1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* |
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5 | * ABSTRACT - dimension, multiplicity, HC, kbase |
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6 | */ |
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7 | |
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8 | #include "kernel/mod2.h" |
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9 | |
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10 | #include "misc/intvec.h" |
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11 | #include "coeffs/numbers.h" |
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12 | |
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13 | #include "kernel/structs.h" |
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14 | #include "kernel/ideals.h" |
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15 | #include "kernel/polys.h" |
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16 | |
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17 | #include "kernel/combinatorics/hutil.h" |
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18 | #include "kernel/combinatorics/hilb.h" |
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19 | #include "kernel/combinatorics/stairc.h" |
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20 | #include "reporter/reporter.h" |
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21 | |
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22 | #ifdef HAVE_SHIFTBBA |
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23 | #include <vector> |
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24 | #include "misc/options.h" |
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25 | #endif |
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26 | |
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27 | VAR int hCo, hMu, hMu2; |
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28 | VAR omBin indlist_bin = omGetSpecBin(sizeof(indlist)); |
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29 | |
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30 | /*0 implementation*/ |
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31 | |
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32 | // dimension |
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33 | |
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34 | void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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35 | varset var, int Nvar) |
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36 | { |
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37 | int dn, iv, rad0, b, c, x; |
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38 | scmon pn; |
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39 | scfmon rn; |
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40 | if (Nrad < 2) |
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41 | { |
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42 | dn = Npure + Nrad; |
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43 | if (dn < hCo) |
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44 | hCo = dn; |
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45 | return; |
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46 | } |
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47 | if (Npure+1 >= hCo) |
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48 | return; |
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49 | iv = Nvar; |
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50 | while(pure[var[iv]]) iv--; |
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51 | hStepR(rad, Nrad, var, iv, &rad0); |
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52 | if (rad0!=0) |
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53 | { |
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54 | iv--; |
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55 | if (rad0 < Nrad) |
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56 | { |
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57 | pn = hGetpure(pure); |
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58 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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59 | hDimSolve(pn, Npure + 1, rn, rad0, var, iv); |
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60 | b = rad0; |
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61 | c = Nrad; |
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62 | hElimR(rn, &rad0, b, c, var, iv); |
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63 | hPure(rn, b, &c, var, iv, pn, &x); |
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64 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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65 | rad0 += (c - b); |
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66 | hDimSolve(pn, Npure + x, rn, rad0, var, iv); |
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67 | } |
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68 | else |
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69 | { |
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70 | hDimSolve(pure, Npure, rad, Nrad, var, iv); |
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71 | } |
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72 | } |
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73 | else |
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74 | hCo = Npure + 1; |
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75 | } |
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76 | |
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77 | int scDimInt(ideal S, ideal Q) |
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78 | { |
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79 | id_Test(S, currRing); |
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80 | if( Q!=NULL ) id_Test(Q, currRing); |
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81 | |
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82 | int mc; |
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83 | hexist = hInit(S, Q, &hNexist); |
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84 | if (!hNexist) |
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85 | return (currRing->N); |
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86 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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87 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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88 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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89 | mc = hisModule; |
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90 | if (!mc) |
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91 | { |
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92 | hrad = hexist; |
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93 | hNrad = hNexist; |
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94 | } |
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95 | else |
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96 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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97 | radmem = hCreate((currRing->N) - 1); |
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98 | hCo = (currRing->N) + 1; |
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99 | loop |
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100 | { |
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101 | if (mc) |
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102 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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103 | if (hNrad) |
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104 | { |
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105 | hNvar = (currRing->N); |
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106 | hRadical(hrad, &hNrad, hNvar); |
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107 | hSupp(hrad, hNrad, hvar, &hNvar); |
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108 | if (hNvar) |
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109 | { |
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110 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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111 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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112 | hLexR(hrad, hNrad, hvar, hNvar); |
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113 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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114 | } |
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115 | } |
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116 | else |
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117 | { |
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118 | hCo = 0; |
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119 | break; |
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120 | } |
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121 | mc--; |
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122 | if (mc <= 0) |
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123 | break; |
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124 | } |
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125 | hKill(radmem, (currRing->N) - 1); |
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126 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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127 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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128 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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129 | hDelete(hexist, hNexist); |
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130 | if (hisModule) |
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131 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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132 | return (currRing->N) - hCo; |
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133 | } |
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134 | |
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135 | int scDimIntRing(ideal vid, ideal Q) |
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136 | { |
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137 | #ifdef HAVE_RINGS |
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138 | if (rField_is_Ring(currRing)) |
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139 | { |
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140 | int i = idPosConstant(vid); |
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141 | if ((i != -1) && (n_IsUnit(pGetCoeff(vid->m[i]),currRing->cf))) |
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142 | { /* ideal v contains unit; dim = -1 */ |
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143 | return(-1); |
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144 | } |
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145 | ideal vv = id_Head(vid,currRing); |
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146 | idSkipZeroes(vv); |
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147 | i = idPosConstant(vid); |
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148 | int d; |
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149 | if(i == -1) |
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150 | { |
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151 | d = scDimInt(vv, Q); |
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152 | if(rField_is_Z(currRing)) |
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153 | d++; |
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154 | } |
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155 | else |
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156 | { |
