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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_LmDelete(poly *p, const ring r)
718 {
719  p_LmCheckPolyRing2(*p, r);
720  poly h = *p;
721  *p = pNext(h);
722  n_Delete(&pGetCoeff(h), r->cf);
723  omFreeBinAddr(h);
724 }
725 static inline poly p_LmDeleteAndNext(poly p, const ring r)
726 {
727  p_LmCheckPolyRing2(p, r);
728  poly pnext = pNext(p);
729  n_Delete(&pGetCoeff(p), r->cf);
730  omFreeBinAddr(p);
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
741 unsigned 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
745 poly p_GetMaxExpP(poly p, ring r);
746 
747 static 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 
770 static inline unsigned long p_GetMaxExp(const poly p, const ring r)
771 {
772  return p_GetMaxExp(p_GetMaxExpL(p, r), r);
773 }
774 
775 static inline unsigned long
776 p_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)
802 static 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
812 static 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
826 static inline poly p_Head(poly p, const ring r)
827 {
828  if (p == NULL) return NULL;
829  p_LmCheckPolyRing1(p, r);
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
840 poly p_CopyPowerProduct(poly p, const ring r);
841 
842 /// returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing
843 static 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
861 static 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 
868 static 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
888 static inline poly p_ShallowCopyDelete(poly p, const ring r, omBin bin)
889 {
890  p_LmCheckPolyRing2(p, r);
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
896 static 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)
906 static 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
918 static 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 
933 static 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
952 static 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
966 static 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
983 static 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
991 static 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
1001 static 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
1011 static 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
1021 static 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 
1030 static 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
1041 static 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
1050 static 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
1058 static 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
1067 static inline poly p_Neg(poly p, const ring r)
1068 {
1069  return r->p_Procs->p_Neg(p, r);
1070 }
1071 
1072 extern poly _p_Mult_q(poly p, poly q, const int copy, const ring r);
1073 // returns p*q, destroys p and q
1074 static 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
1111 static 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
1143 static 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 
1165 static 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
1172 static 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
1179 static 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
1189 static 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  ***************************************************************/
1200 static inline char* p_String(poly p, ring p_ring)
1201 {
1202  return p_String(p, p_ring, p_ring);
1203 }
1204 static inline void p_String0(poly p, ring p_ring)
1205 {
1206  p_String0(p, p_ring, p_ring);
1207 }
1208 static inline void p_Write(poly p, ring p_ring)
1209 {
1210  p_Write(p, p_ring, p_ring);
1211 }
1212 static inline void p_Write0(poly p, ring p_ring)
1213 {
1214  p_Write0(p, p_ring, p_ring);
1215 }
1216 static 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) \
1225 do \
1226 { \
1227  int _cmp = p_LmCmp(p,q,r); \
1228  if (_cmp == 0) actionE; \
1229  if (_cmp == 1) actionG; \
1230  actionS; \
1231 } \
1232 while(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
1252 static 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 }
1262 static 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)
1273 static 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 
1280 static 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 }
1290 static inline poly p_Init(const ring r)
1291 {
1292  return p_Init(r, r->PolyBin);
1293 }
1294 
1295 static inline poly p_LmInit(poly p, const ring r)
1296 {
1297  p_LmCheckPolyRing1(p, r);
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 }
1306 static 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 }
1323 static 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
1332 static inline poly p_GetExp_k_n(poly p, int l, int k, const ring r)
1333 {
1334  if (p == NULL) return NULL;
1335  p_LmCheckPolyRing1(p, r);
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
1353 static inline poly p_LmShallowCopyDelete(poly p, const ring r)
1354 {
1355  p_LmCheckPolyRing1(p, r);
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);
1361  omFreeBinAddr(p);
1362  return new_p;
1363 }
1364 
1365 /***************************************************************
1366  *
1367  * Operation on ExpVectors
1368  *
1369  ***************************************************************/
1370 // ExpVector(p1) += ExpVector(p2)
1371 static 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);
1382  p_MemAdd_NegWeightAdjust(p1, r);
1383 }
1384 // ExpVector(pr) = ExpVector(p1) + ExpVector(p2)
1385 static 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);
1397  p_MemAdd_NegWeightAdjust(pr, r);
1398 }
1399 // ExpVector(p1) -= ExpVector(p2)
1400 static 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);
1412  p_MemSub_NegWeightAdjust(p1, r);
1413 }
1414 
1415 // ExpVector(p1) += ExpVector(p2) - ExpVector(p3)
1416 static 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)
1434 static 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);
1446  p_MemSub_NegWeightAdjust(pr, r);
1447 }
1448 
1449 static 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 
1467 static inline long p_Totaldegree(poly p, const ring r)
1468 {
1469  p_LmCheckPolyRing1(p, r);
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 
1480 static inline void p_GetExpV(poly p, int *ev, const ring r)
1481 {
1482  p_LmCheckPolyRing1(p, r);
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
1489 static inline void p_GetExpVL(poly p, int64 *ev, const ring r)
1490 {
1491  p_LmCheckPolyRing1(p, r);
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
1496 static inline int64 p_GetExpVLV(poly p, int64 *ev, const ring r)
1497 {
1498  p_LmCheckPolyRing1(p, r);
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
1504 static inline void p_SetExpV(poly p, int *ev, const ring r)
1505 {
1506  p_LmCheckPolyRing1(p, r);
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 }
1513 static inline void p_SetExpVL(poly p, int64 *ev, const ring r)
1514 {
1515  p_LmCheckPolyRing1(p, r);
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
1524 static inline void p_SetExpVLV(poly p, int64 *ev, int64 comp, const ring r)
1525 {
1526  p_LmCheckPolyRing1(p, r);
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 
1540 static inline int p_LmCmp(poly p, poly q, const ring r)
1541 {
1542  p_LmCheckPolyRing1(p, r);
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
1581 static 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
1607 static 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
1629 static 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
1645 static 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
1662 static 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
1671 static 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
1679 BOOLEAN 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)))
1695 static 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 
1707 static 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
1733 static 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 
1782 static 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
1803 static 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 }
1822 static 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 }
1828 static inline BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r,const int start, const int end)
1829 {
1830  p_LmCheckPolyRing1(b, r);
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
1837 static 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 }
1843 static 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 }
1849 static inline BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, const ring r)
1850 {
1851  p_LmCheckPolyRing1(a, r);
1852  p_LmCheckPolyRing1(b, r);
1853  return _p_LmDivisibleByNoComp(a, b, r);
1854 }
1855 
1856 static 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 
1863 static inline BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
1864 {
1865  p_LmCheckPolyRing1(b, r);
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 
1872 static 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 }
1881 static inline BOOLEAN p_DivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1882 {
1883  pIfThen1(b!=NULL, p_LmCheckPolyRing1(b, r_b));
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 }
1890 static 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 
1897 static 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);
1901  p_LmCheckPolyRing1(b, 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 
1917 static 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);
1921  p_LmCheckPolyRing1(b, 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 
1937 static 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
1965 static 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 
1971 static 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)?!
