p_polys.cc File Reference

#include <ctype.h>
#include "misc/auxiliary.h"
#include "misc/options.h"
#include "misc/intvec.h"
#include "coeffs/longrat.h"
#include "coeffs/numbers.h"
#include "polys/PolyEnumerator.h"
#include "polys/ext_fields/transext.h"
#include "polys/ext_fields/algext.h"
#include "polys/weight.h"
#include "polys/simpleideals.h"
#include "ring.h"
#include "p_polys.h"
#include "polys/templates/p_MemCmp.h"
#include "polys/templates/p_MemAdd.h"
#include "polys/templates/p_MemCopy.h"
#include "nc/nc.h"
#include "nc/sca.h"
#include "polys/shiftop.h"
#include "clapsing.h"
#include "polys/templates/p_Delete__T.cc"

Go to the source code of this file.

Macros
#define	TRANSEXT_PRIVATES
#define	MYTEST   0
#define	CLEARENUMERATORS   1
#define	Sy_bit_L(x)   (((unsigned long)1L)<<(x))
#define	LINKAGE
#define	p_Delete__T   p_ShallowDelete
#define	n_Delete__T(n, r)   do {} while (0)

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)
void	p_Setm_General (poly p, const ring r)
void	p_Setm_Syz (poly p, ring r, int *Components, long *ShiftedComponents)
void	p_Setm_Dummy (poly p, const ring r)
void	p_Setm_TotalDegree (poly p, const ring r)
void	p_Setm_WFirstTotalDegree (poly p, const ring r)
p_SetmProc	p_GetSetmProc (const ring r)
long	p_Deg (poly a, const ring r)
long	p_WFirstTotalDegree (poly p, const ring r)
long	p_WTotaldegree (poly p, const ring r)
long	p_DegW (poly p, const int *w, const ring R)
int	p_Weight (int i, const ring r)
long	p_WDegree (poly p, const ring r)
long	pLDeg0 (poly p, int *l, const ring r)
long	pLDeg0c (poly p, int *l, const ring r)
long	pLDegb (poly p, int *l, const ring r)
long	pLDeg1 (poly p, int *l, const ring r)
long	pLDeg1c (poly p, int *l, const ring r)
long	pLDeg1_Deg (poly p, int *l, const ring r)
long	pLDeg1c_Deg (poly p, int *l, const ring r)
long	pLDeg1_Totaldegree (poly p, int *l, const ring r)
long	pLDeg1c_Totaldegree (poly p, int *l, const ring r)
long	pLDeg1_WFirstTotalDegree (poly p, int *l, const ring r)
long	pLDeg1c_WFirstTotalDegree (poly p, int *l, const ring r)
static unsigned long	p_GetMaxExpL2 (unsigned long l1, unsigned long l2, const ring r, unsigned long number_of_exp)
static unsigned long	p_GetMaxExpL2 (unsigned long l1, unsigned long l2, const ring r)
poly	p_GetMaxExpP (poly p, const 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 More...
unsigned long	p_GetMaxExpL (poly p, const ring r, unsigned long l_max)
	return the maximal exponent of p in form of the maximal long var More...
BOOLEAN	p_OneComp (poly p, const ring r)
	return TRUE if all monoms have the same component More...
int	p_IsPurePower (const poly p, const ring r)
	return i, if head depends only on var(i) More...
int	p_IsUnivariate (poly p, const ring r)
	return i, if poly depends only on var(i) More...
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) More...
poly	p_ISet (long i, const ring r)
	returns the poly representing the integer i More...
poly	p_One (const ring r)
void	p_Split (poly p, poly *h)
BOOLEAN	p_HasNotCF (poly p1, poly p2, const ring r)
BOOLEAN	p_HasNotCFRing (poly p1, poly p2, const ring r)
const char *	p_Read (const char *st, poly &rc, const ring r)
poly	p_mInit (const char *st, BOOLEAN &ok, const ring r)
poly	p_NSet (number n, const ring r)
	returns the poly representing the number n, destroys n More...
poly	p_MDivide (poly a, poly b, const ring r)
poly	p_Div_nn (poly p, const number n, const ring r)
poly	p_Div_mm (poly p, const poly m, const ring r)
	divide polynomial by monomial More...
poly	p_DivideM (poly a, poly b, const ring r)
poly	pp_DivideM (poly a, poly b, 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 More...
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)
void	p_LmDeleteAndNextRat (poly *p, int ishift, ring r)
poly	p_GetCoeffRat (poly p, int ishift, ring r)
void	p_ContentRat (poly &ph, 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: More...
poly	p_Diff (poly a, int k, const ring r)
static poly	p_DiffOpM (poly a, poly b, BOOLEAN multiply, const ring r)
poly	p_DiffOp (poly a, poly b, BOOLEAN multiply, const ring r)
poly	p_Sub (poly p1, poly p2, const ring r)
static poly	p_MonPower (poly p, int exp, const ring r)
static void	p_MonMult (poly p, poly q, const ring r)
static poly	p_MonMultC (poly p, poly q, const ring rr)
static number *	pnBin (int exp, const ring r)
static void	pnFreeBin (number *bin, int exp, const coeffs r)
static poly	p_TwoMonPower (poly p, int exp, const ring r)
static poly	p_Pow (poly p, int i, const ring r)
static poly	p_Pow_charp (poly p, int i, const ring r)
poly	p_Power (poly p, int i, const ring r)
void	p_Content (poly ph, const ring r)
void	p_Content_n (poly ph, number &c, const ring r)
void	p_ContentForGB (poly ph, const ring r)
void	p_SimpleContent (poly ph, int smax, const ring r)
number	p_InitContent (poly ph, const ring r)
poly	p_Cleardenom (poly p, const ring r)
void	p_Cleardenom_n (poly ph, const ring r, number &c)
void	p_ProjectiveUnique (poly ph, const ring r)
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_VectorHasUnitB (poly p, int *k, const ring r)
void	p_VectorHasUnit (poly p, int *k, int *len, const ring r)
poly	p_TakeOutComp1 (poly *p, int k, const ring r)
poly	p_TakeOutComp (poly *p, int k, const ring r)
void	p_TakeOutComp (poly *r_p, long comp, poly *r_q, int *lq, const ring r)
void	p_DeleteComp (poly *p, int k, 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)
	vector to already allocated array (len>=p_MaxComp(v,r)) More...
void	p_Vec2Polys (poly v, poly **p, int *len, const ring r)
void	pSetDegProcs (ring r, pFDegProc new_FDeg, pLDegProc new_lDeg)
void	pRestoreDegProcs (ring r, pFDegProc old_FDeg, pLDegProc old_lDeg)
static long	pModDeg (poly p, ring r)
void	p_SetModDeg (intvec *w, ring r)
void	pEnlargeSet (poly **p, int l, int increment)
void	p_Norm (poly p1, const ring r)
void	p_Normalize (poly p, const ring r)
static void	p_SplitAndReversePoly (poly p, int n, poly *non_zero, poly *zero, const ring r)
static poly	p_Subst1 (poly p, int n, const ring r)
static poly	p_Subst2 (poly p, int n, number e, const ring r)
static poly	p_Subst0 (poly p, int n, const ring r)
poly	p_Subst (poly p, int n, poly e, const ring r)
poly	n_PermNumber (const number z, const int *par_perm, const int, 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, int OldPar, BOOLEAN use_mult)
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)
int	p_MinDeg (poly p, intvec *w, const ring R)
static poly	p_Invers (int n, poly u, intvec *w, const ring R)
poly	p_Series (int n, poly p, poly u, intvec *w, const ring R)
BOOLEAN	p_EqualPolys (poly p1, poly p2, const ring r)
static BOOLEAN	p_ExpVectorEqual (poly p1, poly p2, const ring r1, const ring r2)
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 More...
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 More...
poly	p_Last (const poly p, int &l, const ring r)
int	p_Var (poly m, const ring r)
int	p_LowVar (poly p, const ring r)
	the minimal index of used variables - 1 More...
void	p_Shift (poly *p, int i, const ring r)
	shifts components of the vector p by i More...
static unsigned long	GetBitFields (const long e, const unsigned int s, const unsigned int n)
unsigned long	p_GetShortExpVector (const poly p, const ring r)
unsigned long	p_GetShortExpVector (const poly p, const poly pp, const ring r)
	p_GetShortExpVector of p * pp More...
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 More...
poly	p_CopyPowerProduct0 (const poly p, number n, const ring r)
	like p_Head, but with coefficient n More...
poly	p_CopyPowerProduct (const poly p, const ring r)
	like p_Head, but with coefficient 1 More...
poly	p_Head0 (const poly p, const ring r)
	like p_Head, but allow NULL coeff More...
int	p_MaxExpPerVar (poly p, int i, const ring r)
	max exponent of variable x_i in p More...

