[ff7993] | 1 | // -*- Mode: C++; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- |
---|
| 2 | /*****************************************************************************\ |
---|
| 3 | * Computer Algebra System SINGULAR |
---|
| 4 | \*****************************************************************************/ |
---|
| 5 | /** @file syzextra.h |
---|
| 6 | * |
---|
| 7 | * Computation of Syzygies |
---|
| 8 | * |
---|
| 9 | * ABSTRACT: Computation of Syzygies due to Schreyer |
---|
| 10 | * |
---|
| 11 | * @author Oleksandr Motsak |
---|
| 12 | * |
---|
| 13 | **/ |
---|
| 14 | /*****************************************************************************/ |
---|
| 15 | |
---|
| 16 | #ifndef SYZEXTRA_H |
---|
| 17 | #define SYZEXTRA_H |
---|
| 18 | |
---|
[026171] | 19 | #include <vector> |
---|
[dd24e5] | 20 | #include <map> |
---|
[026171] | 21 | |
---|
[ff7993] | 22 | // include basic definitions |
---|
| 23 | #include "singularxx_defs.h" |
---|
| 24 | |
---|
| 25 | struct spolyrec; |
---|
| 26 | typedef struct spolyrec polyrec; |
---|
| 27 | typedef polyrec * poly; |
---|
| 28 | |
---|
| 29 | struct ip_sring; |
---|
| 30 | typedef struct ip_sring * ring; |
---|
| 31 | |
---|
| 32 | struct sip_sideal; |
---|
| 33 | typedef struct sip_sideal * ideal; |
---|
| 34 | |
---|
[4eba3ad] | 35 | class idrec; |
---|
| 36 | typedef idrec * idhdl; |
---|
[ff7993] | 37 | |
---|
| 38 | BEGIN_NAMESPACE_SINGULARXX BEGIN_NAMESPACE(SYZEXTRA) |
---|
| 39 | |
---|
[204092] | 40 | poly leadmonom(const poly p, const ring r); |
---|
[ff7993] | 41 | |
---|
[cd5fefc] | 42 | /// return the tail of a given polynomial or vector |
---|
| 43 | /// returns NULL if input is NULL, otherwise |
---|
| 44 | /// the result is a new polynomial/vector in the ring r |
---|
| 45 | poly p_Tail(const poly p, const ring r); |
---|
| 46 | |
---|
| 47 | |
---|
| 48 | /// return the tail of a given ideal or module |
---|
| 49 | /// returns NULL if input is NULL, otherwise |
---|
| 50 | /// the result is a new ideal/module in the ring r |
---|
| 51 | /// NOTE: the resulting rank is autocorrected |
---|
| 52 | ideal id_Tail(const ideal id, const ring r); |
---|
| 53 | |
---|
[92992c] | 54 | /// inplace sorting of the module (ideal) id wrt <_(c,ds) |
---|
[204092] | 55 | void Sort_c_ds(const ideal id, const ring r); |
---|
| 56 | |
---|
| 57 | |
---|
[4eba3ad] | 58 | |
---|
| 59 | |
---|
| 60 | |
---|
| 61 | /// Computation attribute storage |
---|
| 62 | struct SchreyerSyzygyComputationFlags |
---|
| 63 | { |
---|
| 64 | SchreyerSyzygyComputationFlags(idhdl rootRingHdl); |
---|
[495328] | 65 | SchreyerSyzygyComputationFlags(const SchreyerSyzygyComputationFlags& attr): |
---|
| 66 | __DEBUG__(attr.__DEBUG__), |
---|
| 67 | // __SYZCHECK__(attr.__SYZCHECK__), |
---|
| 68 | __LEAD2SYZ__(attr.__LEAD2SYZ__), __TAILREDSYZ__(attr.__TAILREDSYZ__), |
---|
