* orig_M, intvec* target_M, |
---|
5207 | ring baseRing, int reduction, int printout) |
---|
5208 | { |
---|
5209 | // save current options |
---|
5210 | BITSET save1 = si_opt_1; |
---|
5211 | if(reduction == 0) |
---|
5212 | { |
---|
5213 | si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis |
---|
5214 | si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions |
---|
5215 | } |
---|
5216 | Set_Error(FALSE); |
---|
5217 | Overflow_Error = FALSE; |
---|
5218 | //BOOLEAN endwalks = FALSE; |
---|
5219 | #ifdef TIME_TEST |
---|
5220 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
5221 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
5222 | tinput = clock(); |
---|
5223 | clock_t tim; |
---|
5224 | #endif |
---|
5225 | nstep=0; |
---|
5226 | int i,nwalk; |
---|
5227 | int nV = baseRing->N; |
---|
5228 | |
---|
5229 | ideal Gomega, M, F, FF, Gomega1, Gomega2, M1; |
---|
5230 | ring newRing; |
---|
5231 | ring XXRing = baseRing; |
---|
5232 | ring targetRing; |
---|
5233 | intvec* ivNull = new intvec(nV); |
---|
5234 | intvec* curr_weight = new intvec(nV); |
---|
5235 | intvec* target_weight = new intvec(nV); |
---|
5236 | intvec* exivlp = Mivlp(nV); |
---|
5237 | /* |
---|
5238 | intvec* tmp_weight = new intvec(nV); |
---|
5239 | for(i=0; i<nV; i++) |
---|
5240 | { |
---|
5241 | (*tmp_weight)[i] = (*orig_M)[i]; |
---|
5242 | } |
---|
5243 | */ |
---|
5244 | for(i=0; i<nV; i++) |
---|
5245 | { |
---|
5246 | (*curr_weight)[i] = (*orig_M)[i]; |
---|
5247 | (*target_weight)[i] = (*target_M)[i]; |
---|
5248 | } |
---|
5249 | #ifndef BUCHBERGER_ALG |
---|
5250 | intvec* hilb_func; |
---|
5251 | // to avoid (1,0,...,0) as the target vector |
---|
5252 | intvec* last_omega = new intvec(nV); |
---|
5253 | for(i=nV-1; i>0; i--) |
---|
5254 | { |
---|
5255 | (*last_omega)[i] = 1; |
---|
5256 | } |
---|
5257 | (*last_omega)[0] = 10000; |
---|
5258 | #endif |
---|
5259 | rComplete(currRing); |
---|
5260 | #ifdef CHECK_IDEAL_MWALK |
---|
5261 | if(printout > 2) |
---|
5262 | { |
---|
5263 | idString(Go,"//** Mwalk: Go"); |
---|
5264 | } |
---|
5265 | #endif |
---|
5266 | |
---|
5267 | if(target_M->length() == nV) |
---|
5268 | { |
---|
5269 | // define the target ring |
---|
5270 | targetRing = VMrDefault(target_weight); |
---|
5271 | } |
---|
5272 | else |
---|
5273 | { |
---|
5274 | targetRing = VMatrDefault(target_M); |
---|
5275 | } |
---|
5276 | if(orig_M->length() == nV) |
---|
5277 | { |
---|
5278 | // define a new ring with ordering "(a(curr_weight),lp) |
---|
5279 | //newRing = VMrDefault(curr_weight); |
---|
5280 | newRing=VMrRefine(target_weight, curr_weight); |
---|
5281 | } |
---|
5282 | else |
---|
5283 | { |
---|
5284 | newRing = VMatrRefine(target_M,curr_weight); //newRing = VMatrDefault(orig_M); |
---|
5285 | } |
---|
5286 | rChangeCurrRing(newRing); |
---|
5287 | if(printout > 2) |
---|
5288 | { |
---|
5289 | Print("\n//** Mrwalk: Current ring r = %s;\n", rString(currRing)); |
---|
5290 | } |
---|
5291 | #ifdef TIME_TEST |
---|
5292 | to = clock(); |
---|
5293 | #endif |
---|
5294 | ideal G = MstdCC(idrMoveR(Go,baseRing,currRing)); |
---|
5295 | #ifdef TIME_TEST |
---|
5296 | tostd = clock()-to; |
---|
5297 | #endif |
---|
5298 | |
---|
5299 | baseRing = currRing; |
---|
5300 | nwalk = 0; |
---|
5301 | |
---|
5302 | while(1) |
---|
5303 | { |
---|
5304 | nwalk ++; |
---|
5305 | nstep ++; |
---|
5306 | //compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
5307 | #ifdef TIME_TEST |
---|
5308 | to = clock(); |
---|
5309 | #endif |
---|
5310 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
5311 | #ifdef TIME_TEST |
---|
5312 | tif = tif + clock()-to; |
---|
5313 | #endif |
---|
5314 | |
---|
5315 | #ifdef CHECK_IDEAL_MWALK |
---|
5316 | if(printout > 1) |
---|
5317 | { |
---|
5318 | idString(Gomega,"//** Mwalk: Gomega"); |
---|
5319 | } |
---|
5320 | #endif |
---|
5321 | |
---|
5322 | if(reduction == 0) |
---|
5323 | { |
---|
5324 | FF = middleOfCone(G,Gomega); |
---|
5325 | if(FF != NULL) |
---|
5326 | { |
---|
5327 | PrintS("middle of Cone"); |
---|
5328 | idDelete(&G); |
---|
5329 | G = idCopy(FF); |
---|
5330 | idDelete(&FF); |
---|
5331 | goto NEXT_VECTOR; |
---|
5332 | } |
---|
5333 | } |
---|
5334 | |
---|
5335 | #ifndef BUCHBERGER_ALG |
---|
5336 | if(isNolVector(curr_weight) == 0) |
---|
5337 | { |
---|
5338 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
5339 | } |
---|
5340 | else |
---|
5341 | { |
---|
5342 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
5343 | } |
---|
5344 | #endif |
---|
5345 | |
---|
5346 | if(nwalk == 1) |
---|
5347 | { |
---|
5348 | if(orig_M->length() == nV) |
---|
5349 | { |
---|
5350 | // define a new ring with ordering "(a(curr_weight),lp) |
---|
5351 | //newRing = VMrDefault(curr_weight); |
---|
5352 | newRing=VMrRefine(target_weight, curr_weight); |
---|
5353 | } |
---|
5354 | else |
---|
5355 | { |
---|
5356 | newRing = VMatrRefine(target_M,curr_weight);//newRing = VMatrDefault(orig_M); |
---|
5357 | } |
---|
5358 | } |
---|
5359 | else |
---|
5360 | { |
---|
5361 | if(target_M->length() == nV) |
---|
5362 | { |
---|
5363 | //define a new ring with ordering "(a(curr_weight),lp)" |
---|
5364 | //newRing = VMrDefault(curr_weight); |
---|
5365 | newRing=VMrRefine(target_weight, curr_weight); |
---|
5366 | } |
---|
5367 | else |
---|
5368 | { |
---|
5369 | //define a new ring with matrix ordering |
---|
5370 | newRing = VMatrRefine(target_M,curr_weight); |
---|
5371 | } |
---|
5372 | } |
---|
5373 | rChangeCurrRing(newRing); |
---|
5374 | if(printout > 2) |
---|
5375 | { |
---|
5376 | Print("\n// Current ring r = %s;\n", rString(currRing)); |
---|
5377 | } |
---|
5378 | Gomega1 = idrMoveR(Gomega, baseRing,currRing); |
---|
5379 | idDelete(&Gomega); |
---|
5380 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
5381 | #ifdef TIME_TEST |
---|
5382 | to = clock(); |
---|
5383 | #endif |
---|
5384 | #ifndef BUCHBERGER_ALG |
---|
5385 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
5386 | delete hilb_func; |
---|
5387 | #else |
---|
5388 | M = kStd(Gomega1,NULL,testHomog,NULL,NULL,0,0,NULL); |
---|
5389 | #endif |
---|
5390 | #ifdef TIME_TEST |
---|
5391 | tstd = tstd + clock() - to; |
---|
5392 | #endif |
---|
5393 | idSkipZeroes(M); |
---|
5394 | #ifdef CHECK_IDEAL_MWALK |
---|
5395 | if(printout > 2) |
---|
5396 | { |
---|
5397 | idString(M, "//** Mwalk: M"); |
---|
5398 | } |
---|
5399 | #endif |
---|
5400 | //change the ring to baseRing |
---|
5401 | rChangeCurrRing(baseRing); |
---|
5402 | M1 = idrMoveR(M, newRing,currRing); |
---|
5403 | idDelete(&M); |
---|
5404 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
5405 | idDelete(&Gomega1); |
---|
5406 | #ifdef TIME_TEST |
---|
5407 | to = clock(); |
---|
5408 | #endif |
---|
5409 | // compute a representation of the generators of submod (M) with respect to those of mod (Gomega), |
---|
5410 | // where Gomega is a reduced Groebner basis w.r.t. the current ring |
---|
5411 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
5412 | #ifdef TIME_TEST |
---|
5413 | tlift = tlift + clock() - to; |
---|
5414 | #endif |
---|
5415 | #ifdef CHECK_IDEAL_MWALK |
---|
5416 | if(printout > 2) |
---|
5417 | { |
---|
5418 | idString(F, "//** Mwalk: F"); |
---|
5419 | } |
---|
5420 | #endif |
---|
5421 | idDelete(&Gomega2); |
---|
5422 | idDelete(&M1); |
---|
5423 | |
---|
5424 | rChangeCurrRing(newRing); // change the ring to newRing |
---|
5425 | G = idrMoveR(F,baseRing,currRing); |
---|
5426 | idDelete(&F); |
---|
5427 | idSkipZeroes(G); |
---|
5428 | |
---|
5429 | #ifdef CHECK_IDEAL_MWALK |
---|
5430 | if(printout > 2) |
---|
5431 | { |
---|
5432 | idString(G, "//** Mwalk: G"); |
---|
5433 | } |
---|
5434 | #endif |
---|
5435 | |
---|
5436 | rChangeCurrRing(targetRing); |
---|
5437 | G = idrMoveR(G,newRing,currRing); |
---|
5438 | // test whether target cone is reached |
---|
5439 | if(reduction !=0 && test_w_in_ConeCC(G,curr_weight) == 1) |
---|
5440 | { |
---|
5441 | baseRing = currRing; |
---|
5442 | break; |
---|
5443 | //endwalks = TRUE; |
---|
5444 | } |
---|
5445 | |
---|
5446 | rChangeCurrRing(newRing); |
---|
5447 | G = idrMoveR(G,targetRing,currRing); |
---|
5448 | baseRing = currRing; |
---|
5449 | |
---|
5450 | NEXT_VECTOR: |
---|
5451 | #ifdef TIME_TEST |
---|
5452 | to = clock(); |
---|
5453 | #endif |
---|
5454 | intvec* next_weight = MwalkNextWeightCC(curr_weight,target_weight,G); |
---|
5455 | #ifdef TIME_TEST |
---|
5456 | tnw = tnw + clock() - to; |
---|
5457 | #endif |
---|
5458 | #ifdef PRINT_VECTORS |
---|
5459 | if(printout > 0) |
---|
5460 | { |
---|
5461 | MivString(curr_weight, target_weight, next_weight); |
---|
5462 | } |
---|
5463 | #endif |
---|
5464 | if(reduction ==0) |
---|
5465 | { |
---|
5466 | if(MivComp(curr_weight,next_weight)==1) |
---|
5467 | { |
---|
5468 | break; |
---|
5469 | } |
---|
5470 | } |
---|
5471 | if(MivComp(target_weight,curr_weight) == 1) |
---|
5472 | { |
---|
5473 | break; |
---|
5474 | } |
---|
5475 | |
---|
5476 | for(i=nV-1; i>=0; i--) |
---|
5477 | { |
---|
5478 | //(*tmp_weight)[i] = (*curr_weight)[i]; |
---|
5479 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
5480 | } |
---|
5481 | delete next_weight; |
---|
5482 | } |
---|
5483 | rChangeCurrRing(XXRing); |
---|
5484 | ideal result = idrMoveR(G,baseRing,currRing); |
---|
5485 | idDelete(&Go); |
---|
5486 | idDelete(&G); |
---|
5487 | //delete tmp_weight; |
---|
5488 | delete ivNull; |
---|
5489 | delete exivlp; |
---|
5490 | #ifndef BUCHBERGER_ALG |
---|
5491 | delete last_omega; |
---|
5492 | #endif |
---|
5493 | #ifdef TIME_TEST |
---|
5494 | TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep); |
---|
5495 | //Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
5496 | //Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
5497 | #endif |
---|
5498 | if(printout > 0) |
---|
5499 | { |
---|
5500 | Print("\n//** Mwalk: Groebner Walk took %d steps.\n", nstep); |
---|
5501 | } |
---|
5502 | si_opt_1 = save1; //set original options |
---|
5503 | return(result); |
---|
5504 | } |
---|
5505 | |
---|
5506 | // THE RANDOM WALK ALGORITHM |
---|
5507 | ideal Mrwalk(ideal Go, intvec* orig_M, intvec* target_M, int weight_rad, int pert_deg, |
---|
5508 | int reduction, int printout) |
---|
5509 | { |
---|
5510 | BITSET save1 = si_opt_1; // save current options |
---|
5511 | if(reduction == 0) |
---|
5512 | { |
---|
5513 | si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis |
---|
5514 | si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions |
---|
5515 | } |
---|
5516 | |
---|
5517 | Set_Error(FALSE); |
---|
5518 | Overflow_Error = FALSE; |
---|
5519 | BOOLEAN endwalks = FALSE; |
---|
5520 | #ifdef TIME_TEST |
---|
5521 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
5522 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
5523 | tinput = clock(); |
---|
5524 | clock_t tim; |
---|
5525 | #endif |
---|
5526 | nstep=0; |
---|
5527 | int i,nwalk;//polylength; |
---|
5528 | int nV = currRing->N; |
---|
5529 | |
---|
5530 | //check that weight radius is valid |
---|
5531 | if(weight_rad < 0) |
---|
5532 | { |
---|
5533 | Werror("Invalid radius.\n"); |
---|
5534 | return NULL; |
---|
5535 | } |
---|
5536 | |
---|
5537 | //check that perturbation degree is valid |
---|
5538 | if(pert_deg > nV || pert_deg < 1) |
---|
5539 | { |
---|
5540 | Werror("Invalid perturbation degree.\n"); |
---|
5541 | return NULL; |
---|
5542 | } |
---|
5543 | |
---|
5544 | ideal Gomega, M, F,FF, Gomega1, Gomega2, M1; |
---|
5545 | ring newRing; |
---|
5546 | ring targetRing; |
---|
5547 | ring baseRing = currRing; |
---|
5548 | ring XXRing = currRing; |
---|
5549 | intvec* iv_M; |
---|
5550 | intvec* ivNull = new intvec(nV); |
---|
5551 | intvec* curr_weight = new intvec(nV); |
---|
5552 | intvec* target_weight = new intvec(nV); |
---|
5553 | intvec* next_weight= new intvec(nV); |
---|
5554 | |
---|
5555 | for(i=0; i<nV; i++) |
---|
5556 | { |
---|
5557 | (*curr_weight)[i] = (*orig_M)[i]; |
---|
5558 | (*target_weight)[i] = (*target_M)[i]; |
---|
5559 | } |
---|
5560 | |
---|
5561 | #ifndef BUCHBERGER_ALG |
---|
5562 | intvec* hilb_func; |
---|
5563 | // to avoid (1,0,...,0) as the target vector |
---|
5564 | intvec* last_omega = new intvec(nV); |
---|
5565 | for(i=nV-1; i>0; i--) |
---|
5566 | { |
---|
5567 | (*last_omega)[i] = 1; |
---|
5568 | } |
---|
5569 | (*last_omega)[0] = 10000; |
---|
5570 | #endif |
---|
5571 | rComplete(currRing); |
---|
5572 | |
---|
5573 | if(target_M->length() == nV) |
---|
5574 | { |
---|
5575 | targetRing = VMrDefault(target_weight); // define the target ring |
---|
5576 | } |
---|
5577 | else |
---|
5578 | { |
---|
5579 | targetRing = VMatrDefault(target_M); |
---|
5580 | } |
---|
5581 | if(orig_M->length() == nV) |
---|
5582 | { |
---|
5583 | //newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp) |
---|
5584 | newRing=VMrRefine(target_weight, curr_weight); |
---|
5585 | } |
---|
5586 | else |
---|
5587 | { |
---|
5588 | newRing = VMatrRefine(target_M,curr_weight);//newRing = VMatrDefault(orig_M); |
---|
5589 | } |
---|
5590 | rChangeCurrRing(newRing); |
---|
5591 | #ifdef TIME_TEST |
---|
5592 | to = clock(); |
---|
5593 | #endif |
---|
5594 | ideal G = MstdCC(idrMoveR(Go,baseRing,currRing)); |
---|
5595 | #ifdef TIME_TEST |
---|
5596 | tostd = clock()-to; |
---|
5597 | #endif |
---|
5598 | baseRing = currRing; |
---|
5599 | nwalk = 0; |
---|
5600 | |
---|
5601 | #ifdef TIME_TEST |
---|
5602 | to = clock(); |
---|
5603 | #endif |
---|
5604 | Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
5605 | #ifdef TIME_TEST |
---|
5606 | tif = tif + clock()-to; //time for computing initial form ideal |
---|
5607 | #endif |
---|
5608 | |
---|
5609 | while(1) |
---|
5610 | { |
---|
5611 | nwalk ++; |
---|
5612 | nstep ++; |
---|
5613 | #ifdef CHECK_IDEAL_MWALK |
---|
5614 | if(printout > 1) |
---|
5615 | { |
---|
5616 | idString(Gomega,"//** Mrwalk: Gomega"); |
---|
5617 | } |
---|
5618 | #endif |
---|
5619 | if(reduction == 0) |
---|
5620 | { |
---|
5621 | FF = middleOfCone(G,Gomega); |
---|
5622 | if(FF != NULL) |
---|
5623 | { |
---|
5624 | idDelete(&G); |
---|
5625 | G = idCopy(FF); |
---|
5626 | idDelete(&FF); |
---|
5627 | goto NEXT_VECTOR; |
---|
5628 | } |
---|
5629 | } |
---|
5630 | #ifndef BUCHBERGER_ALG |
---|
5631 | if(isNolVector(curr_weight) == 0) |
---|
5632 | { |
---|
5633 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
5634 | } |
---|
5635 | else |
---|
5636 | { |
---|
5637 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
5638 | } |
---|
5639 | #endif |
---|
5640 | if(nwalk == 1) |
---|
5641 | { |
---|
5642 | if(orig_M->length() == nV) |
---|
5643 | { |
---|
5644 | /*newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)*/ |
---|
5645 | newRing=VMrRefine(target_weight, curr_weight); |
---|
5646 | } |
---|
5647 | else |
---|
5648 | { |
---|
5649 | newRing = VMatrRefine(target_M,curr_weight);//newRing = VMatrDefault(orig_M); |
---|
5650 | } |
---|
5651 | } |
---|
5652 | else |
---|
5653 | { |
---|
5654 | if(target_M->length() == nV) |
---|
5655 | { |
---|
5656 | /*newRing = VMrDefault(curr_weight); // define a new ring with ordering "(a(curr_weight),lp)*/ |
---|
5657 | newRing=VMrRefine(target_weight, curr_weight); |
---|
5658 | } |
---|
5659 | else |
---|
5660 | { |
---|
5661 | newRing = VMatrRefine(target_M,curr_weight); |
---|
5662 | } |
---|
5663 | } |
---|
5664 | rChangeCurrRing(newRing); |
---|
5665 | Gomega1 = idrMoveR(Gomega, baseRing,currRing); |
---|
5666 | idDelete(&Gomega); |
---|
5667 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
5668 | #ifdef TIME_TEST |
---|
5669 | to = clock(); |
---|
5670 | #endif |
---|
5671 | #ifndef BUCHBERGER_ALG |
---|
5672 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
5673 | delete hilb_func; |
---|
5674 | #else |
---|
5675 | M = kStd(Gomega1,NULL,testHomog,NULL,NULL,0,0,NULL); |
---|
5676 | #endif |
---|
5677 | #ifdef TIME_TEST |
---|
5678 | tstd = tstd + clock() - to; |
---|
5679 | #endif |
---|
5680 | idSkipZeroes(M); |
---|
5681 | #ifdef CHECK_IDEAL_MWALK |
---|
5682 | if(printout > 2) |
---|
5683 | { |
---|
5684 | idString(M, "//** Mrwalk: M"); |
---|
5685 | } |
---|
5686 | #endif |
---|
5687 | //change the ring to baseRing |
---|
5688 | rChangeCurrRing(baseRing); |
---|
5689 | M1 = idrMoveR(M, newRing,currRing); |
---|
5690 | idDelete(&M); |
---|
5691 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
5692 | idDelete(&Gomega1); |
---|
5693 | #ifdef TIME_TEST |
---|
5694 | to = clock(); |
---|
5695 | #endif |
---|
5696 | // compute a representation of the generators of submod (M) with respect to those of mod (Gomega), |
---|
5697 | // where Gomega is a reduced Groebner basis w.r.t. the current ring |
---|
5698 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
5699 | #ifdef TIME_TEST |
---|
5700 | tlift = tlift + clock() - to; |
---|
5701 | #endif |
---|
5702 | #ifdef CHECK_IDEAL_MWALK |
---|
5703 | if(printout > 2) |
---|
5704 | { |
---|
5705 | idString(F,"//** Mrwalk: F"); |
---|
5706 | } |
---|
5707 | #endif |
---|
5708 | idDelete(&Gomega2); |
---|
5709 | idDelete(&M1); |
---|
5710 | rChangeCurrRing(newRing); // change the ring to newRing |
---|
5711 | G = idrMoveR(F,baseRing,currRing); |
---|
5712 | idDelete(&F); |
---|
5713 | baseRing = currRing; |
---|
5714 | #ifdef TIME_TEST |
---|
5715 | to = clock(); |
---|
5716 | tstd = tstd + clock() - to; |
---|
5717 | #endif |
---|
5718 | idSkipZeroes(G); |
---|
5719 | #ifdef CHECK_IDEAL_MWALK |
---|
5720 | if(printout > 2) |
---|
5721 | { |
---|
5722 | idString(G,"//** Mrwalk: G"); |
---|
5723 | } |
---|
5724 | #endif |
---|
5725 | |
---|
5726 | rChangeCurrRing(targetRing); |
---|
5727 | G = idrMoveR(G,newRing,currRing); |
---|
5728 | |
---|
5729 | // test whether target cone is reached |
---|
5730 | if(reduction !=0 && test_w_in_ConeCC(G,curr_weight) == 1) |
---|
5731 | { |
---|
5732 | baseRing = currRing; |
---|
5733 | break; |
---|
5734 | } |
---|
5735 | |
---|
5736 | rChangeCurrRing(newRing); |
---|
5737 | G = idrMoveR(G,targetRing,currRing); |
---|
5738 | baseRing = currRing; |
---|
5739 | |
---|
5740 | NEXT_VECTOR: |
---|
5741 | #ifdef TIME_TEST |
---|
5742 | to = clock(); |
---|
5743 | #endif |
---|
5744 | next_weight = MwalkNextWeightCC(curr_weight,target_weight,G); |
---|
5745 | #ifdef TIME_TEST |
---|
5746 | tnw = tnw + clock() - to; |
---|
5747 | #endif |
---|
5748 | |
---|
5749 | #ifdef TIME_TEST |
---|
5750 | to = clock(); |
---|
5751 | #endif |
---|
5752 | Gomega = MwalkInitialForm(G, next_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
5753 | #ifdef TIME_TEST |
---|
5754 | tif = tif + clock()-to; //time for computing initial form ideal |
---|
5755 | #endif |
---|
5756 | |
---|
5757 | //lengthpoly(Gomega) = 1 if there is a polynomial in Gomega with at least 3 monomials and 0 otherwise |
---|
5758 | //polylength = lengthpoly(Gomega); |
---|
5759 | if(lengthpoly(Gomega) > 0) |
---|
5760 | { |
---|
5761 | //there is a polynomial in Gomega with at least 3 monomials, |
---|
5762 | //low-dimensional facet of the cone |
---|
5763 | delete next_weight; |
---|
5764 | if(target_M->length() == nV) |
---|
5765 | { |
---|
5766 | //iv_M = MivMatrixOrder(curr_weight); |
---|
5767 | iv_M = MivMatrixOrderRefine(curr_weight,target_M); |
---|
5768 | } |
---|
5769 | else |
---|
5770 | { |
---|
5771 | iv_M = MivMatrixOrderRefine(curr_weight,target_M); |
---|
5772 | } |
---|
5773 | #ifdef TIME_TEST |
---|
5774 | to = clock(); |
---|
5775 | #endif |
---|
5776 | next_weight = MWalkRandomNextWeight(G, iv_M, target_weight, weight_rad, pert_deg); |
---|
5777 | #ifdef TIME_TEST |
---|
5778 | tnw = tnw + clock() - to; |
---|
5779 | #endif |
---|
5780 | idDelete(&Gomega); |
---|
5781 | #ifdef TIME_TEST |
---|
5782 | to = clock(); |
---|
5783 | #endif |
---|
5784 | Gomega = MwalkInitialForm(G, next_weight); |
---|
5785 | #ifdef TIME_TEST |
---|
5786 | tif = tif + clock()-to; //time for computing initial form ideal |
