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rmodulon.cc
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1 /****************************************
2 * Computer Algebra System SINGULAR *
3 ****************************************/
4 /*
5 * ABSTRACT: numbers modulo n
6 */
7 #include "misc/auxiliary.h"
8 
9 #include "misc/mylimits.h"
10 #include "misc/prime.h" // IsPrime
11 #include "reporter/reporter.h"
12 
13 #include "coeffs/si_gmp.h"
14 #include "coeffs/coeffs.h"
15 #include "coeffs/modulop.h"
16 #include "coeffs/rintegers.h"
17 #include "coeffs/numbers.h"
18 
19 #include "coeffs/mpr_complex.h"
20 
21 #include "coeffs/longrat.h"
22 #include "coeffs/rmodulon.h"
23 
24 #include <string.h>
25 
26 #ifdef HAVE_RINGS
27 
28 void nrnWrite (number a, const coeffs);
29 #ifdef LDEBUG
30 BOOLEAN nrnDBTest (number a, const char *f, const int l, const coeffs r);
31 #endif
32 
34 
36 {
37  const char start[]="ZZ/bigint(";
38  const int start_len=strlen(start);
39  if (strncmp(s,start,start_len)==0)
40  {
41  s+=start_len;
42  mpz_t z;
43  mpz_init(z);
44  s=nEatLong(s,z);
45  ZnmInfo info;
46  info.base=z;
47  info.exp= 1;
48  while ((*s!='\0') && (*s!=')')) s++;
49  // expect ")" or ")^exp"
50  if (*s=='\0') { mpz_clear(z); return NULL; }
51  if (((*s)==')') && (*(s+1)=='^'))
52  {
53  s=s+2;
54  int i;
55  s=nEati(s,&i,0);
56  info.exp=(unsigned long)i;
57  return nInitChar(n_Znm,(void*) &info);
58  }
59  else
60  return nInitChar(n_Zn,(void*) &info);
61  }
62  else return NULL;
63 }
64 
66 static char* nrnCoeffName(const coeffs r)
67 {
69  size_t l = (size_t)mpz_sizeinbase(r->modBase, 10) + 2;
70  char* s = (char*) omAlloc(l);
71  l+=24;
72  nrnCoeffName_buff=(char*)omAlloc(l);
73  s= mpz_get_str (s, 10, r->modBase);
74  int ll;
75  if (nCoeff_is_Zn(r))
76  {
77  if (strlen(s)<10)
78  ll=snprintf(nrnCoeffName_buff,l,"ZZ/(%s)",s);
79  else
80  ll=snprintf(nrnCoeffName_buff,l,"ZZ/bigint(%s)",s);
81  }
82  else if (nCoeff_is_Ring_PtoM(r))
83  ll=snprintf(nrnCoeffName_buff,l,"ZZ/(bigint(%s)^%lu)",s,r->modExponent);
84  assume(ll<(int)l); // otherwise nrnCoeffName_buff too small
85  omFreeSize((ADDRESS)s, l-22);
86  return nrnCoeffName_buff;
87 }
88 
89 static BOOLEAN nrnCoeffIsEqual(const coeffs r, n_coeffType n, void * parameter)
90 {
91  /* test, if r is an instance of nInitCoeffs(n,parameter) */
92  ZnmInfo *info=(ZnmInfo*)parameter;
93  return (n==r->type) && (r->modExponent==info->exp)
94  && (mpz_cmp(r->modBase,info->base)==0);
95 }
96 
97 static void nrnKillChar(coeffs r)
98 {
99  mpz_clear(r->modNumber);
100  mpz_clear(r->modBase);
101  omFreeBin((void *) r->modBase, gmp_nrz_bin);
102  omFreeBin((void *) r->modNumber, gmp_nrz_bin);
103 }
104 
105 static coeffs nrnQuot1(number c, const coeffs r)
106 {
107  coeffs rr;
108  long ch = r->cfInt(c, r);
109  mpz_t a,b;
110  mpz_init_set(a, r->modNumber);
111  mpz_init_set_ui(b, ch);
112  mpz_t gcd;
113  mpz_init(gcd);
114  mpz_gcd(gcd, a,b);
115  if(mpz_cmp_ui(gcd, 1) == 0)
116  {
117  WerrorS("constant in q-ideal is coprime to modulus in ground ring");
118  WerrorS("Unable to create qring!");
119  return NULL;
120  }
121  if(r->modExponent == 1)
122  {
123  ZnmInfo info;
124  info.base = gcd;
125  info.exp = (unsigned long) 1;
126  rr = nInitChar(n_Zn, (void*)&info);
127  }
128  else
129  {
130  ZnmInfo info;
131  info.base = r->modBase;
132  int kNew = 1;
133  mpz_t baseTokNew;
134  mpz_init(baseTokNew);
135  mpz_set(baseTokNew, r->modBase);
136  while(mpz_cmp(gcd, baseTokNew) > 0)
137  {
138  kNew++;
139  mpz_mul(baseTokNew, baseTokNew, r->modBase);
140  }
141  //printf("\nkNew = %i\n",kNew);
142  info.exp = kNew;
143  mpz_clear(baseTokNew);
144  rr = nInitChar(n_Znm, (void*)&info);
145  }
146  mpz_clear(gcd);
147  return(rr);
148 }
149 
150 static number nrnCopy(number a, const coeffs)
151 {
152  mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin);
153  mpz_init_set(erg, (mpz_ptr) a);
154  return (number) erg;
155 }
156 
157 /*
158  * create a number from int
159  */
160 static number nrnInit(long i, const coeffs r)
161 {
162  mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin);
163  mpz_init_set_si(erg, i);
164  mpz_mod(erg, erg, r->modNumber);
165  return (number) erg;
166 }
167 
168 /*
169  * convert a number to int
170  */
171 static long nrnInt(number &n, const coeffs)
172 {
173  return mpz_get_si((mpz_ptr) n);
174 }
175 
176 #if SI_INTEGER_VARIANT==2
177 #define nrnDelete nrzDelete
178 #define nrnSize nrzSize
179 #else
180 static void nrnDelete(number *a, const coeffs)
181 {
182  if (*a != NULL)
183  {
184  mpz_clear((mpz_ptr) *a);
185  omFreeBin((void *) *a, gmp_nrz_bin);
186  *a = NULL;
187  }
188 }
189 static int nrnSize(number a, const coeffs)
190 {
191  mpz_ptr p=(mpz_ptr)a;
192  int s=p->_mp_alloc;
193  if (s==1) s=(mpz_cmp_ui(p,0)!=0);
194  return s;
195 }
196 #endif
197 /*
198  * Multiply two numbers
199  */
200 static number nrnMult(number a, number b, const coeffs r)
201 {
202  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
203  mpz_init(erg);
204  mpz_mul(erg, (mpz_ptr)a, (mpz_ptr) b);
205  mpz_mod(erg, erg, r->modNumber);
206  return (number) erg;
207 }
208 
