ffields.cc File Reference

#include "misc/auxiliary.h"
#include "misc/mylimits.h"
#include "misc/sirandom.h"
#include "misc/prime.h"
#include "reporter/reporter.h"
#include "coeffs/coeffs.h"
#include "coeffs/numbers.h"
#include "coeffs/longrat.h"
#include "coeffs/ffields.h"
#include "coeffs/modulop.h"
#include <cmath>
#include <errno.h>

Go to the source code of this file.

Macros
#define	nfTest(N, R)   nfDBTest(N,__FILE__,__LINE__, R)
#define	sixteenlog2   11.09035489

Functions
static BOOLEAN	nfDBTest (number a, const char *f, const int l, const coeffs r)
static BOOLEAN	nfIsZero (number a, const coeffs r)
static BOOLEAN	nfIsMOne (number a, const coeffs r)
static BOOLEAN	nfGreaterZero (number k, const coeffs r)
static number	nfMult (number a, number b, const coeffs r)
static number	nfInit (long i, const coeffs r)
static number	nfParameter (int i, const coeffs)
static int	nfParDeg (number n, const coeffs r)
static long	nfInt (number &n, const coeffs r)
static number	nfAdd (number a, number b, const coeffs R)
static number	nfNeg (number c, const coeffs r)
static number	nfSub (number a, number b, const coeffs r)
static BOOLEAN	nfIsOne (number a, const coeffs r)
static number	nfDiv (number a, number b, const coeffs r)
static number	nfInvers (number c, const coeffs r)
static BOOLEAN	nfGreater (number a, number b, const coeffs r)
static BOOLEAN	nfEqual (number a, number b, const coeffs r)
static void	nfWriteLong (number a, const coeffs r)
static void	nfWriteShort (number a, const coeffs r)
static void	nfPower (number a, int i, number *result, const coeffs r)
static const char *	nfEati (const char *s, int *i, const coeffs r)
static const char *	nfRead (const char *s, number *a, const coeffs r)
int	gf_tab_numdigits62 (int q)
int	convertback62 (char *p, int n)
void	nfShowMipo (const coeffs r)
	Show the mininimal polynom.... NOTE: this is used by char * sleftv::String(void *d, BOOLEAN typed, int dim) (from Singular/subexpr.cc) for printing minpoly. More...
static void	nfReadMipo (char *s)
static void	nfReadTable (const int c, const coeffs r)
static number	nfMapP (number c, const coeffs, const coeffs dst)
static number	nfMapGG (number c, const coeffs src, const coeffs)
static number	nfMapGGrev (number c, const coeffs src, const coeffs)
static number	nfMapMPZ (number c, const coeffs, const coeffs dst)
static number	nfInitMPZ (mpz_t m, const coeffs cf)
static number	nfMapViaInt (number c, const coeffs src, const coeffs dst)
static nMapFunc	nfSetMap (const coeffs src, const coeffs dst)
static BOOLEAN	nfCoeffIsEqual (const coeffs, n_coeffType, void *)
static void	nfKillChar (coeffs r)
static char *	nfCoeffName (const coeffs r)
static number	nfRandom (siRandProc p, number, number, const coeffs cf)
static void	nfCoeffWrite (const coeffs r, BOOLEAN details)
BOOLEAN	nfInitChar (coeffs r, void *parameter)

Variables
const unsigned short	fftable []
STATIC_VAR int	nfMinPoly [16]
STATIC_VAR int	nfMapGG_factor

Macro Definition Documentation

nfTest

#define nfTest	(		N,
			R
	)		nfDBTest(N,__FILE__,__LINE__, R)

Definition at line 127 of file ffields.cc.

sixteenlog2

#define sixteenlog2   11.09035489

Function Documentation

convertback62()

int convertback62	(	char *	p,
		int	n
	)

Definition at line 50 of file gf_tabutil.cc.

