1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /*************************************************************** |
---|
5 | * File: p_polys.cc |
---|
6 | * Purpose: implementation of ring independent poly procedures? |
---|
7 | * Author: obachman (Olaf Bachmann) |
---|
8 | * Created: 8/00 |
---|
9 | * Version: $Id$ |
---|
10 | *******************************************************************/ |
---|
11 | |
---|
12 | #include <ctype.h> |
---|
13 | |
---|
14 | |
---|
15 | #include <omalloc/omalloc.h> |
---|
16 | #include <misc/auxiliary.h> |
---|
17 | #include <misc/options.h> |
---|
18 | #include <misc/intvec.h> |
---|
19 | |
---|
20 | #include <coeffs/longrat.h> // ??? |
---|
21 | |
---|
22 | #include "weight.h" |
---|
23 | #include "simpleideals.h" |
---|
24 | |
---|
25 | #include "monomials/ring.h" |
---|
26 | #include "monomials/p_polys.h" |
---|
27 | #include <polys/templates/p_MemCmp.h> |
---|
28 | #include <polys/templates/p_MemAdd.h> |
---|
29 | #include <polys/templates/p_MemCopy.h> |
---|
30 | |
---|
31 | |
---|
32 | // #include <???/ideals.h> |
---|
33 | // #include <???/int64vec.h> |
---|
34 | |
---|
35 | #ifndef NDEBUG |
---|
36 | // #include <???/febase.h> |
---|
37 | #endif |
---|
38 | |
---|
39 | #ifdef HAVE_PLURAL |
---|
40 | #include "nc/nc.h" |
---|
41 | #include "nc/sca.h" |
---|
42 | #endif |
---|
43 | |
---|
44 | #include "coeffrings.h" |
---|
45 | #ifdef HAVE_FACTORY |
---|
46 | #include "clapsing.h" |
---|
47 | #endif |
---|
48 | |
---|
49 | /*************************************************************** |
---|
50 | * |
---|
51 | * Completing what needs to be set for the monomial |
---|
52 | * |
---|
53 | ***************************************************************/ |
---|
54 | // this is special for the syz stuff |
---|
55 | static int* _components = NULL; |
---|
56 | static long* _componentsShifted = NULL; |
---|
57 | static int _componentsExternal = 0; |
---|
58 | |
---|
59 | BOOLEAN pSetm_error=0; |
---|
60 | |
---|
61 | #ifndef NDEBUG |
---|
62 | # define MYTEST 0 |
---|
63 | #else /* ifndef NDEBUG */ |
---|
64 | # define MYTEST 0 |
---|
65 | #endif /* ifndef NDEBUG */ |
---|
66 | |
---|
67 | void p_Setm_General(poly p, const ring r) |
---|
68 | { |
---|
69 | p_LmCheckPolyRing(p, r); |
---|
70 | int pos=0; |
---|
71 | if (r->typ!=NULL) |
---|
72 | { |
---|
73 | loop |
---|
74 | { |
---|
75 | long ord=0; |
---|
76 | sro_ord* o=&(r->typ[pos]); |
---|
77 | switch(o->ord_typ) |
---|
78 | { |
---|
79 | case ro_dp: |
---|
80 | { |
---|
81 | int a,e; |
---|
82 | a=o->data.dp.start; |
---|
83 | e=o->data.dp.end; |
---|
84 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r); |
---|
85 | p->exp[o->data.dp.place]=ord; |
---|
86 | break; |
---|
87 | } |
---|
88 | case ro_wp_neg: |
---|
89 | ord=POLY_NEGWEIGHT_OFFSET; |
---|
90 | // no break; |
---|
91 | case ro_wp: |
---|
92 | { |
---|
93 | int a,e; |
---|
94 | a=o->data.wp.start; |
---|
95 | e=o->data.wp.end; |
---|
96 | int *w=o->data.wp.weights; |
---|
97 | #if 1 |
---|
98 | for(int i=a;i<=e;i++) ord+=p_GetExp(p,i,r)*w[i-a]; |
---|
99 | #else |
---|
100 | long ai; |
---|
101 | int ei,wi; |
---|
102 | for(int i=a;i<=e;i++) |
---|
103 | { |
---|
104 | ei=p_GetExp(p,i,r); |
---|
105 | wi=w[i-a]; |
---|
106 | ai=ei*wi; |
---|
107 | if (ai/ei!=wi) pSetm_error=TRUE; |
---|
108 | ord+=ai; |
---|
109 | if (ord<ai) pSetm_error=TRUE; |
---|
110 | } |
---|
111 | #endif |
---|
112 | p->exp[o->data.wp.place]=ord; |
---|
113 | break; |
---|
114 | } |
---|
115 | case ro_wp64: |
---|
116 | { |
---|
117 | int64 ord=0; |
---|
118 | int a,e; |
---|
119 | a=o->data.wp64.start; |
---|
120 | e=o->data.wp64.end; |
---|
121 | int64 *w=o->data.wp64.weights64; |
---|
122 | int64 ei,wi,ai; |
---|
123 | for(int i=a;i<=e;i++) |
---|
124 | { |
---|
125 | //Print("exp %d w %d \n",p_GetExp(p,i,r),(int)w[i-a]); |
---|
126 | //ord+=((int64)p_GetExp(p,i,r))*w[i-a]; |
---|
127 | ei=(int64)p_GetExp(p,i,r); |
---|
128 | wi=w[i-a]; |
---|
129 | ai=ei*wi; |
---|
130 | if(ei!=0 && ai/ei!=wi) |
---|
131 | { |
---|
132 | pSetm_error=TRUE; |
---|
133 | #if SIZEOF_LONG == 4 |
---|
134 | Print("ai %lld, wi %lld\n",ai,wi); |
---|
135 | #else |
---|
136 | Print("ai %ld, wi %ld\n",ai,wi); |
---|
137 | #endif |
---|
138 | } |
---|
139 | ord+=ai; |
---|
140 | if (ord<ai) |
---|
141 | { |
---|
142 | pSetm_error=TRUE; |
---|
143 | #if SIZEOF_LONG == 4 |
---|
144 | Print("ai %lld, ord %lld\n",ai,ord); |
---|
145 | #else |
---|
146 | Print("ai %ld, ord %ld\n",ai,ord); |
---|
147 | #endif |
---|
148 | } |
---|
149 | } |
---|
150 | int64 mask=(int64)0x7fffffff; |
---|
151 | long a_0=(long)(ord&mask); //2^31 |
---|
152 | long a_1=(long)(ord >>31 ); /*(ord/(mask+1));*/ |
---|
153 | |
---|
154 | //Print("mask: %x, ord: %d, a_0: %d, a_1: %d\n" |
---|
155 | //,(int)mask,(int)ord,(int)a_0,(int)a_1); |
---|
156 | //Print("mask: %d",mask); |
---|
157 | |
---|
158 | p->exp[o->data.wp64.place]=a_1; |
---|
159 | p->exp[o->data.wp64.place+1]=a_0; |
---|
160 | // if(p_Setm_error) Print("***************************\n |
---|
161 | // ***************************\n |
---|
162 | // **WARNING: overflow error**\n |
---|
163 | // ***************************\n |
---|
164 | // ***************************\n"); |
---|
165 | break; |
---|
166 | } |
---|
167 | case ro_cp: |
---|
168 | { |
---|
169 | int a,e; |
---|
170 | a=o->data.cp.start; |
---|
171 | e=o->data.cp.end; |
---|
172 | int pl=o->data.cp.place; |
---|
173 | for(int i=a;i<=e;i++) { p->exp[pl]=p_GetExp(p,i,r); pl++; } |
---|
174 | break; |
---|
175 | } |
---|
176 | case ro_syzcomp: |
---|
177 | { |
---|
178 | int c=p_GetComp(p,r); |
---|
179 | long sc = c; |
---|
180 | int* Components = (_componentsExternal ? _components : |
---|
181 | o->data.syzcomp.Components); |
---|
182 | long* ShiftedComponents = (_componentsExternal ? _componentsShifted: |
---|
183 | o->data.syzcomp.ShiftedComponents); |
---|
184 | if (ShiftedComponents != NULL) |
---|
185 | { |
---|
186 | assume(Components != NULL); |
---|
187 | assume(c == 0 || Components[c] != 0); |
---|
188 | sc = ShiftedComponents[Components[c]]; |
---|
189 | assume(c == 0 || sc != 0); |
---|
190 | } |
---|
191 | p->exp[o->data.syzcomp.place]=sc; |
---|
192 | break; |
---|
193 | } |
---|
194 | case ro_syz: |
---|
195 | { |
---|
196 | const unsigned long c = p_GetComp(p, r); |
---|
197 | const short place = o->data.syz.place; |
---|
198 | const int limit = o->data.syz.limit; |
---|
199 | |
---|
200 | if (c > limit) |
---|
201 | p->exp[place] = o->data.syz.curr_index; |
---|
202 | else if (c > 0) |
---|
203 | { |
---|
204 | assume( (1 <= c) && (c <= limit) ); |
---|
205 | p->exp[place]= o->data.syz.syz_index[c]; |
---|
206 | } |
---|
207 | else |
---|
208 | { |
---|
209 | assume(c == 0); |
---|
210 | p->exp[place]= 0; |
---|
211 | } |
---|
212 | break; |
---|
213 | } |
---|
214 | // Prefix for Induced Schreyer ordering |
---|
215 | case ro_isTemp: // Do nothing?? (to be removed into suffix later on...?) |
---|
216 | { |
---|
217 | assume(p != NULL); |
---|
218 | |
---|
219 | #ifndef NDEBUG |
---|
220 | #if MYTEST |
---|
221 | Print("p_Setm_General: isTemp ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
---|
222 | #endif |
---|
223 | #endif |
---|
224 | int c = p_GetComp(p, r); |
---|
225 | |
---|
226 | assume( c >= 0 ); |
---|
227 | |
---|
228 | // Let's simulate case ro_syz above.... |
---|
229 | // Should accumulate (by Suffix) and be a level indicator |
---|
230 | const int* const pVarOffset = o->data.isTemp.pVarOffset; |
---|
231 | |
---|
232 | assume( pVarOffset != NULL ); |
---|
233 | |
---|
234 | // TODO: Can this be done in the suffix??? |
---|
235 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
---|
236 | { |
---|
237 | const int vo = pVarOffset[i]; |
---|
238 | if( vo != -1) // TODO: optimize: can be done once! |
---|
239 | { |
---|
240 | // Hans! Please don't break it again! p_SetExp(p, ..., r, vo) is correct: |
---|
241 | p_SetExp(p, p_GetExp(p, i, r), r, vo); // copy put them verbatim |
---|
242 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
---|
243 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
---|
244 | } |
---|
245 | } |
---|
246 | #ifndef NDEBUG |
---|
247 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
---|
248 | { |
---|
249 | const int vo = pVarOffset[i]; |
---|
250 | if( vo != -1) // TODO: optimize: can be done once! |
---|
251 | { |
---|
252 | // Hans! Please don't break it again! p_GetExp(p, r, vo) is correct: |
---|
253 | assume( p_GetExp(p, r, vo) == p_GetExp(p, i, r) ); // copy put them verbatim |
---|
254 | } |
---|
255 | } |
---|
256 | #if MYTEST |
---|
257 | // if( p->exp[o->data.isTemp.start] > 0 ) |
---|
258 | // { |
---|
259 | // PrintS("Initial Value: "); p_DebugPrint(p, r, r, 1); |
---|
260 | // } |
---|
261 | #endif |
---|
262 | #endif |
---|
263 | break; |
---|
264 | } |
---|
265 | |
---|
266 | // Suffix for Induced Schreyer ordering |
---|
267 | case ro_is: |
---|
268 | { |
---|
269 | #ifndef NDEBUG |
---|
270 | #if MYTEST |
---|
271 | Print("p_Setm_General: ro_is ord: pos: %d, p: ", pos); p_DebugPrint(p, r, r, 1); |
---|
272 | #endif |
---|
273 | #endif |
---|
274 | |
---|
275 | assume(p != NULL); |
---|
276 | |
---|
277 | int c = p_GetComp(p, r); |
---|
278 | |
---|
279 | assume( c >= 0 ); |
---|
280 | const ideal F = o->data.is.F; |
---|
281 | const int limit = o->data.is.limit; |
---|
282 | |
---|
283 | if( F != NULL && c > limit ) |
---|
284 | { |
---|
285 | #ifndef NDEBUG |
---|
286 | #if MYTEST |
---|
287 | Print("p_Setm_General: ro_is : in rSetm: pos: %d, c: %d > limit: %d\n", c, pos, limit); // p_DebugPrint(p, r, r, 1); |
---|
288 | #endif |
---|
289 | #endif |
---|
290 | |
---|
291 | c -= limit; |
---|
292 | assume( c > 0 ); |
---|
293 | c--; |
---|
294 | |
---|
295 | assume( c < IDELEMS(F) ); // What about others??? |
---|
296 | |
---|
297 | const poly pp = F->m[c]; // get reference monomial!!! |
---|
298 | |
---|
299 | #ifndef NDEBUG |
---|
300 | #if MYTEST |
---|
301 | Print("Respective F[c - %d: %d] pp: ", limit, c); |
---|
302 | p_DebugPrint(pp, r, r, 1); |
---|
303 | #endif |
---|
304 | #endif |
---|
305 | |
---|
306 | |
---|
307 | assume(pp != NULL); |
---|
308 | if(pp == NULL) break; |
---|
309 | |
---|
310 | const int start = o->data.is.start; |
---|
311 | const int end = o->data.is.end; |
---|
312 | |
---|
313 | assume(start <= end); |
---|
314 | |
---|
315 | // const int limit = o->data.is.limit; |
---|
316 | assume( limit >= 0 ); |
---|
317 | |
---|
318 | // const int st = o->data.isTemp.start; |
---|
319 | |
---|
320 | if( c > limit ) |
---|
321 | p->exp[start] = 1; |
---|
322 | // else |
---|
323 | // p->exp[start] = 0; |
---|
324 | |
---|
325 | |
---|
326 | #ifndef NDEBUG |
---|
327 | Print("p_Setm_General: is(-Temp-) :: c: %d, limit: %d, [st:%d] ===>>> %ld\n", c, limit, start, p->exp[start]); |
---|
328 | #endif |
---|
329 | |
---|
330 | |
---|
331 | for( int i = start; i <= end; i++) // v[0] may be here... |
---|
332 | p->exp[i] += pp->exp[i]; // !!!!!!!! ADD corresponding LT(F) |
---|
333 | |
---|
334 | |
---|
335 | |
---|
336 | |
---|
337 | #ifndef NDEBUG |
---|
338 | const int* const pVarOffset = o->data.is.pVarOffset; |
---|
339 | |
---|
340 | assume( pVarOffset != NULL ); |
---|
341 | |
---|
342 | for( int i = 1; i <= r->N; i++ ) // No v[0] here!!! |
---|
343 | { |
---|
344 | const int vo = pVarOffset[i]; |
---|
345 | if( vo != -1) // TODO: optimize: can be done once! |
---|
346 | // Hans! Please don't break it again! p_GetExp(p/pp, r, vo) is correct: |
---|
347 | assume( p_GetExp(p, r, vo) == (p_GetExp(p, i, r) + p_GetExp(pp, r, vo)) ); |
---|
348 | } |
---|
349 | // TODO: how to check this for computed values??? |
---|
350 | #endif |
---|
351 | } else |
---|
352 | { |
---|
353 | const int* const pVarOffset = o->data.is.pVarOffset; |
---|
354 | |
---|
355 | // What about v[0] - component: it will be added later by |
---|
356 | // suffix!!! |
---|
357 | // TODO: Test it! |
---|
358 | const int vo = pVarOffset[0]; |
---|
359 | if( vo != -1 ) |
---|
360 | p->exp[vo] = c; // initial component v[0]! |
---|
361 | |
---|
362 | #ifndef NDEBUG |
---|
363 | #if MYTEST |
---|
364 | Print("p_Setm_General: ro_is :: c: %d <= limit: %d, vo: %d, exp: %d\n", c, limit, vo, p->exp[vo]); |
---|
365 | p_DebugPrint(p, r, r, 1); |
---|
366 | #endif |
---|
367 | #endif |
---|
368 | } |
---|
369 | |
---|
370 | |
---|
371 | break; |
---|
372 | } |
---|
373 | default: |
---|
374 | dReportError("wrong ord in rSetm:%d\n",o->ord_typ); |
---|
375 | return; |
---|
376 | } |
---|
377 | pos++; |
---|
378 | if (pos == r->OrdSize) return; |
---|
379 | } |
---|
380 | } |
---|
381 | } |
---|
382 | |
---|
383 | void p_Setm_Syz(poly p, ring r, int* Components, long* ShiftedComponents) |
---|
384 | { |
---|
385 | _components = Components; |
---|
386 | _componentsShifted = ShiftedComponents; |
---|
387 | _componentsExternal = 1; |
---|
388 | p_Setm_General(p, r); |
---|
389 | _componentsExternal = 0; |
---|
390 | } |
---|
391 | |
---|
392 | // dummy for lp, ls, etc |
---|
393 | void p_Setm_Dummy(poly p, const ring r) |
---|
394 | { |
---|
395 | p_LmCheckPolyRing(p, r); |
---|
396 | } |
---|
397 | |
---|
398 | // for dp, Dp, ds, etc |
---|
399 | void p_Setm_TotalDegree(poly p, const ring r) |
---|
400 | { |
---|
401 | p_LmCheckPolyRing(p, r); |
---|
402 | p->exp[r->pOrdIndex] = p_Totaldegree(p, r); |
---|
403 | } |
---|
404 | |
---|
405 | // for wp, Wp, ws, etc |
---|
406 | void p_Setm_WFirstTotalDegree(poly p, const ring r) |
---|
407 | { |
---|
408 | p_LmCheckPolyRing(p, r); |
---|
409 | p->exp[r->pOrdIndex] = p_WFirstTotalDegree(p, r); |
---|
410 | } |
---|
411 | |
---|
412 | p_SetmProc p_GetSetmProc(ring r) |
---|
413 | { |
---|
414 | // covers lp, rp, ls, |
---|
415 | if (r->typ == NULL) return p_Setm_Dummy; |
---|
416 | |
---|
417 | if (r->OrdSize == 1) |
---|
418 | { |
---|
419 | if (r->typ[0].ord_typ == ro_dp && |
---|
420 | r->typ[0].data.dp.start == 1 && |
---|
421 | r->typ[0].data.dp.end == r->N && |
---|
422 | r->typ[0].data.dp.place == r->pOrdIndex) |
---|
423 | return p_Setm_TotalDegree; |
---|
424 | if (r->typ[0].ord_typ == ro_wp && |
---|
425 | r->typ[0].data.wp.start == 1 && |
---|
426 | r->typ[0].data.wp.end == r->N && |
---|
427 | r->typ[0].data.wp.place == r->pOrdIndex && |
---|
428 | r->typ[0].data.wp.weights == r->firstwv) |
---|
429 | return p_Setm_WFirstTotalDegree; |
---|
430 | } |
---|
431 | return p_Setm_General; |
---|
432 | } |
---|
433 | |
---|
434 | |
---|
435 | /* -------------------------------------------------------------------*/ |
---|
436 | /* several possibilities for pFDeg: the degree of the head term */ |
---|
437 | |
