1 | #include <kernel/polys.h> |
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2 | #include <kernel/kstd1.h> |
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3 | #include <libpolys/coeffs/longrat.h> |
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4 | #include <libpolys/polys/clapsing.h> |
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5 | #include <bbcone.h> |
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6 | |
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7 | |
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8 | poly initial(poly p) |
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9 | { |
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10 | poly g = p; |
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11 | poly h = p_Head(g,currRing); |
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12 | poly f = h; |
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13 | long d = p_Deg(g,currRing); |
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14 | pIter(g); |
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15 | while ((g != NULL) && (p_Deg(g,currRing) == d)) |
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16 | { |
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17 | pNext(h) = p_Head(g,currRing); |
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18 | pIter(h); |
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19 | pIter(g); |
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20 | } |
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21 | return(f); |
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22 | } |
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23 | |
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24 | |
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25 | BOOLEAN initial(leftv res, leftv args) |
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26 | { |
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27 | leftv u = args; |
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28 | if ((u != NULL) && (u->Typ() == POLY_CMD)) |
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29 | { |
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30 | leftv v = u->next; |
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31 | if (v == NULL) |
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32 | { |
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33 | poly p = (poly) u->Data(); |
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34 | res->rtyp = POLY_CMD; |
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35 | res->data = (void*) initial(p); |
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36 | return FALSE; |
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37 | } |
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38 | } |
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39 | if ((u != NULL) && (u->Typ() == IDEAL_CMD)) |
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40 | { |
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41 | leftv v = u->next; |
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42 | if (v == NULL) |
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43 | { |
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44 | ideal I = (ideal) u->Data(); |
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45 | ideal inI = idInit(IDELEMS(I)); |
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46 | for (int i=0; i<IDELEMS(I); i++) |
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47 | inI->m[i]=initial(I->m[i]); |
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48 | res->rtyp = IDEAL_CMD; |
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49 | res->data = (void*) inI; |
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50 | return FALSE; |
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51 | } |
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52 | } |
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53 | WerrorS("initial: unexpected parameters"); |
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54 | return TRUE; |
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55 | } |
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56 | |
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57 | |
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58 | BOOLEAN homogeneitySpace(leftv res, leftv args) |
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59 | { |
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60 | leftv u = args; |
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61 | if ((u != NULL) && (u->Typ() == IDEAL_CMD)) |
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62 | { |
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63 | leftv v = u->next; |
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64 | if (v == NULL) |
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65 | { |
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66 | int n = currRing->N; |
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67 | ideal I = (ideal) u->Data(); |
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68 | poly g; |
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69 | int* leadexpv = (int*) omAlloc((n+1)*sizeof(int)); |
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70 | int* tailexpv = (int*) omAlloc((n+1)*sizeof(int)); |
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71 | gfan::ZVector leadexpw = gfan::ZVector(n); |
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72 | gfan::ZVector tailexpw = gfan::ZVector(n); |
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73 | gfan::ZMatrix equations = gfan::ZMatrix(0,n); |
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74 | for (int i=0; i<IDELEMS(I); i++) |
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75 | { |
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76 | g = (poly) I->m[i]; pGetExpV(g,leadexpv); |
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77 | leadexpw = intStar2ZVector(n, leadexpv); |
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78 | pIter(g); |
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79 | while (g != NULL) |
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80 | { |
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81 | pGetExpV(g,tailexpv); |
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82 | tailexpw = intStar2ZVector(n, tailexpv); |
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83 | equations.appendRow(leadexpw-tailexpw); |
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84 | pIter(g); |
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85 | } |
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86 | } |
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87 | gfan::ZCone* gCone = new gfan::ZCone(gfan::ZMatrix(0, equations.getWidth()),equations); |
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88 | omFreeSize(leadexpv,(n+1)*sizeof(int)); |
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89 | omFreeSize(tailexpv,(n+1)*sizeof(int)); |
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90 | |
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91 | res->rtyp = coneID; |
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92 | res->data = (void*) gCone; |
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93 | return FALSE; |
