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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 short *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 #if 1
215 // currently only used by Singular/janet
216 void p_SimpleContent(poly p, int s, const ring r);
217 number p_InitContent(poly ph, const ring r);
218 #endif
219 
220 poly p_Cleardenom(poly p, const ring r);
221 void p_Cleardenom_n(poly p, const ring r,number &c);
222 //number p_GetAllDenom(poly ph, const ring r);// unused
223 
224 int p_Size( poly p, const ring r );
225 
226 // homogenizes p by multiplying certain powers of the varnum-th variable
227 poly p_Homogen (poly p, int varnum, const ring r);
228 
229 BOOLEAN p_IsHomogeneous (poly p, const ring r);
230 
231 // Setm
232 static inline void p_Setm(poly p, const ring r)
233 {
234  p_CheckRing2(r);
235  r->p_Setm(p, r);
236 }
237 
238 p_SetmProc p_GetSetmProc(const ring r);
239 
240 poly p_Subst(poly p, int n, poly e, const ring r);
241 
242 // TODO:
243 #define p_SetmComp p_Setm
244 
245 // component
246 static inline unsigned long p_SetComp(poly p, unsigned long c, ring r)
247 {
248  p_LmCheckPolyRing2(p, r);
249  if (r->pCompIndex>=0) __p_GetComp(p,r) = c;
250  return c;
251 }
252 // sets component of poly a to i
253 static inline void p_SetCompP(poly p, int i, ring r)
254 {
255  if (p != NULL)
256  {
257  p_Test(p, r);
259  {
260  do
261  {
262  p_SetComp(p, i, r);
263  p_SetmComp(p, r);
264  pIter(p);
265  }
266  while (p != NULL);
267  }
268  else
269  {
270  do
271  {
272  p_SetComp(p, i, r);
273  pIter(p);
274  }
275  while(p != NULL);
276  }
277  }
278 }
279 
280 static inline void p_SetCompP(poly p, int i, ring lmRing, ring tailRing)
281 {
282  if (p != NULL)
283  {
284  p_SetComp(p, i, lmRing);
285  p_SetmComp(p, lmRing);
286  p_SetCompP(pNext(p), i, tailRing);
287  }
288 }
289 
290 // returns maximal column number in the modul element a (or 0)
291 static inline long p_MaxComp(poly p, ring lmRing, ring tailRing)
292 {
293  long result,i;
294 
295  if(p==NULL) return 0;
296  result = p_GetComp(p, lmRing);
297  if (result != 0)
298  {
299  loop
300  {
301  pIter(p);
302  if(p==NULL) break;
303  i = p_GetComp(p, tailRing);
304  if (i>result) result = i;
305  }
306  }
307  return result;
308 }
309 
310 static inline long p_MaxComp(poly p,ring lmRing) {return p_MaxComp(p,lmRing,lmRing);}
311 
312 static inline long p_MinComp(poly p, ring lmRing, ring tailRing)
313 {
314  long result,i;
315 
316  if(p==NULL) return 0;
317  result = p_GetComp(p,lmRing);
318  if (result != 0)
319  {
320  loop
321  {
322  pIter(p);
323  if(p==NULL) break;
324  i = p_GetComp(p,tailRing);
325  if (i<result) result = i;
326  }
327  }
328  return result;
329 }
330 
331 static inline long p_MinComp(poly p,ring lmRing) {return p_MinComp(p,lmRing,lmRing);}
332 
333 
334 static inline poly pReverse(poly p)
335 {
336  if (p == NULL || pNext(p) == NULL) return p;
337 
338  poly q = pNext(p), // == pNext(p)
339  qn;
340  pNext(p) = NULL;
341  do
342  {
343  qn = pNext(q);
344  pNext(q) = p;
345  p = q;
346  q = qn;
347  }
348  while (qn != NULL);
349  return p;
350 }
351 void pEnlargeSet(poly**p, int length, int increment);
352 
353 
354 /***************************************************************
355  *
356  * I/O
357  *
358  ***************************************************************/
359 /// print p according to ShortOut in lmRing & tailRing
360 void p_String0(poly p, ring lmRing, ring tailRing);
361 char* p_String(poly p, ring lmRing, ring tailRing);
362 void p_Write(poly p, ring lmRing, ring tailRing);
363 void p_Write0(poly p, ring lmRing, ring tailRing);
364 void p_wrp(poly p, ring lmRing, ring tailRing);
365 
366 /// print p in a short way, if possible
367 void p_String0Short(const poly p, ring lmRing, ring tailRing);
368 
369 /// print p in a long way
370 void p_String0Long(const poly p, ring lmRing, ring tailRing);
371 
372 
373 /***************************************************************
374  *
375  * Degree stuff -- see p_polys.cc for explainations
376  *
377  ***************************************************************/
378 
379 static inline long p_FDeg(const poly p, const ring r) { return r->pFDeg(p,r); }
380 static inline long p_LDeg(const poly p, int *l, const ring r) { return r->pLDeg(p,l,r); }
381 
382 long p_WFirstTotalDegree(poly p, ring r);
383 long p_WTotaldegree(poly p, const ring r);
384 long p_WDegree(poly p,const ring r);
385 long pLDeg0(poly p,int *l, ring r);
386 long pLDeg0c(poly p,int *l, ring r);
387 long pLDegb(poly p,int *l, ring r);
388 long pLDeg1(poly p,int *l, ring r);
389 long pLDeg1c(poly p,int *l, ring r);
390 long pLDeg1_Deg(poly p,int *l, ring r);
391 long pLDeg1c_Deg(poly p,int *l, ring r);
392 long pLDeg1_Totaldegree(poly p,int *l, ring r);
393 long pLDeg1c_Totaldegree(poly p,int *l, ring r);
394 long pLDeg1_WFirstTotalDegree(poly p,int *l, ring r);
395 long pLDeg1c_WFirstTotalDegree(poly p,int *l, ring r);
396 
397 BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r);
398 
399 /// same as the usual p_EqualPolys for polys belonging to *equal* rings
400 BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r1, const ring r2);
401 
402 long p_Deg(poly a, const ring r);
403 
404 
405 /***************************************************************
406  *
407  * Primitives for accessing and setting fields of a poly
408  *
409  ***************************************************************/
410 
411 static inline number p_SetCoeff(poly p, number n, ring r)
412 {
413  p_LmCheckPolyRing2(p, r);
414  n_Delete(&(p->coef), r->cf);
415  (p)->coef=n;
416  return n;
417 }
418 
419 // order
420 static inline long p_GetOrder(poly p, ring r)
421 {
422  p_LmCheckPolyRing2(p, r);
423  if (r->typ==NULL) return ((p)->exp[r->pOrdIndex]);
424  int i=0;
425  loop
426  {
427  switch(r->typ[i].ord_typ)
428  {
429  case ro_am:
430  case ro_wp_neg:
431  return ((p->exp[r->pOrdIndex])-POLY_NEGWEIGHT_OFFSET);
432  case ro_syzcomp:
433  case ro_syz:
434  case ro_cp:
435  i++;
436  break;
437  //case ro_dp:
438  //case ro_wp:
439  default:
440  return ((p)->exp[r->pOrdIndex]);
441  }
442  }
443 }
444 
445 
446 static inline unsigned long p_AddComp(poly p, unsigned long v, ring r)
447 {
448  p_LmCheckPolyRing2(p, r);
450  return __p_GetComp(p,r) += v;
451 }
452 static inline unsigned long p_SubComp(poly p, unsigned long v, ring r)
453 {
454  p_LmCheckPolyRing2(p, r);
456  _pPolyAssume2(__p_GetComp(p,r) >= v,p,r);
457  return __p_GetComp(p,r) -= v;
458 }
459 
460 #ifndef HAVE_EXPSIZES
461 
462 /// get a single variable exponent
463 /// @Note:
464 /// the integer VarOffset encodes:
465 /// 1. the position of a variable in the exponent vector p->exp (lower 24 bits)
466 /// 2. number of bits to shift to the right in the upper 8 bits (which takes at most 6 bits for 64 bit)
467 /// Thus VarOffset always has 2 zero higher bits!
468 static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
469 {
470  pAssume2((VarOffset >> (24 + 6)) == 0);
471 #if 0
472  int pos=(VarOffset & 0xffffff);
473  int bitpos=(VarOffset >> 24);
474  unsigned long exp=(p->exp[pos] >> bitmask) & iBitmask;
475  return exp;
476 #else
477  return (long)
478  ((p->exp[(VarOffset & 0xffffff)] >> (VarOffset >> 24))
479  & iBitmask);
480 #endif
481 }
482 
483 
484 /// set a single variable exponent
485 /// @Note:
486 /// VarOffset encodes the position in p->exp @see p_GetExp
487 static inline unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
488 {
489  pAssume2(e>=0);
490  pAssume2(e<=iBitmask);
491  pAssume2((VarOffset >> (24 + 6)) == 0);
492 
493  // shift e to the left:
494  REGISTER int shift = VarOffset >> 24;
495  unsigned long ee = e << shift /*(VarOffset >> 24)*/;
496  // find the bits in the exponent vector
497  REGISTER int offset = (VarOffset & 0xffffff);
498  // clear the bits in the exponent vector:
499  p->exp[offset] &= ~( iBitmask << shift );
500  // insert e with |
501  p->exp[ offset ] |= ee;
502  return e;
503 }
504 
505 
506 #else // #ifdef HAVE_EXPSIZES // EXPERIMENTAL!!!
507 
508 static inline unsigned long BitMask(unsigned long bitmask, int twobits)
509 {
510  // bitmask = 00000111111111111
511  // 0 must give bitmask!
