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1 /*****************************************
2 * Computer Algebra System SINGULAR *
3 *****************************************/
4 
5 /*
6 * ABSTRACT: interface to coefficient aritmetics
7 */
8 
9 #include <string.h>
10 #include <stdlib.h>
11 
12 #include "misc/auxiliary.h"
13 #include "misc/mylimits.h"
14 #include "factory/factory.h"
15 
16 #include "reporter/reporter.h"
17 
18 #include "coeffs/coeffs.h"
19 #include "coeffs/numbers.h"
20 
21 #include "coeffs/longrat.h"
22 #include "coeffs/modulop.h"
23 #include "coeffs/gnumpfl.h"
24 #include "coeffs/gnumpc.h"
25 #include "coeffs/ffields.h"
26 #include "coeffs/shortfl.h"
27 #include "coeffs/ntupel.h"
28 #include "coeffs/flintcf_Qrat.h"
29 
30 #ifdef HAVE_RINGS
31 #include "coeffs/rmodulo2m.h"
32 #include "coeffs/rmodulon.h"
33 #include "coeffs/rintegers.h"
34 #endif
35 
36 #ifdef HAVE_POLYEXTENSIONS
39 #endif
40 
41 
42 //static int characteristic = 0;
43 //extern int IsPrime(int p);
44 
46 
47 void nNew(number* d) { *d=NULL; }
48 
49 
50 static void ndDelete(number* d, const coeffs) { *d=NULL; }
51 static number ndAnn(number, const coeffs) { return NULL;}
52 static char* ndCoeffString(const coeffs r)
53 {
54  return omStrDup(r->cfCoeffName(r));
55 }
56 static void ndCoeffWrite(const coeffs r,BOOLEAN)
57 {
58  PrintS(r->cfCoeffName(r));
59 }
60 static char* ndCoeffName(const coeffs r)
61 {
62  STATIC_VAR char s[20];
63  snprintf(s,11,"Coeffs(%d)",r->type);
64  return s;
65 }
66 static void ndInpMult(number &a, number b, const coeffs r)
67 {
68  number n=r->cfMult(a,b,r);
69  r->cfDelete(&a,r);
70  a=n;
71 }
72 static void ndInpAdd(number &a, number b, const coeffs r)
73 {
74  number n=r->cfAdd(a,b,r);
75  r->cfDelete(&a,r);
76  a=n;
77 }
78 
79 static void ndPower(number a, int i, number * res, const coeffs r)
80 {
81  if (i==0)
82  {
83  *res = r->cfInit(1, r);
84  }
85  else if (i==1)
86  {
87  *res = r->cfCopy(a, r);
88  }
89  else if (i==2)
90  {
91  *res = r->cfMult(a, a, r);
92  }
93  else if (i<0)
94  {
95  number b = r->cfInvers(a, r);
96  ndPower(b, -i, res, r);
97  r->cfDelete(&b, r);
98  }
99  else
100  {
101  ndPower(a, i/2, res, r);
102  r->cfInpMult(*res, *res, r);
103  if (i&1)
104  {
105  r->cfInpMult(*res, a, r);
106  }
107  }
108 }
109 static number ndInvers(number a, const coeffs r)
110 {
111  number one=r->cfInit(1,r);
112  number res=r->cfDiv(one,a,r);
113  r->cfDelete(&one,r);
114  return res;
115 }
116 
117 static BOOLEAN ndIsUnit_Ring(number a, const coeffs r)
118 { return r->cfIsOne(a,r)|| r->cfIsMOne(a,r); }
119 static BOOLEAN ndIsUnit_Field(number a, const coeffs r)
120 { return !r->cfIsZero(a,r); }
121 static number ndGetUnit_Ring(number, const coeffs r)
122 { return r->cfInit(1,r); }
123 #ifdef LDEBUG
124 // static void nDBDummy1(number* d,char *, int) { *d=NULL; }
125 static BOOLEAN ndDBTest(number, const char *, const int, const coeffs){ return TRUE; }
126 #endif
127 
128 static number ndFarey(number,number,const coeffs r)
129 {
130  Werror("farey not implemented for %s (c=%d)",r->cfCoeffName(r),getCoeffType(r));
131  return NULL;
132 }
133 static number ndChineseRemainder(number *,number *,int,BOOLEAN,CFArray&,const coeffs r)
134 {
135  Werror("ChineseRemainder not implemented for %s (c=%d)",r->cfCoeffName(r),getCoeffType(r));
136  return r->cfInit(0,r);
137 }
138 
139 static int ndParDeg(number n, const coeffs r)
140 {
141  return (-r->cfIsZero(n,r));
142 }
143 
144 static number ndParameter(const int, const coeffs r)
145 {
146  return r->cfInit(1,r);
147 }
148 
149 BOOLEAN n_IsZeroDivisor( number a, const coeffs r)
150 {
151  BOOLEAN ret = n_IsZero(a, r);
152  int c = n_GetChar(r);
153  if (ret || (c==0) || (r->is_field))
154  return ret; /*n_IsZero(a, r)*/
155  number ch = n_Init( c, r );
156  number g = n_Gcd( ch, a, r );
157  ret = !n_IsOne (g, r);
158  n_Delete(&ch, r);
159  n_Delete(&g, r);
160  return ret;
161 }
162 
163 void ndNormalize(number&, const coeffs) { }
164 static number ndReturn0(number, const coeffs r) { return r->cfInit(0,r); }
165 number ndGcd(number, number, const coeffs r) { return r->cfInit(1,r); }
166 static number ndIntMod(number, number, const coeffs r) { return r->cfInit(0,r); }
167 static number ndGetDenom(number &, const coeffs r) { return r->cfInit(1,r); }
168 static number ndGetNumerator(number &a,const coeffs r) { return r->cfCopy(a,r); }
169 static int ndSize(number a, const coeffs r) { return (int)r->cfIsZero(a,r)==FALSE; }
170 
171 static void ndClearContent(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs r)
172 {
173  assume(r != NULL);
174 
175  // no fractions
176  assume(!( nCoeff_is_Q(r) ));
177  // all coeffs are given by integers!!!
