1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /* |
---|
5 | * ABSTRACT - all basic methods to manipulate ideals |
---|
6 | */ |
---|
7 | |
---|
8 | /* includes */ |
---|
9 | |
---|
10 | #include <kernel/mod2.h> |
---|
11 | |
---|
12 | #include <omalloc/omalloc.h> |
---|
13 | |
---|
14 | #include <misc/options.h> |
---|
15 | #include <misc/intvec.h> |
---|
16 | |
---|
17 | #include <coeffs/coeffs.h> |
---|
18 | #include <coeffs/numbers.h> |
---|
19 | // #include <coeffs/longrat.h> |
---|
20 | |
---|
21 | |
---|
22 | #include <polys/monomials/ring.h> |
---|
23 | #include <polys/matpol.h> |
---|
24 | #include <polys/weight.h> |
---|
25 | #include <polys/sparsmat.h> |
---|
26 | #include <polys/prCopy.h> |
---|
27 | #include <polys/nc/nc.h> |
---|
28 | |
---|
29 | |
---|
30 | #include <kernel/ideals.h> |
---|
31 | |
---|
32 | #include <kernel/polys.h> |
---|
33 | |
---|
34 | #include <kernel/GBEngine/kstd1.h> |
---|
35 | #include <kernel/GBEngine/syz.h> |
---|
36 | |
---|
37 | |
---|
38 | /* #define WITH_OLD_MINOR */ |
---|
39 | |
---|
40 | /*0 implementation*/ |
---|
41 | |
---|
42 | /*2 |
---|
43 | *returns a minimized set of generators of h1 |
---|
44 | */ |
---|
45 | ideal idMinBase (ideal h1) |
---|
46 | { |
---|
47 | ideal h2, h3,h4,e; |
---|
48 | int j,k; |
---|
49 | int i,l,ll; |
---|
50 | intvec * wth; |
---|
51 | BOOLEAN homog; |
---|
52 | if(rField_is_Ring(currRing)) |
---|
53 | { |
---|
54 | WarnS("minbase applies only to the local or homogeneous case over coefficient fields"); |
---|
55 | e=idCopy(h1); |
---|
56 | return e; |
---|
57 | } |
---|
58 | homog = idHomModule(h1,currRing->qideal,&wth); |
---|
59 | if (rHasGlobalOrdering(currRing)) |
---|
60 | { |
---|
61 | if(!homog) |
---|
62 | { |
---|
63 | WarnS("minbase applies only to the local or homogeneous case over coefficient fields"); |
---|
64 | e=idCopy(h1); |
---|
65 | return e; |
---|
66 | } |
---|
67 | else |
---|
68 | { |
---|
69 | ideal re=kMin_std(h1,currRing->qideal,(tHomog)homog,&wth,h2,NULL,0,3); |
---|
70 | idDelete(&re); |
---|
71 | return h2; |
---|
72 | } |
---|
73 | } |
---|
74 | e=idInit(1,h1->rank); |
---|
75 | if (idIs0(h1)) |
---|
76 | { |
---|
77 | return e; |
---|
78 | } |
---|
79 | pEnlargeSet(&(e->m),IDELEMS(e),15); |
---|
80 | IDELEMS(e) = 16; |
---|
81 | h2 = kStd(h1,currRing->qideal,isNotHomog,NULL); |
---|
82 | h3 = idMaxIdeal(1); |
---|
83 | h4=idMult(h2,h3); |
---|
84 | idDelete(&h3); |
---|
85 | h3=kStd(h4,currRing->qideal,isNotHomog,NULL); |
---|
86 | k = IDELEMS(h3); |
---|
87 | while ((k > 0) && (h3->m[k-1] == NULL)) k--; |
---|
88 | j = -1; |
---|
89 | l = IDELEMS(h2); |
---|
90 | while ((l > 0) && (h2->m[l-1] == NULL)) l--; |
---|
91 | for (i=l-1; i>=0; i--) |
---|
92 | { |
---|
93 | if (h2->m[i] != NULL) |
---|
94 | { |
---|
95 | ll = 0; |
---|
96 | while ((ll < k) && ((h3->m[ll] == NULL) |
---|
97 | || !pDivisibleBy(h3->m[ll],h2->m[i]))) |
---|
98 | ll++; |
---|
99 | if (ll >= k) |
---|
100 | { |
---|
101 | j++; |
---|
102 | if (j > IDELEMS(e)-1) |
---|
103 | { |
---|
104 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
105 | IDELEMS(e) += 16; |
---|
106 | } |
---|
107 | e->m[j] = pCopy(h2->m[i]); |
---|
108 | } |
---|
109 | } |
---|
110 | } |
---|
111 | idDelete(&h2); |
---|
112 | idDelete(&h3); |
---|
113 | idDelete(&h4); |
---|
114 | if (currRing->qideal!=NULL) |
---|
115 | { |
---|
116 | h3=idInit(1,e->rank); |
---|
117 | h2=kNF(h3,currRing->qideal,e); |
---|
118 | idDelete(&h3); |
---|
119 | idDelete(&e); |
---|
120 | e=h2; |
---|
121 | } |
---|
122 | idSkipZeroes(e); |
---|
123 | return e; |
---|
124 | } |
---|
125 | |
---|
126 | |
---|
127 | /*2 |
---|
128 | *initialized a field with r numbers between beg and end for the |
---|
129 | *procedure idNextChoise |
---|
130 | */ |
---|
131 | ideal idSectWithElim (ideal h1,ideal h2) |
---|
132 | // does not destroy h1,h2 |
---|
133 | { |
---|
134 | if (TEST_OPT_PROT) PrintS("intersect by elimination method\n"); |
---|
135 | assume(!idIs0(h1)); |
---|
136 | assume(!idIs0(h2)); |
---|
137 | assume(IDELEMS(h1)<=IDELEMS(h2)); |
---|
138 | assume(id_RankFreeModule(h1,currRing)==0); |
---|
139 | assume(id_RankFreeModule(h2,currRing)==0); |
---|
140 | // add a new variable: |
---|
141 | int j; |
---|
142 | ring origRing=currRing; |
---|
143 | ring r=rCopy0(origRing); |
---|
144 | r->N++; |
---|
145 | r->block0[0]=1; |
---|
146 | r->block1[0]= r->N; |
---|
147 | omFree(r->order); |
---|
148 | r->order=(int*)omAlloc0(3*sizeof(int*)); |
---|
149 | r->order[0]=ringorder_dp; |
---|
150 | r->order[1]=ringorder_C; |
---|
151 | char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr)); |
---|
152 | for (j=0;j<r->N-1;j++) names[j]=r->names[j]; |
---|
153 | names[r->N-1]=omStrDup("@"); |
---|
154 | omFree(r->names); |
---|
155 | r->names=names; |
---|
156 | rComplete(r,TRUE); |
---|
157 | // fetch h1, h2 |
---|
158 | ideal h; |
---|
159 | h1=idrCopyR(h1,origRing,r); |
---|
160 | h2=idrCopyR(h2,origRing,r); |
---|
161 | // switch to temp. ring r |
---|
162 | rChangeCurrRing(r); |
---|
163 | // create 1-t, t |
---|
164 | poly omt=p_One(currRing); |
---|
165 | p_SetExp(omt,r->N,1,currRing); |
---|
166 | poly t=p_Copy(omt,currRing); |
---|
167 | p_Setm(omt,currRing); |
---|
168 | omt=p_Neg(omt,currRing); |
---|
169 | omt=p_Add_q(omt,pOne(),currRing); |
---|
170 | // compute (1-t)*h1 |
---|
171 | h1=(ideal)mp_MultP((matrix)h1,omt,currRing); |
---|
172 | // compute t*h2 |
---|
173 | h2=(ideal)mp_MultP((matrix)h2,pCopy(t),currRing); |
---|
174 | // (1-t)h1 + t*h2 |
---|
175 | h=idInit(IDELEMS(h1)+IDELEMS(h2),1); |
---|
176 | int l; |
---|
177 | for (l=IDELEMS(h1)-1; l>=0; l--) |
---|
178 | { |
---|
179 | h->m[l] = h1->m[l]; h1->m[l]=NULL; |
---|
180 | } |
---|
181 | j=IDELEMS(h1); |
---|
182 | for (l=IDELEMS(h2)-1; l>=0; l--) |
---|
183 | { |
---|
184 | h->m[l+j] = h2->m[l]; h2->m[l]=NULL; |
---|
185 | } |
---|
186 | idDelete(&h1); |
---|
187 | idDelete(&h2); |
---|
188 | // eliminate t: |
---|
189 | |
---|
190 | ideal res=idElimination(h,t); |
---|
191 | // cleanup |
---|
192 | idDelete(&h); |
---|
193 | if (res!=NULL) res=idrMoveR(res,r,origRing); |
---|
194 | rChangeCurrRing(origRing); |
---|
195 | rDelete(r); |
---|
196 | return res; |
---|
197 | } |
---|
198 | /*2 |
---|
199 | * h3 := h1 intersect h2 |
---|
200 | */ |
---|
201 | ideal idSect (ideal h1,ideal h2) |
---|
202 | { |
---|
203 | int i,j,k,length; |
---|
204 | int flength = id_RankFreeModule(h1,currRing); |
---|
205 | int slength = id_RankFreeModule(h2,currRing); |
---|
206 | int rank=si_max(h1->rank,h2->rank); |
---|
207 | if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank); |
---|
208 | |
---|
209 | ideal first,second,temp,temp1,result; |
---|
210 | poly p,q; |
---|
211 | |
---|
212 | if (IDELEMS(h1)<IDELEMS(h2)) |
---|
213 | { |
---|
214 | first = h1; |
---|
215 | second = h2; |
---|
216 | } |
---|
217 | else |
---|
218 | { |
---|
219 | first = h2; |
---|
220 | second = h1; |
---|
221 | int t=flength; flength=slength; slength=t; |
---|
222 | } |
---|
223 | length = si_max(flength,slength); |
---|
224 | if (length==0) |
---|
225 | { |
---|
226 | if ((currRing->qideal==NULL) |
---|
227 | && (currRing->OrdSgn==1) |
---|
228 | && (!rIsPluralRing(currRing)) |
---|
229 | && ((TEST_V_INTERSECT_ELIM) || (!TEST_V_INTERSECT_SYZ))) |
---|
230 | return idSectWithElim(first,second); |
---|
231 | else length = 1; |
---|
232 | } |
---|
233 | if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n"); |
---|
234 | j = IDELEMS(first); |
---|
235 | |
---|
236 | ring orig_ring=currRing; |
---|
237 | ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
238 | rSetSyzComp(length, syz_ring); |
---|
239 | |
---|
240 | while ((j>0) && (first->m[j-1]==NULL)) j--; |
---|
241 | temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j); |
---|
242 | k = 0; |
---|
243 | for (i=0;i<j;i++) |
---|
244 | { |
---|
245 | if (first->m[i]!=NULL) |
---|
246 | { |
---|
247 | if (syz_ring==orig_ring) |
---|
248 | temp->m[k] = pCopy(first->m[i]); |
---|
249 | else |
---|
250 | temp->m[k] = prCopyR(first->m[i], orig_ring, syz_ring); |
---|
251 | q = pOne(); |
---|
252 | pSetComp(q,i+1+length); |
---|
253 | pSetmComp(q); |
---|
254 | if (flength==0) p_Shift(&(temp->m[k]),1,currRing); |
---|
255 | p = temp->m[k]; |
---|
256 | while (pNext(p)!=NULL) pIter(p); |
---|
257 | pNext(p) = q; |
---|
258 | k++; |
---|
259 | } |
---|
260 | } |
---|
261 | for (i=0;i<IDELEMS(second);i++) |
---|
262 | { |
---|
263 | if (second->m[i]!=NULL) |
---|
264 | { |
---|
265 | if (syz_ring==orig_ring) |
---|
266 | temp->m[k] = pCopy(second->m[i]); |
---|
267 | else |
---|
268 | temp->m[k] = prCopyR(second->m[i], orig_ring,currRing); |
---|
269 | if (slength==0) p_Shift(&(temp->m[k]),1,currRing); |
---|
270 | k++; |
---|
271 | } |
---|
272 | } |
---|
273 | intvec *w=NULL; |
---|
274 | temp1 = kStd(temp,currRing->qideal,testHomog,&w,NULL,length); |
---|
275 | if (w!=NULL) delete w; |
---|
276 | idDelete(&temp); |
---|
277 | if(syz_ring!=orig_ring) |
---|
278 | rChangeCurrRing(orig_ring); |
---|
279 | |
---|
280 | result = idInit(IDELEMS(temp1),rank); |
---|
281 | j = 0; |
---|
282 | for (i=0;i<IDELEMS(temp1);i++) |
---|
283 | { |
---|
284 | if ((temp1->m[i]!=NULL) |
---|
285 | && (p_GetComp(temp1->m[i],syz_ring)>length)) |
---|
286 | { |
---|
287 | if(syz_ring==orig_ring) |
---|
288 | { |
---|
289 | p = temp1->m[i]; |
---|
290 | } |
---|
291 | else |
---|
292 | { |
---|
293 | p = prMoveR(temp1->m[i], syz_ring,orig_ring); |
---|
294 | } |
---|
295 | temp1->m[i]=NULL; |
---|
296 | while (p!=NULL) |
---|
297 | { |
---|
298 | q = pNext(p); |
---|
299 | pNext(p) = NULL; |
---|
300 | k = pGetComp(p)-1-length; |
---|
301 | pSetComp(p,0); |
---|
302 | pSetmComp(p); |
---|
303 | /* Warning! multiply only from the left! it's very important for Plural */ |
---|
304 | result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k]))); |
---|
305 | p = q; |
---|
306 | } |
---|
307 | j++; |
---|
308 | } |
---|
309 | } |
---|
310 | if(syz_ring!=orig_ring) |
---|
311 | { |
---|
312 | rChangeCurrRing(syz_ring); |
---|
313 | idDelete(&temp1); |
---|
314 | rChangeCurrRing(orig_ring); |
---|
315 | rDelete(syz_ring); |
---|
316 | } |
---|
317 | else |
---|
318 | { |
---|
319 | idDelete(&temp1); |
---|
320 | } |
---|
321 | |
---|
322 | idSkipZeroes(result); |
---|
323 | if (TEST_OPT_RETURN_SB) |
---|
324 | { |
---|
325 | w=NULL; |
---|
326 | temp1=kStd(result,currRing->qideal,testHomog,&w); |
---|
327 | if (w!=NULL) delete w; |
---|
328 | idDelete(&result); |
---|
329 | idSkipZeroes(temp1); |
---|
330 | return temp1; |
---|
331 | } |
