1 | /**************************************** |
---|
2 | * Computer Algebra System SINGULAR * |
---|
3 | ****************************************/ |
---|
4 | /* $Id: ideals.cc,v 1.9 1997-06-17 09:44:22 Singular Exp $ */ |
---|
5 | /* |
---|
6 | * ABSTRACT - all basic methods to manipulate ideals |
---|
7 | */ |
---|
8 | |
---|
9 | /* includes */ |
---|
10 | #include "mod2.h" |
---|
11 | #include "tok.h" |
---|
12 | #include "mmemory.h" |
---|
13 | #include "febase.h" |
---|
14 | #include "numbers.h" |
---|
15 | #include "polys.h" |
---|
16 | #include "ipid.h" |
---|
17 | #include "ring.h" |
---|
18 | #include "kstd1.h" |
---|
19 | #include "matpol.h" |
---|
20 | #include "weight.h" |
---|
21 | #include "intvec.h" |
---|
22 | #include "syz.h" |
---|
23 | #include "ideals.h" |
---|
24 | #include "lists.h" |
---|
25 | |
---|
26 | |
---|
27 | static poly * idpower; |
---|
28 | /*collects the monomials in makemonoms, must be allocated befor*/ |
---|
29 | static int idpowerpoint; |
---|
30 | /*index of the actual monomial in idpower*/ |
---|
31 | static poly * givenideal; |
---|
32 | /*the ideal from which a power is computed*/ |
---|
33 | |
---|
34 | /*0 implementation*/ |
---|
35 | |
---|
36 | /*2 |
---|
37 | * initialise an ideal |
---|
38 | */ |
---|
39 | #ifdef MDEBUG |
---|
40 | ideal idDBInit(int idsize, int rank, char *f, int l) |
---|
41 | #else |
---|
42 | ideal idInit(int idsize, int rank) |
---|
43 | #endif |
---|
44 | { |
---|
45 | /*- initialise an ideal -*/ |
---|
46 | #ifdef MDEBUG |
---|
47 | ideal hh = (ideal )mmDBAllocBlock(sizeof(*hh),f,l); |
---|
48 | #else |
---|
49 | ideal hh = (ideal )Alloc(sizeof(*hh)); |
---|
50 | #endif |
---|
51 | hh->nrows = 1; |
---|
52 | hh->rank = rank; |
---|
53 | IDELEMS(hh) = idsize; |
---|
54 | if (idsize>0) |
---|
55 | { |
---|
56 | #ifdef MDEBUG |
---|
57 | hh->m = (poly *)mmDBAllocBlock0(idsize*sizeof(poly),f,l); |
---|
58 | #else |
---|
59 | hh->m = (poly *)Alloc0(idsize*sizeof(poly)); |
---|
60 | #endif |
---|
61 | } |
---|
62 | else |
---|
63 | hh->m=NULL; |
---|
64 | return hh; |
---|
65 | } |
---|
66 | |
---|
67 | /*2 |
---|
68 | * initialise the maximal ideal (at 0) |
---|
69 | */ |
---|
70 | ideal idMaxIdeal (void) |
---|
71 | { |
---|
72 | int l; |
---|
73 | ideal hh=NULL; |
---|
74 | |
---|
75 | hh=idInit(pVariables,1); |
---|
76 | for (l=0; l<pVariables; l++) |
---|
77 | { |
---|
78 | hh->m[l] = pOne(); |
---|
79 | pSetExp(hh->m[l],l+1,1); |
---|
80 | pSetm(hh->m[l]); |
---|
81 | } |
---|
82 | return hh; |
---|
83 | } |
---|
84 | |
---|
85 | /*2 |
---|
86 | * deletes an ideal/matrix |
---|
87 | */ |
---|
88 | void idDelete (ideal * h) |
---|
89 | { |
---|
90 | int j; |
---|
91 | if (*h == NULL) return ; |
---|
92 | j=(*h)->nrows*(*h)->ncols; |
---|
93 | if (j>0) |
---|
94 | { |
---|
95 | do |
---|
96 | { |
---|
97 | pDelete(&((*h)->m[--j])); |
---|
98 | } |
---|
99 | while (j>0); |
---|
100 | Free((ADDRESS)((*h)->m),sizeof(poly)*(*h)->nrows*(*h)->ncols); |
---|
101 | } |
---|
102 | Free((ADDRESS)*h,sizeof(**h)); |
---|
103 | *h=NULL; |
---|
104 | } |
---|
105 | |
---|
106 | /*2 |
---|
107 | *gives an ideal the minimal possible size |
---|
108 | */ |
---|
109 | void idSkipZeroes (ideal ide) |
---|
110 | { |
---|
111 | int j,k; |
---|
112 | j = -1; |
---|
113 | for (k=0; k<IDELEMS(ide); k++) |
---|
114 | { |
---|
115 | if (ide->m[k] != NULL) |
---|
116 | { |
---|
117 | j++; |
---|
118 | ide->m[j] = ide->m[k]; |
---|
119 | } |
---|
120 | } |
---|
121 | if (j == -1) |
---|
122 | j = 0; |
---|
123 | else |
---|
124 | { |
---|
125 | for (k=j+1; k<IDELEMS(ide); k++) |
---|
126 | ide->m[k] = NULL; |
---|
127 | } |
---|
128 | pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide)); |
---|
129 | IDELEMS(ide) = j+1; |
---|
130 | } |
---|
131 | |
---|
132 | /*2 |
---|
133 | * ideal id = (id[i]) |
---|
134 | * result is leadcoeff(id[i]) = 1 |
---|
135 | */ |
---|
136 | void idNorm(ideal id) |
---|
137 | { |
---|
138 | for (int i=0; i<IDELEMS(id); i++) |
---|
139 | { |
---|
140 | if (id->m[i] != NULL) |
---|
141 | { |
---|
142 | pNorm(id->m[i]); |
---|
143 | } |
---|
144 | } |
---|
145 | } |
---|
146 | |
---|
147 | /*2 |
---|
148 | * ideal id = (id[i]), c any number |
---|
149 | * if id[i] = c*id[j] then id[j] is deleted for j > i |
---|
150 | */ |
---|
151 | void idDelMultiples(ideal id) |
---|
152 | { |
---|
153 | int i, j, t; |
---|
154 | int k = IDELEMS(id), l = k; |
---|
155 | for (i=k-2; i>=0; i--) |
---|
156 | { |
---|
157 | if (id->m[i]!=NULL) |
---|
158 | { |
---|
159 | for (j=l-1; j>i; j--) |
---|
160 | { |
---|
161 | if ((id->m[j]!=NULL) |
---|
162 | && (pComparePolys(id->m[i], id->m[j]))) |
---|
163 | { |
---|
164 | pDelete(&id->m[j]); |
---|
165 | l--; |
---|
166 | for(t=j; t<l; t++) |
---|
167 | { |
---|
168 | id->m[t] = id->m[t+1]; |
---|
169 | } |
---|
170 | } |
---|
171 | } |
---|
172 | } |
---|
173 | } |
---|
174 | if (l != k) |
---|
175 | { |
---|
176 | pEnlargeSet(&id->m, k, l-k); |
---|
177 | IDELEMS(id) = l; |
---|
178 | } |
---|
179 | } |
---|
180 | |
---|
181 | /*2 |
---|
182 | * ideal id = (id[i]) |
---|
183 | * if id[i] = id[j] then id[j] is deleted for j > i |
---|
184 | */ |
---|
185 | void idDelEquals(ideal id) |
---|
186 | { |
---|
187 | int i, j, t; |
---|
188 | int k = IDELEMS(id), l = k; |
---|
189 | for (i=k-2; i>=0; i--) |
---|
190 | { |
---|
191 | for (j=l-1; j>i; j--) |
---|
192 | { |
---|
193 | if (pEqualPolys(id->m[i], id->m[j])) |
---|
194 | { |
---|
195 | pDelete(&id->m[j]); |
---|
196 | l--; |
---|
197 | for(t=j; t<l; t++) |
---|
198 | { |
---|
199 | id->m[t] = id->m[t+1]; |
---|
200 | } |
---|
201 | } |
---|
202 | } |
---|
203 | } |
---|
204 | if (l != k) |
---|
205 | { |
---|
206 | pEnlargeSet(&id->m, k, l-k); |
---|
207 | IDELEMS(id) = l; |
---|
208 | } |
---|
209 | } |
---|
210 | |
---|
211 | /*2 |
---|
212 | * copy an ideal |
---|
213 | */ |
---|
214 | #ifdef MDEBUG |
---|
215 | ideal idDBCopy(ideal h1,char *f,int l) |
---|
216 | #else |
---|
217 | ideal idCopy (ideal h1) |
---|
218 | #endif |
---|
219 | { |
---|
220 | int i; |
---|
221 | ideal h2; |
---|
222 | |
---|
223 | //#ifdef TEST |
---|
224 | if (h1 == NULL) |
---|
225 | { |
---|
226 | #ifdef MDEBUG |
---|
227 | h2=idDBInit(1,1,f,l); |
---|
228 | #else |
---|
229 | h2=idInit(1,1); |
---|
230 | #endif |
---|
231 | } |
---|
232 | else |
---|
233 | //#endif |
---|
234 | { |
---|
235 | #ifdef MDEBUG |
---|
236 | h2=idDBInit(IDELEMS(h1),h1->rank,f,l); |
---|
237 | #else |
---|
238 | h2=idInit(IDELEMS(h1),h1->rank); |
---|
239 | #endif |
---|
240 | for (i=IDELEMS(h1)-1; i>=0; i--) |
---|
241 | #ifdef MDEBUG |
---|
242 | h2->m[i] = pDBCopy(h1->m[i],f,l); |
---|
243 | #else |
---|
244 | h2->m[i] = pCopy(h1->m[i]); |
---|
245 | #endif |
---|
246 | } |
---|
247 | return h2; |
---|
248 | } |
---|
249 | |
---|
250 | #ifdef PDEBUG |
---|
251 | void idDBTest(ideal h1,char *f,int l) |
---|
252 | { |
---|
253 | int i; |
---|
254 | |
---|
255 | if (h1 != NULL) |
---|
256 | { |
---|
257 | mmTestP(h1,sizeof(*h1)); |
---|
258 | for (i=IDELEMS(h1)-1; i>=0; i--) |
---|
259 | pDBTest(h1->m[i],f,l); |
---|
260 | } |
---|
261 | } |
---|
262 | #endif |
---|
263 | |
---|
264 | /*3 |
---|
265 | * for idSort: compare a and b revlex inclusive module comp. |
---|
266 | */ |
---|
267 | static int pComp_RevLex(poly a, poly b) |
---|
268 | { |
---|
269 | int l=pVariables; |
---|
270 | while ((l>=0) && (pGetExp(a,l)==pGetExp(b,l))) l--; |
---|
271 | if (l<0) |
---|
272 | return 0; |
---|
273 | else if (pGetExp(a,l)>pGetExp(b,l)) |
---|
274 | return 1; |
---|
275 | else |
---|
276 | return -1; |
---|
277 | } |
---|
278 | |
---|
279 | /*2 |
---|
280 | *sorts the ideal w.r.t. the actual ringordering |
---|
281 | *uses lex-ordering when nolex = FALSE |
---|
282 | */ |
---|
283 | intvec *idSort(ideal id,BOOLEAN nolex) |
---|
284 | { |
---|
285 | poly p,q; |
---|
286 | intvec * result = new intvec(IDELEMS(id)); |
---|
287 | int i, j, actpos=0, newpos, l; |
---|
288 | int diff, olddiff, lastcomp, newcomp; |
---|
289 | BOOLEAN notFound; |
---|
290 | |
---|
291 | pCompProc oldComp=pComp0; |
---|
292 | |
---|
293 | if (!nolex) pComp0=pComp_RevLex; |
---|
294 | |
---|
295 | for (i=0;i<IDELEMS(id);i++) |
---|
296 | { |
---|
297 | if (id->m[i]!=NULL) |
---|
298 | { |
---|
299 | notFound = TRUE; |
---|
300 | newpos = actpos / 2; |
---|
301 | diff = (actpos+1) / 2; |
---|
302 | diff = (diff+1) / 2; |
---|
303 | lastcomp = pComp0(id->m[i],id->m[(*result)[newpos]]); |
---|
304 | if (lastcomp<0) |
---|
305 | { |
---|
306 | newpos -= diff; |
---|
307 | } |
---|
308 | else if (lastcomp>0) |
---|
309 | { |
---|
310 | newpos += diff; |
---|
311 | } |
---|
312 | else |
---|
313 | { |
---|
314 | notFound = FALSE; |
---|
315 | } |
---|
316 | while ((newpos>=0) && (newpos<actpos) && (notFound)) |
---|
317 | { |
---|
318 | newcomp = pComp0(id->m[i],id->m[(*result)[newpos]]); |
---|
319 | olddiff = diff; |
---|
320 | if (diff>1) |
---|
321 | { |
---|
322 | diff = (diff+1) / 2; |
---|
323 | if ((newcomp==1) |
---|
324 | && (actpos-newpos>1) |
---|
325 | && (diff>1) |
---|
326 | && (newpos+diff>=actpos)) |
---|
327 | { |
---|
328 | diff = actpos-newpos-1; |
---|
329 | } |
---|
330 | else if ((newcomp==-1) |
---|
331 | && (diff>1) |
---|
332 | && (newpos<diff)) |
---|
333 | { |
---|
334 | diff = newpos; |
---|
335 | } |
---|
336 | } |
---|
337 | if (newcomp<0) |
---|
338 | { |
---|
339 | if ((olddiff==1) && (lastcomp>0)) |
---|
340 | notFound = FALSE; |
---|
341 | else |
---|
342 | newpos -= diff; |
---|
343 | } |
---|
344 | else if (newcomp>0) |
---|
345 | { |
---|
346 | if ((olddiff==1) && (lastcomp<0)) |
---|
347 | { |
---|
348 | notFound = FALSE; |
---|
349 | newpos++; |
---|
350 | } |
---|
351 | else |
---|
352 | { |
---|
353 | newpos += diff; |
---|
354 | } |
---|
355 | } |
---|
356 | else |
---|
357 | { |
---|
358 | notFound = FALSE; |
---|
359 | } |
---|
360 | lastcomp = newcomp; |
---|
361 | if (diff==0) notFound=FALSE; /*hs*/ |
---|
362 | } |
---|
363 | if (newpos<0) newpos = 0; |
---|
364 | if (newpos>=actpos) |
---|
365 | { |
---|
366 | (*result)[actpos] = i; |
---|
367 | } |
---|
368 | else |
---|
369 | { |
---|
370 | for (j=actpos;j>newpos;j--) |
---|
371 | { |
---|
372 | (*result)[j] = (*result)[j-1]; |
---|
373 | } |
---|
374 | (*result)[newpos] = i; |
---|
375 | } |
---|
376 | actpos++; |
---|
377 | } |
---|
378 | } |
---|
379 | for (j=0;j<actpos;j++) (*result)[j]++; |
---|
380 | pComp0=oldComp; |
---|
381 | return result; |
---|
382 | } |
---|
383 | |
---|
384 | /*2 |
---|
385 | * concat the lists h1 and h2 without zeros |
---|
386 | */ |
---|
387 | ideal idSimpleAdd (ideal h1,ideal h2) |
---|
388 | { |
---|
389 | int i,j,r,l; |
---|
390 | ideal result; |
---|
391 | |
---|
392 | if (h1==NULL) return idCopy(h2); |
---|
393 | if (h2==NULL) return idCopy(h1); |
---|
394 | j = IDELEMS(h1); |
---|
395 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
---|
396 | i = IDELEMS(h2); |
---|
397 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
---|
398 | if (i+j==0) |
---|
399 | result = idInit(1,1); |
---|
400 | else |
---|
401 | result=idInit(i+j,1); |
---|
402 | if (h1->rank<h2->rank) |
---|
403 | result->rank = h2->rank; |
---|
404 | else |
---|
405 | result->rank = h1->rank; |
---|
406 | if (i+j==0) return result; |
---|
407 | r = 0; |
---|
408 | for (l=0; l<j; l++) |
---|
409 | { |
---|
410 | result->m[r] = pCopy(h1->m[l]); |