{
    int r = 0;
    for ( int j = 0; j < n; j++ )
        r = r * 62 + convback62( p[j] );
    return r;
}

gf_tab_numdigits62()

int gf_tab_numdigits62

(

int

q

)

Definition at line 12 of file gf_tabutil.cc.

{
    if ( q < 62 )
        return 1;
    else  if ( q < 62*62 )
        return 2;
    else
        return 3;
}

nfAdd()

static number nfAdd ( number  a, number  b, const coeffs  R  )

static

Definition at line 254 of file ffields.cc.

{
/*4 z^a+z^b=z^b*(z^(a-b)+1), if a>=b; *
*          =z^a*(z^(b-a)+1)  if a<b  */
#ifdef LDEBUG
  nfTest(a, R);
  nfTest(b, R);
#endif
  if ((long)R->m_nfCharQ == (long)a) return b;
  if ((long)R->m_nfCharQ == (long)b) return a;
  long zb,zab,r;
  if ((long)a >= (long)b)
  {
    zb = (long)b;
    zab = (long)a-(long)b;
  }
  else
  {
    zb = (long)a;
    zab = (long)b-(long)a;
  }
#ifdef LDEBUG
  nfTest((number)zab, R);
#endif
  if (R->m_nfPlus1Table[zab]==R->m_nfCharQ) r=(long)R->m_nfCharQ; /*if z^(a-b)+1 =0*/
  else
  {
    r= zb+(long)R->m_nfPlus1Table[zab];
    if(r>=(long)R->m_nfCharQ1) r-=(long)R->m_nfCharQ1;
  }
#ifdef LDEBUG
  nfTest((number)r, R);
#endif
  return (number)r;
}

nfCoeffIsEqual()

static BOOLEAN nfCoeffIsEqual ( const coeffs  r, n_coeffType  n, void *  parameter  )

static

Definition at line 844 of file ffields.cc.

{
  if (n==n_GF) {
    GFInfo* p = (GFInfo *)(parameter);
    int c = (int)pow ((double)p->GFChar, (double)p->GFDegree);
    if ((c == r->m_nfCharQ) && (strcmp(n_ParameterNames(r)[0], p->GFPar_name) == 0))
      return TRUE;
  }
  return FALSE;
}

nfCoeffName()

static char * nfCoeffName ( const coeffs  r )

static

Definition at line 816 of file ffields.cc.

{
  STATIC_VAR char nfCoeffName_buf[32];
  const char *p=n_ParameterNames(r)[0];
  nfCoeffName_buf[31]='\0';
  snprintf(nfCoeffName_buf,31,"%d,%s",r->m_nfCharQ,p);
  return nfCoeffName_buf;
}

nfCoeffWrite()

static void nfCoeffWrite ( const coeffs  r, BOOLEAN  details  )

static

Definition at line 830 of file ffields.cc.

{
  // m_nfCharQ = p^k where p is the characteristic (r->CharP) and k is GFDegree
  Print("ZZ/%d[%s]",r->m_nfCharQ,n_ParameterNames(r)[0]);
  if ( details )
  {
    StringSetS("\n//   minpoly        : ");
    nfShowMipo(r);
    StringAppendS("");
    char *s=StringEndS(); PrintS(s); omFree(s);
  }
  else PrintS("//   minpoly        : ...");
}

nfDBTest()

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

static

Definition at line 107 of file ffields.cc.

{
  assume( r->m_nfPlus1Table != NULL );
  if (((long)a<0L) || ((long)a>(long)r->m_nfCharQ))
  {
    Print("wrong %d in %s:%d\n",(int)((long)a),f,l);
    return FALSE;
  }
  int i=0;
  do
  {
    if (r->m_nfPlus1Table[i]>r->m_nfCharQ)
    {
      Print("wrong table %d=%d in %s:%d\n",i,r->m_nfPlus1Table[i],f,l);
      return FALSE;
    }
    i++;
  } while (i<r->m_nfCharQ);
  return TRUE;
}

nfDiv()

static number nfDiv ( number  a, number  b, const coeffs  r  )

