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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
47void nNew(number* d) { *d=NULL; }
48
49
50static void ndDelete(number* d, const coeffs) { *d=NULL; }
51static number ndAnn(number, const coeffs) { return NULL;}
52static char* ndCoeffString(const coeffs r)
53{
54 return omStrDup(r->cfCoeffName(r));
55}
56static void ndCoeffWrite(const coeffs r,BOOLEAN)
57{
58 PrintS(r->cfCoeffName(r));
59}
60static char* ndCoeffName(const coeffs r)
61{
62 STATIC_VAR char s[20];
63 snprintf(s,11,"Coeffs(%d)",r->type);
64 return s;
65}
66static 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}
72void 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
79static 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}
109static 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}
116static number ndInvers_Ring(number a, const coeffs r)
117{
118 if (!r->cfIsUnit(a,r)) Print("ndInvers_Ring used with non-unit\n");
119 number one=r->cfInit(1,r);
120 number res=r->cfDiv(one,a,r);
121 r->cfDelete(&one,r);
122 return res;
123}
124
125static BOOLEAN ndIsUnit_Ring(number a, const coeffs r)
126{ return r->cfIsOne(a,r)|| r->cfIsMOne(a,r); }
127static BOOLEAN ndIsUnit_Field(number a, const coeffs r)
128{ return !r->cfIsZero(a,r); }
129static number ndGetUnit_Ring(number, const coeffs r)
130{ return r->cfInit(1,r); }
131static number ndRandom(siRandProc p, number p1, number p2, const coeffs cf)
132{ return cf->cfInit(p(),cf); }
133static number ndEucNorm(number a, const coeffs cf)
134{ return cf->cfInit(cf->cfSize(a,cf),cf); }
135#ifdef LDEBUG
136// static void nDBDummy1(number* d,char *, int) { *d=NULL; }
137static BOOLEAN ndDBTest(number, const char *, const int, const coeffs){ return TRUE; }
138#endif
139
140static number ndFarey(number,number,const coeffs r)
141{
142 Werror("farey not implemented for %s (c=%d)",r->cfCoeffName(r),getCoeffType(r));
143 return NULL;
144}
145static number ndXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
146{
147 Werror("XExtGcd not implemented for %s (c=%d)",r->cfCoeffName(r),getCoeffType(r));
148 return NULL;
149}
150static number ndChineseRemainder(number *,number *,int,BOOLEAN,CFArray&,const coeffs r)
151{
152 Werror("ChineseRemainder not implemented for %s (c=%d)",r->cfCoeffName(r),getCoeffType(r));
153 return r->cfInit(0,r);
154}
155number ndReadFd( const ssiInfo *f, const coeffs r)
156{
157 Warn("ReadFd not implemented for %s (c=%d)",r->cfCoeffName(r),getCoeffType(r));
158 return NULL;
159}
160
161static void ndWriteFd(number a, const ssiInfo *f, const coeffs r)
162{
163 Warn("WriteFd not implemented for %s (c=%d)",r->cfCoeffName(r),getCoeffType(r));
164}
165
166static int ndParDeg(number n, const coeffs r)
167{
168 return (-r->cfIsZero(n,r));
169}
170
171static number ndParameter(const int, const coeffs r)
172{
173 return r->cfInit(1,r);
174}
175
176BOOLEAN n_IsZeroDivisor( number a, const coeffs r)
177{
178 BOOLEAN ret = n_IsZero(a, r);
179 int c = n_GetChar(r);
180 if (ret || (c==0) || (r->is_field))
181 return ret; /*n_IsZero(a, r)*/
182 number ch = n_Init( c, r );
183 number g = n_Gcd( ch, a, r );
184 ret = !n_IsOne (g, r);
185 n_Delete(&ch, r);
186 n_Delete(&g, r);
187 return ret;
188}
189
190void ndNormalize(number&, const coeffs) { }
191static number ndReturn0(number, const coeffs r) { return r->cfInit(0,r); }
192number ndGcd(number, number, const coeffs r) { return r->cfInit(1,r); }
193static number ndIntMod(number, number, const coeffs r) { return r->cfInit(0,r); }
194static number ndGetDenom(number &, const coeffs r) { return r->cfInit(1,r); }
195static number ndGetNumerator(number &a,const coeffs r) { return r->cfCopy(a,r); }
196static int ndSize(number a, const coeffs r) { return (int)r->cfIsZero(a,r)==FALSE; }
197
198static void ndClearContent(ICoeffsEnumerator& numberCollectionEnumerator, number& c, const coeffs r)
199{
200 assume(r != NULL);
201
202 // no fractions
203 assume(!( nCoeff_is_Q(r) ));
204 // all coeffs are given by integers!!!
