1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: hdegree.cc,v 1.12 1998-04-08 10:01:58 pohl 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 "numbers.h" |
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19 | #include "hutil.h" |
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20 | #include "stairc.h" |
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21 | |
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22 | static int hCo, hMu, hMu2; |
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23 | |
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24 | /*0 implementation*/ |
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25 | |
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26 | // dimension |
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27 | |
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28 | static void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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29 | varset var, int Nvar) |
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30 | { |
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31 | int dn, iv, rad0, b, c, x; |
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32 | scmon pn; |
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33 | scfmon rn; |
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34 | if (Nrad < 2) |
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35 | { |
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36 | dn = Npure + Nrad; |
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37 | if (dn < hCo) |
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38 | hCo = dn; |
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39 | return; |
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40 | } |
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41 | if (Npure+1 >= hCo) |
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42 | return; |
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43 | iv = Nvar; |
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44 | while(pure[var[iv]]) iv--; |
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45 | hStepR(rad, Nrad, var, iv, &rad0); |
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46 | if (rad0!=0) |
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47 | { |
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48 | iv--; |
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49 | if (rad0 < Nrad) |
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50 | { |
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51 | pn = hGetpure(pure); |
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52 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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53 | hDimSolve(pn, Npure + 1, rn, rad0, var, iv); |
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54 | b = rad0; |
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55 | c = Nrad; |
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56 | hElimR(rn, &rad0, b, c, var, iv); |
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57 | hPure(rn, b, &c, var, iv, pn, &x); |
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58 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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59 | rad0 += (c - b); |
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60 | hDimSolve(pn, Npure + x, rn, rad0, var, iv); |
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61 | } |
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62 | else |
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63 | { |
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64 | hDimSolve(pure, Npure, rad, Nrad, var, iv); |
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65 | } |
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66 | } |
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67 | else |
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68 | hCo = Npure + 1; |
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69 | } |
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70 | |
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71 | int scDimInt(ideal S, ideal Q) |
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72 | { |
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73 | Exponent_t mc; |
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74 | hexist = hInit(S, Q, &hNexist); |
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75 | if (!hNexist) |
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76 | return pVariables; |
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77 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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78 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
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79 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
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80 | mc = hisModule; |
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81 | if (!mc) |
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82 | { |
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83 | hrad = hexist; |
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84 | hNrad = hNexist; |
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85 | } |
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86 | else |
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87 | hrad = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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88 | radmem = hCreate(pVariables - 1); |
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89 | hCo = pVariables + 1; |
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90 | loop |
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91 | { |
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92 | if (mc) |
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93 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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94 | if (hNrad) |
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95 | { |
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96 | hNvar = pVariables; |
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97 | hRadical(hrad, &hNrad, hNvar); |
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98 | hSupp(hrad, hNrad, hvar, &hNvar); |
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99 | if (hNvar) |
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100 | { |
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101 | memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t)); |
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102 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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103 | hLexR(hrad, hNrad, hvar, hNvar); |
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104 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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105 | } |
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106 | } |
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107 | else |
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108 | { |
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109 | hCo = 0; |
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110 | break; |
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111 | } |
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112 | mc--; |
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113 | if (mc <= 0) |
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114 | break; |
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115 | } |
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116 | hKill(radmem, pVariables - 1); |
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117 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
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118 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
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119 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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120 | hDelete(hexist, hNexist); |
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121 | if (hisModule) |
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122 | Free((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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123 | return pVariables - hCo; |
