[ff7993] | 1 | // -*- Mode: C++; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- |
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| 2 | /*****************************************************************************\ |
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| 3 | * Computer Algebra System SINGULAR |
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| 4 | \*****************************************************************************/ |
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| 5 | /** @file syzextra.h |
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| 6 | * |
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| 7 | * Computation of Syzygies |
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| 8 | * |
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| 9 | * ABSTRACT: Computation of Syzygies due to Schreyer |
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| 10 | * |
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| 11 | * @author Oleksandr Motsak |
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| 12 | * |
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| 13 | **/ |
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| 14 | /*****************************************************************************/ |
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| 15 | |
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| 16 | #ifndef SYZEXTRA_H |
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| 17 | #define SYZEXTRA_H |
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| 18 | |
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| 19 | // include basic definitions |
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| 20 | #include "singularxx_defs.h" |
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| 21 | |
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| 22 | struct spolyrec; |
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| 23 | typedef struct spolyrec polyrec; |
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| 24 | typedef polyrec * poly; |
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| 25 | |
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| 26 | struct ip_sring; |
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| 27 | typedef struct ip_sring * ring; |
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| 28 | |
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| 29 | struct sip_sideal; |
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| 30 | typedef struct sip_sideal * ideal; |
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| 31 | |
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[4eba3ad] | 32 | class idrec; |
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| 33 | typedef idrec * idhdl; |
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[ff7993] | 34 | |
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| 35 | BEGIN_NAMESPACE_SINGULARXX BEGIN_NAMESPACE(SYZEXTRA) |
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| 36 | |
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[204092] | 37 | poly leadmonom(const poly p, const ring r); |
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[ff7993] | 38 | |
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[cd5fefc] | 39 | /// return the tail of a given polynomial or vector |
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| 40 | /// returns NULL if input is NULL, otherwise |
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| 41 | /// the result is a new polynomial/vector in the ring r |
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| 42 | poly p_Tail(const poly p, const ring r); |
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| 43 | |
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| 44 | |
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| 45 | /// return the tail of a given ideal or module |
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| 46 | /// returns NULL if input is NULL, otherwise |
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| 47 | /// the result is a new ideal/module in the ring r |
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| 48 | /// NOTE: the resulting rank is autocorrected |
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| 49 | ideal id_Tail(const ideal id, const ring r); |
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| 50 | |
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[92992c] | 51 | /// inplace sorting of the module (ideal) id wrt <_(c,ds) |
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[204092] | 52 | void Sort_c_ds(const ideal id, const ring r); |
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| 53 | |
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| 54 | |
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[4eba3ad] | 55 | |
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| 56 | |
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| 57 | |
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| 58 | /// Computation attribute storage |
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| 59 | struct SchreyerSyzygyComputationFlags |
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| 60 | { |
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| 61 | SchreyerSyzygyComputationFlags(idhdl rootRingHdl); |
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| 62 | |
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| 63 | /// output all the intermediate states |
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| 64 | const bool __DEBUG__; // DebugOutput; |
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| 65 | |
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| 66 | /// ? |
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| 67 | const bool __SYZCHECK__; // CheckSyzygyProperty; |
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| 68 | |
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| 69 | /// ? |
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| 70 | const bool __LEAD2SYZ__; // TwoLeadingSyzygyTerms; |
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| 71 | |
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| 72 | /// Reduce syzygy tails wrt the leading syzygy terms |
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| 73 | const bool __TAILREDSYZ__; // TailReducedSyzygies; |
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| 74 | |
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| 75 | /// Use the usual NF's S-poly reduction while dropping lower order terms |
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| 76 | const bool __HYBRIDNF__; // UseHybridNF |
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| 77 | |
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| 78 | }; |
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| 79 | |
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| 80 | |
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| 81 | |
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[7088f18] | 82 | /** @class SchreyerSyzygyComputation syzextra.h |
