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 | #ifdef HAVE_CONFIG_H |
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9 | #include "config.h" |
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10 | #endif /* HAVE_CONFIG_H */ |
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11 | #include <kernel/mod2.h> |
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12 | |
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13 | |
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14 | #include <kernel/structs.h> |
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15 | #include <kernel/febase.h> |
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16 | #include <omalloc/omalloc.h> |
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17 | #include <kernel/ideals.h> |
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18 | #include <kernel/polys.h> |
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19 | #include <misc/intvec.h> |
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20 | #include <coeffs/numbers.h> |
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21 | #include <kernel/hutil.h> |
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22 | #include <kernel/stairc.h> |
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23 | |
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24 | int hCo, hMu, hMu2; |
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25 | omBin indlist_bin = omGetSpecBin(sizeof(indlist)); |
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26 | |
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27 | /*0 implementation*/ |
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28 | |
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29 | // dimension |
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30 | |
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31 | void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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32 | varset var, int Nvar) |
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33 | { |
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34 | int dn, iv, rad0, b, c, x; |
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35 | scmon pn; |
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36 | scfmon rn; |
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37 | if (Nrad < 2) |
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38 | { |
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39 | dn = Npure + Nrad; |
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40 | if (dn < hCo) |
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41 | hCo = dn; |
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42 | return; |
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43 | } |
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44 | if (Npure+1 >= hCo) |
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45 | return; |
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46 | iv = Nvar; |
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47 | while(pure[var[iv]]) iv--; |
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48 | hStepR(rad, Nrad, var, iv, &rad0); |
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49 | if (rad0!=0) |
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50 | { |
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51 | iv--; |
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52 | if (rad0 < Nrad) |
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53 | { |
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54 | pn = hGetpure(pure); |
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55 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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56 | hDimSolve(pn, Npure + 1, rn, rad0, var, iv); |
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57 | b = rad0; |
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58 | c = Nrad; |
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59 | hElimR(rn, &rad0, b, c, var, iv); |
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60 | hPure(rn, b, &c, var, iv, pn, &x); |
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61 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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62 | rad0 += (c - b); |
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63 | hDimSolve(pn, Npure + x, rn, rad0, var, iv); |
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64 | } |
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65 | else |
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66 | { |
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67 | hDimSolve(pure, Npure, rad, Nrad, var, iv); |
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68 | } |
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69 | } |
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70 | else |
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71 | hCo = Npure + 1; |
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72 | } |
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73 | |
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74 | int scDimInt(ideal S, ideal Q) |
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75 | { |
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76 | int mc; |
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77 | hexist = hInit(S, Q, &hNexist); |
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78 | if (!hNexist) |
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79 | return (currRing->N); |
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80 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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81 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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82 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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83 | mc = hisModule; |
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84 | if (!mc) |
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85 | { |
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86 | hrad = hexist; |
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87 | hNrad = hNexist; |
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88 | } |
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89 | else |
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90 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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91 | radmem = hCreate((currRing->N) - 1); |
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92 | hCo = (currRing->N) + 1; |
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93 | loop |
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94 | { |
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95 | if (mc) |
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96 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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97 | if (hNrad) |
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98 | { |
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99 | hNvar = (currRing->N); |
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100 | hRadical(hrad, &hNrad, hNvar); |
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101 | hSupp(hrad, hNrad, hvar, &hNvar); |
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102 | if (hNvar) |
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103 | { |
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104 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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105 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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106 | hLexR(hrad, hNrad, hvar, hNvar); |
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107 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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108 | } |
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109 | } |
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110 | else |
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111 | { |
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112 | hCo = 0; |
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113 | break; |
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114 | } |
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115 | mc--; |
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116 | if (mc <= 0) |
