1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: f5gb.h,v 1.31 2009-03-01 20:31:54 ederc Exp $ */ |
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5 | /* |
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6 | * ABSTRACT: f5gb interface |
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7 | */ |
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8 | #ifndef F5_HEADER |
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9 | #define F5_HEADER |
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10 | |
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11 | #ifdef HAVE_F5 |
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12 | #include "f5data.h" |
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13 | #include "f5lists.h" |
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14 | |
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15 | |
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16 | /* |
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17 | ====================================================== |
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18 | sort polynomials in ideal i by decreasing total degree |
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19 | ====================================================== |
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20 | */ |
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21 | void qsortDegree(poly* left, poly* right); |
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22 | |
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23 | /* |
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24 | ============================================== |
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25 | generating the list lp of ideal generators and |
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26 | test if 1 is in lp(return 1) or not(return 0) |
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27 | ============================================== |
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28 | */ |
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29 | void generate_input_list(LPoly* lp, ideal id, poly one); |
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30 | |
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31 | /* |
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32 | ================================================== |
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33 | computes incrementally gbs of subsets of the input |
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34 | gb{f_m} -> gb{f_m,f_(m-1)} -> gb{f_m,...,f_1} |
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35 | ================================================== |
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36 | */ |
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37 | LList* F5inc(int i, poly f_i, LList* gPrev, ideal gbPrev, poly ONE, LTagList* lTag, RList* rules, RTagList* rTag); |
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38 | |
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39 | /* |
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40 | ================================================================ |
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41 | computes a list of critical pairs for the next reduction process |
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42 | first element in gPrev is always the newest element which must |
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43 | build critical pairs with all other elements in gPrev |
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44 | ================================================================ |
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45 | */ |
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46 | void criticalPair(LList* gPrev, CList* critPairs, LTagList* lTag, RTagList* rTag, RList* rules); |
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47 | |
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48 | /* |
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49 | ================================================================ |
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50 | computes a list of critical pairs for the next reduction process |
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51 | first element in gPrev is always the newest element which must |
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52 | build critical pairs with all other elements in gPrev |
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53 | this is a special version for reduction() in which the first |
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54 | generator of the critical pair is not tested by criterion2() |
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55 | as there are no rules added until then to test for |
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56 | ================================================================ |
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57 | */ |
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58 | void criticalPairRed(LList* gPrev, CList* critPairs, LTagList* lTag, RTagList* rTag, RList* rules); |
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59 | |
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60 | /* |
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61 | ======================================== |
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62 | Criterion 1, i.e. Faugere's F5 Criterion |
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63 | ======================================== |
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64 | */ |
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65 | bool criterion1(LList* gPrev, poly t, LNode* l, LTagList* lTag); |
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66 | |
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67 | /* |
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68 | ===================================== |
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69 | Criterion 2, i.e. Rewritten Criterion |
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70 | ===================================== |
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71 | */ |
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72 | bool criterion2(poly t, LNode* l, RList* rules, RTagList* rTag); |
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73 | |
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74 | /* |
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75 | ========================================================================================================== |
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76 | Criterion 2, i.e. Rewritten Criterion, for its second call in sPols(), with added lastRuleTested parameter |
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77 | ========================================================================================================== |
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78 | */ |
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79 | bool criterion2(poly t, LPoly* l, RList* rules, Rule* testedRule); |
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80 | |
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81 | /* |
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82 | ================================== |
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83 | Computation of S-Polynomials in F5 |
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84 | ================================== |
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85 | */ |
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86 | void computeSPols(CNode* first, RTagList* rTag, RList* rules, LList* sPolyList); |
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87 | |
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88 | /* |
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89 | ======================================================================== |
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90 | reduction including subalgorithm topReduction() using Faugere's criteria |
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91 | ======================================================================== |
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92 | */ |
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93 | void reduction(LList* sPolyList, CList* critPairs, LList* gPrev, RList* rules, LTagList* lTag, RTagList* rTag, |
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94 | ideal gbPrev); |
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95 | |
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96 | /* |
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97 | ===================================================================================== |
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98 | top reduction in F5, i.e. reduction of a given S-polynomial by labeled polynomials of |
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99 | the same index whereas the labels are taken into account |
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100 | ===================================================================================== |
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101 | */ |
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102 | void topReduction(LNode* l, LList* sPolyList, LList* gPrev, RList* rules, LTagList* lTag, RTagList* rTag, ideal gbPrev); |
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103 | |
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104 | /* |
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105 | ===================================================================== |
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106 | subalgorithm to find a possible reductor for the labeled polynomial l |
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107 | ===================================================================== |
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108 | */ |
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109 | LNode* findReductor(LNode* l, LNode* gPrevRedCheck, LList* gPrev, RList* rules, LTagList* lTag,RTagList* rTag); |
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110 | |
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111 | /* |
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112 | ====================================== |
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113 | main function of our F5 implementation |
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114 | ====================================== |
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115 | */ |
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116 | ideal F5main(ideal i, ring r); |
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117 | |
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118 | #endif |
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119 | #endif |
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