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94 | } |
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95 | } |
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96 | WerrorS("homogeneitySpace: unexpected parameters"); |
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97 | return TRUE; |
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98 | } |
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99 | |
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100 | |
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101 | BOOLEAN groebnerCone(leftv res, leftv args) |
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102 | { |
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103 | leftv u = args; |
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104 | if ((u != NULL) && (u->Typ() == IDEAL_CMD)) |
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105 | { |
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106 | leftv v = u->next; |
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107 | if (v == NULL) |
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108 | { |
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109 | int n = currRing->N; |
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110 | ideal I = (ideal) u->Data(); |
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111 | poly g = NULL; |
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112 | int* leadexpv = (int*) omAlloc((n+1)*sizeof(int)); |
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113 | int* tailexpv = (int*) omAlloc((n+1)*sizeof(int)); |
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114 | gfan::ZVector leadexpw = gfan::ZVector(n); |
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115 | gfan::ZVector tailexpw = gfan::ZVector(n); |
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116 | gfan::ZMatrix inequalities = gfan::ZMatrix(0,n); |
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117 | gfan::ZMatrix equations = gfan::ZMatrix(0,n); |
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118 | long d; |
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119 | for (int i=0; i<IDELEMS(I); i++) |
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120 | { |
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121 | g = (poly) I->m[i]; pGetExpV(g,leadexpv); |
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122 | leadexpw = intStar2ZVector(n, leadexpv); |
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123 | pIter(g); |
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124 | d = p_Deg(g,currRing); |
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125 | while ((g != NULL) && (p_Deg(g,currRing) == d)) |
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126 | { |
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127 | pGetExpV(g,tailexpv); |
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128 | tailexpw = intStar2ZVector(n, tailexpv); |
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129 | equations.appendRow(leadexpw-tailexpw); |
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130 | pIter(g); |
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131 | } |
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132 | |
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133 | if (g != NULL) |
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134 | { |
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135 | while (g != NULL) |
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136 | { |
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137 | pGetExpV(g,tailexpv); |
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138 | tailexpw = intStar2ZVector(n, tailexpv); |
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139 | inequalities.appendRow(leadexpw-tailexpw); |
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140 | pIter(g); |
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141 | } |
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142 | } |
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143 | } |
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144 | gfan::ZCone* gCone = new gfan::ZCone(inequalities,equations); |
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145 | omFreeSize(leadexpv,(n+1)*sizeof(int)); |
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146 | omFreeSize(tailexpv,(n+1)*sizeof(int)); |
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147 | |
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148 | res->rtyp = coneID; |
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149 | res->data = (void*) gCone; |
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150 | return FALSE; |
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151 | } |
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152 | } |
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153 | WerrorS("groebnerCone: unexpected parameters"); |
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154 | return TRUE; |
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155 | } |
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156 | |
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157 | |
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158 | gfan::ZCone* maximalGroebnerCone(const ring &r, const ideal &I) |
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159 | { |
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160 | int n = rVar(r); |
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161 | poly g = NULL; |
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162 | int* leadexpv = (int*) omAlloc((n+1)*sizeof(int)); |
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163 | int* tailexpv = (int*) omAlloc((n+1)*sizeof(int)); |
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164 | gfan::ZVector leadexpw = gfan::ZVector(n); |
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165 | gfan::ZVector tailexpw = gfan::ZVector(n); |
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166 | gfan::ZMatrix inequalities = gfan::ZMatrix(0,n); |
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167 | for (int i=0; i<IDELEMS(I); i++) |
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168 | { |
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169 | g = (poly) I->m[i]; pGetExpV(g,leadexpv); |
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170 | leadexpw = intStar2ZVector(n, leadexpv); |
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171 | pIter(g); |
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172 | while (g != NULL) |
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173 | { |
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174 | pGetExpV(g,tailexpv); |
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175 | tailexpw = intStar2ZVector(n, tailexpv); |
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176 | inequalities.appendRow(leadexpw-tailexpw); |
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177 | pIter(g); |
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178 | } |
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179 | } |
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180 | omFreeSize(leadexpv,(n+1)*sizeof(int)); |
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181 | omFreeSize(tailexpv,(n+1)*sizeof(int)); |
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182 | return new gfan::ZCone(inequalities,gfan::ZMatrix(0, inequalities.getWidth())); |