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117 | break; |
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118 | } |
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119 | hKill(radmem, (currRing->N) - 1); |
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120 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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121 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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122 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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123 | hDelete(hexist, hNexist); |
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124 | if (hisModule) |
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125 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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126 | return (currRing->N) - hCo; |
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127 | } |
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128 | |
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129 | // independent set |
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130 | static scmon hInd; |
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131 | |
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132 | static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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133 | varset var, int Nvar) |
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134 | { |
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135 | int dn, iv, rad0, b, c, x; |
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136 | scmon pn; |
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137 | scfmon rn; |
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138 | if (Nrad < 2) |
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139 | { |
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140 | dn = Npure + Nrad; |
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141 | if (dn < hCo) |
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142 | { |
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143 | hCo = dn; |
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144 | for (iv=(currRing->N); iv; iv--) |
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145 | { |
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146 | if (pure[iv]) |
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147 | hInd[iv] = 0; |
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148 | else |
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149 | hInd[iv] = 1; |
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150 | } |
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151 | if (Nrad) |
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152 | { |
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153 | pn = *rad; |
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154 | iv = Nvar; |
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155 | loop |
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156 | { |
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157 | x = var[iv]; |
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158 | if (pn[x]) |
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159 | { |
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160 | hInd[x] = 0; |
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161 | break; |
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162 | } |
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163 | iv--; |
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164 | } |
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165 | } |
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166 | } |
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167 | return; |
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168 | } |
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169 | if (Npure+1 >= hCo) |
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170 | return; |
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171 | iv = Nvar; |
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172 | while(pure[var[iv]]) iv--; |
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173 | hStepR(rad, Nrad, var, iv, &rad0); |
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174 | if (rad0) |
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175 | { |
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176 | iv--; |
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177 | if (rad0 < Nrad) |
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178 | { |
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179 | pn = hGetpure(pure); |
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180 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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181 | pn[var[iv + 1]] = 1; |
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182 | hIndSolve(pn, Npure + 1, rn, rad0, var, iv); |
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183 | pn[var[iv + 1]] = 0; |
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184 | b = rad0; |
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185 | c = Nrad; |
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186 | hElimR(rn, &rad0, b, c, var, iv); |
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187 | hPure(rn, b, &c, var, iv, pn, &x); |
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188 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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189 | rad0 += (c - b); |
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190 | hIndSolve(pn, Npure + x, rn, rad0, var, iv); |
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191 | } |
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192 | else |
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193 | { |
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194 | hIndSolve(pure, Npure, rad, Nrad, var, iv); |
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195 | } |
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196 | } |
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197 | else |
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198 | { |
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199 | hCo = Npure + 1; |
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200 | for (x=(currRing->N); x; x--) |
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201 | { |
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202 | if (pure[x]) |
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203 | hInd[x] = 0; |
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204 | else |
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205 | hInd[x] = 1; |
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206 | } |
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207 | hInd[var[iv]] = 0; |
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208 | } |
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209 | } |
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210 | |
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211 | intvec * scIndIntvec(ideal S, ideal Q) |
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212 | { |
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213 | intvec *Set=new intvec((currRing->N)); |
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214 | int mc,i; |
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215 | hexist = hInit(S, Q, &hNexist); |
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216 | if (hNexist==0) |
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217 | { |
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218 | for(i=0; i<(currRing->N); i++) |
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219 | (*Set)[i]=1; |
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220 | return Set; |
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221 | } |
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222 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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223 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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224 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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225 | hInd = (scmon)omAlloc0((1 + (currRing->N)) * sizeof(int)); |
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226 | mc = hisModule; |
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227 | if (mc==0) |
