old.gring.cc File Reference

#include <misc/auxiliary.h>
#include "nc.h"
#include "sca.h"
#include "gb_hack.h"
#include <polys/monomials/ring.h>
#include <coeffs/numbers.h>
#include <polys/coeffrings.h>
#include <misc/options.h>
#include <polys/monomials/p_polys.h>
#include <polys/simpleideals.h>
#include <polys/matpol.h>
#include <polys/kbuckets.h>
#include <polys/sbuckets.h>
#include <polys/prCopy.h>
#include <polys/operations/p_Mult_q.h>
#include "summator.h"
#include "ncSAMult.h"
#include "ncSAFormula.h"

Go to the source code of this file.

Macros
#define	MYTEST   0
#define	OUTPUT   0
#define	PLURAL_INTERNAL_DECLARATIONS
#define	freeT(A, v)   omFreeSize((ADDRESS)A,(v+1)*sizeof(int))
#define	freeN(A, k)   omFreeSize((ADDRESS)A,k*sizeof(number))

Functions
poly	nc_p_CopyGet (poly a, const ring r)
poly	nc_p_CopyPut (poly a, const ring r)
poly	nc_p_Bracket_qq (poly p, const poly q, const ring r)
	returns [p,q], destroys p More...
int &	getNCExtensions ()
int	setNCExtensions (int iMask)
bool	ncExtensions (int iMask)
poly	gnc_pp_Mult_mm (const poly p, const poly m, const ring r, poly &last)
poly	gnc_p_Mult_mm (poly p, const poly m, const ring r)
poly	gnc_mm_Mult_p (const poly m, poly p, const ring r)
poly	gnc_mm_Mult_pp (const poly m, const poly p, const ring r)
poly	gnc_CreateSpolyOld (const poly p1, const poly p2, const ring r)
poly	gnc_ReduceSpolyOld (const poly p1, poly p2, const ring r)
poly	gnc_CreateSpolyNew (const poly p1, const poly p2, const ring r)
poly	gnc_ReduceSpolyNew (const poly p1, poly p2, const ring r)
void	gnc_kBucketPolyRedNew (kBucket_pt b, poly p, number *c)
void	gnc_kBucketPolyRed_ZNew (kBucket_pt b, poly p, number *c)
void	gnc_kBucketPolyRedOld (kBucket_pt b, poly p, number *c)
void	gnc_kBucketPolyRed_ZOld (kBucket_pt b, poly p, number *c)
void	nc_CleanUp (nc_struct *p)
void	nc_rCleanUp (ring r)
poly	p_Lcm (const poly a, const poly b, const long lCompM, const ring r)
poly	p_Lcm (const poly a, const poly b, const ring r)
poly	nc_p_Minus_mm_Mult_qq (poly p, const poly m, const poly q, int &shorter, const poly, const ring r)
	for p_Minus_mm_Mult_qq in pInline2.h More...
poly	nc_p_Plus_mm_Mult_qq (poly p, const poly m, const poly q, int &lp, const int, const ring r)
poly	_gnc_p_Mult_q (poly p, poly q, const int copy, const ring r)
poly	_nc_p_Mult_q (poly pPolyP, poly pPolyQ, const ring rRing)
	general NC-multiplication with destruction More...
poly	_nc_pp_Mult_qq (const poly pPolyP, const poly pPolyQ, const ring rRing)
	general NC-multiplication without destruction More...
poly	gnc_mm_Mult_nn (int *F, int *G, const ring r)
poly	gnc_mm_Mult_uu (int *F, int jG, int bG, const ring r)
poly	gnc_uu_Mult_ww (int i, int a, int j, int b, const ring r)
poly	gnc_p_Mult_mm_Common (poly p, const poly m, int side, const ring r)
poly	gnc_pp_Mult_mm (const poly p, const poly m, const ring r)
poly	gnc_uu_Mult_ww_vert (int i, int a, int j, int b, const ring r)
static poly	gnc_uu_Mult_ww_formula (int i, int a, int j, int b, const ring r)
poly	gnc_uu_Mult_ww_horvert (int i, int a, int j, int b, const ring r)
poly	nc_CreateShortSpoly (poly p1, poly p2, const ring r)
void	nc_PolyPolyRedOld (poly &b, poly p, number *c, const ring r)
void	nc_PolyPolyRedNew (poly &b, poly p, number *c, const ring r)
void	nc_PolyPolyRed (poly &b, poly p, number *c, const ring r)
poly	nc_mm_Bracket_nn (poly m1, poly m2, const ring r)
	returns [m1,m2] for two monoms, destroys nothing without coeffs More...
matrix	nc_PrintMat (int a, int b, ring r, int metric)
	returns matrix with the info on noncomm multiplication More...
void	nc_CleanUp (ring r)
void	nc_rKill (ring r)
	complete destructor More...
BOOLEAN	nc_CheckSubalgebra (poly PolyVar, ring r)
BOOLEAN	gnc_CheckOrdCondition (matrix D, ring r)
BOOLEAN	gnc_InitMultiplication (ring r, bool bSetupQuotient=false)
BOOLEAN	nc_CallPlural (matrix CCC, matrix DDD, poly CCN, poly DDN, ring r, bool bSetupQuotient, bool bCopyInput, bool bBeQuiet, ring curr, bool dummy_ring)
	returns TRUE if there were errors analyze inputs, check them for consistency detects nc_type, DO NOT initialize multiplication but call for it at the end checks the ordering condition and evtl. NDC NOTE: all the data belong to the curr, we change r which may be the same ring, and must have the same representation! More...
bool	nc_rCopy (ring res, const ring r, bool bSetupQuotient)
static void	gnc_p_ProcsSet (ring rGR, p_Procs_s *p_Procs)
void	nc_p_ProcsSet (ring rGR, p_Procs_s *p_Procs)
poly	nc_pSubst (poly p, int n, poly e, const ring r)
	substitute the n-th variable by e in p destroy p e is not a constant More...
ring	nc_rCreateNCcomm (ring r)
poly	p_CopyEmbed (poly p, ring srcRing, int shift, int, ring dstRing)
BOOLEAN	rIsLikeOpposite (ring rBase, ring rCandidate)
	checks whether rings rBase and rCandidate could be opposite to each other returns TRUE if it is so More...
poly	pOppose (ring Rop, poly p, const ring dst)
	opposes a vector p from Rop to currRing (dst!) More...
ideal	idOppose (ring Rop, ideal I, const ring dst)
	opposes a module I from Rop to currRing(dst) More...
bool	nc_SetupQuotient (ring rGR, const ring rG, bool bCopy)

Variables
int	iNCExtensions = SCAMASK | NOFORMULAMASK

Macro Definition Documentation

#define freeN	(		A,
			k
	)		omFreeSize((ADDRESS)A,k*sizeof(number))

Definition at line 95 of file old.gring.cc.

#define freeT	(		A,
			v
	)		omFreeSize((ADDRESS)A,(v+1)*sizeof(int))

Definition at line 94 of file old.gring.cc.

#define MYTEST   0

Definition at line 11 of file old.gring.cc.

#define OUTPUT   0

Definition at line 12 of file old.gring.cc.

#define PLURAL_INTERNAL_DECLARATIONS

Definition at line 26 of file old.gring.cc.

Function Documentation

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

Definition at line 236 of file old.gring.cc.

{
  poly res=NULL;
  poly qq,pp;
  if (copy)
  {
    qq=p_Copy(q,r);
    pp=p_Copy(p,r);
  }
  else
  {
    qq=q;
    pp=p;
  }
  while (qq!=NULL)
  {
    res=p_Add_q(res, pp_Mult_mm(pp, qq, r), r); // p_Head(qq, r)?
    qq=p_LmDeleteAndNext(qq,r);
  }
  p_Delete(&pp,r);
  return(res);
}

poly _nc_p_Mult_q	(	poly	pPolyP,
		poly	pPolyQ,
		const ring	rRing
	)

general NC-multiplication with destruction

Definition at line 261 of file old.gring.cc.

{
  assume( rIsPluralRing(rRing) );
#ifdef PDEBUG
  p_Test(pPolyP, rRing);
  p_Test(pPolyQ, rRing);
#endif
#ifdef RDEBUG
  rTest(rRing);
#endif

  int lp, lq;

  pqLength(pPolyP, pPolyQ, lp, lq, MIN_LENGTH_BUCKET);

  bool bUsePolynomial = TEST_OPT_NOT_BUCKETS || (si_max(lp, lq) < MIN_LENGTH_BUCKET); // ???

  CPolynomialSummator sum(rRing, bUsePolynomial);

  if (lq <= lp) // ?
  {
    // always length(q) times "p * q[j]"
    for( ; pPolyQ!=NULL; pPolyQ  = p_LmDeleteAndNext( pPolyQ, rRing ) )
      sum += pp_Mult_mm( pPolyP, pPolyQ, rRing);

    p_Delete( &pPolyP, rRing );
  } else
  {
    // always length(p) times "p[i] * q"
    for( ; pPolyP!=NULL; pPolyP  = p_LmDeleteAndNext( pPolyP, rRing ) )
      sum += nc_mm_Mult_pp( pPolyP, pPolyQ, rRing);

    p_Delete( &pPolyQ, rRing );
  }

  return(sum);
}

poly _nc_pp_Mult_qq	(	const poly	pPolyP,
		const poly	pPolyQ,
		const ring	rRing
	)

general NC-multiplication without destruction

Definition at line 300 of file old.gring.cc.

{
  assume( rIsPluralRing(rRing) );
#ifdef PDEBUG
  p_Test(pPolyP, rRing);
  p_Test(pPolyQ, rRing);
#endif
#ifdef RDEBUG
  rTest(rRing);
#endif

  int lp, lq;

  pqLength(pPolyP, pPolyQ, lp, lq, MIN_LENGTH_BUCKET);

  bool bUsePolynomial = TEST_OPT_NOT_BUCKETS || (si_max(lp, lq) < MIN_LENGTH_BUCKET); // ???

  CPolynomialSummator sum(rRing, bUsePolynomial);

  if (lq <= lp) // ?
  {
    // always length(q) times "p * q[j]"
    for( poly q = pPolyQ; q !=NULL; q = pNext(q) )
      sum += pp_Mult_mm(pPolyP, q, rRing);
  } else
  {
    // always length(p) times "p[i] * q"
    for( poly p = pPolyP; p !=NULL; p = pNext(p) )
      sum += nc_mm_Mult_pp( p, pPolyQ, rRing);
  }

  return(sum);
}

int& getNCExtensions

(

)

Definition at line 75 of file old.gring.cc.

{
  return (iNCExtensions);
}

BOOLEAN gnc_CheckOrdCondition	(	matrix	D,
		ring	r
	)

Definition at line 2679 of file old.gring.cc.

{
  /* analyze D: an upper triangular matrix of polys */
  /* check the ordering condition for D */
//  ring save = currRing;
//  int WeChangeRing = 0;
//  if (r != currRing)
//  {
//    rChangeCurrRing(r);
//    WeChangeRing = 1;
//  }
  poly p,q;
  int i,j;
  int report = 0;
  for(i=1; i<r->N; i++)
  {
    for(j=i+1; j<=r->N; j++)
    {
      p = nc_p_CopyGet(MATELEM(D,i,j),r);
      if ( p != NULL)
      {
         q = p_One(r);
         p_SetExp(q,i,1,r);
         p_SetExp(q,j,1,r);
         p_Setm(q,r);
         if (p_LmCmp(q,p,r) != 1) /* i.e. lm(p)==xy < lm(q)==D_ij  */
           {
              Werror("Bad ordering at %d,%d\n",i,j);
#if 0 /*Singularg should not differ from Singular except in error case*/
      p_Write(p,r);
      p_Write(q,r);
#endif
              report = 1;
           }
         p_Delete(&q,r);
         p_Delete(&p,r);
         p = NULL;
      }
    }
  }
//  if ( WeChangeRing )
//    rChangeCurrRing(save);
  return(report);
}

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

Definition at line 1605 of file old.gring.cc.