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157 | if(n_IsUnit(pGetCoeff(vv->m[i]),currRing->cf)) |
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158 | d = -1; |
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159 | else |
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160 | d = scDimInt(vv, Q); |
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161 | } |
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162 | //Anne's Idea for std(4,2x) = 0 bug |
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163 | int dcurr = d; |
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164 | for(unsigned ii=0;ii<(unsigned)IDELEMS(vv);ii++) |
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165 | { |
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166 | if(vv->m[ii] != NULL && !n_IsUnit(pGetCoeff(vv->m[ii]),currRing->cf)) |
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167 | { |
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168 | ideal vc = idCopy(vv); |
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169 | poly c = pInit(); |
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170 | pSetCoeff0(c,nCopy(pGetCoeff(vv->m[ii]))); |
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171 | idInsertPoly(vc,c); |
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172 | idSkipZeroes(vc); |
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173 | for(unsigned jj = 0;jj<(unsigned)IDELEMS(vc)-1;jj++) |
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174 | { |
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175 | if((vc->m[jj]!=NULL) |
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176 | && (n_DivBy(pGetCoeff(vc->m[jj]),pGetCoeff(c),currRing->cf))) |
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177 | { |
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178 | pDelete(&vc->m[jj]); |
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179 | } |
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180 | } |
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181 | idSkipZeroes(vc); |
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182 | i = idPosConstant(vc); |
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183 | if (i != -1) pDelete(&vc->m[i]); |
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184 | dcurr = scDimInt(vc, Q); |
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185 | // the following assumes the ground rings to be either zero- or one-dimensional |
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186 | if((i==-1) && rField_is_Z(currRing)) |
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187 | { |
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188 | // should also be activated for other euclidean domains as groundfield |
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189 | dcurr++; |
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190 | } |
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191 | idDelete(&vc); |
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192 | } |
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193 | if(dcurr > d) |
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194 | d = dcurr; |
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195 | } |
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196 | idDelete(&vv); |
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197 | return d; |
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198 | } |
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199 | #endif |
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200 | return scDimInt(vid,Q); |
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201 | } |
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202 | |
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203 | // independent set |
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204 | STATIC_VAR scmon hInd; |
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205 | |
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206 | static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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207 | varset var, int Nvar) |
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208 | { |
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209 | int dn, iv, rad0, b, c, x; |
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210 | scmon pn; |
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211 | scfmon rn; |
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212 | if (Nrad < 2) |
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213 | { |
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214 | dn = Npure + Nrad; |
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215 | if (dn < hCo) |
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216 | { |
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217 | hCo = dn; |
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218 | for (iv=(currRing->N); iv; iv--) |
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219 | { |
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220 | if (pure[iv]) |
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221 | hInd[iv] = 0; |
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222 | else |
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223 | hInd[iv] = 1; |
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224 | } |
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225 | if (Nrad) |
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226 | { |
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227 | pn = *rad; |
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228 | iv = Nvar; |
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229 | loop |
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230 | { |
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231 | x = var[iv]; |
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232 | if (pn[x]) |
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233 | { |
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234 | hInd[x] = 0; |
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235 | break; |
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236 | } |
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237 | iv--; |
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238 | } |
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239 | } |
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240 | } |
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241 | return; |
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242 | } |
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243 | if (Npure+1 >= hCo) |
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244 | return; |
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245 | iv = Nvar; |
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246 | while(pure[var[iv]]) iv--; |
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247 | hStepR(rad, Nrad, var, iv, &rad0); |
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248 | if (rad0) |
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249 | { |
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250 | iv--; |
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251 | if (rad0 < Nrad) |
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252 | { |
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253 | pn = hGetpure(pure); |
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254 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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255 | pn[var[iv + 1]] = 1; |
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256 | hIndSolve(pn, Npure + 1, rn, rad0, var, iv); |
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257 | pn[var[iv + 1]] = 0; |
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258 | b = rad0; |
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259 | c = Nrad; |
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260 | hElimR(rn, &rad0, b, c, var, iv); |
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261 | hPure(rn, b, &c, var, iv, pn, &x); |
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262 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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263 | rad0 += (c - b); |
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264 | hIndSolve(pn, Npure + x, rn, rad0, var, iv); |
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265 | } |
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266 | else |
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267 | { |
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268 | hIndSolve(pure, Npure, rad, Nrad, var, iv); |
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269 | } |
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270 | } |
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271 | else |
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272 | { |
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273 | hCo = Npure + 1; |
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274 | for (x=(currRing->N); x; x--) |
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275 | { |
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276 | if (pure[x]) |
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277 | hInd[x] = 0; |
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278 | else |
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279 | hInd[x] = 1; |
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280 | } |
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281 | hInd[var[iv]] = 0; |
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282 | } |
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283 | } |
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284 | |
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285 | intvec * scIndIntvec(ideal S, ideal Q) |
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286 | { |
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287 | id_Test(S, currRing); |
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288 | if( Q!=NULL ) id_Test(Q, currRing); |
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289 | |
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290 | intvec *Set=new intvec((currRing->N)); |
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291 | int mc,i; |
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292 | hexist = hInit(S, Q, &hNexist); |
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293 | if (hNexist==0) |
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294 | { |
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295 | for(i=0; i<(currRing->N); i++) |
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296 | (*Set)[i]=1; |
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297 | return Set; |
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298 | } |
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299 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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300 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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301 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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302 | hInd = (scmon)omAlloc0((1 + (currRing->N)) * sizeof(int)); |
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303 | mc = hisModule; |
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304 | if (mc==0) |
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305 | { |
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306 | hrad = hexist; |
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307 | hNrad = hNexist; |
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308 | } |
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309 | else |
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310 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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311 | radmem = hCreate((currRing->N) - 1); |
