algext.h File Reference

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

Go to the source code of this file.

Data Structures
struct	AlgExtInfo
	struct for passing initialization parameters to naInitChar More...

Functions
nMapFunc	naSetMap (const coeffs src, const coeffs dst)
	Get a mapping function from src into the domain of this type (n_algExt).
BOOLEAN	naInitChar (coeffs cf, void *infoStruct)
	Initialize the coeffs object.
BOOLEAN	n2pInitChar (coeffs cf, void *infoStruct)
int	naIsParam (number, const coeffs)
	if m == var(i)/1 => return i,
poly	p_ExtGcd (poly p, poly &pFactor, poly q, poly &qFactor, ring r)
	assumes that p and q are univariate polynomials in r, mentioning the same variable; assumes a global monomial ordering in r; assumes that not both p and q are NULL; returns the gcd of p and q; moreover, afterwards pFactor and qFactor contain appropriate factors such that gcd(p, q) = p * pFactor + q * qFactor; leaves p and q unmodified
char *	naCoeffName (const coeffs r)

---

Data Structure Documentation

AlgExtInfo

struct AlgExtInfo

struct for passing initialization parameters to naInitChar

Definition at line 37 of file algext.h.

Data Fields
ring	r

Function Documentation

n2pInitChar()

BOOLEAN n2pInitChar	(	coeffs	cf,
		void *	infoStruct )

first check whether cf->extRing != NULL and delete old ring???

Definition at line 1687 of file algext.cc.

{
  assume( infoStruct != NULL );
 
  AlgExtInfo *e = (AlgExtInfo *)infoStruct;
  /// first check whether cf->extRing != NULL and delete old ring???
 
  assume(e->r                     != NULL);      // extRing;
  assume(e->r->cf                 != NULL);      // extRing->cf;
 
  assume( cf != NULL );
 
  rIncRefCnt(e->r); // increase the ref.counter for the ground poly. ring!
  const ring R = e->r; // no copy!
  cf->extRing  = R;
 
  /* propagate characteristic up so that it becomes
     directly accessible in cf: */
  cf->ch = R->cf->ch;
  cf->is_field=FALSE;
  cf->is_domain=TRUE;
 
  cf->cfCoeffName    = n2pCoeffName;
 
  cf->cfGreaterZero  = naGreaterZero;
  cf->cfGreater      = naGreater;
  cf->cfEqual        = naEqual;
  cf->cfIsZero       = naIsZero;
  cf->cfIsOne        = naIsOne;
  cf->cfIsMOne       = naIsMOne;
  cf->cfInit         = naInit;
  cf->cfInitMPZ      = naInitMPZ;
  cf->cfFarey        = naFarey;
  cf->cfChineseRemainder= naChineseRemainder;
  cf->cfInt          = naInt;
  cf->cfInpNeg       = naNeg;
  cf->cfAdd          = naAdd;
  cf->cfInpAdd       = naInpAdd;
  cf->cfSub          = naSub;
  cf->cfMult         = n2pMult;
  cf->cfDiv          = n2pDiv;
  cf->cfPower        = n2pPower;
  cf->cfCopy         = naCopy;
 
  cf->cfWriteLong        = naWriteLong;
 
  if( rCanShortOut(n2pRing) )
    cf->cfWriteShort = naWriteShort;
  else
    cf->cfWriteShort = naWriteLong;
 
  cf->cfRead         = n2pRead;
  cf->cfDelete       = naDelete;
  cf->cfSetMap       = naSetMap;
  //cf->cfGetDenom     = naGetDenom; // use nd*
  //cf->cfGetNumerator = naGetNumerator; // use nd*
  cf->cfRePart       = naCopy;
  cf->cfCoeffWrite   = n2pCoeffWrite;
  cf->cfNormalize    = n2pNormalize;
  cf->cfKillChar     = naKillChar;
#ifdef LDEBUG
  cf->cfDBTest       = naDBTest;
#endif
  cf->cfGcd          = naGcd;
  cf->cfNormalizeHelper          = naLcmContent;
  cf->cfSize         = naSize;
  cf->nCoeffIsEqual  = n2pCoeffIsEqual;
  cf->cfInvers       = n2pInvers;
  cf->convFactoryNSingN=naConvFactoryNSingN;
  cf->convSingNFactoryN=naConvSingNFactoryN;
  cf->cfParDeg = naParDeg;
 
  cf->iNumberOfParameters = rVar(R);
  cf->pParameterNames = (const char**)R->names;
  cf->cfParameter = naParameter;
  cf->has_simple_Inverse=FALSE;
  /* cf->has_simple_Alloc= FALSE; */
 
  if( nCoeff_is_Q(R->cf) )
  {
    cf->cfClearContent = naClearContent;
    cf->cfClearDenominators = naClearDenominators;
  }
 
  return FALSE;
}

naCoeffName()

char * naCoeffName

(

const coeffs

r

)

Definition at line 1390 of file algext.cc.