---|
438 | /* comptible with ordering */ |
---|
439 | long p_Deg(poly a, const ring r) |
---|
440 | { |
---|
441 | p_LmCheckPolyRing(a, r); |
---|
442 | assume(p_GetOrder(a, r) == p_WTotaldegree(a, r)); |
---|
443 | return p_GetOrder(a, r); |
---|
444 | } |
---|
445 | |
---|
446 | // p_WTotalDegree for weighted orderings |
---|
447 | // whose first block covers all variables |
---|
448 | long p_WFirstTotalDegree(poly p, const ring r) |
---|
449 | { |
---|
450 | int i; |
---|
451 | long sum = 0; |
---|
452 | |
---|
453 | for (i=1; i<= r->firstBlockEnds; i++) |
---|
454 | { |
---|
455 | sum += p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
456 | } |
---|
457 | return sum; |
---|
458 | } |
---|
459 | |
---|
460 | /*2 |
---|
461 | * compute the degree of the leading monomial of p |
---|
462 | * with respect to weigths from the ordering |
---|
463 | * the ordering is not compatible with degree so do not use p->Order |
---|
464 | */ |
---|
465 | long p_WTotaldegree(poly p, const ring r) |
---|
466 | { |
---|
467 | p_LmCheckPolyRing(p, r); |
---|
468 | int i, k; |
---|
469 | long j =0; |
---|
470 | |
---|
471 | // iterate through each block: |
---|
472 | for (i=0;r->order[i]!=0;i++) |
---|
473 | { |
---|
474 | int b0=r->block0[i]; |
---|
475 | int b1=r->block1[i]; |
---|
476 | switch(r->order[i]) |
---|
477 | { |
---|
478 | case ringorder_M: |
---|
479 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
480 | { // in jedem block: |
---|
481 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]*r->OrdSgn; |
---|
482 | } |
---|
483 | break; |
---|
484 | case ringorder_wp: |
---|
485 | case ringorder_ws: |
---|
486 | case ringorder_Wp: |
---|
487 | case ringorder_Ws: |
---|
488 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
489 | { // in jedem block: |
---|
490 | j+= p_GetExp(p,k,r)*r->wvhdl[i][k - b0 /*r->block0[i]*/]; |
---|
491 | } |
---|
492 | break; |
---|
493 | case ringorder_lp: |
---|
494 | case ringorder_ls: |
---|
495 | case ringorder_rs: |
---|
496 | case ringorder_dp: |
---|
497 | case ringorder_ds: |
---|
498 | case ringorder_Dp: |
---|
499 | case ringorder_Ds: |
---|
500 | case ringorder_rp: |
---|
501 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
502 | { |
---|
503 | j+= p_GetExp(p,k,r); |
---|
504 | } |
---|
505 | break; |
---|
506 | case ringorder_a64: |
---|
507 | { |
---|
508 | int64* w=(int64*)r->wvhdl[i]; |
---|
509 | for (k=0;k<=(b1 /*r->block1[i]*/ - b0 /*r->block0[i]*/);k++) |
---|
510 | { |
---|
511 | //there should be added a line which checks if w[k]>2^31 |
---|
512 | j+= p_GetExp(p,k+1, r)*(long)w[k]; |
---|
513 | } |
---|
514 | //break; |
---|
515 | return j; |
---|
516 | } |
---|
517 | case ringorder_c: |
---|
518 | case ringorder_C: |
---|
519 | case ringorder_S: |
---|
520 | case ringorder_s: |
---|
521 | case ringorder_IS: |
---|
522 | case ringorder_aa: |
---|
523 | break; |
---|
524 | case ringorder_a: |
---|
525 | for (k=b0 /*r->block0[i]*/;k<=b1 /*r->block1[i]*/;k++) |
---|
526 | { // only one line |
---|
527 | j+= p_GetExp(p,k, r)*r->wvhdl[i][ k- b0 /*r->block0[i]*/]; |
---|
528 | } |
---|
529 | //break; |
---|
530 | return j; |
---|
531 | |
---|
532 | #ifndef NDEBUG |
---|
533 | default: |
---|
534 | Print("missing order %d in p_WTotaldegree\n",r->order[i]); |
---|
535 | break; |
---|
536 | #endif |
---|
537 | } |
---|
538 | } |
---|
539 | return j; |
---|
540 | } |
---|
541 | |
---|
542 | long p_DegW(poly p, const short *w, const ring R) |
---|
543 | { |
---|
544 | long r=~0L; |
---|
545 | |
---|
546 | while (p!=NULL) |
---|
547 | { |
---|
548 | long t=totaldegreeWecart_IV(p,R,w); |
---|
549 | if (t>r) r=t; |
---|
550 | pIter(p); |
---|
551 | } |
---|
552 | return r; |
---|
553 | } |
---|
554 | |
---|
555 | int p_Weight(int i, const ring r) |
---|
556 | { |
---|
557 | if ((r->firstwv==NULL) || (i>r->firstBlockEnds)) |
---|
558 | { |
---|
559 | return 1; |
---|
560 | } |
---|
561 | return r->firstwv[i-1]; |
---|
562 | } |
---|
563 | |
---|
564 | long p_WDegree(poly p, const ring r) |
---|
565 | { |
---|
566 | if (r->firstwv==NULL) return p_Totaldegree(p, r); |
---|
567 | p_LmCheckPolyRing(p, r); |
---|
568 | int i; |
---|
569 | long j =0; |
---|
570 | |
---|
571 | for(i=1;i<=r->firstBlockEnds;i++) |
---|
572 | j+=p_GetExp(p, i, r)*r->firstwv[i-1]; |
---|
573 | |
---|
574 | for (;i<=r->N;i++) |
---|
575 | j+=p_GetExp(p,i, r)*p_Weight(i, r); |
---|
576 | |
---|
577 | return j; |
---|
578 | } |
---|
579 | |
---|
580 | |
---|
581 | /* ---------------------------------------------------------------------*/ |
---|
582 | /* several possibilities for pLDeg: the maximal degree of a monomial in p*/ |
---|
583 | /* compute in l also the pLength of p */ |
---|
584 | |
---|
585 | /*2 |
---|
586 | * compute the length of a polynomial (in l) |
---|
587 | * and the degree of the monomial with maximal degree: the last one |
---|
588 | */ |
---|
589 | long pLDeg0(poly p,int *l, const ring r) |
---|
590 | { |
---|
591 | p_CheckPolyRing(p, r); |
---|
592 | long k= p_GetComp(p, r); |
---|
593 | int ll=1; |
---|
594 | |
---|
595 | if (k > 0) |
---|
596 | { |
---|
597 | while ((pNext(p)!=NULL) && (p_GetComp(pNext(p), r)==k)) |
---|
598 | { |
---|
599 | pIter(p); |
---|
600 | ll++; |
---|
601 | } |
---|
602 | } |
---|
603 | else |
---|
604 | { |
---|
605 | while (pNext(p)!=NULL) |
---|
606 | { |
---|
607 | pIter(p); |
---|
608 | ll++; |
---|
609 | } |
---|
610 | } |
---|
611 | *l=ll; |
---|
612 | return r->pFDeg(p, r); |
---|
613 | } |
---|
614 | |
---|
615 | /*2 |
---|
616 | * compute the length of a polynomial (in l) |
---|
617 | * and the degree of the monomial with maximal degree: the last one |
---|
618 | * but search in all components before syzcomp |
---|
619 | */ |
---|
620 | long pLDeg0c(poly p,int *l, const ring r) |
---|
621 | { |
---|
622 | assume(p!=NULL); |
---|
623 | #ifdef PDEBUG |
---|
624 | _p_Test(p,r,PDEBUG); |
---|
625 | #endif |
---|
626 | p_CheckPolyRing(p, r); |
---|
627 | long o; |
---|
628 | int ll=1; |
---|
629 | |
---|
630 | if (! rIsSyzIndexRing(r)) |
---|
631 | { |
---|
632 | while (pNext(p) != NULL) |
---|
633 | { |
---|
634 | pIter(p); |
---|
635 | ll++; |
---|
636 | } |
---|
637 | o = r->pFDeg(p, r); |
---|
638 | } |
---|
639 | else |
---|
640 | { |
---|
641 | int curr_limit = rGetCurrSyzLimit(r); |
---|
642 | poly pp = p; |
---|
643 | while ((p=pNext(p))!=NULL) |
---|
644 | { |
---|
645 | if (p_GetComp(p, r)<=curr_limit/*syzComp*/) |
---|
646 | ll++; |
---|
647 | else break; |
---|
648 | pp = p; |
---|
649 | } |
---|
650 | #ifdef PDEBUG |
---|
651 | _p_Test(pp,r,PDEBUG); |
---|
652 | #endif |
---|
653 | o = r->pFDeg(pp, r); |
---|
654 | } |
---|
655 | *l=ll; |
---|
656 | return o; |
---|
657 | } |
---|
658 | |
---|
659 | /*2 |
---|
660 | * compute the length of a polynomial (in l) |
---|
661 | * and the degree of the monomial with maximal degree: the first one |
---|
662 | * this works for the polynomial case with degree orderings |
---|
663 | * (both c,dp and dp,c) |
---|
664 | */ |
---|
665 | long pLDegb(poly p,int *l, const ring r) |
---|
666 | { |
---|
667 | p_CheckPolyRing(p, r); |
---|
668 | long k= p_GetComp(p, r); |
---|
669 | long o = r->pFDeg(p, r); |
---|
670 | int ll=1; |
---|
671 | |
---|
672 | if (k != 0) |
---|
673 | { |
---|
674 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
675 | { |
---|
676 | ll++; |
---|
677 | } |
---|
678 | } |
---|
679 | else |
---|
680 | { |
---|
681 | while ((p=pNext(p)) !=NULL) |
---|
682 | { |
---|
683 | ll++; |
---|
684 | } |
---|
685 | } |
---|
686 | *l=ll; |
---|
687 | return o; |
---|
688 | } |
---|
689 | |
---|
690 | /*2 |
---|
691 | * compute the length of a polynomial (in l) |
---|
692 | * and the degree of the monomial with maximal degree: |
---|
693 | * this is NOT the last one, we have to look for it |
---|
694 | */ |
---|
695 | long pLDeg1(poly p,int *l, const ring r) |
---|
696 | { |
---|
697 | p_CheckPolyRing(p, r); |
---|
698 | long k= p_GetComp(p, r); |
---|
699 | int ll=1; |
---|
700 | long t,max; |
---|
701 | |
---|
702 | max=r->pFDeg(p, r); |
---|
703 | if (k > 0) |
---|
704 | { |
---|
705 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
706 | { |
---|
707 | t=r->pFDeg(p, r); |
---|
708 | if (t>max) max=t; |
---|
709 | ll++; |
---|
710 | } |
---|
711 | } |
---|
712 | else |
---|
713 | { |
---|
714 | while ((p=pNext(p))!=NULL) |
---|
715 | { |
---|
716 | t=r->pFDeg(p, r); |
---|
717 | if (t>max) max=t; |
---|
718 | ll++; |
---|
719 | } |
---|
720 | } |
---|
721 | *l=ll; |
---|
722 | return max; |
---|
723 | } |
---|
724 | |
---|
725 | /*2 |
---|
726 | * compute the length of a polynomial (in l) |
---|
727 | * and the degree of the monomial with maximal degree: |
---|
728 | * this is NOT the last one, we have to look for it |
---|
729 | * in all components |
---|
730 | */ |
---|
731 | long pLDeg1c(poly p,int *l, const ring r) |
---|
732 | { |
---|
733 | p_CheckPolyRing(p, r); |
---|
734 | int ll=1; |
---|
735 | long t,max; |
---|
736 | |
---|
737 | max=r->pFDeg(p, r); |
---|
738 | if (rIsSyzIndexRing(r)) |
---|
739 | { |
---|
740 | long limit = rGetCurrSyzLimit(r); |
---|
741 | while ((p=pNext(p))!=NULL) |
---|
742 | { |
---|
743 | if (p_GetComp(p, r)<=limit) |
---|
744 | { |
---|
745 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
746 | ll++; |
---|
747 | } |
---|
748 | else break; |
---|
749 | } |
---|
750 | } |
---|
751 | else |
---|
752 | { |
---|
753 | while ((p=pNext(p))!=NULL) |
---|
754 | { |
---|
755 | if ((t=r->pFDeg(p, r))>max) max=t; |
---|
756 | ll++; |
---|
757 | } |
---|
758 | } |
---|
759 | *l=ll; |
---|
760 | return max; |
---|
761 | } |
---|
762 | |
---|
763 | // like pLDeg1, only pFDeg == pDeg |
---|
764 | long pLDeg1_Deg(poly p,int *l, const ring r) |
---|
765 | { |
---|
766 | assume(r->pFDeg == p_Deg); |
---|
767 | p_CheckPolyRing(p, r); |
---|
768 | long k= p_GetComp(p, r); |
---|
769 | int ll=1; |
---|
770 | long t,max; |
---|
771 | |
---|
772 | max=p_GetOrder(p, r); |
---|
773 | if (k > 0) |
---|
774 | { |
---|
775 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
776 | { |
---|
777 | t=p_GetOrder(p, r); |
---|
778 | if (t>max) max=t; |
---|
779 | ll++; |
---|
780 | } |
---|
781 | } |
---|
782 | else |
---|
783 | { |
---|
784 | while ((p=pNext(p))!=NULL) |
---|
785 | { |
---|
786 | t=p_GetOrder(p, r); |
---|
787 | if (t>max) max=t; |
---|
788 | ll++; |
---|
789 | } |
---|
790 | } |
---|
791 | *l=ll; |
---|
792 | return max; |
---|
793 | } |
---|
794 | |
---|
795 | long pLDeg1c_Deg(poly p,int *l, const ring r) |
---|
796 | { |
---|
797 | assume(r->pFDeg == p_Deg); |
---|
798 | p_CheckPolyRing(p, r); |
---|
799 | int ll=1; |
---|
800 | long t,max; |
---|
801 | |
---|
802 | max=p_GetOrder(p, r); |
---|
803 | if (rIsSyzIndexRing(r)) |
---|
804 | { |
---|
805 | long limit = rGetCurrSyzLimit(r); |
---|
806 | while ((p=pNext(p))!=NULL) |
---|
807 | { |
---|
808 | if (p_GetComp(p, r)<=limit) |
---|
809 | { |
---|
810 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
811 | ll++; |
---|
812 | } |
---|
813 | else break; |
---|
814 | } |
---|
815 | } |
---|
816 | else |
---|
817 | { |
---|
818 | while ((p=pNext(p))!=NULL) |
---|
819 | { |
---|
820 | if ((t=p_GetOrder(p, r))>max) max=t; |
---|
821 | ll++; |
---|
822 | } |
---|
823 | } |
---|
824 | *l=ll; |
---|
825 | return max; |
---|
826 | } |
---|
827 | |
---|
828 | // like pLDeg1, only pFDeg == pTotoalDegree |
---|
829 | long pLDeg1_Totaldegree(poly p,int *l, const ring r) |
---|
830 | { |
---|
831 | p_CheckPolyRing(p, r); |
---|
832 | long k= p_GetComp(p, r); |
---|
833 | int ll=1; |
---|
834 | long t,max; |
---|
835 | |
---|
836 | max=p_Totaldegree(p, r); |
---|
837 | if (k > 0) |
---|
838 | { |
---|
839 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
840 | { |
---|
841 | t=p_Totaldegree(p, r); |
---|
842 | if (t>max) max=t; |
---|
843 | ll++; |
---|
844 | } |
---|
845 | } |
---|
846 | else |
---|
847 | { |
---|
848 | while ((p=pNext(p))!=NULL) |
---|
849 | { |
---|
850 | t=p_Totaldegree(p, r); |
---|
851 | if (t>max) max=t; |
---|
852 | ll++; |
---|
853 | } |
---|
854 | } |
---|
855 | *l=ll; |
---|
856 | return max; |
---|
857 | } |
---|
858 | |
---|
859 | long pLDeg1c_Totaldegree(poly p,int *l, const ring r) |
---|
860 | { |
---|
861 | p_CheckPolyRing(p, r); |
---|
862 | int ll=1; |
---|
863 | long t,max; |
---|
864 | |
---|
865 | max=p_Totaldegree(p, r); |
---|
866 | if (rIsSyzIndexRing(r)) |
---|
867 | { |
---|
868 | long limit = rGetCurrSyzLimit(r); |
---|
869 | while ((p=pNext(p))!=NULL) |
---|
870 | { |
---|
871 | if (p_GetComp(p, r)<=limit) |
---|
872 | { |
---|
873 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
874 | ll++; |
---|
875 | } |
---|
876 | else break; |
---|
877 | } |
---|
878 | } |
---|
879 | else |
---|
880 | { |
---|
881 | while ((p=pNext(p))!=NULL) |
---|
882 | { |
---|
883 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
884 | ll++; |
---|
885 | } |
---|
886 | } |
---|
887 | *l=ll; |
---|
888 | return max; |
---|
889 | } |
---|
890 | |
---|
891 | // like pLDeg1, only pFDeg == p_WFirstTotalDegree |
---|
892 | long pLDeg1_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
893 | { |
---|
894 | p_CheckPolyRing(p, r); |
---|
895 | long k= p_GetComp(p, r); |
---|
896 | int ll=1; |
---|
897 | long t,max; |
---|
898 | |
---|
899 | max=p_WFirstTotalDegree(p, r); |
---|
900 | if (k > 0) |
---|
901 | { |
---|
902 | while (((p=pNext(p))!=NULL) && (p_GetComp(p, r)==k)) |
---|
903 | { |
---|
904 | t=p_WFirstTotalDegree(p, r); |
---|
905 | if (t>max) max=t; |
---|
906 | ll++; |
---|
907 | } |
---|
908 | } |
---|
909 | else |
---|
910 | { |
---|
911 | while ((p=pNext(p))!=NULL) |
---|
912 | { |
---|
913 | t=p_WFirstTotalDegree(p, r); |
---|
914 | if (t>max) max=t; |
---|
915 | ll++; |
---|
916 | } |
---|
917 | } |
---|
918 | *l=ll; |
---|
919 | return max; |
---|
920 | } |
---|
921 | |
---|
922 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, const ring r) |
---|
923 | { |
---|
924 | p_CheckPolyRing(p, r); |
---|
925 | int ll=1; |
---|
926 | long t,max; |
---|
927 | |
---|
928 | max=p_WFirstTotalDegree(p, r); |
---|
929 | if (rIsSyzIndexRing(r)) |
---|
930 | { |
---|
931 | long limit = rGetCurrSyzLimit(r); |
---|
932 | while ((p=pNext(p))!=NULL) |
---|
933 | { |
---|
934 | if (p_GetComp(p, r)<=limit) |
---|
935 | { |
---|
936 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
937 | ll++; |
---|
938 | } |
---|
939 | else break; |
---|
940 | } |
---|
941 | } |
---|
942 | else |
---|
943 | { |
---|
944 | while ((p=pNext(p))!=NULL) |
---|
945 | { |
---|
946 | if ((t=p_Totaldegree(p, r))>max) max=t; |
---|
947 | ll++; |
---|
948 | } |
---|
949 | } |
---|
950 | *l=ll; |
---|