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228 | { |
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229 | hrad = hexist; |
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230 | hNrad = hNexist; |
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231 | } |
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232 | else |
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233 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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234 | radmem = hCreate((currRing->N) - 1); |
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235 | hCo = (currRing->N) + 1; |
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236 | loop |
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237 | { |
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238 | if (mc!=0) |
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239 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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240 | if (hNrad!=0) |
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241 | { |
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242 | hNvar = (currRing->N); |
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243 | hRadical(hrad, &hNrad, hNvar); |
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244 | hSupp(hrad, hNrad, hvar, &hNvar); |
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245 | if (hNvar!=0) |
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246 | { |
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247 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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248 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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249 | hLexR(hrad, hNrad, hvar, hNvar); |
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250 | hIndSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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251 | } |
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252 | } |
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253 | else |
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254 | { |
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255 | hCo = 0; |
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256 | break; |
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257 | } |
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258 | mc--; |
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259 | if (mc <= 0) |
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260 | break; |
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261 | } |
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262 | for(i=0; i<(currRing->N); i++) |
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263 | (*Set)[i] = hInd[i+1]; |
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264 | hKill(radmem, (currRing->N) - 1); |
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265 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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266 | omFreeSize((ADDRESS)hInd, (1 + (currRing->N)) * sizeof(int)); |
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267 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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268 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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269 | hDelete(hexist, hNexist); |
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270 | if (hisModule) |
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271 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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272 | return Set; |
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273 | } |
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274 | |
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275 | indset ISet, JSet; |
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276 | |
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277 | static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar) |
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278 | { |
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279 | int k1, i; |
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280 | k1 = var[Nvar]; |
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281 | i = 0; |
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282 | loop |
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283 | { |
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284 | if (rad[i][k1]==0) |
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285 | return FALSE; |
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286 | i++; |
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287 | if (i == Nrad) |
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288 | return TRUE; |
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289 | } |
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290 | } |
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291 | |
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292 | static void hIndep(scmon pure) |
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293 | { |
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294 | int iv; |
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295 | intvec *Set; |
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296 | |
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297 | Set = ISet->set = new intvec((currRing->N)); |
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298 | for (iv=(currRing->N); iv!=0 ; iv--) |
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299 | { |
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300 | if (pure[iv]) |
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301 | (*Set)[iv-1] = 0; |
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302 | else |
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303 | (*Set)[iv-1] = 1; |
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304 | } |
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305 | ISet = ISet->nx = (indset)omAlloc0Bin(indlist_bin); |
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306 | hMu++; |
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307 | } |
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308 | |
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309 | void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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310 | varset var, int Nvar) |
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311 | { |
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312 | int dn, iv, rad0, b, c, x; |
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313 | scmon pn; |
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314 | scfmon rn; |
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315 | if (Nrad < 2) |
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316 | { |
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317 | dn = Npure + Nrad; |
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318 | if (dn == hCo) |
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319 | { |
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320 | if (Nrad==0) |
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321 | hIndep(pure); |
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322 | else |
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323 | { |
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324 | pn = *rad; |
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325 | for (iv = Nvar; iv!=0; iv--) |
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326 | { |
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327 | x = var[iv]; |
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328 | if (pn[x]) |
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329 | { |
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330 | pure[x] = 1; |
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331 | hIndep(pure); |
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332 | pure[x] = 0; |
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333 | } |
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334 | } |
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335 | } |
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336 | } |
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337 | return; |
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338 | } |
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339 | iv = Nvar; |
