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ffields.cc
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1 /****************************************
2 * Computer Algebra System SINGULAR *
3 ****************************************/
4 /*
5 * ABSTRACT: finite fields with a none-prime number of elements (via tables)
6 */
7 #include "misc/auxiliary.h"
8 #include "omalloc/omalloc.h"
9 
10 #include "misc/mylimits.h"
11 #include "misc/sirandom.h"
12 #include "misc/prime.h"
13 
14 #include "reporter/reporter.h"
15 
16 #include "coeffs/coeffs.h"
17 #include "coeffs/numbers.h"
18 #include "coeffs/longrat.h"
19 #include "coeffs/ffields.h"
20 
21 #include <cmath>
22 #include <errno.h>
23 
24 #ifdef LDEBUG
25 BOOLEAN nfDBTest (number a, const char *f, const int l, const coeffs r);
26 #endif
27 
28 //unsigned short *nfPlus1Table=NULL; /* the table i=log(z^i) -> log(z^i+1) */
29 
30 /* the q's from the table 'fftable' */
31 const unsigned short fftable[]={
32  4, 8, 16, 32, 64, 128, 256, 512,1024,2048,4096,8192,16384, 32768,
33 /*2^2 2^3 2^4 2^5 2^6 2^7 2^8 2^9 2^10 2^11 2^12 2^13 2^14 2^15*/
34  9, 27, 81,243,729,2187, 6561,19683,59049,
35 /*3^2 3^3 3^4 3^5 3^6 3^7 3^8 3^9 3^10*/
36  25,125,625,3125,15625,
37 /*5^2 5^3 5^4 5^5 5^6*/
38  49,343,2401,16807,
39 /*7^2 7^3 7^4 7^5*/
40  121,1331, 14641,
41 /*11^2 11^3 11^4*/
42  169, 2197, 28561,
43 /*13^2 13^3 13^4*/
44  289, 4913,
45 /*17^2 17^3*/
46  361, 6859,
47 /*19^2 19^3*/
48  529, 12167,
49 /*23^2 23^3*/
50  841, 24389,
51 /*29^2 29^3*/
52  961, 29791,
53 /*31^2 31^3*/
54  1369, 50653,
55 /*37^2 37^3*/
56  1681, /*41^2*/
57  1849, /*43^2*/
58  2209, /*47^2*/
59  2809, /*53^2*/
60  3481, /*59^2*/
61  3721, /*61^2*/
62  4489, /*67^2*/
63  5041, /*71^2*/
64  5329, /*73^2*/
65  6241, /*79^2*/
66  6889, /*83^2*/
67  7921, /*89^2*/
68  9409, /*97^2*/
69  10201, /*101^2*/
70  10609, /*103^2*/
71  11449, /*107^2*/
72  11881, /*109^2*/
73  12769, /*113^2*/
74  16129, /*127^2*/
75  17161, /*131^2*/
76  18769, /*137^2*/
77  19321, /*139^2*/
78  22201, /*149^2*/
79  22801, /*151^2*/
80  24649, /*157^2*/
81  26569, /*163^2*/
82  27889, /*167^2*/
83  29929, /*173^2*/
84  32041, /*179^2*/
85  32761, /*181^2*/
86  36481, /*191^2*/
87  37249, /*193^2*/
88  38809, /*197^2*/
89  39601, /*199^2*/
90  49729, /*223^2*/
91  44521, /*211^2*/
92  51529, /*227^2*/
93  52441, /*229^2*/
94  54289, /*233^2*/
95  57121, /*239^2*/
96  58081, /*241^2*/
97  63001, /*251^2*/
98  0 };
99 
100 /*1
101 * numbers in GF(p^n):
102 * let nfCharQ=q=nfCharP^n=p^n
103 * GF(q)\{0} will be generated by powers of an element Z
104 * Z^i will be represented by the int i, 1 by the int 0, 0 by the int q=nfChar
105 */
106 
107 #ifdef LDEBUG
108 /*2
109 * debugging: is a a valid representation of a number ?
110 */
111 BOOLEAN nfDBTest (number a, const char *f, const int l, const coeffs r)
112 {
113  assume( r->m_nfPlus1Table != NULL );
114  if (((long)a<0L) || ((long)a>(long)r->m_nfCharQ))
115  {
116  Print("wrong %d in %s:%d\n",(int)((long)a),f,l);
117  return FALSE;
118  }
119  int i=0;
120  do
121  {
122  if (r->m_nfPlus1Table[i]>r->m_nfCharQ)
123  {
124  Print("wrong table %d=%d in %s:%d\n",i,r->m_nfPlus1Table[i],f,l);
125  return FALSE;
126  }
127  i++;
128  } while (i<r->m_nfCharQ);
129  return TRUE;
130 }
131 #define nfTest(N, R) nfDBTest(N,__FILE__,__LINE__, R)
132 #endif
133 
134 /*2
135 * a == 0 ?
136 */
137 static BOOLEAN nfIsZero (number a, const coeffs r)
138 {
139 #ifdef LDEBUG
140  nfTest(a, r);
141 #endif
142  return (long)r->m_nfCharQ == (long)a;
143 }
144 
145 /*2
146 * a == -1 ?
