transext.cc File Reference

#include <misc/auxiliary.h>
#include <omalloc/omalloc.h>
#include <factory/factory.h>
#include <reporter/reporter.h>
#include <coeffs/coeffs.h>
#include <coeffs/numbers.h>
#include <coeffs/longrat.h>
#include <polys/monomials/ring.h>
#include <polys/monomials/p_polys.h>
#include <polys/simpleideals.h>
#include <polys/clapsing.h>
#include <polys/clapconv.h>
#include <polys/prCopy.h>
#include "transext.h"
#include "algext.h"
#include <polys/PolyEnumerator.h>

Go to the source code of this file.

Data Structures
struct	NTNumConverter

Macros
#define	TRANSEXT_PRIVATES
#define	ADD_COMPLEXITY   1
	complexity increase due to + and - More...
#define	MULT_COMPLEXITY   2
	complexity increase due to * and / More...
#define	DIFF_COMPLEXITY   2
	complexity increase due to * and / More...
#define	BOUND_COMPLEXITY   10
	maximum complexity of a number More...
#define	NUMIS1(f)   (p_IsOne(NUM(f), cf->extRing))
	TRUE iff num. represents 1. More...
#define	COM(f)   f->complexity
#define	ntTest(a)   ntDBTest(a,__FILE__,__LINE__,cf)
#define	ntRing   cf->extRing
#define	ntCoeffs   cf->extRing->cf

Functions
BOOLEAN	ntDBTest (number a, const char *f, const int l, const coeffs r)
BOOLEAN	ntGreaterZero (number a, const coeffs cf)
	forward declarations More...
BOOLEAN	ntGreater (number a, number b, const coeffs cf)
BOOLEAN	ntEqual (number a, number b, const coeffs cf)
BOOLEAN	ntIsOne (number a, const coeffs cf)
BOOLEAN	ntIsMOne (number a, const coeffs cf)
BOOLEAN	ntIsZero (number a, const coeffs cf)
number	ntInit (long i, const coeffs cf)
long	ntInt (number &a, const coeffs cf)
number	ntNeg (number a, const coeffs cf)
	this is in-place, modifies a More...
number	ntInvers (number a, const coeffs cf)
number	ntAdd (number a, number b, const coeffs cf)
number	ntSub (number a, number b, const coeffs cf)
number	ntMult (number a, number b, const coeffs cf)
number	ntDiv (number a, number b, const coeffs cf)
void	ntPower (number a, int exp, number *b, const coeffs cf)
number	ntCopy (number a, const coeffs cf)
void	ntWriteLong (number &a, const coeffs cf)
void	ntWriteShort (number &a, const coeffs cf)
number	ntRePart (number a, const coeffs cf)
number	ntImPart (number a, const coeffs cf)
number	ntGetDenom (number &a, const coeffs cf)
	TODO: normalization of a!? More...
number	ntGetNumerator (number &a, const coeffs cf)
	TODO: normalization of a!? More...
number	ntGcd (number a, number b, const coeffs cf)
number	ntNormalizeHelper (number a, number b, const coeffs cf)
int	ntSize (number a, const coeffs cf)
void	ntDelete (number *a, const coeffs cf)
void	ntCoeffWrite (const coeffs cf, BOOLEAN details)
const char *	ntRead (const char *s, number *a, const coeffs cf)
static BOOLEAN	ntCoeffIsEqual (const coeffs cf, n_coeffType n, void *param)
void	heuristicGcdCancellation (number a, const coeffs cf)
void	definiteGcdCancellation (number a, const coeffs cf, BOOLEAN simpleTestsHaveAlreadyBeenPerformed)
	modifies a More...
void	handleNestedFractionsOverQ (fraction f, const coeffs cf)
static coeffs	nCoeff_bottom (const coeffs r, int &height)
number	ntInit (poly p, const coeffs cf)
	takes over p! More...
number	ntDiff (number a, number d, const coeffs cf)
void	ntNormalize (number &a, const coeffs cf)
number	ntMap00 (number a, const coeffs src, const coeffs dst)
number	ntMapZ0 (number a, const coeffs src, const coeffs dst)
number	ntMapP0 (number a, const coeffs src, const coeffs dst)
number	ntCopyMap (number a, const coeffs cf, const coeffs dst)
number	ntGenMap (number a, const coeffs cf, const coeffs dst)
number	ntCopyAlg (number a, const coeffs cf, const coeffs dst)
number	ntGenAlg (number a, const coeffs cf, const coeffs dst)
number	ntMap0P (number a, const coeffs src, const coeffs dst)
number	ntMapPP (number a, const coeffs src, const coeffs dst)
number	ntMapUP (number a, const coeffs src, const coeffs dst)
nMapFunc	ntSetMap (const coeffs src, const coeffs dst)
	Get a mapping function from src into the domain of this type (n_transExt) More...
void	ntKillChar (coeffs cf)
number	ntConvFactoryNSingN (const CanonicalForm n, const coeffs cf)
CanonicalForm	ntConvSingNFactoryN (number n, BOOLEAN, const coeffs cf)
static int	ntParDeg (number a, const coeffs cf)
static number	ntParameter (const int iParameter, const coeffs cf)
	return the specified parameter as a number in the given trans.ext. More...
int	ntIsParam (number m, const coeffs cf)
	if m == var(i)/1 => return i, More...
static void	ntClearContent (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
static void	ntClearDenominators (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
number	ntChineseRemainder (number *x, number *q, int rl, BOOLEAN sym, const coeffs cf)
number	ntFarey (number p, number n, const coeffs cf)
BOOLEAN	ntInitChar (coeffs cf, void *infoStruct)
	Initialize the coeffs object. More...

Variables
static const n_coeffType	ID = n_transExt
	Our own type! More...
omBin	fractionObjectBin = omGetSpecBin(sizeof(fractionObject))

Macro Definition Documentation

#define ADD_COMPLEXITY   1

complexity increase due to + and -

Definition at line 64 of file transext.cc.

#define BOUND_COMPLEXITY   10

maximum complexity of a number

Definition at line 67 of file transext.cc.

#define COM

(

f

)

f->complexity

Definition at line 72 of file transext.cc.

#define DIFF_COMPLEXITY   2

complexity increase due to * and /

Definition at line 66 of file transext.cc.

#define MULT_COMPLEXITY   2

complexity increase due to * and /

Definition at line 65 of file transext.cc.

#define ntCoeffs   cf->extRing->cf

Definition at line 93 of file transext.cc.

#define ntRing   cf->extRing

Definition at line 87 of file transext.cc.

#define ntTest

(

a

)

ntDBTest(a,__FILE__,__LINE__,cf)

Definition at line 76 of file transext.cc.

#define NUMIS1

(

f

)

(p_IsOne(NUM(f), cf->extRing))

TRUE iff num. represents 1.

Definition at line 70 of file transext.cc.

#define TRANSEXT_PRIVATES

Definition at line 35 of file transext.cc.

Function Documentation

void definiteGcdCancellation	(	number	a,
		const coeffs	cf,
		BOOLEAN	simpleTestsHaveAlreadyBeenPerformed
	)

modifies a

Definition at line 1246 of file transext.cc.

{
  ntTest(a); // !!!!

  fraction f = (fraction)a;

  if (IS0(a)) return;
  if (!simpleTestsHaveAlreadyBeenPerformed)
  {
    if (DENIS1(f) || NUMIS1(f)) { COM(f) = 0; return; }

    /* check whether NUM(f) = DEN(f), and - if so - replace 'a' by 1 */
    if (p_EqualPolys(NUM(f), DEN(f), ntRing))
    { /* numerator and denominator are both != 1 */
      p_Delete(&NUM(f), ntRing); NUM(f) = p_ISet(1, ntRing);
      p_Delete(&DEN(f), ntRing); DEN(f) = NULL;
      COM(f) = 0;
      ntTest(a); // !!!!
      return;
    }
  }
  /*if (rField_is_Q(ntRing))
  {
    number c=n_Copy(pGetCoeff(NUM(f)),ntCoeffs);
    poly p=pNext(NUM(f));
    while((p!=NULL)&&(!n_IsOne(c,ntCoeffs)))
    {
      number cc=n_Gcd(c,pGetCoeff(p),ntCoeffs);
      n_Delete(&c,ntCoeffs);
      c=cc;
      pIter(p);
    };
    p=DEN(f);
    while((p!=NULL)&&(!n_IsOne(c,ntCoeffs)))
    {
      number cc=n_Gcd(c,pGetCoeff(p),ntCoeffs);
      n_Delete(&c,ntCoeffs);
      c=cc;
      pIter(p);
    };
    if(!n_IsOne(c,ntCoeffs))
    {
      p=NUM(f);
      do
      {
        number cc=n_Div(pGetCoeff(p),c,ntCoeffs);
        n_Normalize(cc,ntCoeffs);
        p_SetCoeff(p,cc,ntRing);
        pIter(p);
      } while(p!=NULL);
      p=DEN(f);
      do
      {
        number cc=n_Div(pGetCoeff(p),c,ntCoeffs);
        n_Normalize(cc,ntCoeffs);
        p_SetCoeff(p,cc,ntRing);
        pIter(p);
      } while(p!=NULL);
      n_Delete(&c,ntCoeffs);
      if(pNext(DEN(f))==NULL)
      {
        if (p_IsOne(DEN(f),ntRing))
        {
          p_LmDelete(&DEN(f),ntRing);
          COM(f)=0;
          return;
        }
        else
        {
          return;
        }
      }
    }
  }*/