951 | return max; |
---|
952 | } |
---|
953 | |
---|
954 | /*************************************************************** |
---|
955 | * |
---|
956 | * Maximal Exponent business |
---|
957 | * |
---|
958 | ***************************************************************/ |
---|
959 | |
---|
960 | static inline unsigned long |
---|
961 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r, |
---|
962 | unsigned long number_of_exp) |
---|
963 | { |
---|
964 | const unsigned long bitmask = r->bitmask; |
---|
965 | unsigned long ml1 = l1 & bitmask; |
---|
966 | unsigned long ml2 = l2 & bitmask; |
---|
967 | unsigned long max = (ml1 > ml2 ? ml1 : ml2); |
---|
968 | unsigned long j = number_of_exp - 1; |
---|
969 | |
---|
970 | if (j > 0) |
---|
971 | { |
---|
972 | unsigned long mask = bitmask << r->BitsPerExp; |
---|
973 | while (1) |
---|
974 | { |
---|
975 | ml1 = l1 & mask; |
---|
976 | ml2 = l2 & mask; |
---|
977 | max |= ((ml1 > ml2 ? ml1 : ml2) & mask); |
---|
978 | j--; |
---|
979 | if (j == 0) break; |
---|
980 | mask = mask << r->BitsPerExp; |
---|
981 | } |
---|
982 | } |
---|
983 | return max; |
---|
984 | } |
---|
985 | |
---|
986 | static inline unsigned long |
---|
987 | p_GetMaxExpL2(unsigned long l1, unsigned long l2, const ring r) |
---|
988 | { |
---|
989 | return p_GetMaxExpL2(l1, l2, r, r->ExpPerLong); |
---|
990 | } |
---|
991 | |
---|
992 | poly p_GetMaxExpP(poly p, const ring r) |
---|
993 | { |
---|
994 | p_CheckPolyRing(p, r); |
---|
995 | if (p == NULL) return p_Init(r); |
---|
996 | poly max = p_LmInit(p, r); |
---|
997 | pIter(p); |
---|
998 | if (p == NULL) return max; |
---|
999 | int i, offset; |
---|
1000 | unsigned long l_p, l_max; |
---|
1001 | unsigned long divmask = r->divmask; |
---|
1002 | |
---|
1003 | do |
---|
1004 | { |
---|
1005 | offset = r->VarL_Offset[0]; |
---|
1006 | l_p = p->exp[offset]; |
---|
1007 | l_max = max->exp[offset]; |
---|
1008 | // do the divisibility trick to find out whether l has an exponent |
---|
1009 | if (l_p > l_max || |
---|
1010 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1011 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
1012 | |
---|
1013 | for (i=1; i<r->VarL_Size; i++) |
---|
1014 | { |
---|
1015 | offset = r->VarL_Offset[i]; |
---|
1016 | l_p = p->exp[offset]; |
---|
1017 | l_max = max->exp[offset]; |
---|
1018 | // do the divisibility trick to find out whether l has an exponent |
---|
1019 | if (l_p > l_max || |
---|
1020 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1021 | max->exp[offset] = p_GetMaxExpL2(l_max, l_p, r); |
---|
1022 | } |
---|
1023 | pIter(p); |
---|
1024 | } |
---|
1025 | while (p != NULL); |
---|
1026 | return max; |
---|
1027 | } |
---|
1028 | |
---|
1029 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max) |
---|
1030 | { |
---|
1031 | unsigned long l_p, divmask = r->divmask; |
---|
1032 | int i; |
---|
1033 | |
---|
1034 | while (p != NULL) |
---|
1035 | { |
---|
1036 | l_p = p->exp[r->VarL_Offset[0]]; |
---|
1037 | if (l_p > l_max || |
---|
1038 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1039 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
1040 | for (i=1; i<r->VarL_Size; i++) |
---|
1041 | { |
---|
1042 | l_p = p->exp[r->VarL_Offset[i]]; |
---|
1043 | // do the divisibility trick to find out whether l has an exponent |
---|
1044 | if (l_p > l_max || |
---|
1045 | (((l_max & divmask) ^ (l_p & divmask)) != ((l_max-l_p) & divmask))) |
---|
1046 | l_max = p_GetMaxExpL2(l_max, l_p, r); |
---|
1047 | } |
---|
1048 | pIter(p); |
---|
1049 | } |
---|
1050 | return l_max; |
---|
1051 | } |
---|
1052 | |
---|
1053 | |
---|
1054 | |
---|
1055 | |
---|
1056 | /*************************************************************** |
---|
1057 | * |
---|
1058 | * Misc things |
---|
1059 | * |
---|
1060 | ***************************************************************/ |
---|
1061 | // returns TRUE, if all monoms have the same component |
---|
1062 | BOOLEAN p_OneComp(poly p, const ring r) |
---|
1063 | { |
---|
1064 | if(p!=NULL) |
---|
1065 | { |
---|
1066 | long i = p_GetComp(p, r); |
---|
1067 | while (pNext(p)!=NULL) |
---|
1068 | { |
---|
1069 | pIter(p); |
---|
1070 | if(i != p_GetComp(p, r)) return FALSE; |
---|
1071 | } |
---|
1072 | } |
---|
1073 | return TRUE; |
---|
1074 | } |
---|
1075 | |
---|
1076 | /*2 |
---|
1077 | *test if a monomial /head term is a pure power |
---|
1078 | */ |
---|
1079 | int p_IsPurePower(const poly p, const ring r) |
---|
1080 | { |
---|
1081 | int i,k=0; |
---|
1082 | |
---|
1083 | for (i=r->N;i;i--) |
---|
1084 | { |
---|
1085 | if (p_GetExp(p,i, r)!=0) |
---|
1086 | { |
---|
1087 | if(k!=0) return 0; |
---|
1088 | k=i; |
---|
1089 | } |
---|
1090 | } |
---|
1091 | return k; |
---|
1092 | } |
---|
1093 | |
---|
1094 | /*2 |
---|
1095 | *test if a polynomial is univariate |
---|
1096 | * return -1 for constant, |
---|
1097 | * 0 for not univariate,s |
---|
1098 | * i if dep. on var(i) |
---|
1099 | */ |
---|
1100 | int p_IsUnivariate(poly p, const ring r) |
---|
1101 | { |
---|
1102 | int i,k=-1; |
---|
1103 | |
---|
1104 | while (p!=NULL) |
---|
1105 | { |
---|
1106 | for (i=r->N;i;i--) |
---|
1107 | { |
---|
1108 | if (p_GetExp(p,i, r)!=0) |
---|
1109 | { |
---|
1110 | if((k!=-1)&&(k!=i)) return 0; |
---|
1111 | k=i; |
---|
1112 | } |
---|
1113 | } |
---|
1114 | pIter(p); |
---|
1115 | } |
---|
1116 | return k; |
---|
1117 | } |
---|
1118 | |
---|
1119 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
---|
1120 | int p_GetVariables(poly p, int * e, const ring r) |
---|
1121 | { |
---|
1122 | int i; |
---|
1123 | int n=0; |
---|
1124 | while(p!=NULL) |
---|
1125 | { |
---|
1126 | n=0; |
---|
1127 | for(i=r->N; i>0; i--) |
---|
1128 | { |
---|
1129 | if(e[i]==0) |
---|
1130 | { |
---|
1131 | if (p_GetExp(p,i,r)>0) |
---|
1132 | { |
---|
1133 | e[i]=1; |
---|
1134 | n++; |
---|
1135 | } |
---|
1136 | } |
---|
1137 | else |
---|
1138 | n++; |
---|
1139 | } |
---|
1140 | if (n==r->N) break; |
---|
1141 | pIter(p); |
---|
1142 | } |
---|
1143 | return n; |
---|
1144 | } |
---|
1145 | |
---|
1146 | |
---|
1147 | /*2 |
---|
1148 | * returns a polynomial representing the integer i |
---|
1149 | */ |
---|
1150 | poly p_ISet(int i, const ring r) |
---|
1151 | { |
---|
1152 | poly rc = NULL; |
---|
1153 | if (i!=0) |
---|
1154 | { |
---|
1155 | rc = p_Init(r); |
---|
1156 | pSetCoeff0(rc,n_Init(i,r->cf)); |
---|
1157 | if (n_IsZero(pGetCoeff(rc),r->cf)) |
---|
1158 | p_LmDelete(&rc,r); |
---|
1159 | } |
---|
1160 | return rc; |
---|
1161 | } |
---|
1162 | |
---|
1163 | /*2 |
---|
1164 | * an optimized version of p_ISet for the special case 1 |
---|
1165 | */ |
---|
1166 | poly p_One(const ring r) |
---|
1167 | { |
---|
1168 | poly rc = p_Init(r); |
---|
1169 | pSetCoeff0(rc,n_Init(1,r->cf)); |
---|
1170 | return rc; |
---|
1171 | } |
---|
1172 | |
---|
1173 | void p_Split(poly p, poly *h) |
---|
1174 | { |
---|
1175 | *h=pNext(p); |
---|
1176 | pNext(p)=NULL; |
---|
1177 | } |
---|
1178 | |
---|
1179 | /*2 |
---|
1180 | * pair has no common factor ? or is no polynomial |
---|
1181 | */ |
---|
1182 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r) |
---|
1183 | { |
---|
1184 | |
---|
1185 | if (p_GetComp(p1,r) > 0 || p_GetComp(p2,r) > 0) |
---|
1186 | return FALSE; |
---|
1187 | int i = rVar(r); |
---|
1188 | loop |
---|
1189 | { |
---|
1190 | if ((p_GetExp(p1, i, r) > 0) && (p_GetExp(p2, i, r) > 0)) |
---|
1191 | return FALSE; |
---|
1192 | i--; |
---|
1193 | if (i == 0) |
---|
1194 | return TRUE; |
---|
1195 | } |
---|
1196 | } |
---|
1197 | |
---|
1198 | /*2 |
---|
1199 | * convert monomial given as string to poly, e.g. 1x3y5z |
---|
1200 | */ |
---|
1201 | const char * p_Read(const char *st, poly &rc, const ring r) |
---|
1202 | { |
---|
1203 | if (r==NULL) { rc=NULL;return st;} |
---|
1204 | int i,j; |
---|
1205 | rc = p_Init(r); |
---|
1206 | const char *s = r->cf->cfRead(st,&(rc->coef),r->cf); |
---|
1207 | if (s==st) |
---|
1208 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
---|
1209 | { |
---|
1210 | j = r_IsRingVar(s,r); |
---|
1211 | if (j >= 0) |
---|
1212 | { |
---|
1213 | p_IncrExp(rc,1+j,r); |
---|
1214 | while (*s!='\0') s++; |
---|
1215 | goto done; |
---|
1216 | } |
---|
1217 | } |
---|
1218 | while (*s!='\0') |
---|
1219 | { |
---|
1220 | char ss[2]; |
---|
1221 | ss[0] = *s++; |
---|
1222 | ss[1] = '\0'; |
---|
1223 | j = r_IsRingVar(ss,r); |
---|
1224 | if (j >= 0) |
---|
1225 | { |
---|
1226 | const char *s_save=s; |
---|
1227 | s = eati(s,&i); |
---|
1228 | if (((unsigned long)i) > r->bitmask) |
---|
1229 | { |
---|
1230 | // exponent to large: it is not a monomial |
---|
1231 | p_LmDelete(&rc,r); |
---|
1232 | return s_save; |
---|
1233 | } |
---|
1234 | p_AddExp(rc,1+j, (long)i, r); |
---|
1235 | } |
---|
1236 | else |
---|
1237 | { |
---|
1238 | // 1st char of is not a varname |
---|
1239 | p_LmDelete(&rc,r); |
---|
1240 | s--; |
---|
1241 | return s; |
---|
1242 | } |
---|
1243 | } |
---|
1244 | done: |
---|
1245 | if (n_IsZero(pGetCoeff(rc),r->cf)) p_LmDelete(&rc,r); |
---|
1246 | else |
---|
1247 | { |
---|
1248 | #ifdef HAVE_PLURAL |
---|
1249 | // in super-commutative ring |
---|
1250 | // squares of anti-commutative variables are zeroes! |
---|
1251 | if(rIsSCA(r)) |
---|
1252 | { |
---|
1253 | const unsigned int iFirstAltVar = scaFirstAltVar(r); |
---|
1254 | const unsigned int iLastAltVar = scaLastAltVar(r); |
---|
1255 | |
---|
1256 | assume(rc != NULL); |
---|
1257 | |
---|
1258 | for(unsigned int k = iFirstAltVar; k <= iLastAltVar; k++) |
---|
1259 | if( p_GetExp(rc, k, r) > 1 ) |
---|
1260 | { |
---|
1261 | p_LmDelete(&rc, r); |
---|
1262 | goto finish; |
---|
1263 | } |
---|
1264 | } |
---|
1265 | #endif |
---|
1266 | |
---|
1267 | p_Setm(rc,r); |
---|
1268 | } |
---|
1269 | finish: |
---|
1270 | return s; |
---|
1271 | } |
---|
1272 | poly p_mInit(const char *st, BOOLEAN &ok, const ring r) |
---|
1273 | { |
---|
1274 | poly p; |
---|
1275 | const char *s=p_Read(st,p,r); |
---|
1276 | if (*s!='\0') |
---|
1277 | { |
---|
1278 | if ((s!=st)&&isdigit(st[0])) |
---|
1279 | { |
---|
1280 | errorreported=TRUE; |
---|
1281 | } |
---|
1282 | ok=FALSE; |
---|
1283 | p_Delete(&p,r); |
---|
1284 | return NULL; |
---|
1285 | } |
---|
1286 | #ifdef PDEBUG |
---|
1287 | _p_Test(p,r,PDEBUG); |
---|
1288 | #endif |
---|
1289 | ok=!errorreported; |
---|
1290 | return p; |
---|
1291 | } |
---|
1292 | |
---|
1293 | /*2 |
---|
1294 | * returns a polynomial representing the number n |
---|
1295 | * destroys n |
---|
1296 | */ |
---|
1297 | poly p_NSet(number n, const ring r) |
---|
1298 | { |
---|
1299 | if (n_IsZero(n,r->cf)) |
---|
1300 | { |
---|
1301 | n_Delete(&n, r->cf); |
---|
1302 | return NULL; |
---|
1303 | } |
---|
1304 | else |
---|
1305 | { |
---|
1306 | poly rc = p_Init(r); |
---|
1307 | pSetCoeff0(rc,n); |
---|
1308 | return rc; |
---|
1309 | } |
---|
1310 | } |
---|
1311 | /*2 |
---|
1312 | * assumes that LM(a) = LM(b)*m, for some monomial m, |
---|
1313 | * returns the multiplicant m, |
---|
1314 | * leaves a and b unmodified |
---|
1315 | */ |
---|
1316 | poly p_Divide(poly a, poly b, const ring r) |
---|
1317 | { |
---|
1318 | assume((p_GetComp(a,r)==p_GetComp(b,r)) || (p_GetComp(b,r)==0)); |
---|
1319 | int i; |
---|
1320 | poly result = p_Init(r); |
---|
1321 | |
---|
1322 | for(i=(int)r->N; i; i--) |
---|
1323 | p_SetExp(result,i, p_GetExp(a,i,r)- p_GetExp(b,i,r),r); |
---|
1324 | p_SetComp(result, p_GetComp(a,r) - p_GetComp(b,r),r); |
---|
1325 | p_Setm(result,r); |
---|
1326 | return result; |
---|
1327 | } |
---|
1328 | |
---|
1329 | poly p_Div_nn(poly p, const number n, const ring r) |
---|
1330 | { |
---|
1331 | pAssume(!n_IsZero(n,r->cf)); |
---|
1332 | p_Test(p, r); |
---|
1333 | |
---|
1334 | poly q = p; |
---|
1335 | while (p != NULL) |
---|
1336 | { |
---|
1337 | number nc = pGetCoeff(p); |
---|
1338 | pSetCoeff0(p, n_Div(nc, n, r->cf)); |
---|
1339 | n_Delete(&nc, r->cf); |
---|
1340 | pIter(p); |
---|
1341 | } |
---|
1342 | p_Test(q, r); |
---|
1343 | return q; |
---|
1344 | } |
---|
1345 | |
---|
1346 | /*2 |
---|
1347 | * divides a by the monomial b, ignores monomials which are not divisible |
---|
1348 | * assumes that b is not NULL, destroyes b |
---|
1349 | */ |
---|
1350 | poly p_DivideM(poly a, poly b, const ring r) |
---|
1351 | { |
---|
1352 | if (a==NULL) { p_Delete(&b,r); return NULL; } |
---|
1353 | poly result=a; |
---|
1354 | poly prev=NULL; |
---|
1355 | int i; |
---|
1356 | #ifdef HAVE_RINGS |
---|
1357 | number inv=pGetCoeff(b); |
---|
1358 | #else |
---|
1359 | number inv=n_Invers(pGetCoeff(b),r->cf); |
---|
1360 | #endif |
---|
1361 | |
---|
1362 | while (a!=NULL) |
---|
1363 | { |
---|
1364 | if (p_DivisibleBy(b,a,r)) |
---|
1365 | { |
---|
1366 | for(i=(int)r->N; i; i--) |
---|
1367 | p_SubExp(a,i, p_GetExp(b,i,r),r); |
---|
1368 | p_SubComp(a, p_GetComp(b,r),r); |
---|
1369 | p_Setm(a,r); |
---|
1370 | prev=a; |
---|
1371 | pIter(a); |
---|
1372 | } |
---|
1373 | else |
---|
1374 | { |
---|
1375 | if (prev==NULL) |
---|
1376 | { |
---|
1377 | p_LmDelete(&result,r); |
---|
1378 | a=result; |
---|
1379 | } |
---|
1380 | else |
---|
1381 | { |
---|
1382 | p_LmDelete(&pNext(prev),r); |
---|
1383 | a=pNext(prev); |
---|
1384 | } |
---|
1385 | } |
---|
1386 | } |
---|
1387 | #ifdef HAVE_RINGS |
---|
1388 | if (n_IsUnit(inv,r->cf)) |
---|
1389 | { |
---|
1390 | inv = n_Invers(inv,r->cf); |
---|
1391 | p_Mult_nn(result,inv,r); |
---|
1392 | n_Delete(&inv, r->cf); |
---|
1393 | } |
---|
1394 | else |
---|
1395 | { |
---|
1396 | p_Div_nn(result,inv,r); |
---|
1397 | } |
---|
1398 | #else |
---|
1399 | p_Mult_nn(result,inv,r); |
---|
1400 | n_Delete(&inv, r->cf); |
---|
1401 | #endif |
---|
1402 | p_Delete(&b, r); |
---|
1403 | return result; |
---|
1404 | } |
---|
1405 | |
---|
1406 | #ifdef HAVE_RINGS |
---|
1407 | /* TRUE iff LT(f) | LT(g) */ |
---|
1408 | BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r) |
---|
1409 | { |
---|
1410 | int exponent; |
---|
1411 | for(int i = (int)rVar(r); i>0; i--) |
---|
1412 | { |
---|
1413 | exponent = p_GetExp(g, i, r) - p_GetExp(f, i, r); |
---|
1414 | if (exponent < 0) return FALSE; |
---|
1415 | } |
---|
1416 | return n_DivBy(pGetCoeff(g), pGetCoeff(f), r->cf); |
---|
1417 | } |
---|
1418 | #endif |
---|
1419 | |
---|
1420 | /*2 |
---|
1421 | * returns the LCM of the head terms of a and b in *m |
---|
1422 | */ |
---|
1423 | void p_Lcm(poly a, poly b, poly m, const ring r) |
---|
1424 | { |
---|
1425 | int i; |
---|
1426 | for (i=rVar(r); i; i--) |
---|
1427 | { |
---|
1428 | p_SetExp(m,i, si_max( p_GetExp(a,i,r), p_GetExp(b,i,r)),r); |
---|
1429 | } |