178 
179  numberCollectionEnumerator.Reset();
180 
181  if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial?
182  {
183  c = n_Init(1, r);
184  return;
185  }
186 
187  number &curr = numberCollectionEnumerator.Current();
188 
189 #ifdef HAVE_RINGS
190  /// TODO: move to a separate implementation
191  if (nCoeff_is_Ring(r))
192  {
193  if (nCoeff_has_Units(r))
194  {
195  c = n_GetUnit(curr, r);
196 
197  if (!n_IsOne(c, r))
198  {
199  number inv = n_Invers(c, r);
200 
201  n_InpMult(curr, inv, r);
202 
203  while( numberCollectionEnumerator.MoveNext() )
204  {
205  number &n = numberCollectionEnumerator.Current();
206  n_Normalize(n, r); // ?
207  n_InpMult(n, inv, r); // TODO: either this or directly divide!!!?
208  }
209 
210  n_Delete(&inv, r);
211  }
212  } else c = n_Init(1, r);
213 
214  return;
215  }
216 #endif
217 
218  assume(!nCoeff_is_Ring(r));
220 
221  n_Normalize(curr, r); // Q: good/bad/ugly??
222 
223  if (!n_IsOne(curr, r))
224  {
225  number t = curr; // takes over the curr! note: not a reference!!!
226 
227  curr = n_Init(1, r); // ???
228 
229  number inv = n_Invers(t, r);
230 
231  while( numberCollectionEnumerator.MoveNext() )
232  {
233  number &n = numberCollectionEnumerator.Current();
234  n_InpMult(n, inv, r); // TODO: either this or directly divide!!!?
235 // n_Normalize(n, r); // ?
236  }
237 
238  n_Delete(&inv, r);
239 
240  c = t;
241  } else
242  c = n_Copy(curr, r); // c == 1 and nothing else to do...
243 }
244 
245 static void ndClearDenominators(ICoeffsEnumerator& /*numberCollectionEnumerator*/, number& d, const coeffs r)
246 {
247  assume( r != NULL );
250 
251  d = n_Init(1, r);
252 }
253 
254 static number ndCopy(number a, const coeffs) { return a; }
255 number ndCopyMap(number a, const coeffs aRing, const coeffs r)
256 {
257  // aRing and r need not be the same, but must be the same representation
258  assume(aRing->rep==r->rep);
260  return a;
261  else
262  return r->cfCopy(a, r);
263 }
264 
265 static void ndKillChar(coeffs) {}
266 static void ndSetChar(const coeffs) {}
267 
268 number nd_Copy(number a, const coeffs r) { return r->cfCopy(a, r); }
269 
270 #ifdef HAVE_RINGS
271 static BOOLEAN ndDivBy(number, number, const coeffs) { return TRUE; } // assume a,b !=0
272 static int ndDivComp(number, number, const coeffs) { return 2; }
273 static number ndExtGcd (number, number, number *, number *, const coeffs r) { return r->cfInit(1,r); }
274 #endif
275 
276 CanonicalForm ndConvSingNFactoryN( number, BOOLEAN /*setChar*/, const coeffs)
277 {
278  CanonicalForm term(0);
279  WerrorS("no conversion to factory");
280  return term;
281 }
282 
283 static number ndConvFactoryNSingN( const CanonicalForm, const coeffs)
284 {
285  WerrorS("no conversion from factory");
286  return NULL;
287 }
288 
289 /**< [in, out] a bigint number >= 0 */
290 /**< [out] the GMP equivalent */
291 /// Converts a non-negative bigint number into a GMP number.