{
#ifdef PDEBUG
  p_Test(p1, r);
  p_Test(p2, r);
#if MYTEST
  Print("p1: "); p_Write(p1, r);
  Print("p2: "); p_Write(p2, r);
#endif
#endif

  const long lCompP1 = p_GetComp(p1,r);
  const long lCompP2 = p_GetComp(p2,r);

  if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0))
  {
#ifdef PDEBUG
    Werror("gnc_CreateSpolyNew: different non-zero components!");
    assume(0);
#endif
    return(NULL);
  }

//   if ((r->GetNC()->type==nc_lie) && pHasNotCF(p1,p2)) /* prod crit */
//   {
//     return(nc_p_Bracket_qq(pCopy(p2),p1));
//   }

//  poly pL=p_One( r);

  poly m1=p_One( r);
  poly m2=p_One( r);

  poly pL = p_Lcm(p1,p2,r);                               // pL = lcm( lm(p1), lm(p2) )


#ifdef PDEBUG
//  p_Test(pL,r);
#endif

  p_ExpVectorDiff(m1, pL, p1, r);                  // m1 = pL / lm(p1)
  //p_SetComp(m1,0,r);
  //p_Setm(m1,r);

#ifdef PDEBUG
  p_Test(m1,r);
#endif
//  assume(p_GetComp(m1,r) == 0);

  p_ExpVectorDiff(m2, pL, p2, r);                  // m2 = pL / lm(p2)

  //p_SetComp(m2,0,r);
  //p_Setm(m2,r);
#ifdef PDEBUG
  p_Test(m2,r);
#endif

#ifdef PDEBUG
#if MYTEST
  Print("m1: "); pWrite(m1);
  Print("m2: "); pWrite(m2);
#endif
#endif


//  assume(p_GetComp(m2,r) == 0);

#ifdef PDEBUG
#if 0
  if(  (p_GetComp(m2,r) != 0) || (p_GetComp(m1,r) != 0) )
  {
    WarnS("gnc_CreateSpolyNew: wrong monomials!");


#ifdef RDEBUG
    PrintS("m1 = "); p_Write(m1, r);
    p_DebugPrint(m1, r);

    PrintS("m2 = "); p_Write(m2, r);
    p_DebugPrint(m2, r);

    PrintS("p1 = "); p_Write(p1, r);
    p_DebugPrint(p1, r);

    PrintS("p2 = "); p_Write(p2, r);
    p_DebugPrint(p2, r);

    PrintS("pL = "); p_Write(pL, r);
    p_DebugPrint(pL, r);
#endif

  }

#endif
#endif

  p_Delete(&pL,r);

  /* zero exponents !? */
  poly M1    = nc_mm_Mult_p(m1,p_Head(p1,r),r); // M1 = m1 * lt(p1)
  poly M2    = nc_mm_Mult_p(m2,p_Head(p2,r),r); // M2 = m2 * lt(p2)

#ifdef PDEBUG
  p_Test(M1,r);
  p_Test(M2,r);

#if MYTEST
  Print("M1: "); pWrite(M1);
  Print("M2: "); pWrite(M2);
#endif
#endif

  if(M1 == NULL || M2 == NULL)
  {
#ifdef PDEBUG
       Print("\np1 = ");
       p_Write(p1, r);

       Print("m1 = ");
       p_Write(m1, r);

       Print("p2 = ");
       p_Write(p2, r);

       Print("m2 = ");
       p_Write(m2, r);

       Werror("ERROR in nc_CreateSpoly: result of multiplication is Zero!\n");
#endif
       return(NULL);
  }

  number C1  = p_GetCoeff(M1,r);      // C1 = lc(M1)
  number C2  = p_GetCoeff(M2,r);      // C2 = lc(M2)

  /* GCD stuff */
  number C = n_SubringGcd(C1, C2, r->cf);           // C = gcd(C1, C2)

  if (!n_IsOne(C, r))                              // if C != 1
  {
    C1=n_Div(C1, C, r);n_Normalize(C1,r);            // C1 = C1 / C
    C2=n_Div(C2, C, r);n_Normalize(C2,r);            // C2 = C2 / C
  }
  else
  {
    C1=n_Copy(C1,r);
    C2=n_Copy(C2,r);
  }

  n_Delete(&C,r); // destroy the number C

  C1=n_InpNeg(C1,r);

//   number MinusOne=n_Init(-1,r);
//   if (n_Equal(C1,MinusOne,r))                   // lc(M1) / gcd( lc(M1), lc(M2)) == -1 ????
//   {
//     M2=p_Add_q(M1,M2,r);                        // ?????
//   }
//   else
//   {
  M1=p_Mult_nn(M1,C2,r);                           // M1 = (C2*lc(p1)) * (lcm(lm(p1),lm(p2)) / lm(p1)) * lm(p1)

#ifdef PDEBUG
  p_Test(M1,r);
#endif

  M2=p_Mult_nn(M2,C1,r);                           // M2 =(-C1*lc(p2)) * (lcm(lm(p1),lm(p2)) / lm(p2)) * lm(p2)



#ifdef PDEBUG
  p_Test(M2,r);

#if MYTEST
  Print("M1: "); pWrite(M1);
  Print("M2: "); pWrite(M2);
#endif
#endif


  M2=p_Add_q(M1,M2,r);                             // M1 is killed, M2 = spoly(lt(p1), lt(p2)) = C2*M1 - C1*M2

#ifdef PDEBUG
  p_Test(M2,r);

#if MYTEST
  Print("M2: "); pWrite(M2);
#endif

#endif

// M2 == 0 for supercommutative algebras!
//   }
//   n_Delete(&MinusOne,r);

  p_SetCoeff(m1,C2,r);                           // lc(m1) = C2!!!
  p_SetCoeff(m2,C1,r);                           // lc(m2) = C1!!!

#ifdef PDEBUG
  p_Test(m1,r);
  p_Test(m2,r);
#endif

//  poly tmp = p_Copy(p1,r);                         // tmp = p1
//  tmp=p_LmDeleteAndNext(tmp,r);                  // tmp = tail(p1)
//#ifdef PDEBUG
//  p_Test(tmp,r);
//#endif

  M1 = nc_mm_Mult_pp(m1, pNext(p1), r);                      // M1 = m1 * tail(p1), delete tmp // ???

#ifdef PDEBUG
  p_Test(M1,r);

#if MYTEST
  Print("M1: "); pWrite(M1);
#endif

#endif

  M2=p_Add_q(M2,M1,r);                           // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1), delete M1
#ifdef PDEBUG
  M1=NULL;
  p_Test(M2,r);

#if MYTEST
  Print("M2: "); pWrite(M2);
#endif

#endif

//  tmp=p_Copy(p2,r);                              // tmp = p2
//  tmp=p_LmDeleteAndNext(tmp,r);                  // tmp = tail(p2)

//#ifdef PDEBUG
//  p_Test(tmp,r);
//#endif

  M1 = nc_mm_Mult_pp(m2, pNext(p2), r);                      // M1 = m2 * tail(p2), detele tmp

#ifdef PDEBUG
  p_Test(M1,r);

#if MYTEST
  Print("M1: "); pWrite(M1);
#endif

#endif

  M2 = p_Add_q(M2,M1,r);                           // M2 = spoly(lt(p1), lt(p2)) + m1 * tail(p1) + m2*tail(p2)

#ifdef PDEBUG
  M1=NULL;
  p_Test(M2,r);

#if MYTEST
  Print("M2: "); pWrite(M2);
#endif

#endif

  p_Delete(&m1,r);  //  => n_Delete(&C1,r);
  p_Delete(&m2,r);  //  => n_Delete(&C2,r);

#ifdef PDEBUG
  p_Test(M2,r);
#endif

  if (M2!=NULL) p_Cleardenom(M2,r);

  return(M2);
}

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

Definition at line 1517 of file old.gring.cc.

{
#ifdef PDEBUG
  if ((p_GetComp(p1,r)!=p_GetComp(p2,r))
  && (p_GetComp(p1,r)!=0)
  && (p_GetComp(p2,r)!=0))
  {
    dReportError("gnc_CreateSpolyOld : different components!");
    return(NULL);
  }
#endif
  if ((ncRingType(r)==nc_lie) && p_HasNotCF(p1,p2, r)) /* prod crit */
  {
    return(nc_p_Bracket_qq(p_Copy(p2, r),p1, r));
  }
  poly pL=p_One(r);
  poly m1=p_One(r);
  poly m2=p_One(r);
  pL = p_Lcm(p1,p2,r);
  p_Setm(pL,r);
#ifdef PDEBUG
  p_Test(pL,r);
#endif
  p_ExpVectorDiff(m1,pL,p1,r);
  //p_SetComp(m1,0,r);
  //p_Setm(m1,r);
#ifdef PDEBUG
  p_Test(m1,r);
#endif
  p_ExpVectorDiff(m2,pL,p2,r);
  //p_SetComp(m2,0,r);
  //p_Setm(m2,r);
#ifdef PDEBUG
  p_Test(m2,r);
#endif
  p_Delete(&pL,r);
  /* zero exponents ! */
  poly M1    = nc_mm_Mult_p(m1,p_Head(p1,r),r);
  number C1  = p_GetCoeff(M1,r);
  poly M2    = nc_mm_Mult_p(m2,p_Head(p2,r),r);
  number C2  = p_GetCoeff(M2,r);
  /* GCD stuff */
  number C = n_SubringGcd(C1,C2,r->cf);
  if (!n_IsOne(C,r))
  {
    C1=n_Div(C1,C, r);n_Normalize(C1,r);
    C2=n_Div(C2,C, r);n_Normalize(C2,r);
  }
  else
  {
    C1=n_Copy(C1, r);
    C2=n_Copy(C2, r);
  }
  n_Delete(&C,r);
  M1=p_Mult_nn(M1,C2,r);
  p_SetCoeff(m1,C2,r);
  if (n_IsMOne(C1,r))
  {
    M2=p_Add_q(M1,M2,r);
  }
  else
  {
    C1=n_InpNeg(C1,r);
    M2=p_Mult_nn(M2,C1,r);
    M2=p_Add_q(M1,M2,r);
    p_SetCoeff(m2,C1,r);
  }
  /* M1 is killed, M2=res = C2 M1 - C1 M2 */
  poly tmp=p_Copy(p1,r);
  tmp=p_LmDeleteAndNext(tmp,r);
  M1=nc_mm_Mult_p(m1,tmp,r);
  tmp=p_Copy(p2,r);
  tmp=p_LmDeleteAndNext(tmp,r);
  M2=p_Add_q(M2,M1,r);
  M1=nc_mm_Mult_p(m2,tmp,r);
  M2=p_Add_q(M2,M1,r);
  p_Delete(&m1,r);
  p_Delete(&m2,r);
  //  n_Delete(&C1,r);
  //  n_Delete(&C2,r);
#ifdef PDEBUG
  p_Test(M2,r);
#endif
  if (M2!=NULL) M2=p_Cleardenom(M2,r);
  //if (M2!=NULL) p_Content(M2); // done by pCleardenom
  return(M2);
}

BOOLEAN gnc_InitMultiplication	(	ring	r,
		bool	bSetupQuotient = false
	)

Definition at line 3087 of file old.gring.cc.

{
  /* returns TRUE if there were errors */
  /* initialize the multiplication: */
  /*  r->GetNC()->MTsize, r->GetNC()->MT, r->GetNC()->COM, */
  /* and r->GetNC()->IsSkewConstant for the skew case */
  if (rVar(r)==1)
  {
    ncRingType(r, nc_comm);
    r->GetNC()->IsSkewConstant=1;
    return FALSE;
  }

//  ring save = currRing;
//  int WeChangeRing = 0;

//  if (currRing!=r)
//  {
//    rChangeCurrRing(r);
//    WeChangeRing = 1;
//  }
//  assume( (currRing == r)
//       && (currRing->GetNC()!=NULL) );   // otherwise we cannot work with all these matrices!

  int i,j;
  r->GetNC()->MT = (matrix *)omAlloc0((r->N*(r->N-1))/2*sizeof(matrix));
  r->GetNC()->MTsize = (int *)omAlloc0((r->N*(r->N-1))/2*sizeof(int));
  id_Test((ideal)r->GetNC()->C, r);
  matrix COM = mp_Copy(r->GetNC()->C, r);
  poly p,q;
  short DefMTsize=7;
  int IsNonComm=0;
//  bool tmpIsSkewConstant = false;

  for(i=1; i<r->N; i++)
  {
    for(j=i+1; j<=r->N; j++)
    {
      if ( MATELEM(r->GetNC()->D,i,j) == NULL ) /* quasicommutative case */
      {
        /* 1x1 mult.matrix */
        r->GetNC()->MTsize[UPMATELEM(i,j,r->N)] = 1;
        r->GetNC()->MT[UPMATELEM(i,j,r->N)] = mpNew(1,1);
      }
      else /* pure noncommutative case */
      {
        /* TODO check the special multiplication properties */
        IsNonComm = 1;
        p_Delete(&(MATELEM(COM,i,j)),r);
        //MATELEM(COM,i,j) = NULL; // done by p_Delete
        r->GetNC()->MTsize[UPMATELEM(i,j,r->N)] = DefMTsize; /* default sizes */
        r->GetNC()->MT[UPMATELEM(i,j,r->N)] = mpNew(DefMTsize, DefMTsize);
      }
      /* set MT[i,j,1,1] to c_i_j*x_i*x_j + D_i_j */
      p = p_One(r);
      if (MATELEM(r->GetNC()->C,i,j)!=NULL)
        p_SetCoeff(p,n_Copy(pGetCoeff(MATELEM(r->GetNC()->C,i,j)),r),r);
      p_SetExp(p,i,1,r);
      p_SetExp(p,j,1,r);
      p_Setm(p,r);
      p_Test(MATELEM(r->GetNC()->D,i,j),r);
      q =  nc_p_CopyGet(MATELEM(r->GetNC()->D,i,j),r);
      p = p_Add_q(p,q,r);
      MATELEM(r->GetNC()->MT[UPMATELEM(i,j,r->N)],1,1) = nc_p_CopyPut(p,r);
      p_Delete(&p,r);
      // p = NULL;// done by p_Delete
    }
  }
  if (ncRingType(r)==nc_undef)
  {
    if (IsNonComm==1)
    {
      //      assume(pN!=NULL);
      //      if ((tmpIsSkewConstant==1) && (nIsOne(pGetCoeff(pN)))) r->GetNC()->type=nc_lie;
      //      else r->GetNC()->type=nc_general;
    }
    if (IsNonComm==0)
    {
      ncRingType(r, nc_skew); // TODO: check whether it is commutative
      r->GetNC()->IsSkewConstant = 0; // true; //tmpIsSkewConstant; //  BUG???
    } else
       assume( FALSE );
  }
  r->GetNC()->COM=COM;

  nc_p_ProcsSet(r, r->p_Procs);

  if(bSetupQuotient) // Test me!!!
    nc_SetupQuotient(r, NULL, false); // no copy!


//  if (save != currRing)
//    rChangeCurrRing(save);

  return FALSE;
}

void gnc_kBucketPolyRed_ZNew	(	kBucket_pt	b,
		poly	p,
		number *	c
	)

Definition at line 2113 of file old.gring.cc.

{
  const ring r = b->bucket_ring;
  // b is multiplied by a constant in this impl.
  number ctmp;
  poly m=p_One(r);
  p_ExpVectorDiff(m,kBucketGetLm(b),p, r);
  //pSetm(m);
#ifdef PDEBUG
  p_Test(m, r);
#endif

  if(p_IsConstant(m,r))
  {
    p_Delete(&m, r);
    ctmp = kBucketPolyRed(b,p,pLength(p),NULL);
  }
  else
  {
    poly pp = nc_mm_Mult_pp(m,p,r);
    number c2;
    p_Cleardenom_n(pp,r,c2);
    p_Delete(&m, r);
    ctmp = kBucketPolyRed(b,pp,pLength(pp),NULL);
    //cc=*c;
    //*c=nMult(*c,c2);
    n_Delete(&c2, r);
    //nDelete(&cc);
    p_Delete(&pp, r);
  }
  if (c!=NULL) *c=ctmp;
  else n_Delete(&ctmp, r);
}

void gnc_kBucketPolyRed_ZOld	(	kBucket_pt	b,
		poly	p,
		number *	c
	)

Definition at line 2080 of file old.gring.cc.

