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p_polys.h
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1/****************************************
2* Computer Algebra System SINGULAR *
3****************************************/
4/***************************************************************
5 * File: p_polys.h
6 * Purpose: declaration of poly stuf which are independent of
7 * currRing
8 * Author: obachman (Olaf Bachmann)
9 * Created: 9/00
10 *******************************************************************/
11/***************************************************************
12 * Purpose: implementation of poly procs which iter over ExpVector
13 * Author: obachman (Olaf Bachmann)
14 * Created: 8/00
15 *******************************************************************/
16#ifndef P_POLYS_H
17#define P_POLYS_H
18
19#include "misc/mylimits.h"
20#include "misc/intvec.h"
21#include "coeffs/coeffs.h"
22
25
29
30#include "polys/sbuckets.h"
31
32#ifdef HAVE_PLURAL
33#include "polys/nc/nc.h"
34#endif
35
36poly p_Farey(poly p, number N, const ring r);
37/*
38* xx,q: arrays of length 0..rl-1
39* xx[i]: SB mod q[i]
40* assume: char=0
41* assume: q[i]!=0
42* destroys xx
43*/
44poly p_ChineseRemainder(poly *xx, number *x,number *q, int rl, CFArray &inv_cache, const ring R);
45/***************************************************************
46 *
47 * Divisiblity tests, args must be != NULL, except for
48 * pDivisbleBy
49 *
50 ***************************************************************/
51unsigned long p_GetShortExpVector(const poly a, const ring r);
52
53/// p_GetShortExpVector of p * pp
54unsigned long p_GetShortExpVector(const poly p, const poly pp, const ring r);
55
56#ifdef HAVE_RINGS
57/*! divisibility check over ground ring (which may contain zero divisors);
58 TRUE iff LT(f) divides LT(g), i.e., LT(f)*c*m = LT(g), for some
59 coefficient c and some monomial m;
60 does not take components into account
61 */
62BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r);
63#endif
64
65/***************************************************************
66 *
67 * Misc things on polys
68 *
69 ***************************************************************/
70
71poly p_One(const ring r);
72
73int p_MinDeg(poly p,intvec *w, const ring R);
74
75long p_DegW(poly p, const int *w, const ring R);
76
77/// return TRUE if all monoms have the same component
78BOOLEAN p_OneComp(poly p, const ring r);
79
80/// return i, if head depends only on var(i)
81int p_IsPurePower(const poly p, const ring r);
82
83/// return i, if poly depends only on var(i)
84int p_IsUnivariate(poly p, const ring r);
85
86/// set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0
87/// return #(e[i]>0)
88int p_GetVariables(poly p, int * e, const ring r);
89
90/// returns the poly representing the integer i
91poly p_ISet(long i, const ring r);
92
93/// returns the poly representing the number n, destroys n
94poly p_NSet(number n, const ring r);
95
96void p_Vec2Polys(poly v, poly**p, int *len, const ring r);
97poly p_Vec2Poly(poly v, int k, const ring r);
98
99/// julia: vector to already allocated array (len=p_MaxComp(v,r))
100void p_Vec2Array(poly v, poly *p, int len, const ring r);
101
102/***************************************************************
103 *
104 * Copying/Deletion of polys: args may be NULL
105 *
106 ***************************************************************/
107
108// simply deletes monomials, does not free coeffs
109void p_ShallowDelete(poly *p, const ring r);
110
111
112
113/***************************************************************
114 *
115 * Copying/Deleteion of polys: args may be NULL
116 * - p/q as arg mean a poly
117 * - m a monomial
118 * - n a number
119 * - pp (resp. qq, mm, nn) means arg is constant
120 * - p (resp, q, m, n) means arg is destroyed
121 *
122 ***************************************************************/
123
124poly p_Sub(poly a, poly b, const ring r);
125
126poly p_Power(poly p, int i, const ring r);
127
128
129/***************************************************************
130 *
131 * PDEBUG stuff
132 *
133 ***************************************************************/
134#ifdef PDEBUG
135// Returns TRUE if m is monom of p, FALSE otherwise
136BOOLEAN pIsMonomOf(poly p, poly m);
137// Returns TRUE if p and q have common monoms
138BOOLEAN pHaveCommonMonoms(poly p, poly q);
139
140// p_Check* routines return TRUE if everything is ok,
141// else, they report error message and return false
142
143// check if Lm(p) is from ring r
144BOOLEAN p_LmCheckIsFromRing(poly p, ring r);
145// check if Lm(p) != NULL, r != NULL and initialized && Lm(p) is from r
146BOOLEAN p_LmCheckPolyRing(poly p, ring r);
147// check if all monoms of p are from ring r
148BOOLEAN p_CheckIsFromRing(poly p, ring r);
149// check r != NULL and initialized && all monoms of p are from r
150BOOLEAN p_CheckPolyRing(poly p, ring r);
151// check if r != NULL and initialized
152BOOLEAN p_CheckRing(ring r);
153// only do check if cond
154
155
156#define pIfThen(cond, check) do {if (cond) {check;}} while (0)
157
158BOOLEAN _p_Test(poly p, ring r, int level);
159BOOLEAN _p_LmTest(poly p, ring r, int level);
160BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level);
161
162#define p_Test(p,r) _p_Test(p, r, PDEBUG)
163#define p_LmTest(p,r) _p_LmTest(p, r, PDEBUG)
164#define pp_Test(p, lmRing, tailRing) _pp_Test(p, lmRing, tailRing, PDEBUG)
165
166#else // ! PDEBUG
167
168#define pIsMonomOf(p, q) (TRUE)
169#define pHaveCommonMonoms(p, q) (TRUE)
170#define p_LmCheckIsFromRing(p,r) (TRUE)
171#define p_LmCheckPolyRing(p,r) (TRUE)
172#define p_CheckIsFromRing(p,r) (TRUE)
173#define p_CheckPolyRing(p,r) (TRUE)
174#define p_CheckRing(r) (TRUE)
175#define P_CheckIf(cond, check) (TRUE)
176
177#define p_Test(p,r) (TRUE)
178#define p_LmTest(p,r) (TRUE)
179#define pp_Test(p, lmRing, tailRing) (TRUE)
180
181#endif
182
183/***************************************************************
184 *
185 * Misc stuff
186 *
187 ***************************************************************/
188/*2
189* returns the length of a polynomial (numbers of monomials)
190*/
191static inline unsigned pLength(poly a)
192{
193 unsigned l = 0;
194 while (a!=NULL)
195 {
196 pIter(a);
197 l++;
198 }
199 return l;
200}
201
202// returns the length of a polynomial (numbers of monomials) and the last mon.
203// respect syzComp
204poly p_Last(const poly a, int &l, const ring r);
205
206/*----------------------------------------------------*/
207
208void p_Norm(poly p1, const ring r);
209void p_Normalize(poly p,const ring r);
210void p_ProjectiveUnique(poly p,const ring r);
211
212void p_ContentForGB(poly p, const ring r);
213void p_Content(poly p, const ring r);
214void p_Content_n(poly p, number &c,const ring r);
215#if 1
216// currently only used by Singular/janet
217void p_SimpleContent(poly p, int s, const ring r);
218number p_InitContent(poly ph, const ring r);
219#endif
220
221poly p_Cleardenom(poly p, const ring r);
222void p_Cleardenom_n(poly p, const ring r,number &c);
223//number p_GetAllDenom(poly ph, const ring r);// unused
224
225int p_Size( poly p, const ring r );
226
227// homogenizes p by multiplying certain powers of the varnum-th variable
228poly p_Homogen (poly p, int varnum, const ring r);
229
230BOOLEAN p_IsHomogeneous (poly p, const ring r);
231
232// Setm
233static inline void p_Setm(poly p, const ring r)
234{
235 p_CheckRing2(r);
236 r->p_Setm(p, r);
237}
238
239p_SetmProc p_GetSetmProc(const ring r);
240
241poly p_Subst(poly p, int n, poly e, const ring r);
242
243// TODO:
244#define p_SetmComp p_Setm
245
246// component
247static inline unsigned long p_SetComp(poly p, unsigned long c, ring r)
248{
250 if (r->pCompIndex>=0) __p_GetComp(p,r) = c;
251 return c;
252}
253// sets component of poly a to i
254static inline void p_SetCompP(poly p, int i, ring r)
255{
256 if (p != NULL)
257 {
258 p_Test(p, r);
260 {
261 do
262 {
263 p_SetComp(p, i, r);
264 p_SetmComp(p, r);
265 pIter(p);
266 }
267 while (p != NULL);
268 }
269 else
270 {
271 do
272 {
273 p_SetComp(p, i, r);
274 pIter(p);
275 }
276 while(p != NULL);
277 }
278 }
279}
280
281static inline void p_SetCompP(poly p, int i, ring lmRing, ring tailRing)
282{
283 if (p != NULL)
284 {
285 p_SetComp(p, i, lmRing);
286 p_SetmComp(p, lmRing);
287 p_SetCompP(pNext(p), i, tailRing);
288 }
289}
290
291// returns maximal column number in the modul element a (or 0)
292static inline long p_MaxComp(poly p, ring lmRing, ring tailRing)
293{
294 long result,i;
295
296 if(p==NULL) return 0;
297 result = p_GetComp(p, lmRing);
298 if (result != 0)
299 {
300 loop
301 {
302 pIter(p);
303 if(p==NULL) break;
304 i = p_GetComp(p, tailRing);
305 if (i>result) result = i;
306 }
307 }
308 return result;
309}
310
311static inline long p_MaxComp(poly p,ring lmRing) {return p_MaxComp(p,lmRing,lmRing);}
312
313static inline long p_MinComp(poly p, ring lmRing, ring tailRing)
314{
315 long result,i;
316
317 if(p==NULL) return 0;
318 result = p_GetComp(p,lmRing);
319 if (result != 0)
320 {
321 loop
322 {
323 pIter(p);
324 if(p==NULL) break;
325 i = p_GetComp(p,tailRing);
326 if (i<result) result = i;
327 }
328 }
329 return result;
330}
331
332static inline long p_MinComp(poly p,ring lmRing) {return p_MinComp(p,lmRing,lmRing);}
333
334
335static inline poly pReverse(poly p)
336{
337 if (p == NULL || pNext(p) == NULL) return p;
338
339 poly q = pNext(p), // == pNext(p)
340 qn;
341 pNext(p) = NULL;
342 do
343 {
344 qn = pNext(q);
345 pNext(q) = p;
346 p = q;
347 q = qn;
348 }
349 while (qn != NULL);
350 return p;
351}
352void pEnlargeSet(poly**p, int length, int increment);
353
354
355/***************************************************************
356 *
357 * I/O
358 *
359 ***************************************************************/
360/// print p according to ShortOut in lmRing & tailRing
361void p_String0(poly p, ring lmRing, ring tailRing);
362char* p_String(poly p, ring lmRing, ring tailRing);
363void p_Write(poly p, ring lmRing, ring tailRing);
364void p_Write0(poly p, ring lmRing, ring tailRing);
365void p_wrp(poly p, ring lmRing, ring tailRing);
366
367/// print p in a short way, if possible
368void p_String0Short(const poly p, ring lmRing, ring tailRing);
369
370/// print p in a long way
371void p_String0Long(const poly p, ring lmRing, ring tailRing);
372
373
374/***************************************************************
375 *
376 * Degree stuff -- see p_polys.cc for explainations
377 *
378 ***************************************************************/
379
380static inline long p_FDeg(const poly p, const ring r) { return r->pFDeg(p,r); }
381static inline long p_LDeg(const poly p, int *l, const ring r) { return r->pLDeg(p,l,r); }
382
383long p_WFirstTotalDegree(poly p, ring r);
384long p_WTotaldegree(poly p, const ring r);
385long p_WDegree(poly p,const ring r);
386long pLDeg0(poly p,int *l, ring r);
387long pLDeg0c(poly p,int *l, ring r);
388long pLDegb(poly p,int *l, ring r);
389long pLDeg1(poly p,int *l, ring r);
390long pLDeg1c(poly p,int *l, ring r);
391long pLDeg1_Deg(poly p,int *l, ring r);
392long pLDeg1c_Deg(poly p,int *l, ring r);
393long pLDeg1_Totaldegree(poly p,int *l, ring r);
394long pLDeg1c_Totaldegree(poly p,int *l, ring r);
395long pLDeg1_WFirstTotalDegree(poly p,int *l, ring r);
396long pLDeg1c_WFirstTotalDegree(poly p,int *l, ring r);
397
398BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r);
399
400/// same as the usual p_EqualPolys for polys belonging to *equal* rings
401BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r1, const ring r2);
402
403long p_Deg(poly a, const ring r);
404
405
406/***************************************************************
407 *
408 * Primitives for accessing and setting fields of a poly
409 *
410 ***************************************************************/
411
412static inline number p_SetCoeff(poly p, number n, ring r)
413{
415 n_Delete(&(p->coef), r->cf);
416 (p)->coef=n;
417 return n;
418}
419
420// order
421static inline long p_GetOrder(poly p, ring r)
422{
424 if (r->typ==NULL) return ((p)->exp[r->pOrdIndex]);
425 int i=0;
426 loop
427 {
428 switch(r->typ[i].ord_typ)
429 {
430 case ro_am:
431 case ro_wp_neg:
432 return ((p->exp[r->pOrdIndex])-POLY_NEGWEIGHT_OFFSET);
433 case ro_syzcomp:
434 case ro_syz:
435 case ro_cp:
436 i++;
437 break;
438 //case ro_dp:
439 //case ro_wp:
440 default:
441 return ((p)->exp[r->pOrdIndex]);
442 }
443 }
444}
445
446
447static inline unsigned long p_AddComp(poly p, unsigned long v, ring r)
448{
451 return __p_GetComp(p,r) += v;
452}
453static inline unsigned long p_SubComp(poly p, unsigned long v, ring r)
454{
457 _pPolyAssume2(__p_GetComp(p,r) >= v,p,r);
458 return __p_GetComp(p,r) -= v;
459}
460
461#ifndef HAVE_EXPSIZES
462
463/// get a single variable exponent
464/// @Note:
465/// the integer VarOffset encodes:
466/// 1. the position of a variable in the exponent vector p->exp (lower 24 bits)
467/// 2. number of bits to shift to the right in the upper 8 bits (which takes at most 6 bits for 64 bit)
468/// Thus VarOffset always has 2 zero higher bits!
