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simpleideals.cc
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1/****************************************
2* Computer Algebra System SINGULAR *
3****************************************/
4/*
5* ABSTRACT - all basic methods to manipulate ideals
6*/
7
8
9/* includes */
10
11
12
13#include "misc/auxiliary.h"
14
15#include "misc/options.h"
16#include "misc/intvec.h"
17
18#include "matpol.h"
19
20#include "monomials/p_polys.h"
21#include "weight.h"
22#include "sbuckets.h"
23#include "clapsing.h"
24
25#include "simpleideals.h"
26
28
30/*collects the monomials in makemonoms, must be allocated befor*/
32/*index of the actual monomial in idpower*/
33
34/// initialise an ideal / module
35ideal idInit(int idsize, int rank)
36{
37 assume( idsize >= 0 && rank >= 0 );
38
40
41 IDELEMS(hh) = idsize; // ncols
42 hh->nrows = 1; // ideal/module!
43
44 hh->rank = rank; // ideal: 1, module: >= 0!
45
46 if (idsize>0)
47 hh->m = (poly *)omAlloc0(idsize*sizeof(poly));
48 else
49 hh->m = NULL;
50
51 return hh;
52}
53
54#ifdef PDEBUG
55// this is only for outputting an ideal within the debugger
56// therefor it accept the otherwise illegal id==NULL
57void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint)
58{
59 assume( debugPrint >= 0 );
60
61 if( id == NULL )
62 PrintS("(NULL)");
63 else
64 {
65 Print("Module of rank %ld,real rank %ld and %d generators.\n",
66 id->rank,id_RankFreeModule(id, lmRing, tailRing),IDELEMS(id));
67
68 int j = (id->ncols*id->nrows) - 1;
69 while ((j > 0) && (id->m[j]==NULL)) j--;
70 for (int i = 0; i <= j; i++)
71 {
72 Print("generator %d: ",i); p_wrp(id->m[i], lmRing, tailRing);PrintLn();
73 }
74 }
75}
76#endif
77
78/// index of generator with leading term in ground ring (if any);
79/// otherwise -1
80int id_PosConstant(ideal id, const ring r)
81{
82 id_Test(id, r);
83 const int N = IDELEMS(id) - 1;
84 const poly * m = id->m + N;
85
86 for (int k = N; k >= 0; --k, --m)
87 {
88 const poly p = *m;
89 if (p!=NULL)
90 if (p_LmIsConstantComp(p, r) == TRUE)
91 return k;
92 }
93
94 return -1;
95}
96
97/// initialise the maximal ideal (at 0)
99{
100 int nvars;
101#ifdef HAVE_SHIFTBBA
102 if (r->isLPring)
103 {
104 nvars = r->isLPring;
105 }
106 else
107#endif
108 {
109 nvars = rVar(r);
110 }
111 ideal hh = idInit(nvars, 1);
112 for (int l=nvars-1; l>=0; l--)
113 {
114 hh->m[l] = p_One(r);
115 p_SetExp(hh->m[l],l+1,1,r);
116 p_Setm(hh->m[l],r);
117 }
118 id_Test(hh, r);
119 return hh;
120}
121
122/// deletes an ideal/module/matrix
124{
125 if (*h == NULL)
126 return;
127
128 id_Test(*h, r);
129
130 const long elems = (long)(*h)->nrows * (long)(*h)->ncols;
131
132 if ( elems > 0 )
133 {
134 assume( (*h)->m != NULL );
135
136 if (r!=NULL)
137 {
138 long j = elems;
139 do
140 {
141 j--;
142 poly pp=((*h)->m[j]);
143 if (pp!=NULL) p_Delete(&pp, r);
144 }
145 while (j>0);
146 }
147
148 omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems);
149 }
150
152 *h=NULL;
153}
154
156{
157 const long elems = IDELEMS(*h);
158
159 assume( (*h)->m != NULL );
160
161 long j = elems;
162 do
163 {
164 j--;
165 poly pp=((*h)->m[j]);
166 if (pp!=NULL) p_Delete(&pp, r);
167 }
168 while (j>0);
169
170 omFree((ADDRESS)((*h)->m));
172 *h=NULL;
173}
174
175
176/// Shallowdeletes an ideal/matrix
178{
179 id_Test(*h, r);
180
181 if (*h == NULL)
182 return;
183
184 int j,elems;
185 elems=j=(*h)->nrows*(*h)->ncols;
186 if (j>0)
187 {
188 assume( (*h)->m != NULL );
189 do
190 {
191 p_ShallowDelete(&((*h)->m[--j]), r);
192 }
193 while (j>0);
194 omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems);
195 }
197 *h=NULL;
198}
199
200/// gives an ideal/module the minimal possible size
202{
203 assume (ide != NULL);
204
205 int k;
206 int j = -1;
207 int idelems=IDELEMS(ide);
209
210 for (k=0; k<idelems; k++)
211 {
212 if (ide->m[k] != NULL)
213 {
214 j++;
215 if (change)
216 {
217 ide->m[j] = ide->m[k];
218 ide->m[k] = NULL;
219 }
220 }
221 else
222 {
223 change=TRUE;
224 }
225 }
226 if (change)
227 {
228 if (j == -1)
229 j = 0;
230 j++;
231 pEnlargeSet(&(ide->m),idelems,j-idelems);
232 IDELEMS(ide) = j;
233 }
234}
235
236int idSkipZeroes0 (ideal ide) /*idSkipZeroes without realloc*/
237{
238 assume (ide != NULL);
239
240 int k;
241 int j = -1;
242 int idelems=IDELEMS(ide);
243
244 k=0;
245 while((k<idelems)&&(ide->m[k] != NULL)) k++;
246 if (k==idelems) return idelems;
247 // now: k: pos of first NULL entry
248 j=k; k=k+1;
249 for (; k<idelems; k++)
250 {
251 if (ide->m[k] != NULL)
252 {
253 ide->m[j] = ide->m[k];
254 ide->m[k] = NULL;
255 j++;
256 }
257 }
258 if (j<=1) return 1;
259 return j;
260}
261
262/// copies the first k (>= 1) entries of the given ideal/module
263/// and returns these as a new ideal/module
264/// (Note that the copied entries may be zero.)
265ideal id_CopyFirstK (const ideal ide, const int k,const ring r)
266{
267 id_Test(ide, r);
268
269 assume( ide != NULL );
270 assume( k <= IDELEMS(ide) );
271
272 ideal newI = idInit(k, ide->rank);
273
274 for (int i = 0; i < k; i++)
275 newI->m[i] = p_Copy(ide->m[i],r);
276
277 return newI;
278}
279
280/// ideal id = (id[i]), result is leadcoeff(id[i]) = 1
281void id_Norm(ideal id, const ring r)
282{
283 id_Test(id, r);
284 for (int i=IDELEMS(id)-1; i>=0; i--)
285 {
286 if (id->m[i] != NULL)
287 {
288 p_Norm(id->m[i],r);
289 }
290 }
291}
292
293/// ideal id = (id[i]), c any unit
294/// if id[i] = c*id[j] then id[j] is deleted for j > i
295void id_DelMultiples(ideal id, const ring r)
296{
297 id_Test(id, r);
298
299 int i, j;
300 int k = IDELEMS(id)-1;
301 for (i=k; i>=0; i--)
302 {
303 if (id->m[i]!=NULL)
304 {
305 for (j=k; j>i; j--)
306 {
307 if (id->m[j]!=NULL)
308 {
309 if (rField_is_Ring(r))
310 {
311 /* if id[j] = c*id[i] then delete id[j].
