1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: hdegree.cc,v 1.4 1997-04-02 15:07:01 Singular Exp $ */ |
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5 | /* |
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6 | * ABSTRACT - dimension, multiplicity, HC, kbase |
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7 | */ |
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8 | |
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9 | #include "mod2.h" |
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10 | #include "tok.h" |
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11 | #include "lists.h" |
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12 | #include "febase.h" |
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13 | #include "mmemory.h" |
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14 | #include "ipid.h" |
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15 | #include "ideals.h" |
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16 | #include "polys.h" |
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17 | #include "intvec.h" |
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18 | #include "hutil.h" |
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19 | #include "stairc.h" |
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20 | |
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21 | static int hCo, hMu, hMu2; |
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22 | |
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23 | /*0 implementation*/ |
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24 | |
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25 | // dimension |
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26 | |
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27 | static void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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28 | varset var, int Nvar) |
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29 | { |
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30 | int dn, iv, rad0, b, c, x; |
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31 | scmon pn; |
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32 | scfmon rn; |
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33 | if (Nrad < 2) |
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34 | { |
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35 | dn = Npure + Nrad; |
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36 | if (dn < hCo) |
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37 | hCo = dn; |
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38 | return; |
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39 | } |
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40 | if (Npure+1 >= hCo) |
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41 | return; |
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42 | iv = Nvar; |
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43 | while(pure[var[iv]]) iv--; |
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44 | hStepR(rad, Nrad, var, iv, &rad0); |
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45 | if (rad0) |
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46 | { |
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47 | iv--; |
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48 | if (rad0 < Nrad) |
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49 | { |
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50 | pn = hGetpure(pure); |
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51 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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52 | hDimSolve(pn, Npure + 1, rn, rad0, var, iv); |
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53 | b = rad0; |
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54 | c = Nrad; |
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55 | hElimR(rn, &rad0, b, c, var, iv); |
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56 | hPure(rn, b, &c, var, iv, pn, &x); |
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57 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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58 | rad0 += (c - b); |
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59 | hDimSolve(pn, Npure + x, rn, rad0, var, iv); |
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60 | } |
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61 | else |
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62 | { |
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63 | hDimSolve(pure, Npure, rad, Nrad, var, iv); |
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64 | } |
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65 | } |
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66 | else |
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67 | hCo = Npure + 1; |
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68 | } |
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69 | |
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70 | int scDimInt(ideal S, ideal Q) |
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71 | { |
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72 | short mc; |
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73 | hexist = hInit(S, Q, &hNexist); |
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74 | if (!hNexist) |
