source: git/kernel/ideals.h @ 61d32c

spielwiese
Last change on this file since 61d32c was 9c1b63, checked in by Motsak Oleksandr <motsak@…>, 15 years ago
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1#ifndef IDEALS_H
2#define IDEALS_H
3/****************************************
4*  Computer Algebra System SINGULAR     *
5****************************************/
6/* $Id: ideals.h,v 1.13 2009-02-12 16:19:23 motsak Exp $ */
7/*
8* ABSTRACT - all basic methods to manipulate ideals
9*/
10#include "structs.h"
11
12#ifdef PDEBUG
13ideal idDBInit (int size, int rank, const char *f, int l);
14#define idInit(A,B) idDBInit(A,B,__FILE__,__LINE__)
15#else
16/*- creates an ideal -*/
17ideal idInit (int size, int rank=1);
18#endif
19/*- deletes an ideal -*/
20#define idDelete(h) id_Delete(h, currRing)
21void id_Delete (ideal* h, ring r);
22void id_ShallowDelete (ideal* h, ring r);
23/* Shows an ideal -- mainly for debugging */
24void idShow(ideal id);
25  /*- initialise an ideal -*/
26ideal idMaxIdeal (int deg);
27  /*- initialise the maximal ideal (at 0) -*/
28void idSkipZeroes (ideal ide);
29  /*gives an ideal the minimal possible size*/
30void idNorm(ideal id);
31void idDelMultiples(ideal id);
32void idDelEquals(ideal id);
33void idDelLmEquals(ideal id);
34void idDelDiv(ideal id);
35BOOLEAN idIsConstant(ideal id);
36
37#ifdef PDEBUG
38void idDBTest(ideal h1, int level, const char *f,const int l);
39#define idTest(A) idDBTest(A, PDEBUG, __FILE__,__LINE__)
40#define idPrint(id) idShow(id)
41#else
42#define idTest(A)  (TRUE)
43#define idPrint(A) ((void)0)
44#endif
45
46ideal id_Copy (ideal h1,const ring r);
47#ifdef PDEBUG
48ideal idDBCopy(ideal h1,const char *f,int l);
49#define idCopy(A) idDBCopy(A,__FILE__,__LINE__)
50#else
51#define idCopy(A) id_Copy(A,currRing)
52#endif
53  /*adds two ideals without simplifying the result*/
54ideal idSimpleAdd (ideal h1,ideal h2);
55  /*adds the quotient ideal*/
56ideal idAdd (ideal h1,ideal h2);
57  /* h1 + h2 */
58ideal idMult (ideal h1,ideal h2);
59  /*hh := h1 * h2*/
60
61BOOLEAN idIs0 (ideal h);
62
63long idRankFreeModule(ideal m, ring lmRing, ring tailRing);
64inline long idRankFreeModule(ideal m, ring r = currRing)
65{return idRankFreeModule(m, r, r);}
66// returns TRUE, if idRankFreeModule(m) > 0
67BOOLEAN idIsModule(ideal m, ring r = currRing);
68BOOLEAN idHomIdeal (ideal id, ideal Q=NULL);
69BOOLEAN idHomModule(ideal m, ideal Q,intvec **w);
70BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w);
71
72ideal idMinBase (ideal h1);
73  /*returns a minimized set of generators of h1*/
74int pLowVar (poly p);
75  /*-the minimal index of used variables - 1-*/
76ideal idDehomogen (ideal id1,poly p,number n);
77  /*dehomogenized the generators of the ideal id1 with the leading
78  monomial of p replaced by n*/
79void pShift (poly * p,int i);
80  /*- verschiebt die Indizes der Modulerzeugenden um i -*/
81void    idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise);
82void    idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise);
83int     idGetNumberOfChoise(int t, int d, int begin, int end, int * choise);
84
85int     binom (int n,int r);
86
87ideal   idFreeModule (int i);
88
89ideal   idSect (ideal h1,ideal h2);
90ideal   idMultSect(resolvente arg, int length);
91
92//ideal   idSyzygies (ideal h1, tHomog h,intvec **w);
93ideal   idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp=TRUE,
94                    BOOLEAN setRegularity=FALSE, int *deg = NULL);
95ideal   idLiftStd  (ideal h1, matrix *m, tHomog h=testHomog);
96
97ideal   idLift (ideal mod, ideal sumod,ideal * rest=NULL,
98             BOOLEAN goodShape=FALSE, BOOLEAN isSB=TRUE,BOOLEAN divide=FALSE,
99             matrix *unit=NULL);
100
101void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R, short *w= NULL );
102
103intvec * idMWLift(ideal mod,intvec * weights);
104
105ideal   idQuot (ideal h1,ideal h2,
106                BOOLEAN h1IsStb=FALSE, BOOLEAN resultIsIdeal=FALSE);
107
108ideal   idPower(ideal gid,int deg);
109
110//ideal   idElimination (ideal h1,poly delVar);
111ideal   idElimination (ideal h1,poly delVar, intvec *hilb=NULL);
112
113poly idMinor(matrix a, int ar, unsigned long which, ideal R=NULL);
114
115ideal   idMinors(matrix a, int ar, ideal R=NULL);
116
117void   idCompactify(ideal id);
118
119ideal idMinEmbedding(ideal arg,BOOLEAN inPlace=FALSE, intvec **w=NULL);
120
121ideal   idHead(ideal h);
122
123ideal   idHomogen(ideal h, int varnum);
124
125BOOLEAN idIsSubModule(ideal id1,ideal id2);
126
127ideal   idVec2Ideal(poly vec);
128
129ideal   idMatrix2Module(matrix mat);
130
131matrix  idModule2Matrix(ideal mod);
132
133matrix  idModule2formatedMatrix(ideal mod,int rows, int cols);
134
135ideal   idSubst(ideal i, int n, poly e);
136
137ideal   idJet(ideal i,int d);
138ideal   idJetW(ideal i,int d, intvec * iv);
139int idMinDegW(ideal M,intvec *w);
140ideal   idSeries(int n,ideal M,matrix U=NULL,intvec *w=NULL);
141
142BOOLEAN idIsZeroDim(ideal i);
143matrix  idDiff(matrix i, int k);
144matrix  idDiffOp(ideal I, ideal J,BOOLEAN multiply=TRUE);
145
146intvec *idSort(ideal id,BOOLEAN nolex=TRUE);
147ideal   idModulo (ideal h1,ideal h2, tHomog h=testHomog, intvec ** w=NULL);
148int     idElem(const ideal F);
149matrix  idCoeffOfKBase(ideal arg, ideal kbase, poly how);
150// transpose a module
151ideal   idTransp(ideal a);
152// version of "ideal idTransp(ideal)" which works within a given ring.
153ideal id_Transp(ideal a, const ring rRing = currRing);
154
155
156intvec *idQHomWeight(ideal id);
157
158void    idNormalize(ideal id);
159
160ideal idXXX (ideal  h1, int k);
161
162poly id_GCD(poly f, poly g, const ring r);
163
164ideal idChineseRemainder(ideal *x, number *q, int rl);
165ideal idChineseRemainder(ideal *x, intvec *iv);
166
167
168ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing = currRing); // image of certain map for BGG
169
170
171
172#endif
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