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312 | hCo = (currRing->N) + 1; |
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313 | loop |
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314 | { |
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315 | if (mc!=0) |
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316 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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317 | if (hNrad!=0) |
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318 | { |
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319 | hNvar = (currRing->N); |
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320 | hRadical(hrad, &hNrad, hNvar); |
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321 | hSupp(hrad, hNrad, hvar, &hNvar); |
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322 | if (hNvar!=0) |
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323 | { |
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324 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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325 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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326 | hLexR(hrad, hNrad, hvar, hNvar); |
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327 | hIndSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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328 | } |
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329 | } |
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330 | else |
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331 | { |
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332 | hCo = 0; |
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333 | break; |
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334 | } |
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335 | mc--; |
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336 | if (mc <= 0) |
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337 | break; |
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338 | } |
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339 | for(i=0; i<(currRing->N); i++) |
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340 | (*Set)[i] = hInd[i+1]; |
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341 | hKill(radmem, (currRing->N) - 1); |
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342 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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343 | omFreeSize((ADDRESS)hInd, (1 + (currRing->N)) * sizeof(int)); |
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344 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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345 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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346 | hDelete(hexist, hNexist); |
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347 | if (hisModule) |
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348 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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349 | return Set; |
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350 | } |
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351 | |
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352 | VAR indset ISet, JSet; |
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353 | |
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354 | static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar) |
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355 | { |
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356 | int k1, i; |
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357 | k1 = var[Nvar]; |
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358 | i = 0; |
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359 | loop |
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360 | { |
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361 | if (rad[i][k1]==0) |
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362 | return FALSE; |
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363 | i++; |
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364 | if (i == Nrad) |
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365 | return TRUE; |
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366 | } |
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367 | } |
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368 | |
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369 | static void hIndep(scmon pure) |
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370 | { |
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371 | int iv; |
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372 | intvec *Set; |
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373 | |
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374 | Set = ISet->set = new intvec((currRing->N)); |
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375 | for (iv=(currRing->N); iv!=0 ; iv--) |
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376 | { |
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377 | (*Set)[iv-1] = (pure[iv]==0); |
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378 | } |
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379 | ISet = ISet->nx = (indset)omAlloc0Bin(indlist_bin); |
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380 | hMu++; |
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381 | } |
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382 | |
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383 | void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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384 | varset var, int Nvar) |
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385 | { |
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386 | int dn, iv, rad0, b, c, x; |
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387 | scmon pn; |
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388 | scfmon rn; |
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389 | if (Nrad < 2) |
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390 | { |
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391 | dn = Npure + Nrad; |
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392 | if (dn == hCo) |
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393 | { |
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394 | if (Nrad==0) |
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395 | hIndep(pure); |
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396 | else |
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397 | { |
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398 | pn = *rad; |
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399 | for (iv = Nvar; iv!=0; iv--) |
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400 | { |
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401 | x = var[iv]; |
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402 | if (pn[x]) |
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403 | { |
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404 | pure[x] = 1; |
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405 | hIndep(pure); |
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406 | pure[x] = 0; |
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407 | } |
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408 | } |
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409 | } |
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410 | } |
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411 | return; |
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412 | } |
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413 | iv = Nvar; |
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414 | dn = Npure+1; |
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415 | if (dn >= hCo) |
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416 | { |
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417 | if (dn > hCo) |
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418 | return; |
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419 | loop |
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420 | { |
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421 | if(!pure[var[iv]]) |
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422 | { |
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423 | if(hNotZero(rad, Nrad, var, iv)) |
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424 | { |
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425 | pure[var[iv]] = 1; |
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426 | hIndep(pure); |
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427 | pure[var[iv]] = 0; |
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428 | } |
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429 | } |
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430 | iv--; |
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431 | if (!iv) |
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432 | return; |
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433 | } |
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434 | } |
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435 | while(pure[var[iv]]) iv--; |
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436 | hStepR(rad, Nrad, var, iv, &rad0); |
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437 | iv--; |
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438 | if (rad0 < Nrad) |
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439 | { |
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440 | pn = hGetpure(pure); |
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441 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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442 | pn[var[iv + 1]] = 1; |
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443 | hIndMult(pn, Npure + 1, rn, rad0, var, iv); |
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444 | pn[var[iv + 1]] = 0; |
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445 | b = rad0; |
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446 | c = Nrad; |
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447 | hElimR(rn, &rad0, b, c, var, iv); |
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448 | hPure(rn, b, &c, var, iv, pn, &x); |
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449 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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450 | rad0 += (c - b); |
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451 | hIndMult(pn, Npure + x, rn, rad0, var, iv); |
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452 | } |
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453 | else |
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454 | { |
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455 | hIndMult(pure, Npure, rad, Nrad, var, iv); |
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456 | } |
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457 | } |
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458 | |
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459 | /*3 |
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460 | * consider indset x := !pure |
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461 | * (for all i) (if(sm(i) > x) return FALSE) |
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462 | * else return TRUE |
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463 | */ |
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464 | static BOOLEAN hCheck1(indset sm, scmon pure) |
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465 | { |
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466 | int iv; |
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467 | intvec *Set; |
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468 | while (sm->nx != NULL) |
