[35aab3] | 1 | #ifndef IDEALS_H |
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| 2 | #define IDEALS_H |
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| 3 | /**************************************** |
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| 4 | * Computer Algebra System SINGULAR * |
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| 5 | ****************************************/ |
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[341696] | 6 | /* $Id$ */ |
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[35aab3] | 7 | /* |
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| 8 | * ABSTRACT - all basic methods to manipulate ideals |
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| 9 | */ |
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[028192] | 10 | // #include <kernel/structs.h> |
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| 11 | |
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[b07ba77] | 12 | //typedef struct sip_sideal * ideal; |
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| 13 | //typedef struct sip_smap * map; |
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| 14 | typedef ideal * resolvente; |
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| 15 | |
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| 16 | |
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| 17 | extern omBin sip_sideal_bin; |
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| 18 | |
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[35aab3] | 19 | /*- creates an ideal -*/ |
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| 20 | ideal idInit (int size, int rank=1); |
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[1919112] | 21 | ideal idCopyFirstK (const ideal ide, const int k); |
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[e9c3b2] | 22 | |
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| 23 | /// delete an ideal |
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[028192] | 24 | // #define idDelete(h) id_Delete(h, currRing) |
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[35aab3] | 25 | void id_Delete (ideal* h, ring r); |
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| 26 | void id_ShallowDelete (ideal* h, ring r); |
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[e9c3b2] | 27 | /*- initialise an ideal -*/ // ? |
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| 28 | |
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| 29 | /// initialise the maximal ideal (at 0) |
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[35aab3] | 30 | ideal idMaxIdeal (int deg); |
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[e9c3b2] | 31 | |
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| 32 | /// gives an ideal the minimal possible size |
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[35aab3] | 33 | void idSkipZeroes (ideal ide); |
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[e9c3b2] | 34 | |
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| 35 | /// index of generator with leading term in ground ring (if any); otherwise -1 |
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[dd5534] | 36 | int idPosConstant (ideal id); |
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[e9c3b2] | 37 | |
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| 38 | /// Count the effective size of an ideal |
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| 39 | /// (without the trailing allocated zero-elements) |
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| 40 | static inline int idSize(const ideal id) |
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| 41 | { |
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| 42 | int j = IDELEMS(id) - 1; |
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| 43 | poly* mm = id->m; |
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| 44 | while ((j >= 0) && (mm[j] == NULL)) j--; |
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| 45 | return (j + 1); |
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[27fc50] | 46 | } |
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[e9c3b2] | 47 | |
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[35aab3] | 48 | void idNorm(ideal id); |
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| 49 | void idDelMultiples(ideal id); |
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| 50 | void idDelEquals(ideal id); |
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| 51 | void idDelLmEquals(ideal id); |
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| 52 | void idDelDiv(ideal id); |
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| 53 | BOOLEAN idIsConstant(ideal id); |
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| 54 | |
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| 55 | #ifdef PDEBUG |
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[85e68dd] | 56 | void idDBTest(ideal h1, int level, const char *f,const int l); |
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[35aab3] | 57 | #define idTest(A) idDBTest(A, PDEBUG, __FILE__,__LINE__) |
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| 58 | #define idPrint(id) idShow(id) |
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| 59 | #else |
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| 60 | #define idTest(A) (TRUE) |
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| 61 | #define idPrint(A) ((void)0) |
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| 62 | #endif |
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| 63 | |
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[d523f3] | 64 | ideal id_Copy (ideal h1,const ring r); |
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[028192] | 65 | #ifdef PDEBUG |
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| 66 | ideal idDBCopy(ideal h1,const char *f,int l,const ring r); |
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| 67 | #define id_DBCopy(A,r) idDBCopy(A,__FILE__,__LINE__,r) |
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| 68 | #define idCopy(A,r) id_DBCopy(A,r) |
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| 69 | #else |
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| 70 | #define idCopy(A,r) id_Copy(A,r) |
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| 71 | #endif |
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| 72 | |
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| 73 | |
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[35aab3] | 74 | /*adds two ideals without simplifying the result*/ |
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| 75 | ideal idSimpleAdd (ideal h1,ideal h2); |
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| 76 | /*adds the quotient ideal*/ |
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| 77 | ideal idAdd (ideal h1,ideal h2); |
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| 78 | /* h1 + h2 */ |
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[ded085] | 79 | BOOLEAN idInsertPoly (ideal h1,poly h2); |
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[e070895] | 80 | /* h1 + h2 */ |
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[2b3caae] | 81 | BOOLEAN idInsertPolyWithTests (ideal h1, const int validEntries, |
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| 82 | const poly h2, const bool zeroOk, const bool duplicateOk); |
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[1a68d1d] | 83 | /* h1 + h2 */ |
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[35aab3] | 84 | ideal idMult (ideal h1,ideal h2); |
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| 85 | /*hh := h1 * h2*/ |
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| 86 | |
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| 87 | BOOLEAN idIs0 (ideal h); |
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| 88 | |
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| 89 | // returns TRUE, if idRankFreeModule(m) > 0 |
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[028192] | 90 | BOOLEAN idIsModule(ideal m, const ring r); |
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[35aab3] | 91 | BOOLEAN idHomIdeal (ideal id, ideal Q=NULL); |
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| 92 | BOOLEAN idHomModule(ideal m, ideal Q,intvec **w); |
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[30b8381] | 93 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w); |
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[35aab3] | 94 | |
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| 95 | ideal idMinBase (ideal h1); |
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| 96 | /*returns a minimized set of generators of h1*/ |
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| 97 | int pLowVar (poly p); |
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| 98 | /*-the minimal index of used variables - 1-*/ |
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| 99 | void pShift (poly * p,int i); |
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| 100 | /*- verschiebt die Indizes der Modulerzeugenden um i -*/ |