---|
411 | r++; |
---|
412 | } |
---|
413 | for (l=0; l<i; l++) |
---|
414 | { |
---|
415 | result->m[r] = pCopy(h2->m[l]); |
---|
416 | r++; |
---|
417 | } |
---|
418 | return result; |
---|
419 | } |
---|
420 | |
---|
421 | /*2 |
---|
422 | * h1 + h2 |
---|
423 | */ |
---|
424 | ideal idAdd (ideal h1,ideal h2) |
---|
425 | { |
---|
426 | ideal result = idSimpleAdd(h1,h2); |
---|
427 | ideal tmp = idCompactify(result); |
---|
428 | |
---|
429 | idDelete(&result); |
---|
430 | return tmp; |
---|
431 | } |
---|
432 | |
---|
433 | /*2 |
---|
434 | * h1 * h2 |
---|
435 | */ |
---|
436 | ideal idMult (ideal h1,ideal h2) |
---|
437 | { |
---|
438 | int i,j,k; |
---|
439 | ideal hh; |
---|
440 | |
---|
441 | j = IDELEMS(h1); |
---|
442 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
---|
443 | i = IDELEMS(h2); |
---|
444 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
---|
445 | j = j * i; |
---|
446 | if (j == 0) |
---|
447 | hh = idInit(1,1); |
---|
448 | else |
---|
449 | hh=idInit(j,1); |
---|
450 | if (h1->rank<h2->rank) |
---|
451 | hh->rank = h2->rank; |
---|
452 | else |
---|
453 | hh->rank = h1->rank; |
---|
454 | if (j==0) return hh; |
---|
455 | k = 0; |
---|
456 | for (i=0; i<IDELEMS(h1); i++) |
---|
457 | { |
---|
458 | if (h1->m[i] != NULL) |
---|
459 | { |
---|
460 | for (j=0; j<IDELEMS(h2); j++) |
---|
461 | { |
---|
462 | if (h2->m[j] != NULL) |
---|
463 | { |
---|
464 | hh->m[k] = pMult(pCopy(h1->m[i]),pCopy(h2->m[j])); |
---|
465 | k++; |
---|
466 | } |
---|
467 | } |
---|
468 | } |
---|
469 | } |
---|
470 | { |
---|
471 | ideal tmp = idCompactify(hh); |
---|
472 | idDelete(&hh); |
---|
473 | return tmp; |
---|
474 | return hh; |
---|
475 | } |
---|
476 | } |
---|
477 | |
---|
478 | /*2 |
---|
479 | *returns true if h is the zero ideal |
---|
480 | */ |
---|
481 | BOOLEAN idIs0 (ideal h) |
---|
482 | { |
---|
483 | int i; |
---|
484 | |
---|
485 | if (h == NULL) return TRUE; |
---|
486 | i = IDELEMS(h); |
---|
487 | while ((i > 0) && (h->m[i-1] == NULL)) |
---|
488 | { |
---|
489 | i--; |
---|
490 | } |
---|
491 | if (i == 0) |
---|
492 | return TRUE; |
---|
493 | else |
---|
494 | return FALSE; |
---|
495 | } |
---|
496 | |
---|
497 | /*2 |
---|
498 | * return the maximal component number found in any polynomial in s |
---|
499 | */ |
---|
500 | int idRankFreeModule (ideal s) |
---|
501 | { |
---|
502 | if (s!=NULL) |
---|
503 | { |
---|
504 | int j=0; |
---|
505 | int l=IDELEMS(s); |
---|
506 | poly *p=s->m; |
---|
507 | int k; |
---|
508 | |
---|
509 | for (; l != 0; l--) |
---|
510 | { |
---|
511 | if (*p!=NULL) |
---|
512 | { |
---|
513 | k = pMaxComp(*p); |
---|
514 | if (k>j) j = k; |
---|
515 | } |
---|
516 | p++; |
---|
517 | } |
---|
518 | return j; |
---|
519 | } |
---|
520 | return -1; |
---|
521 | } |
---|
522 | |
---|
523 | /*2 |
---|
524 | *returns true if id is homogenous with respect to the aktual weights |
---|
525 | */ |
---|
526 | BOOLEAN idHomIdeal (ideal id, ideal Q) |
---|
527 | { |
---|
528 | int i; |
---|
529 | BOOLEAN b; |
---|
530 | if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE; |
---|
531 | i = 0; |
---|
532 | b = TRUE; |
---|
533 | while ((i < IDELEMS(id)) && b) |
---|
534 | { |
---|
535 | b = pIsHomogeneous(id->m[i]); |
---|
536 | i++; |
---|
537 | } |
---|
538 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
---|
539 | { |
---|
540 | i=0; |
---|
541 | while ((i < IDELEMS(Q)) && b) |
---|
542 | { |
---|
543 | b = pIsHomogeneous(Q->m[i]); |
---|
544 | i++; |
---|
545 | } |
---|
546 | } |
---|
547 | return b; |
---|
548 | } |
---|
549 | |
---|
550 | /*2 |
---|
551 | *returns a minimized set of generators of h1 |
---|
552 | */ |
---|
553 | ideal idMinBase (ideal h1) |
---|
554 | { |
---|
555 | ideal h2, h3,h4,e; |
---|
556 | int j,k; |
---|
557 | int i,l,ll; |
---|
558 | intvec * wth; |
---|
559 | BOOLEAN homog; |
---|
560 | |
---|
561 | homog = idHomModule(h1,currQuotient,&wth); |
---|
562 | if ((currRing->OrdSgn == 1) && (!homog)) |
---|
563 | { |
---|
564 | Warn("minbase applies only to the local or homogeneous case"); |
---|
565 | e=idCopy(h1); |
---|
566 | return e; |
---|
567 | } |
---|
568 | if ((currRing->OrdSgn == 1) && (homog)) |
---|
569 | { |
---|
570 | lists re=min_std(h1,currQuotient,(tHomog)homog,&wth,NULL,0,2); |
---|
571 | h2 = (ideal)re->m[1].data; |
---|
572 | re->m[1].data = NULL; |
---|
573 | re->m[1].rtyp = NONE; |
---|
574 | re->Clean(); |
---|
575 | return h2; |
---|
576 | } |
---|
577 | e=idInit(1,h1->rank); |
---|
578 | if (idIs0(h1)) |
---|
579 | { |
---|
580 | return e; |
---|
581 | } |
---|
582 | pEnlargeSet(&(e->m),IDELEMS(e),15); |
---|
583 | IDELEMS(e) = 16; |
---|
584 | h2 = std(h1,currQuotient,isNotHomog,NULL); |
---|
585 | h3 = idMaxIdeal(); |
---|
586 | h4=idMult(h2,h3); |
---|
587 | idDelete(&h3); |
---|
588 | h3=std(h4,currQuotient,isNotHomog,NULL); |
---|
589 | k = IDELEMS(h3); |
---|
590 | while ((k > 0) && (h3->m[k-1] == NULL)) k--; |
---|
591 | j = -1; |
---|
592 | l = IDELEMS(h2); |
---|
593 | while ((l > 0) && (h2->m[l-1] == NULL)) l--; |
---|
594 | for (i=l-1; i>=0; i--) |
---|
595 | { |
---|
596 | if (h2->m[i] != NULL) |
---|
597 | { |
---|
598 | ll = 0; |
---|
599 | while ((ll < k) && ((h3->m[ll] == NULL) |
---|
600 | || !pDivisibleBy(h3->m[ll],h2->m[i]))) |
---|
601 | ll++; |
---|
602 | if (ll >= k) |
---|
603 | { |
---|
604 | j++; |
---|
605 | if (j > IDELEMS(e)-1) |
---|
606 | { |
---|
607 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
608 | IDELEMS(e) += 16; |
---|
609 | } |
---|
610 | e->m[j] = pCopy(h2->m[i]); |
---|
611 | } |
---|
612 | } |
---|
613 | } |
---|
614 | idDelete(&h2); |
---|
615 | idDelete(&h3); |
---|
616 | idDelete(&h4); |
---|
617 | if (currQuotient!=NULL) |
---|
618 | { |
---|
619 | h3=idInit(1,e->rank); |
---|
620 | h2=kNF(h3,currQuotient,e); |
---|
621 | idDelete(&h3); |
---|
622 | idDelete(&e); |
---|
623 | e=h2; |
---|
624 | } |
---|
625 | idSkipZeroes(e); |
---|
626 | return e; |
---|
627 | } |
---|
628 | |
---|
629 | /*2 |
---|
630 | *the minimal index of used variables - 1 |
---|
631 | */ |
---|
632 | int pLowVar (poly p) |
---|
633 | { |
---|
634 | int k,l,lex; |
---|
635 | |
---|
636 | if (p == NULL) return -1; |
---|
637 | |
---|
638 | k = 32000;/*a very large dummy value*/ |
---|
639 | while (p != NULL) |
---|
640 | { |
---|
641 | l = 1; |
---|
642 | lex = pGetExp(p,l); |
---|
643 | while ((l <= pVariables) && (lex == 0)) |
---|
644 | { |
---|
645 | l++; |
---|
646 | lex = pGetExp(p,l); |
---|
647 | } |
---|
648 | l--; |
---|
649 | if (l < k) k = l; |
---|
650 | pIter(p); |
---|
651 | } |
---|
652 | return k; |
---|
653 | } |
---|
654 | |
---|
655 | /*3 |
---|
656 | *multiplies p with t (!cas) or (t-1) |
---|
657 | *the index of t is:1, so we have to shift all variables |
---|
658 | *p is NOT in the actual ring, it has no t |
---|
659 | */ |
---|
660 | static poly pMultWithT (poly p,BOOLEAN cas) |
---|
661 | { |
---|
662 | /*qp is the working pointer in p*/ |
---|
663 | /*result is the result, qresult is the working pointer*/ |
---|
664 | /*pp is p in the actual ring(shifted), qpp the working pointer*/ |
---|
665 | poly result,qp,pp; |
---|
666 | poly qresult=NULL; |
---|
667 | poly qpp=NULL; |
---|
668 | int i,j,lex; |
---|
669 | number n; |
---|
670 | |
---|
671 | pp = NULL; |
---|
672 | result = NULL; |
---|
673 | qp = p; |
---|
674 | while (qp != NULL) |
---|
675 | { |
---|
676 | i = 0; |
---|
677 | if (result == NULL) |
---|
678 | {/*first monomial*/ |
---|
679 | result = pNew(); |
---|
680 | qresult = result; |
---|
681 | } |
---|
682 | else |
---|
683 | { |
---|
684 | qresult->next = pNew(); |
---|
685 | pIter(qresult); |
---|
686 | } |
---|
687 | for (j=pVariables-1; j>0; j--) |
---|
688 | { |
---|
689 | lex = pGetExp(qp,j); |
---|
690 | pSetExp(qresult,j+1,lex);/*copy all variables*/ |
---|
691 | } |
---|
692 | lex = pGetComp(qp); |
---|
693 | pSetComp(qresult,lex); |
---|
694 | n=nCopy(pGetCoeff(qp)); |
---|
695 | pSetCoeff0(qresult,n); |
---|
696 | qresult->next = NULL; |
---|
697 | pSetm(qresult); |
---|
698 | /*qresult is now qp brought into the actual ring*/ |
---|
699 | if (cas) |
---|
700 | { /*case: mult with t-1*/ |
---|
701 | pSetExp(qresult,1,0); |
---|
702 | pSetm(qresult); |
---|
703 | if (pp == NULL) |
---|
704 | { /*first monomial*/ |
---|
705 | pp = pCopy(qresult); |
---|
706 | qpp = pp; |
---|
707 | } |
---|
708 | else |
---|
709 | { |
---|
710 | qpp->next = pCopy(qresult); |
---|
711 | pIter(qpp); |
---|
712 | } |
---|
713 | pGetCoeff(qpp)=nNeg(pGetCoeff(qpp)); |
---|
714 | /*now qpp contains -1*qp*/ |
---|
715 | } |
---|
716 | pSetExp(qresult,1,1);/*this is mult. by t*/ |
---|
717 | pSetm(qresult); |
---|
718 | pIter(qp); |
---|
719 | } |
---|
720 | /* |
---|
721 | *now p is processed: |
---|
722 | *result contains t*p |
---|
723 | * if cas: pp contains -1*p (in the new ring) |
---|
724 | */ |
---|
725 | if (cas) qresult->next = pp; |
---|
726 | /* else qresult->next = NULL;*/ |
---|
727 | return result; |
---|
728 | } |
---|
729 | |
---|
730 | /*3 |
---|
731 | *deletes the place of t in p (t: variable with index 1) |
---|
732 | *p is NOT in the actual ring: it has pVariables+1 variables |
---|
733 | */ |
---|
734 | static poly pDivByT (poly * p,int size) |
---|
735 | { |
---|
736 | |
---|
737 | poly result=NULL, |
---|
738 | resultp=NULL , /** working pointer in result **/ |
---|
739 | pp; |
---|
740 | int i,j; |
---|
741 | |
---|
742 | while (*p != NULL) |
---|
743 | { |
---|
744 | i = 0; |
---|
745 | if (result == NULL) |
---|
746 | {/*the first monomial*/ |
---|
747 | result = pNew(); |
---|
748 | resultp = result; |
---|
749 | resultp->next = NULL; |
---|
750 | } |
---|
751 | else |
---|
752 | { |
---|
753 | resultp->next = pNew(); |
---|
754 | pIter(resultp); |
---|
755 | resultp->next = NULL; |
---|
756 | } |
---|
757 | for (j=1; j<=pVariables; j++) |
---|
758 | { |
---|
759 | pSetExp(resultp,j,pGetExp(*p,j+1)); |
---|
760 | } |
---|
761 | pSetComp(resultp,pGetComp(*p)); |
---|
762 | pSetCoeff0(resultp,pGetCoeff(*p)); |
---|
763 | pSetm(resultp); |
---|
764 | pp = (*p)->next; |
---|
765 | Free((ADDRESS)*p,size); |
---|
766 | *p = pp; |
---|
767 | } |
---|
768 | return result; |
---|
769 | } |
---|
770 | |
---|
771 | /*2 |
---|
772 | *dehomogenized the generators of the ideal id1 with the leading |
---|
773 | *monomial of p replaced by n |
---|
774 | */ |
---|
775 | ideal idDehomogen (ideal id1,poly p,number n) |
---|
776 | { |
---|
777 | int i; |
---|
778 | ideal result; |
---|
779 | |
---|
780 | if (idIs0(id1)) |
---|
781 | { |
---|
782 | return idInit(1,id1->rank); |
---|
783 | } |
---|
784 | result=idInit(IDELEMS(id1),id1->rank); |
---|
785 | for (i=0; i<IDELEMS(id1); i++) |
---|
786 | { |
---|
787 | result->m[i] = pDehomogen(id1->m[i],p,n); |
---|
788 | } |
---|
789 | return result; |
---|
790 | } |
---|
791 | |
---|
792 | /*2 |
---|
793 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
794 | */ |
---|
795 | void pShift (poly * p,int i) |
---|
796 | { |
---|
797 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
798 | int j = pMaxComp(*p),k = pMinComp(*p); |
---|
799 | |
---|
800 | if (j+i < 0) return ; |
---|
801 | while (qp1 != NULL) |
---|
802 | { |
---|
803 | if ((pGetComp(qp1)+i > 0) || ((j == -i) && (j == k))) |
---|
804 | { |
---|
805 | pSetComp(qp1,pGetComp(qp1)+i); |
---|
806 | qp2 = qp1; |
---|
807 | pIter(qp1); |
---|