1979 static 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 
1986 static 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 
1999 static 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 
2007 static 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 }
2026 void p_Split(poly p, poly * r); /*p => IN(p), r => REST(p) */
2027 BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r);
2028 BOOLEAN p_HasNotCFRing(poly p1, poly p2, const ring r);
2029 poly p_mInit(const char *s, BOOLEAN &ok, const ring r); /* monom s -> poly, interpreter */
2030 const char * p_Read(const char *s, poly &p,const ring r); /* monom -> poly */
2031 poly p_MDivide(poly a, poly b, const ring r);
2032 poly p_DivideM(poly a, poly b, const ring r);
2033 poly pp_DivideM(poly a, poly b, const ring r);
2034 poly 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
2037 void 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
2039 poly p_Lcm(const poly a, const poly b, const ring r);
2040 
2041 #ifdef HAVE_RATGRING
2042 poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r);
2043 poly p_GetCoeffRat(poly p, int ishift, ring r);
2044 void p_LmDeleteAndNextRat(poly *p, int ishift, ring r);
2045 void p_ContentRat(poly &ph, const ring r);
2046 #endif /* ifdef HAVE_RATGRING */
2047 
2048 
2049 poly p_Diff(poly a, int k, const ring r);
2050 poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r);
2051 int 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
2066 poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r);
2067 
2068 /* syszygy stuff */
2069 BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r);
2070 void p_VectorHasUnit(poly p, int * k, int * len, const ring r);
2071 poly 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
2075 void 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
2078 poly p_TakeOutComp(poly * p, int k, const ring r);
2079 
2080 void 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
2090 void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg = NULL);
2091 // restores pFDeg and pLDeg:
2092 void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg);
2093 
2094 /*-------------pComp for syzygies:-------------------*/
2095 void p_SetModDeg(intvec *w, ring r);
2096 
2097 /*------------ Jet ----------------------------------*/
2098 poly pp_Jet(poly p, int m, const ring R);
2099 poly p_Jet(poly p, int m,const ring R);
2100 poly pp_JetW(poly p, int m, int *w, const ring R);
2101 poly p_JetW(poly p, int m, int *w, const ring R);
2102 
2103 poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst);
2104 
2105 poly 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 /*----------------------------------------------------*/
2110 poly p_Series(int n,poly p,poly u, intvec *w, const ring R);
2111 
2112 /*----------------------------------------------------*/
2113 int p_Var(poly mi, const ring r);
2114 /// the minimal index of used variables - 1
2115 int p_LowVar (poly p, const ring r);
2116 
2117 /*----------------------------------------------------*/
2118 /// shifts components of the vector p by i
2119 void p_Shift (poly * p,int i, const ring r);
2120 /*----------------------------------------------------*/
2121 
2122 int p_Compare(const poly a, const poly b, const ring R);
2123 
2124 /// polynomial gcd for f=mon
2125 poly p_GcdMon(poly f, poly g, const ring r);
2126 
2127 /// divide polynomial by monomial
2128 poly p_Div_mm(poly p, const poly m, const ring r);
2129 
2130 
2131 /// max exponent of variable x_i in p
2132 int p_MaxExpPerVar(poly p, int i, const ring r);
2133 #endif // P_POLYS_H
2134 
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)
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
g
Definition: cfModGcd.cc:4092
CanonicalForm b
Definition: cfModGcd.cc:4105
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: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
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: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:4384
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:4966
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:4602
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:4706
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:5004
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:3984
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
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:4412
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
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:4732
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:4474
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:5017
int p_Var(poly mi, const ring r)
Definition: p_polys.cc:4682
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:4932
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
const char * p_Read(const char *s, poly &p, const ring r)
Definition: p_polys.cc:1365
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:4524
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:4053
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
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: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:4156
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:4647
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:4807
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:4429
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:4456
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:4538
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:1910
static BOOLEAN rField_is_Ring(const ring r)
Definition: ring.h:489
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