32 4, 8, 16, 32, 64, 128, 256, 512,1024,2048,4096,8192,16384, 32768,
34 9, 27, 81,243,729,2187, 6561,19683,59049,
36 25,125,625,3125,15625,
114 if (((
long)a<0L) || ((
long)a>(
long)r->m_nfCharQ))
116 Print(
"wrong %d in %s:%d\n",(
int)((
long)a),f,l);
122 if (r->m_nfPlus1Table[i]>r->m_nfCharQ)
124 Print(
"wrong table %d=%d in %s:%d\n",i,r->m_nfPlus1Table[i],f,l);
128 }
while (i<r->m_nfCharQ);
131 #define nfTest(N, R) nfDBTest(N,__FILE__,__LINE__, R) 142 return (
long)r->m_nfCharQ == (long)a;
153 if (0L == (
long)a)
return FALSE;
154 return (
long)r->m_nfM1 == (long)a;
177 if (((
long)a == (
long)r->m_nfCharQ) || ((
long)b == (
long)r->m_nfCharQ))
178 return (number)(long)r->m_nfCharQ;
180 int i=(
int)((long)a+(
long)
b);
181 if (
i>=r->m_nfCharQ1)
i-=r->m_nfCharQ1;
185 return (number)(long)i;
196 if (i==0)
return (number)(long)r->m_nfCharQ;
197 while (i < 0) i += r->m_nfCharP;
198 while (i >= r->m_nfCharP) i -= r->m_nfCharP;
199 if (i==0)
return (number)(long)r->m_nfCharQ;
203 c=r->m_nfPlus1Table[c];
207 nfTest((number)(
long)c, r);
209 return (number)(long)c;
233 if((
long)r->m_nfCharQ == (
long)n)
return -1;
234 return (
int)((long)n);
243 unsigned short nn=(
unsigned short)(
long)n;
244 if (nn==r->m_nfCharQ)
return 0;
246 while ((c!=nn)&&(i<r->m_nfCharP))
248 c=r->m_nfPlus1Table[c];
266 if ((
long)R->m_nfCharQ == (
long)a)
return b;
267 if ((
long)R->m_nfCharQ == (
long)b)
return a;
269 if ((
long)a >= (
long)b)
272 zab = (long)a-(
long)
b;
277 zab = (long)b-(
long)a;
282 if (R->m_nfPlus1Table[zab]==R->m_nfCharQ) r=(long)R->m_nfCharQ;
285 r= zb+(
long)R->m_nfPlus1Table[zab];
286 if(r>=(
long)R->m_nfCharQ1) r-=(
long)R->m_nfCharQ1;
303 if ((
long)r->m_nfCharQ == (
long)c)
return c;
304 long i=(long)c+(
long)r->m_nfM1;
305 if (i>=(
long)r->m_nfCharQ1) i-=(
long)r->m_nfCharQ1;
317 number mb =
nfNeg(b, r);
318 return nfAdd(a,mb,r);
329 return 0L == (long)a;
340 if ((
long)b==(
long)r->m_nfCharQ)
343 return (number)((long)r->m_nfCharQ);
348 if ((
long)a==(
long)r->m_nfCharQ)
349 return (number)((long)r->m_nfCharQ);
351 long s = (long)a - (
long)
b;
353 s += (long)r->m_nfCharQ1;
368 if ((
long)c==(
long)r->m_nfCharQ)
371 return (number)((long)r->m_nfCharQ);
374 nfTest(((number)((
long)r->m_nfCharQ1-(
long)c)), r);
376 return (number)((long)r->m_nfCharQ1-(
long)c);
388 return (
long)a != (long)b;
400 return (
long)a == (long)b;
418 unsigned short nn=(
unsigned short)(
long)a;
419 while ((c!=nn)&&(i<r->m_nfCharQ))
421 c=r->m_nfPlus1Table[c];
452 unsigned short nn=(
unsigned short)(
long)a;
453 while ((c!=nn)&&(i<r->m_nfCharQ))
455 c=r->m_nfPlus1Table[c];
480 *result = (number)0L;
489 if ((
long)a == (long)r->m_nfCharQ) rl=(long)r->m_nfCharQ;
490 else rl=((
long)a*(long)i) % (long)r->m_nfCharQ1;
491 *result = (number)rl;
503 if (*s >=
'0' && *s <=
'9')
510 if (*i > (
MAX_INT_VAL / 10)) *i = *i % r->m_nfCharP;
512 while (*s >=
'0' && *s <=
'9');
513 if (*i >= r->m_nfCharP) *i = *i % r->m_nfCharP;
539 const int N = strlen(nf_Parameter);