808 | } |
---|
809 | else |
---|
810 | { |
---|
811 | if (qp2 == *p) |
---|
812 | { |
---|
813 | pIter(*p); |
---|
814 | qp2->next = NULL; |
---|
815 | pDelete(&qp2); |
---|
816 | qp2 = *p; |
---|
817 | qp1 = *p; |
---|
818 | } |
---|
819 | else |
---|
820 | { |
---|
821 | qp2->next = qp1->next; |
---|
822 | qp1->next = NULL; |
---|
823 | pDelete(&qp1); |
---|
824 | qp1 = qp2->next; |
---|
825 | } |
---|
826 | } |
---|
827 | } |
---|
828 | } |
---|
829 | |
---|
830 | /*2 |
---|
831 | *initialized a field with r numbers between beg and end for the |
---|
832 | *procedure idNextChoise |
---|
833 | */ |
---|
834 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
835 | { |
---|
836 | /*returns the first choise of r numbers between beg and end*/ |
---|
837 | int i; |
---|
838 | for (i=0; i<r; i++) |
---|
839 | { |
---|
840 | choise[i] = 0; |
---|
841 | } |
---|
842 | if (r <= end-beg+1) |
---|
843 | for (i=0; i<r; i++) |
---|
844 | { |
---|
845 | choise[i] = beg+i; |
---|
846 | } |
---|
847 | if (r > end-beg+1) |
---|
848 | *endch = TRUE; |
---|
849 | else |
---|
850 | *endch = FALSE; |
---|
851 | } |
---|
852 | |
---|
853 | /*2 |
---|
854 | *returns the next choise of r numbers between beg and end |
---|
855 | */ |
---|
856 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
857 | { |
---|
858 | int i = r-1,j; |
---|
859 | while ((i >= 0) && (choise[i] == end)) |
---|
860 | { |
---|
861 | i--; |
---|
862 | end--; |
---|
863 | } |
---|
864 | if (i == -1) |
---|
865 | *endch = TRUE; |
---|
866 | else |
---|
867 | { |
---|
868 | choise[i]++; |
---|
869 | for (j=i+1; j<r; j++) |
---|
870 | { |
---|
871 | choise[j] = choise[i]+j-i; |
---|
872 | } |
---|
873 | *endch = FALSE; |
---|
874 | } |
---|
875 | } |
---|
876 | |
---|
877 | /*2 |
---|
878 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
879 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
880 | * w.r.t. the algorithm of construction |
---|
881 | */ |
---|
882 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
883 | { |
---|
884 | int * localchoise,i,result=0; |
---|
885 | BOOLEAN b=FALSE; |
---|
886 | |
---|
887 | if (d<=1) return 1; |
---|
888 | localchoise=(int*)Alloc((d-1)*sizeof(int)); |
---|
889 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
890 | while (!b) |
---|
891 | { |
---|
892 | result++; |
---|
893 | i = 0; |
---|
894 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
895 | if (i>=t) |
---|
896 | { |
---|
897 | i = t+1; |
---|
898 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
899 | if (i>=d) |
---|
900 | { |
---|
901 | Free((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
902 | return result; |
---|
903 | } |
---|
904 | } |
---|
905 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
906 | } |
---|
907 | Free((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
908 | return 0; |
---|
909 | } |
---|
910 | |
---|
911 | /*2 |
---|
912 | *computes the binomial coefficient |
---|
913 | */ |
---|
914 | int binom (int n,int r) |
---|
915 | { |
---|
916 | int i,result; |
---|
917 | |
---|
918 | if (r==0) return 1; |
---|
919 | if (n-r<r) return binom(n,n-r); |
---|
920 | result = n-r+1; |
---|
921 | for (i=2;i<=r;i++) |
---|
922 | { |
---|
923 | result *= n-r+i; |
---|
924 | result /= i; |
---|
925 | } |
---|
926 | return result; |
---|
927 | } |
---|
928 | |
---|
929 | /*2 |
---|
930 | *the free module of rank i |
---|
931 | */ |
---|
932 | ideal idFreeModule (int i) |
---|
933 | { |
---|
934 | int j; |
---|
935 | ideal h; |
---|
936 | |
---|
937 | h=idInit(i,i); |
---|
938 | for (j=0; j<i; j++) |
---|
939 | { |
---|
940 | h->m[j] = pOne(); |
---|
941 | pSetComp(h->m[j],j+1); |
---|
942 | } |
---|
943 | return h; |
---|
944 | } |
---|
945 | |
---|
946 | /*2 |
---|
947 | * h3 := h1 intersect h2 |
---|
948 | */ |
---|
949 | ideal idSect (ideal h1,ideal h2) |
---|
950 | { |
---|
951 | ideal first=h2,second=h1,temp,temp1,result; |
---|
952 | int i,j,k,flength,slength,length,rank=min(h1->rank,h2->rank); |
---|
953 | intvec *w; |
---|
954 | poly p,q; |
---|
955 | |
---|
956 | if ((idIs0(h1)) && (idIs0(h2))) return idInit(1,rank); |
---|
957 | if (IDELEMS(h1)<IDELEMS(h2)) |
---|
958 | { |
---|
959 | first = h1; |
---|
960 | second = h2; |
---|
961 | } |
---|
962 | flength = idRankFreeModule(first); |
---|
963 | slength = idRankFreeModule(second); |
---|
964 | length = max(flength,slength); |
---|
965 | if (length==0) |
---|
966 | { |
---|
967 | length = 1; |
---|
968 | } |
---|
969 | temp = idInit(IDELEMS(first),1); |
---|
970 | j = IDELEMS(temp); |
---|
971 | while ((j>0) && (first->m[j-1]==NULL)) j--; |
---|
972 | k = 0; |
---|
973 | for (i=0;i<j;i++) |
---|
974 | { |
---|
975 | if (first->m[i]!=NULL) |
---|
976 | { |
---|
977 | temp->m[k] = pCopy(first->m[i]); |
---|
978 | q = pOne(); |
---|
979 | pSetComp(q,i+1+length); |
---|
980 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
981 | p = temp->m[k]; |
---|
982 | while (pNext(p)) pIter(p); |
---|
983 | pNext(p) = q; |
---|
984 | k++; |
---|
985 | } |
---|
986 | } |
---|
987 | pEnlargeSet(&(temp->m),IDELEMS(temp),j+IDELEMS(second)-IDELEMS(temp)); |
---|
988 | IDELEMS(temp) = j+IDELEMS(second); |
---|
989 | for (i=0;i<IDELEMS(second);i++) |
---|
990 | { |
---|
991 | if (second->m[i]!=NULL) |
---|
992 | { |
---|
993 | temp->m[k] = pCopy(second->m[i]); |
---|
994 | if (slength==0) pShift(&(temp->m[k]),1); |
---|
995 | k++; |
---|
996 | } |
---|
997 | } |
---|
998 | pSetSyzComp(length); |
---|
999 | temp1 = std(temp,currQuotient,testHomog,&w,NULL,length); |
---|
1000 | if (w!=NULL) delete w; |
---|
1001 | pSetSyzComp(0); |
---|
1002 | idDelete(&temp); |
---|
1003 | result = idInit(IDELEMS(temp1),rank); |
---|
1004 | j = 0; |
---|
1005 | for (i=0;i<IDELEMS(temp1);i++) |
---|
1006 | { |
---|
1007 | if ((temp1->m[i]!=NULL) |
---|
1008 | && (pGetComp(temp1->m[i])>length)) |
---|
1009 | { |
---|
1010 | p = temp1->m[i]; |
---|
1011 | //PrintS("die Syzygie ist: ");pWrite(p); |
---|
1012 | temp1->m[i] = NULL; |
---|
1013 | while (p!=NULL) |
---|
1014 | { |
---|
1015 | q = pNext(p); |
---|
1016 | pNext(p) = NULL; |
---|
1017 | k = pGetComp(p)-1-length; |
---|
1018 | pSetComp(p,0); |
---|
1019 | //PrintS("das %d-te Element: ",k);pWrite(first->m[k]); |
---|
1020 | result->m[j] = pAdd(result->m[j],pMult(pCopy(first->m[k]),p)); |
---|
1021 | p = q; |
---|
1022 | } |
---|
1023 | //PrintS("Generator ist: ");pWrite(result->m[j]); |
---|
1024 | j++; |
---|
1025 | } |
---|
1026 | } |
---|
1027 | idSkipZeroes(result); |
---|
1028 | return result; |
---|
1029 | } |
---|
1030 | |
---|
1031 | /*2 |
---|
1032 | * ideal/module intersection for a list of objects |
---|
1033 | * given as 'resolvente' |
---|
1034 | */ |
---|
1035 | ideal idMultSect(resolvente arg, int length) |
---|
1036 | { |
---|
1037 | int i,j=0,k=0,syzComp,l,maxrk=-1,realrki; |
---|
1038 | ideal bigmat,tempstd,result; |
---|
1039 | poly p; |
---|
1040 | int isIdeal=0; |
---|
1041 | intvec * w=NULL; |
---|
1042 | |
---|
1043 | /* find 0-ideals and max rank -----------------------------------*/ |
---|
1044 | for (i=0;i<length;i++) |
---|
1045 | { |
---|
1046 | if (!idIs0(arg[i])) |
---|
1047 | { |
---|
1048 | realrki=idRankFreeModule(arg[i]); |
---|
1049 | k++; |
---|
1050 | j += IDELEMS(arg[i]); |
---|
1051 | if (realrki>maxrk) maxrk = realrki; |
---|
1052 | } |
---|
1053 | else |
---|
1054 | { |
---|
1055 | if (arg[i]!=NULL) |
---|
1056 | { |
---|
1057 | return idInit(1,arg[i]->rank); |
---|
1058 | } |
---|
1059 | } |
---|
1060 | } |
---|
1061 | if (maxrk == 0) |
---|
1062 | { |
---|
1063 | isIdeal = 1; |
---|
1064 | maxrk = 1; |
---|
1065 | } |
---|
1066 | /* init -----------------------------------------------------------*/ |
---|
1067 | j += maxrk; |
---|
1068 | bigmat = idInit(j,(k+1)*maxrk); |
---|
1069 | syzComp = k*maxrk; |
---|
1070 | pSetSyzComp(syzComp); |
---|
1071 | /* create unit matrices ------------------------------------------*/ |
---|
1072 | for (i=0;i<maxrk;i++) |
---|
1073 | { |
---|
1074 | for (j=0;j<=k;j++) |
---|
1075 | { |
---|
1076 | p = pOne(); |
---|
1077 | pSetComp(p,i+1+j*maxrk); |
---|
1078 | pSetm(p); |
---|
1079 | bigmat->m[i] = pAdd(bigmat->m[i],p); |
---|
1080 | } |
---|
1081 | } |
---|
1082 | /* enter given ideals ------------------------------------------*/ |
---|
1083 | i = maxrk; |
---|
1084 | k = 0; |
---|
1085 | for (j=0;j<length;j++) |
---|
1086 | { |
---|
1087 | if (arg[j]!=NULL) |
---|
1088 | { |
---|
1089 | for (l=0;l<IDELEMS(arg[j]);l++) |
---|
1090 | { |
---|
1091 | if (arg[j]->m[l]!=NULL) |
---|
1092 | { |
---|
1093 | bigmat->m[i] = pCopy(arg[j]->m[l]); |
---|
1094 | pShift(&(bigmat->m[i]),k*maxrk+isIdeal); |
---|
1095 | i++; |
---|
1096 | } |
---|
1097 | } |
---|
1098 | k++; |
---|
1099 | } |
---|
1100 | } |
---|
1101 | /* std computation --------------------------------------------*/ |
---|
1102 | tempstd = std(bigmat,currQuotient,testHomog,&w,NULL,syzComp); |
---|
1103 | if (w!=NULL) delete w; |
---|
1104 | idDelete(&bigmat); |
---|
1105 | pSetSyzComp(0); |
---|
1106 | /* interprete result ----------------------------------------*/ |
---|
1107 | result = idInit(8,maxrk); |
---|
1108 | k = 0; |
---|
1109 | for (j=0;j<IDELEMS(tempstd);j++) |
---|
1110 | { |
---|
1111 | if ((tempstd->m[j]!=NULL) && (pGetComp(tempstd->m[j])>syzComp)) |
---|
1112 | { |
---|
1113 | if (k>=IDELEMS(result)) |
---|
1114 | { |
---|
1115 | pEnlargeSet(&(result->m),IDELEMS(result),8); |
---|
1116 | IDELEMS(result) += 8; |
---|
1117 | } |
---|
1118 | p = tempstd->m[j]; |
---|
1119 | tempstd->m[j] = NULL; |
---|
1120 | pShift(&p,-syzComp-isIdeal); |
---|
1121 | result->m[k] = p; |
---|
1122 | k++; |
---|
1123 | } |
---|
1124 | } |
---|
1125 | /* clean up ----------------------------------------------------*/ |
---|
1126 | idDelete(&tempstd); |
---|
1127 | idSkipZeroes(result); |
---|
1128 | return result; |
---|
1129 | } |
---|
1130 | |
---|
1131 | /*2 |
---|
1132 | *computes the rank of the free module in which h1 embeds |
---|
1133 | */ |
---|
1134 | int lengthFreeModule (ideal h1) |
---|
1135 | { |
---|
1136 | int i,j,k; |
---|
1137 | |
---|
1138 | if (idIs0(h1)) return 0; |
---|
1139 | k = -1; |
---|
1140 | for (i=0; i<IDELEMS(h1); i++) |
---|
1141 | { |
---|
1142 | j = pMaxComp(h1->m[i]); |
---|
1143 | if (j>k) k = j; |
---|
1144 | } |
---|
1145 | return k; |
---|
1146 | } |
---|
1147 | |
---|
1148 | /*2 |
---|
1149 | *computes syzygies of h1, |
---|
1150 | *if quot != NULL it computes in the quotient ring modulo "quot" |
---|
1151 | */ |
---|
1152 | ideal idPrepare (ideal h1,ideal quot, tHomog h, |
---|
1153 | int* syzcomp, int *quotgen, int *quotdim, intvec **w) |
---|
1154 | { |
---|
1155 | ideal h2, h3; |
---|
1156 | int i; |
---|
1157 | int j,k; |
---|
1158 | poly p,q; |
---|
1159 | BOOLEAN orderChanged=FALSE; |
---|
1160 | |
---|
1161 | if (idIs0(h1)) return NULL; |
---|
1162 | k = lengthFreeModule(h1); |
---|
1163 | if (*syzcomp<k) *syzcomp = k; |
---|
1164 | h2 = NULL; |
---|
1165 | h2=idCopy(h1); |
---|
1166 | i = IDELEMS(h2)-1; |
---|
1167 | //while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
1168 | if (k == 0) |
---|
1169 | { |
---|
1170 | for (j=0; j<=i; j++) pShift(&(h2->m[j]),1); |
---|
1171 | *syzcomp = 1; |
---|
1172 | } |
---|
1173 | h2->rank = *syzcomp+i+1; |
---|
1174 | for (j=0; j<=i; j++) |
---|
1175 | { |
---|
1176 | p = h2->m[j]; |
---|
1177 | q = pOne(); |
---|
1178 | #ifdef DRING |
---|