---|
5787 | #endif |
---|
5788 | delete iv_M; |
---|
5789 | } |
---|
5790 | |
---|
5791 | // test whether target weight vector is reached |
---|
5792 | if(MivComp(next_weight, ivNull) == 1 || MivComp(target_weight,curr_weight) == 1) |
---|
5793 | { |
---|
5794 | baseRing = currRing; |
---|
5795 | delete next_weight; |
---|
5796 | break; |
---|
5797 | } |
---|
5798 | if(reduction ==0) |
---|
5799 | { |
---|
5800 | if(MivComp(curr_weight,next_weight)==1) |
---|
5801 | { |
---|
5802 | break; |
---|
5803 | } |
---|
5804 | } |
---|
5805 | #ifdef PRINT_VECTORS |
---|
5806 | if(printout > 0) |
---|
5807 | { |
---|
5808 | MivString(curr_weight, target_weight, next_weight); |
---|
5809 | } |
---|
5810 | #endif |
---|
5811 | |
---|
5812 | for(i=nV-1; i>=0; i--) |
---|
5813 | { |
---|
5814 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
5815 | } |
---|
5816 | delete next_weight; |
---|
5817 | } |
---|
5818 | baseRing = currRing; |
---|
5819 | rChangeCurrRing(XXRing); |
---|
5820 | ideal result = idrMoveR(G,baseRing,currRing); |
---|
5821 | idDelete(&G); |
---|
5822 | delete ivNull; |
---|
5823 | #ifndef BUCHBERGER_ALG |
---|
5824 | delete last_omega; |
---|
5825 | #endif |
---|
5826 | if(printout > 0) |
---|
5827 | { |
---|
5828 | Print("\n//** Mrwalk: Groebner Walk took %d steps.\n", nstep); |
---|
5829 | } |
---|
5830 | #ifdef TIME_TEST |
---|
5831 | TimeString(tinput, tostd, tif, tstd, tlift, tred, tnw, nstep); |
---|
5832 | //Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
5833 | //Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
5834 | #endif |
---|
5835 | si_opt_1 = save1; //set original options |
---|
5836 | return(result); |
---|
5837 | } |
---|
5838 | |
---|
5839 | /**************************************************************/ |
---|
5840 | /* Implementation of the perturbation walk algorithm */ |
---|
5841 | /**************************************************************/ |
---|
5842 | /* If the perturbed target weight vector or an intermediate weight vector |
---|
5843 | doesn't stay in the correct Groebner cone, we have only |
---|
5844 | a reduced Groebner basis for the given ideal with respect to |
---|
5845 | a monomial order which differs to the given order. |
---|
5846 | Then we have to compute the wanted reduced Groebner basis for it. |
---|
5847 | For this, we can use |
---|
5848 | 1) the improved Buchberger algorithm or |
---|
5849 | 2) the changed perturbation walk algorithm with a decreased degree. |
---|
5850 | */ |
---|
5851 | // if nP = 0 use kStd, else call LastGB |
---|
5852 | ideal Mpwalk(ideal Go, int op_deg, int tp_deg,intvec* curr_weight, |
---|
5853 | intvec* target_weight, int nP, int reduction, int printout) |
---|
5854 | { |
---|
5855 | BITSET save1 = si_opt_1; // save current options |
---|
5856 | if(reduction == 0) |
---|
5857 | { |
---|
5858 | si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis |
---|
5859 | si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions |
---|
5860 | } |
---|
5861 | Set_Error(FALSE ); |
---|
5862 | Overflow_Error = FALSE; |
---|
5863 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
5864 | #ifdef TIME_TEST |
---|
5865 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
5866 | xtextra=0; |
---|
5867 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
5868 | tinput = clock(); |
---|
5869 | |
---|
5870 | clock_t tim; |
---|
5871 | #endif |
---|
5872 | nstep = 0; |
---|
5873 | int i, ntwC=1, ntestw=1, nV = currRing->N; |
---|
5874 | |
---|
5875 | //check that perturbation degree is valid |
---|
5876 | if(op_deg < 1 || tp_deg < 1 || op_deg > nV || tp_deg > nV) |
---|
5877 | { |
---|
5878 | Werror("Invalid perturbation degree.\n"); |
---|
5879 | return NULL; |
---|
5880 | } |
---|
5881 | |
---|
5882 | BOOLEAN endwalks = FALSE; |
---|
5883 | ideal Gomega, M, F, FF, G, Gomega1, Gomega2, M1,F1,Eresult,ssG; |
---|
5884 | ring newRing, oldRing, TargetRing; |
---|
5885 | intvec* iv_M_dp; |
---|
5886 | intvec* iv_M_lp; |
---|
5887 | intvec* exivlp = Mivlp(nV); |
---|
5888 | intvec* orig_target = target_weight; |
---|
5889 | intvec* pert_target_vector = target_weight; |
---|
5890 | intvec* ivNull = new intvec(nV); |
---|
5891 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
5892 | #ifndef BUCHBERGER_ALG |
---|
5893 | intvec* hilb_func; |
---|
5894 | #endif |
---|
5895 | intvec* next_weight; |
---|
5896 | |
---|
5897 | // to avoid (1,0,...,0) as the target vector |
---|
5898 | intvec* last_omega = new intvec(nV); |
---|
5899 | for(i=nV-1; i>0; i--) |
---|
5900 | (*last_omega)[i] = 1; |
---|
5901 | (*last_omega)[0] = 10000; |
---|
5902 | |
---|
5903 | ring XXRing = currRing; |
---|
5904 | #ifdef TIME_TEST |
---|
5905 | to = clock(); |
---|
5906 | #endif |
---|
5907 | // perturbs the original vector |
---|
5908 | if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp" |
---|
5909 | { |
---|
5910 | G = MstdCC(Go); |
---|
5911 | #ifdef TIME_TEST |
---|
5912 | tostd = clock()-to; |
---|
5913 | #endif |
---|
5914 | if(op_deg != 1){ |
---|
5915 | iv_M_dp = MivMatrixOrderdp(nV); |
---|
5916 | //ivString(iv_M_dp, "iv_M_dp"); |
---|
5917 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
5918 | } |
---|
5919 | } |
---|
5920 | else |
---|
5921 | { |
---|
5922 | //define ring order := (a(curr_weight),lp); |
---|
5923 | /* |
---|
5924 | if (rParameter(currRing) != NULL) |
---|
5925 | DefRingPar(curr_weight); |
---|
5926 | else |
---|
5927 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
5928 | */ |
---|
5929 | rChangeCurrRing(VMrRefine(target_weight,curr_weight)); |
---|
5930 | |
---|
5931 | G = idrMoveR(Go, XXRing,currRing); |
---|
5932 | G = MstdCC(G); |
---|
5933 | #ifdef TIME_TEST |
---|
5934 | tostd = clock()-to; |
---|
5935 | #endif |
---|
5936 | if(op_deg != 1){ |
---|
5937 | iv_M_dp = MivMatrixOrder(curr_weight); |
---|
5938 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
5939 | } |
---|
5940 | } |
---|
5941 | delete iv_dp; |
---|
5942 | if(op_deg != 1) delete iv_M_dp; |
---|
5943 | |
---|
5944 | ring HelpRing = currRing; |
---|
5945 | |
---|
5946 | // perturbs the target weight vector |
---|
5947 | if(tp_deg > 1 && tp_deg <= nV) |
---|
5948 | { |
---|
5949 | /* |
---|
5950 | if (rParameter(currRing) != NULL) |
---|
5951 | DefRingPar(target_weight); |
---|
5952 | else |
---|
5953 | rChangeCurrRing(VMrDefault(target_weight)); |
---|
5954 | */ |
---|
5955 | rChangeCurrRing(VMrRefine(target_weight,curr_weight)); |
---|
5956 | |
---|
5957 | TargetRing = currRing; |
---|
5958 | ssG = idrMoveR(G,HelpRing,currRing); |
---|
5959 | if(MivSame(target_weight, exivlp) == 1) |
---|
5960 | { |
---|
5961 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
5962 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
5963 | } |
---|
5964 | else |
---|
5965 | { |
---|
5966 | iv_M_lp = MivMatrixOrder(target_weight); |
---|
5967 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
5968 | } |
---|
5969 | delete iv_M_lp; |
---|
5970 | pert_target_vector = target_weight; |
---|
5971 | rChangeCurrRing(HelpRing); |
---|
5972 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
5973 | } |
---|
5974 | if(printout > 0) |
---|
5975 | { |
---|
5976 | Print("\n//** Mpwalk: Perturbation Walk of degree (%d,%d):",op_deg,tp_deg); |
---|
5977 | #ifdef PRINT_VECTORS |
---|
5978 | ivString(curr_weight, "//** Mpwalk: new current weight"); |
---|
5979 | ivString(target_weight, "//** Mpwalk: new target weight"); |
---|
5980 | #endif |
---|
5981 | } |
---|
5982 | while(1) |
---|
5983 | { |
---|
5984 | nstep ++; |
---|
5985 | #ifdef TIME_TEST |
---|
5986 | to = clock(); |
---|
5987 | #endif |
---|
5988 | // compute an initial form ideal of <G> w.r.t. the weight vector |
---|
5989 | // "curr_weight" |
---|
5990 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
5991 | #ifdef TIME_TEST |
---|
5992 | tif = tif + clock()-to; |
---|
5993 | #endif |
---|
5994 | #ifdef CHECK_IDEAL_MWALK |
---|
5995 | if(printout > 1) |
---|
5996 | { |
---|
5997 | idString(Gomega,"//** Mpwalk: Gomega"); |
---|
5998 | } |
---|
5999 | #endif |
---|
6000 | if(reduction == 0 && nstep > 1) |
---|
6001 | { |
---|
6002 | FF = middleOfCone(G,Gomega); |
---|
6003 | if(FF != NULL) |
---|
6004 | { |
---|
6005 | idDelete(&G); |
---|
6006 | G = idCopy(FF); |
---|
6007 | idDelete(&FF); |
---|
6008 | goto NEXT_VECTOR; |
---|
6009 | } |
---|
6010 | } |
---|
6011 | |
---|
6012 | #ifdef ENDWALKS |
---|
6013 | if(endwalks == TRUE) |
---|
6014 | { |
---|
6015 | if(printout > 0) |
---|
6016 | { |
---|
6017 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6018 | } |
---|
6019 | //idElements(G, "G"); |
---|
6020 | //headidString(G, "G"); |
---|
6021 | } |
---|
6022 | #endif |
---|
6023 | |
---|
6024 | #ifndef BUCHBERGER_ALG |
---|
6025 | if(isNolVector(curr_weight) == 0) |
---|
6026 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
6027 | else |
---|
6028 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
6029 | #endif // BUCHBERGER_ALG |
---|
6030 | |
---|
6031 | oldRing = currRing; |
---|
6032 | |
---|
6033 | // define a new ring with ordering "(a(curr_weight),lp) |
---|
6034 | /* |
---|
6035 | if (rParameter(currRing) != NULL) |
---|
6036 | DefRingPar(curr_weight); |
---|
6037 | else |
---|
6038 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
6039 | */ |
---|
6040 | rChangeCurrRing(VMrRefine(target_weight,curr_weight)); |
---|
6041 | |
---|
6042 | newRing = currRing; |
---|
6043 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
6044 | |
---|
6045 | #ifdef ENDWALKS |
---|
6046 | if(endwalks==TRUE) |
---|
6047 | { |
---|
6048 | if(printout > 0) |
---|
6049 | { |
---|
6050 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6051 | //idElements(Gomega1, "Gw"); |
---|
6052 | //headidString(Gomega1, "headGw"); |
---|
6053 | PrintS("\n// compute a rGB of Gw:\n"); |
---|
6054 | } |
---|
6055 | #ifndef BUCHBERGER_ALG |
---|
6056 | ivString(hilb_func, "w"); |
---|
6057 | #endif |
---|
6058 | } |
---|
6059 | #endif |
---|
6060 | #ifdef TIME_TEST |
---|
6061 | tim = clock(); |
---|
6062 | to = clock(); |
---|
6063 | #endif |
---|
6064 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
6065 | #ifdef BUCHBERGER_ALG |
---|
6066 | M = MstdhomCC(Gomega1); |
---|
6067 | #else |
---|
6068 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
6069 | delete hilb_func; |
---|
6070 | #endif |
---|
6071 | |
---|
6072 | if(endwalks == TRUE) |
---|
6073 | { |
---|
6074 | #ifdef TIME_TEST |
---|
6075 | xtstd = xtstd+clock()-to; |
---|
6076 | #endif |
---|
6077 | #ifdef ENDWALKS |
---|
6078 | if(printout > 1) |
---|
6079 | { |
---|
6080 | Print("\n// time for the last std(Gw) = %.2f sec\n", |
---|
6081 | ((double) clock())/1000000 -((double)tim) /1000000); |
---|
6082 | } |
---|
6083 | #endif |
---|
6084 | } |
---|
6085 | else |
---|
6086 | { |
---|
6087 | #ifdef TIME_TEST |
---|
6088 | tstd=tstd+clock()-to; |
---|
6089 | #endif |
---|
6090 | } |
---|
6091 | #ifdef CHECK_IDEAL_MWALK |
---|
6092 | if(printout > 2) |
---|
6093 | { |
---|
6094 | idString(M,"//** Mpwalk: M"); |
---|
6095 | } |
---|
6096 | #endif |
---|
6097 | // change the ring to oldRing |
---|
6098 | rChangeCurrRing(oldRing); |
---|
6099 | M1 = idrMoveR(M, newRing,currRing); |
---|
6100 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
6101 | #ifdef TIME_TEST |
---|
6102 | to=clock(); |
---|
6103 | #endif |
---|
6104 | /* compute a representation of the generators of submod (M) |
---|
6105 | with respect to those of mod (Gomega). |
---|
6106 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
6107 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
6108 | #ifdef TIME_TEST |
---|
6109 | if(endwalks == FALSE) |
---|
6110 | tlift = tlift+clock()-to; |
---|
6111 | else |
---|
6112 | xtlift=clock()-to; |
---|
6113 | #endif |
---|
6114 | #ifdef CHECK_IDEAL_MWALK |
---|
6115 | if(printout > 2) |
---|
6116 | { |
---|
6117 | idString(F,"//** Mpwalk: F"); |
---|
6118 | } |
---|
6119 | #endif |
---|
6120 | |
---|
6121 | idDelete(&M1); |
---|
6122 | idDelete(&Gomega2); |
---|
6123 | idDelete(&G); |
---|
6124 | |
---|
6125 | // change the ring to newRing |
---|
6126 | rChangeCurrRing(newRing); |
---|
6127 | if(reduction == 0) |
---|
6128 | { |
---|
6129 | G = idrMoveR(F,oldRing,currRing); |
---|
6130 | } |
---|
6131 | else |
---|
6132 | { |
---|
6133 | F1 = idrMoveR(F, oldRing,currRing); |
---|
6134 | if(printout > 2) |
---|
6135 | { |
---|
6136 | PrintS("\n //** Mpwalk: reduce the Groebner basis.\n"); |
---|
6137 | } |
---|
6138 | #ifdef TIME_TEST |
---|
6139 | to=clock(); |
---|
6140 | #endif |
---|
6141 | G = kInterRedCC(F1, NULL); |
---|
6142 | #ifdef TIME_TEST |
---|
6143 | if(endwalks == FALSE) |
---|
6144 | tred = tred+clock()-to; |
---|
6145 | else |
---|
6146 | xtred=clock()-to; |
---|
6147 | #endif |
---|
6148 | idDelete(&F1); |
---|
6149 | } |
---|
6150 | if(endwalks == TRUE) |
---|
6151 | break; |
---|
6152 | |
---|
6153 | NEXT_VECTOR: |
---|
6154 | #ifdef TIME_TEST |
---|
6155 | to=clock(); |
---|
6156 | #endif |
---|
6157 | // compute a next weight vector |
---|
6158 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
6159 | #ifdef TIME_TEST |
---|
6160 | tnw=tnw+clock()-to; |
---|
6161 | #endif |
---|
6162 | #ifdef PRINT_VECTORS |
---|
6163 | if(printout > 0) |
---|
6164 | { |
---|
6165 | MivString(curr_weight, target_weight, next_weight); |
---|
6166 | } |
---|
6167 | #endif |
---|
6168 | |
---|
6169 | if(Overflow_Error == TRUE) |
---|
6170 | { |
---|
6171 | ntwC = 0; |
---|
6172 | //ntestomega = 1; |
---|
6173 | //Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6174 | //idElements(G, "G"); |
---|
6175 | delete next_weight; |
---|
6176 | goto FINISH_160302; |
---|
6177 | } |
---|
6178 | if(MivComp(next_weight, ivNull) == 1){ |
---|
6179 | newRing = currRing; |
---|
6180 | delete next_weight; |
---|
6181 | //Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6182 | break; |
---|
6183 | } |
---|
6184 | if(MivComp(next_weight, target_weight) == 1) |
---|
6185 | endwalks = TRUE; |
---|
6186 | |
---|
6187 | for(i=nV-1; i>=0; i--) |
---|
6188 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
6189 | |
---|
6190 | delete next_weight; |
---|
6191 | }//end of while-loop |
---|
6192 | |
---|
6193 | if(tp_deg != 1) |
---|
6194 | { |
---|
6195 | FINISH_160302: |
---|
6196 | if(MivSame(orig_target, exivlp) == 1) { |
---|
6197 | /* if (rParameter(currRing) != NULL) |
---|
6198 | DefRingParlp(); |
---|
6199 | else |
---|
6200 | VMrDefaultlp(); |
---|
6201 | else |
---|
6202 | if (rParameter(currRing) != NULL) |
---|
6203 | DefRingPar(orig_target); |
---|
6204 | else*/ |
---|
6205 | rChangeCurrRing(VMrDefault(orig_target)); |
---|
6206 | } |
---|
6207 | TargetRing=currRing; |
---|
6208 | F1 = idrMoveR(G, newRing,currRing); |
---|
6209 | /* |
---|
6210 | #ifdef CHECK_IDEAL_MWALK |
---|
6211 | headidString(G, "G"); |
---|
6212 | #endif |
---|
6213 | */ |
---|
6214 | |
---|
6215 | // check whether the pertubed target vector stays in the correct cone |
---|
6216 | if(ntwC != 0){ |
---|
6217 | ntestw = test_w_in_ConeCC(F1, pert_target_vector); |
---|
6218 | } |
---|
6219 | |
---|
6220 | if( ntestw != 1 || ntwC == 0) |
---|
6221 | { |
---|
6222 | if(ntestw != 1 && printout >2) |
---|
6223 | { |
---|
6224 | ivString(pert_target_vector, "tau"); |
---|
6225 | PrintS("\n// ** perturbed target vector doesn't stay in cone!!"); |
---|
6226 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6227 | //idElements(F1, "G"); |
---|
6228 | } |
---|
6229 | // LastGB is "better" than the kStd subroutine |
---|
6230 | to=clock(); |
---|
6231 | ideal eF1; |
---|
6232 | if(nP == 0 || tp_deg == 1 || MivSame(orig_target, exivlp) != 1){ |
---|
6233 | // PrintS("\n// ** calls \"std\" to compute a GB"); |
---|
6234 | eF1 = MstdCC(F1); |
---|
6235 | idDelete(&F1); |
---|
6236 | } |
---|
6237 | else { |
---|
6238 | // PrintS("\n// ** calls \"LastGB\" to compute a GB"); |
---|
6239 | rChangeCurrRing(newRing); |
---|
6240 | ideal F2 = idrMoveR(F1, TargetRing,currRing); |
---|
6241 | eF1 = LastGB(F2, curr_weight, tp_deg-1); |
---|
6242 | F2=NULL; |
---|
6243 | } |
---|
6244 | xtextra=clock()-to; |
---|
6245 | ring exTargetRing = currRing; |
---|
6246 | |
---|
6247 | rChangeCurrRing(XXRing); |
---|
6248 | Eresult = idrMoveR(eF1, exTargetRing,currRing); |
---|
6249 | } |
---|
6250 | else{ |
---|
6251 | rChangeCurrRing(XXRing); |
---|
6252 | Eresult = idrMoveR(F1, TargetRing,currRing); |
---|
6253 | } |
---|
6254 | } |
---|
6255 | else { |
---|
6256 | rChangeCurrRing(XXRing); |
---|
6257 | Eresult = idrMoveR(G, newRing,currRing); |
---|
6258 | } |
---|
6259 | si_opt_1 = save1; //set original options, e. g. option(RedSB) |
---|
6260 | delete ivNull; |
---|
6261 | if(tp_deg != 1) |
---|
6262 | delete target_weight; |
---|
6263 | |
---|
6264 | if(op_deg != 1 ) |
---|
6265 | delete curr_weight; |
---|
6266 | |
---|
6267 | delete exivlp; |
---|
6268 | delete last_omega; |
---|
6269 | |
---|
6270 | #ifdef TIME_TEST |
---|
6271 | TimeStringFractal(tinput, tostd, tif+xtif, tstd+xtstd,0, tlift+xtlift, tred+xtred, |
---|
6272 | tnw+xtnw); |
---|
6273 | |
---|
6274 | //Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
6275 | //Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep, Overflow_Error); |
---|
6276 | #endif |
---|
6277 | if(printout > 0) |
---|
6278 | { |
---|
6279 | Print("\n//** Mpwalk: Perturbation Walk took %d steps.\n", nstep); |
---|
6280 | } |
---|
6281 | return(Eresult); |
---|
6282 | } |
---|
6283 | |
---|
6284 | /******************************************************* |
---|
6285 | * THE PERTURBATION WALK ALGORITHM WITH RANDOM ELEMENT * |
---|
6286 | *******************************************************/ |
---|
6287 | ideal Mprwalk(ideal Go, intvec* orig_M, intvec* target_M, int weight_rad, |
---|
6288 | int op_deg, int tp_deg, int nP, int reduction, int printout) |
---|
6289 | { |
---|
6290 | BITSET save1 = si_opt_1; // save current options |
---|
6291 | if(reduction == 0) |
---|
6292 | { |
---|
6293 | si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis |
---|
6294 | si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions |
---|
6295 | } |
---|
6296 | Set_Error(FALSE); |
---|
6297 | Overflow_Error = FALSE; |
---|
6298 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
6299 | #ifdef TIME_TEST |
---|
6300 | clock_t tinput, tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0; |
---|
6301 | xtextra=0; |
---|
6302 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; |
---|
6303 | tinput = clock(); |
---|
6304 | |
---|
6305 | clock_t tim; |
---|
6306 | #endif |
---|
6307 | nstep = 0; |
---|
6308 | int i, ntwC=1, ntestw=1, nV = currRing->N; //polylength |
---|
6309 | |
---|
6310 | //check that weight radius is valid |
---|
6311 | if(weight_rad < 0) |
---|
6312 | { |
---|
6313 | Werror("Invalid radius.\n"); |
---|
6314 | return NULL; |
---|
6315 | } |
---|
6316 | |
---|
6317 | //check that perturbation degree is valid |
---|
6318 | if(op_deg < 1 || tp_deg < 1 || op_deg > nV || tp_deg > nV) |
---|
6319 | { |
---|
6320 | Werror("Invalid perturbation degree.\n"); |
---|
6321 | return NULL; |
---|
6322 | } |
---|
6323 | |
---|
6324 | BOOLEAN endwalks = FALSE; |
---|
6325 | |
---|
6326 | ideal Gomega, M, F, FF, G, Gomega1, Gomega2, M1,F1,Eresult,ssG; |
---|
6327 | ring newRing, oldRing, TargetRing; |
---|
6328 | intvec* iv_M; |
---|
6329 | intvec* iv_M_dp; |
---|
6330 | intvec* iv_M_lp; |
---|
6331 | intvec* exivlp = Mivlp(nV); |
---|
6332 | intvec* curr_weight = new intvec(nV); |
---|
6333 | intvec* target_weight = new intvec(nV); |
---|
6334 | for(i=0; i<nV; i++) |
---|
6335 | { |
---|
6336 | (*curr_weight)[i] = (*orig_M)[i]; |
---|
6337 | (*target_weight)[i] = (*target_M)[i]; |
---|
6338 | } |
---|
6339 | intvec* orig_target = target_weight; |
---|
6340 | intvec* pert_target_vector = target_weight; |
---|
6341 | intvec* ivNull = new intvec(nV); |
---|
6342 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
