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 <omalloc/omalloc.h> |
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11 | #include <misc/intvec.h> |
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12 | #include <coeffs/numbers.h> |
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13 | |
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14 | #include <kernel/structs.h> |
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15 | #include <kernel/ideals.h> |
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16 | #include <kernel/polys.h> |
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17 | |
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18 | #include <kernel/combinatorics/hutil.h> |
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19 | #include <kernel/combinatorics/hilb.h> |
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20 | #include <kernel/combinatorics/stairc.h> |
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21 | |
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22 | int hCo, hMu, hMu2; |
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23 | omBin indlist_bin = omGetSpecBin(sizeof(indlist)); |
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24 | |
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25 | /*0 implementation*/ |
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26 | |
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27 | // dimension |
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28 | |
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29 | void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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30 | varset var, int Nvar) |
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31 | { |
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32 | int dn, iv, rad0, b, c, x; |
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33 | scmon pn; |
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34 | scfmon rn; |
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35 | if (Nrad < 2) |
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36 | { |
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37 | dn = Npure + Nrad; |
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38 | if (dn < hCo) |
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39 | hCo = dn; |
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40 | return; |
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41 | } |
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42 | if (Npure+1 >= hCo) |
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43 | return; |
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44 | iv = Nvar; |
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45 | while(pure[var[iv]]) iv--; |
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46 | hStepR(rad, Nrad, var, iv, &rad0); |
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47 | if (rad0!=0) |
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48 | { |
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49 | iv--; |
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50 | if (rad0 < Nrad) |
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51 | { |
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52 | pn = hGetpure(pure); |
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53 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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54 | hDimSolve(pn, Npure + 1, rn, rad0, var, iv); |
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55 | b = rad0; |
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56 | c = Nrad; |
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57 | hElimR(rn, &rad0, b, c, var, iv); |
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58 | hPure(rn, b, &c, var, iv, pn, &x); |
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59 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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60 | rad0 += (c - b); |
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61 | hDimSolve(pn, Npure + x, rn, rad0, var, iv); |
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62 | } |
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63 | else |
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64 | { |
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65 | hDimSolve(pure, Npure, rad, Nrad, var, iv); |
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66 | } |
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67 | } |
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68 | else |
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69 | hCo = Npure + 1; |
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70 | } |
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71 | |
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72 | int scDimInt(ideal S, ideal Q) |
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73 | { |
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74 | id_Test(S, currRing); |
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75 | if( Q!=NULL ) id_Test(Q, currRing); |
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76 | |
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77 | int mc; |
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78 | hexist = hInit(S, Q, &hNexist, currRing); |
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79 | if (!hNexist) |
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80 | return (currRing->N); |
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81 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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82 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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83 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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84 | mc = hisModule; |
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85 | if (!mc) |
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86 | { |
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87 | hrad = hexist; |
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88 | hNrad = hNexist; |
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89 | } |
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90 | else |
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91 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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92 | radmem = hCreate((currRing->N) - 1); |
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93 | hCo = (currRing->N) + 1; |
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94 | loop |
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95 | { |
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96 | if (mc) |
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97 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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98 | if (hNrad) |
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99 | { |
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100 | hNvar = (currRing->N); |
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101 | hRadical(hrad, &hNrad, hNvar); |
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102 | hSupp(hrad, hNrad, hvar, &hNvar); |
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103 | if (hNvar) |
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104 | { |
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105 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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106 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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107 | hLexR(hrad, hNrad, hvar, hNvar); |
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108 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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109 | } |
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110 | } |
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111 | else |
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112 | { |
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113 | hCo = 0; |
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114 | break; |
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115 | } |
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116 | mc--; |
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117 | if (mc <= 0) |
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118 | break; |
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119 | } |
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120 | hKill(radmem, (currRing->N) - 1); |