205
206 numberCollectionEnumerator.Reset();
207
208 if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial?
209 {
210 c = n_Init(1, r);
211 return;
212 }
213
214 number &curr = numberCollectionEnumerator.Current();
215
216#ifdef HAVE_RINGS
217 /// TODO: move to a separate implementation
218 if (nCoeff_is_Ring(r))
219 {
220 if (nCoeff_has_Units(r))
221 {
222 c = n_GetUnit(curr, r);
223
224 if (!n_IsOne(c, r))
225 {
226 number inv = n_Invers(c, r);
227
228 n_InpMult(curr, inv, r);
229
230 while( numberCollectionEnumerator.MoveNext() )
231 {
232 number &n = numberCollectionEnumerator.Current();
233 n_Normalize(n, r); // ?
234 n_InpMult(n, inv, r); // TODO: either this or directly divide!!!?
235 }
236
237 n_Delete(&inv, r);
238 }
239 } else c = n_Init(1, r);
240
241 return;
242 }
243#endif
244
247
248 n_Normalize(curr, r); // Q: good/bad/ugly??
249
250 if (!n_IsOne(curr, r))
251 {
252 number t = curr; // takes over the curr! note: not a reference!!!
253
254 curr = n_Init(1, r); // ???
255
256 number inv = n_Invers(t, r);
257
258 while( numberCollectionEnumerator.MoveNext() )
259 {
260 number &n = numberCollectionEnumerator.Current();
261 n_InpMult(n, inv, r); // TODO: either this or directly divide!!!?
262// n_Normalize(n, r); // ?
263 }
264
265 n_Delete(&inv, r);
266
267 c = t;
268 } else
269 c = n_Copy(curr, r); // c == 1 and nothing else to do...
270}
271
272static void ndClearDenominators(ICoeffsEnumerator& /*numberCollectionEnumerator*/, number& d, const coeffs r)
273{
274 assume( r != NULL );
277
278 d = n_Init(1, r);
279}
280
281static number ndCopy(number a, const coeffs) { return a; }
282number ndCopyMap(number a, const coeffs aRing, const coeffs r)
283{
284 // aRing and r need not be the same, but must be the same representation
285 assume(aRing->rep==r->rep);
287 return a;
288 else
289 return r->cfCopy(a, r);
290}
291
292static void ndKillChar(coeffs) {}
293static void ndSetChar(const coeffs) {}
294
295number nd_Copy(number a, const coeffs r) { return r->cfCopy(a, r); }
296
297#ifdef HAVE_RINGS
298static BOOLEAN ndDivBy(number, number, const coeffs) { return TRUE; } // assume a,b !=0
299static int ndDivComp(number, number, const coeffs) { return 2; }
300static number ndExtGcd (number, number, number *, number *, const coeffs r) { return r->cfInit(1,r); }
301#endif
302
304{
306 WerrorS("no conversion to factory");
307 return term;
308}
309
310static number ndConvFactoryNSingN( const CanonicalForm, const coeffs)
311{
312 WerrorS("no conversion from factory");
313 return NULL;
314}
315
316/**< [in, out] a bigint number >= 0 */
317/**< [out] the GMP equivalent */
318/// Converts a non-negative bigint number into a GMP number.
