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Data Structures | |
struct | const_ideal |
The following sip_sideal structure has many different uses thoughout Singular. Basic use-cases for it are: More... | |
struct | const_map |
struct | ideal_list |
Macros | |
#define | IDELEMS(i) ((i)->ncols) |
#define | id_Init(s, r, R) idInit(s,r) |
#define | id_Elem(F, R) idElem(F) |
#define | id_Test(A, lR) id_DBTest(A, PDEBUG, __FILE__,__LINE__, lR, lR) |
#define | id_LmTest(A, lR) id_DBLmTest(A, PDEBUG, __FILE__,__LINE__, lR) |
#define | id_Print(id, lR, tR) idShow(id, lR, tR) |
Functions | |
ideal | idInit (int size, int rank=1) |
creates an ideal / module | |
void | id_Delete (ideal *h, ring r) |
deletes an ideal/module/matrix | |
void | id_Delete0 (ideal *h, ring r) |
void | id_ShallowDelete (ideal *h, ring r) |
Shallowdeletes an ideal/matrix. | |
void | idSkipZeroes (ideal ide) |
gives an ideal/module the minimal possible size | |
int | idSkipZeroes0 (ideal ide) |
static int | idElem (const ideal F) |
number of non-zero polys in F | |
void | id_Normalize (ideal id, const ring r) |
normialize all polys in id | |
int | id_MinDegW (ideal M, intvec *w, const ring r) |
void | id_DBTest (ideal h1, int level, const char *f, const int l, const ring lR, const ring tR) |
Internal verification for ideals/modules and dense matrices! | |
void | id_DBLmTest (ideal h1, int level, const char *f, const int l, const ring r) |
Internal verification for ideals/modules and dense matrices! | |
ideal | id_Copy (ideal h1, const ring r) |
copy an ideal | |
ideal | id_SimpleAdd (ideal h1, ideal h2, const ring r) |
concat the lists h1 and h2 without zeros | |
ideal | id_Add (ideal h1, ideal h2, const ring r) |
h1 + h2 | |
ideal | id_Power (ideal given, int exp, const ring r) |
BOOLEAN | idIs0 (ideal h) |
returns true if h is the zero ideal | |
long | id_RankFreeModule (ideal m, ring lmRing, ring tailRing) |
return the maximal component number found in any polynomial in s | |
static long | id_RankFreeModule (ideal m, ring r) |
ideal | id_FreeModule (int i, const ring r) |
the free module of rank i | |
int | id_PosConstant (ideal id, const ring r) |
index of generator with leading term in ground ring (if any); otherwise -1 | |
ideal | id_Head (ideal h, const ring r) |
returns the ideals of initial terms | |
ideal | id_MaxIdeal (const ring r) |
initialise the maximal ideal (at 0) | |
ideal | id_MaxIdeal (int deg, const ring r) |
ideal | id_CopyFirstK (const ideal ide, const int k, const ring r) |
copies the first k (>= 1) entries of the given ideal/module and returns these as a new ideal/module (Note that the copied entries may be zero.) | |
void | id_DelMultiples (ideal id, const ring r) |
ideal id = (id[i]), c any unit if id[i] = c*id[j] then id[j] is deleted for j > i | |
void | id_Norm (ideal id, const ring r) |
ideal id = (id[i]), result is leadcoeff(id[i]) = 1 | |
void | id_DelEquals (ideal id, const ring r) |
ideal id = (id[i]) if id[i] = id[j] then id[j] is deleted for j > i | |
void | id_DelLmEquals (ideal id, const ring r) |
Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i. | |
void | id_DelDiv (ideal id, const ring r) |
delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., delete id[i], if LT(i) == coeff*mon*LT(j) | |
BOOLEAN | id_IsConstant (ideal id, const ring r) |
test if the ideal has only constant polynomials NOTE: zero ideal/module is also constant | |
intvec * | id_Sort (const ideal id, const BOOLEAN nolex, const ring r) |