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75 | return pVariables; |
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76 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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77 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
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78 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(short)); |
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79 | mc = hisModule; |
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80 | if (!mc) |
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81 | { |
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82 | hrad = hexist; |
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83 | hNrad = hNexist; |
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84 | } |
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85 | else |
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86 | hrad = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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87 | radmem = hCreate(pVariables - 1); |
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88 | hCo = pVariables + 1; |
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89 | loop |
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90 | { |
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91 | if (mc) |
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92 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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93 | if (hNrad) |
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94 | { |
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95 | hNvar = pVariables; |
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96 | hRadical(hrad, &hNrad, hNvar); |
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97 | hSupp(hrad, hNrad, hvar, &hNvar); |
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98 | if (hNvar) |
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99 | { |
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100 | memset(hpure, 0, (pVariables + 1) * sizeof(short)); |
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101 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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102 | hLexR(hrad, hNrad, hvar, hNvar); |
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103 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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104 | } |
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105 | } |
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106 | else |
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107 | { |
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108 | hCo = 0; |
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109 | break; |
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110 | } |
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111 | mc--; |
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112 | if (mc <= 0) |
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113 | break; |
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114 | } |
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115 | hKill(radmem, pVariables - 1); |
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116 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(short)); |
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117 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
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118 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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119 | Free((ADDRESS)hexist, hNexist * sizeof(scmon)); |
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120 | if (hisModule) |
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121 | Free((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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122 | return pVariables - hCo; |
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123 | } |
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124 | |
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125 | // independent set |
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126 | static scmon hInd; |
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127 | |
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128 | static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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129 | varset var, int Nvar) |
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130 | { |
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131 | int dn, iv, rad0, b, c, x; |
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132 | scmon pn; |
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133 | scfmon rn; |
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134 | if (Nrad < 2) |
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135 | { |
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136 | dn = Npure + Nrad; |
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137 | if (dn < hCo) |
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138 | { |
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139 | hCo = dn; |
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140 | for (iv=pVariables; iv; iv--) |
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141 | { |
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142 | if (pure[iv]) |