209 static void nrnPower(number a, int i, number * result, const coeffs r)
210 {
211  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
212  mpz_init(erg);
213  mpz_powm_ui(erg, (mpz_ptr)a, i, r->modNumber);
214  *result = (number) erg;
215 }
216 
217 static number nrnAdd(number a, number b, const coeffs r)
218 {
219  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
220  mpz_init(erg);
221  mpz_add(erg, (mpz_ptr)a, (mpz_ptr) b);
222  mpz_mod(erg, erg, r->modNumber);
223  return (number) erg;
224 }
225 
226 static number nrnSub(number a, number b, const coeffs r)
227 {
228  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
229  mpz_init(erg);
230  mpz_sub(erg, (mpz_ptr)a, (mpz_ptr) b);
231  mpz_mod(erg, erg, r->modNumber);
232  return (number) erg;
233 }
234 
235 static BOOLEAN nrnIsZero(number a, const coeffs)
236 {
237  return 0 == mpz_cmpabs_ui((mpz_ptr)a, 0);
238 }
239 
240 static number nrnNeg(number c, const coeffs r)
241 {
242  if( !nrnIsZero(c, r) )
243  // Attention: This method operates in-place.
244  mpz_sub((mpz_ptr)c, r->modNumber, (mpz_ptr)c);
245  return c;
246 }
247 
248 static number nrnInvers(number c, const coeffs r)
249 {
250  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
251  mpz_init(erg);
252  if (nrnIsZero(c,r))
253  {
254  WerrorS(nDivBy0);
255  }
256  else
257  {
258  mpz_invert(erg, (mpz_ptr)c, r->modNumber);
259  }
260  return (number) erg;
261 }
262 
263 /*
264  * Give the largest k, such that a = x * k, b = y * k has
265  * a solution.
266  * a may be NULL, b not
267  */
268 static number nrnGcd(number a, number b, const coeffs r)
269 {
270  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
271  mpz_init_set(erg, r->modNumber);
272  if (a != NULL) mpz_gcd(erg, erg, (mpz_ptr)a);
273  mpz_gcd(erg, erg, (mpz_ptr)b);
274  if(mpz_cmp(erg,r->modNumber)==0)
275  {
276  mpz_clear(erg);
278  return nrnInit(0,r);
279  }
280  return (number)erg;
281 }
282 
283 /*
284  * Give the smallest k, such that a * x = k = b * y has a solution
285  * TODO: lcm(gcd,gcd) better than gcd(lcm) ?
286  */
287 static number nrnLcm(number a, number b, const coeffs r)
288 {
289  number erg = nrnGcd(NULL, a, r);
290  number tmp = nrnGcd(NULL, b, r);
291  mpz_lcm((mpz_ptr)erg, (mpz_ptr)erg, (mpz_ptr)tmp);
292  nrnDelete(&tmp, r);
293  return (number)erg;
294 }
295 
296 /* Not needed any more, but may have room for improvement
297  number nrnGcd3(number a,number b, number c,ring r)
298 {
299  mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin);
300  mpz_init(erg);
301  if (a == NULL) a = (number)r->modNumber;
302  if (b == NULL) b = (number)r->modNumber;
303  if (c == NULL) c = (number)r->modNumber;
304  mpz_gcd(erg, (mpz_ptr)a, (mpz_ptr)b);
305  mpz_gcd(erg, erg, (mpz_ptr)c);
306  mpz_gcd(erg, erg, r->modNumber);
307  return (number)erg;
308 }
309 */
310 
311 /*
312  * Give the largest k, such that a = x * k, b = y * k has
313  * a solution and r, s, s.t. k = s*a + t*b
314  * CF: careful: ExtGcd is wrong as implemented (or at least may not
315  * give you what you want:
316  * ExtGcd(5, 10 modulo 12):
317  * the gcdext will return 5 = 1*5 + 0*10
318  * however, mod 12, the gcd should be 1
319  */
320 static number nrnExtGcd(number a, number b, number *s, number *t, const coeffs r)
321 {
322  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
323  mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin);
324  mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin);
325  mpz_init(erg);
326  mpz_init(bs);
327  mpz_init(bt);
328  mpz_gcdext(erg, bs, bt, (mpz_ptr)a, (mpz_ptr)b);
329  mpz_mod(bs, bs, r->modNumber);
330  mpz_mod(bt, bt, r->modNumber);
331  *s = (number)bs;
332  *t = (number)bt;
333  return (number)erg;
334 }
335 
336 static BOOLEAN nrnIsOne(number a, const coeffs)
337 {
338  return 0 == mpz_cmp_si((mpz_ptr)a, 1);
339 }
340 
341 static BOOLEAN nrnEqual(number a, number b, const coeffs)
342 {
343  return 0 == mpz_cmp((mpz_ptr)a, (mpz_ptr)b);
344 }
345 
346 static number nrnGetUnit(number k, const coeffs r)
347 {
348  if (mpz_divisible_p(r->modNumber, (mpz_ptr)k)) return nrnInit(1,r);
349 
350  mpz_ptr unit = (mpz_ptr)nrnGcd(NULL, k, r);
351  mpz_tdiv_q(unit, (mpz_ptr)k, unit);
352  mpz_ptr gcd = (mpz_ptr)nrnGcd(NULL, (number)unit, r);
353  if (!nrnIsOne((number)gcd,r))
354  {
355  mpz_ptr ctmp;
356  // tmp := unit^2
357  mpz_ptr tmp = (mpz_ptr) nrnMult((number) unit,(number) unit,r);
358  // gcd_new := gcd(tmp, 0)
359  mpz_ptr gcd_new = (mpz_ptr) nrnGcd(NULL, (number) tmp, r);
360  while (!nrnEqual((number) gcd_new,(number) gcd,r))
361  {
362  // gcd := gcd_new
363  ctmp = gcd;
364  gcd = gcd_new;
365  gcd_new = ctmp;
366  // tmp := tmp * unit
367  mpz_mul(tmp, tmp, unit);
368  mpz_mod(tmp, tmp, r->modNumber);
369  // gcd_new := gcd(tmp, 0)
370  mpz_gcd(gcd_new, tmp, r->modNumber);
371  }
372  // unit := unit + modNumber / gcd_new
373  mpz_tdiv_q(tmp, r->modNumber, gcd_new);
374  mpz_add(unit, unit, tmp);
375  mpz_mod(unit, unit, r->modNumber);
376  nrnDelete((number*) &gcd_new, r);
377  nrnDelete((number*) &tmp, r);
378  }
379  nrnDelete((number*) &gcd, r);
380  return (number)unit;
381 }
382 
383 /* XExtGcd returns a unimodular matrix ((s,t)(u,v)) sth.
