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simpleideals.h
Go to the documentation of this file.
1#ifndef SIMPLEIDEALS_H
2#define SIMPLEIDEALS_H
3/****************************************
4* Computer Algebra System SINGULAR *
5****************************************/
6/*
7* ABSTRACT - all basic methods to manipulate ideals
8*/
10#include "polys/matpol.h"
11
12/// The following sip_sideal structure has many different uses
13/// throughout Singular. Basic use-cases for it are:
14/// * ideal/module: nrows = 1, ncols >=0 and rank:1 for ideals, rank>=0 for modules
15/// * matrix: nrows, ncols >=0, rank == nrows! see mp_* procedures
16/// NOTE: the m member point to memory chunk of size (ncols*nrows*sizeof(poly)) or is NULL
18{
19 poly* m;
20 long rank;
21 int nrows;
22 int ncols;
23 #define IDELEMS(i) ((i)->ncols)
24};
25/* the settings of rank, nrows, ncols, m , entries:
26 * for IDEAL_CMD: 1 1 n size n poly (n>=0)
27 * for MODUL_CMD: r 1 n size n vector of rank<=r (n>=0, r>=0)
28 * for MATRIX_CMD r r c size r*c poly (r>=0, c>=0)
29 * for MAP_CMD: char* 1 n size n poly (n>=0)
30 */
31
33{
34 poly *m;
35 char *preimage;
36 int nrows;
37 int ncols;
38};
39
40//typedef struct sip_smap * map;
41
42struct sideal_list;
43typedef struct sideal_list * ideal_list;
44
46{
47 ideal_list next;
48 ideal d;
49#ifdef KDEBUG
50 int nr;
51#endif
52};
53
55
56/// creates an ideal / module
57ideal idInit (int size, int rank=1);
58#define id_Init(s,r,R) idInit(s,r)
59
60/*- deletes an ideal -*/
61void id_Delete (ideal* h, ring r);
62void id_Delete0 (ideal* h, ring r);
63void id_ShallowDelete (ideal* h, ring r);
64void idSkipZeroes (ideal ide);
65int idSkipZeroes0 (ideal ide);
66 /*gives an ideal the minimal possible size*/
67
68/// number of non-zero polys in F
69static inline int idElem(const ideal F)
70{
71 int i=0;
72 for(int j=IDELEMS(F)-1;j>=0;j--)
73 {
74 if ((F->m)[j]!=NULL) i++;
75 }
76 return i;
77}
78
79#define id_Elem(F,R) idElem(F)
80
81/// normialize all polys in id
82void id_Normalize(ideal id, const ring r);
83
84int id_MinDegW(ideal M,intvec *w, const ring r);
85
86#ifdef PDEBUG
87void id_DBTest(ideal h1, int level, const char *f,const int l, const ring lR, const ring tR );
88void id_DBLmTest(ideal h1, int level, const char *f,const int l, const ring r);
89#define id_Test(A, lR) id_DBTest(A, PDEBUG, __FILE__,__LINE__, lR, lR)
90#define id_LmTest(A, lR) id_DBLmTest(A, PDEBUG, __FILE__,__LINE__, lR)
91#else
92#define id_Test(A, lR) do {} while (0)
93#define id_LmTest(A, lR) do {} while (0)
94#endif
95
96ideal id_Copy (ideal h1,const ring r);
97
98 /*adds two ideals without simplifying the result*/
99ideal id_SimpleAdd (ideal h1,ideal h2, const ring r);
100 /*adds the quotient ideal*/
101ideal id_Add (ideal h1,ideal h2,const ring r);
102 /* h1 + h2 */
103
104ideal id_Power(ideal given,int exp, const ring r);
105BOOLEAN idIs0 (ideal h);
106BOOLEAN idIsMonomial (ideal h);
107
108BOOLEAN id_IsModule(ideal A, const ring src);
109long id_RankFreeModule(ideal m, ring lmRing, ring tailRing);
110static inline long id_RankFreeModule(ideal m, ring r)
111{return id_RankFreeModule(m, r, r);}
112
113ideal id_FreeModule (int i, const ring r);
114int idElem(const ideal F);
115int id_PosConstant(ideal id, const ring r);
116ideal id_Head(ideal h,const ring r);
117ideal id_MaxIdeal (const ring r);
118ideal id_MaxIdeal(int deg, const ring r);
119ideal id_CopyFirstK (const ideal ide, const int k,const ring r);
120void id_DelMultiples(ideal id, const ring r);
121void id_Norm(ideal id, const ring r);
122void id_DelEquals(ideal id, const ring r);
123void id_DelLmEquals(ideal id, const ring r);
124void id_DelDiv(ideal id, const ring r);
125BOOLEAN id_IsConstant(ideal id, const ring r);
126
127/// sorts the ideal w.r.t. the actual ringordering
128/// uses lex-ordering when nolex = FALSE
129intvec *id_Sort(const ideal id, const BOOLEAN nolex, const ring r);
130
131/// transpose a module
132ideal id_Transp(ideal a, const ring rRing);
133
134void id_Compactify(ideal id, const ring r);
135ideal id_Mult (ideal h1,ideal h2, const ring r);
136ideal id_Homogen(ideal h, int varnum,const ring r);
137ideal id_HomogenDP(ideal h, int varnum,const ring r);
138BOOLEAN id_HomIdeal (ideal id, ideal Q, const ring r);
139BOOLEAN id_HomIdealDP (ideal id, ideal Q, const ring r);
140BOOLEAN id_HomIdealW (ideal id, ideal Q, const intvec *w, const ring r);
141BOOLEAN id_HomModuleW (ideal id, ideal Q, const intvec *w, const intvec *module_w, const ring r);
