1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /* $Id$ */ |
---|
5 | /* |
---|
6 | * ABSTRACT - all basic methods to manipulate ideals |
---|
7 | */ |
---|
8 | |
---|
9 | |
---|
10 | /* includes */ |
---|
11 | #include "config.h" |
---|
12 | #include <misc/auxiliary.h> |
---|
13 | #include <misc/options.h> |
---|
14 | #include <omalloc/omalloc.h> |
---|
15 | #include <polys/monomials/p_polys.h> |
---|
16 | #include <misc/intvec.h> |
---|
17 | #include <polys/simpleideals.h> |
---|
18 | |
---|
19 | /*2 |
---|
20 | * initialise an ideal |
---|
21 | */ |
---|
22 | ideal idInit(int idsize, int rank) |
---|
23 | { |
---|
24 | /*- initialise an ideal -*/ |
---|
25 | ideal hh = (ideal )omAllocBin(sip_sideal_bin); |
---|
26 | hh->nrows = 1; |
---|
27 | hh->rank = rank; |
---|
28 | IDELEMS(hh) = idsize; |
---|
29 | if (idsize>0) |
---|
30 | { |
---|
31 | hh->m = (poly *)omAlloc0(idsize*sizeof(poly)); |
---|
32 | } |
---|
33 | else |
---|
34 | hh->m=NULL; |
---|
35 | return hh; |
---|
36 | } |
---|
37 | |
---|
38 | #ifdef PDEBUG |
---|
39 | // this is only for outputting an ideal within the debugger |
---|
40 | void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint) |
---|
41 | { |
---|
42 | assume( debugPrint >= 0 ); |
---|
43 | |
---|
44 | if( id == NULL ) |
---|
45 | PrintS("(NULL)"); |
---|
46 | else |
---|
47 | { |
---|
48 | Print("Module of rank %ld,real rank %ld and %d generators.\n", |
---|
49 | id->rank,id_RankFreeModule(id, lmRing, tailRing),IDELEMS(id)); |
---|
50 | |
---|
51 | int j = (id->ncols*id->nrows) - 1; |
---|
52 | while ((j > 0) && (id->m[j]==NULL)) j--; |
---|
53 | for (int i = 0; i <= j; i++) |
---|
54 | { |
---|
55 | Print("generator %d: ",i); p_DebugPrint(id->m[i], lmRing, tailRing, debugPrint); |
---|
56 | } |
---|
57 | } |
---|
58 | } |
---|
59 | #endif |
---|
60 | |
---|
61 | /* index of generator with leading term in ground ring (if any); |
---|
62 | otherwise -1 */ |
---|
63 | int id_PosConstant(ideal id, const ring r) |
---|
64 | { |
---|
65 | int k; |
---|
66 | for (k = IDELEMS(id)-1; k>=0; k--) |
---|
67 | { |
---|
68 | if (p_LmIsConstantComp(id->m[k], r) == TRUE) |
---|
69 | return k; |
---|
70 | } |
---|
71 | return -1; |
---|
72 | } |
---|
73 | |
---|
74 | /*2 |
---|
75 | * initialise the maximal ideal (at 0) |
---|
76 | */ |
---|
77 | ideal id_MaxIdeal (const ring r) |
---|
78 | { |
---|
79 | int l; |
---|
80 | ideal hh=NULL; |
---|
81 | |
---|
82 | hh=idInit(rVar(r),1); |
---|
83 | for (l=0; l<rVar(r); l++) |
---|
84 | { |
---|
85 | hh->m[l] = p_One(r); |
---|
86 | p_SetExp(hh->m[l],l+1,1,r); |
---|
87 | p_Setm(hh->m[l],r); |
---|
88 | } |
---|
89 | return hh; |
---|
90 | } |
---|
91 | |
---|
92 | /*2 |
---|
93 | * deletes an ideal/matrix |
---|
94 | */ |
---|
95 | void id_Delete (ideal * h, ring r) |
---|
96 | { |
---|
97 | int j,elems; |
---|
98 | if (*h == NULL) |
---|
99 | return; |
---|
100 | elems=j=(*h)->nrows*(*h)->ncols; |
---|
101 | if (j>0) |
---|
102 | { |
---|
103 | do |
---|
104 | { |
---|
105 | p_Delete(&((*h)->m[--j]), r); |
---|
106 | } |
---|
107 | while (j>0); |
---|
108 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
---|
109 | } |
---|
110 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
---|
111 | *h=NULL; |
---|
112 | } |
---|
113 | |
---|
114 | |
---|
115 | /*2 |
---|
116 | * Shallowdeletes an ideal/matrix |
---|
117 | */ |
---|
118 | void id_ShallowDelete (ideal *h, ring r) |
---|
119 | { |
---|
120 | int j,elems; |
---|
121 | if (*h == NULL) |
---|
122 | return; |
---|
123 | elems=j=(*h)->nrows*(*h)->ncols; |
---|
124 | if (j>0) |
---|
125 | { |
---|
126 | do |
---|
127 | { |
---|
128 | p_ShallowDelete(&((*h)->m[--j]), r); |
---|
129 | } |
---|
130 | while (j>0); |
---|
131 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
---|
132 | } |
---|
133 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
---|
134 | *h=NULL; |
---|
135 | } |
---|
136 | |
---|
137 | /*2 |
---|
138 | *gives an ideal the minimal possible size |
---|
139 | */ |
---|
140 | void idSkipZeroes (ideal ide) |
---|
141 | { |
---|
142 | int k; |
---|
143 | int j = -1; |
---|
144 | BOOLEAN change=FALSE; |
---|
145 | for (k=0; k<IDELEMS(ide); k++) |
---|
146 | { |
---|
147 | if (ide->m[k] != NULL) |
---|
148 | { |
---|
149 | j++; |
---|
150 | if (change) |
---|
151 | { |
---|
152 | ide->m[j] = ide->m[k]; |
---|
153 | } |
---|
154 | } |
---|
155 | else |
---|
156 | { |
---|
157 | change=TRUE; |
---|
158 | } |
---|
159 | } |
---|
160 | if (change) |
---|
161 | { |
---|
162 | if (j == -1) |
---|
163 | j = 0; |
---|
164 | else |
---|
165 | { |
---|
166 | for (k=j+1; k<IDELEMS(ide); k++) |
---|
167 | ide->m[k] = NULL; |
---|
168 | } |
---|
169 | pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide)); |
---|
170 | IDELEMS(ide) = j+1; |
---|
171 | } |
---|
172 | } |
---|
173 | |
---|
174 | /*2 |
---|
175 | * copies the first k (>= 1) entries of the given ideal |
---|
176 | * and returns these as a new ideal |
---|
177 | * (Note that the copied polynomials may be zero.) |
---|
178 | */ |
---|
179 | ideal id_CopyFirstK (const ideal ide, const int k,const ring r) |
---|
180 | { |
---|
181 | ideal newI = idInit(k, 0); |
---|
182 | for (int i = 0; i < k; i++) |
---|
183 | newI->m[i] = p_Copy(ide->m[i],r); |
---|
184 | return newI; |
---|
185 | } |
---|
186 | |
---|
187 | /*2 |
---|
188 | * ideal id = (id[i]) |
---|
189 | * result is leadcoeff(id[i]) = 1 |
---|
190 | */ |
---|
191 | void id_Norm(ideal id, const ring r) |
---|
192 | { |
---|
193 | for (int i=IDELEMS(id)-1; i>=0; i--) |
---|
194 | { |
---|
195 | if (id->m[i] != NULL) |
---|
196 | { |
---|
197 | p_Norm(id->m[i],r); |
---|
198 | } |
---|
199 | } |
---|
200 | } |
---|
201 | |
---|
202 | /*2 |
---|
203 | * ideal id = (id[i]), c any unit |
---|
204 | * if id[i] = c*id[j] then id[j] is deleted for j > i |
---|
205 | */ |
---|
206 | void id_DelMultiples(ideal id, const ring r) |
---|
207 | { |
---|
208 | int i, j; |
---|
209 | int k = IDELEMS(id)-1; |
---|
210 | for (i=k; i>=0; i--) |
---|
211 | { |
---|
212 | if (id->m[i]!=NULL) |
---|
213 | { |
---|
214 | for (j=k; j>i; j--) |
---|
215 | { |
---|
216 | if (id->m[j]!=NULL) |
---|
217 | { |
---|
218 | #ifdef HAVE_RINGS |
---|
219 | if (rField_is_Ring(r)) |
---|
220 | { |
---|
221 | /* if id[j] = c*id[i] then delete id[j]. |
---|
222 | In the below cases of a ground field, we |
---|
223 | check whether id[i] = c*id[j] and, if so, |
---|
224 | delete id[j] for historical reasons (so |
---|
225 | that previous output does not change) */ |
---|
226 | if (p_ComparePolys(id->m[j], id->m[i],r)) p_Delete(&id->m[j],r); |
---|
227 | } |
---|
228 | else |
---|
229 | { |
---|
230 | if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r); |
---|
231 | } |
---|
232 | #else |
---|
233 | if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r); |
---|
234 | #endif |
---|
235 | } |
---|
236 | } |
---|
237 | } |
---|
238 | } |
---|
239 | } |
---|
240 | |
---|
241 | /*2 |
---|
242 | * ideal id = (id[i]) |
---|
243 | * if id[i] = id[j] then id[j] is deleted for j > i |
---|
244 | */ |
---|
245 | void id_DelEquals(ideal id, const ring r) |
---|
246 | { |
---|
247 | int i, j; |
---|
248 | int k = IDELEMS(id)-1; |
---|
249 | for (i=k; i>=0; i--) |
---|
250 | { |
---|
251 | if (id->m[i]!=NULL) |
---|
252 | { |
---|
253 | for (j=k; j>i; j--) |
---|
254 | { |
---|
255 | if ((id->m[j]!=NULL) |
---|
256 | && (p_EqualPolys(id->m[i], id->m[j],r))) |
---|
257 | { |
---|
258 | p_Delete(&id->m[j],r); |
---|
259 | } |
---|
260 | } |
---|
261 | } |
---|
262 | } |
---|
263 | } |
---|
264 | |
---|
265 | // |
---|
266 | // Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i |
---|
267 | // |
---|
268 | void id_DelLmEquals(ideal id, const ring r) |
---|
269 | { |
---|
270 | int i, j; |
---|
271 | int k = IDELEMS(id)-1; |
---|
272 | for (i=k; i>=0; i--) |
---|
273 | { |
---|
274 | if (id->m[i] != NULL) |
---|
275 | { |
---|
276 | for (j=k; j>i; j--) |
---|
277 | { |
---|
278 | if ((id->m[j] != NULL) |
---|
279 | && p_LmEqual(id->m[i], id->m[j],r) |
---|
280 | #ifdef HAVE_RINGS |
---|
281 | && n_IsUnit(pGetCoeff(id->m[i]),r->cf) && n_IsUnit(pGetCoeff(id->m[j]),r->cf) |
---|
282 | #endif |
---|
283 | ) |
---|
284 | { |
---|
285 | p_Delete(&id->m[j],r); |
---|
286 | } |
---|
287 | } |
---|
288 | } |
---|
289 | } |
---|
290 | } |
---|
291 | |
---|
292 | // |
---|
293 | // delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., |
---|
294 | // delete id[i], if LT(i) == coeff*mon*LT(j) |
---|
295 | // |
---|
296 | void id_DelDiv(ideal id, const ring r) |
---|
297 | { |
---|
298 | int i, j; |
---|
299 | int k = IDELEMS(id)-1; |
---|
300 | for (i=k; i>=0; i--) |
---|
301 | { |
---|
302 | if (id->m[i] != NULL) |
---|
303 | { |
---|
304 | for (j=k; j>i; j--) |
---|
305 | { |
---|
306 | if (id->m[j]!=NULL) |
---|
307 | { |
---|
308 | #ifdef HAVE_RINGS |
---|
309 | if (rField_is_Ring(r)) |
---|
310 | { |
---|
311 | if (p_DivisibleByRingCase(id->m[i], id->m[j],r)) |
---|
312 | { |
---|
313 | p_Delete(&id->m[j],r); |
---|
314 | } |
---|
315 | else if (p_DivisibleByRingCase(id->m[j], id->m[i],r)) |
---|
316 | { |
---|
317 | p_Delete(&id->m[i],r); |
---|
318 | break; |
---|
319 | } |
---|
320 | } |
---|
321 | else |
---|
322 | { |
---|
323 | #endif |
---|
324 | /* the case of a ground field: */ |
---|
325 | if (p_DivisibleBy(id->m[i], id->m[j],r)) |
---|
326 | { |
---|
327 | p_Delete(&id->m[j],r); |
---|
328 | } |
---|
329 | else if (p_DivisibleBy(id->m[j], id->m[i],r)) |
---|
330 | { |
---|
331 | p_Delete(&id->m[i],r); |
---|
332 | break; |
---|
333 | } |
---|
334 | #ifdef HAVE_RINGS |
---|
335 | } |
---|
336 | #endif |
---|
337 | } |
---|
338 | } |
---|
339 | } |
---|
340 | } |
---|
341 | } |
---|
342 | |
---|
343 | /*2 |
---|
344 | *test if the ideal has only constant polynomials |
---|
345 | */ |
---|
346 | BOOLEAN id_IsConstant(ideal id, const ring r) |
---|
347 | { |
---|
348 | int k; |
---|
349 | for (k = IDELEMS(id)-1; k>=0; k--) |
---|
350 | { |
---|
351 | if (!p_IsConstantPoly(id->m[k],r)) |
---|
352 | return FALSE; |
---|
353 | } |
---|
354 | return TRUE; |
---|
355 | } |
---|
356 | |
---|
357 | /*2 |
---|
358 | * copy an ideal |
---|
359 | */ |
---|
360 | #ifdef PDEBUG |
---|
361 | ideal id_DBCopy(ideal h1,const char *f,int l, const ring r) |
---|
362 | { |
---|
363 | int i; |
---|
364 | ideal h2; |
---|
365 | |
---|
366 | id_DBTest(h1,PDEBUG,f,l,r); |