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121 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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122 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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123 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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124 | hDelete(hexist, hNexist); |
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125 | if (hisModule) |
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126 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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127 | return (currRing->N) - hCo; |
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128 | } |
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129 | |
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130 | // independent set |
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131 | static scmon hInd; |
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132 | |
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133 | static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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134 | varset var, int Nvar) |
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135 | { |
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136 | int dn, iv, rad0, b, c, x; |
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137 | scmon pn; |
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138 | scfmon rn; |
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139 | if (Nrad < 2) |
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140 | { |
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141 | dn = Npure + Nrad; |
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142 | if (dn < hCo) |
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143 | { |
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144 | hCo = dn; |
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145 | for (iv=(currRing->N); iv; iv--) |
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146 | { |
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147 | if (pure[iv]) |
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148 | hInd[iv] = 0; |
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149 | else |
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150 | hInd[iv] = 1; |
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151 | } |
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152 | if (Nrad) |
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153 | { |
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154 | pn = *rad; |
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155 | iv = Nvar; |
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156 | loop |
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157 | { |
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158 | x = var[iv]; |
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159 | if (pn[x]) |
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160 | { |
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161 | hInd[x] = 0; |
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162 | break; |
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163 | } |
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164 | iv--; |
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165 | } |
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166 | } |
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167 | } |
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168 | return; |
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169 | } |
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170 | if (Npure+1 >= hCo) |
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171 | return; |
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172 | iv = Nvar; |
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173 | while(pure[var[iv]]) iv--; |
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174 | hStepR(rad, Nrad, var, iv, &rad0); |
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175 | if (rad0) |
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176 | { |
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177 | iv--; |
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178 | if (rad0 < Nrad) |
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179 | { |
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180 | pn = hGetpure(pure); |
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181 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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182 | pn[var[iv + 1]] = 1; |
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183 | hIndSolve(pn, Npure + 1, rn, rad0, var, iv); |
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184 | pn[var[iv + 1]] = 0; |
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185 | b = rad0; |
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186 | c = Nrad; |
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187 | hElimR(rn, &rad0, b, c, var, iv); |
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188 | hPure(rn, b, &c, var, iv, pn, &x); |
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189 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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190 | rad0 += (c - b); |
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191 | hIndSolve(pn, Npure + x, rn, rad0, var, iv); |
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192 | } |
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193 | else |
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194 | { |
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195 | hIndSolve(pure, Npure, rad, Nrad, var, iv); |
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196 | } |
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197 | } |
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198 | else |
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199 | { |
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200 | hCo = Npure + 1; |
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201 | for (x=(currRing->N); x; x--) |
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202 | { |
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203 | if (pure[x]) |
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204 | hInd[x] = 0; |
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205 | else |
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206 | hInd[x] = 1; |
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207 | } |
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208 | hInd[var[iv]] = 0; |
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209 | } |
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210 | } |
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211 | |
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212 | intvec * scIndIntvec(ideal S, ideal Q) |
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213 | { |
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214 | id_Test(S, currRing); |
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215 | if( Q!=NULL ) id_Test(Q, currRing); |
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216 | |
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217 | intvec *Set=new intvec((currRing->N)); |
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218 | int mc,i; |
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219 | hexist = hInit(S, Q, &hNexist, currRing); |
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220 | if (hNexist==0) |
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221 | { |
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222 | for(i=0; i<(currRing->N); i++) |
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223 | (*Set)[i]=1; |
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224 | return Set; |
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225 | } |
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226 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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227 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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228 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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229 | hInd = (scmon)omAlloc0((1 + (currRing->N)) * sizeof(int)); |
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230 | mc = hisModule; |
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231 | if (mc==0) |
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232 | { |
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233 | hrad = hexist; |
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234 | hNrad = hNexist; |