6343 | #ifndef BUCHBERGER_ALG |
---|
6344 | intvec* hilb_func; |
---|
6345 | #endif |
---|
6346 | intvec* next_weight; |
---|
6347 | |
---|
6348 | // to avoid (1,0,...,0) as the target vector |
---|
6349 | intvec* last_omega = new intvec(nV); |
---|
6350 | for(i=nV-1; i>0; i--) |
---|
6351 | (*last_omega)[i] = 1; |
---|
6352 | (*last_omega)[0] = 10000; |
---|
6353 | |
---|
6354 | ring XXRing = currRing; |
---|
6355 | |
---|
6356 | // perturbs the original vector |
---|
6357 | if(orig_M->length() == nV) |
---|
6358 | { |
---|
6359 | if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) := "dp" |
---|
6360 | { |
---|
6361 | #ifdef TIME_TEST |
---|
6362 | to = clock(); |
---|
6363 | #endif |
---|
6364 | G = MstdCC(Go); |
---|
6365 | #ifdef TIME_TEST |
---|
6366 | tostd = clock()-to; |
---|
6367 | #endif |
---|
6368 | if(op_deg != 1) |
---|
6369 | { |
---|
6370 | iv_M_dp = MivMatrixOrderdp(nV); |
---|
6371 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
6372 | } |
---|
6373 | } |
---|
6374 | else |
---|
6375 | { |
---|
6376 | //define ring order := (a(curr_weight),lp); |
---|
6377 | if (rParameter(currRing) != NULL) |
---|
6378 | DefRingPar(curr_weight); |
---|
6379 | else |
---|
6380 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
6381 | |
---|
6382 | G = idrMoveR(Go, XXRing,currRing); |
---|
6383 | #ifdef TIME_TEST |
---|
6384 | to = clock(); |
---|
6385 | #endif |
---|
6386 | G = MstdCC(G); |
---|
6387 | #ifdef TIME_TEST |
---|
6388 | tostd = clock()-to; |
---|
6389 | #endif |
---|
6390 | if(op_deg != 1) |
---|
6391 | { |
---|
6392 | iv_M_dp = MivMatrixOrder(curr_weight); |
---|
6393 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
6394 | } |
---|
6395 | } |
---|
6396 | } |
---|
6397 | else |
---|
6398 | { |
---|
6399 | rChangeCurrRing(VMatrDefault(orig_M)); |
---|
6400 | G = idrMoveR(Go, XXRing,currRing); |
---|
6401 | #ifdef TIME_TEST |
---|
6402 | to = clock(); |
---|
6403 | #endif |
---|
6404 | G = MstdCC(G); |
---|
6405 | #ifdef TIME_TEST |
---|
6406 | tostd = clock()-to; |
---|
6407 | #endif |
---|
6408 | if(op_deg != 1) |
---|
6409 | { |
---|
6410 | curr_weight = MPertVectors(G, orig_M, op_deg); |
---|
6411 | } |
---|
6412 | } |
---|
6413 | |
---|
6414 | delete iv_dp; |
---|
6415 | if(op_deg != 1) delete iv_M_dp; |
---|
6416 | |
---|
6417 | ring HelpRing = currRing; |
---|
6418 | |
---|
6419 | // perturbs the target weight vector |
---|
6420 | if(target_M->length() == nV) |
---|
6421 | { |
---|
6422 | if(tp_deg > 1 && tp_deg <= nV) |
---|
6423 | { |
---|
6424 | if (rParameter(currRing) != NULL) |
---|
6425 | DefRingPar(target_weight); |
---|
6426 | else |
---|
6427 | rChangeCurrRing(VMrDefault(target_weight)); |
---|
6428 | |
---|
6429 | TargetRing = currRing; |
---|
6430 | ssG = idrMoveR(G,HelpRing,currRing); |
---|
6431 | if(MivSame(target_weight, exivlp) == 1) |
---|
6432 | { |
---|
6433 | iv_M_lp = MivMatrixOrderlp(nV); |
---|
6434 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
6435 | } |
---|
6436 | else |
---|
6437 | { |
---|
6438 | iv_M_lp = MivMatrixOrder(target_weight); |
---|
6439 | target_weight = MPertVectors(ssG, iv_M_lp, tp_deg); |
---|
6440 | } |
---|
6441 | delete iv_M_lp; |
---|
6442 | pert_target_vector = target_weight; |
---|
6443 | rChangeCurrRing(HelpRing); |
---|
6444 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
6445 | } |
---|
6446 | } |
---|
6447 | else |
---|
6448 | { |
---|
6449 | if(tp_deg > 1 && tp_deg <= nV) |
---|
6450 | { |
---|
6451 | rChangeCurrRing(VMatrDefault(target_M)); |
---|
6452 | TargetRing = currRing; |
---|
6453 | ssG = idrMoveR(G,HelpRing,currRing); |
---|
6454 | target_weight = MPertVectors(ssG, target_M, tp_deg); |
---|
6455 | } |
---|
6456 | } |
---|
6457 | if(printout > 0) |
---|
6458 | { |
---|
6459 | Print("\n//** Mprwalk: Random Perturbation Walk of degree (%d,%d):",op_deg,tp_deg); |
---|
6460 | ivString(curr_weight, "//** Mprwalk: new current weight"); |
---|
6461 | ivString(target_weight, "//** Mprwalk: new target weight"); |
---|
6462 | } |
---|
6463 | |
---|
6464 | #ifdef TIME_TEST |
---|
6465 | to = clock(); |
---|
6466 | #endif |
---|
6467 | Gomega = MwalkInitialForm(G, curr_weight); // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
6468 | #ifdef TIME_TEST |
---|
6469 | tif = tif + clock()-to; //time for computing initial form ideal |
---|
6470 | #endif |
---|
6471 | |
---|
6472 | while(1) |
---|
6473 | { |
---|
6474 | nstep ++; |
---|
6475 | #ifdef CHECK_IDEAL_MWALK |
---|
6476 | if(printout > 1) |
---|
6477 | { |
---|
6478 | idString(Gomega,"//** Mprwalk: Gomega"); |
---|
6479 | } |
---|
6480 | #endif |
---|
6481 | |
---|
6482 | if(reduction == 0 && nstep > 1) |
---|
6483 | { |
---|
6484 | FF = middleOfCone(G,Gomega); |
---|
6485 | if(FF != NULL) |
---|
6486 | { |
---|
6487 | idDelete(&G); |
---|
6488 | G = idCopy(FF); |
---|
6489 | idDelete(&FF); |
---|
6490 | goto NEXT_VECTOR; |
---|
6491 | } |
---|
6492 | } |
---|
6493 | |
---|
6494 | #ifdef ENDWALKS |
---|
6495 | if(endwalks == TRUE) |
---|
6496 | { |
---|
6497 | if(printout > 0) |
---|
6498 | { |
---|
6499 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6500 | //idElements(G, "G"); |
---|
6501 | //headidString(G, "G"); |
---|
6502 | } |
---|
6503 | } |
---|
6504 | #endif |
---|
6505 | |
---|
6506 | #ifndef BUCHBERGER_ALG |
---|
6507 | if(isNolVector(curr_weight) == 0) |
---|
6508 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
6509 | else |
---|
6510 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
6511 | #endif // BUCHBERGER_ALG |
---|
6512 | |
---|
6513 | oldRing = currRing; |
---|
6514 | |
---|
6515 | if(target_M->length() == nV) |
---|
6516 | {/* |
---|
6517 | // define a new ring with ordering "(a(curr_weight),lp) |
---|
6518 | if (rParameter(currRing) != NULL) |
---|
6519 | DefRingPar(curr_weight); |
---|
6520 | else |
---|
6521 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
6522 | */ |
---|
6523 | rChangeCurrRing(VMrRefine(target_M,curr_weight)); |
---|
6524 | } |
---|
6525 | else |
---|
6526 | { |
---|
6527 | rChangeCurrRing(VMatrRefine(target_M,curr_weight)); |
---|
6528 | } |
---|
6529 | newRing = currRing; |
---|
6530 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
6531 | #ifdef ENDWALKS |
---|
6532 | if(endwalks == TRUE) |
---|
6533 | { |
---|
6534 | if(printout > 0) |
---|
6535 | { |
---|
6536 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6537 | |
---|
6538 | //idElements(Gomega1, "Gw"); |
---|
6539 | //headidString(Gomega1, "headGw"); |
---|
6540 | |
---|
6541 | PrintS("\n// compute a rGB of Gw:\n"); |
---|
6542 | } |
---|
6543 | #ifndef BUCHBERGER_ALG |
---|
6544 | ivString(hilb_func, "w"); |
---|
6545 | #endif |
---|
6546 | } |
---|
6547 | #endif |
---|
6548 | #ifdef TIME_TEST |
---|
6549 | tim = clock(); |
---|
6550 | to = clock(); |
---|
6551 | #endif |
---|
6552 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
6553 | #ifdef BUCHBERGER_ALG |
---|
6554 | M = MstdhomCC(Gomega1); |
---|
6555 | #else |
---|
6556 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
6557 | delete hilb_func; |
---|
6558 | #endif |
---|
6559 | #ifdef CHECK_IDEAL_MWALK |
---|
6560 | if(printout > 2) |
---|
6561 | { |
---|
6562 | idString(M,"//** Mprwalk: M"); |
---|
6563 | } |
---|
6564 | #endif |
---|
6565 | #ifdef TIME_TEST |
---|
6566 | if(endwalks == TRUE) |
---|
6567 | { |
---|
6568 | xtstd = xtstd+clock()-to; |
---|
6569 | #ifdef ENDWALKS |
---|
6570 | Print("\n// time for the last std(Gw) = %.2f sec\n", |
---|
6571 | ((double) clock())/1000000 -((double)tim) /1000000); |
---|
6572 | #endif |
---|
6573 | } |
---|
6574 | else |
---|
6575 | tstd=tstd+clock()-to; |
---|
6576 | #endif |
---|
6577 | /* change the ring to oldRing */ |
---|
6578 | rChangeCurrRing(oldRing); |
---|
6579 | M1 = idrMoveR(M, newRing,currRing); |
---|
6580 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
6581 | #ifdef TIME_TEST |
---|
6582 | to=clock(); |
---|
6583 | #endif |
---|
6584 | /* compute a representation of the generators of submod (M) |
---|
6585 | with respect to those of mod (Gomega). |
---|
6586 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
6587 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
6588 | #ifdef TIME_TEST |
---|
6589 | if(endwalks == FALSE) |
---|
6590 | tlift = tlift+clock()-to; |
---|
6591 | else |
---|
6592 | xtlift=clock()-to; |
---|
6593 | #endif |
---|
6594 | #ifdef CHECK_IDEAL_MWALK |
---|
6595 | if(printout > 2) |
---|
6596 | { |
---|
6597 | idString(F,"//** Mprwalk: F"); |
---|
6598 | } |
---|
6599 | #endif |
---|
6600 | |
---|
6601 | idDelete(&M1); |
---|
6602 | idDelete(&Gomega2); |
---|
6603 | idDelete(&G); |
---|
6604 | |
---|
6605 | // change the ring to newRing |
---|
6606 | rChangeCurrRing(newRing); |
---|
6607 | if(reduction == 0) |
---|
6608 | { |
---|
6609 | G = idrMoveR(F,oldRing,currRing); |
---|
6610 | } |
---|
6611 | else |
---|
6612 | { |
---|
6613 | F1 = idrMoveR(F, oldRing,currRing); |
---|
6614 | if(printout > 2) |
---|
6615 | { |
---|
6616 | PrintS("\n //** Mprwalk: reduce the Groebner basis.\n"); |
---|
6617 | } |
---|
6618 | #ifdef TIME_TEST |
---|
6619 | to=clock(); |
---|
6620 | #endif |
---|
6621 | G = kInterRedCC(F1, NULL); |
---|
6622 | #ifdef TIME_TEST |
---|
6623 | if(endwalks == FALSE) |
---|
6624 | tred = tred+clock()-to; |
---|
6625 | else |
---|
6626 | xtred=clock()-to; |
---|
6627 | #endif |
---|
6628 | idDelete(&F1); |
---|
6629 | } |
---|
6630 | |
---|
6631 | if(endwalks == TRUE) |
---|
6632 | break; |
---|
6633 | |
---|
6634 | NEXT_VECTOR: |
---|
6635 | #ifdef TIME_TEST |
---|
6636 | to = clock(); |
---|
6637 | #endif |
---|
6638 | next_weight = next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
6639 | #ifdef TIME_TEST |
---|
6640 | tnw = tnw + clock() - to; |
---|
6641 | #endif |
---|
6642 | |
---|
6643 | #ifdef TIME_TEST |
---|
6644 | to = clock(); |
---|
6645 | #endif |
---|
6646 | // compute an initial form ideal of <G> w.r.t. "next_vector" |
---|
6647 | Gomega = MwalkInitialForm(G, next_weight); |
---|
6648 | #ifdef TIME_TEST |
---|
6649 | tif = tif + clock()-to; //time for computing initial form ideal |
---|
6650 | #endif |
---|
6651 | |
---|
6652 | //lengthpoly(Gomega) = 1 if there is a polynomial in Gomega with at least 3 monomials and 0 otherwise |
---|
6653 | if(lengthpoly(Gomega) > 0) |
---|
6654 | { |
---|
6655 | if(printout > 1) |
---|
6656 | { |
---|
6657 | Print("\n Mpwalk: there is a polynomial in Gomega with at least 3 monomials.\n"); |
---|
6658 | } |
---|
6659 | // low-dimensional facet of the cone |
---|
6660 | delete next_weight; |
---|
6661 | if(target_M->length() == nV) |
---|
6662 | { |
---|
6663 | iv_M = MivMatrixOrder(curr_weight); |
---|
6664 | } |
---|
6665 | else |
---|
6666 | { |
---|
6667 | iv_M = MivMatrixOrderRefine(curr_weight,target_M); |
---|
6668 | } |
---|
6669 | #ifdef TIME_TEST |
---|
6670 | to = clock(); |
---|
6671 | #endif |
---|
6672 | next_weight = MWalkRandomNextWeight(G, iv_M, target_weight, weight_rad, op_deg); |
---|
6673 | #ifdef TIME_TEST |
---|
6674 | tnw = tnw + clock() - to; |
---|
6675 | #endif |
---|
6676 | idDelete(&Gomega); |
---|
6677 | #ifdef TIME_TEST |
---|
6678 | to = clock(); |
---|
6679 | #endif |
---|
6680 | Gomega = MwalkInitialForm(G, next_weight); |
---|
6681 | #ifdef TIME_TEST |
---|
6682 | tif = tif + clock()-to; //time for computing initial form ideal |
---|
6683 | #endif |
---|
6684 | delete iv_M; |
---|
6685 | } |
---|
6686 | |
---|
6687 | #ifdef PRINT_VECTORS |
---|
6688 | if(printout > 0) |
---|
6689 | { |
---|
6690 | MivString(curr_weight, target_weight, next_weight); |
---|
6691 | } |
---|
6692 | #endif |
---|
6693 | |
---|
6694 | if(Overflow_Error == TRUE) |
---|
6695 | { |
---|
6696 | ntwC = 0; |
---|
6697 | //Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6698 | //idElements(G, "G"); |
---|
6699 | delete next_weight; |
---|
6700 | goto FINISH_160302; |
---|
6701 | } |
---|
6702 | if(MivComp(next_weight, ivNull) == 1){ |
---|
6703 | newRing = currRing; |
---|
6704 | delete next_weight; |
---|
6705 | //Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6706 | break; |
---|
6707 | } |
---|
6708 | if(MivComp(next_weight, target_weight) == 1) |
---|
6709 | endwalks = TRUE; |
---|
6710 | |
---|
6711 | for(i=nV-1; i>=0; i--) |
---|
6712 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
6713 | |
---|
6714 | delete next_weight; |
---|
6715 | }// end of while-loop |
---|
6716 | |
---|
6717 | if(tp_deg != 1) |
---|
6718 | { |
---|
6719 | FINISH_160302: |
---|
6720 | if(target_M->length() == nV) |
---|
6721 | { |
---|
6722 | if(MivSame(orig_target, exivlp) == 1) |
---|
6723 | if (rParameter(currRing) != NULL) |
---|
6724 | DefRingParlp(); |
---|
6725 | else |
---|
6726 | VMrDefaultlp(); |
---|
6727 | else |
---|
6728 | if (rParameter(currRing) != NULL) |
---|
6729 | DefRingPar(orig_target); |
---|
6730 | else |
---|
6731 | rChangeCurrRing(VMrDefault(orig_target)); |
---|
6732 | } |
---|
6733 | else |
---|
6734 | { |
---|
6735 | rChangeCurrRing(VMatrDefault(target_M)); |
---|
6736 | } |
---|
6737 | TargetRing=currRing; |
---|
6738 | F1 = idrMoveR(G, newRing,currRing); |
---|
6739 | |
---|
6740 | // check whether the pertubed target vector stays in the correct cone |
---|
6741 | if(ntwC != 0) |
---|
6742 | { |
---|
6743 | ntestw = test_w_in_ConeCC(F1, pert_target_vector); |
---|
6744 | } |
---|
6745 | if(ntestw != 1 || ntwC == 0) |
---|
6746 | { |
---|
6747 | if(ntestw != 1 && printout > 2) |
---|
6748 | { |
---|
6749 | #ifdef PRINT_VECTORS |
---|
6750 | ivString(pert_target_vector, "tau"); |
---|
6751 | #endif |
---|
6752 | PrintS("\n// **Mprwalk: perturbed target vector doesn't stay in cone."); |
---|
6753 | Print("\n// ring r%d = %s;\n", nstep, rString(currRing)); |
---|
6754 | //idElements(F1, "G"); |
---|
6755 | } |
---|
6756 | // LastGB is "better" than the kStd subroutine |
---|
6757 | #ifdef TIME_TEST |
---|
6758 | to=clock(); |
---|
6759 | #endif |
---|
6760 | ideal eF1; |
---|
6761 | if(nP == 0 || tp_deg == 1 || MivSame(orig_target, exivlp) != 1 || target_M->length() != nV) |
---|
6762 | { |
---|
6763 | if(printout > 2) |
---|
6764 | { |
---|
6765 | PrintS("\n// ** Mprwalk: Call \"std\" to compute a Groebner basis.\n"); |
---|
6766 | } |
---|
6767 | eF1 = MstdCC(F1); |
---|
6768 | idDelete(&F1); |
---|
6769 | } |
---|
6770 | else |
---|
6771 | { |
---|
6772 | if(printout > 2) |
---|
6773 | { |
---|
6774 | PrintS("\n// **Mprwalk: Call \"LastGB\" to compute a Groebner basis.\n"); |
---|
6775 | } |
---|
6776 | rChangeCurrRing(newRing); |
---|
6777 | ideal F2 = idrMoveR(F1, TargetRing,currRing); |
---|
6778 | eF1 = LastGB(F2, curr_weight, tp_deg-1); |
---|
6779 | F2=NULL; |
---|
6780 | } |
---|
6781 | #ifdef TIME_TEST |
---|
6782 | xtextra=clock()-to; |
---|
6783 | #endif |
---|
6784 | ring exTargetRing = currRing; |
---|
6785 | |
---|
6786 | rChangeCurrRing(XXRing); |
---|
6787 | Eresult = idrMoveR(eF1, exTargetRing,currRing); |
---|
6788 | } |
---|
6789 | else |
---|
6790 | { |
---|
6791 | rChangeCurrRing(XXRing); |
---|
6792 | Eresult = idrMoveR(F1, TargetRing,currRing); |
---|
6793 | } |
---|
6794 | } |
---|
6795 | else |
---|
6796 | { |
---|
6797 | rChangeCurrRing(XXRing); |
---|
6798 | Eresult = idrMoveR(G, newRing,currRing); |
---|
6799 | } |
---|
6800 | si_opt_1 = save1; //set original options, e. g. option(RedSB) |
---|
6801 | delete ivNull; |
---|
6802 | if(tp_deg != 1) |
---|
6803 | delete target_weight; |
---|
6804 | |
---|
6805 | if(op_deg != 1 ) |
---|
6806 | delete curr_weight; |
---|
6807 | |
---|
6808 | delete exivlp; |
---|
6809 | delete last_omega; |
---|
6810 | |
---|
6811 | #ifdef TIME_TEST |
---|
6812 | TimeStringFractal(tinput, tostd, tif+xtif, tstd+xtstd,0, tlift+xtlift, tred+xtred, |
---|
6813 | tnw+xtnw); |
---|
6814 | |
---|
6815 | //Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
6816 | //Print("\n// It took %d steps and Overflow_Error? (%d)\n", nstep, Overflow_Error); |
---|
6817 | #endif |
---|
6818 | |
---|
6819 | if(printout > 0) |
---|
6820 | { |
---|
6821 | Print("\n//** Mprwalk: Perturbation Walk took %d steps.\n", nstep); |
---|
6822 | } |
---|
6823 | return(Eresult); |
---|
6824 | } |
---|
6825 | |
---|
6826 | intvec* XivNull; |
---|
6827 | |
---|
6828 | /***************************** |
---|
6829 | * define a matrix (1 ... 1) * |
---|
6830 | *****************************/ |
---|
6831 | intvec* MMatrixone(int nV) |
---|
6832 | { |
---|
6833 | int i,j; |
---|
6834 | intvec* ivM = new intvec(nV*nV); |
---|
6835 | |
---|
6836 | for(i=0; i<nV; i++) |
---|
6837 | for(j=0; j<nV; j++) |
---|
6838 | (*ivM)[i*nV + j] = 1; |
---|
6839 | |
---|
6840 | return(ivM); |
---|
6841 | } |
---|
6842 | |
---|
6843 | int nnflow; |
---|
6844 | int Xcall; |
---|
6845 | int Xngleich; |
---|
6846 | |
---|
6847 | /*********************************************************************** |
---|
6848 | * Perturb the start weight vector at the top level, i.e. nlev = 1 * |
---|
6849 | ***********************************************************************/ |
---|
6850 | static ideal rec_fractal_call(ideal G, int nlev, intvec* ivtarget, |
---|
6851 | int reduction, int printout) |
---|
6852 | { |
---|
6853 | Overflow_Error = FALSE; |
---|
6854 | if(printout >0) |
---|
6855 | { |
---|
6856 | Print("\n\n// Entering the %d-th recursion:", nlev); |
---|
6857 | } |
---|
6858 | int i, nV = currRing->N; |
---|
6859 | ring new_ring, testring; |
---|
6860 | //ring extoRing; |
---|
6861 | ideal Gomega, Gomega1, Gomega2, FF, F, F1, Gresult, Gresult1, G1, Gt; |
---|
6862 | int nwalks = 0; |
---|
6863 | intvec* Mwlp; |
---|
6864 | #ifndef BUCHBERGER_ALG |
---|
6865 | intvec* hilb_func; |
---|
6866 | #endif |
---|
6867 | //intvec* extXtau; |
---|
6868 | intvec* next_vect; |
---|
6869 | intvec* omega2 = new intvec(nV); |
---|
6870 | intvec* omtmp = new intvec(nV); |
---|
6871 | //intvec* altomega = new intvec(nV); |
---|
6872 | |
---|
6873 | for(i = nV -1; i>=0; i--)//Aenderung!! |
---|
6874 | { |
---|
6875 | (*omtmp)[i] = (*ivtarget)[i]; |
---|
6876 | } |
---|
6877 | //BOOLEAN isnewtarget = FALSE; |
---|
6878 | |
---|
6879 | // to avoid (1,0,...,0) as the target vector (Hans) |
---|
6880 | intvec* last_omega = new intvec(nV); |
---|
6881 | for(i=nV-1; i>0; i--) |
---|
6882 | (*last_omega)[i] = 1; |
---|
6883 | (*last_omega)[0] = 10000; |
---|
6884 | |
---|
6885 | intvec* omega = new intvec(nV); |
---|
6886 | for(i=0; i<nV; i++) { |
---|
6887 | if(Xsigma->length() == nV) |
---|
6888 | (*omega)[i] = (*Xsigma)[i]; |
---|
6889 | else |
---|
6890 | (*omega)[i] = (*Xsigma)[(nV*(nlev-1))+i]; |
---|
6891 | |
---|
6892 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
6893 | } |
---|
6894 | |
---|
6895 | if(nlev == 1) Xcall = 1; |
---|
6896 | else Xcall = 0; |
---|
6897 | |
---|
6898 | ring oRing = currRing; |
---|
6899 | |
---|
6900 | while(1) |
---|
6901 | { |
---|
6902 | #ifdef FIRST_STEP_FRACTAL |
---|
6903 | // perturb the current weight vector only on the top level or |
---|
6904 | // after perturbation of the both vectors, nlev = 2 as the top level |
---|
6905 | if((nlev == 1 && Xcall == 0) || (nlev == 2 && Xngleich == 1)) |
---|
6906 | if(islengthpoly2(G) == 1) |
---|
6907 | { |
---|
6908 | Mwlp = MivWeightOrderlp(omega); |
---|
6909 | Xsigma = Mfpertvector(G, Mwlp); |
---|
6910 | delete Mwlp; |
---|
6911 | Overflow_Error = FALSE; |
---|
6912 | } |
---|
6913 | #endif |
---|
6914 | nwalks ++; |
---|
6915 | NEXT_VECTOR_FRACTAL: |
---|
6916 | #ifdef TIME_TEST |
---|
6917 | to=clock(); |
---|
6918 | #endif |
---|
6919 | // determine the next border |
---|
6920 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
6921 | #ifdef TIME_TEST |
---|
6922 | xtnw=xtnw+clock()-to; |
---|
6923 | #endif |
---|
6924 | oRing = currRing; |
---|
6925 | |
---|
6926 | // We only perturb the current target vector at the recursion level 1 |
---|
6927 | if(Xngleich == 0 && nlev == 1) //(ngleich == 0) important, e.g. ex2, ex3 |
---|