---|
332 | else //temp1=kInterRed(result,currRing->qideal); |
---|
333 | return result; |
---|
334 | } |
---|
335 | |
---|
336 | /*2 |
---|
337 | * ideal/module intersection for a list of objects |
---|
338 | * given as 'resolvente' |
---|
339 | */ |
---|
340 | ideal idMultSect(resolvente arg, int length) |
---|
341 | { |
---|
342 | int i,j=0,k=0,syzComp,l,maxrk=-1,realrki; |
---|
343 | ideal bigmat,tempstd,result; |
---|
344 | poly p; |
---|
345 | int isIdeal=0; |
---|
346 | intvec * w=NULL; |
---|
347 | |
---|
348 | /* find 0-ideals and max rank -----------------------------------*/ |
---|
349 | for (i=0;i<length;i++) |
---|
350 | { |
---|
351 | if (!idIs0(arg[i])) |
---|
352 | { |
---|
353 | realrki=id_RankFreeModule(arg[i],currRing); |
---|
354 | k++; |
---|
355 | j += IDELEMS(arg[i]); |
---|
356 | if (realrki>maxrk) maxrk = realrki; |
---|
357 | } |
---|
358 | else |
---|
359 | { |
---|
360 | if (arg[i]!=NULL) |
---|
361 | { |
---|
362 | return idInit(1,arg[i]->rank); |
---|
363 | } |
---|
364 | } |
---|
365 | } |
---|
366 | if (maxrk == 0) |
---|
367 | { |
---|
368 | isIdeal = 1; |
---|
369 | maxrk = 1; |
---|
370 | } |
---|
371 | /* init -----------------------------------------------------------*/ |
---|
372 | j += maxrk; |
---|
373 | syzComp = k*maxrk; |
---|
374 | |
---|
375 | ring orig_ring=currRing; |
---|
376 | ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
377 | rSetSyzComp(syzComp, syz_ring); |
---|
378 | |
---|
379 | bigmat = idInit(j,(k+1)*maxrk); |
---|
380 | /* create unit matrices ------------------------------------------*/ |
---|
381 | for (i=0;i<maxrk;i++) |
---|
382 | { |
---|
383 | for (j=0;j<=k;j++) |
---|
384 | { |
---|
385 | p = pOne(); |
---|
386 | pSetComp(p,i+1+j*maxrk); |
---|
387 | pSetmComp(p); |
---|
388 | bigmat->m[i] = pAdd(bigmat->m[i],p); |
---|
389 | } |
---|
390 | } |
---|
391 | /* enter given ideals ------------------------------------------*/ |
---|
392 | i = maxrk; |
---|
393 | k = 0; |
---|
394 | for (j=0;j<length;j++) |
---|
395 | { |
---|
396 | if (arg[j]!=NULL) |
---|
397 | { |
---|
398 | for (l=0;l<IDELEMS(arg[j]);l++) |
---|
399 | { |
---|
400 | if (arg[j]->m[l]!=NULL) |
---|
401 | { |
---|
402 | if (syz_ring==orig_ring) |
---|
403 | bigmat->m[i] = pCopy(arg[j]->m[l]); |
---|
404 | else |
---|
405 | bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring,currRing); |
---|
406 | p_Shift(&(bigmat->m[i]),k*maxrk+isIdeal,currRing); |
---|
407 | i++; |
---|
408 | } |
---|
409 | } |
---|
410 | k++; |
---|
411 | } |
---|
412 | } |
---|
413 | /* std computation --------------------------------------------*/ |
---|
414 | tempstd = kStd(bigmat,currRing->qideal,testHomog,&w,NULL,syzComp); |
---|
415 | if (w!=NULL) delete w; |
---|
416 | idDelete(&bigmat); |
---|
417 | |
---|
418 | if(syz_ring!=orig_ring) |
---|
419 | rChangeCurrRing(orig_ring); |
---|
420 | |
---|
421 | /* interprete result ----------------------------------------*/ |
---|
422 | result = idInit(IDELEMS(tempstd),maxrk); |
---|
423 | k = 0; |
---|
424 | for (j=0;j<IDELEMS(tempstd);j++) |
---|
425 | { |
---|
426 | if ((tempstd->m[j]!=NULL) && (p_GetComp(tempstd->m[j],syz_ring)>syzComp)) |
---|
427 | { |
---|
428 | if (syz_ring==orig_ring) |
---|
429 | p = pCopy(tempstd->m[j]); |
---|
430 | else |
---|
431 | p = prCopyR(tempstd->m[j], syz_ring,currRing); |
---|
432 | p_Shift(&p,-syzComp-isIdeal,currRing); |
---|
433 | result->m[k] = p; |
---|
434 | k++; |
---|
435 | } |
---|
436 | } |
---|
437 | /* clean up ----------------------------------------------------*/ |
---|
438 | if(syz_ring!=orig_ring) |
---|
439 | rChangeCurrRing(syz_ring); |
---|
440 | idDelete(&tempstd); |
---|
441 | if(syz_ring!=orig_ring) |
---|
442 | { |
---|
443 | rChangeCurrRing(orig_ring); |
---|
444 | rDelete(syz_ring); |
---|
445 | } |
---|
446 | idSkipZeroes(result); |
---|
447 | return result; |
---|
448 | } |
---|
449 | |
---|
450 | /*2 |
---|
451 | *computes syzygies of h1, |
---|
452 | *if quot != NULL it computes in the quotient ring modulo "quot" |
---|
453 | *works always in a ring with ringorder_s |
---|
454 | */ |
---|
455 | static ideal idPrepare (ideal h1, tHomog hom, int syzcomp, intvec **w) |
---|
456 | { |
---|
457 | ideal h2, h3; |
---|
458 | int j,k; |
---|
459 | poly p,q; |
---|
460 | |
---|
461 | if (idIs0(h1)) return NULL; |
---|
462 | k = id_RankFreeModule(h1,currRing); |
---|
463 | h2=idCopy(h1); |
---|
464 | int i = IDELEMS(h2); |
---|
465 | if (k == 0) |
---|
466 | { |
---|
467 | id_Shift(h2,1,currRing); |
---|
468 | k = 1; |
---|
469 | } |
---|
470 | if (syzcomp<k) |
---|
471 | { |
---|
472 | Warn("syzcomp too low, should be %d instead of %d",k,syzcomp); |
---|
473 | syzcomp = k; |
---|
474 | rSetSyzComp(k,currRing); |
---|
475 | } |
---|
476 | h2->rank = syzcomp+i; |
---|
477 | |
---|
478 | //if (hom==testHomog) |
---|
479 | //{ |
---|
480 | // if(idHomIdeal(h1,currRing->qideal)) |
---|
481 | // { |
---|
482 | // hom=TRUE; |
---|
483 | // } |
---|
484 | //} |
---|
485 | |
---|
486 | for (j=0; j<i; j++) |
---|
487 | { |
---|
488 | p = h2->m[j]; |
---|
489 | q = pOne(); |
---|
490 | pSetComp(q,syzcomp+1+j); |
---|
491 | pSetmComp(q); |
---|
492 | if (p!=NULL) |
---|
493 | { |
---|
494 | while (pNext(p)) pIter(p); |
---|
495 | p->next = q; |
---|
496 | } |
---|
497 | else |
---|
498 | h2->m[j]=q; |
---|
499 | } |
---|
500 | |
---|
501 | idTest(h2); |
---|
502 | |
---|
503 | h3 = kStd(h2,currRing->qideal,hom,w,NULL,syzcomp); |
---|
504 | |
---|
505 | idDelete(&h2); |
---|
506 | return h3; |
---|
507 | } |
---|
508 | |
---|
509 | /*2 |
---|
510 | * compute the syzygies of h1 in R/quot, |
---|
511 | * weights of components are in w |
---|
512 | * if setRegularity, return the regularity in deg |
---|
513 | * do not change h1, w |
---|
514 | */ |
---|
515 | ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp, |
---|
516 | BOOLEAN setRegularity, int *deg) |
---|
517 | { |
---|
518 | ideal s_h1; |
---|
519 | int j, k, length=0,reg; |
---|
520 | BOOLEAN isMonomial=TRUE; |
---|
521 | int ii, idElemens_h1; |
---|
522 | |
---|
523 | assume(h1 != NULL); |
---|
524 | |
---|
525 | idElemens_h1=IDELEMS(h1); |
---|
526 | #ifdef PDEBUG |
---|
527 | for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]); |
---|
528 | #endif |
---|
529 | if (idIs0(h1)) |
---|
530 | { |
---|
531 | ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/); |
---|
532 | return result; |
---|
533 | } |
---|
534 | int slength=(int)id_RankFreeModule(h1,currRing); |
---|
535 | k=si_max(1,slength /*id_RankFreeModule(h1)*/); |
---|
536 | |
---|
537 | assume(currRing != NULL); |
---|
538 | ring orig_ring=currRing; |
---|
539 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
540 | |
---|
541 | if (setSyzComp) |
---|
542 | rSetSyzComp(k,syz_ring); |
---|
543 | |
---|
544 | if (orig_ring != syz_ring) |
---|
545 | { |
---|
546 | s_h1=idrCopyR_NoSort(h1,orig_ring,syz_ring); |
---|
547 | } |
---|
548 | else |
---|
549 | { |
---|
550 | s_h1 = h1; |
---|
551 | } |
---|
552 | |
---|
553 | idTest(s_h1); |
---|
554 | |
---|
555 | ideal s_h3=idPrepare(s_h1,h,k,w); // main (syz) GB computation |
---|
556 | |
---|
557 | if (s_h3==NULL) |
---|
558 | { |
---|
559 | return idFreeModule( idElemens_h1 /*IDELEMS(h1)*/); |
---|
560 | } |
---|
561 | |
---|
562 | if (orig_ring != syz_ring) |
---|
563 | { |
---|
564 | idDelete(&s_h1); |
---|
565 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
566 | { |
---|
567 | if (s_h3->m[j] != NULL) |
---|
568 | { |
---|
569 | if (p_MinComp(s_h3->m[j],syz_ring) > k) |
---|
570 | p_Shift(&s_h3->m[j], -k,syz_ring); |
---|
571 | else |
---|
572 | p_Delete(&s_h3->m[j],syz_ring); |
---|
573 | } |
---|
574 | } |
---|
575 | idSkipZeroes(s_h3); |
---|
576 | s_h3->rank -= k; |
---|
577 | rChangeCurrRing(orig_ring); |
---|
578 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring); |
---|
579 | rDelete(syz_ring); |
---|
580 | #ifdef HAVE_PLURAL |
---|
581 | if (rIsPluralRing(orig_ring)) |
---|
582 | { |
---|
583 | id_DelMultiples(s_h3,orig_ring); |
---|
584 | idSkipZeroes(s_h3); |
---|
585 | } |
---|
586 | #endif |
---|
587 | idTest(s_h3); |
---|
588 | return s_h3; |
---|
589 | } |
---|
590 | |
---|
591 | ideal e = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
592 | |
---|
593 | for (j=IDELEMS(s_h3)-1; j>=0; j--) |
---|
594 | { |
---|
595 | if (s_h3->m[j] != NULL) |
---|
596 | { |
---|
597 | if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
598 | { |
---|
599 | e->m[j] = s_h3->m[j]; |
---|
600 | isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL); |
---|
601 | p_Delete(&pNext(s_h3->m[j]),syz_ring); |
---|
602 | s_h3->m[j] = NULL; |
---|
603 | } |
---|
604 | } |
---|
605 | } |
---|
606 | |
---|
607 | idSkipZeroes(s_h3); |
---|
608 | idSkipZeroes(e); |
---|
609 | |
---|
610 | if ((deg != NULL) |
---|
611 | && (!isMonomial) |
---|
612 | && (!TEST_OPT_NOTREGULARITY) |
---|
613 | && (setRegularity) |
---|
614 | && (h==isHomog) |
---|
615 | && (!rIsPluralRing(currRing)) |
---|
616 | && (!rField_is_Ring(currRing)) |
---|
617 | ) |
---|
618 | { |
---|
619 | ring dp_C_ring = rAssure_dp_C(syz_ring); // will do rChangeCurrRing later |
---|
620 | if (dp_C_ring != syz_ring) |
---|
621 | { |
---|
622 | rChangeCurrRing(dp_C_ring); |
---|
623 | e = idrMoveR_NoSort(e, syz_ring, dp_C_ring); |
---|
624 | } |
---|
625 | resolvente res = sySchreyerResolvente(e,-1,&length,TRUE, TRUE); |
---|
626 | intvec * dummy = syBetti(res,length,®, *w); |
---|
627 | *deg = reg+2; |
---|
628 | delete dummy; |
---|
629 | for (j=0;j<length;j++) |
---|
630 | { |
---|
631 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
632 | } |
---|
633 | omFreeSize((ADDRESS)res,length*sizeof(ideal)); |
---|
634 | idDelete(&e); |
---|
635 | if (dp_C_ring != syz_ring) |
---|
636 | { |
---|
637 | rChangeCurrRing(syz_ring); |
---|
638 | rDelete(dp_C_ring); |
---|
639 | } |
---|
640 | } |
---|
641 | else |
---|
642 | { |
---|
643 | idDelete(&e); |
---|
644 | } |
---|
645 | idTest(s_h3); |
---|
646 | if (currRing->qideal != NULL) |
---|
647 | { |
---|
648 | ideal ts_h3=kStd(s_h3,currRing->qideal,h,w); |
---|
649 | idDelete(&s_h3); |
---|
650 | s_h3 = ts_h3; |
---|
651 | } |
---|
652 | return s_h3; |
---|
653 | } |
---|
654 | |
---|
655 | /*2 |
---|
656 | */ |
---|
657 | ideal idXXX (ideal h1, int k) |
---|
658 | { |
---|
659 | ideal s_h1; |
---|
660 | intvec *w=NULL; |
---|
661 | |
---|
662 | assume(currRing != NULL); |
---|
663 | ring orig_ring=currRing; |
---|
664 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
665 | |
---|
666 | rSetSyzComp(k,syz_ring); |
---|
667 | |
---|
668 | if (orig_ring != syz_ring) |