---|
367 | //#ifdef TEST |
---|
368 | if (h1 == NULL) |
---|
369 | { |
---|
370 | h2=idDBInit(1,1,f,l); |
---|
371 | } |
---|
372 | else |
---|
373 | //#endif |
---|
374 | { |
---|
375 | h2=idDBInit(IDELEMS(h1),h1->rank,f,l); |
---|
376 | for (i=IDELEMS(h1)-1; i>=0; i--) |
---|
377 | h2->m[i] = p_Copy(h1->m[i],r); |
---|
378 | } |
---|
379 | return h2; |
---|
380 | } |
---|
381 | #else |
---|
382 | ideal id_Copy(ideal h1, const ring r) |
---|
383 | { |
---|
384 | int i; |
---|
385 | ideal h2; |
---|
386 | |
---|
387 | //#ifdef TEST |
---|
388 | if (h1 == NULL) |
---|
389 | { |
---|
390 | h2=idInit(1,1); |
---|
391 | } |
---|
392 | else |
---|
393 | //#endif |
---|
394 | { |
---|
395 | h2=idInit(IDELEMS(h1),h1->rank); |
---|
396 | for (i=IDELEMS(h1)-1; i>=0; i--) |
---|
397 | h2->m[i] = p_Copy(h1->m[i],r); |
---|
398 | } |
---|
399 | return h2; |
---|
400 | } |
---|
401 | #endif |
---|
402 | |
---|
403 | #ifdef PDEBUG |
---|
404 | void id_DBTest(ideal h1, int level, const char *f,const int l, const ring r) |
---|
405 | { |
---|
406 | int i; |
---|
407 | |
---|
408 | if (h1 != NULL) |
---|
409 | { |
---|
410 | // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix |
---|
411 | omCheckAddrSize(h1,sizeof(*h1)); |
---|
412 | omdebugAddrSize(h1->m,h1->ncols*h1->nrows*sizeof(poly)); |
---|
413 | /* to be able to test matrices: */ |
---|
414 | for (i=(h1->ncols*h1->nrows)-1; i>=0; i--) |
---|
415 | _p_Test(h1->m[i], r, level); |
---|
416 | int new_rk=id_RankFreeModule(h1,r); |
---|
417 | if(new_rk > h1->rank) |
---|
418 | { |
---|
419 | dReportError("wrong rank %d (should be %d) in %s:%d\n", |
---|
420 | h1->rank, new_rk, f,l); |
---|
421 | omPrintAddrInfo(stderr, h1, " for ideal"); |
---|
422 | h1->rank=new_rk; |
---|
423 | } |
---|
424 | } |
---|
425 | } |
---|
426 | #endif |
---|
427 | |
---|
428 | /*3 |
---|
429 | * for idSort: compare a and b revlex inclusive module comp. |
---|
430 | */ |
---|
431 | static int p_Comp_RevLex(poly a, poly b,BOOLEAN nolex, const ring R) |
---|
432 | { |
---|
433 | if (b==NULL) return 1; |
---|
434 | if (a==NULL) return -1; |
---|
435 | |
---|
436 | if (nolex) |
---|
437 | { |
---|
438 | int r=p_LmCmp(a,b,R); |
---|
439 | if (r!=0) return r; |
---|
440 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf); |
---|
441 | r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */ |
---|
442 | n_Delete(&h, R->cf); |
---|
443 | return r; |
---|
444 | } |
---|
445 | int l=rVar(R); |
---|
446 | while ((l>0) && (p_GetExp(a,l,R)==p_GetExp(b,l,R))) l--; |
---|
447 | if (l==0) |
---|
448 | { |
---|
449 | if (p_GetComp(a,R)==p_GetComp(b,R)) |
---|
450 | { |
---|
451 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf); |
---|
452 | int r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */ |
---|
453 | n_Delete(&h,R->cf); |
---|
454 | return r; |
---|
455 | } |
---|
456 | if (p_GetComp(a,R)>p_GetComp(b,R)) return 1; |
---|
457 | } |
---|
458 | else if (p_GetExp(a,l,R)>p_GetExp(b,l,R)) |
---|
459 | return 1; |
---|
460 | return -1; |
---|
461 | } |
---|
462 | |
---|
463 | /*2 |
---|
464 | *sorts the ideal w.r.t. the actual ringordering |
---|
465 | *uses lex-ordering when nolex = FALSE |
---|
466 | */ |
---|
467 | intvec *id_Sort(ideal id,BOOLEAN nolex, const ring r) |
---|
468 | { |
---|
469 | poly p,q; |
---|
470 | intvec * result = new intvec(IDELEMS(id)); |
---|
471 | int i, j, actpos=0, newpos, l; |
---|
472 | int diff, olddiff, lastcomp, newcomp; |
---|
473 | BOOLEAN notFound; |
---|
474 | |
---|
475 | for (i=0;i<IDELEMS(id);i++) |
---|
476 | { |
---|
477 | if (id->m[i]!=NULL) |
---|
478 | { |
---|
479 | notFound = TRUE; |
---|
480 | newpos = actpos / 2; |
---|
481 | diff = (actpos+1) / 2; |
---|
482 | diff = (diff+1) / 2; |
---|
483 | lastcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
---|
484 | if (lastcomp<0) |
---|
485 | { |
---|
486 | newpos -= diff; |
---|
487 | } |
---|
488 | else if (lastcomp>0) |
---|
489 | { |
---|
490 | newpos += diff; |
---|
491 | } |
---|
492 | else |
---|
493 | { |
---|
494 | notFound = FALSE; |
---|
495 | } |
---|
496 | //while ((newpos>=0) && (newpos<actpos) && (notFound)) |
---|
497 | while (notFound && (newpos>=0) && (newpos<actpos)) |
---|
498 | { |
---|
499 | newcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
---|
500 | olddiff = diff; |
---|
501 | if (diff>1) |
---|
502 | { |
---|
503 | diff = (diff+1) / 2; |
---|
504 | if ((newcomp==1) |
---|
505 | && (actpos-newpos>1) |
---|
506 | && (diff>1) |
---|
507 | && (newpos+diff>=actpos)) |
---|
508 | { |
---|
509 | diff = actpos-newpos-1; |
---|
510 | } |
---|
511 | else if ((newcomp==-1) |
---|
512 | && (diff>1) |
---|
513 | && (newpos<diff)) |
---|
514 | { |
---|
515 | diff = newpos; |
---|
516 | } |
---|
517 | } |
---|
518 | if (newcomp<0) |
---|
519 | { |
---|
520 | if ((olddiff==1) && (lastcomp>0)) |
---|
521 | notFound = FALSE; |
---|
522 | else |
---|
523 | newpos -= diff; |
---|
524 | } |
---|
525 | else if (newcomp>0) |
---|
526 | { |
---|
527 | if ((olddiff==1) && (lastcomp<0)) |
---|
528 | { |
---|
529 | notFound = FALSE; |
---|
530 | newpos++; |
---|
531 | } |
---|
532 | else |
---|
533 | { |
---|
534 | newpos += diff; |
---|
535 | } |
---|
536 | } |
---|
537 | else |
---|
538 | { |
---|
539 | notFound = FALSE; |
---|
540 | } |
---|
541 | lastcomp = newcomp; |
---|
542 | if (diff==0) notFound=FALSE; /*hs*/ |
---|
543 | } |
---|
544 | if (newpos<0) newpos = 0; |
---|
545 | if (newpos>actpos) newpos = actpos; |
---|
546 | while ((newpos<actpos) && (p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r)==0)) |
---|
547 | newpos++; |
---|
548 | for (j=actpos;j>newpos;j--) |
---|
549 | { |
---|
550 | (*result)[j] = (*result)[j-1]; |
---|
551 | } |
---|
552 | (*result)[newpos] = i; |
---|
553 | actpos++; |
---|
554 | } |
---|
555 | } |
---|
556 | for (j=0;j<actpos;j++) (*result)[j]++; |
---|
557 | return result; |
---|
558 | } |
---|
559 | |
---|
560 | /*2 |
---|
561 | * concat the lists h1 and h2 without zeros |
---|
562 | */ |
---|
563 | ideal id_SimpleAdd (ideal h1,ideal h2, const ring R) |
---|
564 | { |
---|
565 | int i,j,r,l; |
---|
566 | ideal result; |
---|
567 | |
---|
568 | if (h1==NULL) return id_Copy(h2,R); |
---|
569 | if (h2==NULL) return id_Copy(h1,R); |
---|
570 | j = IDELEMS(h1)-1; |
---|
571 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
572 | i = IDELEMS(h2)-1; |
---|
573 | while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
574 | r = si_max(h1->rank,h2->rank); |
---|
575 | if (i+j==(-2)) |
---|
576 | return idInit(1,r); |
---|
577 | else |
---|
578 | result=idInit(i+j+2,r); |
---|
579 | for (l=j; l>=0; l--) |
---|
580 | { |
---|
581 | result->m[l] = p_Copy(h1->m[l],R); |
---|
582 | } |
---|
583 | r = i+j+1; |
---|
584 | for (l=i; l>=0; l--, r--) |
---|
585 | { |
---|
586 | result->m[r] = p_Copy(h2->m[l],R); |
---|
587 | } |
---|
588 | return result; |
---|
589 | } |
---|
590 | |
---|
591 | /*2 |
---|
592 | * insert h2 into h1 (if h2 is not the zero polynomial) |
---|
593 | * return TRUE iff h2 was indeed inserted |
---|
594 | */ |
---|
595 | BOOLEAN idInsertPoly (ideal h1, poly h2) |
---|
596 | { |
---|
597 | if (h2==NULL) return FALSE; |
---|
598 | int j = IDELEMS(h1)-1; |
---|
599 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
600 | j++; |
---|
601 | if (j==IDELEMS(h1)) |
---|
602 | { |
---|
603 | pEnlargeSet(&(h1->m),IDELEMS(h1),16); |
---|
604 | IDELEMS(h1)+=16; |
---|
605 | } |
---|
606 | h1->m[j]=h2; |
---|
607 | return TRUE; |
---|
608 | } |
---|
609 | |
---|
610 | /*2 |
---|
611 | * insert h2 into h1 depending on the two boolean parameters: |
---|
612 | * - if zeroOk is true, then h2 will also be inserted when it is zero |
---|
613 | * - if duplicateOk is true, then h2 will also be inserted when it is |
---|
614 | * already present in h1 |
---|
615 | * return TRUE iff h2 was indeed inserted |
---|
616 | */ |
---|
617 | BOOLEAN id_InsertPolyWithTests (ideal h1, const int validEntries, |
---|
618 | const poly h2, const bool zeroOk, const bool duplicateOk, const ring r) |
---|
619 | { |
---|
620 | if ((!zeroOk) && (h2 == NULL)) return FALSE; |
---|
621 | if (!duplicateOk) |
---|
622 | { |
---|
623 | bool h2FoundInH1 = false; |
---|
624 | int i = 0; |
---|
625 | while ((i < validEntries) && (!h2FoundInH1)) |
---|
626 | { |
---|
627 | h2FoundInH1 = p_EqualPolys(h1->m[i], h2,r); |
---|
628 | i++; |
---|
629 | } |
---|
630 | if (h2FoundInH1) return FALSE; |
---|
631 | } |
---|
632 | if (validEntries == IDELEMS(h1)) |
---|
633 | { |
---|
634 | pEnlargeSet(&(h1->m), IDELEMS(h1), 16); |
---|
635 | IDELEMS(h1) += 16; |
---|
636 | } |
---|
637 | h1->m[validEntries] = h2; |
---|
638 | return TRUE; |
---|
639 | } |
---|
640 | |
---|
641 | /*2 |
---|
642 | * h1 + h2 |
---|
643 | */ |
---|
644 | ideal id_Add (ideal h1,ideal h2, const ring r) |
---|
645 | { |
---|
646 | ideal result = id_SimpleAdd(h1,h2,r); |
---|
647 | id_Compactify(result,r); |
---|
648 | return result; |
---|
649 | } |
---|
650 | |
---|
651 | /*2 |
---|
652 | * h1 * h2 |
---|
653 | */ |
---|
654 | ideal id_Mult (ideal h1,ideal h2, const ring r) |
---|
655 | { |
---|
656 | int i,j,k; |
---|
657 | ideal hh; |
---|
658 | |
---|
659 | j = IDELEMS(h1); |
---|
660 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
---|
661 | i = IDELEMS(h2); |
---|
662 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
---|
663 | j = j * i; |
---|
664 | if (j == 0) |
---|
665 | hh = idInit(1,1); |
---|
666 | else |
---|
667 | hh=idInit(j,1); |
---|
668 | if (h1->rank<h2->rank) |
---|
669 | hh->rank = h2->rank; |
---|
670 | else |
---|
671 | hh->rank = h1->rank; |
---|
672 | if (j==0) return hh; |
---|
673 | k = 0; |
---|
674 | for (i=0; i<IDELEMS(h1); i++) |
---|
675 | { |
---|
676 | if (h1->m[i] != NULL) |
---|
677 | { |
---|
678 | for (j=0; j<IDELEMS(h2); j++) |
---|
679 | { |
---|
680 | if (h2->m[j] != NULL) |
---|
681 | { |
---|
682 | hh->m[k] = pp_Mult_qq(h1->m[i],h2->m[j],r); |
---|
683 | k++; |
---|
684 | } |
---|
685 | } |
---|
686 | } |
---|
687 | } |
---|
688 | { |
---|
689 | id_Compactify(hh,r); |
---|
690 | return hh; |
---|
691 | } |
---|
692 | } |
---|
693 | |
---|
694 | /*2 |
---|
695 | *returns true if h is the zero ideal |
---|
696 | */ |
---|
697 | BOOLEAN idIs0 (ideal h) |
---|
698 | { |
---|
699 | int i; |
---|
700 | |
---|
701 | if (h == NULL) return TRUE; |
---|
702 | i = IDELEMS(h)-1; |
---|