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124 | } |
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125 | |
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126 | // independent set |
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127 | static scmon hInd; |
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128 | |
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129 | static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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130 | varset var, int Nvar) |
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131 | { |
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132 | int dn, iv, rad0, b, c, x; |
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133 | scmon pn; |
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134 | scfmon rn; |
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135 | if (Nrad < 2) |
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136 | { |
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137 | dn = Npure + Nrad; |
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138 | if (dn < hCo) |
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139 | { |
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140 | hCo = dn; |
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141 | for (iv=pVariables; iv; iv--) |
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142 | { |
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143 | if (pure[iv]) |
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144 | hInd[iv] = 0; |
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145 | else |
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146 | hInd[iv] = 1; |
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147 | } |
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148 | if (Nrad) |
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149 | { |
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150 | pn = *rad; |
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151 | iv = Nvar; |
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152 | loop |
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153 | { |
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154 | x = var[iv]; |
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155 | if (pn[x]) |
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156 | { |
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157 | hInd[x] = 0; |
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158 | break; |
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159 | } |
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160 | iv--; |
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161 | } |
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162 | } |
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163 | } |
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164 | return; |
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165 | } |
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166 | if (Npure+1 >= hCo) |
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167 | return; |
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168 | iv = Nvar; |
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169 | while(pure[var[iv]]) iv--; |
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170 | hStepR(rad, Nrad, var, iv, &rad0); |
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171 | if (rad0) |
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172 | { |
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173 | iv--; |
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174 | if (rad0 < Nrad) |
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175 | { |
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176 | pn = hGetpure(pure); |
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177 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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178 | pn[var[iv + 1]] = 1; |
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179 | hIndSolve(pn, Npure + 1, rn, rad0, var, iv); |
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180 | pn[var[iv + 1]] = 0; |
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181 | b = rad0; |
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182 | c = Nrad; |
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183 | hElimR(rn, &rad0, b, c, var, iv); |
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184 | hPure(rn, b, &c, var, iv, pn, &x); |
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185 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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186 | rad0 += (c - b); |
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187 | hIndSolve(pn, Npure + x, rn, rad0, var, iv); |
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188 | } |
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189 | else |
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190 | { |
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191 | hIndSolve(pure, Npure, rad, Nrad, var, iv); |
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192 | } |
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193 | } |
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194 | else |
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195 | { |
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196 | hCo = Npure + 1; |
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197 | for (x=pVariables; x; x--) |
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198 | { |
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199 | if (pure[x]) |
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200 | hInd[x] = 0; |
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201 | else |
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202 | hInd[x] = 1; |
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203 | } |
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204 | hInd[var[iv]] = 0; |
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205 | } |
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206 | } |
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207 | |
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208 | intvec * scIndIntvec(ideal S, ideal Q) |
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209 | { |
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210 | intvec *Set=new intvec(pVariables); |
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211 | Exponent_t mc,i; |
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212 | hexist = hInit(S, Q, &hNexist); |
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213 | if (hNexist==0) |
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214 | { |
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215 | for(i=0; i<pVariables; i++) |
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216 | (*Set)[i]=1; |
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217 | return Set; |
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218 | } |
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219 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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220 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
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221 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
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222 | hInd = (scmon)Alloc((1 + pVariables) * sizeof(Exponent_t)); |
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223 | mc = hisModule; |
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224 | if (mc==0) |
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225 | { |
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226 | hrad = hexist; |
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227 | hNrad = hNexist; |
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228 | } |
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229 | else |
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230 | hrad = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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231 | radmem = hCreate(pVariables - 1); |
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232 | hCo = pVariables + 1; |
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233 | loop |
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234 | { |
