[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[7ba059] | 4 | /* $Id: polys.cc,v 1.26 2007-07-24 12:29:31 Singular Exp $ */ |
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[35aab3] | 5 | |
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| 6 | /* |
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| 7 | * ABSTRACT - all basic methods to manipulate polynomials |
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| 8 | */ |
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| 9 | |
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| 10 | /* includes */ |
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| 11 | #include <stdio.h> |
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| 12 | #include <string.h> |
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| 13 | #include <ctype.h> |
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| 14 | #include "mod2.h" |
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| 15 | #include "structs.h" |
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| 16 | #include "omalloc.h" |
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| 17 | #include "febase.h" |
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| 18 | #include "numbers.h" |
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| 19 | #include "polys.h" |
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| 20 | #include "ring.h" |
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| 21 | |
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[68349d] | 22 | #ifdef HAVE_PLURAL |
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| 23 | #include "gring.h" |
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[5d7a3b] | 24 | #include "sca.h" |
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[68349d] | 25 | #endif |
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| 26 | |
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[35aab3] | 27 | /* ----------- global variables, set by pSetGlobals --------------------- */ |
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| 28 | /* computes length and maximal degree of a POLYnomial */ |
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| 29 | pLDegProc pLDeg; |
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| 30 | /* computes the degree of the initial term, used for std */ |
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| 31 | pFDegProc pFDeg; |
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| 32 | /* the monomial ordering of the head monomials a and b */ |
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| 33 | /* returns -1 if a comes before b, 0 if a=b, 1 otherwise */ |
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| 34 | |
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| 35 | int pVariables; // number of variables |
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| 36 | |
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| 37 | /* 1 for polynomial ring, -1 otherwise */ |
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| 38 | int pOrdSgn; |
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| 39 | // it is of type int, not BOOLEAN because it is also in ip |
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| 40 | /* TRUE if the monomial ordering is not compatible with pFDeg */ |
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| 41 | BOOLEAN pLexOrder; |
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| 42 | |
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| 43 | /* ----------- global variables, set by procedures from hecke/kstd1 ----- */ |
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| 44 | /* the highest monomial below pHEdge */ |
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| 45 | poly ppNoether = NULL; |
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| 46 | |
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| 47 | /* -------------------------------------------------------- */ |
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| 48 | /*2 |
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| 49 | * change all global variables to fit the description of the new ring |
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| 50 | */ |
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| 51 | |
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| 52 | |
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[8c5988] | 53 | void pSetGlobals(const ring r, BOOLEAN complete) |
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[35aab3] | 54 | { |
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| 55 | int i; |
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| 56 | if (ppNoether!=NULL) pDelete(&ppNoether); |
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| 57 | pVariables = r->N; |
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| 58 | pOrdSgn = r->OrdSgn; |
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| 59 | pFDeg=r->pFDeg; |
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| 60 | pLDeg=r->pLDeg; |
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| 61 | pLexOrder=r->LexOrder; |
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| 62 | |
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| 63 | if (complete) |
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| 64 | { |
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| 65 | test &= ~ TEST_RINGDEP_OPTS; |
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| 66 | test |= r->options; |
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| 67 | } |
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| 68 | } |
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| 69 | |
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| 70 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
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| 71 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
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| 72 | // only uses pFDeg (and not pDeg, or pTotalDegree, etc) |
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| 73 | void pSetDegProcs(pFDegProc new_FDeg, pLDegProc new_lDeg) |
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| 74 | { |
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| 75 | assume(new_FDeg != NULL); |
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| 76 | pFDeg = new_FDeg; |
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| 77 | currRing->pFDeg = new_FDeg; |
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| 78 | |
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| 79 | if (new_lDeg == NULL) |
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| 80 | new_lDeg = currRing->pLDegOrig; |
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| 81 | |
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| 82 | pLDeg = new_lDeg; |
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| 83 | currRing->pLDeg = new_lDeg; |
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| 84 | } |
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| 85 | |
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| 86 | |
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| 87 | // restores pFDeg and pLDeg: |