Variables
STATIC_VAR int *	_components = NULL
STATIC_VAR long *	_componentsShifted = NULL
STATIC_VAR int	_componentsExternal = 0
VAR BOOLEAN	pSetm_error =0
STATIC_VAR pFDegProc	pOldFDeg
STATIC_VAR pLDegProc	pOldLDeg
STATIC_VAR BOOLEAN	pOldLexOrder

Macro Definition Documentation

CLEARENUMERATORS

#define CLEARENUMERATORS   1

Definition at line 2418 of file p_polys.cc.

LINKAGE

#define LINKAGE

Definition at line 4960 of file p_polys.cc.

MYTEST

#define MYTEST   0

Definition at line 153 of file p_polys.cc.

n_Delete__T

#define n_Delete__T	(		n,
			r
	)		do {} while (0)

Definition at line 4964 of file p_polys.cc.

p_Delete__T

#define p_Delete__T   p_ShallowDelete

Definition at line 4962 of file p_polys.cc.

Sy_bit_L

#define Sy_bit_L

(

x

)

(((unsigned long)1L)<<(x))

TRANSEXT_PRIVATES

#define TRANSEXT_PRIVATES

Definition at line 24 of file p_polys.cc.

Function Documentation

GetBitFields()

static unsigned long GetBitFields ( const long  e, const unsigned int  s, const unsigned int  n  )

inlinestatic

Definition at line 4813 of file p_polys.cc.

{
#define Sy_bit_L(x)     (((unsigned long)1L)<<(x))
  unsigned int i = 0;
  unsigned long  ev = 0L;
  assume(n > 0 && s < BIT_SIZEOF_LONG);
  do
  {
    assume(s+i < BIT_SIZEOF_LONG);
    if (e > (long) i) ev |= Sy_bit_L(s+i);
    else break;
    i++;
  }
  while (i < n);
  return ev;
}

n_PermNumber()

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

Definition at line 4092 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_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 2910 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	ph,
		const ring	r,
		number &	c
	)

Definition at line 3019 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_Compare()

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

Definition at line 4972 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 4641 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	ph,
		const ring	r
	)

Definition at line 2291 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_Content_n()

void p_Content_n	(	poly	ph,
		number &	c,
		const ring	r
	)

Definition at line 2349 of file p_polys.cc.