{
  const ring r = b->bucket_ring;
  // b is multiplied by a constant in this impl.
  number ctmp;
  poly m=p_One(r);
  p_ExpVectorDiff(m,kBucketGetLm(b),p, r);
  //pSetm(m);
#ifdef PDEBUG
  p_Test(m, r);
#endif
  if(p_IsConstant(m,r))
  {
    p_Delete(&m, r);
    ctmp = kBucketPolyRed(b,p,pLength(p),NULL);
  }
  else
  {
    poly pp = nc_mm_Mult_pp(m,p,r);
    number c2;
    p_Cleardenom_n(pp,r,c2);
    p_Delete(&m, r);
    ctmp = kBucketPolyRed(b,pp,pLength(pp),NULL);
    //cc=*c;
    //*c=nMult(*c,c2);
    n_Delete(&c2, r);
    //nDelete(&cc);
    p_Delete(&pp, r);
  }
  if (c!=NULL) *c=ctmp;
  else n_Delete(&ctmp, r);
}

void gnc_kBucketPolyRedNew	(	kBucket_pt	b,
		poly	p,
		number *	c
	)

Definition at line 2000 of file old.gring.cc.

{
  const ring r = b->bucket_ring;
#ifdef PDEBUG
//   Print(">*");
#endif

#ifdef KDEBUG
  if( !kbTest(b) )Werror("nc_kBucketPolyRed: broken bucket!");
#endif

#ifdef PDEBUG
  p_Test(p, r);
#if MYTEST
  Print("p: "); p_Write(p, r);
#endif
#endif

  // b will not be multiplied by any constant in this impl.
  // ==> *c=1
  if (c!=NULL) *c=n_Init(1, r);
  poly m = p_One(r);
  const poly pLmB = kBucketGetLm(b); // no new copy!

  assume( pLmB != NULL );

#ifdef PDEBUG
  p_Test(pLmB, r);

#if MYTEST
  Print("pLmB: "); p_Write(pLmB, r);
#endif
#endif

  p_ExpVectorDiff(m, pLmB, p, r);
  //pSetm(m);

#ifdef PDEBUG
  p_Test(m, r);
#if MYTEST
  Print("m: "); p_Write(m, r);
#endif
#endif

  poly pp = nc_mm_Mult_pp(m, p, r);
  p_Delete(&m, r);

  assume( pp != NULL );
  const number n = p_GetCoeff(pp, r); // bug!

  if (!n_IsMOne(n, r) ) // does this improve performance??!? also see below... // TODO: check later on.
  // if n == -1 => nn = 1 and -1/n
  {
    number nn=n_InpNeg(n_Invers(n, r), r);
    number t = n_Mult(nn,p_GetCoeff(pLmB, r), r);
    n_Delete(&nn, r);
    pp = p_Mult_nn(pp,t,r);
    n_Delete(&t, r);
  }
  else
  {
    pp = p_Mult_nn(pp,p_GetCoeff(pLmB, r), r);
  }

  int l = pLength(pp);

#ifdef PDEBUG
  p_Test(pp, r);
//   Print("PP: "); pWrite(pp);
#endif

  kBucket_Add_q(b,pp,&l);


#ifdef PDEBUG
//   Print("*>");
#endif
}

void gnc_kBucketPolyRedOld	(	kBucket_pt	b,
		poly	p,
		number *	c
	)

Definition at line 1967 of file old.gring.cc.

{
  const ring r = b->bucket_ring;
  // b will not be multiplied by any constant in this impl.
  // ==> *c=1
  if (c!=NULL) *c=n_Init(1, r);
  poly m=p_One(r);
  p_ExpVectorDiff(m,kBucketGetLm(b),p, r);
  //pSetm(m);
#ifdef PDEBUG
  p_Test(m, r);
#endif
  poly pp= nc_mm_Mult_pp(m,p, r);
  assume(pp!=NULL);
  p_Delete(&m, r);
  number n=p_GetCoeff(pp, r);
  number nn;
  if (!n_IsMOne(n, r))
  {
    nn=n_InpNeg(n_Invers(n, r), r);
    n= n_Mult(nn,p_GetCoeff(kBucketGetLm(b), r), r);
    n_Delete(&nn, r);
    pp=p_Mult_nn(pp,n,r);
    n_Delete(&n, r);
  }
  else
  {
    pp=p_Mult_nn(pp,p_GetCoeff(kBucketGetLm(b), r),r);
  }
  int l=pLength(pp);
  kBucket_Add_q(b,pp,&l);
}

poly gnc_mm_Mult_nn	(	int *	F,
		int *	G,
		const ring	r
	)

Definition at line 460 of file old.gring.cc.

{
  poly out=NULL;
  int i,j;
  int iF,jG,iG;
  int rN=r->N;

  int *F=(int *)omAlloc0((rN+1)*sizeof(int));
  int *G=(int *)omAlloc0((rN+1)*sizeof(int));

  memcpy(F, F0,(rN+1)*sizeof(int));
  // pExpVectorCopy(F,F0);
  memcpy(G, G0,(rN+1)*sizeof(int));
  //  pExpVectorCopy(G,G0);
  F[0]=0;
  G[0]=0;

  iF=rN;
  while ((F[iF]==0)&&(iF>=1)) iF--; /* last exp_num of F */
  if (iF==0) /* F0 is zero vector */
  {
    out=p_One(r);
    p_SetExpV(out,G0,r);
    p_Setm(out,r);
    freeT(F,rN);
    freeT(G,rN);
    return(out);
  }
  jG=1;
  while ((G[jG]==0)&&(jG<rN)) jG++;  /* first exp_num of G */
  iG=rN;
  while ((G[iG]==0)&&(iG>1)) iG--;  /* last exp_num of G */

  out=p_One(r);

  if (iF<=jG)
    /* i.e. no mixed exp_num , MERGE case */
  {
    { for(int ii=rN;ii>0;ii--) F[ii]+=G[ii]; }
    p_SetExpV(out,F,r);
    p_Setm(out,r);
    freeT(F,rN);
    freeT(G,rN);
    return(out);
  }

  number cff=n_Init(1,r);
  number tmp_num=NULL;
  int cpower=0;

  if (ncRingType(r)==nc_skew)
  {
    if (r->GetNC()->IsSkewConstant==1)
    {
      int tpower=0;
      for(j=jG; j<=iG; j++)
      {
        if (G[j]!=0)
        {
          cpower = 0;
          for(i=j+1; i<=iF; i++)
          {
            cpower = cpower + F[i];
          }
          cpower = cpower*G[j]; // bug! here may happen an arithmetic overflow!!!
          tpower = tpower + cpower;
        }
      }
      cff = n_Copy(p_GetCoeff(MATELEM(r->GetNC()->COM,1,2),r),r);
      n_Power(cff,tpower,&tmp_num, r);
      n_Delete(&cff,r);
      cff = tmp_num;
    }
    else /* skew commutative with nonequal coeffs */
    {
      number totcff=n_Init(1,r);
      for(j=jG; j<=iG; j++)
      {
        if (G[j]!=0)
        {
          cpower = 0;
          for(i=j+1; i<=iF; i++)
          {
            if (F[i]!=0)
            {
              cpower = F[i]*G[j]; // bug! overflow danger!!!
              cff = n_Copy(p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r),r);
              n_Power(cff,cpower,&tmp_num, r);
              cff = n_Mult(totcff,tmp_num, r);
              n_Delete(&totcff, r);
              n_Delete(&tmp_num, r);
              totcff = n_Copy(cff,r);
              n_Delete(&cff,r);
            }
          } /* end 2nd for */
        }
      }
      cff=totcff;
    }
    { for(int ii=rN;ii>0;ii--) F[ii]+=G[ii]; }
    p_SetExpV(out,F,r);
    p_Setm(out,r);
    p_SetCoeff(out,cff,r);
    freeT(F,rN);
    freeT(G,rN);
    return(out);
  } /* end nc_skew */

  /* now we have to destroy out! */
  p_Delete(&out,r);

  if (iG==jG)
    /* g is univariate monomial */
  {
    /*    if (ri->GetNC()->type==nc_skew) -- postpone to TU */
    out = gnc_mm_Mult_uu(F,jG,G[jG],r);
    freeT(F,rN);
    freeT(G,rN);
    return(out);
  }

  int *Prv=(int *)omAlloc0((rN+1)*sizeof(int));
  int *Nxt=(int *)omAlloc0((rN+1)*sizeof(int));

  int *log=(int *)omAlloc0((rN+1)*sizeof(int));
  int cnt=0; int cnf=0;

  /* splitting F wrt jG */
  for (i=1;i<=jG;i++)
  {
    Prv[i]=F[i]; Nxt[i]=0; /* mult at the very end */
    if (F[i]!=0) cnf++;
  }

  if (cnf==0) freeT(Prv,rN);

  for (i=jG+1;i<=rN;i++)
  {
    Nxt[i]=F[i];
    /*    if (cnf!=0)  Prv[i]=0; */
    if (F[i]!=0)
    {
      cnt++;
    }              /* effective part for F */
  }
  freeT(F,rN);
  cnt=0;

  for (i=1;i<=rN;i++)
  {
    if (G[i]!=0)
    {
     cnt++;
     log[cnt]=i;
     }               /* lG for G */
   }

/* ---------------------- A C T I O N ------------------------ */
  poly D=NULL;
  poly Rout=NULL;
  number *c=(number *)omAlloc0((rN+1)*sizeof(number));
  c[0]=n_Init(1,r);

  int *Op=Nxt;
  int *On=G;
  int *U=(int *)omAlloc0((rN+1)*sizeof(int));

  for (i=jG;i<=rN;i++) U[i]=Nxt[i]+G[i];  /* make leadterm */
  Nxt=NULL;
  G=NULL;
  cnt=1;
  int t=0;
  poly w=NULL;
  poly Pn=p_One(r);
  p_SetExpV(Pn,On,r);
  p_Setm(Pn,r);

  while (On[iG]!=0)
  {
     t=log[cnt];

     w=gnc_mm_Mult_uu(Op,t,On[t],r);
     c[cnt]=n_Mult(c[cnt-1],p_GetCoeff(w,r),r);
     D = pNext(w);  /* getting coef and rest D */
     p_LmDelete(&w,r);
     w=NULL;

     Op[t] += On[t];   /* update exp_vectors */
     On[t] = 0;

     if (t!=iG)    /* not the last step */
     {
       p_SetExpV(Pn,On,r);
       p_Setm(Pn,r);
#ifdef PDEBUG
       p_Test(Pn,r);
#endif

//       if (pNext(D)==0)
// is D a monomial? could be postponed higher
//       {
//       Rout=nc_mm_Mult_nn(D,Pn,r);
//       }
//       else
//       {
       Rout=gnc_p_Mult_mm(D,Pn,r);
//       }
     }
     else
     {
       Rout=D;
       D=NULL;
     }

     if (Rout!=NULL)
     {
       Rout=p_Mult_nn(Rout,c[cnt-1],r); /* Rest is ready */
       out=p_Add_q(out,Rout,r);
       Rout=NULL;
     }
     cnt++;
  }
  freeT(On,rN);
  freeT(Op,rN);
  p_Delete(&Pn,r);
  omFreeSize((ADDRESS)log,(rN+1)*sizeof(int));

  /* leadterm and Prv-part */

  Rout=p_One(r);
  /* U is lead.monomial */
  U[0]=0;
  p_SetExpV(Rout,U,r);
  p_Setm(Rout,r);  /* use again this name Rout */
#ifdef PDEBUG
  p_Test(Rout,r);
#endif
  p_SetCoeff(Rout,c[cnt-1],r);
  out=p_Add_q(out,Rout,r);
  freeT(U,rN);
  freeN(c,rN+1);
  if (cnf!=0)  /* Prv is non-zero vector */
  {
    Rout=p_One(r);
    Prv[0]=0;
    p_SetExpV(Rout,Prv,r);
    p_Setm(Rout,r);
#ifdef PDEBUG
    p_Test(Rout,r);
#endif
    out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */
    freeT(Prv,rN);
    p_Delete(&Rout,r);
  }
  return (out);
}

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

Definition at line 448 of file old.gring.cc.

{
  return( gnc_p_Mult_mm_Common(p, m, 0, r) );
}

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

Definition at line 453 of file old.gring.cc.

{
  return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 0, r) );
}

poly gnc_mm_Mult_uu	(	int *	F,
		int	jG,
		int	bG,
		const ring	r
	)

Definition at line 719 of file old.gring.cc.