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235 | } |
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236 | else |
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237 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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238 | radmem = hCreate((currRing->N) - 1); |
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239 | hCo = (currRing->N) + 1; |
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240 | loop |
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241 | { |
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242 | if (mc!=0) |
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243 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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244 | if (hNrad!=0) |
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245 | { |
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246 | hNvar = (currRing->N); |
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247 | hRadical(hrad, &hNrad, hNvar); |
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248 | hSupp(hrad, hNrad, hvar, &hNvar); |
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249 | if (hNvar!=0) |
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250 | { |
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251 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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252 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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253 | hLexR(hrad, hNrad, hvar, hNvar); |
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254 | hIndSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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255 | } |
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256 | } |
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257 | else |
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258 | { |
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259 | hCo = 0; |
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260 | break; |
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261 | } |
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262 | mc--; |
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263 | if (mc <= 0) |
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264 | break; |
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265 | } |
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266 | for(i=0; i<(currRing->N); i++) |
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267 | (*Set)[i] = hInd[i+1]; |
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268 | hKill(radmem, (currRing->N) - 1); |
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269 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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270 | omFreeSize((ADDRESS)hInd, (1 + (currRing->N)) * sizeof(int)); |
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271 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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272 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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273 | hDelete(hexist, hNexist); |
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274 | if (hisModule) |
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275 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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276 | return Set; |
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277 | } |
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278 | |
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279 | indset ISet, JSet; |
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280 | |
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281 | static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar) |
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282 | { |
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283 | int k1, i; |
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284 | k1 = var[Nvar]; |
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285 | i = 0; |
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286 | loop |
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287 | { |
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288 | if (rad[i][k1]==0) |
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289 | return FALSE; |
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290 | i++; |
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291 | if (i == Nrad) |
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292 | return TRUE; |
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293 | } |
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294 | } |
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295 | |
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296 | static void hIndep(scmon pure) |
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297 | { |
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298 | int iv; |
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299 | intvec *Set; |
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300 | |
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301 | Set = ISet->set = new intvec((currRing->N)); |
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302 | for (iv=(currRing->N); iv!=0 ; iv--) |
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303 | { |
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304 | if (pure[iv]) |
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305 | (*Set)[iv-1] = 0; |
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306 | else |
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307 | (*Set)[iv-1] = 1; |
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308 | } |
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309 | ISet = ISet->nx = (indset)omAlloc0Bin(indlist_bin); |
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310 | hMu++; |
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311 | } |
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312 | |
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313 | void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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314 | varset var, int Nvar) |
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315 | { |
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316 | int dn, iv, rad0, b, c, x; |
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317 | scmon pn; |
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318 | scfmon rn; |
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319 | if (Nrad < 2) |
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320 | { |
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321 | dn = Npure + Nrad; |
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322 | if (dn == hCo) |
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323 | { |
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324 | if (Nrad==0) |
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325 | hIndep(pure); |
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326 | else |
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327 | { |
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328 | pn = *rad; |
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329 | for (iv = Nvar; iv!=0; iv--) |
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330 | { |
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331 | x = var[iv]; |
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332 | if (pn[x]) |
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333 | { |
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334 | pure[x] = 1; |
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335 | hIndep(pure); |
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336 | pure[x] = 0; |
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337 | } |
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338 | } |
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339 | } |
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340 | } |
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341 | return; |
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342 | } |
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343 | iv = Nvar; |
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344 | dn = Npure+1; |
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345 | if (dn >= hCo) |
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346 | { |
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347 | if (dn > hCo) |
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348 | return; |
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349 | loop |
