1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* |
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5 | * ABSTRACT: resolutions |
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6 | */ |
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7 | |
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8 | #include <kernel/GBEngine/syz.h> |
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9 | #include <omalloc/omalloc.h> |
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10 | #include <coeffs/numbers.h> |
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11 | #include <kernel/polys.h> |
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12 | #include <kernel/ideals.h> |
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13 | |
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14 | #include <vector> |
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15 | #include <map> |
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16 | |
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17 | #ifdef __GNUC__ |
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18 | #define likely(X) (__builtin_expect(X, 1)) |
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19 | #define unlikely(X) (__builtin_expect(X, 0)) |
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20 | #else |
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21 | #define likely(X) (X) |
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22 | #define unlikely(X) (X) |
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23 | #endif |
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24 | |
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25 | static inline void update_variables(std::vector<bool> &variables, |
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26 | const ideal L) |
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27 | { |
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28 | const ring R = currRing; |
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29 | const int l = IDELEMS(L)-1; |
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30 | int k; |
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31 | for (int j = R->N; j > 0; j--) { |
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32 | if (variables[j-1]) { |
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33 | for (k = l; k >= 0; k--) { |
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34 | if (p_GetExp(L->m[k], j, R) > 0) { |
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35 | break; |
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36 | } |
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37 | } |
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38 | if (k < 0) { // no break |
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39 | variables[j-1] = false; |
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40 | } |
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41 | } |
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42 | } |
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43 | } |
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44 | |
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45 | static inline bool check_variables(const std::vector<bool> &variables, |
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46 | const poly m) |
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47 | { |
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48 | const ring R = currRing; |
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49 | for (int j = R->N; j > 0; j--) { |
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50 | if (variables[j-1] && p_GetExp(m, j, R) > 0) { |
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51 | return true; |
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52 | } |
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53 | } |
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54 | return false; |
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55 | } |
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56 | |
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57 | typedef struct { |
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58 | poly lt; |
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59 | unsigned long sev; |
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60 | unsigned int comp; |
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61 | } lt_struct; |
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62 | |
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63 | typedef std::vector<lt_struct> lts_vector; |
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64 | typedef std::map<long, lts_vector> lts_hash; |
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65 | |
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66 | static void initialize_lts_hash(lts_hash &C, const ideal L) |
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67 | { |
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68 | const ring R = currRing; |
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69 | const unsigned int n_elems = IDELEMS(L); |
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70 | for (unsigned int k = 0; k < n_elems; k++) { |
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71 | const poly a = L->m[k]; |
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72 | C[p_GetComp(a, R)].push_back((lt_struct){a, p_GetShortExpVector(a, R), |
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73 | k}); |
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74 | } |
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75 | } |
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76 | |
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77 | #define delete_lts_hash(C) C->clear() |
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78 | |
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79 | poly FindReducer(const poly multiplier, const poly t, const lts_hash *m_div) |
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80 | { |
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81 | const ring r = currRing; |
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82 | lts_hash::const_iterator m_itr = m_div->find(p_GetComp(t, currRing)); |
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83 | if (m_itr == m_div->end()) { |
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84 | return NULL; |
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85 | } |
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86 | lts_vector::const_iterator m_current = (m_itr->second).begin(); |
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87 | lts_vector::const_iterator m_finish = (m_itr->second).end(); |
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88 | const poly q = p_New(r); |
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89 | pNext(q) = NULL; |
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90 | p_MemSum_LengthGeneral(q->exp, multiplier->exp, t->exp, r->ExpL_Size); |
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91 | const unsigned long m_not_sev = ~p_GetShortExpVector(q, r); |
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92 | for( ; m_current != m_finish; ++m_current) { |
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93 | if (m_current->sev & m_not_sev |