static

Definition at line 331 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(b, r);
#endif
  if ((long)b==(long)r->m_nfCharQ)
  {
    WerrorS(nDivBy0);
    return (number)((long)r->m_nfCharQ);
  }
#ifdef LDEBUG
  nfTest(a, r);
#endif
  if ((long)a==(long)r->m_nfCharQ)
    return (number)((long)r->m_nfCharQ);
  /*else*/
  long s = (long)a - (long)b;
  if (s < 0L)
    s += (long)r->m_nfCharQ1;
#ifdef LDEBUG
  nfTest((number)s, r);
#endif
  return (number)s;
}

nfEati()

static const char * nfEati ( const char *  s, int *  i, const coeffs  r  )

inlinestatic

Definition at line 497 of file ffields.cc.

{
  return nEati((char *)s,i,r->m_nfCharP);
}

nfEqual()

static BOOLEAN nfEqual ( number  a, number  b, const coeffs  r  )

static

Definition at line 390 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(a, r);
  nfTest(b, r);
#endif
  return (long)a == (long)b;
}

nfGreater()

static BOOLEAN nfGreater ( number  a, number  b, const coeffs  r  )

static

Definition at line 378 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(a, r);
  nfTest(b, r);
#endif
  return (long)a != (long)b;
}

nfGreaterZero()

static BOOLEAN nfGreaterZero ( number  k, const coeffs  r  )

static

Definition at line 156 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(k, r);
#endif
  return !nfIsZero(k, r) && !nfIsMOne(k, r);
}

nfInit()

static number nfInit ( long  i, const coeffs  r  )

static

Definition at line 187 of file ffields.cc.

{
  assume( r->m_nfPlus1Table != NULL );
  // Hmm .. this is just to prevent initialization
  // from nfInitChar to go into an infinite loop
  if (i==0) return (number)(long)r->m_nfCharQ;
  while (i <  0)    i += r->m_nfCharP;
  while (i >= r->m_nfCharP) i -= r->m_nfCharP;
  if (i==0) return (number)(long)r->m_nfCharQ;
  unsigned short c=0;
  while (i>1)
  {
    c=r->m_nfPlus1Table[c];
    i--;
  }
#ifdef LDEBUG
  nfTest((number)(long)c, r);
#endif
  return (number)(long)c;
}

nfInitChar()

BOOLEAN nfInitChar	(	coeffs	r,
		void *	parameter
	)

Definition at line 854 of file ffields.cc.

{
  // the variables:
  assume( getCoeffType(r) == n_GF );
 
  GFInfo* p = (GFInfo *)(parameter);
  assume (p->GFChar > 0);
  assume (p->GFDegree > 0);
  if(p->GFChar > (2<<15))
  {
#ifndef SING_NDEBUG
    WarnS("illegal characteristic");
#endif
    return TRUE;
  }
 
  const double check= log ((double) (p->GFChar));
 
  #define sixteenlog2 11.09035489
  if( (p->GFDegree * check) > sixteenlog2 )
  {
#ifndef SING_NDEBUG
    Warn("Sorry: illegal size: %u ^ %u", p->GFChar, p->GFDegree );
#endif
    return TRUE;
  }
 
  r->is_field=TRUE;
  r->is_domain=TRUE;
  r->rep=n_rep_gf;
  //r->cfInitChar=npInitChar;
  r->cfKillChar=nfKillChar;
  r->nCoeffIsEqual=nfCoeffIsEqual;
  r->cfCoeffName=nfCoeffName;
 
