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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 
24 #include "polys/monomials/ring.h"
25 
29 
30 #include "polys/sbuckets.h"
31 
32 #ifdef HAVE_PLURAL
33 #include "polys/nc/nc.h"
34 #endif
35 
36 poly 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 */
44 poly 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  ***************************************************************/
51 unsigned long p_GetShortExpVector(const poly a, const ring r);
52 
53 /// p_GetShortExpVector of p * pp
54 unsigned 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  */
62 BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r);
63 #endif
64 
65 /***************************************************************
66  *
67  * Misc things on polys
68  *
69  ***************************************************************/
70 
71 poly p_One(const ring r);
72 
73 int p_MinDeg(poly p,intvec *w, const ring R);
74 
75 long p_DegW(poly p, const int *w, const ring R);
76 
77 /// return TRUE if all monoms have the same component
78 BOOLEAN p_OneComp(poly p, const ring r);
79 
80 /// return i, if head depends only on var(i)
81 int p_IsPurePower(const poly p, const ring r);
82 
83 /// return i, if poly depends only on var(i)
84 int 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)
88 int p_GetVariables(poly p, int * e, const ring r);
89 
90 /// returns the poly representing the integer i
91 poly p_ISet(long i, const ring r);
92 
93 /// returns the poly representing the number n, destroys n
94 poly p_NSet(number n, const ring r);
95 
96 void p_Vec2Polys(poly v, poly**p, int *len, const ring r);
97 poly p_Vec2Poly(poly v, int k, const ring r);
98 
99 /// julia: vector to already allocated array (len=p_MaxComp(v,r))
100 void 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
109 void 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 
124 poly p_Sub(poly a, poly b, const ring r);
125 
126 poly 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
136 BOOLEAN pIsMonomOf(poly p, poly m);
137 // Returns TRUE if p and q have common monoms
138 BOOLEAN 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
144 BOOLEAN p_LmCheckIsFromRing(poly p, ring r);
145 // check if Lm(p) != NULL, r != NULL and initialized && Lm(p) is from r
146 BOOLEAN p_LmCheckPolyRing(poly p, ring r);
147 // check if all monoms of p are from ring r
148 BOOLEAN p_CheckIsFromRing(poly p, ring r);
149 // check r != NULL and initialized && all monoms of p are from r
150 BOOLEAN p_CheckPolyRing(poly p, ring r);
151 // check if r != NULL and initialized
152 BOOLEAN p_CheckRing(ring r);
153 // only do check if cond
154 
155 
156 #define pIfThen(cond, check) do {if (cond) {check;}} while (0)
157 
158 BOOLEAN _p_Test(poly p, ring r, int level);
159 BOOLEAN _p_LmTest(poly p, ring r, int level);
160 BOOLEAN _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 */
191 static 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
204 poly p_Last(const poly a, int &l, const ring r);
205 
206 /*----------------------------------------------------*/
207 
208 void p_Norm(poly p1, const ring r);
209 void p_Normalize(poly p,const ring r);
210 void p_ProjectiveUnique(poly p,const ring r);
211 
212 void p_ContentForGB(poly p, const ring r);
213 void p_Content(poly p, const ring r);
214 void p_Content_n(poly p, number &c,const ring r);
215 #if 1
216 // currently only used by Singular/janet
217 void p_SimpleContent(poly p, int s, const ring r);
218 number p_InitContent(poly ph, const ring r);
219 #endif
220 
221 poly p_Cleardenom(poly p, const ring r);
222 void p_Cleardenom_n(poly p, const ring r,number &c);
223 //number p_GetAllDenom(poly ph, const ring r);// unused
224 
225 int p_Size( poly p, const ring r );
226 
227 // homogenizes p by multiplying certain powers of the varnum-th variable
228 poly p_Homogen (poly p, int varnum, const ring r);
229 
230 BOOLEAN p_IsHomogeneous (poly p, const ring r);
231 
232 // Setm
233 static inline void p_Setm(poly p, const ring r)
234 {
235  p_CheckRing2(r);
236  r->p_Setm(p, r);
237 }
238 
239 p_SetmProc p_GetSetmProc(const ring r);
240 
241 poly p_Subst(poly p, int n, poly e, const ring r);
242 
243 // TODO:
244 #define p_SetmComp p_Setm
245 
246 // component
247 static inline unsigned long p_SetComp(poly p, unsigned long c, ring r)
248 {
249  p_LmCheckPolyRing2(p, r);
250  if (r->pCompIndex>=0) __p_GetComp(p,r) = c;
251  return c;
252 }
253 // sets component of poly a to i
254 static 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 
281 static 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)
292 static 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 
311 static inline long p_MaxComp(poly p,ring lmRing) {return p_MaxComp(p,lmRing,lmRing);}
312 
313 static 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 
332 static inline long p_MinComp(poly p,ring lmRing) {return p_MinComp(p,lmRing,lmRing);}
333 
334 
335 static 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 }
352 void 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
361 void p_String0(poly p, ring lmRing, ring tailRing);
362 char* p_String(poly p, ring lmRing, ring tailRing);
363 void p_Write(poly p, ring lmRing, ring tailRing);
364 void p_Write0(poly p, ring lmRing, ring tailRing);
365 void p_wrp(poly p, ring lmRing, ring tailRing);
366 
367 /// print p in a short way, if possible
368 void p_String0Short(const poly p, ring lmRing, ring tailRing);
369 
370 /// print p in a long way
371 void 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 
380 static inline long p_FDeg(const poly p, const ring r) { return r->pFDeg(p,r); }
381 static inline long p_LDeg(const poly p, int *l, const ring r) { return r->pLDeg(p,l,r); }
382 
383 long p_WFirstTotalDegree(poly p, ring r);
384 long p_WTotaldegree(poly p, const ring r);
385 long p_WDegree(poly p,const ring r);
386 long pLDeg0(poly p,int *l, ring r);
387 long pLDeg0c(poly p,int *l, ring r);
388 long pLDegb(poly p,int *l, ring r);
389 long pLDeg1(poly p,int *l, ring r);
390 long pLDeg1c(poly p,int *l, ring r);
391 long pLDeg1_Deg(poly p,int *l, ring r);
392 long pLDeg1c_Deg(poly p,int *l, ring r);
393 long pLDeg1_Totaldegree(poly p,int *l, ring r);
394 long pLDeg1c_Totaldegree(poly p,int *l, ring r);
395 long pLDeg1_WFirstTotalDegree(poly p,int *l, ring r);
396 long pLDeg1c_WFirstTotalDegree(poly p,int *l, ring r);
397 
398 BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r);
399 
400 /// same as the usual p_EqualPolys for polys belonging to *equal* rings
401 BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r1, const ring r2);
402 
403 long p_Deg(poly a, const ring r);
404 
405 
406 /***************************************************************
407  *
408  * Primitives for accessing and setting fields of a poly
409  *
410  ***************************************************************/
411 
412 static inline number p_SetCoeff(poly p, number n, ring r)
413 {
414  p_LmCheckPolyRing2(p, r);
415  n_Delete(&(p->coef), r->cf);
416  (p)->coef=n;
417  return n;
418 }
419 
420 // order
421 static inline long p_GetOrder(poly p, ring r)
422 {
423  p_LmCheckPolyRing2(p, r);
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 
447 static inline unsigned long p_AddComp(poly p, unsigned long v, ring r)
448 {
449  p_LmCheckPolyRing2(p, r);
451  return __p_GetComp(p,r) += v;
452 }
453 static inline unsigned long p_SubComp(poly p, unsigned long v, ring r)
454 {
455  p_LmCheckPolyRing2(p, r);
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!
