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polys.h File Reference

Compatiblity layer for legacy polynomial operations (over currRing) More...

#include "polys/monomials/ring.h"
#include "polys/monomials/p_polys.h"
#include "coeffs/numbers.h"

Go to the source code of this file.

Macros

#define pSetCoeff(p, n)   p_SetCoeff(p,n,currRing)
 deletes old coeff before setting the new one More...
 
#define pGetOrder(p)   p_GetOrder(p, currRing)
 Order. More...
 
#define pGetComp(p)   (int)__p_GetComp(p, currRing)
 Component. More...
 
#define pSetComp(p, v)   p_SetComp(p,v, currRing)
 
#define pGetExp(p, i)   p_GetExp(p, i, currRing)
 Exponent. More...
 
#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)
 
#define pNew()   p_New(currRing)
 allocates the space for a new monomial – no initialization !!! More...
 
#define pInit()   p_Init(currRing,currRing->PolyBin)
 allocates a new monomial and initializes everything to 0 More...
 
#define pLmInit(p)   p_LmInit(p, currRing)
 like pInit, except that expvector is initialized to that of p, p must be != NULL More...
 
#define pHead(p)   p_Head(p, currRing)
 returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL More...
 
#define pLmFreeAndNext(p)   p_LmFreeAndNext(p, currRing)
 assumes p != NULL, deletes p, returns pNext(p) More...
 
#define pLmDelete(p)   p_LmDelete(p, currRing)
 assume p != NULL, deletes Lm(p)->coef and Lm(p) More...
 
#define pLmDeleteAndNext(p)   p_LmDeleteAndNext(p, currRing)
 like pLmDelete, returns pNext(p) More...
 
#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)
 
#define pGetExpV(p, e)   p_GetExpV(p, e, 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. More...
 
#define pSetExpV(p, e)   p_SetExpV(p, e, currRing)
 
#define pLmCmp(p, q)   p_LmCmp(p,q,currRing)
 returns 0|1|-1 if p=q|p>q|p<q w.r.t monomial ordering More...
 
#define pLmCmpAction(p, q, actionE, actionG, actionS)    _p_LmCmpAction(p,q,currRing, actionE, actionG,actionS)
 executes axtionE|actionG|actionS if p=q|p>q|p<q w.r.t monomial ordering action should be a "goto ..." More...
 
#define pLmEqual(p1, p2)   p_ExpVectorEqual(p1, p2, currRing)
 
#define pCmp(p1, p2)   p_Cmp(p1, p2, currRing)
 pCmp: args may be NULL returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2))) More...
 
#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)
 
#define pDivisibleBy(a, b)   p_DivisibleBy(a,b,currRing)
 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; More...
 
#define pLmDivisibleBy(a, b)   p_LmDivisibleBy(a,b,currRing)
 like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL More...
 
#define pLmDivisibleByNoComp(a, b)   p_LmDivisibleByNoComp(a,b,currRing)
 like pLmDivisibleBy, does not check components More...
 
#define pLmShortDivisibleBy(a, sev_a, b, not_sev_b)    p_LmShortDivisibleBy(a, sev_a, b, not_sev_b, currRing)
 Divisibility tests based on Short Exponent vectors sev_a == pGetShortExpVector(a) not_sev_b == ~ pGetShortExpVector(b) More...
 
#define pLmRingShortDivisibleBy(a, sev_a, b, not_sev_b)    p_LmRingShortDivisibleBy(a, sev_a, b, not_sev_b, currRing)
 
#define pGetShortExpVector(a)   p_GetShortExpVector(a, currRing)
 returns the "Short Exponent Vector" – used to speed up divisibility tests (see polys-impl.cc ) More...
 
#define pDivisibleByRingCase(f, g)   p_DivisibleByRingCase(f,g,currRing)
 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 *‍/ More...
 
#define pCopy(p)   p_Copy(p, currRing)
 return a copy of the poly More...
 
#define pDelete(p_ptr)   p_Delete(p_ptr, currRing)
 
#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)
 
#define ppMult_Coeff_mm_DivSelect(p, m)   pp_Mult_Coeff_mm_DivSelect(p, m, currRing)
 
#define pSortMerger(p)   p_SortMerge(p, currRing)
 sorts p, assumes all monomials in p are different More...
 
#define pSort(p)   p_SortMerge(p, currRing)
 
#define pSortAdd(p)   p_SortAdd(p, currRing)
 sorts p, p may have equal monomials More...
 
#define pSortCompCorrect(p)   pSort(p)
 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. More...
 
#define pIsConstantComp(p)   p_IsConstantComp(p, currRing)
 return true if p is either NULL, or if all exponents of p are 0, Comp of p might be != 0 More...
 
#define pIsConstant(p)   p_IsConstant(p,currRing)
 like above, except that Comp must be 0 More...
 
#define pIsUnit(p)   p_IsUnit(p,currRing)
 return true if the Lm is a constant <>0 More...
 
#define pLmIsConstantComp(p)   p_LmIsConstantComp(p, currRing)
 like above, except that p must be != NULL More...
 
#define pLmIsConstant(p)   p_LmIsConstant(p,currRing)
 
#define pIsConstantPoly(p)   p_IsConstantPoly(p, currRing)
 return TRUE if all monomials of p are constant More...
 
#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)
 
#define pHasNotCFRing(p1, p2)   p_HasNotCFRing(p1,p2,currRing)
 
#define pHasNotCF(p1, p2)   p_HasNotCF(p1,p2,currRing)
 
#define pSplit(p, r)   p_Split(p,r)
 
#define pSetm(p)   p_Setm(p, currRing)
 
#define pSetmComp(p)   p_Setm(p, currRing)
 TODO: More...
 
#define pWeight(i)   p_Weight(i,currRing)
 
#define pWTotaldegree(p)   p_WTotaldegree(p,currRing)
 
#define pWDegree(p)   p_WDegree(p,currRing)
 
#define pSub(a, b)   p_Sub(a,b,currRing)
 
#define pmInit(a, b)   p_mInit(a,b,currRing)
 
#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)
 
#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)
 
#define pHomogen(p, varnum)   p_Homogen(p,varnum,currRing)
 homogenizes p by multiplying certain powers of the varnum-th variable More...
 
#define pIsHomogen(p)   p_IsHomogen(p,currRing)
 
#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)
 
#define pDeleteComp(p, k)   p_DeleteComp(p,k,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 pDegW(p, w)   p_DegW(p,w,currRing)
 Deprecated: only for compatibility with older code! More...
 
#define pVar(m)   p_Var(m,currRing)
 
#define pEqualPolys(p1, p2)   p_EqualPolys(p1,p2,currRing)
 
#define pTest(p)   _p_Test(p, currRing, PDEBUG)
 
#define pLmTest(p)   _p_LmTest(p, currRing, PDEBUG)
 

Typedefs

typedef poly * polyset
 

Functions

void rChangeCurrRing (ring r)
 
static void pLmFree (poly p)
 frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced More...
 
static void pLmFree (poly *p)
 like pLmFree, but advances p More...
 
poly p_Divide (poly a, poly b, const ring r)
 polynomial division a/b, ignoring the rest via singclap_pdivide resp. idLift destroyes a,b More...
 
