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, hMu2; |
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28 | VAR long hMu; |
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29 | VAR omBin indlist_bin = omGetSpecBin(sizeof(indlist)); |
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30 | |
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31 | /*0 implementation*/ |
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32 | |
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33 | // dimension |
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34 | |
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35 | void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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36 | varset var, int Nvar) |
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37 | { |
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38 | int dn, iv, rad0, b, c, x; |
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39 | scmon pn; |
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40 | scfmon rn; |
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41 | if (Nrad < 2) |
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42 | { |
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43 | dn = Npure + Nrad; |
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44 | if (dn < hCo) |
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45 | hCo = dn; |
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46 | return; |
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47 | } |
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48 | if (Npure+1 >= hCo) |
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49 | return; |
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50 | iv = Nvar; |
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51 | while(pure[var[iv]]) iv--; |
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52 | hStepR(rad, Nrad, var, iv, &rad0); |
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53 | if (rad0!=0) |
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54 | { |
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55 | iv--; |
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56 | if (rad0 < Nrad) |
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57 | { |
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58 | pn = hGetpure(pure); |
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59 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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60 | hDimSolve(pn, Npure + 1, rn, rad0, var, iv); |
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61 | b = rad0; |
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62 | c = Nrad; |
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63 | hElimR(rn, &rad0, b, c, var, iv); |
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64 | hPure(rn, b, &c, var, iv, pn, &x); |
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65 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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66 | rad0 += (c - b); |
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67 | hDimSolve(pn, Npure + x, rn, rad0, var, iv); |
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68 | } |
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69 | else |
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70 | { |
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71 | hDimSolve(pure, Npure, rad, Nrad, var, iv); |
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72 | } |
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73 | } |
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74 | else |
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75 | hCo = Npure + 1; |
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76 | } |
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77 | |
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78 | int scDimInt(ideal S, ideal Q) |
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79 | { |
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80 | id_Test(S, currRing); |
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81 | if( Q!=NULL ) id_Test(Q, currRing); |
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82 | |
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83 | int mc; |
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84 | hexist = hInit(S, Q, &hNexist); |
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85 | if (!hNexist) |
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86 | return (currRing->N); |
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87 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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88 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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89 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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90 | mc = hisModule; |
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91 | if (!mc) |
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92 | { |
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93 | hrad = hexist; |
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94 | hNrad = hNexist; |
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95 | } |
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96 | else |
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97 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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98 | radmem = hCreate((currRing->N) - 1); |
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99 | hCo = (currRing->N) + 1; |
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100 | loop |
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101 | { |
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102 | if (mc) |
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103 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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104 | if (hNrad) |
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105 | { |
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106 | hNvar = (currRing->N); |
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107 | hRadical(hrad, &hNrad, hNvar); |
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108 | hSupp(hrad, hNrad, hvar, &hNvar); |
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109 | if (hNvar) |
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110 | { |
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111 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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112 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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113 | hLexR(hrad, hNrad, hvar, hNvar); |
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114 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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115 | } |
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116 | } |
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117 | else |
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118 | { |
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119 | hCo = 0; |
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120 | break; |
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121 | } |
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122 | mc--; |
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123 | if (mc <= 0) |
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124 | break; |
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125 | } |
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126 | hKill(radmem, (currRing->N) - 1); |
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127 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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128 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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129 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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130 | hDelete(hexist, hNexist); |
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131 | if (hisModule) |
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132 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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133 | return (currRing->N) - hCo; |
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134 | } |
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135 | |
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136 | int scDimIntRing(ideal vid, ideal Q) |
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137 | { |
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138 | #ifdef HAVE_RINGS |
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139 | if (rField_is_Ring(currRing)) |
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140 | { |
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141 | int i = idPosConstant(vid); |
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142 | if ((i != -1) && (n_IsUnit(pGetCoeff(vid->m[i]),currRing->cf))) |
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143 | { /* ideal v contains unit; dim = -1 */ |
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144 | return(-1); |
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145 | } |
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146 | ideal vv = id_Head(vid,currRing); |
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147 | idSkipZeroes(vv); |
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148 | i = idPosConstant(vid); |
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149 | int d; |
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150 | if(i == -1) |
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151 | { |
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152 | d = scDimInt(vv, Q); |
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153 | if(rField_is_Z(currRing)) |
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154 | d++; |
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155 | } |
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156 | else |
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157 | { |
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158 | if(n_IsUnit(pGetCoeff(vv->m[i]),currRing->cf)) |
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159 | d = -1; |
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160 | else |
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161 | d = scDimInt(vv, Q); |
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162 | } |
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163 | //Anne's Idea for std(4,2x) = 0 bug |
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164 | int dcurr = d; |
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165 | for(unsigned ii=0;ii<(unsigned)IDELEMS(vv);ii++) |
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166 | { |
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167 | if(vv->m[ii] != NULL && !n_IsUnit(pGetCoeff(vv->m[ii]),currRing->cf)) |
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168 | { |
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169 | ideal vc = idCopy(vv); |
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170 | poly c = pInit(); |
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171 | pSetCoeff0(c,nCopy(pGetCoeff(vv->m[ii]))); |
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172 | idInsertPoly(vc,c); |
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173 | idSkipZeroes(vc); |
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174 | for(unsigned jj = 0;jj<(unsigned)IDELEMS(vc)-1;jj++) |
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175 | { |
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176 | if((vc->m[jj]!=NULL) |
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177 | && (n_DivBy(pGetCoeff(vc->m[jj]),pGetCoeff(c),currRing->cf))) |
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178 | { |
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179 | pDelete(&vc->m[jj]); |
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180 | } |
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181 | } |
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182 | idSkipZeroes(vc); |
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183 | i = idPosConstant(vc); |
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184 | if (i != -1) pDelete(&vc->m[i]); |
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185 | dcurr = scDimInt(vc, Q); |
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186 | // the following assumes the ground rings to be either zero- or one-dimensional |
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187 | if((i==-1) && rField_is_Z(currRing)) |
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188 | { |
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189 | // should also be activated for other euclidean domains as groundfield |
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190 | dcurr++; |
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191 | } |
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192 | idDelete(&vc); |
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193 | } |