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183 | } |
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184 | |
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185 | |
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186 | BOOLEAN maximalGroebnerCone(leftv res, leftv args) |
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187 | { |
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188 | leftv u = args; |
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189 | if ((u != NULL) && (u->Typ() == IDEAL_CMD)) |
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190 | { |
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191 | leftv v = u->next; |
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192 | if (v == NULL) |
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193 | { |
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194 | ideal I = (ideal) u->Data(); |
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195 | res->rtyp = coneID; |
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196 | res->data = (void*) maximalGroebnerCone(currRing, I); |
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197 | return FALSE; |
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198 | } |
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199 | } |
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200 | WerrorS("maximalGroebnerCone: unexpected parameters"); |
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201 | return TRUE; |
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202 | } |
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203 | |
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204 | /*** |
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205 | * If 1, replaces all occuring t with prime p, |
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206 | * where theoretically feasable. |
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207 | * Also computes GCD over integers than |
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208 | * over univariate polynomials |
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209 | **/ |
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210 | #define T_TO_P 0 |
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211 | |
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212 | /*** |
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213 | * Suppose I=g_0,...,g_{n-1}. |
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214 | * This function uses bubble sort to sorts g_1,...,g_{n-1} |
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215 | * such that lm(g_1)>...>lm(g_{n-1}) |
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216 | **/ |
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217 | static inline void sortingLaterGenerators(ideal I) |
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218 | { |
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219 | poly cache; int i; int n=IDELEMS(I); int newn; |
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220 | do |
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221 | { |
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222 | newn=0; |
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223 | for (i=2; i<n; i++) |
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224 | { |
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225 | if (pLmCmp(I->m[i-1],I->m[i])<0) |
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226 | { |
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227 | cache=I->m[i-1]; |
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228 | I->m[i-1]=I->m[i]; |
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229 | I->m[i]=cache; |
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230 | newn = i; |
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231 | } |
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232 | } |
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233 | n=newn; |
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234 | } while(n); |
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235 | } |
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236 | |
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237 | |
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238 | /*** |
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239 | * replaces coefficients in g of lowest degree in t |
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240 | * divisible by p with a suitable power of t |
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241 | **/ |
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242 | static bool preduce(poly g, const number p) |
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243 | { |
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244 | // go along g and look for relevant terms. |
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245 | // monomials in x which have been checked are tracked in done. |
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246 | // because we assume the leading coefficient of g is 1, |
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247 | // the leading term does not need to be considered. |
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248 | poly done = p_LmInit(g,currRing); |
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249 | p_SetExp(done,1,0,currRing); p_SetCoeff(done,n_Init(1,currRing->cf),currRing); |
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250 | p_Setm(done,currRing); |
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251 | poly doneEnd = done; |
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252 | poly doneCache; |
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253 | number dnumber; long d; |
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254 | poly subst; number ppower; |
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255 | while(pNext(g)) |
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256 | { |
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257 | // check whether next term needs to be reduced: |
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258 | // first, check whether monomial in x has come up yet |
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259 | for (doneCache=done; doneCache; pIter(doneCache)) |
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260 | { |
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261 | if (p_LmDivisibleBy(doneCache,pNext(g),currRing)) |
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262 | break; |
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263 | } |
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264 | if (!doneCache) // if for loop did not terminate prematurely, |
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265 | // then the monomial in x is new |
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266 | { |
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267 | // second, check whether coefficient is divisible by p |
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268 | if (n_DivBy(p_GetCoeff(pNext(g),currRing->cf),p,currRing->cf)) |
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269 | { |
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270 | // reduce the term with respect to p-t: |