469static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
470{
471 pAssume2((VarOffset >> (24 + 6)) == 0);
472#if 0
473 int pos=(VarOffset & 0xffffff);
474 int bitpos=(VarOffset >> 24);
475 unsigned long exp=(p->exp[pos] >> bitmask) & iBitmask;
476 return exp;
477#else
478 return (long)
479 ((p->exp[(VarOffset & 0xffffff)] >> (VarOffset >> 24))
480 & iBitmask);
481#endif
482}
483
484
485/// set a single variable exponent
486/// @Note:
487/// VarOffset encodes the position in p->exp @see p_GetExp
488static inline unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
489{
490 pAssume2(e>=0);
491 pAssume2(e<=iBitmask);
492 pAssume2((VarOffset >> (24 + 6)) == 0);
493
494 // shift e to the left:
495 REGISTER int shift = VarOffset >> 24;
496 unsigned long ee = e << shift /*(VarOffset >> 24)*/;
497 // find the bits in the exponent vector
498 REGISTER int offset = (VarOffset & 0xffffff);
499 // clear the bits in the exponent vector:
500 p->exp[offset] &= ~( iBitmask << shift );
501 // insert e with |
502 p->exp[ offset ] |= ee;
503 return e;
504}
505
506
507#else // #ifdef HAVE_EXPSIZES // EXPERIMENTAL!!!
508
509static inline unsigned long BitMask(unsigned long bitmask, int twobits)
510{
511 // bitmask = 00000111111111111
512 // 0 must give bitmask!
513 // 1, 2, 3 - anything like 00011..11
514 pAssume2((twobits >> 2) == 0);
515 static const unsigned long _bitmasks[4] = {-1, 0x7fff, 0x7f, 0x3};
516 return bitmask & _bitmasks[twobits];
517}
518
519
520/// @Note: we may add some more info (6 ) into VarOffset and thus encode
521static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
522{
523 int pos =(VarOffset & 0xffffff);
524 int hbyte= (VarOffset >> 24); // the highest byte
525 int bitpos = hbyte & 0x3f; // last 6 bits
526 long bitmask = BitMask(iBitmask, hbyte >> 6);
527
528 long exp=(p->exp[pos] >> bitpos) & bitmask;
529 return exp;
530
531}
532
533static inline long p_SetExp(poly p, const long e, const unsigned long iBitmask, const int VarOffset)
534{
535 pAssume2(e>=0);
536 pAssume2(e <= BitMask(iBitmask, VarOffset >> 30));
537
538 // shift e to the left:
539 REGISTER int hbyte = VarOffset >> 24;
540 int bitmask = BitMask(iBitmask, hbyte >> 6);
541 REGISTER int shift = hbyte & 0x3f;
542 long ee = e << shift;
543 // find the bits in the exponent vector
544 REGISTER int offset = (VarOffset & 0xffffff);
545 // clear the bits in the exponent vector:
546 p->exp[offset] &= ~( bitmask << shift );
547 // insert e with |
548 p->exp[ offset ] |= ee;
549 return e;
550}
551
552#endif // #ifndef HAVE_EXPSIZES
553
554
555static inline long p_GetExp(const poly p, const ring r, const int VarOffset)
556{
558 pAssume2(VarOffset != -1);
559 return p_GetExp(p, r->bitmask, VarOffset);
560}
561
562static inline long p_SetExp(poly p, const long e, const ring r, const int VarOffset)
563{
565 pAssume2(VarOffset != -1);
566 return p_SetExp(p, e, r->bitmask, VarOffset);
567}
568
569
570
571/// get v^th exponent for a monomial
572static inline long p_GetExp(const poly p, const int v, const ring r)
573{
575 pAssume2(v>0 && v <= r->N);
576 pAssume2(r->VarOffset[v] != -1);
577 return p_GetExp(p, r->bitmask, r->VarOffset[v]);
578}
579
580
581/// set v^th exponent for a monomial
582static inline long p_SetExp(poly p, const int v, const long e, const ring r)
583{
585 pAssume2(v>0 && v <= r->N);
586 pAssume2(r->VarOffset[v] != -1);
587 return p_SetExp(p, e, r->bitmask, r->VarOffset[v]);
588}
589
590// the following should be implemented more efficiently
591static inline long p_IncrExp(poly p, int v, ring r)
592{
594 int e = p_GetExp(p,v,r);
595 e++;
596 return p_SetExp(p,v,e,r);
597}
598static inline long p_DecrExp(poly p, int v, ring r)
599{
601 int e = p_GetExp(p,v,r);
602 pAssume2(e > 0);
603 e--;
604 return p_SetExp(p,v,e,r);
605}
606static inline long p_AddExp(poly p, int v, long ee, ring r)
607{
609 int e = p_GetExp(p,v,r);
610 e += ee;
611 return p_SetExp(p,v,e,r);
612}
613static inline long p_SubExp(poly p, int v, long ee, ring r)
614{
616 long e = p_GetExp(p,v,r);
617 pAssume2(e >= ee);
618 e -= ee;
619 return p_SetExp(p,v,e,r);
620}
621static inline long p_MultExp(poly p, int v, long ee, ring r)
622{
624 long e = p_GetExp(p,v,r);
625 e *= ee;
626 return p_SetExp(p,v,e,r);
627}
628
629static inline long p_GetExpSum(poly p1, poly p2, int i, ring r)
630{
631 p_LmCheckPolyRing2(p1, r);
632 p_LmCheckPolyRing2(p2, r);
633 return p_GetExp(p1,i,r) + p_GetExp(p2,i,r);
634}
635static inline long p_GetExpDiff(poly p1, poly p2, int i, ring r)
636{
637 return p_GetExp(p1,i,r) - p_GetExp(p2,i,r);
638}
639
640static inline int p_Comp_k_n(poly a, poly b, int k, ring r)
641{
642 if ((a==NULL) || (b==NULL) ) return FALSE;
643 p_LmCheckPolyRing2(a, r);
645 pAssume2(k > 0 && k <= r->N);
646 int i=k;
647 for(;i<=r->N;i++)
648 {
649 if (p_GetExp(a,i,r) != p_GetExp(b,i,r)) return FALSE;
650 // if (a->exp[(r->VarOffset[i] & 0xffffff)] != b->exp[(r->VarOffset[i] & 0xffffff)]) return FALSE;
651 }
652 return TRUE;
653}
654
655
656/***************************************************************
657 *
658 * Allocation/Initalization/Deletion
659 *
660 ***************************************************************/
661#if (OM_TRACK > 2) && defined(OM_TRACK_CUSTOM)
662static inline poly p_New(const ring r, omBin bin)
663#else
664static inline poly p_New(const ring /*r*/, omBin bin)
665#endif
666{
667 p_CheckRing2(r);
668 pAssume2(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
669 poly p;
670 omTypeAllocBin(poly, p, bin);
671 p_SetRingOfLm(p, r);
672 return p;
673}
674
675static inline poly p_New(ring r)
676{
677 return p_New(r, r->PolyBin);
678}
679
680#if PDEBUG > 2
681static inline void p_LmFree(poly p, ring r)
682#else
683static inline void p_LmFree(poly p, ring)
684#endif
685{
688}
689#if PDEBUG > 2
690static inline void p_LmFree(poly *p, ring r)
691#else
692static inline void p_LmFree(poly *p, ring)
693#endif
694{
696 poly h = *p;
697 *p = pNext(h);
699}
700#if PDEBUG > 2
701static inline poly p_LmFreeAndNext(poly p, ring r)
702#else
703static inline poly p_LmFreeAndNext(poly p, ring)
704#endif
705{
707 poly pnext = pNext(p);
709 return pnext;
710}
711static inline void p_LmDelete(poly p, const ring r)
712{
714 n_Delete(&pGetCoeff(p), r->cf);
716}
717static inline void p_LmDelete(poly *p, const ring r)
718{
720 poly h = *p;
721 *p = pNext(h);
722 n_Delete(&pGetCoeff(h), r->cf);
724}
725static inline poly p_LmDeleteAndNext(poly p, const ring r)
726{
728 poly pnext = pNext(p);
729 n_Delete(&pGetCoeff(p), r->cf);
731 return pnext;
732}
733
734/***************************************************************
735 *
736 * Misc routines
737 *
738 ***************************************************************/
739
740/// return the maximal exponent of p in form of the maximal long var
741unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max = 0);
742
743/// return monomial r such that GetExp(r,i) is maximum of all
744/// monomials in p; coeff == 0, next == NULL, ord is not set
745poly p_GetMaxExpP(poly p, ring r);
746
747static inline unsigned long p_GetMaxExp(const unsigned long l, const ring r)
748{
749 unsigned long bitmask = r->bitmask;
750 unsigned long max = (l & bitmask);
751 unsigned long j = r->ExpPerLong - 1;
752
753 if (j > 0)
754 {
755 unsigned long i = r->BitsPerExp;
756 long e;
757 loop
758 {
759 e = ((l >> i) & bitmask);
760 if ((unsigned long) e > max)
761 max = e;
762 j--;
763 if (j==0) break;
764 i += r->BitsPerExp;
765 }
766 }
767 return max;
768}
769
770static inline unsigned long p_GetMaxExp(const poly p, const ring r)
771{
772 return p_GetMaxExp(p_GetMaxExpL(p, r), r);
773}
774
775static inline unsigned long
776p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps)
777{
778 const unsigned long bitmask = r->bitmask;
779 unsigned long sum = (l & bitmask);
780 unsigned long j = number_of_exps - 1;
781
782 if (j > 0)
783 {
784 unsigned long i = r->BitsPerExp;
785 loop
786 {
787 sum += ((l >> i) & bitmask);
788 j--;
789 if (j==0) break;
790 i += r->BitsPerExp;
791 }
792 }
793 return sum;
794}
795
796/***************************************************************
797 *
798 * Dispatcher to r->p_Procs, they do the tests/checks
799 *
800 ***************************************************************/
801/// returns a copy of p (without any additional testing)
802static inline poly p_Copy_noCheck(poly p, const ring r)
803{
804 /*assume(p!=NULL);*/
805 assume(r != NULL);
806 assume(r->p_Procs != NULL);
807 assume(r->p_Procs->p_Copy != NULL);
808 return r->p_Procs->p_Copy(p, r);
809}
810
811/// returns a copy of p
812static inline poly p_Copy(poly p, const ring r)
813{
814 if (p!=NULL)
815 {
816 p_Test(p,r);
817 const poly pp = p_Copy_noCheck(p, r);
818 p_Test(pp,r);
819 return pp;
820 }
821 else
822 return NULL;
823}
824
825/// copy the i(leading) term of p
826static inline poly p_Head(poly p, const ring r)
827{
828 if (p == NULL) return NULL;
830 poly np;
831 omTypeAllocBin(poly, np, r->PolyBin);
832 p_SetRingOfLm(np, r);
833 memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
834 pNext(np) = NULL;
835 pSetCoeff0(np, n_Copy(pGetCoeff(p), r->cf));
836 return np;
837}
838
839/// like p_Head, but with coefficient 1
840poly p_CopyPowerProduct(poly p, const ring r);
841
842/// returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing
843static inline poly p_Copy(poly p, const ring lmRing, const ring tailRing)
844{
845 if (p != NULL)
846 {
847#ifndef PDEBUG
848 if (tailRing == lmRing)
849 return p_Copy_noCheck(p, tailRing);
850#endif
851 poly pres = p_Head(p, lmRing);
852 if (pNext(p)!=NULL)
853 pNext(pres) = p_Copy_noCheck(pNext(p), tailRing);
854 return pres;
855 }
856 else
857 return NULL;
858}
859
860// deletes *p, and sets *p to NULL
861static inline void p_Delete(poly *p, const ring r)
862{
863 assume( p!= NULL );
864 assume( r!= NULL );
865 if ((*p)!=NULL) r->p_Procs->p_Delete(p, r);
866}
867
868static inline void p_Delete(poly *p, const ring lmRing, const ring tailRing)
869{
870 assume( p!= NULL );
871 if (*p != NULL)
872 {
873#ifndef PDEBUG
874 if (tailRing == lmRing)
875 {