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| 88 | extern void pRestoreDegProcs(pFDegProc old_FDeg, pLDegProc old_lDeg) |
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| 89 | { |
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| 90 | assume(old_FDeg != NULL && old_lDeg != NULL); |
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| 91 | pFDeg = old_FDeg; |
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| 92 | currRing->pFDeg = old_FDeg; |
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| 93 | pLDeg = old_lDeg; |
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| 94 | currRing->pLDeg = old_lDeg; |
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| 95 | } |
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| 96 | |
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| 97 | /*2 |
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| 98 | * assumes that the head term of b is a multiple of the head term of a |
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| 99 | * and return the multiplicant *m |
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| 100 | */ |
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| 101 | poly pDivide(poly a, poly b) |
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| 102 | { |
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| 103 | int i; |
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| 104 | poly result = pInit(); |
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| 105 | |
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| 106 | for(i=(int)pVariables; i; i--) |
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| 107 | pSetExp(result,i, pGetExp(a,i)- pGetExp(b,i)); |
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| 108 | pSetComp(result, pGetComp(a) - pGetComp(b)); |
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| 109 | pSetm(result); |
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| 110 | return result; |
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| 111 | } |
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| 112 | |
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[206e158] | 113 | #ifdef HAVE_RINGS //TODO Oliver |
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[8251cc] | 114 | #define pDiv_nn(p, n) p_Div_nn(p, n, currRing) |
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| 115 | |
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| 116 | poly p_Div_nn(poly p, const number n, const ring r) |
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| 117 | { |
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| 118 | pAssume(!n_IsZero(n,r)); |
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| 119 | p_Test(p, r); |
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| 120 | |
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| 121 | poly q = p; |
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| 122 | while (p != NULL) |
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| 123 | { |
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| 124 | number nc = pGetCoeff(p); |
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| 125 | pSetCoeff0(p, n_Div(nc, n, r)); |
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| 126 | n_Delete(&nc, r); |
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| 127 | pIter(p); |
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| 128 | } |
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| 129 | p_Test(q, r); |
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| 130 | return q; |
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| 131 | } |
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| 132 | #endif |
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| 133 | |
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[35aab3] | 134 | /*2 |
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| 135 | * divides a by the monomial b, ignores monomials which are not divisible |
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| 136 | * assumes that b is not NULL |
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| 137 | */ |
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| 138 | poly pDivideM(poly a, poly b) |
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| 139 | { |
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| 140 | if (a==NULL) return NULL; |
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| 141 | poly result=a; |
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| 142 | poly prev=NULL; |
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| 143 | int i; |
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[009d80] | 144 | #ifdef HAVE_RINGS |
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| 145 | number inv=pGetCoeff(b); |
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[8251cc] | 146 | #else |
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[35aab3] | 147 | number inv=nInvers(pGetCoeff(b)); |
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[8251cc] | 148 | #endif |
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[35aab3] | 149 | |
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| 150 | while (a!=NULL) |
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| 151 | { |
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| 152 | if (pDivisibleBy(b,a)) |
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| 153 | { |
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| 154 | for(i=(int)pVariables; i; i--) |
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| 155 | pSubExp(a,i, pGetExp(b,i)); |
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| 156 | pSubComp(a, pGetComp(b)); |
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| 157 | pSetm(a); |
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| 158 | prev=a; |
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| 159 | pIter(a); |
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| 160 | } |
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| 161 | else |
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| 162 | { |
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| 163 | if (prev==NULL) |
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| 164 | { |
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| 165 | pDeleteLm(&result); |
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| 166 | a=result; |
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| 167 | } |
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| 168 | else |
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| 169 | { |
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| 170 | pDeleteLm(&pNext(prev)); |
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| 171 | a=pNext(prev); |
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| 172 | } |
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| 173 | } |
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| 174 | } |
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[009d80] | 175 | #ifdef HAVE_RINGS |
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| 176 | pDiv_nn(result,inv); |