{
  poly out=NULL;
  int i;
  number num=NULL;

  int rN=r->N;
  int iF=r->N;
  while ((F[iF]==0)&&(iF>0)) iF-- ;   /* last exponent_num of F */

  if (iF==0)  /* F==zero vector in other words */
  {
   out=p_One(r);
   p_SetExp(out,jG,bG,r);
   p_Setm(out,r);
   return(out);
  }

  int jF=1;
  while ((F[jF]==0)&&(jF<=rN)) jF++;  /* first exp of F */

  if (iF<=jG)                       /* i.e. no mixed exp_num */
  {
    out=p_One(r);
    F[jG]=F[jG]+bG;
    p_SetExpV(out,F,r);
    p_Setm(out,r);
    return(out);
  }

  if (iF==jF)              /* uni times uni */
  {
   out=gnc_uu_Mult_ww(iF,F[iF],jG,bG,r);
   return(out);
  }

  /* Now: F is mono with >=2 exponents, jG<iF */
  /* check the quasi-commutative case */
//   matrix LCOM=r->GetNC()->COM;
//   number rescoef=n_Init(1,r);
//   number tmpcoef=n_Init(1,r);
//   int tmpint;
//   i=iF;
//   while (i>=jG+1)
//     /* all the non-zero exponents */
//   {
//     if (MATELEM(LCOM,jG,i)!=NULL)
//     {
//       tmpcoef=pGetCoeff(MATELEM(LCOM,jG,i));
//       tmpint=(int)F[i];
//       nPower(tmpcoef,F[i],&tmpcoef);
//       rescoef=nMult(rescoef,tmpcoef);
//       i--;
//     }
//     else
//     {
//       if (F[i]!=0) break;
//     }
//   }
//   if (iF==i)
//   /* no action took place*/
//   {

//   }
//   else /* power the result up to bG */
//   {
//     nPower(rescoef,bG,&rescoef);
//     /* + cleanup, post-processing */
//   }

  int *Prv=(int*)omAlloc0((rN+1)*sizeof(int));
  int *Nxt=(int*)omAlloc0((rN+1)*sizeof(int));
  int *lF=(int *)omAlloc0((rN+1)*sizeof(int));

  int cnt=0; int cnf=0;
  /* splitting F wrt jG */
  for (i=1;i<=jG;i++) /* mult at the very end */
  {
    Prv[i]=F[i]; Nxt[i]=0;
    if (F[i]!=0) cnf++;
  }

  if (cnf==0)
  {
    freeT(Prv,rN); Prv = NULL;
  }

  for (i=jG+1;i<=rN;i++)
  {
    Nxt[i]=F[i];
    if (cnf!=0) { Prv[i]=0;}
    if (F[i]!=0)
    {
      cnt++;
      lF[cnt]=i;
    }                 /* eff_part,lF_for_F */
  }

  if (cnt==1) /* Nxt consists of 1 nonzero el-t only */
  {
    int q=lF[1];
    poly Rout=p_One(r);
    out=gnc_uu_Mult_ww(q,Nxt[q],jG,bG,r);

    freeT(Nxt,rN);  Nxt = NULL;

    if (cnf!=0)
    {
       Prv[0]=0;
       p_SetExpV(Rout,Prv,r);
       p_Setm(Rout,r);

#ifdef PDEBUG
       p_Test(Rout,r);
#endif

       freeT(Prv,rN);
       Prv = NULL;

       out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */
    }

    freeT(lF,rN);
    lF = NULL;

    p_Delete(&Rout,r);

    assume(Nxt == NULL);
    assume(lF == NULL);
    assume(Prv == NULL);

    return (out);
  }
/* -------------------- MAIN ACTION --------------------- */

  poly D=NULL;
  poly Rout=NULL;
  number *c=(number *)omAlloc0((cnt+2)*sizeof(number));
  c[cnt+1]=n_Init(1,r);
  i=cnt+2;         /* later in freeN */
  int *Op=Nxt;

  int *On=(int *)omAlloc0((rN+1)*sizeof(int));
  int *U=(int *)omAlloc0((rN+1)*sizeof(int));


  //  pExpVectorCopy(U,Nxt);
  memcpy(U, Nxt,(rN+1)*sizeof(int));
  U[jG] = U[jG] + bG;

  /* Op=Nxt and initial On=(0); */
  Nxt=NULL;

  poly Pp;
  poly Pn;
  int t=0;
  int first=lF[1];
  int nlast=lF[cnt];
  int kk=0;
  /*  cnt--;   */
  /* now lF[cnt] should be <=iF-1 */

  while (Op[first]!=0)
  {
     t=lF[cnt];   /* cnt as it was computed */

     poly w=gnc_uu_Mult_ww(t,Op[t],jG,bG,r);
     c[cnt]=n_Copy(p_GetCoeff(w,r),r);
     D = pNext(w);  /* getting coef and rest D */
     p_LmDelete(&w,r);
     w=NULL;

     Op[t]= 0;
     Pp=p_One(r);
     p_SetExpV(Pp,Op,r);
     p_Setm(Pp,r);

     if (t<nlast)
     {
       kk=lF[cnt+1];
       On[kk]=F[kk];

       Pn=p_One(r);
       p_SetExpV(Pn,On,r);
       p_Setm(Pn,r);

       if (t!=first)   /* typical expr */
       {
         w=gnc_p_Mult_mm(D,Pn,r);
         Rout=gnc_mm_Mult_p(Pp,w,r);
         w=NULL;
       }
       else                   /* last step */
       {
         On[t]=0;
         p_SetExpV(Pn,On,r);
         p_Setm(Pn,r);
         Rout=gnc_p_Mult_mm(D,Pn,r);
       }
#ifdef PDEBUG
       p_Test(Pp,r);
#endif
       p_Delete(&Pn,r);
     }
     else                     /* first step */
     {
       Rout=gnc_mm_Mult_p(Pp,D,r);
     }
#ifdef PDEBUG
     p_Test(Pp,r);
#endif
     p_Delete(&Pp,r);
     num=n_Mult(c[cnt+1],c[cnt],r);
     n_Delete(&c[cnt],r);
     c[cnt]=num;
     Rout=p_Mult_nn(Rout,c[cnt+1],r); /* Rest is ready */
     out=p_Add_q(out,Rout,r);
     Pp=NULL;
     cnt--;
  }
  /* only to feel safe:*/
  Pn=Pp=NULL;
  freeT(On,rN);
  freeT(Op,rN);

/* leadterm and Prv-part with coef 1 */
/*  U[0]=exp; */
/*  U[jG]=U[jG]+bG;  */
/* make leadterm */
/* ??????????? we have done it already :-0 */

  Rout=p_One(r);
  p_SetExpV(Rout,U,r);
  p_Setm(Rout,r);  /* use again this name */
  p_SetCoeff(Rout,c[cnt+1],r);  /* last computed coef */

  out=p_Add_q(out,Rout,r);

  Rout=NULL;

  freeT(U, rN);
  freeN(c, i);
  freeT(lF, rN);

  if (cnf!=0)
  {
    Rout=p_One(r);
    p_SetExpV(Rout,Prv,r);
    p_Setm(Rout,r);
    freeT(Prv, rN);
    out=gnc_mm_Mult_p(Rout,out,r); /* getting the final result */
    p_Delete(&Rout,r);
  }

  return (out);
}

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

Definition at line 443 of file old.gring.cc.

{
  return( gnc_p_Mult_mm_Common(p, m, 1, r) );
}

poly gnc_p_Mult_mm_Common	(	poly	p,
		const poly	m,
		int	side,
		const ring	r
	)

Definition at line 347 of file old.gring.cc.

{
  if ((p==NULL) || (m==NULL)) return NULL;
  /*  if (pNext(p)==NULL) return(nc_mm_Mult_nn(p,pCopy(m),r)); */
  /* excluded  - the cycle will do it anyway - OK. */
  if (p_IsConstant(m,r)) return(p_Mult_nn(p,p_GetCoeff(m,r),r));

#ifdef PDEBUG
  p_Test(p,r);
  p_Test(m,r);
#endif
  poly v=NULL;
  int rN=r->N;
  int *P=(int *)omAlloc0((rN+1)*sizeof(int));
  int *M=(int *)omAlloc0((rN+1)*sizeof(int));
  /* coefficients: */
  number cP,cM,cOut;
  p_GetExpV(m, M, r);
  cM=p_GetCoeff(m,r);
  /* components:*/
  const int expM=p_GetComp(m,r);
  int expP=0;
  int expOut=0;
  /* bucket constraints: */
  int UseBuckets=1;
  if (pLength(p)< MIN_LENGTH_BUCKET || TEST_OPT_NOT_BUCKETS) UseBuckets=0;

  CPolynomialSummator sum(r, UseBuckets == 0);

  while (p!=NULL)
  {
#ifdef PDEBUG
    p_Test(p,r);
#endif
    expP=p_GetComp(p,r);
    if (expP==0)
    {
      expOut=expM;
    }
    else
    {
      if (expM==0)
      {
        expOut=expP;
#ifdef PDEBUG
        if (side)
        {
          Print("gnc_p_Mult_mm: Multiplication in the left module from the right");
        }
#endif
      }
      else
      {
        /* REPORT_ERROR */
#ifdef PDEBUG
        const char* s;
        if (side==1) s="gnc_p_Mult_mm";
        else s="gnc_mm_Mult_p";
        Print("%s: exponent mismatch %d and %d\n",s,expP,expM);
#endif
        expOut=0;
      }
    }
    p_GetExpV(p,P,r);
    cP=p_GetCoeff(p,r);
    cOut=n_Mult(cP,cM,r);
    if (side==1)
    {
      v = gnc_mm_Mult_nn(P, M, r);
    }
    else
    {
      v = gnc_mm_Mult_nn(M, P, r);
    }
    v = p_Mult_nn(v,cOut,r);
    n_Delete(&cOut,r);
    p_SetCompP(v,expOut,r);

    sum += v;

    p_LmDelete(&p,r);
  }
  freeT(P,rN);
  freeT(M,rN);

  return(sum);
}

static void gnc_p_ProcsSet ( ring  rGR, p_Procs_s *  p_Procs  )

inlinestatic

Definition at line 3187 of file old.gring.cc.

{
  // "commutative"
  p_Procs->p_Mult_mm  = rGR->p_Procs->p_Mult_mm  = gnc_p_Mult_mm;
  p_Procs->pp_Mult_mm = rGR->p_Procs->pp_Mult_mm = gnc_pp_Mult_mm;
  p_Procs->p_Minus_mm_Mult_qq = rGR->p_Procs->p_Minus_mm_Mult_qq = nc_p_Minus_mm_Mult_qq;

  // non-commutaitve multiplication by monomial from the left
  rGR->GetNC()->p_Procs.mm_Mult_p   = gnc_mm_Mult_p;
  rGR->GetNC()->p_Procs.mm_Mult_pp  = gnc_mm_Mult_pp;

#if 0
  // Previous Plural's implementation...
  rGR->GetNC()->p_Procs.SPoly       = gnc_CreateSpolyOld;
  rGR->GetNC()->p_Procs.ReduceSPoly = gnc_ReduceSpolyOld;

  rGR->GetNC()->p_Procs.BucketPolyRed  = gnc_kBucketPolyRedOld;
  rGR->GetNC()->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZOld;
#else
  // A bit cleaned up and somewhat rewritten functions...
  rGR->GetNC()->p_Procs.SPoly       = gnc_CreateSpolyNew;
  rGR->GetNC()->p_Procs.ReduceSPoly = gnc_ReduceSpolyNew;

  rGR->GetNC()->p_Procs.BucketPolyRed  = gnc_kBucketPolyRedNew;
  rGR->GetNC()->p_Procs.BucketPolyRed_Z= gnc_kBucketPolyRed_ZNew;
#endif

  // warning: ISO C++ forbids casting between pointer-to-function and pointer-to-object?
  if (rHasLocalOrMixedOrdering(rGR))
    rGR->GetNC()->p_Procs.GB = cast_A_to_vptr(gnc_gr_mora);
  else
    rGR->GetNC()->p_Procs.GB = cast_A_to_vptr(gnc_gr_bba);

///////////  rGR->GetNC()->p_Procs.GB          = gnc_gr_bba; // bba even for local case!
// old ///    r->GetNC()->GB()            = gnc_gr_bba;
//   rGR->GetNC()->p_Procs.GlobalGB    = gnc_gr_bba;
//   rGR->GetNC()->p_Procs.LocalGB     = gnc_gr_mora;
//  const ring save = currRing; if( save != r ) rChangeCurrRing(r);
//  ideal res = gnc_gr_bba(F, Q, w, hilb, strat/*, r*/);
//  if( save != r )     rChangeCurrRing(save);     return (res);


#if 0
    // Old Stuff
    p_Procs->p_Mult_mm   = gnc_p_Mult_mm;
    _p_procs->p_Mult_mm  = gnc_p_Mult_mm;

    p_Procs->pp_Mult_mm  = gnc_pp_Mult_mm;
    _p_procs->pp_Mult_mm = gnc_pp_Mult_mm;

    p_Procs->p_Minus_mm_Mult_qq = NULL; // gnc_p_Minus_mm_Mult_qq_ign;
    _p_procs->p_Minus_mm_Mult_qq= NULL; // gnc_p_Minus_mm_Mult_qq_ign;

    r->GetNC()->mmMultP()       = gnc_mm_Mult_p;
    r->GetNC()->mmMultPP()      = gnc_mm_Mult_pp;

    r->GetNC()->SPoly()         = gnc_CreateSpoly;
    r->GetNC()->ReduceSPoly()   = gnc_ReduceSpoly;

#endif
}

poly gnc_pp_Mult_mm	(	const poly	p,
		const poly	m,
		const ring	r,
		poly &	last
	)

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

Definition at line 438 of file old.gring.cc.

{
  return( gnc_p_Mult_mm_Common(p_Copy(p,r), m, 1, r) );
}

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

Definition at line 1444 of file old.gring.cc.

{
  assume(p_LmDivisibleBy(p1, p2, r));

  const long lCompP1 = p_GetComp(p1,r);
  const long lCompP2 = p_GetComp(p2,r);

  if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0))
  {
#ifdef PDEBUG
    Werror("gnc_ReduceSpolyNew: different non-zero components!");
#endif
    return(NULL);
  }

  poly m = p_One(r);
  p_ExpVectorDiff(m, p2, p1, r);
  //p_Setm(m,r);
#ifdef PDEBUG
  p_Test(m,r);
#endif

  /* pSetComp(m,r)=0? */
  poly   N  = nc_mm_Mult_p(m, p_Head(p1,r), r);

  number C  = p_GetCoeff(N,  r);
  number cF = p_GetCoeff(p2, r);

  /* GCD stuff */
  number cG = n_SubringGcd(C, cF, r->cf);

  if (!n_IsOne(cG, r))
  {
    cF = n_Div(cF, cG, r); n_Normalize(cF, r);
    C  = n_Div(C,  cG, r); n_Normalize(C, r);
  }
  else
  {
    cF = n_Copy(cF, r);
    C  = n_Copy(C, r);
  }
  n_Delete(&cG,r);

  p2 = p_Mult_nn(p2, C, r); // p2 !!!
  p_Test(p2,r);
  n_Delete(&C,r);
  n_Delete(&cG,r);

  poly out = nc_mm_Mult_pp(m, pNext(p1), r);
  p_Delete(&m,r);

  N = p_Add_q(N, out, r);
  p_Test(N,r);

  if (!n_IsMOne(cF,r)) // ???
  {
    cF = n_InpNeg(cF,r);
    N  = p_Mult_nn(N, cF, r);
    p_Test(N,r);
  }
  n_Delete(&cF,r);

  out = p_Add_q(p2,N,r); // delete N, p2
  p_Test(out,r);
  if ( out!=NULL ) p_Content(out,r);
  return(out);
}

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

Definition at line 1388 of file old.gring.cc.