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| 101 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise); |
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| 102 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise); |
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| 103 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise); |
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| 104 | |
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| 105 | int binom (int n,int r); |
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| 106 | |
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| 107 | ideal idFreeModule (int i); |
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| 108 | |
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| 109 | ideal idSect (ideal h1,ideal h2); |
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| 110 | ideal idMultSect(resolvente arg, int length); |
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| 111 | |
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| 112 | //ideal idSyzygies (ideal h1, tHomog h,intvec **w); |
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| 113 | ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp=TRUE, |
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| 114 | BOOLEAN setRegularity=FALSE, int *deg = NULL); |
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[81dab73] | 115 | ideal idLiftStd (ideal h1, matrix *m, tHomog h=testHomog, ideal *syz=NULL); |
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[35aab3] | 116 | |
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| 117 | ideal idLift (ideal mod, ideal sumod,ideal * rest=NULL, |
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| 118 | BOOLEAN goodShape=FALSE, BOOLEAN isSB=TRUE,BOOLEAN divide=FALSE, |
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| 119 | matrix *unit=NULL); |
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| 120 | |
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| 121 | void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R, short *w= NULL ); |
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| 122 | |
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| 123 | intvec * idMWLift(ideal mod,intvec * weights); |
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| 124 | |
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| 125 | ideal idQuot (ideal h1,ideal h2, |
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| 126 | BOOLEAN h1IsStb=FALSE, BOOLEAN resultIsIdeal=FALSE); |
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| 127 | |
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| 128 | ideal idPower(ideal gid,int deg); |
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| 129 | |
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| 130 | //ideal idElimination (ideal h1,poly delVar); |
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| 131 | ideal idElimination (ideal h1,poly delVar, intvec *hilb=NULL); |
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| 132 | |
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[0a64b14] | 133 | poly idMinor(matrix a, int ar, unsigned long which, ideal R=NULL); |
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| 134 | |
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[35aab3] | 135 | ideal idMinors(matrix a, int ar, ideal R=NULL); |
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| 136 | |
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[10ea45f] | 137 | void idCompactify(ideal id); |
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[35aab3] | 138 | |
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[cf108d] | 139 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace=FALSE, intvec **w=NULL); |
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[35aab3] | 140 | |
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| 141 | ideal idHead(ideal h); |
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| 142 | |
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| 143 | ideal idHomogen(ideal h, int varnum); |
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| 144 | |
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| 145 | BOOLEAN idIsSubModule(ideal id1,ideal id2); |
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| 146 | |
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| 147 | ideal idVec2Ideal(poly vec); |
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| 148 | |
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| 149 | ideal idMatrix2Module(matrix mat); |
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| 150 | |
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| 151 | matrix idModule2Matrix(ideal mod); |
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| 152 | |
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| 153 | matrix idModule2formatedMatrix(ideal mod,int rows, int cols); |
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| 154 | |
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| 155 | ideal idSubst(ideal i, int n, poly e); |
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| 156 | |
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| 157 | ideal idJet(ideal i,int d); |
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| 158 | ideal idJetW(ideal i,int d, intvec * iv); |
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| 159 | int idMinDegW(ideal M,intvec *w); |
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| 160 | ideal idSeries(int n,ideal M,matrix U=NULL,intvec *w=NULL); |
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| 161 | |
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| 162 | BOOLEAN idIsZeroDim(ideal i); |
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| 163 | matrix idDiff(matrix i, int k); |
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| 164 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply=TRUE); |
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| 165 | |
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| 166 | intvec *idSort(ideal id,BOOLEAN nolex=TRUE); |
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[cf108d] | 167 | ideal idModulo (ideal h1,ideal h2, tHomog h=testHomog, intvec ** w=NULL); |
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[b3930d] | 168 | int idElem(const ideal F); |
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[35aab3] | 169 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how); |
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[90a60f] | 170 | // transpose a module |
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[35aab3] | 171 | ideal idTransp(ideal a); |
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[90a60f] | 172 | // version of "ideal idTransp(ideal)" which works within a given ring. |
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[028192] | 173 | ideal id_Transp(ideal a, const ring rRing); |
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[90a60f] | 174 | |
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[35aab3] | 175 | intvec *idQHomWeight(ideal id); |
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| 176 | |
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| 177 | void idNormalize(ideal id); |
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| 178 | |
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| 179 | ideal idXXX (ideal h1, int k); |
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[225d94] | 180 | |
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| 181 | poly id_GCD(poly f, poly g, const ring r); |
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[bba835] | 182 | |
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| 183 | ideal idChineseRemainder(ideal *x, number *q, int rl); |
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[3580b7] | 184 | //ideal idChineseRemainder(ideal *x, intvec *iv); /* currently unused */ |
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[3149a5] | 185 | ideal idFarey(ideal x, number N); |
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[90a60f] | 186 | |
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[028192] | 187 | ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing); // image of certain map for BGG |
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[90a60f] | 188 | |
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[e9c3b2] | 189 | #ifdef PDEBUG |
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[1a4313] | 190 | /* Shows an ideal -- only for debugging */ |
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[028192] | 191 | void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint = 0); |
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[e9c3b2] | 192 | #else |
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| 193 | #define idShow(id, lmRing, tailRing, debugPrint) ((void)0) |
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[1a4313] | 194 | #endif |
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[35aab3] | 195 | #endif |
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