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143 | hInd[iv] = 0; |
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144 | else |
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145 | hInd[iv] = 1; |
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146 | } |
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147 | if (Nrad) |
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148 | { |
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149 | pn = *rad; |
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150 | iv = Nvar; |
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151 | loop |
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152 | { |
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153 | x = var[iv]; |
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154 | if (pn[x]) |
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155 | { |
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156 | hInd[x] = 0; |
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157 | break; |
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158 | } |
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159 | iv--; |
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160 | } |
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161 | } |
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162 | } |
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163 | return; |
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164 | } |
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165 | if (Npure+1 >= hCo) |
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166 | return; |
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167 | iv = Nvar; |
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168 | while(pure[var[iv]]) iv--; |
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169 | hStepR(rad, Nrad, var, iv, &rad0); |
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170 | if (rad0) |
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171 | { |
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172 | iv--; |
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173 | if (rad0 < Nrad) |
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174 | { |
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175 | pn = hGetpure(pure); |
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176 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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177 | pn[var[iv + 1]] = 1; |
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178 | hIndSolve(pn, Npure + 1, rn, rad0, var, iv); |
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179 | pn[var[iv + 1]] = 0; |
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180 | b = rad0; |
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181 | c = Nrad; |
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182 | hElimR(rn, &rad0, b, c, var, iv); |
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183 | hPure(rn, b, &c, var, iv, pn, &x); |
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184 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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185 | rad0 += (c - b); |
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186 | hIndSolve(pn, Npure + x, rn, rad0, var, iv); |
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187 | } |
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188 | else |
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189 | { |
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190 | hIndSolve(pure, Npure, rad, Nrad, var, iv); |
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191 | } |
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192 | } |
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193 | else |
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194 | { |
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195 | hCo = Npure + 1; |
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196 | for (x=pVariables; x; x--) |
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197 | { |
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198 | if (pure[x]) |
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199 | hInd[x] = 0; |
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200 | else |
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201 | hInd[x] = 1; |
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202 | } |
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203 | hInd[var[iv]] = 0; |
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204 | } |
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205 | } |
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206 | |
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207 | intvec * scIndIntvec(ideal S, ideal Q) |
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208 | { |
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209 | intvec *Set=new intvec(pVariables); |
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210 | short mc,i; |
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211 | hexist = hInit(S, Q, &hNexist); |
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212 | if (!hNexist) |
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213 | { |
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214 | for(i=0; i<pVariables; i++) |
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215 | (*Set)[i]=1; |