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271 | // divide coefficient by p, remove old term, |
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272 | // add t multiple of old term |
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273 | dnumber = n_Div(p_GetCoeff(pNext(g),currRing->cf),p,currRing->cf); |
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274 | d = n_Int(dnumber,currRing->cf); |
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275 | n_Delete(&dnumber,currRing->cf); |
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276 | if (!d) |
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277 | { |
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278 | p_Delete(&done,currRing); |
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279 | WerrorS("initialReduction: overflow in a t-exponent"); |
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280 | return true; |
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281 | } |
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282 | subst=p_LmInit(pNext(g),currRing); |
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283 | if (d>0) |
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284 | { |
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285 | p_AddExp(subst,1,d,currRing); |
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286 | p_SetCoeff(subst,n_Init(1,currRing->cf),currRing); |
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287 | } |
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288 | else |
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289 | { |
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290 | p_AddExp(subst,1,-d,currRing); |
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291 | p_SetCoeff(subst,n_Init(-1,currRing->cf),currRing); |
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292 | } |
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293 | p_Setm(subst,currRing); pTest(subst); |
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294 | pNext(g)=p_LmDeleteAndNext(pNext(g),currRing); |
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295 | pNext(g)=p_Add_q(pNext(g),subst,currRing); |
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296 | pTest(pNext(g)); |
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297 | } |
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298 | // either way, add monomial in x to done |
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299 | pNext(doneEnd)=p_LmInit(pNext(g),currRing); |
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300 | pIter(doneEnd); |
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301 | p_SetExp(doneEnd,1,0,currRing); |
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302 | p_SetCoeff(doneEnd,n_Init(1,currRing->cf),currRing); |
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303 | p_Setm(doneEnd,currRing); |
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304 | } |
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305 | pIter(g); |
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306 | } |
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307 | p_Delete(&done,currRing); |
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308 | return false; |
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309 | } |
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310 | |
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311 | |
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312 | #ifndef NDEBUG |
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313 | BOOLEAN preduce(leftv res, leftv args) |
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314 | { |
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315 | leftv u = args; |
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316 | if ((u != NULL) && (u->Typ() == POLY_CMD)) |
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317 | { |
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318 | poly g; bool b; |
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319 | number p = n_Init(3,currRing->cf); |
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320 | omUpdateInfo(); |
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321 | Print("usedBytes=%ld\n",om_Info.UsedBytes); |
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322 | g = (poly) u->CopyD(); |
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323 | b = preduce(g,p); |
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324 | p_Delete(&g,currRing); |
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325 | if (b) return TRUE; |
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326 | omUpdateInfo(); |
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327 | Print("usedBytes=%ld\n",om_Info.UsedBytes); |
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328 | n_Delete(&p,currRing->cf); |
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329 | res->rtyp = NONE; |
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330 | res->data = NULL; |
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331 | return FALSE; |
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332 | } |
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333 | return TRUE; |
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334 | } |
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335 | #endif //NDEBUG |
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336 | |
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337 | |
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338 | /*** |
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339 | * Returns the highest term in g with the matching x-monomial to m |
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340 | * or, if it does not exist, the NULL pointer |
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341 | **/ |
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342 | static poly highestMatchingX(poly g, const poly m) |
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343 | { |
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344 | pTest(g); pTest(m); |
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345 | poly xalpha=p_LmInit(m,currRing); |
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346 | |
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347 | // go along g and find the first term |
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348 | // with the same monomial in x as xalpha |
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349 | while (g) |
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350 | { |
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351 | p_SetExp(xalpha,1,p_GetExp(g,1,currRing),currRing); |
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352 | p_Setm(xalpha,currRing); |
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353 | if (p_LmEqual(g,xalpha,currRing)) |
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354 | break; |
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355 | pIter(g); |
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356 | } |
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357 | |
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358 | // gCache now either points at the wanted term |
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359 | // or is NULL |
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360 | p_Delete(&xalpha,currRing); |
