ideals.h
Go to the documentation of this file.
1 #ifndef IDEALS_H
2 #define IDEALS_H
3 /****************************************
4 * Computer Algebra System SINGULAR *
5 ****************************************/
6 /*
7 * ABSTRACT - all basic methods to manipulate ideals
8 */
9 
10 #include <polys/monomials/ring.h>
12 #include <polys/simpleideals.h>
13 
14 extern ring currRing;
15 
16 #include <kernel/structs.h> // for tHomog
17 
18 //typedef struct sip_sideal * ideal;
19 //typedef struct sip_smap * map;
20 typedef ideal * resolvente;
21 
22 inline ideal idCopyFirstK (const ideal ide, const int k)
23 {
24  return id_CopyFirstK(ide, k, currRing);
25 }
26 
27 void idKeepFirstK(ideal ide, const int k);
28 void idDelEquals(ideal id);
29 
30 /// delete an ideal
31 inline void idDelete (ideal* h)
32 {
33  id_Delete(h, currRing);
34 }
35 
36 /// initialise the maximal ideal (at 0)
37 //ideal id_MaxIdeal(int deg, const ring r);
38 #define idMaxIdeal(D) id_MaxIdeal(D,currRing)
39 
40 /// index of generator with leading term in ground ring (if any); otherwise -1
41 //int id_PosConstant(ideal id, const ring r)
42 #define idPosConstant(I) id_PosConstant(I,currRing)
43 
44 /// Count the effective size of an ideal
45 /// (without the trailing allocated zero-elements)
46 static inline int idSize(const ideal id)
47 {
48  int j = IDELEMS(id) - 1;
49  poly* mm = id->m;
50  while ((j >= 0) && (mm[j] == NULL)) j--;
51  return (j + 1);
52 }
53 
54 
55 //BOOLEAN id_IsConstant(ideal id, const ring r);
56 #define idIsConstant(I) id_IsConstant(I,currRing)
57 
58 #define idSimpleAdd(A,B) id_SimpleAdd(A,B,currRing)
59 
60 ideal id_Copy (ideal h1, const ring r);
61 
62 #define idPrint(id) id_Print(id, currRing, currRing)
63 #define idTest(id) id_Test(id, currRing)
64 
65 #if 0
66 
67 // ifdef PDEBUG // Sorry: the following was lost........ :((((((((
68 ideal idDBCopy(ideal h1,const char *f,int l,const ring r);
69 #define id_DBCopy(A,r) idDBCopy(A,__FILE__,__LINE__,r)
70 
71 inline ideal idCopy(ideal A)
72 {
73  return id_DBCopy(A,currRing); // well, just for now... ok? Macros can't have default args values :(
74 }
75 #else
76 inline ideal idCopy(ideal A)
77 {
78  return id_Copy(A, currRing);
79 }
80 #endif
81 
82 
83 /// h1 + h2
84 inline ideal idAdd (ideal h1, ideal h2)
85 {
86  return id_Add(h1, h2, currRing);
87 }
88 
89 BOOLEAN idInsertPoly (ideal h1,poly h2); /* h1 + h2 */
90 inline BOOLEAN idInsertPolyWithTests (ideal h1, const int validEntries, const poly h2, const bool zeroOk, const bool duplicateOk)
91 {
92  return id_InsertPolyWithTests (h1, validEntries, h2, zeroOk, duplicateOk, currRing);
93 }
94 
95 
96 /* h1 + h2 */
97 
98 /// hh := h1 * h2
99 inline ideal idMult (ideal h1, ideal h2)
100 {
101  return id_Mult(h1, h2, currRing);
102 }
103 
104 BOOLEAN idIs0 (ideal h);
105 
106 inline BOOLEAN idHomIdeal (ideal id, ideal Q=NULL)
107 {
108  return id_HomIdeal(id, Q, currRing);
109 }
110 
111 inline BOOLEAN idHomModule(ideal m, ideal Q,intvec **w)
112 {
113  return id_HomModule(m, Q, w, currRing);
114 }
115 
116 BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w);
117 
118 ideal idMinBase (ideal h1);
119  /*returns a minimized set of generators of h1*/
120 void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise);
121 void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise);
122 int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise);
123 
124 int binom (int n,int r);
125 
126 inline ideal idFreeModule (int i)
127 {
128  return id_FreeModule (i, currRing);
129 }
130 
131 
132 ideal idSect (ideal h1,ideal h2);
133 ideal idMultSect(resolvente arg, int length);
134 
135 //ideal idSyzygies (ideal h1, tHomog h,intvec **w);
136 ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp=TRUE,
137  BOOLEAN setRegularity=FALSE, int *deg = NULL);
138 ideal idLiftStd (ideal h1, matrix *m, tHomog h=testHomog, ideal *syz=NULL);
139 
140 ideal idLift (ideal mod, ideal sumod,ideal * rest=NULL,
141  BOOLEAN goodShape=FALSE, BOOLEAN isSB=TRUE,BOOLEAN divide=FALSE,
142  matrix *unit=NULL);
143 
144 void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R, short *w= NULL );