319static void ndMPZ(mpz_t result, number &n, const coeffs r)
320{
321 mpz_init_set_si( result, r->cfInt(n, r) );
322}
324static number ndInitMPZ(mpz_t m, const coeffs r)
325{
326 return r->cfInit( mpz_get_si(m), r);
327}
329static const char *ndRead(const char * s, number *, const coeffs r)
330{
331 Werror("cfRead is undefined for %s",nCoeffString(r));
332 return s;
334static nMapFunc ndSetMap(const coeffs src, const coeffs dst)
335{
336 if (src==dst) return ndCopyMap;
337 Werror("cfSetMap is undefined for %s",nCoeffString(dst));
338 return NULL;
339}
341static BOOLEAN ndCoeffIsEqual(const coeffs r, n_coeffType n, void *)
342{
343 /* test, if r is an instance of nInitCoeffs(n,parameter) */
344 /* if parameter is not needed */
345 return (n==r->type);
346}
348static number ndQuotRem (number a, number b, number * r, const coeffs R)
349{
350 // implementation for a field: r: 0, result: n_Div
351 assume(R->is_field);
352 *r=n_Init(0,R);
353 return n_Div(a,b,R);
357{ NULL, /*n_unknown */
358 npInitChar, /* n_Zp */
359 nlInitChar, /* n_Q */
360 nrInitChar, /* n_R */
361 nfInitChar, /* n_GF */
362 ngfInitChar, /* n_long_R */
363 #ifdef HAVE_POLYEXTENSIONS
364 n2pInitChar, /* n_polyExt */
365 naInitChar, /* n_algExt */
366 ntInitChar, /* n_transExt */
367 #else
368 NULL, /* n_polyExt */
369 NULL, /* n_algExt */
370 NULL, /* n_transExt */
371 #endif
372 ngcInitChar, /* n_long_C */
373 nnInitChar, /* n_nTupel */
374 #ifdef HAVE_RINGS
375 nrzInitChar, /* n_Z */
376 nrnInitChar, /* n_Zn */
377 nrnInitChar, /* n_Znm */
378 nr2mInitChar, /* n_Z2m */
379 #else
380 NULL, /* n_Z */
381 NULL, /* n_Zn */
382 NULL, /* n_Znm */
383 NULL, /* n_Z2m */
384 #endif
385 flintQrat_InitChar, /* n_FlintQrat */
386 NULL /* n_CF */
387};
390/*2
391* init operations for coeffs r
393coeffs nInitChar(n_coeffType t, void * parameter)
394{
396
397 while((n!=NULL) && (n->nCoeffIsEqual!=NULL) && (!n->nCoeffIsEqual(n,t,parameter)))
398 n=n->next;
399
400 if (n==NULL)
401 {
402 n=(n_Procs_s*)omAlloc0(sizeof(n_Procs_s));
403 n->next=cf_root;
404 n->ref=1;
405 n->type=t;
406
407 // default entries (different from NULL) for some routines:
409 n->cfSize = ndSize;
413 n->cfDelete= ndDelete;
414 n->cfAnn = ndAnn;
417 n->cfCoeffName = ndCoeffName; // should alway be changed!
420 n->cfCopy = ndCopy;
421 n->cfIntMod=ndIntMod; /* dummy !! */
423 n->cfGcd = ndGcd;
424 n->cfNormalizeHelper = ndGcd; /* tricky, isn't it ?*/
425 n->cfLcm = ndGcd; /* tricky, isn't it ?*/
426 n->cfInitMPZ = ndInitMPZ;
427 n->cfMPZ = ndMPZ;
428 n->cfPower = ndPower;
429 n->cfQuotRem = ndQuotRem;
430 n->cfInvers = ndInvers;
431 n->cfRandom = ndRandom;
432
433 n->cfKillChar = ndKillChar; /* dummy */
434 n->cfSetChar = ndSetChar; /* dummy */
435 // temp. removed to catch all the coeffs which miss to implement this!
