source: git/kernel/polys.h @ cf5fc11

fieker-DuValspielwiese
Last change on this file since cf5fc11 was cf5fc11, checked in by Hans Schönemann <hannes@…>, 19 years ago
*hannes: pCleardenom_n git-svn-id: file:///usr/local/Singular/svn/trunk@7694 2c84dea3-7e68-4137-9b89-c4e89433aadc
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1#ifndef POLYS_H
2#define POLYS_H
3/****************************************
4*  Computer Algebra System SINGULAR     *
5****************************************/
6/* $Id: polys.h,v 1.3 2005-01-27 16:42:15 Singular Exp $ */
7/*
8* ABSTRACT - all basic methods to manipulate polynomials of the
9             currRing
10*/
11
12#include "p_polys.h"
13/*
14 Some general remarks:
15 We divide poly operations into roughly 4 categories:
16 Level 2: operations on monomials/polynomials with constant time,
17          or operations which are just dispatchers to other
18          poly routines
19          - implemented in: pInline2.h
20          - debugging only if PDEBUG >= 2
21          - normally inlined, unless PDEBUG >= 2 || NO_INLINE2
22 Level 1: operations on monomials with time proportional to length
23          - implemented in: pInline1.h
24          - debugging only if PDEBUG >= 1
25          - normally inlined, unless PDEBUG >= 1 || NO_INLINE1
26 Level 0: short operations on polynomials with time proportional to
27          length of poly
28          - implemented in pInline0.cc
29          - debugging if PDEBUG
30          - normally _not_ inlined: can be forced with
31            #define DO_PINLINE0
32            #include "pInline0.h"
33 Misc   : operations on polynomials which do not fit in any of the
34          above categories
35          - implemented in: polys*.cc
36          - never inlined
37          - debugging if PDEBUG >= 0
38
39 You can set PDEBUG on a per-file basis, before including "mod2.h" like
40   #define PDEBUG 2
41   #include "mod2.h"
42 However, PDEBUG will only be in effect, if !NDEBUG.
43
44 All p_* operations take as last argument a ring
45 and are ring independent. Their corresponding p* operations are usually
46 just macros to the respective p_*(..,currRing).
47
48*/
49
50/***************************************************************
51 *
52 * Primitives for accessing and setting fields of a poly
53 * poly must be != NULL
54 *
55 ***************************************************************/
56// deletes old coeff before setting the new one
57#define pSetCoeff(p,n)      p_SetCoeff(p,n,currRing)
58
59// Order
60#define pGetOrder(p)        p_GetOrder(p, currRing)
61// don't use this
62#define pSetOrder(p, o)     p_SetOrder(p, o, currRing)
63
64// Component
65#define pGetComp(p)         _p_GetComp(p, currRing)
66#define pSetComp(p,v)       p_SetComp(p,v, currRing)
67#define pIncrComp(p)        p_IncrComp(p,currRing)
68#define pDecrComp(p)        p_DecrComp(p,currRing)
69#define pAddComp(p,v)       p_AddComp(p,v,currRing)
70#define pSubComp(p,v)       p_SubComp(p,v,currRing)
71
72// Exponent
73#define pGetExp(p,i)        p_GetExp(p, i, currRing)
74#define pSetExp(p,i,v)      p_SetExp(p, i, v, currRing)
75#define pIncrExp(p,i)       p_IncrExp(p,i, currRing)
76#define pDecrExp(p,i)       p_DecrExp(p,i, currRing)
77#define pAddExp(p,i,v)      p_AddExp(p,i,v, currRing)
78#define pSubExp(p,i,v)      p_SubExp(p,i,v, currRing)
79#define pMultExp(p,i,v)     p_MultExp(p,i,v, currRing)
80#define pGetExpSum(p1, p2, i)    p_GetExpSum(p1, p2, i, currRing)
81#define pGetExpDiff(p1, p2, i)   p_GetExpDiff(p1, p2, i, currRing)
82
83/***************************************************************
84 *
85 * Allocation/Initalization/Deletion
86 * except for pDeleteLm and pHead, all polys must be != NULL
87 *
88 ***************************************************************/
89// allocates the space for a new monomial -- no initialization !!!
