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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 static 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  return mpz_size1((mpz_ptr)a);
192 }
193 #endif
194 /*
195  * Multiply two numbers
196  */
197 static number nrnMult(number a, number b, const coeffs r)
198 {
199  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
200  mpz_init(erg);
201  mpz_mul(erg, (mpz_ptr)a, (mpz_ptr) b);
202  mpz_mod(erg, erg, r->modNumber);
203  return (number) erg;
204 }
205 
206 static void nrnInpMult(number &a, number b, const coeffs r)
207 {
208  mpz_mul((mpz_ptr)a, (mpz_ptr)a, (mpz_ptr) b);
209  mpz_mod((mpz_ptr)a, (mpz_ptr)a, r->modNumber);
210 }
211 
212 static void nrnPower(number a, int i, number * result, const coeffs r)
213 {
214  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
215  mpz_init(erg);
216  mpz_powm_ui(erg, (mpz_ptr)a, i, r->modNumber);
217  *result = (number) erg;
218 }
219 
220 static number nrnAdd(number a, number b, const coeffs r)
221 {
222  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
223  mpz_init(erg);
224  mpz_add(erg, (mpz_ptr)a, (mpz_ptr) b);
225  mpz_mod(erg, erg, r->modNumber);
226  return (number) erg;
227 }
228 
229 static void nrnInpAdd(number &a, number b, const coeffs r)
230 {
231  mpz_add((mpz_ptr)a, (mpz_ptr)a, (mpz_ptr) b);
232  mpz_mod((mpz_ptr)a, (mpz_ptr)a, r->modNumber);
233 }
234 
235 static number nrnSub(number a, number b, const coeffs r)
236 {
237  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
238  mpz_init(erg);
239  mpz_sub(erg, (mpz_ptr)a, (mpz_ptr) b);
240  mpz_mod(erg, erg, r->modNumber);
241  return (number) erg;
242 }
243 
244 static BOOLEAN nrnIsZero(number a, const coeffs)
245 {
246  return 0 == mpz_sgn1((mpz_ptr)a);
247 }
248 
249 static number nrnNeg(number c, const coeffs r)
250 {
251  if( !nrnIsZero(c, r) )
252  // Attention: This method operates in-place.
253  mpz_sub((mpz_ptr)c, r->modNumber, (mpz_ptr)c);
254  return c;
255 }
256 
257 static number nrnInvers(number c, const coeffs r)
258 {
259  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
260  mpz_init(erg);
261  if (nrnIsZero(c,r))
262  {
263  WerrorS(nDivBy0);
264  }
265  else
266  {
267  mpz_invert(erg, (mpz_ptr)c, r->modNumber);
268  }
269  return (number) erg;
270 }
271 
272 /*
273  * Give the largest k, such that a = x * k, b = y * k has
274  * a solution.
275  * a may be NULL, b not
276  */
277 static number nrnGcd(number a, number b, const coeffs r)
278 {
279  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
280  mpz_init_set(erg, r->modNumber);
281  if (a != NULL) mpz_gcd(erg, erg, (mpz_ptr)a);
282  mpz_gcd(erg, erg, (mpz_ptr)b);
283  if(mpz_cmp(erg,r->modNumber)==0)
284  {
285  mpz_clear(erg);
287  return nrnInit(0,r);
288  }
289  return (number)erg;
290 }
291 
292 /*
293  * Give the smallest k, such that a * x = k = b * y has a solution
294  * TODO: lcm(gcd,gcd) better than gcd(lcm) ?
295  */
296 static number nrnLcm(number a, number b, const coeffs r)
297 {
298  number erg = nrnGcd(NULL, a, r);
299  number tmp = nrnGcd(NULL, b, r);
300  mpz_lcm((mpz_ptr)erg, (mpz_ptr)erg, (mpz_ptr)tmp);
301  nrnDelete(&tmp, r);
302  return (number)erg;
303 }
304 
305 /* Not needed any more, but may have room for improvement
306  number nrnGcd3(number a,number b, number c,ring r)
307 {
308  mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin);
309  mpz_init(erg);
310  if (a == NULL) a = (number)r->modNumber;
311  if (b == NULL) b = (number)r->modNumber;
312  if (c == NULL) c = (number)r->modNumber;
313  mpz_gcd(erg, (mpz_ptr)a, (mpz_ptr)b);
314  mpz_gcd(erg, erg, (mpz_ptr)c);
315  mpz_gcd(erg, erg, r->modNumber);
316  return (number)erg;
317 }
318 */
319 
320 /*
321  * Give the largest k, such that a = x * k, b = y * k has
322  * a solution and r, s, s.t. k = s*a + t*b
323  * CF: careful: ExtGcd is wrong as implemented (or at least may not
324  * give you what you want:
325  * ExtGcd(5, 10 modulo 12):
326  * the gcdext will return 5 = 1*5 + 0*10
327  * however, mod 12, the gcd should be 1
328  */
329 static number nrnExtGcd(number a, number b, number *s, number *t, const coeffs r)
330 {
331  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
332  mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin);
333  mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin);
334  mpz_init(erg);
335  mpz_init(bs);
336  mpz_init(bt);
337  mpz_gcdext(erg, bs, bt, (mpz_ptr)a, (mpz_ptr)b);
338  mpz_mod(bs, bs, r->modNumber);
339  mpz_mod(bt, bt, r->modNumber);
340  *s = (number)bs;
341  *t = (number)bt;
342  return (number)erg;
343 }
344 
345 static BOOLEAN nrnIsOne(number a, const coeffs)
346 {
347  return 0 == mpz_cmp_si((mpz_ptr)a, 1);
348 }
349 
350 static BOOLEAN nrnEqual(number a, number b, const coeffs)
351 {
352  return 0 == mpz_cmp((mpz_ptr)a, (mpz_ptr)b);
353 }
354 
355 static number nrnGetUnit(number k, const coeffs r)
356 {
357  if (mpz_divisible_p(r->modNumber, (mpz_ptr)k)) return nrnInit(1,r);
358 
359  mpz_ptr unit = (mpz_ptr)nrnGcd(NULL, k, r);
360  mpz_tdiv_q(unit, (mpz_ptr)k, unit);
361  mpz_ptr gcd = (mpz_ptr)nrnGcd(NULL, (number)unit, r);
362  if (!nrnIsOne((number)gcd,r))
363  {
364  mpz_ptr ctmp;
365  // tmp := unit^2
366  mpz_ptr tmp = (mpz_ptr) nrnMult((number) unit,(number) unit,r);
367  // gcd_new := gcd(tmp, 0)
368  mpz_ptr gcd_new = (mpz_ptr) nrnGcd(NULL, (number) tmp, r);
369  while (!nrnEqual((number) gcd_new,(number) gcd,r))
370  {
371  // gcd := gcd_new
372  ctmp = gcd;
373  gcd = gcd_new;
374  gcd_new = ctmp;
375  // tmp := tmp * unit
376  mpz_mul(tmp, tmp, unit);
377  mpz_mod(tmp, tmp, r->modNumber);
378  // gcd_new := gcd(tmp, 0)
379  mpz_gcd(gcd_new, tmp, r->modNumber);
380  }
381  // unit := unit + modNumber / gcd_new
382  mpz_tdiv_q(tmp, r->modNumber, gcd_new);
383  mpz_add(unit, unit, tmp);
384  mpz_mod(unit, unit, r->modNumber);
385  nrnDelete((number*) &gcd_new, r);
386  nrnDelete((number*) &tmp, r);
387  }
388  nrnDelete((number*) &gcd, r);
389  return (number)unit;
390 }
391 
392 /* XExtGcd returns a unimodular matrix ((s,t)(u,v)) sth.
393  * (a,b)^t ((st)(uv)) = (g,0)^t
394  * Beware, the ExtGcd will not necessaairly do this.
395  * Problem: if g = as+bt then (in Z/nZ) it follows NOT that
396  * 1 = (a/g)s + (b/g) t
397  * due to the zero divisors.
398  */
399 
400 //#define CF_DEB;
401 static number nrnXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
402 {
403  number xx;
404 #ifdef CF_DEB
405  StringSetS("XExtGcd of ");
406  nrnWrite(a, r);
407  StringAppendS("\t");
408  nrnWrite(b, r);
409  StringAppendS(" modulo ");
410  nrnWrite(xx = (number)r->modNumber, r);
411  Print("%s\n", StringEndS());
412 #endif
413 
414  mpz_ptr one = (mpz_ptr)omAllocBin(gmp_nrz_bin);
415  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
416  mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin);
417  mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin);
418  mpz_ptr bu = (mpz_ptr)omAllocBin(gmp_nrz_bin);
419  mpz_ptr bv = (mpz_ptr)omAllocBin(gmp_nrz_bin);
420  mpz_init(erg);
421  mpz_init(one);
422  mpz_init_set(bs, (mpz_ptr) a);
423  mpz_init_set(bt, (mpz_ptr) b);
424  mpz_init(bu);
425  mpz_init(bv);
426  mpz_gcd(erg, bs, bt);
427 
428 #ifdef CF_DEB
429  StringSetS("1st gcd:");
430  nrnWrite(xx= (number)erg, r);
431 #endif
432 
433  mpz_gcd(erg, erg, r->modNumber);
434 
435  mpz_div(bs, bs, erg);
436  mpz_div(bt, bt, erg);
437 
438 #ifdef CF_DEB
439  Print("%s\n", StringEndS());
440  StringSetS("xgcd: ");
441 #endif
442 
443  mpz_gcdext(one, bu, bv, bs, bt);
444  number ui = nrnGetUnit(xx = (number) one, r);
445 #ifdef CF_DEB
446  n_Write(xx, r);
447  StringAppendS("\t");
448  n_Write(ui, r);
449  Print("%s\n", StringEndS());
450 #endif
451  nrnDelete(&xx, r);
452  if (!nrnIsOne(ui, r))
453  {
454 #ifdef CF_DEB
455  PrintS("Scaling\n");
456 #endif
457  number uii = nrnInvers(ui, r);
458  nrnDelete(&ui, r);