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94 | || unlikely(!(_p_LmDivisibleByNoComp(m_current->lt, q, r)))) { |
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95 | continue; |
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96 | } |
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97 | const poly p = m_current->lt; |
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98 | const int k = m_current->comp; |
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99 | p_MemAdd_NegWeightAdjust(q, r); |
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100 | p_ExpVectorDiff(q, q, p, r); // (LM(product) / LM(L[k])) |
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101 | p_SetComp(q, k + 1, r); |
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102 | p_Setm(q, r); |
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103 | number n = n_Mult(p_GetCoeff(multiplier, r), p_GetCoeff(t, r), r); |
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104 | p_SetCoeff0(q, n_InpNeg(n, r), r); |
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105 | return q; |
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106 | } |
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107 | p_LmFree(q, r); |
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108 | return NULL; |
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109 | } |
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110 | |
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111 | static poly TraverseTail_test(poly multiplier, const int tail, |
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112 | const ideal previous_module, const std::vector<bool> &variables, |
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113 | const lts_hash *m_div); |
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114 | |
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115 | static inline poly ReduceTerm_test(poly multiplier, poly term4reduction, |
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116 | const ideal previous_module, const std::vector<bool> &variables, |
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117 | const lts_hash *m_div) |
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118 | { |
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119 | const ring r = currRing; |
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120 | poly s = FindReducer(multiplier, term4reduction, m_div); |
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121 | if( s == NULL ) |
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122 | { |
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123 | return NULL; |
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124 | } |
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125 | const int c = p_GetComp(s, r) - 1; |
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126 | const poly t |
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127 | = TraverseTail_test(s, c, previous_module, variables, m_div); |
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128 | if( t != NULL ) |
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129 | s = p_Add_q(s, t, r); |
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130 | return s; |
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131 | } |
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132 | |
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133 | static poly ComputeImage_test(poly multiplier, const int t, |
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134 | const ideal previous_module, const std::vector<bool> &variables, |
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135 | const lts_hash *m_div) |
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136 | { |
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137 | const poly tail = previous_module->m[t]->next; |
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138 | if(tail != NULL) |
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139 | { |
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140 | if (!check_variables(variables, multiplier)) |
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141 | { |
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142 | return NULL; |
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143 | } |
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144 | sBucket_pt sum = sBucketCreate(currRing); |
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145 | for(poly p = tail; p != NULL; p = pNext(p)) // iterate over the tail |
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146 | { |
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147 | const poly rt = ReduceTerm_test(multiplier, p, previous_module, |
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148 | variables, m_div); |
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149 | sBucket_Add_p(sum, rt, pLength(rt)); |
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150 | } |
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151 | poly s; |
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152 | int l; |
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153 | sBucketClearAdd(sum, &s, &l); |
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154 | sBucketDestroy(&sum); |
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155 | return s; |
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156 | } |
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157 | return NULL; |
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158 | } |
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159 | |
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160 | #define CACHE 1 |
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161 | |
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162 | #if CACHE |
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163 | struct CCacheCompare_test |
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164 | { |
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165 | inline bool operator() (const poly& l, const poly& r) |
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166 | const |
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167 | { |
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168 | return (p_LmCmp(l, r, currRing) == -1); |
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169 | } |
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170 | }; |
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171 | |
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172 | typedef std::map<poly, poly, CCacheCompare_test> |
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173 | TP2PCache_test; |
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174 | typedef std::map<int, TP2PCache_test> TCache_test; |
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175 | |
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176 | static TCache_test m_cache_test; |
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177 | |
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178 | // note: we don't need to keep the coeffs of those terms which are lifted to 0 |
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179 | |
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180 | static void delete_cache() |
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181 | { |
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182 | for (TCache_test::iterator it = m_cache_test.begin(); |