---|
669 | { |
---|
670 | s_h1=idrCopyR_NoSort(h1,orig_ring, syz_ring); |
---|
671 | } |
---|
672 | else |
---|
673 | { |
---|
674 | s_h1 = h1; |
---|
675 | } |
---|
676 | |
---|
677 | ideal s_h3=kStd(s_h1,NULL,testHomog,&w,NULL,k); |
---|
678 | |
---|
679 | if (s_h3==NULL) |
---|
680 | { |
---|
681 | return idFreeModule(IDELEMS(h1)); |
---|
682 | } |
---|
683 | |
---|
684 | if (orig_ring != syz_ring) |
---|
685 | { |
---|
686 | idDelete(&s_h1); |
---|
687 | idSkipZeroes(s_h3); |
---|
688 | rChangeCurrRing(orig_ring); |
---|
689 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring); |
---|
690 | rDelete(syz_ring); |
---|
691 | idTest(s_h3); |
---|
692 | return s_h3; |
---|
693 | } |
---|
694 | |
---|
695 | idSkipZeroes(s_h3); |
---|
696 | idTest(s_h3); |
---|
697 | return s_h3; |
---|
698 | } |
---|
699 | |
---|
700 | /* |
---|
701 | *computes a standard basis for h1 and stores the transformation matrix |
---|
702 | * in ma |
---|
703 | */ |
---|
704 | ideal idLiftStd (ideal h1, matrix* ma, tHomog hi, ideal * syz) |
---|
705 | { |
---|
706 | int i, j, t, inputIsIdeal=id_RankFreeModule(h1,currRing); |
---|
707 | long k; |
---|
708 | poly p=NULL, q; |
---|
709 | intvec *w=NULL; |
---|
710 | |
---|
711 | idDelete((ideal*)ma); |
---|
712 | BOOLEAN lift3=FALSE; |
---|
713 | if (syz!=NULL) { lift3=TRUE; idDelete(syz); } |
---|
714 | if (idIs0(h1)) |
---|
715 | { |
---|
716 | *ma=mpNew(1,0); |
---|
717 | if (lift3) |
---|
718 | { |
---|
719 | *syz=idFreeModule(IDELEMS(h1)); |
---|
720 | } |
---|
721 | return idInit(1,h1->rank); |
---|
722 | } |
---|
723 | |
---|
724 | BITSET save2; |
---|
725 | SI_SAVE_OPT2(save2); |
---|
726 | |
---|
727 | k=si_max(1L,id_RankFreeModule(h1,currRing)); |
---|
728 | |
---|
729 | if ((k==1) && (!lift3)) si_opt_2 |=Sy_bit(V_IDLIFT); |
---|
730 | |
---|
731 | ring orig_ring = currRing; |
---|
732 | ring syz_ring = rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
733 | rSetSyzComp(k,syz_ring); |
---|
734 | |
---|
735 | ideal s_h1=h1; |
---|
736 | |
---|
737 | if (orig_ring != syz_ring) |
---|
738 | s_h1 = idrCopyR_NoSort(h1,orig_ring,syz_ring); |
---|
739 | else |
---|
740 | s_h1 = h1; |
---|
741 | |
---|
742 | ideal s_h3=idPrepare(s_h1,hi,k,&w); // main (syz) GB computation |
---|
743 | |
---|
744 | ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
745 | |
---|
746 | if (lift3) (*syz)=idInit(IDELEMS(s_h3),IDELEMS(h1)); |
---|
747 | |
---|
748 | if (w!=NULL) delete w; |
---|
749 | i = 0; |
---|
750 | |
---|
751 | // now sort the result, SB : leave in s_h3 |
---|
752 | // T: put in s_h2 |
---|
753 | // syz: put in *syz |
---|
754 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
755 | { |
---|
756 | if (s_h3->m[j] != NULL) |
---|
757 | { |
---|
758 | //if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
759 | if (pGetComp(s_h3->m[j]) <= k) // syz_ring == currRing |
---|
760 | { |
---|
761 | i++; |
---|
762 | q = s_h3->m[j]; |
---|
763 | while (pNext(q) != NULL) |
---|
764 | { |
---|
765 | if (pGetComp(pNext(q)) > k) |
---|
766 | { |
---|
767 | s_h2->m[j] = pNext(q); |
---|
768 | pNext(q) = NULL; |
---|
769 | } |
---|
770 | else |
---|
771 | { |
---|
772 | pIter(q); |
---|
773 | } |
---|
774 | } |
---|
775 | if (!inputIsIdeal) p_Shift(&(s_h3->m[j]), -1,currRing); |
---|
776 | } |
---|
777 | else |
---|
778 | { |
---|
779 | // we a syzygy here: |
---|
780 | if (lift3) |
---|
781 | { |
---|
782 | p_Shift(&s_h3->m[j], -k,currRing); |
---|
783 | (*syz)->m[j]=s_h3->m[j]; |
---|
784 | s_h3->m[j]=NULL; |
---|
785 | } |
---|
786 | else |
---|
787 | p_Delete(&(s_h3->m[j]),currRing); |
---|
788 | } |
---|
789 | } |
---|
790 | } |
---|
791 | idSkipZeroes(s_h3); |
---|
792 | //extern char * iiStringMatrix(matrix im, int dim,char ch); |
---|
793 | //PrintS("SB: ----------------------------------------\n"); |
---|
794 | //PrintS(iiStringMatrix((matrix)s_h3,k,'\n')); |
---|
795 | //PrintLn(); |
---|
796 | //PrintS("T: ----------------------------------------\n"); |
---|
797 | //PrintS(iiStringMatrix((matrix)s_h2,h1->rank,'\n')); |
---|
798 | //PrintLn(); |
---|
799 | |
---|
800 | if (lift3) idSkipZeroes(*syz); |
---|
801 | |
---|
802 | j = IDELEMS(s_h1); |
---|
803 | |
---|
804 | |
---|
805 | if (syz_ring!=orig_ring) |
---|
806 | { |
---|
807 | idDelete(&s_h1); |
---|
808 | rChangeCurrRing(orig_ring); |
---|
809 | } |
---|
810 | |
---|
811 | *ma = mpNew(j,i); |
---|
812 | |
---|
813 | i = 1; |
---|
814 | for (j=0; j<IDELEMS(s_h2); j++) |
---|
815 | { |
---|
816 | if (s_h2->m[j] != NULL) |
---|
817 | { |
---|
818 | q = prMoveR( s_h2->m[j], syz_ring,orig_ring); |
---|
819 | s_h2->m[j] = NULL; |
---|
820 | |
---|
821 | if (q!=NULL) |
---|
822 | { |
---|
823 | q=pReverse(q); |
---|
824 | while (q != NULL) |
---|
825 | { |
---|
826 | p = q; |
---|
827 | pIter(q); |
---|
828 | pNext(p) = NULL; |
---|
829 | t=pGetComp(p); |
---|
830 | pSetComp(p,0); |
---|
831 | pSetmComp(p); |
---|
832 | MATELEM(*ma,t-k,i) = pAdd(MATELEM(*ma,t-k,i),p); |
---|
833 | } |
---|
834 | } |
---|
835 | i++; |
---|
836 | } |
---|
837 | } |
---|
838 | idDelete(&s_h2); |
---|
839 | |
---|
840 | for (i=0; i<IDELEMS(s_h3); i++) |
---|
841 | { |
---|
842 | s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], syz_ring,orig_ring); |
---|
843 | } |
---|
844 | if (lift3) |
---|
845 | { |
---|
846 | for (i=0; i<IDELEMS(*syz); i++) |
---|
847 | { |
---|
848 | (*syz)->m[i] = prMoveR_NoSort((*syz)->m[i], syz_ring,orig_ring); |
---|
849 | } |
---|
850 | } |
---|
851 | |
---|
852 | if (syz_ring!=orig_ring) rDelete(syz_ring); |
---|
853 | SI_RESTORE_OPT2(save2); |
---|
854 | return s_h3; |
---|
855 | } |
---|
856 | |
---|
857 | static void idPrepareStd(ideal s_temp, int k) |
---|
858 | { |
---|
859 | int j,rk=id_RankFreeModule(s_temp,currRing); |
---|
860 | poly p,q; |
---|
861 | |
---|
862 | if (rk == 0) |
---|
863 | { |
---|
864 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
865 | { |
---|
866 | if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1); |
---|
867 | } |
---|
868 | k = si_max(k,1); |
---|
869 | } |
---|
870 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
871 | { |
---|
872 | if (s_temp->m[j]!=NULL) |
---|
873 | { |
---|
874 | p = s_temp->m[j]; |
---|
875 | q = pOne(); |
---|
876 | //pGetCoeff(q)=nInpNeg(pGetCoeff(q)); //set q to -1 |
---|
877 | pSetComp(q,k+1+j); |
---|
878 | pSetmComp(q); |
---|
879 | while (pNext(p)) pIter(p); |
---|
880 | pNext(p) = q; |
---|
881 | } |
---|
882 | } |
---|
883 | s_temp->rank = k+IDELEMS(s_temp); |
---|
884 | } |
---|
885 | |
---|
886 | /*2 |
---|
887 | *computes a representation of the generators of submod with respect to those |
---|
888 | * of mod |
---|
889 | */ |
---|
890 | |
---|
891 | ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape, |
---|
892 | BOOLEAN isSB, BOOLEAN divide, matrix *unit) |
---|
893 | { |
---|
894 | int lsmod =id_RankFreeModule(submod,currRing), j, k; |
---|
895 | int comps_to_add=0; |
---|
896 | poly p; |
---|
897 | |
---|
898 | if (idIs0(submod)) |
---|
899 | { |
---|
900 | if (unit!=NULL) |
---|
901 | { |
---|
902 | *unit=mpNew(1,1); |
---|
903 | MATELEM(*unit,1,1)=pOne(); |
---|
904 | } |
---|
905 | if (rest!=NULL) |
---|
906 | { |
---|
907 | *rest=idInit(1,mod->rank); |
---|
908 | } |
---|
909 | return idInit(1,mod->rank); |
---|
910 | } |
---|
911 | if (idIs0(mod)) /* and not idIs0(submod) */ |
---|
912 | { |
---|
913 | WerrorS("2nd module does not lie in the first"); |
---|
914 | return NULL; |
---|
915 | } |
---|
916 | if (unit!=NULL) |
---|
917 | { |
---|
918 | comps_to_add = IDELEMS(submod); |
---|
919 | while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL)) |
---|
920 | comps_to_add--; |
---|
921 | } |
---|
922 | k=si_max(id_RankFreeModule(mod,currRing),id_RankFreeModule(submod,currRing)); |
---|
923 | if ((k!=0) && (lsmod==0)) lsmod=1; |
---|
924 | k=si_max(k,(int)mod->rank); |
---|
925 | if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; } |
---|
926 | |
---|
927 | ring orig_ring=currRing; |
---|
928 | ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
929 | rSetSyzComp(k,syz_ring); |
---|
930 | |
---|
931 | ideal s_mod, s_temp; |
---|
932 | if (orig_ring != syz_ring) |
---|
933 | { |
---|
934 | s_mod = idrCopyR_NoSort(mod,orig_ring,syz_ring); |
---|
935 | s_temp = idrCopyR_NoSort(submod,orig_ring,syz_ring); |
---|
936 | } |
---|
937 | else |
---|
938 | { |
---|
939 | s_mod = mod; |
---|
940 | s_temp = idCopy(submod); |
---|
941 | } |
---|
942 | ideal s_h3; |
---|
943 | if (isSB) |
---|
944 | { |
---|
945 | s_h3 = idCopy(s_mod); |
---|
946 | idPrepareStd(s_h3, k+comps_to_add); |
---|
947 | } |
---|
948 | else |
---|
949 | { |
---|
950 | s_h3 = idPrepare(s_mod,(tHomog)FALSE,k+comps_to_add,NULL); |
---|
951 | } |
---|
952 | if (!goodShape) |
---|
953 | { |
---|
954 | for (j=0;j<IDELEMS(s_h3);j++) |
---|
955 | { |
---|
956 | if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k)) |
---|
957 | p_Delete(&(s_h3->m[j]),currRing); |
---|
958 | } |
---|
959 | } |
---|
960 | idSkipZeroes(s_h3); |
---|
961 | if (lsmod==0) |
---|
962 | { |
---|
963 | id_Shift(s_temp,1,currRing); |
---|
964 | } |
---|
965 | if (unit!=NULL) |
---|
966 | { |
---|
967 | for(j = 0;j<comps_to_add;j++) |
---|
968 | { |
---|
969 | p = s_temp->m[j]; |
---|
970 | if (p!=NULL) |
---|
971 | { |
---|
972 | while (pNext(p)!=NULL) pIter(p); |
---|
973 | pNext(p) = pOne(); |
---|
974 | pIter(p); |
---|
975 | pSetComp(p,1+j+k); |
---|
976 | pSetmComp(p); |
---|
977 | p = pNeg(p); |
---|
978 | } |
---|
979 | } |
---|
980 | s_temp->rank += (k+comps_to_add); |
---|
981 | } |
---|
982 | ideal s_result = kNF(s_h3,currRing->qideal,s_temp,k); |
---|
983 | s_result->rank = s_h3->rank; |
---|
984 | ideal s_rest = idInit(IDELEMS(s_result),k); |
---|
985 | idDelete(&s_h3); |
---|
986 | idDelete(&s_temp); |
---|
987 | |
---|
988 | for (j=0;j<IDELEMS(s_result);j++) |
---|
989 | { |
---|
990 | if (s_result->m[j]!=NULL) |
---|
991 | { |
---|
992 | if (pGetComp(s_result->m[j])<=k) |
---|
993 | { |
---|
994 | if (!divide) |
---|
995 | { |
---|
996 | if (isSB) |
---|
997 | { |
---|
998 | WarnS("first module not a standardbasis\n" |
---|
999 | "// ** or second not a proper submodule"); |
---|
1000 | } |
---|
1001 | else |
---|
1002 | WerrorS("2nd module does not lie in the first"); |
---|
1003 | idDelete(&s_result); |
---|
1004 | idDelete(&s_rest); |
---|
1005 | s_result=idInit(IDELEMS(submod),submod->rank); |
---|
1006 | break; |
---|
1007 | } |
---|
1008 | else |
---|
1009 | { |
---|
1010 | p = s_rest->m[j] = s_result->m[j]; |
---|
1011 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p); |
---|