6928 | if (MivComp(next_vect, omega2) == 1) |
---|
6929 | { |
---|
6930 | // to dispense with taking initial (and lifting/interreducing |
---|
6931 | // after the call of recursion |
---|
6932 | if(printout > 0) |
---|
6933 | { |
---|
6934 | Print("\n//** rec_fractal_call: Perturb the both vectors with degree %d.",nlev); |
---|
6935 | //idElements(G, "G"); |
---|
6936 | } |
---|
6937 | |
---|
6938 | Xngleich = 1; |
---|
6939 | nlev +=1; |
---|
6940 | |
---|
6941 | if(ivtarget->length() == nV) |
---|
6942 | { |
---|
6943 | /* |
---|
6944 | if (rParameter(currRing) != NULL) |
---|
6945 | DefRingPar(omtmp); |
---|
6946 | else |
---|
6947 | rChangeCurrRing(VMrDefault(omtmp)); |
---|
6948 | */ |
---|
6949 | rChangeCurrRing(VMrRefine(ivtarget,omtmp)); |
---|
6950 | } |
---|
6951 | else |
---|
6952 | { |
---|
6953 | //rChangeCurrRing(VMatrDefault(ivtarget)); |
---|
6954 | rChangeCurrRing(VMatrRefine(ivtarget,omtmp)); |
---|
6955 | } |
---|
6956 | testring = currRing; |
---|
6957 | Gt = idrMoveR(G, oRing,currRing); |
---|
6958 | |
---|
6959 | // perturb the original target vector w.r.t. the current GB |
---|
6960 | if(ivtarget->length() == nV) |
---|
6961 | { |
---|
6962 | delete Xtau; |
---|
6963 | Xtau = NewVectorlp(Gt); |
---|
6964 | } |
---|
6965 | else |
---|
6966 | { |
---|
6967 | delete Xtau; |
---|
6968 | Xtau = Mfpertvector(Gt,ivtarget); |
---|
6969 | } |
---|
6970 | |
---|
6971 | rChangeCurrRing(oRing); |
---|
6972 | G = idrMoveR(Gt, testring,currRing); |
---|
6973 | |
---|
6974 | // perturb the current vector w.r.t. the current GB |
---|
6975 | Mwlp = MivWeightOrderlp(omega); |
---|
6976 | Xsigma = Mfpertvector(G, Mwlp); |
---|
6977 | delete Mwlp; |
---|
6978 | |
---|
6979 | for(i=nV-1; i>=0; i--) { |
---|
6980 | (*omega2)[i] = (*Xtau)[nV+i]; |
---|
6981 | (*omega)[i] = (*Xsigma)[nV+i]; |
---|
6982 | } |
---|
6983 | |
---|
6984 | delete next_vect; |
---|
6985 | #ifdef TIME_TEST |
---|
6986 | to=clock(); |
---|
6987 | #endif |
---|
6988 | // to avoid the value of Overflow_Error that occur in Mfpertvector |
---|
6989 | Overflow_Error = FALSE; |
---|
6990 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
6991 | #ifdef TIME_TEST |
---|
6992 | xtnw=xtnw+clock()-to; |
---|
6993 | #endif |
---|
6994 | }// end of (if MivComp(next_vect, omega2) == 1) |
---|
6995 | |
---|
6996 | #ifdef PRINT_VECTORS |
---|
6997 | if(printout > 0) |
---|
6998 | { |
---|
6999 | MivString(omega, omega2, next_vect); |
---|
7000 | } |
---|
7001 | #endif |
---|
7002 | |
---|
7003 | // check whether the the computed vector is in the correct cone. |
---|
7004 | // If no, compute the reduced Groebner basis of an omega-homogeneous |
---|
7005 | // ideal with Buchberger's algorithm and stop this recursion step |
---|
7006 | if(Overflow_Error == TRUE || test_w_in_ConeCC(G, next_vect) != 1) //e.g. Example s7, cyc6 |
---|
7007 | { |
---|
7008 | delete next_vect; |
---|
7009 | if(ivtarget->length() == nV) |
---|
7010 | { |
---|
7011 | /* |
---|
7012 | if (rParameter(currRing) != NULL) |
---|
7013 | DefRingPar(omtmp); |
---|
7014 | else |
---|
7015 | rChangeCurrRing(VMrDefault(omtmp)); |
---|
7016 | */ |
---|
7017 | rChangeCurrRing(VMrRefine(ivtarget,omtmp)); |
---|
7018 | } |
---|
7019 | else |
---|
7020 | { |
---|
7021 | //rChangeCurrRing(VMatrDefault(ivtarget)); |
---|
7022 | rChangeCurrRing(VMatrRefine(ivtarget,omtmp)); |
---|
7023 | } |
---|
7024 | #ifdef TEST_OVERFLOW |
---|
7025 | Gt = idrMoveR(G, oRing,currRing); |
---|
7026 | Gt = NULL; return(Gt); |
---|
7027 | #endif |
---|
7028 | if(printout > 0) |
---|
7029 | { |
---|
7030 | Print("\n//** rec_fractal_call: Applying Buchberger's algorithm in ring r = %s;", |
---|
7031 | rString(currRing)); |
---|
7032 | } |
---|
7033 | #ifdef TIME_TEST |
---|
7034 | to=clock(); |
---|
7035 | #endif |
---|
7036 | Gt = idrMoveR(G, oRing,currRing); |
---|
7037 | G1 = MstdCC(Gt); |
---|
7038 | #ifdef TIME_TEST |
---|
7039 | xtextra=xtextra+clock()-to; |
---|
7040 | #endif |
---|
7041 | Gt = NULL; |
---|
7042 | |
---|
7043 | delete omega2; |
---|
7044 | //delete altomega; |
---|
7045 | if(printout > 0) |
---|
7046 | { |
---|
7047 | Print("\n//** rec_fractal_call: Overflow. (4) Leaving the %d-th recursion with %d steps.\n", |
---|
7048 | nlev, nwalks); |
---|
7049 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
7050 | } |
---|
7051 | |
---|
7052 | nnflow ++; |
---|
7053 | Overflow_Error = FALSE; |
---|
7054 | return (G1); |
---|
7055 | } |
---|
7056 | |
---|
7057 | /* If the perturbed target vector stays in the correct cone, |
---|
7058 | return the current GB, |
---|
7059 | otherwise, return the computed GB by the Buchberger-algorithm. |
---|
7060 | Then we update the perturbed target vectors w.r.t. this GB. */ |
---|
7061 | |
---|
7062 | /* the computed vector is equal to the origin vector, since |
---|
7063 | t is not defined */ |
---|
7064 | |
---|
7065 | if (MivComp(next_vect, XivNull) == 1) |
---|
7066 | { |
---|
7067 | if(ivtarget->length() == nV) |
---|
7068 | { |
---|
7069 | /* |
---|
7070 | if (rParameter(currRing) != NULL) |
---|
7071 | DefRingPar(omtmp); |
---|
7072 | else |
---|
7073 | rChangeCurrRing(VMrDefault(omtmp)); |
---|
7074 | */ |
---|
7075 | rChangeCurrRing(VMrRefine(ivtarget,omtmp)); |
---|
7076 | } |
---|
7077 | else |
---|
7078 | { |
---|
7079 | //rChangeCurrRing(VMatrDefault(ivtarget)); |
---|
7080 | rChangeCurrRing(VMatrRefine(ivtarget,omtmp)); |
---|
7081 | } |
---|
7082 | |
---|
7083 | testring = currRing; |
---|
7084 | Gt = idrMoveR(G, oRing,currRing); |
---|
7085 | if(test_w_in_ConeCC(Gt, omega2) == 1) |
---|
7086 | { |
---|
7087 | delete omega2; |
---|
7088 | delete next_vect; |
---|
7089 | //delete altomega; |
---|
7090 | if(printout > 0) |
---|
7091 | { |
---|
7092 | Print("\n//** rec_fractal_call: Correct cone. (5) Leaving the %d-th recursion with %d steps.\n", |
---|
7093 | nlev, nwalks); |
---|
7094 | } |
---|
7095 | if(printout>2) |
---|
7096 | { |
---|
7097 | idString(Gt,"//** rec_fractal_call: Gt"); |
---|
7098 | } |
---|
7099 | return (Gt); |
---|
7100 | } |
---|
7101 | else |
---|
7102 | { |
---|
7103 | if(printout > 0) |
---|
7104 | { |
---|
7105 | Print("\n//** rec_fractal_call: Wrong cone. Tau doesn't stay in the correct cone.\n"); |
---|
7106 | } |
---|
7107 | |
---|
7108 | #ifndef MSTDCC_FRACTAL |
---|
7109 | intvec* Xtautmp; |
---|
7110 | if(ivtarget->length() == nV) |
---|
7111 | { |
---|
7112 | Xtautmp = Mfpertvector(Gt, MivMatrixOrder(omtmp)); |
---|
7113 | } |
---|
7114 | else |
---|
7115 | { |
---|
7116 | Xtautmp = Mfpertvector(Gt, ivtarget); |
---|
7117 | } |
---|
7118 | #ifdef TEST_OVERFLOW |
---|
7119 | if(Overflow_Error == TRUE) |
---|
7120 | Gt = NULL; return(Gt); |
---|
7121 | #endif |
---|
7122 | |
---|
7123 | if(MivSame(Xtau, Xtautmp) == 1) |
---|
7124 | { |
---|
7125 | if(printout > 0) |
---|
7126 | { |
---|
7127 | Print("\n//** rec_fractal_call: Updated vectors are equal to the old vectors.\n"); |
---|
7128 | } |
---|
7129 | delete Xtautmp; |
---|
7130 | goto FRACTAL_MSTDCC; |
---|
7131 | } |
---|
7132 | |
---|
7133 | Xtau = Xtautmp; |
---|
7134 | Xtautmp = NULL; |
---|
7135 | |
---|
7136 | for(i=nV-1; i>=0; i--) |
---|
7137 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
7138 | |
---|
7139 | rChangeCurrRing(oRing); |
---|
7140 | G = idrMoveR(Gt, testring,currRing); |
---|
7141 | |
---|
7142 | goto NEXT_VECTOR_FRACTAL; |
---|
7143 | #endif |
---|
7144 | |
---|
7145 | FRACTAL_MSTDCC: |
---|
7146 | if(printout > 0) |
---|
7147 | { |
---|
7148 | Print("\n//** rec_fractal_call: Wrong cone. Applying Buchberger's algorithm in ring = %s.\n", |
---|
7149 | rString(currRing)); |
---|
7150 | } |
---|
7151 | #ifdef TIME_TEST |
---|
7152 | to=clock(); |
---|
7153 | #endif |
---|
7154 | G = MstdCC(Gt); |
---|
7155 | #ifdef TIME_TEST |
---|
7156 | xtextra=xtextra+clock()-to; |
---|
7157 | #endif |
---|
7158 | oRing = currRing; |
---|
7159 | |
---|
7160 | // update the original target vector w.r.t. the current GB |
---|
7161 | if(ivtarget->length() == nV) |
---|
7162 | { |
---|
7163 | /* |
---|
7164 | if(MivSame(Xivinput, Xivlp) == 1) |
---|
7165 | if (rParameter(currRing) != NULL) |
---|
7166 | DefRingParlp(); |
---|
7167 | else |
---|
7168 | VMrDefaultlp(); |
---|
7169 | else |
---|
7170 | if (rParameter(currRing) != NULL) |
---|
7171 | DefRingPar(Xivinput); |
---|
7172 | else |
---|
7173 | rChangeCurrRing(VMrDefault(Xivinput)); |
---|
7174 | */ |
---|
7175 | rChangeCurrRing(VMrRefine(ivtarget,Xivinput)); |
---|
7176 | } |
---|
7177 | else |
---|
7178 | { |
---|
7179 | rChangeCurrRing(VMatrRefine(ivtarget,Xivinput)); |
---|
7180 | } |
---|
7181 | testring = currRing; |
---|
7182 | Gt = idrMoveR(G, oRing,currRing); |
---|
7183 | |
---|
7184 | // perturb the original target vector w.r.t. the current GB |
---|
7185 | if(ivtarget->length() == nV) |
---|
7186 | { |
---|
7187 | delete Xtau; |
---|
7188 | Xtau = NewVectorlp(Gt); |
---|
7189 | } |
---|
7190 | else |
---|
7191 | { |
---|
7192 | delete Xtau; |
---|
7193 | Xtau = Mfpertvector(Gt,ivtarget); |
---|
7194 | } |
---|
7195 | |
---|
7196 | rChangeCurrRing(oRing); |
---|
7197 | G = idrMoveR(Gt, testring,currRing); |
---|
7198 | |
---|
7199 | delete omega2; |
---|
7200 | delete next_vect; |
---|
7201 | //delete altomega; |
---|
7202 | if(printout > 0) |
---|
7203 | { |
---|
7204 | Print("\n//** rec_fractal_call: Vectors updated. (6) Leaving the %d-th recursion with %d steps.\n", |
---|
7205 | nlev, nwalks); |
---|
7206 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
7207 | } |
---|
7208 | if(Overflow_Error == TRUE) |
---|
7209 | nnflow ++; |
---|
7210 | |
---|
7211 | Overflow_Error = FALSE; |
---|
7212 | return(G); |
---|
7213 | } |
---|
7214 | }// end of (if next_vect==nullvector) |
---|
7215 | |
---|
7216 | for(i=nV-1; i>=0; i--) { |
---|
7217 | //(*altomega)[i] = (*omega)[i]; |
---|
7218 | (*omega)[i] = (*next_vect)[i]; |
---|
7219 | } |
---|
7220 | delete next_vect; |
---|
7221 | #ifdef TIME_TEST |
---|
7222 | to=clock(); |
---|
7223 | #endif |
---|
7224 | // Take the initial form of <G> w.r.t. omega |
---|
7225 | Gomega = MwalkInitialForm(G, omega); |
---|
7226 | #ifdef TIME_TEST |
---|
7227 | xtif=xtif+clock()-to; |
---|
7228 | #endif |
---|
7229 | #ifdef CHECK_IDEAL_MWALK |
---|
7230 | if(printout > 1) |
---|
7231 | { |
---|
7232 | idString(Gomega,"//** rec_fractal_call: Gomega"); |
---|
7233 | } |
---|
7234 | #endif |
---|
7235 | if(reduction == 0) |
---|
7236 | { |
---|
7237 | // Check whether the intermediate weight vector lies in the interior of the cone. |
---|
7238 | // If so, only perform reductions. Otherwise apply Buchberger's algorithm. |
---|
7239 | FF = middleOfCone(G,Gomega); |
---|
7240 | if( FF != NULL) |
---|
7241 | { |
---|
7242 | idDelete(&G); |
---|
7243 | G = idCopy(FF); |
---|
7244 | idDelete(&FF); |
---|
7245 | // Compue next vector. |
---|
7246 | goto NEXT_VECTOR_FRACTAL; |
---|
7247 | } |
---|
7248 | } |
---|
7249 | |
---|
7250 | #ifndef BUCHBERGER_ALG |
---|
7251 | if(isNolVector(omega) == 0) |
---|
7252 | hilb_func = hFirstSeries(Gomega,NULL,NULL,omega,currRing); |
---|
7253 | else |
---|
7254 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
7255 | #endif |
---|
7256 | |
---|
7257 | if(ivtarget->length() == nV) |
---|
7258 | { |
---|
7259 | /* |
---|
7260 | if (rParameter(currRing) != NULL) |
---|
7261 | DefRingPar(omega); |
---|
7262 | else |
---|
7263 | rChangeCurrRing(VMrDefault(omega)); |
---|
7264 | */ |
---|
7265 | rChangeCurrRing(VMrRefine(ivtarget,omega)); |
---|
7266 | } |
---|
7267 | else |
---|
7268 | { |
---|
7269 | rChangeCurrRing(VMatrRefine(ivtarget,omega)); |
---|
7270 | } |
---|
7271 | Gomega1 = idrMoveR(Gomega, oRing,currRing); |
---|
7272 | |
---|
7273 | // Maximal recursion depth, to compute a red. GB |
---|
7274 | // Fractal walk with the alternative recursion |
---|
7275 | // alternative recursion |
---|
7276 | if(nlev == Xnlev || lengthpoly(Gomega1) == 0) |
---|
7277 | { |
---|
7278 | if(printout > 1) |
---|
7279 | { |
---|
7280 | Print("\n//** rec_fractal_call: Maximal recursion depth.\n"); |
---|
7281 | } |
---|
7282 | #ifdef TIME_TEST |
---|
7283 | to=clock(); |
---|
7284 | #endif |
---|
7285 | #ifdef BUCHBERGER_ALG |
---|
7286 | Gresult = MstdhomCC(Gomega1); |
---|
7287 | #else |
---|
7288 | Gresult =kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,omega); |
---|
7289 | delete hilb_func; |
---|
7290 | #endif |
---|
7291 | #ifdef TIME_TEST |
---|
7292 | xtstd=xtstd+clock()-to; |
---|
7293 | #endif |
---|
7294 | } |
---|
7295 | else |
---|
7296 | { |
---|
7297 | rChangeCurrRing(oRing); |
---|
7298 | Gomega1 = idrMoveR(Gomega1, oRing,currRing); |
---|
7299 | Gresult = rec_fractal_call(idCopy(Gomega1),nlev+1,omega,reduction,printout); |
---|
7300 | } |
---|
7301 | #ifdef CHECK_IDEAL_MWALK |
---|
7302 | if(printout > 2) |
---|
7303 | { |
---|
7304 | idString(Gresult,"//** rec_fractal_call: M"); |
---|
7305 | } |
---|
7306 | #endif |
---|
7307 | //convert a Groebner basis from a ring to another ring |
---|
7308 | new_ring = currRing; |
---|
7309 | |
---|
7310 | rChangeCurrRing(oRing); |
---|
7311 | Gresult1 = idrMoveR(Gresult, new_ring,currRing); |
---|
7312 | Gomega2 = idrMoveR(Gomega1, new_ring,currRing); |
---|
7313 | #ifdef TIME_TEST |
---|
7314 | to=clock(); |
---|
7315 | #endif |
---|
7316 | // Lifting process |
---|
7317 | F = MLifttwoIdeal(Gomega2, Gresult1, G); |
---|
7318 | #ifdef TIME_TEST |
---|
7319 | xtlift=xtlift+clock()-to; |
---|
7320 | #endif |
---|
7321 | #ifdef CHECK_IDEAL_MWALK |
---|
7322 | if(printout > 2) |
---|
7323 | { |
---|
7324 | idString(F,"//** rec_fractal_call: F"); |
---|
7325 | } |
---|
7326 | #endif |
---|
7327 | id_Normalize(F,currRing); |
---|
7328 | idDelete(&Gresult1); |
---|
7329 | idDelete(&Gomega2); |
---|
7330 | idDelete(&G); |
---|
7331 | |
---|
7332 | rChangeCurrRing(new_ring); |
---|
7333 | G = idrMoveR(F,oRing,currRing); |
---|
7334 | /* |
---|
7335 | F1 = idrMoveR(F, oRing,currRing); |
---|
7336 | #ifdef TIME_TEST |
---|
7337 | to=clock(); |
---|
7338 | #endif |
---|
7339 | // Interreduce G |
---|
7340 | G = kInterRedCC(F1, NULL); |
---|
7341 | #ifdef TIME_TEST |
---|
7342 | xtred=xtred+clock()-to; |
---|
7343 | #endif |
---|
7344 | idDelete(&F1); |
---|
7345 | */ |
---|
7346 | } |
---|
7347 | } |
---|
7348 | |
---|
7349 | /************************************************************************ |
---|
7350 | * Perturb the start weight vector at the top level with random element * |
---|
7351 | ************************************************************************/ |
---|
7352 | static ideal rec_r_fractal_call(ideal G, int nlev, intvec* ivtarget, |
---|
7353 | int weight_rad, int reduction, int printout) |
---|
7354 | { |
---|
7355 | Overflow_Error = FALSE; |
---|
7356 | //Print("\n\n// Entering the %d-th recursion:", nlev); |
---|
7357 | |
---|
7358 | int nwalks = 0,i,nV=currRing->N;//polylength |
---|
7359 | ring new_ring, testring; |
---|
7360 | //ring extoRing; |
---|
7361 | ideal Gomega, Gomega1, Gomega2, F, FF, F1, Gresult, Gresult1, G1, Gt; |
---|
7362 | intvec* Mwlp; |
---|
7363 | #ifndef BUCHBERGER_ALG |
---|
7364 | intvec* hilb_func; |
---|
7365 | #endif |
---|
7366 | // intvec* extXtau; |
---|
7367 | intvec* next_vect; |
---|
7368 | intvec* iv_M; |
---|
7369 | intvec* omega2 = new intvec(nV); |
---|
7370 | intvec* omtmp = new intvec(nV); |
---|
7371 | intvec* altomega = new intvec(nV); |
---|
7372 | |
---|
7373 | //BOOLEAN isnewtarget = FALSE; |
---|
7374 | |
---|
7375 | for(i = nV -1; i>=0; i--) |
---|
7376 | { |
---|
7377 | (*omtmp)[i] = (*ivtarget)[i]; |
---|
7378 | } |
---|
7379 | // to avoid (1,0,...,0) as the target vector (Hans) |
---|
7380 | intvec* last_omega = new intvec(nV); |
---|
7381 | for(i=nV-1; i>0; i--) |
---|
7382 | (*last_omega)[i] = 1; |
---|
7383 | (*last_omega)[0] = 10000; |
---|
7384 | |
---|
7385 | intvec* omega = new intvec(nV); |
---|
7386 | for(i=0; i<nV; i++) { |
---|
7387 | if(Xsigma->length() == nV) |
---|
7388 | (*omega)[i] = (*Xsigma)[i]; |
---|
7389 | else |
---|
7390 | (*omega)[i] = (*Xsigma)[(nV*(nlev-1))+i]; |
---|
7391 | |
---|
7392 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
7393 | } |
---|
7394 | |
---|
7395 | if(nlev == 1) Xcall = 1; |
---|
7396 | else Xcall = 0; |
---|
7397 | |
---|
7398 | ring oRing = currRing; |
---|
7399 | |
---|
7400 | while(1) |
---|
7401 | { |
---|
7402 | #ifdef FIRST_STEP_FRACTAL |
---|
7403 | /* |
---|
7404 | perturb the current weight vector only on the top level or |
---|
7405 | after perturbation of the both vectors, nlev = 2 as the top level |
---|
7406 | */ |
---|
7407 | if((nlev == 1 && Xcall == 0) || (nlev == 2 && Xngleich == 1)) |
---|
7408 | if(islengthpoly2(G) == 1) |
---|
7409 | { |
---|
7410 | Mwlp = MivWeightOrderlp(omega); |
---|
7411 | Xsigma = Mfpertvector(G, Mwlp); |
---|
7412 | delete Mwlp; |
---|
7413 | Overflow_Error = FALSE; |
---|
7414 | } |
---|
7415 | #endif |
---|
7416 | nwalks ++; |
---|
7417 | NEXT_VECTOR_FRACTAL: |
---|
7418 | #ifdef TIME_TEST |
---|
7419 | to=clock(); |
---|
7420 | #endif |
---|
7421 | /* determine the next border */ |
---|
7422 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
7423 | #ifdef TIME_TEST |
---|
7424 | xtnw=xtnw+clock()-to; |
---|
7425 | #endif |
---|
7426 | if(lengthpoly(MwalkInitialForm(G, next_vect)) > 0 && G->m[0] != NULL) |
---|
7427 | { |
---|
7428 | if(printout > 0) |
---|
7429 | { |
---|
7430 | PrintS("\n**// rec_r_fractal_call: there is a polynomial in Gomega with at least 3 monomials.\n"); |
---|
7431 | } |
---|
7432 | delete next_vect; |
---|
7433 | iv_M = MivMatrixOrder(omega); |
---|
7434 | #ifdef TIME_TEST |
---|
7435 | to=clock(); |
---|
7436 | #endif |
---|
7437 | next_vect = MWalkRandomNextWeight(G,iv_M,omega2,weight_rad,nlev); |
---|
7438 | #ifdef TIME_TEST |
---|
7439 | xtnw=xtnw+clock()-to; |
---|
7440 | #endif |
---|
7441 | if(isNegNolVector(next_vect) == 1) |
---|
7442 | { |
---|
7443 | delete next_vect; |
---|
7444 | #ifdef TIME_TEST |
---|
7445 | to=clock(); |
---|
7446 | #endif |
---|
7447 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
7448 | #ifdef TIME_TEST |
---|
7449 | xtnw=xtnw+clock()-to; |
---|
7450 | #endif |
---|
7451 | } |
---|
7452 | } |
---|
7453 | oRing = currRing; |
---|
7454 | |
---|
7455 | // We only perturb the current target vector at the recursion level 1 |
---|
7456 | if(Xngleich == 0 && nlev == 1) //(ngleich == 0) important, e.g. ex2, ex3 |
---|
7457 | if (MivComp(next_vect, omega2) == 1) |
---|
7458 | { |
---|
7459 | // to dispense with taking initials and lifting/interreducing |
---|
7460 | // after the call of recursion. |
---|
7461 | if(printout > 0) |
---|
7462 | { |
---|
7463 | Print("\n//** rec_r_fractal_call: Perturb both vectors with degree %d.",nlev); |
---|
7464 | //idElements(G, "G"); |
---|
7465 | } |
---|
7466 | Xngleich = 1; |
---|
7467 | nlev +=1; |
---|
7468 | if(ivtarget->length() == nV) |
---|
7469 | { |
---|
7470 | /* |
---|
7471 | if (rParameter(currRing) != NULL) |
---|
7472 | DefRingPar(omtmp); |
---|
7473 | else |
---|
7474 | rChangeCurrRing(VMrDefault(omtmp)); |
---|
7475 | */ |
---|
7476 | rChangeCurrRing(VMrRefine(ivtarget,omtmp)); |
---|
7477 | } |
---|
7478 | else |
---|
7479 | { |
---|
7480 | //rChangeCurrRing(VMatrDefault(ivtarget)); |
---|
7481 | rChangeCurrRing(VMatrRefine(ivtarget,omtmp)); |
---|
7482 | } |
---|
7483 | testring = currRing; |
---|
7484 | Gt = idrMoveR(G, oRing,currRing); |
---|
7485 | |
---|
7486 | // perturb the original target vector w.r.t. the current GB |
---|
7487 | if(ivtarget->length() == nV) |
---|
7488 | { |
---|
7489 | delete Xtau; |
---|
7490 | Xtau = NewVectorlp(Gt); |
---|
7491 | } |
---|
7492 | else |
---|
7493 | { |
---|
7494 | delete Xtau; |
---|
7495 | Xtau = Mfpertvector(Gt,ivtarget); |
---|
7496 | } |
---|
7497 | |
---|
7498 | rChangeCurrRing(oRing); |
---|
7499 | G = idrMoveR(Gt,testring,currRing); |
---|
7500 | |
---|
7501 | // perturb the current vector w.r.t. the current GB |
---|