  r->cfMult  = nfMult;
  r->cfSub   = nfSub;
  r->cfAdd   = nfAdd;
  r->cfDiv   = nfDiv;
  //r->cfIntMod= ndIntMod;
  r->cfExactDiv= nfDiv;
  r->cfInit = nfInit;
  r->cfInitMPZ = nfInitMPZ;
  //r->cfSize  = ndSize;
  r->cfInt  = nfInt;
  #ifdef HAVE_RINGS
  //r->cfDivComp = NULL; // only for ring stuff
  //r->cfIsUnit = NULL; // only for ring stuff
  //r->cfGetUnit = NULL; // only for ring stuff
  //r->cfExtGcd = NULL; // only for ring stuff
  // r->cfDivBy = NULL; // only for ring stuff
  #endif
  r->cfInpNeg   = nfNeg;
  r->cfInvers= nfInvers;
  //r->cfCopy  = ndCopy;
  //r->cfRePart = ndCopy;
  //r->cfImPart = ndReturn0;
 
  r->cfWriteLong = nfWriteLong;
  r->cfRead = nfRead;
  //r->cfNormalize=ndNormalize;
  r->cfGreater = nfGreater;
  r->cfEqual = nfEqual;
  r->cfIsZero = nfIsZero;
  r->cfIsOne = nfIsOne;
  r->cfIsMOne = nfIsMOne;
  r->cfGreaterZero = nfGreaterZero;
  r->cfPower = nfPower;
  //r->cfGcd  = ndGcd;
  //r->cfLcm  = ndGcd;
  //r->cfDelete= ndDelete;
  r->cfSetMap = nfSetMap;
  //r->cfName = ndName;
  // debug stuff
  r->cfCoeffWrite=nfCoeffWrite;
 
  r->cfParDeg = nfParDeg;
 
  r->cfRandom = nfRandom;
 
#ifdef LDEBUG
  r->cfDBTest=nfDBTest;
#endif
 
 
  const char * name = p->GFPar_name;
 
  r->m_nfCharQ = 0;
  r->m_nfCharP = p->GFChar;
  r->m_nfCharQ1 = 0;
 
  r->iNumberOfParameters = 1;
  r->cfParameter = nfParameter;
 
  char ** pParameterNames = (char **) omAlloc(sizeof(char *));
  assume( pParameterNames != NULL );
  pParameterNames[0] = omStrDup(name);
  assume( pParameterNames[0] != NULL );
 
  r->pParameterNames = (const char**)pParameterNames;
 
  r->m_nfPlus1Table= NULL;
 
  if (strlen(name) > 1)
    r->cfWriteShort = nfWriteLong;
  else
    r->cfWriteShort = nfWriteShort;
 
  r->has_simple_Alloc=TRUE;
  r->has_simple_Inverse=TRUE;
 
  int c = (int)pow ((double)p->GFChar, (double)p->GFDegree);
 
  nfReadTable(c, r);
 
  if( r->m_nfPlus1Table == NULL )
  {
    Werror("reading table for field with %d elements failed",c);
    return TRUE;
  }
 
 
  assume (r -> m_nfCharQ > 0);
 
  r->ch = r->m_nfCharP;
  assume( r->m_nfPlus1Table != NULL );
 
  return FALSE;
}

nfInitMPZ()

static number nfInitMPZ ( mpz_t  m, const coeffs  cf  )

static

Definition at line 728 of file ffields.cc.

{
  mpz_t tmp;
  mpz_init(tmp);
  mpz_mod_ui(tmp,m,cf->m_nfCharP);
  long l=mpz_get_si(tmp);
  return nfInit(l,cf);
}

nfInt()

static long nfInt ( number &  n, const coeffs  r  )

static

Definition at line 236 of file ffields.cc.

{
  unsigned short c=0;
  unsigned short nn=(unsigned short)(long)n;
  if (nn==r->m_nfCharQ) return 0;
  long i=1; /* 1==a^0 */
  while ((c!=nn)&&(i<r->m_nfCharP))
  {
    c=r->m_nfPlus1Table[c];
    i++;
  }
  if (c==nn) return i;
  else       return 0;
}

nfInvers()

static number nfInvers ( number  c, const coeffs  r  )

