p_polys.h File Reference

#include "misc/mylimits.h"
#include "misc/intvec.h"
#include "coeffs/coeffs.h"
#include "polys/monomials/monomials.h"
#include "polys/monomials/ring.h"
#include "polys/templates/p_MemAdd.h"
#include "polys/templates/p_MemCmp.h"
#include "polys/templates/p_Procs.h"
#include "polys/sbuckets.h"
#include "polys/nc/nc.h"

Go to the source code of this file.

Macros
#define	pIfThen(cond, check)   do {if (cond) {check;}} while (0)
#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)
#define	p_SetmComp   p_Setm
#define	__p_Mult_nn(p, n, r)   r->p_Procs->p_Mult_nn(p, n, r)
#define	__pp_Mult_nn(p, n, r)   r->p_Procs->pp_Mult_nn(p, n, r)
#define	_p_LmCmpAction(p, q, r, actionE, actionG, actionS)
#define	pDivAssume(x)   do {} while (0)
#define	p_LmCmpAction(p, q, r, actionE, actionG, actionS)    _p_LmCmpAction(p, q, r, actionE, actionG, actionS)
#define	p_LmEqual(p1, p2, r)   p_ExpVectorEqual(p1, p2, r)

Functions
poly	p_Farey (poly p, number N, const ring r)
poly	p_ChineseRemainder (poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
unsigned long	p_GetShortExpVector (const poly a, const ring r)
unsigned long	p_GetShortExpVector0 (const poly a, const ring r)
unsigned long	p_GetShortExpVector1 (const poly a, const ring r)
BOOLEAN	p_DivisibleByRingCase (poly f, poly g, const ring r)
	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
poly	p_One (const ring r)
int	p_MinDeg (poly p, intvec *w, const ring R)
long	p_DegW (poly p, const int *w, const ring R)
BOOLEAN	p_OneComp (poly p, const ring r)
	return TRUE if all monoms have the same component
int	p_IsPurePower (const poly p, const ring r)
	return i, if head depends only on var(i)
int	p_IsUnivariate (poly p, const ring r)
	return i, if poly depends only on var(i)
int	p_GetVariables (poly p, int *e, 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)
poly	p_ISet (long i, const ring r)
	returns the poly representing the integer i
poly	p_NSet (number n, const ring r)
	returns the poly representing the number n, destroys n
void	p_Vec2Polys (poly v, poly **p, int *len, const ring r)
poly	p_Vec2Poly (poly v, int k, const ring r)
void	p_Vec2Array (poly v, poly *p, int len, const ring r)
	julia: vector to already allocated array (len=p_MaxComp(v,r))
void	p_ShallowDelete (poly *p, const ring r)
poly	p_Sub (poly a, poly b, const ring r)
poly	p_Power (poly p, int i, const ring r)
BOOLEAN	pIsMonomOf (poly p, poly m)
BOOLEAN	pHaveCommonMonoms (poly p, poly q)
BOOLEAN	p_LmCheckIsFromRing (poly p, ring r)
BOOLEAN	p_LmCheckPolyRing (poly p, ring r)
BOOLEAN	p_CheckIsFromRing (poly p, ring r)
BOOLEAN	p_CheckPolyRing (poly p, ring r)
BOOLEAN	p_CheckRing (ring r)
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)
static int	pLength (poly a)
poly	p_Last (const poly a, int &l, const ring r)
void	p_Norm (poly p1, const ring r)
void	p_Normalize (poly p, const ring r)
void	p_ProjectiveUnique (poly p, const ring r)
void	p_ContentForGB (poly p, const ring r)
void	p_Content (poly p, const ring r)
void	p_SimpleContent (poly p, int s, const ring r)
number	p_InitContent (poly ph, const ring r)
poly	p_Cleardenom (poly p, const ring r)
void	p_Cleardenom_n (poly p, const ring r, number &c)
int	p_Size (poly p, const ring r)
poly	p_Homogen (poly p, int varnum, const ring r)
BOOLEAN	p_IsHomogeneous (poly p, const ring r)
BOOLEAN	p_IsHomogeneousW (poly p, const intvec *w, const ring r)
BOOLEAN	p_IsHomogeneousW (poly p, const intvec *w, const intvec *module_w, const ring r)
static void	p_Setm (poly p, const ring r)
p_SetmProc	p_GetSetmProc (const ring r)
poly	p_Subst (poly p, int n, poly e, const ring r)
static unsigned long	p_SetComp (poly p, unsigned long c, ring r)
static void	p_SetCompP (poly p, int i, ring r)
static void	p_SetCompP (poly p, int i, ring lmRing, ring tailRing)
static long	p_MaxComp (poly p, ring lmRing, ring tailRing)
static long	p_MaxComp (poly p, ring lmRing)
static long	p_MinComp (poly p, ring lmRing, ring tailRing)
static long	p_MinComp (poly p, ring lmRing)
static poly	pReverse (poly p)
void	pEnlargeSet (poly **p, int length, int increment)
void	p_String0 (poly p, ring lmRing, ring tailRing)
	print p according to ShortOut in lmRing & tailRing
char *	p_String (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)
void	p_String0Short (const poly p, ring lmRing, ring tailRing)
	print p in a short way, if possible
void	p_String0Long (const poly p, ring lmRing, ring tailRing)
	print p in a long way
static long	p_FDeg (const poly p, const ring r)
static long	p_LDeg (const poly p, int *l, const ring r)
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)
BOOLEAN	p_EqualPolys (poly p1, poly p2, const ring r1, const ring r2)
	same as the usual p_EqualPolys for polys belonging to equal rings
long	p_Deg (poly a, const ring r)
static number	p_SetCoeff (poly p, number n, ring r)
static long	p_GetOrder (poly p, ring r)
static unsigned long	p_AddComp (poly p, unsigned long v, ring r)
static unsigned long	p_SubComp (poly p, unsigned long v, ring r)
static long	p_GetExp (const poly p, const unsigned long iBitmask, const int VarOffset)
	get a single variable exponent @Note: the integer VarOffset encodes:
static unsigned long	p_SetExp (poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
	set a single variable exponent @Note: VarOffset encodes the position in p->exp
static long	p_GetExp (const poly p, const ring r, const int VarOffset)
static long	p_SetExp (poly p, const long e, const ring r, const int VarOffset)
static long	p_GetExp (const poly p, const int v, const ring r)
	get v^th exponent for a monomial
static long	p_SetExp (poly p, const int v, const long e, const ring r)
	set v^th exponent for a monomial
static long	p_IncrExp (poly p, int v, ring r)
static long	p_DecrExp (poly p, int v, ring r)
static long	p_AddExp (poly p, int v, long ee, ring r)
static long	p_SubExp (poly p, int v, long ee, ring r)
static long	p_MultExp (poly p, int v, long ee, ring r)
static long	p_GetExpSum (poly p1, poly p2, int i, ring r)
static long	p_GetExpDiff (poly p1, poly p2, int i, ring r)
static int	p_Comp_k_n (poly a, poly b, int k, ring r)
static poly	p_New (const ring, omBin bin)
static poly	p_New (ring r)
static void	p_LmFree (poly p, ring)
static void	p_LmFree (poly *p, ring)
static poly	p_LmFreeAndNext (poly p, ring)
static void	p_LmDelete (poly p, const ring r)
static void	p_LmDelete0 (poly p, const ring r)
static void	p_LmDelete (poly *p, const ring r)
static poly	p_LmDeleteAndNext (poly p, const ring r)
unsigned long	p_GetMaxExpL (poly p, const ring r, unsigned long l_max=0)
	return the maximal exponent of p in form of the maximal long var
poly	p_GetMaxExpP (poly p, ring r)
	return monomial r such that GetExp(r,i) is maximum of all monomials in p; coeff == 0, next == NULL, ord is not set
static unsigned long	p_GetMaxExp (const unsigned long l, const ring r)
static unsigned long	p_GetMaxExp (const poly p, const ring r)
static unsigned long	p_GetTotalDegree (const unsigned long l, const ring r, const int number_of_exps)
static poly	p_Copy_noCheck (poly p, const ring r)
	returns a copy of p (without any additional testing)
static poly	p_Copy (poly p, const ring r)
	returns a copy of p
static poly	p_Head (const poly p, const ring r)
	copy the (leading) term of p
poly	p_Head0 (const poly p, const ring r)
	like p_Head, but allow NULL coeff
poly	p_CopyPowerProduct (const poly p, const ring r)
	like p_Head, but with coefficient 1
poly	p_CopyPowerProduct0 (const poly p, const number n, const ring r)
	like p_Head, but with coefficient n
static poly	p_Copy (poly p, const ring lmRing, const ring tailRing)
	returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing
static void	p_Delete (poly *p, const ring r)
static void	p_Delete (poly *p, const ring lmRing, const ring tailRing)
static poly	p_ShallowCopyDelete (poly p, const ring r, omBin bin)
static poly	p_Add_q (poly p, poly q, const ring r)
static poly	p_Add_q (poly p, poly q, int &lp, int lq, const ring r)
	like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q)
static poly	p_Mult_nn (poly p, number n, const ring r)
static poly	p_Mult_nn (poly p, number n, const ring lmRing, const ring tailRing)
static poly	pp_Mult_nn (poly p, number n, const ring r)
static BOOLEAN	p_LmIsConstantComp (const poly p, const ring r)
static BOOLEAN	p_LmIsConstant (const poly p, const ring r)
static poly	pp_Mult_mm (poly p, poly m, const ring r)
static poly	pp_mm_Mult (poly p, poly m, const ring r)
static poly	p_Mult_mm (poly p, poly m, const ring r)
static poly	p_mm_Mult (poly p, poly m, const ring r)
static poly	p_Minus_mm_Mult_qq (poly p, const poly m, const poly q, int &lp, int lq, const poly spNoether, const ring r)
static poly	p_Minus_mm_Mult_qq (poly p, const poly m, const poly q, const ring r)
static poly	pp_Mult_Coeff_mm_DivSelect (poly p, const poly m, const ring r)
static poly	pp_Mult_Coeff_mm_DivSelect (poly p, int &lp, const poly m, const ring r)
static poly	p_Neg (poly p, const ring r)
poly	_p_Mult_q (poly p, poly q, const int copy, const ring r)
	Returns: p * q, Destroys: if !copy then p, q Assumes: pLength(p) >= 2 pLength(q) >=2, !rIsPluralRing(r)
static poly	p_Mult_q (poly p, poly q, const ring r)
static poly	pp_Mult_qq (poly p, poly q, const ring r)
static poly	p_Plus_mm_Mult_qq (poly p, poly m, poly q, int &lp, int lq, const ring r)
static poly	p_Plus_mm_Mult_qq (poly p, poly m, poly q, const ring r)
static poly	p_Merge_q (poly p, poly q, const ring r)
static poly	p_SortAdd (poly p, const ring r, BOOLEAN revert=FALSE)
static poly	p_SortMerge (poly p, const ring r, BOOLEAN revert=FALSE)
static char *	p_String (poly p, ring p_ring)
static void	p_String0 (poly p, ring p_ring)
static void	p_Write (poly p, ring p_ring)
static void	p_Write0 (poly p, ring p_ring)
static void	p_wrp (poly p, ring p_ring)
static void	p_MemAdd_NegWeightAdjust (poly p, const ring r)
static void	p_MemSub_NegWeightAdjust (poly p, const ring r)
static void	p_ExpVectorCopy (poly d_p, poly s_p, const ring r)
static poly	p_Init (const ring r, omBin bin)
static poly	p_Init (const ring r)
static poly	p_LmInit (poly p, const ring r)
static poly	p_LmInit (poly s_p, const ring s_r, const ring d_r, omBin d_bin)
static poly	p_LmInit (poly s_p, const ring s_r, const ring d_r)
static poly	p_GetExp_k_n (poly p, int l, int k, const ring r)
static poly	p_LmShallowCopyDelete (poly p, const ring r)
static void	p_ExpVectorAdd (poly p1, poly p2, const ring r)
static void	p_ExpVectorSum (poly pr, poly p1, poly p2, const ring r)
static void	p_ExpVectorSub (poly p1, poly p2, const ring r)
static void	p_ExpVectorAddSub (poly p1, poly p2, poly p3, const ring r)
static void	p_ExpVectorDiff (poly pr, poly p1, poly p2, const ring r)
static BOOLEAN	p_ExpVectorEqual (poly p1, poly p2, const ring r)
static long	p_Totaldegree (poly p, const ring r)
static void	p_GetExpV (poly p, int *ev, const ring r)
static void	p_GetExpVL (poly p, int64 *ev, const ring r)
static int64	p_GetExpVLV (poly p, int64 *ev, const ring r)
static void	p_SetExpV (poly p, int *ev, const ring r)
static void	p_SetExpVL (poly p, int64 *ev, const ring r)
static void	p_SetExpVLV (poly p, int64 *ev, int64 comp, const ring r)
static int	p_LmCmp (poly p, poly q, const ring r)
static int	p_LtCmp (poly p, poly q, const ring r)
static int	p_LtCmpNoAbs (poly p, poly q, const ring r)
static int	p_LtCmpOrdSgnDiffM (poly p, poly q, const ring r)
static int	p_LtCmpOrdSgnDiffP (poly p, poly q, const ring r)
static int	p_LtCmpOrdSgnEqM (poly p, poly q, const ring r)
static int	p_LtCmpOrdSgnEqP (poly p, poly q, const ring r)
BOOLEAN	p_ComparePolys (poly p1, poly p2, const ring r)
	returns TRUE if p1 is a skalar multiple of p2 assume p1 != NULL and p2 != NULL
static int	p_Cmp (poly p1, poly p2, ring r)
static int	p_CmpPolys (poly p1, poly p2, ring r)
static BOOLEAN	_p_LmDivisibleByNoComp (poly a, poly b, const ring r)
	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 BOOLEAN	_p_LmDivisibleByNoComp (poly a, const ring r_a, poly b, const ring r_b)
static BOOLEAN	_p_LmDivisibleByNoCompPart (poly a, const ring r_a, poly b, const ring r_b, const int start, const int end)
static BOOLEAN	_p_LmDivisibleByPart (poly a, const ring r_a, poly b, const ring r_b, const int start, const int end)
static BOOLEAN	p_LmDivisibleByPart (poly a, poly b, const ring r, const int start, const int end)
static BOOLEAN	_p_LmDivisibleBy (poly a, poly b, const ring r)
static BOOLEAN	p_LmDivisibleByNoComp (poly a, poly b, const ring r)
static BOOLEAN	p_LmDivisibleByNoComp (poly a, const ring ra, poly b, const ring rb)
static BOOLEAN	p_LmDivisibleBy (poly a, poly b, const ring r)
static BOOLEAN	p_DivisibleBy (poly a, poly b, const ring r)
static BOOLEAN	p_LmShortDivisibleBy (poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
static BOOLEAN	p_LmShortDivisibleByNoComp (poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
static BOOLEAN	p_IsConstantComp (const poly p, const ring r)
	like the respective p_LmIs* routines, except that p might be empty
static BOOLEAN	p_IsConstant (const poly p, const ring r)
static BOOLEAN	p_IsOne (const poly p, const ring R)
	either poly(1) or gen(k)?!
static BOOLEAN	p_IsConstantPoly (const poly p, const ring r)
static BOOLEAN	p_IsUnit (const poly p, const ring r)
static BOOLEAN	p_LmExpVectorAddIsOk (const poly p1, const poly p2, const ring r)
void	p_Split (poly p, poly *r)
BOOLEAN	p_HasNotCF (poly p1, poly p2, const ring r)
BOOLEAN	p_HasNotCFRing (poly p1, poly p2, const ring r)
poly	p_mInit (const char *s, BOOLEAN &ok, const ring r)
const char *	p_Read (const char *s, poly &p, const ring r)
poly	p_MDivide (poly a, poly b, const ring r)
poly	p_DivideM (poly a, poly b, const ring r)
poly	pp_DivideM (poly a, poly b, const ring r)
poly	p_Div_nn (poly p, const number n, const ring r)
void	p_Lcm (const poly a, const poly b, poly m, const ring r)
poly	p_Lcm (const poly a, const poly b, const ring r)
poly	p_LcmRat (const poly a, const poly b, const long lCompM, const ring r)
poly	p_GetCoeffRat (poly p, int ishift, ring r)
void	p_LmDeleteAndNextRat (poly *p, int ishift, ring r)
void	p_ContentRat (poly &ph, 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)
poly	p_PolyDiv (poly &p, const poly divisor, const BOOLEAN needResult, const ring r)
	assumes that p and divisor are univariate polynomials in r, mentioning the same variable; assumes divisor != NULL; p may be NULL; assumes a global monomial ordering in r; performs polynomial division of p by divisor:
BOOLEAN	p_VectorHasUnitB (poly p, int *k, const ring r)
void	p_VectorHasUnit (poly p, int *k, int *len, const ring r)
void	p_TakeOutComp (poly *p, long comp, poly *q, int *lq, 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.
poly	p_TakeOutComp (poly *p, int k, const ring r)
void	p_DeleteComp (poly *p, int k, const ring r)
void	pSetDegProcs (ring r, pFDegProc new_FDeg, pLDegProc new_lDeg=NULL)
void	pRestoreDegProcs (ring r, pFDegProc old_FDeg, pLDegProc old_lDeg)
void	p_SetModDeg (intvec *w, ring r)
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, int *w, const ring R)
poly	p_JetW (poly p, int m, int *w, const ring R)
poly	n_PermNumber (const number z, const int *par_perm, const int OldPar, const ring src, const ring dst)
poly	p_PermPoly (poly p, const int *perm, const ring OldRing, const ring dst, nMapFunc nMap, const int *par_perm=NULL, int OldPar=0, BOOLEAN use_mult=FALSE)
poly	p_Series (int n, poly p, poly u, intvec *w, const ring R)
int	p_Var (poly mi, const ring r)
int	p_LowVar (poly p, const ring r)
	the minimal index of used variables - 1
void	p_Shift (poly *p, int i, const ring r)
	shifts components of the vector p by i
int	p_Compare (const poly a, const poly b, const ring R)
poly	p_GcdMon (poly f, poly g, const ring r)
	polynomial gcd for f=mon
poly	p_Div_mm (poly p, const poly m, const ring r)
	divide polynomial by monomial
int	p_MaxExpPerVar (poly p, int i, const ring r)
	max exponent of variable x_i in p

Macro Definition Documentation

__p_Mult_nn

#define __p_Mult_nn	(		p,
			n,
			r
	)		r->p_Procs->p_Mult_nn(p, n, r)

Definition at line 971 of file p_polys.h.

__pp_Mult_nn

#define __pp_Mult_nn	(		p,
			n,
			r
	)		r->p_Procs->pp_Mult_nn(p, n, r)

Definition at line 1002 of file p_polys.h.

_p_LmCmpAction

#define _p_LmCmpAction	(		p,
			q,
			r,
			actionE,
			actionG,
			actionS
	)

Value:

 p_MemCmp_LengthGeneral_OrdGeneral(p->exp, q->exp, r->CmpL_Size, r->ordsgn,    \
                                   actionE, actionG, actionS)

Definition at line 1276 of file p_polys.h.

                           {} while (0)
 
 
 
/***************************************************************
 *
 * 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);
  memcpy(d_p->exp, s_p->exp, r->ExpL_Size*sizeof(long));
}
 
static inline poly p_Init(const ring r, omBin bin)
{
  p_CheckRing1(r);
  pAssume1(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
  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);
  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
  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 (unsigned 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);
}
 
// 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);
  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
  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;
}
 
// simialar to p_ShallowCopyDelete but does it only for leading monomial
static inline poly p_LmShallowCopyDelete(poly p, const ring r)
{
  p_LmCheckPolyRing1(p, r);
  pAssume1(omSizeWOfBin(bin) == omSizeWOfBin(r->PolyBin));
  poly new_p = p_New(r);
  memcpy(new_p->exp, p->exp, r->ExpL_Size*sizeof(long));
  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(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(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_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);
 
  unsigned 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!=0);
  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->ExpPerLong);
  for (unsigned i=r->VarL_Size-1; i!=0; i--)
  {
    s += p_GetTotalDegree(p->exp[r->VarL_Offset[i]], r,r->ExpPerLong);
  }
  return (long)s;
}
 
static inline void p_GetExpV(poly p, int *ev, const ring r)
{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      ev[j] = p_GetExp(p, j, r);
 
  ev[0] = p_GetComp(p, r);
}
// p_GetExpVL is used in Singular,jl
static inline void p_GetExpVL(poly p, int64 *ev, const ring r)
{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      ev[j-1] = p_GetExp(p, j, r);
}
// p_GetExpVLV is used in Singular,jl
static inline int64 p_GetExpVLV(poly p, int64 *ev, const ring r)
{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      ev[j-1] = p_GetExp(p, j, r);
  return (int64)p_GetComp(p,r);
}
// p_GetExpVL is used in Singular,jl
static inline void p_SetExpV(poly p, int *ev, const ring r)
{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      p_SetExp(p, j, ev[j], r);
 
  if(ev[0]!=0) p_SetComp(p, ev[0],r);
  p_Setm(p, r);
}
static inline void p_SetExpVL(poly p, int64 *ev, const ring r)
{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      p_SetExp(p, j, ev[j-1], r);
  p_SetComp(p, 0,r);
 
  p_Setm(p, r);
}
 
// p_SetExpVLV is used in Singular,jl
static inline void p_SetExpVLV(poly p, int64 *ev, int64 comp, const ring r)
{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      p_SetExp(p, j, ev[j-1], r);
  p_SetComp(p, comp,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);
 
  const unsigned long* _s1 = ((unsigned long*) p->exp);
  const unsigned long* _s2 = ((unsigned long*) q->exp);
  REGISTER unsigned long _v1;
  REGISTER unsigned long _v2;
  const unsigned long _l = r->CmpL_Size;
 
  REGISTER unsigned long _i=0;
 
  LengthGeneral_OrdGeneral_LoopTop:
  _v1 = _s1[_i];
  _v2 = _s2[_i];
  if (_v1 == _v2)
  {
    _i++;
    if (_i == _l) return 0;
    goto LengthGeneral_OrdGeneral_LoopTop;
  }
  const long* _ordsgn = (long*) r->ordsgn;
#if 1 /* two variants*/
  if (_v1 > _v2)
  {
    return _ordsgn[_i];
  }
  return -(_ordsgn[_i]);
#else
   if (_v1 > _v2)
   {
     if (_ordsgn[_i] == 1) return 1;
     return -1;
   }
   if (_ordsgn[_i] == 1) return -1;
   return 1;
#endif
}
 
// The coefficient will be compared in absolute value
static inline int p_LtCmp(poly p, poly q, const ring r)
{
  int res = p_LmCmp(p,q,r);
  if(res == 0)
  {
    if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
      return res;
    number pc = n_Copy(p_GetCoeff(p,r),r->cf);
    number qc = n_Copy(p_GetCoeff(q,r),r->cf);
    if(!n_GreaterZero(pc,r->cf))
      pc = n_InpNeg(pc,r->cf);
    if(!n_GreaterZero(qc,r->cf))
      qc = n_InpNeg(qc,r->cf);
    if(n_Greater(pc,qc,r->cf))
      res = 1;
    else if(n_Greater(qc,pc,r->cf))
      res = -1;
    else if(n_Equal(pc,qc,r->cf))
      res = 0;
    n_Delete(&pc,r->cf);
    n_Delete(&qc,r->cf);
  }
  return res;
}
 
// The coefficient will be compared in absolute value
static inline int p_LtCmpNoAbs(poly p, poly q, const ring r)
{
  int res = p_LmCmp(p,q,r);
  if(res == 0)
  {
    if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
      return res;
    number pc = p_GetCoeff(p,r);
    number qc = p_GetCoeff(q,r);
    if(n_Greater(pc,qc,r->cf))
      res = 1;
    if(n_Greater(qc,pc,r->cf))
      res = -1;
    if(n_Equal(pc,qc,r->cf))
      res = 0;
  }
  return res;
}
 
#ifdef HAVE_RINGS
// This is the equivalent of pLmCmp(p,q) != -currRing->OrdSgn for rings
// It is used in posInTRing
static inline int p_LtCmpOrdSgnDiffM(poly p, poly q, const ring r)
{
  return(p_LtCmp(p,q,r) == r->OrdSgn);
}
#endif
 
#ifdef HAVE_RINGS
// This is the equivalent of pLmCmp(p,q) != currRing->OrdSgn for rings
// It is used in posInTRing
static inline int p_LtCmpOrdSgnDiffP(poly p, poly q, const ring r)
{
  if(r->OrdSgn == 1)
  {
    return(p_LmCmp(p,q,r) == -1);
  }
  else
  {
    return(p_LtCmp(p,q,r) != -1);
  }
}
#endif
 
#ifdef HAVE_RINGS
// This is the equivalent of pLmCmp(p,q) == -currRing->OrdSgn for rings
// It is used in posInTRing
static inline int p_LtCmpOrdSgnEqM(poly p, poly q, const ring r)
{
  return(p_LtCmp(p,q,r) == -r->OrdSgn);
}
#endif
 