292 static void ndMPZ(mpz_t result, number &n, const coeffs r)
293 {
294  mpz_init_set_si( result, r->cfInt(n, r) );
295 }
296 
297 static number ndInitMPZ(mpz_t m, const coeffs r)
298 {
299  return r->cfInit( mpz_get_si(m), r);
300 }
301 
302 
303 static BOOLEAN ndCoeffIsEqual(const coeffs r, n_coeffType n, void *)
304 {
305  /* test, if r is an instance of nInitCoeffs(n,parameter) */
306  /* if parameter is not needed */
307  return (n==r->type);
308 }
309 
310 static number ndQuotRem (number a, number b, number * r, const coeffs R)
311 {
312  // implementation for a field: r: 0, result: n_Div
313  assume(R->is_field);
314  *r=n_Init(0,R);
315  return n_Div(a,b,R);
316 }
319 { NULL, /*n_unknown */
320  npInitChar, /* n_Zp */
321  nlInitChar, /* n_Q */
322  nrInitChar, /* n_R */
323  nfInitChar, /* n_GF */
324  ngfInitChar, /* n_long_R */
325  #ifdef HAVE_POLYEXTENSIONS
326  n2pInitChar, /* n_polyExt */
327  naInitChar, /* n_algExt */
328  ntInitChar, /* n_transExt */
329  #else
330  NULL, /* n_polyExt */
331  NULL, /* n_algExt */
332  NULL, /* n_transExt */
333  #endif
334  ngcInitChar, /* n_long_C */
335  nnInitChar, /* n_nTupel */
336  #ifdef HAVE_RINGS
337  nrzInitChar, /* n_Z */
338  nrnInitChar, /* n_Zn */
339  nrnInitChar, /* n_Znm */
340  nr2mInitChar, /* n_Z2m */
341  #else
342  NULL, /* n_Z */
343  NULL, /* n_Zn */
344  NULL, /* n_Znm */
345  NULL, /* n_Z2m */
346  #endif
347  flintQrat_InitChar, /* n_FlintQrat */
348  NULL /* n_CF */
349 };
350 
352 /*2
353 * init operations for coeffs r
354 */
355 coeffs nInitChar(n_coeffType t, void * parameter)
356 {
357  n_Procs_s *n=cf_root;
358 
359  while((n!=NULL) && (n->nCoeffIsEqual!=NULL) && (!n->nCoeffIsEqual(n,t,parameter)))
360  n=n->next;
361 
362  if (n==NULL)
363  {
364  n=(n_Procs_s*)omAlloc0(sizeof(n_Procs_s));
365  n->next=cf_root;
366  n->ref=1;
367  n->type=t;
368 
369  // default entries (different from NULL) for some routines:
371  n->cfSize = ndSize;
374  n->cfImPart=ndReturn0;
375  n->cfDelete= ndDelete;
376  n->cfAnn = ndAnn;
379  n->cfCoeffName = ndCoeffName; // should alway be changed!
380  n->cfInpMult=ndInpMult;
381  n->cfInpAdd=ndInpAdd;
382  n->cfCopy = ndCopy;
383  n->cfIntMod=ndIntMod; /* dummy !! */
385  n->cfGcd = ndGcd;
386  n->cfNormalizeHelper = ndGcd; /* tricky, isn't it ?*/
387  n->cfLcm = ndGcd; /* tricky, isn't it ?*/
388  n->cfInitMPZ = ndInitMPZ;
389  n->cfMPZ = ndMPZ;
390  n->cfPower = ndPower;
391  n->cfQuotRem = ndQuotRem;
392  n->cfInvers = ndInvers;
393 
394  n->cfKillChar = ndKillChar; /* dummy */
395  n->cfSetChar = ndSetChar; /* dummy */
396  // temp. removed to catch all the coeffs which miss to implement this!
397 
399  n->cfFarey = ndFarey;
400  n->cfParDeg = ndParDeg;
401 
403 
406 
407  //n->cfIsUnit = ndIsUnit;
408 #ifdef HAVE_RINGS
409  n->cfDivComp = ndDivComp;
410  n->cfDivBy = ndDivBy;
411  n->cfExtGcd = ndExtGcd;
412  //n->cfGetUnit = ndGetUnit_Ring;// set afterwards
413 #endif
414 
415 #ifdef LDEBUG
416  n->cfDBTest=ndDBTest;
417 #endif
418 
421 
422  BOOLEAN nOK=TRUE;
423  // init
424  if ((t<=nLastCoeffs) && (nInitCharTable[t]!=NULL))
425  nOK = (nInitCharTable[t])(n,parameter);
426  else
427  Werror("Sorry: the coeff type [%d] was not registered: it is missing in nInitCharTable", (int)t);
428  if (nOK)
429  {
430  omFreeSize(n,sizeof(*n));
431  return NULL;
432  }
433  cf_root=n;
434  // post init settings:
435  if (n->cfRePart==NULL) n->cfRePart=n->cfCopy;
436  if (n->cfExactDiv==NULL) n->cfExactDiv=n->cfDiv;
437  if (n->cfSubringGcd==NULL) n->cfSubringGcd=n->cfGcd;
438  if (n->cfIsUnit==NULL)
439  {
440  if (n->is_field) n->cfIsUnit=ndIsUnit_Field;
441  else n->cfIsUnit=ndIsUnit_Ring;
442  }
443  #ifdef HAVE_RINGS
444  if (n->cfGetUnit==NULL)
445  {
446  if (n->is_field) n->cfGetUnit=n->cfCopy;
447  else n->cfGetUnit=ndGetUnit_Ring;
448  }
449  #endif
450 
451  if(n->cfWriteShort==NULL)
452  n->cfWriteShort = n->cfWriteLong;
453 
455  assume(n->cfSetChar!=NULL);
457  assume(n->cfMult!=NULL);
458  assume(n->cfSub!=NULL);
459  assume(n->cfAdd!=NULL);
460  assume(n->cfDiv!=NULL);
461  assume(n->cfIntMod!=NULL);
462  assume(n->cfExactDiv!=NULL);
463  assume(n->cfInit!=NULL);
464  assume(n->cfInitMPZ!=NULL);
465  assume(n->cfSize!=NULL);
466  assume(n->cfInt!=NULL);
467  assume(n->cfMPZ!=NULL);
468  //assume(n->n->cfDivComp!=NULL);
469  //assume(n->cfIsUnit!=NULL);
470  //assume(n->cfGetUnit!=NULL);