static

Definition at line 359 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(c, r);
#endif
  if ((long)c==(long)r->m_nfCharQ)
  {
    WerrorS(nDivBy0);
    return (number)((long)r->m_nfCharQ);
  }
#ifdef LDEBUG
  nfTest(((number)((long)r->m_nfCharQ1-(long)c)), r);
#endif
  return (number)((long)r->m_nfCharQ1-(long)c);
}

nfIsMOne()

static BOOLEAN nfIsMOne ( number  a, const coeffs  r  )

static

Definition at line 144 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(a, r);
#endif
  if (0L == (long)a) return FALSE; /* special handling of char 2*/
  return (long)r->m_nfM1 == (long)a;
}

nfIsOne()

static BOOLEAN nfIsOne ( number  a, const coeffs  r  )

static

Definition at line 320 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(a, r);
#endif
  return 0L == (long)a;
}

nfIsZero()

static BOOLEAN nfIsZero ( number  a, const coeffs  r  )

static

Definition at line 133 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(a, r);
#endif
  return (long)r->m_nfCharQ == (long)a;
}

nfKillChar()

static void nfKillChar ( coeffs  r )

static

Definition at line 808 of file ffields.cc.

{
  char** p = (char**)n_ParameterNames(r);
  /* only one parameter */
  omFree( (ADDRESS)p[0] );
  omFreeSize((ADDRESS)p, sizeof(char*));
}

nfMapGG()

static number nfMapGG ( number  c, const coeffs  src, const  coeffs  )

static

Definition at line 700 of file ffields.cc.

{
  int i=(long)c;
  i*= nfMapGG_factor;
  while (i >src->m_nfCharQ1) i-=src->m_nfCharQ1;
  return (number)((long)i);
}

nfMapGGrev()

static number nfMapGGrev ( number  c, const coeffs  src, const  coeffs  )

static

Definition at line 710 of file ffields.cc.

{
  int ex=(int)((long)c);
  if ((ex % nfMapGG_factor)==0)
    return (number)(((long)ex) / ((long)nfMapGG_factor));
  else
    return (number)(long)src->m_nfCharQ; /* 0 */
}

nfMapMPZ()

static number nfMapMPZ ( number  c, const  coeffs, const coeffs  dst  )

static

Definition at line 719 of file ffields.cc.

{
  mpz_t tmp;
  mpz_init(tmp);
  mpz_mod_ui(tmp,(mpz_ptr)c,dst->m_nfCharP);
  long l=mpz_get_si(tmp);
  return nfInit(l,dst);
}

nfMapP()

static number nfMapP ( number  c, const  coeffs, const coeffs  dst  )

static

Definition at line 691 of file ffields.cc.

{
  return nfInit((int)((long)c), dst);
}

nfMapViaInt()

static number nfMapViaInt ( number  c, const coeffs  src, const coeffs  dst  )

static

Definition at line 737 of file ffields.cc.

{
  long i=src->cfInt(c,src);
  if (i==0) return (number)(long)dst->m_nfCharQ;
  while (i <  0)    i += dst->m_nfCharP;
  while (i >= dst->m_nfCharP) i -= dst->m_nfCharP;
  return nfInit(i,dst);
}

nfMult()

static number nfMult ( number  a, number  b, const coeffs  r  )

static

Definition at line 167 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(a, r);
  nfTest(b, r);
#endif
  if (((long)a == (long)r->m_nfCharQ) || ((long)b == (long)r->m_nfCharQ))
    return (number)(long)r->m_nfCharQ;
  /*else*/
  int i=(int)((long)a+(long)b);
  if (i>=r->m_nfCharQ1) i-=r->m_nfCharQ1;
#ifdef LDEBUG
  nfTest((number)(long)i, r);
#endif
  return (number)(long)i;
}

nfNeg()

static number nfNeg ( number  c, const coeffs  r  )

static

Definition at line 293 of file ffields.cc.