876 p_Delete(p, tailRing);
877 return;
878 }
879#endif
880 if (pNext(*p) != NULL)
881 p_Delete(&pNext(*p), tailRing);
882 p_LmDelete(p, lmRing);
883 }
884}
885
886// copys monomials of p, allocates new monomials from bin,
887// deletes monomials of p
888static inline poly p_ShallowCopyDelete(poly p, const ring r, omBin bin)
889{
891 pAssume2(omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
892 return r->p_Procs->p_ShallowCopyDelete(p, r, bin);
893}
894
895// returns p+q, destroys p and q
896static inline poly p_Add_q(poly p, poly q, const ring r)
897{
898 assume( (p != q) || (p == NULL && q == NULL) );
899 if (q==NULL) return p;
900 if (p==NULL) return q;
901 int shorter;
902 return r->p_Procs->p_Add_q(p, q, shorter, r);
903}
904
905/// like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q)
906static inline poly p_Add_q(poly p, poly q, int &lp, int lq, const ring r)
907{
908 assume( (p != q) || (p == NULL && q == NULL) );
909 if (q==NULL) return p;
910 if (p==NULL) { lp=lq; return q; }
911 int shorter;
912 poly res = r->p_Procs->p_Add_q(p, q, shorter, r);
913 lp += lq - shorter;
914 return res;
915}
916
917// returns p*n, destroys p
918static inline poly p_Mult_nn(poly p, number n, const ring r)
919{
920 if (p==NULL) return NULL;
921 if (n_IsOne(n, r->cf))
922 return p;
923 else if (n_IsZero(n, r->cf))
924 {
925 p_Delete(&p, r); // NOTE: without p_Delete - memory leak!
926 return NULL;
927 }
928 else
929 return r->p_Procs->p_Mult_nn(p, n, r);
930}
931#define __p_Mult_nn(p,n,r) r->p_Procs->p_Mult_nn(p, n, r)
932
933static inline poly p_Mult_nn(poly p, number n, const ring lmRing,
934 const ring tailRing)
935{
936 assume(p!=NULL);
937#ifndef PDEBUG
938 if (lmRing == tailRing)
939 return p_Mult_nn(p, n, tailRing);
940#endif
941 poly pnext = pNext(p);
942 pNext(p) = NULL;
943 p = lmRing->p_Procs->p_Mult_nn(p, n, lmRing);
944 if (pnext!=NULL)
945 {
946 pNext(p) = tailRing->p_Procs->p_Mult_nn(pnext, n, tailRing);
947 }
948 return p;
949}
950
951// returns p*n, does not destroy p
952static inline poly pp_Mult_nn(poly p, number n, const ring r)
953{
954 if (p==NULL) return NULL;
955 if (n_IsOne(n, r->cf))
956 return p_Copy(p, r);
957 else if (n_IsZero(n, r->cf))
958 return NULL;
959 else
960 return r->p_Procs->pp_Mult_nn(p, n, r);
961}
962#define __pp_Mult_nn(p,n,r) r->p_Procs->pp_Mult_nn(p, n, r)
963
964// test if the monomial is a constant as a vector component
965// i.e., test if all exponents are zero
966static inline BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
967{
968 //p_LmCheckPolyRing(p, r);
969 int i = r->VarL_Size - 1;
970
971 do
972 {
973 if (p->exp[r->VarL_Offset[i]] != 0)
974 return FALSE;
975 i--;
976 }
977 while (i >= 0);
978 return TRUE;
979}
980
981// test if monomial is a constant, i.e. if all exponents and the component
982// is zero
983static inline BOOLEAN p_LmIsConstant(const poly p, const ring r)
984{
985 if (p_LmIsConstantComp(p, r))
986 return (p_GetComp(p, r) == 0);
987 return FALSE;
988}
989
990// returns Copy(p)*m, does neither destroy p nor m
991static inline poly pp_Mult_mm(poly p, poly m, const ring r)
992{
993 if (p==NULL) return NULL;
994 if (p_LmIsConstant(m, r))
995 return __pp_Mult_nn(p, pGetCoeff(m), r);
996 else
997 return r->p_Procs->pp_Mult_mm(p, m, r);
998}
999
1000// returns m*Copy(p), does neither destroy p nor m
1001static inline poly pp_mm_Mult(poly p, poly m, const ring r)
1002{
1003 if (p==NULL) return NULL;
1004 if (p_LmIsConstant(m, r))
1005 return __pp_Mult_nn(p, pGetCoeff(m), r);
1006 else
1007 return r->p_Procs->pp_mm_Mult(p, m, r);
1008}
1009
1010// returns p*m, destroys p, const: m
1011static inline poly p_Mult_mm(poly p, poly m, const ring r)
1012{
1013 if (p==NULL) return NULL;
1014 if (p_LmIsConstant(m, r))
1015 return __p_Mult_nn(p, pGetCoeff(m), r);
1016 else
1017 return r->p_Procs->p_Mult_mm(p, m, r);
1018}
1019
1020// returns m*p, destroys p, const: m
1021static inline poly p_mm_Mult(poly p, poly m, const ring r)
1022{
1023 if (p==NULL) return NULL;
1024 if (p_LmIsConstant(m, r))
1025 return __p_Mult_nn(p, pGetCoeff(m), r);
1026 else
1027 return r->p_Procs->p_mm_Mult(p, m, r);
1028}
1029
1030static inline poly p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, int lq,
1031 const poly spNoether, const ring r)
1032{
1033 int shorter;
1034 const poly res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, spNoether, r);
1035 lp += lq - shorter;
1036// assume( lp == pLength(res) );
1037 return res;
1038}
1039
1040// return p - m*Copy(q), destroys p; const: p,m
1041static inline poly p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, const ring r)
1042{
1043 int shorter;
1044
1045 return r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
1046}
1047
1048
1049// returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
1050static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r)
1051{
1052 int shorter;
1053 return r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
1054}
1055
1056// returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
1057// if lp is length of p on input then lp is length of returned poly on output
1058static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, int &lp, const poly m, const ring r)
1059{
1060 int shorter;
1061 poly pp = r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
1062 lp -= shorter;
1063 return pp;
1064}
1065
1066// returns -p, destroys p
1067static inline poly p_Neg(poly p, const ring r)
1068{
1069 return r->p_Procs->p_Neg(p, r);
1070}
1071
1072extern poly _p_Mult_q(poly p, poly q, const int copy, const ring r);
1073// returns p*q, destroys p and q
1074static inline poly p_Mult_q(poly p, poly q, const ring r)
1075{
1076 assume( (p != q) || (p == NULL && q == NULL) );
1077
1078 if (p == NULL)
1079 {
1080 p_Delete(&q, r);
1081 return NULL;
1082 }
1083 if (q == NULL)
1084 {
1085 p_Delete(&p, r);
1086 return NULL;
1087 }
1088
1089 if (pNext(p) == NULL)
1090 {
1091 q = r->p_Procs->p_mm_Mult(q, p, r);
1092 p_LmDelete(&p, r);
1093 return q;
1094 }
1095
1096 if (pNext(q) == NULL)
1097 {
1098 p = r->p_Procs->p_Mult_mm(p, q, r);
1099 p_LmDelete(&q, r);
1100 return p;
1101 }
1102#if defined(HAVE_PLURAL) || defined(HAVE_SHIFTBBA)
1103 if (rIsNCRing(r))
1104 return _nc_p_Mult_q(p, q, r);
1105 else
1106#endif
1107 return _p_Mult_q(p, q, 0, r);
1108}
1109
1110// returns p*q, does neither destroy p nor q
1111static inline poly pp_Mult_qq(poly p, poly q, const ring r)
1112{
1113 if (p == NULL || q == NULL) return NULL;
1114
1115 if (pNext(p) == NULL)
1116 {
1117 return r->p_Procs->pp_mm_Mult(q, p, r);
1118 }
1119
1120 if (pNext(q) == NULL)
1121 {
1122 return r->p_Procs->pp_Mult_mm(p, q, r);
1123 }
1124
1125 poly qq = q;
1126 if (p == q)
1127 qq = p_Copy(q, r);
1128
1129 poly res;
1130#if defined(HAVE_PLURAL) || defined(HAVE_SHIFTBBA)
1131 if (rIsNCRing(r))
1132 res = _nc_pp_Mult_qq(p, qq, r);
1133 else
1134#endif
1135 res = _p_Mult_q(p, qq, 1, r);
1136
1137 if (qq != q)
1138 p_Delete(&qq, r);
1139 return res;
1140}
1141
1142// returns p + m*q destroys p, const: q, m
1143static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq,
1144 const ring r)
1145{
1146#ifdef HAVE_PLURAL
1147 if (rIsPluralRing(r))
1148 return nc_p_Plus_mm_Mult_qq(p, m, q, lp, lq, r);
1149#endif
1150
1151// this should be implemented more efficiently
1152 poly res;
1153 int shorter;
1154 number n_old = pGetCoeff(m);
1155 number n_neg = n_Copy(n_old, r->cf);
1156 n_neg = n_InpNeg(n_neg, r->cf);
1157 pSetCoeff0(m, n_neg);
1158 res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
1159 lp = (lp + lq) - shorter;
1160 pSetCoeff0(m, n_old);
1161 n_Delete(&n_neg, r->cf);
1162 return res;
1163}
1164
1165static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, const ring r)
1166{
1167 int lp = 0, lq = 0;
1168 return p_Plus_mm_Mult_qq(p, m, q, lp, lq, r);
1169}
1170
1171// returns merged p and q, assumes p and q have no monomials which are equal
1172static inline poly p_Merge_q(poly p, poly q, const ring r)
1173{
1174 assume( (p != q) || (p == NULL && q == NULL) );
1175 return r->p_Procs->p_Merge_q(p, q, r);
1176}
1177
1178// like p_SortMerge, except that p may have equal monimals
1179static inline poly p_SortAdd(poly p, const ring r, BOOLEAN revert= FALSE)
1180{
1181 if (revert) p = pReverse(p);
1182 return sBucketSortAdd(p, r);
1183}
1184
1185// sorts p using bucket sort: returns sorted poly
1186// assumes that monomials of p are all different
1187// reverses it first, if revert == TRUE, use this if input p is "almost" sorted
1188// correctly
1189static inline poly p_SortMerge(poly p, const ring r, BOOLEAN revert= FALSE)
1190{
1191 if (revert) p = pReverse(p);
1192 return sBucketSortMerge(p, r);
1193}
1194
1195/***************************************************************
1196 *
1197 * I/O
1198 *
1199 ***************************************************************/
1200static inline char* p_String(poly p, ring p_ring)
1201{
1202 return p_String(p, p_ring, p_ring);
1203}
1204static inline void p_String0(poly p, ring p_ring)
1205{
1206 p_String0(p, p_ring, p_ring);
1207}
1208static inline void p_Write(poly p, ring p_ring)
1209{
1210 p_Write(p, p_ring, p_ring);
1211}
1212static inline void p_Write0(poly p, ring p_ring)
1213{
1214 p_Write0(p, p_ring, p_ring);
1215}
1216static inline void p_wrp(poly p, ring p_ring)
1217{
1218 p_wrp(p, p_ring, p_ring);
1219}
1220
1221
1222#if PDEBUG > 0
1223
1224#define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
1225do \
1226{ \
1227 int _cmp = p_LmCmp(p,q,r); \
1228 if (_cmp == 0) actionE; \
1229 if (_cmp == 1) actionG; \
1230 actionS; \
1231} \
1232while(0)
1233
1234#else
1235
1236#define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
1237 p_MemCmp_LengthGeneral_OrdGeneral(p->exp, q->exp, r->CmpL_Size, r->ordsgn, \
1238 actionE, actionG, actionS)
1239
1240#endif
1241
1242#define pDivAssume(x) do {} while (0)
1243
1244
1245
1246/***************************************************************
1247 *
1248 * Allocation/Initalization/Deletion
1249 *
1250 ***************************************************************/