469 static 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
488 static 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 
509 static 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
521 static 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 
533 static 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 
555 static inline long p_GetExp(const poly p, const ring r, const int VarOffset)
556 {
557  p_LmCheckPolyRing2(p, r);
558  pAssume2(VarOffset != -1);
559  return p_GetExp(p, r->bitmask, VarOffset);
560 }
561 
562 static inline long p_SetExp(poly p, const long e, const ring r, const int VarOffset)
563 {
564  p_LmCheckPolyRing2(p, r);
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
572 static inline long p_GetExp(const poly p, const int v, const ring r)
573 {
574  p_LmCheckPolyRing2(p, r);
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
582 static inline long p_SetExp(poly p, const int v, const long e, const ring r)
583 {
584  p_LmCheckPolyRing2(p, r);
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
591 static inline long p_IncrExp(poly p, int v, ring r)
592 {
593  p_LmCheckPolyRing2(p, r);
594  int e = p_GetExp(p,v,r);
595  e++;
596  return p_SetExp(p,v,e,r);
597 }
598 static inline long p_DecrExp(poly p, int v, ring r)
599 {
600  p_LmCheckPolyRing2(p, r);
601  int e = p_GetExp(p,v,r);
602  pAssume2(e > 0);
603  e--;
604  return p_SetExp(p,v,e,r);
605 }
606 static inline long p_AddExp(poly p, int v, long ee, ring r)
607 {
608  p_LmCheckPolyRing2(p, r);
609  int e = p_GetExp(p,v,r);
610  e += ee;
611  return p_SetExp(p,v,e,r);
612 }
613 static inline long p_SubExp(poly p, int v, long ee, ring r)
614 {
615  p_LmCheckPolyRing2(p, r);
616  long e = p_GetExp(p,v,r);
617  pAssume2(e >= ee);
618  e -= ee;
619  return p_SetExp(p,v,e,r);
620 }
621 static inline long p_MultExp(poly p, int v, long ee, ring r)
622 {
623  p_LmCheckPolyRing2(p, r);
624  long e = p_GetExp(p,v,r);
625  e *= ee;
626  return p_SetExp(p,v,e,r);
627 }
628 
629 static 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 }
635 static 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 
640 static 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);
644  p_LmCheckPolyRing2(b, 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)
662 static inline poly p_New(const ring r, omBin bin)
663 #else
664 static 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 
675 static inline poly p_New(ring r)
676 {
677  return p_New(r, r->PolyBin);
678 }
679 
680 #if PDEBUG > 2
681 static inline void p_LmFree(poly p, ring r)
682 #else
683 static inline void p_LmFree(poly p, ring)
684 #endif
685 {
686  p_LmCheckPolyRing2(p, r);
687  omFreeBinAddr(p);
688 }
689 #if PDEBUG > 2
690 static inline void p_LmFree(poly *p, ring r)
691 #else
692 static inline void p_LmFree(poly *p, ring)
693 #endif
694 {
695  p_LmCheckPolyRing2(*p, r);
696  poly h = *p;
697  *p = pNext(h);
698  omFreeBinAddr(h);
699 }
700 #if PDEBUG > 2
701 static inline poly p_LmFreeAndNext(poly p, ring r)
702 #else
703 static inline poly p_LmFreeAndNext(poly p, ring)
704 #endif
705 {
706  p_LmCheckPolyRing2(p, r);
707  poly pnext = pNext(p);
708  omFreeBinAddr(p);
709  return pnext;
710 }
711 static inline void p_LmDelete(poly p, const ring r)
712 {
713  p_LmCheckPolyRing2(p, r);
714  n_Delete(&pGetCoeff(p), r->cf);
715  omFreeBinAddr(p);
716 }
717 static inline void p_LmDelete0(poly p, const ring r)
718 {
719  p_LmCheckPolyRing2(p, r);
720  if (pGetCoeff(p)!=NULL) n_Delete(&pGetCoeff(p), r->cf);
721  omFreeBinAddr(p);
722 }
723 static inline void p_LmDelete(poly *p, const ring r)
724 {
725  p_LmCheckPolyRing2(*p, r);
726  poly h = *p;
727  *p = pNext(h);
728  n_Delete(&pGetCoeff(h), r->cf);
729  omFreeBinAddr(h);
730 }
731 static inline poly p_LmDeleteAndNext(poly p, const ring r)
732 {
733  p_LmCheckPolyRing2(p, r);
734  poly pnext = pNext(p);
735  n_Delete(&pGetCoeff(p), r->cf);
736  omFreeBinAddr(p);
737  return pnext;
738 }
739 
740 /***************************************************************
741  *
742  * Misc routines
743  *
744  ***************************************************************/
745 
746 /// return the maximal exponent of p in form of the maximal long var
747 unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max = 0);
748 
749 /// return monomial r such that GetExp(r,i) is maximum of all
750 /// monomials in p; coeff == 0, next == NULL, ord is not set
751 poly p_GetMaxExpP(poly p, ring r);
752 
753 static inline unsigned long p_GetMaxExp(const unsigned long l, const ring r)
754 {
755  unsigned long bitmask = r->bitmask;
756  unsigned long max = (l & bitmask);
757  unsigned long j = r->ExpPerLong - 1;
758 
759  if (j > 0)
760  {
761  unsigned long i = r->BitsPerExp;
762  long e;
763  loop
764  {
765  e = ((l >> i) & bitmask);
766  if ((unsigned long) e > max)
767  max = e;
768  j--;
769  if (j==0) break;
770  i += r->BitsPerExp;
771  }
772  }
773  return max;
774 }
775 
776 static inline unsigned long p_GetMaxExp(const poly p, const ring r)
777 {
778  return p_GetMaxExp(p_GetMaxExpL(p, r), r);
779 }
780 
781 static inline unsigned long
782 p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps)
783 {
784  const unsigned long bitmask = r->bitmask;
785  unsigned long sum = (l & bitmask);
786  unsigned long j = number_of_exps - 1;
787 
788  if (j > 0)
789  {
790  unsigned long i = r->BitsPerExp;
791  loop
792  {
793  sum += ((l >> i) & bitmask);
794  j--;
795  if (j==0) break;
796  i += r->BitsPerExp;
797  }
798  }
799  return sum;
800 }
801 
802 /***************************************************************
803  *
804  * Dispatcher to r->p_Procs, they do the tests/checks
805  *
806  ***************************************************************/
807 /// returns a copy of p (without any additional testing)
808 static inline poly p_Copy_noCheck(poly p, const ring r)
809 {
810  /*assume(p!=NULL);*/
811  assume(r != NULL);
812  assume(r->p_Procs != NULL);
813  assume(r->p_Procs->p_Copy != NULL);
814  return r->p_Procs->p_Copy(p, r);
815 }
816 
817 /// returns a copy of p
818 static inline poly p_Copy(poly p, const ring r)
819 {
820  if (p!=NULL)
821  {
822  p_Test(p,r);
823  const poly pp = p_Copy_noCheck(p, r);
824  p_Test(pp,r);
825  return pp;
826  }
827  else
828  return NULL;
829 }
830 
831 /// copy the (leading) term of p
832 static inline poly p_Head(const poly p, const ring r)
833 {
834  if (p == NULL) return NULL;
835  p_LmCheckPolyRing1(p, r);
836  poly np;
837  omTypeAllocBin(poly, np, r->PolyBin);
838  p_SetRingOfLm(np, r);
839  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
840  pNext(np) = NULL;
841  pSetCoeff0(np, n_Copy(pGetCoeff(p), r->cf));
842  return np;
843 }
844 
845 /// like p_Head, but allow NULL coeff
846 poly p_Head0(const poly p, const ring r);
847 
848 /// like p_Head, but with coefficient 1
849 poly p_CopyPowerProduct(const poly p, const ring r);
850 
851 /// like p_Head, but with coefficient n
852 poly p_CopyPowerProduct0(const poly p, const number n, const ring r);
853 
854 /// returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing
855 static inline poly p_Copy(poly p, const ring lmRing, const ring tailRing)
856 {
857  if (p != NULL)
858  {
859 #ifndef PDEBUG
860  if (tailRing == lmRing)
861  return p_Copy_noCheck(p, tailRing);
862 #endif
863  poly pres = p_Head(p, lmRing);
864  if (pNext(p)!=NULL)
865  pNext(pres) = p_Copy_noCheck(pNext(p), tailRing);
866  return pres;
867  }
868  else
869  return NULL;
870 }
871 
872 // deletes *p, and sets *p to NULL
873 static inline void p_Delete(poly *p, const ring r)
874 {
875  assume( p!= NULL );
876  assume( r!= NULL );
877  if ((*p)!=NULL) r->p_Procs->p_Delete(p, r);
878 }
879 
880 static inline void p_Delete(poly *p, const ring lmRing, const ring tailRing)
881 {
882  assume( p!= NULL );
883  if (*p != NULL)
884  {
885 #ifndef PDEBUG
886  if (tailRing == lmRing)
887  {
888  p_Delete(p, tailRing);
889  return;
890  }
891 #endif
892  if (pNext(*p) != NULL)
893  p_Delete(&pNext(*p), tailRing);
894  p_LmDelete(p, lmRing);
895  }
896 }
897 
898 // copys monomials of p, allocates new monomials from bin,
899 // deletes monomials of p
900 static inline poly p_ShallowCopyDelete(poly p, const ring r, omBin bin)
901 {
902  p_LmCheckPolyRing2(p, r);
903  pAssume2(omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
904  return r->p_Procs->p_ShallowCopyDelete(p, r, bin);
905 }
906 
907 // returns p+q, destroys p and q
908 static inline poly p_Add_q(poly p, poly q, const ring r)
909 {
910  assume( (p != q) || (p == NULL && q == NULL) );
911  if (q==NULL) return p;
912  if (p==NULL) return q;
913  int shorter;
914  return r->p_Procs->p_Add_q(p, q, shorter, r);
915 }
916 
917 /// like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q)
918 static inline poly p_Add_q(poly p, poly q, int &lp, int lq, const ring r)
919 {
920  assume( (p != q) || (p == NULL && q == NULL) );
921  if (q==NULL) return p;
922  if (p==NULL) { lp=lq; return q; }
923  int shorter;
924  poly res = r->p_Procs->p_Add_q(p, q, shorter, r);
925  lp += lq - shorter;
926  return res;
927 }
928 
929 // returns p*n, destroys p
930 static inline poly p_Mult_nn(poly p, number n, const ring r)
931 {
932  if (p==NULL) return NULL;
933  if (n_IsOne(n, r->cf))
934  return p;
935  else if (n_IsZero(n, r->cf))
936  {
937  p_Delete(&p, r); // NOTE: without p_Delete - memory leak!