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361 | pTest(g); |
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362 | return g; |
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363 | } |
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364 | |
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365 | |
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366 | /*** |
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367 | * Given g with lm(g)=t^\beta x^\alpha, returns g_\alpha |
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368 | **/ |
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369 | static poly powerSeriesCoeff(poly g) |
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370 | { |
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371 | // the first term obviously is part of our output |
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372 | // so we copy it... |
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373 | poly xalpha=p_LmInit(g,currRing); |
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374 | poly coeff=p_One(currRing); |
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375 | p_SetCoeff(coeff,n_Copy(p_GetCoeff(g,currRing),currRing->cf),currRing); |
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376 | p_SetExp(coeff,1,p_GetExp(g,1,currRing),currRing); |
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377 | p_Setm(coeff,currRing); |
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378 | |
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379 | // ..and proceed with the remaining terms, |
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380 | // appending the relevant terms to coeff via coeffCache |
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381 | poly coeffCache=coeff; |
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382 | pIter(g); |
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383 | while (g) |
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384 | { |
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385 | p_SetExp(xalpha,1,p_GetExp(g,1,currRing),currRing); |
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386 | p_Setm(xalpha,currRing); |
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387 | if (p_LmEqual(g,xalpha,currRing)) |
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388 | { |
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389 | pNext(coeffCache)=p_Init(currRing); |
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390 | pIter(coeffCache); |
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391 | p_SetCoeff(coeffCache,n_Copy(p_GetCoeff(g,currRing),currRing->cf),currRing); |
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392 | p_SetExp(coeffCache,1,p_GetExp(g,1,currRing),currRing); |
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393 | p_Setm(coeffCache,currRing); |
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394 | } |
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395 | pIter(g); |
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396 | } |
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397 | |
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398 | p_Delete(&xalpha,currRing); |
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399 | return coeff; |
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400 | } |
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401 | |
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402 | |
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403 | /*** |
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404 | * divides g by t^b knowing that each term of g |
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405 | * is divisible by t^b, i.e. no divisibility checks |
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406 | * needed |
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407 | **/ |
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408 | static void divideByT(poly g, const long b) |
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409 | { |
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410 | while (g) |
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411 | { |
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412 | p_SetExp(g,1,p_GetExp(g,1,currRing)-b,currRing); |
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413 | p_Setm(g,currRing); |
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414 | pIter(g); |
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415 | } |
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416 | } |
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417 | |
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418 | |
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419 | static void divideByGcd(poly &g) |
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420 | { |
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421 | // first determine all g_\alpha |
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422 | // as alpha runs over all exponent vectors |
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423 | // of monomials in x occuring in g |
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424 | |
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425 | // gAlpha will store all g_\alpha, |
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426 | // the first term will, for comparison purposes for now, |
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427 | // also keep their monomial in x. |
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428 | // we assume that the weight on the x are positive |
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429 | // so that the x won't make the monomial smaller |
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430 | ideal gAlphaFront = idInit(pLength(g)); |
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431 | gAlphaFront->m[0] = p_Head(g,currRing); |
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432 | p_SetExp(gAlphaFront->m[0],1,0,currRing); |
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433 | p_Setm(gAlphaFront->m[0],currRing); |
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434 | ideal gAlphaEnd = idInit(pLength(g)); |
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435 | gAlphaEnd->m[0] = gAlphaFront->m[0]; |
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436 | unsigned long gAlpha_sev[pLength(g)]; |
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437 | gAlpha_sev[0] = p_GetShortExpVector(g,currRing); |
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438 | long beta[pLength(g)]; |
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439 | beta[0] = p_GetExp(g,1,currRing); |
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440 | int count=0; |
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441 | |
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442 | poly current = pNext(g); unsigned long current_not_sev; |
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443 | int i; |
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444 | while (current) |
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445 | { |
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446 | // see whether the monomial in x of current already came up |