1251// adjustments for negative weights
1252static inline void p_MemAdd_NegWeightAdjust(poly p, const ring r)
1253{
1254 if (r->NegWeightL_Offset != NULL)
1255 {
1256 for (int i=r->NegWeightL_Size-1; i>=0; i--)
1257 {
1258 p->exp[r->NegWeightL_Offset[i]] -= POLY_NEGWEIGHT_OFFSET;
1259 }
1260 }
1261}
1262static inline void p_MemSub_NegWeightAdjust(poly p, const ring r)
1263{
1264 if (r->NegWeightL_Offset != NULL)
1265 {
1266 for (int i=r->NegWeightL_Size-1; i>=0; i--)
1267 {
1268 p->exp[r->NegWeightL_Offset[i]] += POLY_NEGWEIGHT_OFFSET;
1269 }
1270 }
1271}
1272// ExpVextor(d_p) = ExpVector(s_p)
1273static inline void p_ExpVectorCopy(poly d_p, poly s_p, const ring r)
1274{
1275 p_LmCheckPolyRing1(d_p, r);
1276 p_LmCheckPolyRing1(s_p, r);
1277 memcpy(d_p->exp, s_p->exp, r->ExpL_Size*sizeof(long));
1278}
1279
1280static inline poly p_Init(const ring r, omBin bin)
1281{
1282 p_CheckRing1(r);
1283 pAssume1(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
1284 poly p;
1285 omTypeAlloc0Bin(poly, p, bin);
1287 p_SetRingOfLm(p, r);
1288 return p;
1289}
1290static inline poly p_Init(const ring r)
1291{
1292 return p_Init(r, r->PolyBin);
1293}
1294
1295static inline poly p_LmInit(poly p, const ring r)
1296{
1298 poly np;
1299 omTypeAllocBin(poly, np, r->PolyBin);
1300 p_SetRingOfLm(np, r);
1301 memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
1302 pNext(np) = NULL;
1303 pSetCoeff0(np, NULL);
1304 return np;
1305}
1306static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r, omBin d_bin)
1307{
1308 p_LmCheckPolyRing1(s_p, s_r);
1309 p_CheckRing(d_r);
1310 pAssume1(d_r->N <= s_r->N);
1311 poly d_p = p_Init(d_r, d_bin);
1312 for (unsigned i=d_r->N; i!=0; i--)
1313 {
1314 p_SetExp(d_p, i, p_GetExp(s_p, i,s_r), d_r);
1315 }
1316 if (rRing_has_Comp(d_r))
1317 {
1318 p_SetComp(d_p, p_GetComp(s_p,s_r), d_r);
1319 }
1320 p_Setm(d_p, d_r);
1321 return d_p;
1322}
1323static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r)
1324{
1325 pAssume1(d_r != NULL);
1326 return p_LmInit(s_p, s_r, d_r, d_r->PolyBin);
1327}
1328
1329// set all exponents l..k to 0, assume exp. k+1..n and 1..l-1 are in
1330// different blocks
1331// set coeff to 1
1332static inline poly p_GetExp_k_n(poly p, int l, int k, const ring r)
1333{
1334 if (p == NULL) return NULL;
1336 poly np;
1337 omTypeAllocBin(poly, np, r->PolyBin);
1338 p_SetRingOfLm(np, r);
1339 memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
1340 pNext(np) = NULL;
1341 pSetCoeff0(np, n_Init(1, r->cf));
1342 int i;
1343 for(i=l;i<=k;i++)
1344 {
1345 //np->exp[(r->VarOffset[i] & 0xffffff)] =0;
1346 p_SetExp(np,i,0,r);
1347 }
1348 p_Setm(np,r);
1349 return np;
1350}
1351
1352// simialar to p_ShallowCopyDelete but does it only for leading monomial
1353static inline poly p_LmShallowCopyDelete(poly p, const ring r)
1354{
1356 pAssume1(omSizeWOfBin(bin) == omSizeWOfBin(r->PolyBin));
1357 poly new_p = p_New(r);
1358 memcpy(new_p->exp, p->exp, r->ExpL_Size*sizeof(long));
1359 pSetCoeff0(new_p, pGetCoeff(p));
1360 pNext(new_p) = pNext(p);
1362 return new_p;
1363}
1364
1365/***************************************************************
1366 *
1367 * Operation on ExpVectors
1368 *
1369 ***************************************************************/
1370// ExpVector(p1) += ExpVector(p2)
1371static inline void p_ExpVectorAdd(poly p1, poly p2, const ring r)
1372{
1373 p_LmCheckPolyRing1(p1, r);
1374 p_LmCheckPolyRing1(p2, r);
1375#if PDEBUG >= 1
1376 for (int i=1; i<=r->N; i++)
1377 pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask);
1378 pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0);
1379#endif
1380
1381 p_MemAdd_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size);
1383}
1384// ExpVector(pr) = ExpVector(p1) + ExpVector(p2)
1385static inline void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r)
1386{
1387 p_LmCheckPolyRing1(p1, r);
1388 p_LmCheckPolyRing1(p2, r);
1389 p_LmCheckPolyRing1(pr, r);
1390#if PDEBUG >= 1
1391 for (int i=1; i<=r->N; i++)
1392 pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask);
1393 pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0);
1394#endif
1395
1396 p_MemSum_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size);
1398}
1399// ExpVector(p1) -= ExpVector(p2)
1400static inline void p_ExpVectorSub(poly p1, poly p2, const ring r)
1401{
1402 p_LmCheckPolyRing1(p1, r);
1403 p_LmCheckPolyRing1(p2, r);
1404#if PDEBUG >= 1
1405 for (int i=1; i<=r->N; i++)
1406 pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r));
1407 pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0 ||
1408 p_GetComp(p1, r) == p_GetComp(p2, r));
1409#endif
1410
1411 p_MemSub_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size);
1413}
1414
1415// ExpVector(p1) += ExpVector(p2) - ExpVector(p3)
1416static inline void p_ExpVectorAddSub(poly p1, poly p2, poly p3, const ring r)
1417{
1418 p_LmCheckPolyRing1(p1, r);
1419 p_LmCheckPolyRing1(p2, r);
1420 p_LmCheckPolyRing1(p3, r);
1421#if PDEBUG >= 1
1422 for (int i=1; i<=r->N; i++)
1423 pAssume1(p_GetExp(p1, i, r) + p_GetExp(p2, i, r) >= p_GetExp(p3, i, r));
1424 pAssume1(p_GetComp(p1, r) == 0 ||
1425 (p_GetComp(p2, r) - p_GetComp(p3, r) == 0) ||
1426 (p_GetComp(p1, r) == p_GetComp(p2, r) - p_GetComp(p3, r)));
1427#endif
1428
1429 p_MemAddSub_LengthGeneral(p1->exp, p2->exp, p3->exp, r->ExpL_Size);
1430 // no need to adjust in case of NegWeights
1431}
1432
1433// ExpVector(pr) = ExpVector(p1) - ExpVector(p2)
1434static inline void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
1435{
1436 p_LmCheckPolyRing1(p1, r);
1437 p_LmCheckPolyRing1(p2, r);
1438 p_LmCheckPolyRing1(pr, r);
1439#if PDEBUG >= 2
1440 for (int i=1; i<=r->N; i++)
1441 pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r));
1442 pAssume1(!rRing_has_Comp(r) || p_GetComp(p1, r) == p_GetComp(p2, r));
1443#endif
1444
1445 p_MemDiff_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size);
1447}
1448
1449static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r)
1450{
1451 p_LmCheckPolyRing1(p1, r);
1452 p_LmCheckPolyRing1(p2, r);
1453
1454 unsigned i = r->ExpL_Size;
1455 unsigned long *ep = p1->exp;
1456 unsigned long *eq = p2->exp;
1457
1458 do
1459 {
1460 i--;
1461 if (ep[i] != eq[i]) return FALSE;
1462 }
1463 while (i!=0);
1464 return TRUE;
1465}
1466
1467static inline long p_Totaldegree(poly p, const ring r)
1468{
1470 unsigned long s = p_GetTotalDegree(p->exp[r->VarL_Offset[0]],
1471 r,
1472 r->ExpPerLong);
1473 for (unsigned i=r->VarL_Size-1; i!=0; i--)
1474 {
1475 s += p_GetTotalDegree(p->exp[r->VarL_Offset[i]], r,r->ExpPerLong);
1476 }
1477 return (long)s;
1478}
1479
1480static inline void p_GetExpV(poly p, int *ev, const ring r)
1481{
1483 for (unsigned j = r->N; j!=0; j--)
1484 ev[j] = p_GetExp(p, j, r);
1485
1486 ev[0] = p_GetComp(p, r);
1487}
1488// p_GetExpVL is used in Singular,jl
1489static inline void p_GetExpVL(poly p, int64 *ev, const ring r)
1490{
1492 for (unsigned j = r->N; j!=0; j--)
1493 ev[j-1] = p_GetExp(p, j, r);
1494}
1495// p_GetExpVLV is used in Singular,jl
1496static inline int64 p_GetExpVLV(poly p, int64 *ev, const ring r)
1497{
1499 for (unsigned j = r->N; j!=0; j--)
1500 ev[j-1] = p_GetExp(p, j, r);
1501 return (int64)p_GetComp(p,r);
1502}
1503// p_GetExpVL is used in Singular,jl
1504static inline void p_SetExpV(poly p, int *ev, const ring r)
1505{
1507 for (unsigned j = r->N; j!=0; j--)
1508 p_SetExp(p, j, ev[j], r);
1509
1510 if(ev[0]!=0) p_SetComp(p, ev[0],r);
1511 p_Setm(p, r);
1512}
1513static inline void p_SetExpVL(poly p, int64 *ev, const ring r)
1514{
1516 for (unsigned j = r->N; j!=0; j--)
1517 p_SetExp(p, j, ev[j-1], r);
1518 p_SetComp(p, 0,r);
1519
1520 p_Setm(p, r);
1521}
1522
1523// p_SetExpVLV is used in Singular,jl
1524static inline void p_SetExpVLV(poly p, int64 *ev, int64 comp, const ring r)
1525{
1527 for (unsigned j = r->N; j!=0; j--)
1528 p_SetExp(p, j, ev[j-1], r);
1529 p_SetComp(p, comp,r);
1530
1531 p_Setm(p, r);
1532}
1533
1534/***************************************************************
1535 *
1536 * Comparison w.r.t. monomial ordering
1537 *
1538 ***************************************************************/
1539
1540static inline int p_LmCmp(poly p, poly q, const ring r)
1541{
1543 p_LmCheckPolyRing1(q, r);
1544
1545 const unsigned long* _s1 = ((unsigned long*) p->exp);
1546 const unsigned long* _s2 = ((unsigned long*) q->exp);
1547 REGISTER unsigned long _v1;
1548 REGISTER unsigned long _v2;
1549 const unsigned long _l = r->CmpL_Size;
1550
1551 REGISTER unsigned long _i=0;
1552
1553 LengthGeneral_OrdGeneral_LoopTop:
1554 _v1 = _s1[_i];
1555 _v2 = _s2[_i];
1556 if (_v1 == _v2)
1557 {
1558 _i++;
1559 if (_i == _l) return 0;
1560 goto LengthGeneral_OrdGeneral_LoopTop;
1561 }
1562 const long* _ordsgn = (long*) r->ordsgn;
1563#if 1 /* two variants*/
1564 if (_v1 > _v2)
1565 {
1566 return _ordsgn[_i];
1567 }
1568 return -(_ordsgn[_i]);
1569#else
1570 if (_v1 > _v2)
1571 {
1572 if (_ordsgn[_i] == 1) return 1;
1573 return -1;
1574 }
1575 if (_ordsgn[_i] == 1) return -1;
1576 return 1;
1577#endif
1578}
1579
1580// The coefficient will be compared in absolute value
1581static inline int p_LtCmp(poly p, poly q, const ring r)
1582{
1583 int res = p_LmCmp(p,q,r);
1584 if(res == 0)
1585 {
1586 if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
1587 return res;
1588 number pc = n_Copy(p_GetCoeff(p,r),r->cf);
1589 number qc = n_Copy(p_GetCoeff(q,r),r->cf);
1590 if(!n_GreaterZero(pc,r->cf))
1591 pc = n_InpNeg(pc,r->cf);
1592 if(!n_GreaterZero(qc,r->cf))
1593 qc = n_InpNeg(qc,r->cf);
1594 if(n_Greater(pc,qc,r->cf))
1595 res = 1;
1596 else if(n_Greater(qc,pc,r->cf))
1597 res = -1;
1598 else if(n_Equal(pc,qc,r->cf))
1599 res = 0;
1600 n_Delete(&pc,r->cf);
1601 n_Delete(&qc,r->cf);
1602 }
1603 return res;
1604}
1605
1606// The coefficient will be compared in absolute value
1607static inline int p_LtCmpNoAbs(poly p, poly q, const ring r)
1608{
1609 int res = p_LmCmp(p,q,r);
1610 if(res == 0)
1611 {
1612 if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
1613 return res;
1614 number pc = p_GetCoeff(p,r);
1615 number qc = p_GetCoeff(q,r);