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,b More...
 
poly p_DivRem (poly a, poly b, poly &rest, const ring r)
 
poly singclap_gcd (poly f, poly g, const ring r)
 polynomial gcd via singclap_gcd_r resp. idSyzygies destroys f and g More...
 
static long pTotaldegree (poly p)
 
char * pString (poly p)
 
void pString0 (poly p)
 
void pWrite (poly p)
 
void pWrite0 (poly p)
 
void wrp (poly p)
 
BOOLEAN pIsHomogeneous (poly p)
 
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 monoms *lq == pLength(*q) On return all components pf *q == 0. More...
 
poly pTakeOutComp (poly *p, int k, const ring R=currRing)
 This is something weird – Don't use it, unless you know what you are doing. More...
 
void pSetPolyComp (poly p, int comp)
 
void pNorm (poly p, const ring R=currRing)
 
BOOLEAN pCompareChain (poly p, poly p1, poly p2, poly lcm, const ring R=currRing)
 Returns TRUE if. More...
 
BOOLEAN pCompareChainPart (poly p, poly p1, poly p2, poly lcm, const ring R=currRing)
 
static poly pLast (poly a, int &length)
 returns the length of a polynomial (numbers of monomials) respect syzComp More...
 
static poly pLast (poly a)
 

Variables

EXTERN_VAR ring currRing
 

Detailed Description

Compatiblity layer for legacy polynomial operations (over currRing)

Macro defines for legacy polynomial operations used in Several involved mathematical algorithms (kernel) and Singular Interpreter and related functionality. They take no ring argument since they work with currRing by default. Notice that they have different prefix: p instead of p_.

See also related global ring variable and the correct ring changeing routine:

Definition in file polys.h.

Macro Definition Documentation

◆ pAdd

#define pAdd (   p,
 
)    p_Add_q(p, q, currRing)

Definition at line 203 of file polys.h.

◆ pAddExp

#define pAddExp (   p,
  i,
  v 
)    p_AddExp(p,i,v, currRing)

Definition at line 45 of file polys.h.

◆ pCmp

#define pCmp (   p1,
  p2 
)    p_Cmp(p1, p2, currRing)

pCmp: args may be NULL returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))

Definition at line 115 of file polys.h.

◆ pCopy

#define pCopy (   p)    p_Copy(p, currRing)

return a copy of the poly

Definition at line 185 of file polys.h.

◆ pDecrExp

#define pDecrExp (   p,
  i 
)    p_DecrExp(p,i, currRing)

Definition at line 44 of file polys.h.

◆ pDegW

#define pDegW (   p,
  w 
)    p_DegW(p,w,currRing)

Deprecated: only for compatibility with older code!

Definition at line 377 of file polys.h.

◆ pDelete

#define pDelete (   p_ptr)    p_Delete(p_ptr, currRing)

Definition at line 186 of file polys.h.

◆ pDeleteComp

#define pDeleteComp (   p,
  k 
)    p_DeleteComp(p,k,currRing)

Definition at line 361 of file polys.h.

◆ pDiff

#define pDiff (   a,
  b 
)    p_Diff(a,b,currRing)

Definition at line 296 of file polys.h.

◆ pDiffOp

#define pDiffOp (   a,
  b,
  m 
)    p_DiffOp(a,b,m,currRing)

Definition at line 297 of file polys.h.

◆ pDivideM

#define pDivideM (   a,
  b 
)    p_DivideM(a,b,currRing)

Definition at line 294 of file polys.h.

◆ pDivisibleBy

#define pDivisibleBy (   a,
  b 
)    p_DivisibleBy(a,b,currRing)

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;

Definition at line 138 of file polys.h.

◆ pDivisibleByRingCase

#define pDivisibleByRingCase (   f,
  g 
)    p_DivisibleByRingCase(f,g,currRing)

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 *‍/

Definition at line 159 of file polys.h.

◆ pEqualPolys

#define pEqualPolys (   p1,
  p2 
)    p_EqualPolys(p1,p2,currRing)

Definition at line 400 of file polys.h.

◆ pExpVectorAdd

#define pExpVectorAdd (   p1,
  p2 
)    p_ExpVectorAdd(p1, p2, currRing)

Definition at line 87 of file polys.h.

◆ pExpVectorAddSub

#define pExpVectorAddSub (   p1,
  p2,
  p3 
)    p_ExpVectorAddSub(p1, p2, p3, currRing)

Definition at line 89 of file polys.h.

◆ pExpVectorCopy

#define pExpVectorCopy (   d_p,
  s_p 
)    p_ExpVectorCopy(d_p, s_p, currRing)

Definition at line 86 of file polys.h.

◆ pExpVectorDiff

#define pExpVectorDiff (   pr,
  p1,
  p2 
)    p_ExpVectorDiff(pr, p1, p2, currRing)

Definition at line 91 of file polys.h.

◆ pExpVectorSub

#define pExpVectorSub (   p1,
  p2 
)    p_ExpVectorSub(p1, p2, currRing)

Definition at line 88 of file polys.h.

◆ pExpVectorSum

#define pExpVectorSum (   pr,
  p1,
  p2 
)    p_ExpVectorSum(pr, p1, p2, currRing)

Definition at line 90 of file polys.h.

◆ pGetComp

#define pGetComp (   p)    (int)__p_GetComp(p, currRing)

Component.

Definition at line 37 of file polys.h.

◆ pGetExp

#define pGetExp (   p,
  i 
)    p_GetExp(p, i, currRing)

Exponent.

Definition at line 41 of file polys.h.

◆ pGetExpDiff

#define pGetExpDiff (   p1,
  p2,
  i 
)    p_GetExpDiff(p1, p2, i, currRing)

Definition at line 49 of file polys.h.

◆ pGetExpSum

#define pGetExpSum (   p1,
  p2,
  i 
)    p_GetExpSum(p1, p2, i, currRing)

Definition at line 48 of file polys.h.

◆ pGetExpV

#define pGetExpV (   p,
 
)    p_GetExpV(p, e, 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.

Definition at line 96 of file polys.h.

◆ pGetOrder

#define pGetOrder (   p)    p_GetOrder(p, currRing)

Order.

Definition at line 34 of file polys.h.

◆ pGetShortExpVector

#define pGetShortExpVector (   a)    p_GetShortExpVector(a, currRing)

returns the "Short Exponent Vector" – used to speed up divisibility tests (see polys-impl.cc )

Definition at line 152 of file polys.h.

◆ pGetVariables

#define pGetVariables (   p,
 
)    p_GetVariables(p, e, currRing)

Definition at line 251 of file polys.h.

◆ pHasNotCF

#define pHasNotCF (   p1,
  p2 
)    p_HasNotCF(p1,p2,currRing)

Definition at line 263 of file polys.h.

◆ pHasNotCFRing

#define pHasNotCFRing (   p1,
  p2 
)    p_HasNotCFRing(p1,p2,currRing)

Definition at line 262 of file polys.h.