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| 177 | #else |
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[35aab3] | 178 | pMult_nn(result,inv); |
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[009d80] | 179 | #endif |
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[35aab3] | 180 | nDelete(&inv); |
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| 181 | pDelete(&b); |
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| 182 | return result; |
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| 183 | } |
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| 184 | |
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| 185 | /*2 |
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| 186 | * returns the LCM of the head terms of a and b in *m |
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| 187 | */ |
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| 188 | void pLcm(poly a, poly b, poly m) |
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| 189 | { |
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| 190 | int i; |
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| 191 | for (i=pVariables; i; i--) |
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| 192 | { |
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| 193 | pSetExp(m,i, si_max( pGetExp(a,i), pGetExp(b,i))); |
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| 194 | } |
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| 195 | pSetComp(m, si_max(pGetComp(a), pGetComp(b))); |
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| 196 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
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| 197 | } |
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| 198 | |
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| 199 | /*2 |
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| 200 | * convert monomial given as string to poly, e.g. 1x3y5z |
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| 201 | */ |
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| 202 | char * p_Read(char *st, poly &rc, ring r) |
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| 203 | { |
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| 204 | if (r==NULL) { rc=NULL;return st;} |
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| 205 | int i,j; |
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| 206 | rc = p_Init(r); |
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| 207 | char *s = r->cf->nRead(st,&(rc->coef)); |
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| 208 | if (s==st) |
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| 209 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
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| 210 | { |
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| 211 | j = r_IsRingVar(s,r); |
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| 212 | if (j >= 0) |
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| 213 | { |
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| 214 | p_IncrExp(rc,1+j,r); |
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| 215 | while (*s!='\0') s++; |
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| 216 | goto done; |
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| 217 | } |
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| 218 | } |
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| 219 | while (*s!='\0') |
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| 220 | { |
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| 221 | char ss[2]; |
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| 222 | ss[0] = *s++; |
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| 223 | ss[1] = '\0'; |
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| 224 | j = r_IsRingVar(ss,r); |
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| 225 | if (j >= 0) |
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| 226 | { |
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[ded4ee] | 227 | char *s_save=s; |
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[35aab3] | 228 | s = eati(s,&i); |
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[ded4ee] | 229 | if (((unsigned long)i) > r->bitmask) |
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| 230 | { |
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[9b10a76] | 231 | // exponent to large: it is not a monomial |
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[b529d9] | 232 | p_DeleteLm(&rc,r); |
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[ded4ee] | 233 | return s_save; |
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| 234 | } |
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[35aab3] | 235 | p_AddExp(rc,1+j, (Exponent_t)i, r); |
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| 236 | } |
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| 237 | else |
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| 238 | { |
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[b529d9] | 239 | // 1st char of is not a varname |
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| 240 | p_DeleteLm(&rc,r); |
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[35aab3] | 241 | s--; |
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| 242 | return s; |
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| 243 | } |
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| 244 | } |
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| 245 | done: |
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| 246 | if (r->cf->nIsZero(pGetCoeff(rc))) p_DeleteLm(&rc,r); |
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| 247 | else |
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| 248 | { |
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[5d7a3b] | 249 | #ifdef HAVE_PLURAL |
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[9b10a76] | 250 | // in super-commutative ring |
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| 251 | // squares of anti-commutative variables are zeroes! |
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| 252 | if(rIsSCA(r)) |
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| 253 | { |
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| 254 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
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| 255 | const unsigned int iLastAltVar = scaLastAltVar(r); |
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| 256 | |
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| 257 | assume(rc != NULL); |
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| 258 | |
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| 259 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
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| 260 | if( p_GetExp(rc, k, r) > 1 ) |
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| 261 | { |
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| 262 | p_DeleteLm(&rc, r); |
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| 263 | goto finish; |
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| 264 | } |