459  ui = uii;
460  mpz_ptr uu = (mpz_ptr)omAllocBin(gmp_nrz_bin);
461  mpz_init_set(uu, (mpz_ptr)ui);
462  mpz_mul(bu, bu, uu);
463  mpz_mul(bv, bv, uu);
464  mpz_clear(uu);
465  omFreeBin(uu, gmp_nrz_bin);
466  }
467  nrnDelete(&ui, r);
468 #ifdef CF_DEB
469  StringSetS("xgcd");
470  nrnWrite(xx= (number)bs, r);
471  StringAppendS("*");
472  nrnWrite(xx= (number)bu, r);
473  StringAppendS(" + ");
474  nrnWrite(xx= (number)bt, r);
475  StringAppendS("*");
476  nrnWrite(xx= (number)bv, r);
477  Print("%s\n", StringEndS());
478 #endif
479 
480  mpz_mod(bs, bs, r->modNumber);
481  mpz_mod(bt, bt, r->modNumber);
482  mpz_mod(bu, bu, r->modNumber);
483  mpz_mod(bv, bv, r->modNumber);
484  *s = (number)bu;
485  *t = (number)bv;
486  *u = (number)bt;
487  *u = nrnNeg(*u, r);
488  *v = (number)bs;
489  return (number)erg;
490 }
491 
492 static BOOLEAN nrnIsMOne(number a, const coeffs r)
493 {
494  if((r->ch==2) && (nrnIsOne(a,r))) return FALSE;
495  mpz_t t; mpz_init_set(t, (mpz_ptr)a);
496  mpz_add_ui(t, t, 1);
497  bool erg = (0 == mpz_cmp(t, r->modNumber));
498  mpz_clear(t);
499  return erg;
500 }
501 
502 static BOOLEAN nrnGreater(number a, number b, const coeffs)
503 {
504  return 0 < mpz_cmp((mpz_ptr)a, (mpz_ptr)b);
505 }
506 
507 static BOOLEAN nrnGreaterZero(number k, const coeffs cf)
508 {
509  if (cf->is_field)
510  {
511  if (mpz_cmp_ui(cf->modBase,2)==0)
512  {
513  return TRUE;
514  }
515  #if 0
516  mpz_t ch2; mpz_init_set(ch2, cf->modBase);
517  mpz_sub_ui(ch2,ch2,1); //cf->modBase is odd
518  mpz_divexact_ui(ch2,ch2,2);
519  if (mpz_cmp(ch2,(mpz_ptr)k)<0)
520  {
521  mpz_clear(ch2);
522  return FALSE;
523  }
524  mpz_clear(ch2);
525  #endif
526  }
527  #if 0
528  else
529  {
530  mpz_t ch2; mpz_init_set(ch2, cf->modBase);
531  mpz_tdiv_q_ui(ch2,ch2,2);
532  if (mpz_cmp(ch2,(mpz_ptr)k)<0)
533  {
534  mpz_clear(ch2);
535  return FALSE;
536  }
537  mpz_clear(ch2);
538  }
539  #endif
540  return 0 < mpz_sgn1((mpz_ptr)k);
541 }
542 
543 static BOOLEAN nrnIsUnit(number a, const coeffs r)
544 {
545  number tmp = nrnGcd(a, (number)r->modNumber, r);
546  bool res = nrnIsOne(tmp, r);
547  nrnDelete(&tmp, r);
548  return res;
549 }
550 
551 static number nrnAnn(number k, const coeffs r)
552 {
553  mpz_ptr tmp = (mpz_ptr) omAllocBin(gmp_nrz_bin);
554  mpz_init(tmp);
555  mpz_gcd(tmp, (mpz_ptr) k, r->modNumber);
556  if (mpz_cmp_si(tmp, 1)==0)
557  {
558  mpz_set_ui(tmp, 0);
559  return (number) tmp;
560  }
561  mpz_divexact(tmp, r->modNumber, tmp);
562  return (number) tmp;
563 }
564 
565 static BOOLEAN nrnDivBy(number a, number b, const coeffs r)
566 {
567  /* b divides a iff b/gcd(a, b) is a unit in the given ring: */
568  number n = nrnGcd(a, b, r);
569  mpz_tdiv_q((mpz_ptr)n, (mpz_ptr)b, (mpz_ptr)n);
570  bool result = nrnIsUnit(n, r);
571  nrnDelete(&n, NULL);
572  return result;
573 }
574 
575 static int nrnDivComp(number a, number b, const coeffs r)
576 {
577  if (nrnEqual(a, b,r)) return 2;
578  if (mpz_divisible_p((mpz_ptr) a, (mpz_ptr) b)) return -1;
579  if (mpz_divisible_p((mpz_ptr) b, (mpz_ptr) a)) return 1;
580  return 0;
581 }
582 
583 static number nrnDiv(number a, number b, const coeffs r)
584 {
585  if (nrnIsZero(b,r))
586  {
587  WerrorS(nDivBy0);
588  return nrnInit(0,r);
589  }
590  else if (r->is_field)
591  {
592  number inv=nrnInvers(b,r);
593  number erg=nrnMult(a,inv,r);
594  nrnDelete(&inv,r);
595  return erg;
596  }
597  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
598  mpz_init(erg);
599  if (mpz_divisible_p((mpz_ptr)a, (mpz_ptr)b))
600  {
601  mpz_divexact(erg, (mpz_ptr)a, (mpz_ptr)b);
602  return (number)erg;
603  }
604  else
605  {
606  mpz_ptr gcd = (mpz_ptr)nrnGcd(a, b, r);
607  mpz_divexact(erg, (mpz_ptr)b, gcd);
608  if (!nrnIsUnit((number)erg, r))
609  {
610  WerrorS("Division not possible, even by cancelling zero divisors.");
611  nrnDelete((number*) &gcd, r);
612  nrnDelete((number*) &erg, r);
613  return (number)NULL;