703 | while ((i >= 0) && (h->m[i] == NULL)) |
---|
704 | { |
---|
705 | i--; |
---|
706 | } |
---|
707 | if (i < 0) |
---|
708 | return TRUE; |
---|
709 | else |
---|
710 | return FALSE; |
---|
711 | } |
---|
712 | |
---|
713 | /*2 |
---|
714 | * return the maximal component number found in any polynomial in s |
---|
715 | */ |
---|
716 | long idRankFreeModule (ideal s, ring lmRing, ring tailRing) |
---|
717 | { |
---|
718 | if (s!=NULL) |
---|
719 | { |
---|
720 | int j=0; |
---|
721 | |
---|
722 | if (rRing_has_Comp(tailRing) && rRing_has_Comp(lmRing)) |
---|
723 | { |
---|
724 | int l=IDELEMS(s); |
---|
725 | poly *p=s->m; |
---|
726 | int k; |
---|
727 | for (; l != 0; l--) |
---|
728 | { |
---|
729 | if (*p!=NULL) |
---|
730 | { |
---|
731 | pp_Test(*p, lmRing, tailRing); |
---|
732 | k = p_MaxComp(*p, lmRing, tailRing); |
---|
733 | if (k>j) j = k; |
---|
734 | } |
---|
735 | p++; |
---|
736 | } |
---|
737 | } |
---|
738 | return j; |
---|
739 | } |
---|
740 | return -1; |
---|
741 | } |
---|
742 | |
---|
743 | BOOLEAN idIsModule(ideal id, ring r) |
---|
744 | { |
---|
745 | if (id != NULL && rRing_has_Comp(r)) |
---|
746 | { |
---|
747 | int j, l = IDELEMS(id); |
---|
748 | for (j=0; j<l; j++) |
---|
749 | { |
---|
750 | if (id->m[j] != NULL && p_GetComp(id->m[j], r) > 0) return TRUE; |
---|
751 | } |
---|
752 | } |
---|
753 | return FALSE; |
---|
754 | } |
---|
755 | |
---|
756 | |
---|
757 | /*2 |
---|
758 | *returns true if id is homogenous with respect to the aktual weights |
---|
759 | */ |
---|
760 | BOOLEAN id_HomIdeal (ideal id, ideal Q, const ring r) |
---|
761 | { |
---|
762 | int i; |
---|
763 | BOOLEAN b; |
---|
764 | if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE; |
---|
765 | i = 0; |
---|
766 | b = TRUE; |
---|
767 | while ((i < IDELEMS(id)) && b) |
---|
768 | { |
---|
769 | b = p_IsHomogeneous(id->m[i],r); |
---|
770 | i++; |
---|
771 | } |
---|
772 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
---|
773 | { |
---|
774 | i=0; |
---|
775 | while ((i < IDELEMS(Q)) && b) |
---|
776 | { |
---|
777 | b = p_IsHomogeneous(Q->m[i],r); |
---|
778 | i++; |
---|
779 | } |
---|
780 | } |
---|
781 | return b; |
---|
782 | } |
---|
783 | |
---|
784 | /*2 |
---|
785 | *the minimal index of used variables - 1 |
---|
786 | */ |
---|
787 | int p_LowVar (poly p, const ring r) |
---|
788 | { |
---|
789 | int k,l,lex; |
---|
790 | |
---|
791 | if (p == NULL) return -1; |
---|
792 | |
---|
793 | k = 32000;/*a very large dummy value*/ |
---|
794 | while (p != NULL) |
---|
795 | { |
---|
796 | l = 1; |
---|
797 | lex = p_GetExp(p,l,r); |
---|
798 | while ((l < rVar(r)) && (lex == 0)) |
---|
799 | { |
---|
800 | l++; |
---|
801 | lex = p_GetExp(p,l,r); |
---|
802 | } |
---|
803 | l--; |
---|
804 | if (l < k) k = l; |
---|
805 | pIter(p); |
---|
806 | } |
---|
807 | return k; |
---|
808 | } |
---|
809 | |
---|
810 | /*3 |
---|
811 | *multiplies p with t (!cas) or (t-1) |
---|
812 | *the index of t is:1, so we have to shift all variables |
---|
813 | *p is NOT in the actual ring, it has no t |
---|
814 | */ |
---|
815 | static poly p_MultWithT (poly p,BOOLEAN cas, const ring r) |
---|
816 | { |
---|
817 | /*qp is the working pointer in p*/ |
---|
818 | /*result is the result, qresult is the working pointer*/ |
---|
819 | /*pp is p in the actual ring(shifted), qpp the working pointer*/ |
---|
820 | poly result,qp,pp; |
---|
821 | poly qresult=NULL; |
---|
822 | poly qpp=NULL; |
---|
823 | int i,j,lex; |
---|
824 | number n; |
---|
825 | |
---|
826 | pp = NULL; |
---|
827 | result = NULL; |
---|
828 | qp = p; |
---|
829 | while (qp != NULL) |
---|
830 | { |
---|
831 | i = 0; |
---|
832 | if (result == NULL) |
---|
833 | {/*first monomial*/ |
---|
834 | result = p_Init(r); |
---|
835 | qresult = result; |
---|
836 | } |
---|
837 | else |
---|
838 | { |
---|
839 | qresult->next = p_Init(r); |
---|
840 | pIter(qresult); |
---|
841 | } |
---|
842 | for (j=rVar(r)-1; j>0; j--) |
---|
843 | { |
---|
844 | lex = p_GetExp(qp,j,r); |
---|
845 | p_SetExp(qresult,j+1,lex,r);/*copy all variables*/ |
---|
846 | } |
---|
847 | lex = p_GetComp(qp,r); |
---|
848 | p_SetComp(qresult,lex,r); |
---|
849 | n=n_Copy(pGetCoeff(qp),r->cf); |
---|
850 | pSetCoeff0(qresult,n); |
---|
851 | qresult->next = NULL; |
---|
852 | p_Setm(qresult,r); |
---|
853 | /*qresult is now qp brought into the actual ring*/ |
---|
854 | if (cas) |
---|
855 | { /*case: mult with t-1*/ |
---|
856 | p_SetExp(qresult,1,0,r); |
---|
857 | p_Setm(qresult,r); |
---|
858 | if (pp == NULL) |
---|
859 | { /*first monomial*/ |
---|
860 | pp = p_Copy(qresult,r); |
---|
861 | qpp = pp; |
---|
862 | } |
---|
863 | else |
---|
864 | { |
---|
865 | qpp->next = p_Copy(qresult,r); |
---|
866 | pIter(qpp); |
---|
867 | } |
---|
868 | pGetCoeff(qpp)=n_Neg(pGetCoeff(qpp),r->cf); |
---|
869 | /*now qpp contains -1*qp*/ |
---|
870 | } |
---|
871 | p_SetExp(qresult,1,1,r);/*this is mult. by t*/ |
---|
872 | p_Setm(qresult,r); |
---|
873 | pIter(qp); |
---|
874 | } |
---|
875 | /* |
---|
876 | *now p is processed: |
---|
877 | *result contains t*p |
---|
878 | * if cas: pp contains -1*p (in the new ring) |
---|
879 | */ |
---|
880 | if (cas) qresult->next = pp; |
---|
881 | /* else qresult->next = NULL;*/ |
---|
882 | return result; |
---|
883 | } |
---|
884 | |
---|
885 | /*2 |
---|
886 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
887 | */ |
---|
888 | void pShift (poly * p,int i) |
---|
889 | { |
---|
890 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
891 | int j = pMaxComp(*p),k = pMinComp(*p); |
---|
892 | |
---|
893 | if (j+i < 0) return ; |
---|
894 | while (qp1 != NULL) |
---|
895 | { |
---|
896 | if ((pGetComp(qp1)+i > 0) || ((j == -i) && (j == k))) |
---|
897 | { |
---|
898 | pAddComp(qp1,i); |
---|
899 | pSetmComp(qp1); |
---|
900 | qp2 = qp1; |
---|
901 | pIter(qp1); |
---|
902 | } |
---|
903 | else |
---|
904 | { |
---|
905 | if (qp2 == *p) |
---|
906 | { |
---|
907 | pIter(*p); |
---|
908 | pLmDelete(&qp2); |
---|
909 | qp2 = *p; |
---|
910 | qp1 = *p; |
---|
911 | } |
---|
912 | else |
---|
913 | { |
---|
914 | qp2->next = qp1->next; |
---|
915 | if (qp1!=NULL) pLmDelete(&qp1); |
---|
916 | qp1 = qp2->next; |
---|
917 | } |
---|
918 | } |
---|
919 | } |
---|
920 | } |
---|
921 | |
---|
922 | /*2 |
---|
923 | *initialized a field with r numbers between beg and end for the |
---|
924 | *procedure idNextChoise |
---|
925 | */ |
---|
926 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
927 | { |
---|
928 | /*returns the first choise of r numbers between beg and end*/ |
---|
929 | int i; |
---|
930 | for (i=0; i<r; i++) |
---|
931 | { |
---|
932 | choise[i] = 0; |
---|
933 | } |
---|
934 | if (r <= end-beg+1) |
---|
935 | for (i=0; i<r; i++) |
---|
936 | { |
---|
937 | choise[i] = beg+i; |
---|
938 | } |
---|
939 | if (r > end-beg+1) |
---|
940 | *endch = TRUE; |
---|
941 | else |
---|
942 | *endch = FALSE; |
---|
943 | } |
---|
944 | |
---|
945 | /*2 |
---|
946 | *returns the next choise of r numbers between beg and end |
---|
947 | */ |
---|
948 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
949 | { |
---|
950 | int i = r-1,j; |
---|
951 | while ((i >= 0) && (choise[i] == end)) |
---|
952 | { |
---|
953 | i--; |
---|
954 | end--; |
---|
955 | } |
---|
956 | if (i == -1) |
---|
957 | *endch = TRUE; |
---|
958 | else |
---|
959 | { |
---|
960 | choise[i]++; |
---|
961 | for (j=i+1; j<r; j++) |
---|
962 | { |
---|
963 | choise[j] = choise[i]+j-i; |
---|
964 | } |
---|
965 | *endch = FALSE; |
---|
966 | } |
---|
967 | } |
---|
968 | |
---|
969 | /*2 |
---|
970 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
971 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
972 | * w.r.t. the algorithm of construction |
---|
973 | */ |
---|
974 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
975 | { |
---|
976 | int * localchoise,i,result=0; |
---|
977 | BOOLEAN b=FALSE; |
---|
978 | |
---|
979 | if (d<=1) return 1; |
---|
980 | localchoise=(int*)omAlloc((d-1)*sizeof(int)); |
---|
981 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
982 | while (!b) |
---|
983 | { |
---|
984 | result++; |
---|
985 | i = 0; |
---|
986 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
987 | if (i>=t) |
---|
988 | { |
---|
989 | i = t+1; |
---|
990 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
991 | if (i>=d) |
---|
992 | { |
---|
993 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
994 | return result; |
---|
995 | } |
---|
996 | } |
---|
997 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
998 | } |
---|
999 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
1000 | return 0; |
---|
1001 | } |
---|
1002 | |
---|
1003 | /*2 |
---|
1004 | *computes the binomial coefficient |
---|
1005 | */ |
---|
1006 | int binom (int n,int r) |
---|
1007 | { |
---|
1008 | int i,result; |
---|
1009 | |
---|
1010 | if (r==0) return 1; |
---|
1011 | if (n-r<r) return binom(n,n-r); |
---|
1012 | result = n-r+1; |
---|
1013 | for (i=2;i<=r;i++) |
---|
1014 | { |
---|
1015 | result *= n-r+i; |
---|
1016 | if (result<0) |
---|
1017 | { |
---|
1018 | WarnS("overflow in binomials"); |
---|
1019 | return 0; |
---|
1020 | } |
---|
1021 | result /= i; |
---|
1022 | } |
---|
1023 | return result; |
---|
1024 | } |
---|
1025 | |
---|
1026 | /*2 |
---|
1027 | *the free module of rank i |
---|
1028 | */ |
---|
1029 | ideal idFreeModule (int i) |
---|
1030 | { |
---|
1031 | int j; |
---|
1032 | ideal h; |
---|
1033 | |
---|
1034 | h=idInit(i,i); |
---|
1035 | for (j=0; j<i; j++) |
---|
1036 | { |
---|
1037 | h->m[j] = p_One(r); |
---|
1038 | pSetComp(h->m[j],j+1); |
---|
1039 | pSetmComp(h->m[j]); |
---|
1040 | } |
---|
1041 | return h; |
---|
1042 | } |
---|
1043 | |
---|
1044 | ideal idSectWithElim (ideal h1,ideal h2) |
---|
1045 | // does not destroy h1,h2 |
---|
1046 | { |
---|
1047 | if (TEST_OPT_PROT) PrintS("intersect by elimination method\n"); |
---|
1048 | assume(!idIs0(h1)); |
---|
1049 | assume(!idIs0(h2)); |
---|
1050 | assume(IDELEMS(h1)<=IDELEMS(h2)); |
---|
1051 | assume(idRankFreeModule(h1)==0); |
---|
1052 | assume(idRankFreeModule(h2)==0); |
---|
1053 | // add a new variable: |
---|
1054 | int j; |
---|
1055 | ring origRing=currRing; |
---|
1056 | ring r=rCopy0(origRing); |
---|
1057 | r->N++; |
---|
1058 | r->block0[0]=1; |
---|
1059 | r->block1[0]= r->N; |
---|
1060 | omFree(r->order); |
