/**************************************** * Computer Algebra System SINGULAR * ****************************************/ /*************************************************************** * File: p_polys.h * Purpose: declaration of poly stuf which are independent of * currRing * Author: obachman (Olaf Bachmann) * Created: 9/00 * Version: $Id$ *******************************************************************/ #ifndef P_POLYS_H #define P_POLYS_H #include #include #include #include #include #include /*************************************************************** * * Primitives for accessing and setting fields of a poly * poly must be != NULL * ***************************************************************/ // next #define pNext(p) ((p)->next) #define pIter(p) ((p) = (p)->next) // coeff #define pGetCoeff(p) ((p)->coef) // deletes old coeff before setting the new one #define pSetCoeff0(p,n) (p)->coef=(n) #define p_GetCoeff(p,r) pGetCoeff(p) #define p_SetCoeff0(p,n,r) pSetCoeff0(p,n) // deletes old p->coef and sets new one static inline number p_SetCoeff(poly p, number n, ring r); // get Order static inline long p_GetOrder(poly p, ring r); // Component static inline unsigned long p_SetComp(poly p, unsigned long c, ring r); static inline unsigned long p_AddComp(poly p, unsigned long v, ring r); static inline unsigned long p_SubComp(poly p, unsigned long v, ring r); // Exponent static inline long p_GetExp(poly p, int v, ring r); static inline long p_SetExp(poly p, int v, long e, ring r); static inline long p_IncrExp(poly p, int v, ring r); static inline long p_DecrExp(poly p, int v, ring r); static inline long p_AddExp(poly p, int v, long ee, ring r); static inline long p_SubExp(poly p, int v, long ee, ring r); static inline long p_MultExp(poly p, int v, long ee, ring r); static inline long p_GetExpSum(poly p1, poly p2, int i, ring r); static inline long p_GetExpDiff(poly p1, poly p2, int i, ring r); /*************************************************************** * * Allocation/Initalization/Deletion * except for pHead, all polys must be != NULL * ***************************************************************/ static inline poly p_New(ring r); static inline poly p_New(ring r, omBin bin); static inline poly p_Init(ring r); static inline poly p_Init(ring r, omBin bin); static inline poly p_LmInit(poly p, ring r); static inline poly p_LmInit(poly s_p, ring s_r, ring d_p); static inline poly p_LmInit(poly s_p, ring s_r, ring d_p, omBin d_bin); static inline poly p_Head(poly p, ring r); static inline void p_LmFree(poly p, ring r); static inline void p_LmFree(poly *p, ring r); static inline poly p_LmFreeAndNext(poly p, ring r); static inline void p_LmDelete(poly p, ring r); static inline void p_LmDelete(poly *p, ring r); static inline poly p_LmDeleteAndNext(poly p, ring r); /*************************************************************** * * Operation on ExpVectors: assumes polys != NULL * ***************************************************************/ // ExpVextor(d_p) = ExpVector(s_p) static inline void p_ExpVectorCopy(poly d_p, poly s_p, ring r); // adjustments for negative weights static inline void p_MemAdd_NegWeightAdjust(poly p, ring r); static inline void p_MemSub_NegWeightAdjust(poly p, ring r); // ExpVector(p1) += ExpVector(p2) static inline void p_ExpVectorAdd(poly p1, poly p2, ring r); // ExpVector(p1) -= ExpVector(p2) static inline void p_ExpVectorSub(poly p1, poly p2, ring r); // ExpVector(p1) += ExpVector(p2) - ExpVector(p3) static inline void p_ExpVectorAddSub(poly p1, poly p2, poly p3, ring r); // ExpVector(pr) = ExpVector(p1) + ExpVector(p2) static inline void p_ExpVectorSum(poly pr, poly p1, poly p2, ring r); /// ExpVector(pr) = ExpVector(p1) + ExpVector(p2) static inline void p_ExpVectorDiff(poly pr, poly p1, poly p2, ring r); /// returns TRUE if ExpVector(p1) == ExpVector(p2), FALSE, otherwise static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, ring r); /// compute the degree of the leading monomial of p /// with respect to weigths 1 /// the ordering may not be compatible with degree so do not use p->Order static inline long p_Totaldegree(poly p, ring r); static inline void p_GetExpV(poly p, int *ev, ring r); static inline void p_SetExpV(poly p, int *ev, ring r); /*************************************************************** * * Comparisons: they are all done without regarding coeffs * ***************************************************************/ static inline int p_LmCmp(poly p, poly q, ring r); #define p_LmCmpAction(p, q, r, actionE, actionG, actionS) \ _p_LmCmpAction(p, q, r, actionE, actionG, actionS) // returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !! #define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r) // pCmp: args may be NULL // returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2))) static inline int p_Cmp(poly p1, poly p2, ring r); /*************************************************************** * * Divisiblity tests, args must be != NULL, except for * pDivisbleBy * ***************************************************************/ static inline BOOLEAN p_DivisibleBy(poly a, poly b, ring r); static inline BOOLEAN p_LmDivisibleBy(poly a, poly b, ring r); static inline BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, ring r); unsigned long p_GetShortExpVector(poly a, ring r); static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, ring r); static inline BOOLEAN p_DivisibleBy(poly a, ring r_a, poly b, ring r_b); static inline BOOLEAN p_LmDivisibleBy(poly a, ring r_a, poly b, ring r_b); static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, ring r_a, poly b, unsigned long not_sev_b, ring r_b); /*************************************************************** * * Misc things on Lm * ***************************************************************/ // test if the monomial is a constant as a vector component // i.e., test if all exponents are zero static inline BOOLEAN p_LmIsConstantComp(const poly p, const ring r); static inline BOOLEAN p_LmIsConstant(const poly p, const ring r); // return TRUE, if p_LmExpVectorAdd stays within ExpBound of ring r, // FALSE, otherwise static inline BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2, ring