1179 | if (pDRING) { pdDFlag(q)=1; pSetm(q); } |
---|
1180 | #endif |
---|
1181 | pSetComp(q,*syzcomp+1+j); |
---|
1182 | if (p!=NULL) |
---|
1183 | { |
---|
1184 | while (pNext(p)) pIter(p); |
---|
1185 | p->next = q; |
---|
1186 | } |
---|
1187 | else |
---|
1188 | h2->m[j]=q; |
---|
1189 | } |
---|
1190 | if ((pOrdSgn!=1) || (h!=TRUE) || (*syzcomp>1)|| (pLexOrder)) |
---|
1191 | { |
---|
1192 | pSetSyzComp(*syzcomp); |
---|
1193 | orderChanged=TRUE; |
---|
1194 | } |
---|
1195 | else |
---|
1196 | { |
---|
1197 | for(j=0;(j<IDELEMS(h2) && (!orderChanged));j++) |
---|
1198 | { |
---|
1199 | if (h2->m[j] != NULL) |
---|
1200 | { |
---|
1201 | p=h2->m[j]; |
---|
1202 | while ((p!=NULL) |
---|
1203 | && (pGetComp(p)<=*syzcomp)) |
---|
1204 | { |
---|
1205 | if (pIsConstantComp(p)) |
---|
1206 | { |
---|
1207 | pSetSyzComp(*syzcomp); |
---|
1208 | orderChanged=TRUE; |
---|
1209 | break; |
---|
1210 | } |
---|
1211 | pIter(p); |
---|
1212 | } |
---|
1213 | } |
---|
1214 | } |
---|
1215 | } |
---|
1216 | // if (orderChanged) PrintS("order changed\n"); |
---|
1217 | // else PrintS("order not changed\n"); |
---|
1218 | #ifdef PDEBUG |
---|
1219 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
1220 | #endif |
---|
1221 | h3=std(h2,quot,h,w,NULL,*syzcomp); |
---|
1222 | //h3->rank = h2->rank; done by std -> initBuchMora -> initS |
---|
1223 | h3->rank-=*syzcomp; |
---|
1224 | idDelete(&h2); |
---|
1225 | if (orderChanged) pSetSyzComp(0); |
---|
1226 | return h3; |
---|
1227 | } |
---|
1228 | |
---|
1229 | ideal idSyzygies (ideal h1,ideal quot, tHomog h,intvec **w) |
---|
1230 | { |
---|
1231 | int d; |
---|
1232 | return idSyzygies(h1,quot,h,w,FALSE,d); |
---|
1233 | } |
---|
1234 | |
---|
1235 | ideal idSyzygies (ideal h1,ideal quot, tHomog h,intvec **w, |
---|
1236 | BOOLEAN setRegularity, int °) |
---|
1237 | { |
---|
1238 | ideal e, h3; |
---|
1239 | poly p; |
---|
1240 | int i, j, k=0, quotdim, quotgen,length=0,reg; |
---|
1241 | BOOLEAN isMonomial=TRUE; |
---|
1242 | |
---|
1243 | #ifdef PDEBUG |
---|
1244 | int ii; |
---|
1245 | for(ii=0;ii<IDELEMS(h1);ii++) pTest(h1->m[ii]); |
---|
1246 | if (quot!=NULL) |
---|
1247 | { |
---|
1248 | for(ii=0;ii<IDELEMS(quot);ii++) pTest(quot->m[ii]); |
---|
1249 | } |
---|
1250 | #endif |
---|
1251 | if (idIs0(h1)) |
---|
1252 | return idFreeModule(IDELEMS(h1)); |
---|
1253 | h3=idPrepare(h1,quot,h,&k,"gen,"dim,w); |
---|
1254 | if (h3==NULL) |
---|
1255 | return idFreeModule(IDELEMS(h1)); |
---|
1256 | i = -1; |
---|
1257 | e=idInit(16,h3->rank); |
---|
1258 | for (j=0; j<IDELEMS(h3); j++) |
---|
1259 | { |
---|
1260 | if (h3->m[j] != NULL) |
---|
1261 | { |
---|
1262 | if (pMinComp(h3->m[j]) > k) |
---|
1263 | { |
---|
1264 | p = h3->m[j]; |
---|
1265 | h3->m[j]=NULL; |
---|
1266 | pShift(&p,-k); |
---|
1267 | if (p!=NULL) |
---|
1268 | { |
---|
1269 | i++; |
---|
1270 | if (i+1 >= IDELEMS(e)) |
---|
1271 | { |
---|
1272 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
1273 | IDELEMS(e) += 16; |
---|
1274 | } |
---|
1275 | e->m[i] = p; |
---|
1276 | } |
---|
1277 | } |
---|
1278 | else |
---|
1279 | { |
---|
1280 | isMonomial=isMonomial && (pNext(h3->m[j])==NULL); |
---|
1281 | pDelete(&pNext(h3->m[j])); |
---|
1282 | } |
---|
1283 | } |
---|
1284 | } |
---|
1285 | if ((!isMonomial) && (!TEST_OPT_NOTREGULARITY) && (setRegularity) && (h==isHomog)) |
---|
1286 | { |
---|
1287 | idSkipZeroes(h3); |
---|
1288 | resolvente res = sySchreyerResolvente(h3,-1,&length,TRUE); |
---|
1289 | intvec * dummy = syBetti(res,length,®, *w); |
---|
1290 | deg = reg+2; |
---|
1291 | delete dummy; |
---|
1292 | for (j=0;j<length;j++) |
---|
1293 | { |
---|
1294 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
1295 | } |
---|
1296 | Free((ADDRESS)res,length*sizeof(ideal)); |
---|
1297 | } |
---|
1298 | idDelete(&h3); |
---|
1299 | idSkipZeroes(e); |
---|
1300 | return e; |
---|
1301 | } |
---|
1302 | |
---|
1303 | /*2 |
---|
1304 | * computes syzygies and minimizes the input (h1) |
---|
1305 | * ONLY used in syMinRes |
---|
1306 | */ |
---|
1307 | ideal idSyzMin (ideal h1,ideal quot, tHomog h,intvec **w, |
---|
1308 | BOOLEAN setRegularity, int °) |
---|
1309 | { |
---|
1310 | ideal e, h3; |
---|
1311 | poly p; |
---|
1312 | intvec * reord; |
---|
1313 | int i, l=0, j, k=0, quotdim, quotgen,length=0,reg; |
---|
1314 | BOOLEAN isMonomial=TRUE; |
---|
1315 | |
---|
1316 | if (idIs0(h1)) |
---|
1317 | return idFreeModule(1); |
---|
1318 | //PrintS("h1 vorher\n"); |
---|
1319 | //for (i=0;i<IDELEMS(h1);i++) |
---|
1320 | //{ |
---|
1321 | //Print("Element %d: ",i);pWrite(h1->m[i]); |
---|
1322 | //} |
---|
1323 | idSkipZeroes(h1); |
---|
1324 | h3=idPrepare(h1,quot,h,&k,"gen,"dim,w); |
---|
1325 | //PrintS("h1 nachher\n"); |
---|
1326 | //for (i=0;i<IDELEMS(h3);i++) |
---|
1327 | //{ |
---|
1328 | //Print("Element %d: ",i);pWrite(h3->m[i]); |
---|
1329 | //} |
---|
1330 | if (h3==NULL) |
---|
1331 | return idFreeModule(1); |
---|
1332 | for (i=IDELEMS(h1);i!=0;i--) |
---|
1333 | pDelete(&(h1->m[i-1])); |
---|
1334 | reord = new intvec(IDELEMS(h1)+1); |
---|
1335 | i = -1; |
---|
1336 | e=idInit(16,h3->rank); |
---|
1337 | for (j=0; j<IDELEMS(h3); j++) |
---|
1338 | { |
---|
1339 | if (h3->m[j] != NULL) |
---|
1340 | { |
---|
1341 | p = h3->m[j]; |
---|
1342 | if (pGetComp(p) > k) |
---|
1343 | { |
---|
1344 | h3->m[j]=NULL; |
---|
1345 | pShift(&p,-k); |
---|
1346 | if (p!=NULL) |
---|
1347 | { |
---|
1348 | i++; |
---|
1349 | if (i+1 >= IDELEMS(e)) |
---|
1350 | { |
---|
1351 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
1352 | IDELEMS(e) += 16; |
---|
1353 | } |
---|
1354 | e->m[i] = p; |
---|
1355 | } |
---|
1356 | } |
---|
1357 | else |
---|
1358 | { |
---|
1359 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p); |
---|
1360 | if (pIsConstantComp(pNext(p))) |
---|
1361 | { |
---|
1362 | (*reord)[pGetComp(pNext(p))-k] = l+1; |
---|
1363 | //Print("Element %d mit Comp %d: ",j,pGetComp(pNext(p))-k); |
---|
1364 | //pWrite(h3->m[j]); |
---|
1365 | h1->m[l] = h3->m[j]; |
---|
1366 | h3->m[j] = pCopy(h1->m[l]); |
---|
1367 | pDelete(&pNext(p)); |
---|
1368 | l++; |
---|
1369 | } |
---|
1370 | isMonomial=isMonomial && (pGetComp(pNext(h3->m[j]))>k); |
---|
1371 | pDelete(&pNext(h3->m[j])); |
---|
1372 | } |
---|
1373 | } |
---|
1374 | } |
---|
1375 | if ((!isMonomial) && (!TEST_OPT_NOTREGULARITY) && (setRegularity) && (h==isHomog)) |
---|
1376 | { |
---|
1377 | idSkipZeroes(h3); |
---|
1378 | resolvente res = sySchreyerResolvente(h3,0,&length); |
---|
1379 | intvec * dummy = syBetti(res,length,®, *w); |
---|
1380 | deg = reg+2; |
---|
1381 | delete dummy; |
---|
1382 | for (j=0;j<length;j++) |
---|
1383 | { |
---|
1384 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
1385 | } |
---|
1386 | Free((ADDRESS)res,length*sizeof(ideal)); |
---|
1387 | } |
---|
1388 | idDelete(&h3); |
---|
1389 | //PrintS("Komponententransformation: "); |
---|
1390 | //reord->show(); |
---|
1391 | //PrintLn(); |
---|
1392 | for (i=IDELEMS(e);i!=0;i--) |
---|
1393 | { |
---|
1394 | if (e->m[i-1]!=NULL) |
---|
1395 | { |
---|
1396 | p = e->m[i-1]; |
---|
1397 | while (p!=NULL) |
---|
1398 | { |
---|
1399 | j = pGetComp(p); |
---|
1400 | pSetComp(p,(*reord)[j]); |
---|
1401 | pIter(p); |
---|
1402 | } |
---|
1403 | e->m[i-1] = pOrdPolySchreyer(e->m[i-1]); |
---|
1404 | } |
---|
1405 | } |
---|
1406 | idSkipZeroes(e); |
---|
1407 | delete reord; |
---|
1408 | return e; |
---|
1409 | } |
---|
1410 | |
---|
1411 | /* |
---|
1412 | *computes a standard basis for h1 and stores the transformation matrix |
---|
1413 | * in ma |
---|
1414 | */ |
---|
1415 | ideal idLiftStd (ideal h1,ideal quot, matrix* ma, tHomog h) |
---|
1416 | { |
---|
1417 | int i, j, k=0, t, quotgen, inputIsIdeal=lengthFreeModule(h1); |
---|
1418 | ideal e, h3; |
---|
1419 | poly p=NULL, q, qq; |
---|
1420 | intvec *w=NULL; |
---|
1421 | |
---|
1422 | idDelete((ideal*)ma); |
---|
1423 | *ma=mpNew(1,0); |
---|
1424 | if (idIs0(h1)) |
---|
1425 | return idInit(1,h1->rank); |
---|
1426 | h3=idPrepare(h1,quot,h,&k,"gen,&i,&w); |
---|
1427 | if (w!=NULL) delete w; |
---|
1428 | i = 0; |
---|
1429 | for (j=0;j<IDELEMS(h3);j++) |
---|
1430 | { |
---|
1431 | if ((h3->m[j] != NULL) && (pMinComp(h3->m[j]) <= k)) |
---|
1432 | i++; |
---|
1433 | } |
---|
1434 | j = IDELEMS(h1); |
---|
1435 | idDelete((ideal*)ma); |
---|
1436 | *ma = mpNew(j,i); |
---|
1437 | i = -1; |
---|
1438 | e=idInit(16,h1->rank); |
---|
1439 | for (j=0; j<IDELEMS(h3); j++) |
---|
1440 | { |
---|
1441 | if ((h3->m[j] != NULL) && (pMinComp(h3->m[j]) <= k)) |
---|
1442 | { |
---|
1443 | q = h3->m[j]; |
---|
1444 | qq=q; |
---|
1445 | h3->m[j]=NULL; |
---|
1446 | while (pNext(q) != NULL) |
---|
1447 | { |
---|
1448 | if (pGetComp(pNext(q)) > k) |
---|
1449 | { |
---|
1450 | p = pNext(q); |
---|
1451 | pNext(q) = pNext(pNext(q)); |
---|
1452 | pNext(p) = NULL; |
---|
1453 | t=pGetComp(p); |
---|
1454 | pSetComp(p,0); |
---|
1455 | MATELEM(*ma,t-k,i+2) = pAdd(MATELEM(*ma,t-k,i+2),p); |
---|
1456 | } |
---|
1457 | else |
---|
1458 | { |
---|
1459 | pIter(q); |
---|
1460 | } |
---|
1461 | } |
---|
1462 | if (!inputIsIdeal) pShift(&qq,-1); |
---|
1463 | //if (quotgen != 0) |
---|
1464 | //{ |
---|
1465 | // q = kNF(quot,qq); |
---|
1466 | // pDelete(&qq); |
---|
1467 | //} |
---|
1468 | //else |
---|
1469 | q = qq; |
---|
1470 | if (q !=NULL) |
---|
1471 | { |
---|
1472 | i++; |
---|
1473 | if (i+1 >= IDELEMS(e)) |
---|
1474 | { |
---|
1475 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
1476 | IDELEMS(e) += 16; |
---|
1477 | } |
---|
1478 | e->m[i] = q; |
---|
1479 | } |
---|
1480 | } |
---|
1481 | } |
---|
1482 | idDelete(&h3); |
---|
1483 | idSkipZeroes(e); |
---|
1484 | return e; |
---|
1485 | } |
---|
1486 | |
---|
1487 | /*2 |
---|
1488 | *computes a representation of the generators of submod with respect to those |
---|
1489 | * of mod |
---|
1490 | */ |
---|
1491 | ideal idLiftNonStB (ideal mod, ideal submod) |
---|
1492 | { |
---|
1493 | int lsmod =idRankFreeModule(submod), i, j, k, quotgen; |
---|
1494 | ideal result, h3, temp; |
---|
1495 | |
---|
1496 | if (idIs0(mod)) |
---|
1497 | return idInit(1,mod->rank); |
---|
1498 | |
---|
1499 | if ((idRankFreeModule(mod)!=0) && (lsmod==0)) lsmod=1; |
---|
1500 | k=lsmod; |
---|
1501 | //idSkipZeroes(mod); |
---|
1502 | h3=idPrepare(mod,currQuotient,(tHomog)FALSE,&k,"gen,&i,NULL); |
---|
1503 | for (j=0;j<IDELEMS(h3);j++) |
---|
1504 | { |
---|
1505 | if ((h3->m[j] != NULL) && (pMinComp(h3->m[j]) > k)) |
---|
1506 | pDelete(&(h3->m[j])); |
---|
1507 | } |
---|
1508 | idSkipZeroes(h3); |
---|
1509 | if (lsmod==0) |
---|
1510 | { |
---|
1511 | temp = idCopy(submod); |
---|
1512 | for (j=IDELEMS(temp);j>0;j--) |
---|
1513 | { |
---|
1514 | if (temp->m[j-1]!=NULL) |
---|
1515 | pShift(&(temp->m[j-1]),1); |
---|
1516 | } |
---|
1517 | } |
---|
1518 | else |
---|
1519 | { |
---|
1520 | temp = submod; |
---|
1521 | } |
---|
1522 | pSetSyzComp(k); |
---|
1523 | result = kNF(h3,currQuotient,temp,k); |
---|
1524 | result->rank = h3->rank; |
---|
1525 | idDelete(&h3); |
---|
1526 | if (lsmod==0) |
---|
1527 | idDelete(&temp); |
---|
1528 | pSetSyzComp(0); |
---|
1529 | for (j=0;j<IDELEMS(result);j++) |
---|
1530 | { |
---|
1531 | if (result->m[j]!=NULL) |
---|
1532 | { |
---|
1533 | if (pGetComp(result->m[j])<=k) |
---|
1534 | { |
---|