---|
1061 | r->order=(int*)omAlloc0(3*sizeof(int*)); |
---|
1062 | r->order[0]=ringorder_dp; |
---|
1063 | r->order[1]=ringorder_C; |
---|
1064 | char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr)); |
---|
1065 | for (j=0;j<r->N-1;j++) names[j]=r->names[j]; |
---|
1066 | names[r->N-1]=omStrDup("@"); |
---|
1067 | omFree(r->names); |
---|
1068 | r->names=names; |
---|
1069 | rComplete(r,TRUE); |
---|
1070 | // fetch h1, h2 |
---|
1071 | ideal h; |
---|
1072 | h1=idrCopyR(h1,origRing,r); |
---|
1073 | h2=idrCopyR(h2,origRing,r); |
---|
1074 | // switch to temp. ring r |
---|
1075 | rChangeCurrRing(r); |
---|
1076 | // create 1-t, t |
---|
1077 | poly omt=p_One(r); |
---|
1078 | pSetExp(omt,r->N,1); |
---|
1079 | poly t=pCopy(omt); |
---|
1080 | pSetm(omt); |
---|
1081 | omt=pNeg(omt); |
---|
1082 | omt=pAdd(omt,p_One(r)); |
---|
1083 | // compute (1-t)*h1 |
---|
1084 | h1=(ideal)mpMultP((matrix)h1,omt); |
---|
1085 | // compute t*h2 |
---|
1086 | h2=(ideal)mpMultP((matrix)h2,pCopy(t)); |
---|
1087 | // (1-t)h1 + t*h2 |
---|
1088 | h=idInit(IDELEMS(h1)+IDELEMS(h2),1); |
---|
1089 | int l; |
---|
1090 | for (l=IDELEMS(h1)-1; l>=0; l--) |
---|
1091 | { |
---|
1092 | h->m[l] = h1->m[l]; h1->m[l]=NULL; |
---|
1093 | } |
---|
1094 | j=IDELEMS(h1); |
---|
1095 | for (l=IDELEMS(h2)-1; l>=0; l--) |
---|
1096 | { |
---|
1097 | h->m[l+j] = h2->m[l]; h2->m[l]=NULL; |
---|
1098 | } |
---|
1099 | idDelete(&h1); |
---|
1100 | idDelete(&h2); |
---|
1101 | // eliminate t: |
---|
1102 | |
---|
1103 | ideal res=idElimination(h,t); |
---|
1104 | // cleanup |
---|
1105 | idDelete(&h); |
---|
1106 | res=idrMoveR(res,r,origRing); |
---|
1107 | rChangeCurrRing(origRing); |
---|
1108 | rKill(r); |
---|
1109 | return res; |
---|
1110 | } |
---|
1111 | |
---|
1112 | /*2 |
---|
1113 | *computes recursively all monomials of a certain degree |
---|
1114 | *in every step the actvar-th entry in the exponential |
---|
1115 | *vector is incremented and the other variables are |
---|
1116 | *computed by recursive calls of makemonoms |
---|
1117 | *if the last variable is reached, the difference to the |
---|
1118 | *degree is computed directly |
---|
1119 | *vars is the number variables |
---|
1120 | *actvar is the actual variable to handle |
---|
1121 | *deg is the degree of the monomials to compute |
---|
1122 | *monomdeg is the actual degree of the monomial in consideration |
---|
1123 | */ |
---|
1124 | static void makemonoms(int vars,int actvar,int deg,int monomdeg) |
---|
1125 | { |
---|
1126 | poly p; |
---|
1127 | int i=0; |
---|
1128 | |
---|
1129 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
1130 | { |
---|
1131 | idpower[idpowerpoint] = p_One(r); |
---|
1132 | monomdeg = 0; |
---|
1133 | } |
---|
1134 | while (i<=deg) |
---|
1135 | { |
---|
1136 | if (deg == monomdeg) |
---|
1137 | { |
---|
1138 | pSetm(idpower[idpowerpoint]); |
---|
1139 | idpowerpoint++; |
---|
1140 | return; |
---|
1141 | } |
---|
1142 | if (actvar == vars) |
---|
1143 | { |
---|
1144 | pSetExp(idpower[idpowerpoint],actvar,deg-monomdeg); |
---|
1145 | pSetm(idpower[idpowerpoint]); |
---|
1146 | pTest(idpower[idpowerpoint]); |
---|
1147 | idpowerpoint++; |
---|
1148 | return; |
---|
1149 | } |
---|
1150 | else |
---|
1151 | { |
---|
1152 | p = pCopy(idpower[idpowerpoint]); |
---|
1153 | makemonoms(vars,actvar+1,deg,monomdeg); |
---|
1154 | idpower[idpowerpoint] = p; |
---|
1155 | } |
---|
1156 | monomdeg++; |
---|
1157 | pSetExp(idpower[idpowerpoint],actvar,pGetExp(idpower[idpowerpoint],actvar)+1); |
---|
1158 | pSetm(idpower[idpowerpoint]); |
---|
1159 | pTest(idpower[idpowerpoint]); |
---|
1160 | i++; |
---|
1161 | } |
---|
1162 | } |
---|
1163 | |
---|
1164 | /*2 |
---|
1165 | *returns the deg-th power of the maximal ideal of 0 |
---|
1166 | */ |
---|
1167 | ideal id_MaxIdeal(int deg, const ring r) |
---|
1168 | { |
---|
1169 | if (deg < 0) |
---|
1170 | { |
---|
1171 | WarnS("maxideal: power must be non-negative"); |
---|
1172 | } |
---|
1173 | if (deg < 1) |
---|
1174 | { |
---|
1175 | ideal I=idInit(1,1); |
---|
1176 | I->m[0]=p_One(r); |
---|
1177 | return I; |
---|
1178 | } |
---|
1179 | if (deg == 1) |
---|
1180 | { |
---|
1181 | return idMaxIdeal(r); |
---|
1182 | } |
---|
1183 | |
---|
1184 | int vars = rVar(r); |
---|
1185 | int i = binom(vars+deg-1,deg); |
---|
1186 | if (i<=0) return idInit(1,1); |
---|
1187 | ideal id=idInit(i,1); |
---|
1188 | idpower = id->m; |
---|
1189 | idpowerpoint = 0; |
---|
1190 | makemonoms(vars,1,deg,0); |
---|
1191 | idpower = NULL; |
---|
1192 | idpowerpoint = 0; |
---|
1193 | return id; |
---|
1194 | } |
---|
1195 | |
---|
1196 | /*2 |
---|
1197 | *computes recursively all generators of a certain degree |
---|
1198 | *of the ideal "givenideal" |
---|
1199 | *elms is the number elements in the given ideal |
---|
1200 | *actelm is the actual element to handle |
---|
1201 | *deg is the degree of the power to compute |
---|
1202 | *gendeg is the actual degree of the generator in consideration |
---|
1203 | */ |
---|
1204 | static void makepotence(int elms,int actelm,int deg,int gendeg) |
---|
1205 | { |
---|
1206 | poly p; |
---|
1207 | int i=0; |
---|
1208 | |
---|
1209 | if ((idpowerpoint == 0) && (actelm ==1)) |
---|
1210 | { |
---|
1211 | idpower[idpowerpoint] = p_One(r); |
---|
1212 | gendeg = 0; |
---|
1213 | } |
---|
1214 | while (i<=deg) |
---|
1215 | { |
---|
1216 | if (deg == gendeg) |
---|
1217 | { |
---|
1218 | idpowerpoint++; |
---|
1219 | return; |
---|
1220 | } |
---|
1221 | if (actelm == elms) |
---|
1222 | { |
---|
1223 | p=pPower(pCopy(givenideal[actelm-1]),deg-gendeg); |
---|
1224 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],p); |
---|
1225 | idpowerpoint++; |
---|
1226 | return; |
---|
1227 | } |
---|
1228 | else |
---|
1229 | { |
---|
1230 | p = pCopy(idpower[idpowerpoint]); |
---|
1231 | makepotence(elms,actelm+1,deg,gendeg); |
---|
1232 | idpower[idpowerpoint] = p; |
---|
1233 | } |
---|
1234 | gendeg++; |
---|
1235 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],pCopy(givenideal[actelm-1])); |
---|
1236 | i++; |
---|
1237 | } |
---|
1238 | } |
---|
1239 | |
---|
1240 | /*2 |
---|
1241 | *returns the deg-th power of the ideal gid |
---|
1242 | */ |
---|
1243 | //ideal idPower(ideal gid,int deg) |
---|
1244 | //{ |
---|
1245 | // int i; |
---|
1246 | // ideal id; |
---|
1247 | // |
---|
1248 | // if (deg < 1) deg = 1; |
---|
1249 | // i = binom(IDELEMS(gid)+deg-1,deg); |
---|
1250 | // id=idInit(i,1); |
---|
1251 | // idpower = id->m; |
---|
1252 | // givenideal = gid->m; |
---|
1253 | // idpowerpoint = 0; |
---|
1254 | // makepotence(IDELEMS(gid),1,deg,0); |
---|
1255 | // idpower = NULL; |
---|
1256 | // givenideal = NULL; |
---|
1257 | // idpowerpoint = 0; |
---|
1258 | // return id; |
---|
1259 | //} |
---|
1260 | static void idNextPotence(ideal given, ideal result, |
---|
1261 | int begin, int end, int deg, int restdeg, poly ap) |
---|
1262 | { |
---|
1263 | poly p; |
---|
1264 | int i; |
---|
1265 | |
---|
1266 | p = pPower(pCopy(given->m[begin]),restdeg); |
---|
1267 | i = result->nrows; |
---|
1268 | result->m[i] = pMult(pCopy(ap),p); |
---|
1269 | //PrintS("."); |
---|
1270 | (result->nrows)++; |
---|
1271 | if (result->nrows >= IDELEMS(result)) |
---|
1272 | { |
---|
1273 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
1274 | IDELEMS(result) += 16; |
---|
1275 | } |
---|
1276 | if (begin == end) return; |
---|
1277 | for (i=restdeg-1;i>0;i--) |
---|
1278 | { |
---|
1279 | p = pPower(pCopy(given->m[begin]),i); |
---|
1280 | p = pMult(pCopy(ap),p); |
---|
1281 | idNextPotence(given, result, begin+1, end, deg, restdeg-i, p); |
---|
1282 | pDelete(&p); |
---|
1283 | } |
---|
1284 | idNextPotence(given, result, begin+1, end, deg, restdeg, ap); |
---|
1285 | } |
---|
1286 | |
---|
1287 | ideal id_Power(ideal given,int exp, const ring r) |
---|
1288 | { |
---|
1289 | ideal result,temp; |
---|
1290 | poly p1; |
---|
1291 | int i; |
---|
1292 | |
---|
1293 | if (idIs0(given)) return idInit(1,1); |
---|
1294 | temp = id_Copy(given,r); |
---|
1295 | idSkipZeroes(temp); |
---|
1296 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
1297 | result = idInit(i,1); |
---|
1298 | result->nrows = 0; |
---|
1299 | //Print("ideal contains %d elements\n",i); |
---|
1300 | p1=p_One(r); |
---|
1301 | idNextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1); |
---|
1302 | p_Delete(&p1,r); |
---|
1303 | id_Delete(&temp,r); |
---|
1304 | result->nrows = 1; |
---|
1305 | id_DelEquals(result,r); |
---|
1306 | idSkipZeroes(result); |
---|
1307 | return result; |
---|
1308 | } |
---|
1309 | |
---|
1310 | /*2 |
---|
1311 | * compute the which-th ar-minor of the matrix a |
---|
1312 | */ |
---|
1313 | poly idMinor(matrix a, int ar, unsigned long which, ideal R) |
---|
1314 | { |
---|
1315 | int i,j,k,size; |
---|
1316 | unsigned long curr; |
---|
1317 | int *rowchoise,*colchoise; |
---|
1318 | BOOLEAN rowch,colch; |
---|
1319 | ideal result; |
---|
1320 | matrix tmp; |
---|
1321 | poly p,q; |
---|
1322 | |
---|
1323 | i = binom(a->rows(),ar); |
---|
1324 | j = binom(a->cols(),ar); |
---|
1325 | |
---|
1326 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1327 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1328 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
1329 | else size=i*j; |
---|
1330 | result=idInit(size,1); |
---|
1331 | tmp=mpNew(ar,ar); |
---|
1332 | k = 0; /* the index in result*/ |
---|
1333 | curr = 0; /* index of current minor */ |
---|
1334 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
1335 | while (!rowch) |
---|
1336 | { |
---|
1337 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
1338 | while (!colch) |
---|
1339 | { |
---|
1340 | if (curr == which) |
---|
1341 | { |
---|
1342 | for (i=1; i<=ar; i++) |
---|
1343 | { |
---|
1344 | for (j=1; j<=ar; j++) |
---|
1345 | { |
---|
1346 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
1347 | } |
---|
1348 | } |
---|
1349 | p = mpDetBareiss(tmp); |
---|
1350 | if (p!=NULL) |
---|
1351 | { |
---|
1352 | if (R!=NULL) |
---|
1353 | { |
---|
1354 | q = p; |
---|
1355 | p = kNF(R,currQuotient,q); |
---|
1356 | pDelete(&q); |
---|
1357 | } |
---|
1358 | /*delete the matrix tmp*/ |
---|
1359 | for (i=1; i<=ar; i++) |
---|
1360 | { |
---|
1361 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
1362 | } |
---|
1363 | idDelete((ideal*)&tmp); |