312 In the below cases of a ground field, we
313 check whether id[i] = c*id[j] and, if so,
314 delete id[j] for historical reasons (so
315 that previous output does not change) */
316 if (p_ComparePolys(id->m[j], id->m[i],r)) p_Delete(&id->m[j],r);
317 }
318 else
319 {
320 if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r);
321 }
322 }
323 }
324 }
325 }
326}
327
328/// ideal id = (id[i])
329/// if id[i] = id[j] then id[j] is deleted for j > i
330void id_DelEquals(ideal id, const ring r)
331{
332 id_Test(id, r);
333
334 int i, j;
335 int k = IDELEMS(id)-1;
336 for (i=k; i>=0; i--)
337 {
338 if (id->m[i]!=NULL)
339 {
340 for (j=k; j>i; j--)
341 {
342 if ((id->m[j]!=NULL)
343 && (p_EqualPolys(id->m[i], id->m[j],r)))
344 {
345 p_Delete(&id->m[j],r);
346 }
347 }
348 }
349 }
350}
351
352/// Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i
353void id_DelLmEquals(ideal id, const ring r)
354{
355 id_Test(id, r);
356
357 int i, j;
358 int k = IDELEMS(id)-1;
359 for (i=k; i>=0; i--)
360 {
361 if (id->m[i] != NULL)
362 {
363 for (j=k; j>i; j--)
364 {
365 if ((id->m[j] != NULL)
366 && p_LmEqual(id->m[i], id->m[j],r)
368 && n_IsUnit(pGetCoeff(id->m[i]),r->cf) && n_IsUnit(pGetCoeff(id->m[j]),r->cf)
369#endif
370 )
371 {
372 p_Delete(&id->m[j],r);
373 }
374 }
375 }
376 }
377}
378
379/// delete id[j], if LT(j) == coeff*mon*LT(i)
380static void id_DelDiv_SEV(ideal id, int k,const ring r)
381{
382 int kk = k+1;
383 long *sev=(long*)omAlloc0(kk*sizeof(long));
384 while(id->m[k]==NULL) k--;
385 BOOLEAN only_lm=r->cf->has_simple_Alloc;
386 if (only_lm)
387 {
388 for (int i=k; i>=0; i--)
389 {
390 if((id->m[i]!=NULL) && (pNext(id->m[i])!=NULL))
391 {
393 break;
394 }
395 }
396 }
397 for (int i=k; i>=0; i--)
398 {
399 if(id->m[i]!=NULL)
400 {
401 sev[i]=p_GetShortExpVector(id->m[i],r);
402 }
403 }
404 if (only_lm)
405 {
406 for (int i=0; i<k; i++)
407 {
408 if (id->m[i] != NULL)
409 {
410 poly m_i=id->m[i];
411 long sev_i=sev[i];
412 for (int j=i+1; j<=k; j++)
413 {
414 if (id->m[j]!=NULL)
415 {
416 if (p_LmShortDivisibleBy(m_i, sev_i,id->m[j],~sev[j],r))
417 {
418 p_LmFree(&id->m[j],r);
419 }
420 else if (p_LmShortDivisibleBy(id->m[j],sev[j], m_i,~sev_i,r))
421 {
422 p_LmFree(&id->m[i],r);
423 break;
424 }
425 }
426 }
427 }
428 }
429 }
430 else
431 {
432 for (int i=0; i<k; i++)
433 {
434 if (id->m[i] != NULL)
435 {
436 poly m_i=id->m[i];
437 long sev_i=sev[i];
438 for (int j=i+1; j<=k; j++)
439 {
440 if (id->m[j]!=NULL)
441 {
442 if (p_LmShortDivisibleBy(m_i, sev_i, id->m[j],~sev[j],r))
443 {
444 p_Delete(&id->m[j],r);
445 }
446 else if (p_LmShortDivisibleBy(id->m[j],sev[j], m_i,~sev_i,r))
447 {
448 p_Delete(&id->m[i],r);
449 break;
450 }
451 }
452 }
453 }
454 }
455 }
456 omFreeSize(sev,kk*sizeof(long));
457}
458
459
460/// delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e.,
461/// delete id[i], if LT(i) == coeff*mon*LT(j)
462void id_DelDiv(ideal id, const ring r)
463{
464 id_Test(id, r);
465
466 int i, j;
467 int k = IDELEMS(id)-1;
468#ifdef HAVE_RINGS
469 if (rField_is_Ring(r))
470 {
471 for (i=k-1; i>=0; i--)
472 {
473 if (id->m[i] != NULL)
474 {
475 for (j=k; j>i; j--)
476 {
477 if (id->m[j]!=NULL)
478 {
479 if (p_DivisibleByRingCase(id->m[i], id->m[j],r))
480 {
481 p_Delete(&id->m[j],r);
482 }
483 else if (p_DivisibleByRingCase(id->m[j], id->m[i],r))
484 {
485 p_Delete(&id->m[i],r);
486 break;
487 }
488 }
489 }
490 }
491 }
492 }
493 else
494#endif
495 {
496 /* the case of a coefficient field: */
497 if (k>9)
498 {
499 id_DelDiv_SEV(id,k,r);
500 return;
501 }
502 for (i=k-1; i>=0; i--)
503 {
504 if (id->m[i] != NULL)
505 {
506 for (j=k; j>i; j--)
507 {
508 if (id->m[j]!=NULL)
509 {
510 if (p_LmDivisibleBy(id->m[i], id->m[j],r))
511 {
512 p_Delete(&id->m[j],r);
513 }
514 else if (p_LmDivisibleBy(id->m[j], id->m[i],r))
515 {
516 p_Delete(&id->m[i],r);
517 break;
518 }
519 }
520 }
521 }
522 }
523 }
524}
525
526/// test if the ideal has only constant polynomials
527/// NOTE: zero ideal/module is also constant
529{
530 id_Test(id, r);
531
532 for (int k = IDELEMS(id)-1; k>=0; k--)
533 {
534 if (!p_IsConstantPoly(id->m[k],r))
535 return FALSE;
536 }
537 return TRUE;
538}
539
540/// copy an ideal
542{
543 id_Test(h1, r);
544
545 ideal h2 = idInit(IDELEMS(h1), h1->rank);
546 for (int i=IDELEMS(h1)-1; i>=0; i--)
547 h2->m[i] = p_Copy(h1->m[i],r);
548 return h2;
549}
550
551#ifdef PDEBUG
552/// Internal verification for ideals/modules and dense matrices!
553void id_DBTest(ideal h1, int level, const char *f,const int l, const ring r, const ring tailRing)
554{
555 if (h1 != NULL)
556 {
557 // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix
558 omCheckAddrSize(h1,sizeof(*h1));
559
560 assume( h1->ncols >= 0 );
561 assume( h1->nrows >= 0 ); // matrix case!
562
563 assume( h1->rank >= 0 );
564
565 const long n = ((long)h1->ncols * (long)h1->nrows);
566
567 assume( !( n > 0 && h1->m == NULL) );
568
569 if( h1->m != NULL && n > 0 )
570 omdebugAddrSize(h1->m, n * sizeof(poly));
571
572 long new_rk = 0; // inlining id_RankFreeModule(h1, r, tailRing);
573
574 /* to be able to test matrices: */
575 for (long i=n - 1; i >= 0; i--)
576 {
577 _pp_Test(h1->m[i], r, tailRing, level);
578 const long k = p_MaxComp(h1->m[i], r, tailRing);
579 if (k > new_rk) new_rk = k;
580 }
581
582 // dense matrices only contain polynomials:
583 // h1->nrows == h1->rank > 1 && new_rk == 0!
584 assume( !( h1->nrows == h1->rank && h1->nrows > 1 && new_rk > 0 ) ); //
585
586 if(new_rk > h1->rank)
587 {
588 dReportError("wrong rank %d (should be %d) in %s:%d\n",
589 h1->rank, new_rk, f,l);
590 omPrintAddrInfo(stderr, h1, " for ideal");
591 h1->rank = new_rk;
592 }
593 }
594 else
595 {
596 Print("error: ideal==NULL in %s:%d\n",f,l);
597 assume( h1 != NULL );
598 }
599}
600#endif
601
602#ifdef PDEBUG
603/// Internal verification for ideals/modules and dense matrices!
604void id_DBLmTest(ideal h1, int level, const char *f,const int l, const ring r)
605{
606 if (h1 != NULL)
607 {
608 // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix
609 omCheckAddrSize(h1,sizeof(*h1));
610
611 assume( h1->ncols >= 0 );
612 assume( h1->nrows >= 0 ); // matrix case!
613
614 assume( h1->rank >= 0 );
615
616 const long n = ((long)h1->ncols * (long)h1->nrows);
617
618 assume( !( n > 0 && h1->m == NULL) );
619
620 if( h1->m != NULL && n > 0 )
621 omdebugAddrSize(h1->m, n * sizeof(poly));
622
623 long new_rk = 0; // inlining id_RankFreeModule(h1, r, tailRing);
624
625 /* to be able to test matrices: */
626 for (long i=n - 1; i >= 0; i--)
627 {
628 if (h1->m[i]!=NULL)
629 {
630 _p_LmTest(h1->m[i], r, level);
631 const long k = p_GetComp(h1->m[i], r);
632 if (k > new_rk) new_rk = k;
633 }
634 }
635
636 // dense matrices only contain polynomials:
637 // h1->nrows == h1->rank > 1 && new_rk == 0!