436
437 n->cfChineseRemainder = ndChineseRemainder; /* not implemented */
438 n->cfFarey = ndFarey; /* not implemented */
439 n->cfParDeg = ndParDeg; /* not implemented */
440 n->cfReadFd = ndReadFd; /* not implemented */
441 n->cfWriteFd = ndWriteFd; /* not implemented */
442
444
447
448 n->cfEucNorm = ndEucNorm;
449#ifdef HAVE_RINGS
450 n->cfDivComp = ndDivComp;
451 n->cfDivBy = ndDivBy;
452 n->cfExtGcd = ndExtGcd;
453 n->cfXExtGcd = ndXExtGcd;
454 //n->cfGetUnit = ndGetUnit_Ring;// set afterwards
455#endif
456
457 // report error, if not redefined
458 n->cfRead=ndRead;
460
461#ifdef LDEBUG
463#endif
464
467
468 BOOLEAN nOK=TRUE;
469 // init
470 if ((t<=nLastCoeffs) && (nInitCharTable[t]!=NULL))
471 nOK = (nInitCharTable[t])(n,parameter);
472 else
473 Werror("Sorry: the coeff type [%d] was not registered: it is missing in nInitCharTable", (int)t);
474 if (nOK)
475 {
476 omFreeSize(n,sizeof(*n));
477 return NULL;
478 }
479 cf_root=n;
480 // post init settings:
481 if (n->cfRePart==NULL) n->cfRePart=n->cfCopy;
482 if (n->cfExactDiv==NULL) n->cfExactDiv=n->cfDiv;
483 if (n->cfSubringGcd==NULL) n->cfSubringGcd=n->cfGcd;
484 if (n->cfWriteShort==NULL) n->cfWriteShort = n->cfWriteLong;
485 if (n->cfIsUnit==NULL)
486 {
488 else n->cfIsUnit=ndIsUnit_Ring;
489 }
490 #ifdef HAVE_RINGS
491 if (n->cfGetUnit==NULL)
492 {
493 if (n->is_field) n->cfGetUnit=n->cfCopy;
495 }
496 if ((n->cfInvers==ndInvers)&&(n->is_field))
497 {
499 }
500 #endif
501
502
503 if(n->cfMult==NULL) PrintS("cfMult missing\n");
504 if(n->cfSub==NULL) PrintS("cfSub missing\n");
505 if(n->cfAdd==NULL) PrintS("cfAdd missing\n");
506 if(n->cfDiv==NULL) PrintS("cfDiv missing\n");
507 if(n->cfExactDiv==NULL) PrintS("cfExactDiv missing\n");
508 if(n->cfInit==NULL) PrintS("cfInit missing\n");
509 if(n->cfInt==NULL) PrintS("cfInt missing\n");
510 if(n->cfIsUnit==NULL) PrintS("cfIsUnit missing\n");
511 if(n->cfGetUnit==NULL) PrintS("cfGetUnit missing\n");
512 if(n->cfInpNeg==NULL) PrintS("cfInpNeg missing\n");
513 if(n->cfXExtGcd==NULL) PrintS("cfXExtGcd missing\n");
514 if(n->cfAnn==NULL) PrintS("cfAnn missing\n");
515 if(n->cfWriteLong==NULL) PrintS("cfWriteLong missing\n");
516
518
519 assume( (n->iNumberOfParameters == 0 && n->pParameterNames == NULL) ||
520 (n->iNumberOfParameters > 0 && n->pParameterNames != NULL) );
521
522
523 if(n->cfGreater==NULL) PrintS("cfGreater missing\n");
524 if(n->cfEqual==NULL) PrintS("cfEqual missing\n");
525 if(n->cfIsZero==NULL) PrintS("cfIsZero missing\n");
526 if(n->cfIsOne==NULL) PrintS("cfIsOne missing\n");
527 if(n->cfIsMOne==NULL) PrintS("cfIsMOne missing\n");
528 if(n->cfGreaterZero==NULL) PrintS("cfGreaterZero missing\n");
529 /* error reporter:
530 if(n->cfRead==ndRead) PrintS("cfRead missing\n");
531 if(n->cfSetMap==ndSetMap) PrintS("cfSetMap missing\n");
532 */
533
534 assume(n->type==t);
535
536#ifndef SING_NDEBUG
537 if(n->cfWriteLong==NULL) Warn("cfWrite is NULL for coeff %d",t);
538 if(n->cfWriteShort==NULL) Warn("cfWriteShort is NULL for coeff %d",t);
539#endif
540 }
541 else
542 {
543 n->ref++;
544 }
545 return n;
546}
548void nKillChar(coeffs r)
549{
550 if (r!=NULL)
