/usr/include/singular/singular/polys/nc/nc.h is in libsingular4-dev-common 1:4.1.0-p3+ds-2build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 | #ifndef POLYS_NC_H
#define POLYS_NC_H
#include <polys/monomials/ring.h>
#include <polys/kbuckets.h>
#ifdef HAVE_PLURAL
// TODO: the following is a part of ring.h... would be nice to have a
// clear public NC interface defined here!
class ip_smatrix;
typedef ip_smatrix * matrix;
matrix nc_PrintMat(int a, int b, ring r, int metric);
enum nc_type
{
nc_error = -1, // Something's gone wrong!
nc_general = 0, /* yx=q xy+... */
nc_skew, /*1*/ /* yx=q xy */
nc_comm, /*2*/ /* yx= xy */
nc_lie, /*3*/ /* yx=xy+... */
nc_undef, /*4*/ /* for internal reasons */
nc_exterior /*5*/ // Exterior Algebra(SCA): yx= -xy & (!:) x^2 = 0
};
// //////////////////////////////////////////////////////
/// checks whether rings rBase and rCandidate
/// could be opposite to each other
/// returns TRUE if it is so
BOOLEAN rIsLikeOpposite(ring rBase, ring rCandidate);
// Macros used to access upper triangle matrices C,D... (which are actually ideals) // afaik
#define UPMATELEM(i,j,nVar) ( (nVar * ((i)-1) - ((i) * ((i)-1))/2 + (j)-1)-(i) )
/// complete destructor
void nc_rKill(ring r);
BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r);
// NC pProcs:
typedef poly (*mm_Mult_p_Proc_Ptr)(const poly m, poly p, const ring r);
typedef poly (*mm_Mult_pp_Proc_Ptr)(const poly m, const poly p, const ring r);
typedef poly (*SPoly_Proc_Ptr)(const poly p1, const poly p2, const ring r);
typedef poly (*SPolyReduce_Proc_Ptr)(const poly p1, poly p2, const ring r);
typedef void (*bucket_Proc_Ptr)(kBucket_pt b, poly p, number *c);
struct nc_pProcs
{
public:
mm_Mult_p_Proc_Ptr mm_Mult_p;
mm_Mult_pp_Proc_Ptr mm_Mult_pp;
bucket_Proc_Ptr BucketPolyRed;
bucket_Proc_Ptr BucketPolyRed_Z;
SPoly_Proc_Ptr SPoly;
SPolyReduce_Proc_Ptr ReduceSPoly;
void* GB; ///< From "gb_hack.h"
// GlobalGB, // BBA
// LocalGB; // MORA
};
class CGlobalMultiplier;
class CFormulaPowerMultiplier;
struct nc_struct
{
nc_type type;
//ring basering; // the ring C,D,.. live in (commutative ring with this NC structure!)
// initial data: square matrices rVar() x rVar()
// logically: upper triangular!!!
// TODO: eliminate this waste of memory!!!!
matrix C;
matrix D;
// computed data:
matrix *MT; // size 0.. (rVar()*rVar()-1)/2
matrix COM;
int *MTsize; // size 0.. (rVar()*rVar()-1)/2
// IsSkewConstant indicates whethere coeffs C_ij are all equal,
// effective together with nc_type=nc_skew
int IsSkewConstant;
private:
// internal data for different implementations
// if dynamic => must be deallocated in destructor (nc_rKill!)
union
{
struct
{
// treat variables from iAltVarsStart till iAltVarsEnd as alternating vars.
// these variables should have odd degree, though that will not be checked
// iAltVarsStart, iAltVarsEnd are only used together with nc_type=nc_exterior
// 1 <= iAltVarsStart <= iAltVarsEnd <= r->N
short iFirstAltVar, iLastAltVar; // = 0 by default
// for factors of super-commutative algebras we need
// the part of general quotient ideal modulo squares!
ideal idSCAQuotient; // = NULL by default. // must be deleted in Kill!