◆ pHead

#define pHead (   p)    p_Head(p, currRing)

returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL

Definition at line 67 of file polys.h.

◆ pHomogen

#define pHomogen (   p,
  varnum 
)    p_Homogen(p,varnum,currRing)

homogenizes p by multiplying certain powers of the varnum-th variable

Definition at line 322 of file polys.h.

◆ pIncrExp

#define pIncrExp (   p,
  i 
)    p_IncrExp(p,i, currRing)

Definition at line 43 of file polys.h.

◆ pInit

#define pInit ( )    p_Init(currRing,currRing->PolyBin)

allocates a new monomial and initializes everything to 0

Definition at line 61 of file polys.h.

◆ pIsConstant

#define pIsConstant (   p)    p_IsConstant(p,currRing)

like above, except that Comp must be 0

Definition at line 238 of file polys.h.

◆ pIsConstantComp

#define pIsConstantComp (   p)    p_IsConstantComp(p, currRing)

return true if p is either NULL, or if all exponents of p are 0, Comp of p might be != 0

Definition at line 236 of file polys.h.

◆ pIsConstantPoly

#define pIsConstantPoly (   p)    p_IsConstantPoly(p, currRing)

return TRUE if all monomials of p are constant

Definition at line 246 of file polys.h.

◆ pISet

#define pISet (   i)    p_ISet(i,currRing)

Definition at line 312 of file polys.h.

◆ pIsHomogen

#define pIsHomogen (   p)    p_IsHomogen(p,currRing)

Definition at line 329 of file polys.h.

◆ pIsPurePower

#define pIsPurePower (   p)    p_IsPurePower(p, currRing)

Definition at line 248 of file polys.h.

◆ pIsUnit

#define pIsUnit (   p)    p_IsUnit(p,currRing)

return true if the Lm is a constant <>0

Definition at line 240 of file polys.h.

◆ pIsUnivariate

#define pIsUnivariate (   p)    p_IsUnivariate(p, currRing)

Definition at line 249 of file polys.h.

◆ pIsVector

#define pIsVector (   p)    (pGetComp(p)>0)

Definition at line 250 of file polys.h.

◆ pJet

#define pJet (   p,
  m 
)    p_Jet(p,m,currRing)

Definition at line 368 of file polys.h.

◆ pJetW

#define pJetW (   p,
  m,
  iv 
)    p_JetW(p,m,iv,currRing)

Definition at line 370 of file polys.h.

◆ pLcm

#define pLcm (   a,
  b,
  m 
)    p_Lcm(a,b,m,currRing)

Definition at line 295 of file polys.h.

◆ pLmCmp

#define pLmCmp (   p,
 
)    p_LmCmp(p,q,currRing)

returns 0|1|-1 if p=q|p>q|p<q w.r.t monomial ordering

Definition at line 105 of file polys.h.

◆ pLmCmpAction

#define pLmCmpAction (   p,
  q,
  actionE,
  actionG,
  actionS 
)     _p_LmCmpAction(p,q,currRing, actionE, actionG,actionS)

executes axtionE|actionG|actionS if p=q|p>q|p<q w.r.t monomial ordering action should be a "goto ..."

Definition at line 108 of file polys.h.

◆ pLmDelete

#define pLmDelete (   p)    p_LmDelete(p, currRing)

assume p != NULL, deletes Lm(p)->coef and Lm(p)

Definition at line 76 of file polys.h.

◆ pLmDeleteAndNext

#define pLmDeleteAndNext (   p)    p_LmDeleteAndNext(p, currRing)

like pLmDelete, returns pNext(p)

Definition at line 78 of file polys.h.

◆ pLmDivisibleBy

#define pLmDivisibleBy (   a,
  b 
)    p_LmDivisibleBy(a,b,currRing)

like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL

Definition at line 140 of file polys.h.

◆ pLmDivisibleByNoComp

#define pLmDivisibleByNoComp (   a,
  b 
)    p_LmDivisibleByNoComp(a,b,currRing)

like pLmDivisibleBy, does not check components

Definition at line 142 of file polys.h.

◆ pLmEqual

#define pLmEqual (   p1,
  p2 
)    p_ExpVectorEqual(p1, p2, currRing)

Definition at line 111 of file polys.h.

◆ pLmFreeAndNext

#define pLmFreeAndNext (   p)    p_LmFreeAndNext(p, currRing)

assumes p != NULL, deletes p, returns pNext(p)

Definition at line 74 of file polys.h.

◆ pLmInit

#define pLmInit (   p)    p_LmInit(p, currRing)

like pInit, except that expvector is initialized to that of p, p must be != NULL

Definition at line 64 of file polys.h.

◆ pLmIsConstant

#define pLmIsConstant (   p)    p_LmIsConstant(p,currRing)

Definition at line 243 of file polys.h.

◆ pLmIsConstantComp

#define pLmIsConstantComp (   p)    p_LmIsConstantComp(p, currRing)

like above, except that p must be != NULL

Definition at line 242 of file polys.h.

◆ pLmRingShortDivisibleBy

#define pLmRingShortDivisibleBy (   a,
  sev_a,
  b,
  not_sev_b 
)     p_LmRingShortDivisibleBy(a, sev_a, b, not_sev_b, currRing)

Definition at line 148 of file polys.h.

◆ pLmShortDivisibleBy

#define pLmShortDivisibleBy (   a,
  sev_a,
  b,
  not_sev_b 
)     p_LmShortDivisibleBy(a, sev_a, b, not_sev_b, currRing)

Divisibility tests based on Short Exponent vectors sev_a == pGetShortExpVector(a) not_sev_b == ~ pGetShortExpVector(b)

Definition at line 146 of file polys.h.

◆ pLmTest

#define pLmTest (   p)    _p_LmTest(p, currRing, PDEBUG)

Definition at line 416 of file polys.h.

◆ pLtCmp

#define pLtCmp (   p,
 
)    p_LtCmp(p,q,currRing)

Definition at line 123 of file polys.h.

◆ pLtCmpNoAbs

#define pLtCmpNoAbs (   p,
 
)    p_LtCmpNoAbs(p,q,currRing)

Definition at line 124 of file polys.h.

◆ pLtCmpOrdSgnDiffM

#define pLtCmpOrdSgnDiffM (   p,
 
)    p_LtCmpOrdSgnDiffM(p,q,currRing)

Definition at line 125 of file polys.h.

◆ pLtCmpOrdSgnDiffP

#define pLtCmpOrdSgnDiffP (   p,
 
)    p_LtCmpOrdSgnDiffP(p,q,currRing)

Definition at line 126 of file polys.h.

◆ pLtCmpOrdSgnEqM

#define pLtCmpOrdSgnEqM (   p,
 
)    p_LtCmpOrdSgnEqM(p,q,currRing)

Definition at line 127 of file polys.h.

◆ pLtCmpOrdSgnEqP

#define pLtCmpOrdSgnEqP (   p,
 
)    p_LtCmpOrdSgnEqP(p,q,currRing)

Definition at line 128 of file polys.h.

