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: f5gb interface |
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6 | */ |
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7 | #ifndef F5_HEADER |
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8 | #define F5_HEADER |
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9 | |
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10 | #ifdef HAVE_F5 |
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11 | #include <kernel/f5data.h> |
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12 | #include <kernel/f5lists.h> |
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13 | |
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14 | |
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15 | /* |
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16 | ====================================================== |
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17 | sort polynomials in ideal i by decreasing total degree |
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18 | ====================================================== |
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19 | */ |
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20 | void qsortDegree(poly* left, poly* right); |
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21 | |
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22 | /*! |
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23 | * ====================================================================== |
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24 | * builds the sum of the entries of the exponent vectors, i.e. the degree |
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25 | * of the corresponding monomial |
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26 | * ====================================================================== |
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27 | */ |
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28 | long sumVector(int* v, int k); |
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29 | |
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30 | /** |
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31 | ========================================================================== |
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32 | compare monomials, i.e. divisibility tests for criterion 1 and criterion 2 |
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33 | ========================================================================== |
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34 | */ |
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35 | bool compareMonomials(int* m1, int** m2, int numberOfRuleOlds); |
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36 | |
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37 | |
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38 | /* |
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39 | ================================================== |
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40 | computes incrementally gbs of subsets of the input |
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41 | gb{f_m} -> gb{f_m,f_(m-1)} -> gb{f_m,...,f_1} |
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42 | ================================================== |
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43 | */ |
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44 | LList* F5inc(int i, poly f_i, LList* gPrev,LList* reducers, ideal gbPrev, poly ONE, LTagList* lTag, RList* rules, RTagList* rTag, int plus ,int termination); |
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45 | |
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46 | /* |
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47 | ================================================================ |
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48 | computes a list of critical pairs for the next reduction process |
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49 | the first element is always "useful" thus the critical pair |
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50 | computed is either "useful" or "useless" depending on the second |
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51 | element which generates the critical pair. |
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52 | first element in gPrev is always the newest element which must |
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53 | build critical pairs with all other elements in gPrev |
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54 | ================================================================ |
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55 | */ |
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56 | void criticalPair(LList* gPrev, CListOld* critPairs, LTagList* lTag, RTagList* rTag, RList* RuleOlds, PList* rejectedGBList, int plus); |
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57 | |
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58 | |
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59 | bool checkDGB(LList* gPrev); |
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60 | |
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61 | |
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62 | /* |
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63 | * Arris Check if we are finished after the current degree step: |
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64 | * Checks all remaining critical pairs, i.e. those of higher degree, |
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65 | * by the two Buchberger criteria. |
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66 | * return value: 0, if all remaining critical pairs are deleted by |
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67 | * Buchberger's criteria |
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68 | * 1, otherwise |
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69 | */ |
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70 | bool arrisCheck(CNode* first,LNode* firstGCurr, long arrisdeg); |
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71 | |
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72 | /* |
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73 | ================================================================ |
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74 | computes a list of critical pairs for the next reduction process |
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75 | the first element is always "useless" thus the critical pair |
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76 | computed is "useless". |
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77 | first element in gPrev is always the newest element which must |
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78 | build critical pairs with all other elements in gPrev |
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79 | ================================================================ |
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80 | */ |
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81 | void criticalPair2(LList* gPrev, CListOld* critPairs, LTagList* lTag, RTagList* rTag, RList* RuleOlds, PList* rejectedGBList); |
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82 | |
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83 | /* |
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84 | ======================================== |
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85 | Criterion 1, i.e. Faugere's F5 Criterion |
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86 | ======================================== |
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87 | */ |
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88 | inline bool criterion1(LList* gPrev, poly t, LNode* l, LTagList* lTag); |
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89 | |
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90 | /* |
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91 | ===================================== |
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92 | Criterion 2, i.e. Rewritten Criterion |
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93 | ===================================== |
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94 | */ |
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95 | inline bool criterion2(int idx, poly t, LNode* l, RList* RuleOlds, RTagList* rTag); |
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96 | |
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97 | /* |