| 69 | __HYBRIDNF__(attr.__HYBRIDNF__), m_rBaseRing(attr.m_rBaseRing) |
---|
| 70 | {} |
---|
| 71 | |
---|
| 72 | |
---|
[4eba3ad] | 73 | /// output all the intermediate states |
---|
| 74 | const bool __DEBUG__; // DebugOutput; |
---|
| 75 | |
---|
[495328] | 76 | // const bool __SYZCHECK__; // CheckSyzygyProperty: never tested here... |
---|
[4eba3ad] | 77 | |
---|
| 78 | /// ? |
---|
| 79 | const bool __LEAD2SYZ__; // TwoLeadingSyzygyTerms; |
---|
| 80 | |
---|
| 81 | /// Reduce syzygy tails wrt the leading syzygy terms |
---|
| 82 | const bool __TAILREDSYZ__; // TailReducedSyzygies; |
---|
| 83 | |
---|
| 84 | /// Use the usual NF's S-poly reduction while dropping lower order terms |
---|
| 85 | const bool __HYBRIDNF__; // UseHybridNF |
---|
| 86 | |
---|
[495328] | 87 | /// global base ring |
---|
| 88 | const ring m_rBaseRing; |
---|
| 89 | |
---|
[4eba3ad] | 90 | }; |
---|
| 91 | |
---|
[026171] | 92 | class SchreyerSyzygyComputation; |
---|
| 93 | |
---|
[495328] | 94 | class CLCM: public SchreyerSyzygyComputationFlags, public std::vector<bool> |
---|
[026171] | 95 | { |
---|
| 96 | public: |
---|
[5cecde] | 97 | CLCM(const ideal& L, const SchreyerSyzygyComputationFlags& flags); |
---|
[026171] | 98 | |
---|
| 99 | bool Check(const poly m) const; |
---|
| 100 | |
---|
| 101 | private: |
---|
| 102 | bool m_compute; |
---|
[5cecde] | 103 | |
---|
| 104 | const unsigned int m_N; ///< number of ring variables |
---|
[026171] | 105 | }; |
---|
[4eba3ad] | 106 | |
---|
| 107 | |
---|
[495328] | 108 | class CReducerFinder: public SchreyerSyzygyComputationFlags |
---|
[dd24e5] | 109 | { |
---|
| 110 | private: |
---|
| 111 | class CLeadingTerm |
---|
| 112 | { |
---|
| 113 | public: |
---|
| 114 | CLeadingTerm(unsigned int id, const poly p, const ring); |
---|
| 115 | |
---|
| 116 | private: |
---|
| 117 | CLeadingTerm(); |
---|
| 118 | |
---|
| 119 | public: |
---|
| 120 | |
---|
| 121 | const unsigned long m_sev; ///< not short exp. vector |
---|
| 122 | // NOTE/TODO: either of the following should be enough: |
---|
| 123 | const unsigned int m_label; ///< index in the main L[] + 1 |
---|
| 124 | const poly m_lt; ///< the leading term itself L[label-1] |
---|
| 125 | }; |
---|
| 126 | |
---|
| 127 | typedef long TComponentKey; |
---|
| 128 | typedef std::vector<const CLeadingTerm*> TReducers; |
---|
| 129 | typedef std::map< TComponentKey, TReducers> CReducersHash; |
---|
| 130 | |
---|
| 131 | public: |
---|
| 132 | /// goes over all leading terms |
---|
[5cecde] | 133 | CReducerFinder(const ideal L, const SchreyerSyzygyComputationFlags& flags); |
---|
| 134 | |
---|
| 135 | void Initialize(const ideal L); |
---|
[dd24e5] | 136 | |
---|
| 137 | ~CReducerFinder(); |
---|
| 138 | |
---|
| 139 | // TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz? |
---|
[5cecde] | 140 | poly FindReducer(const poly product, const poly syzterm, const CReducerFinder& checker) const; |
---|