384  * (a,b)^t ((st)(uv)) = (g,0)^t
385  * Beware, the ExtGcd will not necessaairly do this.
386  * Problem: if g = as+bt then (in Z/nZ) it follows NOT that
387  * 1 = (a/g)s + (b/g) t
388  * due to the zero divisors.
389  */
390 
391 //#define CF_DEB;
392 static number nrnXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
393 {
394  number xx;
395 #ifdef CF_DEB
396  StringSetS("XExtGcd of ");
397  nrnWrite(a, r);
398  StringAppendS("\t");
399  nrnWrite(b, r);
400  StringAppendS(" modulo ");
401  nrnWrite(xx = (number)r->modNumber, r);
402  Print("%s\n", StringEndS());
403 #endif
404 
405  mpz_ptr one = (mpz_ptr)omAllocBin(gmp_nrz_bin);
406  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
407  mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin);
408  mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin);
409  mpz_ptr bu = (mpz_ptr)omAllocBin(gmp_nrz_bin);
410  mpz_ptr bv = (mpz_ptr)omAllocBin(gmp_nrz_bin);
411  mpz_init(erg);
412  mpz_init(one);
413  mpz_init_set(bs, (mpz_ptr) a);
414  mpz_init_set(bt, (mpz_ptr) b);
415  mpz_init(bu);
416  mpz_init(bv);
417  mpz_gcd(erg, bs, bt);
418 
419 #ifdef CF_DEB
420  StringSetS("1st gcd:");
421  nrnWrite(xx= (number)erg, r);
422 #endif
423 
424  mpz_gcd(erg, erg, r->modNumber);
425 
426  mpz_div(bs, bs, erg);
427  mpz_div(bt, bt, erg);
428 
429 #ifdef CF_DEB
430  Print("%s\n", StringEndS());
431  StringSetS("xgcd: ");
432 #endif
433 
434  mpz_gcdext(one, bu, bv, bs, bt);
435  number ui = nrnGetUnit(xx = (number) one, r);
436 #ifdef CF_DEB
437  n_Write(xx, r);
438  StringAppendS("\t");
439  n_Write(ui, r);
440  Print("%s\n", StringEndS());
441 #endif
442  nrnDelete(&xx, r);
443  if (!nrnIsOne(ui, r))
444  {
445 #ifdef CF_DEB
446  PrintS("Scaling\n");
447 #endif
448  number uii = nrnInvers(ui, r);
449  nrnDelete(&ui, r);
450  ui = uii;
451  mpz_ptr uu = (mpz_ptr)omAllocBin(gmp_nrz_bin);
452  mpz_init_set(uu, (mpz_ptr)ui);
453  mpz_mul(bu, bu, uu);
454  mpz_mul(bv, bv, uu);
455  mpz_clear(uu);
456  omFreeBin(uu, gmp_nrz_bin);
457  }
458  nrnDelete(&ui, r);
459 #ifdef CF_DEB
460  StringSetS("xgcd");
461  nrnWrite(xx= (number)bs, r);
462  StringAppendS("*");
463  nrnWrite(xx= (number)bu, r);
464  StringAppendS(" + ");
465  nrnWrite(xx= (number)bt, r);
466  StringAppendS("*");
467  nrnWrite(xx= (number)bv, r);
468  Print("%s\n", StringEndS());
469 #endif
470 
471  mpz_mod(bs, bs, r->modNumber);
472  mpz_mod(bt, bt, r->modNumber);
473  mpz_mod(bu, bu, r->modNumber);
474  mpz_mod(bv, bv, r->modNumber);
475  *s = (number)bu;
476  *t = (number)bv;
477  *u = (number)bt;
478  *u = nrnNeg(*u, r);
479  *v = (number)bs;
480  return (number)erg;
481 }
482 
483 static BOOLEAN nrnIsMOne(number a, const coeffs r)
484 {
485  if((r->ch==2) && (nrnIsOne(a,r))) return FALSE;
486  mpz_t t; mpz_init_set(t, (mpz_ptr)a);
487  mpz_add_ui(t, t, 1);
488  bool erg = (0 == mpz_cmp(t, r->modNumber));
489  mpz_clear(t);
490  return erg;
491 }
492 
493 static BOOLEAN nrnGreater(number a, number b, const coeffs)
494 {
495  return 0 < mpz_cmp((mpz_ptr)a, (mpz_ptr)b);
496 }
497 
498 static BOOLEAN nrnGreaterZero(number k, const coeffs cf)
499 {
500  if (cf->is_field)
501  {
502  if (mpz_cmp_ui(cf->modBase,2)==0)
503  {
504  return TRUE;
505  }
506  #if 0
507  mpz_t ch2; mpz_init_set(ch2, cf->modBase);
508  mpz_sub_ui(ch2,ch2,1); //cf->modBase is odd
509  mpz_divexact_ui(ch2,ch2,2);
510  if (mpz_cmp(ch2,(mpz_ptr)k)<0)
511  {
512  mpz_clear(ch2);
513  return FALSE;
514  }
515  mpz_clear(ch2);
516  #endif
517  }
518  #if 0
519  else
520  {
521  mpz_t ch2; mpz_init_set(ch2, cf->modBase);
522  mpz_tdiv_q_ui(ch2,ch2,2);
523  if (mpz_cmp(ch2,(mpz_ptr)k)<0)
524  {
525  mpz_clear(ch2);
526  return FALSE;
527  }
528  mpz_clear(ch2);
529  }
530  #endif
531  return 0 < mpz_sgn1((mpz_ptr)k);
532 }
533 
534 static BOOLEAN nrnIsUnit(number a, const coeffs r)
535 {
536  number tmp = nrnGcd(a, (number)r->modNumber, r);
537  bool res = nrnIsOne(tmp, r);
538  nrnDelete(&tmp, r);
539  return res;
540 }
541 
542 static number nrnAnn(number k, const coeffs r)
543 {
544  mpz_ptr tmp = (mpz_ptr) omAllocBin(gmp_nrz_bin);