  /* here we assume: NUM(f), DEN(f) !=NULL, in Z_a reqp. Z/p_a */
  poly pGcd = singclap_gcd_and_divide(NUM(f), DEN(f), ntRing);
  if (p_IsConstant(pGcd, ntRing)
  && n_IsOne(p_GetCoeff(pGcd, ntRing), ntCoeffs)
  )
  { /* gcd = 1; nothing to cancel;
       Suppose the given rational function field is over Q. Although the
       gcd is 1, we may have produced fractional coefficients in NUM(f),
       DEN(f), or both, due to previous arithmetics. The next call will
       remove those nested fractions, in case there are any. */
    if (nCoeff_is_Zp(ntCoeffs))
    {
      NUM (f) = p_Div_nn (NUM (f), p_GetCoeff (DEN(f),ntRing), ntRing);
      if (p_IsConstant (DEN (f), ntRing))
      {
        p_Delete(&DEN (f), ntRing);
        DEN (f) = NULL;
      }
      else
      {
        p_Norm (DEN (f),ntRing);
      }
    } else if (nCoeff_is_Q(ntCoeffs)) handleNestedFractionsOverQ(f, cf);
  }
  else
  { /* We divide both NUM(f) and DEN(f) by the gcd which is known
       to be != 1. */
    if (p_IsConstant(DEN(f), ntRing) &&
        n_IsOne(p_GetCoeff(DEN(f), ntRing), ntCoeffs))
    {
      /* DEN(f) = 1 needs to be represented by NULL! */
      p_Delete(&DEN(f), ntRing);
      DEN(f) = NULL;
    }
    else
    {
      if (nCoeff_is_Zp(ntCoeffs))
      {
        NUM (f) = p_Div_nn (NUM (f), p_GetCoeff (DEN(f),ntRing), ntRing);
        if (p_IsConstant (DEN (f), ntRing))
        {
          p_Delete(&DEN (f), ntRing);
          DEN (f) = NULL;
        }
        else
        {
          p_Norm (DEN (f),ntRing);
        }
      }
    }
  }
  COM(f) = 0;
  p_Delete(&pGcd, ntRing);

  if( DEN(f) != NULL )
    if( !n_GreaterZero(pGetCoeff(DEN(f)), ntCoeffs) )
    {
      NUM(f) = p_Neg(NUM(f), ntRing);
      DEN(f) = p_Neg(DEN(f), ntRing);
      if (p_IsConstant(DEN(f), ntRing) &&
        n_IsOne(p_GetCoeff(DEN(f), ntRing), ntCoeffs))
      {
        /* DEN(f) = 1 needs to be represented by NULL! */
        p_Delete(&DEN(f), ntRing);
        DEN (f) = NULL;
      }
    }
  ntTest(a); // !!!!
}

void handleNestedFractionsOverQ	(	fraction	f,
		const coeffs	cf
	)

Definition at line 1100 of file transext.cc.

{
  assume(nCoeff_is_Q(ntCoeffs));
  assume(!IS0(f));
  assume(!DENIS1(f));

  { /* step (1); see documentation of this procedure above */
    number lcmOfDenominators = n_Init(1, ntCoeffs);
    number c; number tmp;
    poly p = NUM(f);
    /* careful when using n_NormalizeHelper!!! It computes the lcm of the numerator
       of the 1st argument and the denominator of the 2nd!!! */
    while (p != NULL)
    {
      c = p_GetCoeff(p, ntRing);
      tmp = n_NormalizeHelper(lcmOfDenominators, c, ntCoeffs);
      n_Delete(&lcmOfDenominators, ntCoeffs);
      lcmOfDenominators = tmp;
      pIter(p);
    }
    p = DEN(f);
    while (p != NULL)
    {
      c = p_GetCoeff(p, ntRing);
      tmp = n_NormalizeHelper(lcmOfDenominators, c, ntCoeffs);
      n_Delete(&lcmOfDenominators, ntCoeffs);
      lcmOfDenominators = tmp;
      pIter(p);
    }
    if (!n_IsOne(lcmOfDenominators, ntCoeffs))
    { /* multiply NUM(f) and DEN(f) with lcmOfDenominators */
      NUM(f) = p_Mult_nn(NUM(f), lcmOfDenominators, ntRing);
      p_Normalize(NUM(f), ntRing);
      DEN(f) = p_Mult_nn(DEN(f), lcmOfDenominators, ntRing);
      p_Normalize(DEN(f), ntRing);
    }
    n_Delete(&lcmOfDenominators, ntCoeffs);
    if (DEN(f)!=NULL)
    { /* step (2); see documentation of this procedure above */
      p = NUM(f);
      number gcdOfCoefficients = n_Copy(p_GetCoeff(p, ntRing), ntCoeffs);
      pIter(p);
      while ((p != NULL) && (!n_IsOne(gcdOfCoefficients, ntCoeffs)))
      {
        c = p_GetCoeff(p, ntRing);
        tmp = n_Gcd(c, gcdOfCoefficients, ntCoeffs);
        n_Delete(&gcdOfCoefficients, ntCoeffs);
        gcdOfCoefficients = tmp;
        pIter(p);
      }
      p = DEN(f);
      while ((p != NULL) && (!n_IsOne(gcdOfCoefficients, ntCoeffs)))
      {
        c = p_GetCoeff(p, ntRing);
        tmp = n_Gcd(c, gcdOfCoefficients, ntCoeffs);
        n_Delete(&gcdOfCoefficients, ntCoeffs);
        gcdOfCoefficients = tmp;
        pIter(p);
      }
      if (!n_IsOne(gcdOfCoefficients, ntCoeffs))
      { /* divide NUM(f) and DEN(f) by gcdOfCoefficients */
        number inverseOfGcdOfCoefficients = n_Invers(gcdOfCoefficients,
                                                     ntCoeffs);
        NUM(f) = p_Mult_nn(NUM(f), inverseOfGcdOfCoefficients, ntRing);
        p_Normalize(NUM(f), ntRing);
        DEN(f) = p_Mult_nn(DEN(f), inverseOfGcdOfCoefficients, ntRing);
        p_Normalize(DEN(f), ntRing);
        n_Delete(&inverseOfGcdOfCoefficients, ntCoeffs);
      }
      n_Delete(&gcdOfCoefficients, ntCoeffs);
    }
  }

  /* Now, due to the above computations, DEN(f) may have become the
     1-polynomial which needs to be represented by NULL: */
  if ((DEN(f) != NULL) &&
      p_IsConstant(DEN(f), ntRing) &&
      n_IsOne(p_GetCoeff(DEN(f), ntRing), ntCoeffs))
  {
    p_Delete(&DEN(f), ntRing); DEN(f) = NULL;
  }

  if( DEN(f) != NULL )
    if( !n_GreaterZero(pGetCoeff(DEN(f)), ntCoeffs) )
    {
      NUM(f) = p_Neg(NUM(f), ntRing);
      DEN(f) = p_Neg(DEN(f), ntRing);
    }

  ntTest((number)f); // TODO!
}

void heuristicGcdCancellation	(	number	a,
		const coeffs	cf
	)

Definition at line 1193 of file transext.cc.

{
//  ntTest(a); // !!!!????
  if (IS0(a)) return;

  fraction f = (fraction)a;
  p_Normalize(NUM(f),ntRing);
  if (DENIS1(f) || NUMIS1(f)) { COM(f) = 0; return; }

  assume( DEN(f) != NULL );
  p_Normalize(DEN(f),ntRing);

  /* check whether NUM(f) = DEN(f), and - if so - replace 'a' by 1 */
  if (p_EqualPolys(NUM(f), DEN(f), ntRing))
  { /* numerator and denominator are both != 1 */
    p_Delete(&NUM(f), ntRing); NUM(f) = p_ISet(1, ntRing);
    p_Delete(&DEN(f), ntRing); DEN(f) = NULL;
    COM(f) = 0;
  }
  else
  {
    if (COM(f) > BOUND_COMPLEXITY)
      definiteGcdCancellation(a, cf, TRUE);

    // TODO: check if it is enough to put the following into definiteGcdCancellation?!
    if( DEN(f) != NULL )
    {
      if( !n_GreaterZero(pGetCoeff(DEN(f)), ntCoeffs) )
      {
        NUM(f) = p_Neg(NUM(f), ntRing);
        DEN(f) = p_Neg(DEN(f), ntRing);
      }
      if (ntCoeffs->has_simple_Inverse)
      {
        if (!n_IsOne(pGetCoeff(DEN(f)),ntCoeffs))
        {
          number inv=n_Invers(pGetCoeff(DEN(f)),ntCoeffs);
          DEN(f)=p_Mult_nn(DEN(f),inv,ntRing);
          NUM(f)=p_Mult_nn(NUM(f),inv,ntRing);
        }
        if(p_LmIsConstant(DEN(f),ntRing))
        {
          p_Delete(&DEN(f),ntRing);
          COM(f)=0;
        }
      }
    }
  }

  ntTest(a);
}

static coeffs nCoeff_bottom ( const coeffs  r, int &  height  )

static

Definition at line 262 of file transext.cc.

{
  assume(r != NULL);
  coeffs cf = r;
  height = 0;
  while (nCoeff_is_Extension(cf))
  {
    assume(cf->extRing != NULL); assume(cf->extRing->cf != NULL);
    cf = cf->extRing->cf;
    height++;
  }
  return cf;
}

number ntAdd	(	number	a,
		number	b,
		const coeffs	cf
	)

Definition at line 815 of file transext.cc.

{
  //check_N(a,cf);
  //check_N(b,cf);
  ntTest(a);
  ntTest(b);
  if (IS0(a)) return ntCopy(b, cf);
  if (IS0(b)) return ntCopy(a, cf);

  fraction fa = (fraction)a;
  fraction fb = (fraction)b;

  poly g = p_Copy(NUM(fa), ntRing);
  if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
  poly h = p_Copy(NUM(fb), ntRing);
  if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing);
  g = p_Add_q(g, h, ntRing);

  if (g == NULL) return NULL;

  poly f;
  if      (DENIS1(fa) && DENIS1(fb))  f = NULL;
  else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing);
  else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing);
  else /* both denom's are != 1 */    f = p_Mult_q(p_Copy(DEN(fa), ntRing),
                                                   p_Copy(DEN(fb), ntRing),
                                                   ntRing);

  fraction result = (fraction)omAllocBin(fractionObjectBin);
  NUM(result) = g;
  DEN(result) = f;
  COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY;
  heuristicGcdCancellation((number)result, cf);

//  ntTest((number)result);

  //check_N((number)result,cf);
  return (number)result;
}

number ntChineseRemainder	(	number *	x,
		number *	q,
		int	rl,
		BOOLEAN	sym,
		const coeffs	cf
	)

Definition at line 2333 of file transext.cc.

{
  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
  int i;

  poly *P=(poly*)omAlloc(rl*sizeof(poly*));
  number *X=(number *)omAlloc(rl*sizeof(number));

  for(i=0;i<rl;i++) P[i]=p_Copy(NUM((fraction)(x[i])),cf->extRing);
  NUM(result)=p_ChineseRemainder(P,X,q,rl,cf->extRing);

  for(i=0;i<rl;i++)
  {
    P[i]=p_Copy(DEN((fraction)(x[i])),cf->extRing);
    if (P[i]==NULL) P[i]=p_One(cf->extRing);
  }
  DEN(result)=p_ChineseRemainder(P,X,q,rl,cf->extRing);

  omFreeSize(X,rl*sizeof(number));
  omFreeSize(P,rl*sizeof(poly*));
  if (p_IsConstant(DEN(result), ntRing)
  && n_IsOne(pGetCoeff(DEN(result)), ntCoeffs))
  {
    p_Delete(&DEN(result),ntRing);
  }
  return ((number)result);
}

static void ntClearContent ( ICoeffsEnumerator &  numberCollectionEnumerator, number &  c, const coeffs  cf  )

static

Definition at line 2100 of file transext.cc.