145 
146 intvec * idMWLift(ideal mod,intvec * weights);
147 
148 ideal idQuot (ideal h1,ideal h2,
149  BOOLEAN h1IsStb=FALSE, BOOLEAN resultIsIdeal=FALSE);
150 
151 // ideal idPower(ideal gid,int deg);
152 
153 //ideal idElimination (ideal h1,poly delVar);
154 ideal idElimination (ideal h1,poly delVar, intvec *hilb=NULL);
155 
156 #ifdef WITH_OLD_MINOR
157 poly idMinor(matrix a, int ar, unsigned long which, ideal R = NULL);
158 #endif
159 ideal idMinors(matrix a, int ar, ideal R = NULL);
160 
161 ideal idMinEmbedding(ideal arg,BOOLEAN inPlace=FALSE, intvec **w=NULL);
162 
163 ideal idHead(ideal h);
164 
165 // ideal idHomogen(ideal h, int varnum);
166 
167 BOOLEAN idIsSubModule(ideal id1,ideal id2);
168 
169 inline ideal idVec2Ideal(poly vec)
170 {
171  return id_Vec2Ideal(vec, currRing);
172 }
173 
174 ideal idSeries(int n,ideal M,matrix U=NULL,intvec *w=NULL);
175 
176 inline BOOLEAN idIsZeroDim(ideal i)
177 {
178  return id_IsZeroDim(i, currRing);
179 }
180 
181 matrix idDiff(matrix i, int k);
182 matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply=TRUE);
183 
184 inline intvec *idSort(ideal id,BOOLEAN nolex=TRUE)
185 {
186  return id_Sort(id, nolex, currRing);
187 }
188 
189 ideal idModulo (ideal h1,ideal h2, tHomog h=testHomog, intvec ** w=NULL);
190 matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how);
191 
192 /// transpose a module
193 inline ideal idTransp(ideal a)
194 {
195  return id_Transp(a, currRing);
196 }
197 
198 // intvec *idQHomWeight(ideal id);
199 
200 ideal idXXX (ideal h1, int k);
201 
202 poly id_GCD(poly f, poly g, const ring r);
203 
204 ideal id_Farey(ideal x, number N, const ring r);
205 
206 ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing); // image of certain map for BGG
207 
208 
209 #endif
ideal id_FreeModule(int i, const ring r)
the free module of rank i
ideal id_Transp(ideal a, const ring rRing)
const poly a
Definition: syzextra.cc:212
ideal idVec2Ideal(poly vec)
Definition: ideals.h:169
CF_NO_INLINE CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
Definition: cf_inline.cc:564
void idLiftW(ideal P, ideal Q, int n, matrix &T, ideal &R, short *w=NULL)
Definition: ideals.cc:1133
#define FALSE
Definition: auxiliary.h:140
ideal idXXX(ideal h1, int k)
Definition: ideals.cc:704
ideal id_Copy(ideal h1, const ring r)
copy an ideal
BOOLEAN id_HomModule(ideal m, ideal Q, intvec **w, const ring R)
BOOLEAN id_HomIdeal(ideal id, ideal Q, const ring r)
const CanonicalForm CFMap CFMap int &both_non_zero int n
Definition: cfEzgcd.cc:52
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
CanonicalForm divide(const CanonicalForm &ff, const CanonicalForm &f, const CFList &as)
ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing)
ideal idModulo(ideal h1, ideal h2, tHomog h=testHomog, intvec **w=NULL)
Definition: ideals.cc:2038
#define TRUE
Definition: auxiliary.h:144
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 * idMWLift(ideal mod, intvec *weights)
Definition: ideals.cc:2178
g
Definition: cfModGcd.cc:4031
int k
Definition: cfEzgcd.cc:93
ideal idLift(ideal mod, ideal sumod, ideal *rest=NULL, BOOLEAN goodShape=FALSE, BOOLEAN isSB=TRUE, BOOLEAN divide=FALSE, matrix *unit=NULL)
Definition: ideals.cc:938
void idDelEquals(ideal id)
Definition: ideals.cc:2650
#define Q
Definition: sirandom.c:25
ideal idLiftStd(ideal h1, matrix *m, tHomog h=testHomog, ideal *syz=NULL)
Definition: ideals.cc:751
intvec * idSort(ideal id, BOOLEAN nolex=TRUE)
Definition: ideals.h:184
ideal idMinBase(ideal h1)
Definition: ideals.cc:53
ideal idHead(ideal h)
ideal idSeries(int n, ideal M, matrix U=NULL, intvec *w=NULL)
Definition: ideals.cc:1936
#define M
Definition: sirandom.c:24
fq_nmod_poly_t * vec
Definition: facHensel.cc:103
const ring r
Definition: syzextra.cc:208
ideal idElimination(ideal h1, poly delVar, intvec *hilb=NULL)
Definition: ideals.cc:1403
ideal idMinEmbedding(ideal arg, BOOLEAN inPlace=FALSE, intvec **w=NULL)
Definition: ideals.cc:2347
Definition: intvec.h:16
void idKeepFirstK(ideal ide, const int k)
keeps the first k (>= 1) entries of the given ideal (Note that the kept polynomials may be zero...
