source: git/kernel/p_polys.h @ 99bdcf

jengelh-datetimespielwiese
Last change on this file since 99bdcf was 99bdcf, checked in by Hans Schoenemann <hannes@…>, 13 years ago
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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 *  Version: $Id$
11 *******************************************************************/
12#ifndef P_POLYS_H
13#define P_POLYS_H
14
15#include <kernel/structs.h>
16#include <kernel/polys-impl.h>
17/*
18 Some general remarks:
19 We divide poly operations into roughly 4 categories:
20 Level 2: operations on monomials/polynomials with constant time,
21          or operations which are just dispatchers to other
22          poly routines
23          - implemented in: pInline2.h
24          - debugging only if PDEBUG >= 2
25          - normally inlined, unless PDEBUG >= 2 || NO_INLINE2
26 Level 1: operations on monomials with time proportional to length
27          - implemented in: pInline1.h
28          - debugging only if PDEBUG >= 1
29          - normally inlined, unless PDEBUG >= 1 || NO_INLINE1
30 Level 0: short operations on polynomials with time proportional to
31          length of poly
32          - implemented in pInline0.cc
33          - debugging if PDEBUG
34          - normally _not_ inlined: can be forced with
35            #define DO_PINLINE0
36            #include "pInline0.h"
37 Misc   : operations on polynomials which do not fit in any of the
38          above categories
39          - implemented in: polys*.cc
40          - never inlined
41          - debugging if PDEBUG >= 0
42
43 You can set PDEBUG on a per-file basis, before including "mod2.h" like
44   #define PDEBUG 2
45   #include "mod2.h"
46 However, PDEBUG will only be in effect, if !NDEBUG.
47*/
48
49/***************************************************************
50 *
51 * Primitives for accessing and setting fields of a poly
52 * poly must be != NULL
53 *
54 ***************************************************************/
55// next
56#define pNext(p)            ((p)->next)
57#define pIter(p)            ((p) = (p)->next)
58
59// coeff
60#define pGetCoeff(p)        ((p)->coef)
61// deletes old coeff before setting the new one
62#define pSetCoeff0(p,n)     (p)->coef=(n)
63#define p_GetCoeff(p,r)     pGetCoeff(p)
64#define p_SetCoeff0(p,n,r)  pSetCoeff0(p,n)
65// deletes old p->coef and sets new one
66PINLINE2 number p_SetCoeff(poly p, number n, ring r);
67
68// get Order
69PINLINE2 long p_GetOrder(poly p, ring r);
70
71// Component
72#define p_GetComp(p, r)     _p_GetComp(p, r)
73PINLINE2 unsigned long p_SetComp(poly p, unsigned long c, ring r);
74PINLINE2 unsigned long p_AddComp(poly p, unsigned long v, ring r);
75PINLINE2 unsigned long p_SubComp(poly p, unsigned long v, ring r);
76
77// Exponent
78PINLINE2 long p_GetExp(poly p, int v, ring r);
79PINLINE2 long p_SetExp(poly p, int v, long e, ring r);
80PINLINE2 long p_IncrExp(poly p, int v, ring r);
81PINLINE2 long p_DecrExp(poly p, int v, ring r);
82PINLINE2 long p_AddExp(poly p, int v, long ee, ring r);
83PINLINE2 long p_SubExp(poly p, int v, long ee, ring r);
84PINLINE2 long p_MultExp(poly p, int v, long ee, ring r);
85PINLINE2 long p_GetExpSum(poly p1, poly p2, int i, ring r);
86PINLINE2 long p_GetExpDiff(poly p1, poly p2, int i, ring r);
87
88/***************************************************************
89 *
90 * Allocation/Initalization/Deletion
91 * except for pHead, all polys must be != NULL
92 *
93 ***************************************************************/
94PINLINE2 poly p_New(ring r);
95PINLINE2 poly p_New(ring r, omBin bin);
96PINLINE1 poly p_Init(ring r);
97PINLINE1 poly p_Init(ring r, omBin bin);
98PINLINE1 poly p_LmInit(poly p, ring r);
99PINLINE1 poly p_LmInit(poly s_p, ring s_r, ring d_p);