512  // 1, 2, 3 - anything like 00011..11
513  pAssume2((twobits >> 2) == 0);
514  static const unsigned long _bitmasks[4] = {-1, 0x7fff, 0x7f, 0x3};
515  return bitmask & _bitmasks[twobits];
516 }
517 
518 
519 /// @Note: we may add some more info (6 ) into VarOffset and thus encode
520 static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
521 {
522  int pos =(VarOffset & 0xffffff);
523  int hbyte= (VarOffset >> 24); // the highest byte
524  int bitpos = hbyte & 0x3f; // last 6 bits
525  long bitmask = BitMask(iBitmask, hbyte >> 6);
526 
527  long exp=(p->exp[pos] >> bitpos) & bitmask;
528  return exp;
529 
530 }
531 
532 static inline long p_SetExp(poly p, const long e, const unsigned long iBitmask, const int VarOffset)
533 {
534  pAssume2(e>=0);
535  pAssume2(e <= BitMask(iBitmask, VarOffset >> 30));
536 
537  // shift e to the left:
538  REGISTER int hbyte = VarOffset >> 24;
539  int bitmask = BitMask(iBitmask, hbyte >> 6);
540  REGISTER int shift = hbyte & 0x3f;
541  long ee = e << shift;
542  // find the bits in the exponent vector
543  REGISTER int offset = (VarOffset & 0xffffff);
544  // clear the bits in the exponent vector:
545  p->exp[offset] &= ~( bitmask << shift );
546  // insert e with |
547  p->exp[ offset ] |= ee;
548  return e;
549 }
550 
551 #endif // #ifndef HAVE_EXPSIZES
552 
553 
554 static inline long p_GetExp(const poly p, const ring r, const int VarOffset)
555 {
556  p_LmCheckPolyRing2(p, r);
557  pAssume2(VarOffset != -1);
558  return p_GetExp(p, r->bitmask, VarOffset);
559 }
560 
561 static inline long p_SetExp(poly p, const long e, const ring r, const int VarOffset)
562 {
563  p_LmCheckPolyRing2(p, r);
564  pAssume2(VarOffset != -1);
565  return p_SetExp(p, e, r->bitmask, VarOffset);
566 }
567 
568 
569 
570 /// get v^th exponent for a monomial
571 static inline long p_GetExp(const poly p, const int v, const ring r)
572 {
573  p_LmCheckPolyRing2(p, r);
574  pAssume2(v>0 && v <= r->N);
575  pAssume2(r->VarOffset[v] != -1);
576  return p_GetExp(p, r->bitmask, r->VarOffset[v]);
577 }
578 
579 
580 /// set v^th exponent for a monomial
581 static inline long p_SetExp(poly p, const int v, const long e, const ring r)
582 {
583  p_LmCheckPolyRing2(p, r);
584  pAssume2(v>0 && v <= r->N);
585  pAssume2(r->VarOffset[v] != -1);
586  return p_SetExp(p, e, r->bitmask, r->VarOffset[v]);
587 }
588 
589 // the following should be implemented more efficiently
590 static inline long p_IncrExp(poly p, int v, ring r)
591 {
592  p_LmCheckPolyRing2(p, r);
593  int e = p_GetExp(p,v,r);
594  e++;
595  return p_SetExp(p,v,e,r);
596 }
597 static inline long p_DecrExp(poly p, int v, ring r)
598 {
599  p_LmCheckPolyRing2(p, r);
600  int e = p_GetExp(p,v,r);
601  pAssume2(e > 0);
602  e--;
603  return p_SetExp(p,v,e,r);
604 }
605 static inline long p_AddExp(poly p, int v, long ee, ring r)
606 {
607  p_LmCheckPolyRing2(p, r);
608  int e = p_GetExp(p,v,r);
609  e += ee;
610  return p_SetExp(p,v,e,r);
611 }
612 static inline long p_SubExp(poly p, int v, long ee, ring r)
613 {
614  p_LmCheckPolyRing2(p, r);
615  long e = p_GetExp(p,v,r);
616  pAssume2(e >= ee);
617  e -= ee;
618  return p_SetExp(p,v,e,r);
619 }
620 static inline long p_MultExp(poly p, int v, long ee, ring r)
621 {
622  p_LmCheckPolyRing2(p, r);
623  long e = p_GetExp(p,v,r);
624  e *= ee;
625  return p_SetExp(p,v,e,r);
626 }
627 
628 static inline long p_GetExpSum(poly p1, poly p2, int i, ring r)
629 {
630  p_LmCheckPolyRing2(p1, r);
631  p_LmCheckPolyRing2(p2, r);
632  return p_GetExp(p1,i,r) + p_GetExp(p2,i,r);
633 }
634 static inline long p_GetExpDiff(poly p1, poly p2, int i, ring r)
635 {
636  return p_GetExp(p1,i,r) - p_GetExp(p2,i,r);
637 }
638 
639 static inline int p_Comp_k_n(poly a, poly b, int k, ring r)
640 {
641  if ((a==NULL) || (b==NULL) ) return FALSE;
642  p_LmCheckPolyRing2(a, r);
643  p_LmCheckPolyRing2(b, r);
644  pAssume2(k > 0 && k <= r->N);
645  int i=k;
646  for(;i<=r->N;i++)
647  {
648  if (p_GetExp(a,i,r) != p_GetExp(b,i,r)) return FALSE;
649  // if (a->exp[(r->VarOffset[i] & 0xffffff)] != b->exp[(r->VarOffset[i] & 0xffffff)]) return FALSE;
650  }
651  return TRUE;
652 }
653 
654 
655 /***************************************************************
656  *
657  * Allocation/Initalization/Deletion
658  *
659  ***************************************************************/
660 #if (OM_TRACK > 2) && defined(OM_TRACK_CUSTOM)
661 static inline poly p_New(const ring r, omBin bin)
662 #else
663 static inline poly p_New(const ring /*r*/, omBin bin)
664 #endif
665 {
666  p_CheckRing2(r);
667  pAssume2(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
668  poly p;
669  omTypeAllocBin(poly, p, bin);
670  p_SetRingOfLm(p, r);
671  return p;
672 }
673 
674 static inline poly p_New(ring r)
675 {
676  return p_New(r, r->PolyBin);
677 }
678 
679 #if PDEBUG > 2
680 static inline void p_LmFree(poly p, ring r)
681 #else
682 static inline void p_LmFree(poly p, ring)
683 #endif
684 {
685  p_LmCheckPolyRing2(p, r);
686  omFreeBinAddr(p);
687 }
688 #if PDEBUG > 2
689 static inline void p_LmFree(poly *p, ring r)
690 #else
691 static inline void p_LmFree(poly *p, ring)
692 #endif
693 {
694  p_LmCheckPolyRing2(*p, r);
695  poly h = *p;
696  *p = pNext(h);
697  omFreeBinAddr(h);
698 }
699 #if PDEBUG > 2
700 static inline poly p_LmFreeAndNext(poly p, ring r)
701 #else
702 static inline poly p_LmFreeAndNext(poly p, ring)
703 #endif
704 {
705  p_LmCheckPolyRing2(p, r);
706  poly pnext = pNext(p);
707  omFreeBinAddr(p);
708  return pnext;
709 }
710 static inline void p_LmDelete(poly p, const ring r)
711 {
712  p_LmCheckPolyRing2(p, r);
713  n_Delete(&pGetCoeff(p), r->cf);
714  omFreeBinAddr(p);
715 }
716 static inline void p_LmDelete(poly *p, const ring r)
717 {
718  p_LmCheckPolyRing2(*p, r);
719  poly h = *p;
720  *p = pNext(h);
721  n_Delete(&pGetCoeff(h), r->cf);
722  omFreeBinAddr(h);
723 }
724 static inline poly p_LmDeleteAndNext(poly p, const ring r)
725 {
726  p_LmCheckPolyRing2(p, r);
727  poly pnext = pNext(p);
728  n_Delete(&pGetCoeff(p), r->cf);
729  omFreeBinAddr(p);
730  return pnext;
731 }
732 
733 /***************************************************************
734  *
735  * Misc routines
736  *
737  ***************************************************************/
738 
739 /// return the maximal exponent of p in form of the maximal long var
740 unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max = 0);
741 
742 /// return monomial r such that GetExp(r,i) is maximum of all
743 /// monomials in p; coeff == 0, next == NULL, ord is not set
744 poly p_GetMaxExpP(poly p, ring r);
745 
746 static inline unsigned long p_GetMaxExp(const unsigned long l, const ring r)
747 {
748  unsigned long bitmask = r->bitmask;
749  unsigned long max = (l & bitmask);
750  unsigned long j = r->ExpPerLong - 1;
751 
752  if (j > 0)
753  {
754  unsigned long i = r->BitsPerExp;
755  long e;
756  loop
757  {
758  e = ((l >> i) & bitmask);
759  if ((unsigned long) e > max)
760  max = e;
761  j--;
762  if (j==0) break;
763  i += r->BitsPerExp;
764  }
765  }
766  return max;
767 }
768 
769 static inline unsigned long p_GetMaxExp(const poly p, const ring r)
770 {
771  return p_GetMaxExp(p_GetMaxExpL(p, r), r);
772 }
773 
774 static inline unsigned long
775 p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps)
776 {
777  const unsigned long bitmask = r->bitmask;
778  unsigned long sum = (l & bitmask);
779  unsigned long j = number_of_exps - 1;
780 
781  if (j > 0)
782  {
783  unsigned long i = r->BitsPerExp;
784  loop
785  {
786  sum += ((l >> i) & bitmask);
787  j--;
788  if (j==0) break;
789  i += r->BitsPerExp;
790  }
791  }
792  return sum;
793 }
794 
795 /***************************************************************
796  *
797  * Dispatcher to r->p_Procs, they do the tests/checks
798  *
799  ***************************************************************/
800 /// returns a copy of p (without any additional testing)
801 static inline poly p_Copy_noCheck(poly p, const ring r)
802 {
803  /*assume(p!=NULL);*/
804  assume(r != NULL);
805  assume(r->p_Procs != NULL);
806  assume(r->p_Procs->p_Copy != NULL);
807  return r->p_Procs->p_Copy(p, r);
808 }
809 
810 /// returns a copy of p
811 static inline poly p_Copy(poly p, const ring r)
812 {
813  if (p!=NULL)
814  {
815  p_Test(p,r);
816  const poly pp = p_Copy_noCheck(p, r);
817  p_Test(pp,r);
818  return pp;
819  }
820  else
821  return NULL;
822 }
823 
824 /// copy the i(leading) term of p
825 static inline poly p_Head(poly p, const ring r)
826 {
827  if (p == NULL) return NULL;
828  p_LmCheckPolyRing1(p, r);
829  poly np;
830  omTypeAllocBin(poly, np, r->PolyBin);
831  p_SetRingOfLm(np, r);
832  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
833  pNext(np) = NULL;
834  pSetCoeff0(np, n_Copy(pGetCoeff(p), r->cf));
835  return np;
836 }
837 
838 /// like p_Head, but with coefficient 1
839 poly p_CopyPowerProduct(poly p, const ring r);
840 
841 /// returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing
842 static inline poly p_Copy(poly p, const ring lmRing, const ring tailRing)
843 {
844  if (p != NULL)
845  {
846 #ifndef PDEBUG
847  if (tailRing == lmRing)
848  return p_Copy_noCheck(p, tailRing);
849 #endif
850  poly pres = p_Head(p, lmRing);
851  if (pNext(p)!=NULL)
852  pNext(pres) = p_Copy_noCheck(pNext(p), tailRing);
853  return pres;
854  }
855  else
856  return NULL;
857 }
858 
859 // deletes *p, and sets *p to NULL
860 static inline void p_Delete(poly *p, const ring r)
861 {
862  assume( p!= NULL );
863  assume( r!= NULL );
864  if ((*p)!=NULL) r->p_Procs->p_Delete(p, r);
865 }
866 
867 static inline void p_Delete(poly *p, const ring lmRing, const ring tailRing)
868 {
869  assume( p!= NULL );
870  if (*p != NULL)
871  {
872 #ifndef PDEBUG
873  if (tailRing == lmRing)
874  {
875  p_Delete(p, tailRing);
876  return;
877  }
878 #endif
879  if (pNext(*p) != NULL)
880  p_Delete(&pNext(*p), tailRing);
881  p_LmDelete(p, lmRing);
882  }
883 }
884 
885 // copys monomials of p, allocates new monomials from bin,
886 // deletes monomials of p
887 static inline poly p_ShallowCopyDelete(poly p, const ring r, omBin bin)
888 {
889  p_LmCheckPolyRing2(p, r);
890  pAssume2(omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
891  return r->p_Procs->p_ShallowCopyDelete(p, r, bin);
892 }
893 
894 // returns p+q, destroys p and q
895 static inline poly p_Add_q(poly p, poly q, const ring r)
896 {
897  assume( (p != q) || (p == NULL && q == NULL) );
898  if (q==NULL) return p;
899  if (p==NULL) return q;
900  int shorter;
901  return r->p_Procs->p_Add_q(p, q, shorter, r);
902 }
903 
904 /// like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q)
905 static inline poly p_Add_q(poly p, poly q, int &lp, int lq, const ring r)
906 {
907  assume( (p != q) || (p == NULL && q == NULL) );
908  if (q==NULL) return p;
909  if (p==NULL) { lp=lq; return q; }
910  int shorter;
911  poly res = r->p_Procs->p_Add_q(p, q, shorter, r);
912  lp += lq - shorter;
913  return res;
914 }
915 
916 // returns p*n, destroys p
917 static inline poly p_Mult_nn(poly p, number n, const ring r)
918 {
919  if (p==NULL) return NULL;
920  if (n_IsOne(n, r->cf))
921  return p;
922  else if (n_IsZero(n, r->cf))
923  {
924  p_Delete(&p, r); // NOTE: without p_Delete - memory leak!