551 {
552 r->ref--;
553 if (r->ref<=0)
554 {
555 n_Procs_s tmp;
556 n_Procs_s* n=&tmp;
557 tmp.next=cf_root;
558 while((n->next!=NULL) && (n->next!=r)) n=n->next;
559 if (n->next==r)
560 {
561 n->next=n->next->next;
562 if (cf_root==r) cf_root=n->next;
563 assume (r->cfKillChar!=NULL); r->cfKillChar(r);
564 omFreeSize((void *)r, sizeof(n_Procs_s));
565 r=NULL;
566 }
567 else
568 {
569 WarnS("cf_root list destroyed");
570 }
571 }
572 }
573}
576{
577 if (n==n_unknown)
578 {
581 {
583 ((int)nLastCoeffs+1)*sizeof(cfInitCharProc));
585 ((int)nLastCoeffs)*sizeof(cfInitCharProc));
586 }
587 else
588 {
590 ((int)nLastCoeffs)*sizeof(cfInitCharProc),
591 (((int)nLastCoeffs)+1)*sizeof(cfInitCharProc));
592 }
593
595 return nLastCoeffs;
596 }
597 else
598 {
599 if (nInitCharTable[n]!=NULL) Print("coeff %d already initialized\n",n);
600 nInitCharTable[n]=p;
601 return n;
602 }
603}
604
605struct nFindCoeffByName_s;
606typedef struct nFindCoeffByName_s* nFindCoeffByName_p;
612 nFindCoeffByName_p next;
613};
615VAR nFindCoeffByName_p nFindCoeffByName_Root=NULL;
617{
618 nFindCoeffByName_p h=(nFindCoeffByName_p)omAlloc0(sizeof(*h));
619 h->p=p;
620 h->n=n;
623}
625coeffs nFindCoeffByName(char *cf_name)
626{
628 // try existings coeffs:
629 while(n!=NULL)
630 {
631 if ((n->cfCoeffName!=NULL)
632 && (strcmp(cf_name,n->cfCoeffName(n))==0)) return n;
633 n=n->next;
634 }
635 // TODO: parametrized cf, e.g. flint:Z/26[a]
636 // try existing types:
637 nFindCoeffByName_p p=nFindCoeffByName_Root;
638 while(p!=NULL)
639 {
640 coeffs cf=p->p(cf_name,p->n);
641 if (cf!=NULL) return cf;
642 p=p->next;
643 }
644 return NULL;
645}
647void n_Print(number& a, const coeffs r)
648{
649 assume(r != NULL);
650 n_Test(a,r);
651
652 StringSetS("");
653 n_Write(a, r);
654 { char* s = StringEndS(); Print("%s", s); omFree(s); }
655}
657char* nEati(char *s, int *i, int m)
658{
659
660 if (((*s) >= '0') && ((*s) <= '9'))
661 {
662 unsigned long ii=0L;
663 do
664 {
665 ii *= 10;
666 ii += *s++ - '0';
667 if ((m!=0) && (ii > (MAX_INT_VAL / 10))) ii = ii % m;
668 }
669 while (((*s) >= '0') && ((*s) <= '9'));
670 if ((m!=0) && (ii>=(unsigned)m)) ii=ii%m;
671 *i=(int)ii;
672 }
673 else (*i) = 1;
674 return s;
675}
676
677/// extracts a long integer from s, returns the rest
678char * nEatLong(char *s, mpz_ptr i)
679{
680 const char * start=s;
681
682 while (*s >= '0' && *s <= '9') s++;
683 if (*s=='\0')
684 {
685 mpz_set_str(i,start,10);
686 }
687 else
688 {
689 char c=*s;
690 *s='\0';
691 mpz_set_str(i,start,10);
692 *s=c;
693 }
694 return s;
695}
696
BOOLEAN naInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
Definition: algext.cc:1388
BOOLEAN n2pInitChar(coeffs cf, void *infoStruct)
Definition: algext.cc:1642
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:4077
g
Definition: cfModGcd.cc:4089
CanonicalForm cf
Definition: cfModGcd.cc:4082
CanonicalForm b
Definition: cfModGcd.cc:4102
FILE * f
Definition: checklibs.c:9
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 char * nCoeffString(const coeffs cf)
TODO: make it a virtual method of coeffs, together with: Decompose & Compose, rParameter & rPar.