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98 | ========================================================================================================== |
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99 | Criterion 2, i.e. Rewritten Criterion, for its second call in sPols(), with added lastRuleOldTested parameter |
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100 | ========================================================================================================== |
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101 | */ |
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102 | inline bool criterion2(poly t, LPolyOld* l, RList* RuleOlds, RuleOld* testedRuleOld); |
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103 | |
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104 | /* |
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105 | * check for useful pairs in the given subset of critical pairs |
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106 | */ |
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107 | int computeUsefulMinDeg(CNode* first); |
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108 | |
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109 | /* |
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110 | ================================== |
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111 | Computation of S-Polynomials in F5 |
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112 | ================================== |
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113 | */ |
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114 | inline void computeSPols(CNode* first, RTagList* rTag, RList* RuleOlds, LList* sPolyList, PList* rejectedGBList); |
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115 | |
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116 | /* |
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117 | ======================================================================== |
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118 | reduction including subalgorithm topReduction() using Faugere's criteria |
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119 | ======================================================================== |
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120 | */ |
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121 | inline void reduction(LList* sPolyList, CListOld* critPairs, LList* gPrev, RList* RuleOlds, LTagList* lTag, RTagList* rTag, |
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122 | ideal gbPrev, PList* rejectedGBList, int plus); |
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123 | |
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124 | /* |
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125 | ======================================================================== |
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126 | reduction including subalgorithm topReduction() using Faugere's criteria |
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127 | ======================================================================== |
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128 | */ |
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129 | inline void newReduction(LList* sPolyList, CListOld* critPairs, LList* gPrev, LList* reducers, RList* rules, LTagList* lTag, RTagList* rTag, ideal gbPrev, int termination, PList* rejectedGBList, int plus); |
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130 | |
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131 | /*! |
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132 | * ================================================================================ |
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133 | * searches for reducers of temp similar to the symbolic preprocessing of F4 and |
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134 | * divides them into a "good" and "bad" part: |
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135 | * |
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136 | * the "good" ones are the reducers which do not corrupt the label of temp, with |
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137 | * these the normal form of temp is computed |
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138 | * |
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139 | * the "bad" ones are the reducers which corrupt the label of temp, they are tested |
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140 | * later on for possible new RuleOlds and S-polynomials to be added to the algorithm |
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141 | * ================================================================================ |
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142 | */ |
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143 | void findReducers(LNode* l, LList* sPolyList, ideal gbPrev, LList* gPrev, LList* reducers, CListOld* critPairs, RList* rules, LTagList* lTag, RTagList* rTag, int termination, PList* rejectedGBList, int plus); |
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144 | |
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145 | /* |
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146 | ===================================================================================== |
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147 | top reduction in F5, i.e. reduction of a given S-polynomial by labeled polynomials of |
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148 | the same index whereas the labels are taken into account |
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149 | ===================================================================================== |
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150 | */ |
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151 | inline void topReduction(LNode* l, LList* sPolyList, LList* gPrev, CListOld* critPairs, RList* RuleOlds, LTagList* lTag, RTagList* rTag, ideal gbPrev, PList* rejectedGBList, int plus); |
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152 | |
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153 | /* |
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154 | ======================================================================================= |
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155 | merging 2 polynomials p & q without requiring that all monomials of p & q are different |
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156 | if there are equal monomials in p & q only one of these monomials (always that of p!) |
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157 | is taken into account |
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158 | ======================================================================================= |
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159 | |
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160 | poly p_MergeEq_q(poly p, poly q, const ring r); |
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161 | */ |
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162 | /* |
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163 | ===================================================================== |
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164 | subalgorithm to find a possible reductor for the labeled polynomial l |
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165 | ===================================================================== |
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166 | */ |
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167 | inline LNode* findReductor(LNode* l, LList* sPolyList, LNode* gPrevRedCheck, LList* gPrev, RList* RuleOlds, LTagList* lTag,RTagList* rTag); |
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168 | |
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169 | /* |
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170 | ====================================== |
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171 | main function of our F5 implementation |
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172 | ====================================== |
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173 | */ |
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174 | ideal F5main(ideal i, ring r, int opt, int plus, int termination); |
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175 | |
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176 | #endif |
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177 | #endif |
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