sorts the ideal w.r.t. the actual ringordering uses lex-ordering when nolex = FALSE | |
ideal | id_Transp (ideal a, const ring rRing) |
transpose a module | |
void | id_Compactify (ideal id, const ring r) |
ideal | id_Mult (ideal h1, ideal h2, const ring r) |
h1 * h2 one h_i must be an ideal (with at least one column) the other h_i may be a module (with no columns at all) | |
ideal | id_Homogen (ideal h, int varnum, const ring r) |
BOOLEAN | id_HomIdeal (ideal id, ideal Q, const ring r) |
BOOLEAN | id_HomIdealW (ideal id, ideal Q, const intvec *w, const ring r) |
BOOLEAN | id_HomModuleW (ideal id, ideal Q, const intvec *w, const intvec *module_w, const ring r) |
BOOLEAN | id_HomModule (ideal m, ideal Q, intvec **w, const ring R) |
BOOLEAN | id_IsZeroDim (ideal I, const ring r) |
ideal | id_Jet (const ideal i, int d, const ring R) |
ideal | id_JetW (const ideal i, int d, intvec *iv, const ring R) |
ideal | id_Subst (ideal id, int n, poly e, const ring r) |
matrix | id_Module2Matrix (ideal mod, const ring R) |
matrix | id_Module2formatedMatrix (ideal mod, int rows, int cols, const ring R) |
ideal | id_ResizeModule (ideal mod, int rows, int cols, const ring R) |
ideal | id_Matrix2Module (matrix mat, const ring R) |
converts mat to module, destroys mat | |
ideal | id_Vec2Ideal (poly vec, const ring R) |
int | id_ReadOutPivot (ideal arg, int *comp, const ring r) |
int | binom (int n, int r) |
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) |
void | idShow (const ideal id, const ring lmRing, const ring tailRing, const int debugPrint=0) |
BOOLEAN | id_InsertPolyWithTests (ideal h1, const int validEntries, const poly h2, const bool zeroOk, const bool duplicateOk, const ring r) |
insert h2 into h1 depending on the two boolean parameters: | |
intvec * | id_QHomWeight (ideal id, const ring r) |
ideal | id_ChineseRemainder (ideal *xx, number *q, int rl, const ring r) |
void | id_Shift (ideal M, int s, const ring r) |
ideal | id_Delete_Pos (const ideal I, const int pos, const ring r) |
poly | id_Array2Vector (poly *m, unsigned n, const ring R) |
for julia: convert an array of poly to vector | |
Variables | |
EXTERN_VAR omBin | sip_sideal_bin |
struct sip_sideal |
The following sip_sideal structure has many different uses thoughout Singular. Basic use-cases for it are:
Definition at line 17 of file simpleideals.h.
Data Fields | ||
---|---|---|
poly * | m | |
int | ncols | |
int | nrows | |
long | rank |
struct sip_smap |
Definition at line 32 of file simpleideals.h.
Data Fields | ||
---|---|---|
poly * | m | |
int | ncols | |
int | nrows | |
char * | preimage |
struct sideal_list |
Definition at line 45 of file simpleideals.h.
Data Fields | ||
---|---|---|
ideal | d | |
ideal_list | next | |
int | nr |
Definition at line 79 of file simpleideals.h.
Definition at line 90 of file simpleideals.h.
Definition at line 89 of file simpleideals.h.
Definition at line 1152 of file simpleideals.cc.
h1 + h2
Definition at line 909 of file simpleideals.cc.
for julia: convert an array of poly to vector
Definition at line 1465 of file simpleideals.cc.
Definition at line 2118 of file simpleideals.cc.
Definition at line 1399 of file simpleideals.cc.
copies the first k (>= 1) entries of the given ideal/module and returns these as a new ideal/module (Note that the copied entries may be zero.)
Definition at line 269 of file simpleideals.cc.
Internal verification for ideals/modules and dense matrices!
Definition at line 608 of file simpleideals.cc.
Internal verification for ideals/modules and dense matrices!