7502 | Mwlp = MivWeightOrderlp(omega); |
---|
7503 | if(ivtarget->length() > nV) |
---|
7504 | { |
---|
7505 | delete Mwlp; |
---|
7506 | Mwlp = MivMatrixOrderRefine(omega,ivtarget); |
---|
7507 | } |
---|
7508 | Xsigma = Mfpertvector(G, Mwlp); |
---|
7509 | delete Mwlp; |
---|
7510 | |
---|
7511 | for(i=nV-1; i>=0; i--) |
---|
7512 | { |
---|
7513 | (*omega2)[i] = (*Xtau)[nV+i]; |
---|
7514 | (*omega)[i] = (*Xsigma)[nV+i]; |
---|
7515 | } |
---|
7516 | |
---|
7517 | delete next_vect; |
---|
7518 | |
---|
7519 | //to avoid the value of Overflow_Error that occur in Mfpertvector |
---|
7520 | Overflow_Error = FALSE; |
---|
7521 | #ifdef TIME_TEST |
---|
7522 | to=clock(); |
---|
7523 | #endif |
---|
7524 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
7525 | #ifdef TIME_TEST |
---|
7526 | xtnw=xtnw+clock()-to; |
---|
7527 | #endif |
---|
7528 | if(lengthpoly(MwalkInitialForm(G, next_vect)) > 0 && G->m[0] != NULL) |
---|
7529 | { |
---|
7530 | // there is a polynomial in Gomega with at least 3 monomials |
---|
7531 | iv_M = MivMatrixOrder(omega); |
---|
7532 | delete next_vect; |
---|
7533 | #ifdef TIME_TEST |
---|
7534 | to=clock(); |
---|
7535 | #endif |
---|
7536 | next_vect = MWalkRandomNextWeight(G,iv_M,omega2,weight_rad,nlev); |
---|
7537 | #ifdef TIME_TEST |
---|
7538 | xtnw=xtnw+clock()-to; |
---|
7539 | #endif |
---|
7540 | delete iv_M; |
---|
7541 | if(isNegNolVector(next_vect) == 1) |
---|
7542 | { |
---|
7543 | delete next_vect; |
---|
7544 | #ifdef TIME_TEST |
---|
7545 | to=clock(); |
---|
7546 | #endif |
---|
7547 | next_vect = MkInterRedNextWeight(omega,omega2,G); |
---|
7548 | #ifdef TIME_TEST |
---|
7549 | xtnw=xtnw+clock()-to; |
---|
7550 | #endif |
---|
7551 | } |
---|
7552 | } |
---|
7553 | } |
---|
7554 | #ifdef PRINT_VECTORS |
---|
7555 | if(printout > 0) |
---|
7556 | { |
---|
7557 | MivString(omega, omega2, next_vect); |
---|
7558 | } |
---|
7559 | #endif |
---|
7560 | |
---|
7561 | /* check whether the the computed vector is in the correct cone |
---|
7562 | If no, the reduced GB of an omega-homogeneous ideal will be |
---|
7563 | computed by Buchberger algorithm and stop this recursion step |
---|
7564 | */ |
---|
7565 | if(Overflow_Error == TRUE || test_w_in_ConeCC(G,next_vect) != 1)//e.g. Example s7, cyc6 |
---|
7566 | { |
---|
7567 | delete next_vect; |
---|
7568 | if(ivtarget->length() == nV) |
---|
7569 | { |
---|
7570 | /* |
---|
7571 | if (rParameter(currRing) != NULL) |
---|
7572 | { |
---|
7573 | DefRingPar(omtmp); |
---|
7574 | } |
---|
7575 | else |
---|
7576 | { |
---|
7577 | rChangeCurrRing(VMrDefault(omtmp)); |
---|
7578 | } |
---|
7579 | */ |
---|
7580 | rChangeCurrRing(VMrRefine(ivtarget,omtmp)); |
---|
7581 | } |
---|
7582 | else |
---|
7583 | { |
---|
7584 | //rChangeCurrRing(VMatrDefault(ivtarget)); |
---|
7585 | rChangeCurrRing(VMatrRefine(ivtarget,omtmp)); |
---|
7586 | } |
---|
7587 | #ifdef TEST_OVERFLOW |
---|
7588 | Gt = idrMoveR(G, oRing,currRing); |
---|
7589 | Gt = NULL; |
---|
7590 | return(Gt); |
---|
7591 | #endif |
---|
7592 | if(printout > 0) |
---|
7593 | { |
---|
7594 | Print("\n//** rec_r_fractal_call: applying Buchberger's algorithm in ring r = %s;", |
---|
7595 | rString(currRing)); |
---|
7596 | } |
---|
7597 | Gt = idrMoveR(G, oRing,currRing); |
---|
7598 | #ifdef TIME_TEST |
---|
7599 | to=clock(); |
---|
7600 | #endif |
---|
7601 | G1 = MstdCC(Gt); |
---|
7602 | #ifdef TIME_TEST |
---|
7603 | xtextra=xtextra+clock()-to; |
---|
7604 | #endif |
---|
7605 | Gt = NULL; |
---|
7606 | |
---|
7607 | delete omega2; |
---|
7608 | delete altomega; |
---|
7609 | if(printout > 0) |
---|
7610 | { |
---|
7611 | Print("\n//** rec_r_fractal_call: (1) Leaving the %d-th recursion with %d steps.\n", |
---|
7612 | nlev, nwalks); |
---|
7613 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
7614 | } |
---|
7615 | nnflow ++; |
---|
7616 | Overflow_Error = FALSE; |
---|
7617 | return (G1); |
---|
7618 | } |
---|
7619 | /* |
---|
7620 | If the perturbed target vector stays in the correct cone, |
---|
7621 | return the current Groebner basis. |
---|
7622 | Otherwise, return the Groebner basis computed with Buchberger's |
---|
7623 | algorithm. |
---|
7624 | Then we update the perturbed target vectors w.r.t. this GB. |
---|
7625 | */ |
---|
7626 | if (MivComp(next_vect, XivNull) == 1) |
---|
7627 | { |
---|
7628 | // The computed vector is equal to the origin vector, |
---|
7629 | // because t is not defined |
---|
7630 | if(ivtarget->length() == nV) |
---|
7631 | { |
---|
7632 | /* |
---|
7633 | if (rParameter(currRing) != NULL) |
---|
7634 | DefRingPar(omtmp); |
---|
7635 | else |
---|
7636 | rChangeCurrRing(VMrDefault(omtmp)); |
---|
7637 | */ |
---|
7638 | rChangeCurrRing(VMrRefine(ivtarget,omtmp)); |
---|
7639 | } |
---|
7640 | else |
---|
7641 | { |
---|
7642 | //rChangeCurrRing(VMatrDefault(ivtarget)); |
---|
7643 | rChangeCurrRing(VMatrRefine(ivtarget,omtmp)); |
---|
7644 | } |
---|
7645 | testring = currRing; |
---|
7646 | Gt = idrMoveR(G, oRing,currRing); |
---|
7647 | |
---|
7648 | if(test_w_in_ConeCC(Gt, omega2) == 1) |
---|
7649 | { |
---|
7650 | delete omega2; |
---|
7651 | delete next_vect; |
---|
7652 | delete altomega; |
---|
7653 | if(printout > 0) |
---|
7654 | { |
---|
7655 | Print("\n//** rec_r_fractal_call: (2) Leaving the %d-th recursion with %d steps.\n", |
---|
7656 | nlev, nwalks); |
---|
7657 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
7658 | } |
---|
7659 | return (Gt); |
---|
7660 | } |
---|
7661 | else |
---|
7662 | { |
---|
7663 | if(printout > 0) |
---|
7664 | { |
---|
7665 | Print("\n//** rec_r_fractal_call: target weight doesn't stay in the correct cone.\n"); |
---|
7666 | } |
---|
7667 | |
---|
7668 | #ifndef MSTDCC_FRACTAL |
---|
7669 | #ifdef PRINT_VECTORS |
---|
7670 | if(printout > 0) |
---|
7671 | { |
---|
7672 | ivString(Xtau, "old Xtau"); |
---|
7673 | } |
---|
7674 | #endif |
---|
7675 | intvec* Xtautmp; |
---|
7676 | if(ivtarget->length() == nV) |
---|
7677 | { |
---|
7678 | Xtautmp = Mfpertvector(Gt, MivMatrixOrder(omtmp)); |
---|
7679 | } |
---|
7680 | else |
---|
7681 | { |
---|
7682 | Xtautmp = Mfpertvector(Gt, ivtarget); |
---|
7683 | } |
---|
7684 | #ifdef TEST_OVERFLOW |
---|
7685 | if(Overflow_Error == TRUE) |
---|
7686 | Gt = NULL; return(Gt); |
---|
7687 | #endif |
---|
7688 | |
---|
7689 | if(MivSame(Xtau, Xtautmp) == 1) |
---|
7690 | { |
---|
7691 | //PrintS("\n// Update vectors are equal to the old vectors!!"); |
---|
7692 | delete Xtautmp; |
---|
7693 | goto FRACTAL_MSTDCC; |
---|
7694 | } |
---|
7695 | |
---|
7696 | Xtau = Xtautmp; |
---|
7697 | Xtautmp = NULL; |
---|
7698 | #ifdef PRINT_VECTORS |
---|
7699 | if(printout > 0) |
---|
7700 | { |
---|
7701 | ivString(Xtau, "new Xtau"); |
---|
7702 | } |
---|
7703 | #endif |
---|
7704 | |
---|
7705 | for(i=nV-1; i>=0; i--) |
---|
7706 | (*omega2)[i] = (*Xtau)[(nlev-1)*nV+i]; |
---|
7707 | |
---|
7708 | //Print("\n// ring tau = %s;", rString(currRing)); |
---|
7709 | rChangeCurrRing(oRing); |
---|
7710 | G = idrMoveR(Gt, testring,currRing); |
---|
7711 | |
---|
7712 | goto NEXT_VECTOR_FRACTAL; |
---|
7713 | #endif |
---|
7714 | |
---|
7715 | FRACTAL_MSTDCC: |
---|
7716 | if(printout > 0) |
---|
7717 | { |
---|
7718 | Print("\n//** rec_r_fractal_call: apply Buchberger's algorithm in ring = %s.\n", |
---|
7719 | rString(currRing)); |
---|
7720 | } |
---|
7721 | #ifdef TIME_TEST |
---|
7722 | to=clock(); |
---|
7723 | #endif |
---|
7724 | G = MstdCC(Gt); |
---|
7725 | #ifdef TIME_TEST |
---|
7726 | xtextra=xtextra+clock()-to; |
---|
7727 | #endif |
---|
7728 | oRing = currRing; |
---|
7729 | |
---|
7730 | // update the original target vector w.r.t. the current GB |
---|
7731 | if(ivtarget->length() == nV) |
---|
7732 | { |
---|
7733 | /* |
---|
7734 | if(MivSame(Xivinput, Xivlp) == 1) |
---|
7735 | if (rParameter(currRing) != NULL) |
---|
7736 | DefRingParlp(); |
---|
7737 | else |
---|
7738 | VMrDefaultlp(); |
---|
7739 | else |
---|
7740 | if (rParameter(currRing) != NULL) |
---|
7741 | DefRingPar(Xivinput); |
---|
7742 | else |
---|
7743 | rChangeCurrRing(VMrDefault(Xivinput)); |
---|
7744 | */ |
---|
7745 | rChangeCurrRing(VMrRefine(ivtarget,Xivinput)); |
---|
7746 | } |
---|
7747 | else |
---|
7748 | { |
---|
7749 | rChangeCurrRing(VMatrRefine(ivtarget,Xivinput)); |
---|
7750 | } |
---|
7751 | testring = currRing; |
---|
7752 | Gt = idrMoveR(G, oRing,currRing); |
---|
7753 | |
---|
7754 | // perturb the original target vector w.r.t. the current GB |
---|
7755 | if(ivtarget->length() == nV) |
---|
7756 | { |
---|
7757 | delete Xtau; |
---|
7758 | Xtau = NewVectorlp(Gt); |
---|
7759 | } |
---|
7760 | else |
---|
7761 | { |
---|
7762 | delete Xtau; |
---|
7763 | Xtau = Mfpertvector(Gt,ivtarget); |
---|
7764 | } |
---|
7765 | |
---|
7766 | rChangeCurrRing(oRing); |
---|
7767 | G = idrMoveR(Gt, testring,currRing); |
---|
7768 | |
---|
7769 | delete omega2; |
---|
7770 | delete next_vect; |
---|
7771 | delete altomega; |
---|
7772 | if(printout > 0) |
---|
7773 | { |
---|
7774 | Print("\n//** rec_r_fractal_call: (3) Leaving the %d-th recursion with %d steps.\n", |
---|
7775 | nlev,nwalks); |
---|
7776 | //Print(" ** Overflow_Error? (%d)", Overflow_Error); |
---|
7777 | } |
---|
7778 | if(Overflow_Error == TRUE) |
---|
7779 | nnflow ++; |
---|
7780 | |
---|
7781 | Overflow_Error = FALSE; |
---|
7782 | return(G); |
---|
7783 | } |
---|
7784 | } //end of if(MivComp(next_vect, XivNull) == 1) |
---|
7785 | |
---|
7786 | for(i=nV-1; i>=0; i--) |
---|
7787 | { |
---|
7788 | (*altomega)[i] = (*omega)[i]; |
---|
7789 | (*omega)[i] = (*next_vect)[i]; |
---|
7790 | } |
---|
7791 | delete next_vect; |
---|
7792 | #ifdef TIME_TEST |
---|
7793 | to=clock(); |
---|
7794 | #endif |
---|
7795 | // Take the initial form of <G> w.r.t. omega |
---|
7796 | Gomega = MwalkInitialForm(G, omega); |
---|
7797 | #ifdef TIME_TEST |
---|
7798 | xtif=xtif+clock()-to; |
---|
7799 | #endif |
---|
7800 | //polylength = 1 if there is a polynomial in Gomega with at least 3 monomials and 0 otherwise |
---|
7801 | //polylength = lengthpoly(Gomega); |
---|
7802 | #ifdef CHECK_IDEAL_MWALK |
---|
7803 | if(printout > 1) |
---|
7804 | { |
---|
7805 | idString(Gomega,"//** rec_r_fractal_call: Gomega"); |
---|
7806 | } |
---|
7807 | #endif |
---|
7808 | if(reduction == 0) |
---|
7809 | { |
---|
7810 | /* Check whether the intermediate weight vector lies in the interior of the cone. |
---|
7811 | * If so, only perform reductions. Otherwise apply Buchberger's algorithm. */ |
---|
7812 | FF = middleOfCone(G,Gomega); |
---|
7813 | if( FF != NULL) |
---|
7814 | { |
---|
7815 | idDelete(&G); |
---|
7816 | G = idCopy(FF); |
---|
7817 | idDelete(&FF); |
---|
7818 | /* Compue next vector. */ |
---|
7819 | goto NEXT_VECTOR_FRACTAL; |
---|
7820 | } |
---|
7821 | } |
---|
7822 | |
---|
7823 | #ifndef BUCHBERGER_ALG |
---|
7824 | if(isNolVector(omega) == 0) |
---|
7825 | hilb_func = hFirstSeries(Gomega,NULL,NULL,omega,currRing); |
---|
7826 | else |
---|
7827 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
7828 | #endif |
---|
7829 | if(ivtarget->length() == nV) |
---|
7830 | { |
---|
7831 | /* |
---|
7832 | if (rParameter(currRing) != NULL) |
---|
7833 | DefRingPar(omega); |
---|
7834 | else |
---|
7835 | rChangeCurrRing(VMrDefault(omega)); |
---|
7836 | */ |
---|
7837 | rChangeCurrRing(VMrRefine(ivtarget,omega)); |
---|
7838 | } |
---|
7839 | else |
---|
7840 | { |
---|
7841 | rChangeCurrRing(VMatrRefine(ivtarget,omega)); |
---|
7842 | } |
---|
7843 | Gomega1 = idrMoveR(Gomega, oRing,currRing); |
---|
7844 | |
---|
7845 | // Maximal recursion depth, to compute a red. GB |
---|
7846 | // Fractal walk with the alternative recursion |
---|
7847 | // alternative recursion |
---|
7848 | if(nlev == Xnlev || lengthpoly(Gomega1) == 0) |
---|
7849 | { |
---|
7850 | #ifdef TIME_TEST |
---|
7851 | to=clock(); |
---|
7852 | #endif |
---|
7853 | #ifdef BUCHBERGER_ALG |
---|
7854 | Gresult = MstdhomCC(Gomega1); |
---|
7855 | #else |
---|
7856 | Gresult =kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,omega); |
---|
7857 | delete hilb_func; |
---|
7858 | #endif |
---|
7859 | #ifdef TIME_TEST |
---|
7860 | xtstd=xtstd+clock()-to; |
---|
7861 | #endif |
---|
7862 | } |
---|
7863 | else |
---|
7864 | { |
---|
7865 | rChangeCurrRing(oRing); |
---|
7866 | Gomega1 = idrMoveR(Gomega1, oRing,currRing); |
---|
7867 | Gresult = rec_r_fractal_call(idCopy(Gomega1),nlev+1,omega,weight_rad,reduction,printout); |
---|
7868 | } |
---|
7869 | #ifdef CHECK_IDEAL_MWALK |
---|
7870 | if(printout > 2) |
---|
7871 | { |
---|
7872 | idString(Gresult,"//** rec_r_fractal_call: M"); |
---|
7873 | } |
---|
7874 | #endif |
---|
7875 | //convert a Groebner basis from a ring to another ring |
---|
7876 | new_ring = currRing; |
---|
7877 | |
---|
7878 | rChangeCurrRing(oRing); |
---|
7879 | Gresult1 = idrMoveR(Gresult, new_ring,currRing); |
---|
7880 | Gomega2 = idrMoveR(Gomega1, new_ring,currRing); |
---|
7881 | #ifdef TIME_TEST |
---|
7882 | to=clock(); |
---|
7883 | #endif |
---|
7884 | // Lifting process |
---|
7885 | F = MLifttwoIdeal(Gomega2, Gresult1, G); |
---|
7886 | #ifdef TIME_TEST |
---|
7887 | xtlift=xtlift+clock()-to; |
---|
7888 | #endif |
---|
7889 | #ifdef CHECK_IDEAL_MWALK |
---|
7890 | if(printout > 2) |
---|
7891 | { |
---|
7892 | idString(F,"//** rec_r_fractal_call: F"); |
---|
7893 | } |
---|
7894 | #endif |
---|
7895 | id_Normalize(F,currRing); |
---|
7896 | idDelete(&Gresult1); |
---|
7897 | idDelete(&Gomega2); |
---|
7898 | idDelete(&G); |
---|
7899 | |
---|
7900 | rChangeCurrRing(new_ring); |
---|
7901 | //F1 = idrMoveR(F, oRing,currRing); |
---|
7902 | G = idrMoveR(F,oRing,currRing); |
---|
7903 | /* |
---|
7904 | #ifdef TIME_TEST |
---|
7905 | to=clock(); |
---|
7906 | #endif |
---|
7907 | // Interreduce G |
---|
7908 | G = kInterRedCC(F1, NULL); |
---|
7909 | #ifdef TIME_TEST |
---|
7910 | xtred=xtred+clock()-to; |
---|
7911 | #endif |
---|
7912 | idDelete(&F1); |
---|
7913 | */ |
---|
7914 | } |
---|
7915 | } |
---|
7916 | |
---|
7917 | |
---|
7918 | /******************************************************************************* |
---|
7919 | * The implementation of the fractal walk algorithm * |
---|
7920 | * * |
---|
7921 | * The main procedure Mfwalk calls the recursive Subroutine * |
---|
7922 | * rec_fractal_call to compute the wanted Groebner basis. * |
---|
7923 | * At the main procedur we compute the reduced Groebner basis w.r.t. a "fast" * |
---|
7924 | * order, e.g. "dp" and a sequence of weight vectors which are row vectors * |
---|
7925 | * of a matrix. This matrix defines the given monomial order, e.g. "lp" * |
---|
7926 | *******************************************************************************/ |
---|
7927 | ideal Mfwalk(ideal G, intvec* ivstart, intvec* ivtarget, |
---|
7928 | int reduction, int printout) |
---|
7929 | { |
---|
7930 | BITSET save1 = si_opt_1; // save current options |
---|
7931 | if(reduction == 0) |
---|
7932 | { |
---|
7933 | si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis |
---|
7934 | //si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions |
---|
7935 | } |
---|
7936 | Set_Error(FALSE); |
---|
7937 | Overflow_Error = FALSE; |
---|
7938 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
7939 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
7940 | |
---|
7941 | nnflow = 0; |
---|
7942 | Xngleich = 0; |
---|
7943 | Xcall = 0; |
---|
7944 | #ifdef TIME_TEST |
---|
7945 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
7946 | xftinput = clock(); |
---|
7947 | #endif |
---|
7948 | ring oldRing = currRing; |
---|
7949 | int i, nV = currRing->N; |
---|
7950 | XivNull = new intvec(nV); |
---|
7951 | Xivinput = ivtarget; |
---|
7952 | ngleich = 0; |
---|
7953 | #ifdef TIME_TEST |
---|
7954 | to=clock(); |
---|
7955 | #endif |
---|
7956 | ideal I = MstdCC(G); |
---|
7957 | G = NULL; |
---|
7958 | #ifdef TIME_TEST |
---|
7959 | xftostd=clock()-to; |
---|
7960 | #endif |
---|
7961 | Xsigma = ivstart; |
---|
7962 | |
---|
7963 | Xnlev=nV; |
---|
7964 | |
---|
7965 | #ifdef FIRST_STEP_FRACTAL |
---|
7966 | ideal Gw = MwalkInitialForm(I, ivstart); |
---|
7967 | for(i=IDELEMS(Gw)-1; i>=0; i--) |
---|
7968 | { |
---|
7969 | if((Gw->m[i]!=NULL) // len >=0 |
---|
7970 | && (Gw->m[i]->next!=NULL) // len >=1 |
---|
7971 | && (Gw->m[i]->next->next!=NULL)) // len >=2 |
---|
7972 | { |
---|
7973 | intvec* iv_dp = MivUnit(nV); // define (1,1,...,1) |
---|
7974 | intvec* Mdp; |
---|
7975 | if(ivstart->length() == nV) |
---|
7976 | { |
---|
7977 | if(MivSame(ivstart, iv_dp) != 1) |
---|
7978 | Mdp = MivWeightOrderdp(ivstart); |
---|
7979 | else |
---|
7980 | Mdp = MivMatrixOrderdp(nV); |
---|
7981 | } |
---|
7982 | else |
---|
7983 | { |
---|
7984 | Mdp = ivstart; |
---|
7985 | } |
---|
7986 | |
---|
7987 | Xsigma = Mfpertvector(I, Mdp); |
---|
7988 | Overflow_Error = FALSE; |
---|
7989 | |
---|
7990 | delete Mdp; |
---|
7991 | delete iv_dp; |
---|
7992 | break; |
---|
7993 | } |
---|
7994 | } |
---|
7995 | idDelete(&Gw); |
---|
7996 | #endif |
---|
7997 | |
---|
7998 | ideal I1; |
---|
7999 | intvec* Mlp; |
---|
8000 | Xivlp = Mivlp(nV); |
---|
8001 | |
---|
8002 | if(ivtarget->length() == nV) |
---|
8003 | { |
---|
8004 | if(MivComp(ivtarget, Xivlp) != 1) |
---|
8005 | { |
---|
8006 | if (rParameter(currRing) != NULL) |
---|
8007 | DefRingPar(ivtarget); |
---|
8008 | else |
---|
8009 | rChangeCurrRing(VMrDefault(ivtarget)); |
---|
8010 | |
---|
8011 | I1 = idrMoveR(I, oldRing,currRing); |
---|
8012 | Mlp = MivWeightOrderlp(ivtarget); |
---|
8013 | Xtau = Mfpertvector(I1, Mlp); |
---|
8014 | } |
---|
8015 | else |
---|
8016 | { |
---|
8017 | if (rParameter(currRing) != NULL) |
---|
8018 | DefRingParlp(); |
---|
8019 | else |
---|
8020 | VMrDefaultlp(); |
---|
8021 | |
---|
8022 | I1 = idrMoveR(I, oldRing,currRing); |
---|
8023 | Mlp = MivMatrixOrderlp(nV); |
---|
8024 | Xtau = Mfpertvector(I1, Mlp); |
---|
8025 | } |
---|
8026 | } |
---|
8027 | else |
---|
8028 | { |
---|
8029 | rChangeCurrRing(VMatrDefault(ivtarget)); |
---|
8030 | I1 = idrMoveR(I,oldRing,currRing); |
---|
8031 | Mlp = ivtarget; |
---|
8032 | Xtau = Mfpertvector(I1, Mlp); |
---|
8033 | } |
---|
8034 | delete Mlp; |
---|
8035 | Overflow_Error = FALSE; |
---|
8036 | |
---|
8037 | //ivString(Xsigma, "Xsigma"); |
---|
8038 | //ivString(Xtau, "Xtau"); |
---|
8039 | |
---|
8040 | id_Delete(&I, oldRing); |
---|
8041 | ring tRing = currRing; |
---|
8042 | if(ivtarget->length() == nV) |
---|
8043 | { |
---|
8044 | /* |
---|
8045 | if (rParameter(currRing) != NULL) |
---|
8046 | DefRingPar(ivstart); |
---|
8047 | else |
---|
8048 | rChangeCurrRing(VMrDefault(ivstart)); |
---|
8049 | */ |
---|
8050 | rChangeCurrRing(VMrRefine(ivtarget,ivstart)); |
---|
8051 | } |
---|
8052 | else |
---|
8053 | { |
---|
8054 | //rChangeCurrRing(VMatrDefault(ivstart)); |
---|
8055 | rChangeCurrRing(VMatrRefine(ivtarget,ivstart)); |
---|
8056 | } |
---|
8057 | |
---|
8058 | I = idrMoveR(I1,tRing,currRing); |
---|
8059 | #ifdef TIME_TEST |
---|
8060 | to=clock(); |
---|
8061 | #endif |
---|
8062 | ideal J = MstdCC(I); |
---|
8063 | idDelete(&I); |
---|
8064 | #ifdef TIME_TEST |
---|
8065 | xftostd=xftostd+clock()-to; |
---|
8066 | #endif |
---|
8067 | ideal resF; |
---|
8068 | ring helpRing = currRing; |
---|
8069 | |
---|
8070 | J = rec_fractal_call(J,1,ivtarget,reduction,printout); |
---|
8071 | //idString(J,"//** Mfwalk: J"); |
---|
8072 | rChangeCurrRing(oldRing); |
---|
8073 | //Print("\n//Mfwalk: (2)\n"); |
---|
8074 | resF = idrMoveR(J, helpRing,currRing); |
---|
8075 | //Print("\n//Mfwalk: (3)\n"); |
---|
8076 | idSkipZeroes(resF); |
---|
8077 | //Print("\n//Mfwalk: (4)\n"); |
---|
8078 | |
---|
8079 | si_opt_1 = save1; //set original options, e. g. option(RedSB) |
---|
8080 | delete Xivlp; |
---|
8081 | //delete Xsigma; |
---|
8082 | delete Xtau; |
---|
8083 | delete XivNull; |
---|
