#ifndef POLYS_H #define POLYS_H /**************************************** * Computer Algebra System SINGULAR * ****************************************/ /* $Id$ */ /* * ABSTRACT - compatiblity layer for all operations with polys */ #include extern ring currRing; extern void rChangeCurrRing(ring r); /*************************************************************** * * Primitives for accessing and setting fields of a poly * poly must be != NULL * ***************************************************************/ // deletes old coeff before setting the new one #define pSetCoeff(p,n) p_SetCoeff(p,n,currRing) // Order #define pGetOrder(p) p_GetOrder(p, currRing) // Component #define pGetComp(p) __p_GetComp(p, currRing) #define pSetComp(p,v) p_SetComp(p,v, currRing) // Exponent #define pGetExp(p,i) p_GetExp(p, i, currRing) #define pSetExp(p,i,v) p_SetExp(p, i, v, currRing) #define pIncrExp(p,i) p_IncrExp(p,i, currRing) #define pDecrExp(p,i) p_DecrExp(p,i, currRing) #define pAddExp(p,i,v) p_AddExp(p,i,v, currRing) #define pSubExp(p,i,v) p_SubExp(p,i,v, currRing) #define pMultExp(p,i,v) p_MultExp(p,i,v, currRing) #define pGetExpSum(p1, p2, i) p_GetExpSum(p1, p2, i, currRing) #define pGetExpDiff(p1, p2, i) p_GetExpDiff(p1, p2, i, currRing) /*************************************************************** * * Allocation/Initalization/Deletion * except for pHead, all polys must be != NULL * ***************************************************************/ // allocates the space for a new monomial -- no initialization !!! #define pNew() p_New(currRing) // allocates a new monomial and initializes everything to 0 #define pInit() p_Init(currRing) // like pInit, except that expvector is initialized to that of p, // p must be != NULL #define pLmInit(p) p_LmInit(p, currRing) // returns newly allocated copy of Lm(p), coef is copied, next=NULL, // p might be NULL #define pHead(p) p_Head(p, currRing) // frees the space of the monomial m, assumes m != NULL // coef is not freed, m is not advanced static inline void pLmFree(poly p) {p_LmFree(p, currRing);} // like pLmFree, but advances p static inline void pLmFree(poly *p) {p_LmFree(p, currRing);} // assumes p != NULL, deletes p, returns pNext(p) #define pLmFreeAndNext(p) p_LmFreeAndNext(p, currRing) // assume p != NULL, deletes Lm(p)->coef and Lm(p) #define pLmDelete(p) p_LmDelete(p, currRing) // like pLmDelete, returns pNext(p) #define pLmDeleteAndNext(p) p_LmDeleteAndNext(p, currRing) /*************************************************************** * * Operation on ExpVectors: assumes polys != NULL * ***************************************************************/ #define pExpVectorCopy(d_p, s_p) p_ExpVectorCopy(d_p, s_p, currRing) #define pExpVectorAdd(p1, p2) p_ExpVectorAdd(p1, p2, currRing) #define pExpVectorSub(p1, p2) p_ExpVectorSub(p1, p2, currRing) #define pExpVectorAddSub(p1, p2, p3)p_ExpVectorAddSub(p1, p2, p3, currRing) #define pExpVectorSum(pr, p1, p2) p_ExpVectorSum(pr, p1, p2, currRing) #define pExpVectorDiff(pr, p1, p2) p_ExpVectorDiff(pr, p1, p2, currRing) // Gets a copy of (resp. set) the exponent vector, where e is assumed // to point to (r->N +1)*sizeof(long) memory. Exponents are // filled in as follows: comp, e_1, .., e_n #define pGetExpV(p, e) p_GetExpV(p, e, currRing) #define pSetExpV(p, e) p_SetExpV(p, e, currRing) /*************************************************************** * * Comparisons: they are all done without regarding coeffs * ***************************************************************/ // returns 0|1|-1 if p=q|p>q|pq|p 0, s.t. b = a + c; #define pDivisibleBy(a, b) p_DivisibleBy(a,b,currRing) // like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL #define pLmDivisibleBy(a,b) p_LmDivisibleBy(a,b,currRing) // like pLmDivisibleBy, does not check components #define pLmDivisibleByNoComp(a, b) p_LmDivisibleByNoComp(a,b,currRing) // Divisibility tests based on Short Exponent vectors // sev_a == pGetShortExpVector(a) // not_sev_b == ~ pGetShortExpVector(b) #define pLmShortDivisibleBy(a, sev_a, b, not_sev_b) \ p_LmShortDivisibleBy(a, sev_a, b, not_sev_b, currRing) #define pLmRingShortDivisibleBy(a, sev_a, b, not_sev_b) \ p_LmRingShortDivisibleBy(a, sev_a, b, not_sev_b, currRing) // returns the "Short Exponent Vector" -- used to speed up divisibility // tests (see polys-impl.cc ) #define pGetShortExpVector(a) p_GetShortExpVector(a, currRing) #ifdef HAVE_RINGS /* divisibility check over ground ring (which may contain zero divisors); TRUE iff LT(f) divides LT(g), i.e., LT(f)*c*m = LT(g), for some coefficient c and some monomial m; does not take components into account */ #define pDivisibleByRingCase(f,g) p_DivisibleByRingCase(f,g,currRing) #endif /*************************************************************** * * Copying/Deleteion of polys: args may be NULL * ***************************************************************/ // return a copy of the poly #define pCopy(p) p_Copy(p, currRing) #define pDelete(p_ptr) p_Delete(p_ptr, currRing) /*************************************************************** * * Copying/Deletion of polys: args may be NULL * - p/q as arg mean a poly * - m a monomial * - n a number * - pp (resp. qq, mm, nn) means arg is constant * - p (resp, q, m, n) means arg is destroyed * ***************************************************************/ #define pNeg(p) p_Neg(p, currRing) #define ppMult_nn(p, n) pp_Mult_nn(p, n, currRing) #define pMult_nn(p, n) p_Mult_nn(p, n, currRing) #define ppMult_mm(p, m) pp_Mult_mm(p, m, currRing) #define pMult_mm(p, m) p_Mult_mm(p, m, currRing) #define pAdd(p, q) p_Add_q(p, q, currRing) #define pPower(p, q) p_Power(p, q, currRing) #define pMinus_mm_Mult_qq(p, m, q) p_Minus_mm_Mult_qq(p, m, q, currRing) #define pPlus_mm_Mult_qq(p, m, q) p_Plus_mm_Mult_qq(p, m, q, currRing) #define pMult(p, q) p_Mult_q(p, q, currRing) #define ppMult_qq(p, q) pp_Mult_qq(p, q, currRing) // p*Coeff(m) for such monomials pm of p, for which m is divisble by pm #define ppMult_Coeff_mm_DivSelect(p, m) pp_Mult_Coeff_mm_DivSelect(p, m, currRing) /************************************************************************* * * Sort routines * *************************************************************************/ // sorts p, assumes all monomials in p are different #define pSortMerger(p) p_SortMerge(p, currRing) #define pSort(p) p_SortMerge(p, currRing) // sorts p, p may have equal monomials #define pSortAdd(p) p_SortAdd(p, currRing) // Assume: If considerd only as poly in any component of p // (say, monomials of other components of p are set to 0), // then p is already sorted correctly #define pSortCompCorrect(p) pSort(p) /*************************************************************** * * Predicates on polys/Lm's * ***************************************************************/ // return true if all p is eihter NULL, or if all exponents // of p are 0 and Comp of p is zero #define pIsConstantComp(p) p_IsConstantComp(p, currRing) // like above, except that Comp might be != 0 #define pIsConstant(p) p_IsConstant(p,currRing) // return true if the Lm is a constant <>0 #define pIsUnit(p) p_IsUnit(p,currRing) // like above, except that p must be != NULL #define pLmIsConstantComp(p) p_LmIsConstantComp(p, currRing) #define pLmIsConstant(p) p_LmIsConstant(p,currRing) // return TRUE if all monomials of p are constant #define pIsConstantPoly(p) p_IsConstantPoly(p, currRing) #define pIsPurePower(p) p_IsPurePower(p, currRing) #define pIsUnivariate(p) p_IsUnivariate(p, currRing) #define pIsVector(p) (pGetComp(p)>0) #define pGetVariables(p,e) p_GetVariables(p, e, currRing) /*************************************************************** * * Old stuff * ***************************************************************/ typedef poly* polyset; extern int pOrdSgn; extern BOOLEAN pLexOrder; extern poly ppNoether; extern BOOLEAN pVectorOut; /*-------------predicate on polys ----------------------*/ #define pHasNotCF(p1,p2) p_HasNotCF(p1,p2,currRing) /*has no common factor ?