938  return NULL;
939  }
940  else
941  return r->p_Procs->p_Mult_nn(p, n, r);
942 }
943 #define __p_Mult_nn(p,n,r) r->p_Procs->p_Mult_nn(p, n, r)
944 
945 static inline poly p_Mult_nn(poly p, number n, const ring lmRing,
946  const ring tailRing)
947 {
948  assume(p!=NULL);
949 #ifndef PDEBUG
950  if (lmRing == tailRing)
951  return p_Mult_nn(p, n, tailRing);
952 #endif
953  poly pnext = pNext(p);
954  pNext(p) = NULL;
955  p = lmRing->p_Procs->p_Mult_nn(p, n, lmRing);
956  if (pnext!=NULL)
957  {
958  pNext(p) = tailRing->p_Procs->p_Mult_nn(pnext, n, tailRing);
959  }
960  return p;
961 }
962 
963 // returns p*n, does not destroy p
964 static inline poly pp_Mult_nn(poly p, number n, const ring r)
965 {
966  if (p==NULL) return NULL;
967  if (n_IsOne(n, r->cf))
968  return p_Copy(p, r);
969  else if (n_IsZero(n, r->cf))
970  return NULL;
971  else
972  return r->p_Procs->pp_Mult_nn(p, n, r);
973 }
974 #define __pp_Mult_nn(p,n,r) r->p_Procs->pp_Mult_nn(p, n, r)
975 
976 // test if the monomial is a constant as a vector component
977 // i.e., test if all exponents are zero
978 static inline BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
979 {
980  //p_LmCheckPolyRing(p, r);
981  int i = r->VarL_Size - 1;
982 
983  do
984  {
985  if (p->exp[r->VarL_Offset[i]] != 0)
986  return FALSE;
987  i--;
988  }
989  while (i >= 0);
990  return TRUE;
991 }
992 
993 // test if monomial is a constant, i.e. if all exponents and the component
994 // is zero
995 static inline BOOLEAN p_LmIsConstant(const poly p, const ring r)
996 {
997  if (p_LmIsConstantComp(p, r))
998  return (p_GetComp(p, r) == 0);
999  return FALSE;
1000 }
1001 
1002 // returns Copy(p)*m, does neither destroy p nor m
1003 static inline poly pp_Mult_mm(poly p, poly m, const ring r)
1004 {
1005  if (p==NULL) return NULL;
1006  if (p_LmIsConstant(m, r))
1007  return __pp_Mult_nn(p, pGetCoeff(m), r);
1008  else
1009  return r->p_Procs->pp_Mult_mm(p, m, r);
1010 }
1011 
1012 // returns m*Copy(p), does neither destroy p nor m
1013 static inline poly pp_mm_Mult(poly p, poly m, const ring r)
1014 {
1015  if (p==NULL) return NULL;
1016  if (p_LmIsConstant(m, r))
1017  return __pp_Mult_nn(p, pGetCoeff(m), r);
1018  else
1019  return r->p_Procs->pp_mm_Mult(p, m, r);
1020 }
1021 
1022 // returns p*m, destroys p, const: m
1023 static inline poly p_Mult_mm(poly p, poly m, const ring r)
1024 {
1025  if (p==NULL) return NULL;
1026  if (p_LmIsConstant(m, r))
1027  return __p_Mult_nn(p, pGetCoeff(m), r);
1028  else
1029  return r->p_Procs->p_Mult_mm(p, m, r);
1030 }
1031 
1032 // returns m*p, destroys p, const: m
1033 static inline poly p_mm_Mult(poly p, poly m, const ring r)
1034 {
1035  if (p==NULL) return NULL;
1036  if (p_LmIsConstant(m, r))
1037  return __p_Mult_nn(p, pGetCoeff(m), r);
1038  else
1039  return r->p_Procs->p_mm_Mult(p, m, r);
1040 }
1041 
1042 static inline poly p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, int lq,
1043  const poly spNoether, const ring r)
1044 {
1045  int shorter;
1046  const poly res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, spNoether, r);
1047  lp += lq - shorter;
1048 // assume( lp == pLength(res) );
1049  return res;
1050 }
1051 
1052 // return p - m*Copy(q), destroys p; const: p,m
1053 static inline poly p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, const ring r)
1054 {
1055  int shorter;
1056 
1057  return r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
1058 }
1059 
1060 
1061 // returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
1062 static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r)
1063 {
1064  int shorter;
1065  return r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
1066 }
1067 
1068 // returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
1069 // if lp is length of p on input then lp is length of returned poly on output
1070 static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, int &lp, const poly m, const ring r)
1071 {
1072  int shorter;
1073  poly pp = r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
1074  lp -= shorter;
1075  return pp;
1076 }
1077 
1078 // returns -p, destroys p
1079 static inline poly p_Neg(poly p, const ring r)
1080 {
1081  return r->p_Procs->p_Neg(p, r);
1082 }
1083 
1084 extern poly _p_Mult_q(poly p, poly q, const int copy, const ring r);
1085 // returns p*q, destroys p and q
1086 static inline poly p_Mult_q(poly p, poly q, const ring r)
1087 {
1088  assume( (p != q) || (p == NULL && q == NULL) );
1089 
1090  if (p == NULL)
1091  {
1092  p_Delete(&q, r);
1093  return NULL;
1094  }
1095  if (q == NULL)
1096  {
1097  p_Delete(&p, r);
1098  return NULL;
1099  }
1100 
1101  if (pNext(p) == NULL)
1102  {
1103  q = r->p_Procs->p_mm_Mult(q, p, r);
1104  p_LmDelete(&p, r);
1105  return q;
1106  }
1107 
1108  if (pNext(q) == NULL)
1109  {
1110  p = r->p_Procs->p_Mult_mm(p, q, r);
1111  p_LmDelete(&q, r);
1112  return p;
1113  }
1114 #if defined(HAVE_PLURAL) || defined(HAVE_SHIFTBBA)
1115  if (rIsNCRing(r))
1116  return _nc_p_Mult_q(p, q, r);
1117  else
1118 #endif
1119  return _p_Mult_q(p, q, 0, r);
1120 }
1121 
1122 // returns p*q, does neither destroy p nor q
1123 static inline poly pp_Mult_qq(poly p, poly q, const ring r)
1124 {
1125  if (p == NULL || q == NULL) return NULL;
1126 
1127  if (pNext(p) == NULL)
1128  {
1129  return r->p_Procs->pp_mm_Mult(q, p, r);
1130  }
1131 
1132  if (pNext(q) == NULL)
1133  {
1134  return r->p_Procs->pp_Mult_mm(p, q, r);
1135  }
1136 
1137  poly qq = q;
1138  if (p == q)
1139  qq = p_Copy(q, r);
1140 
1141  poly res;
1142 #if defined(HAVE_PLURAL) || defined(HAVE_SHIFTBBA)
1143  if (rIsNCRing(r))
1144  res = _nc_pp_Mult_qq(p, qq, r);
1145  else
1146 #endif
1147  res = _p_Mult_q(p, qq, 1, r);
1148 
1149  if (qq != q)
1150  p_Delete(&qq, r);
1151  return res;
1152 }
1153 
1154 // returns p + m*q destroys p, const: q, m
1155 static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq,
1156  const ring r)
1157 {
1158 #ifdef HAVE_PLURAL
1159  if (rIsPluralRing(r))
1160  return nc_p_Plus_mm_Mult_qq(p, m, q, lp, lq, r);
1161 #endif
1162 
1163 // this should be implemented more efficiently
1164  poly res;
1165  int shorter;
1166  number n_old = pGetCoeff(m);
1167  number n_neg = n_Copy(n_old, r->cf);
1168  n_neg = n_InpNeg(n_neg, r->cf);
1169  pSetCoeff0(m, n_neg);
1170  res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
1171  lp = (lp + lq) - shorter;
1172  pSetCoeff0(m, n_old);
1173  n_Delete(&n_neg, r->cf);
1174  return res;
1175 }
1176 
1177 static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, const ring r)
1178 {
1179  int lp = 0, lq = 0;
1180  return p_Plus_mm_Mult_qq(p, m, q, lp, lq, r);
1181 }
1182 
1183 // returns merged p and q, assumes p and q have no monomials which are equal
1184 static inline poly p_Merge_q(poly p, poly q, const ring r)
1185 {
1186  assume( (p != q) || (p == NULL && q == NULL) );
1187  return r->p_Procs->p_Merge_q(p, q, r);
1188 }
1189 
1190 // like p_SortMerge, except that p may have equal monimals
1191 static inline poly p_SortAdd(poly p, const ring r, BOOLEAN revert= FALSE)
1192 {
1193  if (revert) p = pReverse(p);
1194  return sBucketSortAdd(p, r);
1195 }
1196 
1197 // sorts p using bucket sort: returns sorted poly
1198 // assumes that monomials of p are all different
1199 // reverses it first, if revert == TRUE, use this if input p is "almost" sorted