471  //assume(n->cfExtGcd!=NULL);
472  assume(n->cfInpNeg!=NULL);
473  assume(n->cfCopy!=NULL);
474 
475  assume(n->cfWriteLong!=NULL);
476  assume(n->cfWriteShort!=NULL);
477 
478  assume(n->iNumberOfParameters>= 0);
479 
480  assume( (n->iNumberOfParameters == 0 && n->pParameterNames == NULL) ||
481  (n->iNumberOfParameters > 0 && n->pParameterNames != NULL) );
482 
483  assume(n->cfParameter!=NULL);
484  assume(n->cfParDeg!=NULL);
485 
486  assume(n->cfRead!=NULL);
487  assume(n->cfNormalize!=NULL);
488  assume(n->cfGreater!=NULL);
489  //assume(n->cfDivBy!=NULL);
490  assume(n->cfEqual!=NULL);
491  assume(n->cfIsZero!=NULL);
492  assume(n->cfIsOne!=NULL);
493  assume(n->cfIsMOne!=NULL);
495  assume(n->cfGetDenom!=NULL);
497  assume(n->cfGcd!=NULL);
499  assume(n->cfDelete!=NULL);
500  assume(n->cfSetMap!=NULL);
501  assume(n->cfInpMult!=NULL);
502 // assume(n->cfInit_bigint!=NULL);
503  assume(n->cfCoeffWrite != NULL);
504 
505  assume(n->cfClearContent != NULL);
507 
508  assume(n->type==t);
509 
510 #ifndef SING_NDEBUG
511  if(n->cfKillChar==NULL) Warn("cfKillChar is NULL for coeff %d",t);
512  if(n->cfWriteLong==NULL) Warn("cfWrite is NULL for coeff %d",t);
513  if(n->cfWriteShort==NULL) Warn("cfWriteShort is NULL for coeff %d",t);
514 #endif
515  }
516  else
517  {
518  n->ref++;
519  }
520  return n;
521 }
522 
523 void nKillChar(coeffs r)
524 {
525  if (r!=NULL)
526  {
527  r->ref--;
528  if (r->ref<=0)
529  {
530  n_Procs_s tmp;
531  n_Procs_s* n=&tmp;
532  tmp.next=cf_root;
533  while((n->next!=NULL) && (n->next!=r)) n=n->next;
534  if (n->next==r)
535  {
536  n->next=n->next->next;
537  if (cf_root==r) cf_root=n->next;
538  assume (r->cfKillChar!=NULL); r->cfKillChar(r);
539  omFreeSize((void *)r, sizeof(n_Procs_s));
540  r=NULL;
541  }
542  else
543  {
544  WarnS("cf_root list destroyed");
545  }
546  }
547  }
548 }
549 
551 {
552  if (n==n_unknown)
553  {
556  {
558  ((int)nLastCoeffs+1)*sizeof(cfInitCharProc));
560  ((int)nLastCoeffs)*sizeof(cfInitCharProc));
561  }
562  else
563  {
565  ((int)nLastCoeffs)*sizeof(cfInitCharProc),
566  (((int)nLastCoeffs)+1)*sizeof(cfInitCharProc));
567  }
568 
570  return nLastCoeffs;
571  }
572  else
573  {
574  if (nInitCharTable[n]!=NULL) Print("coeff %d already initialized\n",n);
575  nInitCharTable[n]=p;
576  return n;
577  }
578 }
579 
580 struct nFindCoeffByName_s;
581 typedef struct nFindCoeffByName_s* nFindCoeffByName_p;
582 
583 struct nFindCoeffByName_s
584 {
587  nFindCoeffByName_p next;
588 };
589 
590 VAR nFindCoeffByName_p nFindCoeffByName_Root=NULL;
592 {
593  nFindCoeffByName_p h=(nFindCoeffByName_p)omAlloc0(sizeof(*h));
594  h->p=p;
595  h->n=n;
596  h->next=nFindCoeffByName_Root;
598 }
599 
600 coeffs nFindCoeffByName(char *cf_name)
601 {
602  n_Procs_s* n=cf_root;
603  // try existings coeffs:
604  while(n!=NULL)
605  {
606  if ((n->cfCoeffName!=NULL)
607  && (strcmp(cf_name,n->cfCoeffName(n))==0)) return n;
608  n=n->next;
609  }
610  // TODO: parametrized cf, e.g. flint:Z/26[a]
611  // try existing types:
612  nFindCoeffByName_p p=nFindCoeffByName_Root;
613  while(p!=NULL)
614  {
615  coeffs cf=p->p(cf_name,p->n);
616  if (cf!=NULL) return cf;
617  p=p->next;
618  }
619  return NULL;
620 }
621 
622 void n_Print(number& a, const coeffs r)
623 {
624  assume(r != NULL);
625  n_Test(a,r);
626 
627  StringSetS("");
628  n_Write(a, r);
629  { char* s = StringEndS(); Print("%s", s); omFree(s); }
630 }
631 
632 char* nEati(char *s, int *i, int m)
633 {
634 
635  if (((*s) >= '0') && ((*s) <= '9'))
636  {
637  unsigned long ii=0L;
638  do
639  {
640  ii *= 10;
641  ii += *s++ - '0';
642  if ((m!=0) && (ii > (MAX_INT_VAL / 10))) ii = ii % m;
643  }
644  while (((*s) >= '0') && ((*s) <= '9'));
645  if ((m!=0) && (ii>=(unsigned)m)) ii=ii%m;
646  *i=(int)ii;
647  }
648  else (*i) = 1;
649  return s;
650 }
651 
652 /// extracts a long integer from s, returns the rest
653 char * nEatLong(char *s, mpz_ptr i)
654 {
655  const char * start=s;
656 
657  while (*s >= '0' && *s <= '9') s++;
658  if (*s=='\0')
659  {
660  mpz_set_str(i,start,10);
661  }
662  else
663  {
664  char c=*s;
665  *s='\0';
666  mpz_set_str(i,start,10);
667  *s=c;
668  }
669  return s;
670 }
671 
BOOLEAN naInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
Definition: algext.cc:1378
BOOLEAN n2pInitChar(coeffs cf, void *infoStruct)
Definition: algext.cc:1633
All the auxiliary stuff.