Definition at line 557 of file simpleideals.cc.
delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., delete id[i], if LT(i) == coeff*mon*LT(j)
Definition at line 466 of file simpleideals.cc.
ideal id = (id[i]) if id[i] = id[j] then id[j] is deleted for j > i
Definition at line 334 of file simpleideals.cc.
deletes an ideal/module/matrix
Definition at line 123 of file simpleideals.cc.
Definition at line 155 of file simpleideals.cc.
Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i.
Definition at line 357 of file simpleideals.cc.
ideal id = (id[i]), c any unit if id[i] = c*id[j] then id[j] is deleted for j > i
Definition at line 299 of file simpleideals.cc.
the free module of rank i
Definition at line 1175 of file simpleideals.cc.
returns the ideals of initial terms
Definition at line 1423 of file simpleideals.cc.
Definition at line 1022 of file simpleideals.cc.
Definition at line 1652 of file simpleideals.cc.
BOOLEAN id_HomModuleW | ( | ideal | id, |
ideal | Q, | ||
const intvec * | w, | ||
const intvec * | module_w, | ||
const ring | r | ||
) |
Definition at line 1443 of file simpleideals.cc.
BOOLEAN id_InsertPolyWithTests | ( | ideal | h1, |
const int | validEntries, | ||
const poly | h2, | ||
const bool | zeroOk, | ||
const bool | duplicateOk, | ||
const ring | r | ||
) |
insert h2 into h1 depending on the two boolean parameters:
Definition at line 881 of file simpleideals.cc.
test if the ideal has only constant polynomials NOTE: zero ideal/module is also constant
Definition at line 532 of file simpleideals.cc.
Definition at line 1936 of file simpleideals.cc.
Definition at line 1775 of file simpleideals.cc.
Definition at line 1788 of file simpleideals.cc.
converts mat to module, destroys mat
Definition at line 1488 of file simpleideals.cc.
initialise the maximal ideal (at 0)
Definition at line 98 of file simpleideals.cc.
Definition at line 1292 of file simpleideals.cc.
Definition at line 1965 of file simpleideals.cc.
Definition at line 1568 of file simpleideals.cc.
Definition at line 1522 of file simpleideals.cc.
h1 * h2 one h_i must be an ideal (with at least one column) the other h_i may be a module (with no columns at all)
Definition at line 922 of file simpleideals.cc.
ideal id = (id[i]), result is leadcoeff(id[i]) = 1
Definition at line 285 of file simpleideals.cc.
normialize all polys in id
Definition at line 1955 of file simpleideals.cc.
index of generator with leading term in ground ring (if any); otherwise -1
Definition at line 80 of file simpleideals.cc.
Definition at line 1373 of file simpleideals.cc.
Definition at line 1889 of file simpleideals.cc.
return the maximal component number found in any polynomial in s
Definition at line 977 of file simpleideals.cc.
Definition at line 108 of file simpleideals.h.
Definition at line 1812 of file simpleideals.cc.
Definition at line 1600 of file simpleideals.cc.
Shallowdeletes an ideal/matrix.
Definition at line 177 of file simpleideals.cc.
Definition at line 2167 of file simpleideals.cc.
concat the lists h1 and h2 without zeros
Definition at line 793 of file simpleideals.cc.
sorts the ideal w.r.t. the actual ringordering uses lex-ordering when nolex = FALSE
Definition at line 698 of file simpleideals.cc.
Definition at line 1637 of file simpleideals.cc.
transpose a module
Definition at line 1985 of file simpleideals.cc.
Definition at line 1456 of file simpleideals.cc.
Definition at line 1094 of file simpleideals.cc.
Definition at line 1120 of file simpleideals.cc.
creates an ideal / module
creates an ideal / module
Definition at line 35 of file simpleideals.cc.
Definition at line 1072 of file simpleideals.cc.
Definition at line 57 of file simpleideals.cc.
gives an ideal/module the minimal possible size
Definition at line 201 of file simpleideals.cc.
Definition at line 240 of file simpleideals.cc.
EXTERN_VAR omBin sip_sideal_bin |
Definition at line 54 of file simpleideals.h.