{
  const coeffs cf=r->cf;
  if (ph==NULL)
  {
    c=n_Init(1,cf);
    return;
  }
  if (pNext(ph)==NULL)
  {
    c=pGetCoeff(ph);
    p_SetCoeff0(ph,n_Init(1,cf),r);
  }
  if ((cf->cfSubringGcd==ndGcd)
  || (cf->cfGcd==ndGcd)) /* trivial gcd*/
  {
    c=n_Init(1,r->cf);
    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:
  c=h;
  // and last: check leading sign:
  if(!n_GreaterZero(pGetCoeff(ph),r->cf))
  {
    c = n_InpNeg(c,r->cf);
    ph = p_Neg(ph,r);
  }
}

p_ContentForGB()

void p_ContentForGB	(	poly	ph,
		const ring	r
	)

Definition at line 2420 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 1740 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_CopyPowerProduct()

poly p_CopyPowerProduct	(	const poly	p,
		const ring	r
	)

like p_Head, but with coefficient 1

Definition at line 5056 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,
		number	n,
		const ring	r
	)

like p_Head, but with coefficient n

Definition at line 5044 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_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_DeleteComp()

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

Definition at line 3622 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 1894 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 1969 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_DiffOpM()

static poly p_DiffOpM ( poly  a, poly  b, BOOLEAN  multiply, const ring  r  )

static

Definition at line 1930 of file p_polys.cc.

{
  int i,j,s;
  number n,h,hh;
  poly p=p_One(r);
  n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf);
  for(i=rVar(r);i>0;i--)
  {
    s=p_GetExp(b,i,r);
    if (s<p_GetExp(a,i,r))
    {
      n_Delete(&n,r->cf);
      p_LmDelete(&p,r);
      return NULL;
    }
    if (multiply)
    {
      for(j=p_GetExp(a,i,r); j>0;j--)
      {
        h = n_Init(s,r->cf);
        hh=n_Mult(n,h,r->cf);
        n_Delete(&h,r->cf);
        n_Delete(&n,r->cf);
        n=hh;
        s--;
      }
      p_SetExp(p,i,s,r);
    }
    else
    {
      p_SetExp(p,i,s-p_GetExp(a,i,r),r);
    }
  }
  p_Setm(p,r);
  /*if (multiply)*/ p_SetCoeff(p,n,r);
  if (n_IsZero(n,r->cf))  p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial
  return p;
}

p_Div_mm()

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

divide polynomial by monomial

Definition at line 1534 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 1501 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 1574 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_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 1638 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 4577 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 4615 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_ExpVectorEqual()

static BOOLEAN p_ExpVectorEqual ( poly  p1, poly  p2, const ring  r1, const ring  r2  )

inlinestatic

Definition at line 4591 of file p_polys.cc.

{
  assume( r1 == r2 || rSamePolyRep(r1, r2) );
 
  p_LmCheckPolyRing1(p1, r1);
  p_LmCheckPolyRing1(p2, r2);
 
  int i = r1->ExpL_Size;
 
  assume( r1->ExpL_Size == r2->ExpL_Size );
 
  unsigned long *ep = p1->exp;
  unsigned long *eq = p2->exp;
 
  do
  {
    i--;
    if (ep[i] != eq[i]) return FALSE;
  }
  while (i);
 
  return TRUE;
}

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_GcdMon()

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

polynomial gcd for f=mon

Definition at line 5006 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 1718 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_GetMaxExpL()

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

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_GetMaxExpL2() [1/2]

static unsigned long p_GetMaxExpL2 ( unsigned long  l1, unsigned long  l2, const ring  r  )

inlinestatic

Definition at line 1133 of file p_polys.cc.

{
  return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong);
}

p_GetMaxExpL2() [2/2]

static unsigned long p_GetMaxExpL2 ( unsigned long  l1, unsigned long  l2, const ring  r, unsigned long  number_of_exp  )

inlinestatic

Definition at line 1107 of file p_polys.cc.

{
  const unsigned long bitmask = r->bitmask;
  unsigned long ml1 = l1 & bitmask;
  unsigned long ml2 = l2 & bitmask;
  unsigned long max = (ml1 > ml2 ? ml1 : ml2);
  unsigned long j = number_of_exp - 1;
 
  if (j > 0)
  {
    unsigned long mask = bitmask << r->BitsPerExp;
    while (1)
    {
      ml1 = l1 & mask;
      ml2 = l2 & mask;
      max |= ((ml1 > ml2 ? ml1 : ml2) & mask);
      j--;
      if (j == 0) break;
      mask = mask << r->BitsPerExp;
    }
  }
  return max;
}

p_GetMaxExpP()

poly p_GetMaxExpP	(	poly	p,
		const 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_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() [1/2]

unsigned long p_GetShortExpVector	(	const poly	p,
		const poly	pp,
		const ring	r
	)

p_GetShortExpVector of p * pp

Definition at line 4899 of file p_polys.cc.

{
  assume(p != NULL);
  assume(pp != 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)
  int j=1;
  unsigned long i = 0L;
 
  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 || p_GetExp(pp,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) + p_GetExp(pp, j,r), i, n);
    i += n;
    j++;
  }
 
  n--;
  while (i<BIT_SIZEOF_LONG)
  {
    ev |= GetBitFields(p_GetExp(p, j,r) + p_GetExp(pp, j,r), i, n);
    i += n;
    j++;
  }
  return ev;
}

p_GetShortExpVector() [2/2]

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

Definition at line 4846 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_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_Head0()

poly p_Head0	(	const poly	p,
		const ring	r
	)

like p_Head, but allow NULL coeff

Definition at line 5062 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 3335 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_InitContent()

number p_InitContent	(	poly	ph,
		const ring	r
	)

Definition at line 2700 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_Invers()

static poly p_Invers ( int  n, poly  u, intvec *  w, const ring  R  )

static

Definition at line 4534 of file p_polys.cc.

