23 #define IDELEMS(i) ((i)->ncols)
58#define id_Init(s,r,R) idInit(s,r)
67static inline int idElem(
const ideal F)
77#define id_Elem(F,R) idElem(F)
85void id_DBTest(ideal h1,
int level,
const char *
f,
const int l,
const ring lR,
const ring tR );
87#define id_Test(A, lR) id_DBTest(A, PDEBUG, __FILE__,__LINE__, lR, lR)
88#define id_LmTest(A, lR) id_DBLmTest(A, PDEBUG, __FILE__,__LINE__, lR)
90#define id_Test(A, lR) do {} while (0)
91#define id_LmTest(A, lR) do {} while (0)
94ideal
id_Copy (ideal h1,
const ring r);
99ideal
id_Add (ideal h1,ideal h2,
const ring r);
117void id_Norm(ideal
id,
const ring r);
128ideal
id_Transp(ideal a,
const ring rRing);
131ideal
id_Mult (ideal h1,ideal h2,
const ring r);
138ideal
id_Jet(
const ideal
i,
int d,
const ring
R);
140ideal
id_Subst(ideal
id,
int n, poly e,
const ring r);
149int binom (
int n,
int r);
157void idShow(
const ideal
id,
const ring lmRing,
const ring tailRing,
const int debugPrint = 0);
158#define id_Print(id, lR, tR) idShow(id, lR, tR)
160#define id_Print(A, lR, tR) do {} while (0)
171 const poly h2,
const bool zeroOk,
172 const bool duplicateOk,
const ring r);
181ideal
id_Delete_Pos(
const ideal I,
const int pos,
const ring r);
const CanonicalForm int s
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
gmp_float exp(const gmp_float &a)
ideal idInit(int size, int rank=1)
creates an ideal / module
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_Add(ideal h1, ideal h2, const ring r)
h1 + h2
ideal id_Vec2Ideal(poly vec, const ring R)
int id_PosConstant(ideal id, const ring r)
index of generator with leading term in ground ring (if any); otherwise -1
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
poly id_Array2Vector(poly *m, unsigned n, const ring R)
for julia: convert an array of poly to vector
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
intvec * id_QHomWeight(ideal id, const ring r)
void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint=0)
void id_Norm(ideal id, const ring r)
ideal id = (id[i]), result is leadcoeff(id[i]) = 1
BOOLEAN id_HomIdeal(ideal id, ideal Q, const ring r)
BOOLEAN id_HomModuleW(ideal id, ideal Q, const intvec *w, const intvec *module_w, const ring r)
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
ideal id_Transp(ideal a, const ring rRing)
transpose a module
ideal id_FreeModule(int i, const ring r)
the free module of rank i
BOOLEAN id_IsZeroDim(ideal I, const ring r)
ideal id_Homogen(ideal h, int varnum, const ring r)
ideal id_Power(ideal given, int exp, const ring r)
matrix id_Module2Matrix(ideal mod, const ring R)
void id_Normalize(ideal id, const ring r)
normialize all polys in id
static int idElem(const ideal F)
number of non-zero polys in F
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
ideal id_Copy(ideal h1, const ring r)
copy an ideal
BOOLEAN id_IsConstant(ideal id, const ring r)
test if the ideal has only constant polynomials NOTE: zero ideal/module is also constant
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
BOOLEAN id_HomIdealW(ideal id, ideal Q, const intvec *w, const ring r)
int id_ReadOutPivot(ideal arg, int *comp, const ring r)
ideal id_MaxIdeal(const ring r)
initialise the maximal ideal (at 0)
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*L...
int id_MinDegW(ideal M, intvec *w, const ring r)
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_ShallowDelete(ideal *h, ring r)
Shallowdeletes an ideal/matrix.
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:
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!
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 (...
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
ideal id_ResizeModule(ideal mod, int rows, int cols, const ring R)
EXTERN_VAR omBin sip_sideal_bin
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
ideal id_Jet(const ideal i, int d, 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 co...
ideal id_Delete_Pos(const ideal I, const int pos, const 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.
ideal id_JetW(const ideal i, int d, intvec *iv, const ring R)
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
void id_Shift(ideal M, int s, const ring r)
int idGetNumberOfChoise(int t, int d, int begin, int end, int *choise)
long id_RankFreeModule(ideal m, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
ideal id_SimpleAdd(ideal h1, ideal h2, const ring r)
concat the lists h1 and h2 without zeros
void id_Compactify(ideal id, const ring r)
BOOLEAN id_HomModule(ideal m, ideal Q, intvec **w, const ring R)
ideal id_Subst(ideal id, int n, poly e, const ring r)
The following sip_sideal structure has many different uses thoughout Singular. Basic use-cases for it...