1535 | WerrorS("2nd module lies not in the first"); |
---|
1536 | idDelete(&result); |
---|
1537 | return idInit(1,1); |
---|
1538 | } |
---|
1539 | else |
---|
1540 | { |
---|
1541 | pShift(&(result->m[j]),-k); |
---|
1542 | pNeg(result->m[j]); |
---|
1543 | } |
---|
1544 | } |
---|
1545 | } |
---|
1546 | return result; |
---|
1547 | } |
---|
1548 | |
---|
1549 | /*2 |
---|
1550 | *computes a representation of the generators of submod with respect to those |
---|
1551 | * of mod which is given as standardbasis, |
---|
1552 | * uses currQuotient as the quotient ideal (if not NULL) |
---|
1553 | */ |
---|
1554 | ideal idLift (ideal mod,ideal submod) |
---|
1555 | { |
---|
1556 | ideal temp, result; |
---|
1557 | int j,k; |
---|
1558 | poly p,q; |
---|
1559 | BOOLEAN reported=FALSE; |
---|
1560 | |
---|
1561 | if (idIs0(mod)) return idInit(1,mod->rank); |
---|
1562 | k = lengthFreeModule(mod); |
---|
1563 | temp=idCopy(mod); |
---|
1564 | if (k == 0) |
---|
1565 | { |
---|
1566 | for (j=0; j<IDELEMS(temp); j++) |
---|
1567 | { |
---|
1568 | if (temp->m[j]!=NULL) pSetCompP(temp->m[j],1); |
---|
1569 | } |
---|
1570 | k = 1; |
---|
1571 | } |
---|
1572 | for (j=0; j<IDELEMS(temp); j++) |
---|
1573 | { |
---|
1574 | if (temp->m[j]!=NULL) |
---|
1575 | { |
---|
1576 | p = temp->m[j]; |
---|
1577 | q = pOne(); |
---|
1578 | pGetCoeff(q)=nNeg(pGetCoeff(q)); //set q to -1 |
---|
1579 | pSetComp(q,k+1+j); |
---|
1580 | while (pNext(p)) pIter(p); |
---|
1581 | pNext(p) = q; |
---|
1582 | } |
---|
1583 | } |
---|
1584 | result=idInit(IDELEMS(submod),submod->rank); |
---|
1585 | pSetSyzComp(k); |
---|
1586 | for (j=0; j<IDELEMS(submod); j++) |
---|
1587 | { |
---|
1588 | if (submod->m[j]!=NULL) |
---|
1589 | { |
---|
1590 | p = pCopy(submod->m[j]); |
---|
1591 | if (pGetComp(p)==0) pSetCompP(p,1); |
---|
1592 | q = kNF(temp,currQuotient,p); |
---|
1593 | pDelete(&p); |
---|
1594 | if (q!=NULL) |
---|
1595 | { |
---|
1596 | if (pMinComp(q)<=k) |
---|
1597 | { |
---|
1598 | if (!reported) |
---|
1599 | { |
---|
1600 | Warn("first module not a standardbasis"); |
---|
1601 | Warn("or second not a proper submodule"); |
---|
1602 | reported=TRUE; |
---|
1603 | } |
---|
1604 | pDelete(&q); |
---|
1605 | } |
---|
1606 | else |
---|
1607 | { |
---|
1608 | pShift(&q,-k); |
---|
1609 | result->m[j] = q; |
---|
1610 | } |
---|
1611 | } |
---|
1612 | } |
---|
1613 | } |
---|
1614 | pSetSyzComp(0); |
---|
1615 | //idSkipZeroes(result); |
---|
1616 | idDelete(&temp); |
---|
1617 | return result; |
---|
1618 | } |
---|
1619 | |
---|
1620 | /*2 |
---|
1621 | *computes the quotient of h1,h2 |
---|
1622 | */ |
---|
1623 | #ifdef OLD_QUOT |
---|
1624 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsSB) |
---|
1625 | { |
---|
1626 | int i,j = 0,l,ll,k,kkk,k1,k2,kmax; |
---|
1627 | ideal h3,h4; |
---|
1628 | poly p,q = NULL; |
---|
1629 | BOOLEAN b = FALSE; |
---|
1630 | |
---|
1631 | k1 = lengthFreeModule(h1); |
---|
1632 | k2 = lengthFreeModule(h2); |
---|
1633 | k=max(k1,k2); |
---|
1634 | if (k==0) { k = 1; b=TRUE; } |
---|
1635 | h4 = idInit(1,1); |
---|
1636 | for (i=0; i<IDELEMS(h2); i++) |
---|
1637 | { |
---|
1638 | if (h2->m[i] != NULL) |
---|
1639 | { |
---|
1640 | p = pCopy(h2->m[i]); |
---|
1641 | if (k2 == 0) |
---|
1642 | pShift(&p,j*k+1); |
---|
1643 | else |
---|
1644 | pShift(&p,j*k); |
---|
1645 | q = pAdd(q,p); |
---|
1646 | j++; |
---|
1647 | } |
---|
1648 | } |
---|
1649 | kmax = j*k+1; |
---|
1650 | p = pOne(); |
---|
1651 | pSetComp(p,kmax); |
---|
1652 | pSetSyzComp(kmax-1); |
---|
1653 | q = pAdd(q,p); |
---|
1654 | h4->m[0] = q; |
---|
1655 | if (k2 == 0) |
---|
1656 | { |
---|
1657 | if (k > IDELEMS(h4)) |
---|
1658 | { |
---|
1659 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
1660 | IDELEMS(h4) = k; |
---|
1661 | } |
---|
1662 | for (i=1; i<k; i++) |
---|
1663 | { |
---|
1664 | p = pCopy(h4->m[i-1]); |
---|
1665 | pShift(&p,1); |
---|
1666 | h4->m[i] = p; |
---|
1667 | } |
---|
1668 | } |
---|
1669 | kkk = IDELEMS(h4); |
---|
1670 | i = IDELEMS(h1); |
---|
1671 | while (h1->m[i-1] == NULL) i--; |
---|
1672 | for (l=0; l<i; l++) |
---|
1673 | { |
---|
1674 | if(h1->m[l]!=NULL) |
---|
1675 | { |
---|
1676 | for (ll=0; ll<j; ll++) |
---|
1677 | { |
---|
1678 | p = pCopy(h1->m[l]); |
---|
1679 | if (k1 == 0) |
---|
1680 | pShift(&p,ll*k+1); |
---|
1681 | else |
---|
1682 | pShift(&p,ll*k); |
---|
1683 | if (kkk >= IDELEMS(h4)) |
---|
1684 | { |
---|
1685 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
1686 | IDELEMS(h4) += 16; |
---|
1687 | } |
---|
1688 | h4->m[kkk] = p; |
---|
1689 | kkk++; |
---|
1690 | } |
---|
1691 | } |
---|
1692 | } |
---|
1693 | h3 = std(h4,currQuotient,(tHomog)FALSE,NULL,NULL,kmax-1); |
---|
1694 | pSetSyzComp(0); |
---|
1695 | idDelete(&h4); |
---|
1696 | for (i=0;i<IDELEMS(h3);i++) |
---|
1697 | { |
---|
1698 | if ((h3->m[i]!=NULL) && (pGetComp(h3->m[i])>=kmax)) |
---|
1699 | { |
---|
1700 | if (b) |
---|
1701 | pShift(&h3->m[i],-kmax); |
---|
1702 | else |
---|
1703 | pShift(&h3->m[i],-kmax+1); |
---|
1704 | } |
---|
1705 | else |
---|
1706 | pDelete(&h3->m[i]); |
---|
1707 | } |
---|
1708 | if (b) |
---|
1709 | h3->rank = 1; |
---|
1710 | else |
---|
1711 | h3->rank = h1->rank; |
---|
1712 | h4=idCompactify(h3); |
---|
1713 | idDelete(&h3); |
---|
1714 | return h4; |
---|
1715 | } |
---|
1716 | #else |
---|
1717 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb) |
---|
1718 | { |
---|
1719 | int i,j = 0,l,ll,k,kkk,k1,k2,kmax; |
---|
1720 | intvec * weights,* weights1; |
---|
1721 | ideal h3,h4,temph1; |
---|
1722 | poly p,q = NULL; |
---|
1723 | BOOLEAN resultIsIdeal = FALSE,addOnlyOne=TRUE; |
---|
1724 | tHomog hom=isNotHomog; |
---|
1725 | BITSET old_test=test; |
---|
1726 | |
---|
1727 | k1 = lengthFreeModule(h1); |
---|
1728 | k2 = lengthFreeModule(h2); |
---|
1729 | if (idIs0(h2)) |
---|
1730 | { |
---|
1731 | if (k1==0) |
---|
1732 | { |
---|
1733 | h3 = idInit(1,1); |
---|
1734 | h3->m[0] = pOne(); |
---|
1735 | } |
---|
1736 | else |
---|
1737 | h3 = idFreeModule(h1->rank); |
---|
1738 | return h3; |
---|
1739 | } |
---|
1740 | k=max(k1,k2); |
---|
1741 | if (k==0) |
---|
1742 | { |
---|
1743 | k = 1; |
---|
1744 | resultIsIdeal=TRUE; |
---|
1745 | } |
---|
1746 | else if ((k1>0)&&(k2>0)) |
---|
1747 | { |
---|
1748 | resultIsIdeal=TRUE; |
---|
1749 | } |
---|
1750 | hom = (tHomog)idHomModule(h1,currQuotient,&weights) ; |
---|
1751 | h4 = idInit(1,1); |
---|
1752 | for (i=0; i<IDELEMS(h2); i++) |
---|
1753 | { |
---|
1754 | if (h2->m[i] != NULL) |
---|
1755 | { |
---|
1756 | p = pCopy(h2->m[i]); |
---|
1757 | if (k2 == 0) |
---|
1758 | pShift(&p,j*k+1); |
---|
1759 | else |
---|
1760 | pShift(&p,j*k); |
---|
1761 | q = pAdd(q,p); |
---|
1762 | j++; |
---|
1763 | } |
---|
1764 | } |
---|
1765 | kmax = j*k+1; |
---|
1766 | p = pOne(); |
---|
1767 | pSetComp(p,kmax); |
---|
1768 | pSetSyzComp(kmax-1); |
---|
1769 | q = pAdd(q,p); |
---|
1770 | h4->m[0] = q; |
---|
1771 | if (k2 == 0) |
---|
1772 | { |
---|
1773 | if (k > IDELEMS(h4)) |
---|
1774 | { |
---|
1775 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
1776 | IDELEMS(h4) = k; |
---|
1777 | } |
---|
1778 | if (k>1) addOnlyOne = FALSE; |
---|
1779 | for (i=1; i<k; i++) |
---|
1780 | { |
---|
1781 | p = pCopy(h4->m[i-1]); |
---|
1782 | pShift(&p,1); |
---|
1783 | h4->m[i] = p; |
---|
1784 | } |
---|
1785 | } |
---|
1786 | kkk = IDELEMS(h4); |
---|
1787 | if (addOnlyOne && (!h1IsStb)) |
---|
1788 | temph1 = std(h1,currQuotient,hom,&weights,NULL); |
---|
1789 | else |
---|
1790 | temph1 = h1; |
---|
1791 | idTest(temph1); |
---|
1792 | i = IDELEMS(temph1); |
---|
1793 | while ((i>0) && (temph1->m[i-1]==NULL)) i--; |
---|
1794 | for (l=0; l<i; l++) |
---|
1795 | { |
---|
1796 | if(temph1->m[l]!=NULL) |
---|
1797 | { |
---|
1798 | for (ll=0; ll<j; ll++) |
---|
1799 | { |
---|
1800 | p = pCopy(temph1->m[l]); |
---|
1801 | if (k1 == 0) |
---|
1802 | pShift(&p,ll*k+1); |
---|
1803 | else |
---|
1804 | pShift(&p,ll*k); |
---|
1805 | if (kkk >= IDELEMS(h4)) |
---|
1806 | { |
---|
1807 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
1808 | IDELEMS(h4) += 16; |
---|
1809 | } |
---|
1810 | h4->m[kkk] = p; |
---|
1811 | kkk++; |
---|
1812 | } |
---|
1813 | } |
---|
1814 | } |
---|
1815 | idTest(h4); |
---|
1816 | if (addOnlyOne) |
---|
1817 | { |
---|
1818 | p = h4->m[0]; |
---|
1819 | for (i=0;i<IDELEMS(h4)-1;i++) |
---|
1820 | { |
---|
1821 | h4->m[i] = h4->m[i+1]; |
---|
1822 | } |
---|
1823 | h4->m[IDELEMS(h4)-1] = p; |
---|
1824 | idSkipZeroes(h4); |
---|
1825 | test |= Sy_bit(OPT_SB_1); |
---|
1826 | } |
---|
1827 | idTest(h4); |
---|
1828 | hom = (tHomog)idHomModule(h4,currQuotient,&weights1); |
---|
1829 | if (addOnlyOne) |
---|
1830 | { |
---|
1831 | h3 = std(h4,currQuotient,hom,&weights1,NULL,kmax-1,IDELEMS(h4)-1); |
---|
1832 | } |
---|
1833 | else |
---|
1834 | { |
---|
1835 | h3 = std(h4,currQuotient,hom,&weights1,NULL,kmax-1); |
---|
1836 | } |
---|
1837 | idTest(h3); |
---|
1838 | idDelete(&h4); |
---|
1839 | pSetSyzComp(0); |
---|
1840 | for (i=0;i<IDELEMS(h3);i++) |
---|
1841 | { |
---|
1842 | if ((h3->m[i]!=NULL) && (pGetComp(h3->m[i])>=kmax)) |
---|
1843 | { |
---|
1844 | if (resultIsIdeal) |
---|
1845 | pShift(&h3->m[i],-kmax); |
---|
1846 | else |
---|
1847 | pShift(&h3->m[i],-kmax+1); |
---|
1848 | } |
---|
1849 | else |
---|
1850 | pDelete(&h3->m[i]); |
---|
1851 | } |
---|
1852 | if (resultIsIdeal) |
---|
1853 | h3->rank = 1; |
---|
1854 | else |
---|
1855 | h3->rank = h1->rank; |
---|
1856 | idTest(h3); |
---|
1857 | idSkipZeroes(h3); |
---|
1858 | //h4=idCompactify(h3); |
---|
1859 | //idDelete(&h3); |
---|
1860 | if ((addOnlyOne) && (!h1IsStb)) |
---|
1861 | idDelete(&temph1); |
---|
1862 | if (weights!=NULL) delete weights; |
---|
1863 | if (weights1!=NULL) delete weights1; |
---|
1864 | test = old_test; |
---|
1865 | return h3; |
---|
1866 | } |
---|
1867 | #endif |
---|
1868 | |
---|
1869 | /*2 |
---|
1870 | *computes recursively all monomials of a certain degree |
---|
1871 | *in every step the actvar-th entry in the exponential |
---|
1872 | *vector is incremented and the other variables are |
---|
1873 | *computed by recursive calls of makemonoms |
---|
1874 | *if the last variable is reached, the difference to the |
---|
1875 | *degree is computed directly |
---|
1876 | *vars is the number variables |
---|
1877 | *actvar is the actual variable to handle |
---|
1878 | *deg is the degree of the monomials to compute |
---|
1879 | *monomdeg is the actual degree of the monomial in consideration |
---|
1880 | */ |
---|
1881 | static void makemonoms(int vars,int actvar,int deg,int monomdeg) |
---|
1882 | { |
---|
1883 | poly p; |
---|
1884 | int i=0; |
---|
1885 | |
---|
1886 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
1887 | { |
---|
1888 | idpower[idpowerpoint] = pOne(); |
---|
1889 | monomdeg = 0; |
---|
1890 | } |
---|
1891 | while (i<=deg) |
---|
1892 | { |
---|
1893 | if (deg == monomdeg) |
---|
1894 | { |
---|
1895 | pSetm(idpower[idpowerpoint]); |
---|
1896 | idpowerpoint++; |
---|
1897 | return; |
---|
1898 | } |
---|
1899 | if (actvar == vars) |
---|
1900 | { |
---|
1901 | pSetExp(idpower[idpowerpoint],actvar,deg-monomdeg); |
---|
1902 | pSetm(idpower[idpowerpoint]); |
---|
1903 | idpowerpoint++; |
---|
1904 | return; |
---|
1905 | } |
---|
1906 | else |
---|
1907 | { |
---|
1908 | p = pCopy(idpower[idpowerpoint]); |
