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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 | MATCOLS(i) ((i)->ncols) |
#define | MATROWS(i) ((i)->nrows) |
#define | MATELEM(mat, i, j) ((mat)->m)[MATCOLS((mat)) * ((i)-1) + (j)-1] |
#define | id_TestTail(A, lR, tR) id_DBTest(A, PDEBUG, __FILE__,__LINE__, lR, tR) |
#define | id_Test(A, lR) id_DBTest(A, PDEBUG, __FILE__,__LINE__, lR, lR) |
#define | id_Print(id, lR, tR) idShow(id, lR, tR) |
Functions | |
ideal | idInit (int size, int rank=1) |
creates an ideal / module More... | |
void | id_Delete (ideal *h, ring r) |
deletes an ideal/module/matrix More... | |
void | id_ShallowDelete (ideal *h, ring r) |
Shallowdeletes an ideal/matrix. More... | |
void | idSkipZeroes (ideal ide) |
gives an ideal/module the minimal possible size More... | |
int | idElem (const ideal F) |
number of non-zero polys in F More... | |
void | id_Normalize (ideal id, const ring r) |
normialize all polys in id More... | |
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! More... | |
ideal | id_Copy (ideal h1, const ring r) |
copy an ideal More... | |
ideal | id_SimpleAdd (ideal h1, ideal h2, const ring r) |
concat the lists h1 and h2 without zeros More... | |
ideal | id_Add (ideal h1, ideal h2, const ring r) |
h1 + h2 More... | |
ideal | id_Power (ideal given, int exp, const ring r) |
BOOLEAN | idIs0 (ideal h) |
returns true if h is the zero ideal More... | |
long | id_RankFreeModule (ideal m, ring lmRing, ring tailRing) |
return the maximal component number found in any polynomial in s More... | |
static long | id_RankFreeModule (ideal m, ring r) |
ideal | id_FreeModule (int i, const ring r) |
the free module of rank i More... | |
int | id_PosConstant (ideal id, const ring r) |
index of generator with leading term in ground ring (if any); otherwise -1 More... | |
ideal | id_Head (ideal h, const ring r) |
returns the ideals of initial terms More... | |
ideal | id_MaxIdeal (const ring r) |
initialise the maximal ideal (at 0) More... | |
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.) More... | |
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 More... | |
void | id_Norm (ideal id, const ring r) |
ideal id = (id[i]), result is leadcoeff(id[i]) = 1 More... | |
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 More... | |
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. More... | |
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) More... | |
BOOLEAN | id_IsConstant (ideal id, const ring r) |
test if the ideal has only constant polynomials NOTE: zero ideal/module is also constant More... | |
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 More... | |
ideal | id_Transp (ideal a, const ring rRing) |
transpose a module More... | |
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) More... | |
ideal | id_Homogen (ideal h, int varnum, const ring r) |
BOOLEAN | id_HomIdeal (ideal id, ideal Q, 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_Matrix2Module (matrix mat, const ring R) |
converts mat to module, destroys mat More... | |
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: More... | |
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 More... | |
Variables | |
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 36 of file simpleideals.h.
Data Fields | ||
---|---|---|
poly * | m | |
int | ncols | |
int | nrows | |
char * | preimage |
struct sideal_list |
Definition at line 49 of file simpleideals.h.
Data Fields | ||
---|---|---|
ideal | d | |
ideal_list | next | |
int | nr |
#define id_Print | ( | id, | |
lR, | |||
tR | |||
) | idShow(id, lR, tR) |
Definition at line 146 of file simpleideals.h.
Definition at line 79 of file simpleideals.h.
Definition at line 78 of file simpleideals.h.
Definition at line 24 of file simpleideals.h.
Definition at line 25 of file simpleideals.h.
Definition at line 27 of file simpleideals.h.