100PINLINE1 poly p_LmInit(poly s_p, ring s_r, ring d_p, omBin d_bin);
101PINLINE1 poly p_Head(poly p, ring r);
102PINLINE2 void p_LmFree(poly p, ring r);
103PINLINE2 void p_LmFree(poly *p, ring r);
104PINLINE2 poly p_LmFreeAndNext(poly p, ring r);
105PINLINE2 void p_LmDelete(poly p, ring r);
106PINLINE2 void p_LmDelete(poly *p, ring r);
107PINLINE2 poly p_LmDeleteAndNext(poly p, ring r);
108
109/***************************************************************
110 *
111 * Operation on ExpVectors: assumes polys != NULL
112 *
113 ***************************************************************/
114// ExpVextor(d_p) = ExpVector(s_p)
115PINLINE1 void p_ExpVectorCopy(poly d_p, poly s_p, ring r);
116// adjustments for negative weights
117PINLINE1 void p_MemAdd_NegWeightAdjust(poly p, ring r);
118PINLINE1 void p_MemSub_NegWeightAdjust(poly p, ring r);
119// ExpVector(p1) += ExpVector(p2)
120PINLINE1 void p_ExpVectorAdd(poly p1, poly p2, ring r);
121// ExpVector(p1) -= ExpVector(p2)
122PINLINE1 void p_ExpVectorSub(poly p1, poly p2, ring r);
123// ExpVector(p1) += ExpVector(p2) - ExpVector(p3)
124PINLINE1 void p_ExpVectorAddSub(poly p1, poly p2, poly p3, ring r);
125// ExpVector(pr) = ExpVector(p1) + ExpVector(p2)
126PINLINE1 void p_ExpVectorSum(poly pr, poly p1, poly p2, ring r);
127// ExpVector(pr) = ExpVector(p1) + ExpVector(p2)
128PINLINE1 void p_ExpVectorDiff(poly pr, poly p1, poly p2, ring r);
129// returns TRUE if ExpVector(p1) == ExpVector(p2), FALSE, otherwise
130PINLINE1 BOOLEAN p_ExpVectorEqual(poly p1, poly p2, ring r);
131// returns sum of all exponents of p
132PINLINE1 long p_Totaldegree(poly p, ring r);
133
134PINLINE1 void p_GetExpV(poly p, int *ev, ring r);
135PINLINE1 void p_SetExpV(poly p, int *ev, ring r);
136
137
138/***************************************************************
139 *
140 * Comparisons: they are all done without regarding coeffs
141 *
142 ***************************************************************/
143PINLINE1 int p_LmCmp(poly p, poly q, ring r);
144#define p_LmCmpAction(p, q, r, actionE, actionG, actionS) \
145  _p_LmCmpAction(p, q, r, actionE, actionG, actionS)
146
147// returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !!
148#define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r)
149
150// pCmp: args may be NULL
151// returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))
152PINLINE2 int p_Cmp(poly p1, poly p2, ring r);
153
154
155/***************************************************************
156 *
157 * Divisiblity tests, args must be != NULL, except for
158 * pDivisbleBy
159 *
160 ***************************************************************/
161PINLINE1 BOOLEAN p_DivisibleBy(poly a, poly b, ring r);
162PINLINE1 BOOLEAN p_LmDivisibleBy(poly a, poly b, ring r);
163PINLINE1 BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, ring r);
164unsigned long p_GetShortExpVector(poly a, ring r);
165PINLINE1 BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a,
166                                      poly b, unsigned long not_sev_b, ring r);
167
168PINLINE1 BOOLEAN p_DivisibleBy(poly a, ring r_a, poly b, ring r_b);
169PINLINE1 BOOLEAN p_LmDivisibleBy(poly a, ring r_a, poly b, ring r_b);
170PINLINE1 BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, ring r_a,
171                                      poly b, unsigned long not_sev_b, ring r_b);
172
173/***************************************************************
174 *
175 * Misc things on Lm
176 *
177 ***************************************************************/
178// test if the monomial is a constant as a vector component
179// i.e., test if all exponents are zero
180PINLINE1 BOOLEAN p_LmIsConstantComp(const poly p, const ring r);
181PINLINE1 BOOLEAN p_LmIsConstant(const poly p, const ring r);