{
  assume(cf != NULL);
  assume(getCoeffType(cf) == ID);
  // all coeffs are given by fractions of polynomails over integers!!!
  // without denominators!!!

  const ring   R = cf->extRing;
  assume(R != NULL);
  const coeffs Q = R->cf;
  assume(Q != NULL);
  assume(nCoeff_is_Q(Q));


  numberCollectionEnumerator.Reset();

  if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial?
  {
    c = ntInit(1, cf);
    return;
  }

  // all coeffs are given by integers after returning from this routine

  // part 1, collect product of all denominators /gcds
  poly cand = NULL;

  do
  {
    number &n = numberCollectionEnumerator.Current();

    ntNormalize(n, cf);

    fraction f = (fraction)n;

    assume( f != NULL );

    const poly den = DEN(f);

    assume( den == NULL ); // ?? / 1 ?

    const poly num = NUM(f);

    if( cand == NULL )
      cand = p_Copy(num, R);
    else
      cand = singclap_gcd(cand, p_Copy(num, R), R); // gcd(cand, num)

    if( p_IsConstant(cand, R) )
      break;
  }
  while( numberCollectionEnumerator.MoveNext() ) ;


  // part2: all coeffs = all coeffs * cand
  if( cand != NULL )
  {
  if( !p_IsConstant(cand, R) )
  {
    c = ntInit(cand, cf);
    numberCollectionEnumerator.Reset();
    while (numberCollectionEnumerator.MoveNext() )
    {
      number &n = numberCollectionEnumerator.Current();
      const number t = ntDiv(n, c, cf); // TODO: rewrite!?
      ntDelete(&n, cf);
      n = t;
    }
  } // else NUM (result) = p_One(R);
  else { p_Delete(&cand, R); cand = NULL; }
  }

  // Quick and dirty fix for constant content clearing: consider numerators???
  CRecursivePolyCoeffsEnumerator<NTNumConverter> itr(numberCollectionEnumerator); // recursively treat the NUM(numbers) as polys!
  number cc;

  n_ClearContent(itr, cc, Q);
  number g = ntInit(p_NSet(cc, R), cf);

  if( cand != NULL )
  {
    number gg = ntMult(g, c, cf);
    ntDelete(&g, cf);
    ntDelete(&c, cf); c = gg;
  } else
    c = g;
  ntTest(c);
}

static void ntClearDenominators ( ICoeffsEnumerator &  numberCollectionEnumerator, number &  c, const coeffs  cf  )

static

Definition at line 2189 of file transext.cc.

{
  assume(cf != NULL);
  assume(getCoeffType(cf) == ID); // both over Q(a) and Zp(a)!
  // all coeffs are given by fractions of polynomails over integers!!!

  numberCollectionEnumerator.Reset();

  if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial?
  {
    c = ntInit(1, cf);
    return;
  }

  // all coeffs are given by integers after returning from this routine

  // part 1, collect product of all denominators /gcds
  poly cand = NULL;

  const ring R = cf->extRing;
  assume(R != NULL);

  const coeffs Q = R->cf;
  assume(Q != NULL);
//  assume(nCoeff_is_Q(Q));

  do
  {
    number &n = numberCollectionEnumerator.Current();

    ntNormalize(n, cf);

    fraction f = (fraction)ntGetDenom (n, cf);

    assume( f != NULL );

    const poly den = NUM(f);

    if( den == NULL ) // ?? / 1 ?
      continue;

    if( cand == NULL )
      cand = p_Copy(den, R);
    else
    {
      // cand === LCM( cand, den )!!!!
      // NOTE: maybe it's better to make the product and clearcontent afterwards!?
      // TODO: move the following to factory?
      poly gcd = singclap_gcd(p_Copy(cand, R), p_Copy(den, R), R); // gcd(cand, den) is monic no mater leading coeffs! :((((
      if (nCoeff_is_Q (Q))
      {
        number LcGcd= n_SubringGcd (p_GetCoeff (cand, R), p_GetCoeff(den, R), Q);
        gcd = p_Mult_nn(gcd, LcGcd, R);
        n_Delete(&LcGcd,Q);
      }
//      assume( n_IsOne(pGetCoeff(gcd), Q) ); // TODO: this may be wrong...
      cand = p_Mult_q(cand, p_Copy(den, R), R); // cand *= den
      const poly t = singclap_pdivide( cand, gcd, R ); // cand' * den / gcd(cand', den)
      p_Delete(&cand, R);
      p_Delete(&gcd, R);
      cand = t;
    }
  }
  while( numberCollectionEnumerator.MoveNext() );

  if( cand == NULL )
  {
    c = ntInit(1, cf);
    return;
  }

  c = ntInit(cand, cf);

  numberCollectionEnumerator.Reset();

  number d = NULL;

  while (numberCollectionEnumerator.MoveNext() )
  {
    number &n = numberCollectionEnumerator.Current();
    number t = ntMult(n, c, cf); // TODO: rewrite!?
    ntDelete(&n, cf);

    ntNormalize(t, cf); // TODO: needed?
    n = t;

    fraction f = (fraction)t;
    assume( f != NULL );

    const poly den = DEN(f);

    if( den != NULL ) // ?? / ?? ?
    {
      assume( p_IsConstant(den, R) );
      assume( pNext(den) == NULL );

      if( d == NULL )
        d = n_Copy(pGetCoeff(den), Q);
      else
      {
        number g = n_NormalizeHelper(d, pGetCoeff(den), Q);
        n_Delete(&d, Q); d = g;
      }
    }
  }

  if( d != NULL )
  {
    numberCollectionEnumerator.Reset();
    while (numberCollectionEnumerator.MoveNext() )
    {
      number &n = numberCollectionEnumerator.Current();
      fraction f = (fraction)n;

      assume( f != NULL );

      const poly den = DEN(f);

      if( den == NULL ) // ?? / 1 ?
        NUM(f) = p_Mult_nn(NUM(f), d, R);
      else
      {
        assume( p_IsConstant(den, R) );
        assume( pNext(den) == NULL );

        number ddd = n_Div(d, pGetCoeff(den), Q); // but be an integer now!!!
        NUM(f) = p_Mult_nn(NUM(f), ddd, R);
        n_Delete(&ddd, Q);

        p_Delete(&DEN(f), R);
        DEN(f) = NULL; // TODO: check if this is needed!?
      }

      assume( DEN(f) == NULL );
    }

    NUM(c) = p_Mult_nn(NUM(c), d, R);
    n_Delete(&d, Q);
  }


  ntTest(c);
}

static BOOLEAN ntCoeffIsEqual ( const coeffs  cf, n_coeffType  n, void *  param  )

static

Definition at line 1471 of file transext.cc.

{
  if (ID != n) return FALSE;
  TransExtInfo *e = (TransExtInfo *)param;
  /* for rational function fields we expect the underlying
     polynomial rings to be IDENTICAL, i.e. the SAME OBJECT;
     this expectation is based on the assumption that we have properly
     registered cf and perform reference counting rather than creating
     multiple copies of the same coefficient field/domain/ring */
  if (ntRing == e->r)
    return TRUE;

  // NOTE: Q(a)[x] && Q(a)[y] should better share the _same_ Q(a)...
  if( rEqual(ntRing, e->r, TRUE) )
  {
    rDelete(e->r);
    return TRUE;
  }

  return FALSE;
}

void ntCoeffWrite	(	const coeffs	cf,
		BOOLEAN	details
	)

Definition at line 721 of file transext.cc.

{
  assume( cf != NULL );

  const ring A = cf->extRing;

  assume( A != NULL );
  assume( A->cf != NULL );

  n_CoeffWrite(A->cf, details);

//  rWrite(A);

  const int P = rVar(A);
  assume( P > 0 );

  Print("//   %d parameter    : ", P);

  for (int nop=0; nop < P; nop ++)
    Print("%s ", rRingVar(nop, A));

  assume( A->qideal == NULL );

  PrintS("\n//   minpoly        : 0\n");

/*
  PrintS("//   Coefficients live in the rational function field\n");
  Print("//   K(");
  for (int i = 0; i < rVar(ntRing); i++)
  {
    if (i > 0) PrintS(" ");
    Print("%s", rRingVar(i, ntRing));
  }
  PrintS(") with\n");
  PrintS("//   K: "); n_CoeffWrite(cf->extRing->cf);
*/
}

number ntConvFactoryNSingN	(	const CanonicalForm	n,
		const coeffs	cf
	)

Definition at line 2022 of file transext.cc.

{
  if (n.isZero()) return NULL;
  poly p=convFactoryPSingP(n,ntRing);
  p_Normalize(p,ntRing);
  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
  NUM(result) = p;
  //DEN(result) = NULL; // done by omAlloc0Bin
  //COM(result) = 0; // done by omAlloc0Bin
  ntTest((number)result);
  return (number)result;
}

CanonicalForm ntConvSingNFactoryN	(	number	n,
		BOOLEAN	,
		const coeffs	cf
	)

Definition at line 2034 of file transext.cc.

{
  ntTest(n);
  if (IS0(n)) return CanonicalForm(0);

  fraction f = (fraction)n;
  return convSingPFactoryP(NUM(f),ntRing);
}

number ntCopy	(	number	a,
		const coeffs	cf
	)

Definition at line 341 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a); // !!!
  if (IS0(a)) return NULL;
  fraction f = (fraction)a;
  poly g = p_Copy(NUM(f), ntRing);
  poly h = NULL; if (!DENIS1(f)) h = p_Copy(DEN(f), ntRing);
  fraction result = (fraction)omAllocBin(fractionObjectBin);
  NUM(result) = g;
  DEN(result) = h;
  COM(result) = COM(f);
  ntTest((number)result);
  return (number)result;
}

number ntCopyAlg	(	number	a,
		const coeffs	cf,
		const coeffs	dst
	)

Definition at line 1862 of file transext.cc.