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447 | // since everything is homogeneous in x and the ordering is local in t, |
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448 | // this comes down to a divisibility test in two stages |
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449 | current_not_sev = ~p_GetShortExpVector(current,currRing); |
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450 | for(i=0; i<=count; i++) |
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451 | { |
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452 | // first stage using short exponent vectors |
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453 | // second stage a proper test |
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454 | if (p_LmShortDivisibleBy(gAlphaFront->m[i],gAlpha_sev[i],current,current_not_sev, currRing) |
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455 | && p_LmDivisibleBy(gAlphaFront->m[i],current,currRing)) |
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456 | { |
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457 | // if it already occured, add the term to the respective entry |
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458 | // without the x part |
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459 | pNext(gAlphaEnd->m[i])=p_Init(currRing); |
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460 | pIter(gAlphaEnd->m[i]); |
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461 | p_SetExp(gAlphaEnd->m[i],1,p_GetExp(current,1,currRing)-beta[i],currRing); |
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462 | p_SetCoeff(gAlphaEnd->m[i],n_Copy(p_GetCoeff(current,currRing),currRing->cf),currRing); |
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463 | p_Setm(gAlphaEnd->m[i],currRing); |
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464 | break; |
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465 | } |
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466 | } |
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467 | if (i>count) |
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468 | { |
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469 | // if it is new, create a new entry for the term |
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470 | // including the monomial in x |
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471 | count++; |
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472 | gAlphaFront->m[count] = p_Head(current,currRing); |
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473 | beta[count] = p_GetExp(current,1,currRing); |
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474 | gAlphaEnd->m[count] = gAlphaFront->m[count]; |
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475 | gAlpha_sev[count] = p_GetShortExpVector(current,currRing); |
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476 | } |
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477 | |
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478 | pIter(current); |
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479 | } |
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480 | |
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481 | if (count) |
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482 | { |
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483 | // now remove all the x in the leading terms |
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484 | // so that gAlpha only contais terms in t |
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485 | int j; long d; |
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486 | for (i=0; i<=count; i++) |
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487 | { |
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488 | for (j=2; j<=currRing->N; j++) |
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489 | p_SetExp(gAlphaFront->m[i],j,0,currRing); |
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490 | p_Setm(gAlphaFront->m[i],currRing); |
---|
491 | gAlphaEnd->m[i]=NULL; |
---|
492 | } |
---|
493 | |
---|
494 | // now compute the gcd over all g_\alpha |
---|
495 | // and set the input to null as they are deleted in the process |
---|
496 | poly gcd = singclap_gcd(gAlphaFront->m[0],gAlphaFront->m[1],currRing); |
---|
497 | gAlphaFront->m[0] = NULL; |
---|
498 | gAlphaFront->m[1] = NULL; |
---|
499 | for(i=2; i<=count; i++) |
---|
500 | { |
---|
501 | gcd = singclap_gcd(gcd,gAlphaFront->m[i],currRing); |
---|
502 | gAlphaFront->m[i] = NULL; |
---|
503 | } |
---|
504 | // divide g by the gcd |
---|
505 | poly h = singclap_pdivide(g,gcd,currRing); |
---|
506 | p_Delete(&gcd,currRing); |
---|
507 | p_Delete(&g,currRing); |
---|
508 | g = h; |
---|
509 | |
---|
510 | id_Delete(&gAlphaFront,currRing); |
---|
511 | id_Delete(&gAlphaEnd,currRing); |
---|
512 | } |
---|
513 | else |
---|
514 | { |
---|
515 | // if g contains only one monomial in x, |
---|
516 | // then we can get rid of all the higher t |
---|
517 | p_Delete(&g,currRing); |
---|
518 | g = gAlphaFront->m[0]; |
---|
519 | pIter(gAlphaFront->m[0]); |
---|
520 | pNext(g)=NULL; |
---|
521 | gAlphaEnd->m[0] = NULL; |
---|
522 | id_Delete(&gAlphaFront,currRing); |
---|
523 | id_Delete(&gAlphaEnd,currRing); |
---|
524 | } |
---|
525 | } |
---|
526 | |
---|
527 | |
---|
528 | /*** |
---|
529 | * 1. For each \alpha\in\NN^n, changes (c_\beta t^\beta + c_{\beta+1} t^{\beta+1} + ...) |
---|
530 | * to (c_\beta + c_{\beta+1}*p + ...) t^\beta |
---|
531 | * 2. Computes the gcd over all (c_\beta + c_{\beta+1}*p + ...) and divides g by it |
---|
532 | **/ |
---|
533 | static void simplify(poly g, const number p) |
---|
534 | { |
---|
535 | // go along g and look for relevant terms. |
---|
536 | // monomials in x which have been checked are tracked in done. |
---|
537 | poly done = p_LmInit(g,currRing); |
---|
538 | p_SetCoeff(done,n_Init(1,currRing->cf),currRing); |
---|
539 | p_Setm(done,currRing); |
---|
540 | poly doneEnd = done; |
---|
541 | poly doneCurrent; |
---|
542 | |
---|
543 | poly subst; number substCoeff, substCoeffCache; |
---|
544 | unsigned long d; |
---|
545 | |
---|
546 | poly gCurrent = g; |
---|
547 | while(pNext(gCurrent)) |
---|
548 | { |
---|
549 | // check whether next term needs to be reduced: |
---|
550 | // first, check whether monomial in x has come up yet |
---|
551 | for (doneCurrent=done; doneCurrent; pIter(doneCurrent)) |
---|
552 | { |
---|
553 | if (p_LmDivisibleBy(doneCurrent,pNext(gCurrent),currRing)) |
---|
554 | break; |
---|
555 | } |
---|
556 | // if the monomial in x already occured, then we want to replace |
---|
557 | // as many t with p as theoretically feasable |
---|
558 | if (doneCurrent) |
---|
559 | { |
---|
560 | // suppose pNext(gCurrent)=3*t5x and doneCurrent=t3x |
---|
561 | // then we want to replace pNext(gCurrent) with 3p2*t3x |
---|
562 | // subst = ?*t3x |
---|
563 | subst = p_LmInit(doneCurrent,currRing); |
---|
564 | // substcoeff = p2 |
---|
565 | n_Power(p,p_GetExp(subst,1,currRing)-p_GetExp(doneCurrent,1,currRing),&substCoeff,currRing->cf); |
---|
566 | // substcoeff = 3p2 |
---|
567 | n_InpMult(substCoeff,p_GetCoeff(pNext(gCurrent),currRing),currRing->cf); |
---|
568 | // subst = 3p2*t3x |
---|
569 | p_SetCoeff(subst,substCoeff,currRing); |
---|
570 | p_Setm(subst,currRing); pTest(subst); |
---|
571 | |
---|
572 | // g = g - pNext(gCurrent) + subst |
---|