147 */
148 static BOOLEAN nfIsMOne (number a, const coeffs r)
149 {
150 #ifdef LDEBUG
151  nfTest(a, r);
152 #endif
153  if (0L == (long)a) return FALSE; /* special handling of char 2*/
154  return (long)r->m_nfM1 == (long)a;
155 }
156 
157 /*2
158 * k >= 0 ?
159 */
160 static BOOLEAN nfGreaterZero (number k, const coeffs r)
161 {
162 #ifdef LDEBUG
163  nfTest(k, r);
164 #endif
165  return !nfIsZero(k, r) && !nfIsMOne(k, r);
166 }
167 
168 /*2
169 * a*b
170 */
171 static number nfMult (number a,number b, const coeffs r)
172 {
173 #ifdef LDEBUG
174  nfTest(a, r);
175  nfTest(b, r);
176 #endif
177  if (((long)a == (long)r->m_nfCharQ) || ((long)b == (long)r->m_nfCharQ))
178  return (number)(long)r->m_nfCharQ;
179  /*else*/
180  int i=(int)((long)a+(long)b);
181  if (i>=r->m_nfCharQ1) i-=r->m_nfCharQ1;
182 #ifdef LDEBUG
183  nfTest((number)(long)i, r);
184 #endif
185  return (number)(long)i;
186 }
187 
188 /*2
189 * int -> number
190 */
191 static number nfInit (long i, const coeffs r)
192 {
193  assume( r->m_nfPlus1Table != NULL );
194  // Hmm .. this is just to prevent initialization
195  // from nfInitChar to go into an infinite loop
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;
200  unsigned short c=0;
201  while (i>1)
202  {
203  c=r->m_nfPlus1Table[c];
204  i--;
205  }
206 #ifdef LDEBUG
207  nfTest((number)(long)c, r);
208 #endif
209  return (number)(long)c;
210 }
211 
212 /*
213 * the generating element `z`
214 */
215 static number nfParameter (int i, const coeffs)
216 {
217  assume(i==1);
218 
219  if( i == 1 )
220  return (number)1;
221 
222  return NULL;
223 }
224 
225 /*2
226 * the degree of the "alg. number"
227 */
228 static int nfParDeg(number n, const coeffs r)
229 {
230 #ifdef LDEBUG
231  nfTest(n, r);
232 #endif
233  if((long)r->m_nfCharQ == (long)n) return -1;
234  return (int)((long)n);
235 }
236 
237 /*2
238 * number -> int
239 */
240 static long nfInt (number &n, const coeffs r )
241 {
242  unsigned short c=0;
243  unsigned short nn=(unsigned short)(long)n;
244  if (nn==r->m_nfCharQ) return 0;
245  long i=1; /* 1==a^0 */
246  while ((c!=nn)&&(i<r->m_nfCharP))
247  {
248  c=r->m_nfPlus1Table[c];
249  i++;
250  }
251  if (c==nn) return i;
252  else return 0;
253 }
254 
255 /*2
256 * a + b
257 */
258 static number nfAdd (number a, number b, const coeffs R)
259 {
260 /*4 z^a+z^b=z^b*(z^(a-b)+1), if a>=b; *
261 * =z^a*(z^(b-a)+1) if a<b */
262 #ifdef LDEBUG
263  nfTest(a, R);
264  nfTest(b, R);
265 #endif
266  if ((long)R->m_nfCharQ == (long)a) return b;
267  if ((long)R->m_nfCharQ == (long)b) return a;
268  long zb,zab,r;
269  if ((long)a >= (long)b)
270  {
271  zb = (long)b;
272  zab = (long)a-(long)b;
273  }
274  else
275  {
276  zb = (long)a;
277  zab = (long)b-(long)a;
278  }
279 #ifdef LDEBUG
280  nfTest((number)zab, R);
281 #endif
282  if (R->m_nfPlus1Table[zab]==R->m_nfCharQ) r=(long)R->m_nfCharQ; /*if z^(a-b)+1 =0*/
283  else
284  {
285  r= zb+(long)R->m_nfPlus1Table[zab];
286  if(r>=(long)R->m_nfCharQ1) r-=(long)R->m_nfCharQ1;
287  }
288 #ifdef LDEBUG
289  nfTest((number)r, R);
290 #endif
291  return (number)r;
292 }
293 
294 /*2
295 * -c
296 */
297 static number nfNeg (number c, const coeffs r)
298 {
299 /*4 -z^c=z^c*(-1)=z^c*nfM1*/
300 #ifdef LDEBUG
301  nfTest(c, r);
302 #endif
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;
306 #ifdef LDEBUG
307  nfTest((number)i, r);
308 #endif
309  return (number)i;
310 }
311 
312 /*2
313 * a - b
314 */
315 static number nfSub (number a, number b, const coeffs r)
316 {
317  number mb = nfNeg(b, r);
318  return nfAdd(a,mb,r);
319 }
320 
321 /*2
322 * a == 1 ?