638 assume( !( h1->nrows == h1->rank && h1->nrows > 1 && new_rk > 0 ) ); //
639
640 if(new_rk > h1->rank)
641 {
642 dReportError("wrong rank %d (should be %d) in %s:%d\n",
643 h1->rank, new_rk, f,l);
644 omPrintAddrInfo(stderr, h1, " for ideal");
645 h1->rank = new_rk;
646 }
647 }
648 else
649 {
650 Print("error: ideal==NULL in %s:%d\n",f,l);
651 assume( h1 != NULL );
652 }
653}
654#endif
655
656/// for idSort: compare a and b revlex inclusive module comp.
657static int p_Comp_RevLex(poly a, poly b,BOOLEAN nolex, const ring R)
658{
659 if (b==NULL) return 1;
660 if (a==NULL) return -1;
661
662 if (nolex)
663 {
664 int r=p_LtCmp(a,b,R);
665 return r;
666 #if 0
667 if (r!=0) return r;
669 r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */
670 n_Delete(&h, R->cf);
671 return r;
672 #endif
673 }
674 int l=rVar(R);
675 while ((l>0) && (p_GetExp(a,l,R)==p_GetExp(b,l,R))) l--;
676 if (l==0)
677 {
678 if (p_GetComp(a,R)==p_GetComp(b,R))
679 {
681 int r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */
682 n_Delete(&h,R->cf);
683 return r;
684 }
685 if (p_GetComp(a,R)>p_GetComp(b,R)) return 1;
686 }
687 else if (p_GetExp(a,l,R)>p_GetExp(b,l,R))
688 return 1;
689 return -1;
690}
691
692// sorts the ideal w.r.t. the actual ringordering
693// uses lex-ordering when nolex = FALSE
694intvec *id_Sort(const ideal id, const BOOLEAN nolex, const ring r)
695{
696 id_Test(id, r);
697
698 intvec * result = new intvec(IDELEMS(id));
699 int i, j, actpos=0, newpos;
702
703 for (i=0;i<IDELEMS(id);i++)
704 {
705 if (id->m[i]!=NULL)
706 {
707 notFound = TRUE;
708 newpos = actpos / 2;
709 diff = (actpos+1) / 2;
710 diff = (diff+1) / 2;
711 lastcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r);
712 if (lastcomp<0)
713 {
714 newpos -= diff;
715 }
716 else if (lastcomp>0)
717 {
718 newpos += diff;
719 }
720 else
721 {
722 notFound = FALSE;
723 }
724 //while ((newpos>=0) && (newpos<actpos) && (notFound))
725 while (notFound && (newpos>=0) && (newpos<actpos))
726 {
727 newcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r);
728 olddiff = diff;
729 if (diff>1)
730 {
731 diff = (diff+1) / 2;
732 if ((newcomp==1)
733 && (actpos-newpos>1)
734 && (diff>1)
735 && (newpos+diff>=actpos))
736 {
737 diff = actpos-newpos-1;
738 }
739 else if ((newcomp==-1)
740 && (diff>1)
741 && (newpos<diff))
742 {
743 diff = newpos;
744 }
745 }
746 if (newcomp<0)
747 {
748 if ((olddiff==1) && (lastcomp>0))
749 notFound = FALSE;
750 else
751 newpos -= diff;
752 }
753 else if (newcomp>0)
754 {
755 if ((olddiff==1) && (lastcomp<0))
756 {
757 notFound = FALSE;
758 newpos++;
759 }
760 else
761 {
762 newpos += diff;
763 }
764 }
765 else
766 {
767 notFound = FALSE;
768 }
770 if (diff==0) notFound=FALSE; /*hs*/
771 }
772 if (newpos<0) newpos = 0;
773 if (newpos>actpos) newpos = actpos;
774 while ((newpos<actpos) && (p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r)==0))
775 newpos++;
776 for (j=actpos;j>newpos;j--)
777 {
778 (*result)[j] = (*result)[j-1];
779 }
780 (*result)[newpos] = i;
781 actpos++;
782 }
783 }
784 for (j=0;j<actpos;j++) (*result)[j]++;
785 return result;
786}
787
788/// concat the lists h1 and h2 without zeros
790{
791 id_Test(h1, R);
792 id_Test(h2, R);
793
794 if ( idIs0(h1) )
795 {
797 if (res->rank<h1->rank) res->rank=h1->rank;
798 return res;
799 }
800 if ( idIs0(h2) )
801 {
803 if (res->rank<h2->rank) res->rank=h2->rank;
804 return res;
805 }
806
807 int j = IDELEMS(h1)-1;
808 while ((j >= 0) && (h1->m[j] == NULL)) j--;
809
810 int i = IDELEMS(h2)-1;
811 while ((i >= 0) && (h2->m[i] == NULL)) i--;
812
813 const int r = si_max(h1->rank, h2->rank);
814
815 ideal result = idInit(i+j+2,r);
816
817 int l;
818
819 for (l=j; l>=0; l--)
820 result->m[l] = p_Copy(h1->m[l],R);
821
822 j = i+j+1;
823 for (l=i; l>=0; l--, j--)
824 result->m[j] = p_Copy(h2->m[l],R);
825
826 return result;
827}
828
829/// insert h2 into h1 (if h2 is not the zero polynomial)
830/// return TRUE iff h2 was indeed inserted
832{
833 if (h2==NULL) return FALSE;
834 assume (h1 != NULL);
835
836 int j = IDELEMS(h1) - 1;
837
838 while ((j >= 0) && (h1->m[j] == NULL)) j--;
839 j++;
840 if (j==IDELEMS(h1))
841 {
842 pEnlargeSet(&(h1->m),IDELEMS(h1),16);
843 IDELEMS(h1)+=16;
844 }
845 h1->m[j]=h2;
846 return TRUE;
847}
848
849/// insert p into I on position pos
851{
852 if (p==NULL) return FALSE;
853 assume (I != NULL);
854
855 int j = IDELEMS(I) - 1;
856
857 while ((j >= 0) && (I->m[j] == NULL)) j--;
858 j++;
859 if (j==IDELEMS(I))
860 {
861 pEnlargeSet(&(I->m),IDELEMS(I),IDELEMS(I)+1);
862 IDELEMS(I)+=1;
863 }
864 for(j = IDELEMS(I)-1;j>pos;j--)
865 I->m[j] = I->m[j-1];
866 I->m[pos]=p;
867 return TRUE;
868}
869
870
871/*! insert h2 into h1 depending on the two boolean parameters:
872 * - if zeroOk is true, then h2 will also be inserted when it is zero
873 * - if duplicateOk is true, then h2 will also be inserted when it is
874 * already present in h1
875 * return TRUE iff h2 was indeed inserted
876 */
878 const poly h2, const bool zeroOk, const bool duplicateOk, const ring r)
879{
880 id_Test(h1, r);
881 p_Test(h2, r);
882
883 if ((!zeroOk) && (h2 == NULL)) return FALSE;
884 if (!duplicateOk)
885 {
886 bool h2FoundInH1 = false;
887 int i = 0;
888 while ((i < validEntries) && (!h2FoundInH1))
889 {
890 h2FoundInH1 = p_EqualPolys(h1->m[i], h2,r);
891 i++;
892 }
893 if (h2FoundInH1) return FALSE;
894 }
895 if (validEntries == IDELEMS(h1))
896 {
897 pEnlargeSet(&(h1->m), IDELEMS(h1), 16);
898 IDELEMS(h1) += 16;
899 }
900 h1->m[validEntries] = h2;
901 return TRUE;
902}
903
904/// h1 + h2
906{
907 id_Test(h1, r);
908 id_Test(h2, r);
909
912 return result;
913}
914
915/// h1 * h2
916/// one h_i must be an ideal (with at least one column)
917/// the other h_i may be a module (with no columns at all)
919{
920 id_Test(h1, R);
921 id_Test(h2, R);
922
923 int j = IDELEMS(h1);
924 while ((j > 0) && (h1->m[j-1] == NULL)) j--;
925
926 int i = IDELEMS(h2);
927 while ((i > 0) && (h2->m[i-1] == NULL)) i--;
928
929 j *= i;
930 int r = si_max( h2->rank, h1->rank );
931 if (j==0)
932 {
933 if ((IDELEMS(h1)>0) && (IDELEMS(h2)>0)) j=1;
934 return idInit(j, r);
935 }
936 ideal hh = idInit(j, r);