◆ pMaxComp

#define pMaxComp (   p)    p_MaxComp(p, currRing)

Definition at line 299 of file polys.h.

◆ pMDivide

#define pMDivide (   a,
  b 
)    p_MDivide(a,b,currRing)

Definition at line 293 of file polys.h.

◆ pMinComp

#define pMinComp (   p)    p_MinComp(p, currRing)

Definition at line 300 of file polys.h.

◆ pMinDeg

#define pMinDeg (   p,
  w 
)    p_MinDeg(p,w,currRing)

Definition at line 371 of file polys.h.

◆ pmInit

#define pmInit (   a,
  b 
)    p_mInit(a,b,currRing)

Definition at line 289 of file polys.h.

◆ pMinus_mm_Mult_qq

#define pMinus_mm_Mult_qq (   p,
  m,
 
)    p_Minus_mm_Mult_qq(p, m, q, currRing)

Definition at line 205 of file polys.h.

◆ pMult

#define pMult (   p,
 
)    p_Mult_q(p, q, currRing)

Definition at line 207 of file polys.h.

◆ pMult_mm

#define pMult_mm (   p,
  m 
)    p_Mult_mm(p, m, currRing)

Definition at line 202 of file polys.h.

◆ pMult_nn

#define pMult_nn (   p,
 
)    p_Mult_nn(p, n, currRing)

Definition at line 200 of file polys.h.

◆ pMultExp

#define pMultExp (   p,
  i,
  v 
)    p_MultExp(p,i,v, currRing)

Definition at line 47 of file polys.h.

◆ pNeg

#define pNeg (   p)    p_Neg(p, currRing)

Definition at line 198 of file polys.h.

◆ pNew

#define pNew ( )    p_New(currRing)

allocates the space for a new monomial – no initialization !!!

Definition at line 59 of file polys.h.

◆ pNormalize

#define pNormalize (   p)    p_Normalize(p,currRing)

Definition at line 317 of file polys.h.

◆ pNSet

#define pNSet (   n)    p_NSet(n,currRing)

Definition at line 313 of file polys.h.

◆ pOne

#define pOne ( )    p_One(currRing)

Definition at line 315 of file polys.h.

◆ pOneComp

#define pOneComp (   p)    p_OneComp(p, currRing)

Definition at line 302 of file polys.h.

◆ ppJet

#define ppJet (   p,
  m 
)    pp_Jet(p,m,currRing)

Definition at line 367 of file polys.h.

◆ ppJetW

#define ppJetW (   p,
  m,
  iv 
)    pp_JetW(p,m,iv,currRing)

Definition at line 369 of file polys.h.

◆ pPlus_mm_Mult_qq

#define pPlus_mm_Mult_qq (   p,
  m,
 
)    p_Plus_mm_Mult_qq(p, m, q, currRing)

Definition at line 206 of file polys.h.

◆ ppMult_Coeff_mm_DivSelect

#define ppMult_Coeff_mm_DivSelect (   p,
  m 
)    pp_Mult_Coeff_mm_DivSelect(p, m, currRing)

Definition at line 210 of file polys.h.

◆ ppMult_mm

#define ppMult_mm (   p,
  m 
)    pp_Mult_mm(p, m, currRing)

Definition at line 201 of file polys.h.

◆ ppMult_nn

#define ppMult_nn (   p,
 
)    pp_Mult_nn(p, n, currRing)

Definition at line 199 of file polys.h.

◆ ppMult_qq

#define ppMult_qq (   p,
 
)    pp_Mult_qq(p, q, currRing)

Definition at line 208 of file polys.h.

◆ pPower

#define pPower (   p,
 
)    p_Power(p, q, currRing)

Definition at line 204 of file polys.h.

◆ pSeries

#define pSeries (   n,
  p,
  u,
  w 
)    p_Series(n,p,u,w,currRing)

Definition at line 372 of file polys.h.

◆ pSetCoeff

#define pSetCoeff (   p,
 
)    p_SetCoeff(p,n,currRing)

deletes old coeff before setting the new one

Definition at line 31 of file polys.h.

◆ pSetComp

#define pSetComp (   p,
  v 
)    p_SetComp(p,v, currRing)

Definition at line 38 of file polys.h.

◆ pSetCompP

#define pSetCompP (   a,
  i 
)    p_SetCompP(a, i, currRing)

Definition at line 303 of file polys.h.

◆ pSetExp

#define pSetExp (   p,
  i,
  v 
)    p_SetExp(p, i, v, currRing)

Definition at line 42 of file polys.h.

◆ pSetExpV

#define pSetExpV (   p,
 
)    p_SetExpV(p, e, currRing)

Definition at line 97 of file polys.h.

◆ pSetm

#define pSetm (   p)    p_Setm(p, currRing)

Definition at line 271 of file polys.h.

◆ pSetmComp

#define pSetmComp (   p)    p_Setm(p, currRing)

TODO:

Definition at line 273 of file polys.h.

◆ pSize

#define pSize (   p)    p_Size(p,currRing)

Definition at line 318 of file polys.h.

◆ pSort

#define pSort (   p)    p_SortMerge(p, currRing)

Definition at line 218 of file polys.h.

◆ pSortAdd

#define pSortAdd (   p)    p_SortAdd(p, currRing)

sorts p, p may have equal monomials

Definition at line 221 of file polys.h.

◆ pSortCompCorrect

#define pSortCompCorrect (   p)    pSort(p)

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.

Definition at line 227 of file polys.h.

◆ pSortMerger

#define pSortMerger (   p)    p_SortMerge(p, currRing)

sorts p, assumes all monomials in p are different

Definition at line 217 of file polys.h.

◆ pSplit

#define pSplit (   p,
 
)    p_Split(p,r)

Definition at line 265 of file polys.h.

◆ pSub

#define pSub (   a,
  b 
)    p_Sub(a,b,currRing)

Definition at line 287 of file polys.h.

◆ pSubExp

#define pSubExp (   p,
  i,
  v 
)    p_SubExp(p,i,v, currRing)

Definition at line 46 of file polys.h.

◆ pSubst

#define pSubst (   p,
  n,
 
)    p_Subst(p,n,e,currRing)

Definition at line 366 of file polys.h.

◆ pTakeOutComp1

#define pTakeOutComp1 (   p,
  k 
)    p_TakeOutComp1(p,k,currRing)

Definition at line 334 of file polys.h.

◆ pTest

#define pTest (   p)    _p_Test(p, currRing, PDEBUG)

Definition at line 415 of file polys.h.

◆ pVar

#define pVar (   m)    p_Var(m,currRing)

Definition at line 381 of file polys.h.

◆ pVectorHasUnit

#define pVectorHasUnit (   p,
  k,
  l 
)    p_VectorHasUnit(p,k,l,currRing)

Definition at line 333 of file polys.h.

◆ pVectorHasUnitB

#define pVectorHasUnitB (   p,
  k 
)    p_VectorHasUnitB(p,k,currRing)

Definition at line 332 of file polys.h.