925  return NULL;
926  }
927  else
928  return r->p_Procs->p_Mult_nn(p, n, r);
929 }
930 #define __p_Mult_nn(p,n,r) r->p_Procs->p_Mult_nn(p, n, r)
931 
932 static inline poly p_Mult_nn(poly p, number n, const ring lmRing,
933  const ring tailRing)
934 {
935  assume(p!=NULL);
936 #ifndef PDEBUG
937  if (lmRing == tailRing)
938  return p_Mult_nn(p, n, tailRing);
939 #endif
940  poly pnext = pNext(p);
941  pNext(p) = NULL;
942  p = lmRing->p_Procs->p_Mult_nn(p, n, lmRing);
943  if (pnext!=NULL)
944  {
945  pNext(p) = tailRing->p_Procs->p_Mult_nn(pnext, n, tailRing);
946  }
947  return p;
948 }
949 
950 // returns p*n, does not destroy p
951 static inline poly pp_Mult_nn(poly p, number n, const ring r)
952 {
953  if (p==NULL) return NULL;
954  if (n_IsOne(n, r->cf))
955  return p_Copy(p, r);
956  else if (n_IsZero(n, r->cf))
957  return NULL;
958  else
959  return r->p_Procs->pp_Mult_nn(p, n, r);
960 }
961 #define __pp_Mult_nn(p,n,r) r->p_Procs->pp_Mult_nn(p, n, r)
962 
963 // test if the monomial is a constant as a vector component
964 // i.e., test if all exponents are zero
965 static inline BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
966 {
967  //p_LmCheckPolyRing(p, r);
968  int i = r->VarL_Size - 1;
969 
970  do
971  {
972  if (p->exp[r->VarL_Offset[i]] != 0)
973  return FALSE;
974  i--;
975  }
976  while (i >= 0);
977  return TRUE;
978 }
979 
980 // test if monomial is a constant, i.e. if all exponents and the component
981 // is zero
982 static inline BOOLEAN p_LmIsConstant(const poly p, const ring r)
983 {
984  if (p_LmIsConstantComp(p, r))
985  return (p_GetComp(p, r) == 0);
986  return FALSE;
987 }
988 
989 // returns Copy(p)*m, does neither destroy p nor m
990 static inline poly pp_Mult_mm(poly p, poly m, const ring r)
991 {
992  if (p==NULL) return NULL;
993  if (p_LmIsConstant(m, r))
994  return __pp_Mult_nn(p, pGetCoeff(m), r);
995  else
996  return r->p_Procs->pp_Mult_mm(p, m, r);
997 }
998 
999 // returns p*m, destroys p, const: m
1000 static inline poly p_Mult_mm(poly p, poly m, const ring r)
1001 {
1002  if (p==NULL) return NULL;
1003  if (p_LmIsConstant(m, r))
1004  return __p_Mult_nn(p, pGetCoeff(m), r);
1005  else
1006  return r->p_Procs->p_Mult_mm(p, m, r);
1007 }
1008 
1009 static inline poly p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, int &lp, int lq,
1010  const poly spNoether, const ring r)
1011 {
1012  int shorter;
1013  const poly res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, spNoether, r);
1014  lp += lq - shorter;
1015 // assume( lp == pLength(res) );
1016  return res;
1017 }
1018 
1019 // return p - m*Copy(q), destroys p; const: p,m
1020 static inline poly p_Minus_mm_Mult_qq(poly p, const poly m, const poly q, const ring r)
1021 {
1022  int shorter;
1023 
1024  return r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
1025 }
1026 
1027 
1028 // returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
1029 static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r)
1030 {
1031  int shorter;
1032  return r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
1033 }
1034 
1035 // returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
1036 // if lp is length of p on input then lp is length of returned poly on output
1037 static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, int &lp, const poly m, const ring r)
1038 {
1039  int shorter;
1040  poly pp = r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r);
1041  lp -= shorter;
1042  return pp;
1043 }
1044 
1045 // returns -p, destroys p
1046 static inline poly p_Neg(poly p, const ring r)
1047 {
1048  return r->p_Procs->p_Neg(p, r);
1049 }
1050 
1051 extern poly _p_Mult_q(poly p, poly q, const int copy, const ring r);
1052 // returns p*q, destroys p and q
1053 static inline poly p_Mult_q(poly p, poly q, const ring r)
1054 {
1055  assume( (p != q) || (p == NULL && q == NULL) );
1056 
1057  if (p == NULL)
1058  {
1059  p_Delete(&q, r);
1060  return NULL;
1061  }
1062  if (q == NULL)
1063  {
1064  p_Delete(&p, r);
1065  return NULL;
1066  }
1067 
1068  if (pNext(p) == NULL)
1069  {
1070  q = r->p_Procs->p_mm_Mult(q, p, r);
1071  p_LmDelete(&p, r);
1072  return q;
1073  }
1074 
1075  if (pNext(q) == NULL)
1076  {
1077  p = r->p_Procs->p_Mult_mm(p, q, r);
1078  p_LmDelete(&q, r);
1079  return p;
1080  }
1081 #ifdef HAVE_PLURAL
1082  if (rIsNCRing(r))
1083  return _nc_p_Mult_q(p, q, r);
1084  else
1085 #endif
1086  return _p_Mult_q(p, q, 0, r);
1087 }
1088 
1089 // returns p*q, does neither destroy p nor q
1090 static inline poly pp_Mult_qq(poly p, poly q, const ring r)
1091 {
1092  if (p == NULL || q == NULL) return NULL;
1093 
1094  if (pNext(p) == NULL)
1095  {
1096  return r->p_Procs->pp_mm_Mult(q, p, r);
1097  }
1098 
1099  if (pNext(q) == NULL)
1100  {
1101  return r->p_Procs->pp_Mult_mm(p, q, r);
1102  }
1103 
1104  poly qq = q;
1105  if (p == q)
1106  qq = p_Copy(q, r);
1107 
1108  poly res;
1109 #ifdef HAVE_PLURAL
1110  if (rIsPluralRing(r))
1111  res = _nc_pp_Mult_qq(p, qq, r);
1112  else
1113 #endif
1114  res = _p_Mult_q(p, qq, 1, r);
1115 
1116  if (qq != q)
1117  p_Delete(&qq, r);
1118  return res;
1119 }
1120 
1121 // returns p + m*q destroys p, const: q, m
1122 static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq,
1123  const ring r)
1124 {
1125 #ifdef HAVE_PLURAL
1126  if (rIsPluralRing(r))
1127  return nc_p_Plus_mm_Mult_qq(p, m, q, lp, lq, r);
1128 #endif
1129 
1130 // this should be implemented more efficiently
1131  poly res;
1132  int shorter;
1133  number n_old = pGetCoeff(m);
1134  number n_neg = n_Copy(n_old, r->cf);
1135  n_neg = n_InpNeg(n_neg, r->cf);
1136  pSetCoeff0(m, n_neg);
1137  res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r);
1138  lp = (lp + lq) - shorter;
1139  pSetCoeff0(m, n_old);
1140  n_Delete(&n_neg, r->cf);
1141  return res;
1142 }
1143 
1144 static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, const ring r)
1145 {
1146  int lp = 0, lq = 0;
1147  return p_Plus_mm_Mult_qq(p, m, q, lp, lq, r);
1148 }
1149 
1150 // returns merged p and q, assumes p and q have no monomials which are equal
1151 static inline poly p_Merge_q(poly p, poly q, const ring r)
1152 {
1153  assume( (p != q) || (p == NULL && q == NULL) );
1154  return r->p_Procs->p_Merge_q(p, q, r);
1155 }
1156 
1157 // like p_SortMerge, except that p may have equal monimals
1158 static inline poly p_SortAdd(poly p, const ring r, BOOLEAN revert= FALSE)
1159 {
1160  if (revert) p = pReverse(p);
1161  return sBucketSortAdd(p, r);
1162 }
1163 
1164 // sorts p using bucket sort: returns sorted poly
1165 // assumes that monomials of p are all different
1166 // reverses it first, if revert == TRUE, use this if input p is "almost" sorted
1167 // correctly
1168 static inline poly p_SortMerge(poly p, const ring r, BOOLEAN revert= FALSE)
1169 {
1170  if (revert) p = pReverse(p);
1171  return sBucketSortMerge(p, r);
1172 }
1173 
1174 /***************************************************************