90#define pNew()          p_New(currRing)
91// allocates a new monomial and initializes everything to 0
92#define pInit()         p_Init(currRing)
93// like pInit, except that expvector is initialized to that of p,
94// p must be != NULL
95#define pLmInit(p)  p_LmInit(p, currRing)
96// returns newly allocated copy of Lm(p), coef is copied, next=NULL,
97// p might be NULL
98#define pHead(p)        p_Head(p, currRing)
99// if *p_ptr != NULL, delete p_ptr->coef, *p_ptr, and set *p_ptr to
100// pNext(*p_ptr)
101static inline void pDeleteLm(poly *p) {p_DeleteLm(p, currRing);}
102// if (p!=NULL) delete p-coef and p
103static inline void pDeleteLm(poly p)  {p_DeleteLm(p, currRing);}
104// frees the space of the monomial m, assumes m != NULL
105// coef is not freed, m is not advanced
106static inline void pLmFree(poly p)    {p_LmFree(p, currRing);}
107// like pLmFree, but advances p
108static inline void pLmFree(poly *p)   {p_LmFree(p, currRing);}
109// assumes p != NULL, deletes p, returns pNext(p)
110#define pLmFreeAndNext(p) p_LmFreeAndNext(p, currRing)
111// assume p != NULL, deletes Lm(p)->coef and Lm(p)
112#define pLmDelete(p)    p_LmDelete(p, currRing)
113// like pLmDelete, returns pNext(p)
114#define pLmDeleteAndNext(p) p_LmDeleteAndNext(p, currRing)
115// used by iparith.cc
116extern poly pHeadProc(poly p);
117
118/***************************************************************
119 *
120 * Operation on ExpVectors: assumes polys != NULL
121 *
122 ***************************************************************/
123
124#define pExpVectorCopy(d_p, s_p)    p_ExpVectorCopy(d_p, s_p, currRing)
125#define pExpVectorAdd(p1, p2)       p_ExpVectorAdd(p1, p2, currRing)
126#define pExpVectorSub(p1, p2)       p_ExpVectorSub(p1, p2, currRing)
127#define pExpVectorAddSub(p1, p2, p3)p_ExpVectorAddSub(p1, p2, p3, currRing)
128#define pExpVectorSum(pr, p1, p2)   p_ExpVectorSum(pr, p1, p2, currRing)
129#define pExpVectorDiff(pr, p1, p2)  p_ExpVectorDiff(pr, p1, p2, currRing)
130#define pExpVectorEqual(p1, p2)     p_ExpVectorEqual(p1, p2, currRing)
131#define pExpVectorQuerSum(p)        p_ExpVectorQuerSum(p, currRing)
132
133// Gets a copy of (resp. set) the exponent vector, where e is assumed
134// to point to (r->N +1)*sizeof(Exponent_t) memory. Exponents are
135// filled in as follows: comp, e_1, .., e_n
136#define pGetExpV(p, e)      p_GetExpV(p, e, currRing)
137#define pSetExpV(p, e)      p_SetExpV(p, e, currRing)
138
139/***************************************************************
140 *
141 * Comparisons: they are all done without regarding coeffs
142 *
143 ***************************************************************/
144// returns 0|1|-1 if p=q|p>q|p<q w.r.t monomial ordering
145#define pLmCmp(p,q)         p_LmCmp(p,q,currRing)
146// executes axtionE|actionG|actionS if p=q|p>q|p<q w.r.t monomial ordering
147// action should be a "goto ..."
