https://github.com/Singular/Sources
Tip revision: be77cf1dd000fb79a2c712ff01d5455661826482 authored by Hans Schoenemann on 19 November 2014, 13:06:05 UTC
chg: changes from spielwiese
chg: changes from spielwiese
Tip revision: be77cf1
ideals.h
#ifndef IDEALS_H
#define IDEALS_H
/****************************************
* Computer Algebra System SINGULAR *
****************************************/
/*
* ABSTRACT - all basic methods to manipulate ideals
*/
#include <kernel/structs.h>
#include <kernel/ring.h>
struct sip_sideal
{
poly* m;
long rank;
int nrows;
int ncols;
#define IDELEMS(i) ((i)->ncols)
};
struct sip_smap
{
poly *m;
char *preimage;
int nrows;
int ncols;
};
struct sideal_list;
typedef struct sideal_list * ideal_list;
struct sideal_list
{
ideal_list next;
ideal d;
#ifndef NDEBUG
int nr;
#endif
};
//typedef struct sip_sideal * ideal;
//typedef struct sip_smap * map;
typedef ideal * resolvente;
extern omBin sip_sideal_bin;
/*- creates an ideal -*/
ideal idInit (int size, int rank=1);
void idKeepFirstK(ideal ide, const int k);
ideal idCopyFirstK (const ideal ide, const int k);
/// delete an ideal
#define idDelete(h) id_Delete(h, currRing)
void id_Delete (ideal* h, ring r);
void id_ShallowDelete (ideal* h, ring r);
/*- initialise an ideal -*/ // ?
/// initialise the maximal ideal (at 0)
ideal idMaxIdeal (int deg);
/// gives an ideal the minimal possible size
void idSkipZeroes (ideal ide);
/// index of generator with leading term in ground ring (if any); otherwise -1
int idPosConstant (ideal id);
/// Count the effective size of an ideal
/// (without the trailing allocated zero-elements)
static inline int idSize(const ideal id)
{
int j = IDELEMS(id) - 1;
poly* mm = id->m;
while ((j >= 0) && (mm[j] == NULL)) j--;
return (j + 1);
}
void idNorm(ideal id);
void idDelMultiples(ideal id);
void idDelEquals(ideal id);
void idDelLmEquals(ideal id);
void idDelDiv(ideal id);
BOOLEAN idIsConstant(ideal id);
#ifdef PDEBUG
void idDBTest(ideal h1, int level, const char *f,const int l);
#define idTest(A) idDBTest(A, PDEBUG, __FILE__,__LINE__)
#define idPrint(id) idShow(id)
#else
#define idTest(A) do {} while (0)
#define idPrint(A) do {} while (0)
#endif
ideal id_Copy (ideal h1,const ring r);
#define idCopy(A) id_Copy(A,currRing)
/*adds two ideals without simplifying the result*/
ideal idSimpleAdd (ideal h1,ideal h2);
/*adds the quotient ideal*/
ideal idAdd (ideal h1,ideal h2);
/* h1 + h2 */
BOOLEAN idInsertPoly (ideal h1,poly h2);
/* h1 + h2 */
BOOLEAN idInsertPolyWithTests (ideal h1, const int validEntries,
const poly h2, const bool zeroOk, const bool duplicateOk);
/* h1 + h2 */
ideal idMult (ideal h1,ideal h2);
/*hh := h1 * h2*/
BOOLEAN idIs0 (ideal h);
long idRankFreeModule(ideal m, ring lmRing, ring tailRing);
inline long idRankFreeModule(ideal m, ring r = currRing)
{return idRankFreeModule(m, r, r);}
// returns TRUE, if idRankFreeModule(m) > 0
BOOLEAN idIsModule(ideal m, ring r = currRing);
BOOLEAN idHomIdeal (ideal id, ideal Q=NULL);
BOOLEAN idHomModule(ideal m, ideal Q,intvec **w);
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w);
ideal idMinBase (ideal h1);
/*returns a minimized set of generators of h1*/
int pLowVar (poly p);
/*-the minimal index of used variables - 1-*/
void pShift (poly * p,int i);
/*- verschiebt die Indizes der Modulerzeugenden um i -*/
void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise);
void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise);
int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise);
int binom (int n,int r);
ideal idFreeModule (int i);
ideal idSect (ideal h1,ideal h2);
ideal idMultSect(resolvente arg, int length);
//ideal idSyzygies (ideal h1, tHomog h,intvec **w);
ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp=TRUE,
BOOLEAN setRegularity=FALSE, int *deg = NULL);
ideal idLiftStd (ideal h1, matrix *m, tHomog h=testHomog, ideal *syz=NULL);
ideal idLift (ideal mod, ideal sumod,ideal * rest=NULL,
BOOLEAN goodShape=FALSE, BOOLEAN isSB=TRUE,BOOLEAN divide=FALSE,
matrix *unit=NULL);
void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R, short *w= NULL );
intvec * idMWLift(ideal mod,intvec * weights);
ideal idQuot (ideal h1,ideal h2,
BOOLEAN h1IsStb=FALSE, BOOLEAN resultIsIdeal=FALSE);
ideal idPower(ideal gid,int deg);
//ideal idElimination (ideal h1,poly delVar);
ideal idElimination (ideal h1,poly delVar, intvec *hilb=NULL);
poly idMinor(matrix a, int ar, unsigned long which, ideal R=NULL);
ideal idMinors(matrix a, int ar, ideal R=NULL);
void idCompactify(ideal id);
ideal idMinEmbedding(ideal arg,BOOLEAN inPlace=FALSE, intvec **w=NULL);
ideal idHead(ideal h);
ideal idHomogen(ideal h, int varnum);
BOOLEAN idIsSubModule(ideal id1,ideal id2);
ideal idVec2Ideal(poly vec);
ideal idMatrix2Module(matrix mat);
matrix idModule2Matrix(ideal mod);
matrix idModule2formatedMatrix(ideal mod,int rows, int cols);
ideal idSubst(ideal i, int n, poly e);
ideal idJet(ideal i,int d);
ideal idJetW(ideal i,int d, intvec * iv);
int idMinDegW(ideal M,intvec *w);
ideal idSeries(int n,ideal M,matrix U=NULL,intvec *w=NULL);
BOOLEAN idIsZeroDim(ideal i);
matrix idDiff(matrix i, int k);
matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply=TRUE);
intvec *idSort(ideal id,BOOLEAN nolex=TRUE);
ideal idModulo (ideal h1,ideal h2, tHomog h=testHomog, intvec ** w=NULL);
int idElem(const ideal F);
matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how);
// transpose a module
ideal idTransp(ideal a);
// version of "ideal idTransp(ideal)" which works within a given ring.
ideal id_Transp(ideal a, const ring rRing = currRing);
intvec *idQHomWeight(ideal id);
void idNormalize(ideal id);
ideal idXXX (ideal h1, int k);
poly id_GCD(poly f, poly g, const ring r);
ideal idChineseRemainder(ideal *x, number *q, int rl);
//ideal idChineseRemainder(ideal *x, intvec *iv); /* currently unused */
ideal idFarey(ideal x, number N);
ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing = currRing); // image of certain map for BGG
#ifdef PDEBUG
/* Shows an ideal -- only for debugging */
void idShow(const ideal id, const ring lmRing = currRing, const ring tailRing = currRing, const int debugPrint = 0);
#else
#define idShow(id, lmRing, tailRing, debugPrint) ((void)0)
#endif
#endif