---|
1430 | p_SetComp(m, si_max(p_GetComp(a,r), p_GetComp(b,r)),r); |
---|
1431 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
---|
1432 | } |
---|
1433 | |
---|
1434 | /* assumes that p and divisor are univariate polynomials in r, |
---|
1435 | mentioning the same variable; |
---|
1436 | assumes divisor != NULL; |
---|
1437 | p may be NULL; |
---|
1438 | assumes a global monomial ordering in r; |
---|
1439 | performs polynomial division of p by divisor: |
---|
1440 | - afterwards p contains the remainder of the division, i.e., |
---|
1441 | p_before = result * divisor + p_afterwards; |
---|
1442 | - if needResult == TRUE, then the method computes and returns 'result', |
---|
1443 | otherwise NULL is returned (This parametrization can be used when |
---|
1444 | one is only interested in the remainder of the division. In this |
---|
1445 | case, the method will be slightly faster.) |
---|
1446 | leaves divisor unmodified */ |
---|
1447 | poly p_PolyDiv(poly &p, poly divisor, BOOLEAN needResult, ring r) |
---|
1448 | { |
---|
1449 | assume(divisor != NULL); |
---|
1450 | if (p == NULL) return NULL; |
---|
1451 | |
---|
1452 | poly result = NULL; |
---|
1453 | number divisorLC = p_GetCoeff(divisor, r); |
---|
1454 | int divisorLE = p_GetExp(divisor, 1, r); |
---|
1455 | while ((p != NULL) && (p_Deg(p, r) >= p_Deg(divisor, r))) |
---|
1456 | { |
---|
1457 | /* determine t = LT(p) / LT(divisor) */ |
---|
1458 | poly t = p_ISet(1, r); |
---|
1459 | number c = n_Div(p_GetCoeff(p, r), divisorLC, r->cf); |
---|
1460 | p_SetCoeff(t, c, r); |
---|
1461 | int e = p_GetExp(p, 1, r) - divisorLE; |
---|
1462 | p_SetExp(t, 1, e, r); |
---|
1463 | p_Setm(t, r); |
---|
1464 | if (needResult) result = p_Add_q(result, p_Copy(t, r), r); |
---|
1465 | p = p_Add_q(p, p_Neg(p_Mult_q(t, p_Copy(divisor, r), r), r), r); |
---|
1466 | } |
---|
1467 | return result; |
---|
1468 | } |
---|
1469 | |
---|
1470 | /* returns NULL if p == NULL, otherwise makes p monic by dividing |
---|
1471 | by its leading coefficient (only done if this is not already 1); |
---|
1472 | this assumes that we are over a ground field so that division |
---|
1473 | is well-defined; |
---|
1474 | modifies p */ |
---|
1475 | void p_Monic(poly &p, ring r) |
---|
1476 | { |
---|
1477 | if (p == NULL) return; |
---|
1478 | poly pp = p; |
---|
1479 | number lc = p_GetCoeff(p, r); |
---|
1480 | if (n_IsOne(lc, r->cf)) return; |
---|
1481 | number lcInverse = n_Invers(lc, r->cf); |
---|
1482 | number n = n_Init(1, r->cf); |
---|
1483 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
1484 | p = pIter(p); |
---|
1485 | while (p != NULL) |
---|
1486 | { |
---|
1487 | number n = n_Mult(p_GetCoeff(p, r), lcInverse, r->cf); |
---|
1488 | p_SetCoeff(p, n, r); // destroys old leading coefficient! |
---|
1489 | p = pIter(p); |
---|
1490 | } |
---|
1491 | n_Delete(&lcInverse, r->cf); |
---|
1492 | p = pp; |
---|
1493 | } |
---|
1494 | |
---|
1495 | /* see p_Gcd; |
---|
1496 | additional assumption: deg(p) >= deg(q); |
---|
1497 | must destroy p and q (unless one of them is returned) */ |
---|
1498 | poly p_GcdHelper(poly &p, poly &q, ring r) |
---|
1499 | { |
---|
1500 | if (q == NULL) |
---|
1501 | { |
---|
1502 | /* We have to make p monic before we return it, so that if the |
---|
1503 | gcd is a unit in the ground field, we will actually return 1. */ |
---|
1504 | p_Monic(p, r); |
---|
1505 | return p; |
---|
1506 | } |
---|
1507 | else |
---|
1508 | { |
---|
1509 | p_PolyDiv(p, q, FALSE, r); |
---|
1510 | return p_GcdHelper(q, p, r); |
---|
1511 | } |
---|
1512 | } |
---|
1513 | |
---|
1514 | /* assumes that p and q are univariate polynomials in r, |
---|
1515 | mentioning the same variable; |
---|
1516 | assumes a global monomial ordering in r; |
---|
1517 | assumes that not both p and q are NULL; |
---|
1518 | returns the gcd of p and q; |
---|
1519 | leaves p and q unmodified */ |
---|
1520 | poly p_Gcd(poly p, poly q, ring r) |
---|
1521 | { |
---|
1522 | assume((p != NULL) || (q != NULL)); |
---|
1523 | |
---|
1524 | poly a = p; poly b = q; |
---|
1525 | if (p_Deg(a, r) < p_Deg(b, r)) { a = q; b = p; } |
---|
1526 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
1527 | return p_GcdHelper(a, b, r); |
---|
1528 | } |
---|
1529 | |
---|
1530 | /* see p_ExtGcd; |
---|
1531 | additional assumption: deg(p) >= deg(q); |
---|
1532 | must destroy p and q (unless one of them is returned) */ |
---|
1533 | poly p_ExtGcdHelper(poly &p, poly &pFactor, poly &q, poly &qFactor, |
---|
1534 | ring r) |
---|
1535 | { |
---|
1536 | if (q == NULL) |
---|
1537 | { |
---|
1538 | qFactor = NULL; |
---|
1539 | pFactor = p_ISet(1, r); |
---|
1540 | p_SetCoeff(pFactor, n_Invers(p_GetCoeff(p, r), r->cf), r); |
---|
1541 | p_Monic(p, r); |
---|
1542 | return p; |
---|
1543 | } |
---|
1544 | else |
---|
1545 | { |
---|
1546 | poly pDivQ = p_PolyDiv(p, q, TRUE, r); |
---|
1547 | poly ppFactor = NULL; poly qqFactor = NULL; |
---|
1548 | poly theGcd = p_ExtGcdHelper(q, qqFactor, p, ppFactor, r); |
---|
1549 | pFactor = ppFactor; |
---|
1550 | qFactor = p_Add_q(qqFactor, |
---|
1551 | p_Neg(p_Mult_q(pDivQ, p_Copy(ppFactor, r), r), r), |
---|
1552 | r); |
---|
1553 | return theGcd; |
---|
1554 | } |
---|
1555 | } |
---|
1556 | |
---|
1557 | /* assumes that p and q are univariate polynomials in r, |
---|
1558 | mentioning the same variable; |
---|
1559 | assumes a global monomial ordering in r; |
---|
1560 | assumes that not both p and q are NULL; |
---|
1561 | returns the gcd of p and q; |
---|
1562 | moreover, afterwards pFactor and qFactor contain appropriate |
---|
1563 | factors such that gcd(p, q) = p * pFactor + q * qFactor; |
---|
1564 | leaves p and q unmodified */ |
---|
1565 | poly p_ExtGcd(poly p, poly &pFactor, poly q, poly &qFactor, ring r) |
---|
1566 | { |
---|
1567 | assume((p != NULL) || (q != NULL)); |
---|
1568 | poly a = p; poly b = q; BOOLEAN aCorrespondsToP = TRUE; |
---|
1569 | if (p_Deg(a, r) < p_Deg(b, r)) |
---|
1570 | { a = q; b = p; aCorrespondsToP = FALSE; } |
---|
1571 | a = p_Copy(a, r); b = p_Copy(b, r); |
---|
1572 | poly aFactor = NULL; poly bFactor = NULL; |
---|
1573 | poly theGcd = p_ExtGcdHelper(a, aFactor, b, bFactor, r); |
---|
1574 | if (aCorrespondsToP) { pFactor = aFactor; qFactor = bFactor; } |
---|
1575 | else { pFactor = bFactor; qFactor = aFactor; } |
---|
1576 | return theGcd; |
---|
1577 | } |
---|
1578 | |
---|
1579 | /*2 |
---|
1580 | * returns the partial differentiate of a by the k-th variable |
---|
1581 | * does not destroy the input |
---|
1582 | */ |
---|
1583 | poly p_Diff(poly a, int k, const ring r) |
---|
1584 | { |
---|
1585 | poly res, f, last; |
---|
1586 | number t; |
---|
1587 | |
---|
1588 | last = res = NULL; |
---|
1589 | while (a!=NULL) |
---|
1590 | { |
---|
1591 | if (p_GetExp(a,k,r)!=0) |
---|
1592 | { |
---|
1593 | f = p_LmInit(a,r); |
---|
1594 | t = n_Init(p_GetExp(a,k,r),r->cf); |
---|
1595 | pSetCoeff0(f,n_Mult(t,pGetCoeff(a),r->cf)); |
---|
1596 | n_Delete(&t,r->cf); |
---|
1597 | if (n_IsZero(pGetCoeff(f),r->cf)) |
---|
1598 | p_LmDelete(&f,r); |
---|
1599 | else |
---|
1600 | { |
---|
1601 | p_DecrExp(f,k,r); |
---|
1602 | p_Setm(f,r); |
---|
1603 | if (res==NULL) |
---|
1604 | { |
---|
1605 | res=last=f; |
---|
1606 | } |
---|
1607 | else |
---|
1608 | { |
---|
1609 | pNext(last)=f; |
---|
1610 | last=f; |
---|
1611 | } |
---|
1612 | } |
---|
1613 | } |
---|
1614 | pIter(a); |
---|
1615 | } |
---|
1616 | return res; |
---|
1617 | } |
---|
1618 | |
---|
1619 | static poly p_DiffOpM(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
1620 | { |
---|
1621 | int i,j,s; |
---|
1622 | number n,h,hh; |
---|
1623 | poly p=p_One(r); |
---|
1624 | n=n_Mult(pGetCoeff(a),pGetCoeff(b),r->cf); |
---|
1625 | for(i=rVar(r);i>0;i--) |
---|
1626 | { |
---|
1627 | s=p_GetExp(b,i,r); |
---|
1628 | if (s<p_GetExp(a,i,r)) |
---|
1629 | { |
---|
1630 | n_Delete(&n,r->cf); |
---|
1631 | p_LmDelete(&p,r); |
---|
1632 | return NULL; |
---|
1633 | } |
---|
1634 | if (multiply) |
---|
1635 | { |
---|
1636 | for(j=p_GetExp(a,i,r); j>0;j--) |
---|
1637 | { |
---|
1638 | h = n_Init(s,r->cf); |
---|
1639 | hh=n_Mult(n,h,r->cf); |
---|
1640 | n_Delete(&h,r->cf); |
---|
1641 | n_Delete(&n,r->cf); |
---|
1642 | n=hh; |
---|
1643 | s--; |
---|
1644 | } |
---|
1645 | p_SetExp(p,i,s,r); |
---|
1646 | } |
---|
1647 | else |
---|
1648 | { |
---|
1649 | p_SetExp(p,i,s-p_GetExp(a,i,r),r); |
---|
1650 | } |
---|
1651 | } |
---|
1652 | p_Setm(p,r); |
---|
1653 | /*if (multiply)*/ p_SetCoeff(p,n,r); |
---|
1654 | if (n_IsZero(n,r->cf)) p=p_LmDeleteAndNext(p,r); // return NULL as p is a monomial |
---|
1655 | return p; |
---|
1656 | } |
---|
1657 | |
---|
1658 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r) |
---|
1659 | { |
---|
1660 | poly result=NULL; |
---|
1661 | poly h; |
---|
1662 | for(;a!=NULL;pIter(a)) |
---|
1663 | { |
---|
1664 | for(h=b;h!=NULL;pIter(h)) |
---|
1665 | { |
---|
1666 | result=p_Add_q(result,p_DiffOpM(a,h,multiply,r),r); |
---|
1667 | } |
---|
1668 | } |
---|
1669 | return result; |
---|
1670 | } |
---|
1671 | /*2 |
---|
1672 | * subtract p2 from p1, p1 and p2 are destroyed |
---|
1673 | * do not put attention on speed: the procedure is only used in the interpreter |
---|
1674 | */ |
---|
1675 | poly p_Sub(poly p1, poly p2, const ring r) |
---|
1676 | { |
---|
1677 | return p_Add_q(p1, p_Neg(p2,r),r); |
---|
1678 | } |
---|
1679 | |
---|
1680 | /*3 |
---|
1681 | * compute for a monomial m |
---|
1682 | * the power m^exp, exp > 1 |
---|
1683 | * destroys p |
---|
1684 | */ |
---|
1685 | static poly p_MonPower(poly p, int exp, const ring r) |
---|
1686 | { |
---|
1687 | int i; |
---|
1688 | |
---|
1689 | if(!n_IsOne(pGetCoeff(p),r->cf)) |
---|
1690 | { |
---|
1691 | number x, y; |
---|
1692 | y = pGetCoeff(p); |
---|
1693 | n_Power(y,exp,&x,r->cf); |
---|
1694 | n_Delete(&y,r->cf); |
---|
1695 | pSetCoeff0(p,x); |
---|
1696 | } |
---|
1697 | for (i=rVar(r); i!=0; i--) |
---|
1698 | { |
---|
1699 | p_MultExp(p,i, exp,r); |
---|
1700 | } |
---|
1701 | p_Setm(p,r); |
---|
1702 | return p; |
---|
1703 | } |
---|
1704 | |
---|
1705 | /*3 |
---|
1706 | * compute for monomials p*q |
---|
1707 | * destroys p, keeps q |
---|
1708 | */ |
---|
1709 | static void p_MonMult(poly p, poly q, const ring r) |
---|
1710 | { |
---|
1711 | number x, y; |
---|
1712 | |
---|
1713 | y = pGetCoeff(p); |
---|
1714 | x = n_Mult(y,pGetCoeff(q),r->cf); |
---|
1715 | n_Delete(&y,r->cf); |
---|
1716 | pSetCoeff0(p,x); |
---|
1717 | //for (int i=pVariables; i!=0; i--) |
---|
1718 | //{ |
---|
1719 | // pAddExp(p,i, pGetExp(q,i)); |
---|
1720 | //} |
---|
1721 | //p->Order += q->Order; |
---|
1722 | p_ExpVectorAdd(p,q,r); |
---|
1723 | } |
---|
1724 | |
---|
1725 | /*3 |
---|
1726 | * compute for monomials p*q |
---|
1727 | * keeps p, q |
---|
1728 | */ |
---|
1729 | static poly p_MonMultC(poly p, poly q, const ring rr) |
---|
1730 | { |
---|
1731 | number x; |
---|
1732 | poly r = p_Init(rr); |
---|
1733 | |
---|
1734 | x = n_Mult(pGetCoeff(p),pGetCoeff(q),rr->cf); |
---|
1735 | pSetCoeff0(r,x); |
---|
1736 | p_ExpVectorSum(r,p, q, rr); |
---|
1737 | return r; |
---|
1738 | } |
---|
1739 | |
---|
1740 | /*3 |
---|
1741 | * create binomial coef. |
---|
1742 | */ |
---|
1743 | static number* pnBin(int exp, const ring r) |
---|
1744 | { |
---|
1745 | int e, i, h; |
---|
1746 | number x, y, *bin=NULL; |
---|
1747 | |
---|
1748 | x = n_Init(exp,r->cf); |
---|
1749 | if (n_IsZero(x,r->cf)) |
---|
1750 | { |
---|
1751 | n_Delete(&x,r->cf); |
---|
1752 | return bin; |
---|
1753 | } |
---|
1754 | h = (exp >> 1) + 1; |
---|
1755 | bin = (number *)omAlloc0(h*sizeof(number)); |
---|
1756 | bin[1] = x; |
---|
1757 | if (exp < 4) |
---|
1758 | return bin; |
---|
1759 | i = exp - 1; |
---|
1760 | for (e=2; e<h; e++) |
---|
1761 | { |
---|
1762 | x = n_Init(i,r->cf); |
---|
1763 | i--; |
---|
1764 | y = n_Mult(x,bin[e-1],r->cf); |
---|
1765 | n_Delete(&x,r->cf); |
---|
1766 | x = n_Init(e,r->cf); |
---|
1767 | bin[e] = n_IntDiv(y,x,r->cf); |
---|
1768 | n_Delete(&x,r->cf); |
---|
1769 | n_Delete(&y,r->cf); |
---|
1770 | } |
---|
1771 | return bin; |
---|
1772 | } |
---|
1773 | |
---|
1774 | static void pnFreeBin(number *bin, int exp,const coeffs r) |
---|
1775 | { |
---|
1776 | int e, h = (exp >> 1) + 1; |
---|
1777 | |
---|
1778 | if (bin[1] != NULL) |
---|
1779 | { |
---|
1780 | for (e=1; e<h; e++) |
---|
1781 | n_Delete(&(bin[e]),r); |
---|
1782 | } |
---|
1783 | omFreeSize((ADDRESS)bin, h*sizeof(number)); |
---|
1784 | } |
---|
1785 | |
---|
1786 | /* |
---|
1787 | * compute for a poly p = head+tail, tail is monomial |
---|
1788 | * (head + tail)^exp, exp > 1 |
---|
1789 | * with binomial coef. |
---|
1790 | */ |
---|
1791 | static poly p_TwoMonPower(poly p, int exp, const ring r) |
---|
1792 | { |
---|
1793 | int eh, e; |
---|
1794 | long al; |
---|
1795 | poly *a; |
---|
1796 | poly tail, b, res, h; |
---|
1797 | number x; |
---|
1798 | number *bin = pnBin(exp,r); |
---|
1799 | |
---|
1800 | tail = pNext(p); |
---|
1801 | if (bin == NULL) |
---|
1802 | { |
---|
1803 | p_MonPower(p,exp,r); |
---|
1804 | p_MonPower(tail,exp,r); |
---|
1805 | #ifdef PDEBUG |
---|
1806 | p_Test(p,r); |
---|
1807 | #endif |
---|
1808 | return p; |
---|
1809 | } |
---|
1810 | eh = exp >> 1; |
---|
1811 | al = (exp + 1) * sizeof(poly); |
---|
1812 | a = (poly *)omAlloc(al); |
---|
1813 | a[1] = p; |
---|
1814 | for (e=1; e<exp; e++) |
---|
1815 | { |
---|
1816 | a[e+1] = p_MonMultC(a[e],p,r); |
---|
1817 | } |
---|
1818 | res = a[exp]; |
---|
1819 | b = p_Head(tail,r); |
---|
1820 | for (e=exp-1; e>eh; e--) |
---|
1821 | { |
---|
1822 | h = a[e]; |
---|
1823 | x = n_Mult(bin[exp-e],pGetCoeff(h),r->cf); |
---|
1824 | p_SetCoeff(h,x,r); |
---|
1825 | p_MonMult(h,b,r); |
---|
1826 | res = pNext(res) = h; |
---|
1827 | p_MonMult(b,tail,r); |
---|
1828 | } |
---|
1829 | for (e=eh; e!=0; e--) |
---|
1830 | { |
---|
1831 | h = a[e]; |
---|
1832 | x = n_Mult(bin[e],pGetCoeff(h),r->cf); |
---|
1833 | p_SetCoeff(h,x,r); |
---|
1834 | p_MonMult(h,b,r); |
---|
1835 | res = pNext(res) = h; |
---|
1836 | p_MonMult(b,tail,r); |
---|
1837 | } |
---|
1838 | p_LmDelete(&tail,r); |
---|
1839 | pNext(res) = b; |
---|
1840 | pNext(b) = NULL; |
---|
1841 | res = a[exp]; |
---|
1842 | omFreeSize((ADDRESS)a, al); |
---|
1843 | pnFreeBin(bin, exp, r->cf); |
---|
1844 | // tail=res; |
---|
1845 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
---|
1846 | // { |
---|
1847 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
---|
1848 | // { |
---|
1849 | // pLmDelete(&pNext(tail)); |
---|
1850 | // } |
---|
1851 | // else |