1200 // correctly
1201 static inline poly p_SortMerge(poly p, const ring r, BOOLEAN revert= FALSE)
1202 {
1203  if (revert) p = pReverse(p);
1204  return sBucketSortMerge(p, r);
1205 }
1206 
1207 /***************************************************************
1208  *
1209  * I/O
1210  *
1211  ***************************************************************/
1212 static inline char* p_String(poly p, ring p_ring)
1213 {
1214  return p_String(p, p_ring, p_ring);
1215 }
1216 static inline void p_String0(poly p, ring p_ring)
1217 {
1218  p_String0(p, p_ring, p_ring);
1219 }
1220 static inline void p_Write(poly p, ring p_ring)
1221 {
1222  p_Write(p, p_ring, p_ring);
1223 }
1224 static inline void p_Write0(poly p, ring p_ring)
1225 {
1226  p_Write0(p, p_ring, p_ring);
1227 }
1228 static inline void p_wrp(poly p, ring p_ring)
1229 {
1230  p_wrp(p, p_ring, p_ring);
1231 }
1232 
1233 
1234 #if PDEBUG > 0
1235 
1236 #define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
1237 do \
1238 { \
1239  int _cmp = p_LmCmp(p,q,r); \
1240  if (_cmp == 0) actionE; \
1241  if (_cmp == 1) actionG; \
1242  actionS; \
1243 } \
1244 while(0)
1245 
1246 #else
1247 
1248 #define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
1249  p_MemCmp_LengthGeneral_OrdGeneral(p->exp, q->exp, r->CmpL_Size, r->ordsgn, \
1250  actionE, actionG, actionS)
1251 
1252 #endif
1253 
1254 #define pDivAssume(x) do {} while (0)
1255 
1256 
1257 
1258 /***************************************************************
1259  *
1260  * Allocation/Initalization/Deletion
1261  *
1262  ***************************************************************/
1263 // adjustments for negative weights
1264 static inline void p_MemAdd_NegWeightAdjust(poly p, const ring r)
1265 {
1266  if (r->NegWeightL_Offset != NULL)
1267  {
1268  for (int i=r->NegWeightL_Size-1; i>=0; i--)
1269  {
1270  p->exp[r->NegWeightL_Offset[i]] -= POLY_NEGWEIGHT_OFFSET;
1271  }
1272  }
1273 }
1274 static inline void p_MemSub_NegWeightAdjust(poly p, const ring r)
1275 {
1276  if (r->NegWeightL_Offset != NULL)
1277  {
1278  for (int i=r->NegWeightL_Size-1; i>=0; i--)
1279  {
1280  p->exp[r->NegWeightL_Offset[i]] += POLY_NEGWEIGHT_OFFSET;
1281  }
1282  }
1283 }
1284 // ExpVextor(d_p) = ExpVector(s_p)
1285 static inline void p_ExpVectorCopy(poly d_p, poly s_p, const ring r)
1286 {
1287  p_LmCheckPolyRing1(d_p, r);
1288  p_LmCheckPolyRing1(s_p, r);
1289  memcpy(d_p->exp, s_p->exp, r->ExpL_Size*sizeof(long));
1290 }
1291 
1292 static inline poly p_Init(const ring r, omBin bin)
1293 {
1294  p_CheckRing1(r);
1295  pAssume1(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
1296  poly p;
1297  omTypeAlloc0Bin(poly, p, bin);
1299  p_SetRingOfLm(p, r);
1300  return p;
1301 }
1302 static inline poly p_Init(const ring r)
1303 {
1304  return p_Init(r, r->PolyBin);
1305 }
1306 
1307 static inline poly p_LmInit(poly p, const ring r)
1308 {
1309  p_LmCheckPolyRing1(p, r);
1310  poly np;
1311  omTypeAllocBin(poly, np, r->PolyBin);
1312  p_SetRingOfLm(np, r);
1313  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
1314  pNext(np) = NULL;
1315  pSetCoeff0(np, NULL);
1316  return np;
1317 }
1318 static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r, omBin d_bin)
1319 {
1320  p_LmCheckPolyRing1(s_p, s_r);
1321  p_CheckRing(d_r);
1322  pAssume1(d_r->N <= s_r->N);
1323  poly d_p = p_Init(d_r, d_bin);
1324  for (unsigned i=d_r->N; i!=0; i--)
1325  {
1326  p_SetExp(d_p, i, p_GetExp(s_p, i,s_r), d_r);
1327  }
1328  if (rRing_has_Comp(d_r))
1329  {
1330  p_SetComp(d_p, p_GetComp(s_p,s_r), d_r);
1331  }
1332  p_Setm(d_p, d_r);
1333  return d_p;
1334 }
1335 static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r)
1336 {
1337  pAssume1(d_r != NULL);
1338  return p_LmInit(s_p, s_r, d_r, d_r->PolyBin);
1339 }
1340 
1341 // set all exponents l..k to 0, assume exp. k+1..n and 1..l-1 are in
1342 // different blocks
1343 // set coeff to 1
1344 static inline poly p_GetExp_k_n(poly p, int l, int k, const ring r)
1345 {
1346  if (p == NULL) return NULL;
1347  p_LmCheckPolyRing1(p, r);
1348  poly np;
1349  omTypeAllocBin(poly, np, r->PolyBin);
1350  p_SetRingOfLm(np, r);
1351  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
1352  pNext(np) = NULL;
1353  pSetCoeff0(np, n_Init(1, r->cf));
1354  int i;
1355  for(i=l;i<=k;i++)
1356  {
1357  //np->exp[(r->VarOffset[i] & 0xffffff)] =0;
1358  p_SetExp(np,i,0,r);
1359  }
1360  p_Setm(np,r);
1361  return np;
1362 }
1363 
1364 // simialar to p_ShallowCopyDelete but does it only for leading monomial
1365 static inline poly p_LmShallowCopyDelete(poly p, const ring r)
1366 {
1367  p_LmCheckPolyRing1(p, r);
1368  pAssume1(omSizeWOfBin(bin) == omSizeWOfBin(r->PolyBin));
1369  poly new_p = p_New(r);
1370  memcpy(new_p->exp, p->exp, r->ExpL_Size*sizeof(long));
1371  pSetCoeff0(new_p, pGetCoeff(p));
1372  pNext(new_p) = pNext(p);
1373  omFreeBinAddr(p);
1374  return new_p;
1375 }
1376 
1377 /***************************************************************
1378  *
1379  * Operation on ExpVectors
1380  *
1381  ***************************************************************/
1382 // ExpVector(p1) += ExpVector(p2)
1383 static inline void p_ExpVectorAdd(poly p1, poly p2, const ring r)
1384 {
1385  p_LmCheckPolyRing1(p1, r);
1386  p_LmCheckPolyRing1(p2, r);
1387 #if PDEBUG >= 1
1388  for (int i=1; i<=r->N; i++)
1389  pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask);
1390  pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0);
1391 #endif
1392 
1393  p_MemAdd_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size);
1394  p_MemAdd_NegWeightAdjust(p1, r);
1395 }
1396 // ExpVector(pr) = ExpVector(p1) + ExpVector(p2)
1397 static inline void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r)
1398 {
1399  p_LmCheckPolyRing1(p1, r);
1400  p_LmCheckPolyRing1(p2, r);
1401  p_LmCheckPolyRing1(pr, r);
1402 #if PDEBUG >= 1
1403  for (int i=1; i<=r->N; i++)
1404  pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask);
1405  pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0);
1406 #endif
1407 
1408  p_MemSum_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size);
1409  p_MemAdd_NegWeightAdjust(pr, r);
1410 }
1411 // ExpVector(p1) -= ExpVector(p2)
1412 static inline void p_ExpVectorSub(poly p1, poly p2, const ring r)
1413 {
1414  p_LmCheckPolyRing1(p1, r);
1415  p_LmCheckPolyRing1(p2, r);
1416 #if PDEBUG >= 1
1417  for (int i=1; i<=r->N; i++)
1418  pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r));
1419  pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0 ||
1420  p_GetComp(p1, r) == p_GetComp(p2, r));
1421 #endif
1422 
1423  p_MemSub_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size);
1424  p_MemSub_NegWeightAdjust(p1, r);
1425 }
1426 
1427 // ExpVector(p1) += ExpVector(p2) - ExpVector(p3)
1428 static inline void p_ExpVectorAddSub(poly p1, poly p2, poly p3, const ring r)
1429 {
1430  p_LmCheckPolyRing1(p1, r);
1431  p_LmCheckPolyRing1(p2, r);
1432  p_LmCheckPolyRing1(p3, r);
1433 #if PDEBUG >= 1
1434  for (int i=1; i<=r->N; i++)
1435  pAssume1(p_GetExp(p1, i, r) + p_GetExp(p2, i, r) >= p_GetExp(p3, i, r));
1436  pAssume1(p_GetComp(p1, r) == 0 ||
1437  (p_GetComp(p2, r) - p_GetComp(p3, r) == 0) ||
1438  (p_GetComp(p1, r) == p_GetComp(p2, r) - p_GetComp(p3, r)));
1439 #endif
1440 
1441  p_MemAddSub_LengthGeneral(p1->exp, p2->exp, p3->exp, r->ExpL_Size);