{
  if(n<0)
    return NULL;
  number u0=n_Invers(pGetCoeff(u),R->cf);
  poly v=p_NSet(u0,R);
  if(n==0)
    return v;
  int *ww=iv2array(w,R);
  poly u1=p_JetW(p_Sub(p_One(R),__p_Mult_nn(u,u0,R),R),n,ww,R);
  if(u1==NULL)
  {
    omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(int));
    return v;
  }
  poly v1=__p_Mult_nn(p_Copy(u1,R),u0,R);
  v=p_Add_q(v,p_Copy(v1,R),R);
  for(int i=n/p_MinDeg(u1,w,R);i>1;i--)
  {
    v1=p_JetW(p_Mult_q(v1,p_Copy(u1,R),R),n,ww,R);
    v=p_Add_q(v,p_Copy(v1,R),R);
  }
  p_Delete(&u1,R);
  p_Delete(&v1,R);
  omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(int));
  return v;
}

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 3384 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_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_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 4451 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 4495 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	p,
		int &	l,
		const ring	r
	)

Definition at line 4686 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 1660 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 1651 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 1673 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);
  n_New(&(p_GetCoeff(m, r)), r);
 
  return(m);
};

p_LmDeleteAndNextRat()

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

Definition at line 1696 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_LowVar()

int p_LowVar	(	poly	p,
		const ring	r
	)

the minimal index of used variables - 1

Definition at line 4745 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_MaxExpPerVar()

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

max exponent of variable x_i in p

Definition at line 5068 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 1488 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_MinDeg()

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

Definition at line 4513 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 *	st,
		BOOLEAN &	ok,
		const ring	r
	)

Definition at line 1442 of file p_polys.cc.

{
  poly p;
  const char *s=p_Read(st,p,r);
  if (*s!='\0')
  {
    if ((s!=st)&&isdigit(st[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;
  return p;
}

p_MonMult()

static void p_MonMult ( poly  p, poly  q, const ring  r  )

static

Definition at line 2020 of file p_polys.cc.

{
  number x, y;
 
  y = pGetCoeff(p);
  x = n_Mult(y,pGetCoeff(q),r->cf);
  n_Delete(&y,r->cf);
  pSetCoeff0(p,x);
  //for (int i=pVariables; i!=0; i--)
  //{
  //  pAddExp(p,i, pGetExp(q,i));
  //}
  //p->Order += q->Order;
  p_ExpVectorAdd(p,q,r);
}

p_MonMultC()

static poly p_MonMultC ( poly  p, poly  q, const ring  rr  )

static

Definition at line 2040 of file p_polys.cc.

{
  number x;
  poly r = p_Init(rr);
 
  x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf);
  pSetCoeff0(r,x);
  p_ExpVectorSum(r,p, q, rr);
  return r;
}

p_MonPower()

static poly p_MonPower ( poly  p, int  exp, const ring  r  )

static

Definition at line 1996 of file p_polys.cc.

{
  int i;
 
  if(!n_IsOne(pGetCoeff(p),r->cf))
  {
    number x, y;
    y = pGetCoeff(p);
    n_Power(y,exp,&x,r->cf);
    n_Delete(&y,r->cf);
    pSetCoeff0(p,x);
  }
  for (i=rVar(r); i!=0; i--)
  {
    p_MultExp(p,i, exp,r);
  }
  p_Setm(p,r);
  return p;
}

p_Norm()

void p_Norm	(	poly	p1,
		const ring	r
	)

Definition at line 3797 of file p_polys.cc.

{
  if (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 (p1!=NULL)
  {
    if (pNext(p1)==NULL)
    {
      p_SetCoeff(p1,n_Init(1,r->cf),r);
      return;
    }
    if (!n_IsOne(pGetCoeff(p1),r->cf))
    {
      number k, c;
      n_Normalize(pGetCoeff(p1),r->cf);
      k = pGetCoeff(p1);
      c = n_Init(1,r->cf);
      pSetCoeff0(p1,c);
      poly h = pNext(p1);
      if (rField_is_Zp(r))
      {
        if (r->cf->ch>32003)
        {
          number inv=n_Invers(k,r->cf);
          while (h!=NULL)
          {
            c=n_Mult(pGetCoeff(h),inv,r->cf);
            // no need to normalize
            p_SetCoeff(h,c,r);
            pIter(h);
          }
          n_Delete(&inv,r->cf);
        }
        else
        {
          while (h!=NULL)
          {
            c=n_Div(pGetCoeff(h),k,r->cf);
            // no need to normalize
            p_SetCoeff(h,c,r);
            pIter(h);
          }
        }
      }
      else
      {
        while (h!=NULL)
        {
          c=n_Div(pGetCoeff(h),k,r->cf);
          // no need to normalize: Z/p, R
          // normalize already in nDiv: Q_a, Z/p_a
          // remains: Q
          if (rField_is_Q(r) && (!n_IsOne(c,r->cf))) 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 3879 of file p_polys.cc.

{
  if ((rField_has_simple_inverse(r))  /* Z/p, GF(p,n), R, long R/C */
  || (r->cf->cfNormalize==ndNormalize)) /* Nemo rings, ...*/
    return;
  while (p!=NULL)
  {
    // no test befor n_Normalize: n_Normalize should fix problems
    n_Normalize(pGetCoeff(p),r->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 1469 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,
		int	OldPar,
		BOOLEAN	use_mult
	)

Definition at line 4195 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_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 1866 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_Pow()

static poly p_Pow ( poly  p, int  i, const ring  r  )

static

Definition at line 2167 of file p_polys.cc.