{
  n_Test(a, cf) ;
  if (n_IsZero(a, cf)) return NULL;
  return ntInit(prCopyR((poly)a, cf->extRing, dst->extRing),dst);
}

number ntCopyMap	(	number	a,
		const coeffs	cf,
		const coeffs	dst
	)

Definition at line 1806 of file transext.cc.

{
  ntTest(a);
  if (IS0(a)) return NULL;

  const ring rSrc = cf->extRing;
  const ring rDst = dst->extRing;

  if( rSrc == rDst )
    return ntCopy(a, dst); // USUALLY WRONG!

  fraction f = (fraction)a;
  poly g = prCopyR(NUM(f), rSrc, rDst);

  poly h = NULL;

  if (!DENIS1(f))
     h = prCopyR(DEN(f), rSrc, rDst);

  fraction result = (fraction)omAllocBin(fractionObjectBin);

  NUM(result) = g;
  DEN(result) = h;
  COM(result) = COM(f);
  //check_N((number)result,dst);
  n_Test((number)result, dst);
  return (number)result;
}

BOOLEAN ntDBTest	(	number	a,
		const char *	f,
		const int	l,
		const coeffs	r
	)

< t != 0 ==> numerator(t) != 0

Definition at line 178 of file transext.cc.

{
  assume(getCoeffType(cf) == ID);

  if (IS0(a)) return TRUE;

  const fraction t = (fraction)a;

  //check_N(a,cf);
  const poly num = NUM(t);
  assume(num != NULL);   /**< t != 0 ==> numerator(t) != 0 */

  p_Test(num, ntRing);

  const poly den = DEN(t);

  if (den != NULL) // !DENIS1(f)
  {
    p_Test(den, ntRing);

    if(p_IsConstant(den, ntRing) && (n_IsOne(pGetCoeff(den), ntCoeffs)))
    {
      Print("?/1 in %s:%d\n",f,l);
      return FALSE;
    }

    if( !n_GreaterZero(pGetCoeff(den), ntCoeffs) )
    {
      Print("negative sign of DEN. of a fraction in %s:%d\n",f,l);
      return FALSE;
    }

    // test that den is over integers!?

  } else
  {  // num != NULL // den == NULL

//    if( COM(t) != 0 )
//    {
//      Print("?//NULL with non-zero complexity: %d in %s:%d\n", COM(t), f, l);
//      return FALSE;
//    }
    // test that nume is over integers!?
  }
  if (getCoeffType(ntCoeffs)==n_Q)
  {
    poly p=num; // !=NULL
    do
    {
      number n=pGetCoeff(p);
      n_Test(n,ntCoeffs);
      if ((!(SR_HDL(n) & SR_INT))&&(n->s==0))
      /* not normalized, just do for the following test*/
      {
        n_Normalize(pGetCoeff(p),ntCoeffs);
        n=pGetCoeff(p);
      }
      if (!(SR_HDL(n) & SR_INT))
      {
        if (n->s<2)
          Print("rational coeff in num: %s:%d\n",f,l);
      }
      pIter(p);
    } while(p!=NULL);
    p=den;
    while(p!=NULL)
    {
      number n=pGetCoeff(p);
      if (!(SR_HDL(n) & SR_INT))
      {
        if (n->s!=3)
          Print("rational coeff in den.:%s:%d\n",f,l);
      }
      pIter(p);
    }
  }
  return TRUE;
}

void ntDelete	(	number *	a,
		const coeffs	cf
	)

Definition at line 283 of file transext.cc.

{
  //check_N(*a,cf);
  ntTest(*a); // !!!
  fraction f = (fraction)(*a);
  if (IS0(f)) return;
  p_Delete(&NUM(f), ntRing);
  if (!DENIS1(f)) p_Delete(&DEN(f), ntRing);
  omFreeBin((ADDRESS)f, fractionObjectBin);
  *a = NULL;
}

number ntDiff	(	number	a,
		number	d,
		const coeffs	cf
	)

Definition at line 759 of file transext.cc.

{
  //check_N(a,cf);
  //check_N(d,cf);
  ntTest(a);
  ntTest(d);

  if (IS0(d))
  {
    WerrorS("ringvar expected");
    return NULL;
  }
  fraction t = (fraction) d;
  if (!DENIS1(t))
  {
    WerrorS("expected differentiation by a variable");
    return NULL;
  }
  int k=p_Var(NUM(t),ntRing);
  if (k==0)
  {
    WerrorS("expected differentiation by a variable");
    return NULL;
  }

  if (IS0(a)) return ntCopy(a, cf);

  fraction fa = (fraction)a;
  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
  if (DENIS1(fa))
  {
     NUM(result) = p_Diff(NUM(fa),k,ntRing);
     //DEN(result) = NULL; // done by ..Alloc0..
     if (NUM(result)==NULL)
     {
       omFreeBin((ADDRESS)result, fractionObjectBin);
       return(NULL);
     }
     COM(result) = COM(fa);
     //check_N((number)result,cf);
     return (number)result;
  }

  poly fg = p_Mult_q(p_Copy(DEN(fa),ntRing),p_Diff(NUM(fa),k,ntRing),ntRing);
  poly gf = p_Mult_q(p_Copy(NUM(fa),ntRing),p_Diff(DEN(fa),k,ntRing),ntRing);
  NUM(result) = p_Sub(fg,gf,ntRing);
  if (NUM(result)==NULL) return(NULL);
  DEN(result) = pp_Mult_qq(DEN(fa), DEN(fa), ntRing);
  COM(result) = COM(fa) + COM(fa) + DIFF_COMPLEXITY;
  heuristicGcdCancellation((number)result, cf);

  //check_N((number)result,cf);
  return (number)result;
}

number ntDiv	(	number	a,
		number	b,
		const coeffs	cf
	)

Definition at line 963 of file transext.cc.

{
  //check_N(a,cf);
  //check_N(b,cf);
  ntTest(a);
  ntTest(b);
  if (IS0(a)) return NULL;
  if (IS0(b)) WerrorS(nDivBy0);

  fraction fa = (fraction)a;
  fraction fb = (fraction)b;

  poly g = p_Copy(NUM(fa), ntRing);
  if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);

  if (g == NULL) return NULL;   /* may happen due to zero divisors */

  poly f = p_Copy(NUM(fb), ntRing);
  if (!DENIS1(fa)) f = p_Mult_q(f, p_Copy(DEN(fa), ntRing), ntRing);

  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
  NUM(result) = g;
  if (!n_GreaterZero(pGetCoeff(f),ntCoeffs))
  {
    g=p_Neg(g,ntRing);
    f=p_Neg(f,ntRing);
    NUM(result) = g;
  }
  if (!p_IsConstant(f,ntRing) || !n_IsOne(pGetCoeff(f),ntCoeffs))
  {
    DEN(result) = f;
  }
  COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY;
  heuristicGcdCancellation((number)result, cf);
//  ntTest((number)result);
  //check_N((number)result,cf);
  return (number)result;
}

BOOLEAN ntEqual	(	number	a,
		number	b,
		const coeffs	cf
	)

simple tests

cheap test if gcd's have been cancelled in both numbers

Definition at line 295 of file transext.cc.

{
  //check_N(a,cf);
  //check_N(b,cf);
  ntTest(a);
  ntTest(b);

  /// simple tests
  if (a == b) return TRUE;
  if ((IS0(a)) && (!IS0(b))) return FALSE;
  if ((IS0(b)) && (!IS0(a))) return FALSE;

  /// cheap test if gcd's have been cancelled in both numbers
  fraction fa = (fraction)a;
  fraction fb = (fraction)b;
  if ((COM(fa) == 1) && (COM(fb) == 1))
  {
    poly f = p_Add_q(p_Copy(NUM(fa), ntRing),
                     p_Neg(p_Copy(NUM(fb), ntRing), ntRing),
                     ntRing);
    if (f != NULL) { p_Delete(&f, ntRing); return FALSE; }
    if (DENIS1(fa) && DENIS1(fb))  return TRUE;
    if (DENIS1(fa) && !DENIS1(fb)) return FALSE;
    if (!DENIS1(fa) && DENIS1(fb)) return FALSE;
    f = p_Add_q(p_Copy(DEN(fa), ntRing),
                p_Neg(p_Copy(DEN(fb), ntRing), ntRing),
                ntRing);
    if (f != NULL) { p_Delete(&f, ntRing); return FALSE; }
    return TRUE;
  }

  /* default: the more expensive multiplication test
              a/b = c/d  <==>  a*d = b*c */
  poly f = p_Copy(NUM(fa), ntRing);
  if (!DENIS1(fb)) f = p_Mult_q(f, p_Copy(DEN(fb), ntRing), ntRing);
  poly g = p_Copy(NUM(fb), ntRing);
  if (!DENIS1(fa)) g = p_Mult_q(g, p_Copy(DEN(fa), ntRing), ntRing);
  poly h = p_Add_q(f, p_Neg(g, ntRing), ntRing);
  if (h == NULL) return TRUE;
  else
  {
    p_Delete(&h, ntRing);
    return FALSE;
  }
}

number ntFarey	(	number	p,
		number	n,
		const coeffs	cf
	)

Definition at line 2361 of file transext.cc.

{
  // n is really a bigint
  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
  NUM(result)=p_Farey(p_Copy(NUM((fraction)p),cf->extRing),n,cf->extRing);
  DEN(result)=p_Farey(p_Copy(DEN((fraction)p),cf->extRing),n,cf->extRing);
  return ((number)result);
}

number ntGcd	(	number	a,
		number	b,
		const coeffs	cf
	)

Definition at line 1581 of file transext.cc.