1012 | s_result->m[j] = pNext(p); |
---|
1013 | pNext(p) = NULL; |
---|
1014 | } |
---|
1015 | } |
---|
1016 | p_Shift(&(s_result->m[j]),-k,currRing); |
---|
1017 | pNeg(s_result->m[j]); |
---|
1018 | } |
---|
1019 | } |
---|
1020 | if ((lsmod==0) && (s_rest!=NULL)) |
---|
1021 | { |
---|
1022 | for (j=IDELEMS(s_rest);j>0;j--) |
---|
1023 | { |
---|
1024 | if (s_rest->m[j-1]!=NULL) |
---|
1025 | { |
---|
1026 | p_Shift(&(s_rest->m[j-1]),-1,currRing); |
---|
1027 | s_rest->m[j-1] = s_rest->m[j-1]; |
---|
1028 | } |
---|
1029 | } |
---|
1030 | } |
---|
1031 | if(syz_ring!=orig_ring) |
---|
1032 | { |
---|
1033 | idDelete(&s_mod); |
---|
1034 | rChangeCurrRing(orig_ring); |
---|
1035 | s_result = idrMoveR_NoSort(s_result, syz_ring, orig_ring); |
---|
1036 | s_rest = idrMoveR_NoSort(s_rest, syz_ring, orig_ring); |
---|
1037 | rDelete(syz_ring); |
---|
1038 | } |
---|
1039 | if (rest!=NULL) |
---|
1040 | *rest = s_rest; |
---|
1041 | else |
---|
1042 | idDelete(&s_rest); |
---|
1043 | //idPrint(s_result); |
---|
1044 | if (unit!=NULL) |
---|
1045 | { |
---|
1046 | *unit=mpNew(comps_to_add,comps_to_add); |
---|
1047 | int i; |
---|
1048 | for(i=0;i<IDELEMS(s_result);i++) |
---|
1049 | { |
---|
1050 | poly p=s_result->m[i]; |
---|
1051 | poly q=NULL; |
---|
1052 | while(p!=NULL) |
---|
1053 | { |
---|
1054 | if(pGetComp(p)<=comps_to_add) |
---|
1055 | { |
---|
1056 | pSetComp(p,0); |
---|
1057 | if (q!=NULL) |
---|
1058 | { |
---|
1059 | pNext(q)=pNext(p); |
---|
1060 | } |
---|
1061 | else |
---|
1062 | { |
---|
1063 | pIter(s_result->m[i]); |
---|
1064 | } |
---|
1065 | pNext(p)=NULL; |
---|
1066 | MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p); |
---|
1067 | if(q!=NULL) p=pNext(q); |
---|
1068 | else p=s_result->m[i]; |
---|
1069 | } |
---|
1070 | else |
---|
1071 | { |
---|
1072 | q=p; |
---|
1073 | pIter(p); |
---|
1074 | } |
---|
1075 | } |
---|
1076 | p_Shift(&s_result->m[i],-comps_to_add,currRing); |
---|
1077 | } |
---|
1078 | } |
---|
1079 | return s_result; |
---|
1080 | } |
---|
1081 | |
---|
1082 | /*2 |
---|
1083 | *computes division of P by Q with remainder up to (w-weighted) degree n |
---|
1084 | *P, Q, and w are not changed |
---|
1085 | */ |
---|
1086 | void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,short *w) |
---|
1087 | { |
---|
1088 | long N=0; |
---|
1089 | int i; |
---|
1090 | for(i=IDELEMS(Q)-1;i>=0;i--) |
---|
1091 | if(w==NULL) |
---|
1092 | N=si_max(N,p_Deg(Q->m[i],currRing)); |
---|
1093 | else |
---|
1094 | N=si_max(N,p_DegW(Q->m[i],w,currRing)); |
---|
1095 | N+=n; |
---|
1096 | |
---|
1097 | T=mpNew(IDELEMS(Q),IDELEMS(P)); |
---|
1098 | R=idInit(IDELEMS(P),P->rank); |
---|
1099 | |
---|
1100 | for(i=IDELEMS(P)-1;i>=0;i--) |
---|
1101 | { |
---|
1102 | poly p; |
---|
1103 | if(w==NULL) |
---|
1104 | p=ppJet(P->m[i],N); |
---|
1105 | else |
---|
1106 | p=ppJetW(P->m[i],N,w); |
---|
1107 | |
---|
1108 | int j=IDELEMS(Q)-1; |
---|
1109 | while(p!=NULL) |
---|
1110 | { |
---|
1111 | if(pDivisibleBy(Q->m[j],p)) |
---|
1112 | { |
---|
1113 | poly p0=p_DivideM(pHead(p),pHead(Q->m[j]),currRing); |
---|
1114 | if(w==NULL) |
---|
1115 | p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N); |
---|
1116 | else |
---|
1117 | p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w); |
---|
1118 | pNormalize(p); |
---|
1119 | if(((w==NULL)&&(p_Deg(p0,currRing)>n))||((w!=NULL)&&(p_DegW(p0,w,currRing)>n))) |
---|
1120 | p_Delete(&p0,currRing); |
---|
1121 | else |
---|
1122 | MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0); |
---|
1123 | j=IDELEMS(Q)-1; |
---|
1124 | } |
---|
1125 | else |
---|
1126 | { |
---|
1127 | if(j==0) |
---|
1128 | { |
---|
1129 | poly p0=p; |
---|
1130 | pIter(p); |
---|
1131 | pNext(p0)=NULL; |
---|
1132 | if(((w==NULL)&&(p_Deg(p0,currRing)>n)) |
---|
1133 | ||((w!=NULL)&&(p_DegW(p0,w,currRing)>n))) |
---|
1134 | p_Delete(&p0,currRing); |
---|
1135 | else |
---|
1136 | R->m[i]=pAdd(R->m[i],p0); |
---|
1137 | j=IDELEMS(Q)-1; |
---|
1138 | } |
---|
1139 | else |
---|
1140 | j--; |
---|
1141 | } |
---|
1142 | } |
---|
1143 | } |
---|
1144 | } |
---|
1145 | |
---|
1146 | /*2 |
---|
1147 | *computes the quotient of h1,h2 : internal routine for idQuot |
---|
1148 | *BEWARE: the returned ideals may contain incorrectly ordered polys ! |
---|
1149 | * |
---|
1150 | */ |
---|
1151 | static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax) |
---|
1152 | { |
---|
1153 | idTest(h1); |
---|
1154 | idTest(h2); |
---|
1155 | |
---|
1156 | ideal temph1; |
---|
1157 | poly p,q = NULL; |
---|
1158 | int i,l,ll,k,kkk,kmax; |
---|
1159 | int j = 0; |
---|
1160 | int k1 = id_RankFreeModule(h1,currRing); |
---|
1161 | int k2 = id_RankFreeModule(h2,currRing); |
---|
1162 | tHomog hom=isNotHomog; |
---|
1163 | k=si_max(k1,k2); |
---|
1164 | if (k==0) |
---|
1165 | k = 1; |
---|
1166 | if ((k2==0) && (k>1)) *addOnlyOne = FALSE; |
---|
1167 | intvec * weights; |
---|
1168 | hom = (tHomog)idHomModule(h1,currRing->qideal,&weights); |
---|
1169 | if /**addOnlyOne &&*/ (/*(*/ !h1IsStb /*)*/) |
---|
1170 | temph1 = kStd(h1,currRing->qideal,hom,&weights,NULL); |
---|
1171 | else |
---|
1172 | temph1 = idCopy(h1); |
---|
1173 | if (weights!=NULL) delete weights; |
---|
1174 | idTest(temph1); |
---|
1175 | /*--- making a single vector from h2 ---------------------*/ |
---|
1176 | for (i=0; i<IDELEMS(h2); i++) |
---|
1177 | { |
---|
1178 | if (h2->m[i] != NULL) |
---|
1179 | { |
---|
1180 | p = pCopy(h2->m[i]); |
---|
1181 | if (k2 == 0) |
---|
1182 | p_Shift(&p,j*k+1,currRing); |
---|
1183 | else |
---|
1184 | p_Shift(&p,j*k,currRing); |
---|
1185 | q = pAdd(q,p); |
---|
1186 | j++; |
---|
1187 | } |
---|
1188 | } |
---|
1189 | *kkmax = kmax = j*k+1; |
---|
1190 | /*--- adding a monomial for the result (syzygy) ----------*/ |
---|
1191 | p = q; |
---|
1192 | while (pNext(p)!=NULL) pIter(p); |
---|
1193 | pNext(p) = pOne(); |
---|
1194 | pIter(p); |
---|
1195 | pSetComp(p,kmax); |
---|
1196 | pSetmComp(p); |
---|
1197 | /*--- constructing the big matrix ------------------------*/ |
---|
1198 | ideal h4 = idInit(16,kmax+k-1); |
---|
1199 | h4->m[0] = q; |
---|
1200 | if (k2 == 0) |
---|
1201 | { |
---|
1202 | if (k > IDELEMS(h4)) |
---|
1203 | { |
---|
1204 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
1205 | IDELEMS(h4) = k; |
---|
1206 | } |
---|
1207 | for (i=1; i<k; i++) |
---|
1208 | { |
---|
1209 | if (h4->m[i-1]!=NULL) |
---|
1210 | { |
---|
1211 | p = p_Copy_noCheck(h4->m[i-1], currRing); p_Shift(&p,1,currRing); |
---|
1212 | // pTest(p); |
---|
1213 | h4->m[i] = p; |
---|
1214 | } |
---|
1215 | } |
---|
1216 | } |
---|
1217 | idSkipZeroes(h4); |
---|
1218 | kkk = IDELEMS(h4); |
---|
1219 | i = IDELEMS(temph1); |
---|
1220 | for (l=0; l<i; l++) |
---|
1221 | { |
---|
1222 | if(temph1->m[l]!=NULL) |
---|
1223 | { |
---|
1224 | for (ll=0; ll<j; ll++) |
---|
1225 | { |
---|
1226 | p = pCopy(temph1->m[l]); |
---|
1227 | if (k1 == 0) |
---|
1228 | p_Shift(&p,ll*k+1,currRing); |
---|
1229 | else |
---|
1230 | p_Shift(&p,ll*k,currRing); |
---|
1231 | if (kkk >= IDELEMS(h4)) |
---|
1232 | { |
---|
1233 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
1234 | IDELEMS(h4) += 16; |
---|
1235 | } |
---|
1236 | h4->m[kkk] = p; |
---|
1237 | kkk++; |
---|
1238 | } |
---|
1239 | } |
---|
1240 | } |
---|
1241 | /*--- if h2 goes in as single vector - the h1-part is just SB ---*/ |
---|
1242 | if (*addOnlyOne) |
---|
1243 | { |
---|
1244 | idSkipZeroes(h4); |
---|
1245 | p = h4->m[0]; |
---|
1246 | for (i=0;i<IDELEMS(h4)-1;i++) |
---|
1247 | { |
---|
1248 | h4->m[i] = h4->m[i+1]; |
---|
1249 | } |
---|
1250 | h4->m[IDELEMS(h4)-1] = p; |
---|
1251 | if(!rField_is_Ring(currRing)) si_opt_1 |= Sy_bit(OPT_SB_1); |
---|
1252 | } |
---|
1253 | idDelete(&temph1); |
---|
1254 | //idTest(h4);//see remark at the beginning |
---|
1255 | return h4; |
---|
1256 | } |
---|
1257 | /*2 |
---|
1258 | *computes the quotient of h1,h2 |
---|
1259 | */ |
---|
1260 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal) |
---|
1261 | { |
---|
1262 | // first check for special case h1:(0) |
---|
1263 | if (idIs0(h2)) |
---|
1264 | { |
---|
1265 | ideal res; |
---|
1266 | if (resultIsIdeal) |
---|
1267 | { |
---|
1268 | res = idInit(1,1); |
---|
1269 | res->m[0] = pOne(); |
---|
1270 | } |
---|
1271 | else |
---|
1272 | res = idFreeModule(h1->rank); |
---|
1273 | return res; |
---|
1274 | } |
---|
1275 | BITSET old_test1; |
---|
1276 | SI_SAVE_OPT1(old_test1); |
---|
1277 | int i, kmax; |
---|
1278 | BOOLEAN addOnlyOne=TRUE; |
---|
1279 | tHomog hom=isNotHomog; |
---|
1280 | intvec * weights1; |
---|
1281 | |
---|
1282 | ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax); |
---|
1283 | |
---|
1284 | hom = (tHomog)idHomModule(s_h4,currRing->qideal,&weights1); |
---|
1285 | |
---|
1286 | ring orig_ring=currRing; |
---|
1287 | ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring); |
---|
1288 | rSetSyzComp(kmax-1,syz_ring); |
---|
1289 | if (orig_ring!=syz_ring) |
---|
1290 | // s_h4 = idrMoveR_NoSort(s_h4,orig_ring, syz_ring); |
---|
1291 | s_h4 = idrMoveR(s_h4,orig_ring, syz_ring); |
---|
1292 | idTest(s_h4); |
---|
1293 | #if 0 |
---|
1294 | void ipPrint_MA0(matrix m, const char *name); |
---|
1295 | matrix m=idModule2Matrix(idCopy(s_h4)); |
---|
1296 | PrintS("start:\n"); |
---|
1297 | ipPrint_MA0(m,"Q"); |
---|
1298 | idDelete((ideal *)&m); |
---|
1299 | PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn(); |
---|
1300 | #endif |
---|
1301 | ideal s_h3; |
---|
1302 | if (addOnlyOne) |
---|
1303 | { |
---|
1304 | s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,0/*kmax-1*/,IDELEMS(s_h4)-1); |
---|
1305 | } |
---|
1306 | else |
---|
1307 | { |
---|
1308 | s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,kmax-1); |
---|
1309 | } |
---|
1310 | SI_RESTORE_OPT1(old_test1); |
---|
1311 | #if 0 |
---|
1312 | // only together with the above debug stuff |
---|
1313 | idSkipZeroes(s_h3); |
---|
1314 | m=idModule2Matrix(idCopy(s_h3)); |
---|
1315 | Print("result, kmax=%d:\n",kmax); |
---|
1316 | ipPrint_MA0(m,"S"); |
---|
1317 | idDelete((ideal *)&m); |
---|
1318 | #endif |
---|
1319 | idTest(s_h3); |
---|
1320 | if (weights1!=NULL) delete weights1; |
---|
1321 | idDelete(&s_h4); |
---|
1322 | |
---|
1323 | for (i=0;i<IDELEMS(s_h3);i++) |
---|
1324 | { |
---|
1325 | if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax)) |
---|
1326 | { |
---|
1327 | if (resultIsIdeal) |
---|
1328 | p_Shift(&s_h3->m[i],-kmax,currRing); |
---|
1329 | else |
---|
1330 | p_Shift(&s_h3->m[i],-kmax+1,currRing); |
---|
1331 | } |
---|
1332 | else |