323 */
324 static BOOLEAN nfIsOne (number a, const coeffs r)
325 {
326 #ifdef LDEBUG
327  nfTest(a, r);
328 #endif
329  return 0L == (long)a;
330 }
331 
332 /*2
333 * a / b
334 */
335 static number nfDiv (number a,number b, const coeffs r)
336 {
337 #ifdef LDEBUG
338  nfTest(b, r);
339 #endif
340  if ((long)b==(long)r->m_nfCharQ)
341  {
342  WerrorS(nDivBy0);
343  return (number)((long)r->m_nfCharQ);
344  }
345 #ifdef LDEBUG
346  nfTest(a, r);
347 #endif
348  if ((long)a==(long)r->m_nfCharQ)
349  return (number)((long)r->m_nfCharQ);
350  /*else*/
351  long s = (long)a - (long)b;
352  if (s < 0L)
353  s += (long)r->m_nfCharQ1;
354 #ifdef LDEBUG
355  nfTest((number)s, r);
356 #endif
357  return (number)s;
358 }
359 
360 /*2
361 * 1 / c
362 */
363 static number nfInvers (number c, const coeffs r)
364 {
365 #ifdef LDEBUG
366  nfTest(c, r);
367 #endif
368  if ((long)c==(long)r->m_nfCharQ)
369  {
370  WerrorS(nDivBy0);
371  return (number)((long)r->m_nfCharQ);
372  }
373 #ifdef LDEBUG
374  nfTest(((number)((long)r->m_nfCharQ1-(long)c)), r);
375 #endif
376  return (number)((long)r->m_nfCharQ1-(long)c);
377 }
378 
379 /*2
380 * a > b ?
381 */
382 static BOOLEAN nfGreater (number a,number b, const coeffs r)
383 {
384 #ifdef LDEBUG
385  nfTest(a, r);
386  nfTest(b, r);
387 #endif
388  return (long)a != (long)b;
389 }
390 
391 /*2
392 * a == b ?
393 */
394 static BOOLEAN nfEqual (number a,number b, const coeffs r)
395 {
396 #ifdef LDEBUG
397  nfTest(a, r);
398  nfTest(b, r);
399 #endif
400  return (long)a == (long)b;
401 }
402 
403 /*2
404 * write via StringAppend
405 */
406 static void nfWriteLong (number a, const coeffs r)
407 {
408 #ifdef LDEBUG
409  nfTest(a, r);
410 #endif
411  if ((long)a==(long)r->m_nfCharQ) StringAppendS("0");
412  else if ((long)a==0L) StringAppendS("1");
413  else if (nfIsMOne(a, r)) StringAppendS("-1");
414  else
415  {
416  int i=1; /* 1==a^0 */
417  unsigned short c=0;
418  unsigned short nn=(unsigned short)(long)a;
419  while ((c!=nn)&&(i<r->m_nfCharQ))
420  {
421  c=r->m_nfPlus1Table[c];
422  i++;
423  }
424  if (c==nn) StringAppend("%d",i);
425  else
426  {
428  if ((long)a!=1L)
429  {
430  StringAppend("^%d",(int)((long)a)); // long output!
431  }
432  }
433  }
434 }
435 
436 
437 /*2
438 * write (shortert output) via StringAppend
439 */
440 static void nfWriteShort (number a, const coeffs r)
441 {
442 #ifdef LDEBUG
443  nfTest(a, r);
444 #endif
445  if ((long)a==(long)r->m_nfCharQ) StringAppendS("0");
446  else if ((long)a==0L) StringAppendS("1");
447  else if (nfIsMOne(a, r)) StringAppendS("-1");
448  else
449  {
450  int i=1; /* 1==a^0 */
451  unsigned short c=0;
452  unsigned short nn=(unsigned short)(long)a;
453  while ((c!=nn)&&(i<r->m_nfCharQ))
454  {
455  c=r->m_nfPlus1Table[c];
456  i++;
457  }
458  if (c==nn) StringAppend("%d",i);
459  else
460  {
462  if ((long)a!=1L)
463  {
464  StringAppend("%d",(int)((long)a));
465  }
466  }
467  }
468 }
469 
470 /*2
471 * c ^ i with i>=0
472 */
473 static void nfPower (number a, int i, number * result, const coeffs r)
474 {
475 #ifdef LDEBUG
476  nfTest(a, r);
477 #endif
478  if (i==0)
479  {
480  *result = (number)0L;
481  }
482  else if (i==1)
483  {
484  *result = a;
485  }
486  else
487  {
488  long rl;
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;
492  }
493 #ifdef LDEBUG
494  nfTest(*result, r);
495 #endif
496 }
497 
498 /*4