int BOOLEAN
Definition: auxiliary.h:87
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
int m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
int p
Definition: cfModGcd.cc:4078
g
Definition: cfModGcd.cc:4090
CanonicalForm cf
Definition: cfModGcd.cc:4083
CanonicalForm b
Definition: cfModGcd.cc:4103
factory's main class
Definition: canonicalform.h:86
virtual reference Current()=0
Gets the current element in the collection (read and write).
virtual void Reset()=0
Sets the enumerator to its initial position: -1, which is before the first element in the collection.
virtual bool MoveNext()=0
Advances the enumerator to the next element of the collection. returns true if the enumerator was suc...
Templated enumerator interface for simple iteration over a generic collection of T's.
Definition: Enumerator.h:125
Definition: int_poly.h:33
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
Definition: coeffs.h:451
static FORCE_INLINE BOOLEAN nCoeff_has_Units(const coeffs r)
returns TRUE, if r is not a field and r has non-trivial units
Definition: coeffs.h:797
static FORCE_INLINE BOOLEAN nCoeff_is_GF(const coeffs r)
Definition: coeffs.h:839
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
Definition: coeffs.h:712
n_coeffType
Definition: coeffs.h:27
@ n_CF
?
Definition: coeffs.h:48
@ n_unknown
Definition: coeffs.h:28
static FORCE_INLINE number n_Gcd(number a, number b, const coeffs r)
in Z: return the gcd of 'a' and 'b' in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ,...
Definition: coeffs.h:664
static FORCE_INLINE number n_Invers(number a, const coeffs r)
return the multiplicative inverse of 'a'; raise an error if 'a' is not invertible
Definition: coeffs.h:564
static FORCE_INLINE BOOLEAN nCoeff_is_numeric(const coeffs r)
Definition: coeffs.h:832
static FORCE_INLINE BOOLEAN nCoeff_is_Zp_a(const coeffs r)
Definition: coeffs.h:859
static FORCE_INLINE BOOLEAN nCoeff_is_Q_algext(const coeffs r)
is it an alg. ext. of Q?
Definition: coeffs.h:914
static FORCE_INLINE number n_Div(number a, number b, const coeffs r)
return the quotient of 'a' and 'b', i.e., a/b; raises an error if 'b' is not invertible in r exceptio...
Definition: coeffs.h:615
static FORCE_INLINE BOOLEAN nCoeff_is_Q(const coeffs r)
Definition: coeffs.h:806
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition: coeffs.h:464
static FORCE_INLINE number n_GetUnit(number n, const coeffs r)
in Z: 1 in Z/kZ (where k is not a prime): largest divisor of n (taken in Z) that is co-prime with k i...
Definition: coeffs.h:532
static FORCE_INLINE BOOLEAN nCoeff_has_simple_Alloc(const coeffs r)
TRUE if n_Delete/n_New are empty operations.
Definition: coeffs.h:906
static FORCE_INLINE BOOLEAN nCoeff_is_Ring(const coeffs r)
Definition: coeffs.h:730
static FORCE_INLINE n_coeffType getCoeffType(const coeffs r)
Returns the type of coeffs domain.
Definition: coeffs.h:421
static FORCE_INLINE int n_GetChar(const coeffs r)
Return the characteristic of the coeff. domain.
Definition: coeffs.h:444
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:455
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 number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
Definition: coeffs.h:538
static FORCE_INLINE BOOLEAN nCoeff_is_algExt(const coeffs r)
TRUE iff r represents an algebraic extension field.
Definition: coeffs.h:910
static FORCE_INLINE void n_InpMult(number &a, number b, const coeffs r)
multiplication of 'a' and 'b'; replacement of 'a' by the product a*b
Definition: coeffs.h:641
static FORCE_INLINE void n_Normalize(number &n, const coeffs r)
inplace-normalization of n; produces some canonical representation of n;
Definition: coeffs.h:578
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
Definition: coeffs.h:468
static FORCE_INLINE BOOLEAN nCoeff_is_transExt(const coeffs r)
TRUE iff r represents a transcendental extension field.