614  }
615  // a / gcd(a,b) * [b / gcd (a,b)]^(-1)
616  mpz_ptr tmp = (mpz_ptr)nrnInvers((number) erg,r);
617  mpz_divexact(erg, (mpz_ptr)a, gcd);
618  mpz_mul(erg, erg, tmp);
619  nrnDelete((number*) &gcd, r);
620  nrnDelete((number*) &tmp, r);
621  mpz_mod(erg, erg, r->modNumber);
622  return (number)erg;
623  }
624 }
625 
626 static number nrnMod(number a, number b, const coeffs r)
627 {
628  /*
629  We need to return the number rr which is uniquely determined by the
630  following two properties:
631  (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z)
632  (2) There exists some k in the integers Z such that a = k * b + rr.
633  Consider g := gcd(n, |b|). Note that then |b|/g is a unit in Z/n.
634  Now, there are three cases:
635  (a) g = 1
636  Then |b| is a unit in Z/n, i.e. |b| (and also b) divides a.
637  Thus rr = 0.
638  (b) g <> 1 and g divides a
639  Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0.
640  (c) g <> 1 and g does not divide a
641  Then denote the division with remainder of a by g as this:
642  a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b|
643  fulfills (1) and (2), i.e. rr := t is the correct result. Hence
644  in this third case, rr is the remainder of division of a by g in Z.
645  Remark: according to mpz_mod: a,b are always non-negative
646  */
647  mpz_ptr g = (mpz_ptr)omAllocBin(gmp_nrz_bin);
648  mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin);
649  mpz_init(g);
650  mpz_init_set_ui(rr, 0);
651  mpz_gcd(g, (mpz_ptr)r->modNumber, (mpz_ptr)b); // g is now as above
652  if (mpz_cmp_si(g, 1L) != 0) mpz_mod(rr, (mpz_ptr)a, g); // the case g <> 1
653  mpz_clear(g);
655  return (number)rr;
656 }
657 
658 /* CF: note that Z/nZ has (at least) two distinct euclidean structures
659  * 1st phi(a) := (a mod n) which is just the structure directly
660  * inherited from Z
661  * 2nd phi(a) := gcd(a, n)
662  * The 1st version is probably faster as everything just comes from Z,
663  * but the 2nd version behaves nicely wrt. to quotient operations
664  * and HNF and such. In agreement with nrnMod we imlement the 2nd here
665  *
666  * For quotrem note that if b exactly divides a, then
667  * min(v_p(a), v_p(n)) >= min(v_p(b), v_p(n))
668  * so if we divide a and b by g:= gcd(a,b,n), then b becomes a
669  * unit mod n/g.
670  * Thus we 1st compute the remainder (similar to nrnMod) and then
671  * the exact quotient.
672  */
673 static number nrnQuotRem(number a, number b, number * rem, const coeffs r)
674 {
675  mpz_t g, aa, bb;
676  mpz_ptr qq = (mpz_ptr)omAllocBin(gmp_nrz_bin);
677  mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin);
678  mpz_init(qq);
679  mpz_init(rr);
680  mpz_init(g);
681  mpz_init_set(aa, (mpz_ptr)a);
682  mpz_init_set(bb, (mpz_ptr)b);
683 
684  mpz_gcd(g, bb, r->modNumber);
685  mpz_mod(rr, aa, g);
686  mpz_sub(aa, aa, rr);
687  mpz_gcd(g, aa, g);
688  mpz_div(aa, aa, g);
689  mpz_div(bb, bb, g);
690  mpz_div(g, r->modNumber, g);
691  mpz_invert(g, bb, g);
692  mpz_mul(qq, aa, g);
693  if (rem)
694  *rem = (number)rr;
695  else {
696  mpz_clear(rr);
697  omFreeBin(rr, gmp_nrz_bin);
698  }
699  mpz_clear(g);
700  mpz_clear(aa);
701  mpz_clear(bb);
702  return (number) qq;
703 }
704 
705 /*
706  * Helper function for computing the module
707  */
708 
710 
711 static number nrnMapModN(number from, const coeffs /*src*/, const coeffs dst)
712 {
713  return nrnMult(from, (number) nrnMapCoef, dst);
714 }
715 
716 static number nrnMap2toM(number from, const coeffs /*src*/, const coeffs dst)
717 {
718  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
719  mpz_init(erg);
720  mpz_mul_ui(erg, nrnMapCoef, (unsigned long)from);
721  mpz_mod(erg, erg, dst->modNumber);
722  return (number)erg;
723 }
724 
725 static number nrnMapZp(number from, const coeffs /*src*/, const coeffs dst)
726 {
727  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
728  mpz_init(erg);
729  // TODO: use npInt(...)