r); /*************************************************************** * * Misc things on polys * ***************************************************************/ // return the maximal exponent of p static inline unsigned long p_GetMaxExp(poly p, ring r); // return the maximal exponent of p in form of the maximal long var unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max = 0); // return monomial r such that GetExp(r,i) is maximum of all // monomials in p; coeff == 0, next == NULL, ord is not set poly p_GetMaxExpP(poly p, ring r); // suppose that l is a long var in r, return maximal exponent of l static inline unsigned long p_GetMaxExp(const unsigned long l, const ring r); // return the TotalDegree of the long var l static inline unsigned long p_GetTotalDegree(const unsigned long l, const ring r); // return the total degree of the long var l containing number_of_exp exponents static inline unsigned long p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps); int p_MinDeg(poly p,intvec *w, const ring R); long p_DegW(poly p, const short *w, const ring R); // like the respective p_LmIs* routines, except that p might be empty static inline BOOLEAN p_IsConstantComp(const poly p, const ring r); static inline BOOLEAN p_IsConstant(const poly p, const ring r); static inline BOOLEAN p_IsConstantPoly(const poly p, const ring r); // return TRUE if all monoms have the same component BOOLEAN p_OneComp(poly p, ring r); // return i, if head depends only on var(i) int p_IsPurePower(const poly p, const ring r); // return i, if poly depends only on var(i) int p_IsUnivariate(poly p, const ring r); // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 // return #(e[i]>0) int p_GetVariables(poly p, int * e, const ring r); // returns the poly representing the integer i poly p_ISet(int i, ring r); // returns the poly representing the number n, destroys n poly p_NSet(number n, ring r); /*************************************************************** * * Copying/Deletion of polys: args may be NULL * ***************************************************************/ // returns a copy of p static inline poly p_Copy(poly p, const ring r); // returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing static inline poly p_Copy(poly p, const ring lmRing, const ring tailRing); // deletes *p, and sets *p to NULL static inline void p_Delete(poly *p, const ring r); static inline void p_Delete(poly *p, const ring lmRing, const ring tailRing); // copys monomials of p, allocates new monomials from bin, // deletes monomoals of p static inline poly p_ShallowCopyDelete(poly p, const ring r, omBin bin); // simial but does it only for leading monomial static inline poly p_LmShallowCopyDelete(poly p, const ring r, omBin bin); // simply deletes monomials, does not free coeffs void p_ShallowDelete(poly *p, const ring r); /*************************************************************** * * Copying/Deleteion 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 * ***************************************************************/ // returns -p, p is destroyed static inline poly p_Neg(poly p, const ring r); // returns p*n, p is const (i.e. copied) static inline poly pp_Mult_nn(poly p, number n, const ring r); // returns p*n, destroys p static inline poly p_Mult_nn(poly p, number n, const ring r); static inline poly p_Mult_nn(poly p, number n, const ring lmRing, const ring tailRing); // returns p*m, does neither destroy p nor m static inline poly pp_Mult_mm(poly p, poly m, const ring r); // returns p*m, destroys p, const: m static inline poly p_Mult_mm(poly p, poly m, const ring r); /// returns p+q, destroys p and q static inline poly p_Add_q(poly p, poly q, const ring r); /// like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q) static inline poly p_Add_q(poly p, poly q, int &lp, int lq, const ring r); poly p_Sub(poly a, poly b, const ring r); // return p - m*q, destroys p; const: q,m static inline poly p_Minus_mm_Mult_qq(poly p, poly m, poly q, const ring r); // like p_Minus_mm_Mult_qq, except that if lp == pLength(lp) lq == pLength(lq) // then lp == pLength(p -m*q) static inline poly p_Minus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, poly spNoether, const ring r); // returns p + m*q destroys p, const: q, m static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, const ring r); // returns p + m*q destroys p, const: q, m static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, const ring r); // returns p*q, destroys p and q static inline poly p_Mult_q(poly p, poly q, const ring r); // returns p*q, does neither destroy p nor q static inline poly pp_Mult_qq(poly p, poly q, const ring r); // returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r); // returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm // if lp is length of p on input then lp is length of returned poly on output static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, int &lp, const poly m, const ring r); // returns merged p and q, assumes p and q have no monomials which are equal static inline poly p_Merge_q(poly p, poly c, const ring r); // sorts p using bucket sort: returns sorted poly // assumes that monomials of p are all different // reverses it first, if revert == TRUE, use this if input p is "almost" sorted // correctly static inline poly p_SortMerge(poly p, const ring r, BOOLEAN revert = FALSE); // like SortMerge, except that p may have equal monimals static inline poly p_SortAdd(poly p, const ring r, BOOLEAN revert = FALSE); poly p_Power(poly p, int i, const ring r); /*************************************************************** * * Misc stuff * ***************************************************************/ void p_Norm(poly p1, const ring r); void p_Normalize(poly p,const ring r); void p_Content(poly p, const ring r); //void p_SimpleContent(poly p, int s, const ring r); poly p_Cleardenom(poly p, const ring r); void p_Cleardenom_n(poly p, const ring r,number &c); number p_GetAllDenom(poly ph, const ring r); int pSize( poly p, const ring r ); // homogenizes p by multiplying certain powers of the varnum-th variable poly p_Homogen (poly p, int varnum, const ring r); BOOLEAN p_IsHomogeneous (poly p, const ring r); static inline void p_Setm(poly p, const ring r); p_SetmProc p_GetSetmProc(ring r); poly p_Subst(poly p, int n, poly e, const ring r); // TODO: #define p_SetmComp p_Setm // sets component of poly a to i, returns length of a static inline void p_SetCompP(poly a, int i, ring r); static inline void p_SetCompP(poly a, int i, ring lmRing, ring tailRing); static inline long p_MaxComp(poly p, ring lmRing, ring tailRing); inline long p_MaxComp(poly p,ring lmRing) {return p_MaxComp(p,lmRing,lmRing);} static inline long p_MinComp(poly p, ring lmRing, ring tailRing); inline long p_MinComp(poly p,ring lmRing) {return p_MinComp(p,lmRing,lmRing);} /*************************************************************** * * poly things which are independent of ring * ***************************************************************/ static inline int pLength(poly a); static inline poly pLast(poly a, int &length); inline poly pLast(poly a) { int l; return pLast(a, l);} static inline poly pReverse(poly p); void pEnlargeSet(poly**p, int length, int increment); /*************************************************************** * * I/O * ***************************************************************/ char* p_String(poly p, ring lmRing, ring tailRing); char* p_String0(poly p, ring lmRing, ring tailRing); void p_Write(poly p, ring lmRing, ring tailRing); void p_Write0(poly p, ring lmRing, ring tailRing); void p_wrp(poly p, ring lmRing, ring tailRing); static inline char* p_String(poly p, ring p_ring); static inline char* p_String0(poly p, ring p_ring); static inline void p_Write(poly p, ring p_ring); static inline void p_Write0(poly p, ring p_ring); static inline void p_wrp(poly p, ring p_ring); /*************************************************************** * * Degree stuff -- see p_polys.cc for explainations * ***************************************************************/ extern pLDegProc pLDeg; extern pFDegProc pFDeg; long p_WFirstTotalDegree(poly p, ring r); long p_WTotaldegree(poly p, const ring r); long p_WDegree(poly p,const ring r); long pLDeg0(poly p,int *l, ring r); long pLDeg0c(poly p,int *l, ring r); long pLDegb(poly p,int *l, ring r); long pLDeg1(poly p,int *l, ring r); long pLDeg1c(poly p,int *l, ring r); long pLDeg1_Deg(poly p,int *l, ring r); long pLDeg1c_Deg(poly p,int *l, ring r); long pLDeg1_Totaldegree(poly p,int *l, ring r); long pLDeg1c_Totaldegree(poly p,int *l, ring r); long pLDeg1_WFirstTotalDegree(poly p,int *l, ring r); long pLDeg1c_WFirstTotalDegree(poly p,int *l, ring r); BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r); long p_Deg(poly a, const ring r); /*************************************************************** * * PDEBUG stuff * ***************************************************************/ #ifdef PDEBUG // Returns TRUE if m is monom of p, FALSE otherwise BOOLEAN pIsMonomOf(poly p, poly m); // Returns TRUE if p and q have common monoms BOOLEAN pHaveCommonMonoms(poly p, poly q); // p_Check* routines return TRUE if everything is ok, // else, they report error message and return false // check if Lm(p) is from ring r BOOLEAN p_LmCheckIsFromRing(poly p, ring r); // check if Lm(p) != NULL, r != NULL and initialized && Lm(p) is from r BOOLEAN p_LmCheckPolyRing(poly p, ring r); // check if all monoms of p are from ring r BOOLEAN p_CheckIsFromRing(poly p, ring r); // check r != NULL and initialized && all monoms of p are from r BOOLEAN p_CheckPolyRing(poly p, ring r); // check if r != NULL and initialized BOOLEAN p_CheckRing(ring r); // only do check if cond #define pIfThen(cond, check) do {if (cond) {check;}} while (0) BOOLEAN _p_Test(poly p, ring r, int level); BOOLEAN _p_LmTest(poly p, ring r, int level); BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level); #define p_Test(p,r) _p_Test(p, r, PDEBUG) #define p_LmTest(p,r) _p_LmTest(p, r, PDEBUG) #define pp_Test(p, lmRing, tailRing) _pp_Test(p, lmRing, tailRing, PDEBUG) #else // ! PDEBUG #define pIsMonomOf(p, q) (TRUE) #define pHaveCommonMonoms(p, q) (TRUE) #define p_LmCheckIsFromRing(p,r) ((void)0) #define p_LmCheckPolyRing(p,r) ((void)0) #define p_CheckIsFromRing(p,r) ((void)0) #define p_CheckPolyRing(p,r) ((void)0) #define p_CheckRing(r) ((void)0) #define P_CheckIf(cond, check) ((void)0) #define p_Test(p,r) (1) #define p_LmTest(p,r) (1) #define pp_Test(p, lmRing, tailRing) (1) #endif /*************************************************************** * * Primitives for accessing and setting fields of a poly * ***************************************************************/ static inline number p_SetCoeff(poly p, number n, ring r) { p_LmCheckPolyRing2(p, r); n_Delete(&(p->coef), r->cf); (p)->coef=n; return n; } // order static inline long p_GetOrder(poly p, ring r) { p_LmCheckPolyRing2(p, r); if (r->typ==NULL) return ((p)->exp[r->pOrdIndex]); int i=0; loop { switch(r->typ[i].ord_typ) { case ro_wp_neg: return (((long)((p)->exp[r->pOrdIndex]))-POLY_NEGWEIGHT_OFFSET); case ro_syzcomp: case ro_syz: case ro_cp: i++; break; //case ro_dp: //case ro_wp: default: return ((p)->exp[r->pOrdIndex]); } } } // Setm static inline void p_Setm(poly p, const ring r) { p_CheckRing2(r); r->p_Setm(p, r); } // component static inline unsigned long p_SetComp(poly p, unsigned long c, ring r) { p_LmCheckPolyRing2(p, r); pAssume2(rRing_has_Comp(r)); __p_GetComp(p,r) = c; return c; } static inline unsigned long p_AddComp(poly p, unsigned long v, ring r) { p_LmCheckPolyRing2(p, r); pAssume2(rRing_has_Comp(r)); return __p_GetComp(p,r) += v; } static inline unsigned long p_SubComp(poly p, unsigned long v, ring r) { p_LmCheckPolyRing2(p, r); pAssume2(rRing_has_Comp(r)); _pPolyAssume2(__p_GetComp(p,r) >= v,p,r); return __p_GetComp(p,r) -= v; } static inline int p_Comp_k_n(poly a, poly b, int k, ring r) { if ((a==NULL) || (b==NULL) ) return FALSE; p_LmCheckPolyRing2(a, r); p_LmCheckPolyRing2(b, r); pAssume2(k > 0 && k <= r->N); int i=k; for(;i<=r->N;i++) { if (p_GetExp(a,i,r) != p_GetExp(b,i,r)) return FALSE; // if (a->exp[(r->VarOffset[i] & 0xffffff)] != b->exp[(r->VarOffset[i] & 0xffffff)]) return FALSE; } return TRUE; } #ifndef HAVE_EXPSIZES /// get a single variable exponent /// @Note: /// the integer VarOffset encodes: /// 1. the