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194 | if(dcurr > d) |
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195 | d = dcurr; |
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196 | } |
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197 | idDelete(&vv); |
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198 | return d; |
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199 | } |
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200 | #endif |
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201 | return scDimInt(vid,Q); |
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202 | } |
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203 | |
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204 | // independent set |
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205 | STATIC_VAR scmon hInd; |
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206 | |
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207 | static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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208 | varset var, int Nvar) |
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209 | { |
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210 | int dn, iv, rad0, b, c, x; |
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211 | scmon pn; |
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212 | scfmon rn; |
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213 | if (Nrad < 2) |
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214 | { |
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215 | dn = Npure + Nrad; |
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216 | if (dn < hCo) |
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217 | { |
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218 | hCo = dn; |
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219 | for (iv=(currRing->N); iv; iv--) |
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220 | { |
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221 | if (pure[iv]) |
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222 | hInd[iv] = 0; |
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223 | else |
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224 | hInd[iv] = 1; |
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225 | } |
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226 | if (Nrad) |
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227 | { |
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228 | pn = *rad; |
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229 | iv = Nvar; |
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230 | loop |
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231 | { |
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232 | x = var[iv]; |
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233 | if (pn[x]) |
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234 | { |
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235 | hInd[x] = 0; |
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236 | break; |
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237 | } |
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238 | iv--; |
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239 | } |
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240 | } |
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241 | } |
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242 | return; |
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243 | } |
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244 | if (Npure+1 >= hCo) |
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245 | return; |
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246 | iv = Nvar; |
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247 | while(pure[var[iv]]) iv--; |
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248 | hStepR(rad, Nrad, var, iv, &rad0); |
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249 | if (rad0) |
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250 | { |
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251 | iv--; |
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252 | if (rad0 < Nrad) |
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253 | { |
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254 | pn = hGetpure(pure); |
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255 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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256 | pn[var[iv + 1]] = 1; |
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257 | hIndSolve(pn, Npure + 1, rn, rad0, var, iv); |
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258 | pn[var[iv + 1]] = 0; |
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259 | b = rad0; |
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260 | c = Nrad; |
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261 | hElimR(rn, &rad0, b, c, var, iv); |
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262 | hPure(rn, b, &c, var, iv, pn, &x); |
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263 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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264 | rad0 += (c - b); |
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265 | hIndSolve(pn, Npure + x, rn, rad0, var, iv); |
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266 | } |
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267 | else |
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268 | { |
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269 | hIndSolve(pure, Npure, rad, Nrad, var, iv); |
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270 | } |
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271 | } |
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272 | else |
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273 | { |
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274 | hCo = Npure + 1; |
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275 | for (x=(currRing->N); x; x--) |
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276 | { |
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277 | if (pure[x]) |
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278 | hInd[x] = 0; |
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279 | else |
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280 | hInd[x] = 1; |
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281 | } |
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282 | hInd[var[iv]] = 0; |
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283 | } |
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284 | } |
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285 | |
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286 | intvec * scIndIntvec(ideal S, ideal Q) |
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287 | { |
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288 | id_Test(S, currRing); |
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289 | if( Q!=NULL ) id_Test(Q, currRing); |
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290 | |
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291 | intvec *Set=new intvec((currRing->N)); |
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292 | int mc,i; |
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293 | hexist = hInit(S, Q, &hNexist); |
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294 | if (hNexist==0) |
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295 | { |
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296 | for(i=0; i<(currRing->N); i++) |
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297 | (*Set)[i]=1; |
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298 | return Set; |
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299 | } |
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300 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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301 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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302 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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303 | hInd = (scmon)omAlloc0((1 + (currRing->N)) * sizeof(int)); |
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304 | mc = hisModule; |
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305 | if (mc==0) |
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306 | { |
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307 | hrad = hexist; |
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308 | hNrad = hNexist; |
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309 | } |
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310 | else |
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311 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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312 | radmem = hCreate((currRing->N) - 1); |
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313 | hCo = (currRing->N) + 1; |
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314 | loop |
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315 | { |
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316 | if (mc!=0) |
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317 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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318 | if (hNrad!=0) |
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319 | { |
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320 | hNvar = (currRing->N); |
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321 | hRadical(hrad, &hNrad, hNvar); |
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322 | hSupp(hrad, hNrad, hvar, &hNvar); |
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323 | if (hNvar!=0) |
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324 | { |
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325 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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326 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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327 | hLexR(hrad, hNrad, hvar, hNvar); |
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328 | hIndSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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329 | } |
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330 | } |
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331 | else |
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332 | { |
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333 | hCo = 0; |
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334 | break; |
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335 | } |
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336 | mc--; |
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337 | if (mc <= 0) |
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338 | break; |
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339 | } |
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340 | for(i=0; i<(currRing->N); i++) |
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341 | (*Set)[i] = hInd[i+1]; |
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342 | hKill(radmem, (currRing->N) - 1); |
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343 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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344 | omFreeSize((ADDRESS)hInd, (1 + (currRing->N)) * sizeof(int)); |
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345 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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346 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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347 | hDelete(hexist, hNexist); |
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348 | if (hisModule) |
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349 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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350 | return Set; |
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351 | } |
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352 | |
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353 | VAR indset ISet, JSet; |
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354 | |
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355 | static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar) |
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356 | { |
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357 | int k1, i; |
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358 | k1 = var[Nvar]; |
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359 | i = 0; |
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360 | loop |
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361 | { |
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362 | if (rad[i][k1]==0) |
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363 | return FALSE; |
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364 | i++; |
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365 | if (i == Nrad) |
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366 | return TRUE; |