Definition at line 26 of file simpleideals.h.
int binom | ( | int | n, |
int | r | ||
) |
Definition at line 912 of file simpleideals.cc.
ideal id_Add | ( | ideal | h1, |
ideal | h2, | ||
const ring | r | ||
) |
poly id_Array2Vector | ( | poly * | m, |
unsigned | n, | ||
const ring | R | ||
) |
ideal id_ChineseRemainder | ( | ideal * | xx, |
number * | q, | ||
int | rl, | ||
const ring | r | ||
) |
Definition at line 1763 of file simpleideals.cc.
void id_Compactify | ( | ideal | id, |
const ring | r | ||
) |
Definition at line 1086 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 225 of file simpleideals.cc.
Internal verification for ideals/modules and dense matrices!
Definition at line 415 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 341 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 290 of file simpleideals.cc.
void id_Delete | ( | ideal * | h, |
ring | r | ||
) |
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 313 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 255 of file simpleideals.cc.
ideal id_FreeModule | ( | int | i, |
const ring | r | ||
) |
ideal id_Head | ( | ideal | h, |
const ring | r | ||
) |
Definition at line 805 of file simpleideals.cc.
Definition at line 1297 of file simpleideals.cc.
ideal id_Homogen | ( | ideal | h, |
int | varnum, | ||
const ring | r | ||
) |
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 685 of file simpleideals.cc.
Definition at line 1581 of file simpleideals.cc.
Definition at line 1433 of file simpleideals.cc.
ideal id_MaxIdeal | ( | const ring | r | ) |
ideal id_MaxIdeal | ( | int | deg, |
const ring | r | ||
) |
Definition at line 1004 of file simpleideals.cc.
Definition at line 1246 of file simpleideals.cc.
Definition at line 1200 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 726 of file simpleideals.cc.
void id_Norm | ( | ideal | id, |
const ring | r | ||
) |
void id_Normalize | ( | ideal | id, |
const ring | r | ||
) |
int id_PosConstant | ( | ideal | id, |
const ring | r | ||
) |
index of generator with leading term in ground ring (if any); otherwise -1
Definition at line 81 of file simpleideals.cc.
ideal id_Power | ( | ideal | given, |
int | exp, | ||
const ring | r | ||
) |
Definition at line 1060 of file simpleideals.cc.
Definition at line 1534 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 781 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 1457 of file simpleideals.cc.
void id_ShallowDelete | ( | ideal * | h, |
ring | r | ||
) |
void id_Shift | ( | ideal | M, |
int | s, | ||
const ring | r | ||
) |
Definition at line 1812 of file simpleideals.cc.
ideal id_SimpleAdd | ( | ideal | h1, |
ideal | h2, | ||
const ring | r | ||
) |
sorts the ideal w.r.t. the actual ringordering uses lex-ordering when nolex = FALSE
Definition at line 502 of file simpleideals.cc.
ideal id_Subst | ( | ideal | id, |
int | n, | ||
poly | e, | ||
const ring | r | ||
) |
Definition at line 1282 of file simpleideals.cc.
ideal id_Transp | ( | ideal | a, |
const ring | rRing | ||
) |
ideal id_Vec2Ideal | ( | poly | vec, |
const ring | R | ||
) |
int idElem | ( | const ideal | F | ) |
void idGetNextChoise | ( | int | r, |
int | end, | ||
BOOLEAN * | endch, | ||
int * | choise | ||
) |
Definition at line 854 of file simpleideals.cc.
int idGetNumberOfChoise | ( | int | t, |
int | d, | ||
int | begin, | ||
int | end, | ||
int * | choise | ||
) |
Definition at line 880 of file simpleideals.cc.
ideal idInit | ( | int | idsize, |
int | rank | ||
) |
void idInitChoise | ( | int | r, |
int | beg, | ||
int | end, | ||
BOOLEAN * | endch, | ||
int * | choise | ||
) |
Definition at line 832 of file simpleideals.cc.
BOOLEAN idIs0 | ( | ideal | h | ) |
Definition at line 58 of file simpleideals.cc.
void idSkipZeroes | ( | ideal | ide | ) |
omBin sip_sideal_bin |
Definition at line 28 of file simpleideals.cc.