499 * read an integer (with reduction mod p)
500 */
501 static const char* nfEati(const char *s, int *i, const coeffs r)
502 {
503  if (*s >= '0' && *s <= '9')
504  {
505  *i = 0;
506  do
507  {
508  *i *= 10;
509  *i += *s++ - '0';
510  if (*i > (MAX_INT_VAL / 10)) *i = *i % r->m_nfCharP;
511  }
512  while (*s >= '0' && *s <= '9');
513  if (*i >= r->m_nfCharP) *i = *i % r->m_nfCharP;
514  }
515  else *i = 1;
516  return s;
517 }
518 
519 /*2
520 * read a number
521 */
522 static const char * nfRead (const char *s, number *a, const coeffs r)
523 {
524  int i;
525  number z;
526  number n;
527 
528  s = nfEati(s, &i, r);
529  z=nfInit(i, r);
530  *a=z;
531  if (*s == '/')
532  {
533  s++;
534  s = nfEati(s, &i, r);
535  n=nfInit(i, r);
536  *a = nfDiv(z,n,r);
537  }
538  const char * const nf_Parameter = n_ParameterNames(r)[0];
539  const int N = strlen(nf_Parameter);
540  if (strncmp(s,nf_Parameter, N)==0)
541  {
542  s += N;
543  if ((*s >= '0') && (*s <= '9'))
544  {
545  s=eati(s,&i);
546  while (i>=r->m_nfCharQ1) i-=r->m_nfCharQ1;
547  }
548  else
549  i=1;
550  z=(number)(long)i;
551  *a=nfMult(*a,z,r);
552  }
553 #ifdef LDEBUG
554  nfTest(*a, r);
555 #endif
556  return s;
557 }
558 
559 int gf_tab_numdigits62 ( int q ); /*factory/gf_tabitil.cc */
560 int convertback62 ( char * p, int n ); /*factory/gf_tabitil.cc */
561 
562 static int nfMinPoly[16];
563 
564 void nfShowMipo(const coeffs r)
565 {
566  int i=nfMinPoly[0];
567  int j=0;
568  loop
569  {
570  j++;
571  if (nfMinPoly[j]!=0)
572  StringAppend("%d*%s^%d",nfMinPoly[j],n_ParameterNames(r)[0],i);
573  i--;
574  if(i<0) break;
575  if (nfMinPoly[j]!=0)
576  StringAppendS("+");
577  }
578 }
579 
580 static void nfReadMipo(char *s)
581 {
582  const char *l=strchr(s,';')+1;
583  char *n;
584  int i=strtol(l,&n,10);
585  l=n;
586  int j=1;
587  nfMinPoly[0]=i;
588  while(i>=0)
589  {
590  nfMinPoly[j]=strtol(l,&n,10);
591  if (l==n) break;
592  l=n;
593  j++;
594  i--;
595  }
596  if (i>=0)
597  {
598  WerrorS("error in reading minpoly from gftables");
599  }
600 }
601 
602 /*2
603 * init global variables from files 'gftables/%d'
604 */
605 static void nfReadTable(const int c, const coeffs r)
606 {
607  //Print("GF(%d)\n",c);
608  if ((c==r->m_nfCharQ)||(c== -r->m_nfCharQ))
609  /*this field is already set*/ return;
610  int i=0;
611 
612  if ((c>255) ||(c!=IsPrime(c)))
613  {
614  while ((fftable[i]!=c) && (fftable[i]!=0))
615  i++;
616 
617  if (fftable[i]==0)
618  {
619  // illegal GF-table size: c
620  return;
621  }
622  }
623 
624  if (r->m_nfCharQ > 1)
625  {
626  omFreeSize( (ADDRESS)r->m_nfPlus1Table,(r->m_nfCharQ+1)*sizeof(unsigned short) );
627  r->m_nfPlus1Table=NULL;
628  }
629  if ((c>1) || (c<0))
630  {
631  if (c>1) r->m_nfCharQ = c;
632  else r->m_nfCharQ = -c;
633  char buf[100];
634  sprintf(buf,"gftables/%d",r->m_nfCharQ);
635  FILE * fp = feFopen(buf,"r",NULL,TRUE);
636  if (fp==NULL)
637  {
638  return;
639  }
640  if(!fgets( buf, sizeof(buf), fp)) return;
641  if(strcmp(buf,"@@ factory GF(q) table @@\n")!=0)
642  {
643  goto err;
644  }
645  if(!fgets( buf, sizeof(buf), fp))
646  {
647  goto err;
648  }
649  int q;
650  int res = -1;
651  do
652  {
653  res = sscanf(buf,"%d %d",&r->m_nfCharP,&q);
654  }
655  while((res < 0) and (errno == EINTR));
656 
657  nfReadMipo(buf);
658  r->m_nfCharQ1=r->m_nfCharQ-1;
659  //Print("nfCharQ=%d,nfCharQ1=%d,mipo=>>%s<<\n",nfCharQ,nfCharQ1,buf);