{
  poly rc = p_Copy(p,r);
  i -= 2;
  do
  {
    rc = p_Mult_q(rc,p_Copy(p,r),r);
    p_Normalize(rc,r);
    i--;
  }
  while (i != 0);
  return p_Mult_q(rc,p,r);
}

p_Pow_charp()

static poly p_Pow_charp ( poly  p, int  i, const ring  r  )

static

Definition at line 2181 of file p_polys.cc.

{
  //assume char_p == i
  poly h=p;
  while(h!=NULL) { p_MonPower(h,i,r);pIter(h);}
  return p;
}

p_Power()

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

Definition at line 2193 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	ph,
		const ring	r
	)

Definition at line 3208 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 *	st,
		poly &	rc,
		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 4563 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_Setm_Dummy()

void p_Setm_Dummy	(	poly	p,
		const ring	r
	)

Definition at line 541 of file p_polys.cc.

{
  p_LmCheckPolyRing(p, r);
}

p_Setm_General()

void p_Setm_General	(	poly	p,
		const ring	r
	)

!!!????? where?????

Definition at line 158 of file p_polys.cc.

{
  p_LmCheckPolyRing(p, r);
  int pos=0;
  if (r->typ!=NULL)
  {
    loop
    {
      unsigned long ord=0;
      sro_ord* o=&(r->typ[pos]);
      switch(o->ord_typ)
      {
        case ro_dp:
        {
          int a,e;
          a=o->data.dp.start;
          e=o->data.dp.end;
          for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r);
          p->exp[o->data.dp.place]=ord;
          break;
        }
        case ro_wp_neg:
          ord=POLY_NEGWEIGHT_OFFSET;
          // no break;
        case ro_wp:
        {
          int a,e;
          a=o->data.wp.start;
          e=o->data.wp.end;
          int *w=o->data.wp.weights;
#if 1
          for(int i=a;i<=e;i++) ord+=((unsigned long)p_GetExp(p,i,r))*((unsigned long)w[i-a]);
#else
          long ai;
          int ei,wi;
          for(int i=a;i<=e;i++)
          {
             ei=p_GetExp(p,i,r);
             wi=w[i-a];
             ai=ei*wi;
             if (ai/ei!=wi) pSetm_error=TRUE;
             ord+=ai;
             if (ord<ai) pSetm_error=TRUE;
          }
#endif
          p->exp[o->data.wp.place]=ord;
          break;
        }
        case ro_am:
        {
          ord = POLY_NEGWEIGHT_OFFSET;
          const short a=o->data.am.start;
          const short e=o->data.am.end;
          const int * w=o->data.am.weights;
#if 1
          for(short i=a; i<=e; i++, w++)
            ord += ((*w) * p_GetExp(p,i,r));
#else
          long ai;
          int ei,wi;
          for(short i=a;i<=e;i++)
          {
             ei=p_GetExp(p,i,r);
             wi=w[i-a];
             ai=ei*wi;
             if (ai/ei!=wi) pSetm_error=TRUE;
             ord += ai;
             if (ord<ai) pSetm_error=TRUE;
          }
#endif
          const int c = p_GetComp(p,r);
 
          const short len_gen= o->data.am.len_gen;
 
          if ((c > 0) && (c <= len_gen))
          {
            assume( w == o->data.am.weights_m );
            assume( w[0] == len_gen );
            ord += w[c];
          }
 
          p->exp[o->data.am.place] = ord;
          break;
        }
      case ro_wp64:
        {
          int64 ord=0;
          int a,e;
          a=o->data.wp64.start;
          e=o->data.wp64.end;
          int64 *w=o->data.wp64.weights64;
          int64 ei,wi,ai;
          for(int i=a;i<=e;i++)
          {
            //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]);
            //ord+=((int64)p_GetExp(p,i,r))*w[i-a];
            ei=(int64)p_GetExp(p,i,r);
            wi=w[i-a];
            ai=ei*wi;
            if(ei!=0 && ai/ei!=wi)
            {
              pSetm_error=TRUE;
              #if SIZEOF_LONG == 4
              Print("ai %lld, wi %lld\n",ai,wi);
              #else
              Print("ai %ld, wi %ld\n",ai,wi);
              #endif
            }
            ord+=ai;
            if (ord<ai)
            {
              pSetm_error=TRUE;
              #if SIZEOF_LONG == 4
              Print("ai %lld, ord %lld\n",ai,ord);
              #else
              Print("ai %ld, ord %ld\n",ai,ord);
              #endif
            }
          }
          #if SIZEOF_LONG == 4
          int64 mask=(int64)0x7fffffff;
          long a_0=(long)(ord&mask); //2^31
          long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/
 
          //Print("mask: %x,  ord: %d,  a_0: %d,  a_1: %d\n"
          //,(int)mask,(int)ord,(int)a_0,(int)a_1);
                    //Print("mask: %d",mask);
 
          p->exp[o->data.wp64.place]=a_1;
          p->exp[o->data.wp64.place+1]=a_0;
          #elif SIZEOF_LONG == 8
          p->exp[o->data.wp64.place]=ord;
          #endif
//            if(p_Setm_error) PrintS("***************************\n"
//                                    "***************************\n"
//                                    "**WARNING: overflow error**\n"
//                                    "***************************\n"
//                                    "***************************\n");
          break;
        }
        case ro_cp:
        {
          int a,e;
          a=o->data.cp.start;
          e=o->data.cp.end;
          int pl=o->data.cp.place;
          for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; }
          break;
        }
        case ro_syzcomp:
        {
          long c=__p_GetComp(p,r);
          long sc = c;
          int* Components = (_componentsExternal ? _components :
                             o->data.syzcomp.Components);
          long* ShiftedComponents = (_componentsExternal ? _componentsShifted:
                                     o->data.syzcomp.ShiftedComponents);
          if (ShiftedComponents != NULL)
          {
            assume(Components != NULL);
            assume(c == 0 || Components[c] != 0);
            sc = ShiftedComponents[Components[c]];
            assume(c == 0 || sc != 0);
          }
          p->exp[o->data.syzcomp.place]=sc;
          break;
        }
        case ro_syz:
        {
          const unsigned long c = __p_GetComp(p, r);
          const short place = o->data.syz.place;
          const int limit = o->data.syz.limit;
 
          if (c > (unsigned long)limit)
            p->exp[place] = o->data.syz.curr_index;
          else if (c > 0)
          {
            assume( (1 <= c) && (c <= (unsigned long)limit) );
            p->exp[place]= o->data.syz.syz_index[c];
          }
          else
          {
            assume(c == 0);
            p->exp[place]= 0;
          }
          break;
        }
        // Prefix for Induced Schreyer ordering
        case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?)
        {
          assume(p != NULL);
 