8084 | //Print("\n//Mfwalk: (5)\n"); |
---|
8085 | #ifdef TIME_TEST |
---|
8086 | TimeStringFractal(xftinput, xftostd, xtif, xtstd, xtextra, |
---|
8087 | xtlift, xtred, xtnw); |
---|
8088 | |
---|
8089 | |
---|
8090 | //Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
8091 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
8092 | Print("\n// the numbers of Overflow_Error (%d)", nnflow); |
---|
8093 | #endif |
---|
8094 | //Print("\n//Mfwalk: (6)\n"); |
---|
8095 | //idString(resF,"//** Mfwalk: resF"); |
---|
8096 | return(idCopy(resF)); |
---|
8097 | } |
---|
8098 | |
---|
8099 | /******************************************************************************* |
---|
8100 | * The implementation of the fractal walk algorithm with random element * |
---|
8101 | * * |
---|
8102 | * The main procedur Mfwalk calls the recursive Subroutine * |
---|
8103 | * rec_r_fractal_call to compute the wanted Groebner basis. * |
---|
8104 | * At the main procedure we compute the reduced Groebner basis w.r.t. a "fast" * |
---|
8105 | * order, e.g. "dp" and a sequence of weight vectors which are row vectors * |
---|
8106 | * of a matrix. This matrix defines the given monomial order, e.g. "lp" * |
---|
8107 | *******************************************************************************/ |
---|
8108 | ideal Mfrwalk(ideal G, intvec* ivstart, intvec* ivtarget, |
---|
8109 | int weight_rad, int reduction, int printout) |
---|
8110 | { |
---|
8111 | BITSET save1 = si_opt_1; // save current options |
---|
8112 | //check that weight radius is valid |
---|
8113 | if(weight_rad < 0) |
---|
8114 | { |
---|
8115 | Werror("Invalid radius.\n"); |
---|
8116 | return NULL; |
---|
8117 | } |
---|
8118 | if(reduction == 0) |
---|
8119 | { |
---|
8120 | si_opt_1 &= (~Sy_bit(OPT_REDSB)); // no reduced Groebner basis |
---|
8121 | si_opt_1 &= (~Sy_bit(OPT_REDTAIL)); // not tail reductions |
---|
8122 | } |
---|
8123 | Set_Error(FALSE); |
---|
8124 | Overflow_Error = FALSE; |
---|
8125 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
8126 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
8127 | |
---|
8128 | nnflow = 0; |
---|
8129 | Xngleich = 0; |
---|
8130 | Xcall = 0; |
---|
8131 | #ifdef TIME_TEST |
---|
8132 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
8133 | xftinput = clock(); |
---|
8134 | #endif |
---|
8135 | ring oldRing = currRing; |
---|
8136 | int i, nV = currRing->N; |
---|
8137 | XivNull = new intvec(nV); |
---|
8138 | Xivinput = ivtarget; |
---|
8139 | ngleich = 0; |
---|
8140 | #ifdef TIME_TEST |
---|
8141 | to=clock(); |
---|
8142 | #endif |
---|
8143 | ideal I = MstdCC(G); |
---|
8144 | G = NULL; |
---|
8145 | #ifdef TIME_TEST |
---|
8146 | xftostd=clock()-to; |
---|
8147 | #endif |
---|
8148 | Xsigma = ivstart; |
---|
8149 | |
---|
8150 | Xnlev=nV; |
---|
8151 | |
---|
8152 | #ifdef FIRST_STEP_FRACTAL |
---|
8153 | ideal Gw = MwalkInitialForm(I, ivstart); |
---|
8154 | for(i=IDELEMS(Gw)-1; i>=0; i--) |
---|
8155 | { |
---|
8156 | if((Gw->m[i]!=NULL) // len >=0 |
---|
8157 | && (Gw->m[i]->next!=NULL) // len >=1 |
---|
8158 | && (Gw->m[i]->next->next!=NULL)) // len >=2 |
---|
8159 | { |
---|
8160 | intvec* iv_dp = MivUnit(nV); // define (1,1,...,1) |
---|
8161 | intvec* Mdp; |
---|
8162 | if(ivstart->length() == nV) |
---|
8163 | { |
---|
8164 | if(MivSame(ivstart, iv_dp) != 1) |
---|
8165 | Mdp = MivWeightOrderdp(ivstart); |
---|
8166 | else |
---|
8167 | Mdp = MivMatrixOrderdp(nV); |
---|
8168 | } |
---|
8169 | else |
---|
8170 | { |
---|
8171 | Mdp = ivstart; |
---|
8172 | } |
---|
8173 | |
---|
8174 | Xsigma = Mfpertvector(I, Mdp); |
---|
8175 | Overflow_Error = FALSE; |
---|
8176 | |
---|
8177 | delete Mdp; |
---|
8178 | delete iv_dp; |
---|
8179 | break; |
---|
8180 | } |
---|
8181 | } |
---|
8182 | idDelete(&Gw); |
---|
8183 | #endif |
---|
8184 | |
---|
8185 | ideal I1; |
---|
8186 | intvec* Mlp; |
---|
8187 | Xivlp = Mivlp(nV); |
---|
8188 | |
---|
8189 | if(ivtarget->length() == nV) |
---|
8190 | { |
---|
8191 | if(MivComp(ivtarget, Xivlp) != 1) |
---|
8192 | { |
---|
8193 | if (rParameter(currRing) != NULL) |
---|
8194 | DefRingPar(ivtarget); |
---|
8195 | else |
---|
8196 | rChangeCurrRing(VMrDefault(ivtarget)); |
---|
8197 | |
---|
8198 | I1 = idrMoveR(I, oldRing,currRing); |
---|
8199 | Mlp = MivWeightOrderlp(ivtarget); |
---|
8200 | Xtau = Mfpertvector(I1, Mlp); |
---|
8201 | } |
---|
8202 | else |
---|
8203 | { |
---|
8204 | if (rParameter(currRing) != NULL) |
---|
8205 | DefRingParlp(); |
---|
8206 | else |
---|
8207 | VMrDefaultlp(); |
---|
8208 | |
---|
8209 | I1 = idrMoveR(I, oldRing,currRing); |
---|
8210 | Mlp = MivMatrixOrderlp(nV); |
---|
8211 | Xtau = Mfpertvector(I1, Mlp); |
---|
8212 | } |
---|
8213 | } |
---|
8214 | else |
---|
8215 | { |
---|
8216 | rChangeCurrRing(VMatrDefault(ivtarget)); |
---|
8217 | I1 = idrMoveR(I,oldRing,currRing); |
---|
8218 | Mlp = ivtarget; |
---|
8219 | Xtau = Mfpertvector(I1, Mlp); |
---|
8220 | } |
---|
8221 | delete Mlp; |
---|
8222 | Overflow_Error = FALSE; |
---|
8223 | |
---|
8224 | //ivString(Xsigma, "Xsigma"); |
---|
8225 | //ivString(Xtau, "Xtau"); |
---|
8226 | |
---|
8227 | id_Delete(&I, oldRing); |
---|
8228 | ring tRing = currRing; |
---|
8229 | if(ivtarget->length() == nV) |
---|
8230 | { |
---|
8231 | /* |
---|
8232 | if (rParameter(currRing) != NULL) |
---|
8233 | DefRingPar(ivstart); |
---|
8234 | else |
---|
8235 | rChangeCurrRing(VMrDefault(ivstart)); |
---|
8236 | */ |
---|
8237 | rChangeCurrRing(VMrRefine(ivtarget,ivstart)); |
---|
8238 | } |
---|
8239 | else |
---|
8240 | { |
---|
8241 | //rChangeCurrRing(VMatrDefault(ivstart)); |
---|
8242 | rChangeCurrRing(VMatrRefine(ivtarget,ivstart)); |
---|
8243 | } |
---|
8244 | |
---|
8245 | I = idrMoveR(I1,tRing,currRing); |
---|
8246 | #ifdef TIME_TEST |
---|
8247 | to=clock(); |
---|
8248 | #endif |
---|
8249 | ideal J = MstdCC(I); |
---|
8250 | idDelete(&I); |
---|
8251 | #ifdef TIME_TEST |
---|
8252 | xftostd=xftostd+clock()-to; |
---|
8253 | #endif |
---|
8254 | ideal resF; |
---|
8255 | ring helpRing = currRing; |
---|
8256 | |
---|
8257 | J = rec_r_fractal_call(J,1,ivtarget,weight_rad,reduction,printout); |
---|
8258 | //idString(J,"//*** Mfrwalk: J"); |
---|
8259 | //Print("\n//** Mfrwalk hier (1)\n"); |
---|
8260 | rChangeCurrRing(oldRing); |
---|
8261 | //Print("\n//** Mfrwalk hier (2)\n"); |
---|
8262 | resF = idrMoveR(J, helpRing,currRing); |
---|
8263 | //Print("\n//** Mfrwalk hier (3)\n"); |
---|
8264 | //idSkipZeroes(resF); |
---|
8265 | //Print("\n//** Mfrwalk hier (4)\n"); |
---|
8266 | si_opt_1 = save1; //set original options, e. g. option(RedSB) |
---|
8267 | delete Xivlp; |
---|
8268 | //delete Xsigma; |
---|
8269 | delete Xtau; |
---|
8270 | delete XivNull; |
---|
8271 | //Print("\n//** Mfrwalk hier (5)\n"); |
---|
8272 | #ifdef TIME_TEST |
---|
8273 | TimeStringFractal(xftinput, xftostd, xtif, xtstd, xtextra, |
---|
8274 | xtlift, xtred, xtnw); |
---|
8275 | |
---|
8276 | |
---|
8277 | // Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
8278 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
8279 | Print("\n// the numbers of Overflow_Error (%d)", nnflow); |
---|
8280 | #endif |
---|
8281 | //Print("\n//** Mfrwalk hier (6)\n"); |
---|
8282 | //idString(resF,"resF"); |
---|
8283 | //Print("\n//** Mfrwalk hier (7)\n"); |
---|
8284 | return(resF); |
---|
8285 | } |
---|
8286 | |
---|
8287 | /******************************************************* |
---|
8288 | * Tran's algorithm * |
---|
8289 | * * |
---|
8290 | * use kStd, if nP = 0, else call Ab_Rec_Pert (LastGB) * |
---|
8291 | *******************************************************/ |
---|
8292 | ideal TranMImprovwalk(ideal G,intvec* curr_weight,intvec* target_tmp, int nP) |
---|
8293 | { |
---|
8294 | #ifdef TIME_TEST |
---|
8295 | clock_t mtim = clock(); |
---|
8296 | #endif |
---|
8297 | Set_Error(FALSE ); |
---|
8298 | Overflow_Error = FALSE; |
---|
8299 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
8300 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
8301 | |
---|
8302 | clock_t tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0, textra=0; |
---|
8303 | #ifdef TIME_TEST |
---|
8304 | clock_t tinput = clock(); |
---|
8305 | #endif |
---|
8306 | int nsteppert=0, i, nV = currRing->N, nwalk=0, npert_tmp=0; |
---|
8307 | int *npert=(int*)omAlloc(2*nV*sizeof(int)); |
---|
8308 | ideal Gomega, M,F, G1, Gomega1, Gomega2, M1, F1; |
---|
8309 | //ring endRing; |
---|
8310 | ring newRing, oldRing, lpRing; |
---|
8311 | intvec* next_weight; |
---|
8312 | intvec* ivNull = new intvec(nV); //define (0,...,0) |
---|
8313 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
8314 | intvec* iv_lp = Mivlp(nV); //define (1,0,...,0) |
---|
8315 | ideal H0; |
---|
8316 | //ideal H1; |
---|
8317 | ideal H2, Glp; |
---|
8318 | int nGB, endwalks = 0, nwalkpert=0, npertstep=0; |
---|
8319 | intvec* Mlp = MivMatrixOrderlp(nV); |
---|
8320 | intvec* vector_tmp = new intvec(nV); |
---|
8321 | #ifndef BUCHBERGER_ALG |
---|
8322 | intvec* hilb_func; |
---|
8323 | #endif |
---|
8324 | // to avoid (1,0,...,0) as the target vector |
---|
8325 | intvec* last_omega = new intvec(nV); |
---|
8326 | for(i=nV-1; i>0; i--) |
---|
8327 | (*last_omega)[i] = 1; |
---|
8328 | (*last_omega)[0] = 10000; |
---|
8329 | |
---|
8330 | // intvec* extra_curr_weight = new intvec(nV); |
---|
8331 | intvec* target_weight = new intvec(nV); |
---|
8332 | for(i=nV-1; i>=0; i--) |
---|
8333 | (*target_weight)[i] = (*target_tmp)[i]; |
---|
8334 | |
---|
8335 | ring XXRing = currRing; |
---|
8336 | newRing = currRing; |
---|
8337 | |
---|
8338 | to=clock(); |
---|
8339 | // compute a red. GB w.r.t. the help ring |
---|
8340 | if(MivComp(curr_weight, iv_dp) == 1) //rOrdStr(currRing) = "dp" |
---|
8341 | G = MstdCC(G); |
---|
8342 | else |
---|
8343 | { |
---|
8344 | //rOrdStr(currRing) = (a(.c_w..),lp,C) |
---|
8345 | if (rParameter(currRing) != NULL) |
---|
8346 | DefRingPar(curr_weight); |
---|
8347 | else |
---|
8348 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
8349 | G = idrMoveR(G, XXRing,currRing); |
---|
8350 | G = MstdCC(G); |
---|
8351 | } |
---|
8352 | tostd=clock()-to; |
---|
8353 | |
---|
8354 | #ifdef REPRESENTATION_OF_SIGMA |
---|
8355 | ideal Gw = MwalkInitialForm(G, curr_weight); |
---|
8356 | |
---|
8357 | if(islengthpoly2(Gw)==1) |
---|
8358 | { |
---|
8359 | intvec* MDp; |
---|
8360 | if(MivComp(curr_weight, iv_dp) == 1) |
---|
8361 | MDp = MatrixOrderdp(nV); //MivWeightOrderlp(iv_dp); |
---|
8362 | else |
---|
8363 | MDp = MivWeightOrderlp(curr_weight); |
---|
8364 | |
---|
8365 | curr_weight = RepresentationMatrix_Dp(G, MDp); |
---|
8366 | |
---|
8367 | delete MDp; |
---|
8368 | |
---|
8369 | ring exring = currRing; |
---|
8370 | |
---|
8371 | if (rParameter(currRing) != NULL) |
---|
8372 | DefRingPar(curr_weight); |
---|
8373 | else |
---|
8374 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
8375 | to=clock(); |
---|
8376 | Gw = idrMoveR(G, exring,currRing); |
---|
8377 | G = MstdCC(Gw); |
---|
8378 | Gw = NULL; |
---|
8379 | tostd=tostd+clock()-to; |
---|
8380 | //ivString(curr_weight,"rep. sigma"); |
---|
8381 | goto COMPUTE_NEW_VECTOR; |
---|
8382 | } |
---|
8383 | |
---|
8384 | idDelete(&Gw); |
---|
8385 | delete iv_dp; |
---|
8386 | #endif |
---|
8387 | |
---|
8388 | |
---|
8389 | while(1) |
---|
8390 | { |
---|
8391 | to=clock(); |
---|
8392 | /* compute an initial form ideal of <G> w.r.t. "curr_vector" */ |
---|
8393 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
8394 | tif=tif+clock()-to; |
---|
8395 | |
---|
8396 | #ifndef BUCHBERGER_ALG |
---|
8397 | if(isNolVector(curr_weight) == 0) |
---|
8398 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
8399 | else |
---|
8400 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
8401 | #endif // BUCHBERGER_ALG |
---|
8402 | |
---|
8403 | oldRing = currRing; |
---|
8404 | |
---|
8405 | /* define a new ring that its ordering is "(a(curr_weight),lp) */ |
---|
8406 | if (rParameter(currRing) != NULL) |
---|
8407 | DefRingPar(curr_weight); |
---|
8408 | else |
---|
8409 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
8410 | |
---|
8411 | newRing = currRing; |
---|
8412 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
8413 | |
---|
8414 | to=clock(); |
---|
8415 | /* compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" */ |
---|
8416 | #ifdef BUCHBERGER_ALG |
---|
8417 | M = MstdhomCC(Gomega1); |
---|
8418 | #else |
---|
8419 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
8420 | delete hilb_func; |
---|
8421 | #endif // BUCHBERGER_ALG |
---|
8422 | tstd=tstd+clock()-to; |
---|
8423 | |
---|
8424 | /* change the ring to oldRing */ |
---|
8425 | rChangeCurrRing(oldRing); |
---|
8426 | M1 = idrMoveR(M, newRing,currRing); |
---|
8427 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
8428 | |
---|
8429 | to=clock(); |
---|
8430 | /* compute a representation of the generators of submod (M) |
---|
8431 | with respect to those of mod (Gomega). |
---|
8432 | Gomega is a reduced Groebner basis w.r.t. the current ring */ |
---|
8433 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
8434 | tlift=tlift+clock()-to; |
---|
8435 | |
---|
8436 | idDelete(&M1); |
---|
8437 | idDelete(&Gomega2); |
---|
8438 | idDelete(&G); |
---|
8439 | |
---|
8440 | /* change the ring to newRing */ |
---|
8441 | rChangeCurrRing(newRing); |
---|
8442 | F1 = idrMoveR(F, oldRing,currRing); |
---|
8443 | |
---|
8444 | to=clock(); |
---|
8445 | /* reduce the Groebner basis <G> w.r.t. new ring */ |
---|
8446 | G = kInterRedCC(F1, NULL); |
---|
8447 | tred=tred+clock()-to; |
---|
8448 | idDelete(&F1); |
---|
8449 | |
---|
8450 | |
---|
8451 | COMPUTE_NEW_VECTOR: |
---|
8452 | newRing = currRing; |
---|
8453 | nwalk++; |
---|
8454 | nwalkpert++; |
---|
8455 | to=clock(); |
---|
8456 | // compute a next weight vector |
---|
8457 | next_weight = MwalkNextWeightCC(curr_weight,target_weight, G); |
---|
8458 | tnw=tnw+clock()-to; |
---|
8459 | #ifdef PRINT_VECTORS |
---|
8460 | MivString(curr_weight, target_weight, next_weight); |
---|
8461 | #endif |
---|
8462 | |
---|
8463 | /* check whether the computed intermediate weight vector is in |
---|
8464 | the correct cone; sometimes it is very big e.g. s7, cyc7. |
---|
8465 | If it is NOT in the correct cone, then compute directly |
---|
8466 | a reduced Groebner basis with respect to the lexicographic ordering |
---|
8467 | for the known Groebner basis that it is computed in the last step. |
---|
8468 | */ |
---|
8469 | //if(test_w_in_ConeCC(G, next_weight) != 1) |
---|
8470 | if(Overflow_Error == TRUE) |
---|
8471 | { |
---|
8472 | OMEGA_OVERFLOW_TRAN_NEW: |
---|
8473 | //Print("\n// takes %d steps!", nwalk-1); |
---|
8474 | //Print("\n//ring lastRing = %s;", rString(currRing)); |
---|
8475 | #ifdef TEST_OVERFLOW |
---|
8476 | goto BE_FINISH; |
---|
8477 | #endif |
---|
8478 | /* |
---|
8479 | #ifdef CHECK_IDEAL_MWALK |
---|
8480 | idElements(G, "G"); |
---|
8481 | //headidString(G, "G"); |
---|
8482 | #endif |
---|
8483 | */ |
---|
8484 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
8485 | if (rParameter(currRing) != NULL) |
---|
8486 | DefRingParlp(); |
---|
8487 | else |
---|
8488 | VMrDefaultlp(); |
---|
8489 | else |
---|
8490 | if (rParameter(currRing) != NULL) |
---|
8491 | DefRingPar(target_tmp); |
---|
8492 | else |
---|
8493 | rChangeCurrRing(VMrDefault(target_tmp)); |
---|
8494 | |
---|
8495 | lpRing = currRing; |
---|
8496 | G1 = idrMoveR(G, newRing,currRing); |
---|
8497 | |
---|
8498 | to=clock(); |
---|
8499 | /*apply kStd or LastGB to compute a lex. red. Groebner basis of <G>*/ |
---|
8500 | if(nP == 0 || MivSame(target_tmp, iv_lp) == 0){ |
---|
8501 | //Print("\n\n// calls \"std in ring r_%d = %s;", nwalk, rString(currRing)); |
---|
8502 | G = MstdCC(G1);//no result for qnt1 |
---|
8503 | } |
---|
8504 | else { |
---|
8505 | rChangeCurrRing(newRing); |
---|
8506 | G1 = idrMoveR(G1, lpRing,currRing); |
---|
8507 | |
---|
8508 | //Print("\n\n// calls \"LastGB\" (%d) to compute a GB", nV-1); |
---|
8509 | G = LastGB(G1, curr_weight, nV-1); //no result for kats7 |
---|
8510 | |
---|
8511 | rChangeCurrRing(lpRing); |
---|
8512 | G = idrMoveR(G, newRing,currRing); |
---|
8513 | } |
---|
8514 | textra=clock()-to; |
---|
8515 | npert[endwalks]=nwalk-npert_tmp; |
---|
8516 | npert_tmp = nwalk; |
---|
8517 | endwalks ++; |
---|
8518 | break; |
---|
8519 | } |
---|
8520 | |
---|
8521 | /* check whether the computed Groebner basis is really a Groebner basis. |
---|
8522 | If not, we perturb the target vector with the maximal "perturbation" |
---|
8523 | degree.*/ |
---|
8524 | if(MivComp(next_weight, target_weight) == 1 || |
---|
8525 | MivComp(next_weight, curr_weight) == 1 ) |
---|
8526 | { |
---|
8527 | //Print("\n//ring r_%d = %s;", nwalk, rString(currRing)); |
---|
8528 | |
---|
8529 | |
---|
8530 | //compute the number of perturbations and its step |
---|
8531 | npert[endwalks]=nwalk-npert_tmp; |
---|
8532 | npert_tmp = nwalk; |
---|
8533 | |
---|
8534 | endwalks ++; |
---|
8535 | |
---|
8536 | /*it is very important if the walk only uses one step, e.g. Fate, liu*/ |
---|
8537 | if(endwalks == 1 && MivComp(next_weight, curr_weight) == 1){ |
---|
8538 | rChangeCurrRing(XXRing); |
---|
8539 | G = idrMoveR(G, newRing,currRing); |
---|
8540 | goto FINISH; |
---|
8541 | } |
---|
8542 | H0 = id_Head(G,currRing); |
---|
8543 | |
---|
8544 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
8545 | if (rParameter(currRing) != NULL) |
---|
8546 | DefRingParlp(); |
---|
8547 | else |
---|
8548 | VMrDefaultlp(); |
---|
8549 | else |
---|
8550 | if (rParameter(currRing) != NULL) |
---|
8551 | DefRingPar(target_tmp); |
---|
8552 | else |
---|
8553 | rChangeCurrRing(VMrDefault(target_tmp)); |
---|
8554 | |
---|
8555 | lpRing = currRing; |
---|
8556 | Glp = idrMoveR(G, newRing,currRing); |
---|
8557 | H2 = idrMoveR(H0, newRing,currRing); |
---|
8558 | |
---|
8559 | /* Apply Lemma 2.2 in Collart et. al (1997) to check whether |
---|
8560 | cone(k-1) is equal to cone(k) */ |
---|
8561 | nGB = 1; |
---|
8562 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
8563 | { |
---|
8564 | poly t; |
---|
8565 | if((t=pSub(pHead(Glp->m[i]), pCopy(H2->m[i]))) != NULL) |
---|
8566 | { |
---|
8567 | pDelete(&t); |
---|
8568 | idDelete(&H2);//5.5.02 |
---|
8569 | nGB = 0; //i.e. Glp is no reduced Groebner basis |
---|
8570 | break; |
---|
8571 | } |
---|
8572 | pDelete(&t); |
---|
8573 | } |
---|
8574 | |
---|
8575 | idDelete(&H2);//5.5.02 |
---|
8576 | |
---|
8577 | if(nGB == 1) |
---|
8578 | { |
---|
8579 | G = Glp; |
---|
8580 | Glp = NULL; |
---|
8581 | break; |
---|
8582 | } |
---|
8583 | |
---|
8584 | /* perturb the target weight vector, if the vector target_tmp |
---|
8585 | stays in many cones */ |
---|
8586 | poly p; |
---|
8587 | BOOLEAN plength3 = FALSE; |
---|
8588 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
8589 | { |
---|
8590 | p = MpolyInitialForm(Glp->m[i], target_tmp); |
---|
8591 | if(p->next != NULL && |
---|
8592 | p->next->next != NULL && |
---|
8593 | p->next->next->next != NULL) |
---|
8594 | { |
---|
8595 | Overflow_Error = FALSE; |
---|
8596 | |
---|
8597 | for(i=0; i<nV; i++) |
---|
8598 | (*vector_tmp)[i] = (*target_weight)[i]; |
---|
8599 | |
---|
8600 | delete target_weight; |
---|
8601 | target_weight = MPertVectors(Glp, Mlp, nV); |
---|
8602 | |
---|
8603 | if(MivComp(vector_tmp, target_weight)==1) |
---|
8604 | { |
---|
8605 | //PrintS("\n// The old and new representaion vector are the same!!"); |
---|
8606 | G = Glp; |
---|
8607 | newRing = currRing; |
---|
8608 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
8609 | } |
---|
8610 | |
---|
8611 | if(Overflow_Error == TRUE) |
---|
8612 | { |
---|
8613 | rChangeCurrRing(newRing); |
---|
8614 | G = idrMoveR(Glp, lpRing,currRing); |
---|
8615 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
8616 | } |
---|