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183 | it != m_cache_test.end(); it++) { |
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184 | TP2PCache_test& T = it->second; |
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185 | for (TP2PCache_test::iterator vit = T.begin(); vit != T.end(); vit++) { |
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186 | p_Delete((&(vit->second)), currRing); |
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187 | p_Delete(const_cast<poly*>(&(vit->first)), currRing); |
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188 | } |
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189 | T.clear(); |
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190 | } |
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191 | m_cache_test.clear(); |
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192 | } |
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193 | #endif // CACHE |
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194 | |
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195 | static poly TraverseTail_test(poly multiplier, const int tail, |
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196 | const ideal previous_module, const std::vector<bool> &variables, |
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197 | const lts_hash *m_div) |
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198 | { |
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199 | const ring& r = currRing; |
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200 | #if CACHE |
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201 | TCache_test::iterator top_itr = m_cache_test.find(tail); |
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202 | if ( top_itr != m_cache_test.end() ) |
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203 | { |
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204 | TP2PCache_test& T = top_itr->second; |
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205 | TP2PCache_test::iterator itr = T.find(multiplier); |
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206 | if( itr != T.end() ) |
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207 | { |
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208 | if( itr->second == NULL ) |
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209 | return (NULL); |
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210 | poly p = p_Copy(itr->second, r); |
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211 | if( !n_Equal( pGetCoeff(multiplier), pGetCoeff(itr->first), r) ) |
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212 | { |
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213 | number n = n_Div( pGetCoeff(multiplier), pGetCoeff(itr->first), r); |
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214 | p = p_Mult_nn(p, n, r); |
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215 | n_Delete(&n, r); |
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216 | } |
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217 | return p; |
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218 | } |
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219 | const poly p = ComputeImage_test(multiplier, tail, previous_module, |
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220 | variables, m_div); |
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221 | itr = T.find(multiplier); |
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222 | if( itr == T.end() ) |
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223 | { |
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224 | T.insert(TP2PCache_test::value_type(p_Head(multiplier, |
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225 | r), p) ); |
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226 | return p_Copy(p, r); |
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227 | } |
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228 | return p; |
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229 | } |
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230 | #endif // CACHE |
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231 | const poly p = ComputeImage_test(multiplier, tail, previous_module, |
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232 | variables, m_div); |
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233 | #if CACHE |
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234 | top_itr = m_cache_test.find(tail); |
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235 | if ( top_itr != m_cache_test.end() ) |
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236 | { |
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237 | TP2PCache_test& T = top_itr->second; |
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238 | TP2PCache_test::iterator itr = T.find(multiplier); |
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239 | if( itr == T.end() ) |
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240 | { |
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241 | T.insert(TP2PCache_test::value_type(p_Head(multiplier, |
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242 | r), p)); |
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243 | return p_Copy(p, r); |
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244 | } |
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245 | return p; |
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246 | } |
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247 | TP2PCache_test T; |
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248 | T.insert(TP2PCache_test::value_type(p_Head(multiplier, r), |
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249 | p)); |
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250 | m_cache_test.insert( TCache_test::value_type(tail, T) ); |
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251 | return p_Copy(p, r); |
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252 | #else |
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253 | return p; |
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254 | #endif // CACHE |
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255 | } |
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256 | |
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257 | static poly lift_ext_LT(const poly a, const ideal previous_module, |
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258 | const std::vector<bool> &variables, const lts_hash *m_div) |
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259 | { |
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260 | const ring R = currRing; |
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261 | poly t1 = ComputeImage_test(a, p_GetComp(a, R)-1, |
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262 | previous_module, variables, m_div); |
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263 | poly t2 = TraverseTail_test(a->next, p_GetComp(a->next, R)-1, |
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264 | previous_module, variables, m_div); |
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265 | t1 = p_Add_q(t1, t2, R); |
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266 | return t1; |
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267 | } |
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268 | |