#ifndef SING_NDEBUG
#if MYTEST
          Print("p_Setm_General: ro_isTemp ord: pos: %d, p: ", pos);  p_wrp(p, r);
#endif
#endif
          int c = p_GetComp(p, r);
 
          assume( c >= 0 );
 
          // Let's simulate case ro_syz above....
          // Should accumulate (by Suffix) and be a level indicator
          const int* const pVarOffset = o->data.isTemp.pVarOffset;
 
          assume( pVarOffset != NULL );
 
          // TODO: Can this be done in the suffix???
          for( int i = 1; i <= r->N; i++ ) // No v[0] here!!!
          {
            const int vo = pVarOffset[i];
            if( vo != -1) // TODO: optimize: can be done once!
            {
              // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct:
              p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim
              // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct:
              assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim
            }
          }
#ifndef SING_NDEBUG
          for( int i = 1; i <= r->N; i++ ) // No v[0] here!!!
          {
            const int vo = pVarOffset[i];
            if( vo != -1) // TODO: optimize: can be done once!
            {
              // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct:
              assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim
            }
          }
#if MYTEST
//          if( p->exp[o->data.isTemp.start] > 0 )
            PrintS("after Values: "); p_wrp(p, r);
#endif
#endif
          break;
        }
 
        // Suffix for Induced Schreyer ordering
        case ro_is:
        {
#ifndef SING_NDEBUG
#if MYTEST
          Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos);  p_wrp(p, r);
#endif
#endif
 
          assume(p != NULL);
 
          int c = p_GetComp(p, r);
 
          assume( c >= 0 );
          const ideal F = o->data.is.F;
          const int limit = o->data.is.limit;
          assume( limit >= 0 );
          const int start = o->data.is.start;
 
          if( F != NULL && c > limit )
          {
#ifndef SING_NDEBUG
#if MYTEST
            Print("p_Setm_General: ro_is : in rSetm: pos: %d, c: %d >  limit: %d\n", c, pos, limit);
            PrintS("preComputed Values: ");
            p_wrp(p, r);
#endif
#endif
//          if( c > limit ) // BUG???
            p->exp[start] = 1;
//          else
//            p->exp[start] = 0;
 
 
            c -= limit;
            assume( c > 0 );
            c--;
 
            if( c >= IDELEMS(F) )
              break;
 
            assume( c < IDELEMS(F) ); // What about others???
 
            const poly pp = F->m[c]; // get reference monomial!!!
 
            if(pp == NULL)
              break;
 
            assume(pp != NULL);
 
#ifndef SING_NDEBUG
#if MYTEST
            Print("Respective F[c - %d: %d] pp: ", limit, c);
            p_wrp(pp, r);
#endif
#endif
 
            const int end = o->data.is.end;
            assume(start <= end);
 
 
//          const int st = o->data.isTemp.start;
 
#ifndef SING_NDEBUG
#if MYTEST
            Print("p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]);
#endif
#endif
 
            // p_ExpVectorAdd(p, pp, r);
 
            for( int i = start; i <= end; i++) // v[0] may be here...
              p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F)
 
            // p_MemAddAdjust(p, ri);
            if (r->NegWeightL_Offset != NULL)
            {
              for (int i=r->NegWeightL_Size-1; i>=0; i--)
              {
                const int _i = r->NegWeightL_Offset[i];
                if( start <= _i && _i <= end )
                  p->exp[_i] -= POLY_NEGWEIGHT_OFFSET;
              }
            }
 
 
#ifndef SING_NDEBUG
            const int* const pVarOffset = o->data.is.pVarOffset;
 
            assume( pVarOffset != NULL );
 
            for( int i = 1; i <= r->N; i++ ) // No v[0] here!!!
            {
              const int vo = pVarOffset[i];
              if( vo != -1) // TODO: optimize: can be done once!
                // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct:
                assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) );
            }
            // TODO: how to check this for computed values???
#if MYTEST
            PrintS("Computed Values: "); p_wrp(p, r);
#endif
#endif
          } else
          {
            p->exp[start] = 0; //!!!!????? where?????
 
            const int* const pVarOffset = o->data.is.pVarOffset;
 
            // What about v[0] - component: it will be added later by
            // suffix!!!
            // TODO: Test it!
            const int vo = pVarOffset[0];
            if( vo != -1 )
              p->exp[vo] = c; // initial component v[0]!
 
#ifndef SING_NDEBUG
#if MYTEST
            Print("ELSE p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo, p->exp[vo]);
            p_wrp(p, r);
#endif
#endif
          }
 
          break;
        }
        default:
          dReportError("wrong ord in rSetm:%d\n",o->ord_typ);
          return;
      }
      pos++;
      if (pos == r->OrdSize) return;
    }
  }
}

p_Setm_Syz()

void p_Setm_Syz	(	poly	p,
		ring	r,
		int *	Components,
		long *	ShiftedComponents
	)

Definition at line 531 of file p_polys.cc.

