1 /*! \file kernel/polys.h Compatiblity layer for legacy polynomial operations (over @ref currRing)
2
3 Macro defines for legacy polynomial operations used in @ref kernel_page and @ref singular_page.
4 They take no ring argument since they work with @ref currRing by default.
5 Notice that they have different prefix: `p` instead of `p_`.
6
7 See also related global ring variable and the correct ring changeing routine:
8 - \ref currRing
9 - \ref rChangeCurrRing
10 */
11
12 #ifndef POLYS_H
13 #define POLYS_H
14
15 #include "polys/monomials/ring.h"
16 #include "polys/monomials/p_polys.h"
17
18 EXTERN_VAR ring currRing;
19 void rChangeCurrRing(ring r);
20
21 #include "coeffs/numbers.h"
22
23 /***************************************************************
24 *
25 * Primitives for accessing and setting fields of a poly
26 * poly must be != NULL
27 *
28 ***************************************************************/
29
30 /// deletes old coeff before setting the new one
31 #define pSetCoeff(p,n) p_SetCoeff(p,n,currRing)
32
33 /// Order
34 #define pGetOrder(p) p_GetOrder(p, currRing)
35
36 /// Component
37 #define pGetComp(p) (int)__p_GetComp(p, currRing)
38 #define pSetComp(p,v) p_SetComp(p,v, currRing)
39
40 /// Exponent
41 #define pGetExp(p,i) p_GetExp(p, i, currRing)
42 #define pSetExp(p,i,v) p_SetExp(p, i, v, currRing)
43 #define pIncrExp(p,i) p_IncrExp(p,i, currRing)
44 #define pDecrExp(p,i) p_DecrExp(p,i, currRing)
45 #define pAddExp(p,i,v) p_AddExp(p,i,v, currRing)
46 #define pSubExp(p,i,v) p_SubExp(p,i,v, currRing)
47 #define pMultExp(p,i,v) p_MultExp(p,i,v, currRing)
48 #define pGetExpSum(p1, p2, i) p_GetExpSum(p1, p2, i, currRing)
49 #define pGetExpDiff(p1, p2, i) p_GetExpDiff(p1, p2, i, currRing)
50
51
52 /***************************************************************
53 *
54 * Allocation/Initalization/Deletion
55 * except for pHead, all polys must be != NULL
56 *
57 ***************************************************************/
58 /// allocates the space for a new monomial -- no initialization !!!
59 #define pNew() p_New(currRing)
60 /// allocates a new monomial and initializes everything to 0
61 #define pInit() p_Init(currRing,currRing->PolyBin)
62 /// like pInit, except that expvector is initialized to that of p,
63 /// p must be != NULL
64 #define pLmInit(p) p_LmInit(p, currRing)
65 /// returns newly allocated copy of Lm(p), coef is copied, next=NULL,
66 /// p might be NULL
67 #define pHead(p) p_Head(p, currRing)
68 /// frees the space of the monomial m, assumes m != NULL
69 /// coef is not freed, m is not advanced
pLmFree(poly p)70 static inline void pLmFree(poly p) {p_LmFree(p, currRing);}
71 /// like pLmFree, but advances p
pLmFree(poly * p)72 static inline void pLmFree(poly *p) {p_LmFree(p, currRing);}
73 /// assumes p != NULL, deletes p, returns pNext(p)
74 #define pLmFreeAndNext(p) p_LmFreeAndNext(p, currRing)
75 /// assume p != NULL, deletes Lm(p)->coef and Lm(p)
76 #define pLmDelete(p) p_LmDelete(p, currRing)
77 /// like pLmDelete, returns pNext(p)
78 #define pLmDeleteAndNext(p) p_LmDeleteAndNext(p, currRing)
79
80 /***************************************************************
81 *
82 * Operation on ExpVectors: assumes polys != NULL
83 *
84 ***************************************************************/
85
86 #define pExpVectorCopy(d_p, s_p) p_ExpVectorCopy(d_p, s_p, currRing)
87 #define pExpVectorAdd(p1, p2) p_ExpVectorAdd(p1, p2, currRing)
88 #define pExpVectorSub(p1, p2) p_ExpVectorSub(p1, p2, currRing)
89 #define pExpVectorAddSub(p1, p2, p3) p_ExpVectorAddSub(p1, p2, p3, currRing)
90 #define pExpVectorSum(pr, p1, p2) p_ExpVectorSum(pr, p1, p2, currRing)
91 #define pExpVectorDiff(pr, p1, p2) p_ExpVectorDiff(pr, p1, p2, currRing)
92
93 /// Gets a copy of (resp. set) the exponent vector, where e is assumed
94 /// to point to (r->N +1)*sizeof(long) memory. Exponents are
95 /// filled in as follows: comp, e_1, .., e_n
96 #define pGetExpV(p, e) p_GetExpV(p, e, currRing)
97 #define pSetExpV(p, e) p_SetExpV(p, e, currRing)
98
99 /***************************************************************
100 *
101 * Comparisons: they are all done without regarding coeffs
102 *
103 ***************************************************************/
104 /// returns 0|1|-1 if p=q|p>q|p<q w.r.t monomial ordering
105 #define pLmCmp(p,q) p_LmCmp(p,q,currRing)
106 /// executes axtionE|actionG|actionS if p=q|p>q|p<q w.r.t monomial ordering
107 /// action should be a "goto ..."