545  mpz_init(tmp);
546  mpz_gcd(tmp, (mpz_ptr) k, r->modNumber);
547  if (mpz_cmp_si(tmp, 1)==0)
548  {
549  mpz_set_ui(tmp, 0);
550  return (number) tmp;
551  }
552  mpz_divexact(tmp, r->modNumber, tmp);
553  return (number) tmp;
554 }
555 
556 static BOOLEAN nrnDivBy(number a, number b, const coeffs r)
557 {
558  /* b divides a iff b/gcd(a, b) is a unit in the given ring: */
559  number n = nrnGcd(a, b, r);
560  mpz_tdiv_q((mpz_ptr)n, (mpz_ptr)b, (mpz_ptr)n);
561  bool result = nrnIsUnit(n, r);
562  nrnDelete(&n, NULL);
563  return result;
564 }
565 
566 static int nrnDivComp(number a, number b, const coeffs r)
567 {
568  if (nrnEqual(a, b,r)) return 2;
569  if (mpz_divisible_p((mpz_ptr) a, (mpz_ptr) b)) return -1;
570  if (mpz_divisible_p((mpz_ptr) b, (mpz_ptr) a)) return 1;
571  return 0;
572 }
573 
574 static number nrnDiv(number a, number b, const coeffs r)
575 {
576  if (nrnIsZero(b,r))
577  {
578  WerrorS(nDivBy0);
579  return nrnInit(0,r);
580  }
581  else if (r->is_field)
582  {
583  number inv=nrnInvers(b,r);
584  number erg=nrnMult(a,inv,r);
585  nrnDelete(&inv,r);
586  return erg;
587  }
588  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
589  mpz_init(erg);
590  if (mpz_divisible_p((mpz_ptr)a, (mpz_ptr)b))
591  {
592  mpz_divexact(erg, (mpz_ptr)a, (mpz_ptr)b);
593  return (number)erg;
594  }
595  else
596  {
597  mpz_ptr gcd = (mpz_ptr)nrnGcd(a, b, r);
598  mpz_divexact(erg, (mpz_ptr)b, gcd);
599  if (!nrnIsUnit((number)erg, r))
600  {
601  WerrorS("Division not possible, even by cancelling zero divisors.");
602  nrnDelete((number*) &gcd, r);
603  nrnDelete((number*) &erg, r);
604  return (number)NULL;
605  }
606  // a / gcd(a,b) * [b / gcd (a,b)]^(-1)
607  mpz_ptr tmp = (mpz_ptr)nrnInvers((number) erg,r);
608  mpz_divexact(erg, (mpz_ptr)a, gcd);
609  mpz_mul(erg, erg, tmp);
610  nrnDelete((number*) &gcd, r);
611  nrnDelete((number*) &tmp, r);
612  mpz_mod(erg, erg, r->modNumber);
613  return (number)erg;
614  }
615 }
616 
617 static number nrnMod(number a, number b, const coeffs r)
618 {
619  /*
620  We need to return the number rr which is uniquely determined by the
621  following two properties:
622  (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z)
623  (2) There exists some k in the integers Z such that a = k * b + rr.
624  Consider g := gcd(n, |b|). Note that then |b|/g is a unit in Z/n.
625  Now, there are three cases:
626  (a) g = 1
627  Then |b| is a unit in Z/n, i.e. |b| (and also b) divides a.
628  Thus rr = 0.
629  (b) g <> 1 and g divides a
630  Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0.
631  (c) g <> 1 and g does not divide a
632  Then denote the division with remainder of a by g as this:
633  a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b|
634  fulfills (1) and (2), i.e. rr := t is the correct result. Hence
635  in this third case, rr is the remainder of division of a by g in Z.
636  Remark: according to mpz_mod: a,b are always non-negative
637  */
638  mpz_ptr g = (mpz_ptr)omAllocBin(gmp_nrz_bin);
639  mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin);
640  mpz_init(g);
641  mpz_init_set_ui(rr, 0);
642  mpz_gcd(g, (mpz_ptr)r->modNumber, (mpz_ptr)b); // g is now as above
643  if (mpz_cmp_si(g, 1L) != 0) mpz_mod(rr, (mpz_ptr)a, g); // the case g <> 1
644  mpz_clear(g);
646  return (number)rr;
647 }
648 
649 /* CF: note that Z/nZ has (at least) two distinct euclidean structures
650  * 1st phi(a) := (a mod n) which is just the structure directly
651  * inherited from Z
652  * 2nd phi(a) := gcd(a, n)
653  * The 1st version is probably faster as everything just comes from Z,
654  * but the 2nd version behaves nicely wrt. to quotient operations
655  * and HNF and such. In agreement with nrnMod we imlement the 2nd here
656  *
657  * For quotrem note that if b exactly divides a, then
658  * min(v_p(a), v_p(n)) >= min(v_p(b), v_p(n))
659  * so if we divide a and b by g:= gcd(a,b,n), then b becomes a
660  * unit mod n/g.
661  * Thus we 1st compute the remainder (similar to nrnMod) and then
662  * the exact quotient.