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340 | dn = Npure+1; |
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341 | if (dn >= hCo) |
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342 | { |
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343 | if (dn > hCo) |
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344 | return; |
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345 | loop |
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346 | { |
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347 | if(!pure[var[iv]]) |
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348 | { |
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349 | if(hNotZero(rad, Nrad, var, iv)) |
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350 | { |
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351 | pure[var[iv]] = 1; |
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352 | hIndep(pure); |
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353 | pure[var[iv]] = 0; |
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354 | } |
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355 | } |
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356 | iv--; |
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357 | if (!iv) |
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358 | return; |
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359 | } |
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360 | } |
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361 | while(pure[var[iv]]) iv--; |
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362 | hStepR(rad, Nrad, var, iv, &rad0); |
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363 | iv--; |
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364 | if (rad0 < Nrad) |
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365 | { |
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366 | pn = hGetpure(pure); |
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367 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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368 | pn[var[iv + 1]] = 1; |
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369 | hIndMult(pn, Npure + 1, rn, rad0, var, iv); |
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370 | pn[var[iv + 1]] = 0; |
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371 | b = rad0; |
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372 | c = Nrad; |
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373 | hElimR(rn, &rad0, b, c, var, iv); |
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374 | hPure(rn, b, &c, var, iv, pn, &x); |
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375 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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376 | rad0 += (c - b); |
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377 | hIndMult(pn, Npure + x, rn, rad0, var, iv); |
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378 | } |
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379 | else |
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380 | { |
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381 | hIndMult(pure, Npure, rad, Nrad, var, iv); |
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382 | } |
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383 | } |
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384 | |
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385 | /*3 |
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386 | * consider indset x := !pure |
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387 | * (for all i) (if(sm(i) > x) return FALSE) |
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388 | * else return TRUE |
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389 | */ |
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390 | static BOOLEAN hCheck1(indset sm, scmon pure) |
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391 | { |
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392 | int iv; |
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393 | intvec *Set; |
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394 | while (sm->nx != NULL) |
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395 | { |
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396 | Set = sm->set; |
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397 | iv=(currRing->N); |
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398 | loop |
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399 | { |
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400 | if (((*Set)[iv-1] == 0) && (pure[iv] == 0)) |
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401 | break; |
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402 | iv--; |
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403 | if (iv == 0) |
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404 | return FALSE; |
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405 | } |
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406 | sm = sm->nx; |
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407 | } |
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408 | return TRUE; |
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409 | } |
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410 | |
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411 | /*3 |
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412 | * consider indset x := !pure |
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413 | * (for all i) if(x > sm(i)) delete sm(i)) |
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414 | * return (place for x) |
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415 | */ |
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416 | static indset hCheck2(indset sm, scmon pure) |
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417 | { |
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418 | int iv; |
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419 | intvec *Set; |
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420 | indset be, a1 = NULL; |
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421 | while (sm->nx != NULL) |
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422 | { |
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423 | Set = sm->set; |
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424 | iv=(currRing->N); |
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425 | loop |
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426 | { |
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427 | if ((pure[iv] == 1) && ((*Set)[iv-1] == 1)) |
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428 | break; |
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429 | iv--; |
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430 | if (iv == 0) |
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431 | { |
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432 | if (a1 == NULL) |
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433 | { |
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434 | a1 = sm; |
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435 | } |
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436 | else |
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437 | { |
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438 | hMu2--; |
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439 | be->nx = sm->nx; |
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440 | delete Set; |
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441 | omFreeBin((ADDRESS)sm, indlist_bin); |
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442 | sm = be; |
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443 | } |
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444 | break; |
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445 | } |
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446 | } |
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447 | be = sm; |
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448 | sm = sm->nx; |
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449 | } |
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450 | if (a1 != NULL) |
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451 | { |
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452 | return a1; |
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453 | } |
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454 | else |