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350 | { |
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351 | if(!pure[var[iv]]) |
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352 | { |
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353 | if(hNotZero(rad, Nrad, var, iv)) |
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354 | { |
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355 | pure[var[iv]] = 1; |
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356 | hIndep(pure); |
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357 | pure[var[iv]] = 0; |
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358 | } |
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359 | } |
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360 | iv--; |
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361 | if (!iv) |
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362 | return; |
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363 | } |
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364 | } |
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365 | while(pure[var[iv]]) iv--; |
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366 | hStepR(rad, Nrad, var, iv, &rad0); |
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367 | iv--; |
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368 | if (rad0 < Nrad) |
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369 | { |
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370 | pn = hGetpure(pure); |
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371 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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372 | pn[var[iv + 1]] = 1; |
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373 | hIndMult(pn, Npure + 1, rn, rad0, var, iv); |
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374 | pn[var[iv + 1]] = 0; |
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375 | b = rad0; |
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376 | c = Nrad; |
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377 | hElimR(rn, &rad0, b, c, var, iv); |
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378 | hPure(rn, b, &c, var, iv, pn, &x); |
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379 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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380 | rad0 += (c - b); |
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381 | hIndMult(pn, Npure + x, rn, rad0, var, iv); |
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382 | } |
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383 | else |
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384 | { |
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385 | hIndMult(pure, Npure, rad, Nrad, var, iv); |
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386 | } |
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387 | } |
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388 | |
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389 | /*3 |
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390 | * consider indset x := !pure |
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391 | * (for all i) (if(sm(i) > x) return FALSE) |
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392 | * else return TRUE |
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393 | */ |
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394 | static BOOLEAN hCheck1(indset sm, scmon pure) |
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395 | { |
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396 | int iv; |
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397 | intvec *Set; |
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398 | while (sm->nx != NULL) |
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399 | { |
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400 | Set = sm->set; |
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401 | iv=(currRing->N); |
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402 | loop |
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403 | { |
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404 | if (((*Set)[iv-1] == 0) && (pure[iv] == 0)) |
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405 | break; |
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406 | iv--; |
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407 | if (iv == 0) |
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408 | return FALSE; |
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409 | } |
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410 | sm = sm->nx; |
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411 | } |
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412 | return TRUE; |
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413 | } |
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414 | |
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415 | /*3 |
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416 | * consider indset x := !pure |
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417 | * (for all i) if(x > sm(i)) delete sm(i)) |
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418 | * return (place for x) |
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419 | */ |
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420 | static indset hCheck2(indset sm, scmon pure) |
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421 | { |
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422 | int iv; |
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423 | intvec *Set; |
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424 | indset be, a1 = NULL; |
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425 | while (sm->nx != NULL) |
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426 | { |
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427 | Set = sm->set; |
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428 | iv=(currRing->N); |
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429 | loop |
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430 | { |
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431 | if ((pure[iv] == 1) && ((*Set)[iv-1] == 1)) |
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432 | break; |
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433 | iv--; |
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434 | if (iv == 0) |
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435 | { |
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436 | if (a1 == NULL) |
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437 | { |
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438 | a1 = sm; |
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439 | } |
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440 | else |
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441 | { |
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442 | hMu2--; |
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443 | be->nx = sm->nx; |
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444 | delete Set; |
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445 | omFreeBin((ADDRESS)sm, indlist_bin); |
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446 | sm = be; |
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447 | } |
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448 | break; |
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449 | } |
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450 | } |
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451 | be = sm; |
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452 | sm = sm->nx; |
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453 | } |
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454 | if (a1 != NULL) |
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455 | { |
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456 | return a1; |
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457 | } |
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458 | else |
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459 | { |
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460 | hMu2++; |
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461 | sm->set = new intvec((currRing->N)); |
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462 | sm->nx = (indset)omAlloc0Bin(indlist_bin); |
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463 | return sm; |
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464 | } |
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465 | } |
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466 | |
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467 | /*2 |