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469 | { |
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470 | Set = sm->set; |
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471 | iv=(currRing->N); |
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472 | loop |
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473 | { |
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474 | if (((*Set)[iv-1] == 0) && (pure[iv] == 0)) |
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475 | break; |
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476 | iv--; |
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477 | if (iv == 0) |
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478 | return FALSE; |
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479 | } |
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480 | sm = sm->nx; |
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481 | } |
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482 | return TRUE; |
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483 | } |
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484 | |
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485 | /*3 |
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486 | * consider indset x := !pure |
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487 | * (for all i) if(x > sm(i)) delete sm(i)) |
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488 | * return (place for x) |
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489 | */ |
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490 | static indset hCheck2(indset sm, scmon pure) |
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491 | { |
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492 | int iv; |
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493 | intvec *Set; |
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494 | indset be, a1 = NULL; |
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495 | while (sm->nx != NULL) |
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496 | { |
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497 | Set = sm->set; |
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498 | iv=(currRing->N); |
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499 | loop |
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500 | { |
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501 | if ((pure[iv] == 1) && ((*Set)[iv-1] == 1)) |
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502 | break; |
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503 | iv--; |
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504 | if (iv == 0) |
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505 | { |
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506 | if (a1 == NULL) |
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507 | { |
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508 | a1 = sm; |
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509 | } |
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510 | else |
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511 | { |
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512 | hMu2--; |
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513 | be->nx = sm->nx; |
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514 | delete Set; |
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515 | omFreeBin((ADDRESS)sm, indlist_bin); |
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516 | sm = be; |
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517 | } |
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518 | break; |
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519 | } |
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520 | } |
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521 | be = sm; |
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522 | sm = sm->nx; |
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523 | } |
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524 | if (a1 != NULL) |
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525 | { |
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526 | return a1; |
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527 | } |
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528 | else |
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529 | { |
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530 | hMu2++; |
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531 | sm->set = new intvec((currRing->N)); |
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532 | sm->nx = (indset)omAlloc0Bin(indlist_bin); |
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533 | return sm; |
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534 | } |
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535 | } |
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536 | |
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537 | /*2 |
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538 | * definition x >= y |
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539 | * x(i) == 0 => y(i) == 0 |
---|
540 | * > ex. j with x(j) == 1 and y(j) == 0 |
---|
541 | */ |
---|
542 | static void hCheckIndep(scmon pure) |
---|
543 | { |
---|
544 | intvec *Set; |
---|
545 | indset res; |
---|
546 | int iv; |
---|
547 | if (hCheck1(ISet, pure)) |
---|
548 | { |
---|
549 | if (hCheck1(JSet, pure)) |
---|
550 | { |
---|
551 | res = hCheck2(JSet,pure); |
---|
552 | if (res == NULL) |
---|
553 | return; |
---|
554 | Set = res->set; |
---|
555 | for (iv=(currRing->N); iv; iv--) |
---|
556 | { |
---|
557 | (*Set)[iv-1] = (pure[iv]==0); |
---|
558 | } |
---|
559 | } |
---|
560 | } |
---|
561 | } |
---|
562 | |
---|
563 | void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
564 | varset var, int Nvar) |
---|
565 | { |
---|
566 | int dn, iv, rad0, b, c, x; |
---|
567 | scmon pn; |
---|
568 | scfmon rn; |
---|
569 | if (Nrad < 2) |
---|
570 | { |
---|
571 | dn = Npure + Nrad; |
---|
572 | if (dn > hCo) |
---|
573 | { |
---|
574 | if (!Nrad) |
---|
575 | hCheckIndep(pure); |
---|
576 | else |
---|
577 | { |
---|
578 | pn = *rad; |
---|
579 | for (iv = Nvar; iv; iv--) |
---|
580 | { |
---|
581 | x = var[iv]; |
---|
582 | if (pn[x]) |
---|
583 | { |
---|
584 | pure[x] = 1; |
---|
585 | hCheckIndep(pure); |
---|
586 | pure[x] = 0; |
---|
587 | } |
---|
588 | } |
---|
589 | } |
---|
590 | } |
---|
591 | return; |
---|
592 | } |
---|
593 | iv = Nvar; |
---|
594 | while(pure[var[iv]]) iv--; |
---|
595 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
596 | iv--; |
---|
597 | if (rad0 < Nrad) |
---|
598 | { |
---|
599 | pn = hGetpure(pure); |
---|
600 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
601 | pn[var[iv + 1]] = 1; |
---|
602 | hIndAllMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
603 | pn[var[iv + 1]] = 0; |
---|
604 | b = rad0; |
---|
605 | c = Nrad; |
---|
606 | hElimR(rn, &rad0, b, c, var, iv); |
---|
607 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
608 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
609 | rad0 += (c - b); |
---|
610 | hIndAllMult(pn, Npure + x, rn, rad0, var, iv); |
---|
611 | } |
---|
612 | else |
---|
613 | { |
---|
614 | hIndAllMult(pure, Npure, rad, Nrad, var, iv); |
---|
615 | } |
---|
616 | } |
---|
617 | |
---|
618 | // multiplicity |
---|
619 | |
---|
620 | static int hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar) |
---|
621 | { |
---|
622 | int iv = Nvar -1, sum, a, a0, a1, b, i; |
---|
623 | int x, x0; |
---|
624 | scmon pn; |
---|
625 | scfmon sn; |
---|
626 | if (!iv) |
---|
627 | return pure[var[1]]; |
---|
628 | else if (!Nstc) |
---|
629 | { |
---|
630 | sum = 1; |
---|
631 | for (i = Nvar; i; i--) |
---|
632 | sum *= pure[var[i]]; |
---|
633 | return sum; |
---|
634 | } |
---|
635 | x = a = 0; |
---|
636 | pn = hGetpure(pure); |
---|
637 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
638 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
639 | int64 t=hZeroMult(pn, sn, a, var, iv); |
---|
640 | if (a == Nstc) |
---|
641 | { |
---|
642 | t *= pure[var[Nvar]]; |
---|
643 | if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t; |
---|
644 | else if (!errorreported) WerrorS("int overflow in vdim 3"); |
---|
645 | return sum; |
---|
646 | /*return pure[var[Nvar]] * hZeroMult(pn, sn, a, var, iv);*/ |
---|
647 | } |
---|
648 | else |
---|
649 | { |
---|
650 | t *= x; |
---|
651 | if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t; |
---|
652 | else if (!errorreported) WerrorS("int overflow in vdim 4"); |
---|
653 | /*sum = x * hZeroMult(pn, sn, a, var, iv);*/ |
---|
654 | } |
---|
655 | b = a; |
---|
656 | loop |
---|
657 | { |
---|
658 | a0 = a; |
---|
659 | x0 = x; |
---|
660 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
661 | hElimS(sn, &b, a0, a, var, iv); |
---|
662 | a1 = a; |
---|
663 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
664 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
665 | b += (a1 - a0); |
---|
666 | if (a < Nstc) |
---|
667 | { |
---|
668 | int64 t=hZeroMult(pn, sn, b, var, iv); |
---|
669 | t *= (x-x0); |
---|
670 | t += sum; |
---|
671 | if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t; |
---|
672 | else if (!errorreported) WerrorS("int overflow in vdim 1"); |
---|
673 | /*sum += (x - x0) * hZeroMult(pn, sn, b, var, iv);*/ |
---|
674 | } |
---|
675 | else |
---|
676 | { |
---|
677 | int64 t=hZeroMult(pn, sn, b, var, iv); |
---|
678 | t *= (pure[var[Nvar]]-x0); |
---|
679 | t += sum; |
---|
680 | if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t; |
---|
681 | else if (!errorreported) WerrorS("int overflow in vdim 2"); |
---|
682 | /*sum += (pure[var[Nvar]] - x0) * hZeroMult(pn, sn, b, var, iv);*/ |
---|
683 | return sum; |
---|
684 | } |
---|
685 | } |
---|
686 | } |
---|
687 | |
---|
688 | static void hProject(scmon pure, varset sel) |
---|
689 | { |
---|
690 | int i, i0, k; |
---|
691 | i0 = 0; |
---|
692 | for (i = 1; i <= (currRing->N); i++) |
---|
693 | { |
---|
694 | if (pure[i]) |
---|
695 | { |
---|
696 | i0++; |
---|
697 | sel[i0] = i; |
---|
698 | } |
---|
699 | } |
---|
700 | i = hNstc; |
---|
701 | memcpy(hwork, hstc, i * sizeof(scmon)); |
---|
702 | hStaircase(hwork, &i, sel, i0); |
---|
703 | if ((i0 > 2) && (i > 10)) |
---|
704 | hOrdSupp(hwork, i, sel, i0); |
---|
705 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
706 | hPure(hwork, 0, &i, sel, i0, hpur0, &k); |
---|
707 | hLexS(hwork, i, sel, i0); |
---|
708 | hMu += hZeroMult(hpur0, hwork, i, sel, i0); |
---|
709 | } |
---|
710 | |
---|
711 | static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
712 | varset var, int Nvar) |
---|
713 | { |
---|
714 | int dn, iv, rad0, b, c, x; |
---|
715 | scmon pn; |
---|
716 | scfmon rn; |
---|
717 | if (Nrad < 2) |
---|
718 | { |
---|
719 | dn = Npure + Nrad; |
---|
720 | if (dn == hCo) |
---|
721 | { |
---|
722 | if (!Nrad) |
---|
723 | hProject(pure, hsel); |
---|
724 | else |
---|
725 | { |
---|
726 | pn = *rad; |
---|
727 | for (iv = Nvar; iv; iv--) |
---|
728 | { |
---|
729 | x = var[iv]; |
---|
730 | if (pn[x]) |
---|
731 | { |
---|
732 | pure[x] = 1; |
---|
733 | hProject(pure, hsel); |
---|
734 | pure[x] = 0; |
---|
735 | } |
---|
736 | } |
---|
737 | } |
---|
738 | } |
---|
739 | return; |
---|
740 | } |
---|
741 | iv = Nvar; |
---|
742 | dn = Npure+1; |
---|
743 | if (dn >= hCo) |
---|
744 | { |
---|
745 | if (dn > hCo) |
---|
746 | return; |
---|
747 | loop |
---|
748 | { |
---|
749 | if(!pure[var[iv]]) |
---|
750 | { |
---|
751 | if(hNotZero(rad, Nrad, var, iv)) |
---|
752 | { |
---|
753 | pure[var[iv]] = 1; |
---|
754 | hProject(pure, hsel); |
---|
755 | pure[var[iv]] = 0; |
---|
756 | } |
---|
757 | } |
---|
758 | iv--; |
---|
759 | if (!iv) |
---|
760 | return; |
---|
761 | } |
---|
762 | } |
---|
763 | while(pure[var[iv]]) iv--; |
---|
764 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
765 | iv--; |
---|
766 | if (rad0 < Nrad) |
---|
767 | { |
---|
768 | pn = hGetpure(pure); |
---|
769 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
770 | pn[var[iv + 1]] = 1; |