---|
1333 | p_Delete(&s_h3->m[i],currRing); |
---|
1334 | } |
---|
1335 | if (resultIsIdeal) |
---|
1336 | s_h3->rank = 1; |
---|
1337 | else |
---|
1338 | s_h3->rank = h1->rank; |
---|
1339 | if(syz_ring!=orig_ring) |
---|
1340 | { |
---|
1341 | rChangeCurrRing(orig_ring); |
---|
1342 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring); |
---|
1343 | rDelete(syz_ring); |
---|
1344 | } |
---|
1345 | idSkipZeroes(s_h3); |
---|
1346 | idTest(s_h3); |
---|
1347 | return s_h3; |
---|
1348 | } |
---|
1349 | |
---|
1350 | /*2 |
---|
1351 | * eliminate delVar (product of vars) in h1 |
---|
1352 | */ |
---|
1353 | ideal idElimination (ideal h1,poly delVar,intvec *hilb) |
---|
1354 | { |
---|
1355 | int i,j=0,k,l; |
---|
1356 | ideal h,hh, h3; |
---|
1357 | int *ord,*block0,*block1; |
---|
1358 | int ordersize=2; |
---|
1359 | int **wv; |
---|
1360 | tHomog hom; |
---|
1361 | intvec * w; |
---|
1362 | ring tmpR; |
---|
1363 | ring origR = currRing; |
---|
1364 | |
---|
1365 | if (delVar==NULL) |
---|
1366 | { |
---|
1367 | return idCopy(h1); |
---|
1368 | } |
---|
1369 | if ((currRing->qideal!=NULL) && rIsPluralRing(origR)) |
---|
1370 | { |
---|
1371 | WerrorS("cannot eliminate in a qring"); |
---|
1372 | return NULL; |
---|
1373 | } |
---|
1374 | if (idIs0(h1)) return idInit(1,h1->rank); |
---|
1375 | #ifdef HAVE_PLURAL |
---|
1376 | if (rIsPluralRing(origR)) |
---|
1377 | /* in the NC case, we have to check the admissibility of */ |
---|
1378 | /* the subalgebra to be intersected with */ |
---|
1379 | { |
---|
1380 | if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */ |
---|
1381 | { |
---|
1382 | if (nc_CheckSubalgebra(delVar,origR)) |
---|
1383 | { |
---|
1384 | WerrorS("no elimination is possible: subalgebra is not admissible"); |
---|
1385 | return NULL; |
---|
1386 | } |
---|
1387 | } |
---|
1388 | } |
---|
1389 | #endif |
---|
1390 | hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL |
---|
1391 | h3=idInit(16,h1->rank); |
---|
1392 | for (k=0;; k++) |
---|
1393 | { |
---|
1394 | if (origR->order[k]!=0) ordersize++; |
---|
1395 | else break; |
---|
1396 | } |
---|
1397 | #if 0 |
---|
1398 | if (rIsPluralRing(origR)) // we have too keep the odering: it may be needed |
---|
1399 | // for G-algebra |
---|
1400 | { |
---|
1401 | for (k=0;k<ordersize-1; k++) |
---|
1402 | { |
---|
1403 | block0[k+1] = origR->block0[k]; |
---|
1404 | block1[k+1] = origR->block1[k]; |
---|
1405 | ord[k+1] = origR->order[k]; |
---|
1406 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
1407 | } |
---|
1408 | } |
---|
1409 | else |
---|
1410 | { |
---|
1411 | block0[1] = 1; |
---|
1412 | block1[1] = (currRing->N); |
---|
1413 | if (origR->OrdSgn==1) ord[1] = ringorder_wp; |
---|
1414 | else ord[1] = ringorder_ws; |
---|
1415 | wv[1]=(int*)omAlloc0((currRing->N)*sizeof(int)); |
---|
1416 | double wNsqr = (double)2.0 / (double)(currRing->N); |
---|
1417 | wFunctional = wFunctionalBuch; |
---|
1418 | int *x= (int * )omAlloc(2 * ((currRing->N) + 1) * sizeof(int)); |
---|
1419 | int sl=IDELEMS(h1) - 1; |
---|
1420 | wCall(h1->m, sl, x, wNsqr); |
---|
1421 | for (sl = (currRing->N); sl!=0; sl--) |
---|
1422 | wv[1][sl-1] = x[sl + (currRing->N) + 1]; |
---|
1423 | omFreeSize((ADDRESS)x, 2 * ((currRing->N) + 1) * sizeof(int)); |
---|
1424 | |
---|
1425 | ord[2]=ringorder_C; |
---|
1426 | ord[3]=0; |
---|
1427 | } |
---|
1428 | #else |
---|
1429 | #endif |
---|
1430 | if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR))) |
---|
1431 | { |
---|
1432 | #if 1 |
---|
1433 | // we change to an ordering: |
---|
1434 | // aa(1,1,1,...,0,0,0),wp(...),C |
---|
1435 | // this seems to be better than version 2 below, |
---|
1436 | // according to Tst/../elimiate_[3568].tat (- 17 %) |
---|
1437 | ord=(int*)omAlloc0(4*sizeof(int)); |
---|
1438 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
1439 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
1440 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
1441 | block0[0] = block0[1] = 1; |
---|
1442 | block1[0] = block1[1] = rVar(origR); |
---|
1443 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1444 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
1445 | // ignore it |
---|
1446 | ord[0] = ringorder_aa; |
---|
1447 | for (j=0;j<rVar(origR);j++) |
---|
1448 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
1449 | BOOLEAN wp=FALSE; |
---|
1450 | for (j=0;j<rVar(origR);j++) |
---|
1451 | if (pWeight(j+1,origR)!=1) { wp=TRUE;break; } |
---|
1452 | if (wp) |
---|
1453 | { |
---|
1454 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1455 | for (j=0;j<rVar(origR);j++) |
---|
1456 | wv[1][j]=pWeight(j+1,origR); |
---|
1457 | ord[1] = ringorder_wp; |
---|
1458 | } |
---|
1459 | else |
---|
1460 | ord[1] = ringorder_dp; |
---|
1461 | #else |
---|
1462 | // we change to an ordering: |
---|
1463 | // a(w1,...wn),wp(1,...0.....),C |
---|
1464 | ord=(int*)omAlloc0(4*sizeof(int)); |
---|
1465 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
1466 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
1467 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
1468 | block0[0] = block0[1] = 1; |
---|
1469 | block1[0] = block1[1] = rVar(origR); |
---|
1470 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1471 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1472 | ord[0] = ringorder_a; |
---|
1473 | for (j=0;j<rVar(origR);j++) |
---|
1474 | wv[0][j]=pWeight(j+1,origR); |
---|
1475 | ord[1] = ringorder_wp; |
---|
1476 | for (j=0;j<rVar(origR);j++) |
---|
1477 | if (pGetExp(delVar,j+1)!=0) wv[1][j]=1; |
---|
1478 | #endif |
---|
1479 | ord[2] = ringorder_C; |
---|
1480 | ord[3] = 0; |
---|
1481 | } |
---|
1482 | else |
---|
1483 | { |
---|
1484 | // we change to an ordering: |
---|
1485 | // aa(....),orig_ordering |
---|
1486 | ord=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
1487 | block0=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
1488 | block1=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
1489 | wv=(int**) omAlloc0(ordersize*sizeof(int**)); |
---|
1490 | for (k=0;k<ordersize-1; k++) |
---|
1491 | { |
---|
1492 | block0[k+1] = origR->block0[k]; |
---|
1493 | block1[k+1] = origR->block1[k]; |
---|
1494 | ord[k+1] = origR->order[k]; |
---|
1495 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
1496 | } |
---|
1497 | block0[0] = 1; |
---|
1498 | block1[0] = rVar(origR); |
---|
1499 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1500 | for (j=0;j<rVar(origR);j++) |
---|
1501 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
1502 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
1503 | // ignore it |
---|
1504 | ord[0] = ringorder_aa; |
---|
1505 | } |
---|
1506 | // fill in tmp ring to get back the data later on |
---|
1507 | tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL |
---|
1508 | //rUnComplete(tmpR); |
---|
1509 | tmpR->p_Procs=NULL; |
---|
1510 | tmpR->order = ord; |
---|
1511 | tmpR->block0 = block0; |
---|
1512 | tmpR->block1 = block1; |
---|
1513 | tmpR->wvhdl = wv; |
---|
1514 | rComplete(tmpR, 1); |
---|
1515 | |
---|
1516 | #ifdef HAVE_PLURAL |
---|
1517 | /* update nc structure on tmpR */ |
---|
1518 | if (rIsPluralRing(origR)) |
---|
1519 | { |
---|
1520 | if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal! |
---|
1521 | { |
---|
1522 | WerrorS("no elimination is possible: ordering condition is violated"); |
---|
1523 | // cleanup |
---|
1524 | rDelete(tmpR); |
---|
1525 | if (w!=NULL) |
---|
1526 | delete w; |
---|
1527 | return NULL; |
---|
1528 | } |
---|
1529 | } |
---|
1530 | #endif |
---|
1531 | // change into the new ring |
---|
1532 | //pChangeRing((currRing->N),currRing->OrdSgn,ord,block0,block1,wv); |
---|
1533 | rChangeCurrRing(tmpR); |
---|
1534 | |
---|
1535 | //h = idInit(IDELEMS(h1),h1->rank); |
---|
1536 | // fetch data from the old ring |
---|
1537 | //for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR); |
---|
1538 | h=idrCopyR(h1,origR,currRing); |
---|
1539 | if (origR->qideal!=NULL) |
---|
1540 | { |
---|
1541 | WarnS("eliminate in q-ring: experimental"); |
---|
1542 | ideal q=idrCopyR(origR->qideal,origR,currRing); |
---|
1543 | ideal s=idSimpleAdd(h,q); |
---|
1544 | idDelete(&h); |
---|
1545 | idDelete(&q); |
---|
1546 | h=s; |
---|
1547 | } |
---|
1548 | // compute kStd |
---|
1549 | #if 1 |
---|
1550 | //rWrite(tmpR);PrintLn(); |
---|
1551 | //BITSET save1; |
---|
1552 | //SI_SAVE_OPT1(save1); |
---|
1553 | //si_opt_1 |=1; |
---|
1554 | //Print("h: %d gen, rk=%d\n",IDELEMS(h),h->rank); |
---|
1555 | //extern char * showOption(); |
---|
1556 | //Print("%s\n",showOption()); |
---|
1557 | hh = kStd(h,NULL,hom,&w,hilb); |
---|
1558 | //SI_RESTORE_OPT1(save1); |
---|
1559 | idDelete(&h); |
---|
1560 | #else |
---|
1561 | extern ideal kGroebner(ideal F, ideal Q); |
---|
1562 | hh=kGroebner(h,NULL); |
---|
1563 | #endif |
---|
1564 | // go back to the original ring |
---|
1565 | rChangeCurrRing(origR); |
---|
1566 | i = IDELEMS(hh)-1; |
---|
1567 | while ((i >= 0) && (hh->m[i] == NULL)) i--; |
---|
1568 | j = -1; |
---|
1569 | // fetch data from temp ring |
---|
1570 | for (k=0; k<=i; k++) |
---|
1571 | { |
---|
1572 | l=(currRing->N); |
---|
1573 | while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--; |
---|
1574 | if (l==0) |
---|
1575 | { |
---|
1576 | j++; |
---|
1577 | if (j >= IDELEMS(h3)) |
---|
1578 | { |
---|
1579 | pEnlargeSet(&(h3->m),IDELEMS(h3),16); |
---|
1580 | IDELEMS(h3) += 16; |
---|
1581 | } |
---|
1582 | h3->m[j] = prMoveR( hh->m[k], tmpR,origR); |
---|
1583 | hh->m[k] = NULL; |
---|
1584 | } |
---|
1585 | } |
---|
1586 | id_Delete(&hh, tmpR); |
---|
1587 | idSkipZeroes(h3); |
---|
1588 | rDelete(tmpR); |
---|
1589 | if (w!=NULL) |
---|
1590 | delete w; |
---|
1591 | return h3; |
---|
1592 | } |
---|
1593 | |
---|
1594 | #ifdef WITH_OLD_MINOR |
---|
1595 | /*2 |
---|
1596 | * compute the which-th ar-minor of the matrix a |
---|
1597 | */ |
---|
1598 | poly idMinor(matrix a, int ar, unsigned long which, ideal R) |
---|
1599 | { |
---|
1600 | int i,j/*,k,size*/; |
---|
1601 | unsigned long curr; |
---|
1602 | int *rowchoise,*colchoise; |
---|
1603 | BOOLEAN rowch,colch; |
---|
1604 | // ideal result; |
---|
1605 | matrix tmp; |
---|
1606 | poly p,q; |
---|
1607 | |
---|
1608 | i = binom(a->rows(),ar); |
---|
1609 | j = binom(a->cols(),ar); |
---|
1610 | |
---|
1611 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1612 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1613 | // if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
1614 | // else size=i*j; |
---|