*/ #define pSplit(p,r) p_Split(p,r) /*p => IN(p), r => REST(p) */ /*-----------the ordering of monomials:-------------*/ #define pSetm(p) p_Setm(p, currRing) // TODO: #define pSetmComp(p) p_Setm(p, currRing) /*************************************************************** * * Degree stuff -- see p_polys.cc for explainations * ***************************************************************/ inline int pWeight(int i, const ring R = currRing){ return p_Weight(i, R); } inline long pDeg(poly p, const ring R = currRing) { return p_Deg(p, R); } static inline long pTotaldegree(poly p) { return p_Totaldegree(p,currRing); } #define pWTotaldegree(p) p_WTotaldegree(p,currRing) #define pWDegree(p) p_WDegree(p,currRing) /*-------------operations on polynomials:------------*/ #define pSub(a,b) p_Sub(a,b,currRing) #define pmInit(a,b) p_mInit(a,b,currRing) // ----------------- define to enable new p_procs -----*/ #define pDivide(a,b) p_Divide(a,b,currRing) #define pLcm(a,b,m) p_Lcm(a,b,m,currRing) #define pDiff(a,b) p_Diff(a,b,currRing) #define pDiffOp(a,b,m) p_DiffOp(a,b,m,currRing) #define pMaxComp(p) p_MaxComp(p, currRing) #define pMinComp(p) p_MinComp(p, currRing) #define pOneComp(p) p_OneComp(p, currRing) #define pSetCompP(a,i) p_SetCompP(a, i, currRing) // let's inline those, so that we can call them from the debugger inline char* pString(poly p) {return p_String(p, currRing, currRing);} inline char* pString0(poly p) {return p_String0(p, currRing, currRing);} inline void pWrite(poly p) {p_Write(p, currRing, currRing);} inline void pWrite0(poly p) {p_Write0(p, currRing, currRing);} inline void wrp(poly p) {p_wrp(p, currRing, currRing);} #define pISet(i) p_ISet(i,currRing) #define pNSet(n) p_NSet(n,currRing) #define pOne() p_One(currRing) #define pNormalize(p) p_Normalize(p,currRing) #define pSize(p) p_Size(p,currRing) // homogenizes p by multiplying certain powers of the varnum-th variable #define pHomogen(p,varnum) p_Homogen(p,varnum,currRing) BOOLEAN pIsHomogeneous (poly p); // // replaces the maximal powers of the leading monomial of p2 in p1 by // // the same powers of n, utility for dehomogenization // #define pDehomogen(p1,p2,n) p_Dehomgen(p1,p2,n,currRing) // #define pIsHomogen(p) p_IsHomggen(p,currRing) #define pIsHomogen(p) p_IsHomogen(p,currRing) /*BOOLEAN pVectorHasUnitM(poly p, int * k);*/ #define pVectorHasUnitB(p,k) p_VectorHasUnitB(p,k,currRing) #define pVectorHasUnit(p,k,l) p_VectorHasUnit(p,k,l,currRing) #define pTakeOutComp1(p,k) p_TakeOutComp1(p,k,currRing) // Splits *p into two polys: *q which consists of all monoms with // component == comp and *p of all other monoms *lq == pLength(*q) // On return all components pf *q == 0 void pTakeOutComp(poly *p, long comp, poly *q, int *lq); // This is something weird -- Don't use it, unless you know what you are doing poly pTakeOutComp(poly * p, int k); /* old spielwiese #define pTakeOutComp(p,k,q,lq) p_TakeOutComp(p,k,q,lq,currRing) // Similar to pTakeOutComp, except that only those components are // taken out whose Order == order // ASSUME: monomial ordering is Order compatible, i.e., if m1, m2 Monoms then // m1 >= m2 ==> pGetOrder(m1) >= pGetOrder(m2) #define pDecrOrdTakeOutComp(p,c,o,q,lq) p_DecrOrdTakeOutComp(p,c,o,q,lq,currRing) */ void pSetPolyComp(poly p, int comp); #define pDeleteComp(p,k) p_DeleteComp(p,k,currRing) #define pNorm(p) p_Norm(p,currRing) #define pSubst(p,n,e) p_Subst(p,n.e,currRing) #define ppJet(p,m) pp_Jet(p,m,currRing) #define pJet(p,m) p_Jet(p,m,currRing) #define ppJetW(p,m,iv) pp_JetW(p,m,iv,currRing) #define pJetW(p,m,iv) p_JetW(p,m,iv,currRing) #define pMinDeg(p,w) p_MinDeg(p,w,currRing) #define pSeries(n,p,u,w) p_series(n,p,u,w,currRing) #define pInvers(n,p,w) p_Invers(n,p,w,currRing) // maximum weigthed degree of all monomials of p, w is indexed from // 1..pVariables #define pDegW(p,w) p_DegW(p,w,currRing) /*-----------type conversions ----------------------------*/ void pVec2Polys(poly v, polyset *p, int *len); #define pVar(m) p_Var(m,currRing) /*-----------specials for spoly-computations--------------*/ BOOLEAN pCompareChain (poly p,poly p1,poly p2,poly lcm); BOOLEAN pCompareChainPart (poly p,poly p1,poly p2,poly lcm); #define pEqualPolys(p1,p2) p_EqualPolys(p1,p2,currRing) /*************************************************************** * * PDEBUG stuff * ***************************************************************/ #ifdef PDEBUG #define pTest(p) _p_Test(p, currRing, PDEBUG) #define pLmTest(p) _p_LmTest(p, currRing, PDEBUG) #else // ! PDEBUG #define pTest(p) ((void)0) #define pLmTest(p) ((void)0) #endif #endif // POLYS_H