---|
1852 | // pIter(tail); |
---|
1853 | // } |
---|
1854 | #ifdef PDEBUG |
---|
1855 | p_Test(res,r); |
---|
1856 | #endif |
---|
1857 | return res; |
---|
1858 | } |
---|
1859 | |
---|
1860 | static poly p_Pow(poly p, int i, const ring r) |
---|
1861 | { |
---|
1862 | poly rc = p_Copy(p,r); |
---|
1863 | i -= 2; |
---|
1864 | do |
---|
1865 | { |
---|
1866 | rc = p_Mult_q(rc,p_Copy(p,r),r); |
---|
1867 | p_Normalize(rc,r); |
---|
1868 | i--; |
---|
1869 | } |
---|
1870 | while (i != 0); |
---|
1871 | return p_Mult_q(rc,p,r); |
---|
1872 | } |
---|
1873 | |
---|
1874 | /*2 |
---|
1875 | * returns the i-th power of p |
---|
1876 | * p will be destroyed |
---|
1877 | */ |
---|
1878 | poly p_Power(poly p, int i, const ring r) |
---|
1879 | { |
---|
1880 | poly rc=NULL; |
---|
1881 | |
---|
1882 | if (i==0) |
---|
1883 | { |
---|
1884 | p_Delete(&p,r); |
---|
1885 | return p_One(r); |
---|
1886 | } |
---|
1887 | |
---|
1888 | if(p!=NULL) |
---|
1889 | { |
---|
1890 | if ( (i > 0) && ((unsigned long ) i > (r->bitmask))) |
---|
1891 | { |
---|
1892 | Werror("exponent %d is too large, max. is %ld",i,r->bitmask); |
---|
1893 | return NULL; |
---|
1894 | } |
---|
1895 | switch (i) |
---|
1896 | { |
---|
1897 | // cannot happen, see above |
---|
1898 | // case 0: |
---|
1899 | // { |
---|
1900 | // rc=pOne(); |
---|
1901 | // pDelete(&p); |
---|
1902 | // break; |
---|
1903 | // } |
---|
1904 | case 1: |
---|
1905 | rc=p; |
---|
1906 | break; |
---|
1907 | case 2: |
---|
1908 | rc=p_Mult_q(p_Copy(p,r),p,r); |
---|
1909 | break; |
---|
1910 | default: |
---|
1911 | if (i < 0) |
---|
1912 | { |
---|
1913 | p_Delete(&p,r); |
---|
1914 | return NULL; |
---|
1915 | } |
---|
1916 | else |
---|
1917 | { |
---|
1918 | #ifdef HAVE_PLURAL |
---|
1919 | if (rIsPluralRing(r)) /* in the NC case nothing helps :-( */ |
---|
1920 | { |
---|
1921 | int j=i; |
---|
1922 | rc = p_Copy(p,r); |
---|
1923 | while (j>1) |
---|
1924 | { |
---|
1925 | rc = p_Mult_q(p_Copy(p,r),rc,r); |
---|
1926 | j--; |
---|
1927 | } |
---|
1928 | p_Delete(&p,r); |
---|
1929 | return rc; |
---|
1930 | } |
---|
1931 | #endif |
---|
1932 | rc = pNext(p); |
---|
1933 | if (rc == NULL) |
---|
1934 | return p_MonPower(p,i,r); |
---|
1935 | /* else: binom ?*/ |
---|
1936 | int char_p=rChar(r); |
---|
1937 | if ((pNext(rc) != NULL) |
---|
1938 | #ifdef HAVE_RINGS |
---|
1939 | || rField_is_Ring(r) |
---|
1940 | #endif |
---|
1941 | ) |
---|
1942 | return p_Pow(p,i,r); |
---|
1943 | if ((char_p==0) || (i<=char_p)) |
---|
1944 | return p_TwoMonPower(p,i,r); |
---|
1945 | poly p_p=p_TwoMonPower(p_Copy(p,r),char_p,r); |
---|
1946 | return p_Mult_q(p_Power(p,i-char_p,r),p_p,r); |
---|
1947 | } |
---|
1948 | /*end default:*/ |
---|
1949 | } |
---|
1950 | } |
---|
1951 | return rc; |
---|
1952 | } |
---|
1953 | |
---|
1954 | /* --------------------------------------------------------------------------------*/ |
---|
1955 | /* content suff */ |
---|
1956 | |
---|
1957 | static number p_InitContent(poly ph, const ring r); |
---|
1958 | static number p_InitContent_a(poly ph, const ring r); |
---|
1959 | |
---|
1960 | void p_Content(poly ph, const ring r) |
---|
1961 | { |
---|
1962 | #ifdef HAVE_RINGS |
---|
1963 | if (rField_is_Ring(r)) |
---|
1964 | { |
---|
1965 | if ((ph!=NULL) && rField_has_Units(r)) |
---|
1966 | { |
---|
1967 | number k = n_GetUnit(pGetCoeff(ph),r->cf); |
---|
1968 | if (!n_IsOne(k,r->cf)) |
---|
1969 | { |
---|
1970 | number tmpGMP = k; |
---|
1971 | k = n_Invers(k,r->cf); |
---|
1972 | n_Delete(&tmpGMP,r->cf); |
---|
1973 | poly h = pNext(ph); |
---|
1974 | p_SetCoeff(ph, n_Mult(pGetCoeff(ph), k,r->cf),r); |
---|
1975 | while (h != NULL) |
---|
1976 | { |
---|
1977 | p_SetCoeff(h, n_Mult(pGetCoeff(h), k,r->cf),r); |
---|
1978 | pIter(h); |
---|
1979 | } |
---|
1980 | } |
---|
1981 | n_Delete(&k,r->cf); |
---|
1982 | } |
---|
1983 | return; |
---|
1984 | } |
---|
1985 | #endif |
---|
1986 | number h,d; |
---|
1987 | poly p; |
---|
1988 | |
---|
1989 | if(TEST_OPT_CONTENTSB) return; |
---|
1990 | if(pNext(ph)==NULL) |
---|
1991 | { |
---|
1992 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
1993 | } |
---|
1994 | else |
---|
1995 | { |
---|
1996 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
1997 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
1998 | if (rField_is_Q(r)) |
---|
1999 | { |
---|
2000 | h=p_InitContent(ph,r); |
---|
2001 | p=ph; |
---|
2002 | } |
---|
2003 | else if (rField_is_Extension(r) |
---|
2004 | && |
---|
2005 | ( |
---|
2006 | (rPar(r)>1) || rMinpolyIsNULL(r) |
---|
2007 | ) |
---|
2008 | ) |
---|
2009 | { |
---|
2010 | h=p_InitContent_a(ph,r); |
---|
2011 | p=ph; |
---|
2012 | } |
---|
2013 | else |
---|
2014 | { |
---|
2015 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
2016 | p = pNext(ph); |
---|
2017 | } |
---|
2018 | while (p!=NULL) |
---|
2019 | { |
---|
2020 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2021 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
2022 | n_Delete(&h,r->cf); |
---|
2023 | h = d; |
---|
2024 | if(n_IsOne(h,r->cf)) |
---|
2025 | { |
---|
2026 | break; |
---|
2027 | } |
---|
2028 | pIter(p); |
---|
2029 | } |
---|
2030 | p = ph; |
---|
2031 | //number tmp; |
---|
2032 | if(!n_IsOne(h,r->cf)) |
---|
2033 | { |
---|
2034 | while (p!=NULL) |
---|
2035 | { |
---|
2036 | //d = nDiv(pGetCoeff(p),h); |
---|
2037 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
2038 | //if (!nEqual(d,tmp)) |
---|
2039 | //{ |
---|
2040 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
2041 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
2042 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
2043 | //} |
---|
2044 | //nDelete(&tmp); |
---|
2045 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
2046 | p_SetCoeff(p,d,r); |
---|
2047 | pIter(p); |
---|
2048 | } |
---|
2049 | } |
---|
2050 | n_Delete(&h,r->cf); |
---|
2051 | #ifdef HAVE_FACTORY |
---|
2052 | if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
2053 | { |
---|
2054 | singclap_divide_content(ph, r); |
---|
2055 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2056 | } |
---|
2057 | #endif |
---|
2058 | if (rField_is_Q_a(r)) |
---|
2059 | { |
---|
2060 | //number hzz = nlInit(1, r->cf); |
---|
2061 | h = nlInit(1, r->cf); |
---|
2062 | p=ph; |
---|
2063 | Werror("longalg missing 1"); |
---|
2064 | #if 0 |
---|
2065 | while (p!=NULL) |
---|
2066 | { // each monom: coeff in Q_a |
---|
2067 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
2068 | poly c_n=c_n_n->z; |
---|
2069 | while (c_n!=NULL) |
---|
2070 | { // each monom: coeff in Q |
---|
2071 | d=nlLcm(hzz,pGetCoeff(c_n),r->extRing->cf); |
---|
2072 | n_Delete(&hzz,r->extRing->cf); |
---|
2073 | hzz=d; |
---|
2074 | pIter(c_n); |
---|
2075 | } |
---|
2076 | c_n=c_n_n->n; |
---|
2077 | while (c_n!=NULL) |
---|
2078 | { // each monom: coeff in Q |
---|
2079 | d=nlLcm(h,pGetCoeff(c_n),r->extRing->cf); |
---|
2080 | n_Delete(&h,r->extRing->cf); |
---|
2081 | h=d; |
---|
2082 | pIter(c_n); |
---|
2083 | } |
---|
2084 | pIter(p); |
---|
2085 | } |
---|
2086 | /* hzz contains the 1/lcm of all denominators in c_n_n->z*/ |
---|
2087 | /* h contains the 1/lcm of all denominators in c_n_n->n*/ |
---|
2088 | number htmp=nlInvers(h,r->extRing->cf); |
---|
2089 | number hzztmp=nlInvers(hzz,r->extRing->cf); |
---|
2090 | number hh=nlMult(hzz,h,r->extRing->cf); |
---|
2091 | nlDelete(&hzz,r->extRing->cf); |
---|
2092 | nlDelete(&h,r->extRing->cf); |
---|
2093 | number hg=nlGcd(hzztmp,htmp,r->extRing->cf); |
---|
2094 | nlDelete(&hzztmp,r->extRing->cf); |
---|
2095 | nlDelete(&htmp,r->extRing->cf); |
---|
2096 | h=nlMult(hh,hg,r->extRing->cf); |
---|
2097 | nlDelete(&hg,r->extRing->cf); |
---|
2098 | nlDelete(&hh,r->extRing->cf); |
---|
2099 | nlNormalize(h,r->extRing->cf); |
---|
2100 | if(!nlIsOne(h,r->extRing->cf)) |
---|
2101 | { |
---|
2102 | p=ph; |
---|
2103 | while (p!=NULL) |
---|
2104 | { // each monom: coeff in Q_a |
---|
2105 | lnumber c_n_n=(lnumber)pGetCoeff(p); |
---|
2106 | poly c_n=c_n_n->z; |
---|
2107 | while (c_n!=NULL) |
---|
2108 | { // each monom: coeff in Q |
---|
2109 | d=nlMult(h,pGetCoeff(c_n),r->extRing->cf); |
---|
2110 | nlNormalize(d,r->extRing->cf); |
---|
2111 | nlDelete(&pGetCoeff(c_n),r->extRing->cf); |
---|
2112 | pGetCoeff(c_n)=d; |
---|
2113 | pIter(c_n); |
---|
2114 | } |
---|
2115 | c_n=c_n_n->n; |
---|
2116 | while (c_n!=NULL) |
---|
2117 | { // each monom: coeff in Q |
---|
2118 | d=nlMult(h,pGetCoeff(c_n),r->extRing->cf); |
---|
2119 | nlNormalize(d,r->extRing->cf); |
---|
2120 | nlDelete(&pGetCoeff(c_n),r->extRing->cf); |
---|
2121 | pGetCoeff(c_n)=d; |
---|
2122 | pIter(c_n); |
---|
2123 | } |
---|
2124 | pIter(p); |
---|
2125 | } |
---|
2126 | } |
---|
2127 | nlDelete(&h,r->extRing->cf); |
---|
2128 | #endif |
---|
2129 | } |
---|
2130 | } |
---|
2131 | } |
---|
2132 | #if 0 // currently not used |
---|
2133 | void p_SimpleContent(poly ph,int smax, const ring r) |
---|
2134 | { |
---|
2135 | if(TEST_OPT_CONTENTSB) return; |
---|
2136 | if (ph==NULL) return; |
---|
2137 | if (pNext(ph)==NULL) |
---|
2138 | { |
---|
2139 | p_SetCoeff(ph,n_Init(1,r_cf),r); |
---|
2140 | return; |
---|
2141 | } |
---|
2142 | if ((pNext(pNext(ph))==NULL)||(!rField_is_Q(r))) |
---|
2143 | { |
---|
2144 | return; |
---|
2145 | } |
---|
2146 | number d=p_InitContent(ph,r); |
---|
2147 | if (nlSize(d,r->cf)<=smax) |
---|
2148 | { |
---|
2149 | //if (TEST_OPT_PROT) PrintS("G"); |
---|
2150 | return; |
---|
2151 | } |
---|
2152 | poly p=ph; |
---|
2153 | number h=d; |
---|
2154 | if (smax==1) smax=2; |
---|
2155 | while (p!=NULL) |
---|
2156 | { |
---|
2157 | #if 0 |
---|
2158 | d=nlGcd(h,pGetCoeff(p),r->cf); |
---|
2159 | nlDelete(&h,r->cf); |
---|
2160 | h = d; |
---|
2161 | #else |
---|
2162 | nlInpGcd(h,pGetCoeff(p),r->cf); |
---|
2163 | #endif |
---|
2164 | if(nlSize(h,r->cf)<smax) |
---|
2165 | { |
---|
2166 | //if (TEST_OPT_PROT) PrintS("g"); |
---|
2167 | return; |
---|
2168 | } |
---|
2169 | pIter(p); |
---|
2170 | } |
---|
2171 | p = ph; |
---|
2172 | if (!nlGreaterZero(pGetCoeff(p),r->cf)) h=nlNeg(h,r->cf); |
---|
2173 | if(nlIsOne(h,r->cf)) return; |
---|
2174 | //if (TEST_OPT_PROT) PrintS("c"); |
---|
2175 | while (p!=NULL) |
---|
2176 | { |
---|
2177 | #if 1 |
---|
2178 | d = nlIntDiv(pGetCoeff(p),h,r->cf); |
---|
2179 | p_SetCoeff(p,d,r); |
---|
2180 | #else |
---|
2181 | nlInpIntDiv(pGetCoeff(p),h,r->cf); |
---|
2182 | #endif |
---|
2183 | pIter(p); |
---|
2184 | } |
---|
2185 | nlDelete(&h,r->cf); |
---|
2186 | } |
---|
2187 | #endif |
---|
2188 | |
---|
2189 | static number p_InitContent(poly ph, const ring r) |
---|
2190 | // only for coefficients in Q |
---|
2191 | #if 0 |
---|
2192 | { |
---|
2193 | assume(!TEST_OPT_CONTENTSB); |
---|
2194 | assume(ph!=NULL); |
---|
2195 | assume(pNext(ph)!=NULL); |
---|
2196 | assume(rField_is_Q(r)); |
---|
2197 | if (pNext(pNext(ph))==NULL) |
---|
2198 | { |
---|
2199 | return nlGetNom(pGetCoeff(pNext(ph)),r->cf); |
---|
2200 | } |
---|
2201 | poly p=ph; |
---|
2202 | number n1=nlGetNom(pGetCoeff(p),r->cf); |
---|
2203 | pIter(p); |
---|
2204 | number n2=nlGetNom(pGetCoeff(p),r->cf); |
---|
2205 | pIter(p); |
---|
2206 | number d; |
---|
2207 | number t; |
---|
2208 | loop |
---|
2209 | { |
---|
2210 | nlNormalize(pGetCoeff(p),r->cf); |
---|
2211 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
2212 | if (nlGreaterZero(t,r->cf)) |
---|
2213 | d=nlAdd(n1,t,r->cf); |
---|
2214 | else |
---|
2215 | d=nlSub(n1,t,r->cf); |
---|
2216 | nlDelete(&t,r->cf); |
---|
2217 | nlDelete(&n1,r->cf); |
---|
2218 | n1=d; |
---|
2219 | pIter(p); |
---|
2220 | if (p==NULL) break; |
---|
2221 | nlNormalize(pGetCoeff(p),r->cf); |
---|
2222 | t=nlGetNom(pGetCoeff(p),r->cf); |
---|
2223 | if (nlGreaterZero(t,r->cf)) |
---|
2224 | d=nlAdd(n2,t,r->cf); |
---|
2225 | else |
---|
2226 | d=nlSub(n2,t,r->cf); |
---|
2227 | nlDelete(&t,r->cf); |
---|
2228 | nlDelete(&n2,r->cf); |
---|
2229 | n2=d; |
---|
2230 | pIter(p); |
---|
2231 | if (p==NULL) break; |
---|
2232 | } |
---|
2233 | d=nlGcd(n1,n2,r->cf); |
---|
2234 | nlDelete(&n1,r->cf); |
---|
2235 | nlDelete(&n2,r->cf); |
---|
2236 | return d; |
---|
2237 | } |
---|
2238 | #else |
---|
2239 | { |
---|
2240 | number d=pGetCoeff(ph); |
---|
2241 | if(SR_HDL(d)&SR_INT) return d; |
---|
2242 | int s=mpz_size1(d->z); |
---|
2243 | int s2=-1; |
---|
2244 | number d2; |
---|
2245 | loop |
---|
2246 | { |
---|
2247 | pIter(ph); |
---|
2248 | if(ph==NULL) |
---|
2249 | { |
---|
2250 | if (s2==-1) return nlCopy(d,r->cf); |
---|
2251 | break; |
---|
2252 | } |
---|
2253 | if (SR_HDL(pGetCoeff(ph))&SR_INT) |
---|
2254 | { |
---|
2255 | s2=s; |
---|
2256 | d2=d; |
---|
2257 | s=0; |
---|
2258 | d=pGetCoeff(ph); |
---|
2259 | if (s2==0) break; |
---|
2260 | } |
---|
2261 | else |
---|
2262 | if (mpz_size1((pGetCoeff(ph)->z))<=s) |
---|
2263 | { |
---|
2264 | s2=s; |
---|
2265 | d2=d; |
---|
2266 | d=pGetCoeff(ph); |
---|
2267 | s=mpz_size1(d->z); |
---|
2268 | } |
---|
2269 | } |
---|
2270 | return nlGcd(d,d2,r->cf); |
---|
2271 | } |
---|
2272 | #endif |
---|
2273 | |
---|
2274 | number p_InitContent_a(poly ph, const ring r) |
---|
2275 | // only for coefficients in K(a)/<minpoly(a)> and K(t_1, t_2, ..., t_n) |
---|
2276 | { |
---|
2277 | number d=pGetCoeff(ph); |
---|
2278 | /* old: int s=n_ParDeg(d,r->cf); new: */ |
---|
2279 | int s = p_Totaldegree((poly)d, r->cf->extRing); |
---|
2280 | if (s <=1) return n_Copy(d,r->cf); |
---|
2281 | int s2=-1; |
---|
2282 | number d2; |
---|
2283 | int ss; |
---|
2284 | loop |
---|
2285 | { |
---|
2286 | pIter(ph); |
---|
2287 | if(ph==NULL) |
---|
2288 | { |
---|
2289 | if (s2==-1) return n_Copy(d,r->cf); |
---|
2290 | break; |
---|
2291 | } |
---|
2292 | /* old: if ((ss=n_ParDeg(pGetCoeff(ph),r->cf))<s) new: */ |
---|
2293 | if ((ss = p_Totaldegree((poly)pGetCoeff(ph), r->cf->extRing)) < s) |
---|
2294 | { |
---|
2295 | s2=s; |
---|
2296 | d2=d; |
---|
2297 | s=ss; |
---|
2298 | d=pGetCoeff(ph); |
---|
2299 | if (s2<=1) break; |
---|
2300 | } |
---|
2301 | } |
---|
2302 | return n_Gcd(d,d2,r->cf); |
---|
2303 | } |
---|
2304 | |
---|
2305 | |
---|
2306 | //void pContent(poly ph) |
---|
2307 | //{ |
---|
2308 | // number h,d; |
---|
2309 | // poly p; |
---|
2310 | // |
---|
2311 | // p = ph; |
---|
2312 | // if(pNext(p)==NULL) |
---|
2313 | // { |
---|
2314 | // pSetCoeff(p,nInit(1)); |
---|
2315 | // } |
---|
2316 | // else |
---|
2317 | // { |
---|
2318 | //#ifdef PDEBUG |
---|
2319 | // if (!pTest(p)) return; |
---|
2320 | //#endif |
---|
2321 | // nNormalize(pGetCoeff(p)); |
---|
2322 | // if(!nGreaterZero(pGetCoeff(ph))) |
---|
2323 | // { |