1616 if(n_Greater(pc,qc,r->cf))
1617 res = 1;
1618 if(n_Greater(qc,pc,r->cf))
1619 res = -1;
1620 if(n_Equal(pc,qc,r->cf))
1621 res = 0;
1622 }
1623 return res;
1624}
1625
1626#ifdef HAVE_RINGS
1627// This is the equivalent of pLmCmp(p,q) != -currRing->OrdSgn for rings
1628// It is used in posInLRing and posInTRing
1629static inline int p_LtCmpOrdSgnDiffM(poly p, poly q, const ring r)
1630{
1631 if(r->OrdSgn == 1)
1632 {
1633 return(p_LtCmp(p,q,r) == 1);
1634 }
1635 else
1636 {
1637 return(p_LmCmp(p,q,r) == -1);
1638 }
1639}
1640#endif
1641
1642#ifdef HAVE_RINGS
1643// This is the equivalent of pLmCmp(p,q) != currRing->OrdSgn for rings
1644// It is used in posInLRing and posInTRing
1645static inline int p_LtCmpOrdSgnDiffP(poly p, poly q, const ring r)
1646{
1647 if(r->OrdSgn == 1)
1648 {
1649 return(p_LmCmp(p,q,r) == -1);
1650 }
1651 else
1652 {
1653 return(p_LtCmp(p,q,r) != -1);
1654 }
1655
1656}
1657#endif
1658
1659#ifdef HAVE_RINGS
1660// This is the equivalent of pLmCmp(p,q) == -currRing->OrdSgn for rings
1661// It is used in posInLRing and posInTRing
1662static inline int p_LtCmpOrdSgnEqM(poly p, poly q, const ring r)
1663{
1664 return(p_LtCmp(p,q,r) == -r->OrdSgn);
1665}
1666#endif
1667
1668#ifdef HAVE_RINGS
1669// This is the equivalent of pLmCmp(p,q) == currRing->OrdSgn for rings
1670// It is used in posInLRing and posInTRing
1671static inline int p_LtCmpOrdSgnEqP(poly p, poly q, const ring r)
1672{
1673 return(p_LtCmp(p,q,r) == r->OrdSgn);
1674}
1675#endif
1676
1677/// returns TRUE if p1 is a skalar multiple of p2
1678/// assume p1 != NULL and p2 != NULL
1679BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r);
1680
1681
1682/***************************************************************
1683 *
1684 * Comparisons: they are all done without regarding coeffs
1685 *
1686 ***************************************************************/
1687#define p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
1688 _p_LmCmpAction(p, q, r, actionE, actionG, actionS)
1689
1690// returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !!
1691#define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r)
1692
1693// pCmp: args may be NULL
1694// returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))
1695static inline int p_Cmp(poly p1, poly p2, ring r)
1696{
1697 if (p2==NULL)
1698 {
1699 if (p1==NULL) return 0;
1700 return 1;
1701 }
1702 if (p1==NULL)
1703 return -1;
1704 return p_LmCmp(p1,p2,r);
1705}
1706
1707static inline int p_CmpPolys(poly p1, poly p2, ring r)
1708{
1709 if (p2==NULL)
1710 {
1711 if (p1==NULL) return 0;
1712 return 1;
1713 }
1714 if (p1==NULL)
1715 return -1;
1716 return p_ComparePolys(p1,p2,r);
1717}
1718
1719
1720/***************************************************************
1721 *
1722 * divisibility
1723 *
1724 ***************************************************************/
1725/// return: FALSE, if there exists i, such that a->exp[i] > b->exp[i]
1726/// TRUE, otherwise
1727/// (1) Consider long vars, instead of single exponents
1728/// (2) Clearly, if la > lb, then FALSE
1729/// (3) Suppose la <= lb, and consider first bits of single exponents in l:
1730/// if TRUE, then value of these bits is la ^ lb
1731/// if FALSE, then la-lb causes an "overflow" into one of those bits, i.e.,
1732/// la ^ lb != la - lb
1733static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, poly b, const ring r)
1734{
1735 int i=r->VarL_Size - 1;
1736 unsigned long divmask = r->divmask;
1737 unsigned long la, lb;
1738
1739 if (r->VarL_LowIndex >= 0)
1740 {
1741 i += r->VarL_LowIndex;
1742 do
1743 {
1744 la = a->exp[i];
1745 lb = b->exp[i];
1746 if ((la > lb) ||
1747 (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
1748 {
1750 return FALSE;
1751 }
1752 i--;
1753 }
1754 while (i>=r->VarL_LowIndex);
1755 }
1756 else
1757 {
1758 do
1759 {
1760 la = a->exp[r->VarL_Offset[i]];
1761 lb = b->exp[r->VarL_Offset[i]];
1762 if ((la > lb) ||
1763 (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
1764 {
1766 return FALSE;
1767 }
1768 i--;
1769 }
1770 while (i>=0);
1771 }
1772/*#ifdef HAVE_RINGS
1773 pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf));
1774 return (!rField_is_Ring(r)) || n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf);
1775#else
1776*/
1778 return TRUE;
1779//#endif
1780}
1781
1782static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, const ring r_a, poly b, const ring r_b)
1783{
1784 int i=r_a->N;
1785 pAssume1(r_a->N == r_b->N);
1786
1787 do
1788 {
1789 if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b))
1790 return FALSE;
1791 i--;
1792 }
1793 while (i);
1794/*#ifdef HAVE_RINGS
1795 return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
1796#else
1797*/
1798 return TRUE;
1799//#endif
1800}
1801
1802#ifdef HAVE_RATGRING
1803static inline BOOLEAN _p_LmDivisibleByNoCompPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end)
1804{
1805 int i=end;
1806 pAssume1(r_a->N == r_b->N);
1807
1808 do
1809 {
1810 if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b))
1811 return FALSE;
1812 i--;
1813 }
1814 while (i>=start);
1815/*#ifdef HAVE_RINGS
1816 return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
1817#else
1818*/
1819 return TRUE;
1820//#endif
1821}
1822static inline BOOLEAN _p_LmDivisibleByPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end)
1823{
1824 if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b))
1825 return _p_LmDivisibleByNoCompPart(a, r_a, b, r_b,start,end);
1826 return FALSE;
1827}
1828static inline BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r,const int start, const int end)
1829{
1831 pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r));
1832 if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
1833 return _p_LmDivisibleByNoCompPart(a, r, b, r,start, end);
1834 return FALSE;
1835}
1836#endif
1837static inline BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r)
1838{
1839 if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
1840 return _p_LmDivisibleByNoComp(a, b, r);
1841 return FALSE;
1842}
1843static inline BOOLEAN _p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1844{
1845 if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b))
1846 return _p_LmDivisibleByNoComp(a, r_a, b, r_b);
1847 return FALSE;
1848}
1849static inline BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, const ring r)
1850{
1851 p_LmCheckPolyRing1(a, r);
1853 return _p_LmDivisibleByNoComp(a, b, r);
1854}
1855
1856static inline BOOLEAN p_LmDivisibleByNoComp(poly a, const ring ra, poly b, const ring rb)
1857{
1858 p_LmCheckPolyRing1(a, ra);
1859 p_LmCheckPolyRing1(b, rb);
1860 return _p_LmDivisibleByNoComp(a, ra, b, rb);
1861}
1862
1863static inline BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
1864{
1866 pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r));
1867 if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
1868 return _p_LmDivisibleByNoComp(a, b, r);
1869 return FALSE;
1870}
1871
1872static inline BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
1873{
1875 pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r));
1876
1877 if (a != NULL && (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)))
1878 return _p_LmDivisibleByNoComp(a,b,r);
1879 return FALSE;
1880}
1881static inline BOOLEAN p_DivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1882{
1884 pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r_a));
1885 if (a != NULL) {
1886 return _p_LmDivisibleBy(a, r_a, b, r_b);
1887 }
1888 return FALSE;
1889}
1890static inline BOOLEAN p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1891{
1892 p_LmCheckPolyRing(a, r_a);
1893 p_LmCheckPolyRing(b, r_b);
1894 return _p_LmDivisibleBy(a, r_a, b, r_b);
1895}
1896
1897static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a,
1898 poly b, unsigned long not_sev_b, const ring r)
1899{
1900 p_LmCheckPolyRing1(a, r);
1902#ifndef PDIV_DEBUG
1903 _pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r);
1904 _pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r);
1905
1906 if (sev_a & not_sev_b)
1907 {
1909 return FALSE;
1910 }
1911 return p_LmDivisibleBy(a, b, r);
1912#else
1913 return pDebugLmShortDivisibleBy(a, sev_a, r, b, not_sev_b, r);
1914#endif
1915}
1916
1917static inline BOOLEAN p_LmShortDivisibleByNoComp(poly a, unsigned long sev_a,
1918 poly b, unsigned long not_sev_b, const ring r)
1919{
1920 p_LmCheckPolyRing1(a, r);
1922#ifndef PDIV_DEBUG
1923 _pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r);
1924 _pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r);
1925
1926 if (sev_a & not_sev_b)
1927 {
1929 return FALSE;
1930 }
1931 return p_LmDivisibleByNoComp(a, b, r);
1932#else
1933 return pDebugLmShortDivisibleByNoComp(a, sev_a, r, b, not_sev_b, r);
1934#endif
1935}
1936
1937static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, const ring r_a,
1938 poly b, unsigned long not_sev_b, const ring r_b)
1939{
1940 p_LmCheckPolyRing1(a, r_a);
1941 p_LmCheckPolyRing1(b, r_b);
1942#ifndef PDIV_DEBUG
1943 _pPolyAssume2(p_GetShortExpVector(a, r_a) == sev_a, a, r_a);
1944 _pPolyAssume2(p_GetShortExpVector(b, r_b) == ~ not_sev_b, b, r_b);
1945
1946 if (sev_a & not_sev_b)
1947 {
1948 pAssume1(_p_LmDivisibleByNoComp(a, r_a, b, r_b) == FALSE);
1949 return FALSE;
1950 }
1951 return _p_LmDivisibleBy(a, r_a, b, r_b);
1952#else
1953 return pDebugLmShortDivisibleBy(a, sev_a, r_a, b, not_sev_b, r_b);
1954#endif
1955}
1956
1957/***************************************************************
1958 *
1959 * Misc things on Lm
1960 *
1961 ***************************************************************/
1962
1963
1964/// like the respective p_LmIs* routines, except that p might be empty
1965static inline BOOLEAN p_IsConstantComp(const poly p, const ring r)
1966{
1967 if (p == NULL) return TRUE;
1968 return (pNext(p)==NULL) && p_LmIsConstantComp(p, r);
1969}
1970
1971static inline BOOLEAN p_IsConstant(const poly p, const ring r)
1972{
1973 if (p == NULL) return TRUE;
1974 p_Test(p, r);
1975 return (pNext(p)==NULL) && p_LmIsConstant(p, r);
1976}
1977
1978/// either poly(1) or gen(k)?!