#ifdef HAVE_RINGS
// This is the equivalent of pLmCmp(p,q) == currRing->OrdSgn for rings
// It is used in posInTRing
static inline int p_LtCmpOrdSgnEqP(poly p, poly q, const ring r)
{
  return(p_LtCmp(p,q,r) == r->OrdSgn);
}
#endif
 
/// returns TRUE if p1 is a skalar multiple of p2
/// assume p1 != NULL and p2 != NULL
BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r);
 
 
/***************************************************************
 *
 * Comparisons: they are all done without regarding coeffs
 *
 ***************************************************************/
#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)
{
  if (p2==NULL)
  {
    if (p1==NULL) return 0;
    return 1;
  }
  if (p1==NULL)
    return -1;
  return p_LmCmp(p1,p2,r);
}
 
static inline int p_CmpPolys(poly p1, poly p2, ring r)
{
  if (p2==NULL)
  {
    if (p1==NULL) return 0;
    return 1;
  }
  if (p1==NULL)
    return -1;
  return p_ComparePolys(p1,p2,r);
}
 
 
/***************************************************************
 *
 * 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) == n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf));
  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 n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
#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_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_LmDivisibleByNoComp(poly a, const ring ra, poly b, const ring rb)
{
  p_LmCheckPolyRing1(a, ra);
  p_LmCheckPolyRing1(b, rb);
  return _p_LmDivisibleByNoComp(a, ra, b, rb);
}
 
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_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_LmShortDivisibleByNoComp(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_LmDivisibleByNoComp(a, b, r);
#else
  return pDebugLmShortDivisibleByNoComp(a, sev_a, r, b, not_sev_b, r);
#endif
}
 
/***************************************************************
 *
 * Misc things on Lm
 *
 ***************************************************************/
 
 
/// 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);
}
 
/// either poly(1)  or gen(k)?!
static inline BOOLEAN p_IsOne(const poly p, const ring R)
{
  if (p == NULL) return FALSE; /* TODO check if 0 == 1 */
  p_Test(p, R);
  return (p_IsConstant(p, R) && n_IsOne(p_GetCoeff(p, R), R->cf));
}
 
static inline BOOLEAN p_IsConstantPoly(const poly p, const ring r)
{
  p_Test(p, r);
  poly pp=p;
  while(pp!=NULL)
  {
    if (! p_LmIsConstantComp(pp, r))
      return FALSE;
    pIter(pp);
  }
  return TRUE;
}
 
static inline BOOLEAN p_IsUnit(const poly p, const ring r)
{
  if (p == NULL) return FALSE;
  if (rField_is_Ring(r))
    return (p_LmIsConstant(p, r) && n_IsUnit(pGetCoeff(p),r->cf));
  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; i<r->VarL_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);
BOOLEAN p_HasNotCFRing(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_MDivide(poly a, poly b, const ring r);
poly      p_DivideM(poly a, poly b, const ring r);
poly      pp_DivideM(poly a, poly b, const ring r);
poly      p_Div_nn(poly p, const number n, const ring r);
 
// returns the LCM of the head terms of a and b in *m, does not p_Setm
void p_Lcm(const poly a, const poly b, poly m, const ring r);
// returns the LCM of the head terms of a and b, does p_Setm
poly p_Lcm(const poly a, const poly b, const ring r);
 
#ifdef HAVE_RATGRING
poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r);
poly p_GetCoeffRat(poly p, int ishift, ring r);
void p_LmDeleteAndNextRat(poly *p, int ishift, ring r);
void p_ContentRat(poly &ph, const ring r);
#endif /* ifdef HAVE_RATGRING */
 
 
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);
 
///   assumes that p and divisor are univariate polynomials in r,
///   mentioning the same variable;
///   assumes divisor != NULL;
///   p may be NULL;
///   assumes a global monomial ordering in r;
///   performs polynomial division of p by divisor:
///     - afterwards p contains the remainder of the division, i.e.,
///       p_before = result * divisor + p_afterwards;
///     - if needResult == TRUE, then the method computes and returns 'result',
///       otherwise NULL is returned (This parametrization can be used when
///       one is only interested in the remainder of the division. In this
///       case, the method will be slightly faster.)
///   leaves divisor unmodified
poly      p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, 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);
/// 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, const ring r);
 
void      p_DeleteComp(poly * p,int k, const ring r);
 
/*-------------ring management:----------------------*/
 
// 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, int *w, const ring R);
poly p_JetW(poly p, int m, int *w, const ring R);
 
poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst);
 
poly p_PermPoly (poly p, const int * perm,const ring OldRing, const ring dst,
                     nMapFunc nMap, const int *par_perm=NULL, int OldPar=0,
                     BOOLEAN use_mult=FALSE);
 
/*----------------------------------------------------*/
poly p_Series(int n,poly p,poly u, intvec *w, const ring R);
 
/*----------------------------------------------------*/
int   p_Var(poly mi, const ring r);
/// the minimal index of used variables - 1
int   p_LowVar (poly p, const ring r);
 
/*----------------------------------------------------*/
/// shifts components of the vector p by i
void p_Shift (poly * p,int i, const ring r);
/*----------------------------------------------------*/
 
int p_Compare(const poly a, const poly b, const ring R);
 
/// polynomial gcd for f=mon
poly p_GcdMon(poly f, poly g, const ring r);
 
/// divide polynomial by monomial
poly p_Div_mm(poly p, const poly m, const ring r);
 
 
/// max exponent of variable x_i in p
int p_MaxExpPerVar(poly p, int i, const ring r);
#endif // P_POLYS_H
 

p_LmCmpAction

#define p_LmCmpAction	(		p,
			q,
			r,
			actionE,
			actionG,
			actionS
	)		_p_LmCmpAction(p, q, r, actionE, actionG, actionS)

Definition at line 1719 of file p_polys.h.

p_LmEqual

#define p_LmEqual	(		p1,
			p2,
			r
	)		p_ExpVectorEqual(p1, p2, r)

Definition at line 1723 of file p_polys.h.

p_LmTest

#define p_LmTest	(		p,
			r
	)		_p_LmTest(p, r, PDEBUG)

Definition at line 162 of file p_polys.h.

p_SetmComp

#define p_SetmComp   p_Setm

Definition at line 244 of file p_polys.h.

p_Test

#define p_Test	(		p,
			r
	)		_p_Test(p, r, PDEBUG)

Definition at line 161 of file p_polys.h.

pDivAssume

#define pDivAssume

(

x

)

do {} while (0)

Definition at line 1282 of file p_polys.h.

pIfThen

#define pIfThen	(		cond,
			check
	)		do {if (cond) {check;}} while (0)

Definition at line 155 of file p_polys.h.

pp_Test

#define pp_Test	(		p,
			lmRing,
			tailRing
	)		_pp_Test(p, lmRing, tailRing, PDEBUG)

Definition at line 163 of file p_polys.h.

Function Documentation

_p_LmDivisibleBy()

static BOOLEAN _p_LmDivisibleBy ( poly  a, poly  b, const ring  r  )

inlinestatic

Definition at line 1871 of file p_polys.h.

{
  if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
    return _p_LmDivisibleByNoComp(a, b, r);
  return FALSE;
}

_p_LmDivisibleByNoComp() [1/2]

static BOOLEAN _p_LmDivisibleByNoComp ( poly  a, const ring  r_a, poly  b, const ring  r_b  )

inlinestatic

Definition at line 1814 of file p_polys.h.

{
  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
}

_p_LmDivisibleByNoComp() [2/2]

static BOOLEAN _p_LmDivisibleByNoComp ( poly  a, poly  b, const ring  r  )

inlinestatic

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

Definition at line 1765 of file p_polys.h.

{
  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) == n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf));
  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
}

_p_LmDivisibleByNoCompPart()

static BOOLEAN _p_LmDivisibleByNoCompPart ( poly  a, const ring  r_a, poly  b, const ring  r_b, const int  start, const int  end  )

inlinestatic

Definition at line 1837 of file p_polys.h.

{
  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 n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
#else
*/
  return TRUE;
//#endif
}

_p_LmDivisibleByPart()

static BOOLEAN _p_LmDivisibleByPart ( poly  a, const ring  r_a, poly  b, const ring  r_b, const int  start, const int  end  )

inlinestatic

Definition at line 1856 of file p_polys.h.

{
  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;
}

_p_LmTest()

BOOLEAN _p_LmTest	(	poly	p,
		ring	r,
		int	level
	)

Definition at line 326 of file pDebug.cc.

{
  if (level < 0 || p == NULL) return TRUE;
  poly pnext = pNext(p);
  pNext(p) = NULL;
  BOOLEAN test_res = _p_Test(p, r, level);
  pNext(p) = pnext;
  return test_res;
}

_p_Mult_q()

poly _p_Mult_q ( poly  p, poly  q, const int  copy, const ring  r  )

extern

Returns: p * q, Destroys: if !copy then p, q Assumes: pLength(p) >= 2 pLength(q) >=2, !rIsPluralRing(r)

Definition at line 313 of file p_Mult_q.cc.

{
  assume(r != NULL);
#ifdef HAVE_RINGS
  if (!nCoeff_is_Domain(r->cf))
    return _p_Mult_q_Normal_ZeroDiv(p, q, copy, r);
#endif
  int lp, lq, l;
  poly pt;
 
  // MIN_LENGTH_FACTORY must be >= MIN_LENGTH_FACTORY_QQ, MIN_FLINT_QQ, MIN_FLINT_Zp 20
  pqLengthApprox(p, q, lp, lq, MIN_LENGTH_FACTORY);
 
  if (lp < lq)
  {
    pt = p;
    p =  q;
    q = pt;
    l = lp;
    lp = lq;
    lq = l;
  }
  BOOLEAN pure_polys=(p_GetComp(p,r)==0) && (p_GetComp(q,r)==0);
  #ifdef HAVE_FLINT
  #if __FLINT_RELEASE >= 20503
  if (lq>MIN_FLINT_QQ)
  {
    fmpq_mpoly_ctx_t ctx;
    if (pure_polys && rField_is_Q(r) && !convSingRFlintR(ctx,r))
    {
      // lq is a lower bound for the length of p and  q
      poly res=Flint_Mult_MP(p,lq,q,lq,ctx,r);
      if (!copy)
      {
        p_Delete(&p,r);
        p_Delete(&q,r);
      }
      return res;
    }
  }
  if (lq>MIN_FLINT_Zp)
  {
    nmod_mpoly_ctx_t ctx;
    if (pure_polys && rField_is_Zp(r) && !convSingRFlintR(ctx,r))
    {
      // lq is a lower bound for the length of p and  q
      poly res=Flint_Mult_MP(p,lq,q,lq,ctx,r);
      if (!copy)
      {
        p_Delete(&p,r);
        p_Delete(&q,r);
      }
      return res;
    }
  }
  if (lq>MIN_FLINT_Z)
  {
    fmpz_mpoly_ctx_t ctx;
    if (pure_polys && rField_is_Z(r) && !convSingRFlintR(ctx,r))
    {
      // lq is a lower bound for the length of p and  q
      poly res=Flint_Mult_MP(p,lq,q,lq,ctx,r);
      if (!copy)
      {
        p_Delete(&p,r);
        p_Delete(&q,r);
      }
      return res;
    }
  }
  #endif
  #endif
  if (lq < MIN_LENGTH_BUCKET || TEST_OPT_NOT_BUCKETS)
    return _p_Mult_q_Normal(p, q, copy, r);
  else if (pure_polys
  && ((r->cf->extRing==NULL)||(r->cf->extRing->qideal!=NULL))
    /* exclude trans. extensions: may contain rat.funct as cf */
  && (((lq >= MIN_LENGTH_FACTORY)
      && (r->cf->convSingNFactoryN!=ndConvSingNFactoryN))
    || ((lq >= MIN_LENGTH_FACTORY_QQ)
      && rField_is_Q(r))))
  {
    poly h=singclap_pmult(p,q,r);
    if (!copy)
    {
      p_Delete(&p,r);
      p_Delete(&q,r);
    }
    return h;
  }
  else
  {
    lp=pLength(p);
    lq=pLength(q);
    return _p_Mult_q_Bucket(p, lp, q, lq, copy, r);
  }
}

_p_Test()

BOOLEAN _p_Test	(	poly	p,
		ring	r,
		int	level
	)

Definition at line 215 of file pDebug.cc.

{
  assume(r->cf !=NULL);
 
  if (PDEBUG > level) level = PDEBUG;
  if (level < 0 || p == NULL) return TRUE;
 
  poly p_prev = NULL;
 
  #ifndef OM_NDEBUG
  #ifndef X_OMALLOC
  // check addr with level+1 so as to check bin/page of addr
  _pPolyAssumeReturnMsg(omTestBinAddrSize(p, (omSizeWOfBin(r->PolyBin))*SIZEOF_LONG, level+1)
                        == omError_NoError, "memory error",p,r);
  #endif
  #endif
 
  pFalseReturn(p_CheckRing(r));
 
  // this checks that p does not contain a loop: rather expensive O(length^2)
  #ifndef OM_NDEBUG
  if (level > 1)
    pFalseReturn(omTestList(p, level) == omError_NoError);
  #endif
 
  int ismod = p_GetComp(p, r) != 0;
 
  while (p != NULL)
  {
    // ring check
    pFalseReturn(p_LmCheckIsFromRing(p, r));
    #ifndef OM_NDEBUG
    #ifndef X_OMALLOC
    // omAddr check
    _pPolyAssumeReturnMsg(omTestBinAddrSize(p, (omSizeWOfBin(r->PolyBin))*SIZEOF_LONG, 1)
                     == omError_NoError, "memory error",p,r);
    #endif
    #endif
    // number/coef check
    _pPolyAssumeReturnMsg(p->coef != NULL || (n_GetChar(r->cf) >= 2), "NULL coef",p,r);
 
    #ifdef LDEBUG
    _pPolyAssumeReturnMsg(n_Test(p->coef,r->cf),"coeff err",p,r);
    #endif
    _pPolyAssumeReturnMsg(!n_IsZero(p->coef, r->cf), "Zero coef",p,r);
 
    // check for valid comp
    _pPolyAssumeReturnMsg(p_GetComp(p, r) >= 0 && (p_GetComp(p, r)<65000), "component out of range ?",p,r);
    // check for mix poly/vec representation
    _pPolyAssumeReturnMsg(ismod == (p_GetComp(p, r) != 0), "mixed poly/vector",p,r);
 
    // special check for ringorder_s/S
    if ((r->typ!=NULL) && (r->typ[0].ord_typ == ro_syzcomp))
    {
      long c1, cc1, ccc1, ec1;
      sro_ord* o = &(r->typ[0]);
 
      c1 = p_GetComp(p, r);
      if (o->data.syzcomp.Components!=NULL)
      {
        cc1 = o->data.syzcomp.Components[c1];
        ccc1 = o->data.syzcomp.ShiftedComponents[cc1];
      }
      else { cc1=0; ccc1=0; }
      _pPolyAssumeReturnMsg(c1 == 0 || cc1 != 0, "Component <-> TrueComponent zero mismatch",p,r);
      _pPolyAssumeReturnMsg(c1 == 0 || ccc1 != 0,"Component <-> ShiftedComponent zero mismatch",p,r);
      ec1 = p->exp[o->data.syzcomp.place];
      //pPolyAssumeReturnMsg(ec1 == ccc1, "Shifted comp out of sync. should %d, is %d");
      if (ec1 != ccc1)
      {
        dPolyReportError(p,r,"Shifted comp out of sync. should %d, is %d",ccc1,ec1);
        return FALSE;
      }
    }
 
    // check that p_Setm works ok
    if (level > 0)
    {
      poly p_should_equal = p_DebugInit(p, r, r);
      _pPolyAssumeReturnMsg(p_ExpVectorEqual(p, p_should_equal, r), "p_Setm field(s) out of sync",p,r);
      p_LmFree(p_should_equal, r);
    }
 
    // check order
    if (p_prev != NULL)
    {
      int cmp = p_LmCmp(p_prev, p, r);
      if (cmp == 0)
      {
        _pPolyAssumeReturnMsg(0, "monoms p and p->next are equal", p_prev, r);
      }
      else
        _pPolyAssumeReturnMsg(p_LmCmp(p_prev, p, r) == 1, "wrong order", p_prev, r);
 
      // check that compare worked sensibly
      if (level > 1 && p_GetComp(p_prev, r) == p_GetComp(p, r))
      {
        int i;
        for (i=r->N; i>0; i--)
        {
          if (p_GetExp(p_prev, i, r) != p_GetExp(p, i, r)) break;
        }
        _pPolyAssumeReturnMsg(i > 0, "Exponents equal but compare different", p_prev, r);
      }
    }
    p_prev = p;
    pIter(p);
  }
  return TRUE;
}

_pp_Test()

BOOLEAN _pp_Test	(	poly	p,
		ring	lmRing,
		ring	tailRing,
		int	level
	)

Definition at line 336 of file pDebug.cc.

{
  if (PDEBUG > level) level = PDEBUG;
  if (level < 0 || p == NULL) return TRUE;
  if (pNext(p) == NULL || lmRing == tailRing) return _p_Test(p, lmRing, level);
 
  pFalseReturn(_p_LmTest(p, lmRing, level));
  pFalseReturn(_p_Test(pNext(p), tailRing, level));
 
  // check that lm > Lm(tail)
  if (level > 1)
  {
    poly lm = p;
    poly tail = p_DebugInit(pNext(p), tailRing, lmRing);
    poly pnext = pNext(lm);
    pNext(lm) = tail;
    BOOLEAN cmp = p_LmCmp(lm, tail, lmRing);
    if (cmp != 1)
      dPolyReportError(lm, lmRing, "wrong order: lm <= Lm(tail)");
    p_LmFree(tail, lmRing);
    pNext(lm) = pnext;
    return (cmp == 1);
  }
  return TRUE;
}

n_PermNumber()

poly n_PermNumber	(	const number	z,
		const int *	par_perm,
		const int	OldPar,
		const ring	src,
		const ring	dst
	)

Definition at line 4027 of file p_polys.cc.

{
#if 0
  PrintS("\nSource Ring: \n");
  rWrite(src);
 
  if(0)
  {
    number zz = n_Copy(z, src->cf);
    PrintS("z: "); n_Write(zz, src);
    n_Delete(&zz, src->cf);
  }
 
  PrintS("\nDestination Ring: \n");
  rWrite(dst);
 
  /*Print("\nOldPar: %d\n", OldPar);
  for( int i = 1; i <= OldPar; i++ )
  {
    Print("par(%d) -> par/var (%d)\n", i, par_perm[i-1]);
  }*/
#endif
  if( z == NULL )
     return NULL;
 
  const coeffs srcCf = src->cf;
  assume( srcCf != NULL );
 
  assume( !nCoeff_is_GF(srcCf) );
  assume( src->cf->extRing!=NULL );
 
  poly zz = NULL;
 
  const ring srcExtRing = srcCf->extRing;
  assume( srcExtRing != NULL );
 
  const coeffs dstCf = dst->cf;
  assume( dstCf != NULL );
 
  if( nCoeff_is_algExt(srcCf) ) // nCoeff_is_GF(srcCf)?
  {
    zz = (poly) z;
    if( zz == NULL ) return NULL;
  }
  else if (nCoeff_is_transExt(srcCf))
  {
    assume( !IS0(z) );
 
    zz = NUM((fraction)z);
    p_Test (zz, srcExtRing);
 
    if( zz == NULL ) return NULL;
    if( !DENIS1((fraction)z) )
    {
      if (!p_IsConstant(DEN((fraction)z),srcExtRing))
        WarnS("Not defined: Cannot map a rational fraction and make a polynomial out of it! Ignoring the denominator.");
    }
  }
  else
  {
    assume (FALSE);
    WerrorS("Number permutation is not implemented for this data yet!");
    return NULL;
  }
 
  assume( zz != NULL );
  p_Test (zz, srcExtRing);
 
  nMapFunc nMap = n_SetMap(srcExtRing->cf, dstCf);
 
  assume( nMap != NULL );
 
  poly qq;
  if ((par_perm == NULL) && (rPar(dst) != 0 && rVar (srcExtRing) > 0))
  {
    int* perm;
    perm=(int *)omAlloc0((rVar(srcExtRing)+1)*sizeof(int));
    for(int i=si_min(rVar(srcExtRing),rPar(dst));i>0;i--)
      perm[i]=-i;
    qq = p_PermPoly(zz, perm, srcExtRing, dst, nMap, NULL, rVar(srcExtRing)-1);
    omFreeSize ((ADDRESS)perm, (rVar(srcExtRing)+1)*sizeof(int));
  }
  else
    qq = p_PermPoly(zz, par_perm-1, srcExtRing, dst, nMap, NULL, rVar (srcExtRing)-1);
 
  if(nCoeff_is_transExt(srcCf)
  && (!DENIS1((fraction)z))
  && p_IsConstant(DEN((fraction)z),srcExtRing))
  {
    number n=nMap(pGetCoeff(DEN((fraction)z)),srcExtRing->cf, dstCf);
    qq=p_Div_nn(qq,n,dst);
    n_Delete(&n,dstCf);
    p_Normalize(qq,dst);
  }
  p_Test (qq, dst);
 
  return qq;
}

p_Add_q() [1/2]

static poly p_Add_q ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 936 of file p_polys.h.

{
  assume( (p != q) || (p == NULL && q == NULL) );
  if (q==NULL) return p;
  if (p==NULL) return q;
  int shorter;
  return r->p_Procs->p_Add_q(p, q, shorter, r);
}

p_Add_q() [2/2]

static poly p_Add_q ( poly  p, poly  q, int &  lp, int  lq, const ring  r  )

inlinestatic

like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q)

Definition at line 946 of file p_polys.h.

{
  assume( (p != q) || (p == NULL && q == NULL) );
  if (q==NULL) return p;
  if (p==NULL) { lp=lq; return q; }
  int shorter;
  poly res = r->p_Procs->p_Add_q(p, q, shorter, r);
  lp += lq - shorter;
  return res;
}

p_AddComp()

static unsigned long p_AddComp ( poly  p, unsigned long  v, ring  r  )

inlinestatic

Definition at line 447 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  pAssume2(rRing_has_Comp(r));
  return __p_GetComp(p,r) += v;
}

p_AddExp()

static long p_AddExp ( poly  p, int  v, long  ee, ring  r  )

inlinestatic

Definition at line 606 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  int e = p_GetExp(p,v,r);
  e += ee;
  return p_SetExp(p,v,e,r);
}

p_CheckIsFromRing()

BOOLEAN p_CheckIsFromRing	(	poly	p,
		ring	r
	)

Definition at line 105 of file pDebug.cc.

{
  while (p!=NULL)
  {
    pFalseReturn(p_LmCheckIsFromRing(p, r));
    pIter(p);
  }
  return TRUE;
}

p_CheckPolyRing()

BOOLEAN p_CheckPolyRing	(	poly	p,
		ring	r
	)

Definition at line 115 of file pDebug.cc.

{
  #ifndef X_OMALLOC
  pAssumeReturn(r != NULL && r->PolyBin != NULL);
  #endif
  return p_CheckIsFromRing(p, r);
}

p_CheckRing()

BOOLEAN p_CheckRing

(

ring

r

)

Definition at line 131 of file pDebug.cc.

{
  #ifndef X_OMALLOC
  pAssumeReturn(r != NULL && r->PolyBin != NULL);
  #endif
  return TRUE;
}

p_ChineseRemainder()

poly p_ChineseRemainder	(	poly *	xx,
		number *	x,
		number *	q,
		int	rl,
		CFArray &	inv_cache,
		const ring	R
	)

Definition at line 88 of file p_polys.cc.

{
  poly r,h,hh;
  int j;
  poly  res_p=NULL;
  loop
  {
    /* search the lead term */
    r=NULL;
    for(j=rl-1;j>=0;j--)
    {
      h=xx[j];
      if ((h!=NULL)
      &&((r==NULL)||(p_LmCmp(r,h,R)==-1)))
        r=h;
    }
    /* nothing found -> return */
    if (r==NULL) break;
    /* create the monomial in h */
    h=p_Head(r,R);
    /* collect the coeffs in x[..]*/
    for(j=rl-1;j>=0;j--)
    {
      hh=xx[j];
      if ((hh!=NULL) && (p_LmCmp(h,hh,R)==0))
      {
        x[j]=pGetCoeff(hh);
        hh=p_LmFreeAndNext(hh,R);
        xx[j]=hh;
      }
      else
        x[j]=n_Init(0, R->cf);
    }
    number n=n_ChineseRemainderSym(x,q,rl,TRUE,inv_cache,R->cf);
    for(j=rl-1;j>=0;j--)
    {
      x[j]=NULL; // n_Init(0...) takes no memory
    }
    if (n_IsZero(n,R->cf)) p_Delete(&h,R);
    else
    {
      //Print("new mon:");pWrite(h);
      p_SetCoeff(h,n,R);
      pNext(h)=res_p;
      res_p=h; // building res_p in reverse order!
    }
  }
  res_p=pReverse(res_p);
  p_Test(res_p, R);
  return res_p;
}

p_Cleardenom()

poly p_Cleardenom	(	poly	p,
		const ring	r
	)

Definition at line 2845 of file p_polys.cc.