660  r->m_nfPlus1Table= (unsigned short *)omAlloc0( (r->m_nfCharQ+1)*sizeof(unsigned short) );
661  int digs = gf_tab_numdigits62( r->m_nfCharQ );
662  char * bufptr;
663  int i = 1;
664  int k;
665  while ( i < r->m_nfCharQ )
666  {
667  (void)fgets( buf, sizeof(buf), fp);
668  //( strlen( buffer ) == (size_t)digs * 30, "illegal table" );
669  bufptr = buf;
670  k = 0;
671  while ( (i < r->m_nfCharQ) && (k < 30) )
672  {
673  r->m_nfPlus1Table[i] = convertback62( bufptr, digs );
674  if(r->m_nfPlus1Table[i]>r->m_nfCharQ)
675  {
676  Print("wrong entry %d: %d(%c%c%c)\n",i,r->m_nfPlus1Table[i],bufptr[0],bufptr[1],bufptr[2]);
677  }
678  bufptr += digs;
679  if (r->m_nfPlus1Table[i]==r->m_nfCharQ)
680  {
681  if(i==r->m_nfCharQ1)
682  {
683  r->m_nfM1=0;
684  }
685  else
686  {
687  r->m_nfM1=i;
688  }
689  }
690  i++; k++;
691  }
692  }
693  r->m_nfPlus1Table[0]=r->m_nfPlus1Table[r->m_nfCharQ1];
694  }
695  else
696  r->m_nfCharQ=0;
697 #ifdef LDEBUG
698  nfTest((number)0, r);
699 #endif
700  return;
701 err:
702  Werror("illegal GF-table %d",r->m_nfCharQ);
703 }
704 
705 /*2
706 * map Z/p -> GF(p,n)
707 */
708 static number nfMapP(number c, const coeffs, const coeffs dst)
709 {
710  return nfInit((int)((long)c), dst);
711 }
712 
713 /*2
714 * map GF(p,n1) -> GF(p,n2), n1 < n2, n1 | n2
715 */
716 static int nfMapGG_factor;
717 static number nfMapGG(number c, const coeffs src, const coeffs)
718 {
719  int i=(long)c;
720  i*= nfMapGG_factor;
721  while (i >src->m_nfCharQ1) i-=src->m_nfCharQ1;
722  return (number)((long)i);
723 }
724 /*2
725 * map GF(p,n1) -> GF(p,n2), n1 > n2, n2 | n1
726 */
727 static number nfMapGGrev(number c, const coeffs src, const coeffs)
728 {
729  int ex=(int)((long)c);
730  if ((ex % nfMapGG_factor)==0)
731  return (number)(((long)ex) / ((long)nfMapGG_factor));
732  else
733  return (number)(long)src->m_nfCharQ; /* 0 */
734 }
735 
736 /*2
737 * set map function nMap ... -> GF(p,n)
738 */
739 static nMapFunc nfSetMap(const coeffs src, const coeffs dst)
740 {
741  if (nCoeff_is_GF(src,src->m_nfCharQ))
742  {
743  return ndCopyMap; /* GF(p,n) -> GF(p,n) */
744  }
745  if (nCoeff_is_GF(src))
746  {
747  const coeffs r = dst;
748  int q=src->ch;
749  if ((src->m_nfCharQ % q)==0) /* GF(p,n1) -> GF(p,n2), n2 > n1 */
750  {
751  // check if n2 is a multiple of n1
752  int n1=1;
753  int qq=r->m_nfCharP;
754  while(qq!=q) { qq *= r->m_nfCharP; n1++; }
755  int n2=1;
756  qq=r->m_nfCharP;
757  while(qq!=src->m_nfCharQ) { qq *= r->m_nfCharP; n2++; }
758  //Print("map %d^%d -> %d^%d\n",r->m_nfCharP,n1,r->m_nfCharP,n2);
759  if ((n2 % n1)==0)
760  {
761  int save_ch=r->m_nfCharQ;
762  nfReadTable(src->m_nfCharQ, r);
763  int nn=r->m_nfPlus1Table[0];
764  nfReadTable(save_ch, r);
765  nfMapGG_factor= r->m_nfPlus1Table[0] / nn;
766  //Print("nfMapGG_factor=%d (%d / %d)\n",nfMapGG_factor, r->m_nfPlus1Table[0], nn);
767  return nfMapGG;
768  }
769  else if ((n1 % n2)==0)
770  {
771  nfMapGG_factor= (n1/n2);
772  return nfMapGGrev;
773  }
774  else
775  return NULL;
776  }
777  }
778  if ((src->rep==n_rep_int) && nCoeff_is_Zp(src,dst->m_nfCharP))
779  {
780  return nfMapP; /* Z/p -> GF(p,n) */
781  }
782 
783  if (src->rep==n_rep_gap_rat) /*Q, Z */
784  {
785  return nlModP; // FIXME? TODO? // extern number nlModP(number q, const coeffs Q, const coeffs Zp); // Map q \in QQ \to Zp // FIXME!