663  */
664 static number nrnQuotRem(number a, number b, number * rem, const coeffs r)
665 {
666  mpz_t g, aa, bb;
667  mpz_ptr qq = (mpz_ptr)omAllocBin(gmp_nrz_bin);
668  mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin);
669  mpz_init(qq);
670  mpz_init(rr);
671  mpz_init(g);
672  mpz_init_set(aa, (mpz_ptr)a);
673  mpz_init_set(bb, (mpz_ptr)b);
674 
675  mpz_gcd(g, bb, r->modNumber);
676  mpz_mod(rr, aa, g);
677  mpz_sub(aa, aa, rr);
678  mpz_gcd(g, aa, g);
679  mpz_div(aa, aa, g);
680  mpz_div(bb, bb, g);
681  mpz_div(g, r->modNumber, g);
682  mpz_invert(g, bb, g);
683  mpz_mul(qq, aa, g);
684  if (rem)
685  *rem = (number)rr;
686  else {
687  mpz_clear(rr);
688  omFreeBin(rr, gmp_nrz_bin);
689  }
690  mpz_clear(g);
691  mpz_clear(aa);
692  mpz_clear(bb);
693  return (number) qq;
694 }
695 
696 /*
697  * Helper function for computing the module
698  */
699 
701 
702 static number nrnMapModN(number from, const coeffs /*src*/, const coeffs dst)
703 {
704  return nrnMult(from, (number) nrnMapCoef, dst);
705 }
706 
707 static number nrnMap2toM(number from, const coeffs /*src*/, const coeffs dst)
708 {
709  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
710  mpz_init(erg);
711  mpz_mul_ui(erg, nrnMapCoef, (unsigned long)from);
712  mpz_mod(erg, erg, dst->modNumber);
713  return (number)erg;
714 }
715 
716 static number nrnMapZp(number from, const coeffs /*src*/, const coeffs dst)
717 {
718  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
719  mpz_init(erg);
720  // TODO: use npInt(...)
721  mpz_mul_si(erg, nrnMapCoef, (unsigned long)from);
722  mpz_mod(erg, erg, dst->modNumber);
723  return (number)erg;
724 }
725 
726 number nrnMapGMP(number from, const coeffs /*src*/, const coeffs dst)
727 {
728  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
729  mpz_init(erg);
730  mpz_mod(erg, (mpz_ptr)from, dst->modNumber);
731  return (number)erg;
732 }
733 
734 static number nrnMapQ(number from, const coeffs src, const coeffs dst)
735 {
736  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
737  nlMPZ(erg, from, src);
738  mpz_mod(erg, erg, dst->modNumber);
739  return (number)erg;
740 }
741 
742 #if SI_INTEGER_VARIANT==3
743 static number nrnMapZ(number from, const coeffs /*src*/, const coeffs dst)
744 {
745  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
746  if (n_Z_IS_SMALL(from))
747  mpz_init_set_si(erg, SR_TO_INT(from));
748  else
749  mpz_init_set(erg, (mpz_ptr) from);
750  mpz_mod(erg, erg, dst->modNumber);
751  return (number)erg;
752 }
753 #elif SI_INTEGER_VARIANT==2
754 
755 static number nrnMapZ(number from, const coeffs src, const coeffs dst)
756 {
757  if (SR_HDL(from) & SR_INT)
758  {
759  long f_i=SR_TO_INT(from);
760  return nrnInit(f_i,dst);
761  }
762  return nrnMapGMP(from,src,dst);
763 }
764 #elif SI_INTEGER_VARIANT==1
765 static number nrnMapZ(number from, const coeffs src, const coeffs dst)
766 {
767  return nrnMapQ(from,src,dst);
768 }
769 #endif
770 void nrnWrite (number a, const coeffs /*cf*/)
771 {
772  char *s,*z;
773  if (a==NULL)
774  {
775  StringAppendS("o");
776  }
777  else
778  {
779  int l=mpz_sizeinbase((mpz_ptr) a, 10) + 2;
780  s=(char*)omAlloc(l);
781  z=mpz_get_str(s,10,(mpz_ptr) a);
782  StringAppendS(z);
783  omFreeSize((ADDRESS)s,l);
784  }
785 }
786 
787 nMapFunc nrnSetMap(const coeffs src, const coeffs dst)
788 {
789  /* dst = nrn */
790  if ((src->rep==n_rep_gmp) && nCoeff_is_Z(src))
791  {
792  return nrnMapZ;
793  }
794  if ((src->rep==n_rep_gap_gmp) /*&& nCoeff_is_Z(src)*/)
795  {
796  return nrnMapZ;
797  }
798  if (src->rep==n_rep_gap_rat) /*&& nCoeff_is_Q(src)) or Z*/
799  {
800  return nrnMapQ;
801  }
802  // Some type of Z/n ring / field
803  if (nCoeff_is_Zn(src) || nCoeff_is_Ring_PtoM(src) ||
804  nCoeff_is_Ring_2toM(src) || nCoeff_is_Zp(src))
805  {
806  if ( (!nCoeff_is_Zp(src))
807  && (mpz_cmp(src->modBase, dst->modBase) == 0)
808  && (src->modExponent == dst->modExponent)) return ndCopyMap;
809  else
810  {
811  mpz_ptr nrnMapModul = (mpz_ptr) omAllocBin(gmp_nrz_bin);
812  // Computing the n of Z/n
813  if (nCoeff_is_Zp(src))
814  {
815  mpz_init_set_si(nrnMapModul, src->ch);
816  }
817  else
818  {
819  mpz_init(nrnMapModul);
820  mpz_set(nrnMapModul, src->modNumber);
821  }
822  // nrnMapCoef = 1 in dst if dst is a subring of src
823  // nrnMapCoef = 0 in dst / src if src is a subring of dst
824  if (nrnMapCoef == NULL)
825  {