{
  assume(p_LmDivisibleBy(p1, p2, r));

#ifdef PDEBUG
  if (p_GetComp(p1,r)!=p_GetComp(p2,r)
  && (p_GetComp(p1,r)!=0)
  && (p_GetComp(p2,r)!=0))
  {
    dReportError("nc_ReduceSpolyOld: different components");
    return(NULL);
  }
#endif
  poly m = p_One(r);
  p_ExpVectorDiff(m,p2,p1,r);
  //p_Setm(m,r);
#ifdef PDEBUG
  p_Test(m,r);
#endif
  /* pSetComp(m,r)=0? */
  poly   N  = nc_mm_Mult_p(m, p_Head(p1,r), r);
  number C  =  p_GetCoeff(N,  r);
  number cF =  p_GetCoeff(p2, r);
  /* GCD stuff */
  number cG = n_SubringGcd(C, cF, r->cf);
  if ( !n_IsOne(cG,r) )
  {
    cF = n_Div(cF, cG, r); n_Normalize(cF, r);
    C  = n_Div(C,  cG, r); n_Normalize(C, r);
  }
  else
  {
    cF = n_Copy(cF, r);
    C  = n_Copy(C, r);
  }
  n_Delete(&cG,r);
  p2 = p_Mult_nn(p2, C, r);
  poly out = nc_mm_Mult_pp(m, pNext(p1), r);
  N = p_Add_q(N, out, r);
  p_Test(p2,r);
  p_Test(N,r);
  if (!n_IsMOne(cF,r))
  {
    cF = n_InpNeg(cF,r);
    N  = p_Mult_nn(N, cF, r);
    p_Test(N,r);
  }
  out = p_Add_q(p2,N,r);
  p_Test(out,r);
  if ( out!=NULL ) p_Content(out,r);
  p_Delete(&m,r);
  n_Delete(&cF,r);
  n_Delete(&C,r);
  return(out);
}

poly gnc_uu_Mult_ww	(	int	i,
		int	a,
		int	j,
		int	b,
		const ring	r
	)

Definition at line 1085 of file old.gring.cc.

{
  /* Check zero exceptions, (q-)commutativity and is there something to do? */
  assume(a!=0);
  assume(b!=0);
  poly out=p_One(r);
  if (i<=j)
  {
    p_SetExp(out,i,a,r);
    p_AddExp(out,j,b,r);
    p_Setm(out,r);
    return(out);
  }/* zero exeptions and usual case */
  /*  if ((a==0)||(b==0)||(i<=j)) return(out); */

  if (MATELEM(r->GetNC()->COM,j,i)!=NULL)
    /* commutative or quasicommutative case */
  {
    p_SetExp(out,i,a,r);
    p_AddExp(out,j,b,r);
    p_Setm(out,r);
    if (n_IsOne(p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r),r)) /* commutative case */
    {
      return(out);
    }
    else
    {
      number tmp_number=p_GetCoeff(MATELEM(r->GetNC()->COM,j,i),r); /* quasicommutative case */
      n_Power(tmp_number,a*b,&tmp_number, r); // BUG! ;-(
      p_SetCoeff(out,tmp_number,r);
      return(out);
    }
  }/* end_of commutative or quasicommutative case */
  p_Delete(&out,r);


  if(ncExtensions(NOCACHEMASK) && !ncExtensions(NOFORMULAMASK)) // don't use cache whenever possible!
  { // without cache!?
    CFormulaPowerMultiplier* FormulaMultiplier = GetFormulaPowerMultiplier(r);
    Enum_ncSAType PairType = _ncSA_notImplemented;

     if( FormulaMultiplier != NULL )
       PairType = FormulaMultiplier->GetPair(j, i);

     if( PairType != _ncSA_notImplemented )
  // //    return FormulaMultiplier->Multiply(j, i, b, a);
       return CFormulaPowerMultiplier::Multiply( PairType, j, i, b, a, r);
  }


  /* we are here if  i>j and variables do not commute or quasicommute */
  /* in fact, now a>=1 and b>=1; and j<i */
  /* now check whether the polynomial is already computed */
  int rN=r->N;
  int vik = UPMATELEM(j,i,rN);
  int cMTsize=r->GetNC()->MTsize[vik];
  int newcMTsize=0;
  newcMTsize=si_max(a,b);

  if (newcMTsize<=cMTsize)
  {
    out =  nc_p_CopyGet(MATELEM(r->GetNC()->MT[vik],a,b),r);
    if (out !=NULL) return (out);
  }
  int k,m;
  if (newcMTsize > cMTsize)
  {
    int inM=(((newcMTsize+6)/7)*7);
    assume (inM>=newcMTsize);
    newcMTsize = inM;
    //    matrix tmp = (matrix)omAlloc0(inM*inM*sizeof(poly));
    matrix tmp = mpNew(newcMTsize,newcMTsize);

    for (k=1;k<=cMTsize;k++)
    {
      for (m=1;m<=cMTsize;m++)
      {
        out = MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m);
        if ( out != NULL )
        {
          MATELEM(tmp,k,m) = out;/*MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m)*/
          //           omCheckAddr(tmp->m);
          MATELEM(r->GetNC()->MT[UPMATELEM(j,i,rN)],k,m)=NULL;
          //           omCheckAddr(r->GetNC()->MT[UPMATELEM(j,i,rN)]->m);
          out=NULL;
        }
      }
    }
    id_Delete((ideal *)&(r->GetNC()->MT[UPMATELEM(j,i,rN)]),r);
    r->GetNC()->MT[UPMATELEM(j,i,rN)] = tmp;
    tmp=NULL;
    r->GetNC()->MTsize[UPMATELEM(j,i,rN)] = newcMTsize;
  }
  /* The update of multiplication matrix is finished */


  return gnc_uu_Mult_ww_formula(i, a, j, b, r);

  out = gnc_uu_Mult_ww_vert(i, a, j, b, r);
  //    out = nc_uu_Mult_ww_horvert(i, a, j, b, r);
  return(out);
}

static poly gnc_uu_Mult_ww_formula ( int  i, int  a, int  j, int  b, const ring  r  )

inlinestatic

Definition at line 1052 of file old.gring.cc.

{
  if(ncExtensions(NOFORMULAMASK))
    return gnc_uu_Mult_ww_vert(i, a, j, b, r);

  CFormulaPowerMultiplier* FormulaMultiplier = GetFormulaPowerMultiplier(r);
  Enum_ncSAType PairType = _ncSA_notImplemented;

  if( FormulaMultiplier != NULL )
    PairType = FormulaMultiplier->GetPair(j, i);


  if( PairType == _ncSA_notImplemented )
    return gnc_uu_Mult_ww_vert(i, a, j, b, r);


 //    return FormulaMultiplier->Multiply(j, i, b, a);
  poly t = CFormulaPowerMultiplier::Multiply( PairType, j, i, b, a, r);

  int rN=r->N;
  matrix cMT = r->GetNC()->MT[UPMATELEM(j,i,rN)];         /* cMT=current MT */


  MATELEM(cMT, a, b) = nc_p_CopyPut(t,r);

  //  t=MATELEM(cMT,a,b);
//  t= nc_p_CopyGet(MATELEM(cMT,a,b),r);
  //  return(p_Copy(t,r));
  /* since the last computed element was cMT[a,b] */
  return(t);
}

poly gnc_uu_Mult_ww_horvert	(	int	i,
		int	a,
		int	j,
		int	b,
		const ring	r
	)

Definition at line 1190 of file old.gring.cc.

{
  int k,m;
  int rN=r->N;
  matrix cMT=r->GetNC()->MT[UPMATELEM(j,i,rN)];         /* cMT=current MT */

  poly x=p_One(r);p_SetExp(x,j,1,r);p_Setm(x,r);/* var(j); */
  poly y=p_One(r);p_SetExp(y,i,1,r);p_Setm(y,r); /*var(i);  for convenience */
#ifdef PDEBUG
  p_Test(x,r);
  p_Test(y,r);
#endif

  poly t=NULL;

  int toXY;
  int toYX;

  if (a==1) /* y*x^b, b>=2 */
  {
    toXY=b-1;
    while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=2)) toXY--;
    for (m=toXY+1;m<=b;m++)
    {
      t=MATELEM(cMT,1,m);
      if (t==NULL)   /* remove after debug */
      {
        t = p_Copy(MATELEM(cMT,1,m-1),r);
        t = gnc_p_Mult_mm(t,x,r);
        MATELEM(cMT,1,m) = t;
        /*        omCheckAddr(cMT->m); */
      }
      else
      {
        /* Error, should never get there */
        WarnS("Error: a=1; MATELEM!=0");
      }
      t=NULL;
    }
    return(p_Copy(MATELEM(cMT,1,b),r));
  }

  if (b==1) /* y^a*x, a>=2 */
  {
    toYX=a-1;
    while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=2)) toYX--;
    for (m=toYX+1;m<=a;m++)
    {
      t=MATELEM(cMT,m,1);
      if (t==NULL)   /* remove after debug */
      {
        t = p_Copy(MATELEM(cMT,m-1,1),r);
        t = gnc_mm_Mult_p(y,t,r);
        MATELEM(cMT,m,1) = t;
        /*        omCheckAddr(cMT->m); */
      }
      else
      {
        /* Error, should never get there */
        WarnS("Error: b=1, MATELEM!=0");
      }
      t=NULL;
    }
    return(p_Copy(MATELEM(cMT,a,1),r));
  }

/* ------------ Main Cycles ----------------------------*/
  /*            a>1, b>1              */

  int dXY=0; int dYX=0;
  /* dXY = distance for computing x-mult, then y-mult */
  /* dYX = distance for computing y-mult, then x-mult */
  int toX=a-1; int toY=b-1; /* toX = to axe X, toY = to axe Y */
  toXY=b-1; toYX=a-1;
  /* if toX==0, toXY = dist. to computed y * x^toXY */
  /* if toY==0, toYX = dist. to computed y^toYX * x */
  while ( (MATELEM(cMT,toX,b)==NULL) && (toX>=1)) toX--;
  if (toX==0) /* the whole column is not computed yet */
  {
    while ( (MATELEM(cMT,1,toXY)==NULL) && (toXY>=1)) toXY--;
    /* toXY >=1 */
    dXY=b-1-toXY;
  }
  dXY=dXY+a-toX; /* the distance to nearest computed y^toX x^b */

  while ( (MATELEM(cMT,a,toY)==NULL) && (toY>=1)) toY--;
  if (toY==0) /* the whole row is not computed yet */
  {
    while ( (MATELEM(cMT,toYX,1)==NULL) && (toYX>=1)) toYX--;
    /* toYX >=1 */
    dYX=a-1-toYX;
  }
  dYX=dYX+b-toY; /* the distance to nearest computed y^a x^toY */

  if (dYX>=dXY)
  {
    /* first x, then y */
    if (toX==0) /* start with the row*/
    {
      for (m=toXY+1;m<=b;m++)
      {
        t=MATELEM(cMT,1,m);
        if (t==NULL)   /* remove after debug */
        {
          t = p_Copy(MATELEM(cMT,1,m-1),r);
          t = gnc_p_Mult_mm(t,x,r);
          MATELEM(cMT,1,m) = t;
          /*        omCheckAddr(cMT->m); */
        }
        else
        {
          /* Error, should never get there */
          WarnS("dYX>=dXY,toXY; MATELEM==0");
        }
        t=NULL;
      }
      toX=1; /* y*x^b is computed */
    }
    /* Now toX>=1 */
    for (k=toX+1;k<=a;k++)
    {
      t=MATELEM(cMT,k,b);
      if (t==NULL)   /* remove after debug */
      {
        t = p_Copy(MATELEM(cMT,k-1,b),r);
        t = gnc_mm_Mult_p(y,t,r);
        MATELEM(cMT,k,b) = t;
        /*        omCheckAddr(cMT->m); */
      }
      else
      {
        /* Error, should never get there */
        WarnS("dYX>=dXY,toX; MATELEM==0");
      }
      t=NULL;
    }
  } /* endif (dYX>=dXY) */


  if (dYX<dXY)
  {
    /* first y, then x */
    if (toY==0) /* start with the column*/
    {
      for (m=toYX+1;m<=a;m++)
      {
        t=MATELEM(cMT,m,1);
        if (t==NULL)   /* remove after debug */
        {
          t = p_Copy(MATELEM(cMT,m-1,1),r);
          t = gnc_mm_Mult_p(y,t,r);
          MATELEM(cMT,m,1) = t;
          /*        omCheckAddr(cMT->m); */
        }
        else
        {
          /* Error, should never get there */
          WarnS("dYX<dXY,toYX; MATELEM==0");
        }
        t=NULL;
      }
      toY=1; /* y^a*x is computed */
    }
    /* Now toY>=1 */
    for (k=toY+1;k<=b;k++)
    {
      t=MATELEM(cMT,a,k);
      if (t==NULL)   /* remove after debug */
      {
        t = p_Copy(MATELEM(cMT,a,k-1),r);
        t = gnc_p_Mult_mm(t,x,r);
        MATELEM(cMT,a,k) = t;
        /*        omCheckAddr(cMT->m); */
      }
      else
      {
        /* Error, should never get there */
        WarnS("dYX<dXY,toY; MATELEM==0");
      }
      t=NULL;
    }
  } /* endif (dYX<dXY) */

  p_Delete(&x,r);
  p_Delete(&y,r);
  t=p_Copy(MATELEM(cMT,a,b),r);
  return(t);  /* since the last computed element was cMT[a,b] */
}

poly gnc_uu_Mult_ww_vert	(	int	i,
		int	a,
		int	j,
		int	b,
		const ring	r
	)

Definition at line 977 of file old.gring.cc.