786  }
787 
788  return NULL; /* default */
789 }
790 
791 static BOOLEAN nfCoeffIsEqual(const coeffs, n_coeffType, void*);
792 
793 static void nfKillChar(coeffs r)
794 {
795  char** p = (char**)n_ParameterNames(r);
796 
797  const int P = n_NumberOfParameters(r);
798 
799  for( int i = 1; i <= P; i++ )
800  if (p[i-1] != NULL)
801  omFree( (ADDRESS)p[i-1] );
802 
803  omFreeSize((ADDRESS)p, P * sizeof(char*));
804 }
805 
806 static char* nfCoeffString(const coeffs r)
807 {
808  const char *p=n_ParameterNames(r)[0];
809  char *s=(char*)omAlloc(11+1+strlen(p));
810  sprintf(s,"%d,%s",r->m_nfCharQ,p);
811  return s;
812 }
813 
814 static char* nfCoeffName(const coeffs r)
815 {
816  static char nfCoeffName_buf[32];
817  const char *p=n_ParameterNames(r)[0];
818  nfCoeffName_buf[31]='\0';
819  snprintf(nfCoeffName_buf,31,"ZZ/%d[%s]",r->m_nfCharQ,p);
820  return nfCoeffName_buf;
821 }
822 
823 static number nfRandom(siRandProc p,number ,number, const coeffs cf)
824 {
825  return (number)(long)(p() %(cf->m_nfCharQ+1));
826 }
827 
828 static void nfCoeffWrite (const coeffs r, BOOLEAN details)
829 {
830  // m_nfCharQ = p^k where p is the characteristic (r->CharP) and k is GFDegree
831  Print("ZZ/%d[%s]",r->m_nfCharQ,n_ParameterNames(r)[0]);
832  if ( details )
833  {
834  StringSetS("\n// minpoly : ");
835  nfShowMipo(r);
836  StringAppendS("");
837  char *s=StringEndS(); PrintS(s); omFree(s);
838  }
839  else PrintS("// minpoly : ...");
840 }
841 
842 static BOOLEAN nfCoeffIsEqual (const coeffs r, n_coeffType n, void * parameter)
843 {
844  if (n==n_GF) {
845  GFInfo* p = (GFInfo *)(parameter);
846  int c = (int)pow ((double)p->GFChar, (double)p->GFDegree);
847  if ((c == r->m_nfCharQ) && (strcmp(n_ParameterNames(r)[0], p->GFPar_name) == 0))
848  return TRUE;
849  }
850  return FALSE;
851 }
852 BOOLEAN nfInitChar(coeffs r, void * parameter)
853 {
854  r->is_field=TRUE;
855  r->is_domain=TRUE;
856  r->rep=n_rep_gf;
857  //r->cfInitChar=npInitChar;
858  r->cfKillChar=nfKillChar;
859  r->nCoeffIsEqual=nfCoeffIsEqual;
860  r->cfCoeffString=nfCoeffString;
861  r->cfCoeffName=nfCoeffName;
862 
863  r->cfMult = nfMult;
864  r->cfSub = nfSub;
865  r->cfAdd = nfAdd;
866  r->cfDiv = nfDiv;
867  //r->cfIntMod= ndIntMod;
868  r->cfExactDiv= nfDiv;
869  r->cfInit = nfInit;
870  //r->cfSize = ndSize;
871  r->cfInt = nfInt;
872  #ifdef HAVE_RINGS
873  //r->cfDivComp = NULL; // only for ring stuff
874  //r->cfIsUnit = NULL; // only for ring stuff
875  //r->cfGetUnit = NULL; // only for ring stuff
876  //r->cfExtGcd = NULL; // only for ring stuff
877  // r->cfDivBy = NULL; // only for ring stuff
878  #endif
879  r->cfInpNeg = nfNeg;
880  r->cfInvers= nfInvers;
881  //r->cfCopy = ndCopy;
882  //r->cfRePart = ndCopy;
883  //r->cfImPart = ndReturn0;
884 
885  r->cfWriteLong = nfWriteLong;
886  r->cfRead = nfRead;
887  //r->cfNormalize=ndNormalize;
888  r->cfGreater = nfGreater;
889  r->cfEqual = nfEqual;
890  r->cfIsZero = nfIsZero;
891  r->cfIsOne = nfIsOne;
892  r->cfIsMOne = nfIsMOne;
893  r->cfGreaterZero = nfGreaterZero;
894  r->cfPower = nfPower;
895  //r->cfGcd = ndGcd;
896  //r->cfLcm = ndGcd;
897  //r->cfDelete= ndDelete;
898  r->cfSetMap = nfSetMap;
899  //r->cfName = ndName;
900  // debug stuff
901  r->cfCoeffWrite=nfCoeffWrite;
902 
903  r->cfParDeg = nfParDeg;
904 
905  r->cfRandom = nfRandom;
906 
907 #ifdef LDEBUG
908  r->cfDBTest=nfDBTest;
909 #endif
910 
911  // the variables:
912  assume( getCoeffType(r) == n_GF );
913 
914  GFInfo* p = (GFInfo *)(parameter);
915  assume (p->GFChar > 0);
916  assume (p->GFDegree > 0);
917 
918  const char * name = p->GFPar_name;
919 
920  r->m_nfCharQ = 0;
921  r->m_nfCharP = p->GFChar;
922  r->m_nfCharQ1 = 0;
923 
924  r->iNumberOfParameters = 1;
925  r->cfParameter = nfParameter;
926 
927  char ** pParameterNames = (char **) omAlloc0(sizeof(char *));
928  pParameterNames[0] = omStrDup(name); //TODO use omAlloc for allocating memory and use strcpy?