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367 | } |
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368 | } |
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369 | |
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370 | static void hIndep(scmon pure) |
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371 | { |
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372 | int iv; |
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373 | intvec *Set; |
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374 | |
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375 | Set = ISet->set = new intvec((currRing->N)); |
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376 | for (iv=(currRing->N); iv!=0 ; iv--) |
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377 | { |
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378 | (*Set)[iv-1] = (pure[iv]==0); |
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379 | } |
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380 | ISet = ISet->nx = (indset)omAlloc0Bin(indlist_bin); |
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381 | hMu++; |
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382 | } |
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383 | |
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384 | void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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385 | varset var, int Nvar) |
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386 | { |
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387 | int dn, iv, rad0, b, c, x; |
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388 | scmon pn; |
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389 | scfmon rn; |
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390 | if (Nrad < 2) |
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391 | { |
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392 | dn = Npure + Nrad; |
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393 | if (dn == hCo) |
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394 | { |
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395 | if (Nrad==0) |
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396 | hIndep(pure); |
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397 | else |
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398 | { |
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399 | pn = *rad; |
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400 | for (iv = Nvar; iv!=0; iv--) |
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401 | { |
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402 | x = var[iv]; |
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403 | if (pn[x]) |
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404 | { |
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405 | pure[x] = 1; |
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406 | hIndep(pure); |
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407 | pure[x] = 0; |
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408 | } |
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409 | } |
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410 | } |
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411 | } |
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412 | return; |
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413 | } |
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414 | iv = Nvar; |
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415 | dn = Npure+1; |
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416 | if (dn >= hCo) |
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417 | { |
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418 | if (dn > hCo) |
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419 | return; |
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420 | loop |
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421 | { |
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422 | if(!pure[var[iv]]) |
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423 | { |
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424 | if(hNotZero(rad, Nrad, var, iv)) |
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425 | { |
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426 | pure[var[iv]] = 1; |
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427 | hIndep(pure); |
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428 | pure[var[iv]] = 0; |
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429 | } |
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430 | } |
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431 | iv--; |
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432 | if (!iv) |
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433 | return; |
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434 | } |
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435 | } |
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436 | while(pure[var[iv]]) iv--; |
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437 | hStepR(rad, Nrad, var, iv, &rad0); |
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438 | iv--; |
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439 | if (rad0 < Nrad) |
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440 | { |
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441 | pn = hGetpure(pure); |
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442 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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443 | pn[var[iv + 1]] = 1; |
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444 | hIndMult(pn, Npure + 1, rn, rad0, var, iv); |
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445 | pn[var[iv + 1]] = 0; |
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446 | b = rad0; |
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447 | c = Nrad; |
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448 | hElimR(rn, &rad0, b, c, var, iv); |
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449 | hPure(rn, b, &c, var, iv, pn, &x); |
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450 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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451 | rad0 += (c - b); |
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452 | hIndMult(pn, Npure + x, rn, rad0, var, iv); |
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453 | } |
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454 | else |
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455 | { |
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456 | hIndMult(pure, Npure, rad, Nrad, var, iv); |
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457 | } |
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458 | } |
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459 | |
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460 | /*3 |
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461 | * consider indset x := !pure |
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462 | * (for all i) (if(sm(i) > x) return FALSE) |
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463 | * else return TRUE |
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464 | */ |
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465 | static BOOLEAN hCheck1(indset sm, scmon pure) |
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466 | { |
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467 | int iv; |
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468 | intvec *Set; |
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469 | while (sm->nx != NULL) |
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470 | { |
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471 | Set = sm->set; |
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472 | iv=(currRing->N); |
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473 | loop |
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474 | { |
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475 | if (((*Set)[iv-1] == 0) && (pure[iv] == 0)) |
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476 | break; |
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477 | iv--; |
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478 | if (iv == 0) |
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479 | return FALSE; |
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480 | } |
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481 | sm = sm->nx; |
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482 | } |
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483 | return TRUE; |
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484 | } |
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485 | |
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486 | /*3 |
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487 | * consider indset x := !pure |
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488 | * (for all i) if(x > sm(i)) delete sm(i)) |
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489 | * return (place for x) |
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490 | */ |
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491 | static indset hCheck2(indset sm, scmon pure) |
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492 | { |
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493 | int iv; |
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494 | intvec *Set; |
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495 | indset be, a1 = NULL; |
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496 | while (sm->nx != NULL) |
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497 | { |
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498 | Set = sm->set; |
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499 | iv=(currRing->N); |
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500 | loop |
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501 | { |
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502 | if ((pure[iv] == 1) && ((*Set)[iv-1] == 1)) |
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503 | break; |
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504 | iv--; |
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505 | if (iv == 0) |
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506 | { |
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507 | if (a1 == NULL) |
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508 | { |
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509 | a1 = sm; |
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510 | } |
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511 | else |
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512 | { |
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513 | hMu2--; |
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514 | be->nx = sm->nx; |
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515 | delete Set; |
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516 | omFreeBin((ADDRESS)sm, indlist_bin); |
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517 | sm = be; |
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518 | } |
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519 | break; |
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520 | } |
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521 | } |
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522 | be = sm; |
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523 | sm = sm->nx; |
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524 | } |
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525 | if (a1 != NULL) |
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526 | { |
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527 | return a1; |
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528 | } |
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529 | else |
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530 | { |
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531 | hMu2++; |
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532 | sm->set = new intvec((currRing->N)); |
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533 | sm->nx = (indset)omAlloc0Bin(indlist_bin); |
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534 | return sm; |
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535 | } |
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536 | } |
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537 | |
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538 | /*2 |
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539 | * definition x >= y |
---|
540 | * x(i) == 0 => y(i) == 0 |
---|
541 | * > ex. j with x(j) == 1 and y(j) == 0 |
---|
542 | */ |
---|
543 | static void hCheckIndep(scmon pure) |
---|
544 | { |
---|
545 | intvec *Set; |
---|
546 | indset res; |
---|
547 | int iv; |
---|
548 | if (hCheck1(ISet, pure)) |
---|
549 | { |
---|
550 | if (hCheck1(JSet, pure)) |
---|
551 | { |
---|
552 | res = hCheck2(JSet,pure); |
---|
553 | if (res == NULL) |
---|
554 | return; |
---|
555 | Set = res->set; |
---|
556 | for (iv=(currRing->N); iv; iv--) |
---|
557 | { |