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[5d7a3b] | 265 | } |
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| 266 | #endif |
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[9b10a76] | 267 | |
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[35aab3] | 268 | p_Setm(rc,r); |
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| 269 | } |
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[9b10a76] | 270 | finish: |
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[35aab3] | 271 | return s; |
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| 272 | } |
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| 273 | |
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| 274 | poly pmInit(char *st, BOOLEAN &ok) |
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| 275 | { |
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| 276 | poly p; |
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| 277 | char *s=p_Read(st,p,currRing); |
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| 278 | if (*s!='\0') |
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| 279 | { |
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| 280 | if ((s!=st)&&isdigit(st[0])) |
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| 281 | { |
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| 282 | errorreported=TRUE; |
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| 283 | } |
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| 284 | ok=FALSE; |
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| 285 | pDelete(&p); |
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| 286 | return NULL; |
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| 287 | } |
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| 288 | ok=!errorreported; |
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| 289 | return p; |
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| 290 | } |
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| 291 | |
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| 292 | /*2 |
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| 293 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
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[5ef9d3] | 294 | *assume: deg(var(varnum))==1 |
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[35aab3] | 295 | */ |
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| 296 | poly pHomogen (poly p, int varnum) |
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| 297 | { |
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| 298 | poly q=NULL, qn; |
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| 299 | int o,ii; |
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| 300 | sBucket_pt bp; |
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| 301 | |
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| 302 | if (p!=NULL) |
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| 303 | { |
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| 304 | if ((varnum < 1) || (varnum > pVariables)) |
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| 305 | { |
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| 306 | return NULL; |
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| 307 | } |
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| 308 | o=pWTotaldegree(p); |
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| 309 | q=pNext(p); |
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| 310 | while (q != NULL) |
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| 311 | { |
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| 312 | ii=pWTotaldegree(q); |
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| 313 | if (ii>o) o=ii; |
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| 314 | pIter(q); |
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| 315 | } |
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| 316 | q = pCopy(p); |
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| 317 | bp = sBucketCreate(currRing); |
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| 318 | while (q != NULL) |
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| 319 | { |
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| 320 | ii = o-pWTotaldegree(q); |
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| 321 | if (ii!=0) |
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| 322 | { |
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| 323 | pAddExp(q,varnum, (Exponent_t)ii); |
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| 324 | pSetm(q); |
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| 325 | } |
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| 326 | qn = pNext(q); |
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| 327 | pNext(q) = NULL; |
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| 328 | sBucket_Add_p(bp, q, 1); |
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| 329 | q = qn; |
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| 330 | } |
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| 331 | sBucketDestroyAdd(bp, &q, &ii); |
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| 332 | } |
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| 333 | return q; |
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| 334 | } |
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| 335 | |
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| 336 | /*2 |
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| 337 | *replaces the maximal powers of the leading monomial of p2 in p1 by |
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| 338 | *the same powers of n, utility for dehomogenization |
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| 339 | */ |
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| 340 | poly pDehomogen (poly p1,poly p2,number n) |
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| 341 | { |
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| 342 | polyset P; |
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| 343 | int SizeOfSet=5; |
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| 344 | int i; |
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| 345 | poly p; |
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| 346 | number nn; |
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| 347 | |
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| 348 | P = (polyset)omAlloc0(5*sizeof(poly)); |
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| 349 | //for (i=0; i<5; i++) |
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| 350 | //{ |
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| 351 | // P[i] = NULL; |
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| 352 | //} |
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| 353 | pCancelPolyByMonom(p1,p2,&P,&SizeOfSet); |
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| 354 | p = P[0]; |
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| 355 | //P[0] = NULL ;// for safety, may be removed later |
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| 356 | for (i=1; i<SizeOfSet; i++) |