---|
2324 | // ph = pNeg(ph); |
---|
2325 | // nNormalize(pGetCoeff(p)); |
---|
2326 | // } |
---|
2327 | // h=pGetCoeff(p); |
---|
2328 | // pIter(p); |
---|
2329 | // while (p!=NULL) |
---|
2330 | // { |
---|
2331 | // nNormalize(pGetCoeff(p)); |
---|
2332 | // if (nGreater(h,pGetCoeff(p))) h=pGetCoeff(p); |
---|
2333 | // pIter(p); |
---|
2334 | // } |
---|
2335 | // h=nCopy(h); |
---|
2336 | // p=ph; |
---|
2337 | // while (p!=NULL) |
---|
2338 | // { |
---|
2339 | // d=n_Gcd(h,pGetCoeff(p)); |
---|
2340 | // nDelete(&h); |
---|
2341 | // h = d; |
---|
2342 | // if(nIsOne(h)) |
---|
2343 | // { |
---|
2344 | // break; |
---|
2345 | // } |
---|
2346 | // pIter(p); |
---|
2347 | // } |
---|
2348 | // p = ph; |
---|
2349 | // //number tmp; |
---|
2350 | // if(!nIsOne(h)) |
---|
2351 | // { |
---|
2352 | // while (p!=NULL) |
---|
2353 | // { |
---|
2354 | // d = nIntDiv(pGetCoeff(p),h); |
---|
2355 | // pSetCoeff(p,d); |
---|
2356 | // pIter(p); |
---|
2357 | // } |
---|
2358 | // } |
---|
2359 | // nDelete(&h); |
---|
2360 | //#ifdef HAVE_FACTORY |
---|
2361 | // if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
2362 | // { |
---|
2363 | // pTest(ph); |
---|
2364 | // singclap_divide_content(ph); |
---|
2365 | // pTest(ph); |
---|
2366 | // } |
---|
2367 | //#endif |
---|
2368 | // } |
---|
2369 | //} |
---|
2370 | #if 0 |
---|
2371 | void p_Content(poly ph, const ring r) |
---|
2372 | { |
---|
2373 | number h,d; |
---|
2374 | poly p; |
---|
2375 | |
---|
2376 | if(pNext(ph)==NULL) |
---|
2377 | { |
---|
2378 | p_SetCoeff(ph,n_Init(1,r->cf),r); |
---|
2379 | } |
---|
2380 | else |
---|
2381 | { |
---|
2382 | n_Normalize(pGetCoeff(ph),r->cf); |
---|
2383 | if(!n_GreaterZero(pGetCoeff(ph),r->cf)) ph = p_Neg(ph,r); |
---|
2384 | h=n_Copy(pGetCoeff(ph),r->cf); |
---|
2385 | p = pNext(ph); |
---|
2386 | while (p!=NULL) |
---|
2387 | { |
---|
2388 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2389 | d=n_Gcd(h,pGetCoeff(p),r->cf); |
---|
2390 | n_Delete(&h,r->cf); |
---|
2391 | h = d; |
---|
2392 | if(n_IsOne(h,r->cf)) |
---|
2393 | { |
---|
2394 | break; |
---|
2395 | } |
---|
2396 | pIter(p); |
---|
2397 | } |
---|
2398 | p = ph; |
---|
2399 | //number tmp; |
---|
2400 | if(!n_IsOne(h,r->cf)) |
---|
2401 | { |
---|
2402 | while (p!=NULL) |
---|
2403 | { |
---|
2404 | //d = nDiv(pGetCoeff(p),h); |
---|
2405 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
2406 | //if (!nEqual(d,tmp)) |
---|
2407 | //{ |
---|
2408 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
2409 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
2410 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
2411 | //} |
---|
2412 | //nDelete(&tmp); |
---|
2413 | d = n_IntDiv(pGetCoeff(p),h,r->cf); |
---|
2414 | p_SetCoeff(p,d,r->cf); |
---|
2415 | pIter(p); |
---|
2416 | } |
---|
2417 | } |
---|
2418 | n_Delete(&h,r->cf); |
---|
2419 | #ifdef HAVE_FACTORY |
---|
2420 | //if ( (n_GetChar(r) == 1) || (n_GetChar(r) < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
2421 | //{ |
---|
2422 | // singclap_divide_content(ph); |
---|
2423 | // if(!n_GreaterZero(pGetCoeff(ph),r)) ph = p_Neg(ph,r); |
---|
2424 | //} |
---|
2425 | #endif |
---|
2426 | } |
---|
2427 | } |
---|
2428 | #endif |
---|
2429 | /* ---------------------------------------------------------------------------*/ |
---|
2430 | /* cleardenom suff */ |
---|
2431 | poly p_Cleardenom(poly ph, const ring r) |
---|
2432 | { |
---|
2433 | poly start=ph; |
---|
2434 | number d, h; |
---|
2435 | poly p; |
---|
2436 | |
---|
2437 | #ifdef HAVE_RINGS |
---|
2438 | if (rField_is_Ring(r)) |
---|
2439 | { |
---|
2440 | p_Content(ph,r); |
---|
2441 | return start; |
---|
2442 | } |
---|
2443 | #endif |
---|
2444 | if (rField_is_Zp(r) && TEST_OPT_INTSTRATEGY) return start; |
---|
2445 | p = ph; |
---|
2446 | if(pNext(p)==NULL) |
---|
2447 | { |
---|
2448 | if (TEST_OPT_CONTENTSB) |
---|
2449 | { |
---|
2450 | number n=n_GetDenom(pGetCoeff(p),r->cf); |
---|
2451 | if (!n_IsOne(n,r->cf)) |
---|
2452 | { |
---|
2453 | number nn=n_Mult(pGetCoeff(p),n,r->cf); |
---|
2454 | n_Normalize(nn,r->cf); |
---|
2455 | p_SetCoeff(p,nn,r); |
---|
2456 | } |
---|
2457 | n_Delete(&n,r->cf); |
---|
2458 | } |
---|
2459 | else |
---|
2460 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
2461 | } |
---|
2462 | else |
---|
2463 | { |
---|
2464 | h = n_Init(1,r->cf); |
---|
2465 | while (p!=NULL) |
---|
2466 | { |
---|
2467 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2468 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2469 | n_Delete(&h,r->cf); |
---|
2470 | h=d; |
---|
2471 | pIter(p); |
---|
2472 | } |
---|
2473 | /* contains the 1/lcm of all denominators */ |
---|
2474 | if(!n_IsOne(h,r->cf)) |
---|
2475 | { |
---|
2476 | p = ph; |
---|
2477 | while (p!=NULL) |
---|
2478 | { |
---|
2479 | /* should be: |
---|
2480 | * number hh; |
---|
2481 | * nGetDenom(p->coef,&hh); |
---|
2482 | * nMult(&h,&hh,&d); |
---|
2483 | * nNormalize(d); |
---|
2484 | * nDelete(&hh); |
---|
2485 | * nMult(d,p->coef,&hh); |
---|
2486 | * nDelete(&d); |
---|
2487 | * nDelete(&(p->coef)); |
---|
2488 | * p->coef =hh; |
---|
2489 | */ |
---|
2490 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2491 | n_Normalize(d,r->cf); |
---|
2492 | p_SetCoeff(p,d,r); |
---|
2493 | pIter(p); |
---|
2494 | } |
---|
2495 | n_Delete(&h,r->cf); |
---|
2496 | if (n_GetChar(r->cf)==1) |
---|
2497 | { |
---|
2498 | loop |
---|
2499 | { |
---|
2500 | h = n_Init(1,r->cf); |
---|
2501 | p=ph; |
---|
2502 | while (p!=NULL) |
---|
2503 | { |
---|
2504 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2505 | n_Delete(&h,r->cf); |
---|
2506 | h=d; |
---|
2507 | pIter(p); |
---|
2508 | } |
---|
2509 | /* contains the 1/lcm of all denominators */ |
---|
2510 | if(!n_IsOne(h,r->cf)) |
---|
2511 | { |
---|
2512 | p = ph; |
---|
2513 | while (p!=NULL) |
---|
2514 | { |
---|
2515 | /* should be: |
---|
2516 | * number hh; |
---|
2517 | * nGetDenom(p->coef,&hh); |
---|
2518 | * nMult(&h,&hh,&d); |
---|
2519 | * nNormalize(d); |
---|
2520 | * nDelete(&hh); |
---|
2521 | * nMult(d,p->coef,&hh); |
---|
2522 | * nDelete(&d); |
---|
2523 | * nDelete(&(p->coef)); |
---|
2524 | * p->coef =hh; |
---|
2525 | */ |
---|
2526 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2527 | n_Normalize(d,r->cf); |
---|
2528 | p_SetCoeff(p,d,r); |
---|
2529 | pIter(p); |
---|
2530 | } |
---|
2531 | n_Delete(&h,r->cf); |
---|
2532 | } |
---|
2533 | else |
---|
2534 | { |
---|
2535 | n_Delete(&h,r->cf); |
---|
2536 | break; |
---|
2537 | } |
---|
2538 | } |
---|
2539 | } |
---|
2540 | } |
---|
2541 | if (h!=NULL) n_Delete(&h,r->cf); |
---|
2542 | |
---|
2543 | p_Content(ph,r); |
---|
2544 | #ifdef HAVE_RATGRING |
---|
2545 | if (rIsRatGRing(r)) |
---|
2546 | { |
---|
2547 | /* quick unit detection in the rational case is done in gr_nc_bba */ |
---|
2548 | pContentRat(ph); |
---|
2549 | start=ph; |
---|
2550 | } |
---|
2551 | #endif |
---|
2552 | } |
---|
2553 | return start; |
---|
2554 | } |
---|
2555 | |
---|
2556 | void p_Cleardenom_n(poly ph,const ring r,number &c) |
---|
2557 | { |
---|
2558 | number d, h; |
---|
2559 | poly p; |
---|
2560 | |
---|
2561 | p = ph; |
---|
2562 | if(pNext(p)==NULL) |
---|
2563 | { |
---|
2564 | c=n_Invers(pGetCoeff(p),r->cf); |
---|
2565 | p_SetCoeff(p,n_Init(1,r->cf),r); |
---|
2566 | } |
---|
2567 | else |
---|
2568 | { |
---|
2569 | h = n_Init(1,r->cf); |
---|
2570 | while (p!=NULL) |
---|
2571 | { |
---|
2572 | n_Normalize(pGetCoeff(p),r->cf); |
---|
2573 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2574 | n_Delete(&h,r->cf); |
---|
2575 | h=d; |
---|
2576 | pIter(p); |
---|
2577 | } |
---|
2578 | c=h; |
---|
2579 | /* contains the 1/lcm of all denominators */ |
---|
2580 | if(!n_IsOne(h,r->cf)) |
---|
2581 | { |
---|
2582 | p = ph; |
---|
2583 | while (p!=NULL) |
---|
2584 | { |
---|
2585 | /* should be: |
---|
2586 | * number hh; |
---|
2587 | * nGetDenom(p->coef,&hh); |
---|
2588 | * nMult(&h,&hh,&d); |
---|
2589 | * nNormalize(d); |
---|
2590 | * nDelete(&hh); |
---|
2591 | * nMult(d,p->coef,&hh); |
---|
2592 | * nDelete(&d); |
---|
2593 | * nDelete(&(p->coef)); |
---|
2594 | * p->coef =hh; |
---|
2595 | */ |
---|
2596 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2597 | n_Normalize(d,r->cf); |
---|
2598 | p_SetCoeff(p,d,r); |
---|
2599 | pIter(p); |
---|
2600 | } |
---|
2601 | if (rField_is_Q_a(r)) |
---|
2602 | { |
---|
2603 | loop |
---|
2604 | { |
---|
2605 | h = n_Init(1,r->cf); |
---|
2606 | p=ph; |
---|
2607 | while (p!=NULL) |
---|
2608 | { |
---|
2609 | d=n_Lcm(h,pGetCoeff(p),r->cf); |
---|
2610 | n_Delete(&h,r->cf); |
---|
2611 | h=d; |
---|
2612 | pIter(p); |
---|
2613 | } |
---|
2614 | /* contains the 1/lcm of all denominators */ |
---|
2615 | if(!n_IsOne(h,r->cf)) |
---|
2616 | { |
---|
2617 | p = ph; |
---|
2618 | while (p!=NULL) |
---|
2619 | { |
---|
2620 | /* should be: |
---|
2621 | * number hh; |
---|
2622 | * nGetDenom(p->coef,&hh); |
---|
2623 | * nMult(&h,&hh,&d); |
---|
2624 | * nNormalize(d); |
---|
2625 | * nDelete(&hh); |
---|
2626 | * nMult(d,p->coef,&hh); |
---|
2627 | * nDelete(&d); |
---|
2628 | * nDelete(&(p->coef)); |
---|
2629 | * p->coef =hh; |
---|
2630 | */ |
---|
2631 | d=n_Mult(h,pGetCoeff(p),r->cf); |
---|
2632 | n_Normalize(d,r->cf); |
---|
2633 | p_SetCoeff(p,d,r); |
---|
2634 | pIter(p); |
---|
2635 | } |
---|
2636 | number t=n_Mult(c,h,r->cf); |
---|
2637 | n_Delete(&c,r->cf); |
---|
2638 | c=t; |
---|
2639 | } |
---|
2640 | else |
---|
2641 | { |
---|
2642 | break; |
---|
2643 | } |
---|
2644 | n_Delete(&h,r->cf); |
---|
2645 | } |
---|
2646 | } |
---|
2647 | } |
---|
2648 | } |
---|
2649 | } |
---|
2650 | |
---|
2651 | number p_GetAllDenom(poly ph, const ring r) |
---|
2652 | { |
---|
2653 | number d=n_Init(1,r->cf); |
---|
2654 | poly p = ph; |
---|
2655 | |
---|
2656 | while (p!=NULL) |
---|
2657 | { |
---|
2658 | number h=n_GetDenom(pGetCoeff(p),r->cf); |
---|
2659 | if (!n_IsOne(h,r->cf)) |
---|
2660 | { |
---|
2661 | number dd=n_Mult(d,h,r->cf); |
---|
2662 | n_Delete(&d,r->cf); |
---|
2663 | d=dd; |
---|
2664 | } |
---|
2665 | n_Delete(&h,r->cf); |
---|
2666 | pIter(p); |
---|
2667 | } |
---|
2668 | return d; |
---|
2669 | } |
---|
2670 | |
---|
2671 | int p_Size(poly p, const ring r) |
---|
2672 | { |
---|
2673 | int count = 0; |
---|
2674 | while ( p != NULL ) |
---|
2675 | { |
---|
2676 | count+= n_Size( pGetCoeff( p ), r->cf ); |
---|
2677 | pIter( p ); |
---|
2678 | } |
---|
2679 | return count; |
---|
2680 | } |
---|
2681 | |
---|
2682 | /*2 |
---|
2683 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
---|
2684 | *assume: deg(var(varnum))==1 |
---|
2685 | */ |
---|
2686 | poly p_Homogen (poly p, int varnum, const ring r) |
---|
2687 | { |
---|
2688 | pFDegProc deg; |
---|
2689 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
2690 | deg=p_Totaldegree; |
---|
2691 | else |
---|
2692 | deg=r->pFDeg; |
---|
2693 | |
---|
2694 | poly q=NULL, qn; |
---|
2695 | int o,ii; |
---|
2696 | sBucket_pt bp; |
---|
2697 | |
---|
2698 | if (p!=NULL) |
---|
2699 | { |
---|
2700 | if ((varnum < 1) || (varnum > rVar(r))) |
---|
2701 | { |
---|
2702 | return NULL; |
---|
2703 | } |
---|
2704 | o=deg(p,r); |
---|
2705 | q=pNext(p); |
---|
2706 | while (q != NULL) |
---|
2707 | { |
---|
2708 | ii=deg(q,r); |
---|
2709 | if (ii>o) o=ii; |
---|
2710 | pIter(q); |
---|
2711 | } |
---|
2712 | q = p_Copy(p,r); |
---|
2713 | bp = sBucketCreate(r); |
---|
2714 | while (q != NULL) |
---|
2715 | { |
---|
2716 | ii = o-deg(q,r); |
---|
2717 | if (ii!=0) |
---|
2718 | { |
---|
2719 | p_AddExp(q,varnum, (long)ii,r); |
---|
2720 | p_Setm(q,r); |
---|
2721 | } |
---|
2722 | qn = pNext(q); |
---|
2723 | pNext(q) = NULL; |
---|
2724 | sBucket_Add_p(bp, q, 1); |
---|
2725 | q = qn; |
---|
2726 | } |
---|
2727 | sBucketDestroyAdd(bp, &q, &ii); |
---|
2728 | } |
---|
2729 | return q; |
---|
2730 | } |
---|
2731 | |
---|
2732 | /*2 |
---|
2733 | *tests if p is homogeneous with respect to the actual weigths |
---|
2734 | */ |
---|
2735 | BOOLEAN p_IsHomogeneous (poly p, const ring r) |
---|
2736 | { |
---|
2737 | poly qp=p; |
---|
2738 | int o; |
---|
2739 | |
---|
2740 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
2741 | pFDegProc d; |
---|
2742 | if (r->pLexOrder && (r->order[0]==ringorder_lp)) |
---|
2743 | d=p_Totaldegree; |
---|
2744 | else |
---|
2745 | d=r->pFDeg; |
---|
2746 | o = d(p,r); |
---|
2747 | do |
---|
2748 | { |
---|
2749 | if (d(qp,r) != o) return FALSE; |
---|
2750 | pIter(qp); |
---|
2751 | } |
---|
2752 | while (qp != NULL); |
---|
2753 | return TRUE; |
---|
2754 | } |
---|
2755 | |
---|
2756 | /*----------utilities for syzygies--------------*/ |
---|
2757 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r) |
---|
2758 | { |
---|
2759 | poly q=p,qq; |
---|
2760 | int i; |
---|
2761 | |
---|
2762 | while (q!=NULL) |
---|
2763 | { |
---|
2764 | if (p_LmIsConstantComp(q,r)) |
---|
2765 | { |
---|
2766 | i = p_GetComp(q,r); |
---|
2767 | qq = p; |
---|
2768 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
2769 | if (qq == q) |
---|
2770 | { |
---|
2771 | *k = i; |
---|
2772 | return TRUE; |
---|
2773 | } |
---|
2774 | else |
---|
2775 | pIter(q); |
---|
2776 | } |
---|
2777 | else pIter(q); |
---|
2778 | } |
---|
2779 | return FALSE; |
---|
2780 | } |
---|
2781 | |
---|
2782 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r) |
---|
2783 | { |
---|
2784 | poly q=p,qq; |
---|
2785 | int i,j=0; |
---|
2786 | |
---|
2787 | *len = 0; |
---|
2788 | while (q!=NULL) |
---|
2789 | { |
---|
2790 | if (p_LmIsConstantComp(q,r)) |
---|
2791 | { |
---|
2792 | i = p_GetComp(q,r); |
---|
2793 | qq = p; |
---|
2794 | while ((qq != q) && (p_GetComp(qq,r) != i)) pIter(qq); |
---|
2795 | if (qq == q) |
---|
2796 | { |
---|
2797 | j = 0; |
---|
2798 | while (qq!=NULL) |
---|
2799 | { |
---|
2800 | if (p_GetComp(qq,r)==i) j++; |
---|
2801 | pIter(qq); |
---|
2802 | } |
---|
2803 | if ((*len == 0) || (j<*len)) |
---|
2804 | { |
---|
2805 | *len = j; |
---|
2806 | *k = i; |
---|
2807 | } |
---|
2808 | } |
---|
2809 | } |
---|
2810 | pIter(q); |
---|
2811 | } |
---|
2812 | } |
---|
2813 | |
---|
2814 | poly p_TakeOutComp1(poly * p, int k, const ring r) |
---|
2815 | { |
---|
2816 | poly q = *p; |
---|
2817 | |
---|
2818 | if (q==NULL) return NULL; |
---|
2819 | |
---|
2820 | poly qq=NULL,result = NULL; |
---|
2821 | |
---|
2822 | if (p_GetComp(q,r)==k) |
---|
2823 | { |
---|
2824 | result = q; /* *p */ |
---|
2825 | while ((q!=NULL) && (p_GetComp(q,r)==k)) |
---|
2826 | { |
---|
2827 | p_SetComp(q,0,r); |
---|
2828 | p_SetmComp(q,r); |
---|
2829 | qq = q; |
---|