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468 | * definition x >= y |
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469 | * x(i) == 0 => y(i) == 0 |
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470 | * > ex. j with x(j) == 1 and y(j) == 0 |
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471 | */ |
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472 | static void hCheckIndep(scmon pure) |
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473 | { |
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474 | intvec *Set; |
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475 | indset res; |
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476 | int iv; |
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477 | if (hCheck1(ISet, pure)) |
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478 | { |
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479 | if (hCheck1(JSet, pure)) |
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480 | { |
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481 | res = hCheck2(JSet,pure); |
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482 | if (res == NULL) |
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483 | return; |
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484 | Set = res->set; |
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485 | for (iv=(currRing->N); iv; iv--) |
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486 | { |
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487 | if (pure[iv]) |
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488 | (*Set)[iv-1] = 0; |
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489 | else |
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490 | (*Set)[iv-1] = 1; |
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491 | } |
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492 | } |
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493 | } |
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494 | } |
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495 | |
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496 | void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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497 | varset var, int Nvar) |
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498 | { |
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499 | int dn, iv, rad0, b, c, x; |
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500 | scmon pn; |
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501 | scfmon rn; |
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502 | if (Nrad < 2) |
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503 | { |
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504 | dn = Npure + Nrad; |
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505 | if (dn > hCo) |
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506 | { |
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507 | if (!Nrad) |
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508 | hCheckIndep(pure); |
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509 | else |
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510 | { |
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511 | pn = *rad; |
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512 | for (iv = Nvar; iv; iv--) |
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513 | { |
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514 | x = var[iv]; |
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515 | if (pn[x]) |
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516 | { |
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517 | pure[x] = 1; |
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518 | hCheckIndep(pure); |
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519 | pure[x] = 0; |
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520 | } |
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521 | } |
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522 | } |
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523 | } |
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524 | return; |
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525 | } |
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526 | iv = Nvar; |
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527 | while(pure[var[iv]]) iv--; |
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528 | hStepR(rad, Nrad, var, iv, &rad0); |
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529 | iv--; |
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530 | if (rad0 < Nrad) |
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531 | { |
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532 | pn = hGetpure(pure); |
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533 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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534 | pn[var[iv + 1]] = 1; |
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535 | hIndAllMult(pn, Npure + 1, rn, rad0, var, iv); |
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536 | pn[var[iv + 1]] = 0; |
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537 | b = rad0; |
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538 | c = Nrad; |
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539 | hElimR(rn, &rad0, b, c, var, iv); |
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540 | hPure(rn, b, &c, var, iv, pn, &x); |
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541 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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542 | rad0 += (c - b); |
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543 | hIndAllMult(pn, Npure + x, rn, rad0, var, iv); |
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544 | } |
---|
545 | else |
---|
546 | { |
---|
547 | hIndAllMult(pure, Npure, rad, Nrad, var, iv); |
---|
548 | } |
---|
549 | } |
---|
550 | |
---|
551 | // multiplicity |
---|
552 | |
---|
553 | static int hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar) |
---|
554 | { |
---|
555 | int iv = Nvar -1, sum, a, a0, a1, b, i; |
---|
556 | int x, x0; |
---|
557 | scmon pn; |
---|
558 | scfmon sn; |
---|
559 | if (!iv) |
---|
560 | return pure[var[1]]; |
---|
561 | else if (!Nstc) |
---|
562 | { |
---|
563 | sum = 1; |
---|
564 | for (i = Nvar; i; i--) |
---|
565 | sum *= pure[var[i]]; |
---|
566 | return sum; |
---|
567 | } |
---|
568 | x = a = 0; |
---|
569 | pn = hGetpure(pure); |
---|
570 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
571 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
572 | if (a == Nstc) |
---|
573 | return pure[var[Nvar]] * hZeroMult(pn, sn, a, var, iv); |
---|
574 | else |
---|
575 | sum = x * hZeroMult(pn, sn, a, var, iv); |
---|
576 | b = a; |
---|
577 | loop |
---|
578 | { |
---|
579 | a0 = a; |
---|
580 | x0 = x; |
---|
581 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
582 | hElimS(sn, &b, a0, a, var, iv); |
---|
583 | a1 = a; |
---|
584 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
585 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
586 | b += (a1 - a0); |
---|
587 | if (a < Nstc) |
---|
588 | { |
---|
589 | sum += (x - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
590 | } |
---|
591 | else |
---|
592 | { |
---|
593 | sum += (pure[var[Nvar]] - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
594 | return sum; |
---|
595 | } |
---|
596 | } |
---|
597 | } |
---|
598 | |
---|
599 | static void hProject(scmon pure, varset sel) |
---|
600 | { |
---|
601 | int i, i0, k; |
---|
602 | i0 = 0; |
---|
603 | for (i = 1; i <= (currRing->N); i++) |
---|
604 | { |
---|
605 | if (pure[i]) |
---|
606 | { |
---|
607 | i0++; |
---|
608 | sel[i0] = i; |
---|
609 | } |
---|
610 | } |
---|
611 | i = hNstc; |
---|
612 | memcpy(hwork, hstc, i * sizeof(scmon)); |
---|
613 | hStaircase(hwork, &i, sel, i0); |
---|
614 | if ((i0 > 2) && (i > 10)) |
---|
615 | hOrdSupp(hwork, i, sel, i0); |
---|
616 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
617 | hPure(hwork, 0, &i, sel, i0, hpur0, &k); |
---|
618 | hLexS(hwork, i, sel, i0); |
---|
619 | hMu += hZeroMult(hpur0, hwork, i, sel, i0); |
---|
620 | } |
---|
621 | |
---|
622 | static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
623 | varset var, int Nvar) |
---|
624 | { |
---|
625 | int dn, iv, rad0, b, c, x; |
---|
626 | scmon pn; |
---|
627 | scfmon rn; |
---|
628 | if (Nrad < 2) |
---|
629 | { |
---|
630 | dn = Npure + Nrad; |
---|
631 | if (dn == hCo) |
---|
632 | { |
---|
633 | if (!Nrad) |
---|
634 | hProject(pure, hsel); |
---|
635 | else |
---|
636 | { |
---|
637 | pn = *rad; |
---|
638 | for (iv = Nvar; iv; iv--) |
---|
639 | { |
---|
640 | x = var[iv]; |
---|
641 | if (pn[x]) |