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269 | /*****************************************************************************/ |
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270 | |
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271 | typedef poly syzHeadFunction(ideal, int, int); |
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272 | |
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273 | static poly syzHeadFrame(const ideal G, const int i, const int j) |
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274 | { |
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275 | const ring r = currRing; |
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276 | const poly f_i = G->m[i]; |
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277 | const poly f_j = G->m[j]; |
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278 | poly head = p_Init(r); |
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279 | pSetCoeff0(head, n_Init(1, r->cf)); |
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280 | long exp_i, exp_j, lcm; |
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281 | for (int k = (int)r->N; k > 0; k--) { |
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282 | exp_i = p_GetExp(f_i, k, r); |
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283 | exp_j = p_GetExp(f_j, k, r); |
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284 | lcm = si_max(exp_i, exp_j); |
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285 | p_SetExp(head, k, lcm-exp_i, r); |
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286 | } |
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287 | p_SetComp(head, i+1, r); |
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288 | p_Setm(head, r); |
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289 | return head; |
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290 | } |
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291 | |
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292 | static poly syzHeadExtFrame(const ideal G, const int i, const int j) |
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293 | { |
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294 | const ring r = currRing; |
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295 | const poly f_i = G->m[i]; |
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296 | const poly f_j = G->m[j]; |
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297 | poly head = p_Init(r); |
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298 | pSetCoeff0(head, n_Init(1, r->cf)); |
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299 | poly head_ext = p_Init(r); |
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300 | pSetCoeff0(head_ext, n_InpNeg(n_Div(pGetCoeff(f_j), pGetCoeff(f_i), r->cf), |
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301 | r->cf)); |
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302 | long exp_i, exp_j, lcm; |
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303 | for (int k = (int)r->N; k > 0; k--) { |
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304 | exp_i = p_GetExp(f_i, k, r); |
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305 | exp_j = p_GetExp(f_j, k, r); |
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306 | lcm = si_max(exp_i, exp_j); |
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307 | p_SetExp(head, k, lcm-exp_i, r); |
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308 | p_SetExp(head_ext, k, lcm-exp_j, r); |
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309 | } |
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310 | p_SetComp(head, i+1, r); |
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311 | p_Setm(head, r); |
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312 | p_SetComp(head_ext, j+1, r); |
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313 | p_Setm(head_ext, r); |
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314 | head->next = head_ext; |
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315 | return head; |
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316 | } |
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317 | |
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318 | typedef ideal syzM_i_Function(ideal, int, syzHeadFunction); |
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319 | |
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320 | static ideal syzM_i_unsorted(const ideal G, const int i, |
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321 | syzHeadFunction *syzHead) |
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322 | { |
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323 | ideal M_i = NULL; |
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324 | int comp = pGetComp(G->m[i]); |
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325 | int ncols = 0; |
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326 | for (int j = i-1; j >= 0; j--) { |
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327 | if (pGetComp(G->m[j]) == comp) ncols++; |
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328 | } |
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329 | if (ncols > 0) { |
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330 | M_i = idInit(ncols, G->ncols); |
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331 | int k = ncols-1; |
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332 | for (int j = i-1; j >= 0; j--) { |
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333 | if (pGetComp(G->m[j]) == comp) { |
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334 | M_i->m[k] = syzHead(G, i, j); |
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335 | k--; |
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336 | } |
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337 | } |
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338 | id_DelDiv(M_i, currRing); |
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339 | idSkipZeroes(M_i); |
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340 | } |
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341 | return M_i; |
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342 | } |
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343 | |
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344 | static ideal syzM_i_sorted(const ideal G, const int i, |
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345 | syzHeadFunction *syzHead) |
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346 | { |
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347 | ideal M_i = NULL; |
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348 | int comp = pGetComp(G->m[i]); |
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349 | int index = i-1; |
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350 | while (pGetComp(G->m[index]) == comp) index--; |
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351 | index++; |
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352 | int ncols = i-index; |
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353 | if (ncols > 0) { |
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354 | M_i = idInit(ncols, G->ncols); |
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355 | for (int j = ncols-1; j >= 0; j--) { |
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356 | M_i->m[j] = syzHead(G, i, j+index); |