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| 83 | * |
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| 84 | * Computing syzygies after Schreyer |
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| 85 | * |
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| 86 | * Storing/accumulating data during the computation requires some global |
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| 87 | * object, like this class. Ideally the above global functions should not |
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| 88 | * be used in favour of this class. |
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| 89 | * |
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| 90 | * @sa Schreyer Syzygy Computation Paper & Talk & Python prototype |
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| 91 | */ |
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| 92 | class SchreyerSyzygyComputation |
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| 93 | { |
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| 94 | public: |
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| 95 | /// Construct a global object for given input data (separated into leads & tails) |
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[4eba3ad] | 96 | SchreyerSyzygyComputation(const ideal idLeads, const ideal idTails, const ring rBaseRing, const SchreyerSyzygyComputationFlags attribues): |
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| 97 | m_rBaseRing(rBaseRing), |
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| 98 | m_idLeads(idLeads), m_idTails(idTails), |
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| 99 | m_syzLeads(NULL), m_syzTails(NULL), m_LS(NULL), m_atttributes(attribues) {} |
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[7088f18] | 100 | |
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| 101 | |
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| 102 | /// Construct a global object for given input data (separated into leads & tails) |
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[4eba3ad] | 103 | SchreyerSyzygyComputation(const ideal idLeads, const ideal idTails, const ideal syzLeads, const ring rBaseRing, const SchreyerSyzygyComputationFlags attribues): |
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| 104 | m_rBaseRing(rBaseRing), |
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| 105 | m_idLeads(idLeads), m_idTails(idTails), |
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| 106 | m_syzLeads(NULL), m_syzTails(NULL), m_LS(syzLeads), m_atttributes(attribues) {} |
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[7088f18] | 107 | |
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| 108 | |
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| 109 | /// Destructor should not destruct the resulting m_syzLeads, m_syzTails. |
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| 110 | ~SchreyerSyzygyComputation(){ CleanUp(); } |
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| 111 | |
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| 112 | /// Read off the results while detaching them from this object |
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| 113 | /// NOTE: no copy! |
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| 114 | inline void ReadOffResult(ideal& syzL, ideal& syzT) |
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| 115 | { |
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| 116 | syzL = m_syzLeads; syzT = m_syzTails; |
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| 117 | |
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| 118 | m_syzLeads = m_syzTails = NULL; // m_LS ? |
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| 119 | } |
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| 120 | |
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| 121 | /// The main driver function: computes |
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| 122 | void ComputeSyzygy(); |
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| 123 | |
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| 124 | /// Computes Syz(leads) or only LEAD of it. |
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| 125 | /// The result is stored into m_syzLeads |
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| 126 | void ComputeLeadingSyzygyTerms(bool bComputeSecondTerms = true); |
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| 127 | |
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[92992c] | 128 | // TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz? |
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[4eba3ad] | 129 | poly FindReducer(poly product, poly syzterm) const; |
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[92992c] | 130 | |
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[4eba3ad] | 131 | poly SchreyerSyzygyNF(poly syz_lead, poly syz_2) const; |
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[92992c] | 132 | |
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| 133 | // TODO: store m * @tail -.-^-.-^-.--> ? |
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[4eba3ad] | 134 | poly TraverseTail(poly multiplier, poly tail) const; |
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[92992c] | 135 | |
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| 136 | // TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ? |
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[4eba3ad] | 137 | poly ReduceTerm(poly multiplier, poly term4reduction, poly syztermCheck) const; |
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[7088f18] | 138 | |
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| 139 | protected: |
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| 140 | |
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| 141 | /// Clean up all the accumulated data |
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| 142 | void CleanUp() {} |
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| 143 | |
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| 144 | private: |
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| 145 | /// global base ring |
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| 146 | const ring m_rBaseRing; |
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| 147 | |
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| 148 | /// input leading terms |
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| 149 | const ideal m_idLeads; |
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| 150 | |
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| 151 | /// input tails |
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| 152 | const ideal m_idTails; |
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| 153 | |
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| 154 | /// output (syzygy) leading terms (+2nd terms?) |
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| 155 | ideal m_syzLeads; |
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| 156 | |
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| 157 | /// output (syzygy) tails |