148#define pLmCmpAction(p,q, actionE, actionG, actionS)  \
149  _p_LmCmpAction(p,q,currRing, actionE, actionG,actionS)
150
151#define pLmEqual(p1, p2)     pExpVectorEqual(p1, p2)
152
153// pCmp: args may be NULL
154// returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))
155#define pCmp(p1, p2)    p_Cmp(p1, p2, currRing)
156
157
158/***************************************************************
159 *
160 * Divisiblity tests, args must be != NULL, except for
161 * pDivisbleBy
162 *
163 ***************************************************************/
164// returns TRUE, if leading monom of a divides leading monom of b
165// i.e., if there exists a expvector c > 0, s.t. b = a + c;
166#define pDivisibleBy(a, b)  p_DivisibleBy(a,b,currRing)
167// like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL
168#define pLmDivisibleBy(a,b)  p_LmDivisibleBy(a,b,currRing)
169// like pLmDivisibleBy, does not check components
170#define pLmDivisibleByNoComp(a, b) p_LmDivisibleByNoComp(a,b,currRing)
171// Divisibility tests based on Short Exponent vectors
172// sev_a     == pGetShortExpVector(a)
173// not_sev_b == ~ pGetShortExpVector(b)
174#define pLmShortDivisibleBy(a, sev_a, b, not_sev_b) \
175  p_LmShortDivisibleBy(a, sev_a, b, not_sev_b, currRing)
176// returns the "Short Exponent Vector" -- used to speed up divisibility
177// tests (see polys-impl.cc )
178#define pGetShortExpVector(a)   p_GetShortExpVector(a, currRing)
179
180/***************************************************************
181 *
182 * Copying/Deleteion of polys: args may be NULL
183 *
184 ***************************************************************/
185// return a copy of the poly
186#define pCopy(p) p_Copy(p, currRing)
187#define pDelete(p_ptr)  p_Delete(p_ptr, currRing)
188
189/***************************************************************
190 *
191 * Copying/Deleteion of polys: args may be NULL
192 *  - p/q as arg mean a poly
193 *  - m a monomial
194 *  - n a number
195 *  - pp (resp. qq, mm, nn) means arg is constant
196 *  - p (resp, q, m, n)     means arg is destroyed
197 *
198 ***************************************************************/
199#define pNeg(p)                     p_Neg(p, currRing)
200#define ppMult_nn(p, n)             pp_Mult_nn(p, n, currRing)
201#define pMult_nn(p, n)              p_Mult_nn(p, n, currRing)
202#define ppMult_mm(p, m)             pp_Mult_mm(p, m, currRing)
203#define pMult_mm(p, m)              p_Mult_mm(p, m, currRing)
204#define pAdd(p, q)                  p_Add_q(p, q, currRing)
205#define pMinus_mm_Mult_qq(p, m, q)  p_Minus_mm_Mult_qq(p, m, q, currRing)
206#define pPlus_mm_Mult_qq(p, m, q)   p_Plus_mm_Mult_qq(p, m, q, currRing)
207#define pMult(p, q)                 p_Mult_q(p, q, currRing)
208#define ppMult_qq(p, q)             pp_Mult_qq(p, q, currRing)
209// p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
210#define ppMult_Coeff_mm_DivSelect(p, m)   pp_Mult_Coeff_mm_DivSelect(p, m, currRing)
211/*************************************************************************
212 *
213 * Sort routines
214 *
215 *************************************************************************/
216// sorts p, assumes all monomials in p are different
217#define pSortMerger(p)          pSort(p)
218#define pSort(p)                p_SortMerge(p, currRing)
219
220// sorts p, p may have equal monomials
221#define pSortAdd(p)             p_SortAdd(p, currRing)
222
223
224// Assume: If considerd only as poly in any component of p
225// (say, monomials of other components of p are set to 0),
226// then p is already sorted correctly
227#define pSortCompCorrect(p) pSort(p)
228
229/***************************************************************
230 *
231 * Predicates on polys/Lm's
232 *
233 ***************************************************************/
234// return true if all p is eihter NULL, or if all exponents
235// of p are 0 and Comp of p is zero
236#define   pIsConstantComp(p)        p_IsConstantComp(p, currRing)
237// like above, except that Comp might be != 0
238#define   pIsConstant(p)            p_IsConstant(p,currRing)
239// return true if the Lm is a constant <>0
240#define   pIsUnit(p)            p_IsUnit(p,currRing)
241// like above, except that p must be != NULL
242#define   pLmIsConstantComp(p)      p_LmIsConstantComp(p, currRing)
243#define   pLmIsConstant(p)          p_LmIsConstant(p,currRing)
244
245// return TRUE if all monomials of p are constant
246#define   pIsConstantPoly(p)        p_IsConstantPoly(p, currRing)
247
248#define   pIsPurePower(p)   p_IsPurePower(p, currRing)
249#define   pIsVector(p)      (pGetComp(p)>0)
250
251
252/***************************************************************
253 *
254 * Old stuff
255 *
256 ***************************************************************/
257
258#define pFetchCopy(r,p)     _pFetchCopy(r,p)
259// Similar to pFetchCopy, except that poly p is deleted
260#define pFetchCopyDelete(r, p) _pFetchCopyDelete(r, p)
261
262typedef poly*   polyset;
263extern int      pVariables;
264extern int      pOrdSgn;
265extern BOOLEAN  pLexOrder;
266extern poly     ppNoether;
267extern BOOLEAN  pVectorOut;
268
269/*-------------predicate on polys ----------------------*/
270BOOLEAN   pHasNotCF(poly p1, poly p2);   /*has no common factor ?*/
271void      pSplit(poly p, poly * r);   /*p => IN(p), r => REST(p) */
272
273
274
275/*-------------ring management:----------------------*/
276//extern void pChangeRing(ring newRing);
277extern void pSetGlobals(ring r, BOOLEAN complete = TRUE);
278// resets the pFDeg and pLDeg: if pLDeg is not given, it is
279// set to currRing->pLDegOrig, i.e. to the respective LDegProc which
280// only uses pFDeg (and not pDeg, or pTotalDegree, etc).