826  nrnMapCoef = (mpz_ptr) omAllocBin(gmp_nrz_bin);
827  mpz_init(nrnMapCoef);
828  }
829  if (mpz_divisible_p(nrnMapModul, dst->modNumber))
830  {
831  mpz_set_ui(nrnMapCoef, 1);
832  }
833  else
834  if (mpz_divisible_p(dst->modNumber,nrnMapModul))
835  {
836  mpz_divexact(nrnMapCoef, dst->modNumber, nrnMapModul);
837  mpz_ptr tmp = dst->modNumber;
838  dst->modNumber = nrnMapModul;
839  if (!nrnIsUnit((number) nrnMapCoef,dst))
840  {
841  dst->modNumber = tmp;
842  nrnDelete((number*) &nrnMapModul, dst);
843  return NULL;
844  }
845  mpz_ptr inv = (mpz_ptr) nrnInvers((number) nrnMapCoef,dst);
846  dst->modNumber = tmp;
847  mpz_mul(nrnMapCoef, nrnMapCoef, inv);
848  mpz_mod(nrnMapCoef, nrnMapCoef, dst->modNumber);
849  nrnDelete((number*) &inv, dst);
850  }
851  else
852  {
853  nrnDelete((number*) &nrnMapModul, dst);
854  return NULL;
855  }
856  nrnDelete((number*) &nrnMapModul, dst);
857  if (nCoeff_is_Ring_2toM(src))
858  return nrnMap2toM;
859  else if (nCoeff_is_Zp(src))
860  return nrnMapZp;
861  else
862  return nrnMapModN;
863  }
864  }
865  return NULL; // default
866 }
867 
868 static number nrnInitMPZ(mpz_t m, const coeffs r)
869 {
870  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
871  mpz_init_set(erg,m);
872  mpz_mod(erg, erg, r->modNumber);
873  return (number) erg;
874 }
875 
876 static void nrnMPZ(mpz_t m, number &n, const coeffs)
877 {
878  mpz_init_set(m, (mpz_ptr)n);
879 }
880 
881 /*
882  * set the exponent (allocate and init tables) (TODO)
883  */
884 
885 static void nrnSetExp(unsigned long m, coeffs r)
886 {
887  /* clean up former stuff */
888  if (r->modNumber != NULL) mpz_clear(r->modNumber);
889 
890  r->modExponent= m;
891  r->modNumber = (mpz_ptr)omAllocBin(gmp_nrz_bin);
892  mpz_init_set (r->modNumber, r->modBase);
893  mpz_pow_ui (r->modNumber, r->modNumber, m);
894 }
895 
896 /* We expect this ring to be Z/n^m for some m > 0 and for some n > 2 which is not a prime. */
897 static void nrnInitExp(unsigned long m, coeffs r)
898 {
899  nrnSetExp(m, r);
900  assume (r->modNumber != NULL);
901 //CF: in general, the modulus is computed somewhere. I don't want to
902 // check it's size before I construct the best ring.
903 // if (mpz_cmp_ui(r->modNumber,2) <= 0)
904 // WarnS("nrnInitExp failed (m in Z/m too small)");
905 }
906 
907 #ifdef LDEBUG
908 BOOLEAN nrnDBTest (number a, const char *f, const int l, const coeffs r)
909 {
910  if ( (mpz_sgn1((mpz_ptr) a) < 0) || (mpz_cmp((mpz_ptr) a, r->modNumber) > 0) )
911  {
912  Warn("mod-n: out of range at %s:%d\n",f,l);
913  return FALSE;
914  }
915  return TRUE;
916 }
917 #endif
918 
919 /*2
920 * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc)
921 */
922 static const char * nlCPEatLongC(char *s, mpz_ptr i)
923 {
924  const char * start=s;
925  if (!(*s >= '0' && *s <= '9'))
926  {
927  mpz_init_set_ui(i, 1);
928  return s;
929  }
930  mpz_init(i);
931  while (*s >= '0' && *s <= '9') s++;
932  if (*s=='\0')
933  {
934  mpz_set_str(i,start,10);
935  }
936  else
937  {
938  char c=*s;
939  *s='\0';
940  mpz_set_str(i,start,10);
941  *s=c;
942  }
943  return s;
944 }
945 
946 static const char * nrnRead (const char *s, number *a, const coeffs r)
947 {
948  mpz_ptr z = (mpz_ptr) omAllocBin(gmp_nrz_bin);
949  {
950  s = nlCPEatLongC((char *)s, z);
951  }
952  mpz_mod(z, z, r->modNumber);
953  if ((*s)=='/')
954  {
955  mpz_ptr n = (mpz_ptr) omAllocBin(gmp_nrz_bin);
956  s++;
957  s=nlCPEatLongC((char*)s,n);
958  if (!nrnIsOne((number)n,r))
959  {
960  *a=nrnDiv((number)z,(number)n,r);
961  mpz_clear(z);
962  omFreeBin((void *)z, gmp_nrz_bin);
963  mpz_clear(n);
964  omFreeBin((void *)n, gmp_nrz_bin);
965  }
966  }
967  else
968  *a = (number) z;
969  return s;
970 }
971 
972 static number nrnConvFactoryNSingN( const CanonicalForm n, const coeffs r)
973 {
974  return nrnInit(n.intval(),r);
975 }
976 
977 static CanonicalForm nrnConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs r )
978 {
979  if (setChar) setCharacteristic( r->ch );
980  return CanonicalForm(nrnInt( n,r ));
981 }
982 
983 /* for initializing function pointers */
985 {
986  assume( (getCoeffType(r) == n_Zn) || (getCoeffType (r) == n_Znm) );
987  ZnmInfo * info= (ZnmInfo *) p;
988  r->modBase= (mpz_ptr)nrnCopy((number)info->base, r); //this circumvents the problem
989  //in bigintmat.cc where we cannot create a "legal" nrn that can be freed.
990  //If we take a copy, we can do whatever we want.