---|
558 | (*Set)[iv-1] = (pure[iv]==0); |
---|
559 | } |
---|
560 | } |
---|
561 | } |
---|
562 | } |
---|
563 | |
---|
564 | void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
565 | varset var, int Nvar) |
---|
566 | { |
---|
567 | int dn, iv, rad0, b, c, x; |
---|
568 | scmon pn; |
---|
569 | scfmon rn; |
---|
570 | if (Nrad < 2) |
---|
571 | { |
---|
572 | dn = Npure + Nrad; |
---|
573 | if (dn > hCo) |
---|
574 | { |
---|
575 | if (!Nrad) |
---|
576 | hCheckIndep(pure); |
---|
577 | else |
---|
578 | { |
---|
579 | pn = *rad; |
---|
580 | for (iv = Nvar; iv; iv--) |
---|
581 | { |
---|
582 | x = var[iv]; |
---|
583 | if (pn[x]) |
---|
584 | { |
---|
585 | pure[x] = 1; |
---|
586 | hCheckIndep(pure); |
---|
587 | pure[x] = 0; |
---|
588 | } |
---|
589 | } |
---|
590 | } |
---|
591 | } |
---|
592 | return; |
---|
593 | } |
---|
594 | iv = Nvar; |
---|
595 | while(pure[var[iv]]) iv--; |
---|
596 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
597 | iv--; |
---|
598 | if (rad0 < Nrad) |
---|
599 | { |
---|
600 | pn = hGetpure(pure); |
---|
601 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
602 | pn[var[iv + 1]] = 1; |
---|
603 | hIndAllMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
604 | pn[var[iv + 1]] = 0; |
---|
605 | b = rad0; |
---|
606 | c = Nrad; |
---|
607 | hElimR(rn, &rad0, b, c, var, iv); |
---|
608 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
609 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
610 | rad0 += (c - b); |
---|
611 | hIndAllMult(pn, Npure + x, rn, rad0, var, iv); |
---|
612 | } |
---|
613 | else |
---|
614 | { |
---|
615 | hIndAllMult(pure, Npure, rad, Nrad, var, iv); |
---|
616 | } |
---|
617 | } |
---|
618 | |
---|
619 | // multiplicity |
---|
620 | |
---|
621 | static long hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar) |
---|
622 | { |
---|
623 | int iv = Nvar -1, a, a0, a1, b, i; |
---|
624 | long sum; |
---|
625 | int x, x0; |
---|
626 | scmon pn; |
---|
627 | scfmon sn; |
---|
628 | if (!iv) |
---|
629 | return pure[var[1]]; |
---|
630 | else if (!Nstc) |
---|
631 | { |
---|
632 | sum = 1; |
---|
633 | for (i = Nvar; i; i--) |
---|
634 | sum *= pure[var[i]]; |
---|
635 | return sum; |
---|
636 | } |
---|
637 | x = a = 0; |
---|
638 | pn = hGetpure(pure); |
---|
639 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
640 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
641 | if (a == Nstc) |
---|
642 | { |
---|
643 | #if SIZEOF_LONG==8 |
---|
644 | return (long)pure[var[Nvar]] * hZeroMult(pn, sn, a, var, iv); |
---|
645 | #else |
---|
646 | int64 t=hZeroMult(pn, sn, a, var, iv); |
---|
647 | t *= pure[var[Nvar]]; |
---|
648 | if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t; |
---|
649 | else if (!errorreported) WerrorS("int overflow in vdim 3"); |
---|
650 | return sum; |
---|
651 | #endif |
---|
652 | } |
---|
653 | else |
---|
654 | { |
---|
655 | #if SIZEOF_LONG==8 |
---|
656 | sum = x * hZeroMult(pn, sn, a, var, iv); |
---|
657 | #else |
---|
658 | int64 t=hZeroMult(pn, sn, a, var, iv); |
---|
659 | t *= x; |
---|
660 | if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t; |
---|
661 | else if (!errorreported) WerrorS("int overflow in vdim 4"); |
---|
662 | #endif |
---|
663 | } |
---|
664 | b = a; |
---|
665 | loop |
---|
666 | { |
---|
667 | a0 = a; |
---|
668 | x0 = x; |
---|
669 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
670 | hElimS(sn, &b, a0, a, var, iv); |
---|
671 | a1 = a; |
---|
672 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
673 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
674 | b += (a1 - a0); |
---|
675 | if (a < Nstc) |
---|
676 | { |
---|
677 | #if SIZEOF_LONG==8 |
---|
678 | sum += (long)(x - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
679 | #else |
---|
680 | int64 t=hZeroMult(pn, sn, b, var, iv); |
---|
681 | t *= (x-x0); |
---|
682 | t += sum; |
---|
683 | if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t; |
---|
684 | else if (!errorreported) WerrorS("int overflow in vdim 1"); |
---|
685 | #endif |
---|
686 | } |
---|
687 | else |
---|
688 | { |
---|
689 | #if SIZEOF_LONG==8 |
---|
690 | sum += (long)(pure[var[Nvar]] - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
691 | #else |
---|
692 | int64 t=hZeroMult(pn, sn, b, var, iv); |
---|
693 | t *= (pure[var[Nvar]]-x0); |
---|
694 | t += sum; |
---|
695 | if ((t>=INT_MIN)&&(t<=INT_MAX)) sum=t; |
---|
696 | else if (!errorreported) WerrorS("int overflow in vdim 2"); |
---|
697 | #endif |
---|
698 | return sum; |
---|
699 | } |
---|
700 | } |
---|
701 | } |
---|
702 | |
---|
703 | static void hProject(scmon pure, varset sel) |
---|
704 | { |
---|
705 | int i, i0, k; |
---|
706 | i0 = 0; |
---|
707 | for (i = 1; i <= (currRing->N); i++) |
---|
708 | { |
---|
709 | if (pure[i]) |
---|
710 | { |
---|
711 | i0++; |
---|
712 | sel[i0] = i; |
---|
713 | } |
---|
714 | } |
---|
715 | i = hNstc; |
---|
716 | memcpy(hwork, hstc, i * sizeof(scmon)); |
---|
717 | hStaircase(hwork, &i, sel, i0); |
---|
718 | if ((i0 > 2) && (i > 10)) |
---|
719 | hOrdSupp(hwork, i, sel, i0); |
---|
720 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
721 | hPure(hwork, 0, &i, sel, i0, hpur0, &k); |
---|
722 | hLexS(hwork, i, sel, i0); |
---|
723 | hMu += hZeroMult(hpur0, hwork, i, sel, i0); |
---|
724 | } |
---|
725 | |
---|
726 | static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
727 | varset var, int Nvar) |
---|
728 | { |
---|
729 | int dn, iv, rad0, b, c, x; |
---|
730 | scmon pn; |
---|
731 | scfmon rn; |
---|
732 | if (Nrad < 2) |
---|
733 | { |
---|
734 | dn = Npure + Nrad; |
---|
735 | if (dn == hCo) |
---|
736 | { |
---|
737 | if (!Nrad) |
---|
738 | hProject(pure, hsel); |
---|
739 | else |
---|
740 | { |
---|
741 | pn = *rad; |
---|
742 | for (iv = Nvar; iv; iv--) |
---|
743 | { |
---|
744 | x = var[iv]; |
---|
745 | if (pn[x]) |
---|
746 | { |
---|
747 | pure[x] = 1; |
---|
748 | hProject(pure, hsel); |
---|
749 | pure[x] = 0; |
---|
750 | } |
---|
751 | } |
---|
752 | } |
---|
753 | } |
---|
754 | return; |
---|
755 | } |
---|
756 | iv = Nvar; |
---|
757 | dn = Npure+1; |
---|
758 | if (dn >= hCo) |
---|
759 | { |
---|
760 | if (dn > hCo) |
---|
761 | return; |
---|
762 | loop |
---|
763 | { |
---|
764 | if(!pure[var[iv]]) |
---|
765 | { |
---|
766 | if(hNotZero(rad, Nrad, var, iv)) |
---|
767 | { |
---|
768 | pure[var[iv]] = 1; |
---|
769 | hProject(pure, hsel); |
---|
770 | pure[var[iv]] = 0; |
---|
771 | } |
---|
772 | } |
---|
773 | iv--; |
---|
774 | if (!iv) |
---|
775 | return; |
---|
776 | } |
---|
777 | } |
---|
778 | while(pure[var[iv]]) iv--; |
---|
779 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
780 | iv--; |
---|
781 | if (rad0 < Nrad) |
---|
782 | { |
---|
783 | pn = hGetpure(pure); |
---|
784 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
785 | pn[var[iv + 1]] = 1; |
---|
786 | hDimMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
787 | pn[var[iv + 1]] = 0; |
---|
788 | b = rad0; |
---|
789 | c = Nrad; |
---|
790 | hElimR(rn, &rad0, b, c, var, iv); |
---|
791 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
792 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
793 | rad0 += (c - b); |
---|
794 | hDimMult(pn, Npure + x, rn, rad0, var, iv); |
---|
795 | } |
---|
796 | else |
---|
797 | { |
---|
798 | hDimMult(pure, Npure, rad, Nrad, var, iv); |
---|
799 | } |
---|
800 | } |
---|
801 | |
---|
802 | static void hDegree(ideal S, ideal Q) |
---|
803 | { |
---|
804 | id_Test(S, currRing); |
---|
805 | if( Q!=NULL ) id_Test(Q, currRing); |
---|
806 | |
---|
807 | int di; |
---|
808 | int mc; |
---|
809 | hexist = hInit(S, Q, &hNexist); |
---|
810 | if (!hNexist) |
---|
811 | { |
---|
812 | hCo = 0; |
---|
813 | hMu = 1; |
---|
814 | return; |
---|
815 | } |
---|
816 | //hWeight(); |
---|
817 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
818 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
819 | hsel = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
820 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
821 | hpur0 = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
822 | mc = hisModule; |
---|
823 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
824 | if (!mc) |
---|
825 | { |
---|
826 | memcpy(hrad, hexist, hNexist * sizeof(scmon)); |
---|
827 | hstc = hexist; |
---|
828 | hNrad = hNstc = hNexist; |
---|
829 | } |
---|
830 | else |
---|
831 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
832 | radmem = hCreate((currRing->N) - 1); |
---|
833 | stcmem = hCreate((currRing->N) - 1); |
---|
834 | hCo = (currRing->N) + 1; |
---|
835 | di = hCo + 1; |
---|
836 | loop |
---|
837 | { |
---|
838 | if (mc) |
---|
839 | { |
---|
840 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
---|
841 | hNstc = hNrad; |
---|
842 | memcpy(hstc, hrad, hNrad * sizeof(scmon)); |
---|
843 | } |
---|
844 | if (hNrad) |
---|
845 | { |
---|
846 | hNvar = (currRing->N); |
---|
847 | hRadical(hrad, &hNrad, hNvar); |
---|
848 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
849 | if (hNvar) |
---|
850 | { |
---|
851 | hCo = hNvar; |
---|
852 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
853 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
854 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
855 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
856 | } |
---|
857 | } |
---|
858 | else |
---|
859 | { |
---|
860 | hNvar = 1; |
---|
861 | hCo = 0; |
---|
862 | } |
---|
863 | if (hCo < di) |
---|
864 | { |
---|
865 | di = hCo; |
---|
866 | hMu = 0; |
---|
867 | } |
---|
868 | if (hNvar && (hCo == di)) |
---|
869 | { |
---|
870 | if (di && (di < (currRing->N))) |
---|
871 | hDimMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
872 | else if (!di) |
---|
873 | hMu++; |
---|
874 | else |
---|
875 | { |
---|
876 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
877 | if ((hNvar > 2) && (hNstc > 10)) |
---|
878 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
879 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
880 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
881 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
882 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
883 | } |
---|
884 | } |
---|
885 | mc--; |
---|
886 | if (mc <= 0) |
---|
887 | break; |
---|
888 | } |
---|
889 | hCo = di; |
---|
890 | hKill(stcmem, (currRing->N) - 1); |
---|
891 | hKill(radmem, (currRing->N) - 1); |
---|
892 | omFreeSize((ADDRESS)hpur0, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
893 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
894 | omFreeSize((ADDRESS)hsel, ((currRing->N) + 1) * sizeof(int)); |
---|
895 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
---|
896 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
897 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
---|
898 | hDelete(hexist, hNexist); |
---|
899 | if (hisModule) |
---|
900 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
901 | } |
---|
902 | |
---|
903 | int scMultInt(ideal S, ideal Q) |
---|
904 | { |
---|
905 | id_Test(S, currRing); |
---|
906 | if( Q!=NULL ) id_Test(Q, currRing); |
---|
907 | |
---|
908 | hDegree(S, Q); |
---|
909 | return hMu; |
---|
910 | } |
---|
911 | |
---|
912 | void scPrintDegree(int co, int mu) |
---|
913 | { |
---|
914 | int di = (currRing->N)-co; |
---|
915 | if (currRing->OrdSgn == 1) |
---|
916 | { |
---|
917 | if (di>0) |
---|
918 | Print("// dimension (proj.) = %d\n// degree (proj.) = %d\n", di-1, mu); |
---|
919 | else |
---|
920 | Print("// dimension (affine) = 0\n// degree (affine) = %d\n", mu); |
---|
921 | } |
---|
922 | else |
---|
923 | Print("// dimension (local) = %d\n// multiplicity = %d\n", di, mu); |
---|
924 | } |
---|
925 | |
---|
926 | void scDegree(ideal S, intvec *modulweight, ideal Q) |
---|
927 | { |
---|
928 | id_Test(S, currRing); |
---|
929 | if( Q!=NULL ) id_Test(Q, currRing); |
---|
930 | |
---|
931 | int co, mu, l; |
---|
932 | intvec *hseries2; |
---|
933 | intvec *hseries1 = hFirstSeries(S, modulweight, Q); |
---|
934 | if (errorreported) return; |
---|
935 | l = hseries1->length()-1; |
---|
936 | if (l > 1) |
---|
937 | hseries2 = hSecondSeries(hseries1); |
---|
938 | else |
---|
939 | hseries2 = hseries1; |
---|
940 | hDegreeSeries(hseries1, hseries2, &co, &mu); |
---|
941 | if ((l == 1) &&(mu == 0)) |
---|
942 | scPrintDegree((currRing->N)+1, 0); |
---|
943 | else |
---|
944 | scPrintDegree(co, mu); |
---|
945 | if (l>1) |
---|
946 | delete hseries1; |
---|
947 | delete hseries2; |
---|
948 | } |
---|
949 | |
---|
950 | long scMult0Int(ideal S, ideal Q) |
---|
951 | { |
---|
952 | id_LmTest(S, currRing); |
---|
953 | if (Q!=NULL) id_LmTest(Q, currRing); |
---|
954 | |
---|
955 | int mc; |
---|
956 | hexist = hInit(S, Q, &hNexist); |
---|
957 | if (!hNexist) |
---|
958 | { |
---|
959 | hMu = -1; |
---|
960 | return -1; |
---|
961 | } |
---|
962 | else |
---|
963 | hMu = 0; |
---|
964 | |
---|
965 | const ring r = currRing; |
---|
966 | |
---|
967 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
968 | hvar = (varset)omAlloc(((r->N) + 1) * sizeof(int)); |
---|
969 | hpur0 = (scmon)omAlloc((1 + ((r->N) * (r->N))) * sizeof(int)); |
---|
970 | mc = hisModule; |
---|
971 | if (!mc) |
---|
972 | { |
---|
973 | hstc = hexist; |
---|
974 | hNstc = hNexist; |
---|
975 | } |
---|
976 | else |
---|
977 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
978 | stcmem = hCreate((r->N) - 1); |