position of a variable in the exponent vector p->exp (lower 24 bits) /// 2. number of bits to shift to the right in the upper 8 bits (which takes at most 6 bits for 64 bit) /// Thus VarOffset always has 2 zero higher bits! static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset) { pAssume2((VarOffset >> (24 + 6)) == 0); #if 0 int pos=(VarOffset & 0xffffff); int bitpos=(VarOffset >> 24); unsigned long exp=(p->exp[pos] >> bitmask) & iBitmask; return exp; #else return (long) ((p->exp[(VarOffset & 0xffffff)] >> (VarOffset >> 24)) & iBitmask); #endif } /// set a single variable exponent /// @Note: /// VarOffset encodes the position in p->exp @see p_GetExp static inline unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset) { pAssume2(e>=0); pAssume2(e<=iBitmask); pAssume2((VarOffset >> (24 + 6)) == 0); // shift e to the left: register int shift = VarOffset >> 24; unsigned long ee = e << shift /*(VarOffset >> 24)*/; // find the bits in the exponent vector register int offset = (VarOffset & 0xffffff); // clear the bits in the exponent vector: p->exp[offset] &= ~( iBitmask << shift ); // insert e with | p->exp[ offset ] |= ee; return e; } #else // #ifdef HAVE_EXPSIZES // EXPERIMENTAL!!! static inline unsigned long BitMask(unsigned long bitmask, int twobits) { // bitmask = 00000111111111111 // 0 must give bitmask! // 1, 2, 3 - anything like 00011..11 pAssume2((twobits >> 2) == 0); static const unsigned long _bitmasks[4] = {-1, 0x7fff, 0x7f, 0x3}; return bitmask & _bitmasks[twobits]; } /// @Note: we may add some more info (6 ) into VarOffset and thus encode static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset) { int pos =(VarOffset & 0xffffff); int hbyte= (VarOffset >> 24); // the highest byte int bitpos = hbyte & 0x3f; // last 6 bits long bitmask = BitMask(iBitmask, hbyte >> 6); long exp=(p->exp[pos] >> bitpos) & bitmask; return exp; } static inline long p_SetExp(poly p, const long e, const unsigned long iBitmask, const int VarOffset) { pAssume2(e>=0); pAssume2(e <= BitMask(iBitmask, VarOffset >> 30)); // shift e to the left: register int hbyte = VarOffset >> 24; int bitmask = BitMask(iBitmask, hbyte >> 6); register int shift = hbyte & 0x3f; long ee = e << shift; // find the bits in the exponent vector register int offset = (VarOffset & 0xffffff); // clear the bits in the exponent vector: p->exp[offset] &= ~( bitmask << shift ); // insert e with | p->exp[ offset ] |= ee; return e; } #endif // #ifndef HAVE_EXPSIZES static inline long p_GetExp(const poly p, const ring r, const int VarOffset) { p_LmCheckPolyRing2(p, r); pAssume2(VarOffset != -1); return p_GetExp(p, r->bitmask, VarOffset); } static inline long p_SetExp(poly p, const long e, const ring r, const int VarOffset) { p_LmCheckPolyRing2(p, r); pAssume2(VarOffset != -1); return p_SetExp(p, e, r->bitmask, VarOffset); } /// get v^th exponent for a monomial static inline long p_GetExp(const poly p, const int v, const ring r) { p_LmCheckPolyRing2(p, r); pAssume2(v>0 && v <= r->N); pAssume2(r->VarOffset[v] != -1); return p_GetExp(p, r->bitmask, r->VarOffset[v]); } /// set v^th exponent for a monomial static inline long p_SetExp(poly p, const int v, const long e, const ring r) { p_LmCheckPolyRing2(p, r); pAssume2(v>0 && v <= r->N); pAssume2(r->VarOffset[v] != -1); return p_SetExp(p, e, r->bitmask, r->VarOffset[v]); } // the following should be implemented more efficiently static inline long p_IncrExp(poly p, int v, ring r) { p_LmCheckPolyRing2(p, r); int e = p_GetExp(p,v,r); e++; return p_SetExp(p,v,e,r); } static inline long p_DecrExp(poly p, int v, ring r) { p_LmCheckPolyRing2(p, r); int e = p_GetExp(p,v,r); pAssume2(e > 0); e--; return p_SetExp(p,v,e,r); } static inline long p_AddExp(poly p, int v, long ee, ring r) { p_LmCheckPolyRing2(p, r); int e = p_GetExp(p,v,r); e += ee; return p_SetExp(p,v,e,r); } static inline long p_SubExp(poly p, int v, long ee, ring r) { p_LmCheckPolyRing2(p, r); long e = p_GetExp(p,v,r); pAssume2(e >= ee); e -= ee; return p_SetExp(p,v,e,r); } static inline long p_MultExp(poly p, int v, long ee, ring r) { p_LmCheckPolyRing2(p, r); long e = p_GetExp(p,v,r); e *= ee; return p_SetExp(p,v,e,r); } static inline long p_GetExpSum(poly p1, poly p2, int i, ring r) { p_LmCheckPolyRing2(p1, r); p_LmCheckPolyRing2(p2, r); return p_GetExp(p1,i,r) + p_GetExp(p2,i,r); } static inline long p_GetExpDiff(poly p1, poly p2, int i, ring r) { return p_GetExp(p1,i,r) - p_GetExp(p2,i,r); } /*************************************************************** * * Allocation/Initalization/Deletion * ***************************************************************/ static inline poly p_New(ring r, omBin bin) { p_CheckRing2(r); pAssume2(bin != NULL && r->PolyBin->sizeW == bin->sizeW); poly p; omTypeAllocBin(poly, p, bin); p_SetRingOfLm(p, r); return p; } static inline poly p_New(ring r) { return p_New(r, r->PolyBin); } static inline void p_LmFree(poly p, ring r) { p_LmCheckPolyRing2(p, r); omFreeBinAddr(p); } static inline void p_LmFree(poly *p, ring r) { p_LmCheckPolyRing2(*p, r); poly h = *p; *p = pNext(h); omFreeBinAddr(h); } static inline poly p_LmFreeAndNext(poly p, ring r) { p_LmCheckPolyRing2(p, r); poly pnext = pNext(p); omFreeBinAddr(p); return pnext; } static inline void p_LmDelete(poly p, const ring r) { p_LmCheckPolyRing2(p, r); n_Delete(&pGetCoeff(p), r->cf); omFreeBinAddr(p); } static inline void p_LmDelete(poly *p, const ring r) { p_LmCheckPolyRing2(*p, r); poly h = *p; *p = pNext(h); n_Delete(&pGetCoeff(h), r->cf); omFreeBinAddr(h); } static inline poly p_LmDeleteAndNext(poly p, const ring r) { p_LmCheckPolyRing2(p, r); poly pnext = pNext(p); n_Delete(&pGetCoeff(p), r->cf); omFreeBinAddr(p); return pnext; } /*************************************************************** * * Misc routines * ***************************************************************/ static inline int p_Cmp(poly p1, poly p2, ring r) { if (p2==NULL) return 1; if (p1==NULL) return -1; return p_LmCmp(p1,p2,r); } static inline unsigned long p_GetMaxExp(const poly p, const ring r) { return p_GetMaxExp(p_GetMaxExpL(p, r), r); } static inline unsigned long p_GetMaxExp(const unsigned long l, const ring r) { unsigned long bitmask = r->bitmask; unsigned