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235 | if (mc!=0) |
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236 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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237 | if (hNrad!=0) |
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238 | { |
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239 | hNvar = pVariables; |
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240 | hRadical(hrad, &hNrad, hNvar); |
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241 | hSupp(hrad, hNrad, hvar, &hNvar); |
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242 | if (hNvar!=0) |
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243 | { |
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244 | memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t)); |
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245 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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246 | hLexR(hrad, hNrad, hvar, hNvar); |
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247 | hIndSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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248 | } |
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249 | } |
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250 | else |
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251 | { |
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252 | hCo = 0; |
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253 | break; |
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254 | } |
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255 | mc--; |
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256 | if (mc <= 0) |
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257 | break; |
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258 | } |
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259 | for(i=0; i<pVariables; i++) |
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260 | (*Set)[i] = hInd[i+1]; |
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261 | hKill(radmem, pVariables - 1); |
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262 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
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263 | Free((ADDRESS)hInd, (1 + pVariables) * sizeof(Exponent_t)); |
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264 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
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265 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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266 | hDelete(hexist, hNexist); |
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267 | if (hisModule) |
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268 | Free((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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269 | return Set; |
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270 | } |
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271 | |
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272 | typedef struct sindlist indlist; |
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273 | typedef indlist * indset; |
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274 | |
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275 | struct sindlist |
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276 | { |
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277 | indset nx; |
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278 | intvec * set; |
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279 | }; |
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280 | indset ISet, JSet; |
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281 | |
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282 | static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar) |
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283 | { |
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284 | int k1, i; |
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285 | k1 = var[Nvar]; |
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286 | i = 0; |
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287 | loop |
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288 | { |
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289 | if (rad[i][k1]==0) |
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290 | return FALSE; |
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291 | i++; |
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292 | if (i == Nrad) |
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293 | return TRUE; |
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294 | } |
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295 | } |
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296 | |
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297 | static void hIndep(scmon pure) |
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298 | { |
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299 | int iv; |
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300 | intvec *Set; |
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301 | |
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302 | Set = ISet->set = new intvec(pVariables); |
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303 | for (iv=pVariables; iv!=0 ; iv--) |
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304 | { |
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305 | if (pure[iv]) |
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306 | (*Set)[iv-1] = 0; |
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307 | else |
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308 | (*Set)[iv-1] = 1; |
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309 | } |
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310 | ISet = ISet->nx = (indset)Alloc0(sizeof(indlist)); |
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311 | hMu++; |
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312 | } |
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313 | |
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314 | static void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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315 | varset var, int Nvar) |
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316 | { |
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317 | int dn, iv, rad0, b, c, x; |
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318 | scmon pn; |
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319 | scfmon rn; |
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320 | if (Nrad < 2) |
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321 | { |
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322 | dn = Npure + Nrad; |
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323 | if (dn == hCo) |
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324 | { |
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325 | if (Nrad==0) |
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326 | hIndep(pure); |
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327 | else |
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328 | { |
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329 | pn = *rad; |
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330 | for (iv = Nvar; iv!=0; iv--) |
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331 | { |
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332 | x = var[iv]; |
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333 | if (pn[x]) |
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334 | { |
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335 | pure[x] = 1; |
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336 | hIndep(pure); |
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337 | pure[x] = 0; |
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338 | } |
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339 | } |
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340 | } |
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341 | } |
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342 | return; |
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343 | } |
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344 | iv = Nvar; |
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345 | dn = Npure+1; |