---|
979 | loop |
---|
980 | { |
---|
981 | if (mc) |
---|
982 | { |
---|
983 | hComp(hexist, hNexist, mc, hstc, &hNstc); |
---|
984 | if (!hNstc) |
---|
985 | { |
---|
986 | hMu = -1; |
---|
987 | break; |
---|
988 | } |
---|
989 | } |
---|
990 | hNvar = (r->N); |
---|
991 | for (int i = hNvar; i; i--) |
---|
992 | hvar[i] = i; |
---|
993 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
994 | hSupp(hstc, hNstc, hvar, &hNvar); |
---|
995 | if ((hNvar == (r->N)) && (hNstc >= (r->N))) |
---|
996 | { |
---|
997 | if ((hNvar > 2) && (hNstc > 10)) |
---|
998 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
999 | memset(hpur0, 0, ((r->N) + 1) * sizeof(int)); |
---|
1000 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
1001 | if (hNpure == hNvar) |
---|
1002 | { |
---|
1003 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
1004 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
1005 | } |
---|
1006 | else |
---|
1007 | hMu = -1; |
---|
1008 | } |
---|
1009 | else if (hNvar) |
---|
1010 | hMu = -1; |
---|
1011 | mc--; |
---|
1012 | if (mc <= 0 || hMu < 0) |
---|
1013 | break; |
---|
1014 | } |
---|
1015 | hKill(stcmem, (r->N) - 1); |
---|
1016 | omFreeSize((ADDRESS)hpur0, (1 + ((r->N) * (r->N))) * sizeof(int)); |
---|
1017 | omFreeSize((ADDRESS)hvar, ((r->N) + 1) * sizeof(int)); |
---|
1018 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
1019 | hDelete(hexist, hNexist); |
---|
1020 | if (hisModule) |
---|
1021 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1022 | return hMu; |
---|
1023 | } |
---|
1024 | |
---|
1025 | // HC |
---|
1026 | |
---|
1027 | STATIC_VAR poly pWork; |
---|
1028 | |
---|
1029 | static void hHedge(poly hEdge) |
---|
1030 | { |
---|
1031 | pSetm(pWork); |
---|
1032 | if (pLmCmp(pWork, hEdge) == currRing->OrdSgn) |
---|
1033 | { |
---|
1034 | for (int i = hNvar; i>0; i--) |
---|
1035 | pSetExp(hEdge,i, pGetExp(pWork,i)); |
---|
1036 | pSetm(hEdge); |
---|
1037 | } |
---|
1038 | } |
---|
1039 | |
---|
1040 | |
---|
1041 | static void hHedgeStep(scmon pure, scfmon stc, |
---|
1042 | int Nstc, varset var, int Nvar,poly hEdge) |
---|
1043 | { |
---|
1044 | int iv = Nvar -1, k = var[Nvar], a, a0, a1, b, i; |
---|
1045 | int x/*, x0*/; |
---|
1046 | scmon pn; |
---|
1047 | scfmon sn; |
---|
1048 | if (iv==0) |
---|
1049 | { |
---|
1050 | pSetExp(pWork, k, pure[k]); |
---|
1051 | hHedge(hEdge); |
---|
1052 | return; |
---|
1053 | } |
---|
1054 | else if (Nstc==0) |
---|
1055 | { |
---|
1056 | for (i = Nvar; i>0; i--) |
---|
1057 | pSetExp(pWork, var[i], pure[var[i]]); |
---|
1058 | hHedge(hEdge); |
---|
1059 | return; |
---|
1060 | } |
---|
1061 | x = a = 0; |
---|
1062 | pn = hGetpure(pure); |
---|
1063 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
1064 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
1065 | if (a == Nstc) |
---|
1066 | { |
---|
1067 | pSetExp(pWork, k, pure[k]); |
---|
1068 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
1069 | return; |
---|
1070 | } |
---|
1071 | else |
---|
1072 | { |
---|
1073 | pSetExp(pWork, k, x); |
---|
1074 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
1075 | } |
---|
1076 | b = a; |
---|
1077 | loop |
---|
1078 | { |
---|
1079 | a0 = a; |
---|
1080 | // x0 = x; |
---|
1081 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
1082 | hElimS(sn, &b, a0, a, var, iv); |
---|
1083 | a1 = a; |
---|
1084 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
1085 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
1086 | b += (a1 - a0); |
---|
1087 | if (a < Nstc) |
---|
1088 | { |
---|
1089 | pSetExp(pWork, k, x); |
---|
1090 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
1091 | } |
---|
1092 | else |
---|
1093 | { |
---|
1094 | pSetExp(pWork, k, pure[k]); |
---|
1095 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
1096 | return; |
---|
1097 | } |
---|
1098 | } |
---|
1099 | } |
---|
1100 | |
---|
1101 | void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge) |
---|
1102 | { |
---|
1103 | id_LmTest(S, currRing); |
---|
1104 | if (Q!=NULL) id_LmTest(Q, currRing); |
---|
1105 | |
---|
1106 | int i; |
---|
1107 | int k = ak; |
---|
1108 | #ifdef HAVE_RINGS |
---|
1109 | if (rField_is_Ring(currRing) && (currRing->OrdSgn == -1)) |
---|
1110 | { |
---|
1111 | //consider just monic generators (over rings with zero-divisors) |
---|
1112 | ideal SS=id_Head(S,currRing); |
---|
1113 | for(i=0;i<=idElem(S);i++) |
---|
1114 | { |
---|
1115 | if((SS->m[i]!=NULL) |
---|
1116 | && ((p_IsPurePower(SS->m[i],currRing)==0) |
---|
1117 | ||(!n_IsUnit(pGetCoeff(SS->m[i]), currRing->cf)))) |
---|
1118 | { |
---|
1119 | p_Delete(&SS->m[i],currRing); |
---|
1120 | } |
---|
1121 | } |
---|
1122 | S=id_Copy(SS,currRing); |
---|
1123 | idSkipZeroes(S); |
---|
1124 | } |
---|
1125 | #if 0 |
---|
1126 | printf("\nThis is HC:\n"); |
---|
1127 | for(int ii=0;ii<=idElem(S);ii++) |
---|
1128 | { |
---|
1129 | pWrite(S->m[ii]); |
---|
1130 | } |
---|
1131 | //getchar(); |
---|
1132 | #endif |
---|
1133 | #endif |
---|
1134 | if(idElem(S) == 0) |
---|
1135 | return; |
---|
1136 | hNvar = (currRing->N); |
---|
1137 | hexist = hInit(S, Q, &hNexist); |
---|
1138 | if (k!=0) |
---|
1139 | hComp(hexist, hNexist, k, hexist, &hNstc); |
---|
1140 | else |
---|
1141 | hNstc = hNexist; |
---|
1142 | assume(hNexist > 0); |
---|
1143 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1144 | hvar = (varset)omAlloc((hNvar + 1) * sizeof(int)); |
---|
1145 | hpure = (scmon)omAlloc((1 + (hNvar * hNvar)) * sizeof(int)); |
---|
1146 | stcmem = hCreate(hNvar - 1); |
---|
1147 | for (i = hNvar; i>0; i--) |
---|
1148 | hvar[i] = i; |
---|
1149 | hStaircase(hexist, &hNstc, hvar, hNvar); |
---|
1150 | if ((hNvar > 2) && (hNstc > 10)) |
---|
1151 | hOrdSupp(hexist, hNstc, hvar, hNvar); |
---|
1152 | memset(hpure, 0, (hNvar + 1) * sizeof(int)); |
---|
1153 | hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure); |
---|
1154 | hLexS(hexist, hNstc, hvar, hNvar); |
---|
1155 | if (hEdge!=NULL) |
---|
1156 | pLmFree(hEdge); |
---|
1157 | hEdge = pInit(); |
---|
1158 | pWork = pInit(); |
---|
1159 | hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge); |
---|
1160 | pSetComp(hEdge,ak); |
---|
1161 | hKill(stcmem, hNvar - 1); |
---|
1162 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
1163 | omFreeSize((ADDRESS)hvar, (hNvar + 1) * sizeof(int)); |
---|
1164 | omFreeSize((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(int)); |
---|
1165 | hDelete(hexist, hNexist); |
---|
1166 | pLmFree(pWork); |
---|
1167 | } |
---|
1168 | |
---|
1169 | |
---|
1170 | |
---|
1171 | // kbase |
---|
1172 | |
---|
1173 | STATIC_VAR poly last; |
---|
1174 | STATIC_VAR scmon act; |
---|
1175 | |
---|
1176 | static void scElKbase() |
---|
1177 | { |
---|
1178 | poly q = pInit(); |
---|
1179 | pSetCoeff0(q,nInit(1)); |
---|
1180 | pSetExpV(q,act); |
---|
1181 | pNext(q) = NULL; |
---|
1182 | last = pNext(last) = q; |
---|
1183 | } |
---|
1184 | |
---|
1185 | static int scMax( int i, scfmon stc, int Nvar) |
---|
1186 | { |
---|
1187 | int x, y=stc[0][Nvar]; |
---|
1188 | for (; i;) |
---|
1189 | { |
---|
1190 | i--; |
---|
1191 | x = stc[i][Nvar]; |
---|
1192 | if (x > y) y = x; |
---|
1193 | } |
---|
1194 | return y; |
---|
1195 | } |
---|
1196 | |
---|
1197 | static int scMin( int i, scfmon stc, int Nvar) |
---|
1198 | { |
---|
1199 | int x, y=stc[0][Nvar]; |
---|
1200 | for (; i;) |
---|
1201 | { |
---|
1202 | i--; |
---|
1203 | x = stc[i][Nvar]; |
---|
1204 | if (x < y) y = x; |
---|
1205 | } |
---|
1206 | return y; |
---|
1207 | } |
---|
1208 | |
---|
1209 | static int scRestrict( int &Nstc, scfmon stc, int Nvar) |
---|
1210 | { |
---|
1211 | int x, y; |
---|
1212 | int i, j, Istc = Nstc; |
---|
1213 | |
---|
1214 | y = MAX_INT_VAL; |
---|
1215 | for (i=Nstc-1; i>=0; i--) |
---|
1216 | { |
---|
1217 | j = Nvar-1; |
---|
1218 | loop |
---|
1219 | { |
---|
1220 | if(stc[i][j] != 0) break; |
---|
1221 | j--; |
---|
1222 | if (j == 0) |
---|
1223 | { |
---|
1224 | Istc--; |
---|
1225 | x = stc[i][Nvar]; |
---|
1226 | if (x < y) y = x; |
---|
1227 | stc[i] = NULL; |
---|
1228 | break; |
---|
1229 | } |
---|
1230 | } |
---|
1231 | } |
---|
1232 | if (Istc < Nstc) |
---|
1233 | { |
---|
1234 | for (i=Nstc-1; i>=0; i--) |
---|
1235 | { |
---|
1236 | if (stc[i] && (stc[i][Nvar] >= y)) |
---|
1237 | { |
---|
1238 | Istc--; |
---|
1239 | stc[i] = NULL; |
---|
1240 | } |
---|
1241 | } |
---|
1242 | j = 0; |
---|
1243 | while (stc[j]) j++; |
---|
1244 | i = j+1; |
---|
1245 | for(; i<Nstc; i++) |
---|
1246 | { |
---|
1247 | if (stc[i]) |
---|
1248 | { |
---|
1249 | stc[j] = stc[i]; |
---|
1250 | j++; |
---|
1251 | } |
---|
1252 | } |
---|
1253 | Nstc = Istc; |
---|
1254 | return y; |
---|
1255 | } |
---|
1256 | else |
---|
1257 | return -1; |
---|
1258 | } |
---|
1259 | |
---|
1260 | static void scAll( int Nvar, int deg) |
---|
1261 | { |
---|
1262 | int i; |
---|
1263 | int d = deg; |
---|
1264 | if (d == 0) |
---|
1265 | { |
---|
1266 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1267 | scElKbase(); |
---|
1268 | return; |
---|
1269 | } |
---|
1270 | if (Nvar == 1) |
---|
1271 | { |
---|
1272 | act[1] = d; |
---|
1273 | scElKbase(); |
---|
1274 | return; |
---|
1275 | } |
---|
1276 | do |
---|
1277 | { |
---|
1278 | act[Nvar] = d; |
---|
1279 | scAll(Nvar-1, deg-d); |
---|
1280 | d--; |
---|
1281 | } while (d >= 0); |
---|
1282 | } |
---|
1283 | |
---|
1284 | static void scAllKbase( int Nvar, int ideg, int deg) |
---|
1285 | { |
---|
1286 | do |
---|
1287 | { |
---|
1288 | act[Nvar] = ideg; |
---|
1289 | scAll(Nvar-1, deg-ideg); |
---|
1290 | ideg--; |
---|
1291 | } while (ideg >= 0); |
---|
1292 | } |
---|
1293 | |
---|
1294 | static void scDegKbase( scfmon stc, int Nstc, int Nvar, int deg) |
---|
1295 | { |
---|
1296 | int Ivar, Istc, i, j; |
---|
1297 | scfmon sn; |
---|
1298 | int x, ideg; |
---|
1299 | |
---|
1300 | if (deg == 0) |
---|
1301 | { |
---|
1302 | for (i=Nstc-1; i>=0; i--) |
---|
1303 | { |
---|
1304 | for (j=Nvar;j;j--){ if(stc[i][j]) break; } |
---|
1305 | if (j==0){return;} |
---|
1306 | } |
---|
1307 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1308 | scElKbase(); |
---|
1309 | return; |
---|
1310 | } |
---|
1311 | if (Nvar == 1) |
---|
1312 | { |
---|
1313 | for (i=Nstc-1; i>=0; i--) if(deg >= stc[i][1]) return; |
---|
1314 | act[1] = deg; |
---|
1315 | scElKbase(); |
---|
1316 | return; |
---|
1317 | } |
---|
1318 | Ivar = Nvar-1; |
---|
1319 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1320 | x = scRestrict(Nstc, sn, Nvar); |
---|
1321 | if (x <= 0) |
---|
1322 | { |
---|
1323 | if (x == 0) return; |
---|
1324 | ideg = deg; |
---|
1325 | } |
---|
1326 | else |
---|
1327 | { |
---|
1328 | if (deg < x) ideg = deg; |
---|
1329 | else ideg = x-1; |
---|
1330 | if (Nstc == 0) |
---|
1331 | { |
---|
1332 | scAllKbase(Nvar, ideg, deg); |
---|
1333 | return; |
---|
1334 | } |
---|
1335 | } |
---|
1336 | loop |
---|
1337 | { |
---|
1338 | x = scMax(Nstc, sn, Nvar); |
---|
1339 | while (ideg >= x) |
---|
1340 | { |
---|
1341 | act[Nvar] = ideg; |
---|
1342 | scDegKbase(sn, Nstc, Ivar, deg-ideg); |
---|
1343 | ideg--; |
---|
1344 | } |
---|
1345 | if (ideg < 0) return; |
---|
1346 | Istc = Nstc; |
---|
1347 | for (i=Nstc-1; i>=0; i--) |
---|
1348 | { |
---|
1349 | if (ideg < sn[i][Nvar]) |
---|
1350 | { |
---|
1351 | Istc--; |
---|
1352 | sn[i] = NULL; |
---|
1353 | } |
---|
1354 | } |
---|
1355 | if (Istc == 0) |
---|
1356 | { |
---|
1357 | scAllKbase(Nvar, ideg, deg); |
---|
1358 | return; |
---|
1359 | } |
---|
1360 | j = 0; |
---|
1361 | while (sn[j]) j++; |
---|
1362 | i = j+1; |
---|
1363 | for (; i<Nstc; i++) |
---|
1364 | { |
---|
1365 | if (sn[i]) |
---|
1366 | { |
---|
1367 | sn[j] = sn[i]; |
---|
1368 | j++; |
---|
1369 | } |
---|
1370 | } |
---|
1371 | Nstc = Istc; |
---|
1372 | } |
---|
1373 | } |
---|
1374 | |
---|
1375 | static void scInKbase( scfmon stc, int Nstc, int Nvar) |
---|
1376 | { |
---|
1377 | int Ivar, Istc, i, j; |
---|
1378 | scfmon sn; |
---|
1379 | int x, ideg; |
---|
1380 | |
---|
1381 | if (Nvar == 1) |
---|
1382 | { |
---|
1383 | ideg = scMin(Nstc, stc, 1); |
---|
1384 | while (ideg > 0) |
---|
1385 | { |
---|
1386 | ideg--; |
---|
1387 | act[1] = ideg; |
---|
1388 | scElKbase(); |
---|
1389 | } |
---|
1390 | return; |
---|
1391 | } |
---|
1392 | Ivar = Nvar-1; |
---|
1393 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1394 | x = scRestrict(Nstc, sn, Nvar); |
---|
1395 | if (x == 0) return; |
---|
1396 | ideg = x-1; |
---|
1397 | loop |
---|
1398 | { |
---|
1399 | x = scMax(Nstc, sn, Nvar); |
---|
1400 | while (ideg >= x) |
---|
1401 | { |
---|
1402 | act[Nvar] = ideg; |
---|
1403 | scInKbase(sn, Nstc, Ivar); |
---|
1404 | ideg--; |
---|
1405 | } |
---|
1406 | if (ideg < 0) return; |
---|
1407 | Istc = Nstc; |
---|
1408 | for (i=Nstc-1; i>=0; i--) |
---|
1409 | { |
---|
1410 | if (ideg < sn[i][Nvar]) |
---|
1411 | { |
---|
1412 | Istc--; |
---|
1413 | sn[i] = NULL; |
---|
1414 | } |
---|
1415 | } |
---|
1416 | j = 0; |
---|
1417 | while (sn[j]) j++; |
---|
1418 | i = j+1; |
---|
1419 | for (; i<Nstc; i++) |
---|
1420 | { |
---|
1421 | if (sn[i]) |
---|
1422 | { |
---|
1423 | sn[j] = sn[i]; |
---|
1424 | j++; |
---|
1425 | } |
---|
1426 | } |
---|
1427 | Nstc = Istc; |
---|
1428 | } |
---|
1429 | } |
---|
1430 | |
---|
1431 | static ideal scIdKbase(poly q, const int rank) |
---|
1432 | { |
---|