long max = (l & bitmask); unsigned long j = r->ExpPerLong - 1; if (j > 0) { unsigned long i = r->BitsPerExp; long e; loop { e = ((l >> i) & bitmask); if ((unsigned long) e > max) max = e; j--; if (j==0) break; i += r->BitsPerExp; } } return max; } static inline unsigned long p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps) { const unsigned long bitmask = r->bitmask; unsigned long sum = (l & bitmask); unsigned long j = number_of_exps - 1; if (j > 0) { unsigned long i = r->BitsPerExp; loop { sum += ((l >> i) & bitmask); j--; if (j==0) break; i += r->BitsPerExp; } } return sum; } static inline unsigned long p_GetTotalDegree(const unsigned long l, const ring r) { return p_GetTotalDegree(l, r, r->ExpPerLong); } /*************************************************************** * * Dispatcher to r->p_Procs, they do the tests/checks * ***************************************************************/ // returns a copy of p static inline poly p_Copy(poly p, const ring r) { #ifdef PDEBUG poly pp= r->p_Procs->p_Copy(p, r); p_Test(pp,r); return pp; #else return r->p_Procs->p_Copy(p, r); #endif } static inline poly p_Copy(poly p, const ring lmRing, const ring tailRing) { #ifndef PDEBUG if (tailRing == lmRing) return tailRing->p_Procs->p_Copy(p, tailRing); #endif if (p != NULL) { poly pres = p_Head(p, lmRing); pNext(pres) = tailRing->p_Procs->p_Copy(pNext(p), tailRing); return pres; } else return NULL; } // deletes *p, and sets *p to NULL static inline void p_Delete(poly *p, const ring r) { r->p_Procs->p_Delete(p, r); } static inline void p_Delete(poly *p, const ring lmRing, const ring tailRing) { #ifndef PDEBUG if (tailRing == lmRing) { tailRing->p_Procs->p_Delete(p, tailRing); return; } #endif if (*p != NULL) { if (pNext(*p) != NULL) tailRing->p_Procs->p_Delete(&pNext(*p), tailRing); p_LmDelete(p, lmRing); } } static inline poly p_ShallowCopyDelete(poly p, const ring r, omBin bin) { p_LmCheckPolyRing2(p, r); pAssume2(r->PolyBin->sizeW == bin->sizeW); return r->p_Procs->p_ShallowCopyDelete(p, r, bin); } // returns p+q, destroys p and q static inline poly p_Add_q(poly p, poly q, const ring r) { int shorter; return r->p_Procs->p_Add_q(p, q, shorter, r); } static inline poly p_Add_q(poly p, poly q, int &lp, int lq, const ring r) { int shorter; poly res = r->p_Procs->p_Add_q(p, q, shorter, r); lp = (lp + lq) - shorter; return res; } // returns p*n, destroys p static inline poly p_Mult_nn(poly p, number n, const ring r) { if (n_IsOne(n, r->cf)) return p; else return r->p_Procs->p_Mult_nn(p, n, r); } static inline poly p_Mult_nn(poly p, number n, const ring lmRing, const ring tailRing) { #ifndef PDEBUG if (lmRing == tailRing) { return p_Mult_nn(p, n, tailRing); } #endif poly pnext = pNext(p); pNext(p) = NULL; p = lmRing->p_Procs->p_Mult_nn(p, n, lmRing); pNext(p) = tailRing->p_Procs->p_Mult_nn(pnext, n, tailRing); return p; } // returns p*n, does not destroy p static inline poly pp_Mult_nn(poly p, number n, const ring r) { if (n_IsOne(n, r->cf)) return p_Copy(p, r); else return r->p_Procs->pp_Mult_nn(p, n, r); } // returns Copy(p)*m, does neither destroy p nor m static inline poly pp_Mult_mm(poly p, poly m, const ring r) { if (p_LmIsConstant(m, r)) return pp_Mult_nn(p, pGetCoeff(m), r); else { poly last; return r->p_Procs->pp_Mult_mm(p, m, r, last); } } // returns p*m, destroys p, const: m static inline poly p_Mult_mm(poly p, poly m, const ring r) { if (p_LmIsConstant(m, r)) return p_Mult_nn(p, pGetCoeff(m), r); else return r->p_Procs->p_Mult_mm(p, m, r); } // return p - m*Copy(q), destroys p; const: p,m static inline poly p_Minus_mm_Mult_qq(poly p, poly m, poly q, const ring r) { #ifdef HAVE_PLURAL if (rIsPluralRing(r)) { int lp, lq; poly spNoether; return nc_p_Minus_mm_Mult_qq(p, m, q, lp, lq, spNoether, r); } #endif int shorter; poly last; return r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r, last); // !!! } static inline poly p_Minus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, poly spNoether, const ring r) { #ifdef HAVE_PLURAL if (rIsPluralRing(r)) return nc_p_Minus_mm_Mult_qq(p, m, q, lp, lq, spNoether, r); #endif int shorter; poly last,res; res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, spNoether, r, last); lp = (lp + lq) - shorter; return res; } static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r) { int shorter; return r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r); } static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, int &lp, const poly m, const ring r) { int shorter; poly pp = r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r); lp -= shorter; return pp; } // returns -p, destroys p static inline poly p_Neg(poly p, const ring r) { return r->p_Procs->p_Neg(p, r); } extern poly _p_Mult_q(poly p, poly q, const int copy, const ring r); // returns p*q, destroys p and q static inline poly p_Mult_q(poly p, poly q, const ring r) { if (p == NULL) { r->p_Procs->p_Delete(&q, r); return NULL; } if (q == NULL) { r->p_Procs->p_Delete(&p, r); return NULL; } if (pNext(p) == NULL) { #ifdef HAVE_PLURAL if (rIsPluralRing(r)) q = nc_mm_Mult_p(p, q, r); else #endif /* HAVE_PLURAL */ q = r->p_Procs->p_Mult_mm(q, p, r); r->p_Procs->p_Delete(&p, r); return q; } if (pNext(q) == NULL) { // NEEDED #ifdef HAVE_PLURAL /* if (rIsPluralRing(r)) p = gnc_p_Mult_mm(p, q, r); // ??? else*/ #endif /* HAVE_PLURAL */ p = r->p_Procs->p_Mult_mm(p, q, r); r->p_Procs->p_Delete(&q, r); return p; } #ifdef HAVE_PLURAL if (rIsPluralRing(r)) return _nc_p_Mult_q(p, q, r); else #endif return _p_Mult_q(p, q, 0, r); } // returns p*q, does neither destroy p nor q static inline poly pp_Mult_qq(poly p, poly q, const ring r) { poly last; if (p == NULL || q == NULL) return NULL; if (pNext(p) == NULL) { #ifdef HAVE_PLURAL if (rIsPluralRing(r)) return nc_mm_Mult_pp(p, q, r); #endif return r->p_Procs->pp_Mult_mm(q, p, r, last); } if (pNext(q) == NULL) { return r->p_Procs->pp_Mult_mm(p, q, r, last); } poly qq = q; if (p == q) qq = p_Copy(q, r); poly res; #ifdef HAVE_PLURAL if (rIsPluralRing(r)) res = _nc_pp_Mult_qq(p, qq, r); else #endif res = _p_Mult_q(p, qq, 1, r); if (qq != q) p_Delete(&qq, r); return res; } // returns p + m*q destroys p, const: q, m static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, const