937
938 int k = 0;
939 for (i=0; i<IDELEMS(h1); i++)
940 {
941 if (h1->m[i] != NULL)
942 {
943 for (j=0; j<IDELEMS(h2); j++)
944 {
945 if (h2->m[j] != NULL)
946 {
947 hh->m[k] = pp_Mult_qq(h1->m[i],h2->m[j],R);
948 k++;
949 }
950 }
951 }
952 }
953
955 return hh;
956}
957
958/// returns true if h is the zero ideal
960{
961 assume (h != NULL); // will fail :(
962// if (h == NULL) return TRUE;
963
964 for( int i = IDELEMS(h)-1; i >= 0; i-- )
965 if(h->m[i] != NULL)
966 return FALSE;
967
968 return TRUE;
969
970}
971
972/// return the maximal component number found in any polynomial in s
974{
975 long j = 0;
976
977 if (rRing_has_Comp(tailRing) && rRing_has_Comp(lmRing))
978 {
979 poly *p=s->m;
980 for (unsigned int l=IDELEMS(s); l > 0; --l, ++p)
981 if (*p != NULL)
982 {
983 pp_Test(*p, lmRing, tailRing);
984 const long k = p_MaxComp(*p, lmRing, tailRing);
985 if (k>j) j = k;
986 }
987 }
988
989 return j; // return -1;
990}
991
992/*2
993*returns true if id is homogenous with respect to the aktual weights
994*/
996{
997 int i;
998 BOOLEAN b;
999 i = 0;
1000 b = TRUE;
1001 while ((i < IDELEMS(id)) && b)
1002 {
1003 b = p_IsHomogeneous(id->m[i],r);
1004 i++;
1005 }
1006 if ((b) && (Q!=NULL) && (IDELEMS(Q)>0))
1007 {
1008 i=0;
1009 while ((i < IDELEMS(Q)) && b)
1010 {
1011 b = p_IsHomogeneous(Q->m[i],r);
1012 i++;
1013 }
1014 }
1015 return b;
1016}
1017
1019{
1020 int i;
1021 BOOLEAN b;
1022 i = 0;
1023 b = TRUE;
1024 while ((i < IDELEMS(id)) && b)
1025 {
1026 b = p_IsHomogeneousW(id->m[i],w,r);
1027 i++;
1028 }
1029 if ((b) && (Q!=NULL) && (IDELEMS(Q)>0))
1030 {
1031 i=0;
1032 while ((i < IDELEMS(Q)) && b)
1033 {
1034 b = p_IsHomogeneousW(Q->m[i],w,r);
1035 i++;
1036 }
1037 }
1038 return b;
1039}
1040
1042{
1043 int i;
1044 BOOLEAN b;
1045 i = 0;
1046 b = TRUE;
1047 while ((i < IDELEMS(id)) && b)
1048 {
1049 b = p_IsHomogeneousW(id->m[i],w,module_w,r);
1050 i++;
1051 }
1052 if ((b) && (Q!=NULL) && (IDELEMS(Q)>0))
1053 {
1054 i=0;
1055 while ((i < IDELEMS(Q)) && b)
1056 {
1057 b = p_IsHomogeneousW(Q->m[i],w,r);
1058 i++;
1059 }
1060 }
1061 return b;
1062}
1063
1064/*2
1065*initialized a field with r numbers between beg and end for the
1066*procedure idNextChoise
1067*/
1068void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise)
1069{
1070 /*returns the first choise of r numbers between beg and end*/
1071 int i;
1072 for (i=0; i<r; i++)
1073 {
1074 choise[i] = 0;
1075 }
1076 if (r <= end-beg+1)
1077 for (i=0; i<r; i++)
1078 {
1079 choise[i] = beg+i;
1080 }
1081 if (r > end-beg+1)
1082 *endch = TRUE;
1083 else
1084 *endch = FALSE;
1085}
1086
1087/*2
1088*returns the next choise of r numbers between beg and end
1089*/
1090void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise)
1091{
1092 int i = r-1,j;
1093 while ((i >= 0) && (choise[i] == end))
1094 {
1095 i--;
1096 end--;
1097 }
1098 if (i == -1)
1099 *endch = TRUE;
1100 else
1101 {
1102 choise[i]++;
1103 for (j=i+1; j<r; j++)
1104 {
1105 choise[j] = choise[i]+j-i;
1106 }
1107 *endch = FALSE;
1108 }
1109}
1110
1111/*2
1112*takes the field choise of d numbers between beg and end, cancels the t-th
1113*entree and searches for the ordinal number of that d-1 dimensional field
1114* w.r.t. the algorithm of construction
1115*/
1116int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise)
1117{
1118 int * localchoise,i,result=0;
1119 BOOLEAN b=FALSE;
1120
1121 if (d<=1) return 1;
1122 localchoise=(int*)omAlloc((d-1)*sizeof(int));
1123 idInitChoise(d-1,begin,end,&b,localchoise);
1124 while (!b)
1125 {
1126 result++;
1127 i = 0;
1128 while ((i<t) && (localchoise[i]==choise[i])) i++;
1129 if (i>=t)
1130 {
1131 i = t+1;
1132 while ((i<d) && (localchoise[i-1]==choise[i])) i++;
1133 if (i>=d)
1134 {
1135 omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int));
1136 return result;
1137 }
1138 }
1139 idGetNextChoise(d-1,end,&b,localchoise);
1140 }
1141 omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int));
1142 return 0;
1143}
1144
1145/*2
1146*computes the binomial coefficient
1147*/
1148int binom (int n,int r)
1149{
1150 int i;
1151 int64 result;
1152
1153 if (r==0) return 1;
1154 if (n-r<r) return binom(n,n-r);
1155 result = n-r+1;
1156 for (i=2;i<=r;i++)
1157 {
1158 result *= n-r+i;
1159 result /= i;
1160 }
1161 if (result>MAX_INT_VAL)
1162 {
1163 WarnS("overflow in binomials");
1164 result=0;
1165 }
1166 return (int)result;
1167}
1168
1169
1170/// the free module of rank i
1172{
1173 assume(i >= 0);
1174 if (r->isLPring)
1175 {
1176 PrintS("In order to address bimodules, the command freeAlgebra should be used.");
1177 }
1178 ideal h = idInit(i, i);
1179
1180 for (int j=0; j<i; j++)
1181 {
1182 h->m[j] = p_One(r);
1183 p_SetComp(h->m[j],j+1,r);
1184 p_SetmComp(h->m[j],r);
1185 }
1186
1187 return h;
1188}
1189
1190/*2
1191*computes recursively all monomials of a certain degree
1192*in every step the actvar-th entry in the exponential
1193*vector is incremented and the other variables are
1194*computed by recursive calls of makemonoms
1195*if the last variable is reached, the difference to the
1196*degree is computed directly
1197*vars is the number variables
1198*actvar is the actual variable to handle
1199*deg is the degree of the monomials to compute
1200*monomdeg is the actual degree of the monomial in consideration
1201*/
1202static void makemonoms(int vars,int actvar,int deg,int monomdeg, const ring r)
1203{
1204 poly p;
1205 int i=0;
1206
1207 if ((idpowerpoint == 0) && (actvar ==1))
1208 {
1210 monomdeg = 0;
1211 }
1212 while (i<=deg)
1213 {
1214 if (deg == monomdeg)
1215 {
1217 idpowerpoint++;
1218 return;
1219 }
1220 if (actvar == vars)
1221 {
1225 idpowerpoint++;
1226 return;
1227 }
1228 else
1229 {
1231 makemonoms(vars,actvar+1,deg,monomdeg,r);
1233 }
1234 monomdeg++;
1238 i++;
1239 }
1240}
1241
1242#ifdef HAVE_SHIFTBBA
1243/*2
1244*computes recursively all letterplace monomials of a certain degree
1245*vars is the number of original variables (lV)
1246*deg is the degree of the monomials to compute
1247*
1248*NOTE: We use idpowerpoint as the last index of the previous call
1249*/
1250static void lpmakemonoms(int vars, int deg, const ring r)
