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#include "polys/monomials/ring.h"
#include "polys/monomials/p_polys.h"
#include "polys/simpleideals.h"
#include "kernel/structs.h"
Go to the source code of this file.
Macros | |
#define | idDelete(H) |
delete an ideal | |
#define | idMaxIdeal(D) |
initialise the maximal ideal (at 0) | |
#define | idPosConstant(I) |
index of generator with leading term in ground ring (if any); otherwise -1 | |
#define | idIsConstant(I) |
#define | idSimpleAdd(A, B) |
#define | idPrint(id) |
#define | idTest(id) |
Typedefs | |
typedef ideal * | resolvente |
Enumerations | |
enum | GbVariant { GbDefault =0 , GbStd , GbSlimgb , GbSba , GbGroebner , GbModstd , GbFfmod , GbNfmod , GbStdSat , GbSingmatic } |
Functions | |
static ideal | idCopyFirstK (const ideal ide, const int k) |
void | idKeepFirstK (ideal ide, const int k) |
keeps the first k (>= 1) entries of the given ideal (Note that the kept polynomials may be zero.) | |
void | idDelEquals (ideal id) |
ideal | id_Copy (ideal h1, const ring r) |
copy an ideal | |
ideal | idCopy (ideal A) |
ideal | idAdd (ideal h1, ideal h2) |
h1 + h2 | |
BOOLEAN | idInsertPoly (ideal h1, poly h2) |
insert h2 into h1 (if h2 is not the zero polynomial) return TRUE iff h2 was indeed inserted | |
BOOLEAN | idInsertPolyOnPos (ideal I, poly p, int pos) |
insert p into I on position pos | |
BOOLEAN | idInsertPolyWithTests (ideal h1, const int validEntries, const poly h2, const bool zeroOk, const bool duplicateOk) |
static ideal | idMult (ideal h1, ideal h2) |
hh := h1 * h2 | |
BOOLEAN | idIs0 (ideal h) |
returns true if h is the zero ideal | |
static BOOLEAN | idHomIdeal (ideal id, ideal Q=NULL) |
static BOOLEAN | idHomModule (ideal m, ideal Q, intvec **w) |
BOOLEAN | idTestHomModule (ideal m, ideal Q, intvec *w) |
ideal | idMinBase (ideal h1, ideal *SB=NULL) |
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, GbVariant a=GbDefault) |
ideal | idMultSect (resolvente arg, int length, GbVariant a=GbDefault) |
ideal | idSyzygies (ideal h1, tHomog h, intvec **w, BOOLEAN setSyzComp=TRUE, BOOLEAN setRegularity=FALSE, int *deg=NULL, GbVariant a=GbDefault) |
ideal | idLiftStd (ideal h1, matrix *m, tHomog h=testHomog, ideal *syz=NULL, GbVariant a=GbDefault, ideal h11=NULL) |
ideal | idLift (ideal mod, ideal submod, ideal *rest=NULL, BOOLEAN goodShape=FALSE, BOOLEAN isSB=TRUE, BOOLEAN divide=FALSE, matrix *unit=NULL, GbVariant a=GbDefault) |
represents the generators of submod in terms of the generators of mod (Matrix(SM)*U-Matrix(rest)) = Matrix(M)*Matrix(result) goodShape: maximal non-zero index in generators of SM <= that of M isSB: generators of M form a Groebner basis divide: allow SM not to be a submodule of M U is an diagonal matrix of units (non-constant only in local rings) rest is: 0 if SM in M, SM if not divide, NF(SM,std(M)) if divide | |
void | idLiftW (ideal P, ideal Q, int n, matrix &T, ideal &R, int *w=NULL) |
ideal | idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb=FALSE, BOOLEAN resultIsIdeal=FALSE) |
ideal | idElimination (ideal h1, poly delVar, intvec *hilb=NULL, GbVariant a=GbDefault) |
ideal | idElimination2 (ideal h1, poly delVar, bigintmat *hilb=NULL, GbVariant a=GbDefault) |
ideal | idMinors (matrix a, int ar, ideal R=NULL) |