◆ pWDegree

#define pWDegree (   p)    p_WDegree(p,currRing)

Definition at line 284 of file polys.h.

◆ pWeight

#define pWeight (   i)    p_Weight(i,currRing)

Definition at line 280 of file polys.h.

◆ pWTotaldegree

#define pWTotaldegree (   p)    p_WTotaldegree(p,currRing)

Definition at line 283 of file polys.h.

Typedef Documentation

◆ polyset

typedef poly* polyset

Definition at line 259 of file polys.h.

Function Documentation

◆ p_Divide()

poly p_Divide ( poly  a,
poly  b,
const ring  r 
)

polynomial division a/b, ignoring the rest via singclap_pdivide resp. idLift destroyes a,b

Definition at line 31 of file polys.cc.

32 {
33  assume(q!=NULL);
34  if (q==NULL)
35  {
36  WerrorS("div. by 0");
37  return NULL;
38  }
39  if (p==NULL)
40  {
41  p_Delete(&q,r);
42  return NULL;
43  }
44  if ((pNext(q)!=NULL)||rIsPluralRing(r))
45  { /* This means that q != 0 consists of at least two terms*/
46  if(p_GetComp(p,r)==0)
47  {
48  if((rFieldType(r)==n_transExt)
49  &&(convSingTrP(p,r))
50  &&(convSingTrP(q,r))
51  &&(!rIsNCRing(r)))
52  {
53  poly res=singclap_pdivide(p, q, r);
54  p_Delete(&p,r);
55  p_Delete(&q,r);
56  return res;
57  }
58  else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN)
59  &&(!rField_is_Ring(r))
60  &&(!rIsNCRing(r)))
61  {
62  poly res=singclap_pdivide(p, q, r);
63  p_Delete(&p,r);
64  p_Delete(&q,r);
65  return res;
66  }
67  else
68  {
69  ideal vi=idInit(1,1); vi->m[0]=q;
70  ideal ui=idInit(1,1); ui->m[0]=p;
71  ideal R; matrix U;
72  ring save_ring=currRing;
73  if (r!=currRing) rChangeCurrRing(r);
74  int save_opt;
75  SI_SAVE_OPT1(save_opt);
76  si_opt_1 &= ~(Sy_bit(OPT_PROT));
77  ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U);
78  SI_RESTORE_OPT1(save_opt);
79  if (r!=save_ring) rChangeCurrRing(save_ring);
81  p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL;
82  id_Delete((ideal *)&T,r);
83  id_Delete((ideal *)&U,r);
84  id_Delete(&R,r);
85  //vi->m[0]=NULL; ui->m[0]=NULL;
86  id_Delete(&vi,r);
87  id_Delete(&ui,r);
88  return p;
89  }
90  }
91  else
92  {
93  int comps=p_MaxComp(p,r);
94  ideal I=idInit(comps,1);
95  poly h;
96  int i;
97  // conversion to a list of polys:
98  while (p!=NULL)
99  {
100  i=p_GetComp(p,r)-1;
101  h=pNext(p);
102  pNext(p)=NULL;
103  p_SetComp(p,0,r);
104  I->m[i]=p_Add_q(I->m[i],p,r);
105  p=h;
106  }
107  // division and conversion to vector:
108  h=NULL;
109  p=NULL;
110  for(i=comps-1;i>=0;i--)
111  {
112  if (I->m[i]!=NULL)
113  {
114  if((rFieldType(r)==n_transExt)
115  &&(convSingTrP(I->m[i],r))
116  &&(convSingTrP(q,r))
117  &&(!rIsNCRing(r)))
118  {
119  h=singclap_pdivide(I->m[i],q,r);
120  }
121  else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN)
122  &&(!rField_is_Ring(r))
123  &&(!rIsNCRing(r)))
124  h=singclap_pdivide(I->m[i],q,r);
125  else
126  {
127  ideal vi=idInit(1,1); vi->m[0]=q;
128  ideal ui=idInit(1,1); ui->m[0]=I->m[i];
129  ideal R; matrix U;
130  ring save_ring=currRing;
131  if (r!=currRing) rChangeCurrRing(r);
132  int save_opt;
133  SI_SAVE_OPT1(save_opt);
134  si_opt_1 &= ~(Sy_bit(OPT_PROT));
135  ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U);
136  SI_RESTORE_OPT1(save_opt);
137  if (r!=save_ring) rChangeCurrRing(save_ring);
138  if (idIs0(R))
139  {
141  p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL;
142  id_Delete((ideal *)&T,r);
143  }
144  else p=NULL;
145  id_Delete((ideal*)&U,r);
146  id_Delete(&R,r);
147  vi->m[0]=NULL; ui->m[0]=NULL;
148  id_Delete(&vi,r);
149  id_Delete(&ui,r);
150  }
151  p_SetCompP(h,i+1,r);
152  p=p_Add_q(p,h,r);
153  }
154  }
155  id_Delete(&I,r);
156  p_Delete(&q,r);
157  return p;
158  }
159  }
160  else
161  { /* This means that q != 0 consists of just one term, or LetterPlace */
162 #ifdef HAVE_RINGS
163  if (pNext(q)!=NULL)
164  {
165  WerrorS("division over a coefficient domain only implemented for terms");
166  return NULL;
167  }
168 #endif
169  return p_DivideM(p,q,r);
170  }
171  return NULL;
172 }
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
int m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
int p
Definition: cfModGcd.cc:4080
BOOLEAN convSingTrP(poly p, const ring r)
Definition: clapconv.cc:352
poly singclap_pdivide(poly f, poly g, const ring r)
Definition: clapsing.cc:590
@ n_transExt
used for all transcendental extensions, i.e., the top-most extension in an extension tower is transce...
Definition: coeffs.h:39
CanonicalForm res
Definition: facAbsFact.cc:60
void WerrorS(const char *s)
Definition: feFopen.cc:24
ideal idLift(ideal mod, ideal submod, ideal *rest, BOOLEAN goodShape, BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
Definition: ideals.cc:1099
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
STATIC_VAR jList * T
Definition: janet.cc:30
STATIC_VAR Poly * h
Definition: janet.cc:971
#define MATELEM(mat, i, j)
1-based access to matrix
Definition: matpol.h:29
#define assume(x)
Definition: mod2.h:387
#define p_GetComp(p, r)
Definition: monomials.h:64
#define pNext(p)
Definition: monomials.h:36
CanonicalForm ndConvSingNFactoryN(number, BOOLEAN, const coeffs)
Definition: numbers.cc:280
#define NULL
Definition: omList.c:12
VAR unsigned si_opt_1
Definition: options.c:5
#define OPT_PROT
Definition: options.h:75
#define SI_SAVE_OPT1(A)
Definition: options.h:21
#define SI_RESTORE_OPT1(A)
Definition: options.h:24
#define Sy_bit(x)
Definition: options.h:31
poly p_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1565
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:896
static void p_SetCompP(poly p, int i, ring r)
Definition: p_polys.h:254
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
Definition: p_polys.h:247
static long p_MaxComp(poly p, ring lmRing, ring tailRing)
Definition: p_polys.h:292
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:861
void rChangeCurrRing(ring r)
Definition: polys.cc:15
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
static BOOLEAN rField_is_Ring(const ring r)
Definition: ring.h:486
static n_coeffType rFieldType(const ring r)
the type of the coefficient filed of r (n_Zp, n_Q, etc)
Definition: ring.h:558
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition: ring.h:400
static BOOLEAN rIsNCRing(const ring r)
Definition: ring.h:421
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition: simpleideals.cc:35
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
matrix id_Module2formatedMatrix(ideal mod, int rows, int cols, const ring R)
#define R
Definition: sirandom.c:27

◆ p_DivRem()

poly p_DivRem ( poly  a,
poly  b,
poly &  rest,
const ring  r 
)

Definition at line 315 of file polys.cc.