991 
992  nrnInitExp (info->exp, r);
993 
994  /* next computation may yield wrong characteristic as r->modNumber
995  is a GMP number */
996  r->ch = mpz_get_ui(r->modNumber);
997 
998  r->is_field=FALSE;
999  r->is_domain=FALSE;
1000  r->rep=n_rep_gmp;
1001 
1002  r->cfInit = nrnInit;
1003  r->cfDelete = nrnDelete;
1004  r->cfCopy = nrnCopy;
1005  r->cfSize = nrnSize;
1006  r->cfInt = nrnInt;
1007  r->cfAdd = nrnAdd;
1008  r->cfSub = nrnSub;
1009  r->cfMult = nrnMult;
1010  r->cfDiv = nrnDiv;
1011  r->cfAnn = nrnAnn;
1012  r->cfIntMod = nrnMod;
1013  r->cfExactDiv = nrnDiv;
1014  r->cfInpNeg = nrnNeg;
1015  r->cfInvers = nrnInvers;
1016  r->cfDivBy = nrnDivBy;
1017  r->cfDivComp = nrnDivComp;
1018  r->cfGreater = nrnGreater;
1019  r->cfEqual = nrnEqual;
1020  r->cfIsZero = nrnIsZero;
1021  r->cfIsOne = nrnIsOne;
1022  r->cfIsMOne = nrnIsMOne;
1023  r->cfGreaterZero = nrnGreaterZero;
1024  r->cfWriteLong = nrnWrite;
1025  r->cfRead = nrnRead;
1026  r->cfPower = nrnPower;
1027  r->cfSetMap = nrnSetMap;
1028  //r->cfNormalize = ndNormalize;
1029  r->cfLcm = nrnLcm;
1030  r->cfGcd = nrnGcd;
1031  r->cfIsUnit = nrnIsUnit;
1032  r->cfGetUnit = nrnGetUnit;
1033  r->cfExtGcd = nrnExtGcd;
1034  r->cfXExtGcd = nrnXExtGcd;
1035  r->cfQuotRem = nrnQuotRem;
1036  r->cfCoeffName = nrnCoeffName;
1037  r->nCoeffIsEqual = nrnCoeffIsEqual;
1038  r->cfKillChar = nrnKillChar;
1039  r->cfQuot1 = nrnQuot1;
1040  r->cfInitMPZ = nrnInitMPZ;
1041  r->cfMPZ = nrnMPZ;
1042 #if SI_INTEGER_VARIANT==2
1043  r->cfWriteFd = nrzWriteFd;
1044  r->cfReadFd = nrzReadFd;
1045 #endif
1046 
1047 #ifdef LDEBUG
1048  r->cfDBTest = nrnDBTest;
1049 #endif
1050  if ((r->modExponent==1)&&(mpz_size1(r->modBase)==1))
1051  {
1052  long p=mpz_get_si(r->modBase);
1053  if ((p<=FACTORY_MAX_PRIME)&&(p==IsPrime(p))) /*factory limit: <2^29*/
1054  {
1055  r->convFactoryNSingN=nrnConvFactoryNSingN;
1056  r->convSingNFactoryN=nrnConvSingNFactoryN;
1057  }
1058  }
1059  return FALSE;
1060 }
1061 
1062 #endif
1063 /* #ifdef HAVE_RINGS */
All the auxiliary stuff.
int BOOLEAN
Definition: auxiliary.h:87
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
void * ADDRESS
Definition: auxiliary.h:119
void FACTORY_PUBLIC setCharacteristic(int c)
Definition: cf_char.cc:28
int l
Definition: cfEzgcd.cc:100
int m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
int k
Definition: cfEzgcd.cc:99
int p
Definition: cfModGcd.cc:4078
g
Definition: cfModGcd.cc:4090
CanonicalForm cf
Definition: cfModGcd.cc:4083
CanonicalForm b
Definition: cfModGcd.cc:4103
FILE * f
Definition: checklibs.c:9
factory's main class
Definition: canonicalform.h:86
long intval() const
conversion functions
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE BOOLEAN nCoeff_is_Z(const coeffs r)
Definition: coeffs.h:816
number ndCopyMap(number a, const coeffs src, const coeffs dst)
Definition: numbers.cc:255
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_PtoM(const coeffs r)
Definition: coeffs.h:727
n_coeffType
Definition: coeffs.h:27
@ n_Znm
only used if HAVE_RINGS is defined
Definition: coeffs.h:45
@ n_Zn
only used if HAVE_RINGS is defined
Definition: coeffs.h:44
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
Definition: numbers.cc:354
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:421
static FORCE_INLINE BOOLEAN nCoeff_is_Zn(const coeffs r)
Definition: coeffs.h:826
static FORCE_INLINE void n_Write(number n, const coeffs r, const BOOLEAN bShortOut=TRUE)
Definition: coeffs.h:591
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
Definition: coeffs.h:800
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_2toM(const coeffs r)
Definition: coeffs.h:724
@ n_rep_gap_rat
(number), see longrat.h
Definition: coeffs.h:111
@ n_rep_gap_gmp
(), see rinteger.h, new impl.
Definition: coeffs.h:112
@ n_rep_gmp
(mpz_ptr), see rmodulon,h
Definition: coeffs.h:115
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:73
#define Print
Definition: emacs.cc:80
#define Warn
Definition: emacs.cc:77
return result
Definition: facAbsBiFact.cc:75
const CanonicalForm int s
Definition: facAbsFact.cc:51
CanonicalForm res
Definition: facAbsFact.cc:60
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
const ExtensionInfo & info
< [in] sqrfree poly
void WerrorS(const char *s)
Definition: feFopen.cc:24
#define STATIC_VAR
Definition: globaldefs.h:7
#define EXTERN_VAR
Definition: globaldefs.h:6
void mpz_mul_si(mpz_ptr r, mpz_srcptr s, long int si)
Definition: longrat.cc:177
void nlMPZ(mpz_t m, number &n, const coeffs r)
Definition: longrat.cc:2819
#define SR_INT
Definition: longrat.h:67
#define SR_TO_INT(SR)
Definition: longrat.h:69
void rem(unsigned long *a, unsigned long *q, unsigned long p, int &dega, int degq)
Definition: minpoly.cc:572
#define assume(x)
Definition: mod2.h:387
#define FACTORY_MAX_PRIME
Definition: modulop.h:38
The main handler for Singular numbers which are suitable for Singular polynomials.