1615 | // result=idInit(size,1); |
---|
1616 | tmp=mpNew(ar,ar); |
---|
1617 | // k = 0; /* the index in result*/ |
---|
1618 | curr = 0; /* index of current minor */ |
---|
1619 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
1620 | while (!rowch) |
---|
1621 | { |
---|
1622 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
1623 | while (!colch) |
---|
1624 | { |
---|
1625 | if (curr == which) |
---|
1626 | { |
---|
1627 | for (i=1; i<=ar; i++) |
---|
1628 | { |
---|
1629 | for (j=1; j<=ar; j++) |
---|
1630 | { |
---|
1631 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
1632 | } |
---|
1633 | } |
---|
1634 | p = mp_DetBareiss(tmp,currRing); |
---|
1635 | if (p!=NULL) |
---|
1636 | { |
---|
1637 | if (R!=NULL) |
---|
1638 | { |
---|
1639 | q = p; |
---|
1640 | p = kNF(R,currRing->qideal,q); |
---|
1641 | p_Delete(&q,currRing); |
---|
1642 | } |
---|
1643 | /*delete the matrix tmp*/ |
---|
1644 | for (i=1; i<=ar; i++) |
---|
1645 | { |
---|
1646 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
1647 | } |
---|
1648 | idDelete((ideal*)&tmp); |
---|
1649 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
1650 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
1651 | return (p); |
---|
1652 | } |
---|
1653 | } |
---|
1654 | curr++; |
---|
1655 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
1656 | } |
---|
1657 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
1658 | } |
---|
1659 | return (poly) 1; |
---|
1660 | } |
---|
1661 | |
---|
1662 | /*2 |
---|
1663 | * compute all ar-minors of the matrix a |
---|
1664 | */ |
---|
1665 | ideal idMinors(matrix a, int ar, ideal R) |
---|
1666 | { |
---|
1667 | int i,j,/*k,*/size; |
---|
1668 | int *rowchoise,*colchoise; |
---|
1669 | BOOLEAN rowch,colch; |
---|
1670 | ideal result; |
---|
1671 | matrix tmp; |
---|
1672 | poly p,q; |
---|
1673 | |
---|
1674 | i = binom(a->rows(),ar); |
---|
1675 | j = binom(a->cols(),ar); |
---|
1676 | |
---|
1677 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1678 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1679 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
1680 | else size=i*j; |
---|
1681 | result=idInit(size,1); |
---|
1682 | tmp=mpNew(ar,ar); |
---|
1683 | // k = 0; /* the index in result*/ |
---|
1684 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
1685 | while (!rowch) |
---|
1686 | { |
---|
1687 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
1688 | while (!colch) |
---|
1689 | { |
---|
1690 | for (i=1; i<=ar; i++) |
---|
1691 | { |
---|
1692 | for (j=1; j<=ar; j++) |
---|
1693 | { |
---|
1694 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
1695 | } |
---|
1696 | } |
---|
1697 | p = mp_DetBareiss(tmp,currRing); |
---|
1698 | if (p!=NULL) |
---|
1699 | { |
---|
1700 | if (R!=NULL) |
---|
1701 | { |
---|
1702 | q = p; |
---|
1703 | p = kNF(R,currRing->qideal,q); |
---|
1704 | p_Delete(&q,currRing); |
---|
1705 | } |
---|
1706 | if (p!=NULL) |
---|
1707 | { |
---|
1708 | if (k>=size) |
---|
1709 | { |
---|
1710 | pEnlargeSet(&result->m,size,32); |
---|
1711 | size += 32; |
---|
1712 | } |
---|
1713 | result->m[k] = p; |
---|
1714 | k++; |
---|
1715 | } |
---|
1716 | } |
---|
1717 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
1718 | } |
---|
1719 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
1720 | } |
---|
1721 | /*delete the matrix tmp*/ |
---|
1722 | for (i=1; i<=ar; i++) |
---|
1723 | { |
---|
1724 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
1725 | } |
---|
1726 | idDelete((ideal*)&tmp); |
---|
1727 | if (k==0) |
---|
1728 | { |
---|
1729 | k=1; |
---|
1730 | result->m[0]=NULL; |
---|
1731 | } |
---|
1732 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
1733 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
1734 | pEnlargeSet(&result->m,size,k-size); |
---|
1735 | IDELEMS(result) = k; |
---|
1736 | return (result); |
---|
1737 | } |
---|
1738 | #else |
---|
1739 | |
---|
1740 | |
---|
1741 | /// compute all ar-minors of the matrix a |
---|
1742 | /// the caller of mpRecMin |
---|
1743 | /// the elements of the result are not in R (if R!=NULL) |
---|
1744 | ideal idMinors(matrix a, int ar, ideal R) |
---|
1745 | { |
---|
1746 | |
---|
1747 | const ring origR=currRing; |
---|
1748 | id_Test((ideal)a, origR); |
---|
1749 | |
---|
1750 | const int r = a->nrows; |
---|
1751 | const int c = a->ncols; |
---|
1752 | |
---|
1753 | if((ar<=0) || (ar>r) || (ar>c)) |
---|
1754 | { |
---|
1755 | Werror("%d-th minor, matrix is %dx%d",ar,r,c); |
---|
1756 | return NULL; |
---|
1757 | } |
---|
1758 | |
---|
1759 | ideal h = id_Matrix2Module(mp_Copy(a,origR),origR); |
---|
1760 | long bound = sm_ExpBound(h,c,r,ar,origR); |
---|
1761 | id_Delete(&h, origR); |
---|
1762 | |
---|
1763 | ring tmpR = sm_RingChange(origR,bound); |
---|
1764 | |
---|
1765 | matrix b = mpNew(r,c); |
---|
1766 | |
---|
1767 | for (int i=r*c-1;i>=0;i--) |
---|
1768 | if (a->m[i] != NULL) |
---|
1769 | b->m[i] = prCopyR(a->m[i],origR,tmpR); |
---|
1770 | |
---|
1771 | id_Test( (ideal)b, tmpR); |
---|
1772 | |
---|
1773 | if (R!=NULL) |
---|
1774 | { |
---|
1775 | R = idrCopyR(R,origR,tmpR); // TODO: overwrites R? memory leak? |
---|
1776 | //if (ar>1) // otherwise done in mpMinorToResult |
---|
1777 | //{ |
---|
1778 | // matrix bb=(matrix)kNF(R,currRing->qideal,(ideal)b); |
---|
1779 | // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols; |
---|
1780 | // idDelete((ideal*)&b); b=bb; |
---|
1781 | //} |
---|
1782 | id_Test( R, tmpR); |
---|
1783 | } |
---|
1784 | |
---|
1785 | |
---|
1786 | ideal result = idInit(32,1); |
---|
1787 | |
---|
1788 | int elems = 0; |
---|
1789 | |
---|
1790 | if(ar>1) |
---|
1791 | mp_RecMin(ar-1,result,elems,b,r,c,NULL,R,tmpR); |
---|
1792 | else |
---|
1793 | mp_MinorToResult(result,elems,b,r,c,R,tmpR); |
---|
1794 | |
---|
1795 | id_Test( (ideal)b, tmpR); |
---|
1796 | |
---|
1797 | id_Delete((ideal *)&b, tmpR); |
---|
1798 | |
---|
1799 | if (R!=NULL) id_Delete(&R,tmpR); |
---|
1800 | |
---|
1801 | idSkipZeroes(result); |
---|
1802 | rChangeCurrRing(origR); |
---|
1803 | result = idrMoveR(result,tmpR,origR); |
---|
1804 | sm_KillModifiedRing(tmpR); |
---|
1805 | idTest(result); |
---|
1806 | return result; |
---|
1807 | } |
---|
1808 | #endif |
---|
1809 | |
---|
1810 | /*2 |
---|
1811 | *returns TRUE if id1 is a submodule of id2 |
---|
1812 | */ |
---|
1813 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
1814 | { |
---|
1815 | int i; |
---|
1816 | poly p; |
---|
1817 | |
---|
1818 | if (idIs0(id1)) return TRUE; |
---|
1819 | for (i=0;i<IDELEMS(id1);i++) |
---|
1820 | { |
---|
1821 | if (id1->m[i] != NULL) |
---|
1822 | { |
---|
1823 | p = kNF(id2,currRing->qideal,id1->m[i]); |
---|
1824 | if (p != NULL) |
---|
1825 | { |
---|
1826 | p_Delete(&p,currRing); |
---|
1827 | return FALSE; |
---|
1828 | } |
---|
1829 | } |
---|
1830 | } |
---|
1831 | return TRUE; |
---|
1832 | } |
---|
1833 | |
---|
1834 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
1835 | { |
---|
1836 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
1837 | if (idIs0(m)) return TRUE; |
---|
1838 | |
---|
1839 | int cmax=-1; |
---|
1840 | int i; |
---|
1841 | poly p=NULL; |
---|
1842 | int length=IDELEMS(m); |
---|
1843 | polyset P=m->m; |
---|
1844 | for (i=length-1;i>=0;i--) |
---|
1845 | { |
---|
1846 | p=P[i]; |
---|
1847 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
1848 | } |
---|
1849 | if (w != NULL) |
---|
1850 | if (w->length()+1 < cmax) |
---|
1851 | { |
---|
1852 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
1853 | return FALSE; |
---|
1854 | } |
---|
1855 | |
---|
1856 | if(w!=NULL) |
---|
1857 | p_SetModDeg(w, currRing); |
---|
1858 | |
---|
1859 | for (i=length-1;i>=0;i--) |
---|
1860 | { |
---|
1861 | p=P[i]; |
---|
1862 | if (p!=NULL) |
---|
1863 | { |
---|
1864 | int d=currRing->pFDeg(p,currRing); |
---|
1865 | loop |
---|
1866 | { |
---|
1867 | pIter(p); |
---|
1868 | if (p==NULL) break; |
---|
1869 | if (d!=currRing->pFDeg(p,currRing)) |
---|
1870 | { |
---|
1871 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
1872 | if(w!=NULL) |
---|
1873 | p_SetModDeg(NULL, currRing); |
---|
1874 | return FALSE; |
---|
1875 | } |
---|
1876 | } |
---|
1877 | } |
---|
1878 | } |
---|
1879 | |
---|
1880 | if(w!=NULL) |
---|
1881 | p_SetModDeg(NULL, currRing); |
---|
1882 | |
---|
1883 | return TRUE; |
---|
1884 | } |
---|
1885 | |
---|
1886 | ideal idSeries(int n,ideal M,matrix U,intvec *w) |
---|
1887 | { |
---|
1888 | for(int i=IDELEMS(M)-1;i>=0;i--) |
---|
1889 | { |
---|
1890 | if(U==NULL) |
---|
1891 | M->m[i]=pSeries(n,M->m[i],NULL,w); |
---|
1892 | else |
---|
1893 | { |
---|
1894 | M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w); |
---|
1895 | MATELEM(U,i+1,i+1)=NULL; |
---|
1896 | } |
---|
1897 | } |
---|
1898 | if(U!=NULL) |
---|
1899 | idDelete((ideal*)&U); |
---|
1900 | return M; |
---|
1901 | } |
---|
1902 | |
---|
1903 | matrix idDiff(matrix i, int k) |
---|
1904 | { |
---|
1905 | int e=MATCOLS(i)*MATROWS(i); |
---|
1906 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
1907 | r->rank=i->rank; |
---|
1908 | int j; |
---|
1909 | for(j=0; j<e; j++) |
---|
1910 | { |
---|
1911 | r->m[j]=pDiff(i->m[j],k); |
---|
1912 | } |
---|
1913 | return r; |
---|
1914 | } |
---|
1915 | |
---|
1916 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
1917 | { |
---|
1918 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
1919 | int i,j; |
---|
1920 | for(i=0; i<IDELEMS(I); i++) |
---|
1921 | { |
---|
1922 | for(j=0; j<IDELEMS(J); j++) |
---|
1923 | { |
---|
1924 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
1925 | } |
---|
1926 | } |
---|
1927 | return r; |
---|
1928 | } |
---|
1929 | |
---|
1930 | /*3 |
---|
1931 | *handles for some ideal operations the ring/syzcomp managment |
---|
1932 | *returns all syzygies (componentwise-)shifted by -syzcomp |
---|
1933 | *or -syzcomp-1 (in case of ideals as input) |
---|
1934 | static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE) |
---|
1935 | { |
---|
1936 | ring orig_ring=currRing; |
---|
1937 | ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); rChangeCurrRing(syz_ring); |
---|
1938 | rSetSyzComp(length, syz_ring); |
---|
1939 | |
---|
1940 | ideal s_temp; |
---|
1941 | if (orig_ring!=syz_ring) |
---|
1942 | s_temp=idrMoveR_NoSort(arg,orig_ring, syz_ring); |
---|
1943 | else |
---|
1944 | s_temp=arg; |
---|
1945 | |
---|
1946 | ideal s_temp1 = kStd(s_temp,currRing->qideal,testHomog,&w,NULL,length); |
---|
1947 | if (w!=NULL) delete w; |
---|
1948 | |
---|
1949 | if (syz_ring!=orig_ring) |
---|
1950 | { |
---|