8617 | |
---|
8618 | plength3 = TRUE; |
---|
8619 | pDelete(&p); |
---|
8620 | break; |
---|
8621 | } |
---|
8622 | pDelete(&p); |
---|
8623 | } |
---|
8624 | |
---|
8625 | if(plength3 == FALSE) |
---|
8626 | { |
---|
8627 | rChangeCurrRing(newRing); |
---|
8628 | G = idrMoveR(Glp, lpRing,currRing); |
---|
8629 | goto TRAN_LIFTING; |
---|
8630 | } |
---|
8631 | |
---|
8632 | |
---|
8633 | npertstep = nwalk; |
---|
8634 | nwalkpert = 1; |
---|
8635 | nsteppert ++; |
---|
8636 | |
---|
8637 | /* |
---|
8638 | Print("\n// Subroutine needs (%d) steps.", nwalk); |
---|
8639 | idElements(Glp, "last G in walk:"); |
---|
8640 | PrintS("\n// ****************************************"); |
---|
8641 | Print("\n// Perturb the original target vector (%d): ", nsteppert); |
---|
8642 | ivString(target_weight, "new target"); |
---|
8643 | PrintS("\n// ****************************************\n"); |
---|
8644 | */ |
---|
8645 | rChangeCurrRing(newRing); |
---|
8646 | G = idrMoveR(Glp, lpRing,currRing); |
---|
8647 | |
---|
8648 | delete next_weight; |
---|
8649 | |
---|
8650 | //Print("\n// ring rNEW = %s;", rString(currRing)); |
---|
8651 | goto COMPUTE_NEW_VECTOR; |
---|
8652 | } |
---|
8653 | |
---|
8654 | TRAN_LIFTING: |
---|
8655 | for(i=nV-1; i>=0; i--) |
---|
8656 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
8657 | |
---|
8658 | delete next_weight; |
---|
8659 | }//while |
---|
8660 | #ifdef TEST_OVERFLOW |
---|
8661 | BE_FINISH: |
---|
8662 | #endif |
---|
8663 | rChangeCurrRing(XXRing); |
---|
8664 | G = idrMoveR(G, lpRing,currRing); |
---|
8665 | |
---|
8666 | FINISH: |
---|
8667 | delete ivNull; |
---|
8668 | delete next_weight; |
---|
8669 | delete iv_lp; |
---|
8670 | omFree(npert); |
---|
8671 | /* |
---|
8672 | #ifdef TIME_TEST |
---|
8673 | Print("\n// Computation took %d steps and %.2f sec", |
---|
8674 | nwalk, ((double) (clock()-mtim)/1000000)); |
---|
8675 | |
---|
8676 | TimeStringFractal(tinput, tostd, tif, tstd, textra, tlift, tred, tnw); |
---|
8677 | |
---|
8678 | // Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
8679 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
8680 | #endif |
---|
8681 | */ |
---|
8682 | return(G); |
---|
8683 | } |
---|
8684 | |
---|
8685 | #if 0 |
---|
8686 | /******************************************************* |
---|
8687 | * Tran's algorithm with random element * |
---|
8688 | * * |
---|
8689 | * use kStd, if nP = 0, else call Ab_Rec_Pert (LastGB) * |
---|
8690 | *******************************************************/ |
---|
8691 | ideal TranMrImprovwalk(ideal G,intvec* curr_weight,intvec* target_tmp, int nP, int weight_rad, int pert_deg) |
---|
8692 | { |
---|
8693 | #ifdef TIME_TEST |
---|
8694 | clock_t mtim = clock(); |
---|
8695 | #endif |
---|
8696 | Set_Error(FALSE ); |
---|
8697 | Overflow_Error = FALSE; |
---|
8698 | //Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
8699 | //Print("\n// ring ro = %s;", rString(currRing)); |
---|
8700 | |
---|
8701 | clock_t tostd, tif=0, tstd=0, tlift=0, tred=0, tnw=0, textra=0; |
---|
8702 | #ifdef TIME_TEST |
---|
8703 | clock_t tinput = clock(); |
---|
8704 | #endif |
---|
8705 | int nsteppert=0, i, nV = currRing->N, nwalk=0, npert_tmp=0; |
---|
8706 | int *npert=(int*)omAlloc(2*nV*sizeof(int)); |
---|
8707 | ideal Gomega, M,F, G1, Gomega1, Gomega2, M1, F1; |
---|
8708 | //ring endRing; |
---|
8709 | ring newRing, oldRing, lpRing; |
---|
8710 | intvec* next_weight; |
---|
8711 | intvec* ivNull = new intvec(nV); //define (0,...,0) |
---|
8712 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
8713 | intvec* iv_lp = Mivlp(nV); //define (1,0,...,0) |
---|
8714 | ideal H0; |
---|
8715 | //ideal H1; |
---|
8716 | ideal H2, Glp; |
---|
8717 | int weight_norm, nGB, endwalks = 0, nwalkpert=0, npertstep=0; |
---|
8718 | intvec* Mlp = MivMatrixOrderlp(nV); |
---|
8719 | intvec* vector_tmp = new intvec(nV); |
---|
8720 | #ifndef BUCHBERGER_ALG |
---|
8721 | intvec* hilb_func; |
---|
8722 | #endif |
---|
8723 | // to avoid (1,0,...,0) as the target vector |
---|
8724 | intvec* last_omega = new intvec(nV); |
---|
8725 | for(i=nV-1; i>0; i--) |
---|
8726 | { |
---|
8727 | (*last_omega)[i] = 1; |
---|
8728 | } |
---|
8729 | (*last_omega)[0] = 10000; |
---|
8730 | |
---|
8731 | //intvec* extra_curr_weight = new intvec(nV); |
---|
8732 | intvec* target_weight = new intvec(nV); |
---|
8733 | for(i=nV-1; i>=0; i--) |
---|
8734 | { |
---|
8735 | (*target_weight)[i] = (*target_tmp)[i]; |
---|
8736 | } |
---|
8737 | ring XXRing = currRing; |
---|
8738 | newRing = currRing; |
---|
8739 | |
---|
8740 | to=clock(); |
---|
8741 | // compute a red. GB w.r.t. the help ring |
---|
8742 | if(MivComp(curr_weight, iv_dp) == 1) |
---|
8743 | { |
---|
8744 | //rOrdStr(currRing) = "dp" |
---|
8745 | G = MstdCC(G); |
---|
8746 | } |
---|
8747 | else |
---|
8748 | { |
---|
8749 | //rOrdStr(currRing) = (a(.c_w..),lp,C) |
---|
8750 | if (rParameter(currRing) != NULL) |
---|
8751 | { |
---|
8752 | DefRingPar(curr_weight); |
---|
8753 | } |
---|
8754 | else |
---|
8755 | { |
---|
8756 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
8757 | } |
---|
8758 | G = idrMoveR(G, XXRing,currRing); |
---|
8759 | G = MstdCC(G); |
---|
8760 | } |
---|
8761 | tostd=clock()-to; |
---|
8762 | |
---|
8763 | #ifdef REPRESENTATION_OF_SIGMA |
---|
8764 | ideal Gw = MwalkInitialForm(G, curr_weight); |
---|
8765 | |
---|
8766 | if(islengthpoly2(Gw)==1) |
---|
8767 | { |
---|
8768 | intvec* MDp; |
---|
8769 | if(MivComp(curr_weight, iv_dp) == 1) |
---|
8770 | { |
---|
8771 | MDp = MatrixOrderdp(nV); //MivWeightOrderlp(iv_dp); |
---|
8772 | } |
---|
8773 | else |
---|
8774 | { |
---|
8775 | MDp = MivWeightOrderlp(curr_weight); |
---|
8776 | } |
---|
8777 | curr_weight = RepresentationMatrix_Dp(G, MDp); |
---|
8778 | |
---|
8779 | delete MDp; |
---|
8780 | |
---|
8781 | ring exring = currRing; |
---|
8782 | |
---|
8783 | if (rParameter(currRing) != NULL) |
---|
8784 | { |
---|
8785 | DefRingPar(curr_weight); |
---|
8786 | } |
---|
8787 | else |
---|
8788 | { |
---|
8789 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
8790 | } |
---|
8791 | to=clock(); |
---|
8792 | Gw = idrMoveR(G, exring,currRing); |
---|
8793 | G = MstdCC(Gw); |
---|
8794 | Gw = NULL; |
---|
8795 | tostd=tostd+clock()-to; |
---|
8796 | //ivString(curr_weight,"rep. sigma"); |
---|
8797 | goto COMPUTE_NEW_VECTOR; |
---|
8798 | } |
---|
8799 | |
---|
8800 | idDelete(&Gw); |
---|
8801 | delete iv_dp; |
---|
8802 | #endif |
---|
8803 | |
---|
8804 | |
---|
8805 | while(1) |
---|
8806 | { |
---|
8807 | to=clock(); |
---|
8808 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
8809 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
8810 | tif=tif+clock()-to; |
---|
8811 | |
---|
8812 | #ifndef BUCHBERGER_ALG |
---|
8813 | if(isNolVector(curr_weight) == 0) |
---|
8814 | { |
---|
8815 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
8816 | } |
---|
8817 | else |
---|
8818 | { |
---|
8819 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
8820 | } |
---|
8821 | #endif // BUCHBERGER_ALG |
---|
8822 | |
---|
8823 | oldRing = currRing; |
---|
8824 | |
---|
8825 | // define a new ring with ordering "(a(curr_weight),lp) |
---|
8826 | if (rParameter(currRing) != NULL) |
---|
8827 | { |
---|
8828 | DefRingPar(curr_weight); |
---|
8829 | } |
---|
8830 | else |
---|
8831 | { |
---|
8832 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
8833 | } |
---|
8834 | newRing = currRing; |
---|
8835 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
8836 | |
---|
8837 | to=clock(); |
---|
8838 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
8839 | #ifdef BUCHBERGER_ALG |
---|
8840 | M = MstdhomCC(Gomega1); |
---|
8841 | #else |
---|
8842 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
8843 | delete hilb_func; |
---|
8844 | #endif |
---|
8845 | tstd=tstd+clock()-to; |
---|
8846 | |
---|
8847 | // change the ring to oldRing |
---|
8848 | rChangeCurrRing(oldRing); |
---|
8849 | M1 = idrMoveR(M, newRing,currRing); |
---|
8850 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
8851 | |
---|
8852 | to=clock(); |
---|
8853 | // compute a representation of the generators of submod (M) with respect to those of mod (Gomega). |
---|
8854 | // Gomega is a reduced Groebner basis w.r.t. the current ring |
---|
8855 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
8856 | tlift=tlift+clock()-to; |
---|
8857 | |
---|
8858 | idDelete(&M1); |
---|
8859 | idDelete(&Gomega2); |
---|
8860 | idDelete(&G); |
---|
8861 | |
---|
8862 | // change the ring to newRing |
---|
8863 | rChangeCurrRing(newRing); |
---|
8864 | F1 = idrMoveR(F, oldRing,currRing); |
---|
8865 | |
---|
8866 | to=clock(); |
---|
8867 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
8868 | G = kInterRedCC(F1, NULL); |
---|
8869 | tred=tred+clock()-to; |
---|
8870 | idDelete(&F1); |
---|
8871 | |
---|
8872 | COMPUTE_NEW_VECTOR: |
---|
8873 | newRing = currRing; |
---|
8874 | nwalk++; |
---|
8875 | nwalkpert++; |
---|
8876 | to=clock(); |
---|
8877 | // compute a next weight vector |
---|
8878 | //next_weight = MwalkNextWeightCC(curr_weight,target_weight, G); |
---|
8879 | next_weight = MWalkRandomNextWeight(G, curr_weight, target_weight, weight_rad, pert_deg); |
---|
8880 | /* |
---|
8881 | next_weight = MkInterRedNextWeight(curr_weight,target_weight,G); |
---|
8882 | |
---|
8883 | if(MivComp(next_weight, target_weight) != 1) |
---|
8884 | { |
---|
8885 | // compute a perturbed next weight vector "next_weight1" |
---|
8886 | intvec* next_weight1 = MkInterRedNextWeight(MPertVectors(G, MivMatrixOrder(curr_weight), pert_deg), target_weight, G); |
---|
8887 | |
---|
8888 | // compare next_weight and next_weight1 |
---|
8889 | ideal G_test = MwalkInitialForm(G, next_weight); |
---|
8890 | ideal G_test1 = MwalkInitialForm(G, next_weight1); |
---|
8891 | if(IDELEMS(G_test1) <= IDELEMS(G_test)) |
---|
8892 | { |
---|
8893 | next_weight = ivCopy(next_weight1); |
---|
8894 | } |
---|
8895 | delete next_weight1; |
---|
8896 | // compute a random next weight vector "next_weight2" |
---|
8897 | intvec* next_weight22 = ivCopy(target_weight); |
---|
8898 | // Print("\n// size of target_weight = %d", sizeof((*target_weight))); |
---|
8899 | k = 0; |
---|
8900 | |
---|
8901 | while(test_w_in_ConeCC(G, next_weight22) == 0 && k < 11) |
---|
8902 | { |
---|
8903 | k++; |
---|
8904 | if(k>10) |
---|
8905 | { |
---|
8906 | break; |
---|
8907 | } |
---|
8908 | weight_norm = 0; |
---|
8909 | while(weight_norm == 0) |
---|
8910 | { |
---|
8911 | for(i=nV-1; i>=0; i--) |
---|
8912 | { |
---|
8913 | // Print("\n// next_weight[%d] = %d", i, (*next_weight)[i]); |
---|
8914 | (*next_weight22)[i] = rand() % 60000 - 30000; |
---|
8915 | weight_norm = weight_norm + (*next_weight22)[i]*(*next_weight22)[i]; |
---|
8916 | } |
---|
8917 | weight_norm = 1 + floor(sqrt(weight_norm)); |
---|
8918 | } |
---|
8919 | for(i=nV-1; i>=0; i--) |
---|
8920 | { |
---|
8921 | if((*next_weight22)[i] < 0) |
---|
8922 | { |
---|
8923 | (*next_weight22)[i] = 1 + (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm); |
---|
8924 | } |
---|
8925 | else |
---|
8926 | { |
---|
8927 | (*next_weight22)[i] = (*curr_weight)[i] + floor(weight_rad*(*next_weight22)[i]/weight_norm); |
---|
8928 | } |
---|
8929 | // Print("\n// next_weight22[%d] = %d", i, (*next_weight22)[i]); |
---|
8930 | } |
---|
8931 | } |
---|
8932 | |
---|
8933 | if(test_w_in_ConeCC(G, next_weight22) == 1) |
---|
8934 | { |
---|
8935 | // compare next_weight and next_weight2 |
---|
8936 | // Print("\n// ZUFALL IM KEGEL"); |
---|
8937 | intvec* next_weight2 = MkInterRedNextWeight(next_weight22, target_weight, G); |
---|
8938 | |
---|
8939 | ideal G_test2 = MwalkInitialForm(G, next_weight2); |
---|
8940 | if(IDELEMS(G_test2) <= IDELEMS(G_test)) |
---|
8941 | { |
---|
8942 | if(IDELEMS(G_test2) <= IDELEMS(G_test1)) |
---|
8943 | { |
---|
8944 | // Print("\n// ZUFALL BENUTZT!\n"); |
---|
8945 | next_weight = ivCopy(next_weight2); |
---|
8946 | } |
---|
8947 | } |
---|
8948 | idDelete(&G_test2); |
---|
8949 | delete next_weight2; |
---|
8950 | } |
---|
8951 | delete next_weight22; |
---|
8952 | idDelete(&G_test); |
---|
8953 | idDelete(&G_test1); |
---|
8954 | }*/ |
---|
8955 | |
---|
8956 | tnw=tnw+clock()-to; |
---|
8957 | #ifdef PRINT_VECTORS |
---|
8958 | MivString(curr_weight, target_weight, next_weight); |
---|
8959 | #endif |
---|
8960 | |
---|
8961 | /* check whether the computed intermediate weight vector is in |
---|
8962 | the correct cone; sometimes it is very big e.g. s7, cyc7. |
---|
8963 | If it is NOT in the correct cone, then compute directly |
---|
8964 | a reduced Groebner basis with respect to the lexicographic ordering |
---|
8965 | for the known Groebner basis that it is computed in the last step. |
---|
8966 | */ |
---|
8967 | //if(test_w_in_ConeCC(G, next_weight) != 1) |
---|
8968 | if(Overflow_Error == TRUE) |
---|
8969 | { |
---|
8970 | OMEGA_OVERFLOW_TRAN_NEW: |
---|
8971 | //Print("\n// takes %d steps!", nwalk-1); |
---|
8972 | //Print("\n//ring lastRing = %s;", rString(currRing)); |
---|
8973 | #ifdef TEST_OVERFLOW |
---|
8974 | goto BE_FINISH; |
---|
8975 | #endif |
---|
8976 | |
---|
8977 | #ifdef CHECK_IDEAL_MWALK |
---|
8978 | idElements(G, "G"); |
---|
8979 | //headidString(G, "G"); |
---|
8980 | #endif |
---|
8981 | |
---|
8982 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
8983 | { |
---|
8984 | if (rParameter(currRing) != NULL) |
---|
8985 | { |
---|
8986 | DefRingParlp(); |
---|
8987 | } |
---|
8988 | else |
---|
8989 | { |
---|
8990 | VMrDefaultlp(); |
---|
8991 | } |
---|
8992 | } |
---|
8993 | else |
---|
8994 | { |
---|
8995 | if (rParameter(currRing) != NULL) |
---|
8996 | { |
---|
8997 | DefRingPar(target_tmp); |
---|
8998 | } |
---|
8999 | else |
---|
9000 | { |
---|
9001 | rChangeCurrRing(VMrDefault(target_tmp)); |
---|
9002 | } |
---|
9003 | } |
---|
9004 | lpRing = currRing; |
---|
9005 | G1 = idrMoveR(G, newRing,currRing); |
---|
9006 | |
---|
9007 | to=clock(); |
---|
9008 | // apply kStd or LastGB to compute a lex. red. Groebner basis of <G> |
---|
9009 | if(nP == 0 || MivSame(target_tmp, iv_lp) == 0) |
---|
9010 | { |
---|
9011 | //Print("\n\n// calls \"std in ring r_%d = %s;", nwalk, rString(currRing)); |
---|
9012 | G = MstdCC(G1);//no result for qnt1 |
---|
9013 | } |
---|
9014 | else |
---|
9015 | { |
---|
9016 | rChangeCurrRing(newRing); |
---|
9017 | G1 = idrMoveR(G1, lpRing,currRing); |
---|
9018 | |
---|
9019 | //Print("\n\n// calls \"LastGB\" (%d) to compute a GB", nV-1); |
---|
9020 | G = LastGB(G1, curr_weight, nV-1); //no result for kats7 |
---|
9021 | |
---|
9022 | rChangeCurrRing(lpRing); |
---|
9023 | G = idrMoveR(G, newRing,currRing); |
---|
9024 | } |
---|
9025 | textra=clock()-to; |
---|
9026 | npert[endwalks]=nwalk-npert_tmp; |
---|
9027 | npert_tmp = nwalk; |
---|
9028 | endwalks ++; |
---|
9029 | break; |
---|
9030 | } |
---|
9031 | |
---|
9032 | // check whether the computed Groebner basis is really a Groebner basis. |
---|
9033 | // If not, we perturb the target vector with the maximal "perturbation" degree. |
---|
9034 | |
---|
9035 | if(MivComp(next_weight, target_weight) == 1 || MivComp(next_weight, curr_weight) == 1 ) |
---|
9036 | { |
---|
9037 | //Print("\n//ring r_%d = %s;", nwalk, rString(currRing)); |
---|
9038 | |
---|
9039 | |
---|
9040 | //compute the number of perturbations and its step |
---|
9041 | npert[endwalks]=nwalk-npert_tmp; |
---|
9042 | npert_tmp = nwalk; |
---|
9043 | |
---|
9044 | endwalks ++; |
---|
9045 | |
---|
9046 | // it is very important if the walk only uses one step, e.g. Fate, liu |
---|
9047 | if(endwalks == 1 && MivComp(next_weight, curr_weight) == 1) |
---|
9048 | { |
---|
9049 | rChangeCurrRing(XXRing); |
---|
9050 | G = idrMoveR(G, newRing,currRing); |
---|
9051 | goto FINISH; |
---|
9052 | } |
---|
9053 | H0 = id_Head(G,currRing); |
---|
9054 | |
---|
9055 | if(MivSame(target_tmp, iv_lp) == 1) |
---|
9056 | { |
---|
9057 | if (rParameter(currRing) != NULL) |
---|
9058 | { |
---|
9059 | DefRingParlp(); |
---|
9060 | } |
---|
9061 | else |
---|
9062 | { |
---|
9063 | VMrDefaultlp(); |
---|
9064 | } |
---|
9065 | } |
---|
9066 | else |
---|
9067 | { |
---|
9068 | if (rParameter(currRing) != NULL) |
---|
9069 | { |
---|
9070 | DefRingPar(target_tmp); |
---|
9071 | } |
---|
9072 | else |
---|
9073 | { |
---|
9074 | rChangeCurrRing(VMrDefault(target_tmp)); |
---|
9075 | } |
---|
9076 | } |
---|
9077 | lpRing = currRing; |
---|
9078 | Glp = idrMoveR(G, newRing,currRing); |
---|
9079 | H2 = idrMoveR(H0, newRing,currRing); |
---|
9080 | |
---|
9081 | // Apply Lemma 2.2 in Collart et. al (1997) to check whether cone(k-1) is equal to cone(k) |
---|
9082 | nGB = 1; |
---|
9083 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
9084 | { |
---|
9085 | poly t; |
---|
9086 | if((t=pSub(pHead(Glp->m[i]), pCopy(H2->m[i]))) != NULL) |
---|
9087 | { |
---|
9088 | pDelete(&t); |
---|
9089 | idDelete(&H2);//5.5.02 |
---|
9090 | nGB = 0; //i.e. Glp is no reduced Groebner basis |
---|
9091 | break; |
---|
9092 | } |
---|
9093 | pDelete(&t); |
---|
9094 | } |
---|
9095 | |
---|
9096 | idDelete(&H2);//5.5.02 |
---|
9097 | |
---|
9098 | if(nGB == 1) |
---|
9099 | { |
---|
9100 | G = Glp; |
---|
9101 | Glp = NULL; |
---|
9102 | break; |
---|
9103 | } |
---|
9104 | |
---|
9105 | // perturb the target weight vector, if the vector target_tmp stays in many cones |
---|
9106 | poly p; |
---|
9107 | BOOLEAN plength3 = FALSE; |
---|
9108 | for(i=IDELEMS(Glp)-1; i>=0; i--) |
---|
9109 | { |
---|
9110 | p = MpolyInitialForm(Glp->m[i], target_tmp); |
---|
9111 | if(p->next != NULL && |
---|
9112 | p->next->next != NULL && |
---|
9113 | p->next->next->next != NULL) |
---|
9114 | { |
---|
9115 | Overflow_Error = FALSE; |
---|
9116 | |
---|
9117 | for(i=0; i<nV; i++) |
---|
9118 | { |
---|
9119 | (*vector_tmp)[i] = (*target_weight)[i]; |
---|
9120 | } |
---|
9121 | delete target_weight; |
---|
9122 | target_weight = MPertVectors(Glp, Mlp, nV); |
---|
9123 | |
---|
9124 | if(MivComp(vector_tmp, target_weight)==1) |
---|
9125 | { |
---|
9126 | //PrintS("\n// The old and new representaion vector are the same!!"); |
---|
9127 | G = Glp; |
---|
9128 | newRing = currRing; |
---|
9129 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
9130 | } |
---|
9131 | |
---|
9132 | if(Overflow_Error == TRUE) |
---|
9133 | { |
---|
9134 | rChangeCurrRing(newRing); |
---|
9135 | G = idrMoveR(Glp, lpRing,currRing); |
---|
9136 | goto OMEGA_OVERFLOW_TRAN_NEW; |
---|
9137 | } |
---|
9138 | |
---|
9139 | plength3 = TRUE; |
---|
9140 | pDelete(&p); |
---|
9141 | break; |
---|
9142 | } |
---|
9143 | pDelete(&p); |
---|
9144 | } |
---|
9145 | |
---|
9146 | if(plength3 == FALSE) |
---|
9147 | { |
---|
9148 | rChangeCurrRing(newRing); |
---|
9149 | G = idrMoveR(Glp, lpRing,currRing); |
---|
9150 | goto TRAN_LIFTING; |
---|
9151 | } |
---|
9152 | |
---|
9153 | |
---|
9154 | npertstep = nwalk; |
---|
9155 | nwalkpert = 1; |
---|
9156 | nsteppert ++; |
---|
9157 | |
---|
9158 | /* |
---|
9159 | Print("\n// Subroutine needs (%d) steps.", nwalk); |
---|
9160 | idElements(Glp, "last G in walk:"); |
---|
9161 | PrintS("\n// ****************************************"); |
---|
9162 | Print("\n// Perturb the original target vector (%d): ", nsteppert); |
---|
9163 | ivString(target_weight, "new target"); |
---|
9164 | PrintS("\n// ****************************************\n"); |
---|
9165 | */ |
---|
9166 | rChangeCurrRing(newRing); |
---|
9167 | G = idrMoveR(Glp, lpRing,currRing); |
---|
9168 | |
---|
9169 | delete next_weight; |
---|
9170 | |
---|
9171 | //Print("\n// ring rNEW = %s;", rString(currRing)); |
---|
9172 | goto COMPUTE_NEW_VECTOR; |
---|
9173 | } |
---|
9174 | |
---|
9175 | TRAN_LIFTING: |
---|
9176 | for(i=nV-1; i>=0; i--) |
---|
9177 | { |
---|
9178 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
9179 | } |
---|