2830 | pIter(q); |
---|
2831 | } |
---|
2832 | *p = q; |
---|
2833 | pNext(qq) = NULL; |
---|
2834 | } |
---|
2835 | if (q==NULL) return result; |
---|
2836 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2837 | while (pNext(q)!=NULL) |
---|
2838 | { |
---|
2839 | if (p_GetComp(pNext(q),r)==k) |
---|
2840 | { |
---|
2841 | if (result==NULL) |
---|
2842 | { |
---|
2843 | result = pNext(q); |
---|
2844 | qq = result; |
---|
2845 | } |
---|
2846 | else |
---|
2847 | { |
---|
2848 | pNext(qq) = pNext(q); |
---|
2849 | pIter(qq); |
---|
2850 | } |
---|
2851 | pNext(q) = pNext(pNext(q)); |
---|
2852 | pNext(qq) =NULL; |
---|
2853 | p_SetComp(qq,0,r); |
---|
2854 | p_SetmComp(qq,r); |
---|
2855 | } |
---|
2856 | else |
---|
2857 | { |
---|
2858 | pIter(q); |
---|
2859 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
2860 | } |
---|
2861 | } |
---|
2862 | return result; |
---|
2863 | } |
---|
2864 | |
---|
2865 | poly p_TakeOutComp(poly * p, int k, const ring r) |
---|
2866 | { |
---|
2867 | poly q = *p,qq=NULL,result = NULL; |
---|
2868 | |
---|
2869 | if (q==NULL) return NULL; |
---|
2870 | BOOLEAN use_setmcomp=rOrd_SetCompRequiresSetm(r); |
---|
2871 | if (p_GetComp(q,r)==k) |
---|
2872 | { |
---|
2873 | result = q; |
---|
2874 | do |
---|
2875 | { |
---|
2876 | p_SetComp(q,0,r); |
---|
2877 | if (use_setmcomp) p_SetmComp(q,r); |
---|
2878 | qq = q; |
---|
2879 | pIter(q); |
---|
2880 | } |
---|
2881 | while ((q!=NULL) && (p_GetComp(q,r)==k)); |
---|
2882 | *p = q; |
---|
2883 | pNext(qq) = NULL; |
---|
2884 | } |
---|
2885 | if (q==NULL) return result; |
---|
2886 | if (p_GetComp(q,r) > k) |
---|
2887 | { |
---|
2888 | p_SubComp(q,1,r); |
---|
2889 | if (use_setmcomp) p_SetmComp(q,r); |
---|
2890 | } |
---|
2891 | poly pNext_q; |
---|
2892 | while ((pNext_q=pNext(q))!=NULL) |
---|
2893 | { |
---|
2894 | if (p_GetComp(pNext_q,r)==k) |
---|
2895 | { |
---|
2896 | if (result==NULL) |
---|
2897 | { |
---|
2898 | result = pNext_q; |
---|
2899 | qq = result; |
---|
2900 | } |
---|
2901 | else |
---|
2902 | { |
---|
2903 | pNext(qq) = pNext_q; |
---|
2904 | pIter(qq); |
---|
2905 | } |
---|
2906 | pNext(q) = pNext(pNext_q); |
---|
2907 | pNext(qq) =NULL; |
---|
2908 | p_SetComp(qq,0,r); |
---|
2909 | if (use_setmcomp) p_SetmComp(qq,r); |
---|
2910 | } |
---|
2911 | else |
---|
2912 | { |
---|
2913 | /*pIter(q);*/ q=pNext_q; |
---|
2914 | if (p_GetComp(q,r) > k) |
---|
2915 | { |
---|
2916 | p_SubComp(q,1,r); |
---|
2917 | if (use_setmcomp) p_SetmComp(q,r); |
---|
2918 | } |
---|
2919 | } |
---|
2920 | } |
---|
2921 | return result; |
---|
2922 | } |
---|
2923 | |
---|
2924 | // Splits *p into two polys: *q which consists of all monoms with |
---|
2925 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
2926 | void p_TakeOutComp(poly *r_p, long comp, poly *r_q, int *lq, const ring r) |
---|
2927 | { |
---|
2928 | spolyrec pp, qq; |
---|
2929 | poly p, q, p_prev; |
---|
2930 | int l = 0; |
---|
2931 | |
---|
2932 | #ifdef HAVE_ASSUME |
---|
2933 | int lp = pLength(*r_p); |
---|
2934 | #endif |
---|
2935 | |
---|
2936 | pNext(&pp) = *r_p; |
---|
2937 | p = *r_p; |
---|
2938 | p_prev = &pp; |
---|
2939 | q = &qq; |
---|
2940 | |
---|
2941 | while(p != NULL) |
---|
2942 | { |
---|
2943 | while (p_GetComp(p,r) == comp) |
---|
2944 | { |
---|
2945 | pNext(q) = p; |
---|
2946 | pIter(q); |
---|
2947 | p_SetComp(p, 0,r); |
---|
2948 | p_SetmComp(p,r); |
---|
2949 | pIter(p); |
---|
2950 | l++; |
---|
2951 | if (p == NULL) |
---|
2952 | { |
---|
2953 | pNext(p_prev) = NULL; |
---|
2954 | goto Finish; |
---|
2955 | } |
---|
2956 | } |
---|
2957 | pNext(p_prev) = p; |
---|
2958 | p_prev = p; |
---|
2959 | pIter(p); |
---|
2960 | } |
---|
2961 | |
---|
2962 | Finish: |
---|
2963 | pNext(q) = NULL; |
---|
2964 | *r_p = pNext(&pp); |
---|
2965 | *r_q = pNext(&qq); |
---|
2966 | *lq = l; |
---|
2967 | #ifdef HAVE_ASSUME |
---|
2968 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
---|
2969 | #endif |
---|
2970 | p_Test(*r_p,r); |
---|
2971 | p_Test(*r_q,r); |
---|
2972 | } |
---|
2973 | |
---|
2974 | void p_DeleteComp(poly * p,int k, const ring r) |
---|
2975 | { |
---|
2976 | poly q; |
---|
2977 | |
---|
2978 | while ((*p!=NULL) && (p_GetComp(*p,r)==k)) p_LmDelete(p,r); |
---|
2979 | if (*p==NULL) return; |
---|
2980 | q = *p; |
---|
2981 | if (p_GetComp(q,r)>k) |
---|
2982 | { |
---|
2983 | p_SubComp(q,1,r); |
---|
2984 | p_SetmComp(q,r); |
---|
2985 | } |
---|
2986 | while (pNext(q)!=NULL) |
---|
2987 | { |
---|
2988 | if (p_GetComp(pNext(q),r)==k) |
---|
2989 | p_LmDelete(&(pNext(q)),r); |
---|
2990 | else |
---|
2991 | { |
---|
2992 | pIter(q); |
---|
2993 | if (p_GetComp(q,r)>k) |
---|
2994 | { |
---|
2995 | p_SubComp(q,1,r); |
---|
2996 | p_SetmComp(q,r); |
---|
2997 | } |
---|
2998 | } |
---|
2999 | } |
---|
3000 | } |
---|
3001 | |
---|
3002 | /*2 |
---|
3003 | * convert a vector to a set of polys, |
---|
3004 | * allocates the polyset, (entries 0..(*len)-1) |
---|
3005 | * the vector will not be changed |
---|
3006 | */ |
---|
3007 | void p_Vec2Polys(poly v, poly* *p, int *len, const ring r) |
---|
3008 | { |
---|
3009 | poly h; |
---|
3010 | int k; |
---|
3011 | |
---|
3012 | *len=p_MaxComp(v,r); |
---|
3013 | if (*len==0) *len=1; |
---|
3014 | *p=(poly*)omAlloc0((*len)*sizeof(poly)); |
---|
3015 | while (v!=NULL) |
---|
3016 | { |
---|
3017 | h=p_Head(v,r); |
---|
3018 | k=p_GetComp(h,r); |
---|
3019 | p_SetComp(h,0,r); |
---|
3020 | (*p)[k-1]=p_Add_q((*p)[k-1],h,r); |
---|
3021 | pIter(v); |
---|
3022 | } |
---|
3023 | } |
---|
3024 | |
---|
3025 | /* -------------------------------------------------------- */ |
---|
3026 | /*2 |
---|
3027 | * change all global variables to fit the description of the new ring |
---|
3028 | */ |
---|
3029 | |
---|
3030 | void p_SetGlobals(const ring r, BOOLEAN complete) |
---|
3031 | { |
---|
3032 | if (r->ppNoether!=NULL) p_Delete(&r->ppNoether,r); |
---|
3033 | |
---|
3034 | if (complete) |
---|
3035 | { |
---|
3036 | test &= ~ TEST_RINGDEP_OPTS; |
---|
3037 | test |= r->options; |
---|
3038 | } |
---|
3039 | } |
---|
3040 | // |
---|
3041 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
3042 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
3043 | // only uses pFDeg (and not p_Deg, or pTotalDegree, etc) |
---|
3044 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg) |
---|
3045 | { |
---|
3046 | assume(new_FDeg != NULL); |
---|
3047 | r->pFDeg = new_FDeg; |
---|
3048 | |
---|
3049 | if (new_lDeg == NULL) |
---|
3050 | new_lDeg = r->pLDegOrig; |
---|
3051 | |
---|
3052 | r->pLDeg = new_lDeg; |
---|
3053 | } |
---|
3054 | |
---|
3055 | // restores pFDeg and pLDeg: |
---|
3056 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg) |
---|
3057 | { |
---|
3058 | assume(old_FDeg != NULL && old_lDeg != NULL); |
---|
3059 | r->pFDeg = old_FDeg; |
---|
3060 | r->pLDeg = old_lDeg; |
---|
3061 | } |
---|
3062 | |
---|
3063 | /*-------- several access procedures to monomials -------------------- */ |
---|
3064 | /* |
---|
3065 | * the module weights for std |
---|
3066 | */ |
---|
3067 | static pFDegProc pOldFDeg; |
---|
3068 | static pLDegProc pOldLDeg; |
---|
3069 | static intvec * pModW; |
---|
3070 | static BOOLEAN pOldLexOrder; |
---|
3071 | |
---|
3072 | static long pModDeg(poly p, ring r) |
---|
3073 | { |
---|
3074 | long d=pOldFDeg(p, r); |
---|
3075 | int c=p_GetComp(p, r); |
---|
3076 | if ((c>0) && ((r->pModW)->range(c-1))) d+= (*(r->pModW))[c-1]; |
---|
3077 | return d; |
---|
3078 | //return pOldFDeg(p, r)+(*pModW)[p_GetComp(p, r)-1]; |
---|
3079 | } |
---|
3080 | |
---|
3081 | void p_SetModDeg(intvec *w, ring r) |
---|
3082 | { |
---|
3083 | if (w!=NULL) |
---|
3084 | { |
---|
3085 | r->pModW = w; |
---|
3086 | pOldFDeg = r->pFDeg; |
---|
3087 | pOldLDeg = r->pLDeg; |
---|
3088 | pOldLexOrder = r->pLexOrder; |
---|
3089 | pSetDegProcs(r,pModDeg); |
---|
3090 | r->pLexOrder = TRUE; |
---|
3091 | } |
---|
3092 | else |
---|
3093 | { |
---|
3094 | r->pModW = NULL; |
---|
3095 | pRestoreDegProcs(r,pOldFDeg, pOldLDeg); |
---|
3096 | r->pLexOrder = pOldLexOrder; |
---|
3097 | } |
---|
3098 | } |
---|
3099 | |
---|
3100 | /*2 |
---|
3101 | * handle memory request for sets of polynomials (ideals) |
---|
3102 | * l is the length of *p, increment is the difference (may be negative) |
---|
3103 | */ |
---|
3104 | void pEnlargeSet(poly* *p, int l, int increment) |
---|
3105 | { |
---|
3106 | poly* h; |
---|
3107 | |
---|
3108 | h=(poly*)omReallocSize((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
---|
3109 | if (increment>0) |
---|
3110 | { |
---|
3111 | //for (i=l; i<l+increment; i++) |
---|
3112 | // h[i]=NULL; |
---|
3113 | memset(&(h[l]),0,increment*sizeof(poly)); |
---|
3114 | } |
---|
3115 | *p=h; |
---|
3116 | } |
---|
3117 | |
---|
3118 | /*2 |
---|
3119 | *divides p1 by its leading coefficient |
---|
3120 | */ |
---|
3121 | void p_Norm(poly p1, const ring r) |
---|
3122 | { |
---|
3123 | #ifdef HAVE_RINGS |
---|
3124 | if (rField_is_Ring(r)) |
---|
3125 | { |
---|
3126 | if (!n_IsUnit(pGetCoeff(p1), r->cf)) return; |
---|
3127 | // Werror("p_Norm not possible in the case of coefficient rings."); |
---|
3128 | } |
---|
3129 | else |
---|
3130 | #endif |
---|
3131 | if (p1!=NULL) |
---|
3132 | { |
---|
3133 | if (pNext(p1)==NULL) |
---|
3134 | { |
---|
3135 | p_SetCoeff(p1,n_Init(1,r->cf),r); |
---|
3136 | return; |
---|
3137 | } |
---|
3138 | poly h; |
---|
3139 | if (!n_IsOne(pGetCoeff(p1),r->cf)) |
---|
3140 | { |
---|
3141 | number k, c; |
---|
3142 | n_Normalize(pGetCoeff(p1),r->cf); |
---|
3143 | k = pGetCoeff(p1); |
---|
3144 | c = n_Init(1,r->cf); |
---|
3145 | pSetCoeff0(p1,c); |
---|
3146 | h = pNext(p1); |
---|
3147 | while (h!=NULL) |
---|
3148 | { |
---|
3149 | c=n_Div(pGetCoeff(h),k,r->cf); |
---|
3150 | // no need to normalize: Z/p, R |
---|
3151 | // normalize already in nDiv: Q_a, Z/p_a |
---|
3152 | // remains: Q |
---|
3153 | if (rField_is_Q(r) && (!n_IsOne(c,r->cf))) n_Normalize(c,r->cf); |
---|
3154 | p_SetCoeff(h,c,r); |
---|
3155 | pIter(h); |
---|
3156 | } |
---|
3157 | n_Delete(&k,r->cf); |
---|
3158 | } |
---|
3159 | else |
---|
3160 | { |
---|
3161 | //if (r->cf->cfNormalize != nDummy2) //TODO: OPTIMIZE |
---|
3162 | { |
---|
3163 | h = pNext(p1); |
---|
3164 | while (h!=NULL) |
---|
3165 | { |
---|
3166 | n_Normalize(pGetCoeff(h),r->cf); |
---|
3167 | pIter(h); |
---|
3168 | } |
---|
3169 | } |
---|
3170 | } |
---|
3171 | } |
---|
3172 | } |
---|
3173 | |
---|
3174 | /*2 |
---|
3175 | *normalize all coefficients |
---|
3176 | */ |
---|
3177 | void p_Normalize(poly p,const ring r) |
---|
3178 | { |
---|
3179 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
3180 | while (p!=NULL) |
---|
3181 | { |
---|
3182 | #ifdef LDEBUG |
---|
3183 | n_Test(pGetCoeff(p), r->cf); |
---|
3184 | #endif |
---|
3185 | n_Normalize(pGetCoeff(p),r->cf); |
---|
3186 | pIter(p); |
---|
3187 | } |
---|
3188 | } |
---|
3189 | |
---|
3190 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
3191 | // Poly with Exp(n) != 0 is reversed |
---|
3192 | static void p_SplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero, const ring r) |
---|
3193 | { |
---|
3194 | if (p == NULL) |
---|
3195 | { |
---|
3196 | *non_zero = NULL; |
---|
3197 | *zero = NULL; |
---|
3198 | return; |
---|
3199 | } |
---|
3200 | spolyrec sz; |
---|
3201 | poly z, n_z, next; |
---|
3202 | z = &sz; |
---|
3203 | n_z = NULL; |
---|
3204 | |
---|
3205 | while(p != NULL) |
---|
3206 | { |
---|
3207 | next = pNext(p); |
---|
3208 | if (p_GetExp(p, n,r) == 0) |
---|
3209 | { |
---|
3210 | pNext(z) = p; |
---|
3211 | pIter(z); |
---|
3212 | } |
---|
3213 | else |
---|
3214 | { |
---|
3215 | pNext(p) = n_z; |
---|
3216 | n_z = p; |
---|
3217 | } |
---|
3218 | p = next; |
---|
3219 | } |
---|
3220 | pNext(z) = NULL; |
---|
3221 | *zero = pNext(&sz); |
---|
3222 | *non_zero = n_z; |
---|
3223 | } |
---|
3224 | /*3 |
---|
3225 | * substitute the n-th variable by 1 in p |
---|
3226 | * destroy p |
---|
3227 | */ |
---|
3228 | static poly p_Subst1 (poly p,int n, const ring r) |
---|
3229 | { |
---|
3230 | poly qq=NULL, result = NULL; |
---|
3231 | poly zero=NULL, non_zero=NULL; |
---|
3232 | |
---|
3233 | // reverse, so that add is likely to be linear |
---|
3234 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
3235 | |
---|
3236 | while (non_zero != NULL) |
---|
3237 | { |
---|
3238 | assume(p_GetExp(non_zero, n,r) != 0); |
---|
3239 | qq = non_zero; |
---|
3240 | pIter(non_zero); |
---|
3241 | qq->next = NULL; |
---|
3242 | p_SetExp(qq,n,0,r); |
---|
3243 | p_Setm(qq,r); |
---|
3244 | result = p_Add_q(result,qq,r); |
---|
3245 | } |
---|
3246 | p = p_Add_q(result, zero,r); |
---|
3247 | p_Test(p,r); |
---|
3248 | return p; |
---|
3249 | } |
---|
3250 | |
---|
3251 | /*3 |
---|
3252 | * substitute the n-th variable by number e in p |
---|
3253 | * destroy p |
---|
3254 | */ |
---|
3255 | static poly p_Subst2 (poly p,int n, number e, const ring r) |
---|
3256 | { |
---|
3257 | assume( ! n_IsZero(e,r->cf) ); |
---|
3258 | poly qq,result = NULL; |
---|
3259 | number nn, nm; |
---|
3260 | poly zero, non_zero; |
---|
3261 | |
---|
3262 | // reverse, so that add is likely to be linear |
---|
3263 | p_SplitAndReversePoly(p, n, &non_zero, &zero,r); |
---|
3264 | |
---|
3265 | while (non_zero != NULL) |
---|
3266 | { |
---|
3267 | assume(p_GetExp(non_zero, n, r) != 0); |
---|
3268 | qq = non_zero; |
---|
3269 | pIter(non_zero); |
---|
3270 | qq->next = NULL; |
---|
3271 | n_Power(e, p_GetExp(qq, n, r), &nn,r->cf); |
---|
3272 | nm = n_Mult(nn, pGetCoeff(qq),r->cf); |
---|
3273 | #ifdef HAVE_RINGS |
---|
3274 | if (n_IsZero(nm,r->cf)) |
---|
3275 | { |
---|
3276 | p_LmFree(&qq,r); |
---|
3277 | n_Delete(&nm,r->cf); |
---|
3278 | } |
---|
3279 | else |
---|
3280 | #endif |
---|
3281 | { |
---|
3282 | p_SetCoeff(qq, nm,r); |
---|
3283 | p_SetExp(qq, n, 0,r); |
---|
3284 | p_Setm(qq,r); |
---|
3285 | result = p_Add_q(result,qq,r); |
---|
3286 | } |
---|
3287 | n_Delete(&nn,r->cf); |
---|
3288 | } |
---|
3289 | p = p_Add_q(result, zero,r); |
---|
3290 | p_Test(p,r); |
---|
3291 | return p; |
---|
3292 | } |
---|
3293 | |
---|
3294 | |
---|
3295 | /* delete monoms whose n-th exponent is different from zero */ |
---|
3296 | static poly p_Subst0(poly p, int n, const ring r) |
---|
3297 | { |
---|
3298 | spolyrec res; |
---|
3299 | poly h = &res; |
---|
3300 | pNext(h) = p; |
---|
3301 | |
---|
3302 | while (pNext(h)!=NULL) |
---|
3303 | { |
---|
3304 | if (p_GetExp(pNext(h),n,r)!=0) |
---|
3305 | { |
---|
3306 | p_LmDelete(&pNext(h),r); |
---|
3307 | } |
---|
3308 | else |
---|
3309 | { |
---|
3310 | pIter(h); |
---|