{
  _components = Components;
  _componentsShifted = ShiftedComponents;
  _componentsExternal = 1;
  p_Setm_General(p, r);
  _componentsExternal = 0;
}

p_Setm_TotalDegree()

void p_Setm_TotalDegree	(	poly	p,
		const ring	r
	)

Definition at line 547 of file p_polys.cc.

{
  p_LmCheckPolyRing(p, r);
  p->exp[r->pOrdIndex] = p_Totaldegree(p, r);
}

p_Setm_WFirstTotalDegree()

void p_Setm_WFirstTotalDegree	(	poly	p,
		const ring	r
	)

Definition at line 554 of file p_polys.cc.

{
  p_LmCheckPolyRing(p, r);
  p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r);
}

p_SetModDeg()

void p_SetModDeg	(	intvec *	w,
		ring	r
	)

Definition at line 3751 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_Shift()

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

shifts components of the vector p by i

Definition at line 4771 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	ph,
		int	smax,
		const ring	r
	)

Definition at line 2629 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 3318 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_Split()

void p_Split	(	poly	p,
		poly *	h
	)

Definition at line 1320 of file p_polys.cc.

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

p_SplitAndReversePoly()

static void p_SplitAndReversePoly ( poly  p, int  n, poly *  non_zero, poly *  zero, const ring  r  )

static

Definition at line 3894 of file p_polys.cc.

{
  if (p == NULL)
  {
    *non_zero = NULL;
    *zero = NULL;
    return;
  }
  spolyrec sz;
  poly z, n_z, next;
  z = &sz;
  n_z = NULL;
 
  while(p != NULL)
  {
    next = pNext(p);
    if (p_GetExp(p, n,r) == 0)
    {
      pNext(z) = p;
      pIter(z);
    }
    else
    {
      pNext(p) = n_z;
      n_z = p;
    }
    p = next;
  }
  pNext(z) = NULL;
  *zero = pNext(&sz);
  *non_zero = n_z;
}

p_Sub()

poly p_Sub	(	poly	p1,
		poly	p2,
		const ring	r
	)

Definition at line 1986 of file p_polys.cc.

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

p_Subst()

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

Definition at line 4023 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_Subst0()

static poly p_Subst0 ( poly  p, int  n, const ring  r  )

static

Definition at line 3998 of file p_polys.cc.

{
  spolyrec res;
  poly h = &res;
  pNext(h) = p;
 
  while (pNext(h)!=NULL)
  {
    if (p_GetExp(pNext(h),n,r)!=0)
    {
      p_LmDelete(&pNext(h),r);
    }
    else
    {
      pIter(h);
    }
  }
  p_Test(pNext(&res),r);
  return pNext(&res);
}

p_Subst1()

static poly p_Subst1 ( poly  p, int  n, const ring  r  )

static

Definition at line 3930 of file p_polys.cc.

{
  poly qq=NULL, result = NULL;
  poly zero=NULL, non_zero=NULL;
 
  // reverse, so that add is likely to be linear
  p_SplitAndReversePoly(p, n, &non_zero, &zero,r);
 
  while (non_zero != NULL)
  {
    assume(p_GetExp(non_zero, n,r) != 0);
    qq = non_zero;
    pIter(non_zero);
    qq->next = NULL;
    p_SetExp(qq,n,0,r);
    p_Setm(qq,r);
    result = p_Add_q(result,qq,r);
  }
  p = p_Add_q(result, zero,r);
  p_Test(p,r);
  return p;
}

p_Subst2()

static poly p_Subst2 ( poly  p, int  n, number  e, const ring  r  )

static

Definition at line 3957 of file p_polys.cc.

{
  assume( ! n_IsZero(e,r->cf) );
  poly qq,result = NULL;
  number nn, nm;
  poly zero, non_zero;
 
  // reverse, so that add is likely to be linear
  p_SplitAndReversePoly(p, n, &non_zero, &zero,r);
 
  while (non_zero != NULL)
  {
    assume(p_GetExp(non_zero, n, r) != 0);
    qq = non_zero;
    pIter(non_zero);
    qq->next = NULL;
    n_Power(e, p_GetExp(qq, n, r), &nn,r->cf);
    nm = n_Mult(nn, pGetCoeff(qq),r->cf);
#ifdef HAVE_RINGS
    if (n_IsZero(nm,r->cf))
    {
      p_LmFree(&qq,r);
      n_Delete(&nm,r->cf);
    }
    else
#endif
    {
      p_SetCoeff(qq, nm,r);
      p_SetExp(qq, n, 0,r);
      p_Setm(qq,r);
      result = p_Add_q(result,qq,r);
    }
    n_Delete(&nn,r->cf);
  }
  p = p_Add_q(result, zero,r);
  p_Test(p,r);
  return p;
}

p_TakeOutComp() [1/2]

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

Definition at line 3513 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 *	r_p,
		long	comp,
		poly *	r_q,
		int *	lq,
		const ring	r
	)

Definition at line 3574 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_TakeOutComp1()

poly p_TakeOutComp1	(	poly *	p,
		int	k,
		const ring	r
	)

Definition at line 3462 of file p_polys.cc.