182
183// return TRUE, if p_LmExpVectorAdd stays within ExpBound of ring r,
184//       FALSE, otherwise
185PINLINE1 BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2, ring r);
186
187/***************************************************************
188 *
189 * Misc things on polys
190 *
191 ***************************************************************/
192// return the maximal exponent of p
193PINLINE2 unsigned long p_GetMaxExp(poly p, ring r);
194// return the maximal exponent of p in form of the maximal long var
195unsigned long p_GetMaxExpL(poly p, ring r, unsigned long l_max = 0);
196// return monomial r such that GetExp(r,i) is maximum of all
197// monomials in p; coeff == 0, next == NULL, ord is not set
198poly p_GetMaxExpP(poly p, ring r);
199
200// suppose that l is a long var in r, return maximal exponent of l
201PINLINE2 unsigned long p_GetMaxExp(unsigned long l, ring r);
202// similar, except assume that l constains number_of_exps exponents
203PINLINE2 unsigned long p_GetMaxExp(const unsigned long l, const ring r, const int number_of_exps);
204
205// return the TotalDegree of the long var l
206PINLINE2 unsigned long p_GetTotalDegree(const unsigned long l, const ring r);
207// return the total degree of the long var l containing number_of_exp exponents
208PINLINE2 unsigned long p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps);
209
210
211// like the respective p_LmIs* routines, except that p might be empty
212PINLINE1 BOOLEAN p_IsConstantComp(const poly p, const ring r);
213PINLINE1 BOOLEAN p_IsConstant(const poly p, const ring r);
214PINLINE0 BOOLEAN p_IsConstantPoly(const poly p, const ring r);
215
216// return TRUE if all monoms have the same component
217BOOLEAN   p_OneComp(poly p, ring r);
218
219// return i, if head depends only on var(i)
220int       p_IsPurePower(const poly p, const ring r);
221
222// return i, if poly depends only on var(i)
223int       p_IsUnivariate(poly p, const ring r);
224
225// set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0
226// return #(e[i]>0)
227int      p_GetVariables(poly p, int * e, const ring r);
228
229// returns the poly representing the integer i
230poly      p_ISet(int i, ring r);
231
232// returns the poly representing the number n, destroys n
233poly      p_NSet(number n, ring r);
234
235/***************************************************************
236 *
237 * Copying/Deletion of polys: args may be NULL
238 *
239 ***************************************************************/
240// returns a copy of p
241PINLINE2 poly p_Copy(poly p, const ring r);
242// returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing
243PINLINE2 poly p_Copy(poly p, const ring lmRing, const ring tailRing);
244// deletes *p, and sets *p to NULL
245PINLINE2 void p_Delete(poly *p, const ring r);
246PINLINE2 void p_Delete(poly *p, const ring lmRing, const ring tailRing);
247
248// copys monomials of p, allocates new monomials from bin,
249// deletes monomoals of p
250PINLINE2 poly p_ShallowCopyDelete(poly p, const ring r, omBin bin);
251// simial but does it only for leading monomial
252PINLINE1 poly p_LmShallowCopyDelete(poly p, const ring r, omBin bin);
253// simply deletes monomials, does not free coeffs
254void p_ShallowDelete(poly *p, const ring r);
255
256 
257
258/***************************************************************
259 *
260 * Copying/Deleteion of polys: args may be NULL
261 *  - p/q as arg mean a poly
262 *  - m a monomial
263 *  - n a number
264 *  - pp (resp. qq, mm, nn) means arg is constant
265 *  - p (resp, q, m, n)     means arg is destroyed
266 *
267 ***************************************************************/
268// returns -p, p is destroyed
269PINLINE2 poly p_Neg(poly p, const ring r);
270
271// returns p*n, p is const (i.e. copied)