1175  *
1176  * I/O
1177  *
1178  ***************************************************************/
1179 static inline char* p_String(poly p, ring p_ring)
1180 {
1181  return p_String(p, p_ring, p_ring);
1182 }
1183 static inline void p_String0(poly p, ring p_ring)
1184 {
1185  p_String0(p, p_ring, p_ring);
1186 }
1187 static inline void p_Write(poly p, ring p_ring)
1188 {
1189  p_Write(p, p_ring, p_ring);
1190 }
1191 static inline void p_Write0(poly p, ring p_ring)
1192 {
1193  p_Write0(p, p_ring, p_ring);
1194 }
1195 static inline void p_wrp(poly p, ring p_ring)
1196 {
1197  p_wrp(p, p_ring, p_ring);
1198 }
1199 
1200 
1201 #if PDEBUG > 0
1202 
1203 #define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
1204 do \
1205 { \
1206  int _cmp = p_LmCmp(p,q,r); \
1207  if (_cmp == 0) actionE; \
1208  if (_cmp == 1) actionG; \
1209  actionS; \
1210 } \
1211 while(0)
1212 
1213 #else
1214 
1215 #define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
1216  p_MemCmp_LengthGeneral_OrdGeneral(p->exp, q->exp, r->CmpL_Size, r->ordsgn, \
1217  actionE, actionG, actionS)
1218 
1219 #endif
1220 
1221 #define pDivAssume(x) do {} while (0)
1222 
1223 
1224 
1225 /***************************************************************
1226  *
1227  * Allocation/Initalization/Deletion
1228  *
1229  ***************************************************************/
1230 // adjustments for negative weights
1231 static inline void p_MemAdd_NegWeightAdjust(poly p, const ring r)
1232 {
1233  if (r->NegWeightL_Offset != NULL)
1234  {
1235  for (int i=r->NegWeightL_Size-1; i>=0; i--)
1236  {
1237  p->exp[r->NegWeightL_Offset[i]] -= POLY_NEGWEIGHT_OFFSET;
1238  }
1239  }
1240 }
1241 static inline void p_MemSub_NegWeightAdjust(poly p, const ring r)
1242 {
1243  if (r->NegWeightL_Offset != NULL)
1244  {
1245  for (int i=r->NegWeightL_Size-1; i>=0; i--)
1246  {
1247  p->exp[r->NegWeightL_Offset[i]] += POLY_NEGWEIGHT_OFFSET;
1248  }
1249  }
1250 }
1251 // ExpVextor(d_p) = ExpVector(s_p)
1252 static inline void p_ExpVectorCopy(poly d_p, poly s_p, const ring r)
1253 {
1254  p_LmCheckPolyRing1(d_p, r);
1255  p_LmCheckPolyRing1(s_p, r);
1256  memcpy(d_p->exp, s_p->exp, r->ExpL_Size*sizeof(long));
1257 }
1258 
1259 static inline poly p_Init(const ring r, omBin bin)
1260 {
1261  p_CheckRing1(r);
1262  pAssume1(bin != NULL && omSizeWOfBin(r->PolyBin) == omSizeWOfBin(bin));
1263  poly p;
1264  omTypeAlloc0Bin(poly, p, bin);
1266  p_SetRingOfLm(p, r);
1267  return p;
1268 }
1269 static inline poly p_Init(const ring r)
1270 {
1271  return p_Init(r, r->PolyBin);
1272 }
1273 
1274 static inline poly p_LmInit(poly p, const ring r)
1275 {
1276  p_LmCheckPolyRing1(p, r);
1277  poly np;
1278  omTypeAllocBin(poly, np, r->PolyBin);
1279  p_SetRingOfLm(np, r);
1280  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
1281  pNext(np) = NULL;
1282  pSetCoeff0(np, NULL);
1283  return np;
1284 }
1285 static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r, omBin d_bin)
1286 {
1287  p_LmCheckPolyRing1(s_p, s_r);
1288  p_CheckRing(d_r);
1289  pAssume1(d_r->N <= s_r->N);
1290  poly d_p = p_Init(d_r, d_bin);
1291  for (unsigned i=d_r->N; i!=0; i--)
1292  {
1293  p_SetExp(d_p, i, p_GetExp(s_p, i,s_r), d_r);
1294  }
1295  if (rRing_has_Comp(d_r))
1296  {
1297  p_SetComp(d_p, p_GetComp(s_p,s_r), d_r);
1298  }
1299  p_Setm(d_p, d_r);
1300  return d_p;
1301 }
1302 static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r)
1303 {
1304  pAssume1(d_r != NULL);
1305  return p_LmInit(s_p, s_r, d_r, d_r->PolyBin);
1306 }
1307 
1308 // set all exponents l..k to 0, assume exp. k+1..n and 1..l-1 are in
1309 // different blocks
1310 // set coeff to 1
1311 static inline poly p_GetExp_k_n(poly p, int l, int k, const ring r)
1312 {
1313  if (p == NULL) return NULL;
1314  p_LmCheckPolyRing1(p, r);
1315  poly np;
1316  omTypeAllocBin(poly, np, r->PolyBin);
1317  p_SetRingOfLm(np, r);
1318  memcpy(np->exp, p->exp, r->ExpL_Size*sizeof(long));
1319  pNext(np) = NULL;
1320  pSetCoeff0(np, n_Init(1, r->cf));
1321  int i;
1322  for(i=l;i<=k;i++)
1323  {
1324  //np->exp[(r->VarOffset[i] & 0xffffff)] =0;
1325  p_SetExp(np,i,0,r);
1326  }
1327  p_Setm(np,r);
1328  return np;
1329 }
1330 
1331 // simialar to p_ShallowCopyDelete but does it only for leading monomial
1332 static inline poly p_LmShallowCopyDelete(poly p, const ring r)
1333 {
1334  p_LmCheckPolyRing1(p, r);
1335  pAssume1(omSizeWOfBin(bin) == omSizeWOfBin(r->PolyBin));
1336  poly new_p = p_New(r);
1337  memcpy(new_p->exp, p->exp, r->ExpL_Size*sizeof(long));
1338  pSetCoeff0(new_p, pGetCoeff(p));
1339  pNext(new_p) = pNext(p);
1340  omFreeBinAddr(p);
1341  return new_p;
1342 }
1343 
1344 /***************************************************************
1345  *
1346  * Operation on ExpVectors
1347  *
1348  ***************************************************************/
1349 // ExpVector(p1) += ExpVector(p2)
1350 static inline void p_ExpVectorAdd(poly p1, poly p2, const ring r)
1351 {
1352  p_LmCheckPolyRing1(p1, r);
1353  p_LmCheckPolyRing1(p2, r);
1354 #if PDEBUG >= 1
1355  for (int i=1; i<=r->N; i++)
1356  pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask);
1357  pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0);
1358 #endif
1359 
1360  p_MemAdd_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size);
1361  p_MemAdd_NegWeightAdjust(p1, r);
1362 }
1363 // ExpVector(pr) = ExpVector(p1) + ExpVector(p2)
1364 static inline void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r)
1365 {
1366  p_LmCheckPolyRing1(p1, r);
1367  p_LmCheckPolyRing1(p2, r);
1368  p_LmCheckPolyRing1(pr, r);
1369 #if PDEBUG >= 1
1370  for (int i=1; i<=r->N; i++)
1371  pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask);
1372  pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0);
1373 #endif
1374 
1375  p_MemSum_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size);
1376  p_MemAdd_NegWeightAdjust(pr, r);
1377 }
1378 // ExpVector(p1) -= ExpVector(p2)
1379 static inline void p_ExpVectorSub(poly p1, poly p2, const ring r)
1380 {
1381  p_LmCheckPolyRing1(p1, r);
1382  p_LmCheckPolyRing1(p2, r);
1383 #if PDEBUG >= 1
1384  for (int i=1; i<=r->N; i++)
1385  pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r));
1386  pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0 ||
1387  p_GetComp(p1, r) == p_GetComp(p2, r));
1388 #endif
1389 
1390  p_MemSub_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size);
1391  p_MemSub_NegWeightAdjust(p1, r);
1392 }
1393 
1394 // ExpVector(p1) += ExpVector(p2) - ExpVector(p3)
1395 static inline void p_ExpVectorAddSub(poly p1, poly p2, poly p3, const ring r)
1396 {
1397  p_LmCheckPolyRing1(p1, r);
1398  p_LmCheckPolyRing1(p2, r);
1399  p_LmCheckPolyRing1(p3, r);
1400 #if PDEBUG >= 1
1401  for (int i=1; i<=r->N; i++)
1402  pAssume1(p_GetExp(p1, i, r) + p_GetExp(p2, i, r) >= p_GetExp(p3, i, r));
1403  pAssume1(p_GetComp(p1, r) == 0 ||
1404  (p_GetComp(p2, r) - p_GetComp(p3, r) == 0) ||