---|
771 | hDimMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
772 | pn[var[iv + 1]] = 0; |
---|
773 | b = rad0; |
---|
774 | c = Nrad; |
---|
775 | hElimR(rn, &rad0, b, c, var, iv); |
---|
776 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
777 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
778 | rad0 += (c - b); |
---|
779 | hDimMult(pn, Npure + x, rn, rad0, var, iv); |
---|
780 | } |
---|
781 | else |
---|
782 | { |
---|
783 | hDimMult(pure, Npure, rad, Nrad, var, iv); |
---|
784 | } |
---|
785 | } |
---|
786 | |
---|
787 | static void hDegree(ideal S, ideal Q) |
---|
788 | { |
---|
789 | id_Test(S, currRing); |
---|
790 | if( Q!=NULL ) id_Test(Q, currRing); |
---|
791 | |
---|
792 | int di; |
---|
793 | int mc; |
---|
794 | hexist = hInit(S, Q, &hNexist); |
---|
795 | if (!hNexist) |
---|
796 | { |
---|
797 | hCo = 0; |
---|
798 | hMu = 1; |
---|
799 | return; |
---|
800 | } |
---|
801 | //hWeight(); |
---|
802 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
803 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
804 | hsel = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
805 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
806 | hpur0 = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
807 | mc = hisModule; |
---|
808 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
809 | if (!mc) |
---|
810 | { |
---|
811 | memcpy(hrad, hexist, hNexist * sizeof(scmon)); |
---|
812 | hstc = hexist; |
---|
813 | hNrad = hNstc = hNexist; |
---|
814 | } |
---|
815 | else |
---|
816 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
817 | radmem = hCreate((currRing->N) - 1); |
---|
818 | stcmem = hCreate((currRing->N) - 1); |
---|
819 | hCo = (currRing->N) + 1; |
---|
820 | di = hCo + 1; |
---|
821 | loop |
---|
822 | { |
---|
823 | if (mc) |
---|
824 | { |
---|
825 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
---|
826 | hNstc = hNrad; |
---|
827 | memcpy(hstc, hrad, hNrad * sizeof(scmon)); |
---|
828 | } |
---|
829 | if (hNrad) |
---|
830 | { |
---|
831 | hNvar = (currRing->N); |
---|
832 | hRadical(hrad, &hNrad, hNvar); |
---|
833 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
834 | if (hNvar) |
---|
835 | { |
---|
836 | hCo = hNvar; |
---|
837 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
838 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
839 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
840 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
841 | } |
---|
842 | } |
---|
843 | else |
---|
844 | { |
---|
845 | hNvar = 1; |
---|
846 | hCo = 0; |
---|
847 | } |
---|
848 | if (hCo < di) |
---|
849 | { |
---|
850 | di = hCo; |
---|
851 | hMu = 0; |
---|
852 | } |
---|
853 | if (hNvar && (hCo == di)) |
---|
854 | { |
---|
855 | if (di && (di < (currRing->N))) |
---|
856 | hDimMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
857 | else if (!di) |
---|
858 | hMu++; |
---|
859 | else |
---|
860 | { |
---|
861 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
862 | if ((hNvar > 2) && (hNstc > 10)) |
---|
863 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
864 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
865 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
866 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
867 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
868 | } |
---|
869 | } |
---|
870 | mc--; |
---|
871 | if (mc <= 0) |
---|
872 | break; |
---|
873 | } |
---|
874 | hCo = di; |
---|
875 | hKill(stcmem, (currRing->N) - 1); |
---|
876 | hKill(radmem, (currRing->N) - 1); |
---|
877 | omFreeSize((ADDRESS)hpur0, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
878 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
879 | omFreeSize((ADDRESS)hsel, ((currRing->N) + 1) * sizeof(int)); |
---|
880 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
---|
881 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
882 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
---|
883 | hDelete(hexist, hNexist); |
---|
884 | if (hisModule) |
---|
885 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
886 | } |
---|
887 | |
---|
888 | int scMultInt(ideal S, ideal Q) |
---|
889 | { |
---|
890 | id_Test(S, currRing); |
---|
891 | if( Q!=NULL ) id_Test(Q, currRing); |
---|
892 | |
---|
893 | hDegree(S, Q); |
---|
894 | return hMu; |
---|
895 | } |
---|
896 | |
---|
897 | void scPrintDegree(int co, int mu) |
---|
898 | { |
---|
899 | int di = (currRing->N)-co; |
---|
900 | if (currRing->OrdSgn == 1) |
---|
901 | { |
---|
902 | if (di>0) |
---|
903 | Print("// dimension (proj.) = %d\n// degree (proj.) = %d\n", di-1, mu); |
---|
904 | else |
---|
905 | Print("// dimension (affine) = 0\n// degree (affine) = %d\n", mu); |
---|
906 | } |
---|
907 | else |
---|
908 | Print("// dimension (local) = %d\n// multiplicity = %d\n", di, mu); |
---|
909 | } |
---|
910 | |
---|
911 | void scDegree(ideal S, intvec *modulweight, ideal Q) |
---|
912 | { |
---|
913 | id_Test(S, currRing); |
---|
914 | if( Q!=NULL ) id_Test(Q, currRing); |
---|
915 | |
---|
916 | int co, mu, l; |
---|
917 | intvec *hseries2; |
---|
918 | intvec *hseries1 = hFirstSeries(S, modulweight, Q); |
---|
919 | if (errorreported) return; |
---|
920 | l = hseries1->length()-1; |
---|
921 | if (l > 1) |
---|
922 | hseries2 = hSecondSeries(hseries1); |
---|
923 | else |
---|
924 | hseries2 = hseries1; |
---|
925 | hDegreeSeries(hseries1, hseries2, &co, &mu); |
---|
926 | if ((l == 1) &&(mu == 0)) |
---|
927 | scPrintDegree((currRing->N)+1, 0); |
---|
928 | else |
---|
929 | scPrintDegree(co, mu); |
---|
930 | if (l>1) |
---|
931 | delete hseries1; |
---|
932 | delete hseries2; |
---|
933 | } |
---|
934 | |
---|
935 | int scMult0Int(ideal S, ideal Q) |
---|
936 | { |
---|
937 | id_LmTest(S, currRing); |
---|
938 | if (Q!=NULL) id_LmTest(Q, currRing); |
---|
939 | |
---|
940 | int mc; |
---|
941 | hexist = hInit(S, Q, &hNexist); |
---|
942 | if (!hNexist) |
---|
943 | { |
---|
944 | hMu = -1; |
---|
945 | return -1; |
---|
946 | } |
---|
947 | else |
---|
948 | hMu = 0; |
---|
949 | |
---|
950 | const ring r = currRing; |
---|
951 | |
---|
952 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
953 | hvar = (varset)omAlloc(((r->N) + 1) * sizeof(int)); |
---|
954 | hpur0 = (scmon)omAlloc((1 + ((r->N) * (r->N))) * sizeof(int)); |
---|
955 | mc = hisModule; |
---|
956 | if (!mc) |
---|
957 | { |
---|
958 | hstc = hexist; |
---|
959 | hNstc = hNexist; |
---|
960 | } |
---|
961 | else |
---|
962 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
963 | stcmem = hCreate((r->N) - 1); |
---|
964 | loop |
---|
965 | { |
---|
966 | if (mc) |
---|
967 | { |
---|
968 | hComp(hexist, hNexist, mc, hstc, &hNstc); |
---|
969 | if (!hNstc) |
---|
970 | { |
---|
971 | hMu = -1; |
---|
972 | break; |
---|
973 | } |
---|
974 | } |
---|
975 | hNvar = (r->N); |
---|
976 | for (int i = hNvar; i; i--) |
---|
977 | hvar[i] = i; |
---|
978 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
979 | hSupp(hstc, hNstc, hvar, &hNvar); |
---|
980 | if ((hNvar == (r->N)) && (hNstc >= (r->N))) |
---|
981 | { |
---|
982 | if ((hNvar > 2) && (hNstc > 10)) |
---|
983 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
984 | memset(hpur0, 0, ((r->N) + 1) * sizeof(int)); |
---|
985 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
986 | if (hNpure == hNvar) |
---|
987 | { |
---|
988 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
989 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
990 | } |
---|
991 | else |
---|
992 | hMu = -1; |
---|
993 | } |
---|
994 | else if (hNvar) |
---|
995 | hMu = -1; |
---|
996 | mc--; |
---|
997 | if (mc <= 0 || hMu < 0) |
---|
998 | break; |
---|
999 | } |
---|
1000 | hKill(stcmem, (r->N) - 1); |
---|
1001 | omFreeSize((ADDRESS)hpur0, (1 + ((r->N) * (r->N))) * sizeof(int)); |
---|
1002 | omFreeSize((ADDRESS)hvar, ((r->N) + 1) * sizeof(int)); |
---|
1003 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
1004 | hDelete(hexist, hNexist); |
---|
1005 | if (hisModule) |
---|
1006 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1007 | return hMu; |
---|
1008 | } |
---|
1009 | |
---|
1010 | // HC |
---|
1011 | |
---|
1012 | STATIC_VAR poly pWork; |
---|
1013 | |
---|
1014 | static void hHedge(poly hEdge) |
---|
1015 | { |
---|
1016 | pSetm(pWork); |
---|
1017 | if (pLmCmp(pWork, hEdge) == currRing->OrdSgn) |
---|
1018 | { |
---|
1019 | for (int i = hNvar; i>0; i--) |
---|
1020 | pSetExp(hEdge,i, pGetExp(pWork,i)); |
---|
1021 | pSetm(hEdge); |
---|
1022 | } |
---|
1023 | } |
---|
1024 | |
---|
1025 | |
---|
1026 | static void hHedgeStep(scmon pure, scfmon stc, |
---|
1027 | int Nstc, varset var, int Nvar,poly hEdge) |
---|
1028 | { |
---|
1029 | int iv = Nvar -1, k = var[Nvar], a, a0, a1, b, i; |
---|
1030 | int x/*, x0*/; |
---|
1031 | scmon pn; |
---|
1032 | scfmon sn; |
---|
1033 | if (iv==0) |
---|
1034 | { |
---|
1035 | pSetExp(pWork, k, pure[k]); |
---|
1036 | hHedge(hEdge); |
---|
1037 | return; |
---|
1038 | } |
---|
1039 | else if (Nstc==0) |
---|
1040 | { |
---|
1041 | for (i = Nvar; i>0; i--) |
---|
1042 | pSetExp(pWork, var[i], pure[var[i]]); |
---|
1043 | hHedge(hEdge); |
---|
1044 | return; |
---|
1045 | } |
---|
1046 | x = a = 0; |
---|
1047 | pn = hGetpure(pure); |
---|
1048 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
1049 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
1050 | if (a == Nstc) |
---|
1051 | { |
---|
1052 | pSetExp(pWork, k, pure[k]); |
---|
1053 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
1054 | return; |
---|
1055 | } |
---|
1056 | else |
---|
1057 | { |
---|
1058 | pSetExp(pWork, k, x); |
---|
1059 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
1060 | } |
---|
1061 | b = a; |
---|
1062 | loop |
---|
1063 | { |
---|
1064 | a0 = a; |
---|
1065 | // x0 = x; |
---|
1066 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
1067 | hElimS(sn, &b, a0, a, var, iv); |
---|
1068 | a1 = a; |
---|
1069 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
1070 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
1071 | b += (a1 - a0); |
---|
1072 | if (a < Nstc) |
---|
1073 | { |
---|
1074 | pSetExp(pWork, k, x); |
---|
1075 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
1076 | } |
---|
1077 | else |
---|
1078 | { |
---|
1079 | pSetExp(pWork, k, pure[k]); |
---|
1080 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
1081 | return; |
---|
1082 | } |
---|
1083 | } |
---|
1084 | } |
---|
1085 | |
---|
1086 | void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge) |
---|
1087 | { |
---|
1088 | id_LmTest(S, currRing); |
---|
1089 | if (Q!=NULL) id_LmTest(Q, currRing); |
---|
1090 | |
---|
1091 | int i; |
---|
1092 | int k = ak; |
---|
1093 | #ifdef HAVE_RINGS |
---|
1094 | if (rField_is_Ring(currRing) && (currRing->OrdSgn == -1)) |
---|
1095 | { |
---|
1096 | //consider just monic generators (over rings with zero-divisors) |
---|
1097 | ideal SS=id_Head(S,currRing); |
---|
1098 | for(i=0;i<=idElem(S);i++) |
---|
1099 | { |
---|
1100 | if((SS->m[i]!=NULL) |
---|
1101 | && ((p_IsPurePower(SS->m[i],currRing)==0) |
---|
1102 | ||(!n_IsUnit(pGetCoeff(SS->m[i]), currRing->cf)))) |
---|
1103 | { |
---|
1104 | p_Delete(&SS->m[i],currRing); |
---|
1105 | } |
---|
1106 | } |
---|
1107 | S=id_Copy(SS,currRing); |
---|
1108 | idSkipZeroes(S); |
---|
1109 | } |
---|
1110 | #if 0 |
---|
1111 | printf("\nThis is HC:\n"); |
---|
1112 | for(int ii=0;ii<=idElem(S);ii++) |
---|
1113 | { |
---|
1114 | pWrite(S->m[ii]); |
---|
1115 | } |
---|
1116 | //getchar(); |
---|
1117 | #endif |
---|
1118 | #endif |
---|
1119 | if(idElem(S) == 0) |
---|
1120 | return; |
---|
1121 | hNvar = (currRing->N); |
---|
1122 | hexist = hInit(S, Q, &hNexist); |
---|
1123 | if (k!=0) |
---|
1124 | hComp(hexist, hNexist, k, hexist, &hNstc); |
---|
1125 | else |
---|
1126 | hNstc = hNexist; |
---|
1127 | assume(hNexist > 0); |
---|
1128 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1129 | hvar = (varset)omAlloc((hNvar + 1) * sizeof(int)); |
---|
1130 | hpure = (scmon)omAlloc((1 + (hNvar * hNvar)) * sizeof(int)); |
---|
1131 | stcmem = hCreate(hNvar - 1); |
---|
1132 | for (i = hNvar; i>0; i--) |