1433 | ideal res = idInit(pLength(q), rank); |
---|
1434 | polyset mm = res->m; |
---|
1435 | do |
---|
1436 | { |
---|
1437 | *mm = q; ++mm; |
---|
1438 | |
---|
1439 | const poly p = pNext(q); |
---|
1440 | pNext(q) = NULL; |
---|
1441 | q = p; |
---|
1442 | |
---|
1443 | } while (q!=NULL); |
---|
1444 | |
---|
1445 | id_Test(res, currRing); // WRONG RANK!!!??? |
---|
1446 | return res; |
---|
1447 | } |
---|
1448 | |
---|
1449 | ideal scKBase(int deg, ideal s, ideal Q, intvec * mv) |
---|
1450 | { |
---|
1451 | if( Q!=NULL) id_Test(Q, currRing); |
---|
1452 | |
---|
1453 | int i, di; |
---|
1454 | poly p; |
---|
1455 | |
---|
1456 | if (deg < 0) |
---|
1457 | { |
---|
1458 | di = scDimInt(s, Q); |
---|
1459 | if (di != 0) |
---|
1460 | { |
---|
1461 | //Werror("KBase not finite"); |
---|
1462 | return idInit(1,s->rank); |
---|
1463 | } |
---|
1464 | } |
---|
1465 | stcmem = hCreate((currRing->N) - 1); |
---|
1466 | hexist = hInit(s, Q, &hNexist); |
---|
1467 | p = last = pInit(); |
---|
1468 | /*pNext(p) = NULL;*/ |
---|
1469 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
1470 | *act = 0; |
---|
1471 | if (!hNexist) |
---|
1472 | { |
---|
1473 | scAll((currRing->N), deg); |
---|
1474 | goto ende; |
---|
1475 | } |
---|
1476 | if (!hisModule) |
---|
1477 | { |
---|
1478 | if (deg < 0) scInKbase(hexist, hNexist, (currRing->N)); |
---|
1479 | else scDegKbase(hexist, hNexist, (currRing->N), deg); |
---|
1480 | } |
---|
1481 | else |
---|
1482 | { |
---|
1483 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1484 | for (i = 1; i <= hisModule; i++) |
---|
1485 | { |
---|
1486 | *act = i; |
---|
1487 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1488 | int deg_ei=deg; |
---|
1489 | if (mv!=NULL) deg_ei -= (*mv)[i-1]; |
---|
1490 | if ((deg < 0) || (deg_ei>=0)) |
---|
1491 | { |
---|
1492 | if (hNstc) |
---|
1493 | { |
---|
1494 | if (deg < 0) scInKbase(hstc, hNstc, (currRing->N)); |
---|
1495 | else scDegKbase(hstc, hNstc, (currRing->N), deg_ei); |
---|
1496 | } |
---|
1497 | else |
---|
1498 | scAll((currRing->N), deg_ei); |
---|
1499 | } |
---|
1500 | } |
---|
1501 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1502 | } |
---|
1503 | ende: |
---|
1504 | hDelete(hexist, hNexist); |
---|
1505 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
1506 | hKill(stcmem, (currRing->N) - 1); |
---|
1507 | pLmFree(&p); |
---|
1508 | if (p == NULL) |
---|
1509 | return idInit(1,s->rank); |
---|
1510 | |
---|
1511 | last = p; |
---|
1512 | return scIdKbase(p, s->rank); |
---|
1513 | } |
---|
1514 | |
---|
1515 | #if 0 //-- alternative implementation of scComputeHC |
---|
1516 | /* |
---|
1517 | void scComputeHCw(ideal ss, ideal Q, int ak, poly &hEdge) |
---|
1518 | { |
---|
1519 | id_LmTest(ss, currRing); |
---|
1520 | if (Q!=NULL) id_LmTest(Q, currRing); |
---|
1521 | |
---|
1522 | int i, di; |
---|
1523 | poly p; |
---|
1524 | |
---|
1525 | if (hEdge!=NULL) |
---|
1526 | pLmFree(hEdge); |
---|
1527 | |
---|
1528 | ideal s=idInit(IDELEMS(ss),ak); |
---|
1529 | for(i=IDELEMS(ss)-1;i>=0;i--) |
---|
1530 | { |
---|
1531 | if (ss->m[i]!=NULL) s->m[i]=pHead(ss->m[i]); |
---|
1532 | } |
---|
1533 | di = scDimInt(s, Q); |
---|
1534 | stcmem = hCreate((currRing->N) - 1); |
---|
1535 | hexist = hInit(s, Q, &hNexist); |
---|
1536 | p = last = pInit(); |
---|
1537 | // pNext(p) = NULL; |
---|
1538 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
1539 | *act = 0; |
---|
1540 | if (!hNexist) |
---|
1541 | { |
---|
1542 | scAll((currRing->N), -1); |
---|
1543 | goto ende; |
---|
1544 | } |
---|
1545 | if (!hisModule) |
---|
1546 | { |
---|
1547 | scInKbase(hexist, hNexist, (currRing->N)); |
---|
1548 | } |
---|
1549 | else |
---|
1550 | { |
---|
1551 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1552 | for (i = 1; i <= hisModule; i++) |
---|
1553 | { |
---|
1554 | *act = i; |
---|
1555 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1556 | if (hNstc) |
---|
1557 | { |
---|
1558 | scInKbase(hstc, hNstc, (currRing->N)); |
---|
1559 | } |
---|
1560 | else |
---|
1561 | scAll((currRing->N), -1); |
---|
1562 | } |
---|
1563 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1564 | } |
---|
1565 | ende: |
---|
1566 | hDelete(hexist, hNexist); |
---|
1567 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
1568 | hKill(stcmem, (currRing->N) - 1); |
---|
1569 | pDeleteLm(&p); |
---|
1570 | idDelete(&s); |
---|
1571 | if (p == NULL) |
---|
1572 | { |
---|
1573 | return; // no HEdge |
---|
1574 | } |
---|
1575 | else |
---|
1576 | { |
---|
1577 | last = p; |
---|
1578 | ideal res=scIdKbase(p, ss->rank); |
---|
1579 | poly p_ind=res->m[0]; int ind=0; |
---|
1580 | for(i=IDELEMS(res)-1;i>0;i--) |
---|
1581 | { |
---|
1582 | if (pCmp(res->m[i],p_ind)==-1) { p_ind=res->m[i]; ind=i; } |
---|
1583 | } |
---|
1584 | assume(p_ind!=NULL); |
---|
1585 | assume(res->m[ind]==p_ind); |
---|
1586 | hEdge=p_ind; |
---|
1587 | res->m[ind]=NULL; |
---|
1588 | nDelete(&pGetCoeff(hEdge)); |
---|
1589 | pGetCoeff(hEdge)=NULL; |
---|
1590 | for(i=(currRing->N);i>0;i--) |
---|
1591 | pIncrExp(hEdge,i); |
---|
1592 | pSetm(hEdge); |
---|
1593 | |
---|
1594 | idDelete(&res); |
---|
1595 | return; |
---|
1596 | } |
---|
1597 | } |
---|
1598 | */ |
---|
1599 | #endif |
---|
1600 | |
---|
1601 | #ifdef HAVE_SHIFTBBA |
---|
1602 | |
---|
1603 | /* |
---|
1604 | * Computation of the Gel'fand-Kirillov Dimension |
---|
1605 | */ |
---|
1606 | |
---|
1607 | #include "polys/shiftop.h" |
---|
1608 | #include <vector> |
---|
1609 | |
---|
1610 | 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) |
---|
1611 | { |
---|
1612 | intvec* G = ivCopy(_G); // modifications must be local |
---|
1613 | |
---|
1614 | if (cache[v] != -2) return cache; // value is already cached |
---|
1615 | |
---|
1616 | visited[v] = TRUE; |
---|
1617 | path.push_back(v); |
---|
1618 | |
---|
1619 | int cycles = 0; |
---|
1620 | for (int w = 0; w < G->cols(); w++) |
---|
1621 | { |
---|
1622 | if (IMATELEM(*G, v + 1, w + 1)) // edge v -> w exists in G |
---|
1623 | { |
---|
1624 | if (!visited[w]) |
---|
1625 | { // continue with w |
---|
1626 | cache = countCycles(G, w, path, visited, cyclic, cache); |
---|
1627 | if (cache[w] == -1) |
---|
1628 | { |
---|
1629 | cache[v] = -1; |
---|
1630 | return cache; |
---|
1631 | } |
---|
1632 | cycles = si_max(cycles, cache[w]); |
---|
1633 | } |
---|
1634 | else |
---|
1635 | { // found new cycle |
---|
1636 | int pathIndexOfW = -1; |
---|
1637 | for (int i = path.size() - 1; i >= 0; i--) { |
---|
1638 | if (cyclic[path[i]] == 1) { // found an already cyclic vertex |
---|
1639 | cache[v] = -1; |
---|
1640 | return cache; |
---|
1641 | } |
---|
1642 | cyclic[path[i]] = TRUE; |
---|
1643 | |
---|
1644 | if (path[i] == w) { // end of the cycle |
---|
1645 | assume(IMATELEM(*G, v + 1, w + 1) != 0); |
---|
1646 | IMATELEM(*G, v + 1, w + 1) = 0; // remove edge v -> w |
---|
1647 | pathIndexOfW = i; |
---|
1648 | break; |
---|
1649 | } else { |
---|
1650 | assume(IMATELEM(*G, path[i - 1] + 1, path[i] + 1) != 0); |
---|
1651 | IMATELEM(*G, path[i - 1] + 1, path[i] + 1) = 0; // remove edge vi-1 -> vi |
---|
1652 | } |
---|
1653 | } |
---|
1654 | assume(pathIndexOfW != -1); // should never happen |
---|
1655 | for (int i = path.size() - 1; i >= pathIndexOfW; i--) { |
---|
1656 | cache = countCycles(G, path[i], path, visited, cyclic, cache); |
---|
1657 | if (cache[path[i]] == -1) |
---|
1658 | { |
---|
1659 | cache[v] = -1; |
---|
1660 | return cache; |
---|
1661 | } |
---|
1662 | cycles = si_max(cycles, cache[path[i]] + 1); |
---|
1663 | } |
---|
1664 | } |
---|
1665 | } |
---|
1666 | } |
---|
1667 | cache[v] = cycles; |
---|
1668 | |
---|
1669 | delete G; |
---|
1670 | return cache; |
---|
1671 | } |
---|
1672 | |
---|
1673 | // -1 is infinity |
---|
1674 | static int graphGrowth(const intvec* G) |
---|
1675 | { |
---|
1676 | // init |
---|
1677 | int n = G->cols(); |
---|
1678 | std::vector<int> path; |
---|
1679 | std::vector<BOOLEAN> visited; |
---|
1680 | std::vector<BOOLEAN> cyclic; |
---|
1681 | std::vector<int> cache; |
---|
1682 | visited.resize(n, FALSE); |
---|
1683 | cyclic.resize(n, FALSE); |
---|
1684 | cache.resize(n, -2); |
---|
1685 | |
---|
1686 | // get max number of cycles |
---|
1687 | int cycles = 0; |
---|
1688 | for (int v = 0; v < n; v++) |
---|
1689 | { |
---|
1690 | cache = countCycles(G, v, path, visited, cyclic, cache); |
---|
1691 | if (cache[v] == -1) |
---|
1692 | return -1; |
---|
1693 | cycles = si_max(cycles, cache[v]); |
---|
1694 | } |
---|
1695 | return cycles; |
---|
1696 | } |
---|
1697 | |
---|
1698 | // ATTENTION: |
---|
1699 | // - `words` contains the words normal modulo M of length n |
---|
1700 | // - `numberOfNormalWords` contains the number of words normal modulo M of length 0 ... n |
---|
1701 | static void _lp_computeNormalWords(ideal words, int& numberOfNormalWords, int length, ideal M, int minDeg, int& last) |
---|
1702 | { |
---|
1703 | if (length <= 0){ |
---|
1704 | poly one = pOne(); |
---|
1705 | if (p_LPDivisibleBy(M, one, currRing)) // 1 \in M => no normal words at all |
---|
1706 | { |
---|
1707 | pDelete(&one); |
---|
1708 | last = -1; |
---|
1709 | numberOfNormalWords = 0; |
---|
1710 | } |
---|
1711 | else |
---|
1712 | { |
---|
1713 | words->m[0] = one; |
---|
1714 | last = 0; |
---|
1715 | numberOfNormalWords = 1; |
---|
1716 | } |
---|
1717 | return; |
---|
1718 | } |
---|
1719 | |
---|
1720 | _lp_computeNormalWords(words, numberOfNormalWords, length - 1, M, minDeg, last); |
---|
1721 | |
---|
1722 | int nVars = currRing->isLPring - currRing->LPncGenCount; |
---|
1723 | int numberOfNewNormalWords = 0; |
---|
1724 | |
---|
1725 | for (int j = nVars - 1; j >= 0; j--) |
---|
1726 | { |
---|
1727 | for (int i = last; i >= 0; i--) |
---|
1728 | { |
---|
1729 | int index = (j * (last + 1)) + i; |
---|
1730 | |
---|
1731 | if (words->m[i] != NULL) |
---|
1732 | { |
---|
1733 | if (j > 0) { |
---|
1734 | words->m[index] = pCopy(words->m[i]); |
---|
1735 | } |
---|
1736 | |
---|
1737 | int varOffset = ((length - 1) * currRing->isLPring) + 1; |
---|
1738 | pSetExp(words->m[index], varOffset + j, 1); |
---|
1739 | pSetm(words->m[index]); |
---|
1740 | pTest(words->m[index]); |
---|
1741 | |
---|
1742 | if (length >= minDeg && p_LPDivisibleBy(M, words->m[index], currRing)) |
---|
1743 | { |
---|
1744 | pDelete(&words->m[index]); |
---|
1745 | words->m[index] = NULL; |
---|
1746 | } |
---|
1747 | else |
---|
1748 | { |
---|
1749 | numberOfNewNormalWords++; |
---|
1750 | } |
---|
1751 | } |
---|
1752 | } |
---|
1753 | } |
---|
1754 | |
---|
1755 | last = nVars * last + nVars - 1; |
---|
1756 | |
---|
1757 | numberOfNormalWords += numberOfNewNormalWords; |
---|
1758 | } |
---|
1759 | |
---|
1760 | static ideal lp_computeNormalWords(int length, ideal M) |
---|
1761 | { |
---|
1762 | long minDeg = IDELEMS(M) > 0 ? pTotaldegree(M->m[0]) : 0; |
---|
1763 | for (int i = 1; i < IDELEMS(M); i++) |
---|
1764 | { |
---|
1765 | minDeg = si_min(minDeg, pTotaldegree(M->m[i])); |
---|
1766 | } |
---|
1767 | |
---|
1768 | int nVars = currRing->isLPring - currRing->LPncGenCount; |
---|
1769 | |
---|
1770 | int maxElems = 1; |
---|
1771 | for (int i = 0; i < length; i++) // maxElems = nVars^n |
---|
1772 | maxElems *= nVars; |
---|
1773 | ideal words = idInit(maxElems); |
---|
1774 | int last, numberOfNormalWords; |
---|
1775 | _lp_computeNormalWords(words, numberOfNormalWords, length, M, minDeg, last); |
---|
1776 | idSkipZeroes(words); |
---|
1777 | return words; |
---|
1778 | } |
---|
1779 | |
---|
1780 | static int lp_countNormalWords(int upToLength, ideal M) |
---|
1781 | { |
---|
1782 | long minDeg = IDELEMS(M) > 0 ? pTotaldegree(M->m[0]) : 0; |
---|
1783 | for (int i = 1; i < IDELEMS(M); i++) |
---|
1784 | { |
---|
1785 | minDeg = si_min(minDeg, pTotaldegree(M->m[i])); |
---|
1786 | } |
---|
1787 | |
---|
1788 | int nVars = currRing->isLPring - currRing->LPncGenCount; |
---|
1789 | |
---|
1790 | int maxElems = 1; |
---|
1791 | for (int i = 0; i < upToLength; i++) // maxElems = nVars^n |
---|
1792 | maxElems *= nVars; |
---|
1793 | ideal words = idInit(maxElems); |
---|
1794 | int last, numberOfNormalWords; |
---|
1795 | _lp_computeNormalWords(words, numberOfNormalWords, upToLength, M, minDeg, last); |
---|
1796 | idDelete(&words); |
---|
1797 | return numberOfNormalWords; |
---|
1798 | } |
---|
1799 | |
---|
1800 | // NULL if graph is undefined |
---|
1801 | intvec* lp_ufnarovskiGraph(ideal G, ideal &standardWords) |
---|
1802 | { |
---|
1803 | long l = 0; |
---|
1804 | for (int i = 0; i < IDELEMS(G); i++) |
---|
1805 | l = si_max(pTotaldegree(G->m[i]), l); |
---|
1806 | l--; |
---|
1807 | if (l <= 0) |
---|
1808 | { |
---|
1809 | WerrorS("Ufnarovski graph not implemented for l <= 0"); |
---|
1810 | return NULL; |
---|
1811 | } |
---|
1812 | int lV = currRing->isLPring; |
---|
1813 | |
---|
1814 | standardWords = lp_computeNormalWords(l, G); |
---|
1815 | |
---|
1816 | int n = IDELEMS(standardWords); |
---|
1817 | intvec* UG = new intvec(n, n, 0); |
---|
1818 | for (int i = 0; i < n; i++) |
---|
1819 | { |
---|
1820 | for (int j = 0; j < n; j++) |
---|
1821 | { |
---|
1822 | poly v = standardWords->m[i]; |
---|
1823 | poly w = standardWords->m[j]; |
---|
1824 | |
---|
1825 | // check whether v*x1 = x2*w (overlap) |
---|
1826 | bool overlap = true; |
---|
1827 | for (int k = 1; k <= (l - 1) * lV; k++) |
---|
1828 | { |
---|