1405  (p_GetComp(p1, r) == p_GetComp(p2, r) - p_GetComp(p3, r)));
1406 #endif
1407 
1408  p_MemAddSub_LengthGeneral(p1->exp, p2->exp, p3->exp, r->ExpL_Size);
1409  // no need to adjust in case of NegWeights
1410 }
1411 
1412 // ExpVector(pr) = ExpVector(p1) - ExpVector(p2)
1413 static inline void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
1414 {
1415  p_LmCheckPolyRing1(p1, r);
1416  p_LmCheckPolyRing1(p2, r);
1417  p_LmCheckPolyRing1(pr, r);
1418 #if PDEBUG >= 2
1419  for (int i=1; i<=r->N; i++)
1420  pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r));
1421  pAssume1(!rRing_has_Comp(r) || p_GetComp(p1, r) == p_GetComp(p2, r));
1422 #endif
1423 
1424  p_MemDiff_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size);
1425  p_MemSub_NegWeightAdjust(pr, r);
1426 }
1427 
1428 static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r)
1429 {
1430  p_LmCheckPolyRing1(p1, r);
1431  p_LmCheckPolyRing1(p2, r);
1432 
1433  unsigned i = r->ExpL_Size;
1434  unsigned long *ep = p1->exp;
1435  unsigned long *eq = p2->exp;
1436 
1437  do
1438  {
1439  i--;
1440  if (ep[i] != eq[i]) return FALSE;
1441  }
1442  while (i!=0);
1443  return TRUE;
1444 }
1445 
1446 static inline long p_Totaldegree(poly p, const ring r)
1447 {
1448  p_LmCheckPolyRing1(p, r);
1449  unsigned long s = p_GetTotalDegree(p->exp[r->VarL_Offset[0]],
1450  r,
1451  r->ExpPerLong);
1452  for (unsigned i=r->VarL_Size-1; i!=0; i--)
1453  {
1454  s += p_GetTotalDegree(p->exp[r->VarL_Offset[i]], r,r->ExpPerLong);
1455  }
1456  return (long)s;
1457 }
1458 
1459 static inline void p_GetExpV(poly p, int *ev, const ring r)
1460 {
1461  p_LmCheckPolyRing1(p, r);
1462  for (unsigned j = r->N; j!=0; j--)
1463  ev[j] = p_GetExp(p, j, r);
1464 
1465  ev[0] = p_GetComp(p, r);
1466 }
1467 // p_GetExpVL is used in Singular,jl
1468 static inline void p_GetExpVL(poly p, int64 *ev, const ring r)
1469 {
1470  p_LmCheckPolyRing1(p, r);
1471  for (unsigned j = r->N; j!=0; j--)
1472  ev[j-1] = p_GetExp(p, j, r);
1473 }
1474 static inline void p_SetExpV(poly p, int *ev, const ring r)
1475 {
1476  p_LmCheckPolyRing1(p, r);
1477  for (unsigned j = r->N; j!=0; j--)
1478  p_SetExp(p, j, ev[j], r);
1479 
1480  if(ev[0]!=0) p_SetComp(p, ev[0],r);
1481  p_Setm(p, r);
1482 }
1483 // p_SetExpVL is used in Singular,jl
1484 static inline void p_SetExpVL(poly p, int64 *ev, const ring r)
1485 {
1486  p_LmCheckPolyRing1(p, r);
1487  for (unsigned j = r->N; j!=0; j--)
1488  p_SetExp(p, j, ev[j], r);
1489 
1490  if(ev[0]!=0) p_SetComp(p, ev[0],r);
1491  p_Setm(p, r);
1492 }
1493 
1494 /***************************************************************
1495  *
1496  * Comparison w.r.t. monomial ordering
1497  *
1498  ***************************************************************/
1499 
1500 static inline int p_LmCmp(poly p, poly q, const ring r)
1501 {
1502  p_LmCheckPolyRing1(p, r);
1503  p_LmCheckPolyRing1(q, r);
1504 
1505  const unsigned long* _s1 = ((unsigned long*) p->exp);
1506  const unsigned long* _s2 = ((unsigned long*) q->exp);
1507  REGISTER unsigned long _v1;
1508  REGISTER unsigned long _v2;
1509  const unsigned long _l = r->CmpL_Size;
1510 
1511  REGISTER unsigned long _i=0;
1512 
1513  LengthGeneral_OrdGeneral_LoopTop:
1514  _v1 = _s1[_i];
1515  _v2 = _s2[_i];
1516  if (_v1 == _v2)
1517  {
1518  _i++;
1519  if (_i == _l) return 0;
1520  goto LengthGeneral_OrdGeneral_LoopTop;
1521  }
1522  const long* _ordsgn = (long*) r->ordsgn;
1523 #if 1 /* two variants*/
1524  if (_v1 > _v2)
1525  {
1526  return _ordsgn[_i];
1527  }
1528  return -(_ordsgn[_i]);
1529 #else
1530  if (_v1 > _v2)
1531  {
1532  if (_ordsgn[_i] == 1) return 1;
1533  return -1;
1534  }
1535  if (_ordsgn[_i] == 1) return -1;
1536  return 1;
1537 #endif
1538 }
1539 
1540 // The coefficient will be compared in absolute value
1541 static inline int p_LtCmp(poly p, poly q, const ring r)
1542 {
1543  int res = p_LmCmp(p,q,r);
1544  if(res == 0)
1545  {
1546  if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
1547  return res;
1548  number pc = n_Copy(p_GetCoeff(p,r),r->cf);
1549  number qc = n_Copy(p_GetCoeff(q,r),r->cf);
1550  if(!n_GreaterZero(pc,r->cf))
1551  pc = n_InpNeg(pc,r->cf);
1552  if(!n_GreaterZero(qc,r->cf))
1553  qc = n_InpNeg(qc,r->cf);
1554  if(n_Greater(pc,qc,r->cf))
1555  res = 1;
1556  else if(n_Greater(qc,pc,r->cf))
1557  res = -1;
1558  else if(n_Equal(pc,qc,r->cf))
1559  res = 0;
1560  n_Delete(&pc,r->cf);
1561  n_Delete(&qc,r->cf);
1562  }
1563  return res;
1564 }
1565 
1566 // The coefficient will be compared in absolute value
1567 static inline int p_LtCmpNoAbs(poly p, poly q, const ring r)
1568 {
1569  int res = p_LmCmp(p,q,r);
1570  if(res == 0)
1571  {
1572  if(p_GetCoeff(p,r) == NULL || p_GetCoeff(q,r) == NULL)
1573  return res;
1574  number pc = p_GetCoeff(p,r);
1575  number qc = p_GetCoeff(q,r);
1576  if(n_Greater(pc,qc,r->cf))
1577  res = 1;
1578  if(n_Greater(qc,pc,r->cf))
1579  res = -1;
1580  if(n_Equal(pc,qc,r->cf))
1581  res = 0;
1582  }
1583  return res;
1584 }
1585 
1586 #ifdef HAVE_RINGS
1587 // This is the equivalent of pLmCmp(p,q) != -currRing->OrdSgn for rings
1588 // It is used in posInLRing and posInTRing
1589 static inline int p_LtCmpOrdSgnDiffM(poly p, poly q, const ring r)
1590 {
1591  if(r->OrdSgn == 1)
1592  {
1593  return(p_LtCmp(p,q,r) == 1);
1594  }
1595  else
1596  {
1597  return(p_LmCmp(p,q,r) == -1);
1598  }
1599 }
1600 #endif
1601 
1602 #ifdef HAVE_RINGS
1603 // This is the equivalent of pLmCmp(p,q) != currRing->OrdSgn for rings
1604 // It is used in posInLRing and posInTRing
1605 static inline int p_LtCmpOrdSgnDiffP(poly p, poly q, const ring r)
1606 {
1607  if(r->OrdSgn == 1)
1608  {
1609  return(p_LmCmp(p,q,r) == -1);
1610  }
1611  else
1612  {
1613  return(p_LtCmp(p,q,r) != -1);
1614  }
1615 
1616 }
1617 #endif
1618 
1619 #ifdef HAVE_RINGS
1620 // This is the equivalent of pLmCmp(p,q) == -currRing->OrdSgn for rings
1621 // It is used in posInLRing and posInTRing
1622 static inline int p_LtCmpOrdSgnEqM(poly p, poly q, const ring r)
1623 {
1624  return(p_LtCmp(p,q,r) == -r->OrdSgn);
1625 }
1626 #endif
1627 
1628 #ifdef HAVE_RINGS
1629 // This is the equivalent of pLmCmp(p,q) == currRing->OrdSgn for rings
1630 // It is used in posInLRing and posInTRing
1631 static inline int p_LtCmpOrdSgnEqP(poly p, poly q, const ring r)
1632 {
1633  return(p_LtCmp(p,q,r) == r->OrdSgn);
1634 }
1635 #endif
1636 
1637 /// returns TRUE if p1 is a skalar multiple of p2
1638 /// assume p1 != NULL and p2 != NULL
1639 BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r);
1640 
1641 
1642 /***************************************************************
1643  *
1644  * Comparisons: they are all done without regarding coeffs
1645  *
1646  ***************************************************************/
1647 #define p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
1648  _p_LmCmpAction(p, q, r, actionE, actionG, actionS)
1649 
1650 // returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !!