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| 357 | { |
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| 358 | if (P[i] != NULL) |
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| 359 | { |
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| 360 | nPower(n,i,&nn); |
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| 361 | pMult_nn(P[i],nn); |
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| 362 | p = pAdd(p,P[i]); |
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| 363 | //P[i] =NULL; // for safety, may be removed later |
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| 364 | nDelete(&nn); |
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| 365 | } |
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| 366 | } |
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| 367 | omFreeSize((ADDRESS)P,SizeOfSet*sizeof(poly)); |
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| 368 | return p; |
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| 369 | } |
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| 370 | |
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| 371 | /*4 |
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| 372 | *Returns the exponent of the maximal power of the leading monomial of |
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| 373 | *p2 in that of p1 |
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| 374 | */ |
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| 375 | static int pGetMaxPower (poly p1,poly p2) |
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| 376 | { |
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| 377 | int i,k,res = 32000; /*a very large integer*/ |
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| 378 | |
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| 379 | if (p1 == NULL) return 0; |
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| 380 | for (i=1; i<=pVariables; i++) |
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| 381 | { |
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| 382 | if ( pGetExp(p2,i) != 0) |
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| 383 | { |
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| 384 | k = pGetExp(p1,i) / pGetExp(p2,i); |
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| 385 | if (k < res) res = k; |
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| 386 | } |
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| 387 | } |
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| 388 | return res; |
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| 389 | } |
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| 390 | |
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| 391 | /*2 |
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| 392 | *Returns as i-th entry of P the coefficient of the (i-1) power of |
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| 393 | *the leading monomial of p2 in p1 |
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| 394 | */ |
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| 395 | void pCancelPolyByMonom (poly p1,poly p2,polyset * P,int * SizeOfSet) |
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| 396 | { |
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| 397 | int maxPow; |
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| 398 | poly p,qp,Coeff; |
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| 399 | |
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| 400 | if (*P == NULL) |
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| 401 | { |
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| 402 | *P = (polyset) omAlloc(5*sizeof(poly)); |
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| 403 | *SizeOfSet = 5; |
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| 404 | } |
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| 405 | p = pCopy(p1); |
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| 406 | while (p != NULL) |
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| 407 | { |
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| 408 | qp = p->next; |
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| 409 | p->next = NULL; |
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| 410 | maxPow = pGetMaxPower(p,p2); |
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| 411 | Coeff = pDivByMonom(p,p2); |
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| 412 | if (maxPow > *SizeOfSet) |
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| 413 | { |
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| 414 | pEnlargeSet(P,*SizeOfSet,maxPow+1-*SizeOfSet); |
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| 415 | *SizeOfSet = maxPow+1; |
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| 416 | } |
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| 417 | (*P)[maxPow] = pAdd((*P)[maxPow],Coeff); |
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| 418 | pDelete(&p); |
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| 419 | p = qp; |
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| 420 | } |
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| 421 | } |
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| 422 | |
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| 423 | /*2 |
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| 424 | *returns the leading monomial of p1 divided by the maximal power of that |
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| 425 | *of p2 |
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| 426 | */ |
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| 427 | poly pDivByMonom (poly p1,poly p2) |
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| 428 | { |
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| 429 | int k, i; |
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| 430 | |
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| 431 | if (p1 == NULL) return NULL; |
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| 432 | k = pGetMaxPower(p1,p2); |
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| 433 | if (k == 0) |
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| 434 | return pHead(p1); |
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| 435 | else |
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| 436 | { |
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| 437 | number n; |
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| 438 | poly p = pInit(); |
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| 439 | |
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| 440 | p->next = NULL; |
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| 441 | for (i=1; i<=pVariables; i++) |
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| 442 | { |
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| 443 | pSetExp(p,i, pGetExp(p1,i)-k* pGetExp(p2,i)); |
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| 444 | } |
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| 445 | nPower(p2->coef,k,&n); |
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| 446 | pSetCoeff0(p,nDiv(p1->coef,n)); |