---|
1364 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
1365 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
1366 | return (p); |
---|
1367 | } |
---|
1368 | } |
---|
1369 | curr++; |
---|
1370 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
1371 | } |
---|
1372 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
1373 | } |
---|
1374 | return (poly) 1; |
---|
1375 | } |
---|
1376 | |
---|
1377 | #ifdef WITH_OLD_MINOR |
---|
1378 | /*2 |
---|
1379 | * compute all ar-minors of the matrix a |
---|
1380 | */ |
---|
1381 | ideal idMinors(matrix a, int ar, ideal R) |
---|
1382 | { |
---|
1383 | int i,j,k,size; |
---|
1384 | int *rowchoise,*colchoise; |
---|
1385 | BOOLEAN rowch,colch; |
---|
1386 | ideal result; |
---|
1387 | matrix tmp; |
---|
1388 | poly p,q; |
---|
1389 | |
---|
1390 | i = binom(a->rows(),ar); |
---|
1391 | j = binom(a->cols(),ar); |
---|
1392 | |
---|
1393 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1394 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1395 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
1396 | else size=i*j; |
---|
1397 | result=idInit(size,1); |
---|
1398 | tmp=mpNew(ar,ar); |
---|
1399 | k = 0; /* the index in result*/ |
---|
1400 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
1401 | while (!rowch) |
---|
1402 | { |
---|
1403 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
1404 | while (!colch) |
---|
1405 | { |
---|
1406 | for (i=1; i<=ar; i++) |
---|
1407 | { |
---|
1408 | for (j=1; j<=ar; j++) |
---|
1409 | { |
---|
1410 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
1411 | } |
---|
1412 | } |
---|
1413 | p = mpDetBareiss(tmp); |
---|
1414 | if (p!=NULL) |
---|
1415 | { |
---|
1416 | if (R!=NULL) |
---|
1417 | { |
---|
1418 | q = p; |
---|
1419 | p = kNF(R,currQuotient,q); |
---|
1420 | pDelete(&q); |
---|
1421 | } |
---|
1422 | if (p!=NULL) |
---|
1423 | { |
---|
1424 | if (k>=size) |
---|
1425 | { |
---|
1426 | pEnlargeSet(&result->m,size,32); |
---|
1427 | size += 32; |
---|
1428 | } |
---|
1429 | result->m[k] = p; |
---|
1430 | k++; |
---|
1431 | } |
---|
1432 | } |
---|
1433 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
1434 | } |
---|
1435 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
1436 | } |
---|
1437 | /*delete the matrix tmp*/ |
---|
1438 | for (i=1; i<=ar; i++) |
---|
1439 | { |
---|
1440 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
1441 | } |
---|
1442 | idDelete((ideal*)&tmp); |
---|
1443 | if (k==0) |
---|
1444 | { |
---|
1445 | k=1; |
---|
1446 | result->m[0]=NULL; |
---|
1447 | } |
---|
1448 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
1449 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
1450 | pEnlargeSet(&result->m,size,k-size); |
---|
1451 | IDELEMS(result) = k; |
---|
1452 | return (result); |
---|
1453 | } |
---|
1454 | #else |
---|
1455 | /*2 |
---|
1456 | * compute all ar-minors of the matrix a |
---|
1457 | * the caller of mpRecMin |
---|
1458 | * the elements of the result are not in R (if R!=NULL) |
---|
1459 | */ |
---|
1460 | ideal idMinors(matrix a, int ar, ideal R) |
---|
1461 | { |
---|
1462 | int elems=0; |
---|
1463 | int r=a->nrows,c=a->ncols; |
---|
1464 | int i; |
---|
1465 | matrix b; |
---|
1466 | ideal result,h; |
---|
1467 | ring origR; |
---|
1468 | ring tmpR; |
---|
1469 | long bound; |
---|
1470 | |
---|
1471 | if((ar<=0) || (ar>r) || (ar>c)) |
---|
1472 | { |
---|
1473 | Werror("%d-th minor, matrix is %dx%d",ar,r,c); |
---|
1474 | return NULL; |
---|
1475 | } |
---|
1476 | h = idMatrix2Module(mpCopy(a)); |
---|
1477 | bound = smExpBound(h,c,r,ar); |
---|
1478 | idDelete(&h); |
---|
1479 | tmpR=smRingChange(&origR,bound); |
---|
1480 | b = mpNew(r,c); |
---|
1481 | for (i=r*c-1;i>=0;i--) |
---|
1482 | { |
---|
1483 | if (a->m[i]) |
---|
1484 | b->m[i] = prCopyR(a->m[i],origR); |
---|
1485 | } |
---|
1486 | if (R!=NULL) |
---|
1487 | { |
---|
1488 | R = idrCopyR(R,origR); |
---|
1489 | //if (ar>1) // otherwise done in mpMinorToResult |
---|
1490 | //{ |
---|
1491 | // matrix bb=(matrix)kNF(R,currQuotient,(ideal)b); |
---|
1492 | // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols; |
---|
1493 | // idDelete((ideal*)&b); b=bb; |
---|
1494 | //} |
---|
1495 | } |
---|
1496 | result=idInit(32,1); |
---|
1497 | if(ar>1) mpRecMin(ar-1,result,elems,b,r,c,NULL,R); |
---|
1498 | else mpMinorToResult(result,elems,b,r,c,R); |
---|
1499 | idDelete((ideal *)&b); |
---|
1500 | if (R!=NULL) idDelete(&R); |
---|
1501 | idSkipZeroes(result); |
---|
1502 | rChangeCurrRing(origR); |
---|
1503 | result = idrMoveR(result,tmpR); |
---|
1504 | smKillModifiedRing(tmpR); |
---|
1505 | idTest(result); |
---|
1506 | return result; |
---|
1507 | } |
---|
1508 | #endif |
---|
1509 | |
---|
1510 | /*2 |
---|
1511 | *skips all zeroes and double elements, searches also for units |
---|
1512 | */ |
---|
1513 | void id_Compactify(ideal id, const ring r) |
---|
1514 | { |
---|
1515 | int i,j; |
---|
1516 | BOOLEAN b=FALSE; |
---|
1517 | |
---|
1518 | i = IDELEMS(id)-1; |
---|
1519 | while ((! b) && (i>=0)) |
---|
1520 | { |
---|
1521 | b=p_IsUnit(id->m[i],r); |
---|
1522 | i--; |
---|
1523 | } |
---|
1524 | if (b) |
---|
1525 | { |
---|
1526 | for(i=IDELEMS(id)-1;i>=0;i--) p_Delete(&id->m[i],r); |
---|
1527 | id->m[0]=p_One(r); |
---|
1528 | } |
---|
1529 | else |
---|
1530 | { |
---|
1531 | id_DelMultiples(id,r); |
---|
1532 | } |
---|
1533 | idSkipZeroes(id); |
---|
1534 | } |
---|
1535 | |
---|
1536 | /*2 |
---|
1537 | *returns TRUE if id1 is a submodule of id2 |
---|
1538 | */ |
---|
1539 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
1540 | { |
---|
1541 | int i; |
---|
1542 | poly p; |
---|
1543 | |
---|
1544 | if (idIs0(id1)) return TRUE; |
---|
1545 | for (i=0;i<IDELEMS(id1);i++) |
---|
1546 | { |
---|
1547 | if (id1->m[i] != NULL) |
---|
1548 | { |
---|
1549 | p = kNF(id2,currQuotient,id1->m[i]); |
---|
1550 | if (p != NULL) |
---|
1551 | { |
---|
1552 | pDelete(&p); |
---|
1553 | return FALSE; |
---|
1554 | } |
---|
1555 | } |
---|
1556 | } |
---|
1557 | return TRUE; |
---|
1558 | } |
---|
1559 | |
---|
1560 | /*2 |
---|
1561 | * returns the ideals of initial terms |
---|
1562 | */ |
---|
1563 | ideal idHead(ideal h) |
---|
1564 | { |
---|
1565 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
1566 | int i; |
---|
1567 | |
---|
1568 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
1569 | { |
---|
1570 | if (h->m[i]!=NULL) m->m[i]=pHead(h->m[i]); |
---|
1571 | } |
---|
1572 | return m; |
---|
1573 | } |
---|
1574 | |
---|
1575 | ideal idHomogen(ideal h, int varnum) |
---|
1576 | { |
---|
1577 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
1578 | int i; |
---|
1579 | |
---|
1580 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
1581 | { |
---|
1582 | m->m[i]=pHomogen(h->m[i],varnum); |
---|
1583 | } |
---|
1584 | return m; |
---|
1585 | } |
---|
1586 | |
---|
1587 | /*------------------type conversions----------------*/ |
---|
1588 | ideal idVec2Ideal(poly vec) |
---|
1589 | { |
---|
1590 | ideal result=idInit(1,1); |
---|
1591 | omFree((ADDRESS)result->m); |
---|
1592 | result->m=NULL; // remove later |
---|
1593 | pVec2Polys(vec, &(result->m), &(IDELEMS(result))); |
---|
1594 | return result; |
---|
1595 | } |
---|
1596 | |
---|
1597 | #define NEW_STUFF |
---|
1598 | #ifndef NEW_STUFF |
---|
1599 | // converts mat to module, destroys mat |
---|
1600 | ideal idMatrix2Module(matrix mat) |
---|
1601 | { |
---|
1602 | int mc=MATCOLS(mat); |
---|
1603 | int mr=MATROWS(mat); |
---|
1604 | ideal result = idInit(si_max(mc,1),si_max(mr,1)); |
---|
1605 | int i,j; |
---|
1606 | poly h; |
---|
1607 | |
---|
1608 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
1609 | { |
---|
1610 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
1611 | { |
---|
1612 | h = MATELEM(mat,i,j+1); |
---|
1613 | if (h!=NULL) |
---|
1614 | { |
---|
1615 | MATELEM(mat,i,j+1)=NULL; |
---|
1616 | pSetCompP(h,i); |
---|
1617 | result->m[j] = pAdd(result->m[j],h); |
---|
1618 | } |
---|
1619 | } |
---|
1620 | } |
---|
1621 | // obachman: need to clean this up |
---|
1622 | idDelete((ideal*) &mat); |
---|
1623 | return result; |
---|
1624 | } |
---|
1625 | #else |
---|
1626 | |
---|
1627 | #include "sbuckets.h" |
---|
1628 | |
---|
1629 | // converts mat to module, destroys mat |
---|
1630 | ideal idMatrix2Module(matrix mat) |
---|
1631 | { |
---|
1632 | int mc=MATCOLS(mat); |
---|
1633 | int mr=MATROWS(mat); |
---|
1634 | ideal result = idInit(si_max(mc,1),si_max(mr,1)); |
---|
1635 | int i,j, l; |
---|
1636 | poly h; |
---|
1637 | poly p; |
---|
1638 | sBucket_pt bucket = sBucketCreate(currRing); |
---|
1639 | |
---|
1640 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
1641 | { |
---|
1642 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
1643 | { |
---|
1644 | h = MATELEM(mat,i,j+1); |
---|
1645 | if (h!=NULL) |
---|
1646 | { |
---|
1647 | l=pLength(h); |
---|
1648 | MATELEM(mat,i,j+1)=NULL; |
---|
1649 | p_SetCompP(h,i, currRing); |
---|
1650 | sBucket_Merge_p(bucket, h, l); |
---|
1651 | } |
---|
1652 | } |
---|
1653 | sBucketClearMerge(bucket, &(result->m[j]), &l); |
---|
1654 | } |
---|
1655 | sBucketDestroy(&bucket); |
---|
1656 | |
---|
1657 | // obachman: need to clean this up |
---|
1658 | idDelete((ideal*) &mat); |
---|
1659 | return result; |
---|
1660 | } |
---|
1661 | #endif |
---|
1662 | |
---|
1663 | /*2 |
---|
1664 | * converts a module into a matrix, destroyes the input |
---|
1665 | */ |
---|
1666 | matrix idModule2Matrix(ideal mod) |
---|
1667 | { |
---|
1668 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
1669 | int i,cp; |
---|
1670 | poly p,h; |
---|
1671 | |
---|
1672 | for(i=0;i<IDELEMS(mod);i++) |
---|
1673 | { |
---|
1674 | p=pReverse(mod->m[i]); |
---|
1675 | mod->m[i]=NULL; |
---|
1676 | while (p!=NULL) |
---|
1677 | { |
---|
1678 | h=p; |
---|
1679 | pIter(p); |
---|
1680 | pNext(h)=NULL; |
---|
1681 | // cp = si_max(1,pGetComp(h)); // if used for ideals too |
---|
1682 | cp = pGetComp(h); |
---|
1683 | pSetComp(h,0); |
---|
1684 | pSetmComp(h); |
---|
1685 | #ifdef TEST |
---|
1686 | if (cp>mod->rank) |
---|
1687 | { |
---|
1688 | Print("## inv. rank %ld -> %d\n",mod->rank,cp); |
---|
1689 | int k,l,o=mod->rank; |
---|
1690 | mod->rank=cp; |
---|
1691 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
1692 | for (l=1; l<=o; l++) |
---|
1693 | { |