{
  const char* const* p=n_ParameterNames(r);
  int l=0;
  int i;
  for(i=0; i<n_NumberOfParameters(r);i++)
  {
    l+=(strlen(p[i])+1);
  }
  STATIC_VAR char s[200];
  s[0]='\0';
  snprintf(s,10+1,"%d",r->ch); /* Fp(a) or Q(a) */
  char tt[2];
  tt[0]=',';
  tt[1]='\0';
  for(i=0; i<n_NumberOfParameters(r);i++)
  {
    strcat(s,tt);
    strcat(s,p[i]);
  }
  return s;
}

naInitChar()

BOOLEAN naInitChar	(	coeffs	cf,
		void *	infoStruct )

Initialize the coeffs object.

first check whether cf->extRing != NULL and delete old ring???

Definition at line 1433 of file algext.cc.

{
  assume( infoStruct != NULL );
 
  AlgExtInfo *e = (AlgExtInfo *)infoStruct;
  /// first check whether cf->extRing != NULL and delete old ring???
 
  assume(e->r                     != NULL);      // extRing;
  assume(e->r->cf                 != NULL);      // extRing->cf;
 
  assume((e->r->qideal            != NULL) &&    // minideal has one
         (IDELEMS(e->r->qideal)   == 1)    &&    // non-zero generator
         (e->r->qideal->m[0]      != NULL)    ); // at m[0];
 
  assume( cf != NULL );
  assume(getCoeffType(cf) == n_algExt);                     // coeff type;
 
  rIncRefCnt(e->r); // increase the ref.counter for the ground poly. ring!
  const ring R = e->r; // no copy!
  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_poly;
 
  #ifdef LDEBUG
  p_Test((poly)naMinpoly, naRing);
  #endif
 
  cf->cfCoeffName    = naCoeffName;
 
  cf->cfGreaterZero  = naGreaterZero;
  cf->cfGreater      = naGreater;
  cf->cfEqual        = naEqual;
  cf->cfIsZero       = naIsZero;
  cf->cfIsOne        = naIsOne;
  cf->cfIsMOne       = naIsMOne;
  cf->cfInit         = naInit;
  cf->cfInitMPZ      = naInitMPZ;
  cf->cfFarey        = naFarey;
  cf->cfChineseRemainder= naChineseRemainder;
  cf->cfInt          = naInt;
  cf->cfInpNeg       = naNeg;
  cf->cfAdd          = naAdd;
  cf->cfSub          = naSub;
  cf->cfMult         = naMult;
  cf->cfInpMult      = naInpMult;
  cf->cfDiv          = naDiv;
  cf->cfExactDiv     = naDiv;
  cf->cfPower        = naPower;
  cf->cfCopy         = naCopy;
 
  cf->cfWriteLong        = naWriteLong;
 
  if( rCanShortOut(naRing) )
    cf->cfWriteShort = naWriteShort;
  else
    cf->cfWriteShort = naWriteLong;
 
  cf->cfRead         = naRead;
  cf->cfDelete       = naDelete;
  cf->cfSetMap       = naSetMap;
  cf->cfRePart       = naCopy;
  cf->cfCoeffWrite   = naCoeffWrite;
  cf->cfNormalize    = naNormalize;
  cf->cfKillChar     = naKillChar;
#ifdef LDEBUG
  cf->cfDBTest       = naDBTest;
#endif
  cf->cfGcd          = naGcd;
  cf->cfNormalizeHelper          = naLcmContent;
  cf->cfSize         = naSize;
  cf->nCoeffIsEqual  = naCoeffIsEqual;
  cf->cfInvers       = naInvers;
  cf->convFactoryNSingN=naConvFactoryNSingN;
  cf->convSingNFactoryN=naConvSingNFactoryN;
  cf->cfParDeg = naParDeg;
 
  cf->iNumberOfParameters = rVar(R);
  cf->pParameterNames = (const char**)R->names;
  cf->cfParameter = naParameter;
  cf->has_simple_Inverse= R->cf->has_simple_Inverse;
  /* cf->has_simple_Alloc= FALSE; */
 
  if( nCoeff_is_Q(R->cf) )
  {
    cf->cfClearContent = naClearContent;
    cf->cfClearDenominators = naClearDenominators;
  }
 
  return FALSE;
}

naIsParam()

int naIsParam	(	number	m,
		const coeffs	cf )

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

Definition at line 1151 of file algext.cc.