{
  ntTest(a);
  ntTest(b);
  if (a==NULL) return ntCopy(b,cf);
  if (b==NULL) return ntCopy(a,cf);
  fraction fa = (fraction)a;
  fraction fb = (fraction)b;

  poly pa = p_Copy(NUM(fa), ntRing);
  poly pb = p_Copy(NUM(fb), ntRing);

  poly pGcd;
  if (nCoeff_is_Q(ntCoeffs))
  {
    if (p_IsConstant(pa,ntRing) && p_IsConstant(pb,ntRing))
    {
      pGcd = pa;
      p_SetCoeff (pGcd, n_SubringGcd (pGetCoeff(pGcd), pGetCoeff(pb), ntCoeffs), ntRing);
    }
    else
    {
      number contentpa, contentpb, tmp;

      contentpb= p_GetCoeff(pb, ntRing);
      pIter(pb);
      while (pb != NULL)
      {
        tmp = n_SubringGcd(contentpb, p_GetCoeff(pb, ntRing) , ntCoeffs);
        n_Delete(&contentpb, ntCoeffs);
        contentpb = tmp;
        pIter(pb);
      }

      contentpa= p_GetCoeff(pa, ntRing);
      pIter(pa);
      while (pa != NULL)
      {
        tmp = n_SubringGcd(contentpa, p_GetCoeff(pa, ntRing), ntCoeffs);
        n_Delete(&contentpa, ntCoeffs);
        contentpa = tmp;
        pIter(pa);
      }

      tmp= n_SubringGcd (contentpb, contentpa, ntCoeffs);
      n_Delete(&contentpa, ntCoeffs);
      n_Delete(&contentpb, ntCoeffs);
      contentpa= tmp;
      p_Delete(&pb, ntRing);
      p_Delete(&pa, ntRing);

      /* singclap_gcd destroys its arguments; we hence need copies: */
      pGcd = singclap_gcd(p_Copy(NUM(fa),ntRing), p_Copy(NUM(fb),ntRing), ntRing);
      pGcd= p_Mult_nn (pGcd, contentpa, ntRing);
      n_Delete(&contentpa, ntCoeffs);
    }
  }
  else
    pGcd = singclap_gcd(pa, pb, cf->extRing);
  /* Note that, over Q, singclap_gcd will remove the denominators in all
     rational coefficients of pa and pb, before starting to compute
     the gcd. Thus, we do not need to ensure that the coefficients of
     pa and pb live in Z; they may well be elements of Q\Z. */

  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
  NUM(result) = pGcd;
  ntTest((number)result); // !!!!
  return (number)result;
}

number ntGenAlg	(	number	a,
		const coeffs	cf,
		const coeffs	dst
	)

Definition at line 1869 of file transext.cc.

{
  n_Test(a, cf) ;
  if (n_IsZero(a, cf)) return NULL;

  const nMapFunc nMap=n_SetMap(cf->extRing->cf,dst->extRing->cf);
  return ntInit(prMapR((poly)a, nMap, cf->extRing, dst->extRing),dst);
}

number ntGenMap	(	number	a,
		const coeffs	cf,
		const coeffs	dst
	)

Definition at line 1835 of file transext.cc.

{
  ntTest(a);
  if (IS0(a)) return NULL;

  const ring rSrc = cf->extRing;
  const ring rDst = dst->extRing;

  const nMapFunc nMap=n_SetMap(rSrc->cf,rDst->cf);
  fraction f = (fraction)a;
  poly g = prMapR(NUM(f), nMap, rSrc, rDst);

  poly h = NULL;

  if (!DENIS1(f))
     h = prMapR(DEN(f), nMap, rSrc, rDst);

  fraction result = (fraction)omAllocBin(fractionObjectBin);

  NUM(result) = g;
  DEN(result) = h;
  COM(result) = COM(f);
  //check_N((number)result,dst);
  n_Test((number)result, dst);
  return (number)result;
}

number ntGetDenom	(	number &	a,
		const coeffs	cf
	)

TODO: normalization of a!?

Definition at line 419 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a);

  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
  //DEN (result)= NULL; // done by ..Alloc0..
  //COM (result)= 0; // done by ..Alloc0..

  if (IS0(a))
  {
    NUM (result) = p_One(ntRing);
    return (number)result;
  }

  definiteGcdCancellation(a, cf, FALSE);

  fraction f = (fraction)a;

  assume( !IS0(f) );

  const BOOLEAN denis1 = DENIS1 (f);

  if( denis1 && (getCoeffType (ntCoeffs) != n_Q) ) // */1 or 0
  {
    NUM (result)= p_One(ntRing);
    ntTest((number)result);
    return (number)result;
  }

  if (!denis1) // */* / Q
  {
    assume( DEN (f) != NULL );

    if (getCoeffType (ntCoeffs) == n_Q)
      handleNestedFractionsOverQ (f, cf);

    ntTest(a);

    if( DEN (f) != NULL ) // is it ?? // 1 now???
    {
      assume( !p_IsOne(DEN (f), ntRing) );

      NUM (result) = p_Copy (DEN (f), ntRing);
      ntTest((number)result);
      return (number)result;
    }
//    NUM (result) = p_One(ntRing); // NOTE: just in order to be sure...
  }

  // */1 / Q
  assume( getCoeffType (ntCoeffs) == n_Q );
  assume( DEN (f) == NULL );

  number g;
//    poly num= p_Copy (NUM (f), ntRing); // ???


  // TODO/NOTE: the following should not be necessary (due to
  // Hannes!) as NUM (f) should be over Z!!!
  CPolyCoeffsEnumerator itr(NUM(f));

  n_ClearDenominators(itr, g, ntCoeffs); // may return -1 :(((

  if( !n_GreaterZero(g, ntCoeffs) )
  {
//     NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :(((
//     g = n_InpNeg(g, ntCoeffs);
    NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :(((
    g = n_InpNeg(g, ntCoeffs);
  }

  // g should be a positive integer now!
  assume( n_GreaterZero(g, ntCoeffs) );

  if( !n_IsOne(g, ntCoeffs) )
  {
    assume( n_GreaterZero(g, ntCoeffs) );
    assume( !n_IsOne(g, ntCoeffs) );

    DEN (f) = p_NSet(g, ntRing); // update COM(f)???
    assume( DEN (f) != NULL );
    COM (f) ++;

    NUM (result)= p_Copy (DEN (f), ntRing);
  }
  else
  { // common denom == 1?
    NUM (result)= p_NSet(g, ntRing); // p_Copy (DEN (f), ntRing);
//  n_Delete(&g, ntCoeffs);
  }

//    if (!p_IsConstant (num, ntRing) && pNext(num) != NULL)
//    else
//      g= p_GetAllDenom (num, ntRing);
//    result= (fraction) ntSetMap (ntCoeffs, cf) (g, ntCoeffs, cf);

  ntTest((number)result);
  //check_N((number)result,cf);
  return (number)result;
}

number ntGetNumerator	(	number &	a,
		const coeffs	cf
	)

TODO: normalization of a!?

Definition at line 358 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a);
  if (IS0(a)) return NULL;

  definiteGcdCancellation(a, cf, FALSE);

  fraction f = (fraction)a;
  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);

  const BOOLEAN denis1= DENIS1 (f);

  if (getCoeffType (ntCoeffs) == n_Q && !denis1)
    handleNestedFractionsOverQ (f, cf);

  if (getCoeffType (ntCoeffs) == n_Q && denis1)
  {
    assume( DEN (f) == NULL );

    number g;
    // TODO/NOTE: the following should not be necessary (due to
    // Hannes!) as NUM (f) should be over Z!!!
    CPolyCoeffsEnumerator itr(NUM(f));


    n_ClearDenominators(itr, g, ntCoeffs);

    if( !n_GreaterZero(g, ntCoeffs) )
    {
      NUM (f) = p_Neg(NUM (f), ntRing); // Ugly :(((
      g = n_InpNeg(g, ntCoeffs);
    }

    // g should be a positive integer now!
    assume( n_GreaterZero(g, ntCoeffs) );

    if( !n_IsOne(g, ntCoeffs) )
    {
      DEN (f) = p_NSet(g, ntRing); // update COM(f)???
      COM (f) ++;
      assume( DEN (f) != NULL );
    }
    else
      n_Delete(&g, ntCoeffs);

    ntTest(a);
  }

  // Call ntNormalize instead of above?!?

  NUM (result) = p_Copy (NUM (f), ntRing); // ???
  //DEN (result) = NULL; // done by ..Alloc0..
  //COM (result) = 0; // done by ..Alloc0..

  ntTest((number)result);
  //check_N((number)result,cf);
  return (number)result;
}

BOOLEAN ntGreater	(	number	a,
		number	b,
		const coeffs	cf
	)

Definition at line 658 of file transext.cc.

{
  //check_N(a,cf);
  //check_N(b,cf);
  ntTest(a);
  ntTest(b);
  number aNumCoeff = NULL; int aNumDeg = 0;
  number aDenCoeff = NULL; int aDenDeg = 0;
  number bNumCoeff = NULL; int bNumDeg = 0;
  number bDenCoeff = NULL; int bDenDeg = 0;
  if (!IS0(a))
  {
    fraction fa = (fraction)a;
    aNumDeg = p_Totaldegree(NUM(fa), ntRing);
    aNumCoeff = p_GetCoeff(NUM(fa), ntRing);
    if (DEN(fa)!=NULL)
    {
      aDenDeg = p_Totaldegree(DEN(fa), ntRing);
      aDenCoeff=p_GetCoeff(DEN(fa),ntRing);
    }
  }
  else return !(ntGreaterZero (b,cf));
  if (!IS0(b))
  {
    fraction fb = (fraction)b;
    bNumDeg = p_Totaldegree(NUM(fb), ntRing);
    bNumCoeff = p_GetCoeff(NUM(fb), ntRing);
    if (DEN(fb)!=NULL)
    {
      bDenDeg = p_Totaldegree(DEN(fb), ntRing);
      bDenCoeff=p_GetCoeff(DEN(fb),ntRing);
    }
  }
  else return ntGreaterZero(a,cf);
  if (aNumDeg-aDenDeg > bNumDeg-bDenDeg) return TRUE;
  if (aNumDeg-aDenDeg < bNumDeg-bDenDeg) return FALSE;
  number aa;
  number bb;
  if (bDenCoeff==NULL) aa=n_Copy(aNumCoeff,ntCoeffs);
  else                 aa=n_Mult(aNumCoeff,bDenCoeff,ntCoeffs);
  if (aDenCoeff==NULL) bb=n_Copy(bNumCoeff,ntCoeffs);
  else                 bb=n_Mult(bNumCoeff,aDenCoeff,ntCoeffs);
  BOOLEAN rr= n_Greater(aa, bb, ntCoeffs);
  n_Delete(&aa,ntCoeffs);
  n_Delete(&bb,ntCoeffs);
  return rr;
}

BOOLEAN ntGreaterZero	(	number	a,
		const coeffs	cf
	)

forward declarations

Definition at line 711 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a);
  if (IS0(a)) return FALSE;
  fraction f = (fraction)a;
  poly g = NUM(f);
  return (!p_LmIsConstant(g,ntRing)|| n_GreaterZero(pGetCoeff(g), ntCoeffs));
}

number ntImPart	(	number	a,
		const coeffs	cf
	)

Definition at line 556 of file transext.cc.