ring r) { #ifdef HAVE_PLURAL if (rIsPluralRing(r)) return nc_p_Plus_mm_Mult_qq(p, m, q, lp, lq, r); #endif // this should be implemented more efficiently poly res, last; int shorter; number n_old = pGetCoeff(m); number n_neg = n_Copy(n_old, r->cf); n_neg = n_Neg(n_neg, r->cf); pSetCoeff0(m, n_neg); res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r, last); lp = (lp + lq) - shorter; pSetCoeff0(m, n_old); n_Delete(&n_neg, r->cf); return res; } static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, const ring r) { int lp = 0, lq = 0; return p_Plus_mm_Mult_qq(p, m, q, lp, lq, r); } static inline poly p_Merge_q(poly p, poly q, const ring r) { return r->p_Procs->p_Merge_q(p, q, r); } static inline poly p_SortAdd(poly p, const ring r, BOOLEAN revert) { if (revert) p = pReverse(p); return sBucketSortAdd(p, r); } static inline poly p_SortMerge(poly p, const ring r, BOOLEAN revert) { if (revert) p = pReverse(p); return sBucketSortMerge(p, r); } /*************************************************************** * * I/O * ***************************************************************/ static inline char* p_String(poly p, ring p_ring) { return p_String(p, p_ring, p_ring); } static inline char* p_String0(poly p, ring p_ring) { return p_String0(p, p_ring, p_ring); } static inline void p_Write(poly p, ring p_ring) { p_Write(p, p_ring, p_ring); } static inline void p_Write0(poly p, ring p_ring) { p_Write0(p, p_ring, p_ring); } static inline void p_wrp(poly p, ring p_ring) { p_wrp(p, p_ring, p_ring); } /*************************************************************** * Purpose: implementation of poly procs which iter over ExpVector * Author: obachman (Olaf Bachmann) * Created: 8/00 * Version: $Id$ *******************************************************************/ #include #include // #include #include #include #if PDEBUG > 0 #define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \ do \ { \ int _cmp = p_LmCmp(p,q,r); \ if (_cmp == 0) actionE; \ if (_cmp == 1) actionG; \ actionS; \ } \ while(0) #else #define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \ p_MemCmp_LengthGeneral_OrdGeneral(p->exp, q->exp, r->CmpL_Size, r->ordsgn, \ actionE, actionG, actionS) #endif #define pDivAssume(x) ((void)0) #include #include #include #include #include /*************************************************************** * * Allocation/Initalization/Deletion * ***************************************************************/ // adjustments for negative weights static inline void p_MemAdd_NegWeightAdjust(poly p, const ring r) { if (r->NegWeightL_Offset != NULL) { for (int i=r->NegWeightL_Size-1; i>=0; i--) { p->exp[r->NegWeightL_Offset[i]] -= POLY_NEGWEIGHT_OFFSET; } } } static inline void p_MemSub_NegWeightAdjust(poly p, const ring r) { if (r->NegWeightL_Offset != NULL) { for (int i=r->NegWeightL_Size-1; i>=0; i--) { p->exp[r->NegWeightL_Offset[i]] += POLY_NEGWEIGHT_OFFSET; } } } // ExpVextor(d_p) = ExpVector(s_p) static inline void p_ExpVectorCopy(poly d_p, poly s_p, const ring r) { p_LmCheckPolyRing1(d_p, r); p_LmCheckPolyRing1(s_p, r); p_MemCopy_LengthGeneral(d_p->exp, s_p->exp, r->ExpL_Size); } static inline poly p_Init(const ring r, omBin bin) { p_CheckRing1(r); pAssume1(bin != NULL && r->PolyBin->sizeW == bin->sizeW); poly p; omTypeAlloc0Bin(poly, p, bin); p_MemAdd_NegWeightAdjust(p, r); p_SetRingOfLm(p, r); return p; } static inline poly p_Init(const ring r) { return p_Init(r, r->PolyBin); } static inline poly p_LmInit(poly p, const ring r) { p_LmCheckPolyRing1(p, r); poly np; omTypeAllocBin(poly, np, r->PolyBin); p_SetRingOfLm(np, r); p_MemCopy_LengthGeneral(np->exp, p->exp, r->ExpL_Size); pNext(np) = NULL; pSetCoeff0(np, NULL); return np; } static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r, omBin d_bin) { p_LmCheckPolyRing1(s_p, s_r); p_CheckRing(d_r); pAssume1(d_r->N <= s_r->N); poly d_p = p_Init(d_r, d_bin); for (int i=d_r->N; i>0; i--) { p_SetExp(d_p, i, p_GetExp(s_p, i,s_r), d_r); } if (rRing_has_Comp(d_r)) { p_SetComp(d_p, p_GetComp(s_p,s_r), d_r); } p_Setm(d_p, d_r); return d_p; } static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r) { pAssume1(d_r != NULL); return p_LmInit(s_p, s_r, d_r, d_r->PolyBin); } static inline poly p_Head(poly p, const ring r) { if (p == NULL) return NULL; p_LmCheckPolyRing1(p, r); poly np; omTypeAllocBin(poly, np, r->PolyBin); p_SetRingOfLm(np, r); p_MemCopy_LengthGeneral(np->exp, p->exp, r->ExpL_Size); pNext(np) = NULL; pSetCoeff0(np, n_Copy(pGetCoeff(p), r->cf)); return np; } // set all exponents l..k to 0, assume exp. k+1..n and 1..l-1 are in // different blocks // set coeff to 1 static inline poly p_GetExp_k_n(poly p, int l, int k, const ring r) { if (p == NULL) return NULL; p_LmCheckPolyRing1(p, r); poly np; omTypeAllocBin(poly, np, r->PolyBin); p_SetRingOfLm(np, r); p_MemCopy_LengthGeneral(np->exp, p->exp, r->ExpL_Size); pNext(np) = NULL; pSetCoeff0(np, n_Init(1, r->cf)); int i; for(i=l;i<=k;i++) { //np->exp[(r->VarOffset[i] & 0xffffff)] =0; p_SetExp(np,i,0,r); } p_Setm(np,r); return np; } static inline poly p_LmShallowCopyDelete(poly p, const ring r, omBin bin) { p_LmCheckPolyRing1(p, r); pAssume1(bin->sizeW == r->PolyBin->sizeW); poly new_p = p_New(r); p_MemCopy_LengthGeneral(new_p->exp, p->exp, r->ExpL_Size); pSetCoeff0(new_p, pGetCoeff(p)); pNext(new_p) = pNext(p); omFreeBinAddr(p); return new_p; } /*************************************************************** * * Operation on ExpVectors * ***************************************************************/ // ExpVector(p1) += ExpVector(p2) static inline void p_ExpVectorAdd(poly p1, poly p2, const ring r) { p_LmCheckPolyRing1(p1, r); p_LmCheckPolyRing1(p2, r); #if PDEBUG >= 1 for (int i=1; i<=r->N; i++) pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask); pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0); #endif p_MemAdd_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size); p_MemAdd_NegWeightAdjust(p1, r); } // ExpVector(p1) -= ExpVector(p2) static inline void p_ExpVectorSub(poly p1, poly p2, const ring r) { p_LmCheckPolyRing1(p1, r); p_LmCheckPolyRing1(p2, r); #if PDEBUG >= 1 for (int