{
  poly q = *p;
 
  if (q==NULL) return NULL;
 
  poly qq=NULL,result = NULL;
  long unsigned kk=k;
  if (__p_GetComp(q,r)==kk)
  {
    result = q; /* *p */
    while ((q!=NULL) && (__p_GetComp(q,r)==kk))
    {
      p_SetComp(q,0,r);
      p_SetmComp(q,r);
      qq = q;
      pIter(q);
    }
    *p = q;
    pNext(qq) = NULL;
  }
  if (q==NULL) return result;
//  if (pGetComp(q) > k) pGetComp(q)--;
  while (pNext(q)!=NULL)
  {
    if (__p_GetComp(pNext(q),r)==kk)
    {
      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);
      p_SetmComp(qq,r);
    }
    else
    {
      pIter(q);
//      if (pGetComp(q) > k) pGetComp(q)--;
    }
  }
  return result;
}

p_TwoMonPower()

static poly p_TwoMonPower ( poly  p, int  exp, const ring  r  )

static

Definition at line 2102 of file p_polys.cc.

{
  int eh, e;
  long al;
  poly *a;
  poly tail, b, res, h;
  number x;
  number *bin = pnBin(exp,r);
 
  tail = pNext(p);
  if (bin == NULL)
  {
    p_MonPower(p,exp,r);
    p_MonPower(tail,exp,r);
    p_Test(p,r);
    return p;
  }
  eh = exp >> 1;
  al = (exp + 1) * sizeof(poly);
  a = (poly *)omAlloc(al);
  a[1] = p;
  for (e=1; e<exp; e++)
  {
    a[e+1] = p_MonMultC(a[e],p,r);
  }
  res = a[exp];
  b = p_Head(tail,r);
  for (e=exp-1; e>eh; e--)
  {
    h = a[e];
    x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf);
    p_SetCoeff(h,x,r);
    p_MonMult(h,b,r);
    res = pNext(res) = h;
    p_MonMult(b,tail,r);
  }
  for (e=eh; e!=0; e--)
  {
    h = a[e];
    x = n_Mult(bin[e],pGetCoeff(h),r->cf);
    p_SetCoeff(h,x,r);
    p_MonMult(h,b,r);
    res = pNext(res) = h;
    p_MonMult(b,tail,r);
  }
  p_LmDelete(&tail,r);
  pNext(res) = b;
  pNext(b) = NULL;
  res = a[exp];
  omFreeSize((ADDRESS)a, al);
  pnFreeBin(bin, exp, r->cf);
//  tail=res;
// while((tail!=NULL)&&(pNext(tail)!=NULL))
// {
//   if(nIsZero(pGetCoeff(pNext(tail))))
//   {
//     pLmDelete(&pNext(tail));
//   }
//   else
//     pIter(tail);
// }
  p_Test(res,r);
  return res;
}

p_Var()

int p_Var	(	poly	m,
		const ring	r
	)

Definition at line 4721 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
	)

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

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

Definition at line 3673 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 3651 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 3703 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 3429 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 3406 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	i,
		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,
		const 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_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	l,
		int	increment
	)

Definition at line 3774 of file p_polys.cc.

{
  poly* h;
 
  if (*p==NULL)
  {
    if (increment==0) return;
    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;
}

pLDeg0()

long pLDeg0	(	poly	p,
		int *	l,
		const 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,
		const 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,
		const 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,
		const 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,
		const 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,
		const 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,
		const 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,
		const 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,
		const 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,
		const 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,
		const 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;
}

pModDeg()

static long pModDeg ( poly  p, ring  r  )

static

Definition at line 3742 of file p_polys.cc.

{
  long d=pOldFDeg(p, r);
  int c=__p_GetComp(p, r);
  if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1];
  return d;
  //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1];
}

pnBin()

static number * pnBin ( int  exp, const ring  r  )

static

Definition at line 2054 of file p_polys.cc.

{
  int e, i, h;
  number x, y, *bin=NULL;
 
  x = n_Init(exp,r->cf);
  if (n_IsZero(x,r->cf))
  {
    n_Delete(&x,r->cf);
    return bin;
  }
  h = (exp >> 1) + 1;
  bin = (number *)omAlloc0(h*sizeof(number));
  bin[1] = x;
  if (exp < 4)
    return bin;
  i = exp - 1;
  for (e=2; e<h; e++)
  {
      x = n_Init(i,r->cf);
      i--;
      y = n_Mult(x,bin[e-1],r->cf);
      n_Delete(&x,r->cf);
      x = n_Init(e,r->cf);
      bin[e] = n_ExactDiv(y,x,r->cf);
      n_Delete(&x,r->cf);
      n_Delete(&y,r->cf);
  }
  return bin;
}

pnFreeBin()

static void pnFreeBin ( number *  bin, int  exp, const coeffs  r  )

static

Definition at line 2085 of file p_polys.cc.

{
  int e, h = (exp >> 1) + 1;
 
  if (bin[1] != NULL)
  {
    for (e=1; e<h; e++)
      n_Delete(&(bin[e]),r);
  }
  omFreeSize((ADDRESS)bin, h*sizeof(number));
}

pp_DivideM()

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

Definition at line 1629 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 4423 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 4468 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;
}

pRestoreDegProcs()

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

Definition at line 3727 of file p_polys.cc.

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

pSetDegProcs()

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

Definition at line 3715 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;
}

Variable Documentation

_components

STATIC_VAR int* _components = NULL

Definition at line 146 of file p_polys.cc.

_componentsExternal

STATIC_VAR int _componentsExternal = 0

Definition at line 148 of file p_polys.cc.

_componentsShifted

STATIC_VAR long* _componentsShifted = NULL

Definition at line 147 of file p_polys.cc.

pOldFDeg

STATIC_VAR pFDegProc pOldFDeg

Definition at line 3738 of file p_polys.cc.

pOldLDeg

STATIC_VAR pLDegProc pOldLDeg

Definition at line 3739 of file p_polys.cc.

pOldLexOrder

STATIC_VAR BOOLEAN pOldLexOrder

Definition at line 3740 of file p_polys.cc.

pSetm_error

VAR BOOLEAN pSetm_error =0

Definition at line 150 of file p_polys.cc.