1251{
1252 assume(deg <= r->N/r->isLPring);
1253 if (deg == 0)
1254 {
1255 idpower[0] = p_One(r);
1256 return;
1257 }
1258 else
1259 {
1260 lpmakemonoms(vars, deg - 1, r);
1261 }
1262
1263 int size = idpowerpoint + 1;
1264 for (int j = 2; j <= vars; j++)
1265 {
1266 for (int i = 0; i < size; i++)
1267 {
1268 idpowerpoint = (j-1)*size + i;
1270 }
1271 }
1272 for (int j = 1; j <= vars; j++)
1273 {
1274 for (int i = 0; i < size; i++)
1275 {
1276 idpowerpoint = (j-1)*size + i;
1277 p_SetExp(idpower[idpowerpoint], ((deg - 1) * r->isLPring) + j, 1, r);
1280 }
1281 }
1282}
1283#endif
1284
1285/*2
1286*returns the deg-th power of the maximal ideal of 0
1287*/
1288ideal id_MaxIdeal(int deg, const ring r)
1289{
1290 if (deg < 1)
1291 {
1292 ideal I=idInit(1,1);
1293 I->m[0]=p_One(r);
1294 return I;
1295 }
1296 if (deg == 1
1298 && !r->isLPring
1299#endif
1300 )
1301 {
1302 return id_MaxIdeal(r);
1303 }
1304
1305 int vars, i;
1306#ifdef HAVE_SHIFTBBA
1307 if (r->isLPring)
1308 {
1309 vars = r->isLPring - r->LPncGenCount;
1310 i = 1;
1311 // i = vars^deg
1312 for (int j = 0; j < deg; j++)
1313 {
1314 i *= vars;
1315 }
1316 }
1317 else
1318#endif
1319 {
1320 vars = rVar(r);
1321 i = binom(vars+deg-1,deg);
1322 }
1323 if (i<=0) return idInit(1,1);
1324 ideal id=idInit(i,1);
1325 idpower = id->m;
1326 idpowerpoint = 0;
1327#ifdef HAVE_SHIFTBBA
1328 if (r->isLPring)
1329 {
1330 lpmakemonoms(vars, deg, r);
1331 }
1332 else
1333#endif
1334 {
1335 makemonoms(vars,1,deg,0,r);
1336 }
1337 idpower = NULL;
1338 idpowerpoint = 0;
1339 return id;
1340}
1341
1343 int begin, int end, int deg, int restdeg, poly ap, const ring r)
1344{
1345 poly p;
1346 int i;
1347
1348 p = p_Power(p_Copy(given->m[begin],r),restdeg,r);
1349 i = result->nrows;
1350 result->m[i] = p_Mult_q(p_Copy(ap,r),p,r);
1351//PrintS(".");
1352 (result->nrows)++;
1353 if (result->nrows >= IDELEMS(result))
1354 {
1355 pEnlargeSet(&(result->m),IDELEMS(result),16);
1356 IDELEMS(result) += 16;
1357 }
1358 if (begin == end) return;
1359 for (i=restdeg-1;i>0;i--)
1360 {
1361 p = p_Power(p_Copy(given->m[begin],r),i,r);
1362 p = p_Mult_q(p_Copy(ap,r),p,r);
1363 id_NextPotence(given, result, begin+1, end, deg, restdeg-i, p,r);
1364 p_Delete(&p,r);
1365 }
1366 id_NextPotence(given, result, begin+1, end, deg, restdeg, ap,r);
1367}
1368
1370{
1372 poly p1;
1373 int i;
1374
1375 if (idIs0(given)) return idInit(1,1);
1376 temp = id_Copy(given,r);
1378 i = binom(IDELEMS(temp)+exp-1,exp);
1379 result = idInit(i,1);
1380 result->nrows = 0;
1381//Print("ideal contains %d elements\n",i);
1382 p1=p_One(r);
1384 p_Delete(&p1,r);
1385 id_Delete(&temp,r);
1386 result->nrows = 1;
1389 return result;
1390}
1391
1392/*2
1393*skips all zeroes and double elements, searches also for units
1394*/
1395void id_Compactify(ideal id, const ring r)
1396{
1397 int i;
1398 BOOLEAN b=FALSE;
1399
1400 i = IDELEMS(id)-1;
1401 while ((! b) && (i>=0))
1402 {
1403 b=p_IsUnit(id->m[i],r);
1404 i--;
1405 }
1406 if (b)
1407 {
1408 for(i=IDELEMS(id)-1;i>=0;i--) p_Delete(&id->m[i],r);
1409 id->m[0]=p_One(r);
1410 }
1411 else
1412 {
1413 id_DelMultiples(id,r);
1414 }
1415 idSkipZeroes(id);
1416}
1417
1418/// returns the ideals of initial terms
1420{
1421 ideal m = idInit(IDELEMS(h),h->rank);
1422
1423 if (r->cf->has_simple_Alloc)
1424 {
1425 for (int i=IDELEMS(h)-1;i>=0; i--)
1426 if (h->m[i]!=NULL)
1427 m->m[i]=p_CopyPowerProduct0(h->m[i],pGetCoeff(h->m[i]),r);
1428 }
1429 else
1430 {
1431 for (int i=IDELEMS(h)-1;i>=0; i--)
1432 if (h->m[i]!=NULL)
1433 m->m[i]=p_Head(h->m[i],r);
1434 }
1435
1436 return m;
1437}
1438
1440{
1441 ideal m = idInit(IDELEMS(h),h->rank);
1442 int i;
1443
1444 for (i=IDELEMS(h)-1;i>=0; i--)
1445 {
1446 m->m[i]=p_Homogen(h->m[i],varnum,r);
1447 }
1448 return m;
1449}
1450
1451/*------------------type conversions----------------*/
1453{
1454 ideal result=idInit(1,1);
1456 p_Vec2Polys(vec, &(result->m), &(IDELEMS(result)),R);
1457 return result;
1458}
1459
1460/// for julia: convert an array of poly to vector
1461poly id_Array2Vector(poly *m, unsigned n, const ring R)
1462{
1463 poly h;
1464 int l;
1465 sBucket_pt bucket = sBucketCreate(R);
1466
1467 for(unsigned j=0;j<n ;j++)
1468 {
1469 h = m[j];
1470 if (h!=NULL)
1471 {
1472 h=p_Copy(h, R);
1473 l=pLength(h);
1474 p_SetCompP(h,j+1, R);
1475 sBucket_Merge_p(bucket, h, l);
1476 }
1477 }
1478 sBucketClearMerge(bucket, &h, &l);
1479 sBucketDestroy(&bucket);
1480 return h;
1481}
1482
1483/// converts mat to module, destroys mat
1485{
1486 int mc=MATCOLS(mat);
1487 int mr=MATROWS(mat);
1488 ideal result = idInit(mc,mr);
1489 int i,j,l;
1490 poly h;
1491 sBucket_pt bucket = sBucketCreate(R);
1492
1493 for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */
1494 {
1495 for (i=0;i<mr /*MATROWS(mat)*/;i++)
1496 {
1497 h = MATELEM0(mat,i,j);
1498 if (h!=NULL)
1499 {
1500 l=pLength(h);
1501 MATELEM0(mat,i,j)=NULL;
1502 p_SetCompP(h,i+1, R);
1503 sBucket_Merge_p(bucket, h, l);
1504 }
1505 }
1506 sBucketClearMerge(bucket, &(result->m[j]), &l);
1507 }
1508 sBucketDestroy(&bucket);
1509
1510 // obachman: need to clean this up
1511 id_Delete((ideal*) &mat,R);
1512 return result;
1513}
1514
1515/*2
1516* converts a module into a matrix, destroyes the input
1517*/
1519{
1520 matrix result = mpNew(mod->rank,IDELEMS(mod));
1521 long i; long cp;
1522 poly p,h;
1523
1524 for(i=0;i<IDELEMS(mod);i++)
1525 {
1526 p=pReverse(mod->m[i]);
1527 mod->m[i]=NULL;
1528 while (p!=NULL)
1529 {
1530 h=p;
1531 pIter(p);
1532 pNext(h)=NULL;
1533 cp = si_max(1L,p_GetComp(h, R)); // if used for ideals too
1534 //cp = p_GetComp(h,R);
1535 p_SetComp(h,0,R);
1536 p_SetmComp(h,R);
1537#ifdef TEST
1538 if (cp>mod->rank)
1539 {
1540 Print("## inv. rank %ld -> %ld\n",mod->rank,cp);
1541 int k,l,o=mod->rank;
1542 mod->rank=cp;
1543 matrix d=mpNew(mod->rank,IDELEMS(mod));
1544 for (l=0; l<o; l++)
1545 {
1546 for (k=0; k<IDELEMS(mod); k++)
1547 {
1550 }
1551 }
1552 id_Delete((ideal *)&result,R);
1553 result=d;
1554 }
1555#endif
1556 MATELEM0(result,cp-1,i) = p_Add_q(MATELEM0(result,cp-1,i),h,R);
1557 }
1558 }
1559 // obachman 10/99: added the following line, otherwise memory leack!