{
  int k,m;
  int rN=r->N;
  const int cMTindex = UPMATELEM(j,i,rN);
  matrix cMT=r->GetNC()->MT[cMTindex];         /* cMT=current MT */

  poly x=p_One(r);p_SetExp(x,j,1,r);p_Setm(x,r);
/* var(j); */
  poly y=p_One(r);p_SetExp(y,i,1,r);p_Setm(y,r);
/*var(i);  for convenience */
#ifdef PDEBUG
  p_Test(x,r);
  p_Test(y,r);
#endif
  poly t=NULL;
/* ------------ Main Cycles ----------------------------*/

  for (k=2;k<=a;k++)
  {
     t = MATELEM(cMT,k,1);

     if (t==NULL)   /* not computed yet */
     {
       t = nc_p_CopyGet(MATELEM(cMT,k-1,1),r);
       //        t=p_Copy(MATELEM(cMT,k-1,1),r);
       t = gnc_mm_Mult_p(y,t,r);
       cMT=r->GetNC()->MT[cMTindex]; // since multiplication can change the MT table...
       assume( t != NULL );
#ifdef PDEBUG
       p_Test(t,r);
#endif
       MATELEM(cMT,k,1) = nc_p_CopyPut(t,r);
       //        omCheckAddr(cMT->m);
       p_Delete(&t,r);
     }
     t=NULL;
  }

  for (m=2;m<=b;m++)
  {
    t = MATELEM(cMT,a,m);
    //     t=MATELEM(cMT,a,m);
    if (t==NULL)   //not computed yet
    {
      t = nc_p_CopyGet(MATELEM(cMT,a,m-1),r);
      assume( t != NULL );
      //      t=p_Copy(MATELEM(cMT,a,m-1),r);
      t = gnc_p_Mult_mm(t,x,r);
      cMT=r->GetNC()->MT[cMTindex]; // since multiplication can change the MT table...
#ifdef PDEBUG
      p_Test(t,r);
#endif
      MATELEM(cMT,a,m) = nc_p_CopyPut(t,r);
      //      MATELEM(cMT,a,m) = t;
      //        omCheckAddr(cMT->m);
      p_Delete(&t,r);
    }
    t=NULL;
  }
  p_Delete(&x,r);
  p_Delete(&y,r);
  t=MATELEM(cMT,a,b);
  assume( t != NULL );

  t= nc_p_CopyGet(t,r);
#ifdef PDEBUG
  p_Test(t,r);
#endif
  //  return(p_Copy(t,r));
  /* since the last computed element was cMT[a,b] */
  return(t);
}

ideal idOppose	(	ring	Rop,
		ideal	I,
		const ring	dst
	)

opposes a module I from Rop to currRing(dst)

Definition at line 3453 of file old.gring.cc.

{
  /* the simplest case:*/
  if ( Rop == dst ) return id_Copy(I, dst);

  /* check Rop == rOpposite(currRing) */
  if (!rIsLikeOpposite(dst, Rop))
  {
    WarnS("an opposite ring should be used");
    return NULL;
  }
  int i;
  ideal idOp = idInit(I->ncols, I->rank);
  for (i=0; i< (I->ncols)*(I->nrows); i++)
  {
    idOp->m[i] = pOppose(Rop,I->m[i], dst);
  }
  id_Test(idOp, dst);
  return idOp;
}

BOOLEAN nc_CallPlural	(	matrix	CCC,
		matrix	DDD,
		poly	CCN,
		poly	DDN,
		ring	r,
		bool	bSetupQuotient,
		bool	bCopyInput,
		bool	bBeQuiet,
		ring	curr,
		bool	dummy_ring
	)

returns TRUE if there were errors analyze inputs, check them for consistency detects nc_type, DO NOT initialize multiplication but call for it at the end checks the ordering condition and evtl. NDC NOTE: all the data belong to the curr, we change r which may be the same ring, and must have the same representation!

Definition at line 2734 of file old.gring.cc.

{
  assume( r != NULL );
  assume( curr != NULL );

  if( !bSetupQuotient)
    assume( (r->qideal == NULL) ); // The basering must NOT be a qring!??

  assume( rSamePolyRep(r, curr) || bCopyInput ); // wrong assumption?


  if( r->N == 1 ) // clearly commutative!!!
  {
    assume(
           ( (CCC != NULL) && (MATCOLS(CCC) == 1) && (MATROWS(CCC) == 1) && (MATELEM(CCC,1,1) == NULL) ) ||
           ( (CCN == NULL) )
          );

    assume(
           ( (DDD != NULL) && (MATCOLS(DDD) == 1) && (MATROWS(DDD) == 1) && (MATELEM(DDD,1,1) == NULL) ) ||
           ( (DDN == NULL) )
          );
    if(!dummy_ring)
    {
      WarnS("commutative ring with 1 variable");
      return FALSE;
    }
  }

  // there must be:
  assume( (CCC != NULL) != (CCN != NULL) ); // exactly one data about coeffs (C).
  assume( !((DDD != NULL) && (DDN != NULL)) ); // at most one data about tails (D).

//  ring save = currRing;
//  if( save != curr )
//    rChangeCurrRing(curr);


#if OUTPUT
  if( CCC != NULL )
  {
    PrintS("nc_CallPlural(), Input data, CCC: \n");
    iiWriteMatrix(CCC, "C", 2, curr, 4);
  }
  if( DDD != NULL )
  {
    PrintS("nc_CallPlural(), Input data, DDD: \n");
    iiWriteMatrix(DDD, "D", 2, curr, 4);
  }
#endif


#ifndef SING_NDEBUG
  id_Test((ideal)CCC, curr);
  id_Test((ideal)DDD, curr);
  p_Test(CCN, curr);
  p_Test(DDN, curr);
#endif

  if( (!bBeQuiet) && (r->GetNC() != NULL) )
    WarnS("going to redefine the algebra structure");

//  if( currRing != r )
//    rChangeCurrRing(r);

  matrix CC = NULL;
  poly CN = NULL;
  matrix C; bool bCnew = false;

  matrix DD = NULL;
  poly DN = NULL;
  matrix D; bool bDnew = false;

  number nN, pN, qN;

  bool IsSkewConstant = false, tmpIsSkewConstant;
  int i, j;

  nc_type nctype = nc_undef;

  //////////////////////////////////////////////////////////////////
  // check the correctness of arguments, without any real chagnes!!!



  // check C
  if ((CCC != NULL) && ( (MATCOLS(CCC)==1) || MATROWS(CCC)==1 ) )
  {
    CN = MATELEM(CCC,1,1);
  }
  else
  {
    if ((CCC != NULL) && ( (MATCOLS(CCC)!=r->N) || (MATROWS(CCC)!=r->N) ))
    {
      Werror("Square %d x %d  matrix expected", r->N, r->N);

//      if( currRing != save )
//        rChangeCurrRing(save);
      return TRUE;
    }
  }
  if (( CCC != NULL) && (CC == NULL)) CC = CCC; // mp_Copy(CCC, ?); // bug!?
  if (( CCN != NULL) && (CN == NULL)) CN = CCN;

  // check D
  if ((DDD != NULL) && ( (MATCOLS(DDD)==1) || MATROWS(DDD)==1 ) )
  {
    DN = MATELEM(DDD,1,1);
  }
  else
  {
    if ((DDD != NULL) && ( (MATCOLS(DDD)!=r->N) || (MATROWS(DDD)!=r->N) ))
    {
      Werror("Square %d x %d  matrix expected",r->N,r->N);

//      if( currRing != save )
//        rChangeCurrRing(save);
      return TRUE;
    }
  }

  if (( DDD != NULL) && (DD == NULL)) DD = DDD; // mp_Copy(DDD, ?); // ???
  if (( DDN != NULL) && (DN == NULL)) DN = DDN;

  // further checks and some analysis:
  // all data in 'curr'!
  if (CN != NULL)       /* create matrix C = CN * Id */
  {
    if (!p_IsConstant(CN,curr))
    {
      Werror("Incorrect input : non-constants are not allowed as coefficients (first argument)");
      return TRUE;
    }
    assume(p_IsConstant(CN,curr));

    nN = p_GetCoeff(CN, curr);
    if (n_IsZero(nN, curr))
    {
      Werror("Incorrect input : zero coefficients are not allowed");

//      if( currRing != save )
//        rChangeCurrRing(save);
      return TRUE;
    }

    if (n_IsOne(nN, curr))
      nctype = nc_lie;
    else
      nctype = nc_general;

    IsSkewConstant = true;

    C = mpNew(r->N,r->N); // ring independent!
    bCnew = true;

    for(i=1; i<r->N; i++)
      for(j=i+1; j<=r->N; j++)
        MATELEM(C,i,j) = prCopyR_NoSort(CN, curr, r); // nc_p_CopyPut(CN, r); // copy CN from curr into r

#ifndef SING_NDEBUG
    id_Test((ideal)C, r);
#endif

  } else
  if ( (CN == NULL) && (CC != NULL) ) /* copy matrix C */
  {
    /* analyze C */

    pN = NULL; /* check the consistency later */

    if( r->N > 1 )
      if ( MATELEM(CC,1,2) != NULL )
        pN = p_GetCoeff(MATELEM(CC,1,2), curr);

    tmpIsSkewConstant = true;

    for(i=1; i<r->N; i++)
      for(j=i+1; j<=r->N; j++)
      {
        if (MATELEM(CC,i,j) == NULL)
          qN = NULL;
        else
        {
          if (!p_IsConstant(MATELEM(CC,i,j),curr))
          {
            Werror("Incorrect input : non-constants are not allowed as coefficients (first argument at [%d, %d])", i, j);
            return TRUE;
          }
          assume(p_IsConstant(MATELEM(CC,i,j),curr));
          qN = p_GetCoeff(MATELEM(CC,i,j),curr);
        }


        if ( qN == NULL )   /* check the consistency: Cij!=0 */
        // find also illegal pN
        {
          Werror("Incorrect input : matrix of coefficients contains zeros in the upper triangle");

//        if( currRing != save )
//            rChangeCurrRing(save);
          return TRUE;
        }

        if (!n_Equal(pN, qN, curr->cf)) tmpIsSkewConstant = false;
      }

    if( bCopyInput )
    {
      C = mp_Copy(CC, curr, r); // Copy C into r!!!???
#ifndef SING_NDEBUG
      id_Test((ideal)C, r);
#endif
      bCnew = true;
    }
    else
      C = CC;

    IsSkewConstant = tmpIsSkewConstant;

    if ( tmpIsSkewConstant && n_IsOne(pN, curr) )
      nctype = nc_lie;
    else
      nctype = nc_general;
  }

  /* initialition of the matrix D */
  if ( DD == NULL ) /* we treat DN only (it could also be NULL) */
  {
    D = mpNew(r->N,r->N); bDnew = true;

    if (DN  == NULL)
    {
      if ( (nctype == nc_lie) || (nctype == nc_undef) )
        nctype = nc_comm; /* it was nc_skew earlier */
      else /* nc_general, nc_skew */
        nctype = nc_skew;
    }
    else /* DN  != NULL */
      for(i=1; i<r->N; i++)
        for(j=i+1; j<=r->N; j++)
          MATELEM(D,i,j) = prCopyR_NoSort(DN, curr, r); // project DN into r->GetNC()->basering!
#ifndef SING_NDEBUG
  id_Test((ideal)D, r);
#endif
  }
  else /* DD != NULL */
  {
    bool b = true; // DD == null ?

    for(int i = 1; (i < r->N) && b; i++)
    for(int j = i+1; (j <= r->N) && b; j++)
      if (MATELEM(DD, i, j) != NULL)
      {
        b = false;
        break;
      }

    if (b) // D == NULL!!!
    {
      if ( (nctype == nc_lie) || (nctype == nc_undef) )
        nctype = nc_comm; /* it was nc_skew earlier */
      else /* nc_general, nc_skew */
        nctype = nc_skew;
    }

    if( bCopyInput )
    {
      D = mp_Copy(DD, curr, r); // Copy DD into r!!!
#ifndef SING_NDEBUG
      id_Test((ideal)D, r);
#endif
      bDnew = true;
    }
    else
      D = DD;
  }

  assume( C != NULL );
  assume( D != NULL );

#if OUTPUT
  PrintS("nc_CallPlural(), Computed data, C: \n");
  iiWriteMatrix(C, "C", 2, r, 4);

  PrintS("nc_CallPlural(), Computed data, D: \n");
  iiWriteMatrix(D, "D", 2, r, 4);

  Print("\nTemporary: type = %d, IsSkewConstant = %d\n", nctype, IsSkewConstant);
#endif


  // check the ordering condition for D (both matrix and poly cases):
  if ( gnc_CheckOrdCondition(D, r) )
  {
    if( bCnew ) mp_Delete( &C, r );
    if( bDnew ) mp_Delete( &D, r );

    Werror("Matrix of polynomials violates the ordering condition");

//    if( currRing != save )
//      rChangeCurrRing(save);
    return TRUE;
  }

  // okay now we are ready for this!!!