---|
1909 | makemonoms(vars,actvar+1,deg,monomdeg); |
---|
1910 | idpower[idpowerpoint] = p; |
---|
1911 | } |
---|
1912 | monomdeg++; |
---|
1913 | pSetExp(idpower[idpowerpoint],actvar,pGetExp(idpower[idpowerpoint],actvar)+1); |
---|
1914 | pSetm(idpower[idpowerpoint]); |
---|
1915 | i++; |
---|
1916 | } |
---|
1917 | } |
---|
1918 | |
---|
1919 | /*2 |
---|
1920 | *returns the deg-th power of the maximal ideal of 0 |
---|
1921 | */ |
---|
1922 | ideal idMaxIdeal(int deg) |
---|
1923 | { |
---|
1924 | if (deg < 0) |
---|
1925 | { |
---|
1926 | WarnS("maxideal: power must be non-negative"); |
---|
1927 | } |
---|
1928 | if (deg < 1) |
---|
1929 | { |
---|
1930 | ideal I=idInit(1,1); |
---|
1931 | I->m[0]=pOne(); |
---|
1932 | return I; |
---|
1933 | } |
---|
1934 | if (deg == 1) |
---|
1935 | { |
---|
1936 | return idMaxIdeal(); |
---|
1937 | } |
---|
1938 | |
---|
1939 | int vars = currRing->N; |
---|
1940 | int i = binom(vars+deg-1,deg); |
---|
1941 | ideal id=idInit(i,1); |
---|
1942 | idpower = id->m; |
---|
1943 | idpowerpoint = 0; |
---|
1944 | makemonoms(vars,1,deg,0); |
---|
1945 | idpower = NULL; |
---|
1946 | idpowerpoint = 0; |
---|
1947 | return id; |
---|
1948 | } |
---|
1949 | |
---|
1950 | /*2 |
---|
1951 | *computes recursively all generators of a certain degree |
---|
1952 | *of the ideal "givenideal" |
---|
1953 | *elms is the number elements in the given ideal |
---|
1954 | *actelm is the actual element to handle |
---|
1955 | *deg is the degree of the power to compute |
---|
1956 | *gendeg is the actual degree of the generator in consideration |
---|
1957 | */ |
---|
1958 | static void makepotence(int elms,int actelm,int deg,int gendeg) |
---|
1959 | { |
---|
1960 | poly p; |
---|
1961 | int i=0; |
---|
1962 | |
---|
1963 | if ((idpowerpoint == 0) && (actelm ==1)) |
---|
1964 | { |
---|
1965 | idpower[idpowerpoint] = pOne(); |
---|
1966 | gendeg = 0; |
---|
1967 | } |
---|
1968 | while (i<=deg) |
---|
1969 | { |
---|
1970 | if (deg == gendeg) |
---|
1971 | { |
---|
1972 | idpowerpoint++; |
---|
1973 | return; |
---|
1974 | } |
---|
1975 | if (actelm == elms) |
---|
1976 | { |
---|
1977 | p=pPower(pCopy(givenideal[actelm-1]),deg-gendeg); |
---|
1978 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],p); |
---|
1979 | idpowerpoint++; |
---|
1980 | return; |
---|
1981 | } |
---|
1982 | else |
---|
1983 | { |
---|
1984 | p = pCopy(idpower[idpowerpoint]); |
---|
1985 | makepotence(elms,actelm+1,deg,gendeg); |
---|
1986 | idpower[idpowerpoint] = p; |
---|
1987 | } |
---|
1988 | gendeg++; |
---|
1989 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],pCopy(givenideal[actelm-1])); |
---|
1990 | i++; |
---|
1991 | } |
---|
1992 | } |
---|
1993 | |
---|
1994 | /*2 |
---|
1995 | *returns the deg-th power of the ideal gid |
---|
1996 | */ |
---|
1997 | //ideal idPower(ideal gid,int deg) |
---|
1998 | //{ |
---|
1999 | // int i; |
---|
2000 | // ideal id; |
---|
2001 | // |
---|
2002 | // if (deg < 1) deg = 1; |
---|
2003 | // i = binom(IDELEMS(gid)+deg-1,deg); |
---|
2004 | // id=idInit(i,1); |
---|
2005 | // idpower = id->m; |
---|
2006 | // givenideal = gid->m; |
---|
2007 | // idpowerpoint = 0; |
---|
2008 | // makepotence(IDELEMS(gid),1,deg,0); |
---|
2009 | // idpower = NULL; |
---|
2010 | // givenideal = NULL; |
---|
2011 | // idpowerpoint = 0; |
---|
2012 | // return id; |
---|
2013 | //} |
---|
2014 | static void idNextPotence(ideal given, ideal result, |
---|
2015 | int begin, int end, int deg, int restdeg, poly ap) |
---|
2016 | { |
---|
2017 | poly p; |
---|
2018 | int i; |
---|
2019 | |
---|
2020 | p = pPower(pCopy(given->m[begin]),restdeg); |
---|
2021 | i = result->nrows; |
---|
2022 | result->m[i] = pMult(pCopy(ap),p); |
---|
2023 | //PrintS("."); |
---|
2024 | (result->nrows)++; |
---|
2025 | if (result->nrows >= IDELEMS(result)) |
---|
2026 | { |
---|
2027 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
2028 | IDELEMS(result) += 16; |
---|
2029 | } |
---|
2030 | if (begin == end) return; |
---|
2031 | for (i=restdeg-1;i>=0;i--) |
---|
2032 | { |
---|
2033 | p = pPower(pCopy(given->m[begin]),i); |
---|
2034 | p = pMult(pCopy(ap),p); |
---|
2035 | idNextPotence(given, result, begin+1, end, deg, restdeg-i, p); |
---|
2036 | pDelete(&p); |
---|
2037 | } |
---|
2038 | } |
---|
2039 | |
---|
2040 | ideal idPower(ideal given,int exp) |
---|
2041 | { |
---|
2042 | ideal result,temp; |
---|
2043 | poly p1; |
---|
2044 | int i; |
---|
2045 | |
---|
2046 | if (idIs0(given)) return idInit(1,1); |
---|
2047 | temp = idCopy(given); |
---|
2048 | idSkipZeroes(temp); |
---|
2049 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
2050 | result = idInit(i,1); |
---|
2051 | result->nrows = 0; |
---|
2052 | //Print("ideal contains %d elements\n",i); |
---|
2053 | p1=pOne(); |
---|
2054 | idNextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1); |
---|
2055 | pDelete(&p1); |
---|
2056 | idDelete(&temp); |
---|
2057 | idSkipZeroes(result); |
---|
2058 | result->nrows = 1; |
---|
2059 | return result; |
---|
2060 | } |
---|
2061 | |
---|
2062 | /*2 |
---|
2063 | * eliminate delVar (product of vars) in h1 |
---|
2064 | */ |
---|
2065 | ideal idElimination (ideal h1,poly delVar,intvec *hilb) |
---|
2066 | { |
---|
2067 | int i,j=0,k,l; |
---|
2068 | ideal h,hh, h3; |
---|
2069 | int *ord,*block0,*block1; |
---|
2070 | int ordersize=2; |
---|
2071 | short **wv; |
---|
2072 | tHomog hom; |
---|
2073 | intvec * w; |
---|
2074 | |
---|
2075 | if (delVar==NULL) |
---|
2076 | { |
---|
2077 | return idCopy(h1); |
---|
2078 | } |
---|
2079 | if (currQuotient!=NULL) |
---|
2080 | { |
---|
2081 | WerrorS("cannot eliminate in a qring"); |
---|
2082 | return idCopy(h1); |
---|
2083 | } |
---|
2084 | if (idIs0(h1)) return idInit(1,h1->rank); |
---|
2085 | hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL |
---|
2086 | h3=idInit(16,h1->rank); |
---|
2087 | for (k=0;; k++) |
---|
2088 | { |
---|
2089 | if (currRing->order[k]!=0) ordersize++; |
---|
2090 | else break; |
---|
2091 | } |
---|
2092 | ord=(int*)Alloc0(ordersize*sizeof(int)); |
---|
2093 | block0=(int*)Alloc(ordersize*sizeof(int)); |
---|
2094 | block1=(int*)Alloc(ordersize*sizeof(int)); |
---|
2095 | for (k=0;; k++) |
---|
2096 | { |
---|
2097 | if (currRing->order[k]!=0) |
---|
2098 | { |
---|
2099 | block0[k+1] = currRing->block0[k]; |
---|
2100 | block1[k+1] = currRing->block1[k]; |
---|
2101 | ord[k+1] = currRing->order[k]; |
---|
2102 | } |
---|
2103 | else |
---|
2104 | break; |
---|
2105 | } |
---|
2106 | block0[0] = 1; |
---|
2107 | block1[0] = pVariables; |
---|
2108 | wv=(short**) Alloc(ordersize*sizeof(short**)); |
---|
2109 | memcpy4(wv+1,currRing->wvhdl,(ordersize-1)*sizeof(short**)); |
---|
2110 | wv[0]=(short*)Alloc0((pVariables+1)*sizeof(short)); |
---|
2111 | for (j=0;j<=pVariables;j++) |
---|
2112 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
2113 | ord[0] = ringorder_a; |
---|
2114 | pChangeRing(pVariables,currRing->OrdSgn,ord,block0,block1,wv); |
---|
2115 | h = idInit(IDELEMS(h1),1); |
---|
2116 | for (k=0;k<IDELEMS(h1);k++) h->m[k] = pOrdPoly(pCopy(h1->m[k])); |
---|
2117 | hh = std(h,NULL,hom,&w,hilb); |
---|
2118 | idDelete(&h); |
---|
2119 | pChangeRing(pVariables,currRing->OrdSgn,currRing->order, |
---|
2120 | currRing->block0,currRing->block1,currRing->wvhdl); |
---|
2121 | i = IDELEMS(hh)-1; |
---|
2122 | while ((i >= 0) && (hh->m[i] == NULL)) i--; |
---|
2123 | j = -1; |
---|
2124 | for (k=0; k<=i; k++) |
---|
2125 | { |
---|
2126 | l=pVariables; |
---|
2127 | while ((l>0) && (pGetExp(hh->m[k],l)*pGetExp(delVar,l)==0)) l--; |
---|
2128 | if (l==0) |
---|
2129 | { |
---|
2130 | j++; |
---|
2131 | if (j >= IDELEMS(h3)) |
---|
2132 | { |
---|
2133 | pEnlargeSet(&(h3->m),IDELEMS(h3),16); |
---|
2134 | IDELEMS(h3) += 16; |
---|
2135 | } |
---|
2136 | //pWrite(hh->m[k]); |
---|
2137 | h3->m[j] = pOrdPoly(hh->m[k]); |
---|
2138 | hh->m[k] = NULL; |
---|
2139 | //pWrite(h3->m[j]); |
---|
2140 | //PrintLn(); |
---|
2141 | } |
---|
2142 | } |
---|
2143 | idDelete(&hh); |
---|
2144 | idSkipZeroes(h3); |
---|
2145 | Free((ADDRESS)wv[0],(pVariables+1)*sizeof(short)); |
---|
2146 | Free((ADDRESS)wv,ordersize*sizeof(short**)); |
---|
2147 | Free((ADDRESS)ord,ordersize*sizeof(int)); |
---|
2148 | Free((ADDRESS)block0,ordersize*sizeof(int)); |
---|
2149 | Free((ADDRESS)block1,ordersize*sizeof(int)); |
---|
2150 | if (w!=NULL) |
---|
2151 | delete w; |
---|
2152 | return h3; |
---|
2153 | } |
---|
2154 | |
---|
2155 | /*2 |
---|
2156 | * compute all ar-minors of the matrix a |
---|
2157 | */ |
---|
2158 | ideal idMinors(matrix a, int ar) |
---|
2159 | { |
---|
2160 | int i,j,k,size; |
---|
2161 | int *rowchoise,*colchoise; |
---|
2162 | BOOLEAN rowch,colch; |
---|
2163 | ideal result; |
---|
2164 | matrix tmp; |
---|
2165 | poly p; |
---|
2166 | |
---|
2167 | i = binom(a->rows(),ar); |
---|
2168 | j = binom(a->cols(),ar); |
---|
2169 | |
---|
2170 | rowchoise=(int *)Alloc(ar*sizeof(int)); |
---|
2171 | colchoise=(int *)Alloc(ar*sizeof(int)); |
---|
2172 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
2173 | else size=i*j; |
---|
2174 | result=idInit(size,1); |
---|
2175 | tmp=mpNew(ar,ar); |
---|
2176 | k = 0; /* the index in result*/ |
---|
2177 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
2178 | while (!rowch) |
---|
2179 | { |
---|
2180 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
2181 | while (!colch) |
---|
2182 | { |
---|
2183 | for (i=1; i<=ar; i++) |
---|
2184 | { |
---|
2185 | for (j=1; j<=ar; j++) |
---|
2186 | { |
---|
2187 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
2188 | } |
---|
2189 | } |
---|
2190 | p = mpDet(tmp); |
---|
2191 | if (p!=NULL) |
---|
2192 | { |
---|
2193 | if (k>=size) |
---|
2194 | { |
---|
2195 | pEnlargeSet(&result->m,size,32); |
---|
2196 | size += 32; |
---|
2197 | } |
---|
2198 | result->m[k] = p; |
---|
2199 | k++; |
---|
2200 | } |
---|
2201 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
2202 | } |
---|
2203 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
2204 | } |
---|
2205 | /*delete the matrix tmp*/ |
---|
2206 | for (i=1; i<=ar; i++) |
---|
2207 | { |
---|
2208 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
2209 | } |
---|
2210 | idDelete((ideal*)&tmp); |
---|
2211 | if (k==0) |
---|
2212 | { |
---|
2213 | k=1; |
---|
2214 | result->m[0]=NULL; |
---|
2215 | } |
---|
2216 | Free((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
2217 | Free((ADDRESS)colchoise,ar*sizeof(int)); |
---|
2218 | pEnlargeSet(&result->m,size,k-size); |
---|
2219 | IDELEMS(result) = k; |
---|
2220 | return (result); |
---|
2221 | } |
---|
2222 | |
---|
2223 | /*2 |
---|
2224 | *returns TRUE if p is a unit element in the current ring |
---|
2225 | */ |
---|
2226 | BOOLEAN pIsUnit(poly p) |
---|
2227 | { |
---|
2228 | poly q=p; |
---|
2229 | int i,j; |
---|
2230 | BOOLEAN b; |
---|
2231 | |
---|
2232 | if (p == NULL) return FALSE; |
---|
2233 | if (currRing->OrdSgn == 1) |
---|
2234 | { |
---|
2235 | for (i=0;i<=pVariables;i++) |
---|
2236 | { |
---|
2237 | j = pGetExp(p,i); |
---|
2238 | if (j != 0) return FALSE; |
---|
2239 | } |
---|
2240 | if (pNext(p) !=NULL) return FALSE; |
---|
2241 | } |
---|
2242 | else |
---|
2243 | { |
---|
2244 | b = FALSE; |
---|
2245 | while ((! b) && (q != NULL)) |
---|
2246 | { |
---|
2247 | i = 0; |
---|
2248 | j = pGetExp(p,i); |