---|
1694 | for (k=1; k<=IDELEMS(mod); k++) |
---|
1695 | { |
---|
1696 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
1697 | MATELEM(result,l,k)=NULL; |
---|
1698 | } |
---|
1699 | } |
---|
1700 | idDelete((ideal *)&result); |
---|
1701 | result=d; |
---|
1702 | } |
---|
1703 | #endif |
---|
1704 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
1705 | } |
---|
1706 | } |
---|
1707 | // obachman 10/99: added the following line, otherwise memory leack! |
---|
1708 | idDelete(&mod); |
---|
1709 | return result; |
---|
1710 | } |
---|
1711 | |
---|
1712 | matrix idModule2formatedMatrix(ideal mod,int rows, int cols) |
---|
1713 | { |
---|
1714 | matrix result = mpNew(rows,cols); |
---|
1715 | int i,cp,r=idRankFreeModule(mod),c=IDELEMS(mod); |
---|
1716 | poly p,h; |
---|
1717 | |
---|
1718 | if (r>rows) r = rows; |
---|
1719 | if (c>cols) c = cols; |
---|
1720 | for(i=0;i<c;i++) |
---|
1721 | { |
---|
1722 | p=pReverse(mod->m[i]); |
---|
1723 | mod->m[i]=NULL; |
---|
1724 | while (p!=NULL) |
---|
1725 | { |
---|
1726 | h=p; |
---|
1727 | pIter(p); |
---|
1728 | pNext(h)=NULL; |
---|
1729 | cp = pGetComp(h); |
---|
1730 | if (cp<=r) |
---|
1731 | { |
---|
1732 | pSetComp(h,0); |
---|
1733 | pSetmComp(h); |
---|
1734 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
1735 | } |
---|
1736 | else |
---|
1737 | pDelete(&h); |
---|
1738 | } |
---|
1739 | } |
---|
1740 | idDelete(&mod); |
---|
1741 | return result; |
---|
1742 | } |
---|
1743 | |
---|
1744 | /*2 |
---|
1745 | * substitute the n-th variable by the monomial e in id |
---|
1746 | * destroy id |
---|
1747 | */ |
---|
1748 | ideal idSubst(ideal id, int n, poly e) |
---|
1749 | { |
---|
1750 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
1751 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
1752 | |
---|
1753 | res->rank = id->rank; |
---|
1754 | for(k--;k>=0;k--) |
---|
1755 | { |
---|
1756 | res->m[k]=pSubst(id->m[k],n,e); |
---|
1757 | id->m[k]=NULL; |
---|
1758 | } |
---|
1759 | idDelete(&id); |
---|
1760 | return res; |
---|
1761 | } |
---|
1762 | |
---|
1763 | BOOLEAN idHomModule(ideal m, ideal Q, intvec **w) |
---|
1764 | { |
---|
1765 | if (w!=NULL) *w=NULL; |
---|
1766 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) return FALSE; |
---|
1767 | if (idIs0(m)) |
---|
1768 | { |
---|
1769 | if (w!=NULL) (*w)=new intvec(m->rank); |
---|
1770 | return TRUE; |
---|
1771 | } |
---|
1772 | |
---|
1773 | long cmax=1,order=0,ord,* diff,diffmin=32000; |
---|
1774 | int *iscom; |
---|
1775 | int i,j; |
---|
1776 | poly p=NULL; |
---|
1777 | pFDegProc d; |
---|
1778 | if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
1779 | d=p_Totaldegree; |
---|
1780 | else |
---|
1781 | d=pFDeg; |
---|
1782 | int length=IDELEMS(m); |
---|
1783 | polyset P=m->m; |
---|
1784 | polyset F=(polyset)omAlloc(length*sizeof(poly)); |
---|
1785 | for (i=length-1;i>=0;i--) |
---|
1786 | { |
---|
1787 | p=F[i]=P[i]; |
---|
1788 | cmax=si_max(cmax,(long)pMaxComp(p)); |
---|
1789 | } |
---|
1790 | cmax++; |
---|
1791 | diff = (long *)omAlloc0(cmax*sizeof(long)); |
---|
1792 | if (w!=NULL) *w=new intvec(cmax-1); |
---|
1793 | iscom = (int *)omAlloc0(cmax*sizeof(int)); |
---|
1794 | i=0; |
---|
1795 | while (i<=length) |
---|
1796 | { |
---|
1797 | if (i<length) |
---|
1798 | { |
---|
1799 | p=F[i]; |
---|
1800 | while ((p!=NULL) && (iscom[pGetComp(p)]==0)) pIter(p); |
---|
1801 | } |
---|
1802 | if ((p==NULL) && (i<length)) |
---|
1803 | { |
---|
1804 | i++; |
---|
1805 | } |
---|
1806 | else |
---|
1807 | { |
---|
1808 | if (p==NULL) /* && (i==length) */ |
---|
1809 | { |
---|
1810 | i=0; |
---|
1811 | while ((i<length) && (F[i]==NULL)) i++; |
---|
1812 | if (i>=length) break; |
---|
1813 | p = F[i]; |
---|
1814 | } |
---|
1815 | //if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
1816 | // order=pTotaldegree(p); |
---|
1817 | //else |
---|
1818 | // order = p->order; |
---|
1819 | // order = pFDeg(p,currRing); |
---|
1820 | order = d(p,currRing) +diff[pGetComp(p)]; |
---|
1821 | //order += diff[pGetComp(p)]; |
---|
1822 | p = F[i]; |
---|
1823 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
1824 | F[i] = NULL; |
---|
1825 | i=0; |
---|
1826 | } |
---|
1827 | while (p!=NULL) |
---|
1828 | { |
---|
1829 | if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
1830 | ord=pTotaldegree(p); |
---|
1831 | else |
---|
1832 | // ord = p->order; |
---|
1833 | ord = pFDeg(p,currRing); |
---|
1834 | if (iscom[pGetComp(p)]==0) |
---|
1835 | { |
---|
1836 | diff[pGetComp(p)] = order-ord; |
---|
1837 | iscom[pGetComp(p)] = 1; |
---|
1838 | /* |
---|
1839 | *PrintS("new diff: "); |
---|
1840 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
1841 | *PrintLn(); |
---|
1842 | *PrintS("new iscom: "); |
---|
1843 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
1844 | *PrintLn(); |
---|
1845 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
1846 | */ |
---|
1847 | } |
---|
1848 | else |
---|
1849 | { |
---|
1850 | /* |
---|
1851 | *PrintS("new diff: "); |
---|
1852 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
1853 | *PrintLn(); |
---|
1854 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
1855 | */ |
---|
1856 | if (order != (ord+diff[pGetComp(p)])) |
---|
1857 | { |
---|
1858 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
1859 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
1860 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
1861 | delete *w;*w=NULL; |
---|
1862 | return FALSE; |
---|
1863 | } |
---|
1864 | } |
---|
1865 | pIter(p); |
---|
1866 | } |
---|
1867 | } |
---|
1868 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
1869 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
1870 | for (i=1;i<cmax;i++) (**w)[i-1]=(int)(diff[i]); |
---|
1871 | for (i=1;i<cmax;i++) |
---|
1872 | { |
---|
1873 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
1874 | } |
---|
1875 | if (w!=NULL) |
---|
1876 | { |
---|
1877 | for (i=1;i<cmax;i++) |
---|
1878 | { |
---|
1879 | (**w)[i-1]=(int)(diff[i]-diffmin); |
---|
1880 | } |
---|
1881 | } |
---|
1882 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
1883 | return TRUE; |
---|
1884 | } |
---|
1885 | |
---|
1886 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
1887 | { |
---|
1888 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
1889 | if (idIs0(m)) return TRUE; |
---|
1890 | |
---|
1891 | int cmax=-1; |
---|
1892 | int i; |
---|
1893 | poly p=NULL; |
---|
1894 | int length=IDELEMS(m); |
---|
1895 | polyset P=m->m; |
---|
1896 | for (i=length-1;i>=0;i--) |
---|
1897 | { |
---|
1898 | p=P[i]; |
---|
1899 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
1900 | } |
---|
1901 | if (w != NULL) |
---|
1902 | if (w->length()+1 < cmax) |
---|
1903 | { |
---|
1904 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
1905 | return FALSE; |
---|
1906 | } |
---|
1907 | |
---|
1908 | if(w!=NULL) |
---|
1909 | pSetModDeg(w); |
---|
1910 | |
---|
1911 | for (i=length-1;i>=0;i--) |
---|
1912 | { |
---|
1913 | p=P[i]; |
---|
1914 | poly q=p; |
---|
1915 | if (p!=NULL) |
---|
1916 | { |
---|
1917 | int d=pFDeg(p,currRing); |
---|
1918 | loop |
---|
1919 | { |
---|
1920 | pIter(p); |
---|
1921 | if (p==NULL) break; |
---|
1922 | if (d!=pFDeg(p,currRing)) |
---|
1923 | { |
---|
1924 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
1925 | if(w!=NULL) |
---|
1926 | pSetModDeg(NULL); |
---|
1927 | return FALSE; |
---|
1928 | } |
---|
1929 | } |
---|
1930 | } |
---|
1931 | } |
---|
1932 | |
---|
1933 | if(w!=NULL) |
---|
1934 | pSetModDeg(NULL); |
---|
1935 | |
---|
1936 | return TRUE; |
---|
1937 | } |
---|
1938 | |
---|
1939 | ideal idJet(ideal i,int d) |
---|
1940 | { |
---|
1941 | ideal r=idInit((i->nrows)*(i->ncols),i->rank); |
---|
1942 | r->nrows = i-> nrows; |
---|
1943 | r->ncols = i-> ncols; |
---|
1944 | //r->rank = i-> rank; |
---|
1945 | int k; |
---|
1946 | for(k=(i->nrows)*(i->ncols)-1;k>=0; k--) |
---|
1947 | { |
---|
1948 | r->m[k]=ppJet(i->m[k],d); |
---|
1949 | } |
---|
1950 | return r; |
---|
1951 | } |
---|
1952 | |
---|
1953 | ideal idJetW(ideal i,int d, intvec * iv) |
---|
1954 | { |
---|
1955 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
1956 | if (ecartWeights!=NULL) |
---|
1957 | { |
---|
1958 | WerrorS("cannot compute weighted jets now"); |
---|
1959 | } |
---|
1960 | else |
---|
1961 | { |
---|
1962 | short *w=iv2array(iv); |
---|
1963 | int k; |
---|
1964 | for(k=0; k<IDELEMS(i); k++) |
---|
1965 | { |
---|
1966 | r->m[k]=ppJetW(i->m[k],d,w); |
---|
1967 | } |
---|
1968 | omFreeSize((ADDRESS)w,(rVar(r)+1)*sizeof(short)); |
---|
1969 | } |
---|
1970 | return r; |
---|
1971 | } |
---|
1972 | |
---|
1973 | int idMinDegW(ideal M,intvec *w) |
---|
1974 | { |
---|
1975 | int d=-1; |
---|
1976 | for(int i=0;i<IDELEMS(M);i++) |
---|
1977 | { |
---|
1978 | int d0=pMinDeg(M->m[i],w); |
---|
1979 | if(-1<d0&&(d0<d||d==-1)) |
---|
1980 | d=d0; |
---|
1981 | } |
---|
1982 | return d; |
---|
1983 | } |
---|
1984 | |
---|
1985 | ideal idSeries(int n,ideal M,matrix U,intvec *w) |
---|
1986 | { |
---|
1987 | for(int i=IDELEMS(M)-1;i>=0;i--) |
---|
1988 | { |
---|
1989 | if(U==NULL) |
---|
1990 | M->m[i]=pSeries(n,M->m[i],NULL,w); |
---|
1991 | else |
---|
1992 | { |
---|
1993 | M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w); |
---|
1994 | MATELEM(U,i+1,i+1)=NULL; |
---|
1995 | } |
---|
1996 | } |
---|
1997 | if(U!=NULL) |
---|
1998 | idDelete((ideal*)&U); |
---|
1999 | return M; |
---|
2000 | } |
---|
2001 | |
---|
2002 | matrix idDiff(matrix i, int k) |
---|
2003 | { |
---|
2004 | int e=MATCOLS(i)*MATROWS(i); |
---|
2005 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
2006 | r->rank=i->rank; |
---|
2007 | int j; |
---|
2008 | for(j=0; j<e; j++) |
---|
2009 | { |
---|
2010 | r->m[j]=pDiff(i->m[j],k); |
---|
2011 | } |
---|
2012 | return r; |
---|
2013 | } |
---|
2014 | |
---|
2015 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
2016 | { |
---|
2017 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
2018 | int i,j; |
---|
2019 | for(i=0; i<IDELEMS(I); i++) |
---|
2020 | { |
---|
2021 | for(j=0; j<IDELEMS(J); j++) |
---|
2022 | { |
---|
2023 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
2024 | } |
---|
2025 | } |
---|
2026 | return r; |
---|
2027 | } |
---|
2028 | |
---|
2029 | int idElem(const ideal F) |
---|
2030 | { |
---|
2031 | int i=0,j=IDELEMS(F)-1; |