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455 | { |
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456 | hMu2++; |
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457 | sm->set = new intvec((currRing->N)); |
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458 | sm->nx = (indset)omAlloc0Bin(indlist_bin); |
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459 | return sm; |
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460 | } |
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461 | } |
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462 | |
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463 | /*2 |
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464 | * definition x >= y |
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465 | * x(i) == 0 => y(i) == 0 |
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466 | * > ex. j with x(j) == 1 and y(j) == 0 |
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467 | */ |
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468 | static void hCheckIndep(scmon pure) |
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469 | { |
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470 | intvec *Set; |
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471 | indset res; |
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472 | int iv; |
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473 | if (hCheck1(ISet, pure)) |
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474 | { |
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475 | if (hCheck1(JSet, pure)) |
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476 | { |
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477 | res = hCheck2(JSet,pure); |
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478 | if (res == NULL) |
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479 | return; |
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480 | Set = res->set; |
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481 | for (iv=(currRing->N); iv; iv--) |
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482 | { |
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483 | if (pure[iv]) |
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484 | (*Set)[iv-1] = 0; |
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485 | else |
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486 | (*Set)[iv-1] = 1; |
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487 | } |
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488 | } |
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489 | } |
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490 | } |
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491 | |
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492 | void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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493 | varset var, int Nvar) |
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494 | { |
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495 | int dn, iv, rad0, b, c, x; |
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496 | scmon pn; |
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497 | scfmon rn; |
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498 | if (Nrad < 2) |
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499 | { |
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500 | dn = Npure + Nrad; |
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501 | if (dn > hCo) |
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502 | { |
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503 | if (!Nrad) |
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504 | hCheckIndep(pure); |
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505 | else |
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506 | { |
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507 | pn = *rad; |
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508 | for (iv = Nvar; iv; iv--) |
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509 | { |
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510 | x = var[iv]; |
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511 | if (pn[x]) |
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512 | { |
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513 | pure[x] = 1; |
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514 | hCheckIndep(pure); |
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515 | pure[x] = 0; |
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516 | } |
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517 | } |
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518 | } |
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519 | } |
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520 | return; |
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521 | } |
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522 | iv = Nvar; |
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523 | while(pure[var[iv]]) iv--; |
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524 | hStepR(rad, Nrad, var, iv, &rad0); |
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525 | iv--; |
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526 | if (rad0 < Nrad) |
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527 | { |
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528 | pn = hGetpure(pure); |
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529 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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530 | pn[var[iv + 1]] = 1; |
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531 | hIndAllMult(pn, Npure + 1, rn, rad0, var, iv); |
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532 | pn[var[iv + 1]] = 0; |
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533 | b = rad0; |
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534 | c = Nrad; |
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535 | hElimR(rn, &rad0, b, c, var, iv); |
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536 | hPure(rn, b, &c, var, iv, pn, &x); |
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537 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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538 | rad0 += (c - b); |
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539 | hIndAllMult(pn, Npure + x, rn, rad0, var, iv); |
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540 | } |
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541 | else |
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542 | { |
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543 | hIndAllMult(pure, Npure, rad, Nrad, var, iv); |
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544 | } |
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545 | } |
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546 | |
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547 | // multiplicity |
---|
548 | |
---|
549 | static int hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar) |
---|
550 | { |
---|
551 | int iv = Nvar -1, sum, a, a0, a1, b, i; |
---|
552 | int x, x0; |
---|
553 | scmon pn; |
---|
554 | scfmon sn; |
---|
555 | if (!iv) |
---|
556 | return pure[var[1]]; |
---|
557 | else if (!Nstc) |
---|
558 | { |
---|
559 | sum = 1; |
---|
560 | for (i = Nvar; i; i--) |
---|
561 | sum *= pure[var[i]]; |
---|
562 | return sum; |
---|
563 | } |
---|
564 | x = a = 0; |
---|
565 | pn = hGetpure(pure); |
---|
566 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
567 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
568 | if (a == Nstc) |
---|
569 | return pure[var[Nvar]] * hZeroMult(pn, sn, a, var, iv); |
---|
570 | else |
---|
571 | sum = x * hZeroMult(pn, sn, a, var, iv); |
---|
572 | b = a; |
---|
573 | loop |
---|
574 | { |
---|
575 | a0 = a; |
---|
576 | x0 = x; |
---|
577 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
578 | hElimS(sn, &b, a0, a, var, iv); |
---|
579 | a1 = a; |
---|
580 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
581 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
582 | b += (a1 - a0); |
---|
583 | if (a < Nstc) |
---|
584 | { |
---|
585 | sum += (x - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
586 | } |
---|
587 | else |
---|
588 | { |
---|
589 | sum += (pure[var[Nvar]] - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
590 | return sum; |
---|
591 | } |
---|
592 | } |
---|
593 | } |
---|
594 | |
---|
595 | static void hProject(scmon pure, varset sel) |
---|
596 | { |