1829 | if (pGetExp(v, k + lV) != pGetExp(w, k)) { |
---|
1830 | overlap = false; |
---|
1831 | break; |
---|
1832 | } |
---|
1833 | } |
---|
1834 | |
---|
1835 | if (overlap) |
---|
1836 | { |
---|
1837 | // create the overlap |
---|
1838 | poly p = pMult(pCopy(v), p_LPVarAt(w, l, currRing)); |
---|
1839 | |
---|
1840 | // check whether the overlap is normal |
---|
1841 | bool normal = true; |
---|
1842 | for (int k = 0; k < IDELEMS(G); k++) |
---|
1843 | { |
---|
1844 | if (p_LPDivisibleBy(G->m[k], p, currRing)) |
---|
1845 | { |
---|
1846 | normal = false; |
---|
1847 | break; |
---|
1848 | } |
---|
1849 | } |
---|
1850 | |
---|
1851 | if (normal) |
---|
1852 | { |
---|
1853 | IMATELEM(*UG, i + 1, j + 1) = 1; |
---|
1854 | } |
---|
1855 | } |
---|
1856 | } |
---|
1857 | } |
---|
1858 | return UG; |
---|
1859 | } |
---|
1860 | |
---|
1861 | // -1 is infinity, -2 is error |
---|
1862 | int lp_gkDim(const ideal _G) |
---|
1863 | { |
---|
1864 | id_Test(_G, currRing); |
---|
1865 | |
---|
1866 | if (rField_is_Ring(currRing)) { |
---|
1867 | WerrorS("GK-Dim not implemented for rings"); |
---|
1868 | return -2; |
---|
1869 | } |
---|
1870 | |
---|
1871 | for (int i=IDELEMS(_G)-1;i>=0; i--) |
---|
1872 | { |
---|
1873 | if (_G->m[i] != NULL) |
---|
1874 | { |
---|
1875 | if (pGetComp(_G->m[i]) != 0) |
---|
1876 | { |
---|
1877 | WerrorS("GK-Dim not implemented for modules"); |
---|
1878 | return -2; |
---|
1879 | } |
---|
1880 | if (pGetNCGen(_G->m[i]) != 0) |
---|
1881 | { |
---|
1882 | WerrorS("GK-Dim not implemented for bi-modules"); |
---|
1883 | return -2; |
---|
1884 | } |
---|
1885 | } |
---|
1886 | } |
---|
1887 | |
---|
1888 | ideal G = id_Head(_G, currRing); // G = LM(G) (and copy) |
---|
1889 | idSkipZeroes(G); // remove zeros |
---|
1890 | id_DelLmEquals(G, currRing); // remove duplicates |
---|
1891 | |
---|
1892 | // check if G is the zero ideal |
---|
1893 | if (IDELEMS(G) == 1 && G->m[0] == NULL) |
---|
1894 | { |
---|
1895 | // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1! |
---|
1896 | int lV = currRing->isLPring; |
---|
1897 | int ncGenCount = currRing->LPncGenCount; |
---|
1898 | if (lV - ncGenCount == 0) |
---|
1899 | { |
---|
1900 | idDelete(&G); |
---|
1901 | return 0; |
---|
1902 | } |
---|
1903 | if (lV - ncGenCount == 1) |
---|
1904 | { |
---|
1905 | idDelete(&G); |
---|
1906 | return 1; |
---|
1907 | } |
---|
1908 | if (lV - ncGenCount >= 2) |
---|
1909 | { |
---|
1910 | idDelete(&G); |
---|
1911 | return -1; |
---|
1912 | } |
---|
1913 | } |
---|
1914 | |
---|
1915 | // get the max deg |
---|
1916 | long maxDeg = 0; |
---|
1917 | for (int i = 0; i < IDELEMS(G); i++) |
---|
1918 | { |
---|
1919 | maxDeg = si_max(maxDeg, pTotaldegree(G->m[i])); |
---|
1920 | |
---|
1921 | // also check whether G = <1> |
---|
1922 | if (pIsConstantComp(G->m[i])) |
---|
1923 | { |
---|
1924 | WerrorS("GK-Dim not defined for 0-ring"); |
---|
1925 | idDelete(&G); |
---|
1926 | return -2; |
---|
1927 | } |
---|
1928 | } |
---|
1929 | |
---|
1930 | // early termination if G \subset X |
---|
1931 | if (maxDeg <= 1) |
---|
1932 | { |
---|
1933 | int lV = currRing->isLPring; |
---|
1934 | int ncGenCount = currRing->LPncGenCount; |
---|
1935 | if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges |
---|
1936 | { |
---|
1937 | idDelete(&G); |
---|
1938 | return 0; |
---|
1939 | } |
---|
1940 | if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop |
---|
1941 | { |
---|
1942 | idDelete(&G); |
---|
1943 | return 1; |
---|
1944 | } |
---|
1945 | if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop |
---|
1946 | { |
---|
1947 | idDelete(&G); |
---|
1948 | return -1; |
---|
1949 | } |
---|
1950 | } |
---|
1951 | |
---|
1952 | ideal standardWords; |
---|
1953 | intvec* UG = lp_ufnarovskiGraph(G, standardWords); |
---|
1954 | if (UG == NULL) |
---|
1955 | { |
---|
1956 | idDelete(&G); |
---|
1957 | return -2; |
---|
1958 | } |
---|
1959 | if (errorreported) |
---|
1960 | { |
---|
1961 | delete UG; |
---|
1962 | idDelete(&G); |
---|
1963 | return -2; |
---|
1964 | } |
---|
1965 | int gkDim = graphGrowth(UG); |
---|
1966 | delete UG; |
---|
1967 | idDelete(&G); |
---|
1968 | return gkDim; |
---|
1969 | } |
---|
1970 | |
---|
1971 | // converts an intvec matrix to a vector<vector<int> > |
---|
1972 | static std::vector<std::vector<int> > iv2vv(intvec* M) |
---|
1973 | { |
---|
1974 | int rows = M->rows(); |
---|
1975 | int cols = M->cols(); |
---|
1976 | |
---|
1977 | std::vector<std::vector<int> > mat(rows, std::vector<int>(cols)); |
---|
1978 | |
---|
1979 | for (int i = 0; i < rows; i++) |
---|
1980 | { |
---|
1981 | for (int j = 0; j < cols; j++) |
---|
1982 | { |
---|
1983 | mat[i][j] = IMATELEM(*M, i + 1, j + 1); |
---|
1984 | } |
---|
1985 | } |
---|
1986 | |
---|
1987 | return mat; |
---|
1988 | } |
---|
1989 | |
---|
1990 | static void vvPrint(const std::vector<std::vector<int> >& mat) |
---|
1991 | { |
---|
1992 | for (int i = 0; i < mat.size(); i++) |
---|
1993 | { |
---|
1994 | for (int j = 0; j < mat[i].size(); j++) |
---|
1995 | { |
---|
1996 | Print("%d ", mat[i][j]); |
---|
1997 | } |
---|
1998 | PrintLn(); |
---|
1999 | } |
---|
2000 | } |
---|
2001 | |
---|
2002 | static void vvTest(const std::vector<std::vector<int> >& mat) |
---|
2003 | { |
---|
2004 | if (mat.size() > 0) |
---|
2005 | { |
---|
2006 | int cols = mat[0].size(); |
---|
2007 | for (int i = 1; i < mat.size(); i++) |
---|
2008 | { |
---|
2009 | if (cols != mat[i].size()) |
---|
2010 | WerrorS("number of cols in matrix inconsistent"); |
---|
2011 | } |
---|
2012 | } |
---|
2013 | } |
---|
2014 | |
---|
2015 | static void vvDeleteRow(std::vector<std::vector<int> >& mat, int row) |
---|
2016 | { |
---|
2017 | mat.erase(mat.begin() + row); |
---|
2018 | } |
---|
2019 | |
---|
2020 | static void vvDeleteColumn(std::vector<std::vector<int> >& mat, int col) |
---|
2021 | { |
---|
2022 | for (int i = 0; i < mat.size(); i++) |
---|
2023 | { |
---|
2024 | mat[i].erase(mat[i].begin() + col); |
---|
2025 | } |
---|
2026 | } |
---|
2027 | |
---|
2028 | static BOOLEAN vvIsRowZero(const std::vector<std::vector<int> >& mat, int row) |
---|
2029 | { |
---|
2030 | for (int i = 0; i < mat[row].size(); i++) |
---|
2031 | { |
---|
2032 | if (mat[row][i] != 0) |
---|
2033 | return FALSE; |
---|
2034 | } |
---|
2035 | return TRUE; |
---|
2036 | } |
---|
2037 | |
---|
2038 | static BOOLEAN vvIsColumnZero(const std::vector<std::vector<int> >& mat, int col) |
---|
2039 | { |
---|
2040 | for (int i = 0; i < mat.size(); i++) |
---|
2041 | { |
---|
2042 | if (mat[i][col] != 0) |
---|
2043 | return FALSE; |
---|
2044 | } |
---|
2045 | return TRUE; |
---|
2046 | } |
---|
2047 | |
---|
2048 | static BOOLEAN vvIsZero(const std::vector<std::vector<int> >& mat) |
---|
2049 | { |
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2050 | for (int i = 0; i < mat.size(); i++) |
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2051 | { |
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2052 | if (!vvIsRowZero(mat, i)) |
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2053 | return FALSE; |
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2054 | } |
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2055 | return TRUE; |
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2056 | } |
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2057 | |
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2058 | static std::vector<std::vector<int> > vvMult(const std::vector<std::vector<int> >& a, const std::vector<std::vector<int> >& b) |
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2059 | { |
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2060 | int ra = a.size(); |
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2061 | int rb = b.size(); |
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2062 | int ca = a.size() > 0 ? a[0].size() : 0; |
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2063 | int cb = b.size() > 0 ? b[0].size() : 0; |
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2064 | |
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2065 | if (ca != rb) |
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2066 | { |
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2067 | WerrorS("matrix dimensions do not match"); |
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2068 | return std::vector<std::vector<int> >(); |
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2069 | } |
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2070 | |
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2071 | std::vector<std::vector<int> > res(ra, std::vector<int>(cb)); |
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2072 | for (int i = 0; i < ra; i++) |
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2073 | { |
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2074 | for (int j = 0; j < cb; j++) |
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2075 | { |
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2076 | int sum = 0; |
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2077 | for (int k = 0; k < ca; k++) |
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2078 | sum += a[i][k] * b[k][j]; |
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2079 | res[i][j] = sum; |
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2080 | } |
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2081 | } |
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2082 | return res; |
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2083 | } |
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2084 | |
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2085 | static BOOLEAN isAcyclic(const intvec* G) |
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2086 | { |
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2087 | // init |
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2088 | int n = G->cols(); |
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2089 | std::vector<int> path; |
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2090 | std::vector<BOOLEAN> visited; |
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2091 | std::vector<BOOLEAN> cyclic; |
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2092 | std::vector<int> cache; |
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2093 | visited.resize(n, FALSE); |
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2094 | cyclic.resize(n, FALSE); |
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2095 | cache.resize(n, -2); |
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2096 | |
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2097 | for (int v = 0; v < n; v++) |
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2098 | { |
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2099 | cache = countCycles(G, v, path, visited, cyclic, cache); |
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2100 | // check that there are 0 cycles from v |
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2101 | if (cache[v] != 0) |
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2102 | return FALSE; |
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2103 | } |
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2104 | return TRUE; |
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2105 | } |
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2106 | |
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2107 | /* |
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2108 | * Computation of the K-Dimension |
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2109 | */ |
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2110 | |
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2111 | // -1 is infinity, -2 is error |
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2112 | int lp_kDim(const ideal _G) |
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2113 | { |
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2114 | if (rField_is_Ring(currRing)) { |
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2115 | WerrorS("K-Dim not implemented for rings"); |
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2116 | return -2; |
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2117 | } |
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2118 | |
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2119 | for (int i=IDELEMS(_G)-1;i>=0; i--) |
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2120 | { |
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2121 | if (_G->m[i] != NULL) |
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2122 | { |
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2123 | if (pGetComp(_G->m[i]) != 0) |
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2124 | { |
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2125 | WerrorS("K-Dim not implemented for modules"); |
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2126 | return -2; |
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2127 | } |
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2128 | if (pGetNCGen(_G->m[i]) != 0) |
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2129 | { |
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2130 | WerrorS("K-Dim not implemented for bi-modules"); |
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2131 | return -2; |