1951 | idDelete(&s_temp); |
---|
1952 | rChangeCurrRing(orig_ring); |
---|
1953 | } |
---|
1954 | |
---|
1955 | idDelete(&temp); |
---|
1956 | ideal temp1=idRingCopy(s_temp1,syz_ring); |
---|
1957 | |
---|
1958 | if (syz_ring!=orig_ring) |
---|
1959 | { |
---|
1960 | rChangeCurrRing(syz_ring); |
---|
1961 | idDelete(&s_temp1); |
---|
1962 | rChangeCurrRing(orig_ring); |
---|
1963 | rDelete(syz_ring); |
---|
1964 | } |
---|
1965 | |
---|
1966 | for (i=0;i<IDELEMS(temp1);i++) |
---|
1967 | { |
---|
1968 | if ((temp1->m[i]!=NULL) |
---|
1969 | && (pGetComp(temp1->m[i])<=length)) |
---|
1970 | { |
---|
1971 | pDelete(&(temp1->m[i])); |
---|
1972 | } |
---|
1973 | else |
---|
1974 | { |
---|
1975 | p_Shift(&(temp1->m[i]),-length,currRing); |
---|
1976 | } |
---|
1977 | } |
---|
1978 | temp1->rank = rk; |
---|
1979 | idSkipZeroes(temp1); |
---|
1980 | |
---|
1981 | return temp1; |
---|
1982 | } |
---|
1983 | */ |
---|
1984 | /*2 |
---|
1985 | * represents (h1+h2)/h2=h1/(h1 intersect h2) |
---|
1986 | */ |
---|
1987 | //ideal idModulo (ideal h2,ideal h1) |
---|
1988 | ideal idModulo (ideal h2,ideal h1, tHomog hom, intvec ** w) |
---|
1989 | { |
---|
1990 | intvec *wtmp=NULL; |
---|
1991 | |
---|
1992 | int i,k,rk,flength=0,slength,length; |
---|
1993 | poly p,q; |
---|
1994 | |
---|
1995 | if (idIs0(h2)) |
---|
1996 | return idFreeModule(si_max(1,h2->ncols)); |
---|
1997 | if (!idIs0(h1)) |
---|
1998 | flength = id_RankFreeModule(h1,currRing); |
---|
1999 | slength = id_RankFreeModule(h2,currRing); |
---|
2000 | length = si_max(flength,slength); |
---|
2001 | if (length==0) |
---|
2002 | { |
---|
2003 | length = 1; |
---|
2004 | } |
---|
2005 | ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2)); |
---|
2006 | if ((w!=NULL)&&((*w)!=NULL)) |
---|
2007 | { |
---|
2008 | //Print("input weights:");(*w)->show(1);PrintLn(); |
---|
2009 | int d; |
---|
2010 | int k; |
---|
2011 | wtmp=new intvec(length+IDELEMS(h2)); |
---|
2012 | for (i=0;i<length;i++) |
---|
2013 | ((*wtmp)[i])=(**w)[i]; |
---|
2014 | for (i=0;i<IDELEMS(h2);i++) |
---|
2015 | { |
---|
2016 | poly p=h2->m[i]; |
---|
2017 | if (p!=NULL) |
---|
2018 | { |
---|
2019 | d = p_Deg(p,currRing); |
---|
2020 | k= pGetComp(p); |
---|
2021 | if (slength>0) k--; |
---|
2022 | d +=((**w)[k]); |
---|
2023 | ((*wtmp)[i+length]) = d; |
---|
2024 | } |
---|
2025 | } |
---|
2026 | //Print("weights:");wtmp->show(1);PrintLn(); |
---|
2027 | } |
---|
2028 | for (i=0;i<IDELEMS(h2);i++) |
---|
2029 | { |
---|
2030 | temp->m[i] = pCopy(h2->m[i]); |
---|
2031 | q = pOne(); |
---|
2032 | pSetComp(q,i+1+length); |
---|
2033 | pSetmComp(q); |
---|
2034 | if(temp->m[i]!=NULL) |
---|
2035 | { |
---|
2036 | if (slength==0) p_Shift(&(temp->m[i]),1,currRing); |
---|
2037 | p = temp->m[i]; |
---|
2038 | while (pNext(p)!=NULL) pIter(p); |
---|
2039 | pNext(p) = q; // will be sorted later correctly |
---|
2040 | } |
---|
2041 | else |
---|
2042 | temp->m[i]=q; |
---|
2043 | } |
---|
2044 | rk = k = IDELEMS(h2); |
---|
2045 | if (!idIs0(h1)) |
---|
2046 | { |
---|
2047 | pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1)); |
---|
2048 | IDELEMS(temp) += IDELEMS(h1); |
---|
2049 | for (i=0;i<IDELEMS(h1);i++) |
---|
2050 | { |
---|
2051 | if (h1->m[i]!=NULL) |
---|
2052 | { |
---|
2053 | temp->m[k] = pCopy(h1->m[i]); |
---|
2054 | if (flength==0) p_Shift(&(temp->m[k]),1,currRing); |
---|
2055 | k++; |
---|
2056 | } |
---|
2057 | } |
---|
2058 | } |
---|
2059 | |
---|
2060 | ring orig_ring=currRing; |
---|
2061 | ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); rChangeCurrRing(syz_ring); |
---|
2062 | // we can use OPT_RETURN_SB only, if syz_ring==orig_ring, |
---|
2063 | // therefore we disable OPT_RETURN_SB for modulo: |
---|
2064 | // (see tr. #701) |
---|
2065 | //if (TEST_OPT_RETURN_SB) |
---|
2066 | // rSetSyzComp(IDELEMS(h2)+length, syz_ring); |
---|
2067 | //else |
---|
2068 | rSetSyzComp(length, syz_ring); |
---|
2069 | ideal s_temp; |
---|
2070 | |
---|
2071 | if (syz_ring != orig_ring) |
---|
2072 | { |
---|
2073 | s_temp = idrMoveR_NoSort(temp, orig_ring, syz_ring); |
---|
2074 | } |
---|
2075 | else |
---|
2076 | { |
---|
2077 | s_temp = temp; |
---|
2078 | } |
---|
2079 | |
---|
2080 | idTest(s_temp); |
---|
2081 | ideal s_temp1 = kStd(s_temp,currRing->qideal,hom,&wtmp,NULL,length); |
---|
2082 | |
---|
2083 | //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn(); |
---|
2084 | if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL)) |
---|
2085 | { |
---|
2086 | delete *w; |
---|
2087 | *w=new intvec(IDELEMS(h2)); |
---|
2088 | for (i=0;i<IDELEMS(h2);i++) |
---|
2089 | ((**w)[i])=(*wtmp)[i+length]; |
---|
2090 | } |
---|
2091 | if (wtmp!=NULL) delete wtmp; |
---|
2092 | |
---|
2093 | for (i=0;i<IDELEMS(s_temp1);i++) |
---|
2094 | { |
---|
2095 | if ((s_temp1->m[i]!=NULL) |
---|
2096 | && (((int)pGetComp(s_temp1->m[i]))<=length)) |
---|
2097 | { |
---|
2098 | p_Delete(&(s_temp1->m[i]),currRing); |
---|
2099 | } |
---|
2100 | else |
---|
2101 | { |
---|
2102 | p_Shift(&(s_temp1->m[i]),-length,currRing); |
---|
2103 | } |
---|
2104 | } |
---|
2105 | s_temp1->rank = rk; |
---|
2106 | idSkipZeroes(s_temp1); |
---|
2107 | |
---|
2108 | if (syz_ring!=orig_ring) |
---|
2109 | { |
---|
2110 | rChangeCurrRing(orig_ring); |
---|
2111 | s_temp1 = idrMoveR_NoSort(s_temp1, syz_ring, orig_ring); |
---|
2112 | rDelete(syz_ring); |
---|
2113 | // Hmm ... here seems to be a memory leak |
---|
2114 | // However, simply deleting it causes memory trouble |
---|
2115 | // idDelete(&s_temp); |
---|
2116 | } |
---|
2117 | else |
---|
2118 | { |
---|
2119 | idDelete(&temp); |
---|
2120 | } |
---|
2121 | idTest(s_temp1); |
---|
2122 | return s_temp1; |
---|
2123 | } |
---|
2124 | |
---|
2125 | /* |
---|
2126 | *computes module-weights for liftings of homogeneous modules |
---|
2127 | */ |
---|
2128 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
2129 | { |
---|
2130 | if (idIs0(mod)) return new intvec(2); |
---|
2131 | int i=IDELEMS(mod); |
---|
2132 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
2133 | intvec *result = new intvec(i+1); |
---|
2134 | while (i>0) |
---|
2135 | { |
---|
2136 | (*result)[i]=currRing->pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])]; |
---|
2137 | } |
---|
2138 | return result; |
---|
2139 | } |
---|
2140 | |
---|
2141 | /*2 |
---|
2142 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
2143 | *with x_max,...,x_1) |
---|
2144 | */ |
---|
2145 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
2146 | { |
---|
2147 | int i; |
---|
2148 | ideal result; |
---|
2149 | |
---|
2150 | if (idIs0(kBase)) return NULL; |
---|
2151 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
2152 | *convert = idSort(kBase,FALSE); |
---|
2153 | for (i=0;i<(*convert)->length();i++) |
---|
2154 | { |
---|
2155 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
2156 | } |
---|
2157 | return result; |
---|
2158 | } |
---|
2159 | |
---|
2160 | /*2 |
---|
2161 | *returns the index of a given monom in the list of the special kbase |
---|
2162 | */ |
---|
2163 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
2164 | { |
---|
2165 | int j=IDELEMS(kbase); |
---|
2166 | |
---|
2167 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
2168 | if (j==0) return -1; |
---|
2169 | int i=(currRing->N); |
---|
2170 | while (i>0) |
---|
2171 | { |
---|
2172 | loop |
---|
2173 | { |
---|
2174 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
2175 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
2176 | j--; |
---|
2177 | if (j==0) return -1; |
---|
2178 | } |
---|
2179 | if (i==1) |
---|
2180 | { |
---|
2181 | while(j>0) |
---|
2182 | { |
---|
2183 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
2184 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
2185 | j--; |
---|
2186 | } |
---|
2187 | } |
---|
2188 | i--; |
---|
2189 | } |
---|
2190 | return -1; |
---|
2191 | } |
---|
2192 | |
---|
2193 | /*2 |
---|
2194 | *decomposes the monom in a part of coefficients described by the |
---|
2195 | *complement of how and a monom in variables occuring in how, the |
---|
2196 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
2197 | *exists) |
---|
2198 | */ |
---|
2199 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
2200 | { |
---|
2201 | int i; |
---|
2202 | poly coeff=pOne(), base=pOne(); |
---|
2203 | |
---|
2204 | for (i=1;i<=(currRing->N);i++) |
---|
2205 | { |
---|
2206 | if (pGetExp(how,i)>0) |
---|
2207 | { |
---|
2208 | pSetExp(base,i,pGetExp(monom,i)); |
---|
2209 | } |
---|
2210 | else |
---|
2211 | { |
---|
2212 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
2213 | } |
---|
2214 | } |
---|
2215 | pSetComp(base,pGetComp(monom)); |
---|
2216 | pSetm(base); |
---|
2217 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
2218 | pSetm(coeff); |
---|
2219 | *pos = idIndexOfKBase(base,kbase); |
---|
2220 | if (*pos<0) |
---|
2221 | p_Delete(&coeff,currRing); |
---|
2222 | p_Delete(&base,currRing); |
---|
2223 | return coeff; |
---|
2224 | } |
---|
2225 | |
---|
2226 | /*2 |
---|
2227 | *returns a matrix A of coefficients with kbase*A=arg |
---|
2228 | *if all monomials in variables of how occur in kbase |
---|
2229 | *the other are deleted |
---|
2230 | */ |
---|
2231 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
2232 | { |
---|
2233 | matrix result; |
---|
2234 | ideal tempKbase; |
---|
2235 | poly p,q; |
---|
2236 | intvec * convert; |
---|
2237 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
2238 | #if 0 |
---|
2239 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
2240 | if (idIs0(arg)) |
---|
2241 | return mpNew(i,1); |
---|
2242 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
2243 | result = mpNew(i,j); |
---|
2244 | #else |
---|
2245 | result = mpNew(i, j); |
---|
2246 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
2247 | #endif |
---|
2248 | |
---|
2249 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
2250 | for (k=0;k<j;k++) |
---|
2251 | { |
---|
2252 | p = arg->m[k]; |
---|
2253 | while (p!=NULL) |
---|
2254 | { |
---|
2255 | q = idDecompose(p,how,tempKbase,&pos); |
---|
2256 | if (pos>=0) |
---|
2257 | { |
---|
2258 | MATELEM(result,(*convert)[pos],k+1) = |
---|
2259 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
2260 | } |
---|
2261 | else |
---|
2262 | p_Delete(&q,currRing); |
---|
2263 | pIter(p); |
---|
2264 | } |
---|
2265 | } |
---|
2266 | idDelete(&tempKbase); |
---|
2267 | return result; |
---|
2268 | } |
---|
2269 | |
---|
2270 | static void idDeleteComps(ideal arg,int* red_comp,int del) |
---|