929 
930  assume( pParameterNames != NULL );
931  assume( pParameterNames[0] != NULL );
932 
933  r->pParameterNames = (const char**)pParameterNames;
934  // NOTE: r->m_nfParameter was replaced by n_ParameterNames(r)[0]
935 
936  // TODO: nfKillChar MUST destroy r->pParameterNames[0] (0-term. string) && r->pParameterNames (array of size 1)
937 
938  r->m_nfPlus1Table= NULL;
939 
940  if (strlen(name) > 1)
941  r->cfWriteShort = nfWriteLong;
942  else
943  r->cfWriteShort = nfWriteShort;
944 
945  r->has_simple_Alloc=TRUE;
946  r->has_simple_Inverse=TRUE;
947 
948  if(p->GFChar > (2<<15))
949  {
950 #ifndef SING_NDEBUG
951  WarnS("illegal characteristic");
952 #endif
953  return TRUE;
954  }
955 
956  const double check= log ((double) (p->GFChar));
957 
958  #define sixteenlog2 11.09035489
959  if( (p->GFDegree * check) > sixteenlog2 )
960  {
961 #ifndef SING_NDEBUG
962  Warn("Sorry: illegal size: %u ^ %u", p->GFChar, p->GFDegree );
963 #endif
964  return TRUE;
965  }
966 
967  int c = (int)pow ((double)p->GFChar, (double)p->GFDegree);
968 
969  nfReadTable(c, r);
970 
971  if( r->m_nfPlus1Table == NULL )
972  {
973  return TRUE;
974  }
975 
976 
977  assume (r -> m_nfCharQ > 0);
978 
979  r->ch = r->m_nfCharP;
980  assume( r->m_nfPlus1Table != NULL );
981 
982  return FALSE;
983 
984 }
985 
getCoeffType
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:422
n_rep_gap_rat
@ n_rep_gap_rat
(number), see longrat.h
Definition: coeffs.h:112
nfSetMap
static nMapFunc nfSetMap(const coeffs src, const coeffs dst)
Definition: ffields.cc:739
FALSE
#define FALSE
Definition: auxiliary.h:94
omalloc.h
nCoeff_is_Zp
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
Definition: coeffs.h:831
StringAppendS
void StringAppendS(const char *st)
Definition: reporter.cc:107
nfCoeffString
static char * nfCoeffString(const coeffs r)
Definition: ffields.cc:806
IsPrime
int IsPrime(int p)
Definition: prime.cc:61
j
int j
Definition: facHensel.cc:105
f
FILE * f
Definition: checklibs.c:9
feFopen
FILE * feFopen(const char *path, const char *mode, char *where, short useWerror, short path_only)
Definition: feFopen.cc:47
omFree
#define omFree(addr)
Definition: omAllocDecl.h:261
k
int k
Definition: cfEzgcd.cc:92
nfCoeffWrite
static void nfCoeffWrite(const coeffs r, BOOLEAN details)
Definition: ffields.cc:828
result
return result
Definition: facAbsBiFact.cc:76
GFInfo
Creation data needed for finite fields.
Definition: coeffs.h:93
ADDRESS
void * ADDRESS
Definition: auxiliary.h:133
LDEBUG
#define LDEBUG
Definition: mod2.h:308
nfIsMOne
static BOOLEAN nfIsMOne(number a, const coeffs r)
Definition: ffields.cc:148
cf
CanonicalForm cf
Definition: cfModGcd.cc:4024
nfParDeg
static int nfParDeg(number n, const coeffs r)
Definition: ffields.cc:228
fftable
const unsigned short fftable[]
Definition: ffields.cc:31
omStrDup
#define omStrDup(s)
Definition: omAllocDecl.h:263
nfPower
static void nfPower(number a, int i, number *result, const coeffs r)
Definition: ffields.cc:473
ndCopyMap
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
Definition: numbers.cc:251
n_GF
@ n_GF
\GF{p^n < 2^16}
Definition: coeffs.h:33
auxiliary.h
nfEati
static const char * nfEati(const char *s, int *i, const coeffs r)
Definition: ffields.cc:501
N
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:49
nCoeff_is_GF
static FORCE_INLINE BOOLEAN nCoeff_is_GF(const coeffs r)
Definition: coeffs.h:853
n_NumberOfParameters
static FORCE_INLINE int n_NumberOfParameters(const coeffs r)
Returns the number of parameters.
Definition: coeffs.h:805
nfRandom
static number nfRandom(siRandProc p, number, number, const coeffs cf)
Definition: ffields.cc:823
reporter.h
nfMapGGrev
static number nfMapGGrev(number c, const coeffs src, const coeffs)
Definition: ffields.cc:727
StringEndS
char * StringEndS()
Definition: reporter.cc:151
n_rep_int
@ n_rep_int
(int), see modulop.h
Definition: coeffs.h:111
gf_tab_numdigits62
int gf_tab_numdigits62(int q)
Definition: gf_tabutil.cc:12
loop
#define loop
Definition: structs.h:78
b
CanonicalForm b
Definition: cfModGcd.cc:4044
nfInvers
static number nfInvers(number c, const coeffs r)
Definition: ffields.cc:363
nfWriteLong
static void nfWriteLong(number a, const coeffs r)
Definition: ffields.cc:406
convertback62
int convertback62(char *p, int n)
Definition: gf_tabutil.cc:50
ffields.h
nfMapGG_factor
static int nfMapGG_factor
Definition: ffields.cc:716
n_coeffType
n_coeffType
Definition: coeffs.h:27
nfIsZero
static BOOLEAN nfIsZero(number a, const coeffs r)
Definition: ffields.cc:137
nfDiv