1651 #define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r)
1652 
1653 // pCmp: args may be NULL
1654 // returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))
1655 static inline int p_Cmp(poly p1, poly p2, ring r)
1656 {
1657  if (p2==NULL)
1658  {
1659  if (p1==NULL) return 0;
1660  return 1;
1661  }
1662  if (p1==NULL)
1663  return -1;
1664  return p_LmCmp(p1,p2,r);
1665 }
1666 
1667 static inline int p_CmpPolys(poly p1, poly p2, ring r)
1668 {
1669  if (p2==NULL)
1670  {
1671  if (p1==NULL) return 0;
1672  return 1;
1673  }
1674  if (p1==NULL)
1675  return -1;
1676  return p_ComparePolys(p1,p2,r);
1677 }
1678 
1679 
1680 /***************************************************************
1681  *
1682  * divisibility
1683  *
1684  ***************************************************************/
1685 /// return: FALSE, if there exists i, such that a->exp[i] > b->exp[i]
1686 /// TRUE, otherwise
1687 /// (1) Consider long vars, instead of single exponents
1688 /// (2) Clearly, if la > lb, then FALSE
1689 /// (3) Suppose la <= lb, and consider first bits of single exponents in l:
1690 /// if TRUE, then value of these bits is la ^ lb
1691 /// if FALSE, then la-lb causes an "overflow" into one of those bits, i.e.,
1692 /// la ^ lb != la - lb
1693 static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, poly b, const ring r)
1694 {
1695  int i=r->VarL_Size - 1;
1696  unsigned long divmask = r->divmask;
1697  unsigned long la, lb;
1698 
1699  if (r->VarL_LowIndex >= 0)
1700  {
1701  i += r->VarL_LowIndex;
1702  do
1703  {
1704  la = a->exp[i];
1705  lb = b->exp[i];
1706  if ((la > lb) ||
1707  (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
1708  {
1710  return FALSE;
1711  }
1712  i--;
1713  }
1714  while (i>=r->VarL_LowIndex);
1715  }
1716  else
1717  {
1718  do
1719  {
1720  la = a->exp[r->VarL_Offset[i]];
1721  lb = b->exp[r->VarL_Offset[i]];
1722  if ((la > lb) ||
1723  (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask)))
1724  {
1726  return FALSE;
1727  }
1728  i--;
1729  }
1730  while (i>=0);
1731  }
1732 /*#ifdef HAVE_RINGS
1733  pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf));
1734  return (!rField_is_Ring(r)) || n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf);
1735 #else
1736 */
1738  return TRUE;
1739 //#endif
1740 }
1741 
1742 static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, const ring r_a, poly b, const ring r_b)
1743 {
1744  int i=r_a->N;
1745  pAssume1(r_a->N == r_b->N);
1746 
1747  do
1748  {
1749  if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b))
1750  return FALSE;
1751  i--;
1752  }
1753  while (i);
1754 /*#ifdef HAVE_RINGS
1755  return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
1756 #else
1757 */
1758  return TRUE;
1759 //#endif
1760 }
1761 
1762 #ifdef HAVE_RATGRING
1763 static inline BOOLEAN _p_LmDivisibleByNoCompPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end)
1764 {
1765  int i=end;
1766  pAssume1(r_a->N == r_b->N);
1767 
1768  do
1769  {
1770  if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b))
1771  return FALSE;
1772  i--;
1773  }
1774  while (i>=start);
1775 /*#ifdef HAVE_RINGS
1776  return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf);
1777 #else
1778 */
1779  return TRUE;
1780 //#endif
1781 }
1782 static inline BOOLEAN _p_LmDivisibleByPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end)
1783 {
1784  if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b))
1785  return _p_LmDivisibleByNoCompPart(a, r_a, b, r_b,start,end);
1786  return FALSE;
1787 }
1788 static inline BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r,const int start, const int end)
1789 {
1790  p_LmCheckPolyRing1(b, r);
1791  pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r));
1792  if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
1793  return _p_LmDivisibleByNoCompPart(a, r, b, r,start, end);
1794  return FALSE;
1795 }
1796 #endif
1797 static inline BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r)
1798 {
1799  if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
1800  return _p_LmDivisibleByNoComp(a, b, r);
1801  return FALSE;
1802 }
1803 static inline BOOLEAN _p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1804 {
1805  if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b))
1806  return _p_LmDivisibleByNoComp(a, r_a, b, r_b);
1807  return FALSE;
1808 }
1809 static inline BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, const ring r)
1810 {
1811  p_LmCheckPolyRing1(a, r);
1812  p_LmCheckPolyRing1(b, r);
1813  return _p_LmDivisibleByNoComp(a, b, r);
1814 }
1815 
1816 static inline BOOLEAN p_LmDivisibleByNoComp(poly a, const ring ra, poly b, const ring rb)
1817 {
1818  p_LmCheckPolyRing1(a, ra);
1819  p_LmCheckPolyRing1(b, rb);
1820  return _p_LmDivisibleByNoComp(a, ra, b, rb);
1821 }
1822 
1823 static inline BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
1824 {
1825  p_LmCheckPolyRing1(b, r);
1826  pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r));
1827  if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))
1828  return _p_LmDivisibleByNoComp(a, b, r);
1829  return FALSE;
1830 }
1831 
1832 static inline BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
1833 {
1835  pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r));
1836 
1837  if (a != NULL && (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)))
1838  return _p_LmDivisibleByNoComp(a,b,r);
1839  return FALSE;
1840 }
1841 static inline BOOLEAN p_DivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1842 {
1843  pIfThen1(b!=NULL, p_LmCheckPolyRing1(b, r_b));
1844  pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r_a));
1845  if (a != NULL) {
1846  return _p_LmDivisibleBy(a, r_a, b, r_b);
1847  }
1848  return FALSE;
1849 }
1850 static inline BOOLEAN p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b)
1851 {
1852  p_LmCheckPolyRing(a, r_a);
1853  p_LmCheckPolyRing(b, r_b);
1854  return _p_LmDivisibleBy(a, r_a, b, r_b);
1855 }
1856 
1857 static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a,
1858  poly b, unsigned long not_sev_b, const ring r)
1859 {
1860  p_LmCheckPolyRing1(a, r);
1861  p_LmCheckPolyRing1(b, r);
1862 #ifndef PDIV_DEBUG
1863  _pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r);
1864  _pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r);
1865 
1866  if (sev_a & not_sev_b)
1867  {
1869  return FALSE;
1870  }
1871  return p_LmDivisibleBy(a, b, r);
1872 #else
1873  return pDebugLmShortDivisibleBy(a, sev_a, r, b, not_sev_b, r);
1874 #endif
1875 }
1876 
1877 static inline BOOLEAN p_LmShortDivisibleByNoComp(poly a, unsigned long sev_a,
1878  poly b, unsigned long not_sev_b, const ring r)
1879 {
1880  p_LmCheckPolyRing1(a, r);
1881  p_LmCheckPolyRing1(b, r);
1882 #ifndef PDIV_DEBUG
1883  _pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r);
1884  _pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r);
1885 
1886  if (sev_a & not_sev_b)
1887  {
1889  return FALSE;
1890  }
1891  return p_LmDivisibleByNoComp(a, b, r);
1892 #else
1893  return pDebugLmShortDivisibleByNoComp(a, sev_a, r, b, not_sev_b, r);
1894 #endif
1895 }
1896 
1897 static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, const ring r_a,
1898  poly b, unsigned long not_sev_b, const ring r_b)
1899 {
1900  p_LmCheckPolyRing1(a, r_a);
1901  p_LmCheckPolyRing1(b, r_b);
1902 #ifndef PDIV_DEBUG
1903  _pPolyAssume2(p_GetShortExpVector(a, r_a) == sev_a, a, r_a);
1904  _pPolyAssume2(p_GetShortExpVector(b, r_b) == ~ not_sev_b, b, r_b);
1905 
1906  if (sev_a & not_sev_b)
1907  {
1908  pAssume1(_p_LmDivisibleByNoComp(a, r_a, b, r_b) == FALSE);
1909  return FALSE;
1910  }
1911  return _p_LmDivisibleBy(a, r_a, b, r_b);
1912 #else
1913  return pDebugLmShortDivisibleBy(a, sev_a, r_a, b, not_sev_b, r_b);
1914 #endif
1915 }
1916 
1917 /***************************************************************
1918  *
1919  * Misc things on Lm
1920  *
1921  ***************************************************************/
1922 
1923 
1924 /// like the respective p_LmIs* routines, except that p might be empty
1925 static inline BOOLEAN p_IsConstantComp(const poly p, const ring r)
1926 {
1927  if (p == NULL) return TRUE;
1928  return (pNext(p)==NULL) && p_LmIsConstantComp(p, r);
1929 }
1930 
1931 static inline BOOLEAN p_IsConstant(const poly p, const ring r)
1932 {
1933  if (p == NULL) return TRUE;
1934  p_Test(p, r);
1935  return (pNext(p)==NULL) && p_LmIsConstant(p, r);
1936 }
1937 
1938 /// either poly(1) or gen(k)?!
1939 static inline BOOLEAN p_IsOne(const poly p, const ring R)
1940 {
1941  p_Test(p, R);
1942  return (p_IsConstant(p, R) && n_IsOne(p_GetCoeff(p, R), R->cf));
1943 }
1944 
1945 static inline BOOLEAN p_IsConstantPoly(const poly p, const ring r)
1946 {
1947  p_Test(p, r);
1948  poly pp=p;
1949  while(pp!=NULL)
1950  {
1951  if (! p_LmIsConstantComp(pp, r))
1952  return FALSE;
1953  pIter(pp);
1954  }
1955  return TRUE;
1956 }
1957 
1958 static inline BOOLEAN p_IsUnit(const poly p, const ring r)
1959 {
1960  if (p == NULL) return FALSE;
1961  if (rField_is_Ring(r))
1962  return (p_LmIsConstant(p, r) && n_IsUnit(pGetCoeff(p),r->cf));
1963  return p_LmIsConstant(p, r);
1964 }
1965 
1966 static inline BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2,
1967  const ring r)
1968 {
1969  p_LmCheckPolyRing(p1, r);
1970  p_LmCheckPolyRing(p2, r);
1971  unsigned long l1, l2, divmask = r->divmask;
1972  int i;
1973 
1974  for (i=0; i<r->VarL_Size; i++)
1975  {
1976  l1 = p1->exp[r->VarL_Offset[i]];
1977  l2 = p2->exp[r->VarL_Offset[i]];
1978  // do the divisiblity trick
1979  if ( (l1 > ULONG_MAX - l2) ||
1980  (((l1 & divmask) ^ (l2 & divmask)) != ((l1 + l2) & divmask)))
1981  return FALSE;
1982  }
1983  return TRUE;
1984 }
1985 void p_Split(poly p, poly * r); /*p => IN(p), r => REST(p) */
1986 BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r);
1987 BOOLEAN p_HasNotCFRing(poly p1, poly p2, const ring r);
1988 poly p_mInit(const char *s, BOOLEAN &ok, const ring r); /* monom s -> poly, interpreter */
1989 const char * p_Read(const char *s, poly &p,const ring r); /* monom -> poly */
1990 poly p_MDivide(poly a, poly b, const ring r);
1991 poly p_DivideM(poly a, poly b, const ring r);
1992 poly p_Div_nn(poly p, const number n, const ring r);
1993 
1994 // returns the LCM of the head terms of a and b in *m, does not p_Setm
1995 void p_Lcm(const poly a, const poly b, poly m, const ring r);
1996 // returns the LCM of the head terms of a and b, does p_Setm
1997 poly p_Lcm(const poly a, const poly b, const ring r);
1998 
1999 #ifdef HAVE_RATGRING
2000 poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r);
2001 poly p_GetCoeffRat(poly p, int ishift, ring r);
2002 void p_LmDeleteAndNextRat(poly *p, int ishift, ring r);
2003 void p_ContentRat(poly &ph, const ring r);
2004 #endif /* ifdef HAVE_RATGRING */
2005 
2006 
2007 poly p_Diff(poly a, int k, const ring r);
2008 poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r);
2009 int p_Weight(int c, const ring r);
2010 
2011 /// assumes that p and divisor are univariate polynomials in r,
2012 /// mentioning the same variable;
2013 /// assumes divisor != NULL;
2014 /// p may be NULL;
2015 /// assumes a global monomial ordering in r;
2016 /// performs polynomial division of p by divisor:
2017 /// - afterwards p contains the remainder of the division, i.e.,
2018 /// p_before = result * divisor + p_afterwards;
2019 /// - if needResult == TRUE, then the method computes and returns 'result',
2020 /// otherwise NULL is returned (This parametrization can be used when
2021 /// one is only interested in the remainder of the division. In this
2022 /// case, the method will be slightly faster.)