{
  if( p == NULL )
    return NULL;
 
  assume( r != NULL );
  assume( r->cf != NULL );
  const coeffs C = r->cf;
 
#if CLEARENUMERATORS
  if( 0 )
  {
    CPolyCoeffsEnumerator itr(p);
    n_ClearDenominators(itr, C);
    n_ClearContent(itr, C); // divide out the content
    p_Test(p, r); n_Test(pGetCoeff(p), C);
    assume(n_GreaterZero(pGetCoeff(p), C)); // ??
//    if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r);
    return p;
  }
#endif
 
  number d, h;
 
  if (rField_is_Ring(r))
  {
    if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r);
    return p;
  }
 
  if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY)
  {
    if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r);
    return p;
  }
 
  assume(p != NULL);
 
  if(pNext(p)==NULL)
  {
    if (!TEST_OPT_CONTENTSB)
      p_SetCoeff(p,n_Init(1,C),r);
    else if(!n_GreaterZero(pGetCoeff(p),C))
      p = p_Neg(p,r);
    return p;
  }
 
  assume(pNext(p)!=NULL);
  poly start=p;
 
#if 0 && CLEARENUMERATORS
//CF: does not seem to work that well..
 
  if( nCoeff_is_Q(C) || nCoeff_is_Q_a(C) )
  {
    CPolyCoeffsEnumerator itr(p);
    n_ClearDenominators(itr, C);
    n_ClearContent(itr, C); // divide out the content
    p_Test(p, r); n_Test(pGetCoeff(p), C);
    assume(n_GreaterZero(pGetCoeff(p), C)); // ??
//    if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r);
    return start;
  }
#endif
 
  if(1)
  {
    // get lcm of all denominators ----------------------------------
    h = n_Init(1,C);
    while (p!=NULL)
    {
      n_Normalize(pGetCoeff(p),C);
      d=n_NormalizeHelper(h,pGetCoeff(p),C);
      n_Delete(&h,C);
      h=d;
      pIter(p);
    }
    /* h now contains the 1/lcm of all denominators */
    if(!n_IsOne(h,C))
    {
      // multiply by the lcm of all denominators
      p = start;
      while (p!=NULL)
      {
        d=n_Mult(h,pGetCoeff(p),C);
        n_Normalize(d,C);
        p_SetCoeff(p,d,r);
        pIter(p);
      }
    }
    n_Delete(&h,C);
    p=start;
 
    p_ContentForGB(p,r);
#ifdef HAVE_RATGRING
    if (rIsRatGRing(r))
    {
      /* quick unit detection in the rational case is done in gr_nc_bba */
      p_ContentRat(p, r);
      start=p;
    }
#endif
  }
 
  if(!n_GreaterZero(pGetCoeff(p),C)) p = p_Neg(p,r);
 
  return start;
}

p_Cleardenom_n()

void p_Cleardenom_n	(	poly	p,
		const ring	r,
		number &	c
	)

Definition at line 2954 of file p_polys.cc.

{
  const coeffs C = r->cf;
  number d, h;
 
  assume( ph != NULL );
 
  poly p = ph;
 
#if CLEARENUMERATORS
  if( 0 )
  {
    CPolyCoeffsEnumerator itr(ph);
 
    n_ClearDenominators(itr, d, C); // multiply with common denom. d
    n_ClearContent(itr, h, C); // divide by the content h
 
    c = n_Div(d, h, C); // d/h
 
    n_Delete(&d, C);
    n_Delete(&h, C);
 
    n_Test(c, C);
 
    p_Test(ph, r); n_Test(pGetCoeff(ph), C);
    assume(n_GreaterZero(pGetCoeff(ph), C)); // ??
/*
    if(!n_GreaterZero(pGetCoeff(ph),C))
    {
      ph = p_Neg(ph,r);
      c = n_InpNeg(c, C);
    }
*/
    return;
  }
#endif
 
 
  if( pNext(p) == NULL )
  {
    if(!TEST_OPT_CONTENTSB)
    {
      c=n_Invers(pGetCoeff(p), C);
      p_SetCoeff(p, n_Init(1, C), r);
    }
    else
    {
      c=n_Init(1,C);
    }
 
    if(!n_GreaterZero(pGetCoeff(ph),C))
    {
      ph = p_Neg(ph,r);
      c = n_InpNeg(c, C);
    }
 
    return;
  }
  if (TEST_OPT_CONTENTSB) { c=n_Init(1,C); return; }
 
  assume( pNext(p) != NULL );
 
#if CLEARENUMERATORS
  if( nCoeff_is_Q(C) || nCoeff_is_Q_a(C) )
  {
    CPolyCoeffsEnumerator itr(ph);
 
    n_ClearDenominators(itr, d, C); // multiply with common denom. d
    n_ClearContent(itr, h, C); // divide by the content h
 
    c = n_Div(d, h, C); // d/h
 
    n_Delete(&d, C);
    n_Delete(&h, C);
 
    n_Test(c, C);
 
    p_Test(ph, r); n_Test(pGetCoeff(ph), C);
    assume(n_GreaterZero(pGetCoeff(ph), C)); // ??
/*
    if(!n_GreaterZero(pGetCoeff(ph),C))
    {
      ph = p_Neg(ph,r);
      c = n_InpNeg(c, C);
    }
*/
    return;
  }
#endif
 
 
 
 
  if(1)
  {
    h = n_Init(1,C);
    while (p!=NULL)
    {
      n_Normalize(pGetCoeff(p),C);
      d=n_NormalizeHelper(h,pGetCoeff(p),C);
      n_Delete(&h,C);
      h=d;
      pIter(p);
    }
    c=h;
    /* contains the 1/lcm of all denominators */
    if(!n_IsOne(h,C))
    {
      p = ph;
      while (p!=NULL)
      {
        /* should be: // NOTE: don't use ->coef!!!!
        * number hh;
        * nGetDenom(p->coef,&hh);
        * nMult(&h,&hh,&d);
        * nNormalize(d);
        * nDelete(&hh);
        * nMult(d,p->coef,&hh);
        * nDelete(&d);
        * nDelete(&(p->coef));
        * p->coef =hh;
        */
        d=n_Mult(h,pGetCoeff(p),C);
        n_Normalize(d,C);
        p_SetCoeff(p,d,r);
        pIter(p);
      }
      if (rField_is_Q_a(r))
      {
        loop
        {
          h = n_Init(1,C);
          p=ph;
          while (p!=NULL)
          {
            d=n_NormalizeHelper(h,pGetCoeff(p),C);
            n_Delete(&h,C);
            h=d;
            pIter(p);
          }
          /* contains the 1/lcm of all denominators */
          if(!n_IsOne(h,C))
          {
            p = ph;
            while (p!=NULL)
            {
              /* should be: // NOTE: don't use ->coef!!!!
              * number hh;
              * nGetDenom(p->coef,&hh);
              * nMult(&h,&hh,&d);
              * nNormalize(d);
              * nDelete(&hh);
              * nMult(d,p->coef,&hh);
              * nDelete(&d);
              * nDelete(&(p->coef));
              * p->coef =hh;
              */
              d=n_Mult(h,pGetCoeff(p),C);
              n_Normalize(d,C);
              p_SetCoeff(p,d,r);
              pIter(p);
            }
            number t=n_Mult(c,h,C);
            n_Delete(&c,C);
            c=t;
          }
          else
          {
            break;
          }
          n_Delete(&h,C);
        }
      }
    }
  }
 
  if(!n_GreaterZero(pGetCoeff(ph),C))
  {
    ph = p_Neg(ph,r);
    c = n_InpNeg(c, C);
  }
 
}

p_Cmp()

static int p_Cmp ( poly  p1, poly  p2, ring  r  )

inlinestatic

Definition at line 1727 of file p_polys.h.

{
  if (p2==NULL)
  {
    if (p1==NULL) return 0;
    return 1;
  }
  if (p1==NULL)
    return -1;
  return p_LmCmp(p1,p2,r);
}

p_CmpPolys()

static int p_CmpPolys ( poly  p1, poly  p2, ring  r  )

inlinestatic

Definition at line 1739 of file p_polys.h.

{
  if (p2==NULL)
  {
    if (p1==NULL) return 0;
    return 1;
  }
  if (p1==NULL)
    return -1;
  return p_ComparePolys(p1,p2,r);
}

p_Comp_k_n()

static int p_Comp_k_n ( poly  a, poly  b, int  k, ring  r  )

inlinestatic

Definition at line 640 of file p_polys.h.

{
  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;
}

p_Compare()

int p_Compare	(	const poly	a,
		const poly	b,
		const ring	R
	)

Definition at line 4896 of file p_polys.cc.

{
  int r=p_Cmp(a,b,R);
  if ((r==0)&&(a!=NULL))
  {
    number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf);
    /* compare lead coeffs */
    r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */
    n_Delete(&h,R->cf);
  }
  else if (a==NULL)
  {
    if (b==NULL)
    {
      /* compare 0, 0 */
      r=0;
    }
    else if(p_IsConstant(b,R))
    {
      /* compare 0, const */
      r = 1-2*n_GreaterZero(pGetCoeff(b),R->cf); /* -1: <, 1: > */
    }
  }
  else if (b==NULL)
  {
    if (p_IsConstant(a,R))
    {
      /* compare const, 0 */
      r = -1+2*n_GreaterZero(pGetCoeff(a),R->cf); /* -1: <, 1: > */
    }
  }
  return(r);
}

p_ComparePolys()

BOOLEAN p_ComparePolys	(	poly	p1,
		poly	p2,
		const ring	r
	)

returns TRUE if p1 is a skalar multiple of p2 assume p1 != NULL and p2 != NULL

Definition at line 4576 of file p_polys.cc.

{
  number n,nn;
  pAssume(p1 != NULL && p2 != NULL);
 
  if (!p_LmEqual(p1,p2,r)) //compare leading mons
      return FALSE;
  if ((pNext(p1)==NULL) && (pNext(p2)!=NULL))
     return FALSE;
  if ((pNext(p2)==NULL) && (pNext(p1)!=NULL))
     return FALSE;
  if (pLength(p1) != pLength(p2))
    return FALSE;
  #ifdef HAVE_RINGS
  if (rField_is_Ring(r))
  {
    if (!n_DivBy(pGetCoeff(p1), pGetCoeff(p2), r->cf)) return FALSE;
  }
  #endif
  n=n_Div(pGetCoeff(p1),pGetCoeff(p2),r->cf);
  while ((p1 != NULL) /*&& (p2 != NULL)*/)
  {
    if ( ! p_LmEqual(p1, p2,r))
    {
        n_Delete(&n, r->cf);
        return FALSE;
    }
    if (!n_Equal(pGetCoeff(p1), nn = n_Mult(pGetCoeff(p2),n, r->cf), r->cf))
    {
      n_Delete(&n, r->cf);
      n_Delete(&nn, r->cf);
      return FALSE;
    }
    n_Delete(&nn, r->cf);
    pIter(p1);
    pIter(p2);
  }
  n_Delete(&n, r->cf);
  return TRUE;
}

p_Content()

void p_Content	(	poly	p,
		const ring	r
	)

Definition at line 2295 of file p_polys.cc.

{
  if (ph==NULL) return;
  const coeffs cf=r->cf;
  if (pNext(ph)==NULL)
  {
    p_SetCoeff(ph,n_Init(1,cf),r);
    return;
  }
  if ((cf->cfSubringGcd==ndGcd)
  || (cf->cfGcd==ndGcd)) /* trivial gcd*/
    return;
  number h;
  if ((rField_is_Q(r))
  || (rField_is_Q_a(r))
  || (rField_is_Zp_a)(r)
  || (rField_is_Z(r))
  )
  {
    h=p_InitContent(ph,r); /* first guess of a gcd of all coeffs */
  }
  else
  {
    h=n_Copy(pGetCoeff(ph),cf);
  }
  poly p;
  if(n_IsOne(h,cf))
  {
    goto content_finish;
  }
  p=ph;
  // take the SubringGcd of all coeffs
  while (p!=NULL)
  {
    n_Normalize(pGetCoeff(p),cf);
    number d=n_SubringGcd(h,pGetCoeff(p),cf);
    n_Delete(&h,cf);
    h = d;
    if(n_IsOne(h,cf))
    {
      goto content_finish;
    }
    pIter(p);
  }
  // if found<>1, divide by it
  p = ph;
  while (p!=NULL)
  {
    number d = n_ExactDiv(pGetCoeff(p),h,cf);
    p_SetCoeff(p,d,r);
    pIter(p);
  }
content_finish:
  n_Delete(&h,r->cf);
  // and last: check leading sign:
  if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r);
}

p_ContentForGB()

void p_ContentForGB	(	poly	p,
		const ring	r
	)

Definition at line 2355 of file p_polys.cc.

{
  if(TEST_OPT_CONTENTSB) return;
  assume( ph != NULL );
 
  assume( r != NULL ); assume( r->cf != NULL );
 
 
#if CLEARENUMERATORS
  if( 0 )
  {
    const coeffs C = r->cf;
      // experimentall (recursive enumerator treatment) of alg. Ext!
    CPolyCoeffsEnumerator itr(ph);
    n_ClearContent(itr, r->cf);
 
    p_Test(ph, r); n_Test(pGetCoeff(ph), C);
    assume(n_GreaterZero(pGetCoeff(ph), C)); // ??
 
      // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r);
    return;
  }
#endif
 
 
#ifdef HAVE_RINGS
  if (rField_is_Ring(r))
  {
    if (rField_has_Units(r))
    {
      number k = n_GetUnit(pGetCoeff(ph),r->cf);
      if (!n_IsOne(k,r->cf))
      {
        number tmpGMP = k;
        k = n_Invers(k,r->cf);
        n_Delete(&tmpGMP,r->cf);
        poly h = pNext(ph);
        p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r);
        while (h != NULL)
        {
          p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r);
          pIter(h);
        }
//        assume( n_GreaterZero(pGetCoeff(ph),r->cf) );
//        if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r);
      }
      n_Delete(&k,r->cf);
    }
    return;
  }
#endif
  number h,d;
  poly p;
 
  if(pNext(ph)==NULL)
  {
    p_SetCoeff(ph,n_Init(1,r->cf),r);
  }
  else
  {
    assume( pNext(ph) != NULL );
#if CLEARENUMERATORS
    if( nCoeff_is_Q(r->cf) )
    {
      // experimentall (recursive enumerator treatment) of alg. Ext!
      CPolyCoeffsEnumerator itr(ph);
      n_ClearContent(itr, r->cf);
 
      p_Test(ph, r); n_Test(pGetCoeff(ph), r->cf);
      assume(n_GreaterZero(pGetCoeff(ph), r->cf)); // ??
 
      // if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r);
      return;
    }
#endif
 
    n_Normalize(pGetCoeff(ph),r->cf);
    if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r);
    if (rField_is_Q(r)||(getCoeffType(r->cf)==n_transExt)) // should not be used anymore if CLEARENUMERATORS is 1
    {
      h=p_InitContent(ph,r);
      p=ph;
    }
    else
    {
      h=n_Copy(pGetCoeff(ph),r->cf);
      p = pNext(ph);
    }
    while (p!=NULL)
    {
      n_Normalize(pGetCoeff(p),r->cf);
      d=n_SubringGcd(h,pGetCoeff(p),r->cf);
      n_Delete(&h,r->cf);
      h = d;
      if(n_IsOne(h,r->cf))
      {
        break;
      }
      pIter(p);
    }
    //number tmp;
    if(!n_IsOne(h,r->cf))
    {
      p = ph;
      while (p!=NULL)
      {
        //d = nDiv(pGetCoeff(p),h);
        //tmp = nExactDiv(pGetCoeff(p),h);
        //if (!nEqual(d,tmp))
        //{
        //  StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/");
        //  nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:");
        //  nWrite(tmp);Print(StringEndS("\n")); // NOTE/TODO: use StringAppendS("\n"); omFree(s);
        //}
        //nDelete(&tmp);
        d = n_ExactDiv(pGetCoeff(p),h,r->cf);
        p_SetCoeff(p,d,r);
        pIter(p);
      }
    }
    n_Delete(&h,r->cf);
    if (rField_is_Q_a(r))
    {
      // special handling for alg. ext.:
      if (getCoeffType(r->cf)==n_algExt)
      {
        h = n_Init(1, r->cf->extRing->cf);
        p=ph;
        while (p!=NULL)
        { // each monom: coeff in Q_a
          poly c_n_n=(poly)pGetCoeff(p);
          poly c_n=c_n_n;
          while (c_n!=NULL)
          { // each monom: coeff in Q
            d=n_NormalizeHelper(h,pGetCoeff(c_n),r->cf->extRing->cf);
            n_Delete(&h,r->cf->extRing->cf);
            h=d;
            pIter(c_n);
          }
          pIter(p);
        }
        /* h contains the 1/lcm of all denominators in c_n_n*/
        //n_Normalize(h,r->cf->extRing->cf);
        if(!n_IsOne(h,r->cf->extRing->cf))
        {
          p=ph;
          while (p!=NULL)
          { // each monom: coeff in Q_a
            poly c_n=(poly)pGetCoeff(p);
            while (c_n!=NULL)
            { // each monom: coeff in Q
              d=n_Mult(h,pGetCoeff(c_n),r->cf->extRing->cf);
              n_Normalize(d,r->cf->extRing->cf);
              n_Delete(&pGetCoeff(c_n),r->cf->extRing->cf);
              pGetCoeff(c_n)=d;
              pIter(c_n);
            }
            pIter(p);
          }
        }
        n_Delete(&h,r->cf->extRing->cf);
      }
      /*else
      {
      // special handling for rat. functions.:
        number hzz =NULL;
        p=ph;
        while (p!=NULL)
        { // each monom: coeff in Q_a (Z_a)
          fraction f=(fraction)pGetCoeff(p);
          poly c_n=NUM(f);
          if (hzz==NULL)
          {
            hzz=n_Copy(pGetCoeff(c_n),r->cf->extRing->cf);
            pIter(c_n);
          }
          while ((c_n!=NULL)&&(!n_IsOne(hzz,r->cf->extRing->cf)))
          { // each monom: coeff in Q (Z)
            d=n_Gcd(hzz,pGetCoeff(c_n),r->cf->extRing->cf);
            n_Delete(&hzz,r->cf->extRing->cf);
            hzz=d;
            pIter(c_n);
          }
          pIter(p);
        }
        // hzz contains the gcd of all numerators in f
        h=n_Invers(hzz,r->cf->extRing->cf);
        n_Delete(&hzz,r->cf->extRing->cf);
        n_Normalize(h,r->cf->extRing->cf);
        if(!n_IsOne(h,r->cf->extRing->cf))
        {
          p=ph;
          while (p!=NULL)
          { // each monom: coeff in Q_a (Z_a)
            fraction f=(fraction)pGetCoeff(p);
            NUM(f)=__p_Mult_nn(NUM(f),h,r->cf->extRing);
            p_Normalize(NUM(f),r->cf->extRing);
            pIter(p);
          }
        }
        n_Delete(&h,r->cf->extRing->cf);
      }*/
    }
  }
  if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r);
}

p_ContentRat()

void p_ContentRat	(	poly &	ph,
		const ring	r
	)

Definition at line 1744 of file p_polys.cc.

{
  // init array of RatLeadCoeffs
  //  poly p_GetCoeffRat(poly p, int ishift, ring r);
 
  int len=pLength(ph);
  poly *C = (poly *)omAlloc0((len+1)*sizeof(poly));  //rat coeffs
  poly *LM = (poly *)omAlloc0((len+1)*sizeof(poly));  // rat lead terms
  int *D = (int *)omAlloc0((len+1)*sizeof(int));  //degrees of coeffs
  int *L = (int *)omAlloc0((len+1)*sizeof(int));  //lengths of coeffs
  int k = 0;
  poly p = p_Copy(ph, r); // ph will be needed below
  int mintdeg = p_Totaldegree(p, r);
  int minlen = len;
  int dd = 0; int i;
  int HasConstantCoef = 0;
  int is = r->real_var_start - 1;
  while (p!=NULL)
  {
    LM[k] = p_GetExp_k_n(p,1,is, r); // need LmRat istead of  p_HeadRat(p, is, currRing); !
    C[k] = p_GetCoeffRat(p, is, r);
    D[k] =  p_Totaldegree(C[k], r);
    mintdeg = si_min(mintdeg,D[k]);
    L[k] = pLength(C[k]);
    minlen = si_min(minlen,L[k]);
    if (p_IsConstant(C[k], r))
    {
      // C[k] = const, so the content will be numerical
      HasConstantCoef = 1;
      // smth like goto cleanup and return(pContent(p));
    }
    p_LmDeleteAndNextRat(&p, is, r);
    k++;
  }
 
  // look for 1 element of minimal degree and of minimal length
  k--;
  poly d;
  int mindeglen = len;
  if (k<=0) // this poly is not a ratgring poly -> pContent
  {
    p_Delete(&C[0], r);
    p_Delete(&LM[0], r);
    p_ContentForGB(ph, r);
    goto cleanup;
  }
 
  int pmindeglen;
  for(i=0; i<=k; i++)
  {
    if (D[i] == mintdeg)
    {
      if (L[i] < mindeglen)
      {
        mindeglen=L[i];
        pmindeglen = i;
      }
    }
  }
  d = p_Copy(C[pmindeglen], r);
  // there are dd>=1 mindeg elements
  // and pmideglen is the coordinate of one of the smallest among them
 
  //  poly g = singclap_gcd(p_Copy(p,r),p_Copy(q,r));
  //  return naGcd(d,d2,currRing);
 
  // adjoin pContentRat here?
  for(i=0; i<=k; i++)
  {
    d=singclap_gcd(d,p_Copy(C[i], r), r);
    if (p_Totaldegree(d, r)==0)
    {
      // cleanup, pContent, return
      p_Delete(&d, r);
      for(;k>=0;k--)
      {
        p_Delete(&C[k], r);
        p_Delete(&LM[k], r);
      }
      p_ContentForGB(ph, r);
      goto cleanup;
    }
  }
  for(i=0; i<=k; i++)
  {
    poly h=singclap_pdivide(C[i],d, r);
    p_Delete(&C[i], r);
    C[i]=h;
  }
 
  // zusammensetzen,
  p=NULL; // just to be sure
  for(i=0; i<=k; i++)
  {
    p = p_Add_q(p, p_Mult_q(C[i],LM[i], r), r);
    C[i]=NULL; LM[i]=NULL;
  }
  p_Delete(&ph, r); // do not need it anymore
  ph = p;
  // aufraeumen, return
cleanup:
  omFree(C);
  omFree(LM);
  omFree(D);
  omFree(L);
}

p_Copy() [1/2]

static poly p_Copy ( poly  p, const ring  lmRing, const ring  tailRing  )

inlinestatic

returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing

Definition at line 883 of file p_polys.h.

{
  if (p != NULL)
  {
#ifndef PDEBUG
    if (tailRing == lmRing)
      return p_Copy_noCheck(p, tailRing);
#endif
    poly pres = p_Head(p, lmRing);
    if (pNext(p)!=NULL)
      pNext(pres) = p_Copy_noCheck(pNext(p), tailRing);
    return pres;
  }
  else
    return NULL;
}

p_Copy() [2/2]

static poly p_Copy ( poly  p, const ring  r  )

inlinestatic

returns a copy of p

Definition at line 846 of file p_polys.h.

{
  if (p!=NULL)
  {
    p_Test(p,r);
    const poly pp = p_Copy_noCheck(p, r);
    p_Test(pp,r);
    return pp;
  }
  else
    return NULL;
}

p_Copy_noCheck()

static poly p_Copy_noCheck ( poly  p, const ring  r  )

inlinestatic

returns a copy of p (without any additional testing)

Definition at line 836 of file p_polys.h.

{
  /*assume(p!=NULL);*/
  assume(r != NULL);
  assume(r->p_Procs != NULL);
  assume(r->p_Procs->p_Copy != NULL);
  return r->p_Procs->p_Copy(p, r);
}

p_CopyPowerProduct()

poly p_CopyPowerProduct	(	const poly	p,
		const ring	r
	)

like p_Head, but with coefficient 1

Definition at line 4980 of file p_polys.cc.

{
  if (p == NULL) return NULL;
  return p_CopyPowerProduct0(p,n_Init(1,r->cf),r);
}

p_CopyPowerProduct0()

poly p_CopyPowerProduct0	(	const poly	p,
		const number	n,
		const ring	r
	)

like p_Head, but with coefficient n

Definition at line 4968 of file p_polys.cc.