1979static inline BOOLEAN p_IsOne(const poly p, const ring R)
1980{
1981 if (p == NULL) return FALSE; /* TODO check if 0 == 1 */
1982 p_Test(p, R);
1983 return (p_IsConstant(p, R) && n_IsOne(p_GetCoeff(p, R), R->cf));
1984}
1985
1986static inline BOOLEAN p_IsConstantPoly(const poly p, const ring r)
1987{
1988 p_Test(p, r);
1989 poly pp=p;
1990 while(pp!=NULL)
1991 {
1992 if (! p_LmIsConstantComp(pp, r))
1993 return FALSE;
1994 pIter(pp);
1995 }
1996 return TRUE;
1997}
1998
1999static inline BOOLEAN p_IsUnit(const poly p, const ring r)
2000{
2001 if (p == NULL) return FALSE;
2002 if (rField_is_Ring(r))
2003 return (p_LmIsConstant(p, r) && n_IsUnit(pGetCoeff(p),r->cf));
2004 return p_LmIsConstant(p, r);
2005}
2006
2007static inline BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2,
2008 const ring r)
2009{
2010 p_LmCheckPolyRing(p1, r);
2011 p_LmCheckPolyRing(p2, r);
2012 unsigned long l1, l2, divmask = r->divmask;
2013 int i;
2014
2015 for (i=0; i<r->VarL_Size; i++)
2016 {
2017 l1 = p1->exp[r->VarL_Offset[i]];
2018 l2 = p2->exp[r->VarL_Offset[i]];
2019 // do the divisiblity trick
2020 if ( (l1 > ULONG_MAX - l2) ||
2021 (((l1 & divmask) ^ (l2 & divmask)) != ((l1 + l2) & divmask)))
2022 return FALSE;
2023 }
2024 return TRUE;
2025}
2026void p_Split(poly p, poly * r); /*p => IN(p), r => REST(p) */
2027BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r);
2028BOOLEAN p_HasNotCFRing(poly p1, poly p2, const ring r);
2029poly p_mInit(const char *s, BOOLEAN &ok, const ring r); /* monom s -> poly, interpreter */
2030const char * p_Read(const char *s, poly &p,const ring r); /* monom -> poly */
2031poly p_MDivide(poly a, poly b, const ring r);
2032poly p_DivideM(poly a, poly b, const ring r);
2033poly pp_DivideM(poly a, poly b, const ring r);
2034poly p_Div_nn(poly p, const number n, const ring r);
2035
2036// returns the LCM of the head terms of a and b in *m, does not p_Setm
2037void p_Lcm(const poly a, const poly b, poly m, const ring r);
2038// returns the LCM of the head terms of a and b, does p_Setm
2039poly p_Lcm(const poly a, const poly b, const ring r);
2040
2041#ifdef HAVE_RATGRING
2042poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r);
2043poly p_GetCoeffRat(poly p, int ishift, ring r);
2044void p_LmDeleteAndNextRat(poly *p, int ishift, ring r);
2045void p_ContentRat(poly &ph, const ring r);
2046#endif /* ifdef HAVE_RATGRING */
2047
2048
2049poly p_Diff(poly a, int k, const ring r);
2050poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r);
2051int p_Weight(int c, const ring r);
2052
2053/// assumes that p and divisor are univariate polynomials in r,
2054/// mentioning the same variable;
2055/// assumes divisor != NULL;
2056/// p may be NULL;
2057/// assumes a global monomial ordering in r;
2058/// performs polynomial division of p by divisor:
2059/// - afterwards p contains the remainder of the division, i.e.,
2060/// p_before = result * divisor + p_afterwards;
2061/// - if needResult == TRUE, then the method computes and returns 'result',
2062/// otherwise NULL is returned (This parametrization can be used when
2063/// one is only interested in the remainder of the division. In this
2064/// case, the method will be slightly faster.)
2065/// leaves divisor unmodified
2066poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r);
2067
2068/* syszygy stuff */
2069BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r);
2070void p_VectorHasUnit(poly p, int * k, int * len, const ring r);
2071poly p_TakeOutComp1(poly * p, int k, const ring r);
2072// Splits *p into two polys: *q which consists of all monoms with
2073// component == comp and *p of all other monoms *lq == pLength(*q)
2074// On return all components pf *q == 0
2075void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r);
2076
2077// This is something weird -- Don't use it, unless you know what you are doing
2078poly p_TakeOutComp(poly * p, int k, const ring r);
2079
2080void p_DeleteComp(poly * p,int k, const ring r);
2081
2082/*-------------ring management:----------------------*/
2083
2084// resets the pFDeg and pLDeg: if pLDeg is not given, it is
2085// set to currRing->pLDegOrig, i.e. to the respective LDegProc which
2086// only uses pFDeg (and not pDeg, or pTotalDegree, etc).
2087// If you use this, make sure your procs does not make any assumptions
2088// on ordering and/or OrdIndex -- otherwise they might return wrong results
2089// on strat->tailRing
2090void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg = NULL);
2091// restores pFDeg and pLDeg:
2092void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg);
2093
2094/*-------------pComp for syzygies:-------------------*/
2095void p_SetModDeg(intvec *w, ring r);
2096
2097/*------------ Jet ----------------------------------*/
2098poly pp_Jet(poly p, int m, const ring R);
2099poly p_Jet(poly p, int m,const ring R);
2100poly pp_JetW(poly p, int m, int *w, const ring R);
2101poly p_JetW(poly p, int m, int *w, const ring R);
2102
2103poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst);
2104
2105poly p_PermPoly (poly p, const int * perm,const ring OldRing, const ring dst,
2106 nMapFunc nMap, const int *par_perm=NULL, int OldPar=0,
2107 BOOLEAN use_mult=FALSE);
2108
2109/*----------------------------------------------------*/
2110poly p_Series(int n,poly p,poly u, intvec *w, const ring R);
2111
2112/*----------------------------------------------------*/
2113int p_Var(poly mi, const ring r);
2114/// the minimal index of used variables - 1
2115int p_LowVar (poly p, const ring r);
2116
2117/*----------------------------------------------------*/
2118/// shifts components of the vector p by i
2119void p_Shift (poly * p,int i, const ring r);
2120/*----------------------------------------------------*/
2121
2122int p_Compare(const poly a, const poly b, const ring R);
2123
2124/// polynomial gcd for f=mon
2125poly p_GcdMon(poly f, poly g, const ring r);
2126
2127/// divide polynomial by monomial
2128poly p_Div_mm(poly p, const poly m, const ring r);
2129
2130
2131/// max exponent of variable x_i in p
2132int p_MaxExpPerVar(poly p, int i, const ring r);
2133#endif // P_POLYS_H
2134
#define NULL
Definition: auxiliary.h:104
long int64
Definition: auxiliary.h:68
int BOOLEAN
Definition: auxiliary.h:87
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
CanonicalForm pp(const CanonicalForm &)
CanonicalForm pp ( const CanonicalForm & f )
Definition: cf_gcd.cc:676
int level(const CanonicalForm &f)
if(both_non_zero==0)
Definition: cfEzgcd.cc:91
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:56
int l
Definition: cfEzgcd.cc:100
int m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
int k
Definition: cfEzgcd.cc:99
Variable x
Definition: cfModGcd.cc:4084
int p
Definition: cfModGcd.cc:4080
f
Definition: cfModGcd.cc:4083
g
Definition: cfModGcd.cc:4092
CanonicalForm b
Definition: cfModGcd.cc:4105
Definition: intvec.h:23
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:452
static FORCE_INLINE BOOLEAN n_IsUnit(number n, const coeffs r)
TRUE iff n has a multiplicative inverse in the given coeff field/ring r.
Definition: coeffs.h:516
static FORCE_INLINE BOOLEAN n_GreaterZero(number n, const coeffs r)
ordered fields: TRUE iff 'n' is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2),...
Definition: coeffs.h:495
static FORCE_INLINE number n_InpNeg(number n, const coeffs r)
in-place negation of n MUST BE USED: n = n_InpNeg(n) (no copy is returned)
Definition: coeffs.h:558
static FORCE_INLINE BOOLEAN n_Greater(number a, number b, const coeffs r)
ordered fields: TRUE iff 'a' is larger than 'b'; in Z/pZ: TRUE iff la > lb, where la and lb are the l...
Definition: coeffs.h:512
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition: coeffs.h:465
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:456
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:539
static FORCE_INLINE BOOLEAN n_Equal(number a, number b, const coeffs r)
TRUE iff 'a' and 'b' represent the same number; they may have different representations.