| 141 | |
---|
| 142 | bool IsDivisible(const poly q) const; |
---|
| 143 | |
---|
| 144 | bool IsNonempty() const { return (m_hash.size() > 0); } |
---|
[dd24e5] | 145 | |
---|
| 146 | private: |
---|
[5cecde] | 147 | ideal m_L; ///< only for debug |
---|
[dd24e5] | 148 | |
---|
| 149 | CReducersHash m_hash; // can also be replaced with a vector indexed by components |
---|
| 150 | }; |
---|
| 151 | |
---|
| 152 | |
---|
| 153 | |
---|
[7088f18] | 154 | /** @class SchreyerSyzygyComputation syzextra.h |
---|
| 155 | * |
---|
| 156 | * Computing syzygies after Schreyer |
---|
| 157 | * |
---|
| 158 | * Storing/accumulating data during the computation requires some global |
---|
| 159 | * object, like this class. Ideally the above global functions should not |
---|
| 160 | * be used in favour of this class. |
---|
| 161 | * |
---|
| 162 | * @sa Schreyer Syzygy Computation Paper & Talk & Python prototype |
---|
| 163 | */ |
---|
[495328] | 164 | class SchreyerSyzygyComputation: public SchreyerSyzygyComputationFlags |
---|
[7088f18] | 165 | { |
---|
[026171] | 166 | friend class CLCM; |
---|
[dd24e5] | 167 | friend class CReducerFinder; |
---|
[026171] | 168 | |
---|
[7088f18] | 169 | public: |
---|
[026171] | 170 | |
---|
[7088f18] | 171 | /// Construct a global object for given input data (separated into leads & tails) |
---|
[495328] | 172 | SchreyerSyzygyComputation(const ideal idLeads, const ideal idTails, const SchreyerSyzygyComputationFlags setting): |
---|
| 173 | SchreyerSyzygyComputationFlags(setting), |
---|
[4eba3ad] | 174 | m_idLeads(idLeads), m_idTails(idTails), |
---|
[495328] | 175 | m_syzLeads(NULL), m_syzTails(NULL), m_LS(NULL), |
---|
[5cecde] | 176 | m_lcm(m_idLeads, setting), m_div(m_idLeads, setting), m_checker(NULL, setting) |
---|
[026171] | 177 | { |
---|
| 178 | } |
---|
[7088f18] | 179 | |
---|
| 180 | /// Construct a global object for given input data (separated into leads & tails) |
---|
[495328] | 181 | SchreyerSyzygyComputation(const ideal idLeads, const ideal idTails, const ideal syzLeads, const SchreyerSyzygyComputationFlags setting): |
---|
| 182 | SchreyerSyzygyComputationFlags(setting), |
---|
[4eba3ad] | 183 | m_idLeads(idLeads), m_idTails(idTails), |
---|
[5cecde] | 184 | m_syzLeads(syzLeads), m_syzTails(NULL), m_LS(syzLeads), |
---|
| 185 | m_lcm(m_idLeads, setting), m_div(m_idLeads, setting), m_checker(NULL, setting) |
---|
[026171] | 186 | { |
---|
[5cecde] | 187 | if( __TAILREDSYZ__ && syzLeads != NULL ) |
---|
| 188 | m_checker.Initialize(syzLeads); |
---|
[026171] | 189 | } |
---|
[7088f18] | 190 | |
---|
| 191 | |
---|
| 192 | /// Destructor should not destruct the resulting m_syzLeads, m_syzTails. |
---|
| 193 | ~SchreyerSyzygyComputation(){ CleanUp(); } |
---|
| 194 | |
---|
| 195 | /// Read off the results while detaching them from this object |
---|
| 196 | /// NOTE: no copy! |
---|