{
  p_LmCheckPolyRing1(p, r);
  poly np;
  omTypeAllocBin(poly, np, r->PolyBin);
  p_SetRingOfLm(np, r);
  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
  pNext(np) = NULL;
  pSetCoeff0(np, n);
  return np;
}

p_DecrExp()

static long p_DecrExp ( poly  p, int  v, ring  r  )

inlinestatic

Definition at line 598 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  int e = p_GetExp(p,v,r);
  pAssume2(e > 0);
  e--;
  return p_SetExp(p,v,e,r);
}

p_Deg()

long p_Deg	(	poly	a,
		const ring	r
	)

Definition at line 587 of file p_polys.cc.

{
  p_LmCheckPolyRing(a, r);
//  assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); // WRONG assume!
  return p_GetOrder(a, r);
}

p_DegW()

long p_DegW	(	poly	p,
		const int *	w,
		const ring	R
	)

Definition at line 690 of file p_polys.cc.

{
  p_Test(p, R);
  assume( w != NULL );
  long r=-LONG_MAX;
 
  while (p!=NULL)
  {
    long t=totaldegreeWecart_IV(p,R,w);
    if (t>r) r=t;
    pIter(p);
  }
  return r;
}

p_Delete() [1/2]

static void p_Delete ( poly *  p, const ring  lmRing, const ring  tailRing  )

inlinestatic

Definition at line 908 of file p_polys.h.

{
  assume( p!= NULL );
  if (*p != NULL)
  {
#ifndef PDEBUG
    if (tailRing == lmRing)
    {
      p_Delete(p, tailRing);
      return;
    }
#endif
    if (pNext(*p) != NULL)
      p_Delete(&pNext(*p), tailRing);
    p_LmDelete(p, lmRing);
  }
}

p_Delete() [2/2]

static void p_Delete ( poly *  p, const ring  r  )

inlinestatic

Definition at line 901 of file p_polys.h.

{
  assume( p!= NULL );
  assume( r!= NULL );
  if ((*p)!=NULL) r->p_Procs->p_Delete(p, r);
}

p_DeleteComp()

void p_DeleteComp	(	poly *	p,
		int	k,
		const ring	r
	)

Definition at line 3544 of file p_polys.cc.

{
  poly q;
  long unsigned kk=k;
 
  while ((*p!=NULL) && (__p_GetComp(*p,r)==kk)) p_LmDelete(p,r);
  if (*p==NULL) return;
  q = *p;
  if (__p_GetComp(q,r)>kk)
  {
    p_SubComp(q,1,r);
    p_SetmComp(q,r);
  }
  while (pNext(q)!=NULL)
  {
    if (__p_GetComp(pNext(q),r)==kk)
      p_LmDelete(&(pNext(q)),r);
    else
    {
      pIter(q);
      if (__p_GetComp(q,r)>kk)
      {
        p_SubComp(q,1,r);
        p_SetmComp(q,r);
      }
    }
  }
}

p_Diff()

poly p_Diff	(	poly	a,
		int	k,
		const ring	r
	)

Definition at line 1898 of file p_polys.cc.

{
  poly res, f, last;
  number t;
 
  last = res = NULL;
  while (a!=NULL)
  {
    if (p_GetExp(a,k,r)!=0)
    {
      f = p_LmInit(a,r);
      t = n_Init(p_GetExp(a,k,r),r->cf);
      pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf));
      n_Delete(&t,r->cf);
      if (n_IsZero(pGetCoeff(f),r->cf))
        p_LmDelete(&f,r);
      else
      {
        p_DecrExp(f,k,r);
        p_Setm(f,r);
        if (res==NULL)
        {
          res=last=f;
        }
        else
        {
          pNext(last)=f;
          last=f;
        }
      }
    }
    pIter(a);
  }
  return res;
}

p_DiffOp()

poly p_DiffOp	(	poly	a,
		poly	b,
		BOOLEAN	multiply,
		const ring	r
	)

Definition at line 1973 of file p_polys.cc.

{
  poly result=NULL;
  poly h;
  for(;a!=NULL;pIter(a))
  {
    for(h=b;h!=NULL;pIter(h))
    {
      result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r);
    }
  }
  return result;
}

p_Div_mm()

poly p_Div_mm	(	poly	p,
		const poly	m,
		const ring	r
	)

divide polynomial by monomial

Definition at line 1538 of file p_polys.cc.

{
  p_Test(p, r);
  p_Test(m, r);
  poly result = p;
  poly prev = NULL;
  number n=pGetCoeff(m);
  while (p!=NULL)
  {
    number nc = n_Div(pGetCoeff(p),n,r->cf);
    n_Normalize(nc,r->cf);
    if (!n_IsZero(nc,r->cf))
    {
      p_SetCoeff(p,nc,r);
      prev=p;
      p_ExpVectorSub(p,m,r);
      pIter(p);
    }
    else
    {
      if (prev==NULL)
      {
        p_LmDelete(&result,r);
        p=result;
      }
      else
      {
        p_LmDelete(&pNext(prev),r);
        p=pNext(prev);
      }
    }
  }
  p_Test(result,r);
  return(result);
}

p_Div_nn()

poly p_Div_nn	(	poly	p,
		const number	n,
		const ring	r
	)

Definition at line 1505 of file p_polys.cc.

{
  pAssume(!n_IsZero(n,r->cf));
  p_Test(p, r);
  poly result = p;
  poly prev = NULL;
  while (p!=NULL)
  {
    number nc = n_Div(pGetCoeff(p),n,r->cf);
    if (!n_IsZero(nc,r->cf))
    {
      p_SetCoeff(p,nc,r);
      prev=p;
      pIter(p);
    }
    else
    {
      if (prev==NULL)
      {
        p_LmDelete(&result,r);
        p=result;
      }
      else
      {
        p_LmDelete(&pNext(prev),r);
        p=pNext(prev);
      }
    }
  }
  p_Test(result,r);
  return(result);
}

p_DivideM()

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

Definition at line 1578 of file p_polys.cc.

{
  if (a==NULL) { p_Delete(&b,r); return NULL; }
  poly result=a;
 
  if(!p_IsConstant(b,r))
  {
    if (rIsNCRing(r))
    {
      WerrorS("p_DivideM not implemented for non-commuative rings");
      return NULL;
    }
    poly prev=NULL;
    while (a!=NULL)
    {
      if (p_DivisibleBy(b,a,r))
      {
        p_ExpVectorSub(a,b,r);
        prev=a;
        pIter(a);
      }
      else
      {
        if (prev==NULL)
        {
          p_LmDelete(&result,r);
          a=result;
        }
        else
        {
          p_LmDelete(&pNext(prev),r);
          a=pNext(prev);
        }
      }
    }
  }
  if (result!=NULL)
  {
    number inv=pGetCoeff(b);
    //if ((!rField_is_Ring(r)) || n_IsUnit(inv,r->cf))
    if (rField_is_Zp(r))
    {
      inv = n_Invers(inv,r->cf);
      __p_Mult_nn(result,inv,r);
      n_Delete(&inv, r->cf);
    }
    else
    {
      result = p_Div_nn(result,inv,r);
    }
  }
  p_Delete(&b, r);
  return result;
}

p_DivisibleBy()

static BOOLEAN p_DivisibleBy ( poly  a, poly  b, const ring  r  )

inlinestatic

Definition at line 1900 of file p_polys.h.

{
  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;
}

p_DivisibleByRingCase()

BOOLEAN p_DivisibleByRingCase	(	poly	f,
		poly	g,
		const ring	r
	)

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 1642 of file p_polys.cc.

{
  int exponent;
  for(int i = (int)rVar(r); i>0; i--)
  {
    exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r);
    if (exponent < 0) return FALSE;
  }
  return n_DivBy(pGetCoeff(g), pGetCoeff(f), r->cf);
}

p_EqualPolys() [1/2]

BOOLEAN p_EqualPolys	(	poly	p1,
		poly	p2,
		const ring	r
	)

Definition at line 4512 of file p_polys.cc.

{
  while ((p1 != NULL) && (p2 != NULL))
  {
    if (! p_LmEqual(p1, p2,r))
      return FALSE;
    if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r->cf ))
      return FALSE;
    pIter(p1);
    pIter(p2);
  }
  return (p1==p2);
}

p_EqualPolys() [2/2]

BOOLEAN p_EqualPolys	(	poly	p1,
		poly	p2,
		const ring	r1,
		const ring	r2
	)

same as the usual p_EqualPolys for polys belonging to equal rings

Definition at line 4550 of file p_polys.cc.

{
  assume( r1 == r2 || rSamePolyRep(r1, r2) ); // will be used in rEqual!
  assume( r1->cf == r2->cf );
 
  while ((p1 != NULL) && (p2 != NULL))
  {
    // returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !!
    // #define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r)
 
    if (! p_ExpVectorEqual(p1, p2, r1, r2))
      return FALSE;
 
    if (! n_Equal(p_GetCoeff(p1,r1), p_GetCoeff(p2,r2), r1->cf ))
      return FALSE;
 
    pIter(p1);
    pIter(p2);
  }
  return (p1==p2);
}

p_ExpVectorAdd()

static void p_ExpVectorAdd ( poly  p1, poly  p2, const ring  r  )

inlinestatic

Definition at line 1411 of file p_polys.h.

{
  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);
}

p_ExpVectorAddSub()

static void p_ExpVectorAddSub ( poly  p1, poly  p2, poly  p3, const ring  r  )

inlinestatic

Definition at line 1456 of file p_polys.h.

{
  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
}

p_ExpVectorCopy()

static void p_ExpVectorCopy ( poly  d_p, poly  s_p, const ring  r  )

inlinestatic

Definition at line 1313 of file p_polys.h.

{
  p_LmCheckPolyRing1(d_p, r);
  p_LmCheckPolyRing1(s_p, r);
  memcpy(d_p->exp, s_p->exp, r->ExpL_Size*sizeof(long));
}

p_ExpVectorDiff()

static void p_ExpVectorDiff ( poly  pr, poly  p1, poly  p2, const ring  r  )

inlinestatic

Definition at line 1474 of file p_polys.h.

{
  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);
}

p_ExpVectorEqual()

static BOOLEAN p_ExpVectorEqual ( poly  p1, poly  p2, const ring  r  )

inlinestatic

Definition at line 1489 of file p_polys.h.

{
  p_LmCheckPolyRing1(p1, r);
  p_LmCheckPolyRing1(p2, r);
 
  unsigned 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!=0);
  return TRUE;
}

p_ExpVectorSub()

static void p_ExpVectorSub ( poly  p1, poly  p2, const ring  r  )

inlinestatic

Definition at line 1440 of file p_polys.h.

{
  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);
}

p_ExpVectorSum()

static void p_ExpVectorSum ( poly  pr, poly  p1, poly  p2, const ring  r  )

inlinestatic

Definition at line 1425 of file p_polys.h.

{
  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);
}

p_Farey()

poly p_Farey	(	poly	p,
		number	N,
		const ring	r
	)

Definition at line 54 of file p_polys.cc.

{
  poly h=p_Copy(p,r);
  poly hh=h;
  while(h!=NULL)
  {
    number c=pGetCoeff(h);
    pSetCoeff0(h,n_Farey(c,N,r->cf));
    n_Delete(&c,r->cf);
    pIter(h);
  }
  while((hh!=NULL)&&(n_IsZero(pGetCoeff(hh),r->cf)))
  {
    p_LmDelete(&hh,r);
  }
  h=hh;
  while((h!=NULL) && (pNext(h)!=NULL))
  {
    if(n_IsZero(pGetCoeff(pNext(h)),r->cf))
    {
      p_LmDelete(&pNext(h),r);
    }
    else pIter(h);
  }
  return hh;
}

p_FDeg()

static long p_FDeg ( const poly  p, const ring  r  )

inlinestatic

Definition at line 380 of file p_polys.h.

{ return r->pFDeg(p,r); }

p_GcdMon()

poly p_GcdMon	(	poly	f,
		poly	g,
		const ring	r
	)

polynomial gcd for f=mon

Definition at line 4930 of file p_polys.cc.

{
  assume(f!=NULL);
  assume(g!=NULL);
  assume(pNext(f)==NULL);
  poly G=p_Head(f,r);
  poly h=g;
  int *mf=(int*)omAlloc((r->N+1)*sizeof(int));
  p_GetExpV(f,mf,r);
  int *mh=(int*)omAlloc((r->N+1)*sizeof(int));
  BOOLEAN const_mon;
  BOOLEAN one_coeff=n_IsOne(pGetCoeff(G),r->cf);
  loop
  {
    if (h==NULL) break;
    if(!one_coeff)
    {
      number n=n_SubringGcd(pGetCoeff(G),pGetCoeff(h),r->cf);
      one_coeff=n_IsOne(n,r->cf);
      p_SetCoeff(G,n,r);
    }
    p_GetExpV(h,mh,r);
    const_mon=TRUE;
    for(unsigned j=r->N;j!=0;j--)
    {
      if (mh[j]<mf[j]) mf[j]=mh[j];
      if (mf[j]>0) const_mon=FALSE;
    }
    if (one_coeff && const_mon) break;
    pIter(h);
  }
  mf[0]=0;
  p_SetExpV(G,mf,r); // included is p_SetComp, p_Setm
  omFreeSize(mf,(r->N+1)*sizeof(int));
  omFreeSize(mh,(r->N+1)*sizeof(int));
  return G;
}

p_GetCoeffRat()

poly p_GetCoeffRat	(	poly	p,
		int	ishift,
		ring	r
	)

Definition at line 1722 of file p_polys.cc.

{
  poly q   = pNext(p);
  poly res; // = p_Head(p,r);
  res = p_GetExp_k_n(p, ishift+1, r->N, r); // does pSetm internally
  p_SetCoeff(res,n_Copy(p_GetCoeff(p,r),r),r);
  poly s;
  long cmp = p_GetComp(p, r);
  while ( (q!= NULL) && (p_Comp_k_n(p, q, ishift+1, r)) && (p_GetComp(q, r) == cmp) )
  {
    s   = p_GetExp_k_n(q, ishift+1, r->N, r);
    p_SetCoeff(s,n_Copy(p_GetCoeff(q,r),r),r);
    res = p_Add_q(res,s,r);
    q   = pNext(q);
  }
  cmp = 0;
  p_SetCompP(res,cmp,r);
  return res;
}

p_GetExp() [1/3]

static long p_GetExp ( const poly  p, const int  v, const ring  r  )

inlinestatic

get v^th exponent for a monomial

Definition at line 572 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  pAssume2(v>0 && v <= r->N);
  pAssume2(r->VarOffset[v] != -1);
  return p_GetExp(p, r->bitmask, r->VarOffset[v]);
}

p_GetExp() [2/3]

static long p_GetExp ( const poly  p, const ring  r, const int  VarOffset  )

inlinestatic

Definition at line 555 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  pAssume2(VarOffset != -1);
  return p_GetExp(p, r->bitmask, VarOffset);
}

p_GetExp() [3/3]

static long p_GetExp ( const poly  p, const unsigned long  iBitmask, const int  VarOffset  )

inlinestatic

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!

Definition at line 469 of file p_polys.h.

{
  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
}

p_GetExp_k_n()

static poly p_GetExp_k_n ( poly  p, int  l, int  k, const ring  r  )

inlinestatic

Definition at line 1372 of file p_polys.h.

{
  if (p == NULL) return NULL;
  p_LmCheckPolyRing1(p, r);
  poly np;
  omTypeAllocBin(poly, np, r->PolyBin);
  p_SetRingOfLm(np, r);
  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
  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;
}

p_GetExpDiff()

static long p_GetExpDiff ( poly  p1, poly  p2, int  i, ring  r  )

inlinestatic

Definition at line 635 of file p_polys.h.

{
  return p_GetExp(p1,i,r) - p_GetExp(p2,i,r);
}

p_GetExpSum()

static long p_GetExpSum ( poly  p1, poly  p2, int  i, ring  r  )

inlinestatic

Definition at line 629 of file p_polys.h.

{
  p_LmCheckPolyRing2(p1, r);
  p_LmCheckPolyRing2(p2, r);
  return p_GetExp(p1,i,r) + p_GetExp(p2,i,r);
}

p_GetExpV()

static void p_GetExpV ( poly  p, int *  ev, const ring  r  )

inlinestatic

Definition at line 1520 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      ev[j] = p_GetExp(p, j, r);
 
  ev[0] = p_GetComp(p, r);
}

p_GetExpVL()

static void p_GetExpVL ( poly  p, int64 *  ev, const ring  r  )

inlinestatic

Definition at line 1529 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      ev[j-1] = p_GetExp(p, j, r);
}

p_GetExpVLV()

static int64 p_GetExpVLV ( poly  p, int64 *  ev, const ring  r  )

inlinestatic

Definition at line 1536 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      ev[j-1] = p_GetExp(p, j, r);
  return (int64)p_GetComp(p,r);
}

p_GetMaxExp() [1/2]

static unsigned long p_GetMaxExp ( const poly  p, const ring  r  )

inlinestatic

Definition at line 804 of file p_polys.h.

{
  return p_GetMaxExp(p_GetMaxExpL(p, r), r);
}

p_GetMaxExp() [2/2]

static unsigned long p_GetMaxExp ( const unsigned long  l, const ring  r  )

inlinestatic

Definition at line 781 of file p_polys.h.

{
  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;
}

p_GetMaxExpL()

unsigned long p_GetMaxExpL	(	poly	p,
		const ring	r,
		unsigned long	l_max = 0
	)

return the maximal exponent of p in form of the maximal long var

Definition at line 1175 of file p_polys.cc.

{
  unsigned long l_p, divmask = r->divmask;
  int i;
 
  while (p != NULL)
  {
    l_p = p->exp[r->VarL_Offset[0]];
    if (l_p > l_max ||
        (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
      l_max = p_GetMaxExpL2(l_max, l_p, r);
    for (i=1; i<r->VarL_Size; i++)
    {
      l_p = p->exp[r->VarL_Offset[i]];
      // do the divisibility trick to find out whether l has an exponent
      if (l_p > l_max ||
          (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
        l_max = p_GetMaxExpL2(l_max, l_p, r);
    }
    pIter(p);
  }
  return l_max;
}

p_GetMaxExpP()

poly p_GetMaxExpP	(	poly	p,
		ring	r
	)

return monomial r such that GetExp(r,i) is maximum of all monomials in p; coeff == 0, next == NULL, ord is not set

Definition at line 1138 of file p_polys.cc.

{
  p_CheckPolyRing(p, r);
  if (p == NULL) return p_Init(r);
  poly max = p_LmInit(p, r);
  pIter(p);
  if (p == NULL) return max;
  int i, offset;
  unsigned long l_p, l_max;
  unsigned long divmask = r->divmask;
 
  do
  {
    offset = r->VarL_Offset[0];
    l_p = p->exp[offset];
    l_max = max->exp[offset];
    // do the divisibility trick to find out whether l has an exponent
    if (l_p > l_max ||
        (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
      max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r);
 
    for (i=1; i<r->VarL_Size; i++)
    {
      offset = r->VarL_Offset[i];
      l_p = p->exp[offset];
      l_max = max->exp[offset];
      // do the divisibility trick to find out whether l has an exponent
      if (l_p > l_max ||
          (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask)))
        max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r);
    }
    pIter(p);
  }
  while (p != NULL);
  return max;
}

p_GetOrder()

static long p_GetOrder ( poly  p, ring  r  )

inlinestatic

Definition at line 421 of file p_polys.h.

{
  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_am:
      case ro_wp_neg:
        return ((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]);
    }
  }
}

p_GetSetmProc()

p_SetmProc p_GetSetmProc

(

const ring

r

)

Definition at line 560 of file p_polys.cc.

{
  // covers lp, rp, ls,
  if (r->typ == NULL) return p_Setm_Dummy;
 
  if (r->OrdSize == 1)
  {
    if (r->typ[0].ord_typ == ro_dp &&
        r->typ[0].data.dp.start == 1 &&
        r->typ[0].data.dp.end == r->N &&
        r->typ[0].data.dp.place == r->pOrdIndex)
      return p_Setm_TotalDegree;
    if (r->typ[0].ord_typ == ro_wp &&
        r->typ[0].data.wp.start == 1 &&
        r->typ[0].data.wp.end == r->N &&
        r->typ[0].data.wp.place == r->pOrdIndex &&
        r->typ[0].data.wp.weights == r->firstwv)
      return p_Setm_WFirstTotalDegree;
  }
  return p_Setm_General;
}

p_GetShortExpVector()

unsigned long p_GetShortExpVector	(	const poly	a,
		const ring	r
	)

Definition at line 4780 of file p_polys.cc.

{
  assume(p != NULL);
  unsigned long ev = 0; // short exponent vector
  unsigned int n = BIT_SIZEOF_LONG / r->N; // number of bits per exp
  unsigned int m1; // highest bit which is filled with (n+1)
  unsigned int i=0;
  int j=1;
 
  if (n == 0)
  {
    if (r->N <2*BIT_SIZEOF_LONG)
    {
      n=1;
      m1=0;
    }
    else
    {
      for (; j<=r->N; j++)
      {
        if (p_GetExp(p,j,r) > 0) i++;
        if (i == BIT_SIZEOF_LONG) break;
      }
      if (i>0)
        ev = ~(0UL) >> (BIT_SIZEOF_LONG - i);
      return ev;
    }
  }
  else
  {
    m1 = (n+1)*(BIT_SIZEOF_LONG - n*r->N);
  }
 
  n++;
  while (i<m1)
  {
    ev |= GetBitFields(p_GetExp(p, j,r), i, n);
    i += n;
    j++;
  }
 
  n--;
  while (i<BIT_SIZEOF_LONG)
  {
    ev |= GetBitFields(p_GetExp(p, j,r), i, n);
    i += n;
    j++;
  }
  return ev;
}

p_GetShortExpVector0()

unsigned long p_GetShortExpVector0	(	const poly	a,
		const ring	r
	)

Definition at line 4831 of file p_polys.cc.

{
  assume(p != NULL);
  assume(r->N >=BIT_SIZEOF_LONG);
  unsigned long ev = 0; // short exponent vector
 
  for (int j=BIT_SIZEOF_LONG; j>0; j--)
  {
    if (p_GetExp(p, j,r)>0)
    ev |= Sy_bitL(j-1);
  }
  return ev;
}

p_GetShortExpVector1()

unsigned long p_GetShortExpVector1	(	const poly	a,
		const ring	r
	)

Definition at line 4846 of file p_polys.cc.

{
  assume(p != NULL);
  assume(r->N <BIT_SIZEOF_LONG);
  assume(2*r->N >=BIT_SIZEOF_LONG);
  unsigned long ev = 0; // short exponent vector
  int rest=r->N;
  int e;
  // 2 bits per exp
  int j=r->N;
  for (; j>BIT_SIZEOF_LONG-r->N; j--)
  {
    if ((e=p_GetExp(p, j,r))>0)
    {
      ev |= Sy_bitL(j-1);
      if (e>1)
      {
        ev|=Sy_bitL(rest+j-1);
      }
    }
  }
  // 1 bit per exp
  for (; j>0; j--)
  {
    if (p_GetExp(p, j,r)>0)
    {
      ev |= Sy_bitL(j-1);
    }
  }
  return ev;
}

p_GetTotalDegree()

static unsigned long p_GetTotalDegree ( const unsigned long  l, const ring  r, const int  number_of_exps  )

inlinestatic

Definition at line 810 of file p_polys.h.

{
  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;
}

p_GetVariables()

int p_GetVariables	(	poly	p,
		int *	e,
		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)

Definition at line 1267 of file p_polys.cc.

{
  int i;
  int n=0;
  while(p!=NULL)
  {
    n=0;
    for(i=r->N; i>0; i--)
    {
      if(e[i]==0)
      {
        if (p_GetExp(p,i,r)>0)
        {
          e[i]=1;
          n++;
        }
      }
      else
        n++;
    }
    if (n==r->N) break;
    pIter(p);
  }
  return n;
}

p_HasNotCF()

BOOLEAN p_HasNotCF	(	poly	p1,
		poly	p2,
		const ring	r
	)

Definition at line 1329 of file p_polys.cc.

{
 
  if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0)
    return FALSE;
  int i = rVar(r);
  loop
  {
    if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0))
      return FALSE;
    i--;
    if (i == 0)
      return TRUE;
  }
}

p_HasNotCFRing()

BOOLEAN p_HasNotCFRing	(	poly	p1,
		poly	p2,
		const ring	r
	)

Definition at line 1345 of file p_polys.cc.

{
 
  if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0)
    return FALSE;
  int i = rVar(r);
  loop
  {
    if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0))
      return FALSE;
    i--;
    if (i == 0) {
      if (n_DivBy(pGetCoeff(p1), pGetCoeff(p2), r->cf) ||
          n_DivBy(pGetCoeff(p2), pGetCoeff(p1), r->cf)) {
        return FALSE;
      } else {
        return TRUE;
      }
    }
  }
}

p_Head()

static poly p_Head ( const poly  p, const ring  r  )

inlinestatic

copy the (leading) term of p

Definition at line 860 of file p_polys.h.