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| 447 | nDelete(&n); |
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| 448 | pSetm(p); |
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| 449 | return p; |
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| 450 | } |
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| 451 | } |
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| 452 | /*----------utilities for syzygies--------------*/ |
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| 453 | poly pTakeOutComp(poly * p, int k) |
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| 454 | { |
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| 455 | poly q = *p,qq=NULL,result = NULL; |
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| 456 | |
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| 457 | if (q==NULL) return NULL; |
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| 458 | if (pGetComp(q)==k) |
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| 459 | { |
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| 460 | result = q; |
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[0ef842] | 461 | do |
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[35aab3] | 462 | { |
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| 463 | pSetComp(q,0); |
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| 464 | pSetmComp(q); |
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| 465 | qq = q; |
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| 466 | pIter(q); |
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| 467 | } |
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[0ef842] | 468 | while ((q!=NULL) && (pGetComp(q)==k)); |
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[35aab3] | 469 | *p = q; |
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| 470 | pNext(qq) = NULL; |
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| 471 | } |
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| 472 | if (q==NULL) return result; |
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| 473 | if (pGetComp(q) > k) |
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| 474 | { |
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| 475 | pDecrComp(q); |
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| 476 | pSetmComp(q); |
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| 477 | } |
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| 478 | poly pNext_q; |
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| 479 | while ((pNext_q=pNext(q))!=NULL) |
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| 480 | { |
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| 481 | if (pGetComp(pNext_q)==k) |
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| 482 | { |
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| 483 | if (result==NULL) |
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| 484 | { |
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| 485 | result = pNext_q; |
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| 486 | qq = result; |
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| 487 | } |
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| 488 | else |
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| 489 | { |
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| 490 | pNext(qq) = pNext_q; |
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| 491 | pIter(qq); |
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| 492 | } |
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| 493 | pNext(q) = pNext(pNext_q); |
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| 494 | pNext(qq) =NULL; |
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| 495 | pSetComp(qq,0); |
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| 496 | pSetmComp(qq); |
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| 497 | } |
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| 498 | else |
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| 499 | { |
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| 500 | /*pIter(q);*/ q=pNext_q; |
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| 501 | if (pGetComp(q) > k) |
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| 502 | { |
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| 503 | pDecrComp(q); |
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| 504 | pSetmComp(q); |
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| 505 | } |
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| 506 | } |
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| 507 | } |
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| 508 | return result; |
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| 509 | } |
---|
| 510 | |
---|
| 511 | // Splits *p into two polys: *q which consists of all monoms with |
---|
| 512 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
| 513 | void pTakeOutComp(poly *r_p, Exponent_t comp, poly *r_q, int *lq) |
---|
| 514 | { |
---|
| 515 | spolyrec pp, qq; |
---|
| 516 | poly p, q, p_prev; |
---|
| 517 | int l = 0; |
---|
| 518 | |
---|
| 519 | #ifdef HAVE_ASSUME |
---|
| 520 | int lp = pLength(*r_p); |
---|
| 521 | #endif |
---|
| 522 | |
---|
| 523 | pNext(&pp) = *r_p; |
---|
| 524 | p = *r_p; |
---|
| 525 | p_prev = &pp; |
---|
| 526 | q = &qq; |
---|
| 527 | |
---|
| 528 | while(p != NULL) |
---|
| 529 | { |
---|
| 530 | while (pGetComp(p) == comp) |
---|
| 531 | { |
---|
| 532 | pNext(q) = p; |
---|
| 533 | pIter(q); |
---|
| 534 | pSetComp(p, 0); |
---|
| 535 | pSetmComp(p); |
---|
| 536 | pIter(p); |
---|
| 537 | l++; |
---|
| 538 | if (p == NULL) |
---|
| 539 | { |
---|
| 540 | pNext(p_prev) = NULL; |
---|
| 541 | goto Finish; |
---|
| 542 | } |
---|
| 543 | } |
---|
| 544 | pNext(p_prev) = p; |
---|
| 545 | p_prev = p; |
---|
| 546 | pIter(p); |
---|
| 547 | } |
---|
| 548 | |
---|
| 549 | Finish: |
---|
| 550 | pNext(q) = NULL; |
---|
| 551 | *r_p = pNext(&pp); |
---|
| 552 | *r_q = pNext(&qq); |
---|
| 553 | *lq = l; |
---|
| 554 | #ifdef HAVE_ASSUME |
---|
| 555 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
| 556 | #endif |
---|
| 557 | pTest(*r_p); |
---|
| 558 | pTest(*r_q); |
---|
| 559 | } |
---|
| 560 | |
---|
| 561 | void pDecrOrdTakeOutComp(poly *r_p, Exponent_t comp, Order_t order, |
---|
| 562 | poly *r_q, int *lq) |
---|
| 563 | { |
---|
| 564 | spolyrec pp, qq; |
---|
| 565 | poly p, q, p_prev; |
---|
| 566 | int l = 0; |
---|
| 567 | |
---|
| 568 | pNext(&pp) = *r_p; |
---|
| 569 | p = *r_p; |
---|
| 570 | p_prev = &pp; |
---|
| 571 | q = &qq; |
---|
| 572 | |
---|
| 573 | #ifdef HAVE_ASSUME |
---|
| 574 | if (p != NULL) |
---|
| 575 | { |
---|
| 576 | while (pNext(p) != NULL) |
---|
| 577 | { |
---|
| 578 | assume(pGetOrder(p) >= pGetOrder(pNext(p))); |
---|
| 579 | pIter(p); |
---|
| 580 | } |
---|
| 581 | } |
---|
| 582 | p = *r_p; |
---|
| 583 | #endif |
---|
| 584 | |
---|
| 585 | while (p != NULL && pGetOrder(p) > order) pIter(p); |
---|
| 586 | |
---|
| 587 | while(p != NULL && pGetOrder(p) == order) |
---|
| 588 | { |
---|
| 589 | while (pGetComp(p) == comp) |