Definition: coeffs.h:959
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
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:73
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
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
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:568
BOOLEAN ngfInitChar(coeffs n, void *parameter)
Initialize r.
Definition: gnumpfl.cc:513
STATIC_VAR Poly * h
Definition: janet.cc:971
BOOLEAN nlInitChar(coeffs r, void *p)
Definition: longrat.cc:3476
#define assume(x)
Definition: mod2.h:389
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:616
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:127
void nRegisterCfByName(cfInitCfByNameProc p, n_coeffType n)
Definition: numbers.cc:615
CanonicalForm ndConvSingNFactoryN(number, BOOLEAN, const coeffs)
Definition: numbers.cc:303
static int ndDivComp(number, number, const coeffs)
Definition: numbers.cc:299
static number ndEucNorm(number a, const coeffs cf)
Definition: numbers.cc:133
VAR nFindCoeffByName_p nFindCoeffByName_Root
Definition: numbers.cc:614
static number ndGetUnit_Ring(number, const coeffs r)
Definition: numbers.cc:129
static BOOLEAN ndDBTest(number, const char *, const int, const coeffs)
Definition: numbers.cc:137
number ndGcd(number, number, const coeffs r)
Definition: numbers.cc:192
static void ndKillChar(coeffs)
Definition: numbers.cc:292
static number ndConvFactoryNSingN(const CanonicalForm, const coeffs)
[in, out] a bigint number >= 0
Definition: numbers.cc:310
static void ndClearDenominators(ICoeffsEnumerator &, number &d, const coeffs r)
Definition: numbers.cc:272
static void ndClearContent(ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs r)
Definition: numbers.cc:198
number ndReadFd(const ssiInfo *f, const coeffs r)
Definition: numbers.cc:155
static int ndParDeg(number n, const coeffs r)
Definition: numbers.cc:166
static BOOLEAN ndCoeffIsEqual(const coeffs r, n_coeffType n, void *)
Definition: numbers.cc:340
VAR n_Procs_s * cf_root
Definition: numbers.cc:45
number ndCopyMap(number a, const coeffs aRing, const coeffs r)
Definition: numbers.cc:282
static BOOLEAN ndIsUnit_Ring(number a, const coeffs r)
Definition: numbers.cc:125
void ndNormalize(number &, const coeffs)
Definition: numbers.cc:190
void n_Print(number &a, const coeffs r)
print a number (BEWARE of string buffers!) mostly for debugging
Definition: numbers.cc:646
nFindCoeffByName_p next
Definition: numbers.cc:611
char * nEati(char *s, int *i, int m)
divide by the first (leading) number and return it, i.e. make monic
Definition: numbers.cc:656
static int ndSize(number a, const coeffs r)
Definition: numbers.cc:196
static number ndIntMod(number, number, const coeffs r)
Definition: numbers.cc:193
void ndInpAdd(number &a, number b, const coeffs r)
Definition: numbers.cc:72
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
Definition: numbers.cc:392
static void ndWriteFd(number a, const ssiInfo *f, const coeffs r)
Definition: numbers.cc:161
static number ndFarey(number, number, const coeffs r)
Definition: numbers.cc:140
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:318
STATIC_VAR n_coeffType nLastCoeffs
Definition: numbers.cc:354
static number ndAnn(number, const coeffs)
Definition: numbers.cc:51
static number ndGetDenom(number &, const coeffs r)
Definition: numbers.cc:194
static void ndDelete(number *d, const coeffs)
Definition: numbers.cc:50
STATIC_VAR cfInitCharProc * nInitCharTable
Definition: numbers.cc:388
n_coeffType n
Definition: numbers.cc:609
static number ndInvers_Ring(number a, const coeffs r)
Definition: numbers.cc:116
static number ndParameter(const int, const coeffs r)
Definition: numbers.cc:171
static number ndXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
Definition: numbers.cc:145
static number ndCopy(number a, const coeffs)
Definition: numbers.cc:281
static void ndInpMult(number &a, number b, const coeffs r)