108 #define pLmCmpAction(p,q, actionE, actionG, actionS) \
109 _p_LmCmpAction(p,q,currRing, actionE, actionG,actionS)
110
111 #define pLmEqual(p1, p2) p_ExpVectorEqual(p1, p2, currRing)
112
113 /// pCmp: args may be NULL
114 /// returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))
115 #define pCmp(p1, p2) p_Cmp(p1, p2, currRing)
116
117 /***************************************************************
118 *
119 * Comparisons: these are all done regarding coeffs
120 *
121 ***************************************************************/
122
123 #define pLtCmp(p,q) p_LtCmp(p,q,currRing)
124 #define pLtCmpNoAbs(p,q) p_LtCmpNoAbs(p,q,currRing)
125 #define pLtCmpOrdSgnDiffM(p,q) p_LtCmpOrdSgnDiffM(p,q,currRing)
126 #define pLtCmpOrdSgnDiffP(p,q) p_LtCmpOrdSgnDiffP(p,q,currRing)
127 #define pLtCmpOrdSgnEqM(p,q) p_LtCmpOrdSgnEqM(p,q,currRing)
128 #define pLtCmpOrdSgnEqP(p,q) p_LtCmpOrdSgnEqP(p,q,currRing)
129
130 /***************************************************************
131 *
132 * Divisiblity tests, args must be != NULL, except for
133 * pDivisbleBy
134 *
135 ***************************************************************/
136 /// returns TRUE, if leading monom of a divides leading monom of b
137 /// i.e., if there exists a expvector c > 0, s.t. b = a + c;
138 #define pDivisibleBy(a, b) p_DivisibleBy(a,b,currRing)
139 /// like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL
140 #define pLmDivisibleBy(a,b) p_LmDivisibleBy(a,b,currRing)
141 /// like pLmDivisibleBy, does not check components
142 #define pLmDivisibleByNoComp(a, b) p_LmDivisibleByNoComp(a,b,currRing)
143 /// Divisibility tests based on Short Exponent vectors
144 /// sev_a == pGetShortExpVector(a)
145 /// not_sev_b == ~ pGetShortExpVector(b)
146 #define pLmShortDivisibleBy(a, sev_a, b, not_sev_b) \
147 p_LmShortDivisibleBy(a, sev_a, b, not_sev_b, currRing)
148 #define pLmRingShortDivisibleBy(a, sev_a, b, not_sev_b) \
149 p_LmRingShortDivisibleBy(a, sev_a, b, not_sev_b, currRing)
150 /// returns the "Short Exponent Vector" -- used to speed up divisibility
151 /// tests (see polys-impl.cc )
152 #define pGetShortExpVector(a) p_GetShortExpVector(a, currRing)
153
154 #ifdef HAVE_RINGS
155 /// divisibility check over ground ring (which may contain zero divisors);
156 /// TRUE iff LT(f) divides LT(g), i.e., LT(f)*c*m = LT(g), for some
157 /// coefficient c and some monomial m;
158 /// does not take components into account */
159 #define pDivisibleByRingCase(f,g) p_DivisibleByRingCase(f,g,currRing)
160 #endif
161
162 /// polynomial division a/b, ignoring the rest
163 /// via singclap_pdivide resp. idLift
164 /// destroyes a,b
165 poly p_Divide(poly a, poly b, const ring r);
166 /// polynomial division a/b, ignoring the rest
167 /// via singclap_pdivide resp. idLift
168 /// does not destroy a,b
169 poly pp_Divide(poly a, poly b, const ring r);
170 poly p_DivRem(poly a, poly b, poly &rest, const ring r); /*julia*/
171
172 /// polynomial gcd
173 /// via singclap_gcd_r resp. idSyzygies
174 /// destroys f and g
175 poly singclap_gcd ( poly f, poly g, const ring r );
176
177
178
179 /***************************************************************
180 *
181 * Copying/Deletion of polys: args may be NULL
182 *
183 ***************************************************************/
184 /// return a copy of the poly
185 #define pCopy(p) p_Copy(p, currRing)
186 #define pDelete(p_ptr) p_Delete(p_ptr, currRing)
187
188 /***************************************************************
189 *
190 * Copying/Deletion of polys: args may be NULL
191 * - p/q as arg mean a poly
192 * - m a monomial
193 * - n a number
194 * - pp (resp. qq, mm, nn) means arg is constant
195 * - p (resp, q, m, n) means arg is destroyed