---|
2249 | while ((i<=pVariables) && (j == 0)) |
---|
2250 | { |
---|
2251 | i++; |
---|
2252 | j = pGetExp(p,i); |
---|
2253 | } |
---|
2254 | if (i>pVariables) b = TRUE; |
---|
2255 | q = pNext(q); |
---|
2256 | } |
---|
2257 | return b; |
---|
2258 | } |
---|
2259 | return TRUE; |
---|
2260 | } |
---|
2261 | |
---|
2262 | /*2 |
---|
2263 | *skips all zeroes and double elements, searches also for units |
---|
2264 | */ |
---|
2265 | ideal idCompactify(ideal id) |
---|
2266 | { |
---|
2267 | ideal result = NULL; |
---|
2268 | int i,j; |
---|
2269 | BOOLEAN b=FALSE; |
---|
2270 | |
---|
2271 | result=idCopy(id); |
---|
2272 | i = 0; |
---|
2273 | while ((! b) && (i<IDELEMS(result))) |
---|
2274 | { |
---|
2275 | b=pIsUnit(result->m[i]); |
---|
2276 | i++; |
---|
2277 | } |
---|
2278 | if (b) |
---|
2279 | { |
---|
2280 | for (i=0;i<IDELEMS(result);i++) |
---|
2281 | pDelete(&result->m[i]); |
---|
2282 | result->m[0]=pOne(); |
---|
2283 | } |
---|
2284 | else |
---|
2285 | { |
---|
2286 | for (i=1;i<IDELEMS(result);i++) |
---|
2287 | { |
---|
2288 | if (result->m[i]!=NULL) |
---|
2289 | { |
---|
2290 | for (j=0;j<i;j++) |
---|
2291 | { |
---|
2292 | if ((result->m[j]!=NULL) |
---|
2293 | && (pComparePolys(result->m[i],result->m[j]))) |
---|
2294 | { |
---|
2295 | pDelete(&(result->m[j])); |
---|
2296 | } |
---|
2297 | } |
---|
2298 | } |
---|
2299 | } |
---|
2300 | } |
---|
2301 | idSkipZeroes(result); |
---|
2302 | return result; |
---|
2303 | } |
---|
2304 | |
---|
2305 | /*2 |
---|
2306 | *returns TRUE if id1 is a submodule of id2 |
---|
2307 | */ |
---|
2308 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
2309 | { |
---|
2310 | int i; |
---|
2311 | poly p; |
---|
2312 | |
---|
2313 | if (idIs0(id1)) return TRUE; |
---|
2314 | for (i=0;i<IDELEMS(id1);i++) |
---|
2315 | { |
---|
2316 | if (id1->m[i] != NULL) |
---|
2317 | { |
---|
2318 | p = kNF(id2,currQuotient,id1->m[i]); |
---|
2319 | if (p != NULL) |
---|
2320 | { |
---|
2321 | pDelete(&p); |
---|
2322 | return FALSE; |
---|
2323 | } |
---|
2324 | } |
---|
2325 | } |
---|
2326 | return TRUE; |
---|
2327 | } |
---|
2328 | |
---|
2329 | /*2 |
---|
2330 | * returns the ideals of initial terms |
---|
2331 | */ |
---|
2332 | ideal idHead(ideal h) |
---|
2333 | { |
---|
2334 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
2335 | int i; |
---|
2336 | |
---|
2337 | for (i=0; i< IDELEMS(h); i++) |
---|
2338 | { |
---|
2339 | if (h->m[i]) m->m[i]=pHead(h->m[i]); |
---|
2340 | } |
---|
2341 | return m; |
---|
2342 | } |
---|
2343 | |
---|
2344 | ideal idHomogen(ideal h, int varnum) |
---|
2345 | { |
---|
2346 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
2347 | int i; |
---|
2348 | |
---|
2349 | for (i=0; i< IDELEMS(h); i++) |
---|
2350 | { |
---|
2351 | m->m[i]=pHomogen(h->m[i],varnum); |
---|
2352 | } |
---|
2353 | return m; |
---|
2354 | } |
---|
2355 | |
---|
2356 | /*------------------type conversions----------------*/ |
---|
2357 | ideal idVec2Ideal(poly vec) |
---|
2358 | { |
---|
2359 | ideal result=idInit(1,1); |
---|
2360 | Free((ADDRESS)result->m,sizeof(poly)); |
---|
2361 | result->m=NULL; // remove later |
---|
2362 | pVec2Polys(vec, &(result->m), &(IDELEMS(result))); |
---|
2363 | return result; |
---|
2364 | } |
---|
2365 | |
---|
2366 | ideal idMatrix2Module(matrix mat) |
---|
2367 | { |
---|
2368 | ideal result = idInit(MATCOLS(mat),MATROWS(mat)); |
---|
2369 | int i,j; |
---|
2370 | poly h; |
---|
2371 | #ifdef DRING |
---|
2372 | poly p; |
---|
2373 | #endif |
---|
2374 | |
---|
2375 | for(j=0;j<MATCOLS(mat);j++) /* j is also index in result->m */ |
---|
2376 | { |
---|
2377 | for (i=1;i<=MATROWS(mat);i++) |
---|
2378 | { |
---|
2379 | h = MATELEM(mat,i,j+1); |
---|
2380 | if (h!=NULL) |
---|
2381 | { |
---|
2382 | MATELEM(mat,i,j+1)=NULL; |
---|
2383 | pSetCompP(h,i); |
---|
2384 | #ifdef DRING |
---|
2385 | pdSetDFlag(h,0); |
---|
2386 | #endif |
---|
2387 | result->m[j] = pAdd(result->m[j],h); |
---|
2388 | } |
---|
2389 | } |
---|
2390 | } |
---|
2391 | return result; |
---|
2392 | } |
---|
2393 | |
---|
2394 | /*2 |
---|
2395 | * converts a module into a matrix, destroyes the input |
---|
2396 | */ |
---|
2397 | matrix idModule2Matrix(ideal mod) |
---|
2398 | { |
---|
2399 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
2400 | int i,cp; |
---|
2401 | poly p,h; |
---|
2402 | |
---|
2403 | for(i=0;i<IDELEMS(mod);i++) |
---|
2404 | { |
---|
2405 | p=mod->m[i]; |
---|
2406 | mod->m[i]=NULL; |
---|
2407 | while (p!=NULL) |
---|
2408 | { |
---|
2409 | h=p; |
---|
2410 | pIter(p); |
---|
2411 | pNext(h)=NULL; |
---|
2412 | // cp = max(1,pGetComp(h)); // if used for ideals too |
---|
2413 | cp = pGetComp(h); |
---|
2414 | pSetComp(h,0); |
---|
2415 | #ifdef TEST |
---|
2416 | if (cp>mod->rank) |
---|
2417 | { |
---|
2418 | Print("## inv. rank %d -> %d\n",mod->rank,cp); |
---|
2419 | int k,l,o=mod->rank; |
---|
2420 | mod->rank=cp; |
---|
2421 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
2422 | for (l=1; l<=o; l++) |
---|
2423 | { |
---|
2424 | for (k=1; k<=IDELEMS(mod); k++) |
---|
2425 | { |
---|
2426 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
2427 | MATELEM(result,l,k)=NULL; |
---|
2428 | } |
---|
2429 | } |
---|
2430 | idDelete((ideal *)&result); |
---|
2431 | result=d; |
---|
2432 | } |
---|
2433 | #endif |
---|
2434 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
2435 | } |
---|
2436 | } |
---|
2437 | return result; |
---|
2438 | } |
---|
2439 | |
---|
2440 | matrix idModule2formatedMatrix(ideal mod,int rows, int cols) |
---|
2441 | { |
---|
2442 | matrix result = mpNew(rows,cols); |
---|
2443 | int i,cp,r=idRankFreeModule(mod),c=IDELEMS(mod); |
---|
2444 | poly p,h; |
---|
2445 | |
---|
2446 | if (r>rows) r = rows; |
---|
2447 | if (c>cols) c = cols; |
---|
2448 | for(i=0;i<c;i++) |
---|
2449 | { |
---|
2450 | p=mod->m[i]; |
---|
2451 | mod->m[i]=NULL; |
---|
2452 | while (p!=NULL) |
---|
2453 | { |
---|
2454 | h=p; |
---|
2455 | pIter(p); |
---|
2456 | pNext(h)=NULL; |
---|
2457 | cp = pGetComp(h); |
---|
2458 | if (cp<=r) |
---|
2459 | { |
---|
2460 | pSetComp(h,0); |
---|
2461 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
2462 | } |
---|
2463 | else |
---|
2464 | pDelete(&h); |
---|
2465 | } |
---|
2466 | } |
---|
2467 | idDelete(&mod); |
---|
2468 | return result; |
---|
2469 | } |
---|
2470 | |
---|
2471 | /*2 |
---|
2472 | * substitute the n-th variable by the monomial e in id |
---|
2473 | * destroy id |
---|
2474 | */ |
---|
2475 | ideal idSubst(ideal id, int n, poly e) |
---|
2476 | { |
---|
2477 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
2478 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
2479 | |
---|
2480 | res->rank = id->rank; |
---|
2481 | for(k--;k>=0;k--) |
---|
2482 | { |
---|
2483 | res->m[k]=pSubst(id->m[k],n,e); |
---|
2484 | id->m[k]=NULL; |
---|
2485 | } |
---|
2486 | idDelete(&id); |
---|
2487 | return res; |
---|
2488 | } |
---|
2489 | |
---|
2490 | BOOLEAN idHomModule(ideal m, ideal Q, intvec **w) |
---|
2491 | { |
---|
2492 | int i,j,cmax=2,order=0,ord,* diff,* iscom,diffmin=32000; |
---|
2493 | poly p=NULL; |
---|
2494 | int length=IDELEMS(m); |
---|
2495 | polyset P=m->m; |
---|
2496 | polyset F; |
---|
2497 | |
---|
2498 | if (w!=NULL) *w=NULL; |
---|
2499 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) return FALSE; |
---|
2500 | if (idIs0(m)) return TRUE; |
---|
2501 | F=(polyset)Alloc(length*sizeof(poly)); |
---|
2502 | for (i=length-1;i>=0;i--) |
---|
2503 | { |
---|
2504 | p=F[i]=P[i]; |
---|
2505 | cmax=max(cmax,pMaxComp(p)+1); |
---|
2506 | } |
---|
2507 | diff = (int *)Alloc0(cmax*sizeof(int)); |
---|
2508 | if (w!=NULL) *w=new intvec(cmax-1); |
---|
2509 | iscom = (int *)Alloc0(cmax*sizeof(int)); |
---|
2510 | i=0; |
---|
2511 | while (i<=length) |
---|
2512 | { |
---|
2513 | if (i<length) |
---|
2514 | { |
---|
2515 | p=F[i]; |
---|
2516 | while ((p!=NULL) && (!iscom[pGetComp(p)])) pIter(p); |
---|
2517 | } |
---|
2518 | if ((p==NULL) && (i<length)) |
---|
2519 | { |
---|
2520 | i++; |
---|
2521 | } |
---|
2522 | else |
---|
2523 | { |
---|
2524 | if (p==NULL) |
---|
2525 | { |
---|
2526 | i=0; |
---|
2527 | while ((i<length) && (F[i]==NULL)) i++; |
---|
2528 | if (i>=length) break; |
---|
2529 | p = F[i]; |
---|
2530 | } |
---|
2531 | //if (pLexOrder) |
---|
2532 | // order=pTotaldegree(p); |
---|
2533 | //else |
---|
2534 | // order = p->order; |
---|
2535 | order = pFDeg(p); |
---|
2536 | order += diff[pGetComp(p)]; |
---|
2537 | p = F[i]; |
---|
2538 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
2539 | F[i] = NULL; |
---|
2540 | i=0; |
---|
2541 | } |
---|
2542 | while (p!=NULL) |
---|
2543 | { |
---|
2544 | //if (pLexOrder) |
---|
2545 | // ord=pTotaldegree(p); |
---|
2546 | //else |
---|
2547 | // ord = p->order; |
---|
2548 | ord = pFDeg(p); |
---|
2549 | if (!iscom[pGetComp(p)]) |
---|
2550 | { |
---|
2551 | diff[pGetComp(p)] = order-ord; |
---|
2552 | iscom[pGetComp(p)] = 1; |
---|
2553 | /* |
---|
2554 | *PrintS("new diff: "); |
---|
2555 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
2556 | *PrintLn(); |
---|
2557 | *PrintS("new iscom: "); |
---|
2558 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
2559 | *PrintLn(); |
---|
2560 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
2561 | */ |
---|
2562 | } |
---|
2563 | else |
---|
2564 | { |
---|
2565 | /* |
---|
2566 | *PrintS("new diff: "); |
---|
2567 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
2568 | *PrintLn(); |
---|
2569 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
2570 | */ |
---|
2571 | if (order != ord+diff[pGetComp(p)]) |
---|
2572 | { |
---|
2573 | Free((ADDRESS) iscom,cmax*sizeof(int)); |
---|
2574 | Free((ADDRESS) diff,cmax*sizeof(int)); |
---|
2575 | Free((ADDRESS) F,length*sizeof(poly)); |
---|
2576 | delete *w;*w=NULL; |
---|
2577 | return FALSE; |
---|
2578 | } |
---|
2579 | } |
---|
2580 | pIter(p); |
---|
2581 | } |
---|
2582 | } |
---|
2583 | Free((ADDRESS) iscom,cmax*sizeof(int)); |
---|
2584 | Free((ADDRESS) F,length*sizeof(poly)); |
---|
2585 | for (i=1;i<cmax;i++) (**w)[i-1]=diff[i]; |
---|
2586 | for (i=1;i<cmax;i++) |
---|
2587 | { |
---|
2588 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
2589 | } |
---|
2590 | for (i=1;i<cmax;i++) |
---|
2591 | { |
---|
2592 | (**w)[i-1]=diff[i]-diffmin; |
---|
2593 | } |
---|
2594 | Free((ADDRESS) diff,cmax*sizeof(int)); |
---|
2595 | return TRUE; |
---|
2596 | } |
---|
2597 | |
---|
2598 | ideal idJet(ideal i,int d) |
---|
2599 | { |
---|
2600 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
2601 | int k; |
---|
2602 | for(k=0; k<IDELEMS(i); k++) |
---|
2603 | { |
---|
2604 | r->m[k]=pJet(i->m[k],d); |
---|
2605 | } |
---|
2606 | return r; |
---|
2607 | } |
---|
2608 | |
---|
2609 | ideal idJetW(ideal i,int d, intvec * iv) |
---|
2610 | { |
---|
2611 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
2612 | if (ecartWeights!=NULL) |
---|
2613 | { |
---|
2614 | WerrorS("cannot compute weighted jets now"); |
---|
2615 | } |
---|
2616 | else |
---|
2617 | { |
---|
2618 | short *w=iv2array(iv); |
---|
2619 | int k; |
---|
2620 | for(k=0; k<IDELEMS(i); k++) |
---|
2621 | { |
---|
2622 | r->m[k]=pJetW(i->m[k],d,w); |
---|
2623 | } |
---|
2624 | Free((ADDRESS)w,(pVariables+1)*sizeof(short)); |
---|
2625 | } |
---|
2626 | return r; |
---|
2627 | } |
---|
2628 | |