9180 | delete next_weight; |
---|
9181 | } // end of while |
---|
9182 | #ifdef TEST_OVERFLOW |
---|
9183 | BE_FINISH: |
---|
9184 | #endif |
---|
9185 | rChangeCurrRing(XXRing); |
---|
9186 | G = idrMoveR(G, lpRing,currRing); |
---|
9187 | |
---|
9188 | FINISH: |
---|
9189 | delete ivNull; |
---|
9190 | delete next_weight; |
---|
9191 | delete iv_lp; |
---|
9192 | omFree(npert); |
---|
9193 | |
---|
9194 | #ifdef TIME_TEST |
---|
9195 | Print("\n// Computation took %d steps and %.2f sec", nwalk, ((double) (clock()-mtim)/1000000)); |
---|
9196 | |
---|
9197 | TimeStringFractal(tinput, tostd, tif, tstd, textra, tlift, tred, tnw); |
---|
9198 | |
---|
9199 | Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
9200 | Print("\n// Overflow_Error? (%d)\n", Overflow_Error); |
---|
9201 | #endif |
---|
9202 | |
---|
9203 | return(G); |
---|
9204 | } |
---|
9205 | #endif |
---|
9206 | |
---|
9207 | /***************************************************************** |
---|
9208 | * compute the reduced Groebner basis of an ideal <Go> w.r.t. lp * |
---|
9209 | *****************************************************************/ |
---|
9210 | static ideal Mpwalk_MAltwalk1(ideal Go, intvec* curr_weight, int tp_deg) |
---|
9211 | { |
---|
9212 | Overflow_Error = FALSE; |
---|
9213 | // BOOLEAN nOverflow_Error = FALSE; |
---|
9214 | clock_t tproc=0; |
---|
9215 | clock_t tinput=clock(); |
---|
9216 | int i, nV = currRing->N; |
---|
9217 | |
---|
9218 | //check that perturbation degree is valid |
---|
9219 | if(tp_deg < 1 || tp_deg > nV) |
---|
9220 | { |
---|
9221 | Werror("Invalid perturbation degree.\n"); |
---|
9222 | return NULL; |
---|
9223 | } |
---|
9224 | |
---|
9225 | int nwalk=0, endwalks=0, ntestwinC=1; |
---|
9226 | int tp_deg_tmp = tp_deg; |
---|
9227 | ideal Gomega, M, F, G, M1, F1, Gomega1, Gomega2, G1; |
---|
9228 | ring newRing, oldRing, TargetRing; |
---|
9229 | intvec* next_weight; |
---|
9230 | intvec* ivNull = new intvec(nV); |
---|
9231 | |
---|
9232 | ring YXXRing = currRing; |
---|
9233 | |
---|
9234 | intvec* iv_M_dpp = MivMatrixOrderlp(nV); |
---|
9235 | intvec* target_weight;// = Mivlp(nV); |
---|
9236 | ideal ssG; |
---|
9237 | |
---|
9238 | // perturb the target vector |
---|
9239 | while(1) |
---|
9240 | { |
---|
9241 | if(Overflow_Error == FALSE) |
---|
9242 | { |
---|
9243 | if (rParameter(currRing) != NULL) |
---|
9244 | { |
---|
9245 | DefRingParlp(); |
---|
9246 | } |
---|
9247 | else |
---|
9248 | { |
---|
9249 | VMrDefaultlp(); |
---|
9250 | } |
---|
9251 | TargetRing = currRing; |
---|
9252 | ssG = idrMoveR(Go,YXXRing,currRing); |
---|
9253 | } |
---|
9254 | Overflow_Error = FALSE; |
---|
9255 | if(tp_deg != 1) |
---|
9256 | { |
---|
9257 | target_weight = MPertVectors(ssG, iv_M_dpp, tp_deg); |
---|
9258 | } |
---|
9259 | else |
---|
9260 | { |
---|
9261 | target_weight = Mivlp(nV); |
---|
9262 | break; |
---|
9263 | } |
---|
9264 | if(Overflow_Error == FALSE) |
---|
9265 | { |
---|
9266 | break; |
---|
9267 | } |
---|
9268 | Overflow_Error = TRUE; |
---|
9269 | tp_deg --; |
---|
9270 | } |
---|
9271 | if(tp_deg != tp_deg_tmp) |
---|
9272 | { |
---|
9273 | Overflow_Error = TRUE; |
---|
9274 | //nOverflow_Error = TRUE; |
---|
9275 | } |
---|
9276 | |
---|
9277 | // Print("\n// tp_deg = %d", tp_deg); |
---|
9278 | // ivString(target_weight, "pert target"); |
---|
9279 | |
---|
9280 | delete iv_M_dpp; |
---|
9281 | #ifndef BUCHBERGER_ALG |
---|
9282 | intvec* hilb_func; |
---|
9283 | #endif |
---|
9284 | // to avoid (1,0,...,0) as the target vector |
---|
9285 | intvec* last_omega = new intvec(nV); |
---|
9286 | for(i=nV-1; i>0; i--) |
---|
9287 | { |
---|
9288 | (*last_omega)[i] = 1; |
---|
9289 | } |
---|
9290 | (*last_omega)[0] = 10000; |
---|
9291 | |
---|
9292 | rChangeCurrRing(YXXRing); |
---|
9293 | G = idrMoveR(ssG, TargetRing,currRing); |
---|
9294 | |
---|
9295 | while(1) |
---|
9296 | { |
---|
9297 | nwalk ++; |
---|
9298 | nstep ++; |
---|
9299 | |
---|
9300 | if(nwalk==1) |
---|
9301 | { |
---|
9302 | goto FIRST_STEP; |
---|
9303 | } |
---|
9304 | to=clock(); |
---|
9305 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
9306 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
9307 | xtif=xtif+clock()-to; |
---|
9308 | |
---|
9309 | #ifndef BUCHBERGER_ALG |
---|
9310 | if(isNolVector(curr_weight) == 0) |
---|
9311 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
9312 | else |
---|
9313 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
9314 | #endif |
---|
9315 | |
---|
9316 | oldRing = currRing; |
---|
9317 | |
---|
9318 | // define a new ring that its ordering is "(a(curr_weight),lp) |
---|
9319 | if (rParameter(currRing) != NULL) |
---|
9320 | { |
---|
9321 | DefRingPar(curr_weight); |
---|
9322 | } |
---|
9323 | else |
---|
9324 | { |
---|
9325 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
9326 | } |
---|
9327 | newRing = currRing; |
---|
9328 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
9329 | /* |
---|
9330 | #ifdef ENDWALKS |
---|
9331 | if(endwalks == 1) |
---|
9332 | { |
---|
9333 | Print("\n// it is %d-th step!!", nwalk); |
---|
9334 | idString(Gomega1, "Gw"); |
---|
9335 | PrintS("\n// compute a rGB of Gw:"); |
---|
9336 | } |
---|
9337 | #endif |
---|
9338 | */ |
---|
9339 | to=clock(); |
---|
9340 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
9341 | #ifdef BUCHBERGER_ALG |
---|
9342 | M = MstdhomCC(Gomega1); |
---|
9343 | #else |
---|
9344 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
9345 | delete hilb_func; |
---|
9346 | #endif // BUCHBERGER_ALG |
---|
9347 | xtstd=xtstd+clock()-to; |
---|
9348 | |
---|
9349 | // change the ring to oldRing |
---|
9350 | rChangeCurrRing(oldRing); |
---|
9351 | M1 = idrMoveR(M, newRing,currRing); |
---|
9352 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
9353 | to=clock(); |
---|
9354 | |
---|
9355 | // if(endwalks == 1){PrintS("\n// Lifting is still working:");} |
---|
9356 | |
---|
9357 | // compute a reduced Groebner basis of <G> w.r.t. "newRing" by the lifting process |
---|
9358 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
9359 | xtlift=xtlift+clock()-to; |
---|
9360 | |
---|
9361 | idDelete(&M1); |
---|
9362 | idDelete(&Gomega2); |
---|
9363 | idDelete(&G); |
---|
9364 | |
---|
9365 | // change the ring to newRing |
---|
9366 | rChangeCurrRing(newRing); |
---|
9367 | F1 = idrMoveR(F, oldRing,currRing); |
---|
9368 | to=clock(); |
---|
9369 | //if(endwalks == 1){ PrintS("\n// InterRed is still working:");} |
---|
9370 | // reduce the Groebner basis <G> w.r.t. the new ring |
---|
9371 | G = kInterRedCC(F1, NULL); |
---|
9372 | xtred=xtred+clock()-to; |
---|
9373 | idDelete(&F1); |
---|
9374 | |
---|
9375 | if(endwalks == 1) |
---|
9376 | break; |
---|
9377 | |
---|
9378 | FIRST_STEP: |
---|
9379 | Overflow_Error=FALSE; |
---|
9380 | to=clock(); |
---|
9381 | // compute a next weight vector |
---|
9382 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
9383 | xtnw=xtnw+clock()-to; |
---|
9384 | #ifdef PRINT_VECTORS |
---|
9385 | MivString(curr_weight, target_weight, next_weight); |
---|
9386 | #endif |
---|
9387 | |
---|
9388 | if(Overflow_Error == TRUE) |
---|
9389 | { |
---|
9390 | delete next_weight; |
---|
9391 | if(tp_deg > 1){ |
---|
9392 | //nOverflow_Error = Overflow_Error; |
---|
9393 | tproc = tproc+clock()-tinput; |
---|
9394 | //Print("\n// A subroutine takes %d steps and calls \"Mpwalk\" (1,%d):", nwalk, tp_deg-1); |
---|
9395 | G1 = Mpwalk_MAltwalk1(G, curr_weight, tp_deg-1); |
---|
9396 | goto MPW_Finish; |
---|
9397 | } |
---|
9398 | else { |
---|
9399 | newRing = currRing; |
---|
9400 | ntestwinC = 0; |
---|
9401 | break; |
---|
9402 | } |
---|
9403 | } |
---|
9404 | |
---|
9405 | if(MivComp(next_weight, ivNull) == 1) |
---|
9406 | { |
---|
9407 | newRing = currRing; |
---|
9408 | delete next_weight; |
---|
9409 | break; |
---|
9410 | } |
---|
9411 | if(MivComp(next_weight, target_weight) == 1) |
---|
9412 | { |
---|
9413 | endwalks = 1; |
---|
9414 | } |
---|
9415 | for(i=nV-1; i>=0; i--) |
---|
9416 | { |
---|
9417 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
9418 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
9419 | } |
---|
9420 | delete next_weight; |
---|
9421 | }//while |
---|
9422 | |
---|
9423 | // check whether the pertubed target vector is correct |
---|
9424 | |
---|
9425 | //define and execute ring with lex. order |
---|
9426 | if (rParameter(currRing) != NULL) |
---|
9427 | { |
---|
9428 | DefRingParlp(); |
---|
9429 | } |
---|
9430 | else |
---|
9431 | { |
---|
9432 | VMrDefaultlp(); |
---|
9433 | } |
---|
9434 | G1 = idrMoveR(G, newRing,currRing); |
---|
9435 | |
---|
9436 | if( test_w_in_ConeCC(G1, target_weight) != 1 || ntestwinC == 0) |
---|
9437 | { |
---|
9438 | //PrintS("\n// The perturbed target vector doesn't STAY in the correct cone!!"); |
---|
9439 | if(tp_deg == 1) |
---|
9440 | { |
---|
9441 | //Print("\n// subroutine takes %d steps and applys \"std\"", nwalk); |
---|
9442 | to=clock(); |
---|
9443 | ideal G2 = MstdCC(G1); |
---|
9444 | xtextra=xtextra+clock()-to; |
---|
9445 | idDelete(&G1); |
---|
9446 | G1 = G2; |
---|
9447 | G2 = NULL; |
---|
9448 | } |
---|
9449 | else |
---|
9450 | { |
---|
9451 | //nOverflow_Error = Overflow_Error; |
---|
9452 | tproc = tproc+clock()-tinput; |
---|
9453 | // Print("\n// B subroutine takes %d steps and calls \"Mpwalk\" (1,%d) :", nwalk, tp_deg-1); |
---|
9454 | G1 = Mpwalk_MAltwalk1(G1, curr_weight, tp_deg-1); |
---|
9455 | } |
---|
9456 | } |
---|
9457 | |
---|
9458 | MPW_Finish: |
---|
9459 | newRing = currRing; |
---|
9460 | rChangeCurrRing(YXXRing); |
---|
9461 | ideal result = idrMoveR(G1, newRing,currRing); |
---|
9462 | |
---|
9463 | delete ivNull; |
---|
9464 | delete target_weight; |
---|
9465 | |
---|
9466 | //Print("\n// \"Mpwalk\" (1,%d) took %d steps and %.2f sec. Overflow_Error (%d)", tp_deg, nwalk, ((double) clock()-tinput)/1000000, nOverflow_Error); |
---|
9467 | //Print("\n// Mprwalk took %d steps. Ring= %s;\n", nwalk, rString(currRing)); |
---|
9468 | return(result); |
---|
9469 | } |
---|
9470 | |
---|
9471 | /******************************************************************* |
---|
9472 | * Implementation of the first alternative Groebner Walk Algorithm * |
---|
9473 | *******************************************************************/ |
---|
9474 | ideal MAltwalk1(ideal Go, int op_deg, int tp_deg, intvec* curr_weight, |
---|
9475 | intvec* target_weight) |
---|
9476 | { |
---|
9477 | Set_Error(FALSE ); |
---|
9478 | Overflow_Error = FALSE; |
---|
9479 | #ifdef TIME_TEST |
---|
9480 | BOOLEAN nOverflow_Error = FALSE; |
---|
9481 | #endif |
---|
9482 | // Print("// pSetm_Error = (%d)", ErrorCheck()); |
---|
9483 | |
---|
9484 | xtif=0; xtstd=0; xtlift=0; xtred=0; xtnw=0; xtextra=0; |
---|
9485 | xftinput = clock(); |
---|
9486 | clock_t tostd, tproc; |
---|
9487 | |
---|
9488 | nstep = 0; |
---|
9489 | int i, nV = currRing->N; |
---|
9490 | int nwalk=0, endwalks=0; |
---|
9491 | int op_tmp = op_deg; |
---|
9492 | ideal Gomega, M, F, G, Gomega1, Gomega2, M1, F1; |
---|
9493 | ring newRing, oldRing; |
---|
9494 | intvec* next_weight; |
---|
9495 | intvec* iv_M_dp; |
---|
9496 | intvec* ivNull = new intvec(nV); |
---|
9497 | intvec* iv_dp = MivUnit(nV);// define (1,1,...,1) |
---|
9498 | intvec* exivlp = Mivlp(nV); |
---|
9499 | //intvec* extra_curr_weight = new intvec(nV); |
---|
9500 | #ifndef BUCHBERGER_ALG |
---|
9501 | intvec* hilb_func; |
---|
9502 | #endif |
---|
9503 | intvec* cw_tmp = curr_weight; |
---|
9504 | |
---|
9505 | // to avoid (1,0,...,0) as the target vector |
---|
9506 | intvec* last_omega = new intvec(nV); |
---|
9507 | for(i=nV-1; i>0; i--) |
---|
9508 | { |
---|
9509 | (*last_omega)[i] = 1; |
---|
9510 | } |
---|
9511 | (*last_omega)[0] = 10000; |
---|
9512 | |
---|
9513 | ring XXRing = currRing; |
---|
9514 | |
---|
9515 | to=clock(); |
---|
9516 | /* compute a pertubed weight vector of the original weight vector. |
---|
9517 | The perturbation degree is recursive decrease until that vector |
---|
9518 | stays inn the correct cone. */ |
---|
9519 | while(1) |
---|
9520 | { |
---|
9521 | if(Overflow_Error == FALSE) |
---|
9522 | { |
---|
9523 | if(MivComp(curr_weight, iv_dp) == 1) |
---|
9524 | { |
---|
9525 | //rOrdStr(currRing) = "dp" |
---|
9526 | if(op_tmp == op_deg) |
---|
9527 | { |
---|
9528 | G = MstdCC(Go); |
---|
9529 | if(op_deg != 1) |
---|
9530 | { |
---|
9531 | iv_M_dp = MivMatrixOrderdp(nV); |
---|
9532 | } |
---|
9533 | } |
---|
9534 | } |
---|
9535 | } |
---|
9536 | else |
---|
9537 | { |
---|
9538 | if(op_tmp == op_deg) |
---|
9539 | { |
---|
9540 | //rOrdStr(currRing) = (a(...),lp,C) |
---|
9541 | if (rParameter(currRing) != NULL) |
---|
9542 | { |
---|
9543 | DefRingPar(cw_tmp); |
---|
9544 | } |
---|
9545 | else |
---|
9546 | { |
---|
9547 | rChangeCurrRing(VMrDefault(cw_tmp)); |
---|
9548 | } |
---|
9549 | G = idrMoveR(Go, XXRing,currRing); |
---|
9550 | G = MstdCC(G); |
---|
9551 | if(op_deg != 1) |
---|
9552 | iv_M_dp = MivMatrixOrder(cw_tmp); |
---|
9553 | } |
---|
9554 | } |
---|
9555 | Overflow_Error = FALSE; |
---|
9556 | if(op_deg != 1) |
---|
9557 | { |
---|
9558 | curr_weight = MPertVectors(G, iv_M_dp, op_deg); |
---|
9559 | } |
---|
9560 | else |
---|
9561 | { |
---|
9562 | curr_weight = cw_tmp; |
---|
9563 | break; |
---|
9564 | } |
---|
9565 | if(Overflow_Error == FALSE) |
---|
9566 | { |
---|
9567 | break; |
---|
9568 | } |
---|
9569 | Overflow_Error = TRUE; |
---|
9570 | op_deg --; |
---|
9571 | } |
---|
9572 | tostd=clock()-to; |
---|
9573 | |
---|
9574 | if(op_tmp != 1 ) |
---|
9575 | delete iv_M_dp; |
---|
9576 | delete iv_dp; |
---|
9577 | |
---|
9578 | if(currRing->order[0] == ringorder_a) |
---|
9579 | goto NEXT_VECTOR; |
---|
9580 | |
---|
9581 | while(1) |
---|
9582 | { |
---|
9583 | nwalk ++; |
---|
9584 | nstep ++; |
---|
9585 | |
---|
9586 | to = clock(); |
---|
9587 | // compute an initial form ideal of <G> w.r.t. "curr_vector" |
---|
9588 | Gomega = MwalkInitialForm(G, curr_weight); |
---|
9589 | xtif=xtif+clock()-to; |
---|
9590 | #if 0 |
---|
9591 | if(Overflow_Error == TRUE) |
---|
9592 | { |
---|
9593 | for(i=nV-1; i>=0; i--) |
---|
9594 | (*curr_weight)[i] = (*extra_curr_weight)[i]; |
---|
9595 | delete extra_curr_weight; |
---|
9596 | |
---|
9597 | newRing = currRing; |
---|
9598 | goto MSTD_ALT1; |
---|
9599 | } |
---|
9600 | #endif |
---|
9601 | #ifndef BUCHBERGER_ALG |
---|
9602 | if(isNolVector(curr_weight) == 0) |
---|
9603 | { |
---|
9604 | hilb_func = hFirstSeries(Gomega,NULL,NULL,curr_weight,currRing); |
---|
9605 | } |
---|
9606 | else |
---|
9607 | { |
---|
9608 | hilb_func = hFirstSeries(Gomega,NULL,NULL,last_omega,currRing); |
---|
9609 | } |
---|
9610 | #endif // BUCHBERGER_ALG |
---|
9611 | |
---|
9612 | oldRing = currRing; |
---|
9613 | |
---|
9614 | // define a new ring which ordering is "(a(curr_weight),lp) |
---|
9615 | if (rParameter(currRing) != NULL) |
---|
9616 | { |
---|
9617 | DefRingPar(curr_weight); |
---|
9618 | } |
---|
9619 | else |
---|
9620 | { |
---|
9621 | rChangeCurrRing(VMrDefault(curr_weight)); |
---|
9622 | } |
---|
9623 | newRing = currRing; |
---|
9624 | Gomega1 = idrMoveR(Gomega, oldRing,currRing); |
---|
9625 | |
---|
9626 | to=clock(); |
---|
9627 | // compute a reduced Groebner basis of <Gomega> w.r.t. "newRing" |
---|
9628 | #ifdef BUCHBERGER_ALG |
---|
9629 | M = MstdhomCC(Gomega1); |
---|
9630 | #else |
---|
9631 | M=kStd(Gomega1,NULL,isHomog,NULL,hilb_func,0,NULL,curr_weight); |
---|
9632 | delete hilb_func; |
---|
9633 | #endif // BUCHBERGER_ALG |
---|
9634 | xtstd=xtstd+clock()-to; |
---|
9635 | |
---|
9636 | // change the ring to oldRing |
---|
9637 | rChangeCurrRing(oldRing); |
---|
9638 | M1 = idrMoveR(M, newRing,currRing); |
---|
9639 | Gomega2 = idrMoveR(Gomega1, newRing,currRing); |
---|
9640 | |
---|
9641 | to=clock(); |
---|
9642 | // compute a reduced Groebner basis of <G> w.r.t. "newRing" by the lifting process |
---|
9643 | F = MLifttwoIdeal(Gomega2, M1, G); |
---|
9644 | xtlift=xtlift+clock()-to; |
---|
9645 | |
---|
9646 | idDelete(&M1); |
---|
9647 | idDelete(&Gomega2); |
---|
9648 | idDelete(&G); |
---|
9649 | |
---|
9650 | // change the ring to newRing |
---|
9651 | rChangeCurrRing(newRing); |
---|
9652 | F1 = idrMoveR(F, oldRing,currRing); |
---|
9653 | if (oldRing!=IDRING(currRingHdl)) rDelete(oldRing); // do not delete the global currRing |
---|
9654 | oldRing=NULL; |
---|
9655 | |
---|
9656 | to=clock(); |
---|
9657 | // reduce the Groebner basis <G> w.r.t. new ring |
---|
9658 | G = kInterRedCC(F1, NULL); |
---|
9659 | xtred=xtred+clock()-to; |
---|
9660 | idDelete(&F1); |
---|
9661 | |
---|
9662 | if(endwalks == 1) |
---|
9663 | { |
---|
9664 | break; |
---|
9665 | } |
---|
9666 | NEXT_VECTOR: |
---|
9667 | to=clock(); |
---|
9668 | // compute a next weight vector |
---|
9669 | next_weight = MkInterRedNextWeight(curr_weight,target_weight, G); |
---|
9670 | xtnw=xtnw+clock()-to; |
---|
9671 | #ifdef PRINT_VECTORS |
---|
9672 | MivString(curr_weight, target_weight, next_weight); |
---|
9673 | #endif |
---|
9674 | if(Overflow_Error == TRUE) |
---|
9675 | { |
---|
9676 | newRing = currRing; |
---|
9677 | |
---|
9678 | if (rParameter(currRing) != NULL) |
---|
9679 | { |
---|
9680 | DefRingPar(target_weight); |
---|
9681 | } |
---|
9682 | else |
---|
9683 | { |
---|
9684 | rChangeCurrRing(VMrDefault(target_weight)); |
---|
9685 | } |
---|
9686 | F1 = idrMoveR(G, newRing,currRing); |
---|
9687 | G = MstdCC(F1); |
---|
9688 | idDelete(&F1); |
---|
9689 | newRing = currRing; |
---|
9690 | break; //for while |
---|
9691 | } |
---|
9692 | |
---|
9693 | |
---|
9694 | /* G is the wanted Groebner basis if next_weight == curr_weight */ |
---|
9695 | if(MivComp(next_weight, ivNull) == 1) |
---|
9696 | { |
---|
9697 | newRing = currRing; |
---|
9698 | delete next_weight; |
---|
9699 | break; //for while |
---|
9700 | } |
---|
9701 | |
---|
9702 | if(MivComp(next_weight, target_weight) == 1) |
---|
9703 | { |
---|
9704 | if(tp_deg == 1 || MivSame(target_weight, exivlp) == 0) |
---|
9705 | endwalks = 1; |
---|
9706 | else |
---|
9707 | { |
---|
9708 | // MSTD_ALT1: |
---|
9709 | #ifdef TIME_TEST |
---|
9710 | nOverflow_Error = Overflow_Error; |
---|
9711 | #endif |
---|
9712 | tproc = clock()-xftinput; |
---|
9713 | |
---|
9714 | //Print("\n// main routine takes %d steps and calls \"Mpwalk\" (1,%d):", nwalk, tp_deg); |
---|
9715 | |
---|
9716 | // compute the red. GB of <G> w.r.t. the lex order by the "recursive-modified" perturbation walk alg (1,tp_deg) |
---|
9717 | G = Mpwalk_MAltwalk1(G, curr_weight, tp_deg); |
---|
9718 | delete next_weight; |
---|
9719 | break; // for while |
---|
9720 | } |
---|
9721 | } |
---|
9722 | |
---|
9723 | //NOT Changed, to free memory |
---|
9724 | for(i=nV-1; i>=0; i--) |
---|
9725 | { |
---|
9726 | //(*extra_curr_weight)[i] = (*curr_weight)[i]; |
---|
9727 | (*curr_weight)[i] = (*next_weight)[i]; |
---|
9728 | } |
---|
9729 | delete next_weight; |
---|
9730 | }//while |
---|
9731 | |
---|
9732 | rChangeCurrRing(XXRing); |
---|
9733 | ideal result = idrMoveR(G, newRing,currRing); |
---|
9734 | id_Delete(&G, newRing); |
---|
9735 | |
---|
9736 | delete ivNull; |
---|
9737 | if(op_deg != 1 ) |
---|
9738 | { |
---|
9739 | delete curr_weight; |
---|
9740 | } |
---|
9741 | delete exivlp; |
---|
9742 | #ifdef TIME_TEST |
---|
9743 | /* |
---|
9744 | Print("\n// \"Main procedure\" took %d steps, %.2f sec. and Overflow_Error(%d)", |
---|
9745 | nwalk, ((double) tproc)/1000000, nOverflow_Error); |
---|
9746 | |
---|
9747 | TimeStringFractal(xftinput, tostd, xtif, xtstd,xtextra, xtlift, xtred, xtnw); |
---|
9748 | */ |
---|
9749 | // Print("\n// pSetm_Error = (%d)", ErrorCheck()); |
---|
9750 | // Print("\n// Overflow_Error? (%d)", Overflow_Error); |
---|
9751 | // Print("\n// Awalk1 took %d steps.\n", nstep); |
---|
9752 | #endif |
---|
9753 | return(result); |
---|
9754 | } |
---|