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;
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];
489 if ((
long)a == (long)r->m_nfCharQ) rl=(long)r->m_nfCharQ;
490 else rl=((
long)a*(long)
i) % (long)r->m_nfCharQ1;
503 if (*
s >=
'0' && *
s <=
'9')
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)
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 )
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);
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++ )
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 : ...");
846 int c = (int)
pow ((
double)
p->GFChar, (double)
p->GFDegree);
868 r->cfExactDiv=
nfDiv;
918 const char *
name =
p->GFPar_name;
921 r->m_nfCharP =
p->GFChar;
924 r->iNumberOfParameters = 1;
927 char ** pParameterNames = (
char **)
omAlloc0(
sizeof(
char *));
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;
948 if(
p->GFChar > (2<<15))
951 WarnS(
"illegal characteristic");
956 const double check=
log ((
double) (
p->GFChar));
958 #define sixteenlog2 11.09035489
962 Warn(
"Sorry: illegal size: %u ^ %u",
p->GFChar,
p->GFDegree );
967 int c = (int)
pow ((
double)
p->GFChar, (double)
p->GFDegree);
971 if( r->m_nfPlus1Table ==
NULL )
977 assume (r -> m_nfCharQ > 0);
979 r->ch = r->m_nfCharP;
Rational pow(const Rational &a, int e)
const CanonicalForm CFMap CFMap & N
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE BOOLEAN nCoeff_is_GF(const coeffs r)
static FORCE_INLINE char const ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
@ n_rep_gap_rat
(number), see longrat.h
@ n_rep_int
(int), see modulop.h
@ n_rep_gf
(int), see ffields.h
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Creation data needed for finite fields.
const CanonicalForm int s
char name(const Variable &v)
void WerrorS(const char *s)
FILE * feFopen(const char *path, const char *mode, char *where, short useWerror, short path_only)
const char * eati(const char *s, int *i)
static BOOLEAN nfIsMOne(number a, const coeffs r)
static int nfMapGG_factor
static number nfAdd(number a, number b, const coeffs R)
int convertback62(char *p, int n)
static nMapFunc nfSetMap(const coeffs src, const coeffs dst)
static void nfReadMipo(char *s)
static number nfInit(long i, const coeffs r)
void nfShowMipo(const coeffs r)
Show the mininimal polynom.... NOTE: this is used by char * sleftv::String(void *d,...
BOOLEAN nfDBTest(number a, const char *f, const int l, const coeffs r)
static char * nfCoeffString(const coeffs r)
int gf_tab_numdigits62(int q)
static void nfKillChar(coeffs r)
static int nfParDeg(number n, const coeffs r)
const unsigned short fftable[]
static long nfInt(number &n, const coeffs r)
static number nfMult(number a, number b, const coeffs r)
static BOOLEAN nfGreaterZero(number k, const coeffs r)
BOOLEAN nfInitChar(coeffs r, void *parameter)
static void nfWriteShort(number a, const coeffs r)
static char * nfCoeffName(const coeffs r)
static number nfSub(number a, number b, const coeffs r)
static number nfRandom(siRandProc p, number, number, const coeffs cf)
static BOOLEAN nfIsOne(number a, const coeffs r)
static void nfCoeffWrite(const coeffs r, BOOLEAN details)
static const char * nfEati(const char *s, int *i, const coeffs r)
static const char * nfRead(const char *s, number *a, const coeffs r)
static BOOLEAN nfGreater(number a, number b, const coeffs r)
static number nfNeg(number c, const coeffs r)
static BOOLEAN nfIsZero(number a, const coeffs r)
static BOOLEAN nfCoeffIsEqual(const coeffs, n_coeffType, void *)
static number nfMapGGrev(number c, const coeffs src, const coeffs)
static BOOLEAN nfEqual(number a, number b, const coeffs r)
static number nfMapP(number c, const coeffs, const coeffs dst)
static void nfReadTable(const int c, const coeffs r)
static void nfWriteLong(number a, const coeffs r)
static number nfDiv(number a, number b, const coeffs r)
static number nfParameter(int i, const coeffs)
static number nfMapGG(number c, const coeffs src, const coeffs)
static number nfInvers(number c, const coeffs r)
static void nfPower(number a, int i, number *result, const coeffs r)
number nlModP(number q, const coeffs, const coeffs Zp)
gmp_float log(const gmp_float &a)
The main handler for Singular numbers which are suitable for Singular polynomials.
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
const char *const nDivBy0
#define omFreeSize(addr, size)
void StringSetS(const char *st)
void StringAppendS(const char *st)
void PrintS(const char *s)
void Werror(const char *fmt,...)
int status int void * buf