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216 | return Set; |
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217 | } |
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218 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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219 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
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220 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(short)); |
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221 | hInd = (scmon)Alloc((1 + pVariables) * sizeof(short)); |
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222 | mc = hisModule; |
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223 | if (!mc) |
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224 | { |
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225 | hrad = hexist; |
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226 | hNrad = hNexist; |
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227 | } |
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228 | else |
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229 | hrad = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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230 | radmem = hCreate(pVariables - 1); |
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231 | hCo = pVariables + 1; |
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232 | loop |
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233 | { |
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234 | if (mc) |
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235 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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236 | if (hNrad) |
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237 | { |
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238 | hNvar = pVariables; |
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239 | hRadical(hrad, &hNrad, hNvar); |
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240 | hSupp(hrad, hNrad, hvar, &hNvar); |
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241 | if (hNvar) |
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242 | { |
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243 | memset(hpure, 0, (pVariables + 1) * sizeof(short)); |
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244 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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245 | hLexR(hrad, hNrad, hvar, hNvar); |
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246 | hIndSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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247 | } |
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248 | } |
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249 | else |
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250 | { |
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251 | hCo = 0; |
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252 | break; |
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253 | } |
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254 | mc--; |
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255 | if (mc <= 0) |
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256 | break; |
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257 | } |
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258 | for(i=0; i<pVariables; i++) |
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259 | (*Set)[i] = hInd[i+1]; |
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260 | hKill(radmem, pVariables - 1); |
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261 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(short)); |
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262 | Free((ADDRESS)hInd, (1 + pVariables) * sizeof(short)); |
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263 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
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264 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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265 | Free((ADDRESS)hexist, hNexist * sizeof(scmon)); |
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266 | if (hisModule) |
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267 | Free((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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268 | return Set; |
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269 | } |
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270 | |
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271 | typedef struct sindlist indlist; |
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272 | typedef indlist * indset; |
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273 | |
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274 | struct sindlist |
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275 | { |
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276 | indset nx; |
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277 | intvec * set; |
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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(pVariables); |
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302 | for (iv=pVariables; iv; 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)Alloc0(sizeof(indlist)); |
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310 | hMu++; |