  // create new non-commutative structure
  nc_struct *nc_new = (nc_struct *)omAlloc0(sizeof(nc_struct));

  ncRingType(nc_new, nctype);

  nc_new->C = C; // if C and D were given by matrices at the beginning they are in r
  nc_new->D = D; // otherwise they should be in r->GetNC()->basering(polynomial * Id_{N})

  nc_new->IsSkewConstant = (IsSkewConstant?1:0);

  // Setup new NC structure!!!
  if (r->GetNC() != NULL)
  {
#ifndef SING_NDEBUG
    WarnS("Changing the NC-structure of an existing NC-ring!!!");
#endif
    nc_rKill(r);
  }

  r->GetNC() = nc_new;

  r->ext_ref=NULL;

//  if( currRing != save )
//    rChangeCurrRing(save);

  return gnc_InitMultiplication(r, bSetupQuotient);
}

BOOLEAN nc_CheckSubalgebra	(	poly	PolyVar,
		ring	r
	)

Definition at line 2620 of file old.gring.cc.

{
//  ring save = currRing;
//  int WeChangeRing = 0;
//  if (currRing != r)
//    rChangeCurrRing(r);
//    WeChangeRing = 1;
//  }
  int rN=r->N;
  int *ExpVar=(int*)omAlloc0((rN+1)*sizeof(int));
  int *ExpTmp=(int*)omAlloc0((rN+1)*sizeof(int));
  p_GetExpV(PolyVar, ExpVar, r);
  int i; int j; int k;
  poly test=NULL;
  int OK=1;
  for (i=1; i<rN; i++)
  {
    if (ExpVar[i]==0) /* i.e. not in PolyVar */
    {
      for (j=i+1; j<=rN; j++)
      {
        if (ExpVar[j]==0)
        {
          test = MATELEM(r->GetNC()->D,i,j);
          while (test!=NULL)
          {
            p_GetExpV(test, ExpTmp, r);
            OK=1;
            for (k=1;k<=rN;k++)
            {
              if (ExpTmp[k]!=0)
              {
                if (ExpVar[k]!=0) OK=0;
              }
            }
            if (!OK)
            {
//              if ( WeChangeRing )
//                rChangeCurrRing(save);
              return(TRUE);
            }
            pIter(test);
          }
        }
      }
    }
  }
  freeT(ExpVar,rN);
  freeT(ExpTmp,rN);
//  if ( WeChangeRing )
//    rChangeCurrRing(save);
  return(FALSE);
}

void nc_CleanUp ( nc_struct *  p )

inline

Definition at line 2513 of file old.gring.cc.

{
  assume(p != NULL);
  omFreeSize((ADDRESS)p,sizeof(nc_struct));
}

void nc_CleanUp ( ring  r )

inline

Definition at line 2519 of file old.gring.cc.

{
  /* small CleanUp of r->GetNC() */
  assume(r != NULL);
  nc_CleanUp(r->GetNC());
  r->GetNC() = NULL;
}

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

Definition at line 1926 of file old.gring.cc.

{
#ifdef PDEBUG
  p_Test(p1, r);
  p_Test(p2, r);
#endif

  const long lCompP1 = p_GetComp(p1,r);
  const long lCompP2 = p_GetComp(p2,r);

  if ((lCompP1!=lCompP2) && (lCompP1!=0) && (lCompP2!=0))
  {
#ifdef PDEBUG
    Werror("nc_CreateShortSpoly: wrong module components!"); // !!!!
#endif
    return(NULL);
  }

  poly m;

#ifdef HAVE_RATGRING
  if ( rIsRatGRing(r))
  {
    /* rational version */
    m = p_LcmRat(p1, p2, si_max(lCompP1, lCompP2), r);
  } else
#endif
  {
    m = p_Lcm(p1, p2, si_max(lCompP1, lCompP2), r);
  }

//  n_Delete(&p_GetCoeff(m, r), r);
//  pSetCoeff0(m, NULL);

#ifdef PDEBUG
//  p_Test(m,r);
#endif

  return(m);
}

poly nc_mm_Bracket_nn	(	poly	m1,
		poly	m2,
		const ring	r
	)

returns [m1,m2] for two monoms, destroys nothing without coeffs

Definition at line 2336 of file old.gring.cc.

{
  if (p_LmIsConstant(m1, r) || p_LmIsConstant(m1, r)) return(NULL);
  if (p_LmCmp(m1,m2, r)==0) return(NULL);
  int rN=r->N;
  int *M1=(int *)omAlloc0((rN+1)*sizeof(int));
  int *M2=(int *)omAlloc0((rN+1)*sizeof(int));
  int *aPREFIX=(int *)omAlloc0((rN+1)*sizeof(int));
  int *aSUFFIX=(int *)omAlloc0((rN+1)*sizeof(int));
  p_GetExpV(m1,M1, r);
  p_GetExpV(m2,M2, r);
  poly res=NULL;
  poly ares=NULL;
  poly bres=NULL;
  poly prefix=NULL;
  poly suffix=NULL;
  int nMin,nMax;
  number nTmp=NULL;
  int i,j,k;
  for (i=1;i<=rN;i++)
  {
    if (M2[i]!=0)
    {
      ares=NULL;
      for (j=1;j<=rN;j++)
      {
        if (M1[j]!=0)
        {
          bres=NULL;
          /* compute [ x_j^M1[j],x_i^M2[i] ] */
          if (i<j) {nMax=j;  nMin=i;} else {nMax=i;  nMin=j;}
          if ( (i==j) || ((MATELEM(r->GetNC()->COM,nMin,nMax)!=NULL) && n_IsOne(p_GetCoeff(MATELEM(r->GetNC()->C,nMin,nMax), r), r) )) /* not (the same exp. or commuting exps)*/
          { bres=NULL; }
          else
          {
            if (i<j) { bres=gnc_uu_Mult_ww(j,M1[j],i,M2[i], r); }
            else bres=gnc_uu_Mult_ww(i,M2[i],j,M1[j], r);
            if (n_IsOne(p_GetCoeff(bres, r), r))
            {
              bres=p_LmDeleteAndNext(bres, r);
            }
            else
            {
              nTmp=n_Sub(p_GetCoeff(bres, r),n_Init(1, r), r);
              p_SetCoeff(bres,nTmp, r); /* only lc ! */
            }
#ifdef PDEBUG
            p_Test(bres, r);
#endif
            if (i>j)  bres=p_Neg(bres, r);
          }
          if (bres!=NULL)
          {
            /* now mult (prefix, bres, suffix) */
            memcpy(aSUFFIX, M1,(rN+1)*sizeof(int));
            memcpy(aPREFIX, M1,(rN+1)*sizeof(int));
            for (k=1;k<=j;k++) aSUFFIX[k]=0;
            for (k=j;k<=rN;k++) aPREFIX[k]=0;
            aSUFFIX[0]=0;
            aPREFIX[0]=0;
            prefix=p_One(r);
            suffix=p_One(r);
            p_SetExpV(prefix,aPREFIX, r);
            p_Setm(prefix, r);
            p_SetExpV(suffix,aSUFFIX, r);
            p_Setm(suffix, r);
            if (!p_LmIsConstant(prefix, r)) bres = gnc_mm_Mult_p(prefix, bres, r);
            if (!p_LmIsConstant(suffix, r)) bres = gnc_p_Mult_mm(bres, suffix, r);
            ares=p_Add_q(ares, bres, r);
            /* What to give free? */
        /* Do we have to free aPREFIX/aSUFFIX? it seems so */
            p_Delete(&prefix, r);
            p_Delete(&suffix, r);
          }
        }
      }
      if (ares!=NULL)
      {
        /* now mult (prefix, bres, suffix) */
        memcpy(aSUFFIX, M2,(rN+1)*sizeof(int));
        memcpy(aPREFIX, M2,(rN+1)*sizeof(int));
        for (k=1;k<=i;k++) aSUFFIX[k]=0;
        for (k=i;k<=rN;k++) aPREFIX[k]=0;
        aSUFFIX[0]=0;
        aPREFIX[0]=0;
        prefix=p_One(r);
        suffix=p_One(r);
        p_SetExpV(prefix,aPREFIX, r);
        p_Setm(prefix, r);
        p_SetExpV(suffix,aSUFFIX, r);
        p_Setm(suffix, r);
        bres=ares;
        if (!p_LmIsConstant(prefix, r)) bres = gnc_mm_Mult_p(prefix, bres, r);
        if (!p_LmIsConstant(suffix, r)) bres = gnc_p_Mult_mm(bres, suffix, r);
        res=p_Add_q(res, bres, r);
        p_Delete(&prefix, r);
        p_Delete(&suffix, r);
      }
    }
  }
  freeT(M1, rN);
  freeT(M2, rN);
  freeT(aPREFIX, rN);
  freeT(aSUFFIX, rN);
#ifdef PDEBUG
  p_Test(res, r);
#endif
   return(res);
}

poly nc_p_Bracket_qq	(	poly	p,
		const poly	q,
		const ring	r
	)

returns [p,q], destroys p

Definition at line 2295 of file old.gring.cc.

{
  assume(p != NULL && q!= NULL);

  if (!rIsPluralRing(r)) return(NULL);
  if (p_ComparePolys(p,q, r)) return(NULL);
  /* Components !? */
  poly Q=NULL;
  number coef=NULL;
  poly pres=NULL;
  int UseBuckets=1;
  if (((pLength(p)< MIN_LENGTH_BUCKET/2) && (pLength(q)< MIN_LENGTH_BUCKET/2))
  || TEST_OPT_NOT_BUCKETS)
    UseBuckets=0;


  CPolynomialSummator sum(r, UseBuckets == 0);

  while (p!=NULL)
  {
    Q=q;
    while(Q!=NULL)
    {
      pres=nc_mm_Bracket_nn(p,Q, r); /* since no coeffs are taken into account there */
      if (pres!=NULL)
      {
        coef = n_Mult(p_GetCoeff(p, r),p_GetCoeff(Q, r), r);
        pres = p_Mult_nn(pres,coef,r);

        sum += pres;
        n_Delete(&coef, r);
      }
      pIter(Q);
    }
    p=p_LmDeleteAndNext(p, r);
  }
  return(sum);
}

poly nc_p_CopyGet	(	poly	a,
		const ring	r
	)

Definition at line 2578 of file old.gring.cc.

{
#ifndef PDEBUG
  p_Test(a, r);
#endif

//  if (r != currRing)
//  {
//#ifdef PDEBUF
//    Werror("nc_p_CopyGet call not in currRing");
//#endif
//    return(NULL);
//  }
  return(p_Copy(a,r));
}

poly nc_p_CopyPut	(	poly	a,
		const ring	r
	)

Definition at line 2599 of file old.gring.cc.

{
#ifndef PDEBUG
  p_Test(a, r);
#endif

//  if (r != currRing)
//  {
//#ifdef PDEBUF
//    Werror("nc_p_CopyGet call not in currRing");
//#endif
//    return(NULL);
//  }

  return(p_Copy(a,r));
}

poly nc_p_Minus_mm_Mult_qq	(	poly	p,
		const poly	m,
		const poly	q,
		int &	shorter,
		const poly	,
		const ring	r
	)

for p_Minus_mm_Mult_qq in pInline2.h

Definition at line 196 of file old.gring.cc.

{
  poly mc  = p_Neg( p_Copy(m, r), r );
  poly mmc = nc_mm_Mult_pp( mc, q, r );
  p_Delete(&mc, r);

  int org_p=pLength(p);
  int org_q=pLength(q);

  p = p_Add_q(p, mmc, r);

  shorter = pLength(p)-org_p-org_q; // ring independent!

  return(p);
}

poly nc_p_Plus_mm_Mult_qq	(	poly	p,
		const poly	m,
		const poly	q,
		int &	lp,
		const int	,
		const ring	r
	)

Definition at line 214 of file old.gring.cc.

{
  p = p_Add_q(p, nc_mm_Mult_pp( m, q, r ), r);

  lp = pLength(p);

  return(p);
}

void nc_p_ProcsSet	(	ring	rGR,
		p_Procs_s *	p_Procs
	)

Definition at line 3251 of file old.gring.cc.

{
  assume(rIsPluralRing(rGR));
  assume(p_Procs!=NULL);

  gnc_p_ProcsSet(rGR, p_Procs);

  if(rIsSCA(rGR) && ncExtensions(SCAMASK) )
  {
    sca_p_ProcsSet(rGR, p_Procs);
  }

  if( ncExtensions(NOPLURALMASK) )
    ncInitSpecialPairMultiplication(rGR);

  if(!rIsSCA(rGR) && !ncExtensions(NOFORMULAMASK))
    ncInitSpecialPowersMultiplication(rGR);

}

void nc_PolyPolyRed	(	poly &	b,
		poly	p,
		number *	c,
		const ring	r
	)

Definition at line 2282 of file old.gring.cc.

{
#if 0
  nc_PolyPolyRedOld(b, p, c, r);
#else
  nc_PolyPolyRedNew(b, p, c, r);
#endif
}

void nc_PolyPolyRedNew ( poly &  b, poly  p, number *  c, const ring  r  )

inline

Definition at line 2182 of file old.gring.cc.

{
#ifdef PDEBUG
  p_Test(b, r);
  p_Test(p, r);
#endif

#if MYTEST
  PrintS("nc_PolyPolyRedNew(");
  p_Write0(b, r);
  PrintS(", ");
  p_Write0(p, r);
  PrintS(", *c): ");
#endif

  // b will not by multiplied by any constant in this impl.
  // ==> *c=1
  if (c!=NULL) *c=n_Init(1, r);

  poly pp = NULL;

  // there is a problem when p is a square(=>0!)

  while((b != NULL) && (pp == NULL))
  {

//    poly pLmB = p_Head(b, r);
    poly m = p_One(r);
    p_ExpVectorDiff(m, b, p, r);
//    pDelete(&pLmB);
  //pSetm(m);

#ifdef PDEBUG
    p_Test(m, r);
    p_Test(b, r);
#endif

    pp = nc_mm_Mult_pp(m, p, r);

#if MYTEST
    PrintS("\n{b': ");
    p_Write0(b, r);
    PrintS(", m: ");
    p_Write0(m, r);
    PrintS(", pp: ");
    p_Write0(pp, r);
    PrintS(" }\n");
#endif

    p_Delete(&m, r); // one m for all tries!