1442  // no need to adjust in case of NegWeights
1443 }
1444 
1445 // ExpVector(pr) = ExpVector(p1) - ExpVector(p2)
1446 static inline void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
1447 {
1448  p_LmCheckPolyRing1(p1, r);
1449  p_LmCheckPolyRing1(p2, r);
1450  p_LmCheckPolyRing1(pr, r);
1451 #if PDEBUG >= 2
1452  for (int i=1; i<=r->N; i++)
1453  pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r));
1454  pAssume1(!rRing_has_Comp(r) || p_GetComp(p1, r) == p_GetComp(p2, r));
1455 #endif
1456 
1457  p_MemDiff_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size);
1458  p_MemSub_NegWeightAdjust(pr, r);
1459 }
1460 
1461 static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r)
1462 {
1463  p_LmCheckPolyRing1(p1, r);
1464  p_LmCheckPolyRing1(p2, r);
1465 
1466  unsigned i = r->ExpL_Size;
1467  unsigned long *ep = p1->exp;
1468  unsigned long *eq = p2->exp;
1469 
1470  do
1471  {
1472  i--;
1473  if (ep[i] != eq[i]) return FALSE;
1474  }
1475  while (i!=0);
1476  return TRUE;
1477 }
1478 
1479 static inline long p_Totaldegree(poly p, const ring r)
1480 {
1481  p_LmCheckPolyRing1(p, r);
1482  unsigned long s = p_GetTotalDegree(p->exp[r->VarL_Offset[0]],
1483  r,
1484  r->ExpPerLong);
1485  for (unsigned i=r->VarL_Size-1; i!=0; i--)
1486  {
1487  s += p_GetTotalDegree(p->exp[r->VarL_Offset[i]], r,r->ExpPerLong);
1488  }
1489  return (long)s;
1490 }
1491 
1492 static inline void p_GetExpV(poly p, int *ev, const ring r)
1493 {
1494  p_LmCheckPolyRing1(p, r);
1495  for (unsigned j = r->N; j!=0; j--)
1496  ev[j] = p_GetExp(p, j, r);
1497 
1498  ev[0] = p_GetComp(p, r);
1499 }
1500 // p_GetExpVL is used in Singular,jl
1501 static inline void p_GetExpVL(poly p, int64 *ev, const ring r)
1502 {
1503  p_LmCheckPolyRing1(p, r);
1504  for (unsigned j = r->N; j!=0; j--)
1505  ev[j-1] = p_GetExp(p, j, r);
1506 }
1507 // p_GetExpVLV is used in Singular,jl
1508 static inline int64 p_GetExpVLV(poly p, int64 *ev, const ring r)
1509 {
1510  p_LmCheckPolyRing1(p, r);
1511  for (unsigned j = r->N; j!=0; j--)
1512  ev[j-1] = p_GetExp(p, j, r);
1513  return (int64)p_GetComp(p,r);
1514 }
1515 // p_GetExpVL is used in Singular,jl
1516 static inline void p_SetExpV(poly p, int *ev, const ring r)
1517 {
1518  p_LmCheckPolyRing1(p, r);
1519  for (unsigned j = r->N; j!=0; j--)
1520  p_SetExp(p, j, ev[j], r);
1521 
1522  if(ev[0]!=0) p_SetComp(p, ev[0],r);
1523  p_Setm(p, r);
1524 }
1525 static inline void p_SetExpVL(poly p, int64 *ev, const ring r)
1526 {
1527  p_LmCheckPolyRing1(p, r);
1528  for (unsigned j = r->N; j!=0; j--)
1529  p_SetExp(p, j, ev[j-1], r);
1530  p_SetComp(p, 0,r);
1531 
1532  p_Setm(p, r);
1533 }
1534 
1535 // p_SetExpVLV is used in Singular,jl
1536 static inline void p_SetExpVLV(poly p, int64 *ev, int64 comp, const ring r)
1537 {
1538  p_LmCheckPolyRing1(p, r);
1539  for (unsigned j = r->N; j!=0; j--)
1540  p_SetExp(p, j, ev[j-1], r);
1541  p_SetComp(p, comp,r);
1542 
1543  p_Setm(p, r);
1544 }
1545 
1546 /***************************************************************
1547  *
1548  * Comparison w.r.t. monomial ordering
1549  *
1550  ***************************************************************/
1551 
1552 static inline int p_LmCmp(poly p, poly q, const ring r)
1553 {
1554  p_LmCheckPolyRing1(p, r);
1555  p_LmCheckPolyRing1(q, r);
1556 
1557  const unsigned long* _s1 = ((unsigned long*) p->exp);
1558  const unsigned long* _s2 = ((unsigned long*) q->exp);
1559  REGISTER unsigned long _v1;
1560  REGISTER unsigned long _v2;
1561  const unsigned long _l = r->CmpL_Size;
1562 
1563  REGISTER unsigned long _i=0;
1564 
1565  LengthGeneral_OrdGeneral_LoopTop:
1566  _v1 = _s1[_i];
1567  _v2 = _s2[_i];
1568  if (_v1 == _v2)
1569  {
1570  _i++;
1571  if (_i == _l) return 0;
1572  goto LengthGeneral_OrdGeneral_LoopTop;
1573  }
1574  const long* _ordsgn = (long*) r->ordsgn;
1575 #if 1 /* two variants*/
1576  if (_v1 > _v2)
1577  {
1578  return _ordsgn[_i];
1579  }
1580  return -(_ordsgn[_i]);
1581 #else
1582  if (_v1 > _v2)
1583  {
1584  if (_ordsgn[_i] == 1) return 1;
1585  return -1;
1586  }
1587  if (_ordsgn[_i] == 1) return -1;
1588  return 1;
1589 #endif
1590 }
1591 
1592 // The coefficient will be compared in absolute value
1593 static inline int p_LtCmp(poly p, poly q, const ring r)
1594 {
1595  int res = p_LmCmp(p,q,r);
1596  if(res == 0)
1597  {
1598  if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
1599  return res;
1600  number pc = n_Copy(p_GetCoeff(p,r),r->cf);
1601  number qc = n_Copy(p_GetCoeff(q,r),r->cf);
1602  if(!n_GreaterZero(pc,r->cf))
1603  pc = n_InpNeg(pc,r->cf);
1604  if(!n_GreaterZero(qc,r->cf))
1605  qc = n_InpNeg(qc,r->cf);
1606  if(n_Greater(pc,qc,r->cf))
1607  res = 1;
1608  else if(n_Greater(qc,pc,r->cf))
1609  res = -1;
1610  else if(n_Equal(pc,qc,r->cf))
1611  res = 0;
1612  n_Delete(&pc,r->cf);
1613  n_Delete(&qc,r->cf);
1614  }
1615  return res;
1616 }
1617 
1618 // The coefficient will be compared in absolute value
1619 static inline int p_LtCmpNoAbs(poly p, poly q, const ring r)
1620 {
1621  int res = p_LmCmp(p,q,r);
1622  if(res == 0)
1623  {
1624  if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
1625  return res;
1626  number pc = p_GetCoeff(p,r);
1627  number qc = p_GetCoeff(q,r);
1628  if(n_Greater(pc,qc,r->cf))
1629  res = 1;
1630  if(n_Greater(qc,pc,r->cf))
1631  res = -1;
1632  if(n_Equal(pc,qc,r->cf))
1633  res = 0;
1634  }
1635  return res;
1636 }
1637 
1638 #ifdef HAVE_RINGS
1639 // This is the equivalent of pLmCmp(p,q) != -currRing->OrdSgn for rings
1640 // It is used in posInLRing and posInTRing
1641 static inline int p_LtCmpOrdSgnDiffM(poly p, poly q, const ring r)
1642 {
1643  if(r->OrdSgn == 1)
1644  {
1645  return(p_LtCmp(p,q,r) == 1);
1646  }
1647  else
1648  {
1649  return(p_LmCmp(p,q,r) == -1);
1650  }
1651 }
1652 #endif
1653 
1654 #ifdef HAVE_RINGS
1655 // This is the equivalent of pLmCmp(p,q) != currRing->OrdSgn for rings
1656 // It is used in posInLRing and posInTRing
1657 static inline int p_LtCmpOrdSgnDiffP(poly p, poly q, const ring r)
1658 {
1659  if(r->OrdSgn == 1)
1660  {
1661  return(p_LmCmp(p,q,r) == -1);
1662  }
1663  else
1664  {
1665  return(p_LtCmp(p,q,r) != -1);
1666  }
1667 
1668 }
1669 #endif
1670 
1671 #ifdef HAVE_RINGS
1672 // This is the equivalent of pLmCmp(p,q) == -currRing->OrdSgn for rings
1673 // It is used in posInLRing and posInTRing
1674 static inline int p_LtCmpOrdSgnEqM(poly p, poly q, const ring r)
1675 {
1676  return(p_LtCmp(p,q,r) == -r->OrdSgn);
1677 }
1678 #endif
1679 
1680 #ifdef HAVE_RINGS
1681 // This is the equivalent of pLmCmp(p,q) == currRing->OrdSgn for rings
1682 // It is used in posInLRing and posInTRing
1683 static inline int p_LtCmpOrdSgnEqP(poly p, poly q, const ring r)
1684 {
1685  return(p_LtCmp(p,q,r) == r->OrdSgn);
1686 }
1687 #endif
1688 
1689 /// returns TRUE if p1 is a skalar multiple of p2
1690 /// assume p1 != NULL and p2 != NULL
1691 BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r);
1692 
1693 
1694 /***************************************************************
1695  *
1696  * Comparisons: they are all done without regarding coeffs
1697  *
1698  ***************************************************************/
1699 #define p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
1700  _p_LmCmpAction(p, q, r, actionE, actionG, actionS)
1701 
1702 // returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !!