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357 | } |
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358 | id_DelDiv(M_i, currRing); |
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359 | idSkipZeroes(M_i); |
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360 | } |
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361 | return M_i; |
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362 | } |
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363 | |
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364 | static ideal idConcat(const ideal* M, const int size, const int rank) |
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365 | { |
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366 | int ncols = 0; |
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367 | for (int i = size-1; i >= 0; i--) { |
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368 | if (M[i] != NULL) { |
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369 | ncols += M[i]->ncols; |
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370 | } |
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371 | } |
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372 | if (ncols == 0) return idInit(1, rank); |
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373 | ideal result = idInit(ncols, rank); |
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374 | int k = ncols-1; |
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375 | for (int i = size-1; i >= 0; i--) { |
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376 | if (M[i] != NULL) { |
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377 | for (int j = M[i]->ncols-1; j >= 0; j--) { |
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378 | result->m[k] = M[i]->m[j]; |
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379 | k--; |
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380 | } |
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381 | } |
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382 | } |
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383 | return result; |
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384 | } |
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385 | |
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386 | #define SORT_MI 1 |
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387 | |
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388 | #if SORT_MI |
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389 | static int compare_Mi(const void* a, const void *b) |
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390 | { |
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391 | const ring r = currRing; |
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392 | poly p_a = *((poly *)a); |
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393 | poly p_b = *((poly *)b); |
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394 | int cmp; |
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395 | int deg_a = p_Deg(p_a, r); |
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396 | int deg_b = p_Deg(p_b, r); |
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397 | cmp = (deg_a > deg_b) - (deg_a < deg_b); |
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398 | if (cmp != 0) { |
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399 | return cmp; |
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400 | } |
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401 | int comp_a = p_GetComp(p_a, r); |
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402 | int comp_b = p_GetComp(p_b, r); |
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403 | cmp = (comp_a > comp_b) - (comp_a < comp_b); |
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404 | if (cmp != 0) { |
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405 | return cmp; |
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406 | } |
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407 | int exp_a[r->N+1]; |
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408 | int exp_b[r->N+1]; |
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409 | p_GetExpV(p_a, exp_a, r); |
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410 | p_GetExpV(p_b, exp_b, r); |
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411 | for (int i = r->N; i > 0; i--) { |
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412 | cmp = (exp_a[i] > exp_b[i]) - (exp_a[i] < exp_b[i]); |
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413 | if (cmp != 0) { |
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414 | return cmp; |
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415 | } |
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416 | } |
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417 | return 0; |
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418 | } |
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419 | #endif // SORT_MI |
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420 | |
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421 | static ideal computeFrame(const ideal G, syzM_i_Function syzM_i, |
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422 | syzHeadFunction *syzHead) |
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423 | { |
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424 | ideal* M = (ideal *)omalloc((G->ncols-1)*sizeof(ideal)); |
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425 | for (int i = G->ncols-2; i >= 0; i--) { |
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426 | M[i] = syzM_i(G, i+1, syzHead); |
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427 | } |
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428 | ideal frame = idConcat(M, G->ncols-1, G->ncols); |
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429 | for (int i = G->ncols-2; i >= 0; i--) { |
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430 | if (M[i] != NULL) { |
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431 | omFreeSize(M[i]->m, IDELEMS(M[i])*sizeof(poly)); |
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432 | omFreeBin(M[i], sip_sideal_bin); |
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433 | } |
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434 | } |
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435 | omFree(M); |
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436 | #if SORT_MI |
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437 | qsort(frame->m, IDELEMS(frame), sizeof(poly), compare_Mi); |
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438 | #endif |
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439 | return frame; |
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440 | } |
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441 | |
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442 | static void computeLiftings(const resolvente res, const int index, |
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443 | std::vector<bool> &variables) |
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444 | { |
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445 | if (index > 1) { // we don't know if the input is a reduced SB |
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446 | update_variables(variables, res[index-1]); |
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447 | } |