1560 id_Delete(&mod,R);
1561 return result;
1562}
1563
1564matrix id_Module2formatedMatrix(ideal mod,int rows, int cols, const ring R)
1565{
1566 matrix result = mpNew(rows,cols);
1567 int i,cp,r=id_RankFreeModule(mod,R),c=IDELEMS(mod);
1568 poly p,h;
1569
1570 if (r>rows) r = rows;
1571 if (c>cols) c = cols;
1572 for(i=0;i<c;i++)
1573 {
1574 p=pReverse(mod->m[i]);
1575 mod->m[i]=NULL;
1576 while (p!=NULL)
1577 {
1578 h=p;
1579 pIter(p);
1580 pNext(h)=NULL;
1581 cp = p_GetComp(h,R);
1582 if (cp<=r)
1583 {
1584 p_SetComp(h,0,R);
1585 p_SetmComp(h,R);
1586 MATELEM0(result,cp-1,i) = p_Add_q(MATELEM0(result,cp-1,i),h,R);
1587 }
1588 else
1589 p_Delete(&h,R);
1590 }
1591 }
1592 id_Delete(&mod,R);
1593 return result;
1594}
1595
1596ideal id_ResizeModule(ideal mod,int rows, int cols, const ring R)
1597{
1598 // columns?
1599 if (cols!=IDELEMS(mod))
1600 {
1601 for(int i=IDELEMS(mod)-1;i>=cols;i--) p_Delete(&mod->m[i],R);
1602 pEnlargeSet(&(mod->m),IDELEMS(mod),cols-IDELEMS(mod));
1603 IDELEMS(mod)=cols;
1604 }
1605 // rows?
1606 if (rows<mod->rank)
1607 {
1608 for(int i=IDELEMS(mod)-1;i>=0;i--)
1609 {
1610 if (mod->m[i]!=NULL)
1611 {
1612 while((mod->m[i]!=NULL) && (p_GetComp(mod->m[i],R)>rows))
1613 mod->m[i]=p_LmDeleteAndNext(mod->m[i],R);
1614 poly p=mod->m[i];
1615 while(pNext(p)!=NULL)
1616 {
1617 if (p_GetComp(pNext(p),R)>rows)
1619 else
1620 pIter(p);
1621 }
1622 }
1623 }
1624 }
1625 mod->rank=rows;
1626 return mod;
1627}
1628
1629/*2
1630* substitute the n-th variable by the monomial e in id
1631* destroy id
1632*/
1633ideal id_Subst(ideal id, int n, poly e, const ring r)
1634{
1635 int k=MATROWS((matrix)id)*MATCOLS((matrix)id);
1637
1638 res->rank = id->rank;
1639 for(k--;k>=0;k--)
1640 {
1641 res->m[k]=p_Subst(id->m[k],n,e,r);
1642 id->m[k]=NULL;
1643 }
1644 id_Delete(&id,r);
1645 return res;
1646}
1647
1649{
1650 if (w!=NULL) *w=NULL;
1651 if ((Q!=NULL) && (!id_HomIdeal(Q,NULL,R))) return FALSE;
1652 if (idIs0(m))
1653 {
1654 if (w!=NULL) (*w)=new intvec(m->rank);
1655 return TRUE;
1656 }
1657
1658 long cmax=1,order=0,ord,* diff,diffmin=32000;
1659 int *iscom;
1660 int i;
1661 poly p=NULL;
1662 pFDegProc d;
1663 if (R->pLexOrder && (R->order[0]==ringorder_lp))
1664 d=p_Totaldegree;
1665 else
1666 d=R->pFDeg;
1667 int length=IDELEMS(m);
1668 poly* P=m->m;
1669 poly* F=(poly*)omAlloc(length*sizeof(poly));
1670 for (i=length-1;i>=0;i--)
1671 {
1672 p=F[i]=P[i];
1674 }
1675 cmax++;
1676 diff = (long *)omAlloc0(cmax*sizeof(long));
1677 if (w!=NULL) *w=new intvec(cmax-1);
1678 iscom = (int *)omAlloc0(cmax*sizeof(int));
1679 i=0;
1680 while (i<=length)
1681 {
1682 if (i<length)
1683 {
1684 p=F[i];
1685 while ((p!=NULL) && (iscom[__p_GetComp(p,R)]==0)) pIter(p);
1686 }
1687 if ((p==NULL) && (i<length))
1688 {
1689 i++;
1690 }
1691 else
1692 {
1693 if (p==NULL) /* && (i==length) */
1694 {
1695 i=0;
1696 while ((i<length) && (F[i]==NULL)) i++;
1697 if (i>=length) break;
1698 p = F[i];
1699 }
1700 //if (pLexOrder && (currRing->order[0]==ringorder_lp))
1701 // order=pTotaldegree(p);
1702 //else
1703 // order = p->order;
1704 // order = pFDeg(p,currRing);
1705 order = d(p,R) +diff[__p_GetComp(p,R)];
1706 //order += diff[pGetComp(p)];
1707 p = F[i];
1708//Print("Actual p=F[%d]: ",i);pWrite(p);
1709 F[i] = NULL;
1710 i=0;
1711 }
1712 while (p!=NULL)
1713 {
1714 if (R->pLexOrder && (R->order[0]==ringorder_lp))
1715 ord=p_Totaldegree(p,R);
1716 else
1717 // ord = p->order;
1718 ord = R->pFDeg(p,R);
1719 if (iscom[__p_GetComp(p,R)]==0)
1720 {
1721 diff[__p_GetComp(p,R)] = order-ord;
1722 iscom[__p_GetComp(p,R)] = 1;
1723/*
1724*PrintS("new diff: ");
1725*for (j=0;j<cmax;j++) Print("%d ",diff[j]);
1726*PrintLn();
1727*PrintS("new iscom: ");
1728*for (j=0;j<cmax;j++) Print("%d ",iscom[j]);
1729*PrintLn();
1730*Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]);
1731*/
1732 }
1733 else
1734 {
1735/*
1736*PrintS("new diff: ");
1737*for (j=0;j<cmax;j++) Print("%d ",diff[j]);
1738*PrintLn();
1739*Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]);
1740*/
1741 if (order != (ord+diff[__p_GetComp(p,R)]))
1742 {
1743 omFreeSize((ADDRESS) iscom,cmax*sizeof(int));
1744 omFreeSize((ADDRESS) diff,cmax*sizeof(long));
1745 omFreeSize((ADDRESS) F,length*sizeof(poly));
1746 delete *w;*w=NULL;
1747 return FALSE;
1748 }
1749 }
1750 pIter(p);
1751 }
1752 }
1753 omFreeSize((ADDRESS) iscom,cmax*sizeof(int));
1754 omFreeSize((ADDRESS) F,length*sizeof(poly));
1755 for (i=1;i<cmax;i++) (**w)[i-1]=(int)(diff[i]);
1756 for (i=1;i<cmax;i++)
1757 {
1758 if (diff[i]<diffmin) diffmin=diff[i];
1759 }
1760 if (w!=NULL)
1761 {
1762 for (i=1;i<cmax;i++)
1763 {
1764 (**w)[i-1]=(int)(diff[i]-diffmin);
1765 }
1766 }
1767 omFreeSize((ADDRESS) diff,cmax*sizeof(long));
1768 return TRUE;
1769}
1770
1771ideal id_Jet(const ideal i,int d, const ring R)
1772{
1773 ideal r=idInit((i->nrows)*(i->ncols),i->rank);
1774 r->nrows = i-> nrows;
1775 r->ncols = i-> ncols;
1776 //r->rank = i-> rank;
1777
1778 for(long k=((long)(i->nrows))*((long)(i->ncols))-1;k>=0; k--)
1779 r->m[k]=pp_Jet(i->m[k],d,R);
1780
1781 return r;
1782}
1783
1784ideal id_Jet0(const ideal i, const ring R)
1785{
1786 ideal r=idInit((i->nrows)*(i->ncols),i->rank);
1787 r->nrows = i-> nrows;
1788 r->ncols = i-> ncols;
1789 //r->rank = i-> rank;
1790
1791 for(long k=((long)(i->nrows))*((long)(i->ncols))-1;k>=0; k--)
1792 r->m[k]=pp_Jet0(i->m[k],R);
1793
1794 return r;
1795}
1796
1797ideal id_JetW(const ideal i,int d, intvec * iv, const ring R)
1798{
1799 ideal r=idInit(IDELEMS(i),i->rank);
1800 if (ecartWeights!=NULL)
1801 {
1802 WerrorS("cannot compute weighted jets now");
1803 }