3311 | } |
---|
3312 | } |
---|
3313 | p_Test(pNext(&res),r); |
---|
3314 | return pNext(&res); |
---|
3315 | } |
---|
3316 | |
---|
3317 | /*2 |
---|
3318 | * substitute the n-th variable by e in p |
---|
3319 | * destroy p |
---|
3320 | */ |
---|
3321 | poly p_Subst(poly p, int n, poly e, const ring r) |
---|
3322 | { |
---|
3323 | if (e == NULL) return p_Subst0(p, n,r); |
---|
3324 | |
---|
3325 | if (p_IsConstant(e,r)) |
---|
3326 | { |
---|
3327 | if (n_IsOne(pGetCoeff(e),r->cf)) return p_Subst1(p,n,r); |
---|
3328 | else return p_Subst2(p, n, pGetCoeff(e),r); |
---|
3329 | } |
---|
3330 | |
---|
3331 | #ifdef HAVE_PLURAL |
---|
3332 | if (rIsPluralRing(r)) |
---|
3333 | { |
---|
3334 | return nc_pSubst(p,n,e,r); |
---|
3335 | } |
---|
3336 | #endif |
---|
3337 | |
---|
3338 | int exponent,i; |
---|
3339 | poly h, res, m; |
---|
3340 | int *me,*ee; |
---|
3341 | number nu,nu1; |
---|
3342 | |
---|
3343 | me=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
3344 | ee=(int *)omAlloc((rVar(r)+1)*sizeof(int)); |
---|
3345 | if (e!=NULL) p_GetExpV(e,ee,r); |
---|
3346 | res=NULL; |
---|
3347 | h=p; |
---|
3348 | while (h!=NULL) |
---|
3349 | { |
---|
3350 | if ((e!=NULL) || (p_GetExp(h,n,r)==0)) |
---|
3351 | { |
---|
3352 | m=p_Head(h,r); |
---|
3353 | p_GetExpV(m,me,r); |
---|
3354 | exponent=me[n]; |
---|
3355 | me[n]=0; |
---|
3356 | for(i=rVar(r);i>0;i--) |
---|
3357 | me[i]+=exponent*ee[i]; |
---|
3358 | p_SetExpV(m,me,r); |
---|
3359 | if (e!=NULL) |
---|
3360 | { |
---|
3361 | n_Power(pGetCoeff(e),exponent,&nu,r->cf); |
---|
3362 | nu1=n_Mult(pGetCoeff(m),nu,r->cf); |
---|
3363 | n_Delete(&nu,r->cf); |
---|
3364 | p_SetCoeff(m,nu1,r); |
---|
3365 | } |
---|
3366 | res=p_Add_q(res,m,r); |
---|
3367 | } |
---|
3368 | p_LmDelete(&h,r); |
---|
3369 | } |
---|
3370 | omFreeSize((ADDRESS)me,(rVar(r)+1)*sizeof(int)); |
---|
3371 | omFreeSize((ADDRESS)ee,(rVar(r)+1)*sizeof(int)); |
---|
3372 | return res; |
---|
3373 | } |
---|
3374 | /*2 |
---|
3375 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
3376 | */ |
---|
3377 | poly p_PermPoly (poly p, int * perm, const ring oldRing, const ring dst, |
---|
3378 | nMapFunc nMap, int *par_perm, int OldPar) |
---|
3379 | { |
---|
3380 | int OldpVariables = oldRing->N; |
---|
3381 | poly result = NULL; |
---|
3382 | poly result_last = NULL; |
---|
3383 | poly aq=NULL; /* the map coefficient */ |
---|
3384 | poly qq; /* the mapped monomial */ |
---|
3385 | |
---|
3386 | while (p != NULL) |
---|
3387 | { |
---|
3388 | if ((OldPar==0)||(rField_is_GF(oldRing))) |
---|
3389 | { |
---|
3390 | qq = p_Init(dst); |
---|
3391 | number n=nMap(pGetCoeff(p),oldRing->cf,dst->cf); |
---|
3392 | if ((!rMinpolyIsNULL(dst)) |
---|
3393 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
3394 | { |
---|
3395 | n_Normalize(n,dst->cf); |
---|
3396 | } |
---|
3397 | pGetCoeff(qq)=n; |
---|
3398 | // coef may be zero: pTest(qq); |
---|
3399 | } |
---|
3400 | else |
---|
3401 | { |
---|
3402 | qq=p_One(dst); |
---|
3403 | WerrorS("longalg missing 2"); |
---|
3404 | #if 0 |
---|
3405 | aq=naPermNumber(pGetCoeff(p),par_perm,OldPar, oldRing); |
---|
3406 | if ((!rMinpolyIsNULL(dst)) |
---|
3407 | && ((rField_is_Zp_a(dst)) || (rField_is_Q_a(dst)))) |
---|
3408 | { |
---|
3409 | p_Normalize(aq,dst); |
---|
3410 | if (aq==NULL) |
---|
3411 | p_SetCoeff(qq,n_Init(0,dst->cf),dst); |
---|
3412 | } |
---|
3413 | p_Test(aq,dst); |
---|
3414 | #endif |
---|
3415 | } |
---|
3416 | if (rRing_has_Comp(dst)) p_SetComp(qq, p_GetComp(p,oldRing),dst); |
---|
3417 | if (n_IsZero(pGetCoeff(qq),dst->cf)) |
---|
3418 | { |
---|
3419 | p_LmDelete(&qq,dst); |
---|
3420 | } |
---|
3421 | else |
---|
3422 | { |
---|
3423 | int i; |
---|
3424 | int mapped_to_par=0; |
---|
3425 | for(i=1; i<=OldpVariables; i++) |
---|
3426 | { |
---|
3427 | int e=p_GetExp(p,i,oldRing); |
---|
3428 | if (e!=0) |
---|
3429 | { |
---|
3430 | if (perm==NULL) |
---|
3431 | { |
---|
3432 | p_SetExp(qq,i, e, dst); |
---|
3433 | } |
---|
3434 | else if (perm[i]>0) |
---|
3435 | p_AddExp(qq,perm[i], e/*p_GetExp( p,i,oldRing)*/, dst); |
---|
3436 | else if (perm[i]<0) |
---|
3437 | { |
---|
3438 | if (rField_is_GF(dst)) |
---|
3439 | { |
---|
3440 | number c=pGetCoeff(qq); |
---|
3441 | number ee=(number)rGetVar(1, dst->cf->extRing); |
---|
3442 | number eee;n_Power(ee,e,&eee,dst->cf); //nfDelete(ee,dst); |
---|
3443 | ee=n_Mult(c,eee,dst->cf); |
---|
3444 | //nfDelete(c,dst);nfDelete(eee,dst); |
---|
3445 | pSetCoeff0(qq,ee); |
---|
3446 | } |
---|
3447 | else |
---|
3448 | { |
---|
3449 | WerrorS("longalg missing 3"); |
---|
3450 | #if 0 |
---|
3451 | lnumber c=(lnumber)pGetCoeff(qq); |
---|
3452 | if (c->z->next==NULL) |
---|
3453 | p_AddExp(c->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/,dst->extRing); |
---|
3454 | else /* more difficult: we have really to multiply: */ |
---|
3455 | { |
---|
3456 | lnumber mmc=(lnumber)naInit(1,dst); |
---|
3457 | p_SetExp(mmc->z,-perm[i],e/*p_GetExp( p,i,oldRing)*/,dst->extRing); |
---|
3458 | p_Setm(mmc->z,dst->extRing->cf); |
---|
3459 | pGetCoeff(qq)=n_Mult((number)c,(number)mmc,dst->cf); |
---|
3460 | n_Delete((number *)&c,dst->cf); |
---|
3461 | n_Delete((number *)&mmc,dst->cf); |
---|
3462 | } |
---|
3463 | mapped_to_par=1; |
---|
3464 | #endif |
---|
3465 | } |
---|
3466 | } |
---|
3467 | else |
---|
3468 | { |
---|
3469 | /* this variable maps to 0 !*/ |
---|
3470 | p_LmDelete(&qq,dst); |
---|
3471 | break; |
---|
3472 | } |
---|
3473 | } |
---|
3474 | } |
---|
3475 | if (mapped_to_par |
---|
3476 | && (!rMinpolyIsNULL(dst))) |
---|
3477 | { |
---|
3478 | number n=pGetCoeff(qq); |
---|
3479 | n_Normalize(n,dst->cf); |
---|
3480 | pGetCoeff(qq)=n; |
---|
3481 | } |
---|
3482 | } |
---|
3483 | pIter(p); |
---|
3484 | #if 1 |
---|
3485 | if (qq!=NULL) |
---|
3486 | { |
---|
3487 | p_Setm(qq,dst); |
---|
3488 | p_Test(aq,dst); |
---|
3489 | p_Test(qq,dst); |
---|
3490 | if (aq!=NULL) qq=p_Mult_q(aq,qq,dst); |
---|
3491 | aq = qq; |
---|
3492 | while (pNext(aq) != NULL) pIter(aq); |
---|
3493 | if (result_last==NULL) |
---|
3494 | { |
---|
3495 | result=qq; |
---|
3496 | } |
---|
3497 | else |
---|
3498 | { |
---|
3499 | pNext(result_last)=qq; |
---|
3500 | } |
---|
3501 | result_last=aq; |
---|
3502 | aq = NULL; |
---|
3503 | } |
---|
3504 | else if (aq!=NULL) |
---|
3505 | { |
---|
3506 | p_Delete(&aq,dst); |
---|
3507 | } |
---|
3508 | } |
---|
3509 | result=p_SortAdd(result,dst); |
---|
3510 | #else |
---|
3511 | // if (qq!=NULL) |
---|
3512 | // { |
---|
3513 | // pSetm(qq); |
---|
3514 | // pTest(qq); |
---|
3515 | // pTest(aq); |
---|
3516 | // if (aq!=NULL) qq=pMult(aq,qq); |
---|
3517 | // aq = qq; |
---|
3518 | // while (pNext(aq) != NULL) pIter(aq); |
---|
3519 | // pNext(aq) = result; |
---|
3520 | // aq = NULL; |
---|
3521 | // result = qq; |
---|
3522 | // } |
---|
3523 | // else if (aq!=NULL) |
---|
3524 | // { |
---|
3525 | // pDelete(&aq); |
---|
3526 | // } |
---|
3527 | //} |
---|
3528 | //p = result; |
---|
3529 | //result = NULL; |
---|
3530 | //while (p != NULL) |
---|
3531 | //{ |
---|
3532 | // qq = p; |
---|
3533 | // pIter(p); |
---|
3534 | // qq->next = NULL; |
---|
3535 | // result = pAdd(result, qq); |
---|
3536 | //} |
---|
3537 | #endif |
---|
3538 | p_Test(result,dst); |
---|
3539 | return result; |
---|
3540 | } |
---|
3541 | /************************************************************** |
---|
3542 | * |
---|
3543 | * Jet |
---|
3544 | * |
---|
3545 | **************************************************************/ |
---|
3546 | |
---|
3547 | poly pp_Jet(poly p, int m, const ring R) |
---|
3548 | { |
---|
3549 | poly r=NULL; |
---|
3550 | poly t=NULL; |
---|
3551 | |
---|
3552 | while (p!=NULL) |
---|
3553 | { |
---|
3554 | if (p_Totaldegree(p,R)<=m) |
---|
3555 | { |
---|
3556 | if (r==NULL) |
---|
3557 | r=p_Head(p,R); |
---|
3558 | else |
---|
3559 | if (t==NULL) |
---|
3560 | { |
---|
3561 | pNext(r)=p_Head(p,R); |
---|
3562 | t=pNext(r); |
---|
3563 | } |
---|
3564 | else |
---|
3565 | { |
---|
3566 | pNext(t)=p_Head(p,R); |
---|
3567 | pIter(t); |
---|
3568 | } |
---|
3569 | } |
---|
3570 | pIter(p); |
---|
3571 | } |
---|
3572 | return r; |
---|
3573 | } |
---|
3574 | |
---|
3575 | poly p_Jet(poly p, int m,const ring R) |
---|
3576 | { |
---|
3577 | poly t=NULL; |
---|
3578 | |
---|
3579 | while((p!=NULL) && (p_Totaldegree(p,R)>m)) p_LmDelete(&p,R); |
---|
3580 | if (p==NULL) return NULL; |
---|
3581 | poly r=p; |
---|
3582 | while (pNext(p)!=NULL) |
---|
3583 | { |
---|
3584 | if (p_Totaldegree(pNext(p),R)>m) |
---|
3585 | { |
---|
3586 | p_LmDelete(&pNext(p),R); |
---|
3587 | } |
---|
3588 | else |
---|
3589 | pIter(p); |
---|
3590 | } |
---|
3591 | return r; |
---|
3592 | } |
---|
3593 | |
---|
3594 | poly pp_JetW(poly p, int m, short *w, const ring R) |
---|
3595 | { |
---|
3596 | poly r=NULL; |
---|
3597 | poly t=NULL; |
---|
3598 | while (p!=NULL) |
---|
3599 | { |
---|
3600 | if (totaldegreeWecart_IV(p,R,w)<=m) |
---|
3601 | { |
---|
3602 | if (r==NULL) |
---|
3603 | r=p_Head(p,R); |
---|
3604 | else |
---|
3605 | if (t==NULL) |
---|
3606 | { |
---|
3607 | pNext(r)=p_Head(p,R); |
---|
3608 | t=pNext(r); |
---|
3609 | } |
---|
3610 | else |
---|
3611 | { |
---|
3612 | pNext(t)=p_Head(p,R); |
---|
3613 | pIter(t); |
---|
3614 | } |
---|
3615 | } |
---|
3616 | pIter(p); |
---|
3617 | } |
---|
3618 | return r; |
---|
3619 | } |
---|
3620 | |
---|
3621 | poly p_JetW(poly p, int m, short *w, const ring R) |
---|
3622 | { |
---|
3623 | while((p!=NULL) && (totaldegreeWecart_IV(p,R,w)>m)) p_LmDelete(&p,R); |
---|
3624 | if (p==NULL) return NULL; |
---|
3625 | poly r=p; |
---|
3626 | while (pNext(p)!=NULL) |
---|
3627 | { |
---|
3628 | if (totaldegreeWecart_IV(pNext(p),R,w)>m) |
---|
3629 | { |
---|
3630 | p_LmDelete(&pNext(p),R); |
---|
3631 | } |
---|
3632 | else |
---|
3633 | pIter(p); |
---|
3634 | } |
---|
3635 | return r; |
---|
3636 | } |
---|
3637 | |
---|
3638 | /*************************************************************/ |
---|
3639 | int p_MinDeg(poly p,intvec *w, const ring R) |
---|
3640 | { |
---|
3641 | if(p==NULL) |
---|
3642 | return -1; |
---|
3643 | int d=-1; |
---|
3644 | while(p!=NULL) |
---|
3645 | { |
---|
3646 | int d0=0; |
---|
3647 | for(int j=0;j<rVar(R);j++) |
---|
3648 | if(w==NULL||j>=w->length()) |
---|
3649 | d0+=p_GetExp(p,j+1,R); |
---|
3650 | else |
---|
3651 | d0+=(*w)[j]*p_GetExp(p,j+1,R); |
---|
3652 | if(d0<d||d==-1) |
---|
3653 | d=d0; |
---|
3654 | pIter(p); |
---|
3655 | } |
---|
3656 | return d; |
---|
3657 | } |
---|
3658 | |
---|
3659 | /***************************************************************/ |
---|
3660 | |
---|
3661 | poly p_Series(int n,poly p,poly u, intvec *w, const ring R) |
---|
3662 | { |
---|
3663 | short *ww=iv2array(w,R); |
---|
3664 | if(p!=NULL) |
---|
3665 | { |
---|
3666 | if(u==NULL) |
---|
3667 | p=p_JetW(p,n,ww,R); |
---|
3668 | else |
---|
3669 | p=p_JetW(p_Mult_q(p,p_Invers(n-p_MinDeg(p,w,R),u,w,R),R),n,ww,R); |
---|
3670 | } |
---|
3671 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
3672 | return p; |
---|
3673 | } |
---|
3674 | |
---|
3675 | poly p_Invers(int n,poly u,intvec *w, const ring R) |
---|
3676 | { |
---|
3677 | if(n<0) |
---|
3678 | return NULL; |
---|
3679 | number u0=n_Invers(pGetCoeff(u),R->cf); |
---|
3680 | poly v=p_NSet(u0,R); |
---|
3681 | if(n==0) |
---|
3682 | return v; |
---|
3683 | short *ww=iv2array(w,R); |
---|
3684 | poly u1=p_JetW(p_Sub(p_One(R),p_Mult_nn(u,u0,R),R),n,ww,R); |
---|
3685 | if(u1==NULL) |
---|
3686 | { |
---|
3687 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
3688 | return v; |
---|
3689 | } |
---|
3690 | poly v1=p_Mult_nn(p_Copy(u1,R),u0,R); |
---|
3691 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
3692 | for(int i=n/p_MinDeg(u1,w,R);i>1;i--) |
---|
3693 | { |
---|
3694 | v1=p_JetW(p_Mult_q(v1,p_Copy(u1,R),R),n,ww,R); |
---|
3695 | v=p_Add_q(v,p_Copy(v1,R),R); |
---|
3696 | } |
---|
3697 | p_Delete(&u1,R); |
---|
3698 | p_Delete(&v1,R); |
---|
3699 | omFreeSize((ADDRESS)ww,(rVar(R)+1)*sizeof(short)); |
---|
3700 | return v; |
---|
3701 | } |
---|
3702 | |
---|
3703 | BOOLEAN p_EqualPolys(poly p1,poly p2, const ring r) |
---|
3704 | { |
---|
3705 | while ((p1 != NULL) && (p2 != NULL)) |
---|
3706 | { |
---|
3707 | if (! p_LmEqual(p1, p2,r)) |
---|
3708 | return FALSE; |
---|
3709 | if (! n_Equal(p_GetCoeff(p1,r), p_GetCoeff(p2,r),r )) |
---|
3710 | return FALSE; |
---|
3711 | pIter(p1); |
---|
3712 | pIter(p2); |
---|
3713 | } |
---|
3714 | return (p1==p2); |
---|
3715 | } |
---|
3716 | |
---|
3717 | /*2 |
---|
3718 | *returns TRUE if p1 is a skalar multiple of p2 |
---|
3719 | *assume p1 != NULL and p2 != NULL |
---|
3720 | */ |
---|
3721 | BOOLEAN p_ComparePolys(poly p1,poly p2, const ring r) |
---|
3722 | { |
---|
3723 | number n,nn; |
---|
3724 | pAssume(p1 != NULL && p2 != NULL); |
---|
3725 | |
---|
3726 | if (!p_LmEqual(p1,p2,r)) //compare leading mons |
---|
3727 | return FALSE; |
---|
3728 | if ((pNext(p1)==NULL) && (pNext(p2)!=NULL)) |
---|
3729 | return FALSE; |
---|
3730 | if ((pNext(p2)==NULL) && (pNext(p1)!=NULL)) |
---|
3731 | return FALSE; |
---|
3732 | if (pLength(p1) != pLength(p2)) |
---|
3733 | return FALSE; |
---|
3734 | #ifdef HAVE_RINGS |
---|
3735 | if (rField_is_Ring(r)) |
---|
3736 | { |
---|
3737 | if (!n_DivBy(p_GetCoeff(p1, r), p_GetCoeff(p2, r), r)) return FALSE; |
---|
3738 | } |
---|
3739 | #endif |
---|
3740 | n=n_Div(p_GetCoeff(p1,r),p_GetCoeff(p2,r),r); |
---|
3741 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
---|
3742 | { |
---|
3743 | if ( ! p_LmEqual(p1, p2,r)) |
---|
3744 | { |
---|
3745 | n_Delete(&n, r); |
---|
3746 | return FALSE; |
---|
3747 | } |
---|
3748 | if (!n_Equal(p_GetCoeff(p1, r), nn = n_Mult(p_GetCoeff(p2, r),n, r), r)) |
---|
3749 | { |
---|
3750 | n_Delete(&n, r); |
---|
3751 | n_Delete(&nn, r); |
---|
3752 | return FALSE; |
---|
3753 | } |
---|
3754 | n_Delete(&nn, r); |
---|
3755 | pIter(p1); |
---|
3756 | pIter(p2); |
---|
3757 | } |
---|
3758 | n_Delete(&n, r); |
---|
3759 | return TRUE; |
---|
3760 | } |
---|
3761 | |
---|
3762 | |
---|
3763 | /*************************************************************** |
---|
3764 | * |
---|
3765 | * p_ShallowDelete |
---|
3766 | * |
---|
3767 | ***************************************************************/ |
---|
3768 | #undef LINKAGE |
---|
3769 | #define LINKAGE |
---|
3770 | #undef p_Delete__T |
---|
3771 | #define p_Delete__T p_ShallowDelete |
---|
3772 | #undef n_Delete__T |
---|
3773 | #define n_Delete__T(n, r) ((void)0) |
---|
3774 | |
---|
3775 | #include <polys/templates/p_Delete__T.cc> |
---|
3776 | |
---|