---|
2032 | |
---|
2033 | while(j>=0) |
---|
2034 | { |
---|
2035 | if ((F->m)[j]!=NULL) i++; |
---|
2036 | j--; |
---|
2037 | } |
---|
2038 | return i; |
---|
2039 | } |
---|
2040 | |
---|
2041 | /* |
---|
2042 | *computes module-weights for liftings of homogeneous modules |
---|
2043 | */ |
---|
2044 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
2045 | { |
---|
2046 | if (idIs0(mod)) return new intvec(2); |
---|
2047 | int i=IDELEMS(mod); |
---|
2048 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
2049 | intvec *result = new intvec(i+1); |
---|
2050 | while (i>0) |
---|
2051 | { |
---|
2052 | (*result)[i]=pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])]; |
---|
2053 | } |
---|
2054 | return result; |
---|
2055 | } |
---|
2056 | |
---|
2057 | /*2 |
---|
2058 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
2059 | *with x_max,...,x_1) |
---|
2060 | */ |
---|
2061 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
2062 | { |
---|
2063 | int i; |
---|
2064 | ideal result; |
---|
2065 | |
---|
2066 | if (idIs0(kBase)) return NULL; |
---|
2067 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
2068 | *convert = idSort(kBase,FALSE); |
---|
2069 | for (i=0;i<(*convert)->length();i++) |
---|
2070 | { |
---|
2071 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
2072 | } |
---|
2073 | return result; |
---|
2074 | } |
---|
2075 | |
---|
2076 | /*2 |
---|
2077 | *returns the index of a given monom in the list of the special kbase |
---|
2078 | */ |
---|
2079 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
2080 | { |
---|
2081 | int j=IDELEMS(kbase); |
---|
2082 | |
---|
2083 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
2084 | if (j==0) return -1; |
---|
2085 | int i=rVar(r); |
---|
2086 | while (i>0) |
---|
2087 | { |
---|
2088 | loop |
---|
2089 | { |
---|
2090 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
2091 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
2092 | j--; |
---|
2093 | if (j==0) return -1; |
---|
2094 | } |
---|
2095 | if (i==1) |
---|
2096 | { |
---|
2097 | while(j>0) |
---|
2098 | { |
---|
2099 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
2100 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
2101 | j--; |
---|
2102 | } |
---|
2103 | } |
---|
2104 | i--; |
---|
2105 | } |
---|
2106 | return -1; |
---|
2107 | } |
---|
2108 | |
---|
2109 | /*2 |
---|
2110 | *decomposes the monom in a part of coefficients described by the |
---|
2111 | *complement of how and a monom in variables occuring in how, the |
---|
2112 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
2113 | *exists) |
---|
2114 | */ |
---|
2115 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
2116 | { |
---|
2117 | int i; |
---|
2118 | poly coeff=p_One(r), base=p_One(r); |
---|
2119 | |
---|
2120 | for (i=1;i<=rVar(r);i++) |
---|
2121 | { |
---|
2122 | if (pGetExp(how,i)>0) |
---|
2123 | { |
---|
2124 | pSetExp(base,i,pGetExp(monom,i)); |
---|
2125 | } |
---|
2126 | else |
---|
2127 | { |
---|
2128 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
2129 | } |
---|
2130 | } |
---|
2131 | pSetComp(base,pGetComp(monom)); |
---|
2132 | pSetm(base); |
---|
2133 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
2134 | pSetm(coeff); |
---|
2135 | *pos = idIndexOfKBase(base,kbase); |
---|
2136 | if (*pos<0) |
---|
2137 | pDelete(&coeff); |
---|
2138 | pDelete(&base); |
---|
2139 | return coeff; |
---|
2140 | } |
---|
2141 | |
---|
2142 | /*2 |
---|
2143 | *returns a matrix A of coefficients with kbase*A=arg |
---|
2144 | *if all monomials in variables of how occur in kbase |
---|
2145 | *the other are deleted |
---|
2146 | */ |
---|
2147 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
2148 | { |
---|
2149 | matrix result; |
---|
2150 | ideal tempKbase; |
---|
2151 | poly p,q; |
---|
2152 | intvec * convert; |
---|
2153 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
2154 | #if 0 |
---|
2155 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
2156 | if (idIs0(arg)) |
---|
2157 | return mpNew(i,1); |
---|
2158 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
2159 | result = mpNew(i,j); |
---|
2160 | #else |
---|
2161 | result = mpNew(i, j); |
---|
2162 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
2163 | #endif |
---|
2164 | |
---|
2165 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
2166 | for (k=0;k<j;k++) |
---|
2167 | { |
---|
2168 | p = arg->m[k]; |
---|
2169 | while (p!=NULL) |
---|
2170 | { |
---|
2171 | q = idDecompose(p,how,tempKbase,&pos); |
---|
2172 | if (pos>=0) |
---|
2173 | { |
---|
2174 | MATELEM(result,(*convert)[pos],k+1) = |
---|
2175 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
2176 | } |
---|
2177 | else |
---|
2178 | pDelete(&q); |
---|
2179 | pIter(p); |
---|
2180 | } |
---|
2181 | } |
---|
2182 | idDelete(&tempKbase); |
---|
2183 | return result; |
---|
2184 | } |
---|
2185 | |
---|
2186 | /*3 |
---|
2187 | * searches for the next unit in the components of the module arg and |
---|
2188 | * returns the first one; |
---|
2189 | */ |
---|
2190 | static int id_ReadOutPivot(ideal arg,int* comp, const ring r) |
---|
2191 | { |
---|
2192 | if (idIs0(arg)) return -1; |
---|
2193 | int i=0,j, generator=-1; |
---|
2194 | int rk_arg=arg->rank; //idRankFreeModule(arg); |
---|
2195 | int * componentIsUsed =(int *)omAlloc((rk_arg+1)*sizeof(int)); |
---|
2196 | poly p; |
---|
2197 | |
---|
2198 | while ((generator<0) && (i<IDELEMS(arg))) |
---|
2199 | { |
---|
2200 | memset(componentIsUsed,0,(rk_arg+1)*sizeof(int)); |
---|
2201 | p = arg->m[i]; |
---|
2202 | while (p!=NULL) |
---|
2203 | { |
---|
2204 | j = p_GetComp(p,r); |
---|
2205 | if (componentIsUsed[j]==0) |
---|
2206 | { |
---|
2207 | #ifdef HAVE_RINGS |
---|
2208 | if (p_LmIsConstantComp(p,r) && |
---|
2209 | (!rField_is_Ring(r) || n_IsUnit(pGetCoeff(p),r->cf))) |
---|
2210 | { |
---|
2211 | #else |
---|
2212 | if (p_LmIsConstantComp(p,r)) |
---|
2213 | { |
---|
2214 | #endif |
---|
2215 | generator = i; |
---|
2216 | componentIsUsed[j] = 1; |
---|
2217 | } |
---|
2218 | else |
---|
2219 | { |
---|
2220 | componentIsUsed[j] = -1; |
---|
2221 | } |
---|
2222 | } |
---|
2223 | else if (componentIsUsed[j]>0) |
---|
2224 | { |
---|
2225 | (componentIsUsed[j])++; |
---|
2226 | } |
---|
2227 | pIter(p); |
---|
2228 | } |
---|
2229 | i++; |
---|
2230 | } |
---|
2231 | i = 0; |
---|
2232 | *comp = -1; |
---|
2233 | for (j=0;j<=rk_arg;j++) |
---|
2234 | { |
---|
2235 | if (componentIsUsed[j]>0) |
---|
2236 | { |
---|
2237 | if ((*comp==-1) || (componentIsUsed[j]<i)) |
---|
2238 | { |
---|
2239 | *comp = j; |
---|
2240 | i= componentIsUsed[j]; |
---|
2241 | } |
---|
2242 | } |
---|
2243 | } |
---|
2244 | omFree(componentIsUsed); |
---|
2245 | return generator; |
---|
2246 | } |
---|
2247 | |
---|
2248 | #if 0 |
---|
2249 | static void idDeleteComp(ideal arg,int red_comp) |
---|
2250 | { |
---|
2251 | int i,j; |
---|
2252 | poly p; |
---|
2253 | |
---|
2254 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
2255 | { |
---|
2256 | p = arg->m[i]; |
---|
2257 | while (p!=NULL) |
---|
2258 | { |
---|
2259 | j = pGetComp(p); |
---|
2260 | if (j>red_comp) |
---|
2261 | { |
---|
2262 | pSetComp(p,j-1); |
---|
2263 | pSetm(p); |
---|
2264 | } |
---|
2265 | pIter(p); |
---|
2266 | } |
---|
2267 | } |
---|
2268 | (arg->rank)--; |
---|
2269 | } |
---|
2270 | #endif |
---|
2271 | |
---|
2272 | static void idDeleteComps(ideal arg,int* red_comp,int del) |
---|
2273 | // red_comp is an array [0..args->rank] |
---|
2274 | { |
---|
2275 | int i,j; |
---|
2276 | poly p; |
---|
2277 | |
---|
2278 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
2279 | { |
---|
2280 | p = arg->m[i]; |
---|
2281 | while (p!=NULL) |
---|
2282 | { |
---|
2283 | j = pGetComp(p); |
---|
2284 | if (red_comp[j]!=j) |
---|
2285 | { |
---|
2286 | pSetComp(p,red_comp[j]); |
---|
2287 | pSetmComp(p); |
---|
2288 | } |
---|
2289 | pIter(p); |
---|
2290 | } |
---|
2291 | } |
---|
2292 | (arg->rank) -= del; |
---|
2293 | } |
---|
2294 | |
---|
2295 | /*2 |
---|
2296 | * returns the presentation of an isomorphic, minimally |
---|
2297 | * embedded module (arg represents the quotient!) |
---|
2298 | */ |
---|
2299 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w, const ring r) |
---|
2300 | { |
---|
2301 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
2302 | int i,next_gen,next_comp; |
---|
2303 | ideal res=arg; |
---|
2304 | if (!inPlace) res = id_Copy(arg,r); |
---|
2305 | res->rank=si_max(res->rank,id_RankFreeModule(res,r)); |
---|
2306 | int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int)); |
---|
2307 | for (i=res->rank;i>=0;i--) red_comp[i]=i; |
---|
2308 | |
---|
2309 | int del=0; |
---|
2310 | loop |
---|
2311 | { |
---|
2312 | next_gen = idReadOutPivot(res,&next_comp); |
---|
2313 | if (next_gen<0) break; |
---|
2314 | del++; |
---|
2315 | syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res)); |
---|
2316 | for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--; |
---|
2317 | if ((w !=NULL)&&(*w!=NULL)) |
---|
2318 | { |
---|
2319 | for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i]; |
---|
2320 | } |
---|
2321 | } |
---|
2322 | |
---|
2323 | idDeleteComps(res,red_comp,del); |
---|
2324 | idSkipZeroes(res); |
---|
2325 | omFree(red_comp); |
---|
2326 | |
---|
2327 | if ((w !=NULL)&&(*w!=NULL) &&(del>0)) |
---|
2328 | { |
---|
2329 | intvec *wtmp=new intvec((*w)->length()-del); |
---|
2330 | for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i]; |
---|
2331 | delete *w; |
---|
2332 | *w=wtmp; |
---|
2333 | } |
---|
2334 | return res; |
---|
2335 | } |
---|
2336 | |
---|
2337 | intvec * idQHomWeight(ideal id) |
---|
2338 | { |
---|
2339 | poly head, tail; |
---|
2340 | int k; |
---|
2341 | int in=IDELEMS(id)-1, ready=0, all=0, |
---|
2342 | coldim=rVar(r), rowmax=2*coldim; |
---|
2343 | if (in<0) return NULL; |
---|
2344 | intvec *imat=new intvec(rowmax+1,coldim,0); |
---|
2345 | |
---|
2346 | do |
---|
2347 | { |
---|
2348 | head = id->m[in--]; |
---|
2349 | if (head!=NULL) |
---|
2350 | { |
---|
2351 | tail = pNext(head); |
---|
2352 | while (tail!=NULL) |
---|
2353 | { |
---|
2354 | all++; |
---|
2355 | for (k=1;k<=coldim;k++) |
---|
2356 | IMATELEM(*imat,all,k) = pGetExpDiff(head,tail,k); |
---|
2357 | if (all==rowmax) |
---|
2358 | { |
---|
2359 | ivTriangIntern(imat, ready, all); |
---|