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| 158 | ideal m_syzTails; |
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| 159 | |
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| 160 | /*mutable?*/ ideal m_LS; ///< leading syzygy terms used for reducing syzygy tails |
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[4eba3ad] | 161 | |
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| 162 | const SchreyerSyzygyComputationFlags m_atttributes; |
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[7088f18] | 163 | }; |
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| 164 | |
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| 165 | |
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| 166 | // The following wrappers are just for testing separate functions on highest level (within schreyer.lib) |
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| 167 | |
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[4eba3ad] | 168 | static inline void ComputeSyzygy(const ideal L, const ideal T, ideal& LL, ideal& TT, const ring R, const SchreyerSyzygyComputationFlags A) |
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[7088f18] | 169 | { |
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[4eba3ad] | 170 | SchreyerSyzygyComputation syz(L, T, R, A); |
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[7088f18] | 171 | syz.ComputeSyzygy(); |
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| 172 | syz.ReadOffResult(LL, TT); |
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| 173 | } |
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| 174 | |
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[4eba3ad] | 175 | static inline ideal ComputeLeadingSyzygyTerms(const ideal& L, const ring R, const SchreyerSyzygyComputationFlags A) |
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[7088f18] | 176 | { |
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[4eba3ad] | 177 | SchreyerSyzygyComputation syz(L, NULL, R, A); |
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[7088f18] | 178 | syz.ComputeLeadingSyzygyTerms(false); |
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| 179 | ideal LL, TT; |
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| 180 | syz.ReadOffResult(LL, TT); |
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| 181 | return LL; // assume TT is NULL! |
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| 182 | } |
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| 183 | |
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[4eba3ad] | 184 | static inline ideal Compute2LeadingSyzygyTerms(const ideal& L, const ring R, const SchreyerSyzygyComputationFlags A) |
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[7088f18] | 185 | { |
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[4eba3ad] | 186 | SchreyerSyzygyComputation syz(L, NULL, R, A); |
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[7088f18] | 187 | syz.ComputeLeadingSyzygyTerms(true); |
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| 188 | ideal LL, TT; |
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| 189 | syz.ReadOffResult(LL, TT); |
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| 190 | return LL; // assume TT is NULL! |
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| 191 | } |
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| 192 | |
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| 193 | static inline poly FindReducer(poly product, poly syzterm, |
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[4eba3ad] | 194 | ideal L, ideal LS, const ring R, const SchreyerSyzygyComputationFlags A) |
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[7088f18] | 195 | { |
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[4eba3ad] | 196 | SchreyerSyzygyComputation syz(L, NULL, LS, R, A); |
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[7088f18] | 197 | return syz.FindReducer(product, syzterm); |
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| 198 | } |
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| 199 | |
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| 200 | static inline poly TraverseTail(poly multiplier, poly tail, |
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[4eba3ad] | 201 | ideal L, ideal T, ideal LS, const ring R, const SchreyerSyzygyComputationFlags A) |
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[7088f18] | 202 | { |
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[4eba3ad] | 203 | SchreyerSyzygyComputation syz(L, T, LS, R, A); |
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[7088f18] | 204 | return syz.TraverseTail(multiplier, tail); |
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| 205 | } |
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| 206 | |
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| 207 | static inline poly ReduceTerm(poly multiplier, poly term4reduction, poly syztermCheck, |
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[4eba3ad] | 208 | ideal L, ideal T, ideal LS, const ring R, const SchreyerSyzygyComputationFlags A) |
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[7088f18] | 209 | { |
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[4eba3ad] | 210 | SchreyerSyzygyComputation syz(L, T, LS, R, A); |
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[7088f18] | 211 | return syz.ReduceTerm(multiplier, term4reduction, syztermCheck); |
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| 212 | } |
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| 213 | |
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| 214 | |
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| 215 | static inline poly SchreyerSyzygyNF(poly syz_lead, poly syz_2, |
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[4eba3ad] | 216 | ideal L, ideal T, ideal LS, const ring R, const SchreyerSyzygyComputationFlags A) |
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[7088f18] | 217 | { |
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[4eba3ad] | 218 | SchreyerSyzygyComputation syz(L, T, LS, R, A); |
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[7088f18] | 219 | return syz.SchreyerSyzygyNF(syz_lead, syz_2); |
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| 220 | } |
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| 221 | |
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| 222 | END_NAMESPACE |
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| 223 | |
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| 224 | END_NAMESPACE_SINGULARXX |
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[ff7993] | 225 | |
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| 226 | #endif |
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| 227 | /* #ifndef SYZEXTRA_H */ |
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| 228 | |
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| 229 | // Vi-modeline: vim: filetype=c:syntax:shiftwidth=2:tabstop=8:textwidth=0:expandtab |
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| 230 | |
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