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311 | } |
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312 | |
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313 | static 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) |
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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; 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=pVariables; |
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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=pVariables; |
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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 | Free((ADDRESS)sm,sizeof(indlist)); |
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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(pVariables); |
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462 | sm->nx = (indset)Alloc0(sizeof(indlist)); |
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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=pVariables; 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 | static 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 | } |
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545 | else |
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546 | { |
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547 | hIndAllMult(pure, Npure, rad, Nrad, var, iv); |
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548 | } |
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549 | } |
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550 | |
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551 | lists scIndIndset(ideal S, BOOLEAN all, ideal Q) |
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552 | { |
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553 | int i; |
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554 | indset save; |
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555 | lists res=(lists)Alloc0(sizeof(slists)); |
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556 | |
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557 | hexist = hInit(S, Q, &hNexist); |
---|
558 | if ((hNexist == 0) || (hisModule!=0)) |
---|
559 | { |
---|
560 | res->Init(0); |
---|
561 | return res; |
---|
562 | } |
---|
563 | save = ISet = (indset)Alloc0(sizeof(indlist)); |
---|
564 | hMu = 0; |
---|
565 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
566 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
567 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(short)); |
---|
568 | hrad = hexist; |
---|
569 | hNrad = hNexist; |
---|
570 | radmem = hCreate(pVariables - 1); |
---|
571 | hCo = pVariables + 1; |
---|
572 | hNvar = pVariables; |
---|
573 | hRadical(hrad, &hNrad, hNvar); |
---|
574 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
575 | if (hNvar) |
---|
576 | { |
---|
577 | hCo = hNvar; |
---|
578 | memset(hpure, 0, (pVariables + 1) * sizeof(short)); |
---|
579 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
580 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
581 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
582 | } |
---|
583 | if (hCo && (hCo < pVariables)) |
---|
584 | { |
---|
585 | hIndMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
586 | } |
---|
587 | if (hMu!=0) |
---|
588 | { |
---|
589 | ISet = save; |
---|
590 | hMu2 = 0; |
---|
591 | if (all && (hCo+1 < pVariables)) |
---|
592 | { |
---|
593 | JSet = (indset)Alloc0(sizeof(indlist)); |
---|
594 | hIndAllMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
595 | i=hMu+hMu2; |
---|
596 | res->Init(i); |
---|
597 | if (hMu2 == 0) |
---|
598 | { |
---|
599 | Free((ADDRESS)JSet,sizeof(indlist)); |
---|
600 | } |
---|
601 | } |
---|
602 | else |
---|
603 | { |
---|
604 | res->Init(hMu); |
---|
605 | } |
---|
606 | for (i=0;i<hMu;i++) |
---|
607 | { |
---|
608 | res->m[i].data = (void *)save->set; |
---|
609 | res->m[i].rtyp = INTVEC_CMD; |
---|
610 | ISet = save; |
---|
611 | save = save->nx; |
---|
612 | Free((ADDRESS)ISet,sizeof(indlist)); |
---|
613 | } |
---|
614 | Free((ADDRESS)save,sizeof(indlist)); |
---|
615 | if (hMu2 != 0) |
---|
616 | { |
---|
617 | save = JSet; |
---|
618 | for (i=hMu;i<hMu+hMu2;i++) |
---|
619 | { |
---|
620 | res->m[i].data = (void *)save->set; |
---|
621 | res->m[i].rtyp = INTVEC_CMD; |
---|
622 | JSet = save; |
---|
623 | save = save->nx; |
---|
624 | Free((ADDRESS)JSet,sizeof(indlist)); |
---|
625 | } |
---|
626 | Free((ADDRESS)save,sizeof(indlist)); |
---|
627 | } |
---|
628 | } |
---|
629 | else |
---|
630 | { |
---|
631 | res->Init(0); |
---|
632 | Free((ADDRESS)ISet, sizeof(indlist)); |
---|
633 | } |
---|
634 | hKill(radmem, pVariables - 1); |
---|
635 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(short)); |
---|
636 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
---|
637 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
638 | Free((ADDRESS)hexist, hNexist * sizeof(scmon)); |
---|
639 | return res; |
---|
640 | } |
---|
641 | |
---|
642 | // multiplicity |
---|
643 | |
---|
644 | static int hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar) |
---|
645 | { |
---|
646 | int iv = Nvar -1, sum, a, a0, a1, b, i; |
---|
647 | short x, x0; |
---|
648 | scmon pn; |
---|
649 | scfmon sn; |
---|
650 | if (!iv) |
---|
651 | return pure[var[1]]; |
---|
652 | else if (!Nstc) |
---|
653 | { |
---|
654 | sum = 1; |
---|
655 | for (i = Nvar; i; i--) |
---|