| 197 | inline void ReadOffResult(ideal& syzL, ideal& syzT) |
---|
| 198 | { |
---|
| 199 | syzL = m_syzLeads; syzT = m_syzTails; |
---|
| 200 | |
---|
| 201 | m_syzLeads = m_syzTails = NULL; // m_LS ? |
---|
| 202 | } |
---|
| 203 | |
---|
| 204 | /// The main driver function: computes |
---|
| 205 | void ComputeSyzygy(); |
---|
| 206 | |
---|
| 207 | /// Computes Syz(leads) or only LEAD of it. |
---|
| 208 | /// The result is stored into m_syzLeads |
---|
| 209 | void ComputeLeadingSyzygyTerms(bool bComputeSecondTerms = true); |
---|
| 210 | |
---|
[4eba3ad] | 211 | poly SchreyerSyzygyNF(poly syz_lead, poly syz_2) const; |
---|
[92992c] | 212 | |
---|
| 213 | // TODO: store m * @tail -.-^-.-^-.--> ? |
---|
[4eba3ad] | 214 | poly TraverseTail(poly multiplier, poly tail) const; |
---|
[92992c] | 215 | |
---|
| 216 | // TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ? |
---|
[4eba3ad] | 217 | poly ReduceTerm(poly multiplier, poly term4reduction, poly syztermCheck) const; |
---|
[7088f18] | 218 | |
---|
[dd24e5] | 219 | public: |
---|
| 220 | /// just for testing via the wrapper below |
---|
| 221 | inline poly _FindReducer(const poly product, const poly syzterm) const |
---|
[5cecde] | 222 | { return m_div.FindReducer(product, syzterm, m_checker); } |
---|
[dd24e5] | 223 | |
---|
[7088f18] | 224 | protected: |
---|
[c7d29b] | 225 | |
---|
| 226 | /// just leading terms |
---|
| 227 | ideal Compute1LeadingSyzygyTerms(); |
---|
| 228 | |
---|
| 229 | /// leading + second terms |
---|
| 230 | ideal Compute2LeadingSyzygyTerms(); |
---|
[026171] | 231 | |
---|
[7088f18] | 232 | /// Clean up all the accumulated data |
---|
| 233 | void CleanUp() {} |
---|
| 234 | |
---|
| 235 | private: |
---|
| 236 | /// input leading terms |
---|
| 237 | const ideal m_idLeads; |
---|
| 238 | |
---|
| 239 | /// input tails |
---|
| 240 | const ideal m_idTails; |
---|
| 241 | |
---|
| 242 | /// output (syzygy) leading terms (+2nd terms?) |
---|
| 243 | ideal m_syzLeads; |
---|
| 244 | |
---|
| 245 | /// output (syzygy) tails |
---|
| 246 | ideal m_syzTails; |
---|
| 247 | |
---|
[026171] | 248 | /// Bitmask for variables occuring in leading terms |
---|
| 249 | const CLCM m_lcm; |
---|
[dd24e5] | 250 | |
---|
| 251 | /// Divisor finder |
---|
| 252 | const CReducerFinder m_div; |
---|
[5cecde] | 253 | |
---|
| 254 | /// for checking tail-terms and makeing them irreducible (wrt m_LS!) |
---|
| 255 | CReducerFinder m_checker; |
---|
| 256 | |
---|
| 257 | /*mutable?*/ ideal m_LS; ///< leading syzygy terms used for reducing syzygy tails |
---|
[7088f18] | 258 | }; |
---|
| 259 | |
---|
| 260 | |
---|
| 261 | // The following wrappers are just for testing separate functions on highest level (within schreyer.lib) |
---|
| 262 | |
---|
[495328] | 263 | static inline void ComputeSyzygy(const ideal L, const ideal T, ideal& LL, ideal& TT, const SchreyerSyzygyComputationFlags A) |
---|