1804 else
1805 {
1806 int *w=iv2array(iv,R);
1807 int k;
1808 for(k=0; k<IDELEMS(i); k++)
1809 {
1810 r->m[k]=pp_JetW(i->m[k],d,w,R);
1811 }
1812 omFreeSize((ADDRESS)w,(rVar(R)+1)*sizeof(int));
1813 }
1814 return r;
1815}
1816
1817#if 0
1818static void idDeleteComp(ideal arg,int red_comp)
1819{
1820 int i,j;
1821 poly p;
1822
1823 for (i=IDELEMS(arg)-1;i>=0;i--)
1824 {
1825 p = arg->m[i];
1826 while (p!=NULL)
1827 {
1828 j = pGetComp(p);
1829 if (j>red_comp)
1830 {
1831 pSetComp(p,j-1);
1832 pSetm(p);
1833 }
1834 pIter(p);
1835 }
1836 }
1837 (arg->rank)--;
1838}
1839#endif
1840
1842{
1843 poly head, tail;
1844 int k;
1845 int in=IDELEMS(id)-1, ready=0, all=0,
1846 coldim=rVar(r), rowmax=2*coldim;
1847 if (in<0) return NULL;
1848 intvec *imat=new intvec(rowmax+1,coldim,0);
1849
1850 do
1851 {
1852 head = id->m[in--];
1853 if (head!=NULL)
1854 {
1855 tail = pNext(head);
1856 while (tail!=NULL)
1857 {
1858 all++;
1859 for (k=1;k<=coldim;k++)
1860 IMATELEM(*imat,all,k) = p_GetExpDiff(head,tail,k,r);
1861 if (all==rowmax)
1862 {
1863 ivTriangIntern(imat, ready, all);
1864 if (ready==coldim)
1865 {
1866 delete imat;
1867 return NULL;
1868 }
1869 }
1870 pIter(tail);
1871 }
1872 }
1873 } while (in>=0);
1874 if (all>ready)
1875 {
1876 ivTriangIntern(imat, ready, all);
1877 if (ready==coldim)
1878 {
1879 delete imat;
1880 return NULL;
1881 }
1882 }
1883 intvec *result = ivSolveKern(imat, ready);
1884 delete imat;
1885 return result;
1886}
1887
1889{
1890 BOOLEAN *UsedAxis=(BOOLEAN *)omAlloc0(rVar(r)*sizeof(BOOLEAN));
1891 int i,n;
1892 poly po;
1894 for(i=IDELEMS(I)-1;i>=0;i--)
1895 {
1896 po=I->m[i];
1897 if ((po!=NULL) &&((n=p_IsPurePower(po,r))!=0)) UsedAxis[n-1]=TRUE;
1898 }
1899 for(i=rVar(r)-1;i>=0;i--)
1900 {
1901 if(UsedAxis[i]==FALSE) {res=FALSE; break;} // not zero-dim.
1902 }
1903 omFreeSize(UsedAxis,rVar(r)*sizeof(BOOLEAN));
1904 return res;
1905}
1906
1907void id_Normalize(ideal I,const ring r) /* for ideal/matrix */
1908{
1909 if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */
1910 int i;
1911 for(i=I->nrows*I->ncols-1;i>=0;i--)
1912 {
1913 p_Normalize(I->m[i],r);
1914 }
1915}
1916
1918{
1919 int d=-1;
1920 for(int i=0;i<IDELEMS(M);i++)
1921 {
1922 if (M->m[i]!=NULL)
1923 {
1924 int d0=p_MinDeg(M->m[i],w,r);
1925 if(-1<d0&&((d0<d)||(d==-1)))
1926 d=d0;
1927 }
1928 }
1929 return d;
1930}
1931
1932// #include "kernel/clapsing.h"
1933
1934/*2
1935* transpose a module
1936*/
1938{
1939 int r = a->rank, c = IDELEMS(a);
1940 ideal b = idInit(r,c);
1941
1942 int i;
1943 for (i=c; i>0; i--)
1944 {
1945 poly p=a->m[i-1];
1946 while(p!=NULL)
1947 {
1948 poly h=p_Head(p, rRing);
1949 int co=__p_GetComp(h, rRing)-1;
1950 p_SetComp(h, i, rRing);
1951 p_Setm(h, rRing);
1952 h->next=b->m[co];
1953 b->m[co]=h;
1954 pIter(p);
1955 }
1956 }
1957 for (i=IDELEMS(b)-1; i>=0; i--)
1958 {
1959 poly p=b->m[i];
1960 if(p!=NULL)
1961 {
1962 b->m[i]=p_SortMerge(p,rRing,TRUE);
1963 }
1964 }
1965 return b;
1966}
1967
1968/*2
1969* The following is needed to compute the image of certain map used in
1970* the computation of cohomologies via BGG
1971* let M = { w_1, ..., w_k }, k = size(M) == ncols(M), n = nvars(currRing).
1972* assuming that nrows(M) <= m*n; the procedure computes:
1973* transpose(M) * transpose( var(1) I_m | ... | var(n) I_m ) :== transpose(module{f_1, ... f_k}),
1974* where f_i = \sum_{j=1}^{m} (w_i, v_j) gen(j), (w_i, v_j) is a `scalar` multiplication.
1975* that is, if w_i = (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) then
1976
1977 (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m)
1978* var_1 ... var_1 | var_2 ... var_2 | ... | var_n ... var(n)
1979* gen_1 ... gen_m | gen_1 ... gen_m | ... | gen_1 ... gen_m
1980+ =>
1981 f_i =
1982
1983 a^1_1 * var(1) * gen(1) + ... + a^1_m * var(1) * gen(m) +
1984 a^2_1 * var(2) * gen(1) + ... + a^2_m * var(2) * gen(m) +
1985 ...
1986 a^n_1 * var(n) * gen(1) + ... + a^n_m * var(n) * gen(m);
1987
1988 NOTE: for every f_i we run only ONCE along w_i saving partial sums into a temporary array of polys of size m
1989*/
1990ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing)
1991{
1992// #ifdef DEBU
1993// WarnS("tensorModuleMult!!!!");
1994
1995 assume(m > 0);
1996 assume(M != NULL);
1997
1998 const int n = rRing->N;
1999
2000 assume(M->rank <= m * n);
2001
2002 const int k = IDELEMS(M);
2003
2004 ideal idTemp = idInit(k,m); // = {f_1, ..., f_k }
2005
2006 for( int i = 0; i < k; i++ ) // for every w \in M
2007 {
2008 poly pTempSum = NULL;
2009
2010 poly w = M->m[i];
2011
2012 while(w != NULL) // for each term of w...
2013 {
2014 poly h = p_Head(w, rRing);
2015
2016 const int gen = __p_GetComp(h, rRing); // 1 ...
2017
2018 assume(gen > 0);
2019 assume(gen <= n*m);
2020
2021 // TODO: write a formula with %, / instead of while!
2022 /*
2023 int c = gen;
2024 int v = 1;
2025 while(c > m)
2026 {
2027 c -= m;
2028 v++;
2029 }
2030 */
2031
2032 int cc = gen % m;
2033 if( cc == 0) cc = m;
2034 int vv = 1 + (gen - cc) / m;
2035
2036// assume( cc == c );
2037// assume( vv == v );
2038
2039 // 1<= c <= m
2040 assume( cc > 0 );
2041 assume( cc <= m );
2042
2043 assume( vv > 0 );
2044 assume( vv <= n );
2045
2046 assume( (cc + (vv-1)*m) == gen );
2047
2048 p_IncrExp(h, vv, rRing); // h *= var(j) && // p_AddExp(h, vv, 1, rRing);
2049 p_SetComp(h, cc, rRing);
2050
2051 p_Setm(h, rRing); // addjust degree after the previous steps!
2052
2053 pTempSum = p_Add_q(pTempSum, h, rRing); // it is slow since h will be usually put to the back of pTempSum!!!
2054
2055 pIter(w);
2056 }
2057
2058 idTemp->m[i] = pTempSum;
2059 }
2060
2061 // simplify idTemp???