272PINLINE2 poly pp_Mult_nn(poly p, number n, const ring r);
273// returns p*n, destroys p
274PINLINE2 poly p_Mult_nn(poly p, number n, const ring r);
275PINLINE2 poly p_Mult_nn(poly p, number n, const ring lmRing, const ring tailRing);
276
277// returns p*m, does neither destroy p nor m
278PINLINE2 poly pp_Mult_mm(poly p, poly m, const ring r);
279// returns p*m, destroys p, const: m
280PINLINE2 poly p_Mult_mm(poly p, poly m, const ring r);
281
282// returns p+q, destroys p and q
283PINLINE2 poly p_Add_q(poly p, poly q, const ring r);
284// like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq)
285// then lp == pLength(p+q)
286PINLINE2 poly p_Add_q(poly p, poly q, int &lp, int lq, const ring r);
287
288// return p - m*q, destroys p; const: q,m
289PINLINE2 poly p_Minus_mm_Mult_qq(poly p, poly m, poly q, const ring r);
290// like p_Minus_mm_Mult_qq, except that if lp == pLength(lp) lq == pLength(lq)
291// then lp == pLength(p -m*q)
292PINLINE2 poly p_Minus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq,
293                                 poly spNoether, const ring r);
294// returns p + m*q destroys p, const: q, m
295PINLINE2 poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, const ring r);
296
297// returns p + m*q destroys p, const: q, m
298PINLINE2 poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq,
299                                const ring r);
300
301// returns p*q, destroys p and q
302PINLINE2 poly p_Mult_q(poly p, poly q, const ring r);
303// returns p*q, does neither destroy p nor q
304PINLINE2 poly pp_Mult_qq(poly p, poly q, const ring r);
305
306// returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
307PINLINE2 poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r);
308
309// returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm
310// if lp is length of p on input then lp is length of returned poly on output
311PINLINE2 poly pp_Mult_Coeff_mm_DivSelect(poly p, int &lp, const poly m, const ring r);
312
313// returns merged p and q, assumes p and q have no monomials which are equal
314PINLINE2 poly p_Merge_q(poly p, poly c, const ring r);
315// sorts p using bucket sort: returns sorted poly
316// assumes that monomials of p are all different
317// reverses it first, if revert == TRUE, use this if input p is "almost" sorted
318// correctly
319PINLINE2 poly p_SortMerge(poly p, const ring r, BOOLEAN revert = FALSE);
320// like SortMerge, except that p may have equal monimals
321PINLINE2 poly p_SortAdd(poly p, const ring r, BOOLEAN revert = FALSE);
322
323/***************************************************************
324 *
325 * Misc stuff
326 *
327 ***************************************************************/
328PINLINE2 void p_Setm(poly p, const ring r);
329p_SetmProc p_GetSetmProc(ring r);
330
331// TODO:
332#define p_SetmComp  p_Setm
333
334// sets component of poly a to i, returns length of a
335PINLINE0   int p_SetCompP(poly a, int i, ring r);
336PINLINE0   int p_SetCompP(poly a, int i, ring lmRing, ring tailRing);
337PINLINE0   long p_MaxComp(poly p, ring lmRing, ring tailRing);
338inline long p_MaxComp(poly p,ring lmRing) {return p_MaxComp(p,lmRing,lmRing);}
339PINLINE0   long p_MinComp(poly p, ring lmRing, ring tailRing);
340inline long p_MinComp(poly p,ring lmRing) {return p_MinComp(p,lmRing,lmRing);}
341
342/***************************************************************
343 *
344 * poly things which are independent of ring
345 *
346 ***************************************************************/
347PINLINE0 int       pLength(poly a);
348PINLINE0 poly      pLast(poly a, int &length);
349inline   poly      pLast(poly a) { int l; return pLast(a, l);}
350PINLINE0 poly pReverse(poly p);
351
352
353/***************************************************************