656 | sum *= pure[var[i]]; |
---|
657 | return sum; |
---|
658 | } |
---|
659 | x = a = 0; |
---|
660 | pn = hGetpure(pure); |
---|
661 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
662 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
663 | if (a == Nstc) |
---|
664 | return pure[var[Nvar]] * hZeroMult(pn, sn, a, var, iv); |
---|
665 | else |
---|
666 | sum = x * hZeroMult(pn, sn, a, var, iv); |
---|
667 | b = a; |
---|
668 | loop |
---|
669 | { |
---|
670 | a0 = a; |
---|
671 | x0 = x; |
---|
672 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
673 | hElimS(sn, &b, a0, a, var, iv); |
---|
674 | a1 = a; |
---|
675 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
676 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
677 | b += (a1 - a0); |
---|
678 | if (a < Nstc) |
---|
679 | { |
---|
680 | sum += (x - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
681 | } |
---|
682 | else |
---|
683 | { |
---|
684 | sum += (pure[var[Nvar]] - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
685 | return sum; |
---|
686 | } |
---|
687 | } |
---|
688 | } |
---|
689 | |
---|
690 | static void hProject(scmon pure, varset sel) |
---|
691 | { |
---|
692 | int i, i0, k; |
---|
693 | i0 = 0; |
---|
694 | for (i = 1; i <= pVariables; i++) |
---|
695 | { |
---|
696 | if (pure[i]) |
---|
697 | { |
---|
698 | i0++; |
---|
699 | sel[i0] = i; |
---|
700 | } |
---|
701 | } |
---|
702 | i = hNstc; |
---|
703 | memcpy(hwork, hstc, i * sizeof(scmon)); |
---|
704 | hStaircase(hwork, &i, sel, i0); |
---|
705 | if ((i0 > 2) && (i > 10)) |
---|
706 | hOrdSupp(hwork, i, sel, i0); |
---|
707 | memset(hpur0, 0, (pVariables + 1) * sizeof(short)); |
---|
708 | hPure(hwork, 0, &i, sel, i0, hpur0, &k); |
---|
709 | hLexS(hwork, i, sel, i0); |
---|
710 | hMu += hZeroMult(hpur0, hwork, i, sel, i0); |
---|
711 | } |
---|
712 | |
---|
713 | static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
714 | varset var, int Nvar) |
---|
715 | { |
---|
716 | int dn, iv, rad0, b, c, x; |
---|
717 | scmon pn; |
---|
718 | scfmon rn; |
---|
719 | if (Nrad < 2) |
---|
720 | { |
---|
721 | dn = Npure + Nrad; |
---|
722 | if (dn == hCo) |
---|
723 | { |
---|
724 | if (!Nrad) |
---|
725 | hProject(pure, hsel); |
---|
726 | else |
---|
727 | { |
---|
728 | pn = *rad; |
---|
729 | for (iv = Nvar; iv; iv--) |
---|
730 | { |
---|
731 | x = var[iv]; |
---|
732 | if (pn[x]) |
---|
733 | { |
---|
734 | pure[x] = 1; |
---|
735 | hProject(pure, hsel); |
---|
736 | pure[x] = 0; |
---|
737 | } |
---|
738 | } |
---|
739 | } |
---|
740 | } |
---|
741 | return; |
---|
742 | } |
---|
743 | iv = Nvar; |
---|
744 | dn = Npure+1; |
---|
745 | if (dn >= hCo) |
---|
746 | { |
---|
747 | if (dn > hCo) |
---|
748 | return; |
---|
749 | loop |
---|
750 | { |
---|
751 | if(!pure[var[iv]]) |
---|
752 | { |
---|
753 | if(hNotZero(rad, Nrad, var, iv)) |
---|
754 | { |
---|
755 | pure[var[iv]] = 1; |
---|
756 | hProject(pure, hsel); |
---|
757 | pure[var[iv]] = 0; |
---|
758 | } |
---|
759 | } |
---|
760 | iv--; |
---|
761 | if (!iv) |
---|
762 | return; |
---|
763 | } |
---|
764 | } |
---|
765 | while(pure[var[iv]]) iv--; |
---|
766 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
767 | iv--; |
---|
768 | if (rad0 < Nrad) |
---|
769 | { |
---|
770 | pn = hGetpure(pure); |
---|
771 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
772 | pn[var[iv + 1]] = 1; |
---|
773 | hDimMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
774 | pn[var[iv + 1]] = 0; |
---|
775 | b = rad0; |
---|
776 | c = Nrad; |
---|
777 | hElimR(rn, &rad0, b, c, var, iv); |
---|
778 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
779 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
780 | rad0 += (c - b); |
---|
781 | hDimMult(pn, Npure + x, rn, rad0, var, iv); |
---|
782 | } |
---|
783 | else |
---|
784 | { |
---|
785 | hDimMult(pure, Npure, rad, Nrad, var, iv); |
---|
786 | } |
---|
787 | } |
---|
788 | |
---|
789 | static void hDegree(ideal S, ideal Q) |
---|
790 | { |
---|
791 | int di; |
---|
792 | short mc; |
---|
793 | hexist = hInit(S, Q, &hNexist); |
---|
794 | if (!hNexist) |
---|
795 | { |
---|
796 | hCo = 0; |
---|
797 | hMu = 1; |
---|
798 | return; |
---|
799 | } |
---|
800 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
801 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
802 | hsel = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
803 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(short)); |
---|
804 | hpur0 = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(short)); |
---|
805 | mc = hisModule; |
---|
806 | hrad = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
807 | if (!mc) |
---|
808 | { |
---|
809 | memcpy(hrad, hexist, hNexist * sizeof(scmon)); |
---|
810 | hstc = hexist; |
---|
811 | hNrad = hNstc = hNexist; |
---|
812 | } |
---|
813 | else |
---|
814 | hstc = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
815 | radmem = hCreate(pVariables - 1); |
---|
816 | stcmem = hCreate(pVariables - 1); |
---|
817 | hCo = pVariables + 1; |
---|
818 | di = hCo + 1; |
---|
819 | loop |
---|
820 | { |
---|
821 | if (mc) |
---|
822 | { |
---|
823 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
---|
824 | hNstc = hNrad; |
---|
825 | memcpy(hstc, hrad, hNrad * sizeof(scmon)); |
---|
826 | } |
---|
827 | if (hNrad) |
---|
828 | { |
---|
829 | hNvar = pVariables; |
---|
830 | hRadical(hrad, &hNrad, hNvar); |
---|
831 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
832 | if (hNvar) |
---|