573 | pNext(gCurrent)=p_LmDeleteAndNext(pNext(gCurrent),currRing); |
---|
574 | g=p_Add_q(g,subst,currRing); |
---|
575 | pTest(pNext(gbeginning)); |
---|
576 | } |
---|
577 | else |
---|
578 | { |
---|
579 | // if the monomial in x is brand new, |
---|
580 | // then we check whether the coefficient is divisible by p |
---|
581 | if (n_DivBy(p_GetCoeff(pNext(gCurrent),currRing->cf),p,currRing->cf)) |
---|
582 | { |
---|
583 | // reduce the term with respect to p-t: |
---|
584 | // suppose pNext(gCurrent)=4p3*tx |
---|
585 | // then we want to replace it with 4*t4x |
---|
586 | // divide 4p3 repeatedly by p until it is not divisible anymore, |
---|
587 | // keeping track on the final value 4 |
---|
588 | // and the number of times it has been divided 3 |
---|
589 | substCoeff = n_Div(p_GetCoeff(pNext(gCurrent),currRing->cf),p,currRing->cf); |
---|
590 | d = 1; |
---|
591 | while (n_DivBy(substCoeff,p,currRing->cf)) |
---|
592 | { |
---|
593 | substCoeffCache = n_Div(p_GetCoeff(pNext(gCurrent),currRing->cf),p,currRing->cf); |
---|
594 | n_Delete(&substCoeff,currRing->cf); |
---|
595 | substCoeff = substCoeffCache; |
---|
596 | d++; |
---|
597 | assume(d>0); // check for overflow |
---|
598 | } |
---|
599 | |
---|
600 | // subst = ?*tx |
---|
601 | subst=p_LmInit(pNext(gCurrent),currRing); |
---|
602 | // subst = ?*t4x |
---|
603 | p_AddExp(subst,1,d,currRing); |
---|
604 | // subst = 4*t4x |
---|
605 | p_SetCoeff(subst,substCoeffCache,currRing); |
---|
606 | p_Setm(subst,currRing); pTest(subst); |
---|
607 | |
---|
608 | // g = g - pNext(gCurrent) + subst |
---|
609 | pNext(gCurrent)=p_LmDeleteAndNext(pNext(gCurrent),currRing); |
---|
610 | pNext(gCurrent)=p_Add_q(pNext(gCurrent),subst,currRing); |
---|
611 | pTest(pNext(gCurrent)); |
---|
612 | } |
---|
613 | |
---|
614 | // either way, add monomial in x with minimal t to done |
---|
615 | pNext(doneEnd)=p_LmInit(pNext(gCurrent),currRing); |
---|
616 | pIter(doneEnd); |
---|
617 | p_SetCoeff(doneEnd,n_Init(1,currRing->cf),currRing); |
---|
618 | p_Setm(doneEnd,currRing); |
---|
619 | } |
---|
620 | pIter(gCurrent); |
---|
621 | } |
---|
622 | p_Delete(&done,currRing); |
---|
623 | } |
---|
624 | |
---|
625 | |
---|
626 | #ifndef NDEBUG |
---|
627 | BOOLEAN divideByGcd(leftv res, leftv args) |
---|
628 | { |
---|
629 | leftv u = args; |
---|
630 | if ((u != NULL) && (u->Typ() == POLY_CMD)) |
---|
631 | { |
---|
632 | poly g; |
---|
633 | omUpdateInfo(); |
---|
634 | Print("usedBytes1=%ld\n",om_Info.UsedBytes); |
---|
635 | g = (poly) u->CopyD(); |
---|
636 | divideByGcd(g); |
---|
637 | p_Delete(&g,currRing); |
---|
638 | omUpdateInfo(); |
---|
639 | Print("usedBytes1=%ld\n",om_Info.UsedBytes); |
---|
640 | res->rtyp = NONE; |
---|
641 | res->data = NULL; |
---|
642 | return FALSE; |
---|
643 | } |
---|
644 | return TRUE; |
---|
645 | } |
---|
646 | #endif //NDEBUG |
---|
647 | |
---|
648 | |
---|
649 | BOOLEAN initialReduction(leftv res, leftv args) |
---|
650 | { |
---|
651 | leftv u = args; |
---|
652 | if ((u != NULL) && (u->Typ() == IDEAL_CMD)) |
---|
653 | { |
---|
654 | leftv v = u->next; |
---|
655 | if (v == NULL) |
---|
656 | { |
---|
657 | ideal I = (ideal) u->Data(); |
---|
658 | |
---|
659 | /*** |
---|
660 | * Suppose I=g_0,...,g_n and g_0=p-t. |
---|
661 | * Step 1: sort elements g_1,...,g_{n-1} such that lm(g_1)>...>lm(g_{n-1}) |
---|
662 | * (the following algorithm is a bubble sort) |
---|
663 | **/ |
---|
664 | sortingLaterGenerators(I); |
---|
665 | |
---|
666 | /*** |
---|
667 | * Step 2: replace coefficient of terms of lowest t-degree divisible by p with t |
---|
668 | **/ |
---|
669 | number p = p_GetCoeff(I->m[0],currRing); |
---|
670 | for (int i=1; i<IDELEMS(I); i++) |
---|
671 | { |
---|
672 | if (preduce(I->m[i],p)) |
---|
673 | return TRUE; |
---|
674 | } |
---|
675 | |
---|
676 | /*** |
---|
677 | * Step 3: the first pass. removing terms with the same monomials in x as lt(g_i) |
---|
678 | * out of g_j for i<j |
---|
679 | **/ |
---|
680 | int i,j; |
---|
681 | poly uniti, unitj; |
---|
682 | for (i=1; i<IDELEMS(I)-1; i++) |
---|
683 | { |
---|
684 | for (j=i+1; j<IDELEMS(I); j++) |
---|
685 | { |
---|
686 | unitj = highestMatchingX(I->m[j],I->m[i]); |
---|
687 | if (unitj) |
---|
688 | { |
---|
689 | unitj = powerSeriesCoeff(unitj); |
---|
690 | divideByT(unitj,p_GetExp(I->m[i],1,currRing)); |
---|
691 | uniti = powerSeriesCoeff(I->m[i]); |
---|
692 | divideByT(uniti,p_GetExp(I->m[i],1,currRing)); |
---|
693 | pTest(unitj); pTest(uniti); pTest(I->m[j]); pTest(I->m[i]); |
---|
694 | I->m[j]=p_Add_q(p_Mult_q(uniti,I->m[j],currRing), |
---|
695 | p_Neg(p_Mult_q(unitj,p_Copy(I->m[i],currRing),currRing),currRing), |
---|
696 | currRing); |
---|
697 | divideByGcd(I->m[j]); |
---|
698 | } |
---|
699 | } |
---|
700 | } |
---|
701 | for (int i=1; i<IDELEMS(I); i++) |
---|
702 | { |
---|
703 | if (preduce(I->m[i],p)) |
---|
704 | return TRUE; |
---|
705 | } |
---|
706 | |
---|
707 | /*** |
---|
708 | * Step 4: the second pass. removing terms divisible by lt(g_j) out of g_i for i<j |
---|
709 | **/ |
---|
710 | for (i=1; i<IDELEMS(I)-1; i++) |
---|
711 | { |
---|
712 | for (j=i+1; j<IDELEMS(I); j++) |
---|
713 | { |
---|
714 | uniti = highestMatchingX(I->m[i],I->m[j]); |
---|
715 | if (uniti && p_GetExp(uniti,1,currRing)>=p_GetExp(I->m[j],1,currRing)) |
---|
716 | { |
---|
717 | uniti = powerSeriesCoeff(uniti); |
---|
718 | divideByT(uniti,p_GetExp(I->m[j],1,currRing)); |
---|
719 | unitj = powerSeriesCoeff(I->m[j]); |
---|
720 | divideByT(unitj,p_GetExp(I->m[j],1,currRing)); |
---|
721 | I->m[i] = p_Add_q(p_Mult_q(unitj,I->m[i],currRing), |
---|
722 | p_Neg(p_Mult_q(uniti,p_Copy(I->m[j],currRing),currRing),currRing), |
---|
723 | currRing); |
---|
724 | divideByGcd(I->m[j]); |
---|
725 | } |
---|
726 | } |
---|
727 | } |
---|
728 | for (int i=1; i<IDELEMS(I); i++) |
---|
729 | { |
---|
730 | if (preduce(I->m[i],p)) |
---|
731 | return TRUE; |
---|
732 | } |
---|
733 | |
---|
734 | res->rtyp = NONE; |
---|
735 | res->data = NULL; |
---|
736 | IDDATA((idhdl)u->data) = (char*) I; |
---|
737 | return FALSE; |
---|
738 | } |
---|
739 | } |
---|
740 | WerrorS("initialReduction: unexpected parameters"); |
---|
741 | return TRUE; |
---|
742 | } |
---|
743 | |
---|
744 | |
---|
745 | #if 0 |
---|
746 | /*** |
---|
747 | * Given a general ring r with any ordering, |
---|
748 | * changes the ordering to a(v),ws(-w) |
---|
749 | **/ |
---|
750 | bool changetoAWSRing(ring r, gfan::ZVector v, gfan::ZVector w) |
---|
751 | { |
---|
752 | omFree(r->order); |
---|
753 | r->order = (int*) omAlloc0(4*sizeof(int)); |
---|
754 | omFree(r->block0); |
---|
755 | r->block0 = (int*) omAlloc0(4*sizeof(int)); |
---|
756 | omFree(r->block1); |
---|
757 | r->block1 = (int*) omAlloc0(4*sizeof(int)); |
---|
758 | for (int i=0; r->wvhdl[i]; i++) |
---|
759 | { omFree(r->wvhdl[i]); } |
---|
760 | omFree(r->wvhdl); |
---|
761 | r->wvhdl = (int**) omAlloc0(4*sizeof(int*)); |
---|
762 | |
---|
763 | bool ok = false; |
---|
764 | r->order[0] = ringorder_a; |
---|
765 | r->block0[0] = 1; |
---|
766 | r->block1[0] = r->N; |
---|
767 | r->wvhdl[0] = ZVectorToIntStar(v,ok); |
---|
768 | r->order[1] = ringorder_ws; |
---|
769 | r->block0[1] = 1; |
---|
770 | r->block1[1] = r->N; |
---|
771 | r->wvhdl[1] = ZVectorToIntStar(w,ok); |
---|
772 | r->order[2]=ringorder_C; |
---|
773 | return ok; |
---|
774 | } |
---|
775 | |
---|
776 | |
---|
777 | /*** |
---|