540 if (strncmp(s,nf_Parameter, N)==0)
543 if ((*s >=
'0') && (*s <=
'9'))
546 while (i>=r->m_nfCharQ1) i-=r->m_nfCharQ1;
582 const char *
l=strchr(s,
';')+1;
584 int i=strtol(l,&n,10);
598 WerrorS(
"error in reading minpoly from gftables");
608 if ((c==r->m_nfCharQ)||(c== -r->m_nfCharQ))
624 if (r->m_nfCharQ > 1)
626 omFreeSize( (
ADDRESS)r->m_nfPlus1Table,(r->m_nfCharQ+1)*
sizeof(
unsigned short) );
627 r->m_nfPlus1Table=
NULL;
631 if (c>1) r->m_nfCharQ = c;
632 else r->m_nfCharQ = -c;
634 sprintf(buf,
"gftables/%d",r->m_nfCharQ);
640 if(!fgets( buf,
sizeof(buf), fp))
return;
641 if(strcmp(buf,
"@@ factory GF(q) table @@\n")!=0)
645 if(!fgets( buf,
sizeof(buf), fp))
653 res = sscanf(buf,
"%d %d",&r->m_nfCharP,&q);
655 while((res < 0) and (errno == EINTR));
658 r->m_nfCharQ1=r->m_nfCharQ-1;
660 r->m_nfPlus1Table= (
unsigned short *)
omAlloc0( (r->m_nfCharQ+1)*
sizeof(
unsigned short) );
665 while ( i < r->m_nfCharQ )
667 (void)fgets( buf,
sizeof(buf),
fp);
671 while ( (i < r->m_nfCharQ) && (k < 30) )
674 if(r->m_nfPlus1Table[i]>r->m_nfCharQ)
676 Print(
"wrong entry %d: %d(%c%c%c)\n",i,r->m_nfPlus1Table[i],bufptr[0],bufptr[1],bufptr[2]);
679 if (r->m_nfPlus1Table[i]==r->m_nfCharQ)
693 r->m_nfPlus1Table[0]=r->m_nfPlus1Table[r->m_nfCharQ1];
702 Werror(
"illegal GF-table %d",r->m_nfCharQ);
710 return nfInit((
int)((
long)c), dst);
721 while (i >src->m_nfCharQ1) i-=src->m_nfCharQ1;
722 return (number)((long)i);
729 int ex=(int)((
long)c);
731 return (number)(((long)ex) / ((long)nfMapGG_factor));
733 return (number)(long)src->m_nfCharQ;
749 if ((src->m_nfCharQ % q)==0)
754 while(qq!=q) { qq *= r->m_nfCharP; n1++; }
757 while(qq!=src->m_nfCharQ) { qq *= r->m_nfCharP; n2++; }
761 int save_ch=r->m_nfCharQ;
763 int nn=r->m_nfPlus1Table[0];
769 else if ((n1 % n2)==0)
799 for(
int i = 1;
i <= P;
i++ )
809 char *
s=(
char*)
omAlloc(11+1+strlen(p));
810 sprintf(s,
"%d,%s",r->m_nfCharQ,p);
816 static char nfCoeffName_buf[32];
818 nfCoeffName_buf[31]=
'\0';
819 snprintf(nfCoeffName_buf,31,
"ZZ/%d[%s]",r->m_nfCharQ,p);
820 return nfCoeffName_buf;
825 return (number)(long)(
p() %(cf->m_nfCharQ+1));
839 else PrintS(
"// minpoly : ...");
868 r->cfExactDiv=
nfDiv;
924 r->iNumberOfParameters = 1;
927 char ** pParameterNames = (
char **)
omAlloc0(
sizeof(
char *));
928 pParameterNames[0] =
omStrDup(name);
933 r->pParameterNames = (
const char**)pParameterNames;
938 r->m_nfPlus1Table=
NULL;
940 if (strlen(name) > 1)
945 r->has_simple_Alloc=
TRUE;
946 r->has_simple_Inverse=
TRUE;
951 WarnS(
"illegal characteristic");
958 #define sixteenlog2 11.09035489 971 if( r->m_nfPlus1Table ==
NULL )
977 assume (r -> m_nfCharQ > 0);
979 r->ch = r->m_nfCharP;
static FORCE_INLINE char const ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
const CanonicalForm int s
const char * eati(const char *s, int *i)
static const char * nfEati(const char *s, int *i, const coeffs r)
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
static BOOLEAN nfCoeffIsEqual(const coeffs, n_coeffType, void *)