2271 | // red_comp is an array [0..args->rank] |
---|
2272 | { |
---|
2273 | int i,j; |
---|
2274 | poly p; |
---|
2275 | |
---|
2276 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
2277 | { |
---|
2278 | p = arg->m[i]; |
---|
2279 | while (p!=NULL) |
---|
2280 | { |
---|
2281 | j = pGetComp(p); |
---|
2282 | if (red_comp[j]!=j) |
---|
2283 | { |
---|
2284 | pSetComp(p,red_comp[j]); |
---|
2285 | pSetmComp(p); |
---|
2286 | } |
---|
2287 | pIter(p); |
---|
2288 | } |
---|
2289 | } |
---|
2290 | (arg->rank) -= del; |
---|
2291 | } |
---|
2292 | |
---|
2293 | /*2 |
---|
2294 | * returns the presentation of an isomorphic, minimally |
---|
2295 | * embedded module (arg represents the quotient!) |
---|
2296 | */ |
---|
2297 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w) |
---|
2298 | { |
---|
2299 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
2300 | int i,next_gen,next_comp; |
---|
2301 | ideal res=arg; |
---|
2302 | if (!inPlace) res = idCopy(arg); |
---|
2303 | res->rank=si_max(res->rank,id_RankFreeModule(res,currRing)); |
---|
2304 | int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int)); |
---|
2305 | for (i=res->rank;i>=0;i--) red_comp[i]=i; |
---|
2306 | |
---|
2307 | int del=0; |
---|
2308 | loop |
---|
2309 | { |
---|
2310 | next_gen = id_ReadOutPivot(res, &next_comp, currRing); |
---|
2311 | if (next_gen<0) break; |
---|
2312 | del++; |
---|
2313 | syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res)); |
---|
2314 | for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--; |
---|
2315 | if ((w !=NULL)&&(*w!=NULL)) |
---|
2316 | { |
---|
2317 | for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i]; |
---|
2318 | } |
---|
2319 | } |
---|
2320 | |
---|
2321 | idDeleteComps(res,red_comp,del); |
---|
2322 | idSkipZeroes(res); |
---|
2323 | omFree(red_comp); |
---|
2324 | |
---|
2325 | if ((w !=NULL)&&(*w!=NULL) &&(del>0)) |
---|
2326 | { |
---|
2327 | int nl=si_max((*w)->length()-del,1); |
---|
2328 | intvec *wtmp=new intvec(nl); |
---|
2329 | for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i]; |
---|
2330 | delete *w; |
---|
2331 | *w=wtmp; |
---|
2332 | } |
---|
2333 | return res; |
---|
2334 | } |
---|
2335 | |
---|
2336 | #include <polys/clapsing.h> |
---|
2337 | |
---|
2338 | #if 0 |
---|
2339 | poly id_GCD(poly f, poly g, const ring r) |
---|
2340 | { |
---|
2341 | ring save_r=currRing; |
---|
2342 | rChangeCurrRing(r); |
---|
2343 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
2344 | intvec *w = NULL; |
---|
2345 | ideal S=idSyzygies(I,testHomog,&w); |
---|
2346 | if (w!=NULL) delete w; |
---|
2347 | poly gg=pTakeOutComp(&(S->m[0]),2); |
---|
2348 | idDelete(&S); |
---|
2349 | poly gcd_p=singclap_pdivide(f,gg,r); |
---|
2350 | p_Delete(&gg,r); |
---|
2351 | rChangeCurrRing(save_r); |
---|
2352 | return gcd_p; |
---|
2353 | } |
---|
2354 | #else |
---|
2355 | poly id_GCD(poly f, poly g, const ring r) |
---|
2356 | { |
---|
2357 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
2358 | intvec *w = NULL; |
---|
2359 | |
---|
2360 | ring save_r = currRing; rChangeCurrRing(r); ideal S=idSyzygies(I,testHomog,&w); rChangeCurrRing(save_r); |
---|
2361 | |
---|
2362 | if (w!=NULL) delete w; |
---|
2363 | poly gg=p_TakeOutComp(&(S->m[0]), 2, r); |
---|
2364 | id_Delete(&S, r); |
---|
2365 | poly gcd_p=singclap_pdivide(f,gg, r); |
---|
2366 | p_Delete(&gg, r); |
---|
2367 | |
---|
2368 | return gcd_p; |
---|
2369 | } |
---|
2370 | #endif |
---|
2371 | |
---|
2372 | #if 0 |
---|
2373 | /*2 |
---|
2374 | * xx,q: arrays of length 0..rl-1 |
---|
2375 | * xx[i]: SB mod q[i] |
---|
2376 | * assume: char=0 |
---|
2377 | * assume: q[i]!=0 |
---|
2378 | * destroys xx |
---|
2379 | */ |
---|
2380 | ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring R) |
---|
2381 | { |
---|
2382 | int cnt=IDELEMS(xx[0])*xx[0]->nrows; |
---|
2383 | ideal result=idInit(cnt,xx[0]->rank); |
---|
2384 | result->nrows=xx[0]->nrows; // for lifting matrices |
---|
2385 | result->ncols=xx[0]->ncols; // for lifting matrices |
---|
2386 | int i,j; |
---|
2387 | poly r,h,hh,res_p; |
---|
2388 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
2389 | for(i=cnt-1;i>=0;i--) |
---|
2390 | { |
---|
2391 | res_p=NULL; |
---|
2392 | loop |
---|
2393 | { |
---|
2394 | r=NULL; |
---|
2395 | for(j=rl-1;j>=0;j--) |
---|
2396 | { |
---|
2397 | h=xx[j]->m[i]; |
---|
2398 | if ((h!=NULL) |
---|
2399 | &&((r==NULL)||(p_LmCmp(r,h,R)==-1))) |
---|
2400 | r=h; |
---|
2401 | } |
---|
2402 | if (r==NULL) break; |
---|
2403 | h=p_Head(r, R); |
---|
2404 | for(j=rl-1;j>=0;j--) |
---|
2405 | { |
---|
2406 | hh=xx[j]->m[i]; |
---|
2407 | if ((hh!=NULL) && (p_LmCmp(r,hh, R)==0)) |
---|
2408 | { |
---|
2409 | x[j]=p_GetCoeff(hh, R); |
---|
2410 | hh=p_LmFreeAndNext(hh, R); |
---|
2411 | xx[j]->m[i]=hh; |
---|
2412 | } |
---|
2413 | else |
---|
2414 | x[j]=n_Init(0, R->cf); // is R->cf really n_Q???, yes! |
---|
2415 | } |
---|
2416 | |
---|
2417 | number n=n_ChineseRemainder(x,q,rl, R->cf); |
---|
2418 | |
---|
2419 | for(j=rl-1;j>=0;j--) |
---|
2420 | { |
---|
2421 | x[j]=NULL; // nlInit(0...) takes no memory |
---|
2422 | } |
---|
2423 | if (n_IsZero(n, R->cf)) p_Delete(&h, R); |
---|
2424 | else |
---|
2425 | { |
---|
2426 | p_SetCoeff(h,n, R); |
---|
2427 | //Print("new mon:");pWrite(h); |
---|
2428 | res_p=p_Add_q(res_p, h, R); |
---|
2429 | } |
---|
2430 | } |
---|
2431 | result->m[i]=res_p; |
---|
2432 | } |
---|
2433 | omFree(x); |
---|
2434 | for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]), R); |
---|
2435 | omFree(xx); |
---|
2436 | return result; |
---|
2437 | } |
---|
2438 | #endif |
---|
2439 | /* currently unsed: |
---|
2440 | ideal idChineseRemainder(ideal *xx, intvec *iv) |
---|
2441 | { |
---|
2442 | int rl=iv->length(); |
---|
2443 | number *q=(number *)omAlloc(rl*sizeof(number)); |
---|
2444 | int i; |
---|
2445 | for(i=0; i<rl; i++) |
---|
2446 | { |
---|
2447 | q[i]=nInit((*iv)[i]); |
---|
2448 | } |
---|
2449 | return idChineseRemainder(xx,q,rl); |
---|
2450 | } |
---|
2451 | */ |
---|
2452 | /* |
---|
2453 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
---|
2454 | */ |
---|
2455 | ideal id_Farey(ideal x, number N, const ring r) |
---|
2456 | { |
---|
2457 | int cnt=IDELEMS(x)*x->nrows; |
---|
2458 | ideal result=idInit(cnt,x->rank); |
---|
2459 | result->nrows=x->nrows; // for lifting matrices |
---|
2460 | result->ncols=x->ncols; // for lifting matrices |
---|
2461 | |
---|
2462 | int i; |
---|
2463 | for(i=cnt-1;i>=0;i--) |
---|
2464 | { |
---|
2465 | result->m[i]=p_Farey(x->m[i],N,r); |
---|
2466 | } |
---|
2467 | return result; |
---|
2468 | } |
---|
2469 | |
---|
2470 | |
---|
2471 | |
---|
2472 | |
---|
2473 | // uses glabl vars via pSetModDeg |
---|
2474 | /* |
---|
2475 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
2476 | { |
---|
2477 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
2478 | if (idIs0(m)) return TRUE; |
---|
2479 | |
---|
2480 | int cmax=-1; |
---|
2481 | int i; |
---|
2482 | poly p=NULL; |
---|
2483 | int length=IDELEMS(m); |
---|
2484 | poly* P=m->m; |
---|
2485 | for (i=length-1;i>=0;i--) |
---|
2486 | { |
---|
2487 | p=P[i]; |
---|
2488 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
2489 | } |
---|
2490 | if (w != NULL) |
---|
2491 | if (w->length()+1 < cmax) |
---|
2492 | { |
---|
2493 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
2494 | return FALSE; |
---|
2495 | } |
---|
2496 | |
---|
2497 | if(w!=NULL) |
---|
2498 | p_SetModDeg(w, currRing); |
---|
2499 | |
---|
2500 | for (i=length-1;i>=0;i--) |
---|
2501 | { |
---|
2502 | p=P[i]; |
---|
2503 | poly q=p; |
---|
2504 | if (p!=NULL) |
---|
2505 | { |
---|
2506 | int d=p_FDeg(p,currRing); |
---|
2507 | loop |
---|
2508 | { |
---|
2509 | pIter(p); |
---|
2510 | if (p==NULL) break; |
---|
2511 | if (d!=p_FDeg(p,currRing)) |
---|
2512 | { |
---|
2513 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
2514 | if(w!=NULL) |
---|
2515 | p_SetModDeg(NULL, currRing); |
---|
2516 | return FALSE; |
---|
2517 | } |
---|
2518 | } |
---|
2519 | } |
---|
2520 | } |
---|
2521 | |
---|
2522 | if(w!=NULL) |
---|
2523 | p_SetModDeg(NULL, currRing); |
---|
2524 | |
---|
2525 | return TRUE; |
---|
2526 | } |
---|
2527 | */ |
---|
2528 | |
---|
2529 | /// keeps the first k (>= 1) entries of the given ideal |
---|
2530 | /// (Note that the kept polynomials may be zero.) |
---|
2531 | void idKeepFirstK(ideal id, const int k) |
---|
2532 | { |
---|
2533 | for (int i = IDELEMS(id)-1; i >= k; i--) |
---|
2534 | { |
---|
2535 | if (id->m[i] != NULL) pDelete(&id->m[i]); |
---|
2536 | } |
---|
2537 | int kk=k; |
---|
2538 | if (k==0) kk=1; /* ideals must have at least one element(0)*/ |
---|
2539 | pEnlargeSet(&(id->m), IDELEMS(id), kk-IDELEMS(id)); |
---|
2540 | IDELEMS(id) = kk; |
---|
2541 | } |
---|
2542 | |
---|
2543 | typedef struct |
---|
2544 | { |
---|
2545 | poly p; |
---|
2546 | int index; |
---|
2547 | } poly_sort; |
---|
2548 | |
---|
2549 | int pCompare_qsort(const void *a, const void *b) |
---|
2550 | { |
---|
2551 | return (p_Compare(((poly_sort *)a)->p, ((poly_sort *)b)->p,currRing)); |
---|
2552 | } |
---|
2553 | |
---|
2554 | void idSort_qsort(poly_sort *id_sort, int idsize) |
---|
2555 | { |
---|
2556 | qsort(id_sort, idsize, sizeof(poly_sort), pCompare_qsort); |
---|
2557 | } |
---|
2558 | |
---|
2559 | /*2 |
---|
2560 | * ideal id = (id[i]) |
---|
2561 | * if id[i] = id[j] then id[j] is deleted for j > i |
---|
2562 | */ |
---|
2563 | void idDelEquals(ideal id) |
---|
2564 | { |
---|
2565 | int idsize = IDELEMS(id); |
---|
2566 | poly_sort *id_sort = (poly_sort *)omAlloc0(idsize*sizeof(poly_sort)); |
---|
2567 | for (int i = 0; i < idsize; i++) |
---|
2568 | { |
---|
2569 | id_sort[i].p = id->m[i]; |
---|
2570 | id_sort[i].index = i; |
---|
2571 | } |
---|
2572 | idSort_qsort(id_sort, idsize); |
---|
2573 | int index, index_i, index_j; |
---|
2574 | int i = 0; |
---|
2575 | for (int j = 1; j < idsize; j++) |
---|
2576 | { |
---|
2577 | if (id_sort[i].p != NULL && pEqualPolys(id_sort[i].p, id_sort[j].p)) |
---|
2578 | { |
---|
2579 | index_i = id_sort[i].index; |
---|
2580 | index_j = id_sort[j].index; |
---|
2581 | if (index_j > index_i) |
---|
2582 | { |
---|
2583 | index = index_j; |
---|
2584 | } |
---|
2585 | else |
---|
2586 | { |
---|
2587 | index = index_i; |
---|
2588 | i = j; |
---|
2589 | } |
---|
2590 | pDelete(&id->m[index]); |
---|
2591 | } |
---|
2592 | else |
---|
2593 | { |
---|
2594 | i = j; |
---|
2595 | } |
---|
2596 | } |
---|
2597 | omFreeSize((ADDRESS)(id_sort), idsize*sizeof(poly_sort)); |
---|
2598 | } |
---|