316 {
317  assume(q!=NULL);
318  rest=NULL;
319  if (q==NULL)
320  {
321  WerrorS("div. by 0");
322  return NULL;
323  }
324  if (p==NULL)
325  {
326  p_Delete(&q,r);
327  return NULL;
328  }
329  if(p_GetComp(p,r)==0)
330  {
331  if((rFieldType(r)==n_transExt)
332  &&(convSingTrP(p,r))
333  &&(convSingTrP(q,r))
334  &&(!rIsNCRing(r)))
335  {
336  poly res=singclap_pdivide(p, q, r);
337  rest=singclap_pmod(p,q,r);
338  p_Delete(&p,r);
339  p_Delete(&q,r);
340  return res;
341  }
342  else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN)
343  &&(!rField_is_Ring(r))
344  &&(!rIsNCRing(r)))
345  {
346  poly res=singclap_pdivide(p, q, r);
347  rest=singclap_pmod(p,q,r);
348  p_Delete(&p,r);
349  p_Delete(&q,r);
350  return res;
351  }
352  else
353  {
354  ideal vi=idInit(1,1); vi->m[0]=q;
355  ideal ui=idInit(1,1); ui->m[0]=p;
356  ideal R; matrix U;
357  ring save_ring=currRing;
358  if (r!=currRing) rChangeCurrRing(r);
359  int save_opt;
360  SI_SAVE_OPT1(save_opt);
361  si_opt_1 &= ~(Sy_bit(OPT_PROT));
362  ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U);
363  SI_RESTORE_OPT1(save_opt);
364  if (r!=save_ring) rChangeCurrRing(save_ring);
366  p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL;
367  id_Delete((ideal *)&T,r);
368  T = id_Module2formatedMatrix(R,1,1,r);
369  rest=MATELEM(T,1,1); MATELEM(T,1,1)=NULL;
370  id_Delete((ideal *)&T,r);
371  id_Delete((ideal *)&U,r);
372  id_Delete(&R,r);
373  //vi->m[0]=NULL; ui->m[0]=NULL;
374  id_Delete(&vi,r);
375  id_Delete(&ui,r);
376  return p;
377  }
378  }
379  return NULL;
380 }
poly singclap_pmod(poly f, poly g, const ring r)
Definition: clapsing.cc:668

◆ pCompareChain()

BOOLEAN pCompareChain ( poly  p,
poly  p1,
poly  p2,
poly  lcm,
const ring  R = currRing 
)

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

Definition at line 17 of file kpolys.cc.

18 {
19  int k, j;
20 
21  if (lcm==NULL) return FALSE;
22 
23  for (j=(R->N); j; j--)
24  if ( p_GetExp(p,j, R) > p_GetExp(lcm,j, R)) return FALSE;
25  if ( pGetComp(p) != pGetComp(lcm)) return FALSE;
26  for (j=(R->N); j; j--)
27  {
28  if (p_GetExp(p1,j, R)!=p_GetExp(lcm,j, R))
29  {
30  if (p_GetExp(p,j, R)!=p_GetExp(lcm,j, R))
31  {
32  for (k=(R->N); k>j; k--)
33  {
34  if ((p_GetExp(p,k, R)!=p_GetExp(lcm,k, R))
35  && (p_GetExp(p2,k, R)!=p_GetExp(lcm,k, R)))
36  return TRUE;
37  }
38  for (k=j-1; k; k--)
39  {
40  if ((p_GetExp(p,k, R)!=p_GetExp(lcm,k, R))
41  && (p_GetExp(p2,k, R)!=p_GetExp(lcm,k, R)))
42  return TRUE;
43  }
44  return FALSE;
45  }
46  }
47  else if (p_GetExp(p2,j, R)!=p_GetExp(lcm,j, R))
48  {
49  if (p_GetExp(p,j, R)!=p_GetExp(lcm,j, R))
50  {
51  for (k=(R->N); k>j; k--)
52  {
53  if ((p_GetExp(p,k, R)!=p_GetExp(lcm,k, R))
54  && (p_GetExp(p1,k, R)!=p_GetExp(lcm,k, R)))
55  return TRUE;
56  }
57  for (k=j-1; k!=0 ; k--)
58  {
59  if ((p_GetExp(p,k, R)!=p_GetExp(lcm,k, R))
60  && (p_GetExp(p1,k, R)!=p_GetExp(lcm,k, R)))
61  return TRUE;
62  }
63  return FALSE;
64  }
65  }
66  }
67  return FALSE;
68 }
int k
Definition: cfEzgcd.cc:99
int j
Definition: facHensel.cc:110
int lcm(unsigned long *l, unsigned long *a, unsigned long *b, unsigned long p, int dega, int degb)
Definition: minpoly.cc:709
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
Definition: p_polys.h:469
#define pGetComp(p)
Component.
Definition: polys.h:37

◆ pCompareChainPart()

BOOLEAN pCompareChainPart ( poly  p,
poly  p1,
poly  p2,
poly  lcm,
const ring  R = currRing 
)

Definition at line 71 of file kpolys.cc.

72 {
73  int k, j;
74 
75  if (lcm==NULL) return FALSE;
76 
77  for (j=R->real_var_end; j>=R->real_var_start; j--)
78  if ( p_GetExp(p,j, R) > p_GetExp(lcm,j, R)) return FALSE;
79  if ( pGetComp(p) != pGetComp(lcm)) return FALSE;
80  for (j=R->real_var_end; j>=R->real_var_start; j--)
81  {
82  if (p_GetExp(p1,j, R)!=p_GetExp(lcm,j, R))
83  {
84  if (p_GetExp(p,j, R)!=p_GetExp(lcm,j, R))
85  {
86  for (k=(R->N); k>j; k--)
87  for (k=R->real_var_end; k>j; k--)
88  {
89  if ((p_GetExp(p,k, R)!=p_GetExp(lcm,k, R))
90  && (p_GetExp(p2,k, R)!=p_GetExp(lcm,k, R)))
91  return TRUE;
92  }
93  for (k=j-1; k>=R->real_var_start; k--)
94  {
95  if ((p_GetExp(p,k, R)!=p_GetExp(lcm,k, R))
96  && (p_GetExp(p2,k, R)!=p_GetExp(lcm,k, R)))
97  return TRUE;
98  }
99  return FALSE;
100  }
101  }
102  else if (p_GetExp(p2,j, R)!=p_GetExp(lcm,j, R))
103  {
104  if (p_GetExp(p,j, R)!=p_GetExp(lcm,j, R))
105  {
106  for (k=R->real_var_end; k>j; k--)
107  {
108  if ((p_GetExp(p,k, R)!=p_GetExp(lcm,k, R))
109  && (p_GetExp(p1,k, R)!=p_GetExp(lcm,k, R)))
110  return TRUE;
111  }
112  for (k=j-1; k>=R->real_var_start; k--)
113  {
114  if ((p_GetExp(p,k, R)!=p_GetExp(lcm,k, R))
115  && (p_GetExp(p1,k, R)!=p_GetExp(lcm,k, R)))
116  return TRUE;
117  }
118  return FALSE;
119  }
120  }
121  }
122  return FALSE;
123 }