---|
1133 | hvar[i] = i; |
---|
1134 | hStaircase(hexist, &hNstc, hvar, hNvar); |
---|
1135 | if ((hNvar > 2) && (hNstc > 10)) |
---|
1136 | hOrdSupp(hexist, hNstc, hvar, hNvar); |
---|
1137 | memset(hpure, 0, (hNvar + 1) * sizeof(int)); |
---|
1138 | hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure); |
---|
1139 | hLexS(hexist, hNstc, hvar, hNvar); |
---|
1140 | if (hEdge!=NULL) |
---|
1141 | pLmFree(hEdge); |
---|
1142 | hEdge = pInit(); |
---|
1143 | pWork = pInit(); |
---|
1144 | hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge); |
---|
1145 | pSetComp(hEdge,ak); |
---|
1146 | hKill(stcmem, hNvar - 1); |
---|
1147 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
1148 | omFreeSize((ADDRESS)hvar, (hNvar + 1) * sizeof(int)); |
---|
1149 | omFreeSize((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(int)); |
---|
1150 | hDelete(hexist, hNexist); |
---|
1151 | pLmFree(pWork); |
---|
1152 | } |
---|
1153 | |
---|
1154 | |
---|
1155 | |
---|
1156 | // kbase |
---|
1157 | |
---|
1158 | STATIC_VAR poly last; |
---|
1159 | STATIC_VAR scmon act; |
---|
1160 | |
---|
1161 | static void scElKbase() |
---|
1162 | { |
---|
1163 | poly q = pInit(); |
---|
1164 | pSetCoeff0(q,nInit(1)); |
---|
1165 | pSetExpV(q,act); |
---|
1166 | pNext(q) = NULL; |
---|
1167 | last = pNext(last) = q; |
---|
1168 | } |
---|
1169 | |
---|
1170 | static int scMax( int i, scfmon stc, int Nvar) |
---|
1171 | { |
---|
1172 | int x, y=stc[0][Nvar]; |
---|
1173 | for (; i;) |
---|
1174 | { |
---|
1175 | i--; |
---|
1176 | x = stc[i][Nvar]; |
---|
1177 | if (x > y) y = x; |
---|
1178 | } |
---|
1179 | return y; |
---|
1180 | } |
---|
1181 | |
---|
1182 | static int scMin( int i, scfmon stc, int Nvar) |
---|
1183 | { |
---|
1184 | int x, y=stc[0][Nvar]; |
---|
1185 | for (; i;) |
---|
1186 | { |
---|
1187 | i--; |
---|
1188 | x = stc[i][Nvar]; |
---|
1189 | if (x < y) y = x; |
---|
1190 | } |
---|
1191 | return y; |
---|
1192 | } |
---|
1193 | |
---|
1194 | static int scRestrict( int &Nstc, scfmon stc, int Nvar) |
---|
1195 | { |
---|
1196 | int x, y; |
---|
1197 | int i, j, Istc = Nstc; |
---|
1198 | |
---|
1199 | y = MAX_INT_VAL; |
---|
1200 | for (i=Nstc-1; i>=0; i--) |
---|
1201 | { |
---|
1202 | j = Nvar-1; |
---|
1203 | loop |
---|
1204 | { |
---|
1205 | if(stc[i][j] != 0) break; |
---|
1206 | j--; |
---|
1207 | if (j == 0) |
---|
1208 | { |
---|
1209 | Istc--; |
---|
1210 | x = stc[i][Nvar]; |
---|
1211 | if (x < y) y = x; |
---|
1212 | stc[i] = NULL; |
---|
1213 | break; |
---|
1214 | } |
---|
1215 | } |
---|
1216 | } |
---|
1217 | if (Istc < Nstc) |
---|
1218 | { |
---|
1219 | for (i=Nstc-1; i>=0; i--) |
---|
1220 | { |
---|
1221 | if (stc[i] && (stc[i][Nvar] >= y)) |
---|
1222 | { |
---|
1223 | Istc--; |
---|
1224 | stc[i] = NULL; |
---|
1225 | } |
---|
1226 | } |
---|
1227 | j = 0; |
---|
1228 | while (stc[j]) j++; |
---|
1229 | i = j+1; |
---|
1230 | for(; i<Nstc; i++) |
---|
1231 | { |
---|
1232 | if (stc[i]) |
---|
1233 | { |
---|
1234 | stc[j] = stc[i]; |
---|
1235 | j++; |
---|
1236 | } |
---|
1237 | } |
---|
1238 | Nstc = Istc; |
---|
1239 | return y; |
---|
1240 | } |
---|
1241 | else |
---|
1242 | return -1; |
---|
1243 | } |
---|
1244 | |
---|
1245 | static void scAll( int Nvar, int deg) |
---|
1246 | { |
---|
1247 | int i; |
---|
1248 | int d = deg; |
---|
1249 | if (d == 0) |
---|
1250 | { |
---|
1251 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1252 | scElKbase(); |
---|
1253 | return; |
---|
1254 | } |
---|
1255 | if (Nvar == 1) |
---|
1256 | { |
---|
1257 | act[1] = d; |
---|
1258 | scElKbase(); |
---|
1259 | return; |
---|
1260 | } |
---|
1261 | do |
---|
1262 | { |
---|
1263 | act[Nvar] = d; |
---|
1264 | scAll(Nvar-1, deg-d); |
---|
1265 | d--; |
---|
1266 | } while (d >= 0); |
---|
1267 | } |
---|
1268 | |
---|
1269 | static void scAllKbase( int Nvar, int ideg, int deg) |
---|
1270 | { |
---|
1271 | do |
---|
1272 | { |
---|
1273 | act[Nvar] = ideg; |
---|
1274 | scAll(Nvar-1, deg-ideg); |
---|
1275 | ideg--; |
---|
1276 | } while (ideg >= 0); |
---|
1277 | } |
---|
1278 | |
---|
1279 | static void scDegKbase( scfmon stc, int Nstc, int Nvar, int deg) |
---|
1280 | { |
---|
1281 | int Ivar, Istc, i, j; |
---|
1282 | scfmon sn; |
---|
1283 | int x, ideg; |
---|
1284 | |
---|
1285 | if (deg == 0) |
---|
1286 | { |
---|
1287 | for (i=Nstc-1; i>=0; i--) |
---|
1288 | { |
---|
1289 | for (j=Nvar;j;j--){ if(stc[i][j]) break; } |
---|
1290 | if (j==0){return;} |
---|
1291 | } |
---|
1292 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1293 | scElKbase(); |
---|
1294 | return; |
---|
1295 | } |
---|
1296 | if (Nvar == 1) |
---|
1297 | { |
---|
1298 | for (i=Nstc-1; i>=0; i--) if(deg >= stc[i][1]) return; |
---|
1299 | act[1] = deg; |
---|
1300 | scElKbase(); |
---|
1301 | return; |
---|
1302 | } |
---|
1303 | Ivar = Nvar-1; |
---|
1304 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1305 | x = scRestrict(Nstc, sn, Nvar); |
---|
1306 | if (x <= 0) |
---|
1307 | { |
---|
1308 | if (x == 0) return; |
---|
1309 | ideg = deg; |
---|
1310 | } |
---|
1311 | else |
---|
1312 | { |
---|
1313 | if (deg < x) ideg = deg; |
---|
1314 | else ideg = x-1; |
---|
1315 | if (Nstc == 0) |
---|
1316 | { |
---|
1317 | scAllKbase(Nvar, ideg, deg); |
---|
1318 | return; |
---|
1319 | } |
---|
1320 | } |
---|
1321 | loop |
---|
1322 | { |
---|
1323 | x = scMax(Nstc, sn, Nvar); |
---|
1324 | while (ideg >= x) |
---|
1325 | { |
---|
1326 | act[Nvar] = ideg; |
---|
1327 | scDegKbase(sn, Nstc, Ivar, deg-ideg); |
---|
1328 | ideg--; |
---|
1329 | } |
---|
1330 | if (ideg < 0) return; |
---|
1331 | Istc = Nstc; |
---|
1332 | for (i=Nstc-1; i>=0; i--) |
---|
1333 | { |
---|
1334 | if (ideg < sn[i][Nvar]) |
---|
1335 | { |
---|
1336 | Istc--; |
---|
1337 | sn[i] = NULL; |
---|
1338 | } |
---|
1339 | } |
---|
1340 | if (Istc == 0) |
---|
1341 | { |
---|
1342 | scAllKbase(Nvar, ideg, deg); |
---|
1343 | return; |
---|
1344 | } |
---|
1345 | j = 0; |
---|
1346 | while (sn[j]) j++; |
---|
1347 | i = j+1; |
---|
1348 | for (; i<Nstc; i++) |
---|
1349 | { |
---|
1350 | if (sn[i]) |
---|
1351 | { |
---|
1352 | sn[j] = sn[i]; |
---|
1353 | j++; |
---|
1354 | } |
---|
1355 | } |
---|
1356 | Nstc = Istc; |
---|
1357 | } |
---|
1358 | } |
---|
1359 | |
---|
1360 | static void scInKbase( scfmon stc, int Nstc, int Nvar) |
---|
1361 | { |
---|
1362 | int Ivar, Istc, i, j; |
---|
1363 | scfmon sn; |
---|
1364 | int x, ideg; |
---|
1365 | |
---|
1366 | if (Nvar == 1) |
---|
1367 | { |
---|
1368 | ideg = scMin(Nstc, stc, 1); |
---|
1369 | while (ideg > 0) |
---|
1370 | { |
---|
1371 | ideg--; |
---|
1372 | act[1] = ideg; |
---|
1373 | scElKbase(); |
---|
1374 | } |
---|
1375 | return; |
---|
1376 | } |
---|
1377 | Ivar = Nvar-1; |
---|
1378 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1379 | x = scRestrict(Nstc, sn, Nvar); |
---|
1380 | if (x == 0) return; |
---|
1381 | ideg = x-1; |
---|
1382 | loop |
---|
1383 | { |
---|
1384 | x = scMax(Nstc, sn, Nvar); |
---|
1385 | while (ideg >= x) |
---|
1386 | { |
---|
1387 | act[Nvar] = ideg; |
---|
1388 | scInKbase(sn, Nstc, Ivar); |
---|
1389 | ideg--; |
---|
1390 | } |
---|
1391 | if (ideg < 0) return; |
---|
1392 | Istc = Nstc; |
---|
1393 | for (i=Nstc-1; i>=0; i--) |
---|
1394 | { |
---|
1395 | if (ideg < sn[i][Nvar]) |
---|
1396 | { |
---|
1397 | Istc--; |
---|
1398 | sn[i] = NULL; |
---|
1399 | } |
---|
1400 | } |
---|
1401 | j = 0; |
---|
1402 | while (sn[j]) j++; |
---|
1403 | i = j+1; |
---|
1404 | for (; i<Nstc; i++) |
---|
1405 | { |
---|
1406 | if (sn[i]) |
---|
1407 | { |
---|
1408 | sn[j] = sn[i]; |
---|
1409 | j++; |
---|
1410 | } |
---|
1411 | } |
---|
1412 | Nstc = Istc; |
---|
1413 | } |
---|
1414 | } |
---|
1415 | |
---|
1416 | static ideal scIdKbase(poly q, const int rank) |
---|
1417 | { |
---|
1418 | ideal res = idInit(pLength(q), rank); |
---|
1419 | polyset mm = res->m; |
---|
1420 | do |
---|
1421 | { |
---|
1422 | *mm = q; ++mm; |
---|
1423 | |
---|
1424 | const poly p = pNext(q); |
---|
1425 | pNext(q) = NULL; |
---|
1426 | q = p; |
---|
1427 | |
---|
1428 | } while (q!=NULL); |
---|
1429 | |
---|
1430 | id_Test(res, currRing); // WRONG RANK!!!??? |
---|
1431 | return res; |
---|
1432 | } |
---|
1433 | |
---|
1434 | ideal scKBase(int deg, ideal s, ideal Q, intvec * mv) |
---|
1435 | { |
---|
1436 | if( Q!=NULL) id_Test(Q, currRing); |
---|
1437 | |
---|
1438 | int i, di; |
---|
1439 | poly p; |
---|
1440 | |
---|
1441 | if (deg < 0) |
---|
1442 | { |
---|
1443 | di = scDimInt(s, Q); |
---|
1444 | if (di != 0) |
---|
1445 | { |
---|
1446 | //Werror("KBase not finite"); |
---|
1447 | return idInit(1,s->rank); |
---|
1448 | } |
---|
1449 | } |
---|
1450 | stcmem = hCreate((currRing->N) - 1); |
---|
1451 | hexist = hInit(s, Q, &hNexist); |
---|
1452 | p = last = pInit(); |
---|
1453 | /*pNext(p) = NULL;*/ |
---|
1454 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
1455 | *act = 0; |
---|
1456 | if (!hNexist) |
---|
1457 | { |
---|
1458 | scAll((currRing->N), deg); |
---|
1459 | goto ende; |
---|
1460 | } |
---|
1461 | if (!hisModule) |
---|
1462 | { |
---|
1463 | if (deg < 0) scInKbase(hexist, hNexist, (currRing->N)); |
---|
1464 | else scDegKbase(hexist, hNexist, (currRing->N), deg); |
---|
1465 | } |
---|
1466 | else |
---|
1467 | { |
---|
1468 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1469 | for (i = 1; i <= hisModule; i++) |
---|
1470 | { |
---|
1471 | *act = i; |
---|
1472 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1473 | int deg_ei=deg; |
---|
1474 | if (mv!=NULL) deg_ei -= (*mv)[i-1]; |
---|
1475 | if ((deg < 0) || (deg_ei>=0)) |
---|
1476 | { |
---|
1477 | if (hNstc) |
---|
1478 | { |
---|
1479 | if (deg < 0) scInKbase(hstc, hNstc, (currRing->N)); |
---|
1480 | else scDegKbase(hstc, hNstc, (currRing->N), deg_ei); |
---|
1481 | } |
---|
1482 | else |
---|
1483 | scAll((currRing->N), deg_ei); |
---|
1484 | } |
---|
1485 | } |
---|
1486 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1487 | } |
---|
1488 | ende: |
---|
1489 | hDelete(hexist, hNexist); |
---|
1490 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
1491 | hKill(stcmem, (currRing->N) - 1); |
---|
1492 | pLmFree(&p); |
---|
1493 | if (p == NULL) |
---|
1494 | return idInit(1,s->rank); |
---|
1495 | |
---|
1496 | last = p; |
---|
1497 | return scIdKbase(p, s->rank); |
---|
1498 | } |
---|
1499 | |
---|
1500 | #if 0 //-- alternative implementation of scComputeHC |
---|
1501 | /* |
---|
1502 | void scComputeHCw(ideal ss, ideal Q, int ak, poly &hEdge) |
---|
1503 | { |
---|
1504 | id_LmTest(ss, currRing); |
---|
1505 | if (Q!=NULL) id_LmTest(Q, currRing); |
---|
1506 | |
---|
1507 | int i, di; |
---|
1508 | poly p; |
---|
1509 | |
---|
1510 | if (hEdge!=NULL) |
---|
1511 | pLmFree(hEdge); |
---|
1512 | |
---|
1513 | ideal s=idInit(IDELEMS(ss),ak); |
---|
1514 | for(i=IDELEMS(ss)-1;i>=0;i--) |
---|
1515 | { |
---|
1516 | if (ss->m[i]!=NULL) s->m[i]=pHead(ss->m[i]); |
---|
1517 | } |
---|
1518 | di = scDimInt(s, Q); |
---|
1519 | stcmem = hCreate((currRing->N) - 1); |
---|
1520 | hexist = hInit(s, Q, &hNexist); |
---|
1521 | p = last = pInit(); |
---|
1522 | // pNext(p) = NULL; |
---|
1523 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
1524 | *act = 0; |
---|
1525 | if (!hNexist) |
---|
1526 | { |
---|
1527 | scAll((currRing->N), -1); |
---|
1528 | goto ende; |
---|
1529 | } |
---|
1530 | if (!hisModule) |
---|
1531 | { |
---|
1532 | scInKbase(hexist, hNexist, (currRing->N)); |
---|
1533 | } |
---|
1534 | else |
---|
1535 | { |
---|
1536 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1537 | for (i = 1; i <= hisModule; i++) |
---|
1538 | { |
---|
1539 | *act = i; |
---|
1540 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1541 | if (hNstc) |
---|
1542 | { |
---|
1543 | scInKbase(hstc, hNstc, (currRing->N)); |
---|
1544 | } |
---|
1545 | else |
---|
1546 | scAll((currRing->N), -1); |
---|
1547 | } |
---|
1548 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1549 | } |
---|
1550 | ende: |
---|
1551 | hDelete(hexist, hNexist); |
---|
1552 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