//    assume( pp != NULL );

    if( pp == NULL )
    {
      b = p_LmDeleteAndNext(b, r);

      if( !p_DivisibleBy(p, b, r) )
        return;

    }
  }

#if MYTEST
  PrintS("{b': ");
  p_Write0(b, r);
  PrintS(", pp: ");
  p_Write0(pp, r);
  PrintS(" }\n");
#endif


  if(b == NULL) return;


  assume(pp != NULL);

  const number n = p_GetCoeff(pp, r); // no new copy

  number nn;

  if (!n_IsMOne(n, r)) // TODO: as above.
  {
    nn=n_InpNeg(n_Invers(n, r), r);
    number t = n_Mult(nn, p_GetCoeff(b, r), r);
    n_Delete(&nn, r);
    pp=p_Mult_nn(pp, t, r);
    n_Delete(&t, r);
  }
  else
  {
    pp=p_Mult_nn(pp, pGetCoeff(b), r);
  }


  b=p_Add_q(b,pp,r);

}

void nc_PolyPolyRedOld ( poly &  b, poly  p, number *  c, const ring  r  )

inline

Definition at line 2148 of file old.gring.cc.

{
  // b will not by multiplied by any constant in this impl.
  // ==> *c=1
  if (c!=NULL) *c=n_Init(1, r);
  poly m=p_One(r);
  p_ExpVectorDiff(m,p_Head(b, r),p, r);
  //pSetm(m);
#ifdef PDEBUG
  p_Test(m, r);
#endif
  poly pp=nc_mm_Mult_pp(m,p,r);
  assume(pp!=NULL);

  p_Delete(&m, r);
  number n=p_GetCoeff(pp, r);
  number nn;
  if (!n_IsMOne(n, r))
  {
    nn=n_InpNeg(n_Invers(n, r), r);
    n =n_Mult(nn,p_GetCoeff(b, r), r);
    n_Delete(&nn, r);
    pp=p_Mult_nn(pp,n,r);
    n_Delete(&n, r);
  }
  else
  {
    pp=p_Mult_nn(pp,p_GetCoeff(b, r),r);
  }
  b=p_Add_q(b,pp,r);
}

matrix nc_PrintMat	(	int	a,
		int	b,
		ring	r,
		int	metric
	)

returns matrix with the info on noncomm multiplication

Definition at line 2446 of file old.gring.cc.

{

  if ( (a==b) || !rIsPluralRing(r) ) return(NULL);
  int i;
  int j;
  if (a>b) {j=b; i=a;}
  else {j=a; i=b;}
  /* i<j */
  int rN=r->N;
  int size=r->GetNC()->MTsize[UPMATELEM(i,j,rN)];
  matrix M = r->GetNC()->MT[UPMATELEM(i,j,rN)];
  /*  return(M); */
/*
  int sizeofres;
  if (metric==0)
  {
    sizeofres=sizeof(int);
  }
  if (metric==1)
  {
    sizeofres=sizeof(number);
  }
*/
  matrix res=mpNew(size,size);
  int s;
  int t;
  int length;
  long totdeg;
  poly p;
  for(s=1;s<=size;s++)
  {
    for(t=1;t<=size;t++)
    {
      p=MATELEM(M,s,t);
      if (p==NULL)
      {
        MATELEM(res,s,t)=0;
      }
      else
      {
        length = pLength(p);
        if (metric==0) /* length */
        {
          MATELEM(res,s,t)= p_ISet(length,r);
        }
        else if (metric==1) /* sum of deg divided by the length */
        {
          totdeg=0;
          while (p!=NULL)
          {
            totdeg=totdeg+p_Deg(p,r);
            pIter(p);
          }
          number ntd = n_Init(totdeg, r);
          number nln = n_Init(length, r);
          number nres= n_Div(ntd,nln, r);
          n_Delete(&ntd, r);
          n_Delete(&nln, r);
          MATELEM(res,s,t)=p_NSet(nres,r);
        }
      }
    }
  }
  return(res);
}

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

substitute the n-th variable by e in p destroy p e is not a constant

Definition at line 3275 of file old.gring.cc.

{
  int rN = r->N;
  int *PRE = (int *)omAlloc0((rN+1)*sizeof(int));
  int *SUF = (int *)omAlloc0((rN+1)*sizeof(int));
  int i,pow;
  number C;
  poly suf,pre;
  poly res = NULL;
  poly out = NULL;
  while ( p!= NULL )
  {
    C =  p_GetCoeff(p, r);
    p_GetExpV(p, PRE, r); /* faster splitting? */
    pow = PRE[n]; PRE[n]=0;
    res = NULL;
    if (pow!=0)
    {
      for (i=n+1; i<=rN; i++)
      {
         SUF[i] = PRE[i];
         PRE[i] = 0;
      }
      res =  p_Power(p_Copy(e, r),pow, r);
      /* multiply with prefix */
      pre = p_One(r);
      p_SetExpV(pre,PRE, r);
      p_Setm(pre, r);
      res = nc_mm_Mult_p(pre,res, r);
      /* multiply with suffix */
      suf = p_One(r);
      p_SetExpV(suf,SUF, r);
      p_Setm(suf, r);
      res = p_Mult_mm(res,suf, r);
      res = p_Mult_nn(res,C, r);
      p_SetComp(res,PRE[0], r);
    }
    else /* pow==0 */
    {
      res = p_Head(p, r);
    }
    p   = p_LmDeleteAndNext(p, r);
    out = p_Add_q(out,res, r);
  }
  freeT(PRE,rN);
  freeT(SUF,rN);
  return(out);
}

void nc_rCleanUp

(

ring

r

)

bool nc_rCopy	(	ring	res,
		const ring	r,
		bool	bSetupQuotient
	)

Definition at line 3075 of file old.gring.cc.

{
  if (nc_CallPlural(r->GetNC()->C, r->GetNC()->D, NULL, NULL, res, bSetupQuotient, true, true, r))
  {
    WarnS("Error occured while coping/setuping the NC structure!"); // No reaction!???
    return true; // error
  }

  return false;
}

ring nc_rCreateNCcomm

(

ring

r

)

Definition at line 3326 of file old.gring.cc.

{
  if (rIsPluralRing(r)) return r;

  ring rr = rCopy(r);

  matrix C = mpNew(rr->N,rr->N); // ring-independent!?!
  matrix D = mpNew(rr->N,rr->N);

  for(int i=1; i<rr->N; i++)
    for(int j=i+1; j<=rr->N; j++)
      MATELEM(C,i,j) = p_One(rr);

  if (nc_CallPlural(C, D, NULL, NULL, rr, false, true, false, rr, TRUE)) // TODO: what about quotient ideal?
    WarnS("Error initializing multiplication!"); // No reaction!???

  return rr;
}

void nc_rKill

(

ring

r

)

complete destructor

Definition at line 2527 of file old.gring.cc.

{
  if( r->GetNC()->GetGlobalMultiplier() != NULL )
  {
    delete r->GetNC()->GetGlobalMultiplier();
    r->GetNC()->GetGlobalMultiplier() = NULL;
  }

  if( r->GetNC()->GetFormulaPowerMultiplier() != NULL )
  {
    delete r->GetNC()->GetFormulaPowerMultiplier();
    r->GetNC()->GetFormulaPowerMultiplier() = NULL;
  }


  int i,j;
  int rN=r->N;
  if ( rN > 1 )
  {
    for(i=1;i<rN;i++)
    {
      for(j=i+1;j<=rN;j++)
      {
        id_Delete((ideal *)&(r->GetNC()->MT[UPMATELEM(i,j,rN)]),r);
      }
    }
    omFreeSize((ADDRESS)r->GetNC()->MT,rN*(rN-1)/2*sizeof(matrix));
    omFreeSize((ADDRESS)r->GetNC()->MTsize,rN*(rN-1)/2*sizeof(int));
    id_Delete((ideal *)&(r->GetNC()->COM),r);
  }
  id_Delete((ideal *)&(r->GetNC()->C),r);
  id_Delete((ideal *)&(r->GetNC()->D),r);

  if( rIsSCA(r) && (r->GetNC()->SCAQuotient() != NULL) )
  {
    id_Delete(&r->GetNC()->SCAQuotient(), r); // Custom SCA destructor!!!
  }


  nc_CleanUp(r);
}

bool nc_SetupQuotient	(	ring	rGR,
		const ring	rG,
		bool	bCopy
	)

Definition at line 3475 of file old.gring.cc.

{
  if( rGR->qideal == NULL )
    return false; // no quotient = no work! done!? What about factors of SCA?

  bool ret = true;
  // currently only super-commutative extension deals with factors.

  if( ncExtensions(SCAMASK)  )
  {
    bool sca_ret = sca_SetupQuotient(rGR, rG, bCopy);

    if(sca_ret) // yes it was dealt with!
      ret = false;
  }

  if( bCopy )
  {
    assume(rIsPluralRing(rGR) == rIsPluralRing(rG));
    assume((rGR->qideal==NULL) == (rG->qideal==NULL));
    assume(rIsSCA(rGR) == rIsSCA(rG));
    assume(ncRingType(rGR) == ncRingType(rG));
  }

  return ret;
}

bool ncExtensions

(

int

iMask

)

Definition at line 87 of file old.gring.cc.

{
  return ((getNCExtensions() & iMask) == iMask);
}

poly p_CopyEmbed	(	poly	p,
		ring	srcRing,
		int	shift,
		int	,
		ring	dstRing
	)

Definition at line 3350 of file old.gring.cc.

{
  if (dstRing == srcRing)
  {
    return(p_Copy(p,dstRing));
  }
  nMapFunc nMap=n_SetMap(srcRing->cf, dstRing->cf);
  poly q;
  //  if ( nMap == nCopy)
  //  {
  //    q = prCopyR(p,srcRing);
  //  }
  //  else
  {
    int *perm = (int *)omAlloc0((rVar(srcRing)+1)*sizeof(int));
    int *par_perm = (int *)omAlloc0((rPar(srcRing)+1)*sizeof(int));
    //    int *par_perm = (int *)omAlloc0((rPar(srcRing)+1)*sizeof(int));
    int i;
    //    if (srcRing->P > 0)
    //    {
    //      for (i=0; i<srcRing->P; i++)
    //  par_perm[i]=-i;
    //    }
    if ((shift<0) || (shift > rVar(srcRing))) // ???
    {
      Werror("bad shifts in p_CopyEmbed");
      return(0);
    }
    for (i=1; i<= srcRing->N; i++)
    {
      perm[i] = shift+i;
    }
    q = p_PermPoly(p,perm,srcRing, dstRing, nMap,par_perm, rPar(srcRing));
  }
  return(q);
}

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

Definition at line 147 of file old.gring.cc.

{
  poly m = // p_One( r);
          p_Init(r);

  const int pVariables = r->N;

  for (int i = pVariables; i!=0; 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);

#ifdef PDEBUG
//  p_Test(m,r);
#endif

  n_New(&(p_GetCoeff(m, r)), r);

  return(m);
}

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

Definition at line 175 of file old.gring.cc.

{
#ifdef PDEBUG
  p_Test(a, r);
  p_Test(b, r);
#endif

  const long lCompP1 = p_GetComp(a, r);
  const long lCompP2 = p_GetComp(b, r);

  const poly m = p_Lcm(a, b, si_max(lCompP1, lCompP2), r);

#ifdef PDEBUG
//  p_Test(m,r);
#endif
  return(m);
}

poly pOppose	(	ring	Rop,
		poly	p,
		const ring	dst
	)

opposes a vector p from Rop to currRing (dst!)

Definition at line 3414 of file old.gring.cc.

{
  /* the simplest case:*/
  if (  Rop == dst )  return(p_Copy(p, dst));
  /* check Rop == rOpposite(currRing) */


  if ( !rIsLikeOpposite(dst, Rop) )
  {
    WarnS("an opposite ring should be used");
    return NULL;
  }

  nMapFunc nMap = n_SetMap(Rop->cf, dst->cf); // reverse?

  /* nMapFunc nMap = nSetMap(Rop);*/
  /* since we know that basefields coinside! */

  // coinside???

  int *perm=(int *)omAlloc0((Rop->N+1)*sizeof(int));
  if (!p_IsConstantPoly(p, Rop))
  {
    /* we know perm exactly */
    int i;
    for(i=1; i<=Rop->N; i++)
    {
      perm[i] = Rop->N+1-i;
    }
  }
  poly res = p_PermPoly(p, perm, Rop, dst, nMap);
  omFreeSize((ADDRESS)perm,(Rop->N+1)*sizeof(int));

  p_Test(res, dst);

  return res;
}

BOOLEAN rIsLikeOpposite	(	ring	rBase,
		ring	rCandidate
	)

checks whether rings rBase and rCandidate could be opposite to each other returns TRUE if it is so

Definition at line 3387 of file old.gring.cc.

{
  /* the same basefield */
  int diagnose = TRUE;
  nMapFunc nMap = n_SetMap(rCandidate->cf, rBase->cf); // reverse?

//////  if (nMap != nCopy) diagnose = FALSE;
  if (nMap == NULL) diagnose = FALSE;


  /* same number of variables */
  if (rBase->N != rCandidate->N) diagnose = FALSE;
  /* nc and comm ring */
  if ( rIsPluralRing(rBase) != rIsPluralRing(rCandidate) ) diagnose = FALSE;
  /* both are qrings */
  /* NO CHECK, since it is used in building opposite qring */
  /*  if ( ((rBase->qideal != NULL) && (rCandidate->qideal == NULL)) */
  /*       || ((rBase->qideal == NULL) && (rCandidate->qideal != NULL)) ) */
  /*  diagnose = FALSE; */
  /* TODO: varnames are e->E etc */
  return diagnose;
}

int setNCExtensions

(

int

iMask

)

Definition at line 80 of file old.gring.cc.

{
  const int iOld = getNCExtensions();
  getNCExtensions() = iMask;
  return (iOld);
}

Variable Documentation

int iNCExtensions = SCAMASK | NOFORMULAMASK

Definition at line 73 of file old.gring.cc.