compute all ar-minors of the matrix a the caller of mpRecMin the elements of the result are not in R (if R!=NULL) | |
ideal | idMinEmbedding (ideal arg, BOOLEAN inPlace=FALSE, intvec **w=NULL) |
ideal | idMinEmbedding_with_map (ideal arg, intvec **w, ideal &trans) |
ideal | idMinEmbedding_with_map_v (ideal arg, intvec **w, ideal &trans, int *red_comp) |
ideal | idHead (ideal h) |
BOOLEAN | idIsSubModule (ideal id1, ideal id2) |
static ideal | idVec2Ideal (poly vec) |
ideal | idSeries (int n, ideal M, matrix U=NULL, intvec *w=NULL) |
static BOOLEAN | idIsZeroDim (ideal i) |
matrix | idDiff (matrix i, int k) |
matrix | idDiffOp (ideal I, ideal J, BOOLEAN multiply=TRUE) |
static intvec * | idSort (ideal id, BOOLEAN nolex=TRUE) |
ideal | idModulo (ideal h1, ideal h2, tHomog h=testHomog, intvec **w=NULL, matrix *T=NULL, GbVariant a=GbDefault) |
matrix | idCoeffOfKBase (ideal arg, ideal kbase, poly how) |
poly | id_GCD (poly f, poly g, const ring r) |
ideal | id_Farey (ideal x, number N, const ring r) |
ideal | id_TensorModuleMult (const int m, const ideal M, const ring rRing) |
ideal | id_Satstd (const ideal I, ideal J, const ring r) |
ideal | id_Sat_principal (const ideal I, ideal J, const ring r) |
ideal | idSaturate_intern (ideal I, ideal J, int &ki, BOOLEAN isIdeal, BOOLEAN isSB) |
ideal | idSaturate (ideal I, ideal J, int &ki, BOOLEAN isIdeal=TRUE) |
ideal | idSaturateGB (ideal I, ideal J, int &ki, BOOLEAN isIdeal=TRUE) |
ideal | id_Homogenize (ideal I, int var_num, const ring r) |
ideal | id_HomogenizeW (ideal I, int var_num, intvec *w, const ring r) |
GbVariant | syGetAlgorithm (char *n, const ring r, const ideal M) |
#define idDelete | ( | H | ) |
delete an ideal
#define idIsConstant | ( | I | ) |
#define idMaxIdeal | ( | D | ) |
initialise the maximal ideal (at 0)
#define idPosConstant | ( | I | ) |
index of generator with leading term in ground ring (if any); otherwise -1
#define idPrint | ( | id | ) |
#define idTest | ( | id | ) |
typedef ideal* resolvente |
enum GbVariant |
Enumerator | |
---|---|
GbDefault | |
GbStd | |
GbSlimgb | |
GbSba | |
GbGroebner | |
GbModstd | |
GbFfmod | |
GbNfmod | |
GbStdSat | |
GbSingmatic |
Definition at line 118 of file ideals.h.
int binom | ( | int | n, |
int | r ) |
Definition at line 1211 of file simpleideals.cc.
ideal id_Copy | ( | ideal | h1, |
const ring | r ) |
copy an ideal
Definition at line 541 of file simpleideals.cc.
ideal id_Farey | ( | ideal | x, |
number | N, | ||
const ring | r ) |
poly id_GCD | ( | poly | f, |
poly | g, | ||
const ring | r ) |
Definition at line 2971 of file ideals.cc.
ideal id_Homogenize | ( | ideal | I, |
int | var_num, | ||
const ring | r ) |
Definition at line 3576 of file ideals.cc.
Definition at line 3621 of file ideals.cc.
Definition at line 3386 of file ideals.cc.
Definition at line 3334 of file ideals.cc.
Definition at line 2065 of file simpleideals.cc.
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inline |
matrix idCoeffOfKBase | ( | ideal | arg, |
ideal | kbase, | ||
poly | how ) |
Definition at line 2639 of file ideals.cc.
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inline |
Definition at line 20 of file ideals.h.
void idDelEquals | ( | ideal | id | ) |
Definition at line 3182 of file ideals.cc.
Definition at line 1855 of file ideals.cc.
Definition at line 1611 of file ideals.cc.