730  mpz_mul_si(erg, nrnMapCoef, (unsigned long)from);
731  mpz_mod(erg, erg, dst->modNumber);
732  return (number)erg;
733 }
734 
735 number nrnMapGMP(number from, const coeffs /*src*/, const coeffs dst)
736 {
737  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
738  mpz_init(erg);
739  mpz_mod(erg, (mpz_ptr)from, dst->modNumber);
740  return (number)erg;
741 }
742 
743 static number nrnMapQ(number from, const coeffs src, const coeffs dst)
744 {
745  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
746  nlMPZ(erg, from, src);
747  mpz_mod(erg, erg, dst->modNumber);
748  return (number)erg;
749 }
750 
751 #if SI_INTEGER_VARIANT==3
752 static number nrnMapZ(number from, const coeffs /*src*/, const coeffs dst)
753 {
754  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
755  if (n_Z_IS_SMALL(from))
756  mpz_init_set_si(erg, SR_TO_INT(from));
757  else
758  mpz_init_set(erg, (mpz_ptr) from);
759  mpz_mod(erg, erg, dst->modNumber);
760  return (number)erg;
761 }
762 #elif SI_INTEGER_VARIANT==2
763 
764 static number nrnMapZ(number from, const coeffs src, const coeffs dst)
765 {
766  if (SR_HDL(from) & SR_INT)
767  {
768  long f_i=SR_TO_INT(from);
769  return nrnInit(f_i,dst);
770  }
771  return nrnMapGMP(from,src,dst);
772 }
773 #elif SI_INTEGER_VARIANT==1
774 static number nrnMapZ(number from, const coeffs src, const coeffs dst)
775 {
776  return nrnMapQ(from,src,dst);
777 }
778 #endif
779 void nrnWrite (number a, const coeffs /*cf*/)
780 {
781  char *s,*z;
782  if (a==NULL)
783  {
784  StringAppendS("o");
785  }
786  else
787  {
788  int l=mpz_sizeinbase((mpz_ptr) a, 10) + 2;
789  s=(char*)omAlloc(l);
790  z=mpz_get_str(s,10,(mpz_ptr) a);
791  StringAppendS(z);
792  omFreeSize((ADDRESS)s,l);
793  }
794 }
795 
796 nMapFunc nrnSetMap(const coeffs src, const coeffs dst)
797 {
798  /* dst = nrn */
799  if ((src->rep==n_rep_gmp) && nCoeff_is_Z(src))
800  {
801  return nrnMapZ;
802  }
803  if ((src->rep==n_rep_gap_gmp) /*&& nCoeff_is_Z(src)*/)
804  {
805  return nrnMapZ;
806  }
807  if (src->rep==n_rep_gap_rat) /*&& nCoeff_is_Q(src)) or Z*/
808  {
809  return nrnMapQ;
810  }
811  // Some type of Z/n ring / field
812  if (nCoeff_is_Zn(src) || nCoeff_is_Ring_PtoM(src) ||
813  nCoeff_is_Ring_2toM(src) || nCoeff_is_Zp(src))
814  {
815  if ( (!nCoeff_is_Zp(src))
816  && (mpz_cmp(src->modBase, dst->modBase) == 0)
817  && (src->modExponent == dst->modExponent)) return ndCopyMap;
818  else
819  {
820  mpz_ptr nrnMapModul = (mpz_ptr) omAllocBin(gmp_nrz_bin);
821  // Computing the n of Z/n
822  if (nCoeff_is_Zp(src))
823  {
824  mpz_init_set_si(nrnMapModul, src->ch);
825  }
826  else
827  {
828  mpz_init(nrnMapModul);
829  mpz_set(nrnMapModul, src->modNumber);
830  }
831  // nrnMapCoef = 1 in dst if dst is a subring of src
832  // nrnMapCoef = 0 in dst / src if src is a subring of dst
833  if (nrnMapCoef == NULL)
834  {
835  nrnMapCoef = (mpz_ptr) omAllocBin(gmp_nrz_bin);
836  mpz_init(nrnMapCoef);
837  }
838  if (mpz_divisible_p(nrnMapModul, dst->modNumber))
839  {
840  mpz_set_ui(nrnMapCoef, 1);
841  }
842  else
843  if (mpz_divisible_p(dst->modNumber,nrnMapModul))
844  {
845  mpz_divexact(nrnMapCoef, dst->modNumber, nrnMapModul);
846  mpz_ptr tmp = dst->modNumber;
847  dst->modNumber = nrnMapModul;
848  if (!nrnIsUnit((number) nrnMapCoef,dst))
849  {
850  dst->modNumber = tmp;
851  nrnDelete((number*) &nrnMapModul, dst);
852  return NULL;
853  }
854  mpz_ptr inv = (mpz_ptr) nrnInvers((number) nrnMapCoef,dst);
855  dst->modNumber = tmp;
856  mpz_mul(nrnMapCoef, nrnMapCoef, inv);
857  mpz_mod(nrnMapCoef, nrnMapCoef, dst->modNumber);
858  nrnDelete((number*) &inv, dst);