{
/*4 -z^c=z^c*(-1)=z^c*nfM1*/
#ifdef LDEBUG
  nfTest(c, r);
#endif
  if ((long)r->m_nfCharQ == (long)c) return c;
  long i=(long)c+(long)r->m_nfM1;
  if (i>=(long)r->m_nfCharQ1) i-=(long)r->m_nfCharQ1;
#ifdef LDEBUG
  nfTest((number)i, r);
#endif
  return (number)i;
}

nfParameter()

static number nfParameter ( int  i, const  coeffs  )

static

Definition at line 211 of file ffields.cc.

{
  assume(i==1);
 
  if( i == 1 )
    return (number)1;
 
  return NULL;
}

nfParDeg()

static int nfParDeg ( number  n, const coeffs  r  )

static

Definition at line 224 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(n, r);
#endif
  if((long)r->m_nfCharQ == (long)n) return -1;
  return (int)((long)n);
}

nfPower()

static void nfPower ( number  a, int  i, number *  result, const coeffs  r  )

static

Definition at line 469 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(a, r);
#endif
  if (i==0)
  {
    *result = (number)0L;
  }
  else if (i==1)
  {
    *result = a;
  }
  else
  {
    long rl;
    if ((long)a == (long)r->m_nfCharQ) rl=(long)r->m_nfCharQ;
    else rl=((long)a*(long)i) % (long)r->m_nfCharQ1;
    *result = (number)rl;
  }
#ifdef LDEBUG
  nfTest(*result, r);
#endif
}

nfRandom()

static number nfRandom ( siRandProc  p, number  , number  , const coeffs  cf  )

static

Definition at line 825 of file ffields.cc.

{
  return (number)(long)(p() %(cf->m_nfCharQ+1));
}

nfRead()

static const char * nfRead ( const char *  s, number *  a, const coeffs  r  )

static

Definition at line 505 of file ffields.cc.

{
  int i;
  number z;
  number n;
 
  s = nfEati(s, &i, r);
  z=nfInit(i, r);
  *a=z;
  if (*s == '/')
  {
    s++;
    s = nfEati(s, &i, r);
    n=nfInit(i, r);
    *a = nfDiv(z,n,r);
  }
  const char * const nf_Parameter = n_ParameterNames(r)[0];
  const int N = strlen(nf_Parameter);
  if (strncmp(s,nf_Parameter, N)==0)
  {
    s += N;
    if ((*s >= '0') && (*s <= '9'))
    {
      s=eati(s,&i);
      while (i>=r->m_nfCharQ1) i-=r->m_nfCharQ1;
    }
    else
      i=1;
    z=(number)(long)i;
    *a=nfMult(*a,z,r);
  }
#ifdef LDEBUG
  nfTest(*a, r);
#endif
  return s;
}

nfReadMipo()

static void nfReadMipo ( char *  s )

static

Definition at line 563 of file ffields.cc.

{
  const char *l=strchr(s,';')+1;
  char *n;
  int i=strtol(l,&n,10);
  l=n;
  int j=1;
  nfMinPoly[0]=i;
  while(i>=0)
  {
    nfMinPoly[j]=strtol(l,&n,10);
    if (l==n) break;
    l=n;
    j++;
    i--;
  }
  if (i>=0)
  {
    WerrorS("error in reading minpoly from gftables");
  }
}

nfReadTable()

static void nfReadTable ( const int  c, const coeffs  r  )

static

Definition at line 588 of file ffields.cc.

{
  //Print("GF(%d)\n",c);
  if ((c==r->m_nfCharQ)||(c== -r->m_nfCharQ))
    /*this field is already set*/  return;
  int i=0;
 
  if ((c>255) ||(c!=IsPrime(c)))
  {
    while ((fftable[i]!=c) && (fftable[i]!=0))
      i++;
 
    if (fftable[i]==0)
    {
      // illegal GF-table size: c
      return;
    }
  }
 