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346 | if (dn >= hCo) |
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347 | { |
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348 | if (dn > hCo) |
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349 | return; |
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350 | loop |
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351 | { |
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352 | if(!pure[var[iv]]) |
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353 | { |
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354 | if(hNotZero(rad, Nrad, var, iv)) |
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355 | { |
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356 | pure[var[iv]] = 1; |
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357 | hIndep(pure); |
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358 | pure[var[iv]] = 0; |
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359 | } |
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360 | } |
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361 | iv--; |
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362 | if (!iv) |
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363 | return; |
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364 | } |
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365 | } |
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366 | while(pure[var[iv]]) iv--; |
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367 | hStepR(rad, Nrad, var, iv, &rad0); |
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368 | iv--; |
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369 | if (rad0 < Nrad) |
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370 | { |
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371 | pn = hGetpure(pure); |
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372 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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373 | pn[var[iv + 1]] = 1; |
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374 | hIndMult(pn, Npure + 1, rn, rad0, var, iv); |
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375 | pn[var[iv + 1]] = 0; |
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376 | b = rad0; |
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377 | c = Nrad; |
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378 | hElimR(rn, &rad0, b, c, var, iv); |
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379 | hPure(rn, b, &c, var, iv, pn, &x); |
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380 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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381 | rad0 += (c - b); |
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382 | hIndMult(pn, Npure + x, rn, rad0, var, iv); |
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383 | } |
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384 | else |
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385 | { |
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386 | hIndMult(pure, Npure, rad, Nrad, var, iv); |
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387 | } |
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388 | } |
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389 | |
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390 | /*3 |
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391 | * consider indset x := !pure |
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392 | * (for all i) (if(sm(i) > x) return FALSE) |
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393 | * else return TRUE |
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394 | */ |
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395 | static BOOLEAN hCheck1(indset sm, scmon pure) |
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396 | { |
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397 | int iv; |
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398 | intvec *Set; |
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399 | while (sm->nx != NULL) |
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400 | { |
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401 | Set = sm->set; |
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402 | iv=pVariables; |
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403 | loop |
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404 | { |
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405 | if (((*Set)[iv-1] == 0) && (pure[iv] == 0)) |
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406 | break; |
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407 | iv--; |
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408 | if (iv == 0) |
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409 | return FALSE; |
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410 | } |
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411 | sm = sm->nx; |
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412 | } |
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413 | return TRUE; |
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414 | } |
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415 | |
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416 | /*3 |
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417 | * consider indset x := !pure |
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418 | * (for all i) if(x > sm(i)) delete sm(i)) |
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419 | * return (place for x) |
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420 | */ |
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421 | static indset hCheck2(indset sm, scmon pure) |
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422 | { |
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423 | int iv; |
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424 | intvec *Set; |
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425 | indset be, a1 = NULL; |
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426 | while (sm->nx != NULL) |
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427 | { |
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428 | Set = sm->set; |
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429 | iv=pVariables; |
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430 | loop |
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431 | { |
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432 | if ((pure[iv] == 1) && ((*Set)[iv-1] == 1)) |
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433 | break; |
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434 | iv--; |
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435 | if (iv == 0) |
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436 | { |
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437 | if (a1 == NULL) |
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438 | { |
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439 | a1 = sm; |
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440 | } |
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441 | else |
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442 | { |
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443 | hMu2--; |
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444 | be->nx = sm->nx; |
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445 | delete Set; |
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446 | Free((ADDRESS)sm,sizeof(indlist)); |
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447 | sm = be; |
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448 | } |
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449 | break; |
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450 | } |
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451 | } |
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452 | be = sm; |
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453 | sm = sm->nx; |
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454 | } |
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455 | if (a1 != NULL) |
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456 | { |
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457 | return a1; |
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458 | } |