---|
597 | int i, i0, k; |
---|
598 | i0 = 0; |
---|
599 | for (i = 1; i <= (currRing->N); i++) |
---|
600 | { |
---|
601 | if (pure[i]) |
---|
602 | { |
---|
603 | i0++; |
---|
604 | sel[i0] = i; |
---|
605 | } |
---|
606 | } |
---|
607 | i = hNstc; |
---|
608 | memcpy(hwork, hstc, i * sizeof(scmon)); |
---|
609 | hStaircase(hwork, &i, sel, i0); |
---|
610 | if ((i0 > 2) && (i > 10)) |
---|
611 | hOrdSupp(hwork, i, sel, i0); |
---|
612 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
613 | hPure(hwork, 0, &i, sel, i0, hpur0, &k); |
---|
614 | hLexS(hwork, i, sel, i0); |
---|
615 | hMu += hZeroMult(hpur0, hwork, i, sel, i0); |
---|
616 | } |
---|
617 | |
---|
618 | static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
619 | varset var, int Nvar) |
---|
620 | { |
---|
621 | int dn, iv, rad0, b, c, x; |
---|
622 | scmon pn; |
---|
623 | scfmon rn; |
---|
624 | if (Nrad < 2) |
---|
625 | { |
---|
626 | dn = Npure + Nrad; |
---|
627 | if (dn == hCo) |
---|
628 | { |
---|
629 | if (!Nrad) |
---|
630 | hProject(pure, hsel); |
---|
631 | else |
---|
632 | { |
---|
633 | pn = *rad; |
---|
634 | for (iv = Nvar; iv; iv--) |
---|
635 | { |
---|
636 | x = var[iv]; |
---|
637 | if (pn[x]) |
---|
638 | { |
---|
639 | pure[x] = 1; |
---|
640 | hProject(pure, hsel); |
---|
641 | pure[x] = 0; |
---|
642 | } |
---|
643 | } |
---|
644 | } |
---|
645 | } |
---|
646 | return; |
---|
647 | } |
---|
648 | iv = Nvar; |
---|
649 | dn = Npure+1; |
---|
650 | if (dn >= hCo) |
---|
651 | { |
---|
652 | if (dn > hCo) |
---|
653 | return; |
---|
654 | loop |
---|
655 | { |
---|
656 | if(!pure[var[iv]]) |
---|
657 | { |
---|
658 | if(hNotZero(rad, Nrad, var, iv)) |
---|
659 | { |
---|
660 | pure[var[iv]] = 1; |
---|
661 | hProject(pure, hsel); |
---|
662 | pure[var[iv]] = 0; |
---|
663 | } |
---|
664 | } |
---|
665 | iv--; |
---|
666 | if (!iv) |
---|
667 | return; |
---|
668 | } |
---|
669 | } |
---|
670 | while(pure[var[iv]]) iv--; |
---|
671 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
672 | iv--; |
---|
673 | if (rad0 < Nrad) |
---|
674 | { |
---|
675 | pn = hGetpure(pure); |
---|
676 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
677 | pn[var[iv + 1]] = 1; |
---|
678 | hDimMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
679 | pn[var[iv + 1]] = 0; |
---|
680 | b = rad0; |
---|
681 | c = Nrad; |
---|
682 | hElimR(rn, &rad0, b, c, var, iv); |
---|
683 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
684 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
685 | rad0 += (c - b); |
---|
686 | hDimMult(pn, Npure + x, rn, rad0, var, iv); |
---|
687 | } |
---|
688 | else |
---|
689 | { |
---|
690 | hDimMult(pure, Npure, rad, Nrad, var, iv); |
---|
691 | } |
---|
692 | } |
---|
693 | |
---|
694 | static void hDegree(ideal S, ideal Q) |
---|
695 | { |
---|
696 | int di; |
---|
697 | int mc; |
---|
698 | hexist = hInit(S, Q, &hNexist); |
---|
699 | if (!hNexist) |
---|
700 | { |
---|
701 | hCo = 0; |
---|
702 | hMu = 1; |
---|
703 | return; |
---|
704 | } |
---|
705 | //hWeight(); |
---|
706 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
707 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
708 | hsel = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
709 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
710 | hpur0 = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
711 | mc = hisModule; |
---|
712 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
713 | if (!mc) |
---|
714 | { |
---|
715 | memcpy(hrad, hexist, hNexist * sizeof(scmon)); |
---|
716 | hstc = hexist; |
---|
717 | hNrad = hNstc = hNexist; |
---|
718 | } |
---|
719 | else |
---|
720 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
721 | radmem = hCreate((currRing->N) - 1); |
---|
722 | stcmem = hCreate((currRing->N) - 1); |
---|
723 | hCo = (currRing->N) + 1; |
---|
724 | di = hCo + 1; |
---|
725 | loop |
---|
726 | { |
---|
727 | if (mc) |
---|
728 | { |
---|
729 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
---|
730 | hNstc = hNrad; |
---|
731 | memcpy(hstc, hrad, hNrad * sizeof(scmon)); |
---|
732 | } |
---|
733 | if (hNrad) |
---|
734 | { |
---|
735 | hNvar = (currRing->N); |
---|
736 | hRadical(hrad, &hNrad, hNvar); |
---|
737 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
738 | if (hNvar) |
---|
739 | { |
---|
740 | hCo = hNvar; |
---|
741 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
742 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
743 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
744 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
745 | } |
---|
746 | } |
---|
747 | else |
---|
748 | { |
---|
749 | hNvar = 1; |
---|
750 | hCo = 0; |
---|
751 | } |
---|
752 | if (hCo < di) |
---|
753 | { |
---|
754 | di = hCo; |
---|
755 | hMu = 0; |
---|
756 | } |
---|
757 | if (hNvar && (hCo == di)) |
---|
758 | { |
---|
759 | if (di && (di < (currRing->N))) |
---|
760 | hDimMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
761 | else if (!di) |
---|
762 | hMu++; |
---|
763 | else |
---|
764 | { |
---|
765 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
766 | if ((hNvar > 2) && (hNstc > 10)) |
---|
767 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
768 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
769 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
770 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
771 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
772 | } |
---|
773 | } |
---|
774 | mc--; |
---|
775 | if (mc <= 0) |
---|
776 | break; |
---|
777 | } |
---|
778 | hCo = di; |
---|
779 | hKill(stcmem, (currRing->N) - 1); |
---|
780 | hKill(radmem, (currRing->N) - 1); |
---|
781 | omFreeSize((ADDRESS)hpur0, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
782 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
783 | omFreeSize((ADDRESS)hsel, ((currRing->N) + 1) * sizeof(int)); |
---|
784 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
---|
785 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
786 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
---|
787 | hDelete(hexist, hNexist); |
---|
788 | if (hisModule) |
---|
789 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
790 | } |
---|
791 | |
---|
792 | int scMultInt(ideal S, ideal Q) |
---|
793 | { |
---|
794 | hDegree(S, Q); |
---|
795 | return hMu; |
---|
796 | } |
---|
797 | |
---|
798 | void scPrintDegree(int co, int mu) |
---|
799 | { |
---|
800 | int di = (currRing->N)-co; |
---|
801 | if (currRing->OrdSgn == 1) |
---|
802 | { |
---|
803 | if (di>0) |
---|
804 | Print("// dimension (proj.) = %d\n// degree (proj.) = %d\n", di-1, mu); |
---|
805 | else |
---|
806 | Print("// dimension (affine) = 0\n// degree (affine) = %d\n", mu); |
---|
807 | } |
---|
808 | else |
---|
809 | Print("// dimension (local) = %d\n// multiplicity = %d\n", di, mu); |
---|
810 | } |
---|
811 | |
---|
812 | void scDegree(ideal S, intvec *modulweight, ideal Q) |
---|
813 | { |
---|
814 | int co, mu, l; |
---|
815 | intvec *hseries2; |
---|
816 | intvec *hseries1 = hFirstSeries(S, modulweight, Q); |
---|
817 | l = hseries1->length()-1; |
---|
818 | if (l > 1) |
---|
819 | hseries2 = hSecondSeries(hseries1); |
---|
820 | else |
---|
821 | hseries2 = hseries1; |
---|
822 | hDegreeSeries(hseries1, hseries2, &co, &mu); |
---|
823 | if ((l == 1) &&(mu == 0)) |
---|
824 | scPrintDegree((currRing->N)+1, 0); |
---|
825 | else |
---|
826 | scPrintDegree(co, mu); |
---|
827 | if (l>1) |
---|
828 | delete hseries1; |
---|
829 | delete hseries2; |
---|
830 | } |
---|
831 | |
---|
832 | static void hDegree0(ideal S, ideal Q) |
---|
833 | { |
---|
834 | int mc; |
---|
835 | hexist = hInit(S, Q, &hNexist); |
---|
836 | if (!hNexist) |
---|
837 | { |
---|
838 | hMu = -1; |
---|
839 | return; |
---|
840 | } |
---|
841 | else |
---|
842 | hMu = 0; |
---|
843 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
844 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
845 | hpur0 = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
846 | mc = hisModule; |
---|
847 | if (!mc) |
---|
848 | { |
---|
849 | hstc = hexist; |
---|
850 | hNstc = hNexist; |
---|
851 | } |
---|
852 | else |
---|
853 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
854 | stcmem = hCreate((currRing->N) - 1); |
---|
855 | loop |
---|
856 | { |
---|
857 | if (mc) |
---|
858 | { |
---|
859 | hComp(hexist, hNexist, mc, hstc, &hNstc); |
---|
860 | if (!hNstc) |
---|
861 | { |
---|
862 | hMu = -1; |
---|
863 | break; |
---|
864 | } |
---|
865 | } |
---|
866 | hNvar = (currRing->N); |
---|
867 | for (int i = hNvar; i; i--) |
---|
868 | hvar[i] = i; |
---|