2062
2064
2066
2067 return(idResult);
2068}
2069
2071{
2072 int cnt=0;int rw=0; int cl=0;
2073 int i,j;
2074 // find max. size of xx[.]:
2075 for(j=rl-1;j>=0;j--)
2076 {
2077 i=IDELEMS(xx[j])*xx[j]->nrows;
2078 if (i>cnt) cnt=i;
2079 if (xx[j]->nrows >rw) rw=xx[j]->nrows; // for lifting matrices
2080 if (xx[j]->ncols >cl) cl=xx[j]->ncols; // for lifting matrices
2081 }
2082 if (rw*cl !=cnt)
2083 {
2084 WerrorS("format mismatch in CRT");
2085 return NULL;
2086 }
2087 ideal result=idInit(cnt,xx[0]->rank);
2088 result->nrows=rw; // for lifting matrices
2089 result->ncols=cl; // for lifting matrices
2090 number *x=(number *)omAlloc(rl*sizeof(number));
2091 poly *p=(poly *)omAlloc(rl*sizeof(poly));
2093 EXTERN_VAR int n_SwitchChinRem; //TEST
2096 for(i=cnt-1;i>=0;i--)
2097 {
2098 for(j=rl-1;j>=0;j--)
2099 {
2100 if(i>=IDELEMS(xx[j])*xx[j]->nrows) // out of range of this ideal
2101 p[j]=NULL;
2102 else
2103 p[j]=xx[j]->m[i];
2104 }
2106 for(j=rl-1;j>=0;j--)
2107 {
2108 if(i<IDELEMS(xx[j])*xx[j]->nrows) xx[j]->m[i]=p[j];
2109 }
2110 }
2112 omFreeSize(p,rl*sizeof(poly));
2113 omFreeSize(x,rl*sizeof(number));
2114 for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]),r);
2115 omFreeSize(xx,rl*sizeof(ideal));
2116 return result;
2117}
2118
2119void id_Shift(ideal M, int s, const ring r)
2120{
2121// id_Test( M, r );
2122
2123// assume( s >= 0 ); // negative is also possible // TODO: verify input ideal in such a case!?
2124
2125 for(int i=IDELEMS(M)-1; i>=0;i--)
2126 p_Shift(&(M->m[i]),s,r);
2127
2128 M->rank += s;
2129
2130// id_Test( M, r );
2131}
2132
2133ideal id_Delete_Pos(const ideal I, const int p, const ring r)
2134{
2135 if ((p<0)||(p>=IDELEMS(I))) return NULL;
2136 ideal ret=idInit(IDELEMS(I)-1,I->rank);
2137 for(int i=0;i<p;i++) ret->m[i]=p_Copy(I->m[i],r);
2138 for(int i=p+1;i<IDELEMS(I);i++) ret->m[i-1]=p_Copy(I->m[i],r);
2139 return ret;
2140}
2141
2142ideal id_PermIdeal(ideal I,int R, int C,const int *perm, const ring src, const ring dst,
2143 nMapFunc nMap, const int *par_perm, int P, BOOLEAN use_mult)
2144{
2145 ideal II=(ideal)mpNew(R,C);
2146 II->rank=I->rank;
2147 for(int i=R*C-1; i>=0; i--)
2148 {
2149 II->m[i]=p_PermPoly(I->m[i],perm,src,dst,nMap,par_perm,P,use_mult);
2150 }
2151 return II;
2152}
All the auxiliary stuff.
long int64
Definition auxiliary.h:68
static int si_max(const int a, const int b)
Definition auxiliary.h:124
int BOOLEAN
Definition auxiliary.h:87
#define TRUE
Definition auxiliary.h:100
#define FALSE
Definition auxiliary.h:96
int size(const CanonicalForm &f, const Variable &v)
int size ( const CanonicalForm & f, const Variable & v )
Definition cf_ops.cc:600
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
CanonicalForm FACTORY_PUBLIC pp(const CanonicalForm &)
CanonicalForm pp ( const CanonicalForm & f )
Definition cf_gcd.cc:676
CanonicalForm head(const CanonicalForm &f)
int level(const CanonicalForm &f)
const CanonicalForm CFMap CFMap & N
Definition cfEzgcd.cc:56
int l
Definition cfEzgcd.cc:100
int m
Definition cfEzgcd.cc:128
int i
Definition cfEzgcd.cc:132
int k
Definition cfEzgcd.cc:99
Variable x
Definition cfModGcd.cc:4090
int p
Definition cfModGcd.cc:4086
cl
Definition cfModGcd.cc:4108
CanonicalForm b
Definition cfModGcd.cc:4111
int int ncols
Definition cf_linsys.cc:32
int nrows
Definition cf_linsys.cc:32
FILE * f
Definition checklibs.c:9
static FORCE_INLINE BOOLEAN n_IsUnit(number n, const coeffs r)
TRUE iff n has a multiplicative inverse in the given coeff field/ring r.
Definition coeffs.h:519
static FORCE_INLINE BOOLEAN n_GreaterZero(number n, const coeffs r)
ordered fields: TRUE iff 'n' is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2),...
Definition coeffs.h:498
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition coeffs.h:468
static FORCE_INLINE number n_Sub(number a, number b, const coeffs r)
return the difference of 'a' and 'b', i.e., a-b
Definition coeffs.h:659
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition coeffs.h:459
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
Definition coeffs.h:80
#define Print
Definition emacs.cc:80
#define WarnS
Definition emacs.cc:78
return result
const CanonicalForm int s
Definition facAbsFact.cc:51
CanonicalForm res
Definition facAbsFact.cc:60
const CanonicalForm & w
Definition facAbsFact.cc:51
fq_nmod_poly_t * vec
Definition facHensel.cc:108
int j
Definition facHensel.cc:110
void WerrorS(const char *s)
Definition feFopen.cc:24
#define STATIC_VAR
Definition globaldefs.h:7
#define EXTERN_VAR
Definition globaldefs.h:6
#define VAR
Definition globaldefs.h:5
static BOOLEAN length(leftv result, leftv arg)
Definition interval.cc:257
void ivTriangIntern(intvec *imat, int &ready, int &all)
Definition intvec.cc:404
intvec * ivSolveKern(intvec *imat, int dimtr)
Definition intvec.cc:442
#define IMATELEM(M, I, J)
Definition intvec.h:85
STATIC_VAR Poly * h
Definition janet.cc:971
poly p_ChineseRemainder(poly *xx, mpz_ptr *x, mpz_ptr *q, int rl, mpz_ptr *C, const ring R)
VAR int n_SwitchChinRem
Definition longrat.cc:3097
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition matpol.cc:37
#define MATELEM0(mat, i, j)
0-based access to matrix
Definition matpol.h:31
#define MATROWS(i)
Definition matpol.h:26
#define MATCOLS(i)
Definition matpol.h:27
#define assume(x)
Definition mod2.h:387
int dReportError(const char *fmt,...)
Definition dError.cc:44
#define p_GetComp(p, r)
Definition monomials.h:64
#define pIter(p)
Definition monomials.h:37
#define pNext(p)
Definition monomials.h:36
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition monomials.h:44
#define __p_GetComp(p, r)
Definition monomials.h:63
#define rRing_has_Comp(r)
Definition monomials.h:266
gmp_float exp(const gmp_float &a)
STATIC_VAR gmp_float * diff
const int MAX_INT_VAL
Definition mylimits.h:12
Definition ap.h:40
#define omFreeSize(addr, size)
#define omAlloc(size)
#define omAllocBin(bin)
#define omdebugAddrSize(addr, size)
#define omCheckAddrSize(addr, size)
#define omFree(addr)
#define omAlloc0(size)
#define omFreeBin(addr, bin)
#define omFreeBinAddr(addr)
#define omGetSpecBin(size)
Definition omBin.h:11
#define NULL
Definition omList.c:12
omBin_t * omBin
Definition omStructs.h:12
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
Definition p_polys.cc:1229
poly pp_Jet(poly p, int m, const ring R)
Definition p_polys.cc:4380
BOOLEAN p_ComparePolys(poly p1, poly p2, const ring r)
returns TRUE if p1 is a skalar multiple of p2 assume p1 != NULL and p2 != NULL
Definition p_polys.cc:4626
BOOLEAN p_DivisibleByRingCase(poly f, poly g, const ring r)
divisibility check over ground ring (which may contain zero divisors); TRUE