281// If you use this, make sure your procs does not make any assumptions
282// on oredering and/or OrdIndex -- otherwise they might return wrong results
283// on strat->tailRing
284extern void pSetDegProcs(pFDegProc new_FDeg, pLDegProc new_lDeg = NULL);
285// restores pFDeg and pLDeg:
286extern void pRestoreDegProcs(pFDegProc old_FDeg, pLDegProc old_lDeg);
287
288/*-----------the ordering of monomials:-------------*/
289#define pSetm(p)    p_Setm(p, currRing)
290// TODO:
291#define pSetmComp   pSetm
292
293/***************************************************************
294 *
295 * Degree stuff -- see p_polys.cc for explainations
296 *
297 ***************************************************************/
298extern pLDegProc pLDeg;
299extern pFDegProc pFDeg;
300int  pWeight(int c, ring r = currRing);
301long pDeg(poly p, ring r = currRing);
302long pTotaldegree(poly p, ring r = currRing);
303long pWTotaldegree(poly p, ring r = currRing);
304long pWDegree(poly p, ring r = currRing);
305long pLDeg0(poly p,int *l, ring r = currRing);
306long pLDeg0c(poly p,int *l, ring r = currRing);
307long pLDegb(poly p,int *l, ring r = currRing);
308long pLDeg1(poly p,int *l, ring r = currRing);
309long pLDeg1c(poly p,int *l, ring r = currRing);
310long pLDeg1_Deg(poly p,int *l, ring r = currRing);
311long pLDeg1c_Deg(poly p,int *l, ring r = currRing);
312long pLDeg1_Totaldegree(poly p,int *l, ring r = currRing);
313long pLDeg1c_Totaldegree(poly p,int *l, ring r = currRing);
314long pLDeg1_WFirstTotalDegree(poly p,int *l, ring r=currRing);
315long pLDeg1c_WFirstTotalDegree(poly p,int *l, ring r=currRing);
316
317/*-------------pComp for syzygies:-------------------*/
318
319void pSetModDeg(intvec *w);
320
321
322
323
324poly      pmInit(char *s, BOOLEAN &ok);     /* monom -> poly, interpreter */
325char *    p_Read(char *s, poly &p, ring r); /* monom -> poly */
326void      ppDelete(poly * a, ring r);
327
328/*-------------operations on polynomials:------------*/
329poly      pSub(poly a, poly b);
330poly      pPower(poly p, int i);
331
332// ----------------- define to enable new p_procs -----*/
333
334poly      pDivide(poly a, poly b);
335poly      pDivideM(poly a, poly b);
336void      pLcm(poly a, poly b, poly m);
337poly      pDiff(poly a, int k);
338poly      pDiffOp(poly a, poly b,BOOLEAN multiply);
339
340#define   pMaxComp(p)   p_MaxComp(p, currRing)
341#define   pMinComp(p)   p_MinComp(p, currRing)
342int pMaxCompProc(poly p);
343
344#define   pOneComp(p)       p_OneComp(p, currRing)
345#define   pSetCompP(a,i)    p_SetCompP(a, i, currRing)
346
347// let's inline those, so that we can call them from the debugger
348inline char*   pString(poly p)    {return p_String(p, currRing, currRing);}
349inline char*   pString0(poly p)   {return p_String0(p, currRing, currRing);}
350inline void    pWrite(poly p)     {p_Write(p, currRing, currRing);}
351inline void    pWrite0(poly p)    {p_Write0(p, currRing, currRing);}
352inline void    wrp(poly p)        {p_wrp(p, currRing, currRing);}
353
354void      pEnlargeSet(polyset *p, int length, int increment);
355#define   pISet(i) p_ISet(i,currRing)
356#define   pNSet(n) p_NSet(n,currRing)
357#define   pOne()   pISet(1)
358
359void      pContent(poly p);
360void      pSimpleContent(poly p, int s);
361void      pCleardenom(poly p);
362void      pCleardenom_n(poly p,number &c);