869 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
870 | hSupp(hstc, hNstc, hvar, &hNvar); |
---|
871 | if ((hNvar == (currRing->N)) && (hNstc >= (currRing->N))) |
---|
872 | { |
---|
873 | if ((hNvar > 2) && (hNstc > 10)) |
---|
874 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
875 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
876 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
877 | if (hNpure == hNvar) |
---|
878 | { |
---|
879 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
880 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
881 | } |
---|
882 | else |
---|
883 | hMu = -1; |
---|
884 | } |
---|
885 | else if (hNvar) |
---|
886 | hMu = -1; |
---|
887 | mc--; |
---|
888 | if (mc <= 0 || hMu < 0) |
---|
889 | break; |
---|
890 | } |
---|
891 | hKill(stcmem, (currRing->N) - 1); |
---|
892 | omFreeSize((ADDRESS)hpur0, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
893 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
---|
894 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
895 | hDelete(hexist, hNexist); |
---|
896 | if (hisModule) |
---|
897 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
898 | } |
---|
899 | |
---|
900 | int scMult0Int(ideal S, ideal Q) |
---|
901 | { |
---|
902 | hDegree0(S, Q); |
---|
903 | return hMu; |
---|
904 | } |
---|
905 | |
---|
906 | |
---|
907 | // HC |
---|
908 | |
---|
909 | static poly pWork; |
---|
910 | |
---|
911 | static void hHedge(poly hEdge) |
---|
912 | { |
---|
913 | pSetm(pWork); |
---|
914 | if (pLmCmp(pWork, hEdge) == currRing->OrdSgn) |
---|
915 | { |
---|
916 | for (int i = hNvar; i>0; i--) |
---|
917 | pSetExp(hEdge,i, pGetExp(pWork,i)); |
---|
918 | pSetm(hEdge); |
---|
919 | } |
---|
920 | } |
---|
921 | |
---|
922 | |
---|
923 | static void hHedgeStep(scmon pure, scfmon stc, |
---|
924 | int Nstc, varset var, int Nvar,poly hEdge) |
---|
925 | { |
---|
926 | int iv = Nvar -1, k = var[Nvar], a, a0, a1, b, i; |
---|
927 | int x/*, x0*/; |
---|
928 | scmon pn; |
---|
929 | scfmon sn; |
---|
930 | if (iv==0) |
---|
931 | { |
---|
932 | pSetExp(pWork, k, pure[k]); |
---|
933 | hHedge(hEdge); |
---|
934 | return; |
---|
935 | } |
---|
936 | else if (Nstc==0) |
---|
937 | { |
---|
938 | for (i = Nvar; i>0; i--) |
---|
939 | pSetExp(pWork, var[i], pure[var[i]]); |
---|
940 | hHedge(hEdge); |
---|
941 | return; |
---|
942 | } |
---|
943 | x = a = 0; |
---|
944 | pn = hGetpure(pure); |
---|
945 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
946 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
947 | if (a == Nstc) |
---|
948 | { |
---|
949 | pSetExp(pWork, k, pure[k]); |
---|
950 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
951 | return; |
---|
952 | } |
---|
953 | else |
---|
954 | { |
---|
955 | pSetExp(pWork, k, x); |
---|
956 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
957 | } |
---|
958 | b = a; |
---|
959 | loop |
---|
960 | { |
---|
961 | a0 = a; |
---|
962 | // x0 = x; |
---|
963 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
964 | hElimS(sn, &b, a0, a, var, iv); |
---|
965 | a1 = a; |
---|
966 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
967 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
968 | b += (a1 - a0); |
---|
969 | if (a < Nstc) |
---|
970 | { |
---|
971 | pSetExp(pWork, k, x); |
---|
972 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
973 | } |
---|
974 | else |
---|
975 | { |
---|
976 | pSetExp(pWork, k, pure[k]); |
---|
977 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
978 | return; |
---|
979 | } |
---|
980 | } |
---|
981 | } |
---|
982 | |
---|
983 | void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge, ring tailRing) |
---|
984 | { |
---|
985 | int i; |
---|
986 | int k = ak; |
---|
987 | hNvar = (currRing->N); |
---|
988 | hexist = hInit(S, Q, &hNexist, tailRing); |
---|
989 | if (k!=0) |
---|
990 | hComp(hexist, hNexist, k, hexist, &hNstc); |
---|
991 | else |
---|
992 | hNstc = hNexist; |
---|
993 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
994 | hvar = (varset)omAlloc((hNvar + 1) * sizeof(int)); |
---|
995 | hpure = (scmon)omAlloc((1 + (hNvar * hNvar)) * sizeof(int)); |
---|
996 | stcmem = hCreate(hNvar - 1); |
---|
997 | for (i = hNvar; i>0; i--) |
---|
998 | hvar[i] = i; |
---|
999 | hStaircase(hexist, &hNstc, hvar, hNvar); |
---|
1000 | if ((hNvar > 2) && (hNstc > 10)) |
---|
1001 | hOrdSupp(hexist, hNstc, hvar, hNvar); |
---|
1002 | memset(hpure, 0, (hNvar + 1) * sizeof(int)); |
---|
1003 | hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure); |
---|
1004 | hLexS(hexist, hNstc, hvar, hNvar); |
---|
1005 | if (hEdge!=NULL) |
---|
1006 | pLmFree(hEdge); |
---|
1007 | hEdge = pInit(); |
---|
1008 | pWork = pInit(); |
---|
1009 | hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge); |
---|
1010 | pSetComp(hEdge,ak); |
---|
1011 | hKill(stcmem, hNvar - 1); |
---|
1012 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
1013 | omFreeSize((ADDRESS)hvar, (hNvar + 1) * sizeof(int)); |
---|
1014 | omFreeSize((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(int)); |
---|
1015 | hDelete(hexist, hNexist); |
---|
1016 | pLmFree(pWork); |
---|
1017 | } |
---|
1018 | |
---|
1019 | |
---|
1020 | |
---|
1021 | // kbase |
---|
1022 | |
---|
1023 | static poly last; |
---|
1024 | static scmon act; |
---|
1025 | |
---|
1026 | static void scElKbase() |
---|
1027 | { |
---|
1028 | poly q = pInit(); |
---|
1029 | pSetCoeff0(q,nInit(1)); |
---|
1030 | pSetExpV(q,act); |
---|
1031 | pNext(q) = NULL; |
---|
1032 | last = pNext(last) = q; |
---|
1033 | } |
---|
1034 | |
---|
1035 | static int scMax( int i, scfmon stc, int Nvar) |
---|
1036 | { |
---|
1037 | int x, y=stc[0][Nvar]; |
---|
1038 | for (; i;) |
---|
1039 | { |
---|
1040 | i--; |
---|
1041 | x = stc[i][Nvar]; |
---|
1042 | if (x > y) y = x; |
---|
1043 | } |
---|
1044 | return y; |
---|
1045 | } |
---|
1046 | |
---|
1047 | static int scMin( int i, scfmon stc, int Nvar) |
---|
1048 | { |
---|
1049 | int x, y=stc[0][Nvar]; |
---|
1050 | for (; i;) |
---|
1051 | { |
---|
1052 | i--; |
---|
1053 | x = stc[i][Nvar]; |
---|
1054 | if (x < y) y = x; |
---|
1055 | } |
---|
1056 | return y; |
---|
1057 | } |
---|
1058 | |
---|
1059 | static int scRestrict( int &Nstc, scfmon stc, int Nvar) |
---|
1060 | { |
---|
1061 | int x, y; |
---|
1062 | int i, j, Istc = Nstc; |
---|
1063 | |
---|
1064 | y = MAX_INT_VAL; |
---|
1065 | for (i=Nstc-1; i>=0; i--) |
---|
1066 | { |
---|
1067 | j = Nvar-1; |
---|
1068 | loop |
---|
1069 | { |
---|
1070 | if(stc[i][j] != 0) break; |
---|
1071 | j--; |
---|
1072 | if (j == 0) |
---|
1073 | { |
---|
1074 | Istc--; |
---|
1075 | x = stc[i][Nvar]; |
---|
1076 | if (x < y) y = x; |
---|
1077 | stc[i] = NULL; |
---|
1078 | break; |
---|
1079 | } |
---|
1080 | } |
---|
1081 | } |
---|
1082 | if (Istc < Nstc) |
---|
1083 | { |
---|
1084 | for (i=Nstc-1; i>=0; i--) |
---|
1085 | { |
---|
1086 | if (stc[i] && (stc[i][Nvar] >= y)) |
---|
1087 | { |
---|
1088 | Istc--; |
---|
1089 | stc[i] = NULL; |
---|
1090 | } |
---|
1091 | } |
---|
1092 | j = 0; |
---|
1093 | while (stc[j]) j++; |
---|
1094 | i = j+1; |
---|
1095 | for(; i<Nstc; i++) |
---|
1096 | { |
---|
1097 | if (stc[i]) |
---|
1098 | { |
---|
1099 | stc[j] = stc[i]; |
---|
1100 | j++; |
---|
1101 | } |
---|
1102 | } |
---|
1103 | Nstc = Istc; |
---|
1104 | return y; |
---|
1105 | } |
---|
1106 | else |
---|
1107 | return -1; |
---|
1108 | } |
---|
1109 | |
---|
1110 | static void scAll( int Nvar, int deg) |
---|
1111 | { |
---|
1112 | int i; |
---|
1113 | int d = deg; |
---|
1114 | if (d == 0) |
---|
1115 | { |
---|
1116 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1117 | scElKbase(); |
---|
1118 | return; |
---|
1119 | } |
---|
1120 | if (Nvar == 1) |
---|
1121 | { |
---|
1122 | act[1] = d; |
---|
1123 | scElKbase(); |
---|
1124 | return; |
---|
1125 | } |
---|
1126 | do |
---|
1127 | { |
---|
1128 | act[Nvar] = d; |
---|
1129 | scAll(Nvar-1, deg-d); |
---|
1130 | d--; |
---|
1131 | } while (d >= 0); |
---|
1132 | } |
---|
1133 | |
---|
1134 | static void scAllKbase( int Nvar, int ideg, int deg) |
---|
1135 | { |
---|
1136 | do |
---|
1137 | { |
---|
1138 | act[Nvar] = ideg; |
---|
1139 | scAll(Nvar-1, deg-ideg); |
---|
1140 | ideg--; |
---|
1141 | } while (ideg >= 0); |
---|
1142 | } |
---|
1143 | |
---|
1144 | static void scDegKbase( scfmon stc, int Nstc, int Nvar, int deg) |
---|
1145 | { |
---|
1146 | int Ivar, Istc, i, j; |
---|
1147 | scfmon sn; |
---|
1148 | int x, ideg; |
---|
1149 | |
---|
1150 | if (deg == 0) |
---|
1151 | { |
---|
1152 | for (i=Nstc-1; i>=0; i--) |
---|
1153 | { |