Definition: coeffs.h:918
#define Print
Definition: emacs.cc:80
#define Warn
Definition: emacs.cc:77
#define WarnS
Definition: emacs.cc:78
return result
Definition: facAbsBiFact.cc:75
const CanonicalForm int s
Definition: facAbsFact.cc:51
CanonicalForm res
Definition: facAbsFact.cc:60
void WerrorS(const char *s)
Definition: feFopen.cc:24
BOOLEAN nfInitChar(coeffs r, void *parameter)
Definition: ffields.cc:858
BOOLEAN flintQrat_InitChar(coeffs cf, void *infoStruct)
#define STATIC_VAR
Definition: globaldefs.h:7
#define VAR
Definition: globaldefs.h:5
BOOLEAN ngcInitChar(coeffs n, void *parameter)
Initialize r (n_long_C)
Definition: gnumpc.cc:554
BOOLEAN ngfInitChar(coeffs n, void *parameter)
Initialize r.
Definition: gnumpfl.cc:499
STATIC_VAR Poly * h
Definition: janet.cc:971
BOOLEAN nlInitChar(coeffs r, void *p)
Definition: longrat.cc:3475
#define assume(x)
Definition: mod2.h:387
BOOLEAN npInitChar(coeffs r, void *p)
Definition: modulop.cc:340
const int MAX_INT_VAL
Definition: mylimits.h:12
The main handler for Singular numbers which are suitable for Singular polynomials.
BOOLEAN nnInitChar(coeffs n, void *p)
Initialize r.
Definition: ntupel.cc:588
static void ndPower(number a, int i, number *res, const coeffs r)
Definition: numbers.cc:79
static BOOLEAN ndIsUnit_Field(number a, const coeffs r)
Definition: numbers.cc:119
void nRegisterCfByName(cfInitCfByNameProc p, n_coeffType n)
Definition: numbers.cc:590
CanonicalForm ndConvSingNFactoryN(number, BOOLEAN, const coeffs)
Definition: numbers.cc:276
static int ndDivComp(number, number, const coeffs)
Definition: numbers.cc:272
VAR nFindCoeffByName_p nFindCoeffByName_Root
Definition: numbers.cc:589
static number ndGetUnit_Ring(number, const coeffs r)
Definition: numbers.cc:121
static BOOLEAN ndDBTest(number, const char *, const int, const coeffs)
Definition: numbers.cc:125
number ndGcd(number, number, const coeffs r)
Definition: numbers.cc:165
static void ndKillChar(coeffs)
Definition: numbers.cc:265
static number ndConvFactoryNSingN(const CanonicalForm, const coeffs)
[in, out] a bigint number >= 0
Definition: numbers.cc:283
static void ndClearDenominators(ICoeffsEnumerator &, number &d, const coeffs r)
Definition: numbers.cc:245
static void ndClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs r)
Definition: numbers.cc:171
static int ndParDeg(number n, const coeffs r)
Definition: numbers.cc:139
static BOOLEAN ndCoeffIsEqual(const coeffs r, n_coeffType n, void *)
Definition: numbers.cc:302
static char * ndCoeffString(const coeffs r)
Definition: numbers.cc:52
VAR n_Procs_s * cf_root
Definition: numbers.cc:45
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
Definition: numbers.cc:255
static BOOLEAN ndIsUnit_Ring(number a, const coeffs r)
Definition: numbers.cc:117
static char * ndCoeffName(const coeffs r)
Definition: numbers.cc:60
void ndNormalize(number &, const coeffs)
Definition: numbers.cc:163
void n_Print(number &a, const coeffs r)
print a number (BEWARE of string buffers!) mostly for debugging
Definition: numbers.cc:621
nFindCoeffByName_p next
Definition: numbers.cc:586
static int ndSize(number a, const coeffs r)
Definition: numbers.cc:169
static number ndIntMod(number, number, const coeffs r)
Definition: numbers.cc:166
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 number ndFarey(number, number, const coeffs r)
Definition: numbers.cc:128
void nNew(number *d)
Definition: numbers.cc:47
static void ndMPZ(mpz_t result, number &n, const coeffs r)
Converts a non-negative bigint number into a GMP number.
