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polys.h
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/*! \file kernel/polys.h Compatibility layer for legacy polynomial operations (over @ref currRing)
Macro defines for legacy polynomial operations used in @ref kernel_page and @ref singular_page.
They take no ring argument since they work with @ref currRing by default.
Notice that they have different prefix: `p` instead of `p_`.
See also related global ring variable and the correct ring changing routine:
- \ref currRing
- \ref rChangeCurrRing
*/
#ifndef POLYS_H
#define POLYS_H
#include "polys/monomials/ring.h"
#include "polys/monomials/p_polys.h"
EXTERN_VAR ring currRing;
EXTERN_VAR coeffs coeffs_BIGINT;
void rChangeCurrRing(ring r);
#include "coeffs/numbers.h"
/***************************************************************
*
* 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) (int)__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/Initialization/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,currRing->PolyBin)
/// 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|p<q w.r.t monomial ordering
#define pLmCmp(p,q) p_LmCmp(p,q,currRing)
/// executes axtionE|actionG|actionS if p=q|p>q|p<q w.r.t monomial ordering
/// action should be a "goto ..."
#define pLmCmpAction(p,q, actionE, actionG, actionS) \
_p_LmCmpAction(p,q,currRing, actionE, actionG,actionS)
#define pLmEqual(p1, p2) p_ExpVectorEqual(p1, p2, currRing)
/// pCmp: args may be NULL
/// returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))
#define pCmp(p1, p2) p_Cmp(p1, p2, currRing)
/***************************************************************
*
* Comparisons: these are all done regarding coeffs
*
***************************************************************/
#define pLtCmp(p,q) p_LtCmp(p,q,currRing)
#define pLtCmpNoAbs(p,q) p_LtCmpNoAbs(p,q,currRing)
#define pLtCmpOrdSgnDiffM(p,q) p_LtCmpOrdSgnDiffM(p,q,currRing)
#define pLtCmpOrdSgnDiffP(p,q) p_LtCmpOrdSgnDiffP(p,q,currRing)
#define pLtCmpOrdSgnEqM(p,q) p_LtCmpOrdSgnEqM(p,q,currRing)
#define pLtCmpOrdSgnEqP(p,q) p_LtCmpOrdSgnEqP(p,q,currRing)
/***************************************************************
*
* Divisiblity tests, args must be != NULL, except for
* pDivisbleBy
*
***************************************************************/
/// returns TRUE, if leading monom of a divides leading monom of b
/// i.e., if there exists a expvector c > 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
/// polynomial division a/b, ignoring the rest
/// via singclap_pdivide resp. idLift
/// destroys a,b
poly p_Divide(poly a, poly b, const ring r);
/// polynomial division a/b, ignoring the rest
/// via singclap_pdivide resp. idLift
/// does not destroy a,b
poly pp_Divide(poly a, poly b, const ring r);
poly p_DivRem(poly a, poly b, poly &rest, const ring r); /*julia*/
/// polynomial gcd
/// via singclap_gcd_r resp. idSyzygies
/// destroys f and g
poly singclap_gcd ( poly f, poly g, const ring r );
/***************************************************************
*
* Copying/Deletion 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 divisible 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 considered 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 p is either NULL, or if all exponents
/// of p are 0, Comp of p might be != 0
#define pIsConstantComp(p) p_IsConstantComp(p, currRing)
/// like above, except that Comp must 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;
/*-------------predicate on polys ----------------------*/
#define pHasNotCFRing(p1,p2) p_HasNotCFRing(p1,p2,currRing)
#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 explanations
*
***************************************************************/
#define pWeight(i) p_Weight(i,currRing)
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 pMDivide(a,b) p_MDivide(a,b,currRing)
#define pDivideM(a,b) p_DivideM(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 void pString0(poly p) {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)
/// 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
inline void pTakeOutComp(poly *p, long comp, poly *q, int *lq, const ring R = currRing)
{
return p_TakeOutComp(p, comp, q, lq, R);
}
/// This is something weird -- Don't use it, unless you know what you are doing
inline poly pTakeOutComp(poly * p, int k, const ring R = currRing)
{
return p_TakeOutComp(p, k, R);
}
/* 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)
inline void pNorm(poly 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)
// maximum weighted degree of all monomials of p, w is indexed from
// 1..pVariables
/// Deprecated: only for compatibility with older code!