  if (r->m_nfCharQ > 1)
  {
    omFreeSize( (ADDRESS)r->m_nfPlus1Table,(r->m_nfCharQ+1)*sizeof(unsigned short) );
    r->m_nfPlus1Table=NULL;
  }
  if ((c>1) || (c<0))
  {
    if (c>1) r->m_nfCharQ = c;
    else     r->m_nfCharQ = -c;
    char buf[100];
    sprintf(buf,"gftables/%d",r->m_nfCharQ);
    FILE * fp = feFopen(buf,"r",NULL,TRUE);
    if (fp==NULL)
    {
      return;
    }
    if(!fgets( buf, sizeof(buf), fp)) return;
    if(strcmp(buf,"@@ factory GF(q) table @@\n")!=0)
    {
      goto err;
    }
    if(!fgets( buf, sizeof(buf), fp))
    {
      goto err;
    }
    int q;
    int res = -1;
    do
    {
      res = sscanf(buf,"%d %d",&r->m_nfCharP,&q);
    }
    while((res < 0) and (errno == EINTR));
 
    nfReadMipo(buf);
    r->m_nfCharQ1=r->m_nfCharQ-1;
    //Print("nfCharQ=%d,nfCharQ1=%d,mipo=>>%s<<\n",nfCharQ,nfCharQ1,buf);
    r->m_nfPlus1Table= (unsigned short *)omAlloc0( (r->m_nfCharQ+1)*sizeof(unsigned short) );
    int digs = gf_tab_numdigits62( r->m_nfCharQ );
    char * bufptr;
    int i = 1;
    int k;
    while ( i < r->m_nfCharQ )
    {
      (void)fgets( buf, sizeof(buf), fp);
      //( strlen( buffer ) == (size_t)digs * 30, "illegal table" );
      bufptr = buf;
      k = 0;
      while ( (i < r->m_nfCharQ) && (k < 30) )
      {
        r->m_nfPlus1Table[i] = convertback62( bufptr, digs );
        if(r->m_nfPlus1Table[i]>r->m_nfCharQ)
        {
          Print("wrong entry %d: %d(%c%c%c)\n",i,r->m_nfPlus1Table[i],bufptr[0],bufptr[1],bufptr[2]);
        }
        bufptr += digs;
        if (r->m_nfPlus1Table[i]==r->m_nfCharQ)
        {
          if(i==r->m_nfCharQ1)
          {
            r->m_nfM1=0;
          }
          else
          {
            r->m_nfM1=i;
          }
        }
        i++; k++;
      }
    }
    r->m_nfPlus1Table[0]=r->m_nfPlus1Table[r->m_nfCharQ1];
  }
  else
    r->m_nfCharQ=0;
#ifdef LDEBUG
  nfTest((number)0, r);
#endif
  return;
err:
  Werror("illegal GF-table %d",r->m_nfCharQ);
}

nfSetMap()

static nMapFunc nfSetMap ( const coeffs  src, const coeffs  dst  )

static

Definition at line 749 of file ffields.cc.

{
  if (nCoeff_is_GF(src))
  {
    const coeffs r = dst;
    int q=src->ch;
    if ((src->m_nfCharQ % q)==0) /* GF(p,n1) -> GF(p,n2), n2 > n1 */
    {
      // check if n2 is a multiple of n1
      int n1=1;
      int qq=r->m_nfCharP;
      while(qq!=q) { qq *= r->m_nfCharP; n1++; }
      int n2=1;
      qq=r->m_nfCharP;
      while(qq!=src->m_nfCharQ) { qq *= r->m_nfCharP; n2++; }
      //Print("map %d^%d -> %d^%d\n",r->m_nfCharP,n1,r->m_nfCharP,n2);
      if ((n2 % n1)==0)
      {
        int save_ch=r->m_nfCharQ;
        nfReadTable(src->m_nfCharQ, r);
        int nn=r->m_nfPlus1Table[0];
        nfReadTable(save_ch, r);
        nfMapGG_factor= r->m_nfPlus1Table[0] / nn;
        //Print("nfMapGG_factor=%d (%d / %d)\n",nfMapGG_factor, r->m_nfPlus1Table[0], nn);
        return nfMapGG;
      }
      else if ((n1 % n2)==0)
      {
        nfMapGG_factor= (n1/n2);
        return nfMapGGrev;
      }
      else
        return NULL;
    }
  }
  if ((src->rep==n_rep_int) && nCoeff_is_Zp(src,dst->m_nfCharP))
  {
    return nfMapP;    /* Z/p -> GF(p,n) */
  }
 