} sca;
} data;
public:
inline nc_type& ncRingType() { return (type); };
inline nc_type ncRingType() const { return (type); };
inline short& FirstAltVar()
{ assume(ncRingType() == nc_exterior); return (data.sca.iFirstAltVar); };
inline short& LastAltVar ()
{ assume(ncRingType() == nc_exterior); return (data.sca.iLastAltVar ); };
inline short FirstAltVar() const
{ assume(ncRingType() == nc_exterior); return (data.sca.iFirstAltVar); };
inline short LastAltVar () const
{ assume(ncRingType() == nc_exterior); return (data.sca.iLastAltVar ); };
inline ideal& SCAQuotient()
{ assume(ncRingType() == nc_exterior); return (data.sca.idSCAQuotient); };
private:
CGlobalMultiplier* m_Multiplier;
CFormulaPowerMultiplier* m_PowerMultiplier;
public:
inline CGlobalMultiplier* GetGlobalMultiplier() const
{ return (m_Multiplier); };
inline CGlobalMultiplier*& GetGlobalMultiplier()
{ return (m_Multiplier); };
inline CFormulaPowerMultiplier* GetFormulaPowerMultiplier() const
{ return (m_PowerMultiplier); };
inline CFormulaPowerMultiplier*& GetFormulaPowerMultiplier()
{ return (m_PowerMultiplier); };
public:
nc_pProcs p_Procs; // NC procedures.
};
// //////////////////////////////////////////////////////////////////////// //
// NC inlines
static inline nc_struct*& GetNC(ring r)
{
return r->GetNC();
}
static inline nc_type& ncRingType(nc_struct* p)
{
assume(p!=NULL);
return (p->ncRingType());
}
static inline nc_type ncRingType(ring r) // Get
{
if(rIsPluralRing(r))
return (ncRingType(r->GetNC()));
else
return (nc_error);
}
static inline void ncRingType(ring r, nc_type t) // Set
{
assume((r != NULL) && (r->GetNC() != NULL));
ncRingType(r->GetNC()) = t;
}
static inline void ncRingType(nc_struct* p, nc_type t) // Set
{
assume(p!=NULL);
ncRingType(p) = t;
}
// //////////////////////////////////////////////////////////////////////// //
// we must always have this test!?
static inline bool rIsSCA(const ring r)
{
#ifdef HAVE_PLURAL
return rIsPluralRing(r) && (ncRingType(r) == nc_exterior);
#else
return false;
#endif
}
// //////////////////////////////////////////////////////////////////////// //
// NC inlines
/// general NC-multiplication with destruction
poly _nc_p_Mult_q(poly p, poly q, const ring r);
/// general NC-multiplication without destruction
poly _nc_pp_Mult_qq(const poly p, const poly q, const ring r);
/// for p_Minus_mm_Mult_qq in pInline2.h
poly nc_p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp,
const poly, const ring r);
// // for p_Plus_mm_Mult_qq in pInline2.h
// returns p + m*q destroys p, const: q, m
poly nc_p_Plus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp,
const int, const ring r);
// returns m*p, does neither destroy p nor m
static inline poly nc_mm_Mult_pp(const poly m, const poly p, const ring r)
{
assume(rIsPluralRing(r));
assume(r->GetNC()->p_Procs.mm_Mult_pp!=NULL);
return r->GetNC()->p_Procs.mm_Mult_pp(m, p, r);
// return pp_Mult_mm( p, m, r);
}
// returns m*p, does destroy p, preserves m
static inline poly nc_mm_Mult_p(const poly m, poly p, const ring r)
{
assume(rIsPluralRing(r));
assume(r->GetNC()->p_Procs.mm_Mult_p!=NULL);
return r->GetNC()->p_Procs.mm_Mult_p(m, p, r);
// return p_Mult_mm( p, m, r);
}
static inline poly nc_CreateSpoly(const poly p1, const poly p2, const ring r)
{
assume(rIsPluralRing(r));
assume(r->GetNC()->p_Procs.SPoly!=NULL);
return r->GetNC()->p_Procs.SPoly(p1, p2, r);
}
// ?