static number nfDiv(number a, number b, const coeffs r)
Definition: ffields.cc:335
nfCoeffName
static char * nfCoeffName(const coeffs r)
Definition: ffields.cc:814
nfRead
static const char * nfRead(const char *s, number *a, const coeffs r)
Definition: ffields.cc:522
TRUE
#define TRUE
Definition: auxiliary.h:98
i
int i
Definition: cfEzgcd.cc:125
res
CanonicalForm res
Definition: facAbsFact.cc:64
nMapFunc
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:74
fp
CanonicalForm fp
Definition: cfModGcd.cc:4043
nfEqual
static BOOLEAN nfEqual(number a, number b, const coeffs r)
Definition: ffields.cc:394
buf
int status int void * buf
Definition: si_signals.h:59
nDivBy0
const char *const nDivBy0
Definition: numbers.h:89
PrintS
void PrintS(const char *s)
Definition: reporter.cc:284
omFreeSize
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
BOOLEAN
int BOOLEAN
Definition: auxiliary.h:85
nfSub
static number nfSub(number a, number b, const coeffs r)
Definition: ffields.cc:315
nfGreater
static BOOLEAN nfGreater(number a, number b, const coeffs r)
Definition: ffields.cc:382
nfIsOne
static BOOLEAN nfIsOne(number a, const coeffs r)
Definition: ffields.cc:324
sixteenlog2
#define sixteenlog2
nfTest
#define nfTest(N, R)
Definition: ffields.cc:131
nfMinPoly
static int nfMinPoly[16]
Definition: ffields.cc:562
coeffs
omAlloc
#define omAlloc(size)
Definition: omAllocDecl.h:210
nlModP
number nlModP(number q, const coeffs, const coeffs Zp)
Definition: longrat.cc:1436
nfShowMipo
void nfShowMipo(const coeffs r)
Show the mininimal polynom.... NOTE: this is used by char * sleftv::String(void *d,...
Definition: ffields.cc:564
nfInit
static number nfInit(long i, const coeffs r)
Definition: ffields.cc:191
nfReadTable
static void nfReadTable(const int c, const coeffs r)
Definition: ffields.cc:605
n_ParameterNames
static FORCE_INLINE const char ** n_ParameterNames(const coeffs r)
Returns a (const!) pointer to (const char*) names of parameters.
Definition: coeffs.h:809
nfAdd
static number nfAdd(number a, number b, const coeffs R)
Definition: ffields.cc:258
nfGreaterZero
static BOOLEAN nfGreaterZero(number k, const coeffs r)
Definition: ffields.cc:160
StringSetS
void StringSetS(const char *st)
Definition: reporter.cc:128
log
gmp_float log(const gmp_float &a)
Definition: mpr_complex.cc:344
prime.h
Print
#define Print
Definition: emacs.cc:80
mylimits.h
nfNeg
static number nfNeg(number c, const coeffs r)
Definition: ffields.cc:297
Werror
void Werror(const char *fmt,...)
Definition: reporter.cc:189
while
while(1)
Definition: libparse.cc:1442
name
char name(const Variable &v)
Definition: factory.h:180
pow
Rational pow(const Rational &a, int e)
Definition: GMPrat.cc:414
WerrorS
void WerrorS(const char *s)
Definition: feFopen.cc:24
nfDBTest
BOOLEAN nfDBTest(number a, const char *f, const int l, const coeffs r)
Definition: ffields.cc:111
n_rep_gf
@ n_rep_gf
(int), see ffields.h
Definition: coeffs.h:120
WarnS
#define WarnS
Definition: emacs.cc:78
assume
#define assume(x)
Definition: mod2.h:390
sirandom.h
NULL
#define NULL
Definition: omList.c:10
check
int check
Definition: libparse.cc:1104
nfInt
static long nfInt(number &n, const coeffs r)
Definition: ffields.cc:240
eati
const char * eati(const char *s, int *i)
Definition: reporter.cc:373
nfMult
static number nfMult(number a, number b, const coeffs r)
Definition: ffields.cc:171
nfInitChar
BOOLEAN nfInitChar(coeffs r, void *parameter)
Definition: ffields.cc:852
l
int l
Definition: cfEzgcd.cc:93
nfMapGG
static number nfMapGG(number c, const coeffs src, const coeffs)
Definition: ffields.cc:717
R
#define R
Definition: sirandom.c:26
Warn
#define Warn
Definition: emacs.cc:77
StringAppend
#define StringAppend
Definition: emacs.cc:79
p
int p
Definition: cfModGcd.cc:4019
nfParameter
static number nfParameter(int i, const coeffs)
Definition: ffields.cc:215
longrat.h
s
const CanonicalForm int s
Definition: facAbsFact.cc:55
nfKillChar
static void nfKillChar(coeffs r)
Definition: ffields.cc:793
siRandProc
int(* siRandProc)()
Definition: sirandom.h:9
nfMapP
static number nfMapP(number c, const coeffs, const coeffs dst)
Definition: ffields.cc:708
nfReadMipo
static void nfReadMipo(char *s)
Definition: ffields.cc:580
numbers.h
nfCoeffIsEqual
static BOOLEAN nfCoeffIsEqual(const coeffs, n_coeffType, void *)
Definition: ffields.cc:842
omAlloc0
#define omAlloc0(size)
Definition: omAllocDecl.h:211
MAX_INT_VAL
const int MAX_INT_VAL
Definition: mylimits.h:12
nfWriteShort
static void nfWriteShort(number a, const coeffs r)
Definition: ffields.cc:440
coeffs.h