---|
| 590 | { |
---|
| 591 | pNext(q) = p; |
---|
| 592 | pIter(q); |
---|
| 593 | pIter(p); |
---|
| 594 | pSetComp(p, 0); |
---|
| 595 | pSetmComp(p); |
---|
| 596 | l++; |
---|
| 597 | if (p == NULL || pGetOrder(p) != order) |
---|
| 598 | { |
---|
| 599 | pNext(p_prev) = p; |
---|
| 600 | goto Finish; |
---|
| 601 | } |
---|
| 602 | } |
---|
| 603 | pNext(p_prev) = p; |
---|
| 604 | p_prev = p; |
---|
| 605 | pIter(p); |
---|
| 606 | } |
---|
| 607 | |
---|
| 608 | Finish: |
---|
| 609 | pNext(q) = NULL; |
---|
| 610 | *r_p = pNext(&pp); |
---|
| 611 | *r_q = pNext(&qq); |
---|
| 612 | *lq = l; |
---|
| 613 | } |
---|
| 614 | |
---|
| 615 | #if 1 |
---|
| 616 | poly pTakeOutComp1(poly * p, int k) |
---|
| 617 | { |
---|
| 618 | poly q = *p; |
---|
| 619 | |
---|
| 620 | if (q==NULL) return NULL; |
---|
| 621 | |
---|
| 622 | poly qq=NULL,result = NULL; |
---|
| 623 | |
---|
| 624 | if (pGetComp(q)==k) |
---|
| 625 | { |
---|
| 626 | result = q; /* *p */ |
---|
| 627 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
| 628 | { |
---|
| 629 | pSetComp(q,0); |
---|
| 630 | pSetmComp(q); |
---|
| 631 | qq = q; |
---|
| 632 | pIter(q); |
---|
| 633 | } |
---|
| 634 | *p = q; |
---|
| 635 | pNext(qq) = NULL; |
---|
| 636 | } |
---|
| 637 | if (q==NULL) return result; |
---|
| 638 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 639 | while (pNext(q)!=NULL) |
---|
| 640 | { |
---|
| 641 | if (pGetComp(pNext(q))==k) |
---|
| 642 | { |
---|
| 643 | if (result==NULL) |
---|
| 644 | { |
---|
| 645 | result = pNext(q); |
---|
| 646 | qq = result; |
---|
| 647 | } |
---|
| 648 | else |
---|
| 649 | { |
---|
| 650 | pNext(qq) = pNext(q); |
---|
| 651 | pIter(qq); |
---|
| 652 | } |
---|
| 653 | pNext(q) = pNext(pNext(q)); |
---|
| 654 | pNext(qq) =NULL; |
---|
| 655 | pSetComp(qq,0); |
---|
| 656 | pSetmComp(qq); |
---|
| 657 | } |
---|
| 658 | else |
---|
| 659 | { |
---|
| 660 | pIter(q); |
---|
| 661 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
| 662 | } |
---|
| 663 | } |
---|
| 664 | return result; |
---|
| 665 | } |
---|
| 666 | #endif |
---|
| 667 | |
---|
| 668 | void pDeleteComp(poly * p,int k) |
---|
| 669 | { |
---|
| 670 | poly q; |
---|
| 671 | |
---|
| 672 | while ((*p!=NULL) && (pGetComp(*p)==k)) pDeleteLm(p); |
---|
| 673 | if (*p==NULL) return; |
---|
| 674 | q = *p; |
---|
| 675 | if (pGetComp(q)>k) |
---|
| 676 | { |
---|
| 677 | pDecrComp(q); |
---|
| 678 | pSetmComp(q); |
---|
| 679 | } |
---|
| 680 | while (pNext(q)!=NULL) |
---|
| 681 | { |
---|
| 682 | if (pGetComp(pNext(q))==k) |
---|
| 683 | pDeleteLm(&(pNext(q))); |
---|
| 684 | else |
---|
| 685 | { |
---|
| 686 | pIter(q); |
---|
| 687 | if (pGetComp(q)>k) |
---|
| 688 | { |
---|
| 689 | pDecrComp(q); |
---|
| 690 | pSetmComp(q); |
---|
| 691 | } |
---|
| 692 | } |
---|
| 693 | } |
---|
| 694 | } |
---|
| 695 | /*----------end of utilities for syzygies--------------*/ |
---|
| 696 | |
---|
| 697 | /*2 |
---|
| 698 | * pair has no common factor ? or is no polynomial |
---|
| 699 | */ |
---|
| 700 | BOOLEAN pHasNotCF(poly p1, poly p2) |
---|
| 701 | { |
---|
| 702 | |
---|
[225d94] | 703 | if (!TEST_OPT_IDLIFT) |
---|
| 704 | { |
---|
| 705 | if (pGetComp(p1) > 0 || pGetComp(p2) > 0) |
---|
| 706 | return FALSE; |
---|
| 707 | } |
---|
[35aab3] | 708 | int i = 1; |
---|
| 709 | loop |
---|
| 710 | { |
---|
| 711 | if ((pGetExp(p1, i) > 0) && (pGetExp(p2, i) > 0)) return FALSE; |
---|
| 712 | if (i == pVariables) return TRUE; |
---|
| 713 | i++; |
---|
| 714 | } |
---|
| 715 | } |
---|
| 716 | |
---|
| 717 | /*2 |
---|
| 718 | *divides p1 by its leading coefficient |
---|
| 719 | */ |
---|
| 720 | void pNorm(poly p1) |
---|
| 721 | { |
---|
| 722 | poly h; |
---|
| 723 | number k, c; |
---|
[009d80] | 724 | #ifdef HAVE_RINGS |
---|
| 725 | if (rField_is_Ring(currRing)) |
---|
[585bbcb] | 726 | { |
---|
[1e579c6] | 727 | if ((p1!=NULL) && rField_has_Units(currRing)) |
---|
[585bbcb] | 728 | { |
---|
| 729 | k = nGetUnit(pGetCoeff(p1)); |
---|
| 730 | if (!nIsOne(k)) |
---|
| 731 | { |
---|
| 732 | c = nDiv(pGetCoeff(p1), k); |
---|
[32a34c2] | 733 | nDelete(&pGetCoeff(p1)); |
---|
[585bbcb] | 734 | pSetCoeff0(p1, c); |
---|
| 735 | h = pNext(p1); |
---|
| 736 | while (h != NULL) |
---|
| 737 | { |
---|
| 738 | c = nDiv(pGetCoeff(h), k); |
---|
[32a34c2] | 739 | nDelete(&pGetCoeff(h)); |
---|
[1e579c6] | 740 | pSetCoeff0(h, c); |
---|
[585bbcb] | 741 | pIter(h); |
---|
| 742 | } |
---|
| 743 | } |
---|
[1e579c6] | 744 | nDelete(&k); |
---|
[585bbcb] | 745 | } |
---|
[1e579c6] | 746 | return; |
---|
[585bbcb] | 747 | } |
---|
[994445] | 748 | else |
---|
[f92547] | 749 | #endif |
---|
[35aab3] | 750 | if (p1!=NULL) |
---|
| 751 | { |
---|
[5e8fe91] | 752 | if (pNext(p1)==NULL) |
---|
| 753 | { |
---|
[98938c] | 754 | pSetCoeff(p1,nInit(1)); |
---|
[5e8fe91] | 755 | return; |
---|
| 756 | } |
---|
[35aab3] | 757 | if (!nIsOne(pGetCoeff(p1))) |
---|
| 758 | { |
---|
| 759 | nNormalize(pGetCoeff(p1)); |
---|
[585bbcb] | 760 | k = pGetCoeff(p1); |
---|
[35aab3] | 761 | c = nInit(1); |
---|
| 762 | pSetCoeff0(p1,c); |
---|
| 763 | h = pNext(p1); |
---|
| 764 | while (h!=NULL) |
---|
| 765 | { |
---|
| 766 | c=nDiv(pGetCoeff(h),k); |
---|
[7ba059] | 767 | // no need to normalize: Z/p, R |
---|
| 768 | // normalize already in nDiv: Q_a, Z/p_a |
---|
| 769 | // remains: Q |
---|
| 770 | if (rField_is_Q() && (!nIsOne(c))) nNormalize(c); |
---|
[35aab3] | 771 | pSetCoeff(h,c); |
---|
| 772 | pIter(h); |
---|
| 773 | } |
---|
| 774 | nDelete(&k); |
---|
| 775 | } |
---|
| 776 | else |
---|
| 777 | { |
---|
| 778 | if (nNormalize != nDummy2) |
---|
| 779 | { |
---|
| 780 | h = pNext(p1); |
---|
| 781 | while (h!=NULL) |
---|
| 782 | { |
---|
| 783 | nNormalize(pGetCoeff(h)); |
---|
| 784 | pIter(h); |
---|
| 785 | } |
---|
| 786 | } |
---|
| 787 | } |
---|
| 788 | } |
---|
| 789 | } |
---|
| 790 | |
---|
| 791 | /*2 |
---|
| 792 | *normalize all coefficients |
---|
| 793 | */ |
---|
[585bbcb] | 794 | void p_Normalize(poly p, ring r) |
---|
[35aab3] | 795 | { |
---|
| 796 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
| 797 | while (p!=NULL) |
---|
| 798 | { |
---|
| 799 | if (currRing==r) {nTest(pGetCoeff(p));} |
---|
| 800 | n_Normalize(pGetCoeff(p),r); |
---|
| 801 | pIter(p); |
---|
| 802 | } |
---|
| 803 | } |
---|
| 804 | |
---|
| 805 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
| 806 | // Poly with Exp(n) != 0 is reversed |
---|
| 807 | static void pSplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero) |
---|
| 808 | { |
---|
| 809 | if (p == NULL) |
---|
| 810 | { |
---|
| 811 | *non_zero = NULL; |
---|
| 812 | *zero = NULL; |
---|
| 813 | return; |
---|
| 814 | } |
---|
| 815 | spolyrec sz; |
---|
| 816 | poly z, n_z, next; |
---|
| 817 | z = &sz; |
---|
| 818 | n_z = NULL; |
---|
| 819 | |
---|
| 820 | while(p != NULL) |
---|
| 821 | { |
---|
| 822 | next = pNext(p); |
---|
| 823 | if (pGetExp(p, n) == 0) |
---|
| 824 | { |
---|
| 825 | pNext(z) = p; |
---|
| 826 | pIter(z); |
---|
| 827 | } |
---|
| 828 | else |
---|
| 829 | { |
---|
| 830 | pNext(p) = n_z; |
---|
| 831 | n_z = p; |
---|
| 832 | } |
---|
| 833 | p = next; |
