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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_ShallowDelete (ideal *h, ring r) |
Shallowdeletes an ideal/matrix. | |
void | idSkipZeroes (ideal ide) |
gives an ideal/module the minimal possible size | |
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) | |
void | id_DelDiv_Sorted (ideal id, const ring r) |
delete id[j], if LT(j) == coeff*mon*LT(i) (j>i) | |
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 68 of file simpleideals.h.
#define id_LmTest | ( | A, | |
lR | |||
) | id_DBLmTest(A, PDEBUG, __FILE__,__LINE__, lR) |
Definition at line 79 of file simpleideals.h.
#define id_Print | ( | id, | |
lR, | |||
tR | |||
) | idShow(id, lR, tR) |
Definition at line 150 of file simpleideals.h.
Definition at line 78 of file simpleideals.h.
Definition at line 23 of file simpleideals.h.
int binom | ( | int | n, |
int | r | ||
) |
Definition at line 1081 of file simpleideals.cc.
ideal id_Add | ( | ideal | h1, |
ideal | h2, | ||
const ring | r | ||
) |
h1 + h2
Definition at line 838 of file simpleideals.cc.
poly id_Array2Vector | ( | poly * | m, |
unsigned | n, | ||
const ring | R | ||
) |
for julia: convert an array of poly to vector
Definition at line 1385 of file simpleideals.cc.
ideal id_ChineseRemainder | ( | ideal * | xx, |
number * | q, | ||
int | rl, | ||
const ring | r | ||
) |
Definition at line 2038 of file simpleideals.cc.
void id_Compactify | ( | ideal | id, |
const ring | r | ||
) |
Definition at line 1328 of file simpleideals.cc.
ideal id_Copy | ( | ideal | h1, |
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.)
Definition at line 237 of file simpleideals.cc.
Internal verification for ideals/modules and dense matrices!
Definition at line 537 of file simpleideals.cc.
Internal verification for ideals/modules and dense matrices!
Definition at line 486 of file simpleideals.cc.
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)
Definition at line 388 of file simpleideals.cc.
void id_DelDiv_Sorted | ( | ideal | id, |
const ring | r | ||
) |
delete id[j], if LT(j) == coeff*mon*LT(i) (j>i)
Definition at line 453 of file simpleideals.cc.
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
Definition at line 302 of file simpleideals.cc.
void id_Delete | ( | ideal * | h, |
ring | r | ||
) |
deletes an ideal/module/matrix
Definition at line 123 of file simpleideals.cc.
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.
Definition at line 325 of file simpleideals.cc.
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
Definition at line 267 of file simpleideals.cc.
ideal id_FreeModule | ( | int | i, |
const ring | r | ||
) |
the free module of rank i
Definition at line 1104 of file simpleideals.cc.
ideal id_Head | ( | ideal | h, |
const ring | r | ||
) |
returns the ideals of initial terms
Definition at line 1352 of file simpleideals.cc.
Definition at line 951 of file simpleideals.cc.
Definition at line 1572 of file simpleideals.cc.
BOOLEAN id_HomModuleW | ( | ideal | id, |
ideal | Q, | ||
const intvec * | w, | ||
const intvec * | module_w, | ||
const ring | r | ||
) |
ideal id_Homogen | ( | ideal | h, |
int | varnum, | ||
const ring | r | ||
) |
Definition at line 1363 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 810 of file simpleideals.cc.
test if the ideal has only constant polynomials NOTE: zero ideal/module is also constant
Definition at line 461 of file simpleideals.cc.
Definition at line 1856 of file simpleideals.cc.
Definition at line 1695 of file simpleideals.cc.
Definition at line 1708 of file simpleideals.cc.
converts mat to module, destroys mat
Definition at line 1408 of file simpleideals.cc.
ideal id_MaxIdeal | ( | const ring | r | ) |
initialise the maximal ideal (at 0)
Definition at line 98 of file simpleideals.cc.
ideal id_MaxIdeal | ( | int | deg, |
const ring | r | ||
) |
Definition at line 1221 of file simpleideals.cc.