i=1; i<=r->N; i++) pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r)); pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0 || p_GetComp(p1, r) == p_GetComp(p2, r)); #endif p_MemSub_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size); p_MemSub_NegWeightAdjust(p1, r); } // ExpVector(p1) += ExpVector(p2) - ExpVector(p3) static inline void p_ExpVectorAddSub(poly p1, poly p2, poly p3, const ring r) { p_LmCheckPolyRing1(p1, r); p_LmCheckPolyRing1(p2, r); p_LmCheckPolyRing1(p3, r); #if PDEBUG >= 1 for (int i=1; i<=r->N; i++) pAssume1(p_GetExp(p1, i, r) + p_GetExp(p2, i, r) >= p_GetExp(p3, i, r)); pAssume1(p_GetComp(p1, r) == 0 || (p_GetComp(p2, r) - p_GetComp(p3, r) == 0) || (p_GetComp(p1, r) == p_GetComp(p2, r) - p_GetComp(p3, r))); #endif p_MemAddSub_LengthGeneral(p1->exp, p2->exp, p3->exp, r->ExpL_Size); // no need to adjust in case of NegWeights } // ExpVector(pr) = ExpVector(p1) + ExpVector(p2) static inline void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r) { p_LmCheckPolyRing1(p1, r); p_LmCheckPolyRing1(p2, r); p_LmCheckPolyRing1(pr, r); #if PDEBUG >= 1 for (int i=1; i<=r->N; i++) pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask); pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0); #endif p_MemSum_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size); p_MemAdd_NegWeightAdjust(pr, r); } // ExpVector(pr) = ExpVector(p1) - ExpVector(p2) static inline void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r) { p_LmCheckPolyRing1(p1, r); p_LmCheckPolyRing1(p2, r); p_LmCheckPolyRing1(pr, r); #if PDEBUG >= 2 for (int i=1; i<=r->N; i++) pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r)); pAssume1(!rRing_has_Comp(r) || p_GetComp(p1, r) == p_GetComp(p2, r)); #endif p_MemDiff_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size); p_MemSub_NegWeightAdjust(pr, r); } static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r) { p_LmCheckPolyRing1(p1, r); p_LmCheckPolyRing1(p2, r); int i = r->ExpL_Size; unsigned long *ep = p1->exp; unsigned long *eq = p2->exp; do { i--; if (ep[i] != eq[i]) return FALSE; } while (i); return TRUE; } static inline long p_Totaldegree(poly p, const ring r) { p_LmCheckPolyRing1(p, r); unsigned long s = p_GetTotalDegree(p->exp[r->VarL_Offset[0]], r, r->MinExpPerLong); for (int i=r->VarL_Size-1; i>0; i--) { s += p_GetTotalDegree(p->exp[r->VarL_Offset[i]], r); } return (long)s; } static inline void p_GetExpV(poly p, int *ev, const ring r) { p_LmCheckPolyRing1(p, r); for (int j = r->N; j; j--) ev[j] = p_GetExp(p, j, r); ev[0] = p_GetComp(p, r); } static inline void p_SetExpV(poly p, int *ev, const ring r) { p_LmCheckPolyRing1(p, r); for (int j = r->N; j; j--) p_SetExp(p, j, ev[j], r); p_SetComp(p, ev[0],r); p_Setm(p, r); } /*************************************************************** * * Comparison w.r.t. monomial ordering * ***************************************************************/ static inline int p_LmCmp(poly p, poly q, const ring r) { p_LmCheckPolyRing1(p, r); p_LmCheckPolyRing1(q, r); p_MemCmp_LengthGeneral_OrdGeneral(p->exp, q->exp, r->CmpL_Size, r->ordsgn, return 0, return 1, return -1); } /*************************************************************** * * divisibility * ***************************************************************/ // return: FALSE, if there exists i, such that a->exp[i] > b->exp[i] // TRUE, otherwise // (1) Consider long vars, instead of single exponents // (2) Clearly, if la > lb, then FALSE // (3) Suppose la <= lb, and consider first bits of single exponents in l: // if TRUE, then value of these bits is la ^ lb // if FALSE, then la-lb causes an "overflow" into one of those bits, i.e., // la ^ lb != la - lb static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, poly b, const ring r) { int i=r->VarL_Size - 1; unsigned long divmask = r->divmask; unsigned long la, lb; if (r->VarL_LowIndex >= 0) { i += r->VarL_LowIndex; do { la = a->exp[i]; lb = b->exp[i]; if ((la > lb) || (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask))) { pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == FALSE); return FALSE; } i--; } while (i>=r->VarL_LowIndex); } else { do { la = a->exp[r->VarL_Offset[i]]; lb = b->exp[r->VarL_Offset[i]]; if ((la > lb) || (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask))) { pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == FALSE); return FALSE; } i--; } while (i>=0); } #ifdef HAVE_RINGS pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == nDivBy(p_GetCoeff(b, r), p_GetCoeff(a, r))); return (!rField_is_Ring(r)) || n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf); #else pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == TRUE); return TRUE; #endif } static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, const ring r_a, poly b, const ring r_b) { int i=r_a->N; pAssume1(r_a->N == r_b->N); do { if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b)) return FALSE; i--; } while (i); #ifdef HAVE_RINGS return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf); #else return TRUE; #endif } #ifdef HAVE_RATGRING static inline BOOLEAN _p_LmDivisibleByNoCompPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end) { int i=end; pAssume1(r_a->N == r_b->N); do { if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b)) return FALSE; i--; } while (i>=start); #ifdef HAVE_RINGS return nDivBy(p_GetCoeff(b, r), p_GetCoeff(a, r)); #else return TRUE; #endif } static inline BOOLEAN _p_LmDivisibleByPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end) { if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b)) return _p_LmDivisibleByNoCompPart(a, r_a, b, r_b,start,end); return FALSE; } static inline BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r,const int start, const int end) { p_LmCheckPolyRing1(b, r); pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r)); if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)) return _p_LmDivisibleByNoCompPart(a, r, b, r,start, end); return FALSE; } #endif static inline BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r) { if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)) return _p_LmDivisibleByNoComp(a, b, r); return FALSE; } static inline BOOLEAN _p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b) { if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b)) return _p_LmDivisibleByNoComp(a, r_a, b, r_b); return FALSE; } static inline BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, const ring r) { p_LmCheckPolyRing1(a, r); p_LmCheckPolyRing1(b, r); return _p_LmDivisibleByNoComp(a, b, r); } static inline BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r) { p_LmCheckPolyRing1(b, r); pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r)); if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)) return _p_LmDivisibleByNoComp(a, b, r); return FALSE; } static inline BOOLEAN p_DivisibleBy(poly a, poly b, const ring r) { pIfThen1(b!