  if (src->rep==n_rep_gap_rat) /*Q, bigint */
  {
    return nlModP; // FIXME? TODO? // extern number nlModP(number q, const coeffs Q, const coeffs Zp); // Map q \in QQ \to Zp // FIXME!
  }
  if (nCoeff_is_Z(src)) /* Z*/
  {
    return nfMapMPZ;
  }
  if (nCoeff_is_Zp(src) && (src->ch==dst->m_nfCharP)) /* Zp*/
  {
    return nfMapViaInt;
  }
 
 
  return NULL;     /* default */
}

nfShowMipo()

void nfShowMipo

(

const coeffs

r

)

Show the mininimal polynom.... NOTE: this is used by char * sleftv::String(void *d, BOOLEAN typed, int dim) (from Singular/subexpr.cc) for printing minpoly.

Definition at line 547 of file ffields.cc.

{
  int i=nfMinPoly[0];
  int j=0;
  loop
  {
    j++;
    if (nfMinPoly[j]!=0)
      StringAppend("%d*%s^%d",nfMinPoly[j],n_ParameterNames(r)[0],i);
    i--;
    if(i<0) break;
    if (nfMinPoly[j]!=0)
      StringAppendS("+");
  }
}

nfSub()

static number nfSub ( number  a, number  b, const coeffs  r  )

static

Definition at line 311 of file ffields.cc.

{
  number mb = nfNeg(b, r);
  return nfAdd(a,mb,r);
}

nfWriteLong()

static void nfWriteLong ( number  a, const coeffs  r  )

static

Definition at line 402 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(a, r);
#endif
  if ((long)a==(long)r->m_nfCharQ)  StringAppendS("0");
  else if ((long)a==0L)   StringAppendS("1");
  else if (nfIsMOne(a, r))   StringAppendS("-1");
  else
  {
    int i=1; /* 1==a^0 */
    unsigned short c=0;
    unsigned short nn=(unsigned short)(long)a;
    while ((c!=nn)&&(i<r->m_nfCharQ))
    {
      c=r->m_nfPlus1Table[c];
      i++;
    }
    if (c==nn) StringAppend("%d",i);
    else
    {
      StringAppendS(n_ParameterNames(r)[0]);
      if ((long)a!=1L)
      {
        StringAppend("^%d",(int)((long)a)); // long output!
      }
    }
  }
}

nfWriteShort()

static void nfWriteShort ( number  a, const coeffs  r  )

static

Definition at line 436 of file ffields.cc.

{
#ifdef LDEBUG
  nfTest(a, r);
#endif
  if ((long)a==(long)r->m_nfCharQ)  StringAppendS("0");
  else if ((long)a==0L)   StringAppendS("1");
  else if (nfIsMOne(a, r))   StringAppendS("-1");
  else
  {
    int i=1; /* 1==a^0 */
    unsigned short c=0;
    unsigned short nn=(unsigned short)(long)a;
    while ((c!=nn)&&(i<r->m_nfCharQ))
    {
      c=r->m_nfPlus1Table[c];
      i++;
    }
    if (c==nn) StringAppend("%d",i);
    else
    {
      StringAppendS(n_ParameterNames(r)[0]);
      if ((long)a!=1L)
      {
        StringAppend("%d",(int)((long)a));
      }
    }
  }
}

Variable Documentation

fftable

const unsigned short fftable[]

Definition at line 27 of file ffields.cc.

nfMapGG_factor

STATIC_VAR int nfMapGG_factor

Definition at line 699 of file ffields.cc.

nfMinPoly

STATIC_VAR int nfMinPoly[16]

Definition at line 545 of file ffields.cc.