◆ pIsHomogeneous()

BOOLEAN pIsHomogeneous ( poly  p)

◆ pLast() [1/2]

static poly pLast ( poly  a)
inlinestatic

Definition at line 407 of file polys.h.

407 { int l; return pLast(a, l); }
int l
Definition: cfEzgcd.cc:100
static poly pLast(poly a, int &length)
returns the length of a polynomial (numbers of monomials) respect syzComp
Definition: polys.h:406

◆ pLast() [2/2]

static poly pLast ( poly  a,
int &  length 
)
inlinestatic

returns the length of a polynomial (numbers of monomials) respect syzComp

Definition at line 406 of file polys.h.

406 { return p_Last (a, length, currRing); }
static BOOLEAN length(leftv result, leftv arg)
Definition: interval.cc:257
poly p_Last(const poly p, int &l, const ring r)
Definition: p_polys.cc:4649
EXTERN_VAR ring currRing
Definition: polys.h:18

◆ pLmFree() [1/2]

static void pLmFree ( poly *  p)
inlinestatic

like pLmFree, but advances p

Definition at line 72 of file polys.h.

72 {p_LmFree(p, currRing);}
static void p_LmFree(poly p, ring)
Definition: p_polys.h:683

◆ pLmFree() [2/2]

static void pLmFree ( poly  p)
inlinestatic

frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced

Definition at line 70 of file polys.h.

70 {p_LmFree(p, currRing);}

◆ pNorm()

void pNorm ( poly  p,
const ring  R = currRing 
)
inline

Definition at line 363 of file polys.h.

363 { p_Norm(p, R); }
void p_Norm(poly p1, const ring r)
Definition: p_polys.cc:3789

◆ 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,b

Definition at line 174 of file polys.cc.

175 {
176  assume(q!=NULL);
177  if (q==NULL)
178  {
179  WerrorS("div. by 0");
180  return NULL;
181  }
182  if (p==NULL)
183  {
184  return NULL;
185  }
186  if ((pNext(q)!=NULL)||rIsPluralRing(r))
187  { /* This means that q != 0 consists of at least two terms*/
188  if(p_GetComp(p,r)==0)
189  {
190  if((rFieldType(r)==n_transExt)
191  &&(convSingTrP(p,r))
192  &&(convSingTrP(q,r))
193  &&(!rIsNCRing(r)))
194  {
195  poly res=singclap_pdivide(p, q, r);
196  return res;
197  }
198  else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN)
199  &&(!rField_is_Ring(r))
200  &&(!rIsNCRing(r)))
201  {
202  poly res=singclap_pdivide(p, q, r);
203  return res;
204  }
205  else
206  {
207  ideal vi=idInit(1,1); vi->m[0]=p_Copy(q,r);
208  ideal ui=idInit(1,1); ui->m[0]=p_Copy(p,r);
209  ideal R; matrix U;
210  ring save_ring=currRing;
211  if (r!=currRing) rChangeCurrRing(r);
212  int save_opt;
213  SI_SAVE_OPT1(save_opt);
214  si_opt_1 &= ~(Sy_bit(OPT_PROT));
215  ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U);
216  SI_RESTORE_OPT1(save_opt);
217  if (r!=save_ring) rChangeCurrRing(save_ring);
219  p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL;
220  id_Delete((ideal *)&T,r);
221  id_Delete((ideal *)&U,r);
222  id_Delete(&R,r);
223  //vi->m[0]=NULL; ui->m[0]=NULL;
224  id_Delete(&vi,r);
225  id_Delete(&ui,r);
226  return p;
227  }
228  }
229  else
230  {
231  p=p_Copy(p,r);
232  int comps=p_MaxComp(p,r);
233  ideal I=idInit(comps,1);
234  poly h;
235  int i;
236  // conversion to a list of polys:
237  while (p!=NULL)
238  {
239  i=p_GetComp(p,r)-1;
240  h=pNext(p);
241  pNext(p)=NULL;
242  p_SetComp(p,0,r);
243  I->m[i]=p_Add_q(I->m[i],p,r);
244  p=h;
245  }
246  // division and conversion to vector:
247  h=NULL;
248  p=NULL;
249  q=p_Copy(q,r);
250  for(i=comps-1;i>=0;i--)
251  {
252  if (I->m[i]!=NULL)
253  {
254  if((rFieldType(r)==n_transExt)
255  &&(convSingTrP(I->m[i],r))
256  &&(convSingTrP(q,r))
257  &&(!rIsNCRing(r)))
258  {
259  h=singclap_pdivide(I->m[i],q,r);
260  }
261  else if ((r->cf->convSingNFactoryN!=ndConvSingNFactoryN)
262  &&(!rField_is_Ring(r))
263  &&(!rIsNCRing(r)))
264  h=singclap_pdivide(I->m[i],q,r);
265  else
266  {
267  ideal vi=idInit(1,1); vi->m[0]=q;
268  ideal ui=idInit(1,1); ui->m[0]=I->m[i];
269  ideal R; matrix U;
270  ring save_ring=currRing;
271  if (r!=currRing) rChangeCurrRing(r);
272  int save_opt;
273  SI_SAVE_OPT1(save_opt);
274  si_opt_1 &= ~(Sy_bit(OPT_PROT));
275  ideal m = idLift(vi,ui,&R, FALSE,TRUE,TRUE,&U);
276  SI_RESTORE_OPT1(save_opt);
277  if (r!=save_ring) rChangeCurrRing(save_ring);
278  if (idIs0(R))
279  {
281  p=MATELEM(T,1,1); MATELEM(T,1,1)=NULL;
282  id_Delete((ideal *)&T,r);
283  }
284  else p=NULL;
285  id_Delete((ideal*)&U,r);
286  id_Delete(&R,r);
287  vi->m[0]=NULL; ui->m[0]=NULL;
288  id_Delete(&vi,r);
289  id_Delete(&ui,r);
290  }
291  p_SetCompP(h,i+1,r);
292  p=p_Add_q(p,h,r);
293  }
294  }
295  id_Delete(&I,r);
296  p_Delete(&q,r);
297  return p;
298  }
299  }
300  else
301  { /* This means that q != 0 consists of just one term,
302  or that r is over a coefficient ring. */
303 #ifdef HAVE_RINGS
304  if (pNext(q)!=NULL)
305  {
306  WerrorS("division over a coefficient domain only implemented for terms");
307  return NULL;
308  }
309 #endif
310  return pp_DivideM(p,q,r);
311  }
312  return NULL;
313 }
poly pp_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1620
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:812

◆ pSetPolyComp()

void pSetPolyComp ( poly  p,
int  comp 
)

◆ pString()

char* pString ( poly  p)
inline

Definition at line 306 of file polys.h.