142BOOLEAN id_HomModule(ideal m, ideal Q, intvec **w, const ring R);
143BOOLEAN id_IsZeroDim(ideal I, const ring r);
144ideal id_Jet(const ideal i,int d, const ring R);
145ideal id_Jet0(const ideal i, const ring R);/*id_Jet(i,0,R)*/
146ideal id_JetW(const ideal i,int d, intvec * iv, const ring R);
147ideal id_Subst(ideal id, int n, poly e, const ring r);
148matrix id_Module2Matrix(ideal mod, const ring R);
149matrix id_Module2formatedMatrix(ideal mod,int rows, int cols, const ring R);
150ideal id_ResizeModule(ideal mod,int rows, int cols, const ring R);
151ideal id_Matrix2Module(matrix mat, const ring R);
152ideal id_Vec2Ideal(poly vec, const ring R);
153
154int binom (int n,int r);
155
156 /*- verschiebt die Indizes der Modulerzeugenden um i -*/
157void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise);
158void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise);
159int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise);
160
161#ifdef PDEBUG
162void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint = 0);
163#define id_Print(id, lR, tR) idShow(id, lR, tR)
164#else
165#define id_Print(A, lR, tR) do {} while (0)
166#endif
167
168
169
170/// insert h2 into h1 depending on the two boolean parameters:
171/// - if zeroOk is true, then h2 will also be inserted when it is zero
172/// - if duplicateOk is true, then h2 will also be inserted when it is
173/// already present in h1
174/// return TRUE iff h2 was indeed inserted
175BOOLEAN id_InsertPolyWithTests (ideal h1, const int validEntries,
176 const poly h2, const bool zeroOk,
177 const bool duplicateOk, const ring r);
178
179
180intvec * id_QHomWeight(ideal id, const ring r);
181
182
183ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r);
184
185void id_Shift(ideal M, int s, const ring r);
186ideal id_Delete_Pos(const ideal I, const int pos, const ring r);
187
188/// for julia: convert an array of poly to vector
189poly id_Array2Vector(poly *m, unsigned n, const ring R);
190
191/// mapping ideals/matrices to other rings
192ideal id_PermIdeal(ideal I,int R, int C,const int *perm, const ring src,
193 const ring dst, nMapFunc nMap, const int *par_perm, int P, BOOLEAN use_mult);
194#endif
int BOOLEAN
Definition auxiliary.h:88
int size(const CanonicalForm &f, const Variable &v)
int size ( const CanonicalForm & f, const Variable & v )
Definition cf_ops.cc:600
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
int level(const CanonicalForm &f)
int l
Definition cfEzgcd.cc:100
int m
Definition cfEzgcd.cc:128
int i
Definition cfEzgcd.cc:132
int k
Definition cfEzgcd.cc:99
FILE * f
Definition checklibs.c:9
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition coeffs.h:80
const CanonicalForm int s
Definition facAbsFact.cc:51
const CanonicalForm & w
Definition facAbsFact.cc:51
fq_nmod_poly_t * vec
Definition facHensel.cc:108
int j
Definition facHensel.cc:110
#define EXTERN_VAR
Definition globaldefs.h:6
STATIC_VAR Poly * h
Definition janet.cc:971
ip_smatrix * matrix
Definition matpol.h:43
gmp_float exp(const gmp_float &a)
#define NULL
Definition omList.c:12
omBin_t * omBin
Definition omStructs.h:12
VAR omBin sip_sideal_bin
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
int binom(int n, int r)
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
BOOLEAN id_IsModule(ideal A, const ring src)
int idSkipZeroes0(ideal ide)
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
ideal_list next
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)
#define IDELEMS(i)
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
void id_Delete0(ideal *h, ring r)
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)
BOOLEAN id_HomIdealDP(ideal id, ideal Q, 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)
ideal id_Jet0(const ideal i, 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)
poly * m
char * preimage
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)
ideal id_HomogenDP(ideal h, int varnum, 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_PermIdeal(ideal I, int R, int C, const int *perm, const ring src, const ring dst, nMapFunc nMap, const int *par_perm, int P, BOOLEAN use_mult)
mapping ideals/matrices to other rings
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 idIsMonomial(ideal h)
returns true if h is generated by monomials
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 throughout Singular. Basic use-cases for i...
#define R
Definition sirandom.c:27
#define A
Definition sirandom.c:24
#define M
Definition sirandom.c:25
#define Q
Definition sirandom.c:26