[7088f18] | 264 | { |
---|
[495328] | 265 | SchreyerSyzygyComputation syz(L, T, A); |
---|
[7088f18] | 266 | syz.ComputeSyzygy(); |
---|
| 267 | syz.ReadOffResult(LL, TT); |
---|
| 268 | } |
---|
| 269 | |
---|
[495328] | 270 | static inline ideal ComputeLeadingSyzygyTerms(const ideal& L, const SchreyerSyzygyComputationFlags A) |
---|
[7088f18] | 271 | { |
---|
[495328] | 272 | SchreyerSyzygyComputation syz(L, NULL, A); |
---|
[7088f18] | 273 | syz.ComputeLeadingSyzygyTerms(false); |
---|
| 274 | ideal LL, TT; |
---|
| 275 | syz.ReadOffResult(LL, TT); |
---|
| 276 | return LL; // assume TT is NULL! |
---|
| 277 | } |
---|
| 278 | |
---|
[495328] | 279 | static inline ideal Compute2LeadingSyzygyTerms(const ideal& L, const SchreyerSyzygyComputationFlags A) |
---|
[7088f18] | 280 | { |
---|
[495328] | 281 | SchreyerSyzygyComputation syz(L, NULL, A); |
---|
[7088f18] | 282 | syz.ComputeLeadingSyzygyTerms(true); |
---|
| 283 | ideal LL, TT; |
---|
| 284 | syz.ReadOffResult(LL, TT); |
---|
| 285 | return LL; // assume TT is NULL! |
---|
| 286 | } |
---|
| 287 | |
---|
| 288 | static inline poly FindReducer(poly product, poly syzterm, |
---|
[495328] | 289 | ideal L, ideal LS, const SchreyerSyzygyComputationFlags A) |
---|
[7088f18] | 290 | { |
---|
[495328] | 291 | SchreyerSyzygyComputation syz(L, NULL, LS, A); |
---|
[dd24e5] | 292 | return syz._FindReducer(product, syzterm); |
---|
[7088f18] | 293 | } |
---|
| 294 | |
---|
| 295 | static inline poly TraverseTail(poly multiplier, poly tail, |
---|
[495328] | 296 | ideal L, ideal T, ideal LS, const SchreyerSyzygyComputationFlags A) |
---|
[7088f18] | 297 | { |
---|
[495328] | 298 | SchreyerSyzygyComputation syz(L, T, LS, A); |
---|
[7088f18] | 299 | return syz.TraverseTail(multiplier, tail); |
---|
| 300 | } |
---|
| 301 | |
---|
| 302 | static inline poly ReduceTerm(poly multiplier, poly term4reduction, poly syztermCheck, |
---|
[495328] | 303 | ideal L, ideal T, ideal LS, const SchreyerSyzygyComputationFlags A) |
---|
[7088f18] | 304 | { |
---|
[495328] | 305 | SchreyerSyzygyComputation syz(L, T, LS, A); |
---|
[7088f18] | 306 | return syz.ReduceTerm(multiplier, term4reduction, syztermCheck); |
---|
| 307 | } |
---|
| 308 | |
---|
| 309 | |
---|
| 310 | static inline poly SchreyerSyzygyNF(poly syz_lead, poly syz_2, |
---|
[495328] | 311 | ideal L, ideal T, ideal LS, const SchreyerSyzygyComputationFlags A) |
---|
[7088f18] | 312 | { |
---|
[495328] | 313 | SchreyerSyzygyComputation syz(L, T, LS, A); |
---|
[7088f18] | 314 | return syz.SchreyerSyzygyNF(syz_lead, syz_2); |
---|
| 315 | } |
---|
| 316 | |
---|
| 317 | END_NAMESPACE |
---|
| 318 | |
---|
| 319 | END_NAMESPACE_SINGULARXX |
---|
[ff7993] | 320 | |
---|
| 321 | #endif |
---|
| 322 | /* #ifndef SYZEXTRA_H */ |
---|
| 323 | |
---|
| 324 | // Vi-modeline: vim: filetype=c:syntax:shiftwidth=2:tabstop=8:textwidth=0:expandtab |
---|
| 325 | |
---|