778 | * Given a ring with ordering a(v'),ws(w'), |
---|
779 | * changes the weights to v,w |
---|
780 | **/ |
---|
781 | bool changeAWSWeights(ring r, gfan::ZVector v, gfan::ZVector w) |
---|
782 | { |
---|
783 | omFree(r->wvhdl[0]); |
---|
784 | omFree(r->wvhdl[1]); |
---|
785 | bool ok = false; |
---|
786 | r->wvhdl[0] = ZVectorToIntStar(v,ok); |
---|
787 | r->wvhdl[1] = ZVectorToIntStar(w,ok); |
---|
788 | return ok; |
---|
789 | } |
---|
790 | |
---|
791 | |
---|
792 | // /*** |
---|
793 | // * Creates an int* representing the transposition of the last two variables |
---|
794 | // **/ |
---|
795 | // static inline int* createPermutationVectorForSaturation(static const ring &r) |
---|
796 | // { |
---|
797 | // int* w = (int*) omAlloc0((rVar(r)+1)*sizeof(int)); |
---|
798 | // for (int i=1; i<=rVar(r)-2; i++) |
---|
799 | // w[i] = i; |
---|
800 | // w[rVar(r)-1] = rVar(r); |
---|
801 | // w[rVar(r)] = rVar(r)-1; |
---|
802 | // } |
---|
803 | |
---|
804 | |
---|
805 | /*** |
---|
806 | * Creates an int* representing the permutation |
---|
807 | * 1 -> 1, ..., i-1 -> i-1, i -> n, i+1 -> n-1, ... , n -> i |
---|
808 | **/ |
---|
809 | static inline int* createPermutationVectorForSaturation(const ring &r, const int i) |
---|
810 | { |
---|
811 | int* sigma = (int*) omAlloc0((rVar(r)+1)*sizeof(int)); |
---|
812 | int j; |
---|
813 | for (j=1; j<i; j++) |
---|
814 | sigma[j] = j; |
---|
815 | for (; j<=rVar(r); j++) |
---|
816 | sigma[j] = rVar(r)-j+i; |
---|
817 | return(sigma); |
---|
818 | } |
---|
819 | |
---|
820 | |
---|
821 | /*** |
---|
822 | * Changes the int* representing the permutation |
---|
823 | * 1 -> 1, ..., i -> i, i+1 -> n, i+2 -> n-1, ... , n -> i+1 |
---|
824 | * to an int* representing the permutation |
---|
825 | * 1 -> 1, ..., i-1 -> i-1, i -> n, i+1 -> n-1, ... , n -> i |
---|
826 | **/ |
---|
827 | static void changePermutationVectorForSaturation(int* sigma, const ring &r, const int i) |
---|
828 | { |
---|
829 | for (int j=i; j<rVar(r); j++) |
---|
830 | sigma[j] = rVar(r)-j+i; |
---|
831 | sigma[rVar(r)] = i; |
---|
832 | } |
---|
833 | |
---|
834 | |
---|
835 | /*** |
---|
836 | * returns a ring in which the weights of the ring variables are permuted |
---|
837 | * if handed over a poly in which the variables are permuted, this is basically |
---|
838 | * as good as permuting the variables of the ring itself. |
---|
839 | **/ |
---|
840 | static ring permuteWeighstOfRingVariables(const ring &r, const int* const sigma) |
---|
841 | { |
---|
842 | ring s = rCopy0(r); |
---|
843 | for (int j=0; j<rVar(r); j++) |
---|
844 | { |
---|
845 | s->wvhdl[0][j] = r->wvhdl[0][sigma[j+1]]; |
---|
846 | s->wvhdl[1][j] = r->wvhdl[1][sigma[j+1]]; |
---|
847 | } |
---|
848 | rComplete(s,1); |
---|
849 | return s; |
---|
850 | } |
---|
851 | |
---|
852 | |
---|
853 | /*** |
---|
854 | * creates a ring s that is a copy of r except with ordering wp(w) |
---|
855 | **/ |
---|
856 | static inline ring createInitialRingForSaturation(const ring &r, const gfan::ZVector &w, bool &ok) |
---|
857 | { |
---|
858 | assume(rVar(r) == (int) w.size()); |
---|
859 | |
---|
860 | ring s = rCopy0(r); int i; |
---|
861 | for (i=0; s->order[i]; i++) |
---|
862 | omFreeSize(s->wvhdl[i],rVar(r)*sizeof(int)); |
---|
863 | i++; |
---|
864 | omFreeSize(s->order,i*sizeof(int)); |
---|
865 | s->order = (int*) omAlloc0(3*sizeof(int)); |
---|
866 | omFreeSize(s->block0,i*sizeof(int)); |
---|
867 | s->block0 = (int*) omAlloc0(3*sizeof(int)); |
---|
868 | omFreeSize(s->block1,i*sizeof(int)); |
---|
869 | s->block1 = (int*) omAlloc0(3*sizeof(int)); |
---|
870 | omFreeSize(s->wvhdl,i*sizeof(int*)); |
---|
871 | s->wvhdl = (int**) omAlloc0(3*sizeof(int*)); |
---|
872 | |
---|
873 | s->order[0] = ringorder_wp; |
---|
874 | s->block0[0] = 1; |
---|
875 | s->block1[0] = rVar(r); |
---|
876 | s->wvhdl[0] = ZVectorToIntStar(w,ok); |
---|
877 | s->order[1]=ringorder_C; |
---|
878 | |
---|
879 | rComplete(s,1); |
---|
880 | return s; |
---|
881 | } |
---|
882 | |
---|
883 | |
---|
884 | /*** |
---|
885 | * Given an weighted homogeneous ideal I with respect to weight w |
---|
886 | * that in standard basis form with respect to the ordering ws(-w), |
---|
887 | * derives the standard basis of I:<x_n>^\infty |
---|
888 | * and returns a long k such that I:<x_n>^\infty=I:<x_n>^k |
---|
889 | **/ |
---|
890 | static long deriveStandardBasisOfSaturation(ideal &I, ring &r) |
---|
891 | { |
---|
892 | long k=0, l; poly current; |
---|
893 | for (int i=0; i<IDELEMS(I); i++) |
---|
894 | { |
---|
895 | current = I->m[i]; |
---|
896 | l = p_GetExp(current,rVar(r),r); |
---|
897 | if (k<l) k=l; |
---|
898 | while (current) |
---|
899 | { |
---|
900 | p_SubExp(current,rVar(r),l,r); p_Setm(current,r); |
---|
901 | pIter(current); |
---|
902 | } |
---|
903 | } |
---|
904 | return k; |
---|
905 | } |
---|
906 | |
---|
907 | |
---|
908 | /*** |
---|
909 | * Given a weighted homogeneous ideal I with respect to weight w |
---|
910 | * with constant first element, |
---|
911 | * returns NULL if I does not contain a monomial |
---|
912 | * otherwise returns the monomial contained in I |
---|
913 | **/ |
---|
914 | poly containsMonomial(const ideal &I, const gfan::ZVector &w) |
---|
915 | { |
---|
916 | assume(rField_is_Ring_Z(currRing)); |
---|
917 | |
---|
918 | // first we switch to the ground field currRing->cf / I->m[0] |
---|
919 | ring r = rCopy0(currRing); |
---|
920 | nKillChar(r->cf); |
---|
921 | r->cf = nInitChar(n_Zp,(void*)(long)n_Int(p_GetCoeff(I->m[0],currRing),currRing->cf)); |
---|
922 | rComplete(r); |
---|
923 | |
---|
924 | ideal J = id_Copy(I, currRing); poly cache; number temp; |
---|
925 | for (int i=0; i<IDELEMS(I); i++) |
---|
926 | { |
---|
927 | cache = J->m[i]; |
---|
928 | while (cache) |
---|
929 | { |
---|
930 | // TODO: temp = npMapGMP(p_GetCoeff(cache,currRing),currRing->cf,r->cf); |
---|
931 | p_SetCoeff(cache,temp,r); pIter(cache); |
---|
932 | } |
---|
933 | } |
---|
934 | |
---|
935 | |
---|
936 | J = kStd(J,NULL,isHomog,NULL); |
---|
937 | |
---|
938 | bool b = false; |
---|
939 | ring s = createInitialRingForSaturation(currRing, w, b); |
---|
940 | if (b) |
---|
941 | { |
---|
942 | WerrorS("containsMonomial: overflow in weight vector"); |
---|
943 | return NULL; |
---|
944 | } |
---|
945 | |
---|
946 | return NULL; |
---|
947 | } |
---|
948 | |
---|
949 | |
---|
950 | gfan::ZCone* startingCone(ideal I) |
---|
951 | { |
---|
952 | I = kStd(I,NULL,isNotHomog,NULL); |
---|
953 | gfan::ZCone* zc = maximalGroebnerCone(currRing,I); |
---|
954 | gfan::ZMatrix rays = zc->extremeRays(); |
---|
955 | gfan::ZVector v; |
---|
956 | for (int i=0; i<rays.getHeight(); i++) |
---|
957 | { |
---|
958 | v = rays[i]; |
---|
959 | } |
---|
960 | return zc; |
---|
961 | } |
---|
962 | #endif |
---|
963 | |
---|
964 | |
---|
965 | void tropical_setup(SModulFunctions* p) |
---|
966 | { |
---|
967 | p->iiAddCproc("","groebnerCone",FALSE,groebnerCone); |
---|
968 | p->iiAddCproc("","maximalGroebnerCone",FALSE,maximalGroebnerCone); |
---|
969 | p->iiAddCproc("","initial",FALSE,initial); |
---|
970 | #ifndef NDEBUG |
---|
971 | p->iiAddCproc("","divideByGcd",FALSE,divideByGcd); |
---|
972 | p->iiAddCproc("","preduce",FALSE,preduce); |
---|
973 | #endif //NDEBUG |
---|
974 | p->iiAddCproc("","initialReduction",FALSE,initialReduction); |
---|
975 | p->iiAddCproc("","homogeneitySpace",FALSE,homogeneitySpace); |
---|
976 | } |
---|