Definition at line 1885 of file simpleideals.cc.
Definition at line 1488 of file simpleideals.cc.
Definition at line 1442 of file simpleideals.cc.
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)
Definition at line 851 of file simpleideals.cc.
void id_Norm | ( | ideal | id, |
const ring | r | ||
) |
ideal id = (id[i]), result is leadcoeff(id[i]) = 1
Definition at line 253 of file simpleideals.cc.
void id_Normalize | ( | ideal | id, |
const ring | r | ||
) |
normialize all polys in id
Definition at line 1875 of file simpleideals.cc.
int id_PosConstant | ( | ideal | id, |
const ring | r | ||
) |
index of generator with leading term in ground ring (if any); otherwise -1
Definition at line 80 of file simpleideals.cc.
ideal id_Power | ( | ideal | given, |
int | exp, | ||
const ring | r | ||
) |
Definition at line 1302 of file simpleideals.cc.
Definition at line 1809 of file simpleideals.cc.
long id_RankFreeModule | ( | ideal | m, |
ring | lmRing, | ||
ring | tailRing | ||
) |
return the maximal component number found in any polynomial in s
Definition at line 906 of file simpleideals.cc.
|
inlinestatic |
Definition at line 97 of file simpleideals.h.
int id_ReadOutPivot | ( | ideal | arg, |
int * | comp, | ||
const ring | r | ||
) |
Definition at line 1732 of file simpleideals.cc.
ideal id_ResizeModule | ( | ideal | mod, |
int | rows, | ||
int | cols, | ||
const ring | R | ||
) |
Definition at line 1520 of file simpleideals.cc.
void id_ShallowDelete | ( | ideal * | h, |
ring | r | ||
) |
Shallowdeletes an ideal/matrix.
Definition at line 157 of file simpleideals.cc.
void id_Shift | ( | ideal | M, |
int | s, | ||
const ring | r | ||
) |
Definition at line 2087 of file simpleideals.cc.
ideal id_SimpleAdd | ( | ideal | h1, |
ideal | h2, | ||
const ring | r | ||
) |
concat the lists h1 and h2 without zeros
Definition at line 722 of file simpleideals.cc.
sorts the ideal w.r.t. the actual ringordering uses lex-ordering when nolex = FALSE
Definition at line 627 of file simpleideals.cc.
ideal id_Subst | ( | ideal | id, |
int | n, | ||
poly | e, | ||
const ring | r | ||
) |
Definition at line 1557 of file simpleideals.cc.
ideal id_Transp | ( | ideal | a, |
const ring | rRing | ||
) |
transpose a module
Definition at line 1905 of file simpleideals.cc.
ideal id_Vec2Ideal | ( | poly | vec, |
const ring | R | ||
) |
Definition at line 1376 of file simpleideals.cc.
int idElem | ( | const ideal | F | ) |
void idGetNextChoise | ( | int | r, |
int | end, | ||
BOOLEAN * | endch, | ||
int * | choise | ||
) |
Definition at line 1023 of file simpleideals.cc.
int idGetNumberOfChoise | ( | int | t, |
int | d, | ||
int | begin, | ||
int | end, | ||
int * | choise | ||
) |
Definition at line 1049 of file simpleideals.cc.
ideal idInit | ( | int | idsize, |
int | rank | ||
) |
creates an ideal / module
creates an ideal / module
Definition at line 35 of file simpleideals.cc.
void idInitChoise | ( | int | r, |
int | beg, | ||
int | end, | ||
BOOLEAN * | endch, | ||
int * | choise | ||
) |
Definition at line 1001 of file simpleideals.cc.
BOOLEAN idIs0 | ( | ideal | h | ) |
Definition at line 57 of file simpleideals.cc.
void idSkipZeroes | ( | ideal | ide | ) |
EXTERN_VAR omBin sip_sideal_bin |
Definition at line 54 of file simpleideals.h.