363void      p_Normalize(poly p, ring r);
364#define   pNormalize(p) p_Normalize(p,currRing)
365
366// homogenizes p by multiplying certain powers of the varnum-th variable
367poly      pHomogen (poly p, int varnum);
368
369// replaces the maximal powers of the leading monomial of p2 in p1 by
370// the same powers of n, utility for dehomogenization
371poly      pDehomogen (poly p1,poly p2,number n);
372BOOLEAN   pIsHomogeneous (poly p);
373
374// returns the leading monomial of p1 divided by the maximal power of
375// that of p2
376poly      pDivByMonom (poly p1,poly p2);
377
378// Returns as i-th entry of P the coefficient of the (i-1) power of
379// the leading monomial of p2 in p1
380void      pCancelPolyByMonom (poly p1,poly p2,polyset * P,int * SizeOfSet);
381
382poly      pPermPoly (poly p, int * perm, ring OldRing, nMapFunc nMap,
383                     int *par_perm=NULL, int OldPar=0);
384
385/*BOOLEAN   pVectorHasUnitM(poly p, int * k);*/
386BOOLEAN   pVectorHasUnitB(poly p, int * k);
387void      pVectorHasUnit(poly p, int * k, int * len);
388poly      pTakeOutComp1(poly * p, int k);
389// Splits *p into two polys: *q which consists of all monoms with
390// component == comp and *p of all other monoms *lq == pLength(*q)
391// On return all components pf *q == 0
392void pTakeOutComp(poly *p, Exponent_t comp, poly *q, int *lq);
393// Similar to pTakeOutComp, except that only those components are
394// taken out whose Order == order
395// ASSUME: monomial ordering is Order compatible, i.e., if m1, m2 Monoms then
396//         m1 >= m2 ==> pGetOrder(m1) >= pGetOrder(m2)
397void pDecrOrdTakeOutComp(poly *p, Exponent_t comp, Order_t order,
398                         poly *q, int *lq);
399// This is something weird -- Don't use it, unless you know what you are doing
400poly      pTakeOutComp(poly * p, int k);
401void      pSetPolyComp(poly p, int comp);
402void      pDeleteComp(poly * p,int k);
403void      pNorm(poly p);
404poly      pSubst(poly p, int n, poly e);
405poly      ppJet(poly p, int m);
406poly      pJet(poly p, int m);
407poly      ppJetW(poly p, int m, short * iv);
408poly      pJetW(poly p, int m, short * iv);
409int pMinDeg(poly p,intvec *w=NULL);
410poly      pSeries(int n,poly p,poly u=NULL,intvec *w=NULL);
411poly      pInvers(int n, poly p,intvec *w=NULL);
412// maximum weigthed degree of all monomials of p, w is indexed from
413// 1..pVariables
414long      pDegW(poly p, short *w);
415
416/*-----------type conversions ----------------------------*/
417poly  pPolys2Vec(polyset p, int len);
418void  pVec2Polys(poly v, polyset *p, int *len);
419int   pVar(poly m);
420
421/*-----------specials for spoly-computations--------------*/
422BOOLEAN pCompareChain (poly p,poly p1,poly p2,poly lcm);
423BOOLEAN pEqualPolys(poly p1,poly p2);
424BOOLEAN pComparePolys(poly p1,poly p2);
425
426
427
428/***************************************************************
429 *
430 * PDEBUG stuff
431 *
432 ***************************************************************/
433#ifdef PDEBUG
434#define pTest(p)        _p_Test(p, currRing, PDEBUG)
435#define pLmTest(p)      _p_LmTest(p, currRing, PDEBUG)
436
437#else // ! PDEBUG
438
439#define pTest(p)        ((void)0)
440#define pLmTest(p)      ((void)0)
441#endif
442
443#endif // POLYS_H
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