Definition: numbers.cc:291
STATIC_VAR n_coeffType nLastCoeffs
Definition: numbers.cc:316
static number ndAnn(number, const coeffs)
Definition: numbers.cc:51
static number ndGetDenom(number &, const coeffs r)
Definition: numbers.cc:167
static void ndDelete(number *d, const coeffs)
Definition: numbers.cc:50
STATIC_VAR cfInitCharProc * nInitCharTable
Definition: numbers.cc:350
n_coeffType n
Definition: numbers.cc:584
static number ndParameter(const int, const coeffs r)
Definition: numbers.cc:144
static number ndCopy(number a, const coeffs)
Definition: numbers.cc:254
static void ndInpMult(number &a, number b, const coeffs r)
Definition: numbers.cc:66
VAR cfInitCharProc nInitCharTableDefault[]
Definition: numbers.cc:317
static number ndChineseRemainder(number *, number *, int, BOOLEAN, CFArray &, const coeffs r)
Definition: numbers.cc:133
coeffs nFindCoeffByName(char *cf_name)
find an existing coeff by its "CoeffName"
Definition: numbers.cc:599
static number ndGetNumerator(number &a, const coeffs r)
Definition: numbers.cc:168
static BOOLEAN ndDivBy(number, number, const coeffs)
Definition: numbers.cc:271
static number ndInitMPZ(mpz_t m, const coeffs r)
Definition: numbers.cc:296
cfInitCfByNameProc p
Definition: numbers.cc:585
char * nEatLong(char *s, mpz_ptr i)
extracts a long integer from s, returns the rest
Definition: numbers.cc:652
static void ndInpAdd(number &a, number b, const coeffs r)
Definition: numbers.cc:72
number nd_Copy(number a, const coeffs r)
Definition: numbers.cc:268
static number ndInvers(number a, const coeffs r)
Definition: numbers.cc:109
BOOLEAN n_IsZeroDivisor(number a, const coeffs r)
Test whether a is a zero divisor in r i.e. not coprime with char. of r very inefficient implementatio...
Definition: numbers.cc:149
static void ndCoeffWrite(const coeffs r, BOOLEAN)
Definition: numbers.cc:56
n_coeffType nRegister(n_coeffType n, cfInitCharProc p)
Definition: numbers.cc:549
static number ndReturn0(number, const coeffs r)
Definition: numbers.cc:164
static number ndExtGcd(number, number, number *, number *, const coeffs r)
Definition: numbers.cc:273
static number ndQuotRem(number a, number b, number *r, const coeffs R)
Definition: numbers.cc:309
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
static void ndSetChar(const coeffs)
Definition: numbers.cc:266
void nKillChar(coeffs r)
undo all initialisations
Definition: numbers.cc:522
coeffs(* cfInitCfByNameProc)(char *s, n_coeffType n)
initialize an object of type coeffs by its name, return NULL otherwise
Definition: numbers.h:97
BOOLEAN(* cfInitCharProc)(coeffs, void *)
initialize an object of type coeff, return FALSE in case of success
Definition: numbers.h:93
#define omStrDup(s)
Definition: omAllocDecl.h:263
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omReallocSize(addr, o_size, size)
Definition: omAllocDecl.h:220
#define omFree(addr)
Definition: omAllocDecl.h:261
#define omAlloc0(size)
Definition: omAllocDecl.h:211
#define NULL
Definition: omList.c:12
void StringSetS(const char *st)
Definition: reporter.cc:128
void PrintS(const char *s)
Definition: reporter.cc:284
char * StringEndS()
Definition: reporter.cc:151
void Werror(const char *fmt,...)
Definition: reporter.cc:189
BOOLEAN nrzInitChar(coeffs r, void *parameter)
BOOLEAN nr2mInitChar(coeffs r, void *p)
Definition: rmodulo2m.cc:770
BOOLEAN nrnInitChar(coeffs r, void *p)
Definition: rmodulon.cc:984
BOOLEAN nrInitChar(coeffs n, void *p)
Initialize r.
Definition: shortfl.cc:658
#define R
Definition: sirandom.c:27
BOOLEAN(* cfIsUnit)(number a, const coeffs r)
Definition: coeffs.h:378
number(* cfChineseRemainder)(number *x, number *q, int rl, BOOLEAN sym, CFArray &inv_cache, const coeffs)
chinese remainder returns X with X mod q[i]=x[i], i=0..rl-1
Definition: coeffs.h:297
number(* cfNormalizeHelper)(number a, number b, const coeffs r)
Definition: coeffs.h:271
int(* cfDivComp)(number a, number b, const coeffs r)
Definition: coeffs.h:377
BOOLEAN(*)(*)(*)(*)(*)(*) cfGreaterZero(number a, const coeffs r)
Definition: coeffs.h:237
number(* cfExtGcd)(number a, number b, number *s, number *t, const coeffs r)
Definition: coeffs.h:248
number(* cfGetUnit)(number a, const coeffs r)
Definition: coeffs.h:379
number(* cfLcm)(number a, number b, const coeffs r)
Definition: coeffs.h:270
number(* cfGetNumerator)(number &n, const coeffs r)
Definition: coeffs.h:241
number(* cfInvers)(number a, const coeffs r)
return 1/a
Definition: coeffs.h:197
number(* cfInit)(long i, const coeffs r)
init with an integer
Definition: coeffs.h:178
int iNumberOfParameters
Number of Parameters in the coeffs (default 0)
Definition: coeffs.h:319
number(* cfInpNeg)(number a, const coeffs r)
changes argument inline: a:= -a return -a! (no copy is returned) the result should be assigned to the...
Definition: coeffs.h:195
number(* cfInitMPZ)(mpz_t i, const coeffs r)
init with a GMP integer
Definition: coeffs.h:181
BOOLEAN is_field
TRUE, if cf is a field.