196 *
197 ***************************************************************/
198 #define pNeg(p) p_Neg(p, currRing)
199 #define ppMult_nn(p, n) pp_Mult_nn(p, n, currRing)
200 #define pMult_nn(p, n) p_Mult_nn(p, n, currRing)
201 #define ppMult_mm(p, m) pp_Mult_mm(p, m, currRing)
202 #define pMult_mm(p, m) p_Mult_mm(p, m, currRing)
203 #define pAdd(p, q) p_Add_q(p, q, currRing)
204 #define pPower(p, q) p_Power(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) p_SortMerge(p, currRing)
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 p is either NULL, or if all exponents
235 /// of p are 0, Comp of p might be != 0
236 #define pIsConstantComp(p) p_IsConstantComp(p, currRing)
237 /// like above, except that Comp must 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 pIsUnivariate(p) p_IsUnivariate(p, currRing)
250 #define pIsVector(p) (pGetComp(p)>0)
251 #define pGetVariables(p,e) p_GetVariables(p, e, currRing)
252
253 /***************************************************************
254 *
255 * Old stuff
256 *
257 ***************************************************************/
258
259 typedef poly* polyset;
260
261 /*-------------predicate on polys ----------------------*/
262 #define pHasNotCFRing(p1,p2) p_HasNotCFRing(p1,p2,currRing)
263 #define pHasNotCF(p1,p2) p_HasNotCF(p1,p2,currRing)
264 /*has no common factor ?*/
265 #define pSplit(p,r) p_Split(p,r)
266 /*p => IN(p), r => REST(p) */
267
268
269
270 /*-----------the ordering of monomials:-------------*/
271 #define pSetm(p) p_Setm(p, currRing)
272 /// TODO:
273 #define pSetmComp(p) p_Setm(p, currRing)
274
275 /***************************************************************
276 *
277 * Degree stuff -- see p_polys.cc for explainations
278 *
279 ***************************************************************/
280 #define pWeight(i) p_Weight(i,currRing)
281
pTotaldegree(poly p)282 static inline long pTotaldegree(poly p) { return p_Totaldegree(p,currRing); }
283 #define pWTotaldegree(p) p_WTotaldegree(p,currRing)
284 #define pWDegree(p) p_WDegree(p,currRing)
285
286 /*-------------operations on polynomials:------------*/
287 #define pSub(a,b) p_Sub(a,b,currRing)
288
289 #define pmInit(a,b) p_mInit(a,b,currRing)
290
291 /* ----------------- define to enable new p_procs -----*/
292
293 #define pMDivide(a,b) p_MDivide(a,b,currRing)
294 #define pDivideM(a,b) p_DivideM(a,b,currRing)
295 #define pLcm(a,b,m) p_Lcm(a,b,m,currRing)
296 #define pDiff(a,b) p_Diff(a,b,currRing)
297 #define pDiffOp(a,b,m) p_DiffOp(a,b,m,currRing)
298
299 #define pMaxComp(p) p_MaxComp(p, currRing)
300 #define pMinComp(p) p_MinComp(p, currRing)
301
302 #define pOneComp(p) p_OneComp(p, currRing)
303 #define pSetCompP(a,i) p_SetCompP(a, i, currRing)
304
305 // let's inline those, so that we can call them from the debugger
pString(poly p)306 inline char* pString(poly p) {return p_String(p, currRing, currRing);}
pString0(poly p)307 inline void pString0(poly p) {p_String0(p, currRing, currRing);}
pWrite(poly p)308 inline void pWrite(poly p) {p_Write(p, currRing, currRing);}
pWrite0(poly p)309 inline void pWrite0(poly p) {p_Write0(p, currRing, currRing);}
wrp(poly p)310 inline void wrp(poly p) {p_wrp(p, currRing, currRing);}
311
312 #define pISet(i) p_ISet(i,currRing)
313 #define pNSet(n) p_NSet(n,currRing)
314
315 #define pOne() p_One(currRing)
316
317 #define pNormalize(p) p_Normalize(p,currRing)
318 #define pSize(p) p_Size(p,currRing)
319
320
321 /// homogenizes p by multiplying certain powers of the varnum-th variable
322 #define pHomogen(p,varnum) p_Homogen(p,varnum,currRing)
323
324 BOOLEAN pIsHomogeneous (poly p);
325 // // replaces the maximal powers of the leading monomial of p2 in p1 by