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459 | else |
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460 | { |
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461 | hMu2++; |
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462 | sm->set = new intvec(pVariables); |
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463 | sm->nx = (indset)Alloc0(sizeof(indlist)); |
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464 | return sm; |
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465 | } |
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466 | } |
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467 | |
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468 | /*2 |
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469 | * definition x >= y |
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470 | * x(i) == 0 => y(i) == 0 |
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471 | * > ex. j with x(j) == 1 and y(j) == 0 |
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472 | */ |
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473 | static void hCheckIndep(scmon pure) |
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474 | { |
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475 | intvec *Set; |
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476 | indset res; |
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477 | int iv; |
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478 | if (hCheck1(ISet, pure)) |
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479 | { |
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480 | if (hCheck1(JSet, pure)) |
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481 | { |
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482 | res = hCheck2(JSet,pure); |
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483 | if (res == NULL) |
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484 | return; |
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485 | Set = res->set; |
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486 | for (iv=pVariables; iv; iv--) |
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487 | { |
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488 | if (pure[iv]) |
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489 | (*Set)[iv-1] = 0; |
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490 | else |
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491 | (*Set)[iv-1] = 1; |
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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 | |
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497 | static void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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498 | varset var, int Nvar) |
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499 | { |
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500 | int dn, iv, rad0, b, c, x; |
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501 | scmon pn; |
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502 | scfmon rn; |
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503 | if (Nrad < 2) |
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504 | { |
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505 | dn = Npure + Nrad; |
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506 | if (dn > hCo) |
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507 | { |
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508 | if (!Nrad) |
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509 | hCheckIndep(pure); |
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510 | else |
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511 | { |
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512 | pn = *rad; |
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513 | for (iv = Nvar; iv; iv--) |
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514 | { |
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515 | x = var[iv]; |
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516 | if (pn[x]) |
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517 | { |
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518 | pure[x] = 1; |
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519 | hCheckIndep(pure); |
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520 | pure[x] = 0; |
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521 | } |
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522 | } |
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523 | } |
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524 | } |
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525 | return; |
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526 | } |
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527 | iv = Nvar; |
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528 | while(pure[var[iv]]) iv--; |
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529 | hStepR(rad, Nrad, var, iv, &rad0); |
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530 | iv--; |
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531 | if (rad0 < Nrad) |
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532 | { |
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533 | pn = hGetpure(pure); |
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534 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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535 | pn[var[iv + 1]] = 1; |
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536 | hIndAllMult(pn, Npure + 1, rn, rad0, var, iv); |
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537 | pn[var[iv + 1]] = 0; |
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538 | b = rad0; |
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539 | c = Nrad; |
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540 | hElimR(rn, &rad0, b, c, var, iv); |
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541 | hPure(rn, b, &c, var, iv, pn, &x); |
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542 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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543 | rad0 += (c - b); |
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544 | hIndAllMult(pn, Npure + x, rn, rad0, var, iv); |
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545 | } |
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546 | else |
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547 | { |
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548 | hIndAllMult(pure, Npure, rad, Nrad, var, iv); |
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549 | } |
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550 | } |
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551 | |
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552 | lists scIndIndset(ideal S, BOOLEAN all, ideal Q) |
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553 | { |
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554 | int i; |
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555 | indset save; |
---|
556 | lists res=(lists)Alloc0(sizeof(slists)); |
---|
557 | |
---|
558 | hexist = hInit(S, Q, &hNexist); |
---|
559 | if ((hNexist == 0) || (hisModule!=0)) |
---|
560 | { |
---|
561 | res->Init(0); |
---|
562 | return res; |
---|
563 | } |
---|
564 | save = ISet = (indset)Alloc0(sizeof(indlist)); |
---|
565 | hMu = 0; |
---|
566 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
567 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
568 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
569 | hrad = hexist; |
---|
570 | hNrad = hNexist; |
---|
571 | radmem = hCreate(pVariables - 1); |
---|
572 | hCo = pVariables + 1; |
---|
573 | hNvar = pVariables; |
---|
574 | hRadical(hrad, &hNrad, hNvar); |
---|
575 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
576 | if (hNvar) |
---|
577 | { |
---|
578 | hCo = hNvar; |
---|
579 | memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
580 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
581 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
582 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
583 | } |
---|
584 | if (hCo && (hCo < pVariables)) |
---|
585 | { |
---|
586 | hIndMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
587 | } |
---|
588 | if (hMu!=0) |
---|
589 | { |
---|
590 | ISet = save; |
---|
591 | hMu2 = 0; |
---|
592 | if (all && (hCo+1 < pVariables)) |