859  }
860  else
861  {
862  nrnDelete((number*) &nrnMapModul, dst);
863  return NULL;
864  }
865  nrnDelete((number*) &nrnMapModul, dst);
866  if (nCoeff_is_Ring_2toM(src))
867  return nrnMap2toM;
868  else if (nCoeff_is_Zp(src))
869  return nrnMapZp;
870  else
871  return nrnMapModN;
872  }
873  }
874  return NULL; // default
875 }
876 
877 static number nrnInitMPZ(mpz_t m, const coeffs r)
878 {
879  mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin);
880  mpz_init_set(erg,m);
881  mpz_mod(erg, erg, r->modNumber);
882  return (number) erg;
883 }
884 
885 static void nrnMPZ(mpz_t m, number &n, const coeffs)
886 {
887  mpz_init_set(m, (mpz_ptr)n);
888 }
889 
890 /*
891  * set the exponent (allocate and init tables) (TODO)
892  */
893 
894 static void nrnSetExp(unsigned long m, coeffs r)
895 {
896  /* clean up former stuff */
897  if (r->modNumber != NULL) mpz_clear(r->modNumber);
898 
899  r->modExponent= m;
900  r->modNumber = (mpz_ptr)omAllocBin(gmp_nrz_bin);
901  mpz_init_set (r->modNumber, r->modBase);
902  mpz_pow_ui (r->modNumber, r->modNumber, m);
903 }
904 
905 /* We expect this ring to be Z/n^m for some m > 0 and for some n > 2 which is not a prime. */
906 static void nrnInitExp(unsigned long m, coeffs r)
907 {
908  nrnSetExp(m, r);
909  assume (r->modNumber != NULL);
910 //CF: in general, the modulus is computed somewhere. I don't want to
911 // check it's size before I construct the best ring.
912 // if (mpz_cmp_ui(r->modNumber,2) <= 0)
913 // WarnS("nrnInitExp failed (m in Z/m too small)");
914 }
915 
916 #ifdef LDEBUG
917 static BOOLEAN nrnDBTest (number a, const char *f, const int l, const coeffs r)
918 {
919  if ( (mpz_sgn1((mpz_ptr) a) < 0) || (mpz_cmp((mpz_ptr) a, r->modNumber) > 0) )
920  {
921  Warn("mod-n: out of range at %s:%d\n",f,l);
922  return FALSE;
923  }
924  return TRUE;
925 }
926 #endif
927 
928 /*2
929 * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc)
930 */
931 static const char * nlCPEatLongC(char *s, mpz_ptr i)
932 {
933  const char * start=s;
934  if (!(*s >= '0' && *s <= '9'))
935  {
936  mpz_init_set_ui(i, 1);
937  return s;
938  }
939  mpz_init(i);
940  while (*s >= '0' && *s <= '9') s++;
941  if (*s=='\0')
942  {
943  mpz_set_str(i,start,10);
944  }
945  else
946  {
947  char c=*s;
948  *s='\0';
949  mpz_set_str(i,start,10);
950  *s=c;
951  }
952  return s;
953 }
954 
955 static const char * nrnRead (const char *s, number *a, const coeffs r)
956 {
957  mpz_ptr z = (mpz_ptr) omAllocBin(gmp_nrz_bin);
958  {
959  s = nlCPEatLongC((char *)s, z);
960  }
961  mpz_mod(z, z, r->modNumber);
962  if ((*s)=='/')
963  {
964  mpz_ptr n = (mpz_ptr) omAllocBin(gmp_nrz_bin);
965  s++;
966  s=nlCPEatLongC((char*)s,n);
967  if (!nrnIsOne((number)n,r))
968  {
969  *a=nrnDiv((number)z,(number)n,r);
970  mpz_clear(z);
971  omFreeBin((void *)z, gmp_nrz_bin);
972  mpz_clear(n);
973  omFreeBin((void *)n, gmp_nrz_bin);
974  }
975  }
976  else
977  *a = (number) z;
978  return s;
979 }
980 
981 static number nrnConvFactoryNSingN( const CanonicalForm n, const coeffs r)
982 {
983  return nrnInit(n.intval(),r);
984 }
985 
986 static CanonicalForm nrnConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs r )
987 {
988  if (setChar) setCharacteristic( r->ch );
989  return CanonicalForm(nrnInt( n,r ));
990 }
991 
992 /* for initializing function pointers */
994 {
995  assume( (getCoeffType(r) == n_Zn) || (getCoeffType (r) == n_Znm) );
996  ZnmInfo * info= (ZnmInfo *) p;
997  r->modBase= (mpz_ptr)nrnCopy((number)info->base, r); //this circumvents the problem
998  //in bigintmat.cc where we cannot create a "legal" nrn that can be freed.