{
  if (p == NULL) return NULL;
  p_LmCheckPolyRing1(p, r);
  poly np;
  omTypeAllocBin(poly, np, r->PolyBin);
  p_SetRingOfLm(np, r);
  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
  pNext(np) = NULL;
  pSetCoeff0(np, n_Copy(pGetCoeff(p), r->cf));
  return np;
}

p_Head0()

poly p_Head0	(	const poly	p,
		const ring	r
	)

like p_Head, but allow NULL coeff

Definition at line 4986 of file p_polys.cc.

{
  if (p==NULL) return NULL;
  if (pGetCoeff(p)==NULL) return p_CopyPowerProduct0(p,NULL,r);
  return p_Head(p,r);
}

p_Homogen()

poly p_Homogen	(	poly	p,
		int	varnum,
		const ring	r
	)

Definition at line 3270 of file p_polys.cc.

{
  pFDegProc deg;
  if (r->pLexOrder && (r->order[0]==ringorder_lp))
    deg=p_Totaldegree;
  else
    deg=r->pFDeg;
 
  poly q=NULL, qn;
  int  o,ii;
  sBucket_pt bp;
 
  if (p!=NULL)
  {
    if ((varnum < 1) || (varnum > rVar(r)))
    {
      return NULL;
    }
    o=deg(p,r);
    q=pNext(p);
    while (q != NULL)
    {
      ii=deg(q,r);
      if (ii>o) o=ii;
      pIter(q);
    }
    q = p_Copy(p,r);
    bp = sBucketCreate(r);
    while (q != NULL)
    {
      ii = o-deg(q,r);
      if (ii!=0)
      {
        p_AddExp(q,varnum, (long)ii,r);
        p_Setm(q,r);
      }
      qn = pNext(q);
      pNext(q) = NULL;
      sBucket_Add_m(bp, q);
      q = qn;
    }
    sBucketDestroyAdd(bp, &q, &ii);
  }
  return q;
}

p_IncrExp()

static long p_IncrExp ( poly  p, int  v, ring  r  )

inlinestatic

Definition at line 591 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  int e = p_GetExp(p,v,r);
  e++;
  return p_SetExp(p,v,e,r);
}

p_Init() [1/2]

static poly p_Init ( const ring  r )

inlinestatic

Definition at line 1330 of file p_polys.h.

{
  return p_Init(r, r->PolyBin);
}

p_Init() [2/2]

static poly p_Init ( const ring  r, omBin  bin  )

inlinestatic

Definition at line 1320 of file p_polys.h.

{
  p_CheckRing1(r);
  pAssume1(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
  poly p;
  omTypeAlloc0Bin(poly, p, bin);
  p_MemAdd_NegWeightAdjust(p, r);
  p_SetRingOfLm(p, r);
  return p;
}

p_InitContent()

number p_InitContent	(	poly	ph,
		const ring	r
	)

Definition at line 2635 of file p_polys.cc.

{
  assume(!TEST_OPT_CONTENTSB);
  assume(ph!=NULL);
  assume(pNext(ph)!=NULL);
  assume(rField_is_Q(r));
  if (pNext(pNext(ph))==NULL)
  {
    return n_GetNumerator(pGetCoeff(pNext(ph)),r->cf);
  }
  poly p=ph;
  number n1=n_GetNumerator(pGetCoeff(p),r->cf);
  pIter(p);
  number n2=n_GetNumerator(pGetCoeff(p),r->cf);
  pIter(p);
  number d;
  number t;
  loop
  {
    nlNormalize(pGetCoeff(p),r->cf);
    t=n_GetNumerator(pGetCoeff(p),r->cf);
    if (nlGreaterZero(t,r->cf))
      d=nlAdd(n1,t,r->cf);
    else
      d=nlSub(n1,t,r->cf);
    nlDelete(&t,r->cf);
    nlDelete(&n1,r->cf);
    n1=d;
    pIter(p);
    if (p==NULL) break;
    nlNormalize(pGetCoeff(p),r->cf);
    t=n_GetNumerator(pGetCoeff(p),r->cf);
    if (nlGreaterZero(t,r->cf))
      d=nlAdd(n2,t,r->cf);
    else
      d=nlSub(n2,t,r->cf);
    nlDelete(&t,r->cf);
    nlDelete(&n2,r->cf);
    n2=d;
    pIter(p);
    if (p==NULL) break;
  }
  d=nlGcd(n1,n2,r->cf);
  nlDelete(&n1,r->cf);
  nlDelete(&n2,r->cf);
  return d;
}
#else
{
  /* ph has al least 2 terms */
  number d=pGetCoeff(ph);
  int s=n_Size(d,r->cf);
  pIter(ph);
  number d2=pGetCoeff(ph);
  int s2=n_Size(d2,r->cf);
  pIter(ph);
  if (ph==NULL)
  {
    if (s<s2) return n_Copy(d,r->cf);
    else      return n_Copy(d2,r->cf);
  }
  do
  {
    number nd=pGetCoeff(ph);
    int ns=n_Size(nd,r->cf);
    if (ns<=2)
    {
      s2=s;
      d2=d;
      d=nd;
      s=ns;
      break;
    }
    else if (ns<s)
    {
      s2=s;
      d2=d;
      d=nd;
      s=ns;
    }
    pIter(ph);
  }
  while(ph!=NULL);
  return n_SubringGcd(d,d2,r->cf);
}

p_IsConstant()

static BOOLEAN p_IsConstant ( const poly  p, const ring  r  )

inlinestatic

Definition at line 1964 of file p_polys.h.

{
  if (p == NULL) return TRUE;
  return (pNext(p)==NULL) && p_LmIsConstant(p, r);
}

p_IsConstantComp()

static BOOLEAN p_IsConstantComp ( const poly  p, const ring  r  )

inlinestatic

like the respective p_LmIs* routines, except that p might be empty

Definition at line 1958 of file p_polys.h.

{
  if (p == NULL) return TRUE;
  return (pNext(p)==NULL) && p_LmIsConstantComp(p, r);
}

p_IsConstantPoly()

static BOOLEAN p_IsConstantPoly ( const poly  p, const ring  r  )

inlinestatic

Definition at line 1978 of file p_polys.h.

{
  p_Test(p, r);
  poly pp=p;
  while(pp!=NULL)
  {
    if (! p_LmIsConstantComp(pp, r))
      return FALSE;
    pIter(pp);
  }
  return TRUE;
}

p_ISet()

poly p_ISet	(	long	i,
		const ring	r
	)

returns the poly representing the integer i

Definition at line 1297 of file p_polys.cc.

{
  poly rc = NULL;
  if (i!=0)
  {
    rc = p_Init(r);
    pSetCoeff0(rc,n_Init(i,r->cf));
    if (n_IsZero(pGetCoeff(rc),r->cf))
      p_LmDelete(&rc,r);
  }
  return rc;
}

p_IsHomogeneous()

BOOLEAN p_IsHomogeneous	(	poly	p,
		const ring	r
	)

Definition at line 3319 of file p_polys.cc.

{
  poly qp=p;
  int o;
 
  if ((p == NULL) || (pNext(p) == NULL)) return TRUE;
  pFDegProc d;
  if (r->pLexOrder && (r->order[0]==ringorder_lp))
    d=p_Totaldegree;
  else
    d=r->pFDeg;
  o = d(p,r);
  do
  {
    if (d(qp,r) != o) return FALSE;
    pIter(qp);
  }
  while (qp != NULL);
  return TRUE;
}

p_IsHomogeneousW() [1/2]

BOOLEAN p_IsHomogeneousW	(	poly	p,
		const intvec *	w,
		const intvec *	module_w,
		const ring	r
	)

Definition at line 3360 of file p_polys.cc.

{
  poly qp=p;
  long o;
 
  if ((p == NULL) || (pNext(p) == NULL)) return TRUE;
  pIter(qp);
  o = totaldegreeWecart_IV(p,r,w->ivGetVec())+(*module_w)[p_GetComp(p,r)];
  do
  {
    long oo=totaldegreeWecart_IV(qp,r,w->ivGetVec())+(*module_w)[p_GetComp(qp,r)];
    if (oo != o) return FALSE;
    pIter(qp);
  }
  while (qp != NULL);
  return TRUE;
}

p_IsHomogeneousW() [2/2]

BOOLEAN p_IsHomogeneousW	(	poly	p,
		const intvec *	w,
		const ring	r
	)

Definition at line 3343 of file p_polys.cc.

{
  poly qp=p;
  long o;
 
  if ((p == NULL) || (pNext(p) == NULL)) return TRUE;
  pIter(qp);
  o = totaldegreeWecart_IV(p,r,w->ivGetVec());
  do
  {
    if (totaldegreeWecart_IV(qp,r,w->ivGetVec()) != o) return FALSE;
    pIter(qp);
  }
  while (qp != NULL);
  return TRUE;
}

p_IsOne()

static BOOLEAN p_IsOne ( const poly  p, const ring  R  )

inlinestatic

either poly(1) or gen(k)?!

Definition at line 1971 of file p_polys.h.

{
  if (p == NULL) return FALSE; /* TODO check if 0 == 1 */
  p_Test(p, R);
  return (p_IsConstant(p, R) && n_IsOne(p_GetCoeff(p, R), R->cf));
}

p_IsPurePower()

int p_IsPurePower	(	const poly	p,
		const ring	r
	)

return i, if head depends only on var(i)

Definition at line 1226 of file p_polys.cc.

{
  int i,k=0;
 
  for (i=r->N;i;i--)
  {
    if (p_GetExp(p,i, r)!=0)
    {
      if(k!=0) return 0;
      k=i;
    }
  }
  return k;
}

p_IsUnit()

static BOOLEAN p_IsUnit ( const poly  p, const ring  r  )

inlinestatic

Definition at line 1991 of file p_polys.h.

{
  if (p == NULL) return FALSE;
  if (rField_is_Ring(r))
    return (p_LmIsConstant(p, r) && n_IsUnit(pGetCoeff(p),r->cf));
  return p_LmIsConstant(p, r);
}

p_IsUnivariate()

int p_IsUnivariate	(	poly	p,
		const ring	r
	)

return i, if poly depends only on var(i)

Definition at line 1247 of file p_polys.cc.

{
  int i,k=-1;
 
  while (p!=NULL)
  {
    for (i=r->N;i;i--)
    {
      if (p_GetExp(p,i, r)!=0)
      {
        if((k!=-1)&&(k!=i)) return 0;
        k=i;
      }
    }
    pIter(p);
  }
  return k;
}

p_Jet()

poly p_Jet	(	poly	p,
		int	m,
		const ring	R
	)

Definition at line 4386 of file p_polys.cc.

{
  while((p!=NULL) && (p_Totaldegree(p,R)>m)) p_LmDelete(&p,R);
  if (p==NULL) return NULL;
  poly r=p;
  while (pNext(p)!=NULL)
  {
    if (p_Totaldegree(pNext(p),R)>m)
    {
      p_LmDelete(&pNext(p),R);
    }
    else
      pIter(p);
  }
  return r;
}

p_JetW()

poly p_JetW	(	poly	p,
		int	m,
		int *	w,
		const ring	R
	)

Definition at line 4430 of file p_polys.cc.

{
  while((p!=NULL) && (totaldegreeWecart_IV(p,R,w)>m)) p_LmDelete(&p,R);
  if (p==NULL) return NULL;
  poly r=p;
  while (pNext(p)!=NULL)
  {
    if (totaldegreeWecart_IV(pNext(p),R,w)>m)
    {
      p_LmDelete(&pNext(p),R);
    }
    else
      pIter(p);
  }
  return r;
}

p_Last()

poly p_Last	(	const poly	a,
		int &	l,
		const ring	r
	)

Definition at line 4621 of file p_polys.cc.

{
  if (p == NULL)
  {
    l = 0;
    return NULL;
  }
  l = 1;
  poly a = p;
  if (! rIsSyzIndexRing(r))
  {
    poly next = pNext(a);
    while (next!=NULL)
    {
      a = next;
      next = pNext(a);
      l++;
    }
  }
  else
  {
    long unsigned curr_limit = rGetCurrSyzLimit(r);
    poly pp = a;
    while ((a=pNext(a))!=NULL)
    {
      if (__p_GetComp(a,r)<=curr_limit/*syzComp*/)
        l++;
      else break;
      pp = a;
    }
    a=pp;
  }
  return a;
}

p_Lcm() [1/2]

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

Definition at line 1664 of file p_polys.cc.

{
  poly m=p_Init(r);
  p_Lcm(a, b, m, r);
  p_Setm(m,r);
  return(m);
}

p_Lcm() [2/2]

void p_Lcm	(	const poly	a,
		const poly	b,
		poly	m,
		const ring	r
	)

Definition at line 1655 of file p_polys.cc.

{
  for (int i=r->N; i; --i)
    p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r);
 
  p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r);
  /* Don't do a pSetm here, otherwise hres/lres chockes */
}

p_LcmRat()

poly p_LcmRat	(	const poly	a,
		const poly	b,
		const long	lCompM,
		const ring	r
	)

Definition at line 1677 of file p_polys.cc.

{
  poly m = // p_One( r);
          p_Init(r);
 
//  const int (currRing->N) = r->N;
 
  //  for (int i = (currRing->N); i>=r->real_var_start; i--)
  for (int i = r->real_var_end; i>=r->real_var_start; i--)
  {
    const int lExpA = p_GetExp (a, i, r);
    const int lExpB = p_GetExp (b, i, r);
 
    p_SetExp (m, i, si_max(lExpA, lExpB), r);
  }
 
  p_SetComp (m, lCompM, r);
  p_Setm(m,r);
  p_GetCoeff(m, r)=NULL;
 
  return(m);
};

p_LDeg()

static long p_LDeg ( const poly  p, int *  l, const ring  r  )

inlinestatic

Definition at line 381 of file p_polys.h.

{ return r->pLDeg(p,l,r); }

p_LmCheckIsFromRing()

BOOLEAN p_LmCheckIsFromRing	(	poly	p,
		ring	r
	)

Definition at line 74 of file pDebug.cc.

{
  if (p != NULL)
  {
    #if (OM_TRACK > 0) && defined(OM_TRACK_CUSTOM)
    void* custom = omGetCustomOfAddr(p);
    if (custom != NULL)
    {
      pPolyAssumeReturnMsg(custom == r ||
                           // be more sloppy for qrings
                           (r->qideal != NULL &&
                            omIsBinPageAddr(p) &&
                            omSizeWOfAddr(p)==omSizeWOfBin(r->PolyBin)) ||
                           rSamePolyRep((ring) custom, r),
                           "monomial not from specified ring",p,r);
      return TRUE;
    }
    else
    #endif
    #ifndef X_OMALLOC
    {
      _pPolyAssumeReturn(omIsBinPageAddr(p),p,r);
      _pPolyAssumeReturn(omSizeWOfAddr(p)==omSizeWOfBin(r->PolyBin),p,r);
      return TRUE;
    }
    return FALSE;
    #endif
  }
  return TRUE;
}

p_LmCheckPolyRing()

BOOLEAN p_LmCheckPolyRing	(	poly	p,
		ring	r
	)

Definition at line 123 of file pDebug.cc.

{
  #ifndef X_OMALLOC
  pAssumeReturn(r != NULL && r->PolyBin != NULL);
  #endif
  pAssumeReturn(p != NULL);
  return p_LmCheckIsFromRing(p, r);
}

p_LmCmp()

static int p_LmCmp ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1580 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  p_LmCheckPolyRing1(q, r);
 
  const unsigned long* _s1 = ((unsigned long*) p->exp);
  const unsigned long* _s2 = ((unsigned long*) q->exp);
  REGISTER unsigned long _v1;
  REGISTER unsigned long _v2;
  const unsigned long _l = r->CmpL_Size;
 
  REGISTER unsigned long _i=0;
 
  LengthGeneral_OrdGeneral_LoopTop:
  _v1 = _s1[_i];
  _v2 = _s2[_i];
  if (_v1 == _v2)
  {
    _i++;
    if (_i == _l) return 0;
    goto LengthGeneral_OrdGeneral_LoopTop;
  }
  const long* _ordsgn = (long*) r->ordsgn;
#if 1 /* two variants*/
  if (_v1 > _v2)
  {
    return _ordsgn[_i];
  }
  return -(_ordsgn[_i]);
#else
   if (_v1 > _v2)
   {
     if (_ordsgn[_i] == 1) return 1;
     return -1;
   }
   if (_ordsgn[_i] == 1) return -1;
   return 1;
#endif
}

p_LmDelete() [1/2]

static void p_LmDelete ( poly *  p, const ring  r  )

inlinestatic

Definition at line 743 of file p_polys.h.

{
  p_LmCheckPolyRing2(*p, r);
  poly h = *p;
  *p = pNext(h);
  n_Delete(&pGetCoeff(h), r->cf);
  #ifdef XALLOC_BIN
  omFreeBin(h,r->PolyBin);
  #else
  omFreeBinAddr(h);
  #endif
}

p_LmDelete() [2/2]

static void p_LmDelete ( poly  p, const ring  r  )

inlinestatic

Definition at line 723 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  n_Delete(&pGetCoeff(p), r->cf);
  #ifdef XALLOC_BIN
  omFreeBin(p,r->PolyBin);
  #else
  omFreeBinAddr(p);
  #endif
}

p_LmDelete0()

static void p_LmDelete0 ( poly  p, const ring  r  )

inlinestatic

Definition at line 733 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  if (pGetCoeff(p)!=NULL) n_Delete(&pGetCoeff(p), r->cf);
  #ifdef XALLOC_BIN
  omFreeBin(p,r->PolyBin);
  #else
  omFreeBinAddr(p);
  #endif
}

p_LmDeleteAndNext()

static poly p_LmDeleteAndNext ( poly  p, const ring  r  )

inlinestatic

Definition at line 755 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  poly pnext = pNext(p);
  n_Delete(&pGetCoeff(p), r->cf);
  #ifdef XALLOC_BIN
  omFreeBin(p,r->PolyBin);
  #else
  omFreeBinAddr(p);
  #endif
  return pnext;
}

p_LmDeleteAndNextRat()

void p_LmDeleteAndNextRat	(	poly *	p,
		int	ishift,
		ring	r
	)

Definition at line 1700 of file p_polys.cc.

{
  /* modifies p*/
  //  Print("start: "); Print(" "); p_wrp(*p,r);
  p_LmCheckPolyRing2(*p, r);
  poly q = p_Head(*p,r);
  const long cmp = p_GetComp(*p, r);
  while ( ( (*p)!=NULL ) && ( p_Comp_k_n(*p, q, ishift+1, r) ) && (p_GetComp(*p, r) == cmp) )
  {
    p_LmDelete(p,r);
    //    Print("while: ");p_wrp(*p,r);Print(" ");
  }
  //  p_wrp(*p,r);Print(" ");
  //  PrintS("end\n");
  p_LmDelete(&q,r);
}

p_LmDivisibleBy()

static BOOLEAN p_LmDivisibleBy ( poly  a, poly  b, const ring  r  )

inlinestatic

Definition at line 1891 of file p_polys.h.

{
  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;
}

p_LmDivisibleByNoComp() [1/2]

static BOOLEAN p_LmDivisibleByNoComp ( poly  a, const ring  ra, poly  b, const ring  rb  )

inlinestatic

Definition at line 1884 of file p_polys.h.

{
  p_LmCheckPolyRing1(a, ra);
  p_LmCheckPolyRing1(b, rb);
  return _p_LmDivisibleByNoComp(a, ra, b, rb);
}

p_LmDivisibleByNoComp() [2/2]

static BOOLEAN p_LmDivisibleByNoComp ( poly  a, poly  b, const ring  r  )

inlinestatic

Definition at line 1877 of file p_polys.h.

{
  p_LmCheckPolyRing1(a, r);
  p_LmCheckPolyRing1(b, r);
  return _p_LmDivisibleByNoComp(a, b, r);
}

p_LmDivisibleByPart()

static BOOLEAN p_LmDivisibleByPart ( poly  a, poly  b, const ring  r, const int  start, const int  end  )

inlinestatic

Definition at line 1862 of file p_polys.h.

{
  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;
}

p_LmExpVectorAddIsOk()

static BOOLEAN p_LmExpVectorAddIsOk ( const poly  p1, const poly  p2, const ring  r  )

inlinestatic

Definition at line 1999 of file p_polys.h.

{
  p_LmCheckPolyRing(p1, r);
  p_LmCheckPolyRing(p2, r);
  unsigned long l1, l2, divmask = r->divmask;
  int i;
 
  for (i=0; i<r->VarL_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;
}

p_LmFree() [1/2]

static void p_LmFree ( poly *  p, ring    )

inlinestatic

Definition at line 696 of file p_polys.h.

{
  p_LmCheckPolyRing2(*p, r);
  poly h = *p;
  *p = pNext(h);
  #ifdef XALLOC_BIN
  omFreeBin(h,r->PolyBin);
  #else
  omFreeBinAddr(h);
  #endif
}

p_LmFree() [2/2]

static void p_LmFree ( poly  p, ring    )

inlinestatic

Definition at line 683 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  #ifdef XALLOC_BIN
  omFreeBin(p,r->PolyBin);
  #else
  omFreeBinAddr(p);
  #endif
}

p_LmFreeAndNext()

static poly p_LmFreeAndNext ( poly  p, ring    )

inlinestatic

Definition at line 711 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  poly pnext = pNext(p);
  #ifdef XALLOC_BIN
  omFreeBin(p,r->PolyBin);
  #else
  omFreeBinAddr(p);
  #endif
  return pnext;
}

p_LmInit() [1/3]

static poly p_LmInit ( poly  p, const ring  r  )

inlinestatic

Definition at line 1335 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  poly np;
  omTypeAllocBin(poly, np, r->PolyBin);
  p_SetRingOfLm(np, r);
  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
  pNext(np) = NULL;
  pSetCoeff0(np, NULL);
  return np;
}

p_LmInit() [2/3]

static poly p_LmInit ( poly  s_p, const ring  s_r, const ring  d_r  )

inlinestatic

Definition at line 1363 of file p_polys.h.

{
  pAssume1(d_r != NULL);
  return p_LmInit(s_p, s_r, d_r, d_r->PolyBin);
}

p_LmInit() [3/3]

static poly p_LmInit ( poly  s_p, const ring  s_r, const ring  d_r, omBin  d_bin  )

inlinestatic

Definition at line 1346 of file p_polys.h.

{
  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 (unsigned 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;
}

p_LmIsConstant()

static BOOLEAN p_LmIsConstant ( const poly  p, const ring  r  )

inlinestatic

Definition at line 1023 of file p_polys.h.

{
  if (p_LmIsConstantComp(p, r))
    return (p_GetComp(p, r) == 0);
  return FALSE;
}

p_LmIsConstantComp()

static BOOLEAN p_LmIsConstantComp ( const poly  p, const ring  r  )

inlinestatic

Definition at line 1006 of file p_polys.h.

{
  //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;
}

p_LmShallowCopyDelete()

static poly p_LmShallowCopyDelete ( poly  p, const ring  r  )

inlinestatic

Definition at line 1393 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  pAssume1(omSizeWOfBin(bin) == omSizeWOfBin(r->PolyBin));
  poly new_p = p_New(r);
  memcpy(new_p->exp, p->exp, r->ExpL_Size*sizeof(long));
  pSetCoeff0(new_p, pGetCoeff(p));
  pNext(new_p) = pNext(p);
  omFreeBinAddr(p);
  return new_p;
}

p_LmShortDivisibleBy()

static BOOLEAN p_LmShortDivisibleBy ( poly  a, unsigned long  sev_a, poly  b, unsigned long  not_sev_b, const ring  r  )

inlinestatic

Definition at line 1910 of file p_polys.h.

{
  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
}

p_LmShortDivisibleByNoComp()

static BOOLEAN p_LmShortDivisibleByNoComp ( poly  a, unsigned long  sev_a, poly  b, unsigned long  not_sev_b, const ring  r  )

inlinestatic

Definition at line 1930 of file p_polys.h.

{
  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_LmDivisibleByNoComp(a, b, r);
#else
  return pDebugLmShortDivisibleByNoComp(a, sev_a, r, b, not_sev_b, r);
#endif
}

p_LowVar()

int p_LowVar	(	poly	p,
		const ring	r
	)

the minimal index of used variables - 1

Definition at line 4680 of file p_polys.cc.

{
  int k,l,lex;
 
  if (p == NULL) return -1;
 
  k = 32000;/*a very large dummy value*/
  while (p != NULL)
  {
    l = 1;
    lex = p_GetExp(p,l,r);
    while ((l < (rVar(r))) && (lex == 0))
    {
      l++;
      lex = p_GetExp(p,l,r);
    }
    l--;
    if (l < k) k = l;
    pIter(p);
  }
  return k;
}

p_LtCmp()

static int p_LtCmp ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1621 of file p_polys.h.