{
  ntTest(a);
  return NULL;
}

number ntInit	(	long	i,
		const coeffs	cf
	)

Definition at line 562 of file transext.cc.

{
  if (i != 0)
  {
    poly p=p_ISet(i, ntRing);
    if (p!=NULL)
    {
      fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
      NUM(result) = p;
      //DEN(result) = NULL; // done by omAlloc0Bin
      //COM(result) = 0; // done by omAlloc0Bin
      ntTest((number)result);
      //check_N((number)result,cf);
      return (number)result;
    }
  }
  return NULL;
}

number ntInit	(	poly	p,
		const coeffs	cf
	)

takes over p!

Definition at line 583 of file transext.cc.

{
  if (p == NULL) return NULL;

  fraction f = (fraction)omAlloc0Bin(fractionObjectBin);

  if (nCoeff_is_Q(ntCoeffs))
  {
    number g;
    // the following is necessary because
    // NUM (f) should be over Z,
    // while p may be over Q
    CPolyCoeffsEnumerator itr(p);

    n_ClearDenominators(itr, g, ntCoeffs);

    if( !n_GreaterZero(g, ntCoeffs) )
    {
      p = p_Neg(p, ntRing);
      g = n_InpNeg(g, ntCoeffs);
    }

    // g should be a positive integer now!
    assume( n_GreaterZero(g, ntCoeffs) );

    if( !n_IsOne(g, ntCoeffs) )
    {
      DEN (f) = p_NSet(g, ntRing);
      p_Normalize(DEN(f), ntRing);
      assume( DEN (f) != NULL );
    }
    else
    {
      //DEN(f) = NULL; // done by omAlloc0
      n_Delete(&g, ntCoeffs);
    }
  }

  p_Normalize(p, ntRing);
  NUM(f) = p;
  //COM(f) = 0; // done by omAlloc0

  //check_N((number)f,cf);
  ntTest((number)f);
  return (number)f;
}

BOOLEAN ntInitChar	(	coeffs	cf,
		void *	infoStruct
	)

Initialize the coeffs object.

Definition at line 2370 of file transext.cc.

{

  assume( infoStruct != NULL );

  TransExtInfo *e = (TransExtInfo *)infoStruct;

  assume( e->r                != NULL);      // extRing;
  assume( e->r->cf            != NULL);      // extRing->cf;
  assume( e->r->qideal == NULL );

  assume( cf != NULL );
  assume(getCoeffType(cf) == ID);                // coeff type;

  ring R = e->r;
  assume(R != NULL);

  R->ref ++; // increase the ref.counter for the ground poly. ring!

  cf->extRing           = R;
  /* propagate characteristic up so that it becomes
     directly accessible in cf: */
  cf->ch = R->cf->ch;

  cf->is_field=TRUE;
  cf->is_domain=TRUE;
  cf->rep=n_rep_rat_fct;

  cf->factoryVarOffset = R->cf->factoryVarOffset + rVar(R);

  cf->cfCoeffString = naCoeffString; // FIXME? TODO? // extern char* naCoeffString(const coeffs r);

  cf->cfGreaterZero  = ntGreaterZero;
  cf->cfGreater      = ntGreater;
  cf->cfEqual        = ntEqual;
  cf->cfIsZero       = ntIsZero;
  cf->cfIsOne        = ntIsOne;
  cf->cfIsMOne       = ntIsMOne;
  cf->cfInit         = ntInit;
  cf->cfFarey        = ntFarey;
  cf->cfChineseRemainder = ntChineseRemainder;
  cf->cfInt          = ntInt;
  cf->cfInpNeg          = ntNeg;
  cf->cfAdd          = ntAdd;
  cf->cfSub          = ntSub;
  cf->cfMult         = ntMult;
  cf->cfDiv          = ntDiv;
  cf->cfExactDiv     = ntDiv;
  cf->cfPower        = ntPower;
  cf->cfCopy         = ntCopy;
  cf->cfWriteLong    = ntWriteLong;
  cf->cfRead         = ntRead;
  cf->cfNormalize    = ntNormalize;
  cf->cfDelete       = ntDelete;
  cf->cfSetMap       = ntSetMap;
  cf->cfGetDenom     = ntGetDenom;
  cf->cfGetNumerator = ntGetNumerator;
  cf->cfRePart       = ntCopy;
  cf->cfImPart       = ntImPart;
  cf->cfCoeffWrite   = ntCoeffWrite;
#ifdef LDEBUG
  cf->cfDBTest       = ntDBTest;
#endif
  //cf->cfGcd          = ntGcd_dummy;
  cf->cfSubringGcd   = ntGcd;
  cf->cfNormalizeHelper = ntNormalizeHelper;
  cf->cfSize         = ntSize;
  cf->nCoeffIsEqual  = ntCoeffIsEqual;
  cf->cfInvers       = ntInvers;
  cf->cfKillChar     = ntKillChar;

  if( rCanShortOut(ntRing) )
    cf->cfWriteShort = ntWriteShort;
  else
    cf->cfWriteShort = ntWriteLong;

  cf->convFactoryNSingN =ntConvFactoryNSingN;
  cf->convSingNFactoryN =ntConvSingNFactoryN;
  cf->cfParDeg = ntParDeg;

  cf->iNumberOfParameters = rVar(R);
  cf->pParameterNames = (const char**)R->names;
  cf->cfParameter = ntParameter;
  cf->has_simple_Inverse= FALSE;
  /* cf->has_simple_Alloc= FALSE; */


  if( nCoeff_is_Q(R->cf) )
    cf->cfClearContent = ntClearContent;

  cf->cfClearDenominators = ntClearDenominators;

  return FALSE;
}

long ntInt	(	number &	a,
		const coeffs	cf
	)

Definition at line 630 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a);
  if (IS0(a)) return 0;
  definiteGcdCancellation(a, cf, FALSE);
  fraction f = (fraction)a;
  if (!DENIS1(f)) return 0;

  const poly aAsPoly = NUM(f);

  if(aAsPoly == NULL)
    return 0;

  if (!p_IsConstant(aAsPoly, ntRing))
    return 0;

  assume( aAsPoly != NULL );

  return n_Int(p_GetCoeff(aAsPoly, ntRing), ntCoeffs);
}

number ntInvers	(	number	a,
		const coeffs	cf
	)

Definition at line 1696 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a);
  if (IS0(a))
  {
    WerrorS(nDivBy0);
    return NULL;
  }
  fraction f = (fraction)a;
  assume( f != NULL );

  fraction result = (fraction)omAlloc0Bin(fractionObjectBin);

  assume( NUM(f) != NULL );
  const poly den = DEN(f);

  if (den == NULL)
    NUM(result) = p_One(ntRing);
  else
    NUM(result) = p_Copy(den, ntRing);

  if( !NUMIS1(f) )
  {
    poly num_f=NUM(f);
    BOOLEAN neg= !n_GreaterZero(pGetCoeff(num_f),ntCoeffs);
    if (neg)
    {
      num_f=p_Neg(p_Copy(num_f, ntRing), ntRing);
      NUM(result)=p_Neg(NUM(result), ntRing);
    }
    else
    {
      num_f=p_Copy(num_f, ntRing);
    }
    DEN(result) = num_f;
    COM(result) = COM(f);
    if (neg)
    {
      if (p_IsOne(num_f, ntRing))
      {
        DEN(result)=NULL;
        //COM(result) = 0;
        p_Delete(&num_f,ntRing);
      }
    }
  }
  //else// Alloc0
  //{
  //  DEN(result) = NULL;
  //  COM(result) = 0;
  //}
  ntTest((number)result); // !!!!
  //check_N((number)result,cf);
  return (number)result;
}

BOOLEAN ntIsMOne	(	number	a,
		const coeffs	cf
	)

Definition at line 530 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a);
  definiteGcdCancellation(a, cf, FALSE);
  fraction f = (fraction)a;
  if ((f==NULL) || (!DENIS1(f))) return FALSE;
  poly g = NUM(f);
  if (!p_IsConstant(g, ntRing)) return FALSE;
  return n_IsMOne(p_GetCoeff(g, ntRing), ntCoeffs);
}

BOOLEAN ntIsOne	(	number	a,
		const coeffs	cf
	)

Definition at line 521 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a); // !!!
  definiteGcdCancellation(a, cf, FALSE);
  fraction f = (fraction)a;
  return (f!=NULL) && DENIS1(f) && NUMIS1(f);
}

int ntIsParam	(	number	m,
		const coeffs	cf
	)

if m == var(i)/1 => return i,

Definition at line 2074 of file transext.cc.

{
  ntTest(m);
  assume(getCoeffType(cf) == ID);

  const ring R = cf->extRing;
  assume( R != NULL );

  fraction f = (fraction)m;

  if( DEN(f) != NULL )
    return 0;

  return p_Var( NUM(f), R );
}

BOOLEAN ntIsZero	(	number	a,
		const coeffs	cf
	)

Definition at line 276 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a); // !!!
  return (IS0(a));
}

void ntKillChar

(

coeffs

cf

)

Definition at line 2017 of file transext.cc.

{
  if ((--cf->extRing->ref) == 0)
    rDelete(cf->extRing);
}

number ntMap00	(	number	a,
		const coeffs	src,
		const coeffs	dst
	)

Definition at line 1754 of file transext.cc.

{
  if (n_IsZero(a, src)) return NULL;
  n_Test(a, src);
  assume(src->rep == dst->extRing->cf->rep);
  if ((SR_HDL(a) & SR_INT) || (a->s==3))
  {
    number res=ntInit(p_NSet(n_Copy(a, src), dst->extRing), dst);
    n_Test(res,dst);
    return res;
  }
  number nn=n_GetDenom(a,src);
  number zz=n_GetNumerator(a,src);
  number res=ntInit(p_NSet(zz,dst->extRing), dst);
  fraction ff=(fraction)res;
  if (n_IsOne(nn,src)) DEN(ff)=NULL;
  else                 DEN(ff)=p_NSet(nn,dst->extRing);
  n_Test((number)ff,dst);
  //check_N((number)ff,dst);
  return (number)ff;
}

number ntMap0P	(	number	a,
		const coeffs	src,
		const coeffs	dst
	)

Definition at line 1879 of file transext.cc.