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2132 | } |
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2133 | } |
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2134 | } |
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2135 | |
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2136 | ideal G = id_Head(_G, currRing); // G = LM(G) (and copy) |
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2137 | if (TEST_OPT_PROT) |
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2138 | Print("%d original generators\n", IDELEMS(G)); |
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2139 | idSkipZeroes(G); // remove zeros |
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2140 | id_DelLmEquals(G, currRing); // remove duplicates |
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2141 | if (TEST_OPT_PROT) |
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2142 | Print("%d non-zero unique generators\n", IDELEMS(G)); |
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2143 | |
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2144 | // check if G is the zero ideal |
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2145 | if (IDELEMS(G) == 1 && G->m[0] == NULL) |
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2146 | { |
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2147 | // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1! |
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2148 | int lV = currRing->isLPring; |
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2149 | int ncGenCount = currRing->LPncGenCount; |
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2150 | if (lV - ncGenCount == 0) |
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2151 | { |
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2152 | idDelete(&G); |
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2153 | return 1; |
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2154 | } |
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2155 | if (lV - ncGenCount == 1) |
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2156 | { |
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2157 | idDelete(&G); |
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2158 | return -1; |
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2159 | } |
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2160 | if (lV - ncGenCount >= 2) |
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2161 | { |
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2162 | idDelete(&G); |
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2163 | return -1; |
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2164 | } |
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2165 | } |
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2166 | |
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2167 | // get the max deg |
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2168 | long maxDeg = 0; |
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2169 | for (int i = 0; i < IDELEMS(G); i++) |
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2170 | { |
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2171 | maxDeg = si_max(maxDeg, pTotaldegree(G->m[i])); |
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2172 | |
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2173 | // also check whether G = <1> |
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2174 | if (pIsConstantComp(G->m[i])) |
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2175 | { |
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2176 | WerrorS("K-Dim not defined for 0-ring"); // TODO is it minus infinity ? |
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2177 | idDelete(&G); |
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2178 | return -2; |
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2179 | } |
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2180 | } |
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2181 | if (TEST_OPT_PROT) |
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2182 | Print("max deg: %ld\n", maxDeg); |
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2183 | |
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2184 | |
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2185 | // for normal words of length minDeg ... maxDeg-1 |
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2186 | // brute-force the normal words |
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2187 | if (TEST_OPT_PROT) |
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2188 | PrintS("Computing normal words normally...\n"); |
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2189 | long numberOfNormalWords = lp_countNormalWords(maxDeg - 1, G); |
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2190 | |
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2191 | if (TEST_OPT_PROT) |
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2192 | Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1); |
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2193 | |
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2194 | // early termination if G \subset X |
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2195 | if (maxDeg <= 1) |
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2196 | { |
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2197 | int lV = currRing->isLPring; |
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2198 | int ncGenCount = currRing->LPncGenCount; |
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2199 | if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges |
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2200 | { |
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2201 | idDelete(&G); |
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2202 | return numberOfNormalWords; |
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2203 | } |
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2204 | if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop |
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2205 | { |
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2206 | idDelete(&G); |
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2207 | return -1; |
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2208 | } |
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2209 | if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop |
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2210 | { |
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2211 | idDelete(&G); |
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2212 | return -1; |
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2213 | } |
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2214 | } |
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2215 | |
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2216 | if (TEST_OPT_PROT) |
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2217 | PrintS("Computing Ufnarovski graph...\n"); |
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2218 | |
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2219 | ideal standardWords; |
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2220 | intvec* UG = lp_ufnarovskiGraph(G, standardWords); |
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2221 | if (UG == NULL) |
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2222 | { |
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2223 | idDelete(&G); |
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2224 | return -2; |
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2225 | } |
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2226 | if (errorreported) |
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2227 | { |
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2228 | delete UG; |
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2229 | idDelete(&G); |
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2230 | return -2; |
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2231 | } |
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2232 | |
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2233 | if (TEST_OPT_PROT) |
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2234 | Print("Ufnarovski graph is %dx%d.\n", UG->rows(), UG->cols()); |
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2235 | |
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2236 | if (TEST_OPT_PROT) |
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2237 | PrintS("Checking whether Ufnarovski graph is acyclic...\n"); |
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2238 | |
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2239 | if (!isAcyclic(UG)) |
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2240 | { |
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2241 | // in this case we have infinitely many normal words |
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2242 | return -1; |
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2243 | } |
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2244 | |
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2245 | std::vector<std::vector<int> > vvUG = iv2vv(UG); |
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2246 | for (int i = 0; i < vvUG.size(); i++) |
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2247 | { |
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2248 | if (vvIsRowZero(vvUG, i) && vvIsColumnZero(vvUG, i)) // i is isolated vertex |
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2249 | { |
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2250 | vvDeleteRow(vvUG, i); |
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2251 | vvDeleteColumn(vvUG, i); |
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2252 | i--; |
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2253 | } |
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2254 | } |
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2255 | if (TEST_OPT_PROT) |
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2256 | Print("Simplified Ufnarovski graph to %dx%d.\n", (int)vvUG.size(), (int)vvUG.size()); |
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2257 | |
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2258 | // for normal words of length >= maxDeg |
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2259 | // use Ufnarovski graph |
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2260 | if (TEST_OPT_PROT) |
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2261 | PrintS("Computing normal words via Ufnarovski graph...\n"); |
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2262 | std::vector<std::vector<int> > UGpower = vvUG; |
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2263 | long nUGpower = 1; |
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2264 | while (!vvIsZero(UGpower)) |
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2265 | { |
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2266 | if (TEST_OPT_PROT) |
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2267 | PrintS("Start count graph entries.\n"); |
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2268 | for (int i = 0; i < UGpower.size(); i++) |
---|
2269 | { |
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2270 | for (int j = 0; j < UGpower[i].size(); j++) |
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2271 | { |
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2272 | numberOfNormalWords += UGpower[i][j]; |
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2273 | } |
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2274 | } |
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2275 | |
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2276 | if (TEST_OPT_PROT) |
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2277 | { |
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2278 | PrintS("Done count graph entries.\n"); |
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2279 | Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1 + nUGpower); |
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2280 | } |
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2281 | |
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2282 | if (TEST_OPT_PROT) |
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2283 | PrintS("Start mat mult.\n"); |
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2284 | UGpower = vvMult(UGpower, vvUG); // TODO: avoid creation of new intvec |
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2285 | if (TEST_OPT_PROT) |
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2286 | PrintS("Done mat mult.\n"); |
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2287 | nUGpower++; |
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2288 | } |
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2289 | |
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2290 | delete UG; |
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2291 | idDelete(&G); |
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2292 | return numberOfNormalWords; |
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2293 | } |
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2294 | #endif |
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