354 *
355 * I/O
356 *
357 ***************************************************************/
358char*     p_String(poly p, ring lmRing, ring tailRing);
359char*     p_String0(poly p, ring lmRing, ring tailRing);
360void      p_Write(poly p, ring lmRing, ring tailRing);
361void      p_Write0(poly p, ring lmRing, ring tailRing);
362void      p_wrp(poly p, ring lmRing, ring tailRing);
363
364PINLINE2 char*     p_String(poly p, ring p_ring);
365PINLINE2 char*     p_String0(poly p, ring p_ring);
366PINLINE2 void      p_Write(poly p, ring p_ring);
367PINLINE2 void      p_Write0(poly p, ring p_ring);
368PINLINE2 void      p_wrp(poly p, ring p_ring);
369
370
371/***************************************************************
372 *
373 * Degree stuff -- see p_polys.cc for explainations
374 *
375 ***************************************************************/
376extern pLDegProc pLDeg;
377extern pFDegProc pFDeg;
378int  pWeight(int i, ring r);
379long pDeg(poly p, ring r);
380long pWFirstTotalDegree(poly p, ring r);
381long pWTotaldegree(poly p, ring r);
382long pWDegree(poly p, ring r);
383long pLDeg0(poly p,int *l, ring r);
384long pLDeg0c(poly p,int *l, ring r);
385long pLDegb(poly p,int *l, ring r);
386long pLDeg1(poly p,int *l, ring r);
387long pLDeg1c(poly p,int *l, ring r);
388long pLDeg1_Deg(poly p,int *l, ring r);
389long pLDeg1c_Deg(poly p,int *l, ring r);
390long pLDeg1_Totaldegree(poly p,int *l, ring r);
391long pLDeg1c_Totaldegree(poly p,int *l, ring r);
392long pLDeg1_WFirstTotalDegree(poly p,int *l, ring r);
393long pLDeg1c_WFirstTotalDegree(poly p,int *l, ring r);
394BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r);
395/***************************************************************
396 *
397 * PDEBUG stuff
398 *
399 ***************************************************************/
400#ifdef PDEBUG
401// Returns TRUE if m is monom of p, FALSE otherwise
402BOOLEAN pIsMonomOf(poly p, poly m);
403// Returns TRUE if p and q have common monoms
404BOOLEAN pHaveCommonMonoms(poly p, poly q);
405
406// p_Check* routines return TRUE if everything is ok,
407// else, they report error message and return false
408
409// check if Lm(p) is from ring r
410BOOLEAN p_LmCheckIsFromRing(poly p, ring r);
411// check if Lm(p) != NULL, r != NULL and initialized && Lm(p) is from r
412BOOLEAN p_LmCheckPolyRing(poly p, ring r);
413// check if all monoms of p are from ring r
414BOOLEAN p_CheckIsFromRing(poly p, ring r);
415// check r != NULL and initialized && all monoms of p are from r
416BOOLEAN p_CheckPolyRing(poly p, ring r);
417// check if r != NULL and initialized
418BOOLEAN p_CheckRing(ring r);
419// only do check if cond
420
421
422#define pIfThen(cond, check) do {if (cond) {check;}} while (0)
423
424BOOLEAN _p_Test(poly p, ring r, int level);
425BOOLEAN _p_LmTest(poly p, ring r, int level);
426BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level);
427
428#define p_Test(p,r)     _p_Test(p, r, PDEBUG)
429#define p_LmTest(p,r)   _p_LmTest(p, r, PDEBUG)
430#define pp_Test(p, lmRing, tailRing)    _pp_Test(p, lmRing, tailRing, PDEBUG)
431
432#else // ! PDEBUG
433
434#define pIsMonomOf(p, q)        (TRUE)
435#define pHaveCommonMonoms(p, q) (TRUE)
436#define p_LmCheckIsFromRing(p,r)  ((void)0)
437#define p_LmCheckPolyRing(p,r)    ((void)0)
438#define p_CheckIsFromRing(p,r)  ((void)0)
439#define p_CheckPolyRing(p,r)    ((void)0)
440#define p_CheckRing(r)          ((void)0)
441#define P_CheckIf(cond, check)  ((void)0)
442
443#define p_Test(p,r)     (1)
444#define p_LmTest(p,r)   (1)
445#define pp_Test(p, lmRing, tailRing) (1)
446
447#endif
448
449#include <kernel/pInline2.h>
450#include <kernel/pInline1.h>
451
452#endif // P_POLYS_H
453
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