Definition: coeffs.h:140
char *(* cfCoeffName)(const coeffs r)
default name of cf, should substitue cfCoeffWrite, cfCoeffString
Definition: coeffs.h:154
nMapFunc(* cfSetMap)(const coeffs src, const coeffs dst)
Definition: coeffs.h:275
number(* cfParameter)(const int i, const coeffs r)
create i^th parameter or NULL if not possible
Definition: coeffs.h:303
void(* cfSetChar)(const coeffs r)
Definition: coeffs.h:161
number(* convFactoryNSingN)(const CanonicalForm n, const coeffs r)
conversion to CanonicalForm(factory) to number
Definition: coeffs.h:315
number(* cfGcd)(number a, number b, const coeffs r)
Definition: coeffs.h:246
number(* cfImPart)(number a, const coeffs r)
Definition: coeffs.h:201
number(* cfFarey)(number p, number n, const coeffs)
rational reconstruction: "best" rational a/b with a/b = p mod n
Definition: coeffs.h:291
coeffs next
Definition: coeffs.h:125
number(* cfCopy)(number a, const coeffs r)
return a copy of a
Definition: coeffs.h:199
int ref
Definition: coeffs.h:126
BOOLEAN(*)(*)(*) cfIsZero(number a, const coeffs r)
Definition: coeffs.h:228
void(* cfKillChar)(coeffs r)
Definition: coeffs.h:159
BOOLEAN(*)(*) cfEqual(number a, number b, const coeffs r)
tests
Definition: coeffs.h:227
numberfunc cfIntMod
Definition: coeffs.h:175
numberfunc cfExactDiv
Definition: coeffs.h:175
void(* cfMPZ)(mpz_t result, number &n, const coeffs r)
Converts a (integer) number n into a GMP number, 0 if impossible.
Definition: coeffs.h:190
BOOLEAN(* nCoeffIsEqual)(const coeffs r, n_coeffType n, void *parameter)
Definition: coeffs.h:145
void(* cfWriteShort)(number a, const coeffs r)
print a given number in a shorter way, if possible e.g. in K(a): a2 instead of a^2
Definition: coeffs.h:208
number(* cfRePart)(number a, const coeffs r)
Definition: coeffs.h:200
void(* cfNormalize)(number &a, const coeffs r)
Definition: coeffs.h:223
numberfunc cfMult
Definition: coeffs.h:175
char *(* cfCoeffString)(const coeffs r)
string output of coeff description
Definition: coeffs.h:151
number(* cfGetDenom)(number &n, const coeffs r)
Definition: coeffs.h:240
void(* cfWriteLong)(number a, const coeffs r)
print a given number (long format)
Definition: coeffs.h:204
number(* cfSubringGcd)(number a, number b, const coeffs r)
Definition: coeffs.h:247
BOOLEAN(*)(*)(*)(*) cfIsOne(number a, const coeffs r)
Definition: coeffs.h:229
number(* cfAnn)(number a, const coeffs r)
Definition: coeffs.h:261
void(* cfPower)(number a, int i, number *result, const coeffs r)
Definition: coeffs.h:239
CanonicalForm(* convSingNFactoryN)(number n, BOOLEAN setChar, const coeffs r)
Definition: coeffs.h:316
long(* cfInt)(number &n, const coeffs r)
convertion to long, 0 if impossible
Definition: coeffs.h:187
BOOLEAN(* cfGreater)(number a, number b, const coeffs r)
Definition: coeffs.h:225
number(* cfQuotRem)(number a, number b, number *rem, const coeffs r)
Definition: coeffs.h:269
void(* cfCoeffWrite)(const coeffs r, BOOLEAN details)
output of coeff description via Print
Definition: coeffs.h:148
void(* cfDelete)(number *a, const coeffs r)
Definition: coeffs.h:272
numberfunc cfSub
Definition: coeffs.h:175
BOOLEAN(* cfDBTest)(number a, const char *f, const int l, const coeffs r)
Test: is "a" a correct number?
Definition: coeffs.h:415
n_coeffType type
Definition: coeffs.h:128
numberfunc cfAdd
Definition: coeffs.h:175
BOOLEAN(*)(*)(*)(*)(*) cfIsMOne(number a, const coeffs r)
Definition: coeffs.h:232
numberfunc cfDiv
Definition: coeffs.h:175
char const ** pParameterNames
array containing the names of Parameters (default NULL)
Definition: coeffs.h:322
int(* cfParDeg)(number x, const coeffs r)
degree for coeffcients: -1 for 0, 0 for "constants", ...
Definition: coeffs.h:300
void(* cfInpMult)(number &a, number b, const coeffs r)
Inplace: a *= b.
Definition: coeffs.h:281
int(* cfSize)(number n, const coeffs r)
how complicated, (0) => 0, or positive
Definition: coeffs.h:184
const char *(* cfRead)(const char *s, number *a, const coeffs r)
Definition: coeffs.h:221
void(* cfInpAdd)(number &a, number b, const coeffs r)
Inplace: a += b.
Definition: coeffs.h:284
BOOLEAN(* cfDivBy)(number a, number b, const coeffs r)
Definition: coeffs.h:381
nCoeffsEnumeratorFunc cfClearContent
function pointer behind n_ClearContent
Definition: coeffs.h:309
nCoeffsEnumeratorFunc cfClearDenominators
function pointer behind n_ClearDenominators
Definition: coeffs.h:312
BOOLEAN ntInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
Definition: transext.cc:2544