static number nfRandom(siRandProc p, number, number, const coeffs cf)
number nlModP(number q, const coeffs, const coeffs Zp)
static number nfDiv(number a, number b, const coeffs r)
static BOOLEAN nfGreaterZero(number k, const coeffs r)
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
static const char * nfRead(const char *s, number *a, const coeffs r)
static int nfMapGG_factor
#define omFreeSize(addr, size)
gmp_float log(const gmp_float &a)
BOOLEAN nfDBTest(number a, const char *f, const int l, const coeffs r)
static number nfSub(number a, number b, const coeffs r)
static BOOLEAN nfIsOne(number a, const coeffs r)
static number nfParameter(int i, const coeffs)
void WerrorS(const char *s)
static number nfNeg(number c, const coeffs r)
static number nfMapGG(number c, const coeffs src, const coeffs)
static void nfKillChar(coeffs r)
static number nfMapP(number c, const coeffs, const coeffs dst)
Creation data needed for finite fields.
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
static void nfPower(number a, int i, number *result, const coeffs r)
static void nfReadMipo(char *s)
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.
Coefficient rings, fields and other domains suitable for Singular polynomials.
const CanonicalForm CFMap CFMap & N
static char * nfCoeffString(const coeffs r)
int gf_tab_numdigits62(int q)
static void nfWriteShort(number a, const coeffs r)
The main handler for Singular numbers which are suitable for Singular polynomials.
void StringSetS(const char *st)
int status int void * buf
static BOOLEAN nfIsZero(number a, const coeffs r)
static number nfAdd(number a, number b, const coeffs R)
void StringAppendS(const char *st)
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
static nMapFunc nfSetMap(const coeffs src, const coeffs dst)
const char *const nDivBy0
FILE * feFopen(const char *path, const char *mode, char *where, short useWerror, short path_only)
void PrintS(const char *s)
char name(const Variable &v)
static FORCE_INLINE BOOLEAN nCoeff_is_GF(const coeffs r)
const unsigned short fftable[]
static number nfMult(number a, number b, const coeffs r)
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
BOOLEAN nfInitChar(coeffs r, void *parameter)
static int nfParDeg(number n, const coeffs r)
static number nfInvers(number c, const coeffs r)
static void nfWriteLong(number a, const coeffs r)
static number nfInit(long i, const coeffs r)
static char * nfCoeffName(const coeffs r)
static number nfMapGGrev(number c, const coeffs src, const coeffs)
static void nfReadTable(const int c, const coeffs r)
static void nfCoeffWrite(const coeffs r, BOOLEAN details)
int convertback62(char *p, int n)
Rational pow(const Rational &a, int e)
static BOOLEAN nfEqual(number a, number b, const coeffs r)
static BOOLEAN nfIsMOne(number a, const coeffs r)
void Werror(const char *fmt,...)
static long nfInt(number &n, const coeffs r)
static BOOLEAN nfGreater(number a, number b, const coeffs r)