#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--------------*/
/// Returns TRUE if
/// * LM(p) | LM(lcm)
/// * LC(p) | LC(lcm) only if ring
/// * Exists i, j:
/// * LE(p, i) != LE(lcm, i)
/// * LE(p1, i) != LE(lcm, i) ==> LCM(p1, p) != lcm
/// * LE(p, j) != LE(lcm, j)
/// * LE(p2, j) != LE(lcm, j) ==> LCM(p2, p) != lcm
BOOLEAN pCompareChain (poly p, poly p1, poly p2, poly lcm, const ring R = currRing);
#ifdef HAVE_RATGRING
BOOLEAN pCompareChainPart (poly p, poly p1, poly p2, poly lcm, const ring R = currRing);
#endif
#define pEqualPolys(p1,p2) p_EqualPolys(p1,p2,currRing)
/// returns the length of a polynomial (numbers of monomials)
/// respect syzComp
static inline poly pLast(poly a, int &length) { return p_Last (a, length, currRing); }
static inline poly pLast(poly a) { int l; return pLast(a, l); }
/***************************************************************
*
* 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) do {} while (0)
#define pLmTest(p) do {} while (0)
#endif
#endif // POLYS_H
BOOLEAN
int BOOLEAN
Definition auxiliary.h:88
l
int l
Definition cfEzgcd.cc:100
k
int k
Definition cfEzgcd.cc:99
p
int p
Definition cfModGcd.cc:4086
g
g
Definition cfModGcd.cc:4098
b
CanonicalForm b
Definition cfModGcd.cc:4111
f
FILE * f
Definition checklibs.c:9
comp
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
Definition facSparseHensel.h:25
EXTERN_VAR
#define EXTERN_VAR
Definition globaldefs.h:6
length
static BOOLEAN length(leftv result, leftv arg)
Definition interval.cc:257
p_TakeOutComp
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition p_polys.cc:3620
lcm
int lcm(unsigned long *l, unsigned long *a, unsigned long *b, unsigned long p, int dega, int degb)
Definition minpoly.cc:709
coeffs
The main handler for Singular numbers which are suitable for Singular polynomials.
lq
Definition lq.h:40
numbers.h
p_Norm
void p_Norm(poly p1, const ring r)
Definition p_polys.cc:3844
p_Last
poly p_Last(const poly p, int &l, const ring r)
Definition p_polys.cc:4775
p_polys.h
p_String
char * p_String(poly p, ring lmRing, ring tailRing)
Definition polys0.cc:322
p_String0
void p_String0(poly p, ring lmRing, ring tailRing)
print p according to ShortOut in lmRing & tailRing
Definition polys0.cc:223
p_Write
void p_Write(poly p, ring lmRing, ring tailRing)
Definition polys0.cc:342
p_Write0
void p_Write0(poly p, ring lmRing, ring tailRing)
Definition polys0.cc:332
p_LmFree
static void p_LmFree(poly p, ring)
Definition p_polys.h:685
p_Totaldegree
static long p_Totaldegree(poly p, const ring r)
Definition p_polys.h:1528
p_wrp
void p_wrp(poly p, ring lmRing, ring tailRing)
Definition polys0.cc:373
coeffs_BIGINT
VAR coeffs coeffs_BIGINT
Definition polys.cc:14
currRing
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition polys.cc:13
pTotaldegree
static long pTotaldegree(poly p)
Definition polys.h:283
pSetPolyComp
void pSetPolyComp(poly p, int comp)
pp_Divide
poly pp_Divide(poly a, poly b, const ring r)
polynomial division a/b, ignoring the rest via singclap_pdivide resp. idLift does not destroy a,...
Definition polys.cc:178
pNorm
void pNorm(poly p)
Definition polys.h:363
p_Divide
poly p_Divide(poly a, poly b, const ring r)
polynomial division a/b, ignoring the rest via singclap_pdivide resp. idLift destroys a,...
Definition polys.cc:34
rChangeCurrRing
void rChangeCurrRing(ring r)
Definition polys.cc:16
pCompareChain
BOOLEAN pCompareChain(poly p, poly p1, poly p2, poly lcm, const ring R=currRing)
Returns TRUE if.
Definition kpolys.cc:17
pWrite0
void pWrite0(poly p)
Definition polys.h:310
pIsHomogeneous
BOOLEAN pIsHomogeneous(poly p)
wrp
void wrp(poly p)
Definition polys.h:311
pLmFree
static void pLmFree(poly p)
frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced
Definition polys.h:71
pWrite
void pWrite(poly p)
Definition polys.h:309
pCompareChainPart
BOOLEAN pCompareChainPart(poly p, poly p1, poly p2, poly lcm, const ring R=currRing)
Definition kpolys.cc:71
p_DivRem
poly p_DivRem(poly a, poly b, poly &rest, const ring r)
Definition polys.cc:343
pString0
void pString0(poly p)
Definition polys.h:308
pLast
static poly pLast(poly a, int &length)
returns the length of a polynomial (numbers of monomials) respect syzComp
Definition polys.h:406
pTakeOutComp
void pTakeOutComp(poly *p, long comp, poly *q, int *lq, const ring R=currRing)
Splits *p into two polys: *q which consists of all monoms with component == comp and *p of all other ...
Definition polys.h:339
pString
char * pString(poly p)
Definition polys.h:307
polyset
poly * polyset
Definition polys.h:260
singclap_gcd
poly singclap_gcd(poly f, poly g, const ring r)
polynomial gcd via singclap_gcd_r resp. idSyzygies destroys f and g
Definition polys.cc:409
ring.h
R
#define R
Definition sirandom.c:27