1703 #define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r)
1704 
1705 // pCmp: args may be NULL
1706 // returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))
1707 static inline int p_Cmp(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_LmCmp(p1,p2,r);
1717 }
1718 
1719 static inline int p_CmpPolys(poly p1, poly p2, ring r)
1720 {
1721  if (p2==NULL)
1722  {
1723  if (p1==NULL) return 0;
1724  return 1;
1725  }
1726  if (p1==NULL)
1727  return -1;
1728  return p_ComparePolys(p1,p2,r);
1729 }
1730 
1731 
1732 /***************************************************************
1733  *
1734  * divisibility
1735  *
1736  ***************************************************************/
1737 /// return: FALSE, if there exists i, such that a->exp[i] > b->exp[i]
1738 /// TRUE, otherwise
1739 /// (1) Consider long vars, instead of single exponents
1740 /// (2) Clearly, if la > lb, then FALSE
1741 /// (3) Suppose la <= lb, and consider first bits of single exponents in l:
1742 /// if TRUE, then value of these bits is la ^ lb
1743 /// if FALSE, then la-lb causes an "overflow" into one of those bits, i.e.,
1744 /// la ^ lb != la - lb
1745 static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, poly b, const ring r)
1746 {
1747  int i=r->VarL_Size - 1;
1748  unsigned long divmask = r->divmask;
1749  unsigned long la, lb;
1750 
1751  if (r->VarL_LowIndex >= 0)
1752  {
1753  i += r->VarL_LowIndex;
1754  do
1755  {
1756  la = a->exp[i];
1757  lb = b->exp[i];
1758  if ((la > lb) ||
1759  (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
1760  {
1762  return FALSE;
1763  }
1764  i--;
1765  }
1766  while (i>=r->VarL_LowIndex);
1767  }
1768  else
1769  {
1770  do
1771  {
1772  la = a->exp[r->VarL_Offset[i]];
1773  lb = b->exp[r->VarL_Offset[i]];
1774  if ((la > lb) ||
1775  (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
1776  {
1778  return FALSE;
1779  }
1780  i--;
1781  }
1782  while (i>=0);
1783  }
1784 /*#ifdef HAVE_RINGS
1785  pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf));
1786  return (!rField_is_Ring(r)) || n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf);
1787 #else
1788 */
1790  return TRUE;
1791 //#endif
1792 }
1793 
1794 static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, const ring r_a, poly b, const ring r_b)
1795 {
1796  int i=r_a->N;
1797  pAssume1(r_a->N == r_b->N);
1798 
1799  do
1800  {
1801  if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b))
1802  return FALSE;
1803  i--;
1804  }
1805  while (i);
1806 /*#ifdef HAVE_RINGS
1807  return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
1808 #else
1809 */
1810  return TRUE;
1811 //#endif
1812 }
1813 
1814 #ifdef HAVE_RATGRING
1815 static inline BOOLEAN _p_LmDivisibleByNoCompPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end)
1816 {
1817  int i=end;
1818  pAssume1(r_a->N == r_b->N);
1819 
1820  do
1821  {
1822  if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b))
1823  return FALSE;
1824  i--;
1825  }
1826  while (i>=start);
1827 /*#ifdef HAVE_RINGS
1828  return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
1829 #else
1830 */
1831  return TRUE;
1832 //#endif
1833 }
1834 static inline BOOLEAN _p_LmDivisibleByPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end)
1835 {
1836  if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b))
1837  return _p_LmDivisibleByNoCompPart(a, r_a, b, r_b,start,end);
1838  return FALSE;
1839 }
1840 static inline BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r,const int start, const int end)
1841 {
1842  p_LmCheckPolyRing1(b, r);
1843  pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r));
1844  if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
1845  return _p_LmDivisibleByNoCompPart(a, r, b, r,start, end);
1846  return FALSE;
1847 }
1848 #endif
1849 static inline BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r)
1850 {
1851  if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
1852  return _p_LmDivisibleByNoComp(a, b, r);
1853  return FALSE;
1854 }
1855 static inline BOOLEAN _p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1856 {
1857  if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b))
1858  return _p_LmDivisibleByNoComp(a, r_a, b, r_b);
1859  return FALSE;
1860 }
1861 static inline BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, const ring r)
1862 {
1863  p_LmCheckPolyRing1(a, r);
1864  p_LmCheckPolyRing1(b, r);
1865  return _p_LmDivisibleByNoComp(a, b, r);
1866 }
1867 
1868 static inline BOOLEAN p_LmDivisibleByNoComp(poly a, const ring ra, poly b, const ring rb)
1869 {
1870  p_LmCheckPolyRing1(a, ra);
1871  p_LmCheckPolyRing1(b, rb);
1872  return _p_LmDivisibleByNoComp(a, ra, b, rb);
1873 }
1874 
1875 static inline BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
1876 {
1877  p_LmCheckPolyRing1(b, r);
1878  pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r));
1879  if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
1880  return _p_LmDivisibleByNoComp(a, b, r);
1881  return FALSE;
1882 }
1883 
1884 static inline BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
1885 {
1887  pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r));
1888 
1889  if (a != NULL && (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)))
1890  return _p_LmDivisibleByNoComp(a,b,r);
1891  return FALSE;
1892 }
1893 static inline BOOLEAN p_DivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1894 {
1895  pIfThen1(b!=NULL, p_LmCheckPolyRing1(b, r_b));
1896  pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r_a));
1897  if (a != NULL) {
1898  return _p_LmDivisibleBy(a, r_a, b, r_b);
1899  }
1900  return FALSE;
1901 }
1902 static inline BOOLEAN p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1903 {
1904  p_LmCheckPolyRing(a, r_a);
1905  p_LmCheckPolyRing(b, r_b);
1906  return _p_LmDivisibleBy(a, r_a, b, r_b);
1907 }
1908 
1909 static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a,
1910  poly b, unsigned long not_sev_b, const ring r)
1911 {
1912  p_LmCheckPolyRing1(a, r);
1913  p_LmCheckPolyRing1(b, r);
1914 #ifndef PDIV_DEBUG
1915  _pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r);
1916  _pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r);
1917 
1918  if (sev_a & not_sev_b)
1919  {
1921  return FALSE;
1922  }
1923  return p_LmDivisibleBy(a, b, r);
1924 #else
1925  return pDebugLmShortDivisibleBy(a, sev_a, r, b, not_sev_b, r);
1926 #endif
1927 }
1928 
1929 static inline BOOLEAN p_LmShortDivisibleByNoComp(poly a, unsigned long sev_a,
1930  poly b, unsigned long not_sev_b, const ring r)
1931 {
1932  p_LmCheckPolyRing1(a, r);
1933  p_LmCheckPolyRing1(b, r);
1934 #ifndef PDIV_DEBUG
1935  _pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r);
1936  _pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r);
1937 
1938  if (sev_a & not_sev_b)
1939  {
1941  return FALSE;
1942  }
1943  return p_LmDivisibleByNoComp(a, b, r);
1944 #else
1945  return pDebugLmShortDivisibleByNoComp(a, sev_a, r, b, not_sev_b, r);
1946 #endif
1947 }
1948 
1949 static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, const ring r_a,
1950  poly b, unsigned long not_sev_b, const ring r_b)
1951 {
1952  p_LmCheckPolyRing1(a, r_a);
1953  p_LmCheckPolyRing1(b, r_b);
1954 #ifndef PDIV_DEBUG
1955  _pPolyAssume2(p_GetShortExpVector(a, r_a) == sev_a, a, r_a);
1956  _pPolyAssume2(p_GetShortExpVector(b, r_b) == ~ not_sev_b, b, r_b);
1957 
1958  if (sev_a & not_sev_b)
1959  {
1960  pAssume1(_p_LmDivisibleByNoComp(a, r_a, b, r_b) == FALSE);
1961  return FALSE;
1962  }
1963  return _p_LmDivisibleBy(a, r_a, b, r_b);
1964 #else
1965  return pDebugLmShortDivisibleBy(a, sev_a, r_a, b, not_sev_b, r_b);
1966 #endif
1967 }
1968 
1969 /***************************************************************
1970  *
1971  * Misc things on Lm
1972  *
1973  ***************************************************************/
1974 
1975 
1976 /// like the respective p_LmIs* routines, except that p might be empty
1977 static inline BOOLEAN p_IsConstantComp(const poly p, const ring r)
1978 {
1979  if (p == NULL) return TRUE;
1980  return (pNext(p)==NULL) && p_LmIsConstantComp(p, r);
1981 }
1982 
1983 static inline BOOLEAN p_IsConstant(const poly p, const ring r)
1984 {
1985  if (p == NULL) return TRUE;
1986  return (pNext(p)==NULL) && p_LmIsConstant(p, r);
1987 }
1988 
1989 /// either poly(1) or gen(k)?!
1990 static inline BOOLEAN p_IsOne(const poly p, const ring R)
1991 {
1992  if (p == NULL) return FALSE; /* TODO check if 0 == 1 */
1993  p_Test(p, R);
1994  return (p_IsConstant(p, R) && n_IsOne(p_GetCoeff(p, R), R->cf));
1995 }
1996 
1997 static inline BOOLEAN p_IsConstantPoly(const poly p, const ring r)
1998 {
1999  p_Test(p, r);
2000  poly pp=p;
2001  while(pp!=NULL)
2002  {
2003  if (! p_LmIsConstantComp(pp, r))
2004  return FALSE;
2005  pIter(pp);
2006  }
2007  return TRUE;
2008 }
2009 
2010 static inline BOOLEAN p_IsUnit(const poly p, const ring r)
2011 {
2012  if (p == NULL) return FALSE;
2013  if (rField_is_Ring(r))
2014  return (p_LmIsConstant(p, r) && n_IsUnit(pGetCoeff(p),r->cf));
2015  return p_LmIsConstant(p, r);
2016 }
2017 
2018 static inline BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2,
2019  const ring r)
2020 {
2021  p_LmCheckPolyRing(p1, r);
2022  p_LmCheckPolyRing(p2, r);
2023  unsigned long l1, l2, divmask = r->divmask;
2024  int i;
2025 
2026  for (i=0; i<r->VarL_Size; i++)
2027  {
2028  l1 = p1->exp[r->VarL_Offset[i]];
2029  l2 = p2->exp[r->VarL_Offset[i]];
2030  // do the divisiblity trick
2031  if ( (l1 > ULONG_MAX - l2) ||
2032  (((l1 & divmask) ^ (l2 & divmask)) != ((l1 + l2) & divmask)))
2033  return FALSE;
2034  }
2035  return TRUE;
2036 }
2037 void p_Split(poly p, poly * r); /*p => IN(p), r => REST(p) */
2038 BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r);
2039 BOOLEAN p_HasNotCFRing(poly p1, poly p2, const ring r);
2040 poly p_mInit(const char *s, BOOLEAN &ok, const ring r); /* monom s -> poly, interpreter */
2041 const char * p_Read(const char *s, poly &p,const ring r); /* monom -> poly */
2042 poly p_MDivide(poly a, poly b, const ring r);
2043 poly p_DivideM(poly a, poly b, const ring r);
2044 poly pp_DivideM(poly a, poly b, const ring r);
2045 poly p_Div_nn(poly p, const number n, const ring r);
2046 
2047 // returns the LCM of the head terms of a and b in *m, does not p_Setm
2048 void p_Lcm(const poly a, const poly b, poly m, const ring r);
2049 // returns the LCM of the head terms of a and b, does p_Setm
2050 poly p_Lcm(const poly a, const poly b, const ring r);
2051 
2052 #ifdef HAVE_RATGRING
2053 poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r);
2054 poly p_GetCoeffRat(poly p, int ishift, ring r);
2055 void p_LmDeleteAndNextRat(poly *p, int ishift, ring r);
2056 void p_ContentRat(poly &ph, const ring r);
2057 #endif /* ifdef HAVE_RATGRING */
2058 
2059 
2060 poly p_Diff(poly a, int k, const ring r);
2061 poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r);
2062 int p_Weight(int c, const ring r);
2063 
2064 /// assumes that p and divisor are univariate polynomials in r,
2065 /// mentioning the same variable;
2066 /// assumes divisor != NULL;
2067 /// p may be NULL;
2068 /// assumes a global monomial ordering in r;
2069 /// performs polynomial division of p by divisor:
2070 /// - afterwards p contains the remainder of the division, i.e.,
2071 /// p_before = result * divisor + p_afterwards;
2072 /// - if needResult == TRUE, then the method computes and returns 'result',
2073 /// otherwise NULL is returned (This parametrization can be used when
2074 /// one is only interested in the remainder of the division. In this
2075 /// case, the method will be slightly faster.)