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448 | lts_hash *hash_previous_module = new lts_hash(); |
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449 | initialize_lts_hash(*hash_previous_module, res[index-1]); |
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450 | for (int j = res[index]->ncols-1; j >= 0; j--) { |
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451 | res[index]->m[j]->next->next = lift_ext_LT(res[index]->m[j], |
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452 | res[index-1], variables, hash_previous_module); |
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453 | } |
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454 | delete_lts_hash(hash_previous_module); |
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455 | delete(hash_previous_module); |
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456 | #if CACHE |
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457 | delete_cache(); |
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458 | #endif // CACHE |
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459 | } |
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460 | |
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461 | static int computeResolution(resolvente &res, const int length, |
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462 | syzHeadFunction *syzHead) |
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463 | { |
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464 | int max_index = length-1; |
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465 | int index = 0; |
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466 | if (!idIs0(res[index]) && index < max_index) { |
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467 | index++; |
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468 | res[index] = computeFrame(res[index-1], syzM_i_unsorted, syzHead); |
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469 | std::vector<bool> variables; |
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470 | variables.resize(currRing->N, true); |
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471 | while (!idIs0(res[index])) { |
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472 | #if 1 |
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473 | computeLiftings(res, index, variables); |
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474 | #endif // LIFT |
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475 | if (index < max_index) { |
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476 | index++; |
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477 | res[index] = computeFrame(res[index-1], syzM_i_sorted, |
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478 | syzHead); |
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479 | } |
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480 | else { |
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481 | break; |
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482 | } |
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483 | } |
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484 | variables.clear(); |
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485 | } |
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486 | max_index = index+1; |
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487 | if (max_index < length) { |
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488 | res = (resolvente)omReallocSize(res, (length+1)*sizeof(ideal), |
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489 | (max_index+1)*sizeof(ideal)); |
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490 | } |
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491 | return max_index; |
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492 | } |
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493 | |
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494 | #define insert_first_term(r, p, q, R) \ |
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495 | do \ |
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496 | { \ |
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497 | p = r; \ |
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498 | q = p->next; \ |
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499 | if (q != NULL && p_LmCmp(p, q, R) != 1) { \ |
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500 | while (q->next != NULL && p_LmCmp(p, q->next, R) == -1) { \ |
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501 | pIter(q); \ |
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502 | } \ |
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503 | r = p->next; \ |
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504 | p->next = q->next; \ |
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505 | q->next = p; \ |
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506 | } \ |
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507 | } \ |
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508 | while (0) |
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509 | |
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510 | static void insert_ext_induced_LTs(const resolvente res, const int length) |
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511 | { |
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512 | const ring R = currRing; |
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513 | poly p, q; |
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514 | for (int i = length-2; i > 0; i--) { |
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515 | for (int j = res[i]->ncols-1; j >= 0; j--) { |
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516 | insert_first_term(res[i]->m[j]->next, p, q, R); |
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517 | insert_first_term(res[i]->m[j], p, q, R); |
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518 | } |
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519 | } |
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520 | } |
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521 | |
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522 | syStrategy syFrank(const ideal arg, int &length, const char *method) |
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523 | { |
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524 | syStrategy result = (syStrategy)omAlloc0(sizeof(ssyStrategy)); |
---|
525 | resolvente res = (resolvente)omAlloc0((length+1)*sizeof(ideal)); |
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526 | res[0] = id_Copy(arg, currRing); |
---|
527 | syzHeadFunction *syzHead; |
---|
528 | if (strcmp(method, "frame") == 0 || strcmp(method, "linear strand") == 0) { |
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529 | syzHead = syzHeadFrame; |
---|
530 | } |
---|
531 | else { |
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532 | syzHead = syzHeadExtFrame; |
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533 | } |
---|
534 | length = computeResolution(res, length, syzHead); |
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535 | insert_ext_induced_LTs(res, length); |
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536 | result->fullres = res; |
---|
537 | result->length = length; |
---|
538 | return result; |
---|
539 | } |
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540 | |
---|