Definition: ideals.cc:2581
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:49
tHomog
Definition: structs.h:37
int j
Definition: myNF.cc:70
ideal idMinors(matrix a, int ar, ideal R=NULL)
compute all ar-minors of the matrix a the caller of mpRecMin the elements of the result are not in R ...
Definition: ideals.cc:1794
matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
Definition: ideals.cc:2281
ideal idFreeModule(int i)
Definition: ideals.h:126
#define A
Definition: sirandom.c:23
poly id_GCD(poly f, poly g, const ring r)
Definition: ideals.cc:2405
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 idMultSect(resolvente arg, int length)
Definition: ideals.cc:350
BOOLEAN idInsertPoly(ideal h1, poly h2)
insert h2 into h1 (if h2 is not the zero polynomial) return TRUE iff h2 was indeed inserted ...
int m
Definition: cfEzgcd.cc:119
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
FILE * f
Definition: checklibs.c:7
int i
Definition: cfEzgcd.cc:123
ideal idSect(ideal h1, ideal h2)
Definition: ideals.cc:211
ideal idTransp(ideal a)
transpose a module
Definition: ideals.h:193
#define IDELEMS(i)
Definition: simpleideals.h:24
ideal idCopy(ideal A)
Definition: ideals.h:76
ideal idMult(ideal h1, ideal h2)
hh := h1 * h2
Definition: ideals.h:99
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...
BOOLEAN idInsertPolyWithTests(ideal h1, const int validEntries, const poly h2, const bool zeroOk, const bool duplicateOk)
Definition: ideals.h:90
#define NULL
Definition: omList.c:10
BOOLEAN idHomIdeal(ideal id, ideal Q=NULL)
Definition: ideals.h:106
ideal idSyzygies(ideal h1, tHomog h, intvec **w, BOOLEAN setSyzComp=TRUE, BOOLEAN setRegularity=FALSE, int *deg=NULL)
Definition: ideals.cc:560
ideal id_Add(ideal h1, ideal h2, const ring r)
h1 + h2
#define R
Definition: sirandom.c:26
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
const CanonicalForm & w
Definition: facAbsFact.cc:55
BOOLEAN idIsZeroDim(ideal i)
Definition: ideals.h:176
Variable x
Definition: cfModGcd.cc:4023
ideal id_Farey(ideal x, number N, const ring r)
Definition: ideals.cc:2505
BOOLEAN idIsSubModule(ideal id1, ideal id2)
Definition: ideals.cc:1863
ideal * resolvente
Definition: ideals.h:20
ideal idQuot(ideal h1, ideal h2, BOOLEAN h1IsStb=FALSE, BOOLEAN resultIsIdeal=FALSE)
Definition: ideals.cc:1310
BOOLEAN id_IsZeroDim(ideal I, 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 (...
matrix idDiffOp(ideal I, ideal J, BOOLEAN multiply=TRUE)
Definition: ideals.cc:1966
int idGetNumberOfChoise(int t, int d, int begin, int end, int *choise)
static int idSize(const ideal id)
Count the effective size of an ideal (without the trailing allocated zero-elements) ...
Definition: ideals.h:46
ideal idAdd(ideal h1, ideal h2)
h1 + h2
Definition: ideals.h:84
ideal id_Vec2Ideal(poly vec, const ring R)
kBucketDestroy & P
Definition: myNF.cc:191
static jList * T
Definition: janet.cc:37
polyrec * poly
Definition: hilb.h:10
static Poly * h
Definition: janet.cc:978
int BOOLEAN
Definition: auxiliary.h:131
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:12
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
Definition: ideals.cc:1884
BOOLEAN idHomModule(ideal m, ideal Q, intvec **w)
Definition: ideals.h:111
int binom(int n, int r)
void idDelete(ideal *h)
delete an ideal
Definition: ideals.h:31
matrix idDiff(matrix i, int k)
Definition: ideals.cc:1953
int l
Definition: cfEzgcd.cc:94
ideal idCopyFirstK(const ideal ide, const int k)
Definition: ideals.h:22