1553 | hKill(stcmem, (currRing->N) - 1); |
---|
1554 | pDeleteLm(&p); |
---|
1555 | idDelete(&s); |
---|
1556 | if (p == NULL) |
---|
1557 | { |
---|
1558 | return; // no HEdge |
---|
1559 | } |
---|
1560 | else |
---|
1561 | { |
---|
1562 | last = p; |
---|
1563 | ideal res=scIdKbase(p, ss->rank); |
---|
1564 | poly p_ind=res->m[0]; int ind=0; |
---|
1565 | for(i=IDELEMS(res)-1;i>0;i--) |
---|
1566 | { |
---|
1567 | if (pCmp(res->m[i],p_ind)==-1) { p_ind=res->m[i]; ind=i; } |
---|
1568 | } |
---|
1569 | assume(p_ind!=NULL); |
---|
1570 | assume(res->m[ind]==p_ind); |
---|
1571 | hEdge=p_ind; |
---|
1572 | res->m[ind]=NULL; |
---|
1573 | nDelete(&pGetCoeff(hEdge)); |
---|
1574 | pGetCoeff(hEdge)=NULL; |
---|
1575 | for(i=(currRing->N);i>0;i--) |
---|
1576 | pIncrExp(hEdge,i); |
---|
1577 | pSetm(hEdge); |
---|
1578 | |
---|
1579 | idDelete(&res); |
---|
1580 | return; |
---|
1581 | } |
---|
1582 | } |
---|
1583 | */ |
---|
1584 | #endif |
---|
1585 | |
---|
1586 | #ifdef HAVE_SHIFTBBA |
---|
1587 | |
---|
1588 | /* |
---|
1589 | * Computation of the Gel'fand-Kirillov Dimension |
---|
1590 | */ |
---|
1591 | |
---|
1592 | #include "polys/shiftop.h" |
---|
1593 | #include <vector> |
---|
1594 | |
---|
1595 | static std::vector<int> countCycles(const intvec* _G, int v, std::vector<int> path, std::vector<BOOLEAN> visited, std::vector<BOOLEAN> cyclic, std::vector<int> cache) |
---|
1596 | { |
---|
1597 | intvec* G = ivCopy(_G); // modifications must be local |
---|
1598 | |
---|
1599 | if (cache[v] != -2) return cache; // value is already cached |
---|
1600 | |
---|
1601 | visited[v] = TRUE; |
---|
1602 | path.push_back(v); |
---|
1603 | |
---|
1604 | int cycles = 0; |
---|
1605 | for (int w = 0; w < G->cols(); w++) |
---|
1606 | { |
---|
1607 | if (IMATELEM(*G, v + 1, w + 1)) // edge v -> w exists in G |
---|
1608 | { |
---|
1609 | if (!visited[w]) |
---|
1610 | { // continue with w |
---|
1611 | cache = countCycles(G, w, path, visited, cyclic, cache); |
---|
1612 | if (cache[w] == -1) |
---|
1613 | { |
---|
1614 | cache[v] = -1; |
---|
1615 | return cache; |
---|
1616 | } |
---|
1617 | cycles = si_max(cycles, cache[w]); |
---|
1618 | } |
---|
1619 | else |
---|
1620 | { // found new cycle |
---|
1621 | int pathIndexOfW = -1; |
---|
1622 | for (int i = path.size() - 1; i >= 0; i--) { |
---|
1623 | if (cyclic[path[i]] == 1) { // found an already cyclic vertex |
---|
1624 | cache[v] = -1; |
---|
1625 | return cache; |
---|
1626 | } |
---|
1627 | cyclic[path[i]] = TRUE; |
---|
1628 | |
---|
1629 | if (path[i] == w) { // end of the cycle |
---|
1630 | assume(IMATELEM(*G, v + 1, w + 1) != 0); |
---|
1631 | IMATELEM(*G, v + 1, w + 1) = 0; // remove edge v -> w |
---|
1632 | pathIndexOfW = i; |
---|
1633 | break; |
---|
1634 | } else { |
---|
1635 | assume(IMATELEM(*G, path[i - 1] + 1, path[i] + 1) != 0); |
---|
1636 | IMATELEM(*G, path[i - 1] + 1, path[i] + 1) = 0; // remove edge vi-1 -> vi |
---|
1637 | } |
---|
1638 | } |
---|
1639 | assume(pathIndexOfW != -1); // should never happen |
---|
1640 | for (int i = path.size() - 1; i >= pathIndexOfW; i--) { |
---|
1641 | cache = countCycles(G, path[i], path, visited, cyclic, cache); |
---|
1642 | if (cache[path[i]] == -1) |
---|
1643 | { |
---|
1644 | cache[v] = -1; |
---|
1645 | return cache; |
---|
1646 | } |
---|
1647 | cycles = si_max(cycles, cache[path[i]] + 1); |
---|
1648 | } |
---|
1649 | } |
---|
1650 | } |
---|
1651 | } |
---|
1652 | cache[v] = cycles; |
---|
1653 | |
---|
1654 | delete G; |
---|
1655 | return cache; |
---|
1656 | } |
---|
1657 | |
---|
1658 | // -1 is infinity |
---|
1659 | static int graphGrowth(const intvec* G) |
---|
1660 | { |
---|
1661 | // init |
---|
1662 | int n = G->cols(); |
---|
1663 | std::vector<int> path; |
---|
1664 | std::vector<BOOLEAN> visited; |
---|
1665 | std::vector<BOOLEAN> cyclic; |
---|
1666 | std::vector<int> cache; |
---|
1667 | visited.resize(n, FALSE); |
---|
1668 | cyclic.resize(n, FALSE); |
---|
1669 | cache.resize(n, -2); |
---|
1670 | |
---|
1671 | // get max number of cycles |
---|
1672 | int cycles = 0; |
---|
1673 | for (int v = 0; v < n; v++) |
---|
1674 | { |
---|
1675 | cache = countCycles(G, v, path, visited, cyclic, cache); |
---|
1676 | if (cache[v] == -1) |
---|
1677 | return -1; |
---|
1678 | cycles = si_max(cycles, cache[v]); |
---|
1679 | } |
---|
1680 | return cycles; |
---|
1681 | } |
---|
1682 | |
---|
1683 | // ATTENTION: |
---|
1684 | // - `words` contains the words normal modulo M of length n |
---|
1685 | // - `numberOfNormalWords` contains the number of words normal modulo M of length 0 ... n |
---|
1686 | static void _lp_computeNormalWords(ideal words, int& numberOfNormalWords, int length, ideal M, int minDeg, int& last) |
---|
1687 | { |
---|
1688 | if (length <= 0){ |
---|
1689 | poly one = pOne(); |
---|
1690 | if (p_LPDivisibleBy(M, one, currRing)) // 1 \in M => no normal words at all |
---|
1691 | { |
---|
1692 | pDelete(&one); |
---|
1693 | last = -1; |
---|
1694 | numberOfNormalWords = 0; |
---|
1695 | } |
---|
1696 | else |
---|
1697 | { |
---|
1698 | words->m[0] = one; |
---|
1699 | last = 0; |
---|
1700 | numberOfNormalWords = 1; |
---|
1701 | } |
---|
1702 | return; |
---|
1703 | } |
---|
1704 | |
---|
1705 | _lp_computeNormalWords(words, numberOfNormalWords, length - 1, M, minDeg, last); |
---|
1706 | |
---|
1707 | int nVars = currRing->isLPring - currRing->LPncGenCount; |
---|
1708 | int numberOfNewNormalWords = 0; |
---|
1709 | |
---|
1710 | for (int j = nVars - 1; j >= 0; j--) |
---|
1711 | { |
---|
1712 | for (int i = last; i >= 0; i--) |
---|
1713 | { |
---|
1714 | int index = (j * (last + 1)) + i; |
---|
1715 | |
---|
1716 | if (words->m[i] != NULL) |
---|
1717 | { |
---|
1718 | if (j > 0) { |
---|
1719 | words->m[index] = pCopy(words->m[i]); |
---|
1720 | } |
---|
1721 | |
---|
1722 | int varOffset = ((length - 1) * currRing->isLPring) + 1; |
---|
1723 | pSetExp(words->m[index], varOffset + j, 1); |
---|
1724 | pSetm(words->m[index]); |
---|
1725 | pTest(words->m[index]); |
---|
1726 | |
---|
1727 | if (length >= minDeg && p_LPDivisibleBy(M, words->m[index], currRing)) |
---|
1728 | { |
---|
1729 | pDelete(&words->m[index]); |
---|
1730 | words->m[index] = NULL; |
---|
1731 | } |
---|
1732 | else |
---|
1733 | { |
---|
1734 | numberOfNewNormalWords++; |
---|
1735 | } |
---|
1736 | } |
---|
1737 | } |
---|
1738 | } |
---|
1739 | |
---|
1740 | last = nVars * last + nVars - 1; |
---|
1741 | |
---|
1742 | numberOfNormalWords += numberOfNewNormalWords; |
---|
1743 | } |
---|
1744 | |
---|
1745 | static ideal lp_computeNormalWords(int length, ideal M) |
---|
1746 | { |
---|
1747 | long minDeg = IDELEMS(M) > 0 ? pTotaldegree(M->m[0]) : 0; |
---|
1748 | for (int i = 1; i < IDELEMS(M); i++) |
---|
1749 | { |
---|
1750 | minDeg = si_min(minDeg, pTotaldegree(M->m[i])); |
---|
1751 | } |
---|
1752 | |
---|
1753 | int nVars = currRing->isLPring - currRing->LPncGenCount; |
---|
1754 | |
---|
1755 | int maxElems = 1; |
---|
1756 | for (int i = 0; i < length; i++) // maxElems = nVars^n |
---|
1757 | maxElems *= nVars; |
---|
1758 | ideal words = idInit(maxElems); |
---|
1759 | int last, numberOfNormalWords; |
---|
1760 | _lp_computeNormalWords(words, numberOfNormalWords, length, M, minDeg, last); |
---|
1761 | idSkipZeroes(words); |
---|
1762 | return words; |
---|
1763 | } |
---|
1764 | |
---|
1765 | static int lp_countNormalWords(int upToLength, ideal M) |
---|
1766 | { |
---|
1767 | long minDeg = IDELEMS(M) > 0 ? pTotaldegree(M->m[0]) : 0; |
---|
1768 | for (int i = 1; i < IDELEMS(M); i++) |
---|
1769 | { |
---|
1770 | minDeg = si_min(minDeg, pTotaldegree(M->m[i])); |
---|
1771 | } |
---|
1772 | |
---|
1773 | int nVars = currRing->isLPring - currRing->LPncGenCount; |
---|
1774 | |
---|
1775 | int maxElems = 1; |
---|
1776 | for (int i = 0; i < upToLength; i++) // maxElems = nVars^n |
---|
1777 | maxElems *= nVars; |
---|
1778 | ideal words = idInit(maxElems); |
---|
1779 | int last, numberOfNormalWords; |
---|
1780 | _lp_computeNormalWords(words, numberOfNormalWords, upToLength, M, minDeg, last); |
---|
1781 | idDelete(&words); |
---|
1782 | return numberOfNormalWords; |
---|
1783 | } |
---|
1784 | |
---|
1785 | // NULL if graph is undefined |
---|
1786 | intvec* lp_ufnarovskiGraph(ideal G, ideal &standardWords) |
---|
1787 | { |
---|
1788 | long l = 0; |
---|
1789 | for (int i = 0; i < IDELEMS(G); i++) |
---|
1790 | l = si_max(pTotaldegree(G->m[i]), l); |
---|
1791 | l--; |
---|
1792 | if (l <= 0) |
---|
1793 | { |
---|
1794 | WerrorS("Ufnarovski graph not implemented for l <= 0"); |
---|
1795 | return NULL; |
---|
1796 | } |
---|
1797 | int lV = currRing->isLPring; |
---|
1798 | |
---|
1799 | standardWords = lp_computeNormalWords(l, G); |
---|
1800 | |
---|
1801 | int n = IDELEMS(standardWords); |
---|
1802 | intvec* UG = new intvec(n, n, 0); |
---|
1803 | for (int i = 0; i < n; i++) |
---|
1804 | { |
---|
1805 | for (int j = 0; j < n; j++) |
---|
1806 | { |
---|
1807 | poly v = standardWords->m[i]; |
---|
1808 | poly w = standardWords->m[j]; |
---|
1809 | |
---|
1810 | // check whether v*x1 = x2*w (overlap) |
---|
1811 | bool overlap = true; |
---|
1812 | for (int k = 1; k <= (l - 1) * lV; k++) |
---|
1813 | { |
---|
1814 | if (pGetExp(v, k + lV) != pGetExp(w, k)) { |
---|
1815 | overlap = false; |
---|
1816 | break; |
---|
1817 | } |
---|
1818 | } |
---|
1819 | |
---|
1820 | if (overlap) |
---|
1821 | { |
---|
1822 | // create the overlap |
---|
1823 | poly p = pMult(pCopy(v), p_LPVarAt(w, l, currRing)); |
---|
1824 | |
---|
1825 | // check whether the overlap is normal |
---|
1826 | bool normal = true; |
---|
1827 | for (int k = 0; k < IDELEMS(G); k++) |
---|
1828 | { |
---|
1829 | if (p_LPDivisibleBy(G->m[k], p, currRing)) |
---|
1830 | { |
---|
1831 | normal = false; |
---|
1832 | break; |
---|
1833 | } |
---|
1834 | } |
---|
1835 | |
---|
1836 | if (normal) |
---|
1837 | { |
---|
1838 | IMATELEM(*UG, i + 1, j + 1) = 1; |
---|
1839 | } |
---|
1840 | } |
---|
1841 | } |
---|
1842 | } |
---|
1843 | return UG; |
---|
1844 | } |
---|
1845 | |
---|
1846 | // -1 is infinity, -2 is error |
---|
1847 | int lp_gkDim(const ideal _G) |
---|
1848 | { |
---|
1849 | id_Test(_G, currRing); |
---|
1850 | |
---|
1851 | if (rField_is_Ring(currRing)) { |
---|
1852 | WerrorS("GK-Dim not implemented for rings"); |
---|
1853 | return -2; |
---|
1854 | } |
---|
1855 | |
---|
1856 | for (int i=IDELEMS(_G)-1;i>=0; i--) |
---|
1857 | { |
---|
1858 | if (_G->m[i] != NULL) |
---|
1859 | { |
---|
1860 | if (pGetComp(_G->m[i]) != 0) |
---|
1861 | { |
---|
1862 | WerrorS("GK-Dim not implemented for modules"); |
---|
1863 | return -2; |
---|
1864 | } |
---|
1865 | if (pGetNCGen(_G->m[i]) != 0) |
---|
1866 | { |
---|
1867 | WerrorS("GK-Dim not implemented for bi-modules"); |
---|
1868 | return -2; |
---|
1869 | } |
---|
1870 | } |
---|
1871 | } |
---|
1872 | |
---|
1873 | ideal G = id_Head(_G, currRing); // G = LM(G) (and copy) |
---|
1874 | idSkipZeroes(G); // remove zeros |
---|
1875 | id_DelLmEquals(G, currRing); // remove duplicates |
---|
1876 | |
---|
1877 | // check if G is the zero ideal |
---|
1878 | if (IDELEMS(G) == 1 && G->m[0] == NULL) |
---|
1879 | { |
---|
1880 | // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1! |
---|
1881 | int lV = currRing->isLPring; |
---|
1882 | int ncGenCount = currRing->LPncGenCount; |
---|
1883 | if (lV - ncGenCount == 0) |
---|
1884 | { |
---|
1885 | idDelete(&G); |
---|
1886 | return 0; |
---|
1887 | } |
---|
1888 | if (lV - ncGenCount == 1) |
---|
1889 | { |
---|
1890 | idDelete(&G); |
---|
1891 | return 1; |
---|
1892 | } |
---|
1893 | if (lV - ncGenCount >= 2) |
---|
1894 | { |
---|
1895 | idDelete(&G); |
---|
1896 | return -1; |
---|
1897 | } |
---|
1898 | } |
---|
1899 | |
---|
1900 | // get the max deg |
---|
1901 | long maxDeg = 0; |
---|
1902 | for (int i = 0; i < IDELEMS(G); i++) |
---|
1903 | { |
---|
1904 | maxDeg = si_max(maxDeg, pTotaldegree(G->m[i])); |
---|
1905 | |
---|
1906 | // also check whether G = <1> |
---|
1907 | if (pIsConstantComp(G->m[i])) |
---|
1908 | { |
---|
1909 | WerrorS("GK-Dim not defined for 0-ring"); |
---|