=NULL, p_LmCheckPolyRing1(b, r)); pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r)); if (a != NULL && (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))) return _p_LmDivisibleByNoComp(a,b,r); return FALSE; } static inline BOOLEAN p_DivisibleBy(poly a, const ring r_a, poly b, const ring r_b) { pIfThen1(b!=NULL, p_LmCheckPolyRing1(b, r_b)); pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r_a)); if (a != NULL) { return _p_LmDivisibleBy(a, r_a, b, r_b); } return FALSE; } static inline BOOLEAN p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b) { p_LmCheckPolyRing(a, r_a); p_LmCheckPolyRing(b, r_b); return _p_LmDivisibleBy(a, r_a, b, r_b); } static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r) { p_LmCheckPolyRing1(a, r); p_LmCheckPolyRing1(b, r); #ifndef PDIV_DEBUG _pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r); _pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r); if (sev_a & not_sev_b) { pAssume1(p_LmDivisibleByNoComp(a, b, r) == FALSE); return FALSE; } return p_LmDivisibleBy(a, b, r); #else return pDebugLmShortDivisibleBy(a, sev_a, r, b, not_sev_b, r); #endif } static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, const ring r_a, poly b, unsigned long not_sev_b, const ring r_b) { p_LmCheckPolyRing1(a, r_a); p_LmCheckPolyRing1(b, r_b); #ifndef PDIV_DEBUG _pPolyAssume2(p_GetShortExpVector(a, r_a) == sev_a, a, r_a); _pPolyAssume2(p_GetShortExpVector(b, r_b) == ~ not_sev_b, b, r_b); if (sev_a & not_sev_b) { pAssume1(_p_LmDivisibleByNoComp(a, r_a, b, r_b) == FALSE); return FALSE; } return _p_LmDivisibleBy(a, r_a, b, r_b); #else return pDebugLmShortDivisibleBy(a, sev_a, r_a, b, not_sev_b, r_b); #endif } /*************************************************************** * * Misc things on Lm * ***************************************************************/ // test if the monomial is a constant as a vector component // i.e., test if all exponents are zero static inline BOOLEAN p_LmIsConstantComp(const poly p, const ring r) { //p_LmCheckPolyRing(p, r); int i = r->VarL_Size - 1; do { if (p->exp[r->VarL_Offset[i]] != 0) return FALSE; i--; } while (i >= 0); return TRUE; } // test if monomial is a constant, i.e. if all exponents and the component // is zero static inline BOOLEAN p_LmIsConstant(const poly p, const ring r) { if (p_LmIsConstantComp(p, r)) return (p_GetComp(p, r) == 0); return FALSE; } // like the respective p_LmIs* routines, except that p might be empty static inline BOOLEAN p_IsConstantComp(const poly p, const ring r) { if (p == NULL) return TRUE; return (pNext(p)==NULL) && p_LmIsConstantComp(p, r); } static inline BOOLEAN p_IsConstant(const poly p, const ring r) { if (p == NULL) return TRUE; return (pNext(p)==NULL) && p_LmIsConstant(p, r); } static inline BOOLEAN p_IsUnit(const poly p, const ring r) { if (p == NULL) return FALSE; #ifdef HAVE_RINGS if (rField_is_Ring(r)) return (p_LmIsConstant(p, r) && nIsUnit(pGetCoeff(p),r->cf)); #endif return p_LmIsConstant(p, r); } static inline BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2, const ring r) { p_LmCheckPolyRing(p1, r); p_LmCheckPolyRing(p2, r); unsigned long l1, l2, divmask = r->divmask; int i; for (i=0; iVarL_Size; i++) { l1 = p1->exp[r->VarL_Offset[i]]; l2 = p2->exp[r->VarL_Offset[i]]; // do the divisiblity trick if ( (l1 > ULONG_MAX - l2) || (((l1 & divmask) ^ (l2 & divmask)) != ((l1 + l2) & divmask))) return FALSE; } return TRUE; } void p_Split(poly p, poly * r); /*p => IN(p), r => REST(p) */ BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r); poly p_mInit(const char *s, BOOLEAN &ok, const ring r); /* monom s -> poly, interpreter */ const char * p_Read(const char *s, poly &p,const ring r); /* monom -> poly */ poly p_Divide(poly a, poly b, const ring r); poly p_DivideM(poly a, poly b, const ring r); void p_Lcm(poly a, poly b, poly m, const ring r); poly p_Diff(poly a, int k, const ring r); poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r); int p_Weight(int c, const ring r); /* syszygy stuff */ BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r); void p_VectorHasUnit(poly p, int * k, int * len, const ring r); poly p_TakeOutComp1(poly * p, int k, const ring r); // 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 p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r); // This is something weird -- Don't use it, unless you know what you are doing poly p_TakeOutComp(poly * p, int k); void p_DeleteComp(poly * p,int k, const ring r); /*-------------ring management:----------------------*/ void p_SetGlobals(const ring r, BOOLEAN complete = TRUE); // resets the pFDeg and pLDeg: if pLDeg is not given, it is // set to currRing->pLDegOrig, i.e. to the respective LDegProc which // only uses pFDeg (and not pDeg, or pTotalDegree, etc). // If you use this, make sure your procs does not make any assumptions // on ordering and/or OrdIndex -- otherwise they might return wrong results // on strat->tailRing void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg = NULL); // restores pFDeg and pLDeg: void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg); /*-------------pComp for syzygies:-------------------*/ void p_SetModDeg(intvec *w, ring r); /*------------ Jet ----------------------------------*/ poly pp_Jet(poly p, int m, const ring R); poly p_Jet(poly p, int m,const ring R); poly pp_JetW(poly p, int m, short *w, const ring R); poly p_JetW(poly p, int m, short *w, const ring R); poly p_PermPoly (poly p, int * perm,const ring OldRing, const ring dst, nMapFunc nMap, int *par_perm=NULL, int OldPar=0); #endif // P_POLYS_H