{
  int res = p_LmCmp(p,q,r);
  if(res == 0)
  {
    if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
      return res;
    number pc = n_Copy(p_GetCoeff(p,r),r->cf);
    number qc = n_Copy(p_GetCoeff(q,r),r->cf);
    if(!n_GreaterZero(pc,r->cf))
      pc = n_InpNeg(pc,r->cf);
    if(!n_GreaterZero(qc,r->cf))
      qc = n_InpNeg(qc,r->cf);
    if(n_Greater(pc,qc,r->cf))
      res = 1;
    else if(n_Greater(qc,pc,r->cf))
      res = -1;
    else if(n_Equal(pc,qc,r->cf))
      res = 0;
    n_Delete(&pc,r->cf);
    n_Delete(&qc,r->cf);
  }
  return res;
}

p_LtCmpNoAbs()

static int p_LtCmpNoAbs ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1647 of file p_polys.h.

{
  int res = p_LmCmp(p,q,r);
  if(res == 0)
  {
    if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
      return res;
    number pc = p_GetCoeff(p,r);
    number qc = p_GetCoeff(q,r);
    if(n_Greater(pc,qc,r->cf))
      res = 1;
    if(n_Greater(qc,pc,r->cf))
      res = -1;
    if(n_Equal(pc,qc,r->cf))
      res = 0;
  }
  return res;
}

p_LtCmpOrdSgnDiffM()

static int p_LtCmpOrdSgnDiffM ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1669 of file p_polys.h.

{
  return(p_LtCmp(p,q,r) == r->OrdSgn);
}

p_LtCmpOrdSgnDiffP()

static int p_LtCmpOrdSgnDiffP ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1678 of file p_polys.h.

{
  if(r->OrdSgn == 1)
  {
    return(p_LmCmp(p,q,r) == -1);
  }
  else
  {
    return(p_LtCmp(p,q,r) != -1);
  }
}

p_LtCmpOrdSgnEqM()

static int p_LtCmpOrdSgnEqM ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1694 of file p_polys.h.

{
  return(p_LtCmp(p,q,r) == -r->OrdSgn);
}

p_LtCmpOrdSgnEqP()

static int p_LtCmpOrdSgnEqP ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1703 of file p_polys.h.

{
  return(p_LtCmp(p,q,r) == r->OrdSgn);
}

p_MaxComp() [1/2]

static long p_MaxComp ( poly  p, ring  lmRing  )

inlinestatic

Definition at line 311 of file p_polys.h.

{return p_MaxComp(p,lmRing,lmRing);}

p_MaxComp() [2/2]

static long p_MaxComp ( poly  p, ring  lmRing, ring  tailRing  )

inlinestatic

Definition at line 292 of file p_polys.h.

{
  long result,i;
 
  if(p==NULL) return 0;
  result = p_GetComp(p, lmRing);
  if (result != 0)
  {
    loop
    {
      pIter(p);
      if(p==NULL) break;
      i = p_GetComp(p, tailRing);
      if (i>result) result = i;
    }
  }
  return result;
}

p_MaxExpPerVar()

int p_MaxExpPerVar	(	poly	p,
		int	i,
		const ring	r
	)

max exponent of variable x_i in p

Definition at line 4992 of file p_polys.cc.

{
  int m=0;
  while(p!=NULL)
  {
    int mm=p_GetExp(p,i,r);
    if (mm>m) m=mm;
    pIter(p);
  }
  return m;
}

p_MDivide()

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

Definition at line 1492 of file p_polys.cc.

{
  assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0));
  int i;
  poly result = p_Init(r);
 
  for(i=(int)r->N; i; i--)
    p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r);
  p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r);
  p_Setm(result,r);
  return result;
}

p_MemAdd_NegWeightAdjust()

static void p_MemAdd_NegWeightAdjust ( poly  p, const ring  r  )

inlinestatic

Definition at line 1292 of file p_polys.h.

{
  if (r->NegWeightL_Offset != NULL)
  {
    for (int i=r->NegWeightL_Size-1; i>=0; i--)
    {
      p->exp[r->NegWeightL_Offset[i]] -= POLY_NEGWEIGHT_OFFSET;
    }
  }
}

p_MemSub_NegWeightAdjust()

static void p_MemSub_NegWeightAdjust ( poly  p, const ring  r  )

inlinestatic

Definition at line 1302 of file p_polys.h.

{
  if (r->NegWeightL_Offset != NULL)
  {
    for (int i=r->NegWeightL_Size-1; i>=0; i--)
    {
      p->exp[r->NegWeightL_Offset[i]] += POLY_NEGWEIGHT_OFFSET;
    }
  }
}

p_Merge_q()

static poly p_Merge_q ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1212 of file p_polys.h.

{
  assume( (p != q) || (p == NULL && q == NULL) );
  return r->p_Procs->p_Merge_q(p, q, r);
}

p_MinComp() [1/2]

static long p_MinComp ( poly  p, ring  lmRing  )

inlinestatic

Definition at line 332 of file p_polys.h.

{return p_MinComp(p,lmRing,lmRing);}

p_MinComp() [2/2]

static long p_MinComp ( poly  p, ring  lmRing, ring  tailRing  )

inlinestatic

Definition at line 313 of file p_polys.h.

{
  long result,i;
 
  if(p==NULL) return 0;
  result = p_GetComp(p,lmRing);
  if (result != 0)
  {
    loop
    {
      pIter(p);
      if(p==NULL) break;
      i = p_GetComp(p,tailRing);
      if (i<result) result = i;
    }
  }
  return result;
}

p_MinDeg()

int p_MinDeg	(	poly	p,
		intvec *	w,
		const ring	R
	)

Definition at line 4448 of file p_polys.cc.

{
  if(p==NULL)
    return -1;
  int d=-1;
  while(p!=NULL)
  {
    int d0=0;
    for(int j=0;j<rVar(R);j++)
      if(w==NULL||j>=w->length())
        d0+=p_GetExp(p,j+1,R);
      else
        d0+=(*w)[j]*p_GetExp(p,j+1,R);
    if(d0<d||d==-1)
      d=d0;
    pIter(p);
  }
  return d;
}

p_mInit()

poly p_mInit	(	const char *	s,
		BOOLEAN &	ok,
		const ring	r
	)

Definition at line 1442 of file p_polys.cc.

{
  poly p;
  char *sst=(char*)st;
  BOOLEAN neg=FALSE;
  if (sst[0]=='-') { neg=TRUE; sst=sst+1; }
  const char *s=p_Read(sst,p,r);
  if (*s!='\0')
  {
    if ((s!=sst)&&isdigit(sst[0]))
    {
      errorreported=TRUE;
    }
    ok=FALSE;
    if (p!=NULL)
    {
      if (pGetCoeff(p)==NULL) p_LmFree(p,r);
      else                    p_LmDelete(p,r);
    }
    return NULL;
  }
  p_Test(p,r);
  ok=!errorreported;
  if (neg) p=p_Neg(p,r);
  return p;
}

p_Minus_mm_Mult_qq() [1/2]

static poly p_Minus_mm_Mult_qq ( poly  p, const poly  m, const poly  q, const ring  r  )

inlinestatic

Definition at line 1081 of file p_polys.h.

{
  int shorter;
 
  return r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
}

p_Minus_mm_Mult_qq() [2/2]

static poly p_Minus_mm_Mult_qq ( poly  p, const poly  m, const poly  q, int &  lp, int  lq, const poly  spNoether, const ring  r  )

inlinestatic

Definition at line 1070 of file p_polys.h.

{
  int shorter;
  const poly res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, spNoether, r);
  lp += lq - shorter;
//  assume( lp == pLength(res) );
  return res;
}

p_mm_Mult()

static poly p_mm_Mult ( poly  p, poly  m, const ring  r  )

inlinestatic

Definition at line 1061 of file p_polys.h.

{
  if (p==NULL) return NULL;
  if (p_LmIsConstant(m, r))
    return __p_Mult_nn(p, pGetCoeff(m), r);
  else
    return r->p_Procs->p_mm_Mult(p, m, r);
}

p_Mult_mm()

static poly p_Mult_mm ( poly  p, poly  m, const ring  r  )

inlinestatic

Definition at line 1051 of file p_polys.h.

{
  if (p==NULL) return NULL;
  if (p_LmIsConstant(m, r))
    return __p_Mult_nn(p, pGetCoeff(m), r);
  else
    return r->p_Procs->p_Mult_mm(p, m, r);
}

p_Mult_nn() [1/2]

static poly p_Mult_nn ( poly  p, number  n, const ring  lmRing, const ring  tailRing  )

inlinestatic

Definition at line 973 of file p_polys.h.

{
  assume(p!=NULL);
#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);
  if (pnext!=NULL)
  {
    pNext(p) = tailRing->p_Procs->p_Mult_nn(pnext, n, tailRing);
  }
  return p;
}

p_Mult_nn() [2/2]

static poly p_Mult_nn ( poly  p, number  n, const ring  r  )

inlinestatic

Definition at line 958 of file p_polys.h.

{
  if (p==NULL) return NULL;
  if (n_IsOne(n, r->cf))
    return p;
  else if (n_IsZero(n, r->cf))
  {
    p_Delete(&p, r); // NOTE: without p_Delete - memory leak!
    return NULL;
  }
  else
    return r->p_Procs->p_Mult_nn(p, n, r);
}

p_Mult_q()

static poly p_Mult_q ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1114 of file p_polys.h.

{
  assume( (p != q) || (p == NULL && q == NULL) );
 
  if (p == NULL)
  {
    p_Delete(&q, r);
    return NULL;
  }
  if (q == NULL)
  {
    p_Delete(&p, r);
    return NULL;
  }
 
  if (pNext(p) == NULL)
  {
    q = r->p_Procs->p_mm_Mult(q, p, r);
    p_LmDelete(&p, r);
    return q;
  }
 
  if (pNext(q) == NULL)
  {
    p = r->p_Procs->p_Mult_mm(p, q, r);
    p_LmDelete(&q, r);
    return p;
  }
#if defined(HAVE_PLURAL) || defined(HAVE_SHIFTBBA)
  if (rIsNCRing(r))
    return _nc_p_Mult_q(p, q, r);
  else
#endif
  return _p_Mult_q(p, q, 0, r);
}

p_MultExp()

static long p_MultExp ( poly  p, int  v, long  ee, ring  r  )

inlinestatic

Definition at line 621 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  long e = p_GetExp(p,v,r);
  e *= ee;
  return p_SetExp(p,v,e,r);
}

p_Neg()

static poly p_Neg ( poly  p, const ring  r  )

inlinestatic

Definition at line 1107 of file p_polys.h.

{
  return r->p_Procs->p_Neg(p, r);
}

p_New() [1/2]

static poly p_New ( const ring  , omBin  bin  )

inlinestatic

Definition at line 664 of file p_polys.h.

{
  p_CheckRing2(r);
  pAssume2(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
  poly p;
  omTypeAllocBin(poly, p, bin);
  p_SetRingOfLm(p, r);
  return p;
}

p_New() [2/2]

static poly p_New ( ring  r )

inlinestatic

Definition at line 675 of file p_polys.h.

{
  return p_New(r, r->PolyBin);
}

p_Norm()

void p_Norm	(	poly	p1,
		const ring	r
	)

Definition at line 3719 of file p_polys.cc.

{
  if (LIKELY(rField_is_Ring(r)))
  {
    if(!n_GreaterZero(pGetCoeff(p1),r->cf)) p1 = p_Neg(p1,r);
    if (!n_IsUnit(pGetCoeff(p1), r->cf)) return;
    // Werror("p_Norm not possible in the case of coefficient rings.");
  }
  else if (LIKELY(p1!=NULL))
  {
    if (UNLIKELY(pNext(p1)==NULL))
    {
      p_SetCoeff(p1,n_Init(1,r->cf),r);
      return;
    }
    if (!n_IsOne(pGetCoeff(p1),r->cf))
    {
      number k = pGetCoeff(p1);
      pSetCoeff0(p1,n_Init(1,r->cf));
      poly h = pNext(p1);
      if (LIKELY(rField_is_Zp(r)))
      {
        if (r->cf->ch>32003)
        {
          number inv=n_Invers(k,r->cf);
          while (h!=NULL)
          {
            number c=n_Mult(pGetCoeff(h),inv,r->cf);
            // no need to normalize
            p_SetCoeff(h,c,r);
            pIter(h);
          }
          // no need for n_Delete for Zp: n_Delete(&inv,r->cf);
        }
        else
        {
          while (h!=NULL)
          {
            number c=n_Div(pGetCoeff(h),k,r->cf);
            // no need to normalize
            p_SetCoeff(h,c,r);
            pIter(h);
          }
        }
      }
      else if(getCoeffType(r->cf)==n_algExt)
      {
        n_Normalize(k,r->cf);
        number inv=n_Invers(k,r->cf);
        while (h!=NULL)
        {
          number c=n_Mult(pGetCoeff(h),inv,r->cf);
          // no need to normalize
          // normalize already in nMult: Zp_a, Q_a
          p_SetCoeff(h,c,r);
          pIter(h);
        }
        n_Delete(&inv,r->cf);
        n_Delete(&k,r->cf);
      }
      else
      {
        n_Normalize(k,r->cf);
        while (h!=NULL)
        {
          number c=n_Div(pGetCoeff(h),k,r->cf);
          // no need to normalize: Z/p, R
          // remains: Q
          if (rField_is_Q(r)) n_Normalize(c,r->cf);
          p_SetCoeff(h,c,r);
          pIter(h);
        }
        n_Delete(&k,r->cf);
      }
    }
    else
    {
      //if (r->cf->cfNormalize != nDummy2) //TODO: OPTIMIZE
      if (rField_is_Q(r))
      {
        poly h = pNext(p1);
        while (h!=NULL)
        {
          n_Normalize(pGetCoeff(h),r->cf);
          pIter(h);
        }
      }
    }
  }
}

p_Normalize()

void p_Normalize	(	poly	p,
		const ring	r
	)

Definition at line 3813 of file p_polys.cc.

{
  const coeffs cf=r->cf;
  /* Z/p, GF(p,n), R, long R/C, Nemo rings */
  if (cf->cfNormalize==ndNormalize)
    return;
  while (p!=NULL)
  {
    // no test befor n_Normalize: n_Normalize should fix problems
    n_Normalize(pGetCoeff(p),cf);
    pIter(p);
  }
}

p_NSet()

poly p_NSet	(	number	n,
		const ring	r
	)

returns the poly representing the number n, destroys n

Definition at line 1473 of file p_polys.cc.

{
  if (n_IsZero(n,r->cf))
  {
    n_Delete(&n, r->cf);
    return NULL;
  }
  else
  {
    poly rc = p_Init(r);
    pSetCoeff0(rc,n);
    return rc;
  }
}

p_One()

poly p_One

(

const ring

r

)

Definition at line 1313 of file p_polys.cc.

{
  poly rc = p_Init(r);
  pSetCoeff0(rc,n_Init(1,r->cf));
  return rc;
}

p_OneComp()

BOOLEAN p_OneComp	(	poly	p,
		const ring	r
	)

return TRUE if all monoms have the same component

Definition at line 1208 of file p_polys.cc.

{
  if(p!=NULL)
  {
    long i = p_GetComp(p, r);
    while (pNext(p)!=NULL)
    {
      pIter(p);
      if(i != p_GetComp(p, r)) return FALSE;
    }
  }
  return TRUE;
}

p_PermPoly()

poly p_PermPoly	(	poly	p,
		const int *	perm,
		const ring	OldRing,
		const ring	dst,
		nMapFunc	nMap,
		const int *	par_perm = NULL,
		int	OldPar = 0,
		BOOLEAN	use_mult = FALSE
	)

Definition at line 4130 of file p_polys.cc.

{
#if 0
    p_Test(p, oldRing);
    PrintS("p_PermPoly::p: "); p_Write(p, oldRing, oldRing);
#endif
  const int OldpVariables = rVar(oldRing);
  poly result = NULL;
  poly result_last = NULL;
  poly aq = NULL; /* the map coefficient */
  poly qq; /* the mapped monomial */
  assume(dst != NULL);
  assume(dst->cf != NULL);
  #ifdef HAVE_PLURAL
  poly tmp_mm=p_One(dst);
  #endif
  while (p != NULL)
  {
    // map the coefficient
    if ( ((OldPar == 0) || (par_perm == NULL) || rField_is_GF(oldRing) || (nMap==ndCopyMap))
    && (nMap != NULL) )
    {
      qq = p_Init(dst);
      assume( nMap != NULL );
      number n = nMap(p_GetCoeff(p, oldRing), oldRing->cf, dst->cf);
      n_Test (n,dst->cf);
      if ( nCoeff_is_algExt(dst->cf) )
        n_Normalize(n, dst->cf);
      p_GetCoeff(qq, dst) = n;// Note: n can be a ZERO!!!
    }
    else
    {
      qq = p_One(dst);
//      aq = naPermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing); // no dst???
//      poly    n_PermNumber(const number z, const int *par_perm, const int P, const ring src, const ring dst)
      aq = n_PermNumber(p_GetCoeff(p, oldRing), par_perm, OldPar, oldRing, dst);
      p_Test(aq, dst);
      if ( nCoeff_is_algExt(dst->cf) )
        p_Normalize(aq,dst);
      if (aq == NULL)
        p_SetCoeff(qq, n_Init(0, dst->cf),dst); // Very dirty trick!!!
      p_Test(aq, dst);
    }
    if (rRing_has_Comp(dst))
       p_SetComp(qq, p_GetComp(p, oldRing), dst);
    if ( n_IsZero(pGetCoeff(qq), dst->cf) )
    {
      p_LmDelete(&qq,dst);
      qq = NULL;
    }
    else
    {
      // map pars:
      int mapped_to_par = 0;
      for(int i = 1; i <= OldpVariables; i++)
      {
        int e = p_GetExp(p, i, oldRing);
        if (e != 0)
        {
          if (perm==NULL)
            p_SetExp(qq, i, e, dst);
          else if (perm[i]>0)
          {
            #ifdef HAVE_PLURAL
            if(use_mult)
            {
              p_SetExp(tmp_mm,perm[i],e,dst);
              p_Setm(tmp_mm,dst);
              qq=p_Mult_mm(qq,tmp_mm,dst);
              p_SetExp(tmp_mm,perm[i],0,dst);
 
            }
            else
            #endif
            p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst);
          }
          else if (perm[i]<0)
          {
            number c = p_GetCoeff(qq, dst);
            if (rField_is_GF(dst))
            {
              assume( dst->cf->extRing == NULL );
              number ee = n_Param(1, dst);
              number eee;
              n_Power(ee, e, &eee, dst->cf); //nfDelete(ee,dst);
              ee = n_Mult(c, eee, dst->cf);
              //nfDelete(c,dst);nfDelete(eee,dst);
              pSetCoeff0(qq,ee);
            }
            else if (nCoeff_is_Extension(dst->cf))
            {
              const int par = -perm[i];
              assume( par > 0 );
//              WarnS("longalg missing 3");
#if 1
              const coeffs C = dst->cf;
              assume( C != NULL );
              const ring R = C->extRing;
              assume( R != NULL );
              assume( par <= rVar(R) );
              poly pcn; // = (number)c
              assume( !n_IsZero(c, C) );
              if( nCoeff_is_algExt(C) )
                 pcn = (poly) c;
               else //            nCoeff_is_transExt(C)
                 pcn = NUM((fraction)c);
              if (pNext(pcn) == NULL) // c->z
                p_AddExp(pcn, -perm[i], e, R);
              else /* more difficult: we have really to multiply: */
              {
                poly mmc = p_ISet(1, R);
                p_SetExp(mmc, -perm[i], e, R);
                p_Setm(mmc, R);
                number nnc;
                // convert back to a number: number nnc = mmc;
                if( nCoeff_is_algExt(C) )
                   nnc = (number) mmc;
                else //            nCoeff_is_transExt(C)
                  nnc = ntInit(mmc, C);
                p_GetCoeff(qq, dst) = n_Mult((number)c, nnc, C);
                n_Delete((number *)&c, C);
                n_Delete((number *)&nnc, C);
              }
              mapped_to_par=1;
#endif
            }
          }
          else
          {
            /* this variable maps to 0 !*/
            p_LmDelete(&qq, dst);
            break;
          }
        }
      }
      if ( mapped_to_par && (qq!= NULL) && nCoeff_is_algExt(dst->cf) )
      {
        number n = p_GetCoeff(qq, dst);
        n_Normalize(n, dst->cf);
        p_GetCoeff(qq, dst) = n;
      }
    }
    pIter(p);
 
#if 0
    p_Test(aq,dst);
    PrintS("aq: "); p_Write(aq, dst, dst);
#endif
 
 
#if 1
    if (qq!=NULL)
    {
      p_Setm(qq,dst);
 
      p_Test(aq,dst);
      p_Test(qq,dst);
 
#if 0
    PrintS("qq: "); p_Write(qq, dst, dst);
#endif
 
      if (aq!=NULL)
         qq=p_Mult_q(aq,qq,dst);
      aq = qq;
      while (pNext(aq) != NULL) pIter(aq);
      if (result_last==NULL)
      {
        result=qq;
      }
      else
      {
        pNext(result_last)=qq;
      }
      result_last=aq;
      aq = NULL;
    }
    else if (aq!=NULL)
    {
      p_Delete(&aq,dst);
    }
  }
  result=p_SortAdd(result,dst);
#else
  //  if (qq!=NULL)
  //  {
  //    pSetm(qq);
  //    pTest(qq);
  //    pTest(aq);
  //    if (aq!=NULL) qq=pMult(aq,qq);
  //    aq = qq;
  //    while (pNext(aq) != NULL) pIter(aq);
  //    pNext(aq) = result;
  //    aq = NULL;
  //    result = qq;
  //  }
  //  else if (aq!=NULL)
  //  {
  //    pDelete(&aq);
  //  }
  //}
  //p = result;
  //result = NULL;
  //while (p != NULL)
  //{
  //  qq = p;
  //  pIter(p);
  //  qq->next = NULL;
  //  result = pAdd(result, qq);
  //}
#endif
  p_Test(result,dst);
#if 0
  p_Test(result,dst);
  PrintS("result: "); p_Write(result,dst,dst);
#endif
  #ifdef HAVE_PLURAL
  p_LmDelete(&tmp_mm,dst);
  #endif
  return result;
}

p_Plus_mm_Mult_qq() [1/2]

static poly p_Plus_mm_Mult_qq ( poly  p, poly  m, poly  q, const ring  r  )

inlinestatic

Definition at line 1205 of file p_polys.h.

{
  int lp = 0, lq = 0;
  return p_Plus_mm_Mult_qq(p, m, q, lp, lq, r);
}

p_Plus_mm_Mult_qq() [2/2]

static poly p_Plus_mm_Mult_qq ( poly  p, poly  m, poly  q, int &  lp, int  lq, const ring  r  )

inlinestatic

Definition at line 1183 of file p_polys.h.

{
#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;
  int shorter;
  number n_old = pGetCoeff(m);
  number n_neg = n_Copy(n_old, r->cf);
  n_neg = n_InpNeg(n_neg, r->cf);
  pSetCoeff0(m, n_neg);
  res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
  lp = (lp + lq) - shorter;
  pSetCoeff0(m, n_old);
  n_Delete(&n_neg, r->cf);
  return res;
}

p_PolyDiv()

poly p_PolyDiv	(	poly &	p,
		const poly	divisor,
		const BOOLEAN	needResult,
		const ring	r
	)

assumes that p and divisor are univariate polynomials in r, mentioning the same variable; assumes divisor != NULL; p may be NULL; assumes a global monomial ordering in r; performs polynomial division of p by divisor:

• afterwards p contains the remainder of the division, i.e., p_before = result * divisor + p_afterwards;
• if needResult == TRUE, then the method computes and returns 'result', otherwise NULL is returned (This parametrization can be used when one is only interested in the remainder of the division. In this case, the method will be slightly faster.) leaves divisor unmodified

Definition at line 1870 of file p_polys.cc.

{
  assume(divisor != NULL);
  if (p == NULL) return NULL;
 
  poly result = NULL;
  number divisorLC = p_GetCoeff(divisor, r);
  int divisorLE = p_GetExp(divisor, 1, r);
  while ((p != NULL) && (p_Deg(p, r) >= p_Deg(divisor, r)))
  {
    /* determine t = LT(p) / LT(divisor) */
    poly t = p_ISet(1, r);
    number c = n_Div(p_GetCoeff(p, r), divisorLC, r->cf);
    n_Normalize(c,r->cf);
    p_SetCoeff(t, c, r);
    int e = p_GetExp(p, 1, r) - divisorLE;
    p_SetExp(t, 1, e, r);
    p_Setm(t, r);
    if (needResult) result = p_Add_q(result, p_Copy(t, r), r);
    p = p_Add_q(p, p_Neg(p_Mult_q(t, p_Copy(divisor, r), r), r), r);
  }
  return result;
}

p_Power()

poly p_Power	(	poly	p,
		int	i,
		const ring	r
	)

Definition at line 2197 of file p_polys.cc.