2023 /// leaves divisor unmodified
2024 poly p_PolyDiv(poly &p, const poly divisor, const BOOLEAN needResult, const ring r);
2025 
2026 /* syszygy stuff */
2027 BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r);
2028 void p_VectorHasUnit(poly p, int * k, int * len, const ring r);
2029 poly p_TakeOutComp1(poly * p, int k, const ring r);
2030 // Splits *p into two polys: *q which consists of all monoms with
2031 // component == comp and *p of all other monoms *lq == pLength(*q)
2032 // On return all components pf *q == 0
2033 void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r);
2034 
2035 // This is something weird -- Don't use it, unless you know what you are doing
2036 poly p_TakeOutComp(poly * p, int k, const ring r);
2037 
2038 void p_DeleteComp(poly * p,int k, const ring r);
2039 
2040 /*-------------ring management:----------------------*/
2041 
2042 // resets the pFDeg and pLDeg: if pLDeg is not given, it is
2043 // set to currRing->pLDegOrig, i.e. to the respective LDegProc which
2044 // only uses pFDeg (and not pDeg, or pTotalDegree, etc).
2045 // If you use this, make sure your procs does not make any assumptions
2046 // on ordering and/or OrdIndex -- otherwise they might return wrong results
2047 // on strat->tailRing
2048 void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg = NULL);
2049 // restores pFDeg and pLDeg:
2050 void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg);
2051 
2052 /*-------------pComp for syzygies:-------------------*/
2053 void p_SetModDeg(intvec *w, ring r);
2054 
2055 /*------------ Jet ----------------------------------*/
2056 poly pp_Jet(poly p, int m, const ring R);
2057 poly p_Jet(poly p, int m,const ring R);
2058 poly pp_JetW(poly p, int m, short *w, const ring R);
2059 poly p_JetW(poly p, int m, short *w, const ring R);
2060 
2061 poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst);
2062 
2063 poly p_PermPoly (poly p, const int * perm,const ring OldRing, const ring dst,
2064  nMapFunc nMap, const int *par_perm=NULL, int OldPar=0,
2065  BOOLEAN use_mult=FALSE);
2066 
2067 /*----------------------------------------------------*/
2068 poly p_Series(int n,poly p,poly u, intvec *w, const ring R);
2069 
2070 /*----------------------------------------------------*/
2071 int p_Var(poly mi, const ring r);
2072 /// the minimal index of used variables - 1
2073 int p_LowVar (poly p, const ring r);
2074 
2075 /*----------------------------------------------------*/
2076 /// shifts components of the vector p by i
2077 void p_Shift (poly * p,int i, const ring r);
2078 /*----------------------------------------------------*/
2079 
2080 int p_Compare(const poly a, const poly b, const ring R);
2081 
2082 /// polynomial gcd for f=mon
2083 poly p_GcdMon(poly f, poly g, const ring r);
2084 
2085 /// divide polynomial by monomial
2086 poly p_Div_mm(poly p, const poly m, const ring r);
2087 #endif // P_POLYS_H
2088 
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:248
int level(const CanonicalForm &f)
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:49
int l
Definition: cfEzgcd.cc:93
int m
Definition: cfEzgcd.cc:121
int i
Definition: cfEzgcd.cc:125
int k
Definition: cfEzgcd.cc:92
Variable x
Definition: cfModGcd.cc:4023
int p
Definition: cfModGcd.cc:4019
g
Definition: cfModGcd.cc:4031
CanonicalForm b
Definition: cfModGcd.cc:4044
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:76
const CanonicalForm int s
Definition: facAbsFact.cc:55
CanonicalForm res
Definition: facAbsFact.cc:64
const CanonicalForm & w
Definition: facAbsFact.cc:55
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:37
CFArray copy(const CFList &list)
write elements of list into an array
int j
Definition: facHensel.cc:105
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:263
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:390
#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:1046
poly p_Diff(poly a, int k, const ring r)
Definition: p_polys.cc:1873
long pLDeg1c_WFirstTotalDegree(poly p, int *l, ring r)
Definition: p_polys.cc:1058
static int p_CmpPolys(poly p1, poly p2, ring r)
Definition: p_polys.h:1667
long pLDeg0(poly p, int *l, ring r)
Definition: p_polys.cc:729
poly p_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1560
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
Definition: p_polys.cc:1216
static long p_GetExpDiff(poly p1, poly p2, int i, ring r)
Definition: p_polys.h:634
static void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r)
Definition: p_polys.h:1364
poly pp_Jet(poly p, int m, const ring R)
Definition: p_polys.cc:4264
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:895
static void p_LmDelete(poly p, const ring r)
Definition: p_polys.h:710
static poly p_Mult_q(poly p, poly q, const ring r)
Definition: p_polys.h:1053
void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg=NULL)
Definition: p_polys.cc:3597
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:1231
poly p_Farey(poly p, number N, const ring r)
Definition: p_polys.cc:50
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:1350
static unsigned long p_SubComp(poly p, unsigned long v, ring r)
Definition: p_polys.h:452
long pLDeg1_Deg(poly p, int *l, ring r)
Definition: p_polys.cc:900
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:3609
long pLDeg1_WFirstTotalDegree(poly p, int *l, ring r)
Definition: p_polys.cc:1028
static long p_SubExp(poly p, int v, long ee, ring r)
Definition: p_polys.h:612
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:1782
static poly p_Head(poly p, const ring r)
copy the i(leading) term of p
Definition: p_polys.h:825
poly p_Sub(poly a, poly b, const ring r)
Definition: p_polys.cc:1965
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:1845
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:1925
int p_Size(poly p, const ring r)
Definition: p_polys.cc:3200
static long p_AddExp(poly p, int v, long ee, ring r)
Definition: p_polys.h:605
static poly p_LmInit(poly p, const ring r)
Definition: p_polys.h:1274
poly p_GcdMon(poly f, poly g, const ring r)
polynomial gcd for f=mon
Definition: p_polys.cc:4846
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:4482
static long p_FDeg(const poly p, const ring r)
Definition: p_polys.h:379
static unsigned long p_GetMaxExp(const unsigned long l, const ring r)
Definition: p_polys.h:746
int p_LowVar(poly p, const ring r)
the minimal index of used variables - 1
Definition: p_polys.cc:4586
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:1617
poly p_CopyPowerProduct(poly p, const ring r)
like p_Head, but with coefficient 1
Definition: p_polys.cc:4884
poly p_Homogen(poly p, int varnum, const ring r)
Definition: p_polys.cc:3217
static void p_ExpVectorCopy(poly d_p, poly s_p, const ring r)
Definition: p_polys.h:1252
poly p_Subst(poly p, int n, poly e, const ring r)
Definition: p_polys.cc:3874
long pLDeg1c_Deg(poly p, int *l, ring r)
Definition: p_polys.cc:931
static int p_Cmp(poly p1, poly p2, ring r)
Definition: p_polys.h:1655
BOOLEAN _p_LmTest(poly p, ring r, int level)
Definition: pDebug.cc:321
#define __pp_Mult_nn(p, n, r)
Definition: p_polys.h:961
static void p_SetExpVL(poly p, int64 *ev, const ring r)
Definition: p_polys.h:1484
BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r)
Definition: p_polys.cc:1319
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:831
static void p_SetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1474
void p_ShallowDelete(poly *p, const ring r)
static poly pp_Mult_mm(poly p, poly m, const ring r)
Definition: p_polys.h:990
static int p_LtCmpNoAbs(poly p, poly q, const ring r)
Definition: p_polys.h:1567
static void p_MemSub_NegWeightAdjust(poly p, const ring r)
Definition: p_polys.h:1241
long p_WFirstTotalDegree(poly p, ring r)
Definition: p_polys.cc:586
int p_Weight(int c, const ring r)
Definition: p_polys.cc:695
static int p_Comp_k_n(poly a, poly b, int k, ring r)
Definition: p_polys.h:639
poly p_ISet(long i, const ring r)
returns the poly representing the integer i
Definition: p_polys.cc:1287
static int p_LtCmpOrdSgnEqP(poly p, poly q, const ring r)
Definition: p_polys.h:1631
void p_ContentForGB(poly p, const ring r)
Definition: p_polys.cc:2315
void p_Vec2Polys(poly v, poly **p, int *len, const ring r)
Definition: p_polys.cc:3582
poly p_DiffOp(poly a, poly b, BOOLEAN multiply, const ring r)
Definition: p_polys.cc:1948
static void p_SetCompP(poly p, int i, ring r)
Definition: p_polys.h:253
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:487
poly p_Jet(poly p, int m, const ring R)
Definition: p_polys.cc:4292
poly p_TakeOutComp1(poly *p, int k, const ring r)
Definition: p_polys.cc:3343
static void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
Definition: p_polys.h:1413
static long p_MinComp(poly p, ring lmRing, ring tailRing)
Definition: p_polys.h:312
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
poly pp_JetW(poly p, int m, short *w, const ring R)
Definition: p_polys.cc:4309
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
Definition: p_polys.cc:4612
static long p_GetExpSum(poly p1, poly p2, int i, ring r)
Definition: p_polys.h:628
poly p_Power(poly p, int i, const ring r)
Definition: p_polys.cc:2172
poly p_Div_nn(poly p, const number n, const ring r)
Definition: p_polys.cc:1487
void p_Normalize(poly p, const ring r)
Definition: p_polys.cc:3732
void p_DeleteComp(poly *p, int k, const ring r)
Definition: p_polys.cc:3503
poly p_MDivide(poly a, poly b, const ring r)
Definition: p_polys.cc:1474
void p_Content(poly p, const ring r)
Definition: p_polys.cc:2270
void p_ProjectiveUnique(poly p, const ring r)
Definition: p_polys.cc:3089