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inline |
Definition at line 111 of file ideals.h.
void idGetNextChoise | ( | int | r, |
int | end, | ||
BOOLEAN * | endch, | ||
int * | choise ) |
Definition at line 1153 of file simpleideals.cc.
int idGetNumberOfChoise | ( | int | t, |
int | d, | ||
int | begin, | ||
int | end, | ||
int * | choise ) |
Definition at line 1179 of file simpleideals.cc.
ideal idHead | ( | ideal | h | ) |
Definition at line 96 of file ideals.h.
void idInitChoise | ( | int | r, |
int | beg, | ||
int | end, | ||
BOOLEAN * | endch, | ||
int * | choise ) |
Definition at line 1131 of file simpleideals.cc.
BOOLEAN idInsertPoly | ( | ideal | h1, |
poly | h2 ) |
insert h2 into h1 (if h2 is not the zero polynomial) return TRUE iff h2 was indeed inserted
Definition at line 831 of file simpleideals.cc.
BOOLEAN idInsertPolyOnPos | ( | ideal | I, |
poly | p, | ||
int | pos ) |
insert p into I on position pos
Definition at line 850 of file simpleideals.cc.
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inline |
Definition at line 75 of file ideals.h.
BOOLEAN idIs0 | ( | ideal | h | ) |
BOOLEAN idIsSubModule | ( | ideal | id1, |
ideal | id2 ) |
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inlinestatic |
void idKeepFirstK | ( | ideal | ide, |
const int | k ) |
keeps the first k (>= 1) entries of the given ideal (Note that the kept polynomials may be zero.)
ideal idLift | ( | ideal | mod, |
ideal | submod, | ||
ideal * | rest = NULL, | ||
BOOLEAN | goodShape = FALSE, | ||
BOOLEAN | isSB = TRUE, | ||
BOOLEAN | divide = FALSE, | ||
matrix * | unit = NULL, | ||
GbVariant | a = GbDefault ) |
represents the generators of submod in terms of the generators of mod (Matrix(SM)*U-Matrix(rest)) = Matrix(M)*Matrix(result) goodShape: maximal non-zero index in generators of SM <= that of M isSB: generators of M form a Groebner basis divide: allow SM not to be a submodule of M U is an diagonal matrix of units (non-constant only in local rings) rest is: 0 if SM in M, SM if not divide, NF(SM,std(M)) if divide
Definition at line 1111 of file ideals.cc.
ideal idLiftStd | ( | ideal | h1, |
matrix * | m, | ||
tHomog | h = testHomog, | ||
ideal * | syz = NULL, | ||
GbVariant | a = GbDefault, | ||
ideal | h11 = NULL ) |
Definition at line 982 of file ideals.cc.
Definition at line 1342 of file ideals.cc.
ideal idMinBase | ( | ideal | h1, |
ideal * | SB = NULL ) |
Definition at line 51 of file ideals.cc.
Definition at line 2824 of file ideals.cc.
ideal idMinEmbedding_with_map | ( | ideal | arg, |
intvec ** | w, | ||
ideal & | trans ) |
Definition at line 2834 of file ideals.cc.
ideal idMinEmbedding_with_map_v | ( | ideal | arg, |
intvec ** | w, | ||
ideal & | trans, | ||
int * | red_comp ) |
Definition at line 2845 of file ideals.cc.
compute all ar-minors of the matrix a the caller of mpRecMin the elements of the result are not in R (if R!=NULL)
Definition at line 2002 of file ideals.cc.
ideal idModulo | ( | ideal | h1, |
ideal | h2, | ||
tHomog | h = testHomog, | ||
intvec ** | w = NULL, | ||
matrix * | T = NULL, | ||
GbVariant | a = GbDefault ) |
Definition at line 2434 of file ideals.cc.
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inlinestatic |
ideal idMultSect | ( | resolvente | arg, |
int | length, | ||
GbVariant | a = GbDefault ) |
Definition at line 472 of file ideals.cc.
Definition at line 1512 of file ideals.cc.
Definition at line 3567 of file ideals.cc.
Definition at line 3466 of file ideals.cc.
Definition at line 315 of file ideals.cc.
ideal idSyzygies | ( | ideal | h1, |
tHomog | h, | ||
intvec ** | w, | ||
BOOLEAN | setSyzComp = TRUE, | ||
BOOLEAN | setRegularity = FALSE, | ||
int * | deg = NULL, | ||
GbVariant | a = GbDefault ) |
Definition at line 836 of file ideals.cc.
Definition at line 2091 of file ideals.cc.
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inlinestatic |
Definition at line 3666 of file ideals.cc.