{
  poly rc=NULL;
 
  if (i==0)
  {
    p_Delete(&p,r);
    return p_One(r);
  }
 
  if(p!=NULL)
  {
    if ( (i > 0) && ((unsigned long ) i > (r->bitmask))
    #ifdef HAVE_SHIFTBBA
    && (!rIsLPRing(r))
    #endif
    )
    {
      Werror("exponent %d is too large, max. is %ld",i,r->bitmask);
      return NULL;
    }
    switch (i)
    {
// cannot happen, see above
//      case 0:
//      {
//        rc=pOne();
//        pDelete(&p);
//        break;
//      }
      case 1:
        rc=p;
        break;
      case 2:
        rc=p_Mult_q(p_Copy(p,r),p,r);
        break;
      default:
        if (i < 0)
        {
          p_Delete(&p,r);
          return NULL;
        }
        else
        {
#ifdef HAVE_PLURAL
          if (rIsNCRing(r)) /* in the NC case nothing helps :-( */
          {
            int j=i;
            rc = p_Copy(p,r);
            while (j>1)
            {
              rc = p_Mult_q(p_Copy(p,r),rc,r);
              j--;
            }
            p_Delete(&p,r);
            return rc;
          }
#endif
          rc = pNext(p);
          if (rc == NULL)
            return p_MonPower(p,i,r);
          /* else: binom ?*/
          int char_p=rInternalChar(r);
          if ((char_p>0) && (i>char_p)
          && ((rField_is_Zp(r,char_p)
            || (rField_is_Zp_a(r,char_p)))))
          {
            poly h=p_Pow_charp(p_Copy(p,r),char_p,r);
            int rest=i-char_p;
            while (rest>=char_p)
            {
              rest-=char_p;
              h=p_Mult_q(h,p_Pow_charp(p_Copy(p,r),char_p,r),r);
            }
            poly res=h;
            if (rest>0)
              res=p_Mult_q(p_Power(p_Copy(p,r),rest,r),h,r);
            p_Delete(&p,r);
            return res;
          }
          if ((pNext(rc) != NULL)
             || rField_is_Ring(r)
             )
            return p_Pow(p,i,r);
          if ((char_p==0) || (i<=char_p))
            return p_TwoMonPower(p,i,r);
          return p_Pow(p,i,r);
        }
      /*end default:*/
    }
  }
  return rc;
}

p_ProjectiveUnique()

void p_ProjectiveUnique	(	poly	p,
		const ring	r
	)

Definition at line 3143 of file p_polys.cc.

{
  if( ph == NULL )
    return;
 
  const coeffs C = r->cf;
 
  number h;
  poly p;
 
  if (nCoeff_is_Ring(C))
  {
    p_ContentForGB(ph,r);
    if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r);
        assume( n_GreaterZero(pGetCoeff(ph),C) );
    return;
  }
 
  if (nCoeff_is_Zp(C) && TEST_OPT_INTSTRATEGY)
  {
    if(!n_GreaterZero(pGetCoeff(ph),C)) ph = p_Neg(ph,r);
    return;
  }
  p = ph;
 
  assume(p != NULL);
 
  if(pNext(p)==NULL) // a monomial
  {
    p_SetCoeff(p, n_Init(1, C), r);
    return;
  }
 
  assume(pNext(p)!=NULL);
 
  if(!nCoeff_is_Q(C) && !nCoeff_is_transExt(C))
  {
    h = p_GetCoeff(p, C);
    number hInv = n_Invers(h, C);
    pIter(p);
    while (p!=NULL)
    {
      p_SetCoeff(p, n_Mult(p_GetCoeff(p, C), hInv, C), r);
      pIter(p);
    }
    n_Delete(&hInv, C);
    p = ph;
    p_SetCoeff(p, n_Init(1, C), r);
  }
 
  p_Cleardenom(ph, r); //removes also Content
 
 
    /* normalize ph over a transcendental extension s.t.
       lead (ph) is > 0 if extRing->cf == Q
       or lead (ph) is monic if extRing->cf == Zp*/
  if (nCoeff_is_transExt(C))
  {
    p= ph;
    h= p_GetCoeff (p, C);
    fraction f = (fraction) h;
    number n=p_GetCoeff (NUM (f),C->extRing->cf);
    if (rField_is_Q (C->extRing))
    {
      if (!n_GreaterZero(n,C->extRing->cf))
      {
        p=p_Neg (p,r);
      }
    }
    else if (rField_is_Zp(C->extRing))
    {
      if (!n_IsOne (n, C->extRing->cf))
      {
        n=n_Invers (n,C->extRing->cf);
        nMapFunc nMap;
        nMap= n_SetMap (C->extRing->cf, C);
        number ninv= nMap (n,C->extRing->cf, C);
        p=__p_Mult_nn (p, ninv, r);
        n_Delete (&ninv, C);
        n_Delete (&n, C->extRing->cf);
      }
    }
    p= ph;
  }
 
  return;
}

p_Read()

const char * p_Read	(	const char *	s,
		poly &	p,
		const ring	r
	)

Definition at line 1370 of file p_polys.cc.

{
  if (r==NULL) { rc=NULL;return st;}
  int i,j;
  rc = p_Init(r);
  const char *s = n_Read(st,&(p_GetCoeff(rc, r)),r->cf);
  if (s==st)
  /* i.e. it does not start with a coeff: test if it is a ringvar*/
  {
    j = r_IsRingVar(s,r->names,r->N);
    if (j >= 0)
    {
      p_IncrExp(rc,1+j,r);
      while (*s!='\0') s++;
      goto done;
    }
  }
  while (*s!='\0')
  {
    char ss[2];
    ss[0] = *s++;
    ss[1] = '\0';
    j = r_IsRingVar(ss,r->names,r->N);
    if (j >= 0)
    {
      const char *s_save=s;
      s = eati(s,&i);
      if (((unsigned long)i) >  r->bitmask/2)
      {
        // exponent to large: it is not a monomial
        p_LmDelete(&rc,r);
        return s_save;
      }
      p_AddExp(rc,1+j, (long)i, r);
    }
    else
    {
      // 1st char of is not a varname
      // We return the parsed polynomial nevertheless. This is needed when
      // we are parsing coefficients in a rational function field.
      s--;
      break;
    }
  }
done:
  if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r);
  else
  {
#ifdef HAVE_PLURAL
    // in super-commutative ring
    // squares of anti-commutative variables are zeroes!
    if(rIsSCA(r))
    {
      const unsigned int iFirstAltVar = scaFirstAltVar(r);
      const unsigned int iLastAltVar  = scaLastAltVar(r);
 
      assume(rc != NULL);
 
      for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++)
        if( p_GetExp(rc, k, r) > 1 )
        {
          p_LmDelete(&rc, r);
          goto finish;
        }
    }
#endif
 
    p_Setm(rc,r);
  }
finish:
  return s;
}

p_Series()

poly p_Series	(	int	n,
		poly	p,
		poly	u,
		intvec *	w,
		const ring	R
	)

Definition at line 4498 of file p_polys.cc.

{
  int *ww=iv2array(w,R);
  if(p!=NULL)
  {
    if(u==NULL)
      p=p_JetW(p,n,ww,R);
    else
      p=p_JetW(p_Mult_q(p,p_Invers(n-p_MinDeg(p,w,R),u,w,R),R),n,ww,R);
  }
  omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(int));
  return p;
}

p_SetCoeff()

static number p_SetCoeff ( poly  p, number  n, ring  r  )

inlinestatic

Definition at line 412 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  n_Delete(&(p->coef), r->cf);
  (p)->coef=n;
  return n;
}

p_SetComp()

static unsigned long p_SetComp ( poly  p, unsigned long  c, ring  r  )

inlinestatic

Definition at line 247 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  if (r->pCompIndex>=0) __p_GetComp(p,r) = c;
  return c;
}

p_SetCompP() [1/2]

static void p_SetCompP ( poly  p, int  i, ring  lmRing, ring  tailRing  )

inlinestatic

Definition at line 281 of file p_polys.h.

{
  if (p != NULL)
  {
    p_SetComp(p, i, lmRing);
    p_SetmComp(p, lmRing);
    p_SetCompP(pNext(p), i, tailRing);
  }
}

p_SetCompP() [2/2]

static void p_SetCompP ( poly  p, int  i, ring  r  )

inlinestatic

Definition at line 254 of file p_polys.h.

{
  if (p != NULL)
  {
    p_Test(p, r);
    if (rOrd_SetCompRequiresSetm(r))
    {
      do
      {
        p_SetComp(p, i, r);
        p_SetmComp(p, r);
        pIter(p);
      }
      while (p != NULL);
    }
    else
    {
      do
      {
        p_SetComp(p, i, r);
        pIter(p);
      }
      while(p != NULL);
    }
  }
}

p_SetExp() [1/3]

static long p_SetExp ( poly  p, const int  v, const long  e, const ring  r  )

inlinestatic

set v^th exponent for a monomial

Definition at line 582 of file p_polys.h.

{
  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]);
}

p_SetExp() [2/3]

static long p_SetExp ( poly  p, const long  e, const ring  r, const int  VarOffset  )

inlinestatic

Definition at line 562 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  pAssume2(VarOffset != -1);
  return p_SetExp(p, e, r->bitmask, VarOffset);
}

p_SetExp() [3/3]

static unsigned long p_SetExp ( poly  p, const unsigned long  e, const unsigned long  iBitmask, const int  VarOffset  )

inlinestatic

set a single variable exponent @Note: VarOffset encodes the position in p->exp

See also

p_GetExp

Definition at line 488 of file p_polys.h.

{
  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;
}

p_SetExpV()

static void p_SetExpV ( poly  p, int *  ev, const ring  r  )

inlinestatic

Definition at line 1544 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      p_SetExp(p, j, ev[j], r);
 
  if(ev[0]!=0) p_SetComp(p, ev[0],r);
  p_Setm(p, r);
}

p_SetExpVL()

static void p_SetExpVL ( poly  p, int64 *  ev, const ring  r  )

inlinestatic

Definition at line 1553 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      p_SetExp(p, j, ev[j-1], r);
  p_SetComp(p, 0,r);
 
  p_Setm(p, r);
}

p_SetExpVLV()

static void p_SetExpVLV ( poly  p, int64 *  ev, int64  comp, const ring  r  )

inlinestatic

Definition at line 1564 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  for (unsigned j = r->N; j!=0; j--)
      p_SetExp(p, j, ev[j-1], r);
  p_SetComp(p, comp,r);
 
  p_Setm(p, r);
}

p_Setm()

static void p_Setm ( poly  p, const ring  r  )

inlinestatic

Definition at line 233 of file p_polys.h.

{
  p_CheckRing2(r);
  r->p_Setm(p, r);
}

p_SetModDeg()

void p_SetModDeg	(	intvec *	w,
		ring	r
	)

Definition at line 3673 of file p_polys.cc.

{
  if (w!=NULL)
  {
    r->pModW = w;
    pOldFDeg = r->pFDeg;
    pOldLDeg = r->pLDeg;
    pOldLexOrder = r->pLexOrder;
    pSetDegProcs(r,pModDeg);
    r->pLexOrder = TRUE;
  }
  else
  {
    r->pModW = NULL;
    pRestoreDegProcs(r,pOldFDeg, pOldLDeg);
    r->pLexOrder = pOldLexOrder;
  }
}

p_ShallowCopyDelete()

static poly p_ShallowCopyDelete ( poly  p, const ring  r, omBin  bin  )

inlinestatic

Definition at line 928 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  pAssume2(omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
  return r->p_Procs->p_ShallowCopyDelete(p, r, bin);
}

p_ShallowDelete()

void p_ShallowDelete	(	poly *	p,
		const ring	r
	)

p_Shift()

void p_Shift	(	poly *	p,
		int	i,
		const ring	r
	)

shifts components of the vector p by i

Definition at line 4706 of file p_polys.cc.

{
  poly qp1 = *p,qp2 = *p;/*working pointers*/
  int     j = p_MaxComp(*p,r),k = p_MinComp(*p,r);
 
  if (j+i < 0) return ;
  BOOLEAN toPoly= ((j == -i) && (j == k));
  while (qp1 != NULL)
  {
    if (toPoly || (__p_GetComp(qp1,r)+i > 0))
    {
      p_AddComp(qp1,i,r);
      p_SetmComp(qp1,r);
      qp2 = qp1;
      pIter(qp1);
    }
    else
    {
      if (qp2 == *p)
      {
        pIter(*p);
        p_LmDelete(&qp2,r);
        qp2 = *p;
        qp1 = *p;
      }
      else
      {
        qp2->next = qp1->next;
        if (qp1!=NULL) p_LmDelete(&qp1,r);
        qp1 = qp2->next;
      }
    }
  }
}

p_SimpleContent()

void p_SimpleContent	(	poly	p,
		int	s,
		const ring	r
	)

Definition at line 2564 of file p_polys.cc.

{
  if(TEST_OPT_CONTENTSB) return;
  if (ph==NULL) return;
  if (pNext(ph)==NULL)
  {
    p_SetCoeff(ph,n_Init(1,r->cf),r);
    return;
  }
  if (pNext(pNext(ph))==NULL)
  {
    return;
  }
  if (!(rField_is_Q(r))
  && (!rField_is_Q_a(r))
  && (!rField_is_Zp_a(r))
  && (!rField_is_Z(r))
  )
  {
    return;
  }
  number d=p_InitContent(ph,r);
  number h=d;
  if (n_Size(d,r->cf)<=smax)
  {
    n_Delete(&h,r->cf);
    //if (TEST_OPT_PROT) PrintS("G");
    return;
  }
 
  poly p=ph;
  if (smax==1) smax=2;
  while (p!=NULL)
  {
#if 1
    d=n_SubringGcd(h,pGetCoeff(p),r->cf);
    n_Delete(&h,r->cf);
    h = d;
#else
    n_InpGcd(h,pGetCoeff(p),r->cf);
#endif
    if(n_Size(h,r->cf)<smax)
    {
      //if (TEST_OPT_PROT) PrintS("g");
      n_Delete(&h,r->cf);
      return;
    }
    pIter(p);
  }
  p = ph;
  if (!n_GreaterZero(pGetCoeff(p),r->cf)) h=n_InpNeg(h,r->cf);
  if(n_IsOne(h,r->cf))
  {
    n_Delete(&h,r->cf);
    return;
  }
  if (TEST_OPT_PROT) PrintS("c");
  while (p!=NULL)
  {
#if 1
    d = n_ExactDiv(pGetCoeff(p),h,r->cf);
    p_SetCoeff(p,d,r);
#else
    STATISTIC(n_ExactDiv); nlInpExactDiv(pGetCoeff(p),h,r->cf); // no such function... ?
#endif
    pIter(p);
  }
  n_Delete(&h,r->cf);
}

p_Size()

int p_Size	(	poly	p,
		const ring	r
	)

Definition at line 3253 of file p_polys.cc.

{
  int count = 0;
  if (r->cf->has_simple_Alloc)
    return pLength(p);
  while ( p != NULL )
  {
    count+= n_Size( pGetCoeff( p ), r->cf );
    pIter( p );
  }
  return count;
}

p_SortAdd()

static poly p_SortAdd ( poly  p, const ring  r, BOOLEAN  revert = FALSE  )

inlinestatic

Definition at line 1219 of file p_polys.h.

{
  if (revert) p = pReverse(p);
  return sBucketSortAdd(p, r);
}

p_SortMerge()

static poly p_SortMerge ( poly  p, const ring  r, BOOLEAN  revert = FALSE  )

inlinestatic

Definition at line 1229 of file p_polys.h.

{
  if (revert) p = pReverse(p);
  return sBucketSortMerge(p, r);
}

p_Split()

void p_Split	(	poly	p,
		poly *	r
	)

Definition at line 1320 of file p_polys.cc.

{
  *h=pNext(p);
  pNext(p)=NULL;
}

p_String() [1/2]

char * p_String	(	poly	p,
		ring	lmRing,
		ring	tailRing
	)

Definition at line 322 of file polys0.cc.

{
  StringSetS("");
  p_String0(p, lmRing, tailRing);
  return StringEndS();
}

p_String() [2/2]

static char * p_String ( poly  p, ring  p_ring  )

inlinestatic

Definition at line 1240 of file p_polys.h.

{
  return p_String(p, p_ring, p_ring);
}

p_String0() [1/2]

void p_String0	(	poly	p,
		ring	lmRing,
		ring	tailRing
	)

print p according to ShortOut in lmRing & tailRing

Definition at line 223 of file polys0.cc.

{
  if (p == NULL)
  {
    StringAppendS("0");
    return;
  }
  p_Normalize(p,lmRing);
  if ((n_GetChar(lmRing->cf) == 0)
  && (nCoeff_is_transExt(lmRing->cf)))
    p_Normalize(p,lmRing); /* Manual/absfact.tst */
#ifdef HAVE_SHIFTBBA
  if(lmRing->isLPring)
  {
    if ((p_GetComp(p, lmRing) == 0) || (!lmRing->VectorOut))
    {
      writemonLP(p,0, lmRing);
      p = pNext(p);
      while (p!=NULL)
      {
        assume((p->coef==NULL)||(!n_IsZero(p->coef,tailRing->cf)));
        if ((p->coef==NULL)||n_GreaterZero(p->coef,tailRing->cf))
          StringAppendS("+");
        writemonLP(p,0, tailRing);
        p = pNext(p);
      }
      return;
    }
  }
  else
#endif
  {
    if ((p_GetComp(p, lmRing) == 0) || (!lmRing->VectorOut))
    {
      writemon(p,0, lmRing);
      p = pNext(p);
      while (p!=NULL)
      {
        assume((p->coef==NULL)||(!n_IsZero(p->coef,tailRing->cf)));
        if ((p->coef==NULL)||n_GreaterZero(p->coef,tailRing->cf))
          StringAppendS("+");
        writemon(p,0, tailRing);
        p = pNext(p);
      }
      return;
    }
  }
 
  long k = 1;
  StringAppendS("[");
#ifdef HAVE_SHIFTBBA
  if(lmRing->isLPring)
  {
    loop
    {
      while (k < p_GetComp(p,lmRing))
      {
        StringAppendS("0,");
        k++;
      }
      writemonLP(p,k,lmRing);
      pIter(p);
      while ((p!=NULL) && (k == p_GetComp(p, tailRing)))
      {
        if (n_GreaterZero(p->coef,tailRing->cf)) StringAppendS("+");
        writemonLP(p,k,tailRing);
        pIter(p);
      }
      if (p == NULL) break;
      StringAppendS(",");
      k++;
    }
  }
  else
#endif
  {
    loop
    {
      while (k < p_GetComp(p,lmRing))
      {
        StringAppendS("0,");
        k++;
      }
      writemon(p,k,lmRing);
      pIter(p);
      while ((p!=NULL) && (k == p_GetComp(p, tailRing)))
      {
        if (n_GreaterZero(p->coef,tailRing->cf)) StringAppendS("+");
        writemon(p,k,tailRing);
        pIter(p);
      }
      if (p == NULL) break;
      StringAppendS(",");
      k++;
    }
  }
  StringAppendS("]");
}

p_String0() [2/2]

static void p_String0 ( poly  p, ring  p_ring  )

inlinestatic

Definition at line 1244 of file p_polys.h.

{
  p_String0(p, p_ring, p_ring);
}

p_String0Long()

void p_String0Long	(	const poly	p,
		ring	lmRing,
		ring	tailRing
	)

print p in a long way

print p in a long way

Definition at line 203 of file polys0.cc.

{
  // NOTE: the following (non-thread-safe!) UGLYNESS
  // (changing naRing->ShortOut for a while) is due to Hans!
  // Just think of other ring using the VERY SAME naRing and possible
  // side-effects...
  // but this is not a problem: i/o is not thread-safe anyway.
  const BOOLEAN bLMShortOut = rShortOut(lmRing);
  const BOOLEAN bTAILShortOut = rShortOut(tailRing);
 
  lmRing->ShortOut = FALSE;
  tailRing->ShortOut = FALSE;
 
  p_String0(p, lmRing, tailRing);
 
  lmRing->ShortOut = bLMShortOut;
  tailRing->ShortOut = bTAILShortOut;
}

p_String0Short()

void p_String0Short	(	const poly	p,
		ring	lmRing,
		ring	tailRing
	)

print p in a short way, if possible

print p in a short way, if possible

Definition at line 184 of file polys0.cc.

{
  // NOTE: the following (non-thread-safe!) UGLYNESS
  // (changing naRing->ShortOut for a while) is due to Hans!
  // Just think of other ring using the VERY SAME naRing and possible
  // side-effects...
  const BOOLEAN bLMShortOut = rShortOut(lmRing);
  const BOOLEAN bTAILShortOut = rShortOut(tailRing);
 
  lmRing->ShortOut = rCanShortOut(lmRing);
  tailRing->ShortOut = rCanShortOut(tailRing);
 
  p_String0(p, lmRing, tailRing);
 
  lmRing->ShortOut = bLMShortOut;
  tailRing->ShortOut = bTAILShortOut;
}

p_Sub()

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

Definition at line 1990 of file p_polys.cc.

{
  return p_Add_q(p1, p_Neg(p2,r),r);
}

p_SubComp()

static unsigned long p_SubComp ( poly  p, unsigned long  v, ring  r  )

inlinestatic

Definition at line 453 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  pAssume2(rRing_has_Comp(r));
  _pPolyAssume2(__p_GetComp(p,r) >= v,p,r);
  return __p_GetComp(p,r) -= v;
}

p_SubExp()

static long p_SubExp ( poly  p, int  v, long  ee, ring  r  )

inlinestatic

Definition at line 613 of file p_polys.h.

{
  p_LmCheckPolyRing2(p, r);
  long e = p_GetExp(p,v,r);
  pAssume2(e >= ee);
  e -= ee;
  return p_SetExp(p,v,e,r);
}

p_Subst()

poly p_Subst	(	poly	p,
		int	n,
		poly	e,
		const ring	r
	)

Definition at line 3958 of file p_polys.cc.

{
#ifdef HAVE_SHIFTBBA
  // also don't even use p_Subst0 for Letterplace
  if (rIsLPRing(r))
  {
    poly subst = p_LPSubst(p, n, e, r);
    p_Delete(&p, r);
    return subst;
  }
#endif
 
  if (e == NULL) return p_Subst0(p, n,r);
 
  if (p_IsConstant(e,r))
  {
    if (n_IsOne(pGetCoeff(e),r->cf)) return p_Subst1(p,n,r);
    else return p_Subst2(p, n, pGetCoeff(e),r);
  }
 
#ifdef HAVE_PLURAL
  if (rIsPluralRing(r))
  {
    return nc_pSubst(p,n,e,r);
  }
#endif
 
  int exponent,i;
  poly h, res, m;
  int *me,*ee;
  number nu,nu1;
 
  me=(int *)omAlloc((rVar(r)+1)*sizeof(int));
  ee=(int *)omAlloc((rVar(r)+1)*sizeof(int));
  if (e!=NULL) p_GetExpV(e,ee,r);
  res=NULL;
  h=p;
  while (h!=NULL)
  {
    if ((e!=NULL) || (p_GetExp(h,n,r)==0))
    {
      m=p_Head(h,r);
      p_GetExpV(m,me,r);
      exponent=me[n];
      me[n]=0;
      for(i=rVar(r);i>0;i--)
        me[i]+=exponent*ee[i];
      p_SetExpV(m,me,r);
      if (e!=NULL)
      {
        n_Power(pGetCoeff(e),exponent,&nu,r->cf);
        nu1=n_Mult(pGetCoeff(m),nu,r->cf);
        n_Delete(&nu,r->cf);
        p_SetCoeff(m,nu1,r);
      }
      res=p_Add_q(res,m,r);
    }
    p_LmDelete(&h,r);
  }
  omFreeSize((ADDRESS)me,(rVar(r)+1)*sizeof(int));
  omFreeSize((ADDRESS)ee,(rVar(r)+1)*sizeof(int));
  return res;
}

p_TakeOutComp() [1/2]

poly p_TakeOutComp	(	poly *	p,
		int	k,
		const ring	r
	)

Definition at line 3435 of file p_polys.cc.

{
  poly q = *p,qq=NULL,result = NULL;
 
  if (q==NULL) return NULL;
  BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r);
  if (__p_GetComp(q,r)==k)
  {
    result = q;
    do
    {
      p_SetComp(q,0,r);
      if (use_setmcomp) p_SetmComp(q,r);
      qq = q;
      pIter(q);
    }
    while ((q!=NULL) && (__p_GetComp(q,r)==k));
    *p = q;
    pNext(qq) = NULL;
  }
  if (q==NULL) return result;
  if (__p_GetComp(q,r) > k)
  {
    p_SubComp(q,1,r);
    if (use_setmcomp) p_SetmComp(q,r);
  }
  poly pNext_q;
  while ((pNext_q=pNext(q))!=NULL)
  {
    if (__p_GetComp(pNext_q,r)==k)
    {
      if (result==NULL)
      {
        result = pNext_q;
        qq = result;
      }
      else
      {
        pNext(qq) = pNext_q;
        pIter(qq);
      }
      pNext(q) = pNext(pNext_q);
      pNext(qq) =NULL;
      p_SetComp(qq,0,r);
      if (use_setmcomp) p_SetmComp(qq,r);
    }
    else
    {
      /*pIter(q);*/ q=pNext_q;
      if (__p_GetComp(q,r) > k)
      {
        p_SubComp(q,1,r);
        if (use_setmcomp) p_SetmComp(q,r);
      }
    }
  }
  return result;
}

p_TakeOutComp() [2/2]

void p_TakeOutComp	(	poly *	p,
		long	comp,
		poly *	q,
		int *	lq,
		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.