---|
| 834 | } |
---|
| 835 | pNext(z) = NULL; |
---|
| 836 | *zero = pNext(&sz); |
---|
| 837 | *non_zero = n_z; |
---|
| 838 | return; |
---|
| 839 | } |
---|
| 840 | |
---|
| 841 | /*3 |
---|
| 842 | * substitute the n-th variable by 1 in p |
---|
| 843 | * destroy p |
---|
| 844 | */ |
---|
| 845 | static poly pSubst1 (poly p,int n) |
---|
| 846 | { |
---|
[788529d] | 847 | poly qq=NULL, result = NULL; |
---|
| 848 | poly zero=NULL, non_zero=NULL; |
---|
[35aab3] | 849 | |
---|
| 850 | // reverse, so that add is likely to be linear |
---|
| 851 | pSplitAndReversePoly(p, n, &non_zero, &zero); |
---|
| 852 | |
---|
| 853 | while (non_zero != NULL) |
---|
| 854 | { |
---|
| 855 | assume(pGetExp(non_zero, n) != 0); |
---|
| 856 | qq = non_zero; |
---|
| 857 | pIter(non_zero); |
---|
| 858 | qq->next = NULL; |
---|
| 859 | pSetExp(qq,n,0); |
---|
| 860 | pSetm(qq); |
---|
| 861 | result = pAdd(result,qq); |
---|
| 862 | } |
---|
| 863 | p = pAdd(result, zero); |
---|
| 864 | pTest(p); |
---|
| 865 | return p; |
---|
| 866 | } |
---|
| 867 | |
---|
| 868 | /*3 |
---|
| 869 | * substitute the n-th variable by number e in p |
---|
| 870 | * destroy p |
---|
| 871 | */ |
---|
| 872 | static poly pSubst2 (poly p,int n, number e) |
---|
| 873 | { |
---|
| 874 | assume( ! nIsZero(e) ); |
---|
| 875 | poly qq,result = NULL; |
---|
| 876 | number nn, nm; |
---|
| 877 | poly zero, non_zero; |
---|
| 878 | |
---|
| 879 | // reverse, so that add is likely to be linear |
---|
| 880 | pSplitAndReversePoly(p, n, &non_zero, &zero); |
---|
| 881 | |
---|
| 882 | while (non_zero != NULL) |
---|
| 883 | { |
---|
| 884 | assume(pGetExp(non_zero, n) != 0); |
---|
| 885 | qq = non_zero; |
---|
| 886 | pIter(non_zero); |
---|
| 887 | qq->next = NULL; |
---|
| 888 | nPower(e, pGetExp(qq, n), &nn); |
---|
| 889 | nm = nMult(nn, pGetCoeff(qq)); |
---|
| 890 | pSetCoeff(qq, nm); |
---|
| 891 | nDelete(&nn); |
---|
| 892 | pSetExp(qq, n, 0); |
---|
| 893 | pSetm(qq); |
---|
| 894 | result = pAdd(result,qq); |
---|
| 895 | } |
---|
| 896 | p = pAdd(result, zero); |
---|
| 897 | pTest(p); |
---|
| 898 | return p; |
---|
| 899 | } |
---|
| 900 | |
---|
| 901 | |
---|
| 902 | /* delete monoms whose n-th exponent is different from zero */ |
---|
| 903 | poly pSubst0(poly p, int n) |
---|
| 904 | { |
---|
| 905 | spolyrec res; |
---|
| 906 | poly h = &res; |
---|
| 907 | pNext(h) = p; |
---|
| 908 | |
---|
| 909 | while (pNext(h)!=NULL) |
---|
| 910 | { |
---|
| 911 | if (pGetExp(pNext(h),n)!=0) |
---|
| 912 | { |
---|
| 913 | pDeleteLm(&pNext(h)); |
---|
| 914 | } |
---|
| 915 | else |
---|
| 916 | { |
---|
| 917 | pIter(h); |
---|
| 918 | } |
---|
| 919 | } |
---|
| 920 | pTest(pNext(&res)); |
---|
| 921 | return pNext(&res); |
---|
| 922 | } |
---|
| 923 | |
---|
| 924 | /*2 |
---|
| 925 | * substitute the n-th variable by e in p |
---|
| 926 | * destroy p |
---|
| 927 | */ |
---|
| 928 | poly pSubst(poly p, int n, poly e) |
---|
| 929 | { |
---|
| 930 | if (e == NULL) return pSubst0(p, n); |
---|
| 931 | |
---|
| 932 | if (pIsConstant(e)) |
---|
| 933 | { |
---|
| 934 | if (nIsOne(pGetCoeff(e))) return pSubst1(p,n); |
---|
| 935 | else return pSubst2(p, n, pGetCoeff(e)); |
---|
| 936 | } |
---|
| 937 | |
---|
[68349d] | 938 | #ifdef HAVE_PLURAL |
---|
| 939 | if (rIsPluralRing(currRing)) |
---|
| 940 | { |
---|
| 941 | return nc_pSubst(p,n,e); |
---|
| 942 | } |
---|
| 943 | #endif |
---|
| 944 | |
---|
[35aab3] | 945 | int exponent,i; |
---|
| 946 | poly h, res, m; |
---|
| 947 | int *me,*ee; |
---|
| 948 | number nu,nu1; |
---|
| 949 | |
---|
| 950 | me=(int *)omAlloc((pVariables+1)*sizeof(int)); |
---|
| 951 | ee=(int *)omAlloc((pVariables+1)*sizeof(int)); |
---|
| 952 | if (e!=NULL) pGetExpV(e,ee); |
---|
| 953 | res=NULL; |
---|
| 954 | h=p; |
---|
| 955 | while (h!=NULL) |
---|
| 956 | { |
---|
| 957 | if ((e!=NULL) || (pGetExp(h,n)==0)) |
---|
| 958 | { |
---|
| 959 | m=pHead(h); |
---|
| 960 | pGetExpV(m,me); |
---|
| 961 | exponent=me[n]; |
---|
| 962 | me[n]=0; |
---|
| 963 | for(i=pVariables;i>0;i--) |
---|
| 964 | me[i]+=exponent*ee[i]; |
---|
| 965 | pSetExpV(m,me); |
---|
| 966 | if (e!=NULL) |
---|
| 967 | { |
---|
| 968 | nPower(pGetCoeff(e),exponent,&nu); |
---|
| 969 | nu1=nMult(pGetCoeff(m),nu); |
---|
| 970 | nDelete(&nu); |
---|
| 971 | pSetCoeff(m,nu1); |
---|
| 972 | } |
---|
| 973 | res=pAdd(res,m); |
---|
| 974 | } |
---|
| 975 | pDeleteLm(&h); |
---|
| 976 | } |
---|
| 977 | omFreeSize((ADDRESS)me,(pVariables+1)*sizeof(int)); |
---|
| 978 | omFreeSize((ADDRESS)ee,(pVariables+1)*sizeof(int)); |
---|
| 979 | return res; |
---|
| 980 | } |
---|
| 981 | |
---|
[a2466f] | 982 | /* Returns TRUE if |
---|
| 983 | * LM(p) | LM(lcm) |
---|
| 984 | * LC(p) | LC(lcm) only if ring |
---|
| 985 | * Exists i, j: |
---|
| 986 | * LE(p, i) != LE(lcm, i) |
---|
| 987 | * LE(p1, i) != LE(lcm, i) ==> LCM(p1, p) != lcm |
---|
| 988 | * LE(p, j) != LE(lcm, j) |
---|
| 989 | * LE(p2, j) != LE(lcm, j) ==> LCM(p2, p) != lcm |
---|
| 990 | */ |
---|
[35aab3] | 991 | BOOLEAN pCompareChain (poly p,poly p1,poly p2,poly lcm) |
---|
| 992 | { |
---|
| 993 | int k, j; |
---|
| 994 | |
---|
| 995 | if (lcm==NULL) return FALSE; |
---|
| 996 | |
---|
| 997 | for (j=pVariables; j; j--) |
---|
| 998 | if ( pGetExp(p,j) > pGetExp(lcm,j)) return FALSE; |
---|
| 999 | if ( pGetComp(p) != pGetComp(lcm)) return FALSE; |
---|
| 1000 | for (j=pVariables; j; j--) |
---|
| 1001 | { |
---|
| 1002 | if (pGetExp(p1,j)!=pGetExp(lcm,j)) |
---|
| 1003 | { |
---|
| 1004 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
| 1005 | { |
---|
| 1006 | for (k=pVariables; k>j; k--) |
---|
| 1007 | { |
---|
| 1008 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
| 1009 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
| 1010 | return TRUE; |
---|
| 1011 | } |
---|
| 1012 | for (k=j-1; k; k--) |
---|
| 1013 | { |
---|
| 1014 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
| 1015 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
| 1016 | return TRUE; |
---|
| 1017 | } |
---|
| 1018 | return FALSE; |
---|
| 1019 | } |
---|
| 1020 | } |
---|
| 1021 | else if (pGetExp(p2,j)!=pGetExp(lcm,j)) |
---|
| 1022 | { |
---|
| 1023 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
| 1024 | { |
---|
| 1025 | for (k=pVariables; k>j; k--) |
---|
| 1026 | { |
---|
| 1027 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
| 1028 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
| 1029 | return TRUE; |
---|
| 1030 | } |
---|
| 1031 | for (k=j-1; k!=0 ; k--) |
---|
| 1032 | { |
---|
| 1033 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
| 1034 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
| 1035 | return TRUE; |
---|
| 1036 | } |
---|
| 1037 | return FALSE; |
---|
| 1038 | } |
---|
| 1039 | } |
---|
| 1040 | } |
---|
| 1041 | return FALSE; |
---|
| 1042 | } |
---|
[7ba059] | 1043 | |
---|
| 1044 | int pSize(poly p) |
---|
| 1045 | { |
---|
| 1046 | int count = 0; |
---|
| 1047 | while ( p != NULL ) |
---|
| 1048 | { |
---|
| 1049 | count+= nSize( pGetCoeff( p ) ); |
---|
| 1050 | pIter( p ); |
---|
| 1051 | } |
---|
| 1052 | return count; |
---|
| 1053 | } |
---|
| 1054 | |
---|