306 {return p_String(p, currRing, currRing);}
char * p_String(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:322

◆ pString0()

void pString0 ( poly  p)
inline

Definition at line 307 of file polys.h.

void p_String0(poly p, ring lmRing, ring tailRing)
print p according to ShortOut in lmRing & tailRing
Definition: polys0.cc:223

◆ pTakeOutComp() [1/2]

poly pTakeOutComp ( poly *  p,
int  k,
const ring  R = currRing 
)
inline

This is something weird – Don't use it, unless you know what you are doing.

Definition at line 346 of file polys.h.

347 {
348  return p_TakeOutComp(p, k, R);
349 }
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition: p_polys.cc:3565

◆ pTakeOutComp() [2/2]

void pTakeOutComp ( poly *  p,
long  comp,
poly *  q,
int *  lq,
const ring  R = currRing 
)
inline

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.

Definition at line 339 of file polys.h.

340 {
341  return p_TakeOutComp(p, comp, q, lq, R);
342 }
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
Definition: lq.h:40

◆ pTotaldegree()

static long pTotaldegree ( poly  p)
inlinestatic

Definition at line 282 of file polys.h.

282 { return p_Totaldegree(p,currRing); }
static long p_Totaldegree(poly p, const ring r)
Definition: p_polys.h:1467

◆ pWrite()

void pWrite ( poly  p)
inline

Definition at line 308 of file polys.h.

void p_Write(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:342

◆ pWrite0()

void pWrite0 ( poly  p)
inline

Definition at line 309 of file polys.h.

void p_Write0(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:332

◆ rChangeCurrRing()

void rChangeCurrRing ( ring  r)

Definition at line 15 of file polys.cc.

16 {
17  //------------ set global ring vars --------------------------------
18  currRing = r;
19  if( r != NULL )
20  {
21  rTest(r);
22  //------------ global variables related to coefficients ------------
23  assume( r->cf!= NULL );
24  nSetChar(r->cf);
25  //------------ global variables related to polys
26  p_SetGlobals(r); // also setting TEST_RINGDEP_OPTS
27  //------------ global variables related to factory -----------------
28  }
29 }
static FORCE_INLINE void nSetChar(const coeffs r)
initialisations after each ring change
Definition: coeffs.h:437
void p_SetGlobals(const ring r, BOOLEAN complete)
set all properties of a new ring - also called by rComplete
Definition: ring.cc:3365
#define rTest(r)
Definition: ring.h:787

◆ 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 at line 382 of file polys.cc.

383 {
384  poly res=NULL;
385 
386  if (f!=NULL)
387  {
388  //if (r->cf->has_simple_Inverse) p_Norm(f,r);
389  if (rField_is_Zp(r)) p_Norm(f,r);
390  else p_Cleardenom(f, r);
391  }
392  if (g!=NULL)
393  {
394  //if (r->cf->has_simple_Inverse) p_Norm(g,r);
395  if (rField_is_Zp(r)) p_Norm(g,r);
396  else p_Cleardenom(g, r);
397  }
398  else return f; // g==0 => gcd=f (but do a p_Cleardenom/pNorm)
399  if (f==NULL) return g; // f==0 => gcd=g (but do a p_Cleardenom/pNorm)
400  if(!rField_is_Ring(r)
401  && (p_IsConstant(f,r)
402  ||p_IsConstant(g,r)))
403  {
404  res=p_One(r);
405  }
406  else if (r->cf->convSingNFactoryN!=ndConvSingNFactoryN)
407  {
408  res=singclap_gcd_r(f,g,r);
409  }
410  else
411  {
412  ideal I=idInit(2,1);
413  I->m[0]=f;
414  I->m[1]=p_Copy(g,r);
415  intvec *w=NULL;
416  ring save_ring=currRing;
417  if (r!=currRing) rChangeCurrRing(r);
418  int save_opt;
419  SI_SAVE_OPT1(save_opt);
420  si_opt_1 &= ~(Sy_bit(OPT_PROT));
421  ideal S1=idSyzygies(I,testHomog,&w);
422  if (w!=NULL) delete w;
423  // expect S1->m[0]=(-g/gcd,f/gcd)
424  if (IDELEMS(S1)!=1) WarnS("error in syzygy computation for GCD");
425  int lp;
426  p_TakeOutComp(&S1->m[0],1,&res,&lp,r);
427  p_Delete(&S1->m[0],r);
428  // GCD is g divided iby (-g/gcd):
429  res=p_Divide(g,res,r);
430  // restore, r, opt:
431  SI_RESTORE_OPT1(save_opt);
432  if (r!=save_ring) rChangeCurrRing(save_ring);
433  // clean the result
434  res=p_Cleardenom(res,r);
435  p_Content(res,r);
436  return res;
437  }
438  p_Delete(&f, r);
439  p_Delete(&g, r);
440  return res;
441 }
g
Definition: cfModGcd.cc:4092
FILE * f
Definition: checklibs.c:9
poly singclap_gcd_r(poly f, poly g, const ring r)
Definition: clapsing.cc:45
Definition: intvec.h:23
#define WarnS
Definition: emacs.cc:78
const CanonicalForm & w
Definition: facAbsFact.cc:51
ideal idSyzygies(ideal h1, tHomog h, intvec **w, BOOLEAN setSyzComp, BOOLEAN setRegularity, int *deg, GbVariant alg)
Definition: ideals.cc:830
void p_Content(poly ph, const ring r)
Definition: p_polys.cc:2282
poly p_Cleardenom(poly p, const ring r)
Definition: p_polys.cc:2900
poly p_One(const ring r)
Definition: p_polys.cc:1308
static BOOLEAN p_IsConstant(const poly p, const ring r)
Definition: p_polys.h:1971
poly p_Divide(poly p, poly q, const ring r)
polynomial division a/b, ignoring the rest via singclap_pdivide resp. idLift destroyes a,...
Definition: polys.cc:31
static BOOLEAN rField_is_Zp(const ring r)
Definition: ring.h:502
#define IDELEMS(i)
Definition: simpleideals.h:23
@ testHomog
Definition: structs.h:43

◆ wrp()

void wrp ( poly  p)
inline

Definition at line 310 of file polys.h.

310 {p_wrp(p, currRing, currRing);}
void p_wrp(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:373

Variable Documentation

◆ currRing

EXTERN_VAR ring currRing

Definition at line 18 of file polys.h.