---|
2629 | matrix idDiff(matrix i, int k) |
---|
2630 | { |
---|
2631 | int e=MATCOLS(i)*MATROWS(i); |
---|
2632 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
2633 | int j; |
---|
2634 | for(j=0; j<e; j++) |
---|
2635 | { |
---|
2636 | r->m[j]=pDiff(i->m[j],k); |
---|
2637 | } |
---|
2638 | return r; |
---|
2639 | } |
---|
2640 | |
---|
2641 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
2642 | { |
---|
2643 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
2644 | int i,j; |
---|
2645 | for(i=0; i<IDELEMS(I); i++) |
---|
2646 | { |
---|
2647 | for(j=0; j<IDELEMS(J); j++) |
---|
2648 | { |
---|
2649 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
2650 | } |
---|
2651 | } |
---|
2652 | return r; |
---|
2653 | } |
---|
2654 | |
---|
2655 | /*2 |
---|
2656 | * represents (h1+h2)/h2=h1/(h1 intersect h2) |
---|
2657 | */ |
---|
2658 | ideal idModulo (ideal h2,ideal h1) |
---|
2659 | { |
---|
2660 | ideal temp,temp1; |
---|
2661 | int i,j,k,rk,flength=0,slength,length; |
---|
2662 | intvec * w; |
---|
2663 | poly p,q; |
---|
2664 | |
---|
2665 | if (idIs0(h2)) |
---|
2666 | return idFreeModule(max(1,h2->ncols)); |
---|
2667 | if (!idIs0(h1)) |
---|
2668 | flength = idRankFreeModule(h1); |
---|
2669 | slength = idRankFreeModule(h2); |
---|
2670 | length = max(flength,slength); |
---|
2671 | if (length==0) |
---|
2672 | { |
---|
2673 | length = 1; |
---|
2674 | } |
---|
2675 | temp = idInit(IDELEMS(h2),1); |
---|
2676 | for (i=0;i<IDELEMS(h2);i++) |
---|
2677 | { |
---|
2678 | temp->m[i] = pCopy(h2->m[i]); |
---|
2679 | q = pOne(); |
---|
2680 | pSetComp(q,i+1+length); |
---|
2681 | if(temp->m[i]!=NULL) |
---|
2682 | { |
---|
2683 | if (slength==0) pShift(&(temp->m[i]),1); |
---|
2684 | p = temp->m[i]; |
---|
2685 | while (pNext(p)!=NULL) pIter(p); |
---|
2686 | pNext(p) = q; |
---|
2687 | } |
---|
2688 | else |
---|
2689 | temp->m[i]=q; |
---|
2690 | } |
---|
2691 | rk = k = IDELEMS(h2); |
---|
2692 | if (!idIs0(h1)) |
---|
2693 | { |
---|
2694 | pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1)); |
---|
2695 | IDELEMS(temp) += IDELEMS(h1); |
---|
2696 | for (i=0;i<IDELEMS(h1);i++) |
---|
2697 | { |
---|
2698 | if (h1->m[i]!=NULL) |
---|
2699 | { |
---|
2700 | temp->m[k] = pCopy(h1->m[i]); |
---|
2701 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
2702 | k++; |
---|
2703 | } |
---|
2704 | } |
---|
2705 | } |
---|
2706 | pSetSyzComp(length); |
---|
2707 | temp1 = std(temp,currQuotient,testHomog,&w,NULL,length); |
---|
2708 | pSetSyzComp(0); |
---|
2709 | idDelete(&temp); |
---|
2710 | if (w!=NULL) delete w; |
---|
2711 | for (i=0;i<IDELEMS(temp1);i++) |
---|
2712 | { |
---|
2713 | if ((temp1->m[i]!=NULL) |
---|
2714 | && (pGetComp(temp1->m[i])<=length)) |
---|
2715 | { |
---|
2716 | pDelete(&(temp1->m[i])); |
---|
2717 | } |
---|
2718 | else |
---|
2719 | { |
---|
2720 | pShift(&(temp1->m[i]),-length); |
---|
2721 | } |
---|
2722 | } |
---|
2723 | idSkipZeroes(temp1); |
---|
2724 | temp1->rank = rk; |
---|
2725 | return temp1; |
---|
2726 | } |
---|
2727 | |
---|
2728 | int idElem(ideal F) |
---|
2729 | { |
---|
2730 | int i=0,j=0; |
---|
2731 | |
---|
2732 | while(j<IDELEMS(F)) |
---|
2733 | { |
---|
2734 | if ((F->m)[j]!=NULL) i++; |
---|
2735 | j++; |
---|
2736 | } |
---|
2737 | return i; |
---|
2738 | } |
---|
2739 | |
---|
2740 | /* |
---|
2741 | *computes module-weights for liftings of homogeneous modules |
---|
2742 | */ |
---|
2743 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
2744 | { |
---|
2745 | if (idIs0(mod)) return new intvec(2); |
---|
2746 | int i=IDELEMS(mod); |
---|
2747 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
2748 | intvec *result = new intvec(i+1); |
---|
2749 | while (i>0) |
---|
2750 | { |
---|
2751 | (*result)[i]=pFDeg(mod->m[i])+(*weights)[pGetComp(mod->m[i])]; |
---|
2752 | } |
---|
2753 | return result; |
---|
2754 | } |
---|
2755 | |
---|
2756 | /*2 |
---|
2757 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
2758 | *with x_max,...,x_1) |
---|
2759 | */ |
---|
2760 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
2761 | { |
---|
2762 | int i; |
---|
2763 | ideal result; |
---|
2764 | |
---|
2765 | if (idIs0(kBase)) return NULL; |
---|
2766 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
2767 | *convert = idSort(kBase,FALSE); |
---|
2768 | for (i=0;i<(*convert)->length();i++) |
---|
2769 | { |
---|
2770 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
2771 | } |
---|
2772 | return result; |
---|
2773 | } |
---|
2774 | |
---|
2775 | /*2 |
---|
2776 | *returns the index of a given monom in the list of the special kbase |
---|
2777 | */ |
---|
2778 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
2779 | { |
---|
2780 | int j=IDELEMS(kbase); |
---|
2781 | |
---|
2782 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
2783 | if (j==0) return -1; |
---|
2784 | int i=pVariables; |
---|
2785 | while (i>=0) |
---|
2786 | { |
---|
2787 | while ((j>0) && (pGetExp(monom,i)<pGetExp(kbase->m[j-1],i))) j--; |
---|
2788 | if ((j==0) || (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i))) return -1; |
---|
2789 | if (i==0) |
---|
2790 | return j-1; |
---|
2791 | else |
---|
2792 | i--; |
---|
2793 | } |
---|
2794 | return -1; |
---|
2795 | } |
---|
2796 | |
---|
2797 | /*2 |
---|
2798 | *decomposes the monom in a part of coefficients described by the |
---|
2799 | *complement of how and a monom in variables occuring in how, the |
---|
2800 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
2801 | *exists) |
---|
2802 | */ |
---|
2803 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
2804 | { |
---|
2805 | int i; |
---|
2806 | poly coeff=pOne(), base=pOne(); |
---|
2807 | |
---|
2808 | for (i=1;i<=pVariables;i++) |
---|
2809 | { |
---|
2810 | if (pGetExp(how,i)>0) |
---|
2811 | { |
---|
2812 | pSetExp(base,i,pGetExp(monom,i)); |
---|
2813 | } |
---|
2814 | else |
---|
2815 | { |
---|
2816 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
2817 | } |
---|
2818 | } |
---|
2819 | pSetComp(base,pGetComp(monom)); |
---|
2820 | pSetm(base); |
---|
2821 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
2822 | pSetm(coeff); |
---|
2823 | *pos = idIndexOfKBase(base,kbase); |
---|
2824 | if (*pos<0) |
---|
2825 | pDelete(&coeff); |
---|
2826 | pDelete(&base); |
---|
2827 | return coeff; |
---|
2828 | } |
---|
2829 | |
---|
2830 | /*2 |
---|
2831 | *returns a matrix A of coefficients with kbase*A=arg |
---|
2832 | *if all monomials in variables of how occur in kbase |
---|
2833 | *the other are deleted |
---|
2834 | */ |
---|
2835 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
2836 | { |
---|
2837 | matrix result; |
---|
2838 | ideal tempKbase; |
---|
2839 | poly p,q; |
---|
2840 | intvec * convert; |
---|
2841 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
2842 | |
---|
2843 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
2844 | if (idIs0(arg)) |
---|
2845 | return mpNew(i,1); |
---|
2846 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
2847 | result = mpNew(i,j); |
---|
2848 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
2849 | for (k=0;k<j;k++) |
---|
2850 | { |
---|
2851 | p = arg->m[k]; |
---|
2852 | while (p!=NULL) |
---|
2853 | { |
---|
2854 | q = idDecompose(p,how,tempKbase,&pos); |
---|
2855 | if (pos>=0) |
---|
2856 | { |
---|
2857 | MATELEM(result,(*convert)[pos],k+1) = |
---|
2858 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
2859 | } |
---|
2860 | else |
---|
2861 | pDelete(&q); |
---|
2862 | p = pIter(p); |
---|
2863 | } |
---|
2864 | } |
---|
2865 | idDelete(&tempKbase); |
---|
2866 | return result; |
---|
2867 | } |
---|
2868 | |
---|
2869 | intvec * idQHomWeights(ideal id) |
---|
2870 | { |
---|
2871 | intvec * imat=new intvec(2*pVariables,pVariables,0); |
---|
2872 | poly actHead=NULL,wPoint=NULL; |
---|
2873 | int actIndex,i=-1,j=1,k; |
---|
2874 | BOOLEAN notReady=TRUE; |
---|
2875 | |
---|
2876 | while (notReady) |
---|
2877 | { |
---|
2878 | if (wPoint==NULL) |
---|
2879 | { |
---|
2880 | i++; |
---|
2881 | while ((i<IDELEMS(id)) |
---|
2882 | && ((id->m[i]==NULL) || (pNext(id->m[i])==NULL))) |
---|
2883 | i++; |
---|
2884 | if (i<IDELEMS(id)) |
---|
2885 | { |
---|
2886 | actHead = id->m[i]; |
---|
2887 | wPoint = pNext(actHead); |
---|
2888 | } |
---|
2889 | } |
---|
2890 | while ((wPoint!=NULL) && (j<=2*pVariables)) |
---|
2891 | { |
---|
2892 | for (k=1;k<=pVariables;k++) |
---|
2893 | IMATELEM(*imat,j,k) += pGetExp(actHead,k)-pGetExp(wPoint,k); |
---|
2894 | pIter(wPoint); |
---|
2895 | j++; |
---|
2896 | } |
---|
2897 | if ((i>=IDELEMS(id)) || (j>2*pVariables)) |
---|
2898 | { |
---|
2899 | ivTriangMat(imat,1,1); |
---|
2900 | j = ivFirstEmptyRow(imat); |
---|
2901 | if ((i>=IDELEMS(id)) || (j>pVariables)) notReady=FALSE; |
---|
2902 | } |
---|
2903 | } |
---|
2904 | intvec *result=NULL; |
---|
2905 | if (j<=pVariables) |
---|
2906 | { |
---|
2907 | result=ivSolveIntMat(imat); |
---|
2908 | } |
---|
2909 | //else |
---|
2910 | //{ |
---|
2911 | // WerrorS("not homogeneous"); |
---|
2912 | //} |
---|
2913 | delete imat; |
---|
2914 | return result; |
---|
2915 | } |
---|
2916 | |
---|
2917 | /*2 |
---|
2918 | * returns the presentation of an isomorphic, minimally |
---|
2919 | * embedded module |
---|
2920 | */ |
---|
2921 | ideal idMinEmbedding(ideal arg) |
---|
2922 | { |
---|
2923 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
2924 | |
---|
2925 | int i,j,k,pC; |
---|
2926 | poly p,q; |
---|
2927 | int rg=arg->rank; |
---|
2928 | ideal res = idCopy(arg); |
---|
2929 | intvec *indexMap=new intvec(rg+1); |
---|
2930 | intvec *toKill=new intvec(rg+1); |
---|
2931 | |
---|
2932 | loop |
---|
2933 | { |
---|
2934 | k = 0; |
---|
2935 | for (i=indexMap->length()-1;i>0;i--) |
---|
2936 | { |
---|
2937 | (*indexMap)[i] = i; |
---|
2938 | (*toKill)[i] = 0; |
---|
2939 | } |
---|
2940 | for (j=IDELEMS(res)-1;j>=0;j--) |
---|
2941 | { |
---|
2942 | if ((res->m[j]!=NULL) && (pIsConstantComp(res->m[j])) && |
---|
2943 | (pNext(res->m[j])==NULL)) |
---|
2944 | { |
---|
2945 | pC = pGetComp(res->m[j]); |
---|
2946 | if ((*toKill)[pC]==0) |
---|
2947 | { |
---|
2948 | rg--; |
---|
2949 | (*toKill)[pC] = 1; |
---|
2950 | for (i=indexMap->length()-1;i>=pC;i--) |
---|
2951 | (*indexMap)[i]--; |
---|
2952 | } |
---|
2953 | pDelete(&(res->m[j])); |
---|
2954 | k++; |
---|
2955 | } |
---|
2956 | } |
---|
2957 | idSkipZeroes(res); |
---|
2958 | if (k==0) break; |
---|
2959 | if (rg>0) |
---|
2960 | { |
---|
2961 | res->rank=rg; |
---|
2962 | for (j=IDELEMS(res)-1;j>=0;j--) |
---|
2963 | { |
---|
2964 | while ((res->m[j]!=NULL) && ((*toKill)[pGetComp(res->m[j])]==1)) |
---|
2965 | pDelete1(&res->m[j]); |
---|
2966 | p = res->m[j]; |
---|
2967 | while ((p!=NULL) && (pNext(p)!=NULL)) |
---|
2968 | { |
---|
2969 | pSetComp(p,(*indexMap)[pGetComp(p)]); |
---|
2970 | while ((pNext(p)!=NULL) && ((*toKill)[pGetComp(pNext(p))]==1)) |
---|
2971 | pDelete1(&pNext(p)); |
---|
2972 | pIter(p); |
---|
2973 | } |
---|
2974 | if (p!=NULL) pSetComp(p,(*indexMap)[pGetComp(p)]); |
---|
2975 | } |
---|
2976 | idSkipZeroes(res); |
---|
2977 | } |
---|
2978 | else |
---|
2979 | { |
---|
2980 | idDelete(&res); |
---|
2981 | res=idFreeModule(1); |
---|
2982 | break; |
---|
2983 | } |
---|
2984 | } |
---|
2985 | delete toKill; |
---|
2986 | delete indexMap; |
---|
2987 | return res; |
---|
2988 | } |
---|