poly nc_CreateShortSpoly(poly p1, poly p2, const ring r);
/* brackets: p will be destroyed... */
poly nc_p_Bracket_qq(poly p, const poly q, const ring r);
static inline poly nc_ReduceSpoly(const poly p1, poly p2, const ring r)
{
assume(rIsPluralRing(r));
assume(r->GetNC()->p_Procs.ReduceSPoly!=NULL);
#ifdef PDEBUG
// assume(p_LmDivisibleBy(p1, p2, r));
#endif
return r->GetNC()->p_Procs.ReduceSPoly(p1, p2, r);
}
void nc_PolyPolyRed(poly &b, poly p, number *c, const ring r);
/*
static inline void nc_PolyReduce(poly &b, const poly p, number *c, const ring r) // nc_PolyPolyRed
{
assume(rIsPluralRing(r));
// assume(r->GetNC()->p_Procs.PolyReduce!=NULL);
// r->GetNC()->p_Procs.PolyReduce(b, p, c, r);
}
*/
static inline void nc_kBucketPolyRed(kBucket_pt b, poly p, number *c)
{
const ring r = b->bucket_ring;
assume(rIsPluralRing(r));
// return gnc_kBucketPolyRedNew(b, p, c);
assume(r->GetNC()->p_Procs.BucketPolyRed!=NULL);
return r->GetNC()->p_Procs.BucketPolyRed(b, p, c);
}
static inline void nc_BucketPolyRed_Z(kBucket_pt b, poly p, number *c)
{
const ring r = b->bucket_ring;
assume(rIsPluralRing(r));
// return gnc_kBucketPolyRed_ZNew(b, p, c);
assume(r->GetNC()->p_Procs.BucketPolyRed_Z!=NULL);
return r->GetNC()->p_Procs.BucketPolyRed_Z(b, p, c);
}
/* subst: */
poly nc_pSubst(poly p, int n, poly e, const ring r);
// the part, related to the interface
// Changes r, Assumes that all other input belongs to curr
BOOLEAN nc_CallPlural(matrix cc, matrix dd, poly cn, poly dn, ring r,
bool bSetupQuotient, //< false
bool bCopyInput, //< true
bool bBeQuiet, //< false
ring curr,
bool dummy_ring = false
/* allow to create a nc-ring with 1 variable*/);
// this function should be used inside QRing definition!
// we go from rG into factor ring rGR with factor ideal rGR->qideal.
bool nc_SetupQuotient(ring rGR, const ring rG = NULL, bool bCopy = false); // rG == NULL means that there is no base G-algebra
BOOLEAN nc_rComplete(const ring src, ring dest, bool bSetupQuotient = true); // in ring.cc
bool nc_rCopy(ring res, const ring r, bool bSetupQuotient);
poly pOppose(ring Rop_src, poly p, const ring Rop_dst);
ideal idOppose(ring Rop_src, ideal I, const ring Rop_dst);
const int GENERICMASK = 0x000; // gnc... must do its dirty job first!
const int SCAMASK = 0x001;
#if 0
static const bool bNoPluralMultiplication = false; // use only formula shortcuts in my OOP Multiplier
// the following make sense only if bNoPluralMultiplication is false:
static const bool bNoFormula = true; // don't use any formula shortcuts
static const bool bNoCache = false; // only formula whenever possible, only make sanse if bNoFormula is false!
#endif
// false, true, false == old "good" Plural
// false, false ==>> Plural + Cache + Direct Formula - not much
// false, false, true ==>> Plural Mult + Direct Formula (no ~cache)
// true, *, * == new OOP multiplication!
const int NOPLURALMASK= 0x002; // bNoPluralMultiplication
const int NOFORMULAMASK=0x004; // bNoFormula
const int NOCACHEMASK = 0x008; // bNoCache
const int TESTSYZSCAMASK = 0x0100 | SCAMASK;
// NCExtensions Mask Property
int& getNCExtensions();
int setNCExtensions(int iMask);
// Test
bool ncExtensions(int iMask); // = 0x0FFFF
#ifdef PLURAL_INTERNAL_DECLARATIONS
// set pProcs table for rGR and global variable p_Procs
// this should be used by p_ProcsSet in p_Procs_Set.h
void nc_p_ProcsSet(ring rGR, p_Procs_s* p_Procs);
#include <polys/matpol.h>
// read only access to NC matrices C/D:
// get C_{i,j}, 1 <= row = i < j = col <= N
static inline poly GetC( const ring r, int i, int j )
{
assume(r!= NULL && rIsPluralRing(r));
const matrix C = GetNC(r)->C;
assume(C != NULL);
const int ncols = C->ncols;
assume( (i > 0) && (i < j) && (j <= ncols) );
return ( C->m[ncols * ((i)-1) + (j)-1] );
}
// get D_{i,j}, 1 <= row = i < j = col <= N
static inline poly GetD( const ring r, int i, int j )
{
assume(r!= NULL && rIsPluralRing(r));
const matrix D = GetNC(r)->D;
assume(D != NULL);
const int ncols = D->ncols;
assume( (i > 0) && (i < j) && (j <= ncols) );
return ( D->m[ncols * ((i)-1) + (j)-1] );
}
#endif // PLURAL_INTERNAL_DECLARATIONS
#endif /* HAVE_PLURAL */
#endif /* POLYS_NC_H */
|