999  //If we take a copy, we can do whatever we want.
1000 
1001  nrnInitExp (info->exp, r);
1002 
1003  /* next computation may yield wrong characteristic as r->modNumber
1004  is a GMP number */
1005  r->ch = mpz_get_ui(r->modNumber);
1006 
1007  r->is_field=FALSE;
1008  r->is_domain=FALSE;
1009  r->rep=n_rep_gmp;
1010 
1011  r->cfInit = nrnInit;
1012  r->cfDelete = nrnDelete;
1013  r->cfCopy = nrnCopy;
1014  r->cfSize = nrnSize;
1015  r->cfInt = nrnInt;
1016  r->cfAdd = nrnAdd;
1017  r->cfInpAdd = nrnInpAdd;
1018  r->cfSub = nrnSub;
1019  r->cfMult = nrnMult;
1020  r->cfInpMult = nrnInpMult;
1021  r->cfDiv = nrnDiv;
1022  r->cfAnn = nrnAnn;
1023  r->cfIntMod = nrnMod;
1024  r->cfExactDiv = nrnDiv;
1025  r->cfInpNeg = nrnNeg;
1026  r->cfInvers = nrnInvers;
1027  r->cfDivBy = nrnDivBy;
1028  r->cfDivComp = nrnDivComp;
1029  r->cfGreater = nrnGreater;
1030  r->cfEqual = nrnEqual;
1031  r->cfIsZero = nrnIsZero;
1032  r->cfIsOne = nrnIsOne;
1033  r->cfIsMOne = nrnIsMOne;
1034  r->cfGreaterZero = nrnGreaterZero;
1035  r->cfWriteLong = nrnWrite;
1036  r->cfRead = nrnRead;
1037  r->cfPower = nrnPower;
1038  r->cfSetMap = nrnSetMap;
1039  //r->cfNormalize = ndNormalize;
1040  r->cfLcm = nrnLcm;
1041  r->cfGcd = nrnGcd;
1042  r->cfIsUnit = nrnIsUnit;
1043  r->cfGetUnit = nrnGetUnit;
1044  r->cfExtGcd = nrnExtGcd;
1045  r->cfXExtGcd = nrnXExtGcd;
1046  r->cfQuotRem = nrnQuotRem;
1047  r->cfCoeffName = nrnCoeffName;
1048  r->nCoeffIsEqual = nrnCoeffIsEqual;
1049  r->cfKillChar = nrnKillChar;
1050  r->cfQuot1 = nrnQuot1;
1051  r->cfInitMPZ = nrnInitMPZ;
1052  r->cfMPZ = nrnMPZ;
1053 #if SI_INTEGER_VARIANT==2
1054  r->cfWriteFd = nrzWriteFd;
1055  r->cfReadFd = nrzReadFd;
1056 #endif
1057 
1058 #ifdef LDEBUG
1059  r->cfDBTest = nrnDBTest;
1060 #endif
1061  if ((r->modExponent==1)&&(mpz_size1(r->modBase)==1))
1062  {
1063  long p=mpz_get_si(r->modBase);
1064  if ((p<=FACTORY_MAX_PRIME)&&(p==IsPrime(p))) /*factory limit: <2^29*/
1065  {
1066  r->convFactoryNSingN=nrnConvFactoryNSingN;
1067  r->convSingNFactoryN=nrnConvSingNFactoryN;
1068  }
1069  }
1070  return FALSE;
1071 }
1072 
1073 #endif
1074 /* #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:813
number ndCopyMap(number a, const coeffs src, const coeffs dst)
Definition: numbers.cc:291
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_PtoM(const coeffs r)
Definition: coeffs.h:724
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:413
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:422
static FORCE_INLINE BOOLEAN nCoeff_is_Zn(const coeffs r)
Definition: coeffs.h:823
static FORCE_INLINE void n_Write(number n, const coeffs r, const BOOLEAN bShortOut=TRUE)
Definition: coeffs.h:588
static FORCE_INLINE BOOLEAN nCoeff_is_Zp(const coeffs r)
Definition: coeffs.h:797
static FORCE_INLINE BOOLEAN nCoeff_is_Ring_2toM(const coeffs r)
Definition: coeffs.h:721
@ 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:389
#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:698
char * nEati(char *s, int *i, int m)
divide by the first (leading) number and return it, i.e. make monic
Definition: numbers.cc:677
const char *const nDivBy0
Definition: numbers.h:89
#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:955
static number nrnMap2toM(number from, const coeffs, const coeffs dst)
Definition: rmodulon.cc:716
static coeffs nrnQuot1(number c, const coeffs r)
Definition: rmodulon.cc:105
static const char * nlCPEatLongC(char *s, mpz_ptr i)
Definition: rmodulon.cc:931
static number nrnInit(long i, const coeffs r)
Definition: rmodulon.cc:160
STATIC_VAR char * nrnCoeffName_buff
Definition: rmodulon.cc:65
static BOOLEAN nrnDBTest(number a, const char *f, const int l, const coeffs r)
Definition: rmodulon.cc:917
static void nrnKillChar(coeffs r)
Definition: rmodulon.cc:97
#define nrnSize
Definition: rmodulon.cc:178
static BOOLEAN nrnGreater(number a, number b, const coeffs)