---|
593 | { |
---|
594 | JSet = (indset)Alloc0(sizeof(indlist)); |
---|
595 | hIndAllMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
596 | i=hMu+hMu2; |
---|
597 | res->Init(i); |
---|
598 | if (hMu2 == 0) |
---|
599 | { |
---|
600 | Free((ADDRESS)JSet,sizeof(indlist)); |
---|
601 | } |
---|
602 | } |
---|
603 | else |
---|
604 | { |
---|
605 | res->Init(hMu); |
---|
606 | } |
---|
607 | for (i=0;i<hMu;i++) |
---|
608 | { |
---|
609 | res->m[i].data = (void *)save->set; |
---|
610 | res->m[i].rtyp = INTVEC_CMD; |
---|
611 | ISet = save; |
---|
612 | save = save->nx; |
---|
613 | Free((ADDRESS)ISet,sizeof(indlist)); |
---|
614 | } |
---|
615 | Free((ADDRESS)save,sizeof(indlist)); |
---|
616 | if (hMu2 != 0) |
---|
617 | { |
---|
618 | save = JSet; |
---|
619 | for (i=hMu;i<hMu+hMu2;i++) |
---|
620 | { |
---|
621 | res->m[i].data = (void *)save->set; |
---|
622 | res->m[i].rtyp = INTVEC_CMD; |
---|
623 | JSet = save; |
---|
624 | save = save->nx; |
---|
625 | Free((ADDRESS)JSet,sizeof(indlist)); |
---|
626 | } |
---|
627 | Free((ADDRESS)save,sizeof(indlist)); |
---|
628 | } |
---|
629 | } |
---|
630 | else |
---|
631 | { |
---|
632 | res->Init(0); |
---|
633 | Free((ADDRESS)ISet, sizeof(indlist)); |
---|
634 | } |
---|
635 | hKill(radmem, pVariables - 1); |
---|
636 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
637 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
---|
638 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
639 | hDelete(hexist, hNexist); |
---|
640 | return res; |
---|
641 | } |
---|
642 | |
---|
643 | // multiplicity |
---|
644 | |
---|
645 | static int hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar) |
---|
646 | { |
---|
647 | int iv = Nvar -1, sum, a, a0, a1, b, i; |
---|
648 | Exponent_t x, x0; |
---|
649 | scmon pn; |
---|
650 | scfmon sn; |
---|
651 | if (!iv) |
---|
652 | return pure[var[1]]; |
---|
653 | else if (!Nstc) |
---|
654 | { |
---|
655 | sum = 1; |
---|
656 | for (i = Nvar; i; i--) |
---|
657 | sum *= pure[var[i]]; |
---|
658 | return sum; |
---|
659 | } |
---|
660 | x = a = 0; |
---|
661 | pn = hGetpure(pure); |
---|
662 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
663 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
664 | if (a == Nstc) |
---|
665 | return pure[var[Nvar]] * hZeroMult(pn, sn, a, var, iv); |
---|
666 | else |
---|
667 | sum = x * hZeroMult(pn, sn, a, var, iv); |
---|
668 | b = a; |
---|
669 | loop |
---|
670 | { |
---|
671 | a0 = a; |
---|
672 | x0 = x; |
---|
673 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
674 | hElimS(sn, &b, a0, a, var, iv); |
---|
675 | a1 = a; |
---|
676 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
677 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
678 | b += (a1 - a0); |
---|
679 | if (a < Nstc) |
---|
680 | { |
---|
681 | sum += (x - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
682 | } |
---|
683 | else |
---|
684 | { |
---|
685 | sum += (pure[var[Nvar]] - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
686 | return sum; |
---|
687 | } |
---|
688 | } |
---|
689 | } |
---|
690 | |
---|
691 | static void hProject(scmon pure, varset sel) |
---|
692 | { |
---|
693 | int i, i0, k; |
---|
694 | i0 = 0; |
---|
695 | for (i = 1; i <= pVariables; i++) |
---|
696 | { |
---|
697 | if (pure[i]) |
---|
698 | { |
---|
699 | i0++; |
---|
700 | sel[i0] = i; |
---|
701 | } |
---|
702 | } |
---|
703 | i = hNstc; |
---|
704 | memcpy(hwork, hstc, i * sizeof(scmon)); |
---|
705 | hStaircase(hwork, &i, sel, i0); |
---|
706 | if ((i0 > 2) && (i > 10)) |
---|
707 | hOrdSupp(hwork, i, sel, i0); |
---|
708 | memset(hpur0, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
709 | hPure(hwork, 0, &i, sel, i0, hpur0, &k); |
---|
710 | hLexS(hwork, i, sel, i0); |
---|
711 | hMu += hZeroMult(hpur0, hwork, i, sel, i0); |
---|
712 | } |
---|
713 | |
---|
714 | static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
715 | varset var, int Nvar) |
---|
716 | { |
---|
717 | int dn, iv, rad0, b, c, x; |
---|
718 | scmon pn; |
---|
719 | scfmon rn; |
---|
720 | if (Nrad < 2) |
---|
721 | { |
---|
722 | dn = Npure + Nrad; |
---|
723 | if (dn == hCo) |
---|
724 | { |
---|
725 | if (!Nrad) |
---|
726 | hProject(pure, hsel); |
---|
727 | else |
---|
728 | { |
---|
729 | pn = *rad; |
---|
730 | for (iv = Nvar; iv; iv--) |
---|
731 | { |
---|
732 | x = var[iv]; |
---|
733 | if (pn[x]) |
---|
734 | { |
---|
735 | pure[x] = 1; |
---|
736 | hProject(pure, hsel); |
---|
737 | pure[x] = 0; |
---|
738 | } |
---|
739 | } |
---|
740 | } |
---|
741 | } |
---|
742 | return; |
---|
743 | } |
---|
744 | iv = Nvar; |
---|
745 | dn = Npure+1; |
---|
746 | if (dn >= hCo) |
---|
747 | { |
---|
748 | if (dn > hCo) |
---|
749 | return; |
---|
750 | loop |
---|
751 | { |
---|
752 | if(!pure[var[iv]]) |
---|
753 | { |
---|
754 | if(hNotZero(rad, Nrad, var, iv)) |
---|
755 | { |
---|
756 | pure[var[iv]] = 1; |
---|
757 | hProject(pure, hsel); |
---|
758 | pure[var[iv]] = 0; |
---|
759 | } |
---|
760 | } |
---|
761 | iv--; |
---|
762 | if (!iv) |
---|
763 | return; |
---|
764 | } |
---|
765 | } |
---|
766 | while(pure[var[iv]]) iv--; |
---|
767 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
768 | iv--; |
---|
769 | if (rad0 < Nrad) |
---|
770 | { |
---|
771 | pn = hGetpure(pure); |
---|
772 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
773 | pn[var[iv + 1]] = 1; |
---|
774 | hDimMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
775 | pn[var[iv + 1]] = 0; |
---|
776 | b = rad0; |
---|
777 | c = Nrad; |
---|
778 | hElimR(rn, &rad0, b, c, var, iv); |
---|
779 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
780 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
781 | rad0 += (c - b); |
---|
782 | hDimMult(pn, Npure + x, rn, rad0, var, iv); |
---|
783 | } |
---|
784 | else |
---|
785 | { |
---|
786 | hDimMult(pure, Npure, rad, Nrad, var, iv); |
---|
787 | } |
---|
788 | } |
---|
789 | |
---|
790 | static void hDegree(ideal S, ideal Q) |
---|
791 | { |
---|
792 | int di; |
---|
793 | Exponent_t mc; |
---|
794 | hexist = hInit(S, Q, &hNexist); |
---|
795 | if (!hNexist) |
---|
796 | { |
---|
797 | hCo = 0; |
---|
798 | hMu = 1; |
---|
799 | return; |
---|
800 | } |
---|
801 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
802 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
803 | hsel = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
804 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
805 | hpur0 = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
806 | mc = hisModule; |
---|
807 | hrad = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
808 | if (!mc) |
---|
809 | { |
---|
810 | memcpy(hrad, hexist, hNexist * sizeof(scmon)); |
---|
811 | hstc = hexist; |
---|
812 | hNrad = hNstc = hNexist; |
---|
813 | } |
---|
814 | else |
---|
815 | hstc = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
816 | radmem = hCreate(pVariables - 1); |
---|
817 | stcmem = hCreate(pVariables - 1); |
---|
818 | hCo = pVariables + 1; |
---|
819 | di = hCo + 1; |
---|
820 | loop |
---|
821 | { |
---|
822 | if (mc) |
---|
823 | { |
---|
824 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
---|
825 | hNstc = hNrad; |
---|
826 | memcpy(hstc, hrad, hNrad * sizeof(scmon)); |
---|
827 | } |
---|
828 | if (hNrad) |
---|
829 | { |
---|
830 | hNvar = pVariables; |
---|
831 | hRadical(hrad, &hNrad, hNvar); |
---|
832 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
833 | if (hNvar) |
---|
834 | { |
---|
835 | hCo = hNvar; |
---|
836 | memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
837 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
838 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
839 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
840 | } |
---|
841 | } |
---|
842 | else |
---|
843 | { |
---|
844 | hNvar = 1; |
---|
845 | hCo = 0; |
---|
846 | } |
---|
847 | if (hCo < di) |
---|
848 | { |
---|
849 | di = hCo; |
---|
850 | hMu = 0; |
---|
851 | } |
---|
852 | if (hNvar && (hCo == di)) |
---|
853 | { |
---|
854 | if (di && (di < pVariables)) |
---|
855 | hDimMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
856 | else if (!di) |
---|
857 | hMu++; |
---|
858 | else |
---|
859 | { |
---|
860 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
861 | if ((hNvar > 2) && (hNstc > 10)) |
---|
862 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
863 | memset(hpur0, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
864 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