326 // // the same powers of n, utility for dehomogenization
327 // #define pDehomogen(p1,p2,n) p_Dehomgen(p1,p2,n,currRing)
328 // #define pIsHomogen(p) p_IsHomggen(p,currRing)
329 #define pIsHomogen(p) p_IsHomogen(p,currRing)
330
331 /*BOOLEAN pVectorHasUnitM(poly p, int * k);*/
332 #define pVectorHasUnitB(p,k) p_VectorHasUnitB(p,k,currRing)
333 #define pVectorHasUnit(p,k,l) p_VectorHasUnit(p,k,l,currRing)
334 #define pTakeOutComp1(p,k) p_TakeOutComp1(p,k,currRing)
335
336 /// Splits *p into two polys: *q which consists of all monoms with
337 /// component == comp and *p of all other monoms *lq == pLength(*q)
338 /// On return all components pf *q == 0
339 inline void pTakeOutComp(poly *p, long comp, poly *q, int *lq, const ring R = currRing)
340 {
341 return p_TakeOutComp(p, comp, q, lq, R);
342 }
343
344
345 /// This is something weird -- Don't use it, unless you know what you are doing
346 inline poly pTakeOutComp(poly * p, int k, const ring R = currRing)
347 {
348 return p_TakeOutComp(p, k, R);
349 }
350
351 /* old spielwiese
352 #define pTakeOutComp(p,k,q,lq) p_TakeOutComp(p,k,q,lq,currRing)
353
354 // Similar to pTakeOutComp, except that only those components are
355 // taken out whose Order == order
356 // ASSUME: monomial ordering is Order compatible, i.e., if m1, m2 Monoms then
357 // m1 >= m2 ==> pGetOrder(m1) >= pGetOrder(m2)
358 #define pDecrOrdTakeOutComp(p,c,o,q,lq) p_DecrOrdTakeOutComp(p,c,o,q,lq,currRing)
359 */
360 void pSetPolyComp(poly p, int comp);
361 #define pDeleteComp(p,k) p_DeleteComp(p,k,currRing)
362
363 inline void pNorm(poly p, const ring R = currRing){ p_Norm(p, R); }
364
365
366 #define pSubst(p,n,e) p_Subst(p,n,e,currRing)
367 #define ppJet(p,m) pp_Jet(p,m,currRing)
368 #define pJet(p,m) p_Jet(p,m,currRing)
369 #define ppJetW(p,m,iv) pp_JetW(p,m,iv,currRing)
370 #define pJetW(p,m,iv) p_JetW(p,m,iv,currRing)
371 #define pMinDeg(p,w) p_MinDeg(p,w,currRing)
372 #define pSeries(n,p,u,w) p_Series(n,p,u,w,currRing)
373 // maximum weigthed degree of all monomials of p, w is indexed from
374 // 1..pVariables
375
376 /// Deprecated: only for compatibility with older code!
377 #define pDegW(p,w) p_DegW(p,w,currRing)
378
379 /*-----------type conversions ----------------------------*/
380 // void pVec2Polys(poly v, polyset *p, int *len);
381 #define pVar(m) p_Var(m,currRing)
382
383 /*-----------specials for spoly-computations--------------*/
384
385 /// Returns TRUE if
386 /// * LM(p) | LM(lcm)
387 /// * LC(p) | LC(lcm) only if ring
388 /// * Exists i, j:
389 /// * LE(p, i) != LE(lcm, i)
390 /// * LE(p1, i) != LE(lcm, i) ==> LCM(p1, p) != lcm
391 /// * LE(p, j) != LE(lcm, j)
392 /// * LE(p2, j) != LE(lcm, j) ==> LCM(p2, p) != lcm
393 BOOLEAN pCompareChain (poly p, poly p1, poly p2, poly lcm, const ring R = currRing);
394
395 #ifdef HAVE_RATGRING
396 BOOLEAN pCompareChainPart (poly p, poly p1, poly p2, poly lcm, const ring R = currRing);
397 #endif
398
399
400 #define pEqualPolys(p1,p2) p_EqualPolys(p1,p2,currRing)
401
402
403
404 /// returns the length of a polynomial (numbers of monomials)
405 /// respect syzComp
pLast(poly a,int & length)406 static inline poly pLast(poly a, int &length) { return p_Last (a, length, currRing); }
pLast(poly a)407 static inline poly pLast(poly a) { int l; return pLast(a, l); }
408
409 /***************************************************************
410 *
411 * PDEBUG stuff
412 *
413 ***************************************************************/
414 #ifdef PDEBUG
415 #define pTest(p) _p_Test(p, currRing, PDEBUG)
416 #define pLmTest(p) _p_LmTest(p, currRing, PDEBUG)
417
418 #else // ! PDEBUG
419
420 #define pTest(p) do {} while (0)
421 #define pLmTest(p) do {} while (0)
422 #endif
423
424 #endif // POLYS_H
425