---|
642 | { |
---|
643 | pure[x] = 1; |
---|
644 | hProject(pure, hsel); |
---|
645 | pure[x] = 0; |
---|
646 | } |
---|
647 | } |
---|
648 | } |
---|
649 | } |
---|
650 | return; |
---|
651 | } |
---|
652 | iv = Nvar; |
---|
653 | dn = Npure+1; |
---|
654 | if (dn >= hCo) |
---|
655 | { |
---|
656 | if (dn > hCo) |
---|
657 | return; |
---|
658 | loop |
---|
659 | { |
---|
660 | if(!pure[var[iv]]) |
---|
661 | { |
---|
662 | if(hNotZero(rad, Nrad, var, iv)) |
---|
663 | { |
---|
664 | pure[var[iv]] = 1; |
---|
665 | hProject(pure, hsel); |
---|
666 | pure[var[iv]] = 0; |
---|
667 | } |
---|
668 | } |
---|
669 | iv--; |
---|
670 | if (!iv) |
---|
671 | return; |
---|
672 | } |
---|
673 | } |
---|
674 | while(pure[var[iv]]) iv--; |
---|
675 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
676 | iv--; |
---|
677 | if (rad0 < Nrad) |
---|
678 | { |
---|
679 | pn = hGetpure(pure); |
---|
680 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
681 | pn[var[iv + 1]] = 1; |
---|
682 | hDimMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
683 | pn[var[iv + 1]] = 0; |
---|
684 | b = rad0; |
---|
685 | c = Nrad; |
---|
686 | hElimR(rn, &rad0, b, c, var, iv); |
---|
687 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
688 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
689 | rad0 += (c - b); |
---|
690 | hDimMult(pn, Npure + x, rn, rad0, var, iv); |
---|
691 | } |
---|
692 | else |
---|
693 | { |
---|
694 | hDimMult(pure, Npure, rad, Nrad, var, iv); |
---|
695 | } |
---|
696 | } |
---|
697 | |
---|
698 | static void hDegree(ideal S, ideal Q) |
---|
699 | { |
---|
700 | id_Test(S, currRing); |
---|
701 | if( Q!=NULL ) id_Test(Q, currRing); |
---|
702 | |
---|
703 | int di; |
---|
704 | int mc; |
---|
705 | hexist = hInit(S, Q, &hNexist, currRing); |
---|
706 | if (!hNexist) |
---|
707 | { |
---|
708 | hCo = 0; |
---|
709 | hMu = 1; |
---|
710 | return; |
---|
711 | } |
---|
712 | //hWeight(); |
---|
713 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
714 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
715 | hsel = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
716 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
717 | hpur0 = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
718 | mc = hisModule; |
---|
719 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
720 | if (!mc) |
---|
721 | { |
---|
722 | memcpy(hrad, hexist, hNexist * sizeof(scmon)); |
---|
723 | hstc = hexist; |
---|
724 | hNrad = hNstc = hNexist; |
---|
725 | } |
---|
726 | else |
---|
727 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
728 | radmem = hCreate((currRing->N) - 1); |
---|
729 | stcmem = hCreate((currRing->N) - 1); |
---|
730 | hCo = (currRing->N) + 1; |
---|
731 | di = hCo + 1; |
---|
732 | loop |
---|
733 | { |
---|
734 | if (mc) |
---|
735 | { |
---|
736 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
---|
737 | hNstc = hNrad; |
---|
738 | memcpy(hstc, hrad, hNrad * sizeof(scmon)); |
---|
739 | } |
---|
740 | if (hNrad) |
---|
741 | { |
---|
742 | hNvar = (currRing->N); |
---|
743 | hRadical(hrad, &hNrad, hNvar); |
---|
744 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
745 | if (hNvar) |
---|
746 | { |
---|
747 | hCo = hNvar; |
---|
748 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
749 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
750 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
751 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
752 | } |
---|
753 | } |
---|
754 | else |
---|
755 | { |
---|
756 | hNvar = 1; |
---|
757 | hCo = 0; |
---|
758 | } |
---|
759 | if (hCo < di) |
---|
760 | { |
---|
761 | di = hCo; |
---|
762 | hMu = 0; |
---|
763 | } |
---|
764 | if (hNvar && (hCo == di)) |
---|
765 | { |
---|
766 | if (di && (di < (currRing->N))) |
---|
767 | hDimMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
768 | else if (!di) |
---|
769 | hMu++; |
---|
770 | else |
---|
771 | { |
---|
772 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
773 | if ((hNvar > 2) && (hNstc > 10)) |
---|
774 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
775 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
776 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
777 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
778 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
779 | } |
---|
780 | } |
---|
781 | mc--; |
---|
782 | if (mc <= 0) |
---|
783 | break; |
---|
784 | } |
---|
785 | hCo = di; |
---|
786 | hKill(stcmem, (currRing->N) - 1); |
---|
787 | hKill(radmem, (currRing->N) - 1); |
---|
788 | omFreeSize((ADDRESS)hpur0, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
789 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
790 | omFreeSize((ADDRESS)hsel, ((currRing->N) + 1) * sizeof(int)); |
---|
791 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
---|
792 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
793 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
---|
794 | hDelete(hexist, hNexist); |
---|
795 | if (hisModule) |
---|
796 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
797 | } |
---|
798 | |
---|
799 | int scMultInt(ideal S, ideal Q) |
---|
800 | { |
---|
801 | id_Test(S, currRing); |
---|
802 | if( Q!=NULL ) id_Test(Q, currRing); |
---|
803 | |
---|
804 | hDegree(S, Q); |
---|
805 | return hMu; |
---|
806 | } |
---|
807 | |
---|
808 | void scPrintDegree(int co, int mu) |
---|
809 | { |
---|
810 | int di = (currRing->N)-co; |
---|
811 | if (currRing->OrdSgn == 1) |
---|
812 | { |
---|
813 | if (di>0) |
---|
814 | Print("// dimension (proj.) = %d\n// degree (proj.) = %d\n", di-1, mu); |
---|
815 | else |
---|
816 | Print("// dimension (affine) = 0\n// degree (affine) = %d\n", mu); |
---|
817 | } |
---|
818 | else |
---|
819 | Print("// dimension (local) = %d\n// multiplicity = %d\n", di, mu); |
---|
820 | } |
---|
821 | |
---|
822 | void scDegree(ideal S, intvec *modulweight, ideal Q) |
---|
823 | { |
---|
824 | id_Test(S, currRing); |
---|
825 | if( Q!=NULL ) id_Test(Q, currRing); |
---|
826 | |
---|
827 | int co, mu, l; |
---|
828 | intvec *hseries2; |
---|
829 | intvec *hseries1 = hFirstSeries(S, modulweight, Q); |
---|
830 | l = hseries1->length()-1; |
---|
831 | if (l > 1) |
---|
832 | hseries2 = hSecondSeries(hseries1); |
---|
833 | else |
---|
834 | hseries2 = hseries1; |
---|
835 | hDegreeSeries(hseries1, hseries2, &co, &mu); |
---|
836 | if ((l == 1) &&(mu == 0)) |
---|
837 | scPrintDegree((currRing->N)+1, 0); |
---|
838 | else |
---|
839 | scPrintDegree(co, mu); |
---|
840 | if (l>1) |
---|
841 | delete hseries1; |
---|
842 | delete hseries2; |
---|
843 | } |
---|
844 | |
---|
845 | static void hDegree0(ideal S, ideal Q, const ring tailRing) |
---|
846 | { |
---|
847 | id_TestTail(S, currRing, tailRing); |
---|
848 | if (Q!=NULL) id_TestTail(Q, currRing, tailRing); |
---|
849 | |
---|
850 | int mc; |
---|
851 | hexist = hInit(S, Q, &hNexist, tailRing); |
---|
852 | if (!hNexist) |
---|
853 | { |
---|
854 | hMu = -1; |
---|
855 | return; |
---|
856 | } |
---|
857 | else |
---|
858 | hMu = 0; |
---|
859 | |
---|
860 | const ring r = currRing; |
---|
861 | |
---|
862 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
863 | hvar = (varset)omAlloc(((r->N) + 1) * sizeof(int)); |
---|
864 | hpur0 = (scmon)omAlloc((1 + ((r->N) * (r->N))) * sizeof(int)); |
---|
865 | mc = hisModule; |
---|
866 | if (!mc) |
---|
867 | { |
---|
868 | hstc = hexist; |
---|
869 | hNstc = hNexist; |
---|
870 | } |
---|
871 | else |
---|
872 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
873 | stcmem = hCreate((r->N) - 1); |
---|
874 | loop |
---|
875 | { |
---|
876 | if (mc) |
---|
877 | { |
---|
878 | hComp(hexist, hNexist, mc, hstc, &hNstc); |
---|
879 | if (!hNstc) |
---|
880 | { |
---|
881 | hMu = -1; |
---|
882 | break; |
---|
883 | } |
---|
884 | } |
---|
885 | hNvar = (r->N); |
---|
886 | for (int i = hNvar; i; i--) |
---|
887 | hvar[i] = i; |
---|
888 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
889 | hSupp(hstc, hNstc, hvar, &hNvar); |
---|
890 | if ((hNvar == (r->N)) && (hNstc >= (r->N))) |
---|
891 | { |
---|
892 | if ((hNvar > 2) && (hNstc > 10)) |
---|
893 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
894 | memset(hpur0, 0, ((r->N) + 1) * sizeof(int)); |
---|
895 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
896 | if (hNpure == hNvar) |
---|
897 | { |
---|
898 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
899 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
900 | } |
---|
901 | else |
---|
902 | hMu = -1; |
---|
903 | } |
---|
904 | else if (hNvar) |
---|
905 | hMu = -1; |
---|
906 | mc--; |
---|
907 | if (mc <= 0 || hMu < 0) |
---|
908 | break; |
---|
909 | } |
---|
910 | hKill(stcmem, (r->N) - 1); |
---|
911 | omFreeSize((ADDRESS)hpur0, (1 + ((r->N) * (r->N))) * sizeof(int)); |