1910 | idDelete(&G); |
---|
1911 | return -2; |
---|
1912 | } |
---|
1913 | } |
---|
1914 | |
---|
1915 | // early termination if G \subset X |
---|
1916 | if (maxDeg <= 1) |
---|
1917 | { |
---|
1918 | int lV = currRing->isLPring; |
---|
1919 | int ncGenCount = currRing->LPncGenCount; |
---|
1920 | if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges |
---|
1921 | { |
---|
1922 | idDelete(&G); |
---|
1923 | return 0; |
---|
1924 | } |
---|
1925 | if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop |
---|
1926 | { |
---|
1927 | idDelete(&G); |
---|
1928 | return 1; |
---|
1929 | } |
---|
1930 | if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop |
---|
1931 | { |
---|
1932 | idDelete(&G); |
---|
1933 | return -1; |
---|
1934 | } |
---|
1935 | } |
---|
1936 | |
---|
1937 | ideal standardWords; |
---|
1938 | intvec* UG = lp_ufnarovskiGraph(G, standardWords); |
---|
1939 | if (UG == NULL) |
---|
1940 | { |
---|
1941 | idDelete(&G); |
---|
1942 | return -2; |
---|
1943 | } |
---|
1944 | if (errorreported) |
---|
1945 | { |
---|
1946 | delete UG; |
---|
1947 | idDelete(&G); |
---|
1948 | return -2; |
---|
1949 | } |
---|
1950 | int gkDim = graphGrowth(UG); |
---|
1951 | delete UG; |
---|
1952 | idDelete(&G); |
---|
1953 | return gkDim; |
---|
1954 | } |
---|
1955 | |
---|
1956 | // converts an intvec matrix to a vector<vector<int> > |
---|
1957 | static std::vector<std::vector<int> > iv2vv(intvec* M) |
---|
1958 | { |
---|
1959 | int rows = M->rows(); |
---|
1960 | int cols = M->cols(); |
---|
1961 | |
---|
1962 | std::vector<std::vector<int> > mat(rows, std::vector<int>(cols)); |
---|
1963 | |
---|
1964 | for (int i = 0; i < rows; i++) |
---|
1965 | { |
---|
1966 | for (int j = 0; j < cols; j++) |
---|
1967 | { |
---|
1968 | mat[i][j] = IMATELEM(*M, i + 1, j + 1); |
---|
1969 | } |
---|
1970 | } |
---|
1971 | |
---|
1972 | return mat; |
---|
1973 | } |
---|
1974 | |
---|
1975 | static void vvPrint(const std::vector<std::vector<int> >& mat) |
---|
1976 | { |
---|
1977 | for (int i = 0; i < mat.size(); i++) |
---|
1978 | { |
---|
1979 | for (int j = 0; j < mat[i].size(); j++) |
---|
1980 | { |
---|
1981 | Print("%d ", mat[i][j]); |
---|
1982 | } |
---|
1983 | PrintLn(); |
---|
1984 | } |
---|
1985 | } |
---|
1986 | |
---|
1987 | static void vvTest(const std::vector<std::vector<int> >& mat) |
---|
1988 | { |
---|
1989 | if (mat.size() > 0) |
---|
1990 | { |
---|
1991 | int cols = mat[0].size(); |
---|
1992 | for (int i = 1; i < mat.size(); i++) |
---|
1993 | { |
---|
1994 | if (cols != mat[i].size()) |
---|
1995 | WerrorS("number of cols in matrix inconsistent"); |
---|
1996 | } |
---|
1997 | } |
---|
1998 | } |
---|
1999 | |
---|
2000 | static void vvDeleteRow(std::vector<std::vector<int> >& mat, int row) |
---|
2001 | { |
---|
2002 | mat.erase(mat.begin() + row); |
---|
2003 | } |
---|
2004 | |
---|
2005 | static void vvDeleteColumn(std::vector<std::vector<int> >& mat, int col) |
---|
2006 | { |
---|
2007 | for (int i = 0; i < mat.size(); i++) |
---|
2008 | { |
---|
2009 | mat[i].erase(mat[i].begin() + col); |
---|
2010 | } |
---|
2011 | } |
---|
2012 | |
---|
2013 | static BOOLEAN vvIsRowZero(const std::vector<std::vector<int> >& mat, int row) |
---|
2014 | { |
---|
2015 | for (int i = 0; i < mat[row].size(); i++) |
---|
2016 | { |
---|
2017 | if (mat[row][i] != 0) |
---|
2018 | return FALSE; |
---|
2019 | } |
---|
2020 | return TRUE; |
---|
2021 | } |
---|
2022 | |
---|
2023 | static BOOLEAN vvIsColumnZero(const std::vector<std::vector<int> >& mat, int col) |
---|
2024 | { |
---|
2025 | for (int i = 0; i < mat.size(); i++) |
---|
2026 | { |
---|
2027 | if (mat[i][col] != 0) |
---|
2028 | return FALSE; |
---|
2029 | } |
---|
2030 | return TRUE; |
---|
2031 | } |
---|
2032 | |
---|
2033 | static BOOLEAN vvIsZero(const std::vector<std::vector<int> >& mat) |
---|
2034 | { |
---|
2035 | for (int i = 0; i < mat.size(); i++) |
---|
2036 | { |
---|
2037 | if (!vvIsRowZero(mat, i)) |
---|
2038 | return FALSE; |
---|
2039 | } |
---|
2040 | return TRUE; |
---|
2041 | } |
---|
2042 | |
---|
2043 | static std::vector<std::vector<int> > vvMult(const std::vector<std::vector<int> >& a, const std::vector<std::vector<int> >& b) |
---|
2044 | { |
---|
2045 | int ra = a.size(); |
---|
2046 | int rb = b.size(); |
---|
2047 | int ca = a.size() > 0 ? a[0].size() : 0; |
---|
2048 | int cb = b.size() > 0 ? b[0].size() : 0; |
---|
2049 | |
---|
2050 | if (ca != rb) |
---|
2051 | { |
---|
2052 | WerrorS("matrix dimensions do not match"); |
---|
2053 | return std::vector<std::vector<int> >(); |
---|
2054 | } |
---|
2055 | |
---|
2056 | std::vector<std::vector<int> > res(ra, std::vector<int>(cb)); |
---|
2057 | for (int i = 0; i < ra; i++) |
---|
2058 | { |
---|
2059 | for (int j = 0; j < cb; j++) |
---|
2060 | { |
---|
2061 | int sum = 0; |
---|
2062 | for (int k = 0; k < ca; k++) |
---|
2063 | sum += a[i][k] * b[k][j]; |
---|
2064 | res[i][j] = sum; |
---|
2065 | } |
---|
2066 | } |
---|
2067 | return res; |
---|
2068 | } |
---|
2069 | |
---|
2070 | static BOOLEAN isAcyclic(const intvec* G) |
---|
2071 | { |
---|
2072 | // init |
---|
2073 | int n = G->cols(); |
---|
2074 | std::vector<int> path; |
---|
2075 | std::vector<BOOLEAN> visited; |
---|
2076 | std::vector<BOOLEAN> cyclic; |
---|
2077 | std::vector<int> cache; |
---|
2078 | visited.resize(n, FALSE); |
---|
2079 | cyclic.resize(n, FALSE); |
---|
2080 | cache.resize(n, -2); |
---|
2081 | |
---|
2082 | for (int v = 0; v < n; v++) |
---|
2083 | { |
---|
2084 | cache = countCycles(G, v, path, visited, cyclic, cache); |
---|
2085 | // check that there are 0 cycles from v |
---|
2086 | if (cache[v] != 0) |
---|
2087 | return FALSE; |
---|
2088 | } |
---|
2089 | return TRUE; |
---|
2090 | } |
---|
2091 | |
---|
2092 | /* |
---|
2093 | * Computation of the K-Dimension |
---|
2094 | */ |
---|
2095 | |
---|
2096 | // -1 is infinity, -2 is error |
---|
2097 | int lp_kDim(const ideal _G) |
---|
2098 | { |
---|
2099 | if (rField_is_Ring(currRing)) { |
---|
2100 | WerrorS("K-Dim not implemented for rings"); |
---|
2101 | return -2; |
---|
2102 | } |
---|
2103 | |
---|
2104 | for (int i=IDELEMS(_G)-1;i>=0; i--) |
---|
2105 | { |
---|
2106 | if (_G->m[i] != NULL) |
---|
2107 | { |
---|
2108 | if (pGetComp(_G->m[i]) != 0) |
---|
2109 | { |
---|
2110 | WerrorS("K-Dim not implemented for modules"); |
---|
2111 | return -2; |
---|
2112 | } |
---|
2113 | if (pGetNCGen(_G->m[i]) != 0) |
---|
2114 | { |
---|
2115 | WerrorS("K-Dim not implemented for bi-modules"); |
---|
2116 | return -2; |
---|
2117 | } |
---|
2118 | } |
---|
2119 | } |
---|
2120 | |
---|
2121 | ideal G = id_Head(_G, currRing); // G = LM(G) (and copy) |
---|
2122 | if (TEST_OPT_PROT) |
---|
2123 | Print("%d original generators\n", IDELEMS(G)); |
---|
2124 | idSkipZeroes(G); // remove zeros |
---|
2125 | id_DelLmEquals(G, currRing); // remove duplicates |
---|
2126 | if (TEST_OPT_PROT) |
---|
2127 | Print("%d non-zero unique generators\n", IDELEMS(G)); |
---|
2128 | |
---|
2129 | // check if G is the zero ideal |
---|
2130 | if (IDELEMS(G) == 1 && G->m[0] == NULL) |
---|
2131 | { |
---|
2132 | // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1! |
---|
2133 | int lV = currRing->isLPring; |
---|
2134 | int ncGenCount = currRing->LPncGenCount; |
---|
2135 | if (lV - ncGenCount == 0) |
---|
2136 | { |
---|
2137 | idDelete(&G); |
---|
2138 | return 1; |
---|
2139 | } |
---|
2140 | if (lV - ncGenCount == 1) |
---|
2141 | { |
---|
2142 | idDelete(&G); |
---|
2143 | return -1; |
---|
2144 | } |
---|
2145 | if (lV - ncGenCount >= 2) |
---|
2146 | { |
---|
2147 | idDelete(&G); |
---|
2148 | return -1; |
---|
2149 | } |
---|
2150 | } |
---|
2151 | |
---|
2152 | // get the max deg |
---|
2153 | long maxDeg = 0; |
---|
2154 | for (int i = 0; i < IDELEMS(G); i++) |
---|
2155 | { |
---|
2156 | maxDeg = si_max(maxDeg, pTotaldegree(G->m[i])); |
---|
2157 | |
---|
2158 | // also check whether G = <1> |
---|
2159 | if (pIsConstantComp(G->m[i])) |
---|
2160 | { |
---|
2161 | WerrorS("K-Dim not defined for 0-ring"); // TODO is it minus infinity ? |
---|
2162 | idDelete(&G); |
---|
2163 | return -2; |
---|
2164 | } |
---|
2165 | } |
---|
2166 | if (TEST_OPT_PROT) |
---|
2167 | Print("max deg: %ld\n", maxDeg); |
---|
2168 | |
---|
2169 | |
---|
2170 | // for normal words of length minDeg ... maxDeg-1 |
---|
2171 | // brute-force the normal words |
---|
2172 | if (TEST_OPT_PROT) |
---|
2173 | PrintS("Computing normal words normally...\n"); |
---|
2174 | long numberOfNormalWords = lp_countNormalWords(maxDeg - 1, G); |
---|
2175 | |
---|
2176 | if (TEST_OPT_PROT) |
---|
2177 | Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1); |
---|
2178 | |
---|
2179 | // early termination if G \subset X |
---|
2180 | if (maxDeg <= 1) |
---|
2181 | { |
---|
2182 | int lV = currRing->isLPring; |
---|
2183 | int ncGenCount = currRing->LPncGenCount; |
---|
2184 | if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges |
---|
2185 | { |
---|
2186 | idDelete(&G); |
---|
2187 | return numberOfNormalWords; |
---|
2188 | } |
---|
2189 | if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop |
---|
2190 | { |
---|
2191 | idDelete(&G); |
---|
2192 | return -1; |
---|
2193 | } |
---|
2194 | if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop |
---|
2195 | { |
---|
2196 | idDelete(&G); |
---|
2197 | return -1; |
---|
2198 | } |
---|
2199 | } |
---|
2200 | |
---|
2201 | if (TEST_OPT_PROT) |
---|
2202 | PrintS("Computing Ufnarovski graph...\n"); |
---|
2203 | |
---|
2204 | ideal standardWords; |
---|
2205 | intvec* UG = lp_ufnarovskiGraph(G, standardWords); |
---|
2206 | if (UG == NULL) |
---|
2207 | { |
---|
2208 | idDelete(&G); |
---|
2209 | return -2; |
---|
2210 | } |
---|
2211 | if (errorreported) |
---|
2212 | { |
---|
2213 | delete UG; |
---|
2214 | idDelete(&G); |
---|
2215 | return -2; |
---|
2216 | } |
---|
2217 | |
---|
2218 | if (TEST_OPT_PROT) |
---|
2219 | Print("Ufnarovski graph is %dx%d.\n", UG->rows(), UG->cols()); |
---|
2220 | |
---|
2221 | if (TEST_OPT_PROT) |
---|
2222 | PrintS("Checking whether Ufnarovski graph is acyclic...\n"); |
---|
2223 | |
---|
2224 | if (!isAcyclic(UG)) |
---|
2225 | { |
---|
2226 | // in this case we have infinitely many normal words |
---|
2227 | return -1; |
---|
2228 | } |
---|
2229 | |
---|
2230 | std::vector<std::vector<int> > vvUG = iv2vv(UG); |
---|
2231 | for (int i = 0; i < vvUG.size(); i++) |
---|
2232 | { |
---|
2233 | if (vvIsRowZero(vvUG, i) && vvIsColumnZero(vvUG, i)) // i is isolated vertex |
---|
2234 | { |
---|
2235 | vvDeleteRow(vvUG, i); |
---|
2236 | vvDeleteColumn(vvUG, i); |
---|
2237 | i--; |
---|
2238 | } |
---|
2239 | } |
---|
2240 | if (TEST_OPT_PROT) |
---|
2241 | Print("Simplified Ufnarovski graph to %dx%d.\n", (int)vvUG.size(), (int)vvUG.size()); |
---|
2242 | |
---|
2243 | // for normal words of length >= maxDeg |
---|
2244 | // use Ufnarovski graph |
---|
2245 | if (TEST_OPT_PROT) |
---|
2246 | PrintS("Computing normal words via Ufnarovski graph...\n"); |
---|
2247 | std::vector<std::vector<int> > UGpower = vvUG; |
---|
2248 | long nUGpower = 1; |
---|
2249 | while (!vvIsZero(UGpower)) |
---|
2250 | { |
---|
2251 | if (TEST_OPT_PROT) |
---|
2252 | PrintS("Start count graph entries.\n"); |
---|
2253 | for (int i = 0; i < UGpower.size(); i++) |
---|
2254 | { |
---|
2255 | for (int j = 0; j < UGpower[i].size(); j++) |
---|
2256 | { |
---|
2257 | numberOfNormalWords += UGpower[i][j]; |
---|
2258 | } |
---|
2259 | } |
---|
2260 | |
---|
2261 | if (TEST_OPT_PROT) |
---|
2262 | { |
---|
2263 | PrintS("Done count graph entries.\n"); |
---|
2264 | Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1 + nUGpower); |
---|
2265 | } |
---|
2266 | |
---|
2267 | if (TEST_OPT_PROT) |
---|
2268 | PrintS("Start mat mult.\n"); |
---|
2269 | UGpower = vvMult(UGpower, vvUG); // TODO: avoid creation of new intvec |
---|
2270 | if (TEST_OPT_PROT) |
---|
2271 | PrintS("Done mat mult.\n"); |
---|
2272 | nUGpower++; |
---|
2273 | } |
---|
2274 | |
---|
2275 | delete UG; |
---|
2276 | idDelete(&G); |
---|
2277 | return numberOfNormalWords; |
---|
2278 | } |
---|
2279 | #endif |
---|