Definition: numbers.cc:66
VAR cfInitCharProc nInitCharTableDefault[]
Definition: numbers.cc:355
static number ndChineseRemainder(number *, number *, int, BOOLEAN, CFArray &, const coeffs r)
Definition: numbers.cc:150
static char * ndCoeffString(const coeffs r)
Definition: numbers.cc:52
coeffs nFindCoeffByName(char *cf_name)
find an existing coeff by its "CoeffName"
Definition: numbers.cc:624
static number ndGetNumerator(number &a, const coeffs r)
Definition: numbers.cc:195
static BOOLEAN ndDivBy(number, number, const coeffs)
Definition: numbers.cc:298
static number ndInitMPZ(mpz_t m, const coeffs r)
Definition: numbers.cc:323
cfInitCfByNameProc p
Definition: numbers.cc:610
number nd_Copy(number a, const coeffs r)
Definition: numbers.cc:295
static nMapFunc ndSetMap(const coeffs src, const coeffs dst)
Definition: numbers.cc:333
static const char * ndRead(const char *s, number *, const coeffs r)
Definition: numbers.cc:328
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:176
static void ndCoeffWrite(const coeffs r, BOOLEAN)
Definition: numbers.cc:56
n_coeffType nRegister(n_coeffType n, cfInitCharProc p)
Definition: numbers.cc:574
static number ndRandom(siRandProc p, number p1, number p2, const coeffs cf)
Definition: numbers.cc:131
static number ndReturn0(number, const coeffs r)
Definition: numbers.cc:191
static number ndExtGcd(number, number, number *, number *, const coeffs r)
Definition: numbers.cc:300
static number ndQuotRem(number a, number b, number *r, const coeffs R)
Definition: numbers.cc:347
static char * ndCoeffName(const coeffs r)
Definition: numbers.cc:60
static void ndSetChar(const coeffs)
Definition: numbers.cc:293
void nKillChar(coeffs r)
undo all initialisations
Definition: numbers.cc:547
char * nEatLong(char *s, mpz_ptr i)
extracts a long integer from s, returns the rest
Definition: numbers.cc:677
coeffs(* cfInitCfByNameProc)(char *s, n_coeffType n)
initialize an object of type coeffs by its name, return NULL otherwise
Definition: numbers.h:98
BOOLEAN(* cfInitCharProc)(coeffs, void *)
initialize an object of type coeff, return FALSE in case of success
Definition: numbers.h:94
#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:797
BOOLEAN nrnInitChar(coeffs r, void *p)
Definition: rmodulon.cc:996
Definition: s_buff.h:21
BOOLEAN nrInitChar(coeffs n, void *p)
Initialize r.
Definition: shortfl.cc:658
#define R
Definition: sirandom.c:27
int(* siRandProc)()
Definition: sirandom.h:9
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
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
number(* cfXExtGcd)(number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
Definition: coeffs.h:256
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
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(* cfEucNorm)(number a, const coeffs r)
Definition: coeffs.h:258
number(* cfAnn)(number a, const coeffs r)
Definition: coeffs.h:261
char *(* cfCoeffString)(const coeffs r)
string output of coeff description
Definition: coeffs.h:151
number(* cfReadFd)(const ssiInfo *f, const coeffs r)
Definition: coeffs.h:278
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
void(* cfWriteFd)(number a, const ssiInfo *f, const coeffs r)
Definition: coeffs.h:277
n_coeffType type
Definition: coeffs.h:128
numberfunc cfAdd
Definition: coeffs.h:175
number(* cfRandom)(siRandProc p, number p1, number p2, const coeffs cf)
a function returning random elements
Definition: coeffs.h:306
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
char *(* cfCoeffName)(const coeffs r)
default name of cf, should substitue cfCoeffWrite, cfCoeffString
Definition: coeffs.h:154
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
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
const char *(* cfRead)(const char *s, number *a, const coeffs r)
Definition: coeffs.h:221
BOOLEAN ntInitChar(coeffs cf, void *infoStruct)
Initialize the coeffs object.
Definition: transext.cc:2636