{
  assume((getCoeffType(cf) == n_algExt)||(getCoeffType(cf) == n_polyExt));
 
  const ring R = cf->extRing;
  assume( R != NULL );
 
  return p_Var( (poly)m, R );
}

naSetMap()

nMapFunc naSetMap	(	const coeffs	src,
		const coeffs	dst )

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

Q or Z --> Q(a)

Z --> Q(a)

Z/p --> Q(a)

Q --> Z/p(a)

Z --> Z/p(a)

Z/p --> Z/p(a)

Z/u --> Z/p(a)

default

Definition at line 1077 of file algext.cc.

{
  /* dst is expected to be an algebraic field extension */
  assume(getCoeffType(dst) == n_algExt);
 
  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 or 0 */
  if (h==0)
  {
    if ((src->rep==n_rep_gap_rat) && nCoeff_is_Q(bDst))
      return naMap00;                            /// Q or Z     -->  Q(a)
    if ((src->rep==n_rep_gap_gmp) && nCoeff_is_Q(bDst))
      return naMapZ0;                            /// Z     -->  Q(a)
    if (nCoeff_is_Zp(src) && nCoeff_is_Q(bDst))
      return naMapP0;                            /// Z/p   -->  Q(a)
    if (nCoeff_is_Q_or_BI(src) && nCoeff_is_Zp(bDst))
      return naMap0P;                            /// Q      --> Z/p(a)
    if ((src->rep==n_rep_gap_gmp) && nCoeff_is_Zp(bDst))
      return naMapZ0;                            /// Z     -->  Z/p(a)
    if (nCoeff_is_Zp(src) && nCoeff_is_Zp(bDst))
    {
      if (src->ch == dst->ch) return naMapPP;    /// Z/p    --> Z/p(a)
      else return naMapUP;                       /// Z/u    --> Z/p(a)
    }
  }
  if (h != 1) return NULL;
  if ((!nCoeff_is_Zp(bDst)) && (!nCoeff_is_Q(bDst))) return NULL;
  if ((!nCoeff_is_Zp(bSrc)) && (!nCoeff_is_Q_or_BI(bSrc))) return NULL;
 
  nMapFunc nMap=n_SetMap(src->extRing->cf,dst->extRing->cf);
  if (rSamePolyRep(src->extRing, dst->extRing) && (strcmp(rRingVar(0, src->extRing), rRingVar(0, dst->extRing)) == 0))
  {
    if (src->type==n_algExt)
       return ndCopyMap; // naCopyMap;         /// K(a)   --> K(a)
    else
       return naCopyTrans2AlgExt;
  }
  else if ((nMap!=NULL) && (strcmp(rRingVar(0,src->extRing),rRingVar(0,dst->extRing))==0) && (rVar (src->extRing) == rVar (dst->extRing)))
  {
    if (src->type==n_algExt)
       return naGenMap; // naCopyMap;         /// K(a)   --> K'(a)
    else
       return naGenTrans2AlgExt;
  }
 
  return NULL;                                           /// default
}

p_ExtGcd()

poly p_ExtGcd	(	poly	p,
		poly &	pFactor,
		poly	q,
		poly &	qFactor,
		ring	r )

assumes that p and q are univariate polynomials in r, mentioning the same variable; assumes a global monomial ordering in r; assumes that not both p and q are NULL; returns the gcd of p and q; moreover, afterwards pFactor and qFactor contain appropriate factors such that gcd(p, q) = p * pFactor + q * qFactor; leaves p and q unmodified

Definition at line 214 of file algext.cc.

{
  assume((p != NULL) || (q != NULL));
  poly a = p; poly b = q; BOOLEAN aCorrespondsToP = TRUE;
  if (p_Deg(a, r) < p_Deg(b, r))
    { a = q; b = p; aCorrespondsToP = FALSE; }
  a = p_Copy(a, r); b = p_Copy(b, r);
  poly aFactor = NULL; poly bFactor = NULL;
  poly theGcd = p_ExtGcdHelper(a, aFactor, b, bFactor, r);
  if (aCorrespondsToP) { pFactor = aFactor; qFactor = bFactor; }
  else                 { pFactor = bFactor; qFactor = aFactor; }
  return theGcd;
}