Definition: coeffs.h:461
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition: coeffs.h:74
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
Definition: coeffs.h:469
return result
Definition: facAbsBiFact.cc:75
const CanonicalForm int s
Definition: facAbsFact.cc:51
CanonicalForm res
Definition: facAbsFact.cc:60
const CanonicalForm & w
Definition: facAbsFact.cc:51
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
CFArray copy(const CFList &list)
write elements of list into an array
int j
Definition: facHensel.cc:110
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
static int max(int a, int b)
Definition: fast_mult.cc:264
static BOOLEAN length(leftv result, leftv arg)
Definition: interval.cc:257
STATIC_VAR int offset
Definition: janet.cc:29
STATIC_VAR Poly * h
Definition: janet.cc:971
poly nc_p_Plus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, const int, const ring r)
Definition: old.gring.cc:168
poly _nc_pp_Mult_qq(const poly p, const poly q, const ring r)
general NC-multiplication without destruction
Definition: old.gring.cc:254
poly _nc_p_Mult_q(poly p, poly q, const ring r)
general NC-multiplication with destruction
Definition: old.gring.cc:215
#define assume(x)
Definition: mod2.h:387
#define p_GetComp(p, r)
Definition: monomials.h:64
#define pIfThen1(cond, check)
Definition: monomials.h:179
#define pIter(p)
Definition: monomials.h:37
#define pNext(p)
Definition: monomials.h:36
#define p_LmCheckPolyRing1(p, r)
Definition: monomials.h:177
#define pAssume1(cond)
Definition: monomials.h:171
#define p_LmCheckPolyRing2(p, r)
Definition: monomials.h:199
#define pSetCoeff0(p, n)
Definition: monomials.h:59
#define p_CheckRing2(r)
Definition: monomials.h:200
#define p_GetCoeff(p, r)
Definition: monomials.h:50
#define p_CheckRing1(r)
Definition: monomials.h:178
#define pAssume2(cond)
Definition: monomials.h:193
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:44
#define _pPolyAssume2(cond, p, r)
Definition: monomials.h:195
#define POLY_NEGWEIGHT_OFFSET
Definition: monomials.h:236
#define __p_GetComp(p, r)
Definition: monomials.h:63
#define p_SetRingOfLm(p, r)
Definition: monomials.h:144
#define rRing_has_Comp(r)
Definition: monomials.h:266
gmp_float exp(const gmp_float &a)
Definition: mpr_complex.cc:357
Definition: lq.h:40
#define omTypeAlloc0Bin(type, addr, bin)
Definition: omAllocDecl.h:204
#define omTypeAllocBin(type, addr, bin)
Definition: omAllocDecl.h:203
#define omFreeBinAddr(addr)
Definition: omAllocDecl.h:258
#define omSizeWOfBin(bin_ptr)
omBin_t * omBin
Definition: omStructs.h:12
#define REGISTER
Definition: omalloc.h:27
BOOLEAN pDebugLmShortDivisibleByNoComp(poly p1, unsigned long sev_1, ring r_1, poly p2, unsigned long not_sev_2, ring r_2)
Definition: pDebug.cc:387
BOOLEAN pDebugLmShortDivisibleBy(poly p1, unsigned long sev_1, ring r_1, poly p2, unsigned long not_sev_2, ring r_2)
Definition: pDebug.cc:364
BOOLEAN p_DebugLmDivisibleByNoComp(poly a, poly b, ring r)
Definition: pDebug.cc:139
#define p_MemDiff_LengthGeneral(r, s1, s2, length)
Definition: p_MemAdd.h:262
#define p_MemSub_LengthGeneral(r, s, length)
Definition: p_MemAdd.h:291
#define p_MemAdd_LengthGeneral(r, s, length)
Definition: p_MemAdd.h:173
#define p_MemAddSub_LengthGeneral(r, s, t, length)
Definition: p_MemAdd.h:312
#define p_MemSum_LengthGeneral(r, s1, s2, length)
Definition: p_MemAdd.h:86
static poly p_Neg(poly p, const ring r)
Definition: p_polys.h:1067
void p_Content_n(poly p, number &c, const ring r)
Definition: p_polys.cc:2339
poly p_Diff(poly a, int k, const ring r)
Definition: p_polys.cc:1885
long pLDeg1c_WFirstTotalDegree(poly p, int *l, ring r)
Definition: p_polys.cc:1063
static int p_CmpPolys(poly p1, poly p2, ring r)
Definition: p_polys.h:1707
long pLDeg0(poly p, int *l, ring r)
Definition: p_polys.cc:734
poly p_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1565
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
Definition: p_polys.cc:1221
static long p_GetExpDiff(poly p1, poly p2, int i, ring r)
Definition: p_polys.h:635
static void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r)
Definition: p_polys.h:1385
poly pp_Jet(poly p, int m, const ring R)
Definition: p_polys.cc:4386
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:896
static void p_LmDelete(poly p, const ring r)
Definition: p_polys.h:711
static poly p_Mult_q(poly p, poly q, const ring r)
Definition: p_polys.h:1074
void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg=NULL)
Definition: p_polys.cc:3707
BOOLEAN pIsMonomOf(poly p, poly m)
Definition: pDebug.cc:163
BOOLEAN p_LmCheckPolyRing(poly p, ring r)
Definition: pDebug.cc:118
static void p_MemAdd_NegWeightAdjust(poly p, const ring r)
Definition: p_polys.h:1252
poly p_Farey(poly p, number N, const ring r)
Definition: p_polys.cc:54
BOOLEAN _p_Test(poly p, ring r, int level)
Definition: pDebug.cc:210
static void p_ExpVectorAdd(poly p1, poly p2, const ring r)
Definition: p_polys.h:1371
static unsigned long p_SubComp(poly p, unsigned long v, ring r)
Definition: p_polys.h:453
long pLDeg1_Deg(poly p, int *l, ring r)
Definition: p_polys.cc:905
BOOLEAN p_CheckIsFromRing(poly p, ring r)
Definition: pDebug.cc:100
void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg)
Definition: p_polys.cc:3719
long pLDeg1_WFirstTotalDegree(poly p, int *l, ring r)
Definition: p_polys.cc:1033
static long p_SubExp(poly p, int v, long ee, ring r)
Definition: p_polys.h:613
static BOOLEAN _p_LmDivisibleByPart(poly a, const ring r_a, poly b, const ring r_b, const int start, const int end)
Definition: p_polys.h:1822
static poly p_Head(poly p, const ring r)
copy the i(leading) term of p
Definition: p_polys.h:826
poly p_Sub(poly a, poly b, const ring r)
Definition: p_polys.cc:1977
poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r)
assumes that p and divisor are univariate polynomials in r, mentioning the same variable; assumes div...
Definition: p_polys.cc:1857
static BOOLEAN p_IsConstantComp(const poly p, const ring r)
like the respective p_LmIs* routines, except that p might be empty
Definition: p_polys.h:1965
int p_Size(poly p, const ring r)
Definition: p_polys.cc:3310
static long p_AddExp(poly p, int v, long ee, ring r)
Definition: p_polys.h:606
static poly p_LmInit(poly p, const ring r)
Definition: p_polys.h:1295
poly p_GcdMon(poly f, poly g, const ring r)
polynomial gcd for f=mon
Definition: p_polys.cc:4968
BOOLEAN p_ComparePolys(poly p1, poly p2, const ring r)
returns TRUE if p1 is a skalar multiple of p2 assume p1 != NULL and p2 != NULL
Definition: p_polys.cc:4604
static long p_FDeg(const poly p, const ring r)
Definition: p_polys.h:380
static unsigned long p_GetMaxExp(const unsigned long l, const ring r)
Definition: p_polys.h:747
int p_LowVar(poly p, const ring r)
the minimal index of used variables - 1
Definition: p_polys.cc:4708
BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r)
divisibility check over ground ring (which may contain zero divisors); TRUE iff LT(f) divides LT(g),...
Definition: p_polys.cc:1629
poly p_CopyPowerProduct(poly p, const ring r)
like p_Head, but with coefficient 1
Definition: p_polys.cc:5006
poly p_Homogen(poly p, int varnum, const ring r)
Definition: p_polys.cc:3327
static void p_ExpVectorCopy(poly d_p, poly s_p, const ring r)
Definition: p_polys.h:1273
poly p_Subst(poly p, int n, poly e, const ring r)
Definition: p_polys.cc:3986
long pLDeg1c_Deg(poly p, int *l, ring r)
Definition: p_polys.cc:936
static int p_Cmp(poly p1, poly p2, ring r)
Definition: p_polys.h:1695
BOOLEAN _p_LmTest(poly p, ring r, int level)
Definition: pDebug.cc:321
#define __pp_Mult_nn(p, n, r)
Definition: p_polys.h:962
static void p_SetExpVL(poly p, int64 *ev, const ring r)
Definition: p_polys.h:1513
char * p_String(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:322
BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r)
Definition: p_polys.cc:1324
void p_String0(poly p, ring lmRing, ring tailRing)
print p according to ShortOut in lmRing & tailRing
Definition: polys0.cc:223
void p_Write(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:342
long pLDeg1(poly p, int *l, ring r)
Definition: p_polys.cc:836
static void p_SetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1504
void p_ShallowDelete(poly *p, const ring r)
static poly pp_mm_Mult(poly p, poly m, const ring r)
Definition: p_polys.h:1001
static poly pp_Mult_mm(poly p, poly m, const ring r)
Definition: p_polys.h:991
static int p_LtCmpNoAbs(poly p, poly q, const ring r)
Definition: p_polys.h:1607
static void p_MemSub_NegWeightAdjust(poly p, const ring r)
Definition: p_polys.h:1262
poly pp_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1620
long p_WFirstTotalDegree(poly p, ring r)
Definition: p_polys.cc:591
int p_Weight(int c, const ring r)
Definition: p_polys.cc:700
static int p_Comp_k_n(poly a, poly b, int k, ring r)
Definition: p_polys.h:640
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
Definition: p_polys.cc:1292
static int p_LtCmpOrdSgnEqP(poly p, poly q, const ring r)
Definition: p_polys.h:1671
void p_ContentForGB(poly p, const ring r)
Definition: p_polys.cc:2410
void p_Vec2Polys(poly v, poly **p, int *len, const ring r)
Definition: p_polys.cc:3692
poly p_DiffOp(poly a, poly b, BOOLEAN multiply, const ring r)
Definition: p_polys.cc:1960
static void p_SetCompP(poly p, int i, ring r)
Definition: p_polys.h:254
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
Definition: p_polys.h:488
poly p_Jet(poly p, int m, const ring R)
Definition: p_polys.cc:4414
poly p_TakeOutComp1(poly *p, int k, const ring r)
Definition: p_polys.cc:3453
static void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
Definition: p_polys.h:1434
const char * p_Read(const char *s, poly &p, const ring r)
Definition: p_polys.cc:1365
static long p_MinComp(poly p, ring lmRing, ring tailRing)
Definition: p_polys.h:313
void p_String0Long(const poly p, ring lmRing, ring tailRing)
print p in a long way
Definition: polys0.cc:203
void p_String0Short(const poly p, ring lmRing, ring tailRing)
print p in a short way, if possible
Definition: polys0.cc:184
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
Definition: p_polys.cc:4734
static long p_GetExpSum(poly p1, poly p2, int i, ring r)
Definition: p_polys.h:629
poly p_Power(poly p, int i, const ring r)
Definition: p_polys.cc:2184
poly p_Div_nn(poly p, const number n, const ring r)
Definition: p_polys.cc:1492
static poly p_mm_Mult(poly p, poly m, const ring r)
Definition: p_polys.h:1021
void p_Normalize(poly p, const ring r)
Definition: p_polys.cc:3842
void p_DeleteComp(poly *p, int k, const ring r)
Definition: p_polys.cc:3613
poly p_MDivide(poly a, poly b, const ring r)
Definition: p_polys.cc:1479
void p_Content(poly p, const ring r)
Definition: p_polys.cc:2282
void p_ProjectiveUnique(poly p, const ring r)
Definition: p_polys.cc:3198
void p_ContentRat(poly &ph, const ring r)
Definition: p_polys.cc:1731
void p_Norm(poly p1, const ring r)
Definition: p_polys.cc:3789
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
Definition: p_polys.h:247
poly p_Div_mm(poly p, const poly m, const ring r)
divide polynomial by monomial
Definition: p_polys.cc:1525
poly p_GetMaxExpP(poly p, ring r)
return monomial r such that GetExp(r,i) is maximum of all monomials in p; coeff == 0,...