833 | { |
---|
834 | hCo = hNvar; |
---|
835 | memset(hpure, 0, (pVariables + 1) * sizeof(short)); |
---|
836 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
837 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
838 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
839 | } |
---|
840 | } |
---|
841 | else |
---|
842 | { |
---|
843 | hNvar = 1; |
---|
844 | hCo = 0; |
---|
845 | } |
---|
846 | if (hCo < di) |
---|
847 | { |
---|
848 | di = hCo; |
---|
849 | hMu = 0; |
---|
850 | } |
---|
851 | if (hNvar && (hCo == di)) |
---|
852 | { |
---|
853 | if (di && (di < pVariables)) |
---|
854 | hDimMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
855 | else if (!di) |
---|
856 | hMu++; |
---|
857 | else |
---|
858 | { |
---|
859 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
860 | if ((hNvar > 2) && (hNstc > 10)) |
---|
861 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
862 | memset(hpur0, 0, (pVariables + 1) * sizeof(short)); |
---|
863 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
864 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
865 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
866 | } |
---|
867 | } |
---|
868 | mc--; |
---|
869 | if (mc <= 0) |
---|
870 | break; |
---|
871 | } |
---|
872 | hCo = di; |
---|
873 | hKill(stcmem, pVariables - 1); |
---|
874 | hKill(radmem, pVariables - 1); |
---|
875 | Free((ADDRESS)hpur0, (1 + (pVariables * pVariables)) * sizeof(short)); |
---|
876 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(short)); |
---|
877 | Free((ADDRESS)hsel, (pVariables + 1) * sizeof(int)); |
---|
878 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
---|
879 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
880 | Free((ADDRESS)hrad, hNexist * sizeof(scmon)); |
---|
881 | Free((ADDRESS)hexist, hNexist * sizeof(scmon)); |
---|
882 | if (hisModule) |
---|
883 | Free((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
884 | } |
---|
885 | |
---|
886 | int scMultInt(ideal S, ideal Q) |
---|
887 | { |
---|
888 | hDegree(S, Q); |
---|
889 | return hMu; |
---|
890 | } |
---|
891 | |
---|
892 | void scDegree(ideal S, ideal Q) |
---|
893 | { |
---|
894 | hDegree(S, Q); |
---|
895 | if (pOrdSgn == 1) |
---|
896 | Print("// codimension = %d\n// dimension = %d\n// degree = %d\n", |
---|
897 | hCo, pVariables - hCo, hMu); |
---|
898 | else |
---|
899 | Print("// codimension = %d\n// dimension = %d\n// multiplicity = %d\n", |
---|
900 | hCo, pVariables - hCo, hMu); |
---|
901 | } |
---|
902 | |
---|
903 | static void hDegree0(ideal S, ideal Q) |
---|
904 | { |
---|
905 | short mc; |
---|
906 | hexist = hInit(S, Q, &hNexist); |
---|
907 | if (!hNexist) |
---|
908 | { |
---|
909 | hMu = -1; |
---|
910 | return; |
---|
911 | } |
---|
912 | else |
---|
913 | hMu = 0; |
---|
914 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
915 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
916 | hpur0 = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(short)); |
---|
917 | mc = hisModule; |
---|
918 | if (!mc) |
---|
919 | { |
---|
920 | hstc = hexist; |
---|
921 | hNstc = hNexist; |
---|
922 | } |
---|
923 | else |
---|
924 | hstc = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
925 | stcmem = hCreate(pVariables - 1); |
---|
926 | loop |
---|
927 | { |
---|
928 | if (mc) |
---|
929 | { |
---|
930 | hComp(hexist, hNexist, mc, hstc, &hNstc); |
---|
931 | if (!hNstc) |
---|
932 | { |
---|
933 | hMu = -1; |
---|
934 | break; |
---|
935 | } |
---|
936 | } |
---|
937 | hNvar = pVariables; |
---|
938 | for (int i = hNvar; i; i--) |
---|
939 | hvar[i] = i; |
---|
940 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
941 | hSupp(hstc, hNstc, hvar, &hNvar); |
---|
942 | if ((hNvar == pVariables) && (hNstc >= pVariables)) |
---|
943 | { |
---|
944 | if ((hNvar > 2) && (hNstc > 10)) |
---|
945 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
946 | memset(hpur0, 0, (pVariables + 1) * sizeof(short)); |
---|
947 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
948 | if (hNpure == hNvar) |
---|
949 | { |
---|
950 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
951 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
952 | } |
---|
953 | else |
---|
954 | hMu = -1; |
---|
955 | } |
---|
956 | else if (hNvar) |
---|
957 | hMu = -1; |
---|
958 | mc--; |
---|
959 | if (mc <= 0 || hMu < 0) |
---|
960 | break; |
---|
961 | } |
---|
962 | hKill(stcmem, pVariables - 1); |
---|
963 | Free((ADDRESS)hpur0, (1 + (pVariables * pVariables)) * sizeof(short)); |
---|
964 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
---|
965 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
966 | Free((ADDRESS)hexist, hNexist * sizeof(scmon)); |
---|
967 | if (hisModule) |
---|
968 | Free((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
969 | } |
---|
970 | |
---|
971 | int scMult0Int(ideal S, ideal Q) |
---|
972 | { |
---|
973 | hDegree0(S, Q); |
---|
974 | return hMu; |
---|
975 | } |
---|
976 | |
---|
977 | |
---|
978 | // HC |
---|
979 | |
---|
980 | static poly pWork; |
---|
981 | |
---|
982 | static void hHedge(poly hEdge) |
---|
983 | { |
---|
984 | pSetm(pWork); |
---|
985 | if (pComp0(pWork, hEdge) == pOrdSgn) |
---|
986 | { |
---|
987 | for (int i = hNvar; i>0; i--) |
---|
988 | hEdge->exp[i] = pWork->exp[i]; |
---|
989 | pGetOrder(hEdge) = pGetOrder(pWork); |
---|
990 | } |
---|
991 | } |
---|
992 | |
---|
993 | |
---|
994 | static void hHedgeStep(scmon pure, scfmon stc, |
---|
995 | int Nstc, varset var, int Nvar,poly hEdge) |