2076 /// leaves divisor unmodified
2077 poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r);
2078 
2079 /* syszygy stuff */
2080 BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r);
2081 void p_VectorHasUnit(poly p, int * k, int * len, const ring r);
2082 poly p_TakeOutComp1(poly * p, int k, const ring r);
2083 // Splits *p into two polys: *q which consists of all monoms with
2084 // component == comp and *p of all other monoms *lq == pLength(*q)
2085 // On return all components pf *q == 0
2086 void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r);
2087 
2088 // This is something weird -- Don't use it, unless you know what you are doing
2089 poly p_TakeOutComp(poly * p, int k, const ring r);
2090 
2091 void p_DeleteComp(poly * p,int k, const ring r);
2092 
2093 /*-------------ring management:----------------------*/
2094 
2095 // resets the pFDeg and pLDeg: if pLDeg is not given, it is
2096 // set to currRing->pLDegOrig, i.e. to the respective LDegProc which
2097 // only uses pFDeg (and not pDeg, or pTotalDegree, etc).
2098 // If you use this, make sure your procs does not make any assumptions
2099 // on ordering and/or OrdIndex -- otherwise they might return wrong results
2100 // on strat->tailRing
2101 void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg = NULL);
2102 // restores pFDeg and pLDeg:
2103 void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg);
2104 
2105 /*-------------pComp for syzygies:-------------------*/
2106 void p_SetModDeg(intvec *w, ring r);
2107 
2108 /*------------ Jet ----------------------------------*/
2109 poly pp_Jet(poly p, int m, const ring R);
2110 poly p_Jet(poly p, int m,const ring R);
2111 poly pp_JetW(poly p, int m, int *w, const ring R);
2112 poly p_JetW(poly p, int m, int *w, const ring R);
2113 
2114 poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst);
2115 
2116 poly p_PermPoly (poly p, const int * perm,const ring OldRing, const ring dst,
2117  nMapFunc nMap, const int *par_perm=NULL, int OldPar=0,
2118  BOOLEAN use_mult=FALSE);
2119 
2120 /*----------------------------------------------------*/
2121 poly p_Series(int n,poly p,poly u, intvec *w, const ring R);
2122 
2123 /*----------------------------------------------------*/
2124 int p_Var(poly mi, const ring r);
2125 /// the minimal index of used variables - 1
2126 int p_LowVar (poly p, const ring r);
2127 
2128 /*----------------------------------------------------*/
2129 /// shifts components of the vector p by i
2130 void p_Shift (poly * p,int i, const ring r);
2131 /*----------------------------------------------------*/
2132 
2133 int p_Compare(const poly a, const poly b, const ring R);
2134 
2135 /// polynomial gcd for f=mon
2136 poly p_GcdMon(poly f, poly g, const ring r);
2137 
2138 /// divide polynomial by monomial
2139 poly p_Div_mm(poly p, const poly m, const ring r);
2140 
2141 
2142 /// max exponent of variable x_i in p
2143 int p_MaxExpPerVar(poly p, int i, const ring r);
2144 #endif // P_POLYS_H
2145 
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 FACTORY_PUBLIC pp(const CanonicalForm &)
CanonicalForm pp ( const CanonicalForm & f )
Definition: cf_gcd.cc:676
int level(const CanonicalForm &f)
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:4082
int p
Definition: cfModGcd.cc:4078
g
Definition: cfModGcd.cc:4090
CanonicalForm b
Definition: cfModGcd.cc:4103
FILE * f
Definition: checklibs.c:9
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:451
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:515
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:494
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:557
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:511
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 void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:455
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 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:460
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 BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
Definition: coeffs.h:468
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
if(yy_init)
Definition: libparse.cc:1420
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
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 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
#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)
#define NULL
Definition: omList.c:12
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:389
BOOLEAN pDebugLmShortDivisibleBy(poly p1, unsigned long sev_1, ring r_1, poly p2, unsigned long not_sev_2, ring r_2)
Definition: pDebug.cc:366
BOOLEAN p_DebugLmDivisibleByNoComp(poly a, poly b, ring r)
Definition: pDebug.cc:141
#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:1079
void p_Content_n(poly p, number &c, const ring r)
Definition: p_polys.cc:2345
poly p_Diff(poly a, int k, const ring r)
Definition: p_polys.cc:1890
long pLDeg1c_WFirstTotalDegree(poly p, int *l, ring r)
Definition: p_polys.cc:1064
static int p_CmpPolys(poly p1, poly p2, ring r)
Definition: p_polys.h:1719
long pLDeg0(poly p, int *l, ring r)
Definition: p_polys.cc:735
poly p_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1570
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
Definition: p_polys.cc:1222
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:1397
poly pp_Jet(poly p, int m, const ring R)
Definition: p_polys.cc:4391
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:908
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:1086
void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg=NULL)
Definition: p_polys.cc:3711
BOOLEAN pIsMonomOf(poly p, poly m)
Definition: pDebug.cc:165
BOOLEAN p_LmCheckPolyRing(poly p, ring r)
Definition: pDebug.cc:120
static void p_MemAdd_NegWeightAdjust(poly p, const ring r)
Definition: p_polys.h:1264
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:212
static void p_ExpVectorAdd(poly p1, poly p2, const ring r)
Definition: p_polys.h:1383
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:906
BOOLEAN p_CheckIsFromRing(poly p, ring r)
Definition: pDebug.cc:102
void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg)
Definition: p_polys.cc:3723
long pLDeg1_WFirstTotalDegree(poly p, int *l, ring r)
Definition: p_polys.cc:1034
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:1834
poly p_Sub(poly a, poly b, const ring r)
Definition: p_polys.cc:1982
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:1862
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:1977
int p_Size(poly p, const ring r)
Definition: p_polys.cc:3314
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:1307
poly p_GcdMon(poly f, poly g, const ring r)
polynomial gcd for f=mon
Definition: p_polys.cc:4974
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:4609
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:753
int p_LowVar(poly p, const ring r)
the minimal index of used variables - 1
Definition: p_polys.cc:4713
poly p_CopyPowerProduct0(const poly p, const number n, const ring r)
like p_Head, but with coefficient n
Definition: p_polys.cc:5012
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:1634
poly p_Homogen(poly p, int varnum, const ring r)
Definition: p_polys.cc:3331
static void p_ExpVectorCopy(poly d_p, poly s_p, const ring r)
Definition: p_polys.h:1285
poly p_Subst(poly p, int n, poly e, const ring r)
Definition: p_polys.cc:3991
static void p_LmDelete0(poly p, const ring r)
Definition: p_polys.h:717
long pLDeg1c_Deg(poly p, int *l, ring r)
Definition: p_polys.cc:937
static int p_Cmp(poly p1, poly p2, ring r)
Definition: p_polys.h:1707
BOOLEAN _p_LmTest(poly p, ring r, int level)
Definition: pDebug.cc:323
#define __pp_Mult_nn(p, n, r)
Definition: p_polys.h:974
static void p_SetExpVL(poly p, int64 *ev, const ring r)
Definition: p_polys.h:1525
BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r)
Definition: p_polys.cc:1325
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:837
poly p_CopyPowerProduct(const poly p, const ring r)
like p_Head, but with coefficient 1
Definition: p_polys.cc:5024
static void p_SetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1516
void p_ShallowDelete(poly *p, const ring r)
static poly pp_mm_Mult(poly p, poly m, const ring r)
Definition: p_polys.h:1013
static poly pp_Mult_mm(poly p, poly m, const ring r)
Definition: p_polys.h:1003
static int p_LtCmpNoAbs(poly p, poly q, const ring r)
Definition: p_polys.h:1619
static void p_MemSub_NegWeightAdjust(poly p, const ring r)
Definition: p_polys.h:1274
poly pp_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1625
long p_WFirstTotalDegree(poly p, ring r)
Definition: p_polys.cc:592
int p_Weight(int c, const ring r)
Definition: p_polys.cc:701
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:1293
static int p_LtCmpOrdSgnEqP(poly p, poly q, const ring r)
Definition: p_polys.h:1683
void p_ContentForGB(poly p, const ring r)
Definition: p_polys.cc:2416
void p_Vec2Polys(poly v, poly **p, int *len, const ring r)
Definition: p_polys.cc:3699
poly p_DiffOp(poly a, poly b, BOOLEAN multiply, const ring r)
Definition: p_polys.cc:1965
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:4419
poly p_TakeOutComp1(poly *p, int k, const ring r)
Definition: p_polys.cc:3458
static void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
Definition: p_polys.h:1446