Definition: p_polys.cc:1133
int p_GetVariables(poly p, int *e, const ring r)
set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 return #(e[i]>0)
Definition: p_polys.cc:1262
static long p_IncrExp(poly p, int v, ring r)
Definition: p_polys.h:591
int p_MinDeg(poly p, intvec *w, const ring R)
Definition: p_polys.cc:4476
static void p_ExpVectorSub(poly p1, poly p2, const ring r)
Definition: p_polys.h:1400
static unsigned long p_AddComp(poly p, unsigned long v, ring r)
Definition: p_polys.h:447
int p_MaxExpPerVar(poly p, int i, const ring r)
max exponent of variable x_i in p
Definition: p_polys.cc:5019
int p_Var(poly mi, const ring r)
Definition: p_polys.cc:4684
poly _p_Mult_q(poly p, poly q, const int copy, const ring r)
Returns: p * q, Destroys: if !copy then p, q Assumes: pLength(p) >= 2 pLength(q) >=2,...
Definition: p_Mult_q.cc:313
int p_Compare(const poly a, const poly b, const ring R)
Definition: p_polys.cc:4934
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:233
#define p_SetmComp
Definition: p_polys.h:244
poly p_mInit(const char *s, BOOLEAN &ok, const ring r)
Definition: p_polys.cc:1437
void p_LmDeleteAndNextRat(poly *p, int ishift, ring r)
Definition: p_polys.cc:1687
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
Definition: p_polys.h:802
static number p_SetCoeff(poly p, number n, ring r)
Definition: p_polys.h:412
static poly p_SortMerge(poly p, const ring r, BOOLEAN revert=FALSE)
Definition: p_polys.h:1189
static poly p_LmShallowCopyDelete(poly p, const ring r)
Definition: p_polys.h:1353
static poly pReverse(poly p)
Definition: p_polys.h:335
static poly p_Merge_q(poly p, poly q, const ring r)
Definition: p_polys.h:1172
long pLDegb(poly p, int *l, ring r)
Definition: p_polys.cc:806
static void p_GetExpVL(poly p, int64 *ev, const ring r)
Definition: p_polys.h:1489
static int p_LtCmp(poly p, poly q, const ring r)
Definition: p_polys.h:1581
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
Definition: p_polys.h:966
static int p_LmCmp(poly p, poly q, const ring r)
Definition: p_polys.h:1540
poly p_Series(int n, poly p, poly u, intvec *w, const ring R)
Definition: p_polys.cc:4526
long p_WTotaldegree(poly p, const ring r)
Definition: p_polys.cc:608
static BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
Definition: p_polys.h:1897
long p_DegW(poly p, const int *w, const ring R)
Definition: p_polys.cc:685
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
Definition: p_polys.h:469
static BOOLEAN p_LmIsConstant(const poly p, const ring r)
Definition: p_polys.h:983
p_SetmProc p_GetSetmProc(const ring r)
Definition: p_polys.cc:555
static long p_MultExp(poly p, int v, long ee, ring r)
Definition: p_polys.h:621
static BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, const ring r)
Definition: p_polys.h:1849
static BOOLEAN p_IsOne(const poly p, const ring R)
either poly(1) or gen(k)?!
Definition: p_polys.h:1979
static BOOLEAN p_IsConstant(const poly p, const ring r)
Definition: p_polys.h:1971
static void p_SetExpVLV(poly p, int64 *ev, int64 comp, const ring r)
Definition: p_polys.h:1524
BOOLEAN p_OneComp(poly p, const ring r)
return TRUE if all monoms have the same component
Definition: p_polys.cc:1203
static BOOLEAN _p_LmDivisibleByNoCompPart(poly a, const ring r_a, poly b, const ring r_b, const int start, const int end)
Definition: p_polys.h:1803
BOOLEAN p_CheckRing(ring r)
Definition: pDebug.cc:126
poly p_Cleardenom(poly p, const ring r)
Definition: p_polys.cc:2900
static BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1837
static unsigned long p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps)
Definition: p_polys.h:776
BOOLEAN p_LmCheckIsFromRing(poly p, ring r)
Definition: pDebug.cc:69
static poly p_New(const ring, omBin bin)
Definition: p_polys.h:664
void p_Split(poly p, poly *r)
Definition: p_polys.cc:1315
poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst)
Definition: p_polys.cc:4055
static poly p_GetExp_k_n(poly p, int l, int k, const ring r)
Definition: p_polys.h:1332
static BOOLEAN p_LmShortDivisibleByNoComp(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
Definition: p_polys.h:1917
static poly pp_Mult_nn(poly p, number n, const ring r)
Definition: p_polys.h:952
poly p_GetCoeffRat(poly p, int ishift, ring r)
Definition: p_polys.cc:1709
BOOLEAN p_VectorHasUnitB(poly p, int *k, const ring r)
Definition: p_polys.cc:3398
poly p_Vec2Poly(poly v, int k, const ring r)
Definition: p_polys.cc:3641
static BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1863
poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r)
Definition: p_polys.cc:1664
static BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1872
static BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r)
Definition: p_polys.h:1449
long pLDeg1_Totaldegree(poly p, int *l, ring r)
Definition: p_polys.cc:970
void p_SetModDeg(intvec *w, ring r)
Definition: p_polys.cc:3743
static poly p_ShallowCopyDelete(poly p, const ring r, omBin bin)
Definition: p_polys.h:888
static int64 p_GetExpVLV(poly p, int64 *ev, const ring r)
Definition: p_polys.h:1496
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition: p_polys.cc:3565
static long p_MaxComp(poly p, ring lmRing, ring tailRing)
Definition: p_polys.h:292
static poly p_Mult_nn(poly p, number n, const ring r)
Definition: p_polys.h:918
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:861
BOOLEAN p_HasNotCFRing(poly p1, poly p2, const ring r)
Definition: p_polys.cc:1340
poly p_One(const ring r)
Definition: p_polys.cc:1308
static long p_DecrExp(poly p, int v, ring r)
Definition: p_polys.h:598
static int p_LtCmpOrdSgnDiffM(poly p, poly q, const ring r)
Definition: p_polys.h:1629
static BOOLEAN _p_LmDivisibleByNoComp(poly a, poly b, const ring r)
return: FALSE, if there exists i, such that a->exp[i] > b->exp[i] TRUE, otherwise (1) Consider long v...
Definition: p_polys.h:1733
void p_VectorHasUnit(poly p, int *k, int *len, const ring r)
Definition: p_polys.cc:3421
static unsigned pLength(poly a)
Definition: p_polys.h:191
static void p_GetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1480
BOOLEAN p_CheckPolyRing(poly p, ring r)
Definition: pDebug.cc:110
void p_Write0(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:332
long pLDeg1c_Totaldegree(poly p, int *l, ring r)
Definition: p_polys.cc:1000
static long p_GetOrder(poly p, ring r)
Definition: p_polys.h:421
int p_IsUnivariate(poly p, const ring r)
return i, if poly depends only on var(i)
Definition: p_polys.cc:1242
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
Definition: p_polys.cc:1460
static poly pp_Mult_qq(poly p, poly q, const ring r)
Definition: p_polys.h:1111
poly p_PermPoly(poly p, const int *perm, const ring OldRing, const ring dst, nMapFunc nMap, const int *par_perm=NULL, int OldPar=0, BOOLEAN use_mult=FALSE)
Definition: p_polys.cc:4158
static int p_LtCmpOrdSgnEqM(poly p, poly q, const ring r)
Definition: p_polys.h:1662
static poly p_LmFreeAndNext(poly p, ring)
Definition: p_polys.h:703
#define pDivAssume(x)
Definition: p_polys.h:1242
static poly p_Mult_mm(poly p, poly m, const ring r)
Definition: p_polys.h:1011
void p_Cleardenom_n(poly p, const ring r, number &c)
Definition: p_polys.cc:3009
long p_WDegree(poly p, const ring r)
Definition: p_polys.cc:709
long pLDeg1c(poly p, int *l, ring r)
Definition: p_polys.cc:872
poly p_Last(const poly a, int &l, const ring r)
Definition: p_polys.cc:4649
static void p_LmFree(poly p, ring)
Definition: p_polys.h:683
static poly p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, int lq, const poly spNoether, const ring r)
Definition: p_polys.h:1030
static poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, const ring r)
Definition: p_polys.h:1143
void pEnlargeSet(poly **p, int length, int increment)
Definition: p_polys.cc:3766
static BOOLEAN p_IsUnit(const poly p, const ring r)
Definition: p_polys.h:1999
static poly p_Init(const ring r, omBin bin)
Definition: p_polys.h:1280
BOOLEAN p_IsHomogeneous(poly p, const ring r)
Definition: p_polys.cc:3376
static poly p_LmDeleteAndNext(poly p, const ring r)
Definition: p_polys.h:725
BOOLEAN pHaveCommonMonoms(poly p, poly q)
Definition: pDebug.cc:173
unsigned long p_GetShortExpVector(const poly a, const ring r)
Definition: p_polys.cc:4809
static poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r)
Definition: p_polys.h:1050
poly pp_JetW(poly p, int m, int *w, const ring R)
Definition: p_polys.cc:4431
static BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r, const int start, const int end)
Definition: p_polys.h:1828
long p_Deg(poly a, const ring r)
Definition: p_polys.cc:582
static poly p_SortAdd(poly p, const ring r, BOOLEAN revert=FALSE)
Definition: p_polys.h:1179
void p_SimpleContent(poly p, int s, const ring r)
Definition: p_polys.cc:2619
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:812
static long p_LDeg(const poly p, int *l, const ring r)
Definition: p_polys.h:381
number p_InitContent(poly ph, const ring r)
Definition: p_polys.cc:2690
void p_Vec2Array(poly v, poly *p, int len, const ring r)
julia: vector to already allocated array (len=p_MaxComp(v,r))
Definition: p_polys.cc:3662
static long p_Totaldegree(poly p, const ring r)
Definition: p_polys.h:1467
unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max=0)
return the maximal exponent of p in form of the maximal long var
Definition: p_polys.cc:1170
static BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2, const ring r)
Definition: p_polys.h:2007
static int p_LtCmpOrdSgnDiffP(poly p, poly q, const ring r)
Definition: p_polys.h:1645
BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level)
Definition: pDebug.cc:331
void p_Lcm(const poly a, const poly b, poly m, const ring r)
Definition: p_polys.cc:1642
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
Definition: p_polys.cc:88
#define p_Test(p, r)
Definition: p_polys.h:162
#define __p_Mult_nn(p, n, r)
Definition: p_polys.h:931
poly p_JetW(poly p, int m, int *w, const ring R)
Definition: p_polys.cc:4458
static BOOLEAN p_IsConstantPoly(const poly p, const ring r)
Definition: p_polys.h:1986
void p_wrp(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:373
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
Definition: p_polys.cc:4540
long pLDeg0c(poly p, int *l, ring r)
Definition: p_polys.cc:765
static void p_ExpVectorAddSub(poly p1, poly p2, poly p3, const ring r)
Definition: p_polys.h:1416
BOOLEAN rOrd_SetCompRequiresSetm(const ring r)
return TRUE if p_SetComp requires p_Setm
Definition: ring.cc:1907
static BOOLEAN rField_is_Ring(const ring r)
Definition: ring.h:486
void(* p_SetmProc)(poly p, const ring r)
Definition: ring.h:39
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition: ring.h:400
long(* pFDegProc)(poly p, ring r)
Definition: ring.h:38
long(* pLDegProc)(poly p, int *length, ring r)
Definition: ring.h:37
@ ro_syz
Definition: ring.h:60
@ ro_cp
Definition: ring.h:58
@ ro_wp_neg
Definition: ring.h:56
@ ro_am
Definition: ring.h:54
@ ro_syzcomp
Definition: ring.h:59
static BOOLEAN rIsNCRing(const ring r)
Definition: ring.h:421
poly sBucketSortMerge(poly p, const ring r)
Sorts p with bucketSort: assumes all monomials of p are different.
Definition: sbuckets.cc:332
poly sBucketSortAdd(poly p, const ring r)
Sorts p with bucketSort: p may have equal monomials.
Definition: sbuckets.cc:368
#define R
Definition: sirandom.c:27
#define loop
Definition: structs.h:80