---|
1154 | for (j=Nvar;j;j--){ if(stc[i][j]) break; } |
---|
1155 | if (j==0){return;} |
---|
1156 | } |
---|
1157 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1158 | scElKbase(); |
---|
1159 | return; |
---|
1160 | } |
---|
1161 | if (Nvar == 1) |
---|
1162 | { |
---|
1163 | for (i=Nstc-1; i>=0; i--) if(deg >= stc[i][1]) return; |
---|
1164 | act[1] = deg; |
---|
1165 | scElKbase(); |
---|
1166 | return; |
---|
1167 | } |
---|
1168 | Ivar = Nvar-1; |
---|
1169 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1170 | x = scRestrict(Nstc, sn, Nvar); |
---|
1171 | if (x <= 0) |
---|
1172 | { |
---|
1173 | if (x == 0) return; |
---|
1174 | ideg = deg; |
---|
1175 | } |
---|
1176 | else |
---|
1177 | { |
---|
1178 | if (deg < x) ideg = deg; |
---|
1179 | else ideg = x-1; |
---|
1180 | if (Nstc == 0) |
---|
1181 | { |
---|
1182 | scAllKbase(Nvar, ideg, deg); |
---|
1183 | return; |
---|
1184 | } |
---|
1185 | } |
---|
1186 | loop |
---|
1187 | { |
---|
1188 | x = scMax(Nstc, sn, Nvar); |
---|
1189 | while (ideg >= x) |
---|
1190 | { |
---|
1191 | act[Nvar] = ideg; |
---|
1192 | scDegKbase(sn, Nstc, Ivar, deg-ideg); |
---|
1193 | ideg--; |
---|
1194 | } |
---|
1195 | if (ideg < 0) return; |
---|
1196 | Istc = Nstc; |
---|
1197 | for (i=Nstc-1; i>=0; i--) |
---|
1198 | { |
---|
1199 | if (ideg < sn[i][Nvar]) |
---|
1200 | { |
---|
1201 | Istc--; |
---|
1202 | sn[i] = NULL; |
---|
1203 | } |
---|
1204 | } |
---|
1205 | if (Istc == 0) |
---|
1206 | { |
---|
1207 | scAllKbase(Nvar, ideg, deg); |
---|
1208 | return; |
---|
1209 | } |
---|
1210 | j = 0; |
---|
1211 | while (sn[j]) j++; |
---|
1212 | i = j+1; |
---|
1213 | for (; i<Nstc; i++) |
---|
1214 | { |
---|
1215 | if (sn[i]) |
---|
1216 | { |
---|
1217 | sn[j] = sn[i]; |
---|
1218 | j++; |
---|
1219 | } |
---|
1220 | } |
---|
1221 | Nstc = Istc; |
---|
1222 | } |
---|
1223 | } |
---|
1224 | |
---|
1225 | static void scInKbase( scfmon stc, int Nstc, int Nvar) |
---|
1226 | { |
---|
1227 | int Ivar, Istc, i, j; |
---|
1228 | scfmon sn; |
---|
1229 | int x, ideg; |
---|
1230 | |
---|
1231 | if (Nvar == 1) |
---|
1232 | { |
---|
1233 | ideg = scMin(Nstc, stc, 1); |
---|
1234 | while (ideg > 0) |
---|
1235 | { |
---|
1236 | ideg--; |
---|
1237 | act[1] = ideg; |
---|
1238 | scElKbase(); |
---|
1239 | } |
---|
1240 | return; |
---|
1241 | } |
---|
1242 | Ivar = Nvar-1; |
---|
1243 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1244 | x = scRestrict(Nstc, sn, Nvar); |
---|
1245 | if (x == 0) return; |
---|
1246 | ideg = x-1; |
---|
1247 | loop |
---|
1248 | { |
---|
1249 | x = scMax(Nstc, sn, Nvar); |
---|
1250 | while (ideg >= x) |
---|
1251 | { |
---|
1252 | act[Nvar] = ideg; |
---|
1253 | scInKbase(sn, Nstc, Ivar); |
---|
1254 | ideg--; |
---|
1255 | } |
---|
1256 | if (ideg < 0) return; |
---|
1257 | Istc = Nstc; |
---|
1258 | for (i=Nstc-1; i>=0; i--) |
---|
1259 | { |
---|
1260 | if (ideg < sn[i][Nvar]) |
---|
1261 | { |
---|
1262 | Istc--; |
---|
1263 | sn[i] = NULL; |
---|
1264 | } |
---|
1265 | } |
---|
1266 | j = 0; |
---|
1267 | while (sn[j]) j++; |
---|
1268 | i = j+1; |
---|
1269 | for (; i<Nstc; i++) |
---|
1270 | { |
---|
1271 | if (sn[i]) |
---|
1272 | { |
---|
1273 | sn[j] = sn[i]; |
---|
1274 | j++; |
---|
1275 | } |
---|
1276 | } |
---|
1277 | Nstc = Istc; |
---|
1278 | } |
---|
1279 | } |
---|
1280 | |
---|
1281 | static ideal scIdKbase() |
---|
1282 | { |
---|
1283 | polyset mm; |
---|
1284 | ideal res; |
---|
1285 | poly p, q = last; |
---|
1286 | int i = pLength(q); |
---|
1287 | res = idInit(i,1); |
---|
1288 | mm = res->m; |
---|
1289 | i = 0; |
---|
1290 | do |
---|
1291 | { |
---|
1292 | mm[i] = q; |
---|
1293 | i++; |
---|
1294 | p = pNext(q); |
---|
1295 | pNext(q) = NULL; |
---|
1296 | q = p; |
---|
1297 | } while (q!=NULL); |
---|
1298 | return res; |
---|
1299 | } |
---|
1300 | |
---|
1301 | ideal scKBase(int deg, ideal s, ideal Q, intvec * mv) |
---|
1302 | { |
---|
1303 | int i, di; |
---|
1304 | poly p; |
---|
1305 | |
---|
1306 | if (deg < 0) |
---|
1307 | { |
---|
1308 | di = scDimInt(s, Q); |
---|
1309 | if (di != 0) |
---|
1310 | { |
---|
1311 | //Werror("KBase not finite"); |
---|
1312 | return idInit(1,s->rank); |
---|
1313 | } |
---|
1314 | } |
---|
1315 | stcmem = hCreate((currRing->N) - 1); |
---|
1316 | hexist = hInit(s, Q, &hNexist); |
---|
1317 | p = last = pInit(); |
---|
1318 | /*pNext(p) = NULL;*/ |
---|
1319 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
1320 | *act = 0; |
---|
1321 | if (!hNexist) |
---|
1322 | { |
---|
1323 | scAll((currRing->N), deg); |
---|
1324 | goto ende; |
---|
1325 | } |
---|
1326 | if (!hisModule) |
---|
1327 | { |
---|
1328 | if (deg < 0) scInKbase(hexist, hNexist, (currRing->N)); |
---|
1329 | else scDegKbase(hexist, hNexist, (currRing->N), deg); |
---|
1330 | } |
---|
1331 | else |
---|
1332 | { |
---|
1333 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1334 | for (i = 1; i <= hisModule; i++) |
---|
1335 | { |
---|
1336 | *act = i; |
---|
1337 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1338 | int deg_ei=deg; |
---|
1339 | if (mv!=NULL) deg_ei -= (*mv)[i-1]; |
---|
1340 | if ((deg < 0) || (deg_ei>=0)) |
---|
1341 | { |
---|
1342 | if (hNstc) |
---|
1343 | { |
---|
1344 | if (deg < 0) scInKbase(hstc, hNstc, (currRing->N)); |
---|
1345 | else scDegKbase(hstc, hNstc, (currRing->N), deg_ei); |
---|
1346 | } |
---|
1347 | else |
---|
1348 | scAll((currRing->N), deg_ei); |
---|
1349 | } |
---|
1350 | } |
---|
1351 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1352 | } |
---|
1353 | ende: |
---|
1354 | hDelete(hexist, hNexist); |
---|
1355 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
1356 | hKill(stcmem, (currRing->N) - 1); |
---|
1357 | pLmDelete(&p); |
---|
1358 | if (p == NULL) |
---|
1359 | return idInit(1,s->rank); |
---|
1360 | else |
---|
1361 | { |
---|
1362 | last = p; |
---|
1363 | ideal res=scIdKbase(); |
---|
1364 | res->rank=s->rank; |
---|
1365 | return res; |
---|
1366 | } |
---|
1367 | } |
---|
1368 | |
---|
1369 | #if 0 //-- alternative implementation of scComputeHC |
---|
1370 | void scComputeHCw(ideal ss, ideal Q, int ak, poly &hEdge, ring tailRing) |
---|
1371 | { |
---|
1372 | int i, di; |
---|
1373 | poly p; |
---|
1374 | |
---|
1375 | if (hEdge!=NULL) |
---|
1376 | pLmFree(hEdge); |
---|
1377 | |
---|
1378 | ideal s=idInit(IDELEMS(ss),ak); |
---|
1379 | for(i=IDELEMS(ss)-1;i>=0;i--) |
---|
1380 | { |
---|
1381 | if (ss->m[i]!=NULL) s->m[i]=pHead(ss->m[i]); |
---|
1382 | } |
---|
1383 | di = scDimInt(s, Q); |
---|
1384 | stcmem = hCreate((currRing->N) - 1); |
---|
1385 | hexist = hInit(s, Q, &hNexist); |
---|
1386 | p = last = pInit(); |
---|
1387 | /*pNext(p) = NULL;*/ |
---|
1388 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
1389 | *act = 0; |
---|
1390 | if (!hNexist) |
---|
1391 | { |
---|
1392 | scAll((currRing->N), -1); |
---|
1393 | goto ende; |
---|
1394 | } |
---|
1395 | if (!hisModule) |
---|
1396 | { |
---|
1397 | scInKbase(hexist, hNexist, (currRing->N)); |
---|
1398 | } |
---|
1399 | else |
---|
1400 | { |
---|
1401 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
1402 | for (i = 1; i <= hisModule; i++) |
---|
1403 | { |
---|
1404 | *act = i; |
---|
1405 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1406 | if (hNstc) |
---|
1407 | { |
---|
1408 | scInKbase(hstc, hNstc, (currRing->N)); |
---|
1409 | } |
---|
1410 | else |
---|
1411 | scAll((currRing->N), -1); |
---|
1412 | } |
---|
1413 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1414 | } |
---|
1415 | ende: |
---|
1416 | hDelete(hexist, hNexist); |
---|
1417 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
1418 | hKill(stcmem, (currRing->N) - 1); |
---|
1419 | pDeleteLm(&p); |
---|
1420 | idDelete(&s); |
---|
1421 | if (p == NULL) |
---|
1422 | { |
---|
1423 | return; // no HEdge |
---|
1424 | } |
---|
1425 | else |
---|
1426 | { |
---|
1427 | last = p; |
---|
1428 | ideal res=scIdKbase(); |
---|
1429 | res->rank=ss->rank; |
---|
1430 | poly p_ind=res->m[0]; int ind=0; |
---|
1431 | for(i=IDELEMS(res)-1;i>0;i--) |
---|
1432 | { |
---|
1433 | if (pCmp(res->m[i],p_ind)==-1) { p_ind=res->m[i]; ind=i; } |
---|
1434 | } |
---|
1435 | assume(p_ind!=NULL); |
---|
1436 | assume(res->m[ind]==p_ind); |
---|
1437 | hEdge=p_ind; |
---|
1438 | res->m[ind]=NULL; |
---|
1439 | nDelete(&pGetCoeff(hEdge)); |
---|
1440 | pGetCoeff(hEdge)=NULL; |
---|
1441 | for(i=(currRing->N);i>0;i--) |
---|
1442 | pIncrExp(hEdge,i); |
---|
1443 | pSetm(hEdge); |
---|
1444 | |
---|
1445 | idDelete(&res); |
---|
1446 | return; |
---|
1447 | } |
---|
1448 | } |
---|
1449 | #endif |
---|