---|
912 | omFreeSize((ADDRESS)hvar, ((r->N) + 1) * sizeof(int)); |
---|
913 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
914 | hDelete(hexist, hNexist); |
---|
915 | if (hisModule) |
---|
916 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
917 | } |
---|
918 | |
---|
919 | int scMult0Int(ideal S, ideal Q, const ring tailRing) |
---|
920 | { |
---|
921 | id_TestTail(S, currRing, tailRing); |
---|
922 | if (Q!=NULL) id_TestTail(Q, currRing, tailRing); |
---|
923 | |
---|
924 | hDegree0(S, Q, tailRing); |
---|
925 | return hMu; |
---|
926 | } |
---|
927 | |
---|
928 | |
---|
929 | // HC |
---|
930 | |
---|
931 | static poly pWork; |
---|
932 | |
---|
933 | static void hHedge(poly hEdge) |
---|
934 | { |
---|
935 | pSetm(pWork); |
---|
936 | if (pLmCmp(pWork, hEdge) == currRing->OrdSgn) |
---|
937 | { |
---|
938 | for (int i = hNvar; i>0; i--) |
---|
939 | pSetExp(hEdge,i, pGetExp(pWork,i)); |
---|
940 | pSetm(hEdge); |
---|
941 | } |
---|
942 | } |
---|
943 | |
---|
944 | |
---|
945 | static void hHedgeStep(scmon pure, scfmon stc, |
---|
946 | int Nstc, varset var, int Nvar,poly hEdge) |
---|
947 | { |
---|
948 | int iv = Nvar -1, k = var[Nvar], a, a0, a1, b, i; |
---|
949 | int x/*, x0*/; |
---|
950 | scmon pn; |
---|
951 | scfmon sn; |
---|
952 | if (iv==0) |
---|
953 | { |
---|
954 | pSetExp(pWork, k, pure[k]); |
---|
955 | hHedge(hEdge); |
---|
956 | return; |
---|
957 | } |
---|
958 | else if (Nstc==0) |
---|
959 | { |
---|
960 | for (i = Nvar; i>0; i--) |
---|
961 | pSetExp(pWork, var[i], pure[var[i]]); |
---|
962 | hHedge(hEdge); |
---|
963 | return; |
---|
964 | } |
---|
965 | x = a = 0; |
---|
966 | pn = hGetpure(pure); |
---|
967 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
968 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
969 | if (a == Nstc) |
---|
970 | { |
---|
971 | pSetExp(pWork, k, pure[k]); |
---|
972 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
973 | return; |
---|
974 | } |
---|
975 | else |
---|
976 | { |
---|
977 | pSetExp(pWork, k, x); |
---|
978 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
979 | } |
---|
980 | b = a; |
---|
981 | loop |
---|
982 | { |
---|
983 | a0 = a; |
---|
984 | // x0 = x; |
---|
985 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
986 | hElimS(sn, &b, a0, a, var, iv); |
---|
987 | a1 = a; |
---|
988 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
989 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
990 | b += (a1 - a0); |
---|
991 | if (a < Nstc) |
---|
992 | { |
---|
993 | pSetExp(pWork, k, x); |
---|
994 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
995 | } |
---|
996 | else |
---|
997 | { |
---|
998 | pSetExp(pWork, k, pure[k]); |
---|
999 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
1000 | return; |
---|
1001 | } |
---|
1002 | } |
---|
1003 | } |
---|
1004 | |
---|
1005 | void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge, ring tailRing) |
---|
1006 | { |
---|
1007 | id_TestTail(S, currRing, tailRing); |
---|
1008 | if (Q!=NULL) id_TestTail(Q, currRing, tailRing); |
---|
1009 | |
---|
1010 | int i; |
---|
1011 | int k = ak; |
---|
1012 | #if HAVE_RINGS |
---|
1013 | if (rField_is_Ring(currRing) && (currRing->OrdSgn == -1)) |
---|
1014 | { |
---|
1015 | //consider just monic generators (over rings with zero-divisors) |
---|
1016 | ideal SS=id_Copy(S,tailRing); |
---|
1017 | for(i=0;i<=idElem(S);i++) |
---|
1018 | { |
---|
1019 | if(p_IsPurePower(SS->m[i],tailRing)==0) |
---|
1020 | { |
---|
1021 | p_Delete(&SS->m[i],tailRing); |
---|
1022 | } |
---|
1023 | } |
---|
1024 | S=id_Copy(SS,tailRing); |
---|
1025 | idSkipZeroes(S); |
---|
1026 | } |
---|
1027 | #if 0 |
---|
1028 | printf("\nThis is HC:\n"); |
---|
1029 | for(int ii=0;ii<=idElem(S);ii++) |
---|
1030 | { |
---|
1031 | pWrite(S->m[ii]); |
---|
1032 | } |
---|
1033 | //getchar(); |
---|
1034 | #endif |
---|
1035 | #endif |
---|
1036 | if(idElem(S) == 0) |
---|
1037 | return; |
---|
1038 | hNvar = (currRing->N); |
---|
1039 | hexist = hInit(S, Q, &hNexist, tailRing); // tailRing? |
---|
1040 | if (k!=0) |
---|
1041 | hComp(hexist, hNexist, k, hexist, &hNstc); |
---|
1042 | else |
---|
1043 | hNstc = hNexist; |
---|
1044 | assume(hNexist > 0); |
---|
1045 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1046 | hvar = (varset)omAlloc((hNvar + 1) * sizeof(int)); |
---|
1047 | hpure = (scmon)omAlloc((1 + (hNvar * hNvar)) * sizeof(int)); |
---|
1048 | stcmem = hCreate(hNvar - 1); |
---|
1049 | for (i = hNvar; i>0; i--) |
---|
1050 | hvar[i] = i; |
---|
1051 | hStaircase(hexist, &hNstc, hvar, hNvar); |
---|
1052 | if ((hNvar > 2) && (hNstc > 10)) |
---|
1053 | hOrdSupp(hexist, hNstc, hvar, hNvar); |
---|
1054 | memset(hpure, 0, (hNvar + 1) * sizeof(int)); |
---|
1055 | hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure); |
---|
1056 | hLexS(hexist, hNstc, hvar, hNvar); |
---|
1057 | if (hEdge!=NULL) |
---|
1058 | pLmFree(hEdge); |
---|
1059 | hEdge = pInit(); |
---|
1060 | pWork = pInit(); |
---|
1061 | hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge); |
---|
1062 | pSetComp(hEdge,ak); |
---|
1063 | hKill(stcmem, hNvar - 1); |
---|
1064 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
1065 | omFreeSize((ADDRESS)hvar, (hNvar + 1) * sizeof(int)); |
---|
1066 | omFreeSize((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(int)); |
---|
1067 | hDelete(hexist, hNexist); |
---|
1068 | pLmFree(pWork); |
---|
1069 | } |
---|
1070 | |
---|
1071 | |
---|
1072 | |
---|
1073 | // kbase |
---|
1074 | |
---|
1075 | static poly last; |
---|
1076 | static scmon act; |
---|
1077 | |
---|
1078 | static void scElKbase() |
---|
1079 | { |
---|
1080 | poly q = pInit(); |
---|
1081 | pSetCoeff0(q,nInit(1)); |
---|
1082 | pSetExpV(q,act); |
---|
1083 | pNext(q) = NULL; |
---|
1084 | last = pNext(last) = q; |
---|
1085 | } |
---|
1086 | |
---|
1087 | static int scMax( int i, scfmon stc, int Nvar) |
---|
1088 | { |
---|
1089 | int x, y=stc[0][Nvar]; |
---|
1090 | for (; i;) |
---|
1091 | { |
---|
1092 | i--; |
---|
1093 | x = stc[i][Nvar]; |
---|
1094 | if (x > y) y = x; |
---|
1095 | } |
---|
1096 | return y; |
---|
1097 | } |
---|
1098 | |
---|
1099 | static int scMin( int i, scfmon stc, int Nvar) |
---|
1100 | { |
---|
1101 | int x, y=stc[0][Nvar]; |
---|
1102 | for (; i;) |
---|
1103 | { |
---|
1104 | i--; |
---|
1105 | x = stc[i][Nvar]; |
---|
1106 | if (x < y) y = x; |
---|
1107 | } |
---|
1108 | return y; |
---|
1109 | } |
---|
1110 | |
---|
1111 | static int scRestrict( int &Nstc, scfmon stc, int Nvar) |
---|
1112 | { |
---|
1113 | int x, y; |
---|
1114 | int i, j, Istc = Nstc; |
---|
1115 | |
---|
1116 | y = MAX_INT_VAL; |
---|
1117 | for (i=Nstc-1; i>=0; i--) |
---|
1118 | { |
---|
1119 | j = Nvar-1; |
---|
1120 | loop |
---|
1121 | { |
---|
1122 | if(stc[i][j] != 0) break; |
---|
1123 | j--; |
---|
1124 | if (j == 0) |
---|
1125 | { |
---|
1126 | Istc--; |
---|
1127 | x = stc[i][Nvar]; |
---|
1128 | if (x < y) y = x; |
---|
1129 | stc[i] = NULL; |
---|
1130 | break; |
---|
1131 | } |
---|
1132 | } |
---|
1133 | } |
---|
1134 | if (Istc < Nstc) |
---|
1135 | { |
---|
1136 | for (i=Nstc-1; i>=0; i--) |
---|
1137 | { |
---|
1138 | if (stc[i] && (stc[i][Nvar] >= y)) |
---|
1139 | { |
---|
1140 | Istc--; |
---|
1141 | stc[i] = NULL; |
---|
1142 | } |
---|
1143 | } |
---|
1144 | j = 0; |
---|
1145 | while (stc[j]) j++; |
---|
1146 | i = j+1; |
---|
1147 | for(; i<Nstc; i++) |
---|
1148 | { |
---|
1149 | if (stc[i]) |
---|
1150 | { |
---|
1151 | stc[j] = stc[i]; |
---|
1152 | j++; |
---|
1153 | } |
---|
1154 | } |
---|
1155 | Nstc = Istc; |
---|
1156 | return y; |
---|
1157 | } |
---|
1158 | else |
---|
1159 | return -1; |
---|
1160 | } |
---|
1161 | |
---|
1162 | static void scAll( int Nvar, int deg) |
---|
1163 | { |
---|
1164 | int i; |
---|
1165 | int d = deg; |
---|
1166 | if (d == 0) |
---|
1167 | { |
---|
1168 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1169 | scElKbase(); |
---|
1170 | return; |
---|
1171 | } |
---|
1172 | if (Nvar == 1) |
---|
1173 | { |
---|
1174 | act[1] = d; |
---|
1175 | scElKbase(); |
---|
1176 | return; |
---|
1177 | } |
---|
1178 | do |
---|
1179 | { |
---|
1180 | act[Nvar] = d; |
---|
1181 | scAll(Nvar-1, deg-d); |
---|
1182 | d--; |
---|
1183 | } while (d >= 0); |
---|
1184 | } |
---|
1185 | |
---|
1186 | static void scAllKbase( int Nvar, int ideg, int deg) |
---|
1187 | { |
---|
1188 | do |
---|
1189 | { |
---|
1190 | act[Nvar] = ideg; |
---|
1191 | scAll(Nvar-1, deg-ideg); |
---|
1192 | ideg--; |
---|
1193 | } while (ideg >= 0); |
---|
1194 | } |
---|
1195 | |
---|
1196 | static void scDegKbase( scfmon stc, int Nstc, int Nvar, int deg) |
---|
1197 | { |
---|
1198 | int Ivar, Istc, i, j; |
---|
1199 | scfmon sn; |
---|
1200 | int x, ideg; |
---|
1201 | |
---|
1202 | if (deg == 0) |
---|
1203 | { |
---|