char * nEatLong(char *s, mpz_ptr i)
extracts a long integer from s, returns the rest
Definition: numbers.cc:652
char * nEati(char *s, int *i, int m)
divide by the first (leading) number and return it, i.e. make monic
Definition: numbers.cc:631
const char *const nDivBy0
Definition: numbers.h:87
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc(size)
Definition: omAllocDecl.h:210
#define omAllocBin(bin)
Definition: omAllocDecl.h:205
#define omFree(addr)
Definition: omAllocDecl.h:261
#define omFreeBin(addr, bin)
Definition: omAllocDecl.h:259
#define NULL
Definition: omList.c:12
omBin_t * omBin
Definition: omStructs.h:12
int IsPrime(int p)
Definition: prime.cc:61
void StringSetS(const char *st)
Definition: reporter.cc:128
void StringAppendS(const char *st)
Definition: reporter.cc:107
void PrintS(const char *s)
Definition: reporter.cc:284
char * StringEndS()
Definition: reporter.cc:151
number nrzReadFd(const ssiInfo *d, const coeffs)
void nrzWriteFd(number n, const ssiInfo *d, const coeffs)
static const char * nrnRead(const char *s, number *a, const coeffs r)
Definition: rmodulon.cc:946
static number nrnMap2toM(number from, const coeffs, const coeffs dst)
Definition: rmodulon.cc:707
static coeffs nrnQuot1(number c, const coeffs r)
Definition: rmodulon.cc:105
static const char * nlCPEatLongC(char *s, mpz_ptr i)
Definition: rmodulon.cc:922
static number nrnInit(long i, const coeffs r)
Definition: rmodulon.cc:160
STATIC_VAR char * nrnCoeffName_buff
Definition: rmodulon.cc:65
static void nrnKillChar(coeffs r)
Definition: rmodulon.cc:97
BOOLEAN nrnDBTest(number a, const char *f, const int l, const coeffs r)
Definition: rmodulon.cc:908
#define nrnSize
Definition: rmodulon.cc:178
static BOOLEAN nrnGreater(number a, number b, const coeffs)
Definition: rmodulon.cc:493
STATIC_VAR mpz_ptr nrnMapCoef
Definition: rmodulon.cc:700
static BOOLEAN nrnIsZero(number a, const coeffs)
Definition: rmodulon.cc:235
static CanonicalForm nrnConvSingNFactoryN(number n, BOOLEAN setChar, const coeffs r)
Definition: rmodulon.cc:977
static number nrnExtGcd(number a, number b, number *s, number *t, const coeffs r)
Definition: rmodulon.cc:320
static void nrnMPZ(mpz_t m, number &n, const coeffs)
Definition: rmodulon.cc:876
static BOOLEAN nrnCoeffIsEqual(const coeffs r, n_coeffType n, void *parameter)
Definition: rmodulon.cc:89
void nrnWrite(number a, const coeffs)
Definition: rmodulon.cc:770
static number nrnMod(number a, number b, const coeffs r)
Definition: rmodulon.cc:617
coeffs nrnInitCfByName(char *s, n_coeffType)
Definition: rmodulon.cc:35
static number nrnMapZ(number from, const coeffs src, const coeffs dst)
Definition: rmodulon.cc:755
static number nrnInitMPZ(mpz_t m, const coeffs r)
Definition: rmodulon.cc:868
static void nrnInitExp(unsigned long m, coeffs r)
Definition: rmodulon.cc:897
static number nrnAnn(number k, const coeffs r)
Definition: rmodulon.cc:542
static char * nrnCoeffName(const coeffs r)
Definition: rmodulon.cc:66
static BOOLEAN nrnIsUnit(number a, const coeffs r)
Definition: rmodulon.cc:534
#define nrnDelete
Definition: rmodulon.cc:177
nMapFunc nrnSetMap(const coeffs src, const coeffs dst)
Definition: rmodulon.cc:787
static number nrnMapZp(number from, const coeffs, const coeffs dst)
Definition: rmodulon.cc:716
static number nrnInvers(number c, const coeffs r)
Definition: rmodulon.cc:248
static number nrnConvFactoryNSingN(const CanonicalForm n, const coeffs r)
Definition: rmodulon.cc:972
static void nrnSetExp(unsigned long m, coeffs r)
Definition: rmodulon.cc:885
static int nrnDivComp(number a, number b, const coeffs r)
Definition: rmodulon.cc:566
static number nrnXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
Definition: rmodulon.cc:392
static BOOLEAN nrnEqual(number a, number b, const coeffs)
Definition: rmodulon.cc:341
static number nrnQuotRem(number a, number b, number *rem, const coeffs r)
Definition: rmodulon.cc:664
static long nrnInt(number &n, const coeffs)
Definition: rmodulon.cc:171
static number nrnMapQ(number from, const coeffs src, const coeffs dst)
Definition: rmodulon.cc:734
EXTERN_VAR omBin gmp_nrz_bin
Definition: rmodulon.cc:33
static BOOLEAN nrnIsOne(number a, const coeffs)
Definition: rmodulon.cc:336
static number nrnCopy(number a, const coeffs)
Definition: rmodulon.cc:150
static number nrnSub(number a, number b, const coeffs r)
Definition: rmodulon.cc:226
static number nrnLcm(number a, number b, const coeffs r)
Definition: rmodulon.cc:287
static number nrnMapModN(number from, const coeffs, const coeffs dst)
Definition: rmodulon.cc:702
static void nrnPower(number a, int i, number *result, const coeffs r)
Definition: rmodulon.cc:209
static number nrnMult(number a, number b, const coeffs r)
Definition: rmodulon.cc:200
static number nrnNeg(number c, const coeffs r)
Definition: rmodulon.cc:240
static number nrnGetUnit(number k, const coeffs r)
Definition: rmodulon.cc:346
number nrnMapGMP(number from, const coeffs, const coeffs dst)
Definition: rmodulon.cc:726
static number nrnDiv(number a, number b, const coeffs r)
Definition: rmodulon.cc:574
static BOOLEAN nrnIsMOne(number a, const coeffs r)
Definition: rmodulon.cc:483
static BOOLEAN nrnDivBy(number a, number b, const coeffs r)
Definition: rmodulon.cc:556
static BOOLEAN nrnGreaterZero(number k, const coeffs cf)
Definition: rmodulon.cc:498
BOOLEAN nrnInitChar(coeffs r, void *p)
Definition: rmodulon.cc:984
static number nrnAdd(number a, number b, const coeffs r)
Definition: rmodulon.cc:217
static number nrnGcd(number a, number b, const coeffs r)
Definition: rmodulon.cc:268
#define mpz_size1(A)
Definition: si_gmp.h:17
#define mpz_sgn1(A)
Definition: si_gmp.h:18
#define SR_HDL(A)
Definition: tgb.cc:35
int gcd(int a, int b)
Definition: walkSupport.cc:836