{
  n_Test(a, src) ;
  if (n_IsZero(a, src)) return NULL;
  // int p = rChar(dst->extRing);

  number q = nlModP(a, src, dst->extRing->cf); // FIXME? TODO? // extern number nlModP(number q, const coeffs Q, const coeffs Zp); // Map q \in QQ \to Zp

  if (n_IsZero(q, dst->extRing->cf))
  {
    n_Delete(&q, dst->extRing->cf);
    return NULL;
  }

  poly g = p_NSet(q, dst->extRing);

  fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
  NUM(f) = g; // DEN(f) = NULL; COM(f) = 0;
  n_Test((number)f, dst);
  //check_N((number)f,dst);
  return (number)f;
}

number ntMapP0	(	number	a,
		const coeffs	src,
		const coeffs	dst
	)

Definition at line 1790 of file transext.cc.

{
  if (n_IsZero(a, src)) return NULL;
  n_Test(a, src);
  /* mapping via intermediate int: */
  int n = n_Int(a, src);
  number q = n_Init(n, dst->extRing->cf);
  if (n_IsZero(q, dst->extRing->cf))
  {
    n_Delete(&q, dst->extRing->cf);
    return NULL;
  }
  return ntInit(p_NSet(q, dst->extRing), dst);
}

number ntMapPP	(	number	a,
		const coeffs	src,
		const coeffs	dst
	)

Definition at line 1903 of file transext.cc.

{
  n_Test(a, src) ;
  if (n_IsZero(a, src)) return NULL;
  assume(src == dst->extRing->cf);
  poly p = p_One(dst->extRing);
  p_SetCoeff(p, n_Copy(a, src), dst->extRing);
  fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
  NUM(f) = p; // DEN(f) = NULL; COM(f) = 0;
  n_Test((number)f, dst);
  //check_N((number)f,dst);
  return (number)f;
}

number ntMapUP	(	number	a,
		const coeffs	src,
		const coeffs	dst
	)

Definition at line 1918 of file transext.cc.

{
  n_Test(a, src) ;
  if (n_IsZero(a, src)) return NULL;
  /* mapping via intermediate int: */
  int n = n_Int(a, src);
  number q = n_Init(n, dst->extRing->cf);
  poly p;
  if (n_IsZero(q, dst->extRing->cf))
  {
    n_Delete(&q, dst->extRing->cf);
    return NULL;
  }
  p = p_One(dst->extRing);
  p_SetCoeff(p, q, dst->extRing);
  fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
  NUM(f) = p; // DEN(f) = NULL; COM(f) = 0;
  n_Test((number)f, dst);
  //check_N((number)f,dst);
  return (number)f;
}

number ntMapZ0	(	number	a,
		const coeffs	src,
		const coeffs	dst
	)

Definition at line 1776 of file transext.cc.

{
  if (n_IsZero(a, src)) return NULL;
  n_Test(a, src);
  nMapFunc nMap=n_SetMap(src,dst->extRing->cf);
  poly p=p_NSet(nMap(a, src,dst->extRing->cf), dst->extRing);
  if (n_IsZero(pGetCoeff(p),dst->extRing->cf))
    p_Delete(&p,dst->extRing);
  number res=ntInit(p, dst);
  n_Test(res,dst);
  return res;
}

number ntMult	(	number	a,
		number	b,
		const coeffs	cf
	)

Definition at line 893 of file transext.cc.

{
  //check_N(a,cf);
  //check_N(b,cf);
  ntTest(a); // !!!?
  ntTest(b); // !!!?

  if (IS0(a) || IS0(b)) return NULL;

  fraction fa = (fraction)a;
  fraction fb = (fraction)b;

  const poly g = pp_Mult_qq(NUM(fa), NUM(fb), ntRing);

  if (g == NULL) return NULL; // may happen due to zero divisors???

  fraction result = (fraction)omAllocBin(fractionObjectBin);

  NUM(result) = g;

  const poly da = DEN(fa);
  const poly db = DEN(fb);


  //check_N((number)result,cf);
  if (db == NULL)
  {
    // b = ? // NULL

    if(da == NULL)
    { // both fa && fb are ?? // NULL!
      assume (da == NULL && db == NULL);
      DEN(result) = NULL;
      COM(result) = 0;
    }
    else
    {
      assume (da != NULL && db == NULL);
      DEN(result) = p_Copy(da, ntRing);
      COM(result) = COM(fa) + MULT_COMPLEXITY;
      heuristicGcdCancellation((number)result, cf);
      //check_N((number)result,cf);
    }
  }
  else
  { // b = ?? / ??
    if (da == NULL)
    { // a == ? // NULL
      assume( db != NULL && da == NULL);
      DEN(result) = p_Copy(db, ntRing);
      COM(result) = COM(fb) + MULT_COMPLEXITY;
      heuristicGcdCancellation((number)result, cf);
      //check_N((number)result,cf);
    }
    else /* both den's are != 1 */
    {
      assume (da != NULL && db != NULL);
      DEN(result) = pp_Mult_qq(da, db, ntRing);
      COM(result) = COM(fa) + COM(fb) + MULT_COMPLEXITY;
      heuristicGcdCancellation((number)result, cf);
      //check_N((number)result,cf);
    }
  }

//  ntTest((number)result);

  //check_N((number)result,cf);
  return (number)result;
}

number ntNeg	(	number	a,
		const coeffs	cf
	)

this is in-place, modifies a

Definition at line 543 of file transext.cc.

{
  //check_N(a,cf);
  ntTest(a);
  if (!IS0(a))
  {
    fraction f = (fraction)a;
    NUM(f) = p_Neg(NUM(f), ntRing);
  }
  ntTest(a);
  return a;
}

void ntNormalize	(	number &	a,
		const coeffs	cf
	)

Definition at line 1455 of file transext.cc.

{
  if ( /*(*/ a!=NULL /*)*/ )
  {
    definiteGcdCancellation(a, cf, FALSE);
    if ((DEN(a)!=NULL)
    &&(!n_GreaterZero(pGetCoeff(DEN(a)),ntCoeffs)))
    {
      NUM(a)=p_Neg(NUM(a),ntRing);
      DEN(a)=p_Neg(DEN(a),ntRing);
    }
  }
  ntTest(a); // !!!!
}

number ntNormalizeHelper	(	number	a,
		number	b,
		const coeffs	cf
	)

Definition at line 1493 of file transext.cc.

{
  ntTest(a);
  ntTest(b);
  fraction fb = (fraction)b;
  if ((b==NULL)||(DEN(fb)==NULL)) return ntCopy(a,cf);
  fraction fa = (fraction)a;
  /* singclap_gcd destroys its arguments; we hence need copies: */
  poly pa = p_Copy(NUM(fa), ntRing);
  poly pb = p_Copy(DEN(fb), ntRing);

  poly pGcd;
  if (nCoeff_is_Q(ntCoeffs))
  {
    if (p_IsConstant(pa,ntRing) && p_IsConstant(pb,ntRing))
    {
      pGcd = pa;
      p_SetCoeff (pGcd, n_Gcd (pGetCoeff(pGcd), pGetCoeff(pb), ntCoeffs), ntRing);
    }
    else
    {
      number contentpa, contentpb, tmp;

      contentpb= p_GetCoeff(pb, ntRing);
      pIter(pb);
      while (pb != NULL)
      {
        tmp = n_SubringGcd(contentpb, p_GetCoeff(pb, ntRing) , ntCoeffs);
        n_Delete(&contentpb, ntCoeffs);
        contentpb = tmp;
        pIter(pb);
      }

      contentpa= p_GetCoeff(pa, ntRing);
      pIter(pa);
      while (pa != NULL)
      {
        tmp = n_SubringGcd(contentpa, p_GetCoeff(pa, ntRing), ntCoeffs);
        n_Delete(&contentpa, ntCoeffs);
        contentpa = tmp;
        pIter(pa);
      }

      tmp= n_SubringGcd (contentpb, contentpa, ntCoeffs);
      n_Delete(&contentpa, ntCoeffs);
      n_Delete(&contentpb, ntCoeffs);
      contentpa= tmp;
      p_Delete(&pb, ntRing);
      p_Delete(&pa, ntRing);

      /* singclap_gcd destroys its arguments; we hence need copies: */
      pGcd = singclap_gcd(p_Copy(NUM(fa),ntRing), p_Copy(DEN(fb),ntRing), ntRing);
      pGcd= p_Mult_nn (pGcd, contentpa, ntRing);
      n_Delete(&contentpa, ntCoeffs);
    }
  }
  else
    pGcd = singclap_gcd(pa, pb, cf->extRing);

  /* Note that, over Q, singclap_gcd will remove the denominators in all
     rational coefficients of pa and pb, before starting to compute
     the gcd. Thus, we do not need to ensure that the coefficients of
     pa and pb live in Z; they may well be elements of Q\Z. */

  if (p_IsConstant(pGcd, ntRing) &&
      n_IsOne(p_GetCoeff(pGcd, ntRing), ntCoeffs))
  { /* gcd = 1; return pa*pb*/
    p_Delete(&pGcd,ntRing);
    fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
    NUM(result) = pp_Mult_qq(NUM(fa),DEN(fb),ntRing);

    ntTest((number)result); // !!!!

    return (number)result;
  }


  /* return pa*pb/gcd */
    poly newNum = singclap_pdivide(NUM(fa), pGcd, ntRing);
    p_Delete(&pGcd,ntRing);
    fraction result = (fraction)omAlloc0Bin(fractionObjectBin);
    NUM(result) = p_Mult_q(p_Copy(DEN(fb),ntRing),newNum,ntRing);
    ntTest((number)result); // !!!!
    return (number)result;

  return NULL;
}

static number ntParameter ( const int  iParameter, const coeffs  cf  )

static

return the specified parameter as a number in the given trans.ext.

Definition at line 2052 of file transext.cc.

{
  assume(getCoeffType(cf) == ID);

  const ring R = cf->extRing;
  assume( R != NULL );
  assume( 0 < iParameter && iParameter <= rVar(R) );

  poly p = p_One(R); p_SetExp(p, iParameter, 1, R); p_Setm(p, R);
  p_Test(p,R);

  fraction f = (fraction)omAlloc0Bin(fractionObjectBin);
  NUM(f) = p;
  //DEN(f) = NULL;
  //COM(f) = 0;

  ntTest((number)f);

  return (number)f;
}

static int ntParDeg ( number  a, const coeffs  cf  )

static

Definition at line 2043 of file transext.cc.