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:4739
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:2189
poly p_Div_nn(poly p, const number n, const ring r)
Definition: p_polys.cc:1497
static poly p_mm_Mult(poly p, poly m, const ring r)
Definition: p_polys.h:1033
void p_Normalize(poly p, const ring r)
Definition: p_polys.cc:3847
void p_DeleteComp(poly *p, int k, const ring r)
Definition: p_polys.cc:3618
poly p_MDivide(poly a, poly b, const ring r)
Definition: p_polys.cc:1484
void p_Content(poly p, const ring r)
Definition: p_polys.cc:2287
void p_ProjectiveUnique(poly p, const ring r)
Definition: p_polys.cc:3204
void p_ContentRat(poly &ph, const ring r)
Definition: p_polys.cc:1736
void p_Norm(poly p1, const ring r)
Definition: p_polys.cc:3793
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:1530
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:1134
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:1263
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:4481
static void p_ExpVectorSub(poly p1, poly p2, const ring r)
Definition: p_polys.h:1412
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:5036
int p_Var(poly mi, const ring r)
Definition: p_polys.cc:4689
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:4940
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:1438
void p_LmDeleteAndNextRat(poly *p, int ishift, ring r)
Definition: p_polys.cc:1692
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
Definition: p_polys.h:808
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:1201
static poly p_LmShallowCopyDelete(poly p, const ring r)
Definition: p_polys.h:1365
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:1184
const char * p_Read(const char *s, poly &p, const ring r)
Definition: p_polys.cc:1366
long pLDegb(poly p, int *l, ring r)
Definition: p_polys.cc:807
static void p_GetExpVL(poly p, int64 *ev, const ring r)
Definition: p_polys.h:1501
static int p_LtCmp(poly p, poly q, const ring r)
Definition: p_polys.h:1593
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
Definition: p_polys.h:978
static poly p_Head(const poly p, const ring r)
copy the (leading) term of p
Definition: p_polys.h:832
static int p_LmCmp(poly p, poly q, const ring r)
Definition: p_polys.h:1552
poly p_Series(int n, poly p, poly u, intvec *w, const ring R)
Definition: p_polys.cc:4531
long p_WTotaldegree(poly p, const ring r)
Definition: p_polys.cc:609
static BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
Definition: p_polys.h:1909
long p_DegW(poly p, const int *w, const ring R)
Definition: p_polys.cc:686
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:995
p_SetmProc p_GetSetmProc(const ring r)
Definition: p_polys.cc:556
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:1861
static BOOLEAN p_IsOne(const poly p, const ring R)
either poly(1) or gen(k)?!
Definition: p_polys.h:1990
static BOOLEAN p_IsConstant(const poly p, const ring r)
Definition: p_polys.h:1983
static void p_SetExpVLV(poly p, int64 *ev, int64 comp, const ring r)
Definition: p_polys.h:1536
BOOLEAN p_OneComp(poly p, const ring r)
return TRUE if all monoms have the same component
Definition: p_polys.cc:1204
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:1815
BOOLEAN p_CheckRing(ring r)
Definition: pDebug.cc:128
poly p_Cleardenom(poly p, const ring r)
Definition: p_polys.cc:2906
static BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1849
static unsigned long p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps)
Definition: p_polys.h:782
BOOLEAN p_LmCheckIsFromRing(poly p, ring r)
Definition: pDebug.cc:71
static poly p_New(const ring, omBin bin)
Definition: p_polys.h:664
void p_Split(poly p, poly *r)
Definition: p_polys.cc:1316
poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst)
Definition: p_polys.cc:4060
static poly p_GetExp_k_n(poly p, int l, int k, const ring r)
Definition: p_polys.h:1344
static BOOLEAN p_LmShortDivisibleByNoComp(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
Definition: p_polys.h:1929
static poly pp_Mult_nn(poly p, number n, const ring r)
Definition: p_polys.h:964
poly p_GetCoeffRat(poly p, int ishift, ring r)
Definition: p_polys.cc:1714
BOOLEAN p_VectorHasUnitB(poly p, int *k, const ring r)
Definition: p_polys.cc:3402
poly p_Vec2Poly(poly v, int k, const ring r)
Definition: p_polys.cc:3647
static BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1875
poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r)
Definition: p_polys.cc:1669
static BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1884
char * p_String(poly p, ring lmRing, ring tailRing)
Definition: polys0.cc:322
static BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r)
Definition: p_polys.h:1461
long pLDeg1_Totaldegree(poly p, int *l, ring r)
Definition: p_polys.cc:971
void p_SetModDeg(intvec *w, ring r)
Definition: p_polys.cc:3747
static poly p_ShallowCopyDelete(poly p, const ring r, omBin bin)
Definition: p_polys.h:900
static int64 p_GetExpVLV(poly p, int64 *ev, const ring r)
Definition: p_polys.h:1508
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition: p_polys.cc:3570
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:930
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:873
BOOLEAN p_HasNotCFRing(poly p1, poly p2, const ring r)
Definition: p_polys.cc:1341
poly p_One(const ring r)
Definition: p_polys.cc:1309
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:1641
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:1745
void p_VectorHasUnit(poly p, int *k, int *len, const ring r)
Definition: p_polys.cc:3425
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:1492
BOOLEAN p_CheckPolyRing(poly p, ring r)
Definition: pDebug.cc:112
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:1001
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:1243
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
Definition: p_polys.cc:1465
static poly pp_Mult_qq(poly p, poly q, const ring r)
Definition: p_polys.h:1123
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:4163
static int p_LtCmpOrdSgnEqM(poly p, poly q, const ring r)
Definition: p_polys.h:1674
static poly p_LmFreeAndNext(poly p, ring)
Definition: p_polys.h:703
#define pDivAssume(x)
Definition: p_polys.h:1254
static poly p_Mult_mm(poly p, poly m, const ring r)
Definition: p_polys.h:1023
void p_Cleardenom_n(poly p, const ring r, number &c)
Definition: p_polys.cc:3015
long p_WDegree(poly p, const ring r)
Definition: p_polys.cc:710
long pLDeg1c(poly p, int *l, ring r)
Definition: p_polys.cc:873
poly p_Last(const poly a, int &l, const ring r)
Definition: p_polys.cc:4654
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:1042
static poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, const ring r)
Definition: p_polys.h:1155
void pEnlargeSet(poly **p, int length, int increment)
Definition: p_polys.cc:3770
static BOOLEAN p_IsUnit(const poly p, const ring r)
Definition: p_polys.h:2010
static poly p_Init(const ring r, omBin bin)
Definition: p_polys.h:1292
BOOLEAN p_IsHomogeneous(poly p, const ring r)
Definition: p_polys.cc:3380
poly p_Head0(const poly p, const ring r)
like p_Head, but allow NULL coeff
Definition: p_polys.cc:5030
static poly p_LmDeleteAndNext(poly p, const ring r)
Definition: p_polys.h:731
BOOLEAN pHaveCommonMonoms(poly p, poly q)
Definition: pDebug.cc:175
unsigned long p_GetShortExpVector(const poly a, const ring r)
Definition: p_polys.cc:4814
static poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r)
Definition: p_polys.h:1062
poly pp_JetW(poly p, int m, int *w, const ring R)
Definition: p_polys.cc:4436
static BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r, const int start, const int end)
Definition: p_polys.h:1840
long p_Deg(poly a, const ring r)
Definition: p_polys.cc:583
static poly p_SortAdd(poly p, const ring r, BOOLEAN revert=FALSE)
Definition: p_polys.h:1191
void p_SimpleContent(poly p, int s, const ring r)
Definition: p_polys.cc:2625
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:818
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:2696
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:3669
static long p_Totaldegree(poly p, const ring r)
Definition: p_polys.h:1479
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:1171
static BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2, const ring r)
Definition: p_polys.h:2018
static int p_LtCmpOrdSgnDiffP(poly p, poly q, const ring r)
Definition: p_polys.h:1657
BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level)
Definition: pDebug.cc:333
void p_Lcm(const poly a, const poly b, poly m, const ring r)
Definition: p_polys.cc:1647
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:943
poly p_JetW(poly p, int m, int *w, const ring R)
Definition: p_polys.cc:4463
static BOOLEAN p_IsConstantPoly(const poly p, const ring r)
Definition: p_polys.h:1997
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:4545
long pLDeg0c(poly p, int *l, ring r)
Definition: p_polys.cc:766
static void p_ExpVectorAddSub(poly p1, poly p2, poly p3, const ring r)
Definition: p_polys.h:1428
BOOLEAN rOrd_SetCompRequiresSetm(const ring r)
return TRUE if p_SetComp requires p_Setm
Definition: ring.cc:1907
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
#define rField_is_Ring(R)
Definition: ring.h:486
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:79