Definition at line 3496 of file p_polys.cc.

{
  spolyrec pp, qq;
  poly p, q, p_prev;
  int l = 0;
 
#ifndef SING_NDEBUG
  int lp = pLength(*r_p);
#endif
 
  pNext(&pp) = *r_p;
  p = *r_p;
  p_prev = &pp;
  q = &qq;
 
  while(p != NULL)
  {
    while (__p_GetComp(p,r) == comp)
    {
      pNext(q) = p;
      pIter(q);
      p_SetComp(p, 0,r);
      p_SetmComp(p,r);
      pIter(p);
      l++;
      if (p == NULL)
      {
        pNext(p_prev) = NULL;
        goto Finish;
      }
    }
    pNext(p_prev) = p;
    p_prev = p;
    pIter(p);
  }
 
  Finish:
  pNext(q) = NULL;
  *r_p = pNext(&pp);
  *r_q = pNext(&qq);
  *lq = l;
#ifndef SING_NDEBUG
  assume(pLength(*r_p) + pLength(*r_q) == (unsigned)lp);
#endif
  p_Test(*r_p,r);
  p_Test(*r_q,r);
}

p_Totaldegree()

static long p_Totaldegree ( poly  p, const ring  r  )

inlinestatic

Definition at line 1507 of file p_polys.h.

{
  p_LmCheckPolyRing1(p, r);
  unsigned long s = p_GetTotalDegree(p->exp[r->VarL_Offset[0]],
                                     r,
                                     r->ExpPerLong);
  for (unsigned i=r->VarL_Size-1; i!=0; i--)
  {
    s += p_GetTotalDegree(p->exp[r->VarL_Offset[i]], r,r->ExpPerLong);
  }
  return (long)s;
}

p_Var()

int p_Var	(	poly	mi,
		const ring	r
	)

Definition at line 4656 of file p_polys.cc.

{
  if (m==NULL) return 0;
  if (pNext(m)!=NULL) return 0;
  int i,e=0;
  for (i=rVar(r); i>0; i--)
  {
    int exp=p_GetExp(m,i,r);
    if (exp==1)
    {
      if (e==0) e=i;
      else return 0;
    }
    else if (exp!=0)
    {
      return 0;
    }
  }
  return e;
}

p_Vec2Array()

void p_Vec2Array	(	poly	v,
		poly *	p,
		int	len,
		const ring	r
	)

julia: vector to already allocated array (len=p_MaxComp(v,r))

julia: vector to already allocated array (len=p_MaxComp(v,r))

Definition at line 3595 of file p_polys.cc.

{
  poly h;
  int k;
 
  for(int i=len-1;i>=0;i--) p[i]=NULL;
  while (v!=NULL)
  {
    h=p_Head(v,r);
    k=__p_GetComp(h,r);
    if (k>len) { Werror("wrong rank:%d, should be %d",len,k); }
    else
    {
      p_SetComp(h,0,r);
      p_Setm(h,r);
      pNext(h)=p[k-1];p[k-1]=h;
    }
    pIter(v);
  }
  for(int i=len-1;i>=0;i--)
  {
    if (p[i]!=NULL) p[i]=pReverse(p[i]);
  }
}

p_Vec2Poly()

poly p_Vec2Poly	(	poly	v,
		int	k,
		const ring	r
	)

Definition at line 3573 of file p_polys.cc.

{
  poly h;
  poly res=NULL;
  long unsigned kk=k;
 
  while (v!=NULL)
  {
    if (__p_GetComp(v,r)==kk)
    {
      h=p_Head(v,r);
      p_SetComp(h,0,r);
      pNext(h)=res;res=h;
    }
    pIter(v);
  }
  if (res!=NULL) res=pReverse(res);
  return res;
}

p_Vec2Polys()

void p_Vec2Polys	(	poly	v,
		poly **	p,
		int *	len,
		const ring	r
	)

Definition at line 3625 of file p_polys.cc.

{
  *len=p_MaxComp(v,r);
  if (*len==0) *len=1;
  *p=(poly*)omAlloc((*len)*sizeof(poly));
  p_Vec2Array(v,*p,*len,r);
}

p_VectorHasUnit()

void p_VectorHasUnit	(	poly	p,
		int *	k,
		int *	len,
		const ring	r
	)

Definition at line 3402 of file p_polys.cc.

{
  poly q=p,qq;
  int j=0;
  long unsigned i;
 
  *len = 0;
  while (q!=NULL)
  {
    if (p_LmIsConstantComp(q,r))
    {
      i = __p_GetComp(q,r);
      qq = p;
      while ((qq != q) && (__p_GetComp(qq,r) != i)) pIter(qq);
      if (qq == q)
      {
       j = 0;
       while (qq!=NULL)
       {
         if (__p_GetComp(qq,r)==i) j++;
         pIter(qq);
       }
       if ((*len == 0) || (j<*len))
       {
         *len = j;
         *k = i;
       }
      }
    }
    pIter(q);
  }
}

p_VectorHasUnitB()

BOOLEAN p_VectorHasUnitB	(	poly	p,
		int *	k,
		const ring	r
	)

Definition at line 3379 of file p_polys.cc.

{
  poly q=p,qq;
  long unsigned i;
 
  while (q!=NULL)
  {
    if (p_LmIsConstantComp(q,r))
    {
      i = __p_GetComp(q,r);
      qq = p;
      while ((qq != q) && (__p_GetComp(qq,r) != i)) pIter(qq);
      if (qq == q)
      {
        *k = i;
        return TRUE;
      }
    }
    pIter(q);
  }
  return FALSE;
}

p_WDegree()

long p_WDegree	(	poly	p,
		const ring	r
	)

Definition at line 714 of file p_polys.cc.

{
  if (r->firstwv==NULL) return p_Totaldegree(p, r);
  p_LmCheckPolyRing(p, r);
  int i;
  long j =0;
 
  for(i=1;i<=r->firstBlockEnds;i++)
    j+=p_GetExp(p, i, r)*r->firstwv[i-1];
 
  for (;i<=rVar(r);i++)
    j+=p_GetExp(p,i, r)*p_Weight(i, r);
 
  return j;
}

p_Weight()

int p_Weight	(	int	c,
		const ring	r
	)

Definition at line 705 of file p_polys.cc.

{
  if ((r->firstwv==NULL) || (i>r->firstBlockEnds))
  {
    return 1;
  }
  return r->firstwv[i-1];
}

p_WFirstTotalDegree()

long p_WFirstTotalDegree	(	poly	p,
		ring	r
	)

Definition at line 596 of file p_polys.cc.

{
  int i;
  long sum = 0;
 
  for (i=1; i<= r->firstBlockEnds; i++)
  {
    sum += p_GetExp(p, i, r)*r->firstwv[i-1];
  }
  return sum;
}

p_Write() [1/2]

void p_Write	(	poly	p,
		ring	lmRing,
		ring	tailRing
	)

Definition at line 342 of file polys0.cc.

{
  p_Write0(p, lmRing, tailRing);
  PrintLn();
}

p_Write() [2/2]

static void p_Write ( poly  p, ring  p_ring  )

inlinestatic

Definition at line 1248 of file p_polys.h.

{
  p_Write(p, p_ring, p_ring);
}

p_Write0() [1/2]

void p_Write0	(	poly	p,
		ring	lmRing,
		ring	tailRing
	)

Definition at line 332 of file polys0.cc.

{
  char *s=p_String(p, lmRing, tailRing);
  PrintS(s);
  omFree(s);
}

p_Write0() [2/2]

static void p_Write0 ( poly  p, ring  p_ring  )

inlinestatic

Definition at line 1252 of file p_polys.h.

{
  p_Write0(p, p_ring, p_ring);
}

p_wrp() [1/2]

void p_wrp	(	poly	p,
		ring	lmRing,
		ring	tailRing
	)

Definition at line 373 of file polys0.cc.

{
  poly r;
 
  if (p==NULL) PrintS("NULL");
  else if (pNext(p)==NULL) p_Write0(p, lmRing);
  else
  {
    r = pNext(pNext(p));
    pNext(pNext(p)) = NULL;
    p_Write0(p, tailRing);
    if (r!=NULL)
    {
      PrintS("+...");
      pNext(pNext(p)) = r;
    }
  }
}

p_wrp() [2/2]

static void p_wrp ( poly  p, ring  p_ring  )

inlinestatic

Definition at line 1256 of file p_polys.h.

{
  p_wrp(p, p_ring, p_ring);
}

p_WTotaldegree()

long p_WTotaldegree	(	poly	p,
		const ring	r
	)

Definition at line 613 of file p_polys.cc.

{
  p_LmCheckPolyRing(p, r);
  int i, k;
  long j =0;
 
  // iterate through each block:
  for (i=0;r->order[i]!=0;i++)
  {
    int b0=r->block0[i];
    int b1=r->block1[i];
    switch(r->order[i])
    {
      case ringorder_M:
        for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++)
        { // in jedem block:
          j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn;
        }
        break;
      case ringorder_am:
        b1=si_min(b1,r->N);
        /* no break, continue as ringorder_a*/
      case ringorder_a:
        for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++)
        { // only one line
          j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/];
        }
        return j*r->OrdSgn;
      case ringorder_wp:
      case ringorder_ws:
      case ringorder_Wp:
      case ringorder_Ws:
        for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++)
        { // in jedem block:
          j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/];
        }
        break;
      case ringorder_lp:
      case ringorder_ls:
      case ringorder_rs:
      case ringorder_dp:
      case ringorder_ds:
      case ringorder_Dp:
      case ringorder_Ds:
      case ringorder_rp:
        for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++)
        {
          j+= p_GetExp(p,k,r);
        }
        break;
      case ringorder_a64:
        {
          int64* w=(int64*)r->wvhdl[i];
          for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++)
          {
            //there should be added a line which checks if w[k]>2^31
            j+= p_GetExp(p,k+1, r)*(long)w[k];
          }
          //break;
          return j;
        }
      case ringorder_c: /* nothing to do*/
      case ringorder_C: /* nothing to do*/
      case ringorder_S: /* nothing to do*/
      case ringorder_s: /* nothing to do*/
      case ringorder_IS: /* nothing to do */
      case ringorder_unspec: /* to make clang happy, does not occur*/
      case ringorder_no: /* to make clang happy, does not occur*/
      case ringorder_L: /* to make clang happy, does not occur*/
      case ringorder_aa: /* ignored by p_WTotaldegree*/
        break;
    /* no default: all orderings covered */
    }
  }
  return  j;
}

pEnlargeSet()

void pEnlargeSet	(	poly **	p,
		int	length,
		int	increment
	)

Definition at line 3696 of file p_polys.cc.

{
  poly* h;
 
  if (increment==0) return;
  if (*p==NULL)
  {
    h=(poly*)omAlloc0(increment*sizeof(poly));
  }
  else
  {
    h=(poly*)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly));
    if (increment>0)
    {
      memset(&(h[l]),0,increment*sizeof(poly));
    }
  }
  *p=h;
}

pHaveCommonMonoms()

BOOLEAN pHaveCommonMonoms	(	poly	p,
		poly	q
	)

Definition at line 178 of file pDebug.cc.

{
  while (p != NULL)
  {
    if (pIsMonomOf(q, p))
    {
      return TRUE;
    }
    pIter(p);
  }
  return FALSE;
}

pIsMonomOf()

BOOLEAN pIsMonomOf	(	poly	p,
		poly	m
	)

Definition at line 168 of file pDebug.cc.

{
  if (m == NULL) return TRUE;
  while (p != NULL)
  {
    if (p == m) return TRUE;
    pIter(p);
  }
  return FALSE;
}

pLDeg0()

long pLDeg0	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 739 of file p_polys.cc.

{
  p_CheckPolyRing(p, r);
  long unsigned k= p_GetComp(p, r);
  int ll=1;
 
  if (k > 0)
  {
    while ((pNext(p)!=NULL) && (__p_GetComp(pNext(p), r)==k))
    {
      pIter(p);
      ll++;
    }
  }
  else
  {
     while (pNext(p)!=NULL)
     {
       pIter(p);
       ll++;
     }
  }
  *l=ll;
  return r->pFDeg(p, r);
}

pLDeg0c()

long pLDeg0c	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 770 of file p_polys.cc.

{
  assume(p!=NULL);
  p_Test(p,r);
  p_CheckPolyRing(p, r);
  long o;
  int ll=1;
 
  if (! rIsSyzIndexRing(r))
  {
    while (pNext(p) != NULL)
    {
      pIter(p);
      ll++;
    }
    o = r->pFDeg(p, r);
  }
  else
  {
    long unsigned curr_limit = rGetCurrSyzLimit(r);
    poly pp = p;
    while ((p=pNext(p))!=NULL)
    {
      if (__p_GetComp(p, r)<=curr_limit/*syzComp*/)
        ll++;
      else break;
      pp = p;
    }
    p_Test(pp,r);
    o = r->pFDeg(pp, r);
  }
  *l=ll;
  return o;
}

pLDeg1()

long pLDeg1	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 841 of file p_polys.cc.

{
  p_CheckPolyRing(p, r);
  long unsigned k= p_GetComp(p, r);
  int ll=1;
  long  t,max;
 
  max=r->pFDeg(p, r);
  if (k > 0)
  {
    while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k))
    {
      t=r->pFDeg(p, r);
      if (t>max) max=t;
      ll++;
    }
  }
  else
  {
    while ((p=pNext(p))!=NULL)
    {
      t=r->pFDeg(p, r);
      if (t>max) max=t;
      ll++;
    }
  }
  *l=ll;
  return max;
}

pLDeg1_Deg()

long pLDeg1_Deg	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 910 of file p_polys.cc.

{
  assume(r->pFDeg == p_Deg);
  p_CheckPolyRing(p, r);
  long unsigned k= p_GetComp(p, r);
  int ll=1;
  long  t,max;
 
  max=p_GetOrder(p, r);
  if (k > 0)
  {
    while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k))
    {
      t=p_GetOrder(p, r);
      if (t>max) max=t;
      ll++;
    }
  }
  else
  {
    while ((p=pNext(p))!=NULL)
    {
      t=p_GetOrder(p, r);
      if (t>max) max=t;
      ll++;
    }
  }
  *l=ll;
  return max;
}

pLDeg1_Totaldegree()

long pLDeg1_Totaldegree	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 975 of file p_polys.cc.

{
  p_CheckPolyRing(p, r);
  long unsigned k= p_GetComp(p, r);
  int ll=1;
  long  t,max;
 
  max=p_Totaldegree(p, r);
  if (k > 0)
  {
    while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k))
    {
      t=p_Totaldegree(p, r);
      if (t>max) max=t;
      ll++;
    }
  }
  else
  {
    while ((p=pNext(p))!=NULL)
    {
      t=p_Totaldegree(p, r);
      if (t>max) max=t;
      ll++;
    }
  }
  *l=ll;
  return max;
}

pLDeg1_WFirstTotalDegree()

long pLDeg1_WFirstTotalDegree	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 1038 of file p_polys.cc.

{
  p_CheckPolyRing(p, r);
  long unsigned k= p_GetComp(p, r);
  int ll=1;
  long  t,max;
 
  max=p_WFirstTotalDegree(p, r);
  if (k > 0)
  {
    while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k))
    {
      t=p_WFirstTotalDegree(p, r);
      if (t>max) max=t;
      ll++;
    }
  }
  else
  {
    while ((p=pNext(p))!=NULL)
    {
      t=p_WFirstTotalDegree(p, r);
      if (t>max) max=t;
      ll++;
    }
  }
  *l=ll;
  return max;
}

pLDeg1c()

long pLDeg1c	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 877 of file p_polys.cc.

{
  p_CheckPolyRing(p, r);
  int ll=1;
  long  t,max;
 
  max=r->pFDeg(p, r);
  if (rIsSyzIndexRing(r))
  {
    long unsigned limit = rGetCurrSyzLimit(r);
    while ((p=pNext(p))!=NULL)
    {
      if (__p_GetComp(p, r)<=limit)
      {
        if ((t=r->pFDeg(p, r))>max) max=t;
        ll++;
      }
      else break;
    }
  }
  else
  {
    while ((p=pNext(p))!=NULL)
    {
      if ((t=r->pFDeg(p, r))>max) max=t;
      ll++;
    }
  }
  *l=ll;
  return max;
}

pLDeg1c_Deg()

long pLDeg1c_Deg	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 941 of file p_polys.cc.

{
  assume(r->pFDeg == p_Deg);
  p_CheckPolyRing(p, r);
  int ll=1;
  long  t,max;
 
  max=p_GetOrder(p, r);
  if (rIsSyzIndexRing(r))
  {
    long unsigned limit = rGetCurrSyzLimit(r);
    while ((p=pNext(p))!=NULL)
    {
      if (__p_GetComp(p, r)<=limit)
      {
        if ((t=p_GetOrder(p, r))>max) max=t;
        ll++;
      }
      else break;
    }
  }
  else
  {
    while ((p=pNext(p))!=NULL)
    {
      if ((t=p_GetOrder(p, r))>max) max=t;
      ll++;
    }
  }
  *l=ll;
  return max;
}

pLDeg1c_Totaldegree()

long pLDeg1c_Totaldegree	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 1005 of file p_polys.cc.

{
  p_CheckPolyRing(p, r);
  int ll=1;
  long  t,max;
 
  max=p_Totaldegree(p, r);
  if (rIsSyzIndexRing(r))
  {
    long unsigned limit = rGetCurrSyzLimit(r);
    while ((p=pNext(p))!=NULL)
    {
      if (__p_GetComp(p, r)<=limit)
      {
        if ((t=p_Totaldegree(p, r))>max) max=t;
        ll++;
      }
      else break;
    }
  }
  else
  {
    while ((p=pNext(p))!=NULL)
    {
      if ((t=p_Totaldegree(p, r))>max) max=t;
      ll++;
    }
  }
  *l=ll;
  return max;
}

pLDeg1c_WFirstTotalDegree()

long pLDeg1c_WFirstTotalDegree	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 1068 of file p_polys.cc.

{
  p_CheckPolyRing(p, r);
  int ll=1;
  long  t,max;
 
  max=p_WFirstTotalDegree(p, r);
  if (rIsSyzIndexRing(r))
  {
    long unsigned limit = rGetCurrSyzLimit(r);
    while ((p=pNext(p))!=NULL)
    {
      if (__p_GetComp(p, r)<=limit)
      {
        if ((t=p_Totaldegree(p, r))>max) max=t;
        ll++;
      }
      else break;
    }
  }
  else
  {
    while ((p=pNext(p))!=NULL)
    {
      if ((t=p_Totaldegree(p, r))>max) max=t;
      ll++;
    }
  }
  *l=ll;
  return max;
}

pLDegb()

long pLDegb	(	poly	p,
		int *	l,
		ring	r
	)

Definition at line 811 of file p_polys.cc.

{
  p_CheckPolyRing(p, r);
  long unsigned k= p_GetComp(p, r);
  long o = r->pFDeg(p, r);
  int ll=1;
 
  if (k != 0)
  {
    while (((p=pNext(p))!=NULL) && (__p_GetComp(p, r)==k))
    {
      ll++;
    }
  }
  else
  {
    while ((p=pNext(p)) !=NULL)
    {
      ll++;
    }
  }
  *l=ll;
  return o;
}

pLength()

static int pLength ( poly  a )

inlinestatic

Definition at line 190 of file p_polys.h.

{
  int l = 0;
  while (a!=NULL)
  {
    pIter(a);
    l++;
  }
  return l;
}

pp_DivideM()

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

Definition at line 1633 of file p_polys.cc.

{
  if (a==NULL) { return NULL; }
  // TODO: better implementation without copying a,b
  return p_DivideM(p_Copy(a,r),p_Head(b,r),r);
}

pp_Jet()

poly pp_Jet	(	poly	p,
		int	m,
		const ring	R
	)

Definition at line 4358 of file p_polys.cc.

{
  poly r=NULL;
  poly t=NULL;
 
  while (p!=NULL)
  {
    if (p_Totaldegree(p,R)<=m)
    {
      if (r==NULL)
        r=p_Head(p,R);
      else
      if (t==NULL)
      {
        pNext(r)=p_Head(p,R);
        t=pNext(r);
      }
      else
      {
        pNext(t)=p_Head(p,R);
        pIter(t);
      }
    }
    pIter(p);
  }
  return r;
}

pp_JetW()

poly pp_JetW	(	poly	p,
		int	m,
		int *	w,
		const ring	R
	)

Definition at line 4403 of file p_polys.cc.

{
  poly r=NULL;
  poly t=NULL;
  while (p!=NULL)
  {
    if (totaldegreeWecart_IV(p,R,w)<=m)
    {
      if (r==NULL)
        r=p_Head(p,R);
      else
      if (t==NULL)
      {
        pNext(r)=p_Head(p,R);
        t=pNext(r);
      }
      else
      {
        pNext(t)=p_Head(p,R);
        pIter(t);
      }
    }
    pIter(p);
  }
  return r;
}

pp_mm_Mult()

static poly pp_mm_Mult ( poly  p, poly  m, const ring  r  )

inlinestatic

Definition at line 1041 of file p_polys.h.

{
  if (p==NULL) return NULL;
  if (p_LmIsConstant(m, r))
    return __pp_Mult_nn(p, pGetCoeff(m), r);
  else
    return r->p_Procs->pp_mm_Mult(p, m, r);
}

pp_Mult_Coeff_mm_DivSelect() [1/2]

static poly pp_Mult_Coeff_mm_DivSelect ( poly  p, const poly  m, const ring  r  )

inlinestatic

Definition at line 1090 of file p_polys.h.

{
  int shorter;
  return r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
}

pp_Mult_Coeff_mm_DivSelect() [2/2]

static poly pp_Mult_Coeff_mm_DivSelect ( poly  p, int &  lp, const poly  m, const ring  r  )

inlinestatic

Definition at line 1098 of file p_polys.h.

{
  int shorter;
  poly pp = r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
  lp -= shorter;
  return pp;
}

pp_Mult_mm()

static poly pp_Mult_mm ( poly  p, poly  m, const ring  r  )

inlinestatic

Definition at line 1031 of file p_polys.h.

{
  if (p==NULL) return NULL;
  if (p_LmIsConstant(m, r))
    return __pp_Mult_nn(p, pGetCoeff(m), r);
  else
    return r->p_Procs->pp_Mult_mm(p, m, r);
}

pp_Mult_nn()

static poly pp_Mult_nn ( poly  p, number  n, const ring  r  )

inlinestatic

Definition at line 992 of file p_polys.h.

{
  if (p==NULL) return NULL;
  if (n_IsOne(n, r->cf))
    return p_Copy(p, r);
  else if (n_IsZero(n, r->cf))
    return NULL;
  else
    return r->p_Procs->pp_Mult_nn(p, n, r);
}

pp_Mult_qq()

static poly pp_Mult_qq ( poly  p, poly  q, const ring  r  )

inlinestatic

Definition at line 1151 of file p_polys.h.

{
  if (p == NULL || q == NULL) return NULL;
 
  if (pNext(p) == NULL)
  {
    return r->p_Procs->pp_mm_Mult(q, p, r);
  }
 
  if (pNext(q) == NULL)
  {
    return r->p_Procs->pp_Mult_mm(p, q, r);
  }
 
  poly qq = q;
  if (p == q)
    qq = p_Copy(q, r);
 
  poly res;
#if defined(HAVE_PLURAL) || defined(HAVE_SHIFTBBA)
  if (rIsNCRing(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;
}

pRestoreDegProcs()

void pRestoreDegProcs	(	ring	r,
		pFDegProc	old_FDeg,
		pLDegProc	old_lDeg
	)

Definition at line 3649 of file p_polys.cc.

{
  assume(old_FDeg != NULL && old_lDeg != NULL);
  r->pFDeg = old_FDeg;
  r->pLDeg = old_lDeg;
}

pReverse()

static poly pReverse ( poly  p )

inlinestatic

Definition at line 335 of file p_polys.h.

{
  if (p == NULL || pNext(p) == NULL) return p;
 
  poly q = pNext(p), // == pNext(p)
    qn;
  pNext(p) = NULL;
  do
  {
    qn = pNext(q);
    pNext(q) = p;
    p = q;
    q = qn;
  }
  while (qn != NULL);
  return p;
}

pSetDegProcs()

void pSetDegProcs	(	ring	r,
		pFDegProc	new_FDeg,
		pLDegProc	new_lDeg = NULL
	)

Definition at line 3637 of file p_polys.cc.

{
  assume(new_FDeg != NULL);
  r->pFDeg = new_FDeg;
 
  if (new_lDeg == NULL)
    new_lDeg = r->pLDegOrig;
 
  r->pLDeg = new_lDeg;
}