{
  ntTest(a);
  if (IS0(a)) return -1;
  fraction fa = (fraction)a;
  return cf->extRing->pFDeg(NUM(fa),cf->extRing);
}

void ntPower	(	number	a,
		int	exp,
		number *	b,
		const coeffs	cf
	)

Definition at line 1010 of file transext.cc.

{
  ntTest(a);

  /* special cases first */
  if (IS0(a))
  {
    if (exp >= 0) *b = NULL;
    else          WerrorS(nDivBy0);
  }
  else if (exp ==  0) { *b = ntInit(1, cf); return;}
  else if (exp ==  1) { *b = ntCopy(a, cf); return;}
  else if (exp == -1) { *b = ntInvers(a, cf); return;}

  int expAbs = exp; if (expAbs < 0) expAbs = -expAbs;

  /* now compute a^expAbs */
  number pow; number t;
  if (expAbs <= 7)
  {
    pow = ntCopy(a, cf);
    for (int i = 2; i <= expAbs; i++)
    {
      t = ntMult(pow, a, cf);
      ntDelete(&pow, cf);
      pow = t;
      heuristicGcdCancellation(pow, cf);
    }
  }
  else
  {
    pow = ntInit(1, cf);
    number factor = ntCopy(a, cf);
    while (expAbs != 0)
    {
      if (expAbs & 1)
      {
        t = ntMult(pow, factor, cf);
        ntDelete(&pow, cf);
        pow = t;
        heuristicGcdCancellation(pow, cf);
      }
      expAbs = expAbs / 2;
      if (expAbs != 0)
      {
        t = ntMult(factor, factor, cf);
        ntDelete(&factor, cf);
        factor = t;
        heuristicGcdCancellation(factor, cf);
      }
    }
    ntDelete(&factor, cf);
  }

  /* invert if original exponent was negative */
  if (exp < 0)
  {
    t = ntInvers(pow, cf);
    ntDelete(&pow, cf);
    pow = t;
  }
  *b = pow;
  ntTest(*b);
  //check_N(*b,cf);
}

const char * ntRead	(	const char *	s,
		number *	a,
		const coeffs	cf
	)

Definition at line 1446 of file transext.cc.

{
  poly p;
  const char * result = p_Read(s, p, ntRing);
  if (p == NULL) *a = NULL;
  else *a = ntInit(p, cf);
  return result;
}

number ntRePart	(	number	a,
		const coeffs	cf
	)

nMapFunc ntSetMap	(	const coeffs	src,
		const coeffs	dst
	)

Get a mapping function from src into the domain of this type (n_transExt)

Q or Z –> Q(T)

Z –> K(T)

Z/p –> Q(T)

Q –> Z/p(T)

Z/p –> Z/p(T)

Z/u –> Z/p(T)

K(T') –> K(T)

K(T') –> K'(T)

K(T') –> K(T)

K(T') –> K'(T)

default

Definition at line 1940 of file transext.cc.

{
  /* dst is expected to be a rational function field */
  assume(getCoeffType(dst) == ID);

  if( src == dst ) return ndCopyMap;

  int h = 0; /* the height of the extension tower given by dst */
  coeffs bDst = nCoeff_bottom(dst, h); /* the bottom field in the tower dst */
  coeffs bSrc = nCoeff_bottom(src, h); /* the bottom field in the tower src */

  /* for the time being, we only provide maps if h = 1 and if b is Q or
     some field Z/pZ: */
  if (h==0)
  {
    if ((src->rep==n_rep_gap_rat) && nCoeff_is_Q(bDst))
      return ntMap00;                                 /// Q or Z   -->  Q(T)
    if (src->rep==n_rep_gap_gmp)
      return ntMapZ0;                                 /// Z   -->  K(T)
    if (nCoeff_is_Zp(src) && nCoeff_is_Q(bDst))
      return ntMapP0;                                 /// Z/p     -->  Q(T)
    if (nCoeff_is_Q(src) && nCoeff_is_Zp(bDst))
      return ntMap0P;                                 /// Q       --> Z/p(T)
    if (nCoeff_is_Zp(src) && nCoeff_is_Zp(bDst))
    {
      if (src->ch == dst->ch) return ntMapPP;         /// Z/p     --> Z/p(T)
      else return ntMapUP;                            /// Z/u     --> Z/p(T)
    }
  }
  if (h != 1) return NULL;
  //if ((!nCoeff_is_Zp(bDst)) && (!nCoeff_is_Q(bDst))) return NULL;

  /* Let T denote the sequence of transcendental extension variables, i.e.,
     K[t_1, ..., t_s] =: K[T];
     Let moreover, for any such sequence T, T' denote any subsequence of T
     of the form t_1, ..., t_w with w <= s. */

  if (rVar(src->extRing) > rVar(dst->extRing))
     return NULL;

  for (int i = 0; i < rVar(src->extRing); i++)
    if (strcmp(rRingVar(i, src->extRing), rRingVar(i, dst->extRing)) != 0)
       return NULL;

  if (src->type==n_transExt)
  {
     if (src->extRing->cf==dst->extRing->cf)
       return ntCopyMap;          /// K(T')   --> K(T)
     else
       return ntGenMap;          /// K(T')   --> K'(T)
  }
  else
  {
     if (src->extRing->cf==dst->extRing->cf)
       return ntCopyAlg;          /// K(T')   --> K(T)
     else
       return ntGenAlg;          /// K(T')   --> K'(T)
  }

  return NULL;                                 /// default
}

int ntSize	(	number	a,
		const coeffs	cf
	)

Definition at line 1657 of file transext.cc.

{
  ntTest(a);
  if (IS0(a)) return -1;
  /* this has been taken from the old implementation of field extensions,
     where we computed the sum of the degrees and the numbers of terms in
     the numerator and denominator of a; so we leave it at that, for the
     time being */
  fraction f = (fraction)a;
  poly p = NUM(f);
  int noOfTerms = 0;
  int numDegree = 0;
  while (p != NULL)
  {
    noOfTerms++;
    int d = 0;
    for (int i = 1; i <= rVar(ntRing); i++)
      d += p_GetExp(p, i, ntRing);
    if (d > numDegree) numDegree = d;
    pIter(p);
  }
  int denDegree = 0;
  if (!DENIS1(f))
  {
    p = DEN(f);
    while (p != NULL)
    {
      noOfTerms++;
      int d = 0;
      for (int i = 1; i <= rVar(ntRing); i++)
        d += p_GetExp(p, i, ntRing);
      if (d > denDegree) denDegree = d;
      pIter(p);
    }
  }
  ntTest(a); // !!!!
  return numDegree + denDegree + noOfTerms;
}

number ntSub	(	number	a,
		number	b,
		const coeffs	cf
	)

Definition at line 855 of file transext.cc.

{
  //check_N(a,cf);
  //check_N(b,cf);
  ntTest(a);
  ntTest(b);
  if (IS0(a)) return ntNeg(ntCopy(b, cf), cf);
  if (IS0(b)) return ntCopy(a, cf);

  fraction fa = (fraction)a;
  fraction fb = (fraction)b;

  poly g = p_Copy(NUM(fa), ntRing);
  if (!DENIS1(fb)) g = p_Mult_q(g, p_Copy(DEN(fb), ntRing), ntRing);
  poly h = p_Copy(NUM(fb), ntRing);
  if (!DENIS1(fa)) h = p_Mult_q(h, p_Copy(DEN(fa), ntRing), ntRing);
  g = p_Add_q(g, p_Neg(h, ntRing), ntRing);

  if (g == NULL) return NULL;

  poly f;
  if      (DENIS1(fa) && DENIS1(fb))  f = NULL;
  else if (!DENIS1(fa) && DENIS1(fb)) f = p_Copy(DEN(fa), ntRing);
  else if (DENIS1(fa) && !DENIS1(fb)) f = p_Copy(DEN(fb), ntRing);
  else /* both den's are != 1 */      f = p_Mult_q(p_Copy(DEN(fa), ntRing),
                                                   p_Copy(DEN(fb), ntRing),
                                                   ntRing);

  fraction result = (fraction)omAllocBin(fractionObjectBin);
  NUM(result) = g;
  DEN(result) = f;
  COM(result) = COM(fa) + COM(fb) + ADD_COMPLEXITY;
  heuristicGcdCancellation((number)result, cf);
//  ntTest((number)result);
  //check_N((number)result,cf);
  return (number)result;
}

void ntWriteLong	(	number &	a,
		const coeffs	cf
	)

Definition at line 1393 of file transext.cc.

{
  ntTest(a);
  definiteGcdCancellation(a, cf, FALSE);
  if (IS0(a))
    StringAppendS("0");
  else
  {
    fraction f = (fraction)a;
    // stole logic from napWrite from kernel/longtrans.cc of legacy singular
    BOOLEAN omitBrackets = p_IsConstant(NUM(f), ntRing);
    if (!omitBrackets) StringAppendS("(");
    p_String0Long(NUM(f), ntRing, ntRing);
    if (!omitBrackets) StringAppendS(")");
    if (!DENIS1(f))
    {
      StringAppendS("/");
      omitBrackets = p_IsConstant(DEN(f), ntRing);
      if (!omitBrackets) StringAppendS("(");
      p_String0Long(DEN(f), ntRing, ntRing);
      if (!omitBrackets) StringAppendS(")");
    }
  }
  ntTest(a); // !!!!
}

void ntWriteShort	(	number &	a,
		const coeffs	cf
	)

Definition at line 1420 of file transext.cc.

{
  ntTest(a);
  definiteGcdCancellation(a, cf, FALSE);
  if (IS0(a))
    StringAppendS("0");
  else
  {
    fraction f = (fraction)a;
    // stole logic from napWrite from kernel/longtrans.cc of legacy singular
    BOOLEAN omitBrackets = p_IsConstant(NUM(f), ntRing);
    if (!omitBrackets) StringAppendS("(");
    p_String0Short(NUM(f), ntRing, ntRing);
    if (!omitBrackets) StringAppendS(")");
    if (!DENIS1(f))
    {
      StringAppendS("/");
      omitBrackets = p_IsConstant(DEN(f), ntRing);
      if (!omitBrackets) StringAppendS("(");
      p_String0Short(DEN(f), ntRing, ntRing);
      if (!omitBrackets) StringAppendS(")");
    }
  }
  ntTest(a);
}

Variable Documentation

omBin fractionObjectBin = omGetSpecBin(sizeof(fractionObject))

Definition at line 96 of file transext.cc.

const n_coeffType ID = n_transExt

static

Our own type!

Definition at line 83 of file transext.cc.