Definition: rmodulon.cc:502
STATIC_VAR mpz_ptr nrnMapCoef
Definition: rmodulon.cc:709
static BOOLEAN nrnIsZero(number a, const coeffs)
Definition: rmodulon.cc:244
static CanonicalForm nrnConvSingNFactoryN(number n, BOOLEAN setChar, const coeffs r)
Definition: rmodulon.cc:986
static number nrnExtGcd(number a, number b, number *s, number *t, const coeffs r)
Definition: rmodulon.cc:329
static void nrnMPZ(mpz_t m, number &n, const coeffs)
Definition: rmodulon.cc:885
static BOOLEAN nrnCoeffIsEqual(const coeffs r, n_coeffType n, void *parameter)
Definition: rmodulon.cc:89
static void nrnInpMult(number &a, number b, const coeffs r)
Definition: rmodulon.cc:206
void nrnWrite(number a, const coeffs)
Definition: rmodulon.cc:779
static number nrnMod(number a, number b, const coeffs r)
Definition: rmodulon.cc:626
coeffs nrnInitCfByName(char *s, n_coeffType)
Definition: rmodulon.cc:35
static number nrnMapZ(number from, const coeffs src, const coeffs dst)
Definition: rmodulon.cc:764
static number nrnInitMPZ(mpz_t m, const coeffs r)
Definition: rmodulon.cc:877
static void nrnInitExp(unsigned long m, coeffs r)
Definition: rmodulon.cc:906
static number nrnAnn(number k, const coeffs r)
Definition: rmodulon.cc:551
static char * nrnCoeffName(const coeffs r)
Definition: rmodulon.cc:66
static BOOLEAN nrnIsUnit(number a, const coeffs r)
Definition: rmodulon.cc:543
#define nrnDelete
Definition: rmodulon.cc:177
nMapFunc nrnSetMap(const coeffs src, const coeffs dst)
Definition: rmodulon.cc:796
static number nrnMapZp(number from, const coeffs, const coeffs dst)
Definition: rmodulon.cc:725
static number nrnInvers(number c, const coeffs r)
Definition: rmodulon.cc:257
static number nrnConvFactoryNSingN(const CanonicalForm n, const coeffs r)
Definition: rmodulon.cc:981
static void nrnSetExp(unsigned long m, coeffs r)
Definition: rmodulon.cc:894
static int nrnDivComp(number a, number b, const coeffs r)
Definition: rmodulon.cc:575
static number nrnXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
Definition: rmodulon.cc:401
static BOOLEAN nrnEqual(number a, number b, const coeffs)
Definition: rmodulon.cc:350
static number nrnQuotRem(number a, number b, number *rem, const coeffs r)
Definition: rmodulon.cc:673
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:743
EXTERN_VAR omBin gmp_nrz_bin
Definition: rmodulon.cc:33
static BOOLEAN nrnIsOne(number a, const coeffs)
Definition: rmodulon.cc:345
static number nrnCopy(number a, const coeffs)
Definition: rmodulon.cc:150
static number nrnSub(number a, number b, const coeffs r)
Definition: rmodulon.cc:235
static number nrnLcm(number a, number b, const coeffs r)
Definition: rmodulon.cc:296
static number nrnMapModN(number from, const coeffs, const coeffs dst)
Definition: rmodulon.cc:711
static void nrnPower(number a, int i, number *result, const coeffs r)
Definition: rmodulon.cc:212
static number nrnMult(number a, number b, const coeffs r)
Definition: rmodulon.cc:197
static number nrnNeg(number c, const coeffs r)
Definition: rmodulon.cc:249
static number nrnGetUnit(number k, const coeffs r)
Definition: rmodulon.cc:355
number nrnMapGMP(number from, const coeffs, const coeffs dst)
Definition: rmodulon.cc:735
static number nrnDiv(number a, number b, const coeffs r)
Definition: rmodulon.cc:583
static BOOLEAN nrnIsMOne(number a, const coeffs r)
Definition: rmodulon.cc:492
static BOOLEAN nrnDivBy(number a, number b, const coeffs r)
Definition: rmodulon.cc:565
static BOOLEAN nrnGreaterZero(number k, const coeffs cf)
Definition: rmodulon.cc:507
BOOLEAN nrnInitChar(coeffs r, void *p)
Definition: rmodulon.cc:993
static number nrnAdd(number a, number b, const coeffs r)
Definition: rmodulon.cc:220
static number nrnGcd(number a, number b, const coeffs r)
Definition: rmodulon.cc:277
static void nrnInpAdd(number &a, number b, const coeffs r)
Definition: rmodulon.cc:229
#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