| 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* $Id: f5gb.h,v 1.30 2009-02-28 21:14:06 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, 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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