865 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
866 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
867 | } |
---|
868 | } |
---|
869 | mc--; |
---|
870 | if (mc <= 0) |
---|
871 | break; |
---|
872 | } |
---|
873 | hCo = di; |
---|
874 | hKill(stcmem, pVariables - 1); |
---|
875 | hKill(radmem, pVariables - 1); |
---|
876 | Free((ADDRESS)hpur0, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
877 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
878 | Free((ADDRESS)hsel, (pVariables + 1) * sizeof(int)); |
---|
879 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
---|
880 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
881 | Free((ADDRESS)hrad, hNexist * sizeof(scmon)); |
---|
882 | hDelete(hexist, hNexist); |
---|
883 | if (hisModule) |
---|
884 | Free((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
885 | } |
---|
886 | |
---|
887 | int scMultInt(ideal S, ideal Q) |
---|
888 | { |
---|
889 | hDegree(S, Q); |
---|
890 | return hMu; |
---|
891 | } |
---|
892 | |
---|
893 | void scDegree(ideal S, ideal Q) |
---|
894 | { |
---|
895 | hDegree(S, Q); |
---|
896 | if (pOrdSgn == 1) |
---|
897 | Print("// codimension = %d\n// dimension = %d\n// degree = %d\n", |
---|
898 | hCo, pVariables - hCo, hMu); |
---|
899 | else |
---|
900 | Print("// codimension = %d\n// dimension = %d\n// multiplicity = %d\n", |
---|
901 | hCo, pVariables - hCo, hMu); |
---|
902 | } |
---|
903 | |
---|
904 | static void hDegree0(ideal S, ideal Q) |
---|
905 | { |
---|
906 | Exponent_t mc; |
---|
907 | hexist = hInit(S, Q, &hNexist); |
---|
908 | if (!hNexist) |
---|
909 | { |
---|
910 | hMu = -1; |
---|
911 | return; |
---|
912 | } |
---|
913 | else |
---|
914 | hMu = 0; |
---|
915 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
916 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
917 | hpur0 = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
918 | mc = hisModule; |
---|
919 | if (!mc) |
---|
920 | { |
---|
921 | hstc = hexist; |
---|
922 | hNstc = hNexist; |
---|
923 | } |
---|
924 | else |
---|
925 | hstc = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
926 | stcmem = hCreate(pVariables - 1); |
---|
927 | loop |
---|
928 | { |
---|
929 | if (mc) |
---|
930 | { |
---|
931 | hComp(hexist, hNexist, mc, hstc, &hNstc); |
---|
932 | if (!hNstc) |
---|
933 | { |
---|
934 | hMu = -1; |
---|
935 | break; |
---|
936 | } |
---|
937 | } |
---|
938 | hNvar = pVariables; |
---|
939 | for (int i = hNvar; i; i--) |
---|
940 | hvar[i] = i; |
---|
941 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
942 | hSupp(hstc, hNstc, hvar, &hNvar); |
---|
943 | if ((hNvar == pVariables) && (hNstc >= pVariables)) |
---|
944 | { |
---|
945 | if ((hNvar > 2) && (hNstc > 10)) |
---|
946 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
947 | memset(hpur0, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
948 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
949 | if (hNpure == hNvar) |
---|
950 | { |
---|
951 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
952 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
953 | } |
---|
954 | else |
---|
955 | hMu = -1; |
---|
956 | } |
---|
957 | else if (hNvar) |
---|
958 | hMu = -1; |
---|
959 | mc--; |
---|
960 | if (mc <= 0 || hMu < 0) |
---|
961 | break; |
---|
962 | } |
---|
963 | hKill(stcmem, pVariables - 1); |
---|
964 | Free((ADDRESS)hpur0, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
965 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
---|
966 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
967 | hDelete(hexist, hNexist); |
---|
968 | if (hisModule) |
---|
969 | Free((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
970 | } |
---|
971 | |
---|
972 | int scMult0Int(ideal S, ideal Q) |
---|
973 | { |
---|
974 | hDegree0(S, Q); |
---|
975 | return hMu; |
---|
976 | } |
---|
977 | |
---|
978 | |
---|
979 | // HC |
---|
980 | |
---|
981 | static poly pWork; |
---|
982 | |
---|
983 | static void hHedge(poly hEdge) |
---|
984 | { |
---|
985 | pSetm(pWork); |
---|
986 | if (pComp0(pWork, hEdge) == pOrdSgn) |
---|
987 | { |
---|
988 | for (int i = hNvar; i>0; i--) |
---|
989 | pSetExp(hEdge,i, pGetExp(pWork,i)); |
---|
990 | pGetOrder(hEdge) = pGetOrder(pWork); |
---|
991 | } |
---|
992 | } |
---|
993 | |
---|
994 | |
---|
995 | static void hHedgeStep(scmon pure, scfmon stc, |
---|
996 | int Nstc, varset var, int Nvar,poly hEdge) |
---|
997 | { |
---|
998 | int iv = Nvar -1, k = var[Nvar], a, a0, a1, b, i; |
---|
999 | Exponent_t x, x0; |
---|
1000 | scmon pn; |
---|
1001 | scfmon sn; |
---|
1002 | if (iv==0) |
---|
1003 | { |
---|
1004 | pSetExp(pWork, k, pure[k]); |
---|
1005 | hHedge(hEdge); |
---|
1006 | return; |
---|
1007 | } |
---|
1008 | else if (Nstc==0) |
---|
1009 | { |
---|
1010 | for (i = Nvar; i>0; i--) |
---|
1011 | pSetExp(pWork, var[i], pure[var[i]]); |
---|
1012 | hHedge(hEdge); |
---|
1013 | return; |
---|
1014 | } |
---|
1015 | x = a = 0; |
---|
1016 | pn = hGetpure(pure); |
---|
1017 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
1018 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
1019 | if (a == Nstc) |
---|
1020 | { |
---|
1021 | pSetExp(pWork, k, pure[k]); |
---|
1022 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
1023 | return; |
---|
1024 | } |
---|
1025 | else |
---|
1026 | { |
---|
1027 | pSetExp(pWork, k, x); |
---|
1028 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
1029 | } |
---|
1030 | b = a; |
---|
1031 | loop |
---|
1032 | { |
---|
1033 | a0 = a; |
---|
1034 | x0 = x; |
---|
1035 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
1036 | hElimS(sn, &b, a0, a, var, iv); |
---|
1037 | a1 = a; |
---|
1038 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
1039 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
1040 | b += (a1 - a0); |
---|
1041 | if (a < Nstc) |
---|
1042 | { |
---|
1043 | pSetExp(pWork, k, x); |
---|
1044 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
1045 | } |
---|
1046 | else |
---|
1047 | { |
---|
1048 | pSetExp(pWork, k, pure[k]); |
---|
1049 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
1050 | return; |
---|
1051 | } |
---|
1052 | } |
---|
1053 | } |
---|
1054 | |
---|
1055 | |
---|
1056 | void scComputeHC(ideal S, int ak, poly &hEdge) |
---|
1057 | { |
---|
1058 | int i; |
---|
1059 | Exponent_t k = ak; |
---|
1060 | hNvar = pVariables; |
---|
1061 | hexist = hInit(S, NULL, &hNexist); |
---|
1062 | if (k!=0) |
---|
1063 | hComp(hexist, hNexist, k, hexist, &hNstc); |
---|
1064 | else |
---|
1065 | hNstc = hNexist; |
---|
1066 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
1067 | hvar = (varset)Alloc((hNvar + 1) * sizeof(int)); |
---|
1068 | hpure = (scmon)Alloc((1 + (hNvar * hNvar)) * sizeof(Exponent_t)); |
---|
1069 | stcmem = hCreate(hNvar - 1); |
---|
1070 | for (i = hNvar; i>0; i--) |
---|
1071 | hvar[i] = i; |
---|
1072 | hStaircase(hexist, &hNstc, hvar, hNvar); |
---|
1073 | if ((hNvar > 2) && (hNstc > 10)) |
---|
1074 | hOrdSupp(hexist, hNstc, hvar, hNvar); |
---|
1075 | memset(hpure, 0, (hNvar + 1) * sizeof(Exponent_t)); |
---|
1076 | hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure); |
---|
1077 | hLexS(hexist, hNstc, hvar, hNvar); |
---|
1078 | if (hEdge!=NULL) |
---|
1079 | pFree1(hEdge); |
---|
1080 | hEdge = pInit(); |
---|
1081 | pWork = pInit(); |
---|
1082 | hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge); |
---|
1083 | pSetComp(hEdge,ak); |
---|
1084 | hKill(stcmem, hNvar - 1); |
---|
1085 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
1086 | Free((ADDRESS)hvar, (hNvar + 1) * sizeof(int)); |
---|
1087 | Free((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(Exponent_t)); |
---|
1088 | hDelete(hexist, hNexist); |
---|
1089 | pFree1(pWork); |
---|
1090 | } |
---|
1091 | |
---|
1092 | |
---|
1093 | // kbase |
---|
1094 | |
---|
1095 | static poly last; |
---|
1096 | static scmon act; |
---|
1097 | |
---|
1098 | static void scElKbase() |
---|
1099 | { |
---|
1100 | poly q = pInit(); |
---|
1101 | pSetCoeff0(q,nInit(1)); |
---|
1102 | pSetExpV(q,act); |
---|
1103 | pNext(q) = NULL; |
---|
1104 | last = pNext(last) = q; |
---|
1105 | } |
---|
1106 | |
---|
1107 | static Exponent_t scMax( int i, scfmon stc, int Nvar) |
---|
1108 | { |
---|
1109 | Exponent_t x, y=stc[0][Nvar]; |
---|
1110 | for (; i;) |
---|
1111 | { |
---|
1112 | i--; |
---|
1113 | x = stc[i][Nvar]; |
---|
1114 | if (x > y) y = x; |
---|
1115 | } |
---|
1116 | return y; |
---|
1117 | } |
---|
1118 | |
---|