void p_ContentRat(poly &ph, const ring r)
Definition: p_polys.cc:1719
void p_Norm(poly p1, const ring r)
Definition: p_polys.cc:3679
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
Definition: p_polys.h:246
poly p_Div_mm(poly p, const poly m, const ring r)
divide polynomial by monomial
Definition: p_polys.cc:1520
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:1128
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:1257
static long p_IncrExp(poly p, int v, ring r)
Definition: p_polys.h:590
int p_MinDeg(poly p, intvec *w, const ring R)
Definition: p_polys.cc:4354
static void p_ExpVectorSub(poly p1, poly p2, const ring r)
Definition: p_polys.h:1379
static unsigned long p_AddComp(poly p, unsigned long v, ring r)
Definition: p_polys.h:446
int p_Var(poly mi, const ring r)
Definition: p_polys.cc:4562
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:273
int p_Compare(const poly a, const poly b, const ring R)
Definition: p_polys.cc:4812
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:232
#define p_SetmComp
Definition: p_polys.h:243
poly p_mInit(const char *s, BOOLEAN &ok, const ring r)
Definition: p_polys.cc:1432
void p_LmDeleteAndNextRat(poly *p, int ishift, ring r)
Definition: p_polys.cc:1675
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
Definition: p_polys.h:801
static number p_SetCoeff(poly p, number n, ring r)
Definition: p_polys.h:411
static poly p_SortMerge(poly p, const ring r, BOOLEAN revert=FALSE)
Definition: p_polys.h:1168
static poly p_LmShallowCopyDelete(poly p, const ring r)
Definition: p_polys.h:1332
static poly pReverse(poly p)
Definition: p_polys.h:334
static poly p_Merge_q(poly p, poly q, const ring r)
Definition: p_polys.h:1151
const char * p_Read(const char *s, poly &p, const ring r)
Definition: p_polys.cc:1360
long pLDegb(poly p, int *l, ring r)
Definition: p_polys.cc:801
static void p_GetExpVL(poly p, int64 *ev, const ring r)
Definition: p_polys.h:1468
static int p_LtCmp(poly p, poly q, const ring r)
Definition: p_polys.h:1541
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
Definition: p_polys.h:965
static int p_LmCmp(poly p, poly q, const ring r)
Definition: p_polys.h:1500
poly p_Series(int n, poly p, poly u, intvec *w, const ring R)
Definition: p_polys.cc:4404
long p_WTotaldegree(poly p, const ring r)
Definition: p_polys.cc:603
static BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
Definition: p_polys.h:1857
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:468
static BOOLEAN p_LmIsConstant(const poly p, const ring r)
Definition: p_polys.h:982
p_SetmProc p_GetSetmProc(const ring r)
Definition: p_polys.cc:550
static long p_MultExp(poly p, int v, long ee, ring r)
Definition: p_polys.h:620
static BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, const ring r)
Definition: p_polys.h:1809
static BOOLEAN p_IsOne(const poly p, const ring R)
either poly(1) or gen(k)?!
Definition: p_polys.h:1939
static BOOLEAN p_IsConstant(const poly p, const ring r)
Definition: p_polys.h:1931
BOOLEAN p_OneComp(poly p, const ring r)
return TRUE if all monoms have the same component
Definition: p_polys.cc:1198
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:1763
BOOLEAN p_CheckRing(ring r)
Definition: pDebug.cc:126
poly p_Cleardenom(poly p, const ring r)
Definition: p_polys.cc:2791
static BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1797
static unsigned long p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps)
Definition: p_polys.h:775
long p_DegW(poly p, const short *w, const ring R)
Definition: p_polys.cc:680
BOOLEAN p_LmCheckIsFromRing(poly p, ring r)
Definition: pDebug.cc:69
static poly p_New(const ring, omBin bin)
Definition: p_polys.h:663
void p_Split(poly p, poly *r)
Definition: p_polys.cc:1310
poly n_PermNumber(const number z, const int *par_perm, const int OldPar, const ring src, const ring dst)
Definition: p_polys.cc:3933
static poly p_GetExp_k_n(poly p, int l, int k, const ring r)
Definition: p_polys.h:1311
poly p_JetW(poly p, int m, short *w, const ring R)
Definition: p_polys.cc:4336
static BOOLEAN p_LmShortDivisibleByNoComp(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
Definition: p_polys.h:1877
static poly pp_Mult_nn(poly p, number n, const ring r)
Definition: p_polys.h:951
poly p_GetCoeffRat(poly p, int ishift, ring r)
Definition: p_polys.cc:1697
BOOLEAN p_VectorHasUnitB(poly p, int *k, const ring r)
Definition: p_polys.cc:3288
poly p_Vec2Poly(poly v, int k, const ring r)
Definition: p_polys.cc:3531
static BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1823
poly p_LcmRat(const poly a, const poly b, const long lCompM, const ring r)
Definition: p_polys.cc:1652
static BOOLEAN p_DivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1832
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:1428
long pLDeg1_Totaldegree(poly p, int *l, ring r)
Definition: p_polys.cc:965
void p_SetModDeg(intvec *w, ring r)
Definition: p_polys.cc:3633
static poly p_ShallowCopyDelete(poly p, const ring r, omBin bin)
Definition: p_polys.h:887
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition: p_polys.cc:3455
static long p_MaxComp(poly p, ring lmRing, ring tailRing)
Definition: p_polys.h:291
static poly p_Mult_nn(poly p, number n, const ring r)
Definition: p_polys.h:917
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:860
BOOLEAN p_HasNotCFRing(poly p1, poly p2, const ring r)
Definition: p_polys.cc:1335
poly p_One(const ring r)
Definition: p_polys.cc:1303
static long p_DecrExp(poly p, int v, ring r)
Definition: p_polys.h:597
static int p_LtCmpOrdSgnDiffM(poly p, poly q, const ring r)
Definition: p_polys.h:1589
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:1693
void p_VectorHasUnit(poly p, int *k, int *len, const ring r)
Definition: p_polys.cc:3311
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:1459
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:995
static long p_GetOrder(poly p, ring r)
Definition: p_polys.h:420
int p_IsUnivariate(poly p, const ring r)
return i, if poly depends only on var(i)
Definition: p_polys.cc:1237
poly p_NSet(number n, const ring r)
returns the poly representing the number n, destroys n
Definition: p_polys.cc:1455
static poly pp_Mult_qq(poly p, poly q, const ring r)
Definition: p_polys.h:1090
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:4036
static int p_LtCmpOrdSgnEqM(poly p, poly q, const ring r)
Definition: p_polys.h:1622
static poly p_LmFreeAndNext(poly p, ring)
Definition: p_polys.h:702
#define pDivAssume(x)
Definition: p_polys.h:1221
static poly p_Mult_mm(poly p, poly m, const ring r)
Definition: p_polys.h:1000
void p_Cleardenom_n(poly p, const ring r, number &c)
Definition: p_polys.cc:2900
long p_WDegree(poly p, const ring r)
Definition: p_polys.cc:704
long pLDeg1c(poly p, int *l, ring r)
Definition: p_polys.cc:867
poly p_Last(const poly a, int &l, const ring r)
Definition: p_polys.cc:4527
static void p_LmFree(poly p, ring)
Definition: p_polys.h:682
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:1009
static poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, const ring r)
Definition: p_polys.h:1122
void pEnlargeSet(poly **p, int length, int increment)
Definition: p_polys.cc:3656
static BOOLEAN p_IsUnit(const poly p, const ring r)
Definition: p_polys.h:1958
static poly p_Init(const ring r, omBin bin)
Definition: p_polys.h:1259
BOOLEAN p_IsHomogeneous(poly p, const ring r)
Definition: p_polys.cc:3266
static poly p_LmDeleteAndNext(poly p, const ring r)
Definition: p_polys.h:724
BOOLEAN pHaveCommonMonoms(poly p, poly q)
Definition: pDebug.cc:173
unsigned long p_GetShortExpVector(const poly a, const ring r)
Definition: p_polys.cc:4687
static poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r)
Definition: p_polys.h:1029
static BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r, const int start, const int end)
Definition: p_polys.h:1788
long p_Deg(poly a, const ring r)
Definition: p_polys.cc:577
static poly p_SortAdd(poly p, const ring r, BOOLEAN revert=FALSE)
Definition: p_polys.h:1158
void p_SimpleContent(poly p, int s, const ring r)
Definition: p_polys.cc:2524
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:811
static long p_LDeg(const poly p, int *l, const ring r)
Definition: p_polys.h:380
number p_InitContent(poly ph, const ring r)
Definition: p_polys.cc:2581
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:3552
static long p_Totaldegree(poly p, const ring r)
Definition: p_polys.h:1446
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:1165
static BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2, const ring r)
Definition: p_polys.h:1966
static int p_LtCmpOrdSgnDiffP(poly p, poly q, const ring r)
Definition: p_polys.h:1605
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:1630
poly p_ChineseRemainder(poly *xx, number *x, number *q, int rl, CFArray &inv_cache, const ring R)
Definition: p_polys.cc:83
#define p_Test(p, r)
Definition: p_polys.h:162
#define __p_Mult_nn(p, n, r)
Definition: p_polys.h:930
static BOOLEAN p_IsConstantPoly(const poly p, const ring r)
Definition: p_polys.h:1945
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:4418
long pLDeg0c(poly p, int *l, ring r)
Definition: p_polys.cc:760
static void p_ExpVectorAddSub(poly p1, poly p2, poly p3, const ring r)
Definition: p_polys.h:1395
BOOLEAN rOrd_SetCompRequiresSetm(const ring r)
return TRUE if p_SetComp requires p_Setm
Definition: ring.cc:1906
static BOOLEAN rField_is_Ring(const ring r)
Definition: ring.h:479
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:397
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:418
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