---|
996 | { |
---|
997 | int iv = Nvar -1, k = var[Nvar], a, a0, a1, b, i; |
---|
998 | short x, x0; |
---|
999 | scmon pn; |
---|
1000 | scfmon sn; |
---|
1001 | if (iv==0) |
---|
1002 | { |
---|
1003 | pSetExp(pWork, k, pure[k]); |
---|
1004 | hHedge(hEdge); |
---|
1005 | return; |
---|
1006 | } |
---|
1007 | else if (Nstc==0) |
---|
1008 | { |
---|
1009 | for (i = Nvar; i>0; i--) |
---|
1010 | pSetExp(pWork, var[i], pure[var[i]]); |
---|
1011 | hHedge(hEdge); |
---|
1012 | return; |
---|
1013 | } |
---|
1014 | x = a = 0; |
---|
1015 | pn = hGetpure(pure); |
---|
1016 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
1017 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
1018 | if (a == Nstc) |
---|
1019 | { |
---|
1020 | pSetExp(pWork, k, pure[k]); |
---|
1021 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
1022 | return; |
---|
1023 | } |
---|
1024 | else |
---|
1025 | { |
---|
1026 | pSetExp(pWork, k, x); |
---|
1027 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
1028 | } |
---|
1029 | b = a; |
---|
1030 | loop |
---|
1031 | { |
---|
1032 | a0 = a; |
---|
1033 | x0 = x; |
---|
1034 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
1035 | hElimS(sn, &b, a0, a, var, iv); |
---|
1036 | a1 = a; |
---|
1037 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
1038 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
1039 | b += (a1 - a0); |
---|
1040 | if (a < Nstc) |
---|
1041 | { |
---|
1042 | pSetExp(pWork, k, x); |
---|
1043 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
1044 | } |
---|
1045 | else |
---|
1046 | { |
---|
1047 | pSetExp(pWork, k, pure[k]); |
---|
1048 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
1049 | return; |
---|
1050 | } |
---|
1051 | } |
---|
1052 | } |
---|
1053 | |
---|
1054 | |
---|
1055 | void scComputeHC(ideal S, int ak, poly &hEdge) |
---|
1056 | { |
---|
1057 | int i; |
---|
1058 | short k = ak; |
---|
1059 | hNvar = pVariables; |
---|
1060 | hexist = hInit(S, NULL, &hNexist); |
---|
1061 | if (k!=0) |
---|
1062 | hComp(hexist, hNexist, k, hexist, &hNstc); |
---|
1063 | else |
---|
1064 | hNstc = hNexist; |
---|
1065 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
1066 | hvar = (varset)Alloc((hNvar + 1) * sizeof(int)); |
---|
1067 | hpure = (scmon)Alloc((1 + (hNvar * hNvar)) * sizeof(short)); |
---|
1068 | stcmem = hCreate(hNvar - 1); |
---|
1069 | for (i = hNvar; i>0; i--) |
---|
1070 | hvar[i] = i; |
---|
1071 | hStaircase(hexist, &hNstc, hvar, hNvar); |
---|
1072 | if ((hNvar > 2) && (hNstc > 10)) |
---|
1073 | hOrdSupp(hexist, hNstc, hvar, hNvar); |
---|
1074 | memset(hpure, 0, (hNvar + 1) * sizeof(short)); |
---|
1075 | hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure); |
---|
1076 | hLexS(hexist, hNstc, hvar, hNvar); |
---|
1077 | if (hEdge!=NULL) |
---|
1078 | pFree1(hEdge); |
---|
1079 | hEdge = pInit(); |
---|
1080 | pWork = pInit(); |
---|
1081 | hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge); |
---|
1082 | pSetComp(hEdge,ak); |
---|
1083 | hKill(stcmem, hNvar - 1); |
---|
1084 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
1085 | Free((ADDRESS)hvar, (hNvar + 1) * sizeof(int)); |
---|
1086 | Free((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(short)); |
---|
1087 | Free((ADDRESS)hexist, hNexist * sizeof(scmon)); |
---|
1088 | pFree1(pWork); |
---|
1089 | } |
---|
1090 | |
---|
1091 | |
---|
1092 | // kbase |
---|
1093 | |
---|
1094 | static polyset Kbase; |
---|
1095 | static int count; |
---|
1096 | |
---|
1097 | static void scInKbase( poly p, int start) |
---|
1098 | { |
---|
1099 | int i, j; |
---|
1100 | poly q; |
---|
1101 | scmon x; |
---|
1102 | for (i = 0; i < hNstc; i++) |
---|
1103 | { |
---|
1104 | x = hstc[i]; |
---|
1105 | j = pVariables; |
---|
1106 | loop |
---|
1107 | { |
---|
1108 | if (x[j] > p->exp[j]) |
---|
1109 | break; |
---|
1110 | j--; |
---|
1111 | if (j==0) |
---|
1112 | { |
---|
1113 | pDelete1(&p); |
---|
1114 | return; |
---|
1115 | } |
---|
1116 | } |
---|
1117 | } |
---|
1118 | pSetm(p); |
---|
1119 | Kbase[count] = p; |
---|
1120 | count++; |
---|
1121 | for (i = start; i <= pVariables; i++) |
---|
1122 | { |
---|
1123 | q = pCopy(p); |
---|
1124 | q->exp[i]++; |
---|
1125 | scInKbase(q, i); |
---|
1126 | } |
---|
1127 | } |
---|
1128 | |
---|
1129 | |
---|
1130 | extern ideal scKBase(ideal s, ideal Q) |
---|
1131 | { |
---|
1132 | int i, a; |
---|
1133 | poly p; |
---|
1134 | ideal res; |
---|
1135 | a = scMult0Int(s, Q); |
---|
1136 | if (a <= 0) |
---|
1137 | return idInit(1,s->rank); |
---|
1138 | res = idInit(a,s->rank); |
---|
1139 | Kbase = res->m; |
---|
1140 | hexist = hInit(s, Q, &hNexist); |
---|
1141 | count = 0; |
---|
1142 | if (!hisModule) |
---|
1143 | { |
---|
1144 | hstc = hexist; |
---|
1145 | hNstc = hNexist; |
---|
1146 | p = pOne(); |
---|
1147 | scInKbase(p, 1); |
---|
1148 | } |
---|
1149 | else |
---|
1150 | { |
---|
1151 | hstc = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
1152 | for (i = 1; i <= hisModule; i++) |
---|
1153 | { |
---|
1154 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1155 | if (hNstc) |
---|
1156 | { |
---|
1157 | p = pOne(); |
---|
1158 | p->exp[0] = i; |
---|
1159 | scInKbase(p, 1); |
---|
1160 | } |
---|
1161 | } |
---|
1162 | Free((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1163 | } |
---|
1164 | Free((ADDRESS)hexist, hNexist * sizeof(scmon)); |
---|
1165 | return res; |
---|
1166 | } |
---|
1167 | |
---|
1168 | |
---|