1204 | for (i=Nstc-1; i>=0; i--) |
---|
1205 | { |
---|
1206 | for (j=Nvar;j;j--){ if(stc[i][j]) break; } |
---|
1207 | if (j==0){return;} |
---|
1208 | } |
---|
1209 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1210 | scElKbase(); |
---|
1211 | return; |
---|
1212 | } |
---|
1213 | if (Nvar == 1) |
---|
1214 | { |
---|
1215 | for (i=Nstc-1; i>=0; i--) if(deg >= stc[i][1]) return; |
---|
1216 | act[1] = deg; |
---|
1217 | scElKbase(); |
---|
1218 | return; |
---|
1219 | } |
---|
1220 | Ivar = Nvar-1; |
---|
1221 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1222 | x = scRestrict(Nstc, sn, Nvar); |
---|
1223 | if (x <= 0) |
---|
1224 | { |
---|
1225 | if (x == 0) return; |
---|
1226 | ideg = deg; |
---|
1227 | } |
---|
1228 | else |
---|
1229 | { |
---|
1230 | if (deg < x) ideg = deg; |
---|
1231 | else ideg = x-1; |
---|
1232 | if (Nstc == 0) |
---|
1233 | { |
---|
1234 | scAllKbase(Nvar, ideg, deg); |
---|
1235 | return; |
---|
1236 | } |
---|
1237 | } |
---|
1238 | loop |
---|
1239 | { |
---|
1240 | x = scMax(Nstc, sn, Nvar); |
---|
1241 | while (ideg >= x) |
---|
1242 | { |
---|
1243 | act[Nvar] = ideg; |
---|
1244 | scDegKbase(sn, Nstc, Ivar, deg-ideg); |
---|
1245 | ideg--; |
---|
1246 | } |
---|
1247 | if (ideg < 0) return; |
---|
1248 | Istc = Nstc; |
---|
1249 | for (i=Nstc-1; i>=0; i--) |
---|
1250 | { |
---|
1251 | if (ideg < sn[i][Nvar]) |
---|
1252 | { |
---|
1253 | Istc--; |
---|
1254 | sn[i] = NULL; |
---|
1255 | } |
---|
1256 | } |
---|
1257 | if (Istc == 0) |
---|
1258 | { |
---|
1259 | scAllKbase(Nvar, ideg, deg); |
---|
1260 | return; |
---|
1261 | } |
---|
1262 | j = 0; |
---|
1263 | while (sn[j]) j++; |
---|
1264 | i = j+1; |
---|
1265 | for (; i<Nstc; i++) |
---|
1266 | { |
---|
1267 | if (sn[i]) |
---|
1268 | { |
---|
1269 | sn[j] = sn[i]; |
---|
1270 | j++; |
---|
1271 | } |
---|
1272 | } |
---|
1273 | Nstc = Istc; |
---|
1274 | } |
---|
1275 | } |
---|
1276 | |
---|
1277 | static void scInKbase( scfmon stc, int Nstc, int Nvar) |
---|
1278 | { |
---|
1279 | int Ivar, Istc, i, j; |
---|
1280 | scfmon sn; |
---|
1281 | int x, ideg; |
---|
1282 | |
---|
1283 | if (Nvar == 1) |
---|
1284 | { |
---|
1285 | ideg = scMin(Nstc, stc, 1); |
---|
1286 | while (ideg > 0) |
---|
1287 | { |
---|
1288 | ideg--; |
---|
1289 | act[1] = ideg; |
---|
1290 | scElKbase(); |
---|
1291 | } |
---|
1292 | return; |
---|
1293 | } |
---|
1294 | Ivar = Nvar-1; |
---|
1295 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1296 | x = scRestrict(Nstc, sn, Nvar); |
---|
1297 | if (x == 0) return; |
---|
1298 | ideg = x-1; |
---|
1299 | loop |
---|
1300 | { |
---|
1301 | x = scMax(Nstc, sn, Nvar); |
---|
1302 | while (ideg >= x) |
---|
1303 | { |
---|
1304 | act[Nvar] = ideg; |
---|
1305 | scInKbase(sn, Nstc, Ivar); |
---|
1306 | ideg--; |
---|
1307 | } |
---|
1308 | if (ideg < 0) return; |
---|
1309 | Istc = Nstc; |
---|
1310 | for (i=Nstc-1; i>=0; i--) |
---|
1311 | { |
---|
1312 | if (ideg < sn[i][Nvar]) |
---|
1313 | { |
---|
1314 | Istc--; |
---|
1315 | sn[i] = NULL; |
---|
1316 | } |
---|
1317 | } |
---|
1318 | j = 0; |
---|
1319 | while (sn[j]) j++; |
---|
1320 | i = j+1; |
---|
1321 | for (; i<Nstc; i++) |
---|
1322 | { |
---|
1323 | if (sn[i]) |
---|
1324 | { |
---|
1325 | sn[j] = sn[i]; |
---|
1326 | j++; |
---|
1327 | } |
---|
1328 | } |
---|
1329 | Nstc = Istc; |
---|
1330 | } |
---|
1331 | } |
---|
1332 | |
---|
1333 | static ideal scIdKbase(poly q, const int rank) |
---|
1334 | { |
---|
1335 | ideal res = idInit(pLength(q), rank); |
---|
1336 | polyset mm = res->m; |
---|
1337 | int i = 0; |
---|
1338 | do |
---|
1339 | { |
---|
1340 | *mm = q; ++mm; |
---|
1341 | |
---|
1342 | const poly p = pNext(q); |
---|
1343 | pNext(q) = NULL; |
---|
1344 | q = p; |
---|
1345 | |
---|
1346 | } while (q!=NULL); |
---|
1347 | |
---|
1348 | id_Test(res, currRing); // WRONG RANK!!!??? |
---|
1349 | return res; |
---|
1350 | } |
---|
1351 | |
---|
1352 | ideal scKBase(int deg, ideal s, ideal Q, intvec * mv) |
---|
1353 | { |
---|
1354 | if( Q!=NULL) id_Test(Q, currRing); |
---|
1355 | |
---|
1356 | int i, di; |
---|
1357 | poly p; |
---|
1358 | |
---|
1359 | if (deg < 0) |
---|
1360 | { |
---|
1361 | di = scDimInt(s, Q); |
---|
1362 | if (di != 0) |
---|
1363 | { |
---|
1364 | //Werror("KBase not finite"); |
---|
1365 | return idInit(1,s->rank); |
---|
1366 | } |
---|
1367 | } |
---|
1368 | stcmem = hCreate((currRing->N) - 1); |
---|
1369 | hexist = hInit(s, Q, &hNexist, currRing); |
---|
1370 | p = last = pInit(); |
---|
1371 | /*pNext(p) = NULL;*/ |
---|
1372 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
1373 | *act = 0; |
---|
1374 | if (!hNexist) |
---|
1375 | { |
---|
1376 | scAll((currRing->N), deg); |
---|
1377 | goto ende; |
---|
1378 | } |
---|
1379 | if (!hisModule) |
---|
1380 | { |
---|
1381 | if (deg < 0) scInKbase(hexist, hNexist, (currRing->N)); |
---|
1382 | else scDegKbase(hexist, hNexist, (currRing->N), deg); |
---|
1383 | } |
---|
1384 | else |
---|
1385 | { |
---|
1386 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1387 | for (i = 1; i <= hisModule; i++) |
---|
1388 | { |
---|
1389 | *act = i; |
---|
1390 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1391 | int deg_ei=deg; |
---|
1392 | if (mv!=NULL) deg_ei -= (*mv)[i-1]; |
---|
1393 | if ((deg < 0) || (deg_ei>=0)) |
---|
1394 | { |
---|
1395 | if (hNstc) |
---|
1396 | { |
---|
1397 | if (deg < 0) scInKbase(hstc, hNstc, (currRing->N)); |
---|
1398 | else scDegKbase(hstc, hNstc, (currRing->N), deg_ei); |
---|
1399 | } |
---|
1400 | else |
---|
1401 | scAll((currRing->N), deg_ei); |
---|
1402 | } |
---|
1403 | } |
---|
1404 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1405 | } |
---|
1406 | ende: |
---|
1407 | hDelete(hexist, hNexist); |
---|
1408 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
1409 | hKill(stcmem, (currRing->N) - 1); |
---|
1410 | pLmDelete(&p); |
---|
1411 | if (p == NULL) |
---|
1412 | return idInit(1,s->rank); |
---|
1413 | |
---|
1414 | last = p; |
---|
1415 | return scIdKbase(p, s->rank); |
---|
1416 | } |
---|
1417 | |
---|
1418 | #if 0 //-- alternative implementation of scComputeHC |
---|
1419 | /* |
---|
1420 | void scComputeHCw(ideal ss, ideal Q, int ak, poly &hEdge, ring tailRing) |
---|
1421 | { |
---|
1422 | id_TestTail(ss, currRing, tailRing); |
---|
1423 | if (Q!=NULL) id_TestTail(Q, currRing, tailRing); |
---|
1424 | |
---|
1425 | int i, di; |
---|
1426 | poly p; |
---|
1427 | |
---|
1428 | if (hEdge!=NULL) |
---|
1429 | pLmFree(hEdge); |
---|
1430 | |
---|
1431 | ideal s=idInit(IDELEMS(ss),ak); |
---|
1432 | for(i=IDELEMS(ss)-1;i>=0;i--) |
---|
1433 | { |
---|
1434 | if (ss->m[i]!=NULL) s->m[i]=pHead(ss->m[i]); |
---|
1435 | } |
---|
1436 | di = scDimInt(s, Q); |
---|
1437 | stcmem = hCreate((currRing->N) - 1); |
---|
1438 | hexist = hInit(s, Q, &hNexist, currRing); |
---|
1439 | p = last = pInit(); |
---|
1440 | // pNext(p) = NULL; |
---|
1441 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
1442 | *act = 0; |
---|
1443 | if (!hNexist) |
---|
1444 | { |
---|
1445 | scAll((currRing->N), -1); |
---|
1446 | goto ende; |
---|
1447 | } |
---|
1448 | if (!hisModule) |
---|
1449 | { |
---|
1450 | scInKbase(hexist, hNexist, (currRing->N)); |
---|
1451 | } |
---|
1452 | else |
---|
1453 | { |
---|
1454 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1455 | for (i = 1; i <= hisModule; i++) |
---|
1456 | { |
---|
1457 | *act = i; |
---|
1458 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1459 | if (hNstc) |
---|
1460 | { |
---|
1461 | scInKbase(hstc, hNstc, (currRing->N)); |
---|
1462 | } |
---|
1463 | else |
---|
1464 | scAll((currRing->N), -1); |
---|
1465 | } |
---|
1466 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1467 | } |
---|
1468 | ende: |
---|
1469 | hDelete(hexist, hNexist); |
---|
1470 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
1471 | hKill(stcmem, (currRing->N) - 1); |
---|
1472 | pDeleteLm(&p); |
---|
1473 | idDelete(&s); |
---|
1474 | if (p == NULL) |
---|
1475 | { |
---|
1476 | return; // no HEdge |
---|
1477 | } |
---|
1478 | else |
---|
1479 | { |
---|
1480 | last = p; |
---|
1481 | ideal res=scIdKbase(p, ss->rank); |
---|
1482 | poly p_ind=res->m[0]; int ind=0; |
---|
1483 | for(i=IDELEMS(res)-1;i>0;i--) |
---|
1484 | { |
---|
1485 | if (pCmp(res->m[i],p_ind)==-1) { p_ind=res->m[i]; ind=i; } |
---|
1486 | } |
---|
1487 | assume(p_ind!=NULL); |
---|
1488 | assume(res->m[ind]==p_ind); |
---|
1489 | hEdge=p_ind; |
---|
1490 | res->m[ind]=NULL; |
---|
1491 | nDelete(&pGetCoeff(hEdge)); |
---|
1492 | pGetCoeff(hEdge)=NULL; |
---|
1493 | for(i=(currRing->N);i>0;i--) |
---|
1494 | pIncrExp(hEdge,i); |
---|
1495 | pSetm(hEdge); |
---|
1496 | |
---|
1497 | idDelete(&res); |
---|
1498 | return; |
---|
1499 | } |
---|
1500 | } |
---|
1501 | */ |
---|
1502 | #endif |
---|