1119 | static Exponent_t scMin( int i, scfmon stc, int Nvar) |
---|
1120 | { |
---|
1121 | Exponent_t x, y=stc[0][Nvar]; |
---|
1122 | for (; i;) |
---|
1123 | { |
---|
1124 | i--; |
---|
1125 | x = stc[i][Nvar]; |
---|
1126 | if (x < y) y = x; |
---|
1127 | } |
---|
1128 | return y; |
---|
1129 | } |
---|
1130 | |
---|
1131 | static Exponent_t scRestrict( int &Nstc, scfmon stc, int Nvar) |
---|
1132 | { |
---|
1133 | Exponent_t x, y; |
---|
1134 | int i, j, Istc = Nstc; |
---|
1135 | |
---|
1136 | y = MAX_EXPONENT; |
---|
1137 | for (i=Nstc-1; i>=0; i--) |
---|
1138 | { |
---|
1139 | j = Nvar-1; |
---|
1140 | loop |
---|
1141 | { |
---|
1142 | if(stc[i][j] != 0) break; |
---|
1143 | j--; |
---|
1144 | if (j == 0) |
---|
1145 | { |
---|
1146 | Istc--; |
---|
1147 | x = stc[i][Nvar]; |
---|
1148 | if (x < y) y = x; |
---|
1149 | stc[i] = NULL; |
---|
1150 | break; |
---|
1151 | } |
---|
1152 | } |
---|
1153 | } |
---|
1154 | if (Istc < Nstc) |
---|
1155 | { |
---|
1156 | for (i=Nstc-1; i>=0; i--) |
---|
1157 | { |
---|
1158 | if (stc[i] && (stc[i][Nvar] >= y)) |
---|
1159 | { |
---|
1160 | Istc--; |
---|
1161 | stc[i] = NULL; |
---|
1162 | } |
---|
1163 | } |
---|
1164 | j = 0; |
---|
1165 | while (stc[j]) j++; |
---|
1166 | i = j+1; |
---|
1167 | for(; i<Nstc; i++) |
---|
1168 | { |
---|
1169 | if (stc[i]) |
---|
1170 | { |
---|
1171 | stc[j] = stc[i]; |
---|
1172 | j++; |
---|
1173 | } |
---|
1174 | } |
---|
1175 | Nstc = Istc; |
---|
1176 | return y; |
---|
1177 | } |
---|
1178 | else |
---|
1179 | return -1; |
---|
1180 | } |
---|
1181 | |
---|
1182 | static void scAll( int Nvar, Exponent_t deg) |
---|
1183 | { |
---|
1184 | int i; |
---|
1185 | Exponent_t d = deg; |
---|
1186 | if (d == 0) |
---|
1187 | { |
---|
1188 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1189 | scElKbase(); |
---|
1190 | return; |
---|
1191 | } |
---|
1192 | if (Nvar == 1) |
---|
1193 | { |
---|
1194 | act[1] = d; |
---|
1195 | scElKbase(); |
---|
1196 | return; |
---|
1197 | } |
---|
1198 | do |
---|
1199 | { |
---|
1200 | act[Nvar] = d; |
---|
1201 | scAll(Nvar-1, deg-d); |
---|
1202 | d--; |
---|
1203 | } while (d >= 0); |
---|
1204 | } |
---|
1205 | |
---|
1206 | static void scAllKbase( int Nvar, Exponent_t ideg, Exponent_t deg) |
---|
1207 | { |
---|
1208 | do |
---|
1209 | { |
---|
1210 | act[Nvar] = ideg; |
---|
1211 | scAll(Nvar-1, deg-ideg); |
---|
1212 | ideg--; |
---|
1213 | } while (ideg >= 0); |
---|
1214 | } |
---|
1215 | |
---|
1216 | static void scDegKbase( scfmon stc, int Nstc, int Nvar, Exponent_t deg) |
---|
1217 | { |
---|
1218 | int Ivar, Istc, i, j; |
---|
1219 | scfmon sn; |
---|
1220 | Exponent_t x, ideg; |
---|
1221 | |
---|
1222 | if (deg == 0) |
---|
1223 | { |
---|
1224 | for (i=Nvar; i; i--) act[i] = 0; |
---|
1225 | scElKbase(); |
---|
1226 | return; |
---|
1227 | } |
---|
1228 | if (Nvar == 1) |
---|
1229 | { |
---|
1230 | for (i=Nstc-1; i>=0; i--) if(deg >= stc[i][1]) return; |
---|
1231 | act[1] = deg; |
---|
1232 | scElKbase(); |
---|
1233 | return; |
---|
1234 | } |
---|
1235 | Ivar = Nvar-1; |
---|
1236 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1237 | x = scRestrict(Nstc, sn, Nvar); |
---|
1238 | if (x <= 0) |
---|
1239 | { |
---|
1240 | if (x == 0) return; |
---|
1241 | ideg = deg; |
---|
1242 | } |
---|
1243 | else |
---|
1244 | { |
---|
1245 | if (deg < x) ideg = deg; |
---|
1246 | else ideg = x-1; |
---|
1247 | if (Nstc == 0) |
---|
1248 | { |
---|
1249 | scAllKbase(Nvar, ideg, deg); |
---|
1250 | return; |
---|
1251 | } |
---|
1252 | } |
---|
1253 | loop |
---|
1254 | { |
---|
1255 | x = scMax(Nstc, sn, Nvar); |
---|
1256 | while (ideg >= x) |
---|
1257 | { |
---|
1258 | act[Nvar] = ideg; |
---|
1259 | scDegKbase(sn, Nstc, Ivar, deg-ideg); |
---|
1260 | ideg--; |
---|
1261 | } |
---|
1262 | if (ideg < 0) return; |
---|
1263 | Istc = Nstc; |
---|
1264 | for (i=Nstc-1; i>=0; i--) |
---|
1265 | { |
---|
1266 | if (ideg < sn[i][Nvar]) |
---|
1267 | { |
---|
1268 | Istc--; |
---|
1269 | sn[i] = NULL; |
---|
1270 | } |
---|
1271 | } |
---|
1272 | if (Istc == 0) |
---|
1273 | { |
---|
1274 | scAllKbase(Nvar, ideg, deg); |
---|
1275 | return; |
---|
1276 | } |
---|
1277 | j = 0; |
---|
1278 | while (sn[j]) j++; |
---|
1279 | i = j+1; |
---|
1280 | for (; i<Nstc; i++) |
---|
1281 | { |
---|
1282 | if (sn[i]) |
---|
1283 | { |
---|
1284 | sn[j] = sn[i]; |
---|
1285 | j++; |
---|
1286 | } |
---|
1287 | } |
---|
1288 | Nstc = Istc; |
---|
1289 | } |
---|
1290 | } |
---|
1291 | |
---|
1292 | static void scInKbase( scfmon stc, int Nstc, int Nvar) |
---|
1293 | { |
---|
1294 | int Ivar, Istc, i, j; |
---|
1295 | scfmon sn; |
---|
1296 | Exponent_t x, ideg; |
---|
1297 | |
---|
1298 | if (Nvar == 1) |
---|
1299 | { |
---|
1300 | ideg = scMin(Nstc, stc, 1); |
---|
1301 | while (ideg > 0) |
---|
1302 | { |
---|
1303 | ideg--; |
---|
1304 | act[1] = ideg; |
---|
1305 | scElKbase(); |
---|
1306 | } |
---|
1307 | return; |
---|
1308 | } |
---|
1309 | Ivar = Nvar-1; |
---|
1310 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
1311 | x = scRestrict(Nstc, sn, Nvar); |
---|
1312 | if (x == 0) return; |
---|
1313 | ideg = x-1; |
---|
1314 | loop |
---|
1315 | { |
---|
1316 | x = scMax(Nstc, sn, Nvar); |
---|
1317 | while (ideg >= x) |
---|
1318 | { |
---|
1319 | act[Nvar] = ideg; |
---|
1320 | scInKbase(sn, Nstc, Ivar); |
---|
1321 | ideg--; |
---|
1322 | } |
---|
1323 | if (ideg < 0) return; |
---|
1324 | Istc = Nstc; |
---|
1325 | for (i=Nstc-1; i>=0; i--) |
---|
1326 | { |
---|
1327 | if (ideg < sn[i][Nvar]) |
---|
1328 | { |
---|
1329 | Istc--; |
---|
1330 | sn[i] = NULL; |
---|
1331 | } |
---|
1332 | } |
---|
1333 | j = 0; |
---|
1334 | while (sn[j]) j++; |
---|
1335 | i = j+1; |
---|
1336 | for (; i<Nstc; i++) |
---|
1337 | { |
---|
1338 | if (sn[i]) |
---|
1339 | { |
---|
1340 | sn[j] = sn[i]; |
---|
1341 | j++; |
---|
1342 | } |
---|
1343 | } |
---|
1344 | Nstc = Istc; |
---|
1345 | } |
---|
1346 | } |
---|
1347 | |
---|
1348 | static ideal scIdKbase() |
---|
1349 | { |
---|
1350 | polyset mm; |
---|
1351 | ideal res; |
---|
1352 | poly p, q = last; |
---|
1353 | int i = pLength(q); |
---|
1354 | res = idInit(i,1); |
---|
1355 | mm = res->m; |
---|
1356 | i = 0; |
---|
1357 | do |
---|
1358 | { |
---|
1359 | mm[i] = q; |
---|
1360 | i++; |
---|
1361 | p = pNext(q); |
---|
1362 | pNext(q) = NULL; |
---|
1363 | q = p; |
---|
1364 | } while (q!=NULL); |
---|
1365 | return res; |
---|
1366 | } |
---|
1367 | |
---|
1368 | extern ideal scKBase(int deg, ideal s, ideal Q) |
---|
1369 | { |
---|
1370 | int i, di; |
---|
1371 | poly p; |
---|
1372 | |
---|
1373 | if (deg < 0) |
---|
1374 | { |
---|
1375 | di = scDimInt(s, Q); |
---|
1376 | if (di != 0) |
---|
1377 | { |
---|
1378 | //Werror("KBase not finite"); |
---|
1379 | return idInit(1,s->rank); |
---|
1380 | } |
---|
1381 | } |
---|
1382 | stcmem = hCreate(pVariables - 1); |
---|
1383 | hexist = hInit(s, Q, &hNexist); |
---|
1384 | p = last = pInit(); |
---|
1385 | /*pNext(p) = NULL;*/ |
---|
1386 | act = (scmon)Alloc((pVariables + 1) * sizeof(Exponent_t)); |
---|
1387 | *act = 0; |
---|
1388 | if (!hNexist) |
---|
1389 | { |
---|
1390 | scAll(pVariables, deg); |
---|
1391 | goto ende; |
---|
1392 | } |
---|
1393 | if (!hisModule) |
---|
1394 | { |
---|
1395 | if (deg < 0) scInKbase(hexist, hNexist, pVariables); |
---|
1396 | else scDegKbase(hexist, hNexist, pVariables, deg); |
---|
1397 | } |
---|
1398 | else |
---|
1399 | { |
---|
1400 | hstc = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
1401 | for (i = 1; i <= hisModule; i++) |
---|
1402 | { |
---|
1403 | *act = i; |
---|
1404 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
1405 | if (hNstc) |
---|
1406 | { |
---|
1407 | if (deg < 0) scInKbase(hstc, hNstc, pVariables); |
---|
1408 | else scDegKbase(hstc, hNstc, pVariables, deg); |
---|
1409 | } |
---|
1410 | else |
---|
1411 | scAll(pVariables, deg); |
---|
1412 | } |
---|
1413 | Free((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
1414 | } |
---|
1415 | ende: |
---|
1416 | hDelete(hexist, hNexist); |
---|
1417 | Free((ADDRESS)act, (pVariables + 1) * sizeof(Exponent_t)); |
---|
1418 | hKill(stcmem, pVariables - 1); |
---|
1419 | pDelete1(&p); |
---|
1420 | if (p == NULL) |
---|
1421 | return idInit(1,s->rank); |
---|
1422 | else |
---|
1423 | { |
---|
1424 | last = p; |
---|
1425 | ideal res=scIdKbase(); |
---|
1426 | res->rank=s->rank; |
---|
1427 | return res; |
---|
1428 | } |
---|
1429 | } |
---|
1430 | |
---|
1431 | |
---|