2360 | if (ready==coldim) |
---|
2361 | { |
---|
2362 | delete imat; |
---|
2363 | return NULL; |
---|
2364 | } |
---|
2365 | } |
---|
2366 | pIter(tail); |
---|
2367 | } |
---|
2368 | } |
---|
2369 | } while (in>=0); |
---|
2370 | if (all>ready) |
---|
2371 | { |
---|
2372 | ivTriangIntern(imat, ready, all); |
---|
2373 | if (ready==coldim) |
---|
2374 | { |
---|
2375 | delete imat; |
---|
2376 | return NULL; |
---|
2377 | } |
---|
2378 | } |
---|
2379 | intvec *result = ivSolveKern(imat, ready); |
---|
2380 | delete imat; |
---|
2381 | return result; |
---|
2382 | } |
---|
2383 | |
---|
2384 | BOOLEAN idIsZeroDim(ideal I) |
---|
2385 | { |
---|
2386 | BOOLEAN *UsedAxis=(BOOLEAN *)omAlloc0(rVar(r)*sizeof(BOOLEAN)); |
---|
2387 | int i,n; |
---|
2388 | poly po; |
---|
2389 | BOOLEAN res=TRUE; |
---|
2390 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
2391 | { |
---|
2392 | po=I->m[i]; |
---|
2393 | if ((po!=NULL) &&((n=pIsPurePower(po))!=0)) UsedAxis[n-1]=TRUE; |
---|
2394 | } |
---|
2395 | for(i=rVar(r)-1;i>=0;i--) |
---|
2396 | { |
---|
2397 | if(UsedAxis[i]==FALSE) {res=FALSE; break;} // not zero-dim. |
---|
2398 | } |
---|
2399 | omFreeSize(UsedAxis,rVar(r)*sizeof(BOOLEAN)); |
---|
2400 | return res; |
---|
2401 | } |
---|
2402 | |
---|
2403 | void id_Normalize(ideal I,const ring r) |
---|
2404 | { |
---|
2405 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
2406 | int i; |
---|
2407 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
2408 | { |
---|
2409 | p_Normalize(I->m[i],r); |
---|
2410 | } |
---|
2411 | } |
---|
2412 | |
---|
2413 | // #include <kernel/clapsing.h> |
---|
2414 | |
---|
2415 | #ifdef HAVE_FACTORY |
---|
2416 | poly id_GCD(poly f, poly g, const ring r) |
---|
2417 | { |
---|
2418 | ring save_r=r; |
---|
2419 | rChangeCurrRing(r); |
---|
2420 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
2421 | intvec *w = NULL; |
---|
2422 | ideal S=idSyzygies(I,testHomog,&w); |
---|
2423 | if (w!=NULL) delete w; |
---|
2424 | poly gg=pTakeOutComp(&(S->m[0]),2); |
---|
2425 | idDelete(&S); |
---|
2426 | poly gcd_p=singclap_pdivide(f,gg); |
---|
2427 | pDelete(&gg); |
---|
2428 | rChangeCurrRing(save_r); |
---|
2429 | return gcd_p; |
---|
2430 | } |
---|
2431 | #endif |
---|
2432 | |
---|
2433 | /*2 |
---|
2434 | * xx,q: arrays of length 0..rl-1 |
---|
2435 | * xx[i]: SB mod q[i] |
---|
2436 | * assume: char=0 |
---|
2437 | * assume: q[i]!=0 |
---|
2438 | * destroys xx |
---|
2439 | */ |
---|
2440 | #ifdef HAVE_FACTORY |
---|
2441 | ideal idChineseRemainder(ideal *xx, number *q, int rl, const ring r) |
---|
2442 | { |
---|
2443 | int cnt=IDELEMS(xx[0])*xx[0]->nrows; |
---|
2444 | ideal result=idInit(cnt,xx[0]->rank); |
---|
2445 | result->nrows=xx[0]->nrows; // for lifting matrices |
---|
2446 | result->ncols=xx[0]->ncols; // for lifting matrices |
---|
2447 | int i,j; |
---|
2448 | poly r,h,hh,res_p; |
---|
2449 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
2450 | for(i=cnt-1;i>=0;i--) |
---|
2451 | { |
---|
2452 | res_p=NULL; |
---|
2453 | loop |
---|
2454 | { |
---|
2455 | r=NULL; |
---|
2456 | for(j=rl-1;j>=0;j--) |
---|
2457 | { |
---|
2458 | h=xx[j]->m[i]; |
---|
2459 | if ((h!=NULL) |
---|
2460 | &&((r==NULL)||(pLmCmp(r,h)==-1))) |
---|
2461 | r=h; |
---|
2462 | } |
---|
2463 | if (r==NULL) break; |
---|
2464 | h=pHead(r); |
---|
2465 | for(j=rl-1;j>=0;j--) |
---|
2466 | { |
---|
2467 | hh=xx[j]->m[i]; |
---|
2468 | if ((hh!=NULL) && (pLmCmp(r,hh)==0)) |
---|
2469 | { |
---|
2470 | x[j]=pGetCoeff(hh); |
---|
2471 | hh=pLmFreeAndNext(hh); |
---|
2472 | xx[j]->m[i]=hh; |
---|
2473 | } |
---|
2474 | else |
---|
2475 | x[j]=nlInit(0, r); |
---|
2476 | } |
---|
2477 | number n=nlChineseRemainder(x,q,rl); |
---|
2478 | for(j=rl-1;j>=0;j--) |
---|
2479 | { |
---|
2480 | x[j]=NULL; // nlInit(0...) takes no memory |
---|
2481 | } |
---|
2482 | if (nlIsZero(n)) pDelete(&h); |
---|
2483 | else |
---|
2484 | { |
---|
2485 | pSetCoeff(h,n); |
---|
2486 | //Print("new mon:");pWrite(h); |
---|
2487 | res_p=pAdd(res_p,h); |
---|
2488 | } |
---|
2489 | } |
---|
2490 | result->m[i]=res_p; |
---|
2491 | } |
---|
2492 | omFree(x); |
---|
2493 | for(i=rl-1;i>=0;i--) idDelete(&(xx[i])); |
---|
2494 | omFree(xx); |
---|
2495 | return result; |
---|
2496 | } |
---|
2497 | #endif |
---|
2498 | /* currently unsed: |
---|
2499 | ideal idChineseRemainder(ideal *xx, intvec *iv) |
---|
2500 | { |
---|
2501 | int rl=iv->length(); |
---|
2502 | number *q=(number *)omAlloc(rl*sizeof(number)); |
---|
2503 | int i; |
---|
2504 | for(i=0; i<rl; i++) |
---|
2505 | { |
---|
2506 | q[i]=nInit((*iv)[i]); |
---|
2507 | } |
---|
2508 | return idChineseRemainder(xx,q,rl); |
---|
2509 | } |
---|
2510 | */ |
---|
2511 | /* |
---|
2512 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
---|
2513 | */ |
---|
2514 | ideal id_Farey(ideal x, number N, const ring r) |
---|
2515 | { |
---|
2516 | int cnt=IDELEMS(x)*x->nrows; |
---|
2517 | ideal result=idInit(cnt,x->rank); |
---|
2518 | result->nrows=x->nrows; // for lifting matrices |
---|
2519 | result->ncols=x->ncols; // for lifting matrices |
---|
2520 | |
---|
2521 | int i; |
---|
2522 | for(i=cnt-1;i>=0;i--) |
---|
2523 | { |
---|
2524 | poly h=p_Copy(x->m[i],r); |
---|
2525 | result->m[i]=h; |
---|
2526 | while(h!=NULL) |
---|
2527 | { |
---|
2528 | number c=pGetCoeff(h); |
---|
2529 | pSetCoeff0(h,nlFarey(c,N)); |
---|
2530 | n_Delete(&c,r->cf); |
---|
2531 | pIter(h); |
---|
2532 | } |
---|
2533 | while((result->m[i]!=NULL)&&(n_IsZero(pGetCoeff(result->m[i]),r->cf))) |
---|
2534 | { |
---|
2535 | p_LmDelete(&(result->m[i]),r); |
---|
2536 | } |
---|
2537 | h=result->m[i]; |
---|
2538 | while((h!=NULL) && (pNext(h)!=NULL)) |
---|
2539 | { |
---|
2540 | if(n_IsZero(pGetCoeff(pNext(h)),r->cf)) |
---|
2541 | { |
---|
2542 | p_LmDelete(&pNext(h),r); |
---|
2543 | } |
---|
2544 | else pIter(h); |
---|
2545 | } |
---|
2546 | } |
---|
2547 | return result; |
---|
2548 | } |
---|
2549 | |
---|
2550 | /*2 |
---|
2551 | * transpose a module |
---|
2552 | */ |
---|
2553 | ideal id_Transp(ideal a, const ring rRing) |
---|
2554 | { |
---|
2555 | int r = a->rank, c = IDELEMS(a); |
---|
2556 | ideal b = idInit(r,c); |
---|
2557 | |
---|
2558 | for (int i=c; i>0; i--) |
---|
2559 | { |
---|
2560 | poly p=a->m[i-1]; |
---|
2561 | while(p!=NULL) |
---|
2562 | { |
---|
2563 | poly h=p_Head(p, rRing); |
---|
2564 | int co=p_GetComp(h, rRing)-1; |
---|
2565 | p_SetComp(h, i, rRing); |
---|
2566 | p_Setm(h, rRing); |
---|
2567 | b->m[co] = p_Add_q(b->m[co], h, rRing); |
---|
2568 | pIter(p); |
---|
2569 | } |
---|
2570 | } |
---|
2571 | return b; |
---|
2572 | } |
---|
2573 | |
---|
2574 | |
---|
2575 | |
---|
2576 | /*2 |
---|
2577 | * The following is needed to compute the image of certain map used in |
---|
2578 | * the computation of cohomologies via BGG |
---|
2579 | * let M = { w_1, ..., w_k }, k = size(M) == ncols(M), n = nvars(currRing). |
---|
2580 | * assuming that nrows(M) <= m*n; the procedure computes: |
---|
2581 | * transpose(M) * transpose( var(1) I_m | ... | var(n) I_m ) :== transpose(module{f_1, ... f_k}), |
---|
2582 | * where f_i = \sum_{j=1}^{m} (w_i, v_j) gen(j), (w_i, v_j) is a `scalar` multiplication. |
---|
2583 | * that is, if w_i = (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) then |
---|
2584 | |
---|
2585 | (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) |
---|
2586 | * var_1 ... var_1 | var_2 ... var_2 | ... | var_n ... var(n) |
---|
2587 | * gen_1 ... gen_m | gen_1 ... gen_m | ... | gen_1 ... gen_m |
---|
2588 | + => |
---|
2589 | f_i = |
---|
2590 | |
---|
2591 | a^1_1 * var(1) * gen(1) + ... + a^1_m * var(1) * gen(m) + |
---|
2592 | a^2_1 * var(2) * gen(1) + ... + a^2_m * var(2) * gen(m) + |
---|
2593 | ... |
---|
2594 | a^n_1 * var(n) * gen(1) + ... + a^n_m * var(n) * gen(m); |
---|
2595 | |
---|
2596 | NOTE: for every f_i we run only ONCE along w_i saving partial sums into a temporary array of polys of size m |
---|
2597 | */ |
---|
2598 | ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing) |
---|
2599 | { |
---|
2600 | // #ifdef DEBU |
---|
2601 | // WarnS("tensorModuleMult!!!!"); |
---|
2602 | |
---|
2603 | assume(m > 0); |
---|
2604 | assume(M != NULL); |
---|
2605 | |
---|
2606 | const int n = rRing->N; |
---|
2607 | |
---|
2608 | assume(M->rank <= m * n); |
---|
2609 | |
---|
2610 | const int k = IDELEMS(M); |
---|
2611 | |
---|
2612 | ideal idTemp = idInit(k,m); // = {f_1, ..., f_k } |
---|
2613 | |
---|
2614 | for( int i = 0; i < k; i++ ) // for every w \in M |
---|
2615 | { |
---|
2616 | poly pTempSum = NULL; |
---|
2617 | |
---|
2618 | poly w = M->m[i]; |
---|
2619 | |
---|
2620 | while(w != NULL) // for each term of w... |
---|
2621 | { |
---|
2622 | poly h = p_Head(w, rRing); |
---|
2623 | |
---|
2624 | const int gen = p_GetComp(h, rRing); // 1 ... |
---|
2625 | |
---|
2626 | assume(gen > 0); |
---|
2627 | assume(gen <= n*m); |
---|
2628 | |
---|
2629 | // TODO: write a formula with %, / instead of while! |
---|
2630 | /* |
---|
2631 | int c = gen; |
---|
2632 | int v = 1; |
---|
2633 | while(c > m) |
---|
2634 | { |
---|
2635 | c -= m; |
---|
2636 | v++; |
---|
2637 | } |
---|
2638 | */ |
---|
2639 | |
---|
2640 | int cc = gen % m; |
---|
2641 | if( cc == 0) cc = m; |
---|
2642 | int vv = 1 + (gen - cc) / m; |
---|
2643 | |
---|
2644 | // assume( cc == c ); |
---|
2645 | // assume( vv == v ); |
---|
2646 | |
---|
2647 | // 1<= c <= m |
---|
2648 | assume( cc > 0 ); |
---|
2649 | assume( cc <= m ); |
---|
2650 | |
---|
2651 | assume( vv > 0 ); |
---|
2652 | assume( vv <= n ); |
---|
2653 | |
---|
2654 | assume( (cc + (vv-1)*m) == gen ); |
---|
2655 | |
---|
2656 | p_IncrExp(h, vv, rRing); // h *= var(j) && // p_AddExp(h, vv, 1, rRing); |
---|
2657 | p_SetComp(h, cc, rRing); |
---|
2658 | |
---|
2659 | p_Setm(h, rRing); // addjust degree after the previous steps! |
---|
2660 | |
---|
2661 | pTempSum = p_Add_q(pTempSum, h, rRing); // it is slow since h will be usually put to the back of pTempSum!!! |
---|
2662 | |
---|
2663 | pIter(w); |
---|
2664 | } |
---|
2665 | |
---|
2666 | idTemp->m[i] = pTempSum; |
---|
2667 | } |
---|
2668 | |
---|
2669 | // simplify idTemp??? |
---|
2670 | |
---|
2671 | ideal idResult = id_Transp(idTemp, rRing); |
---|
2672 | |
---|
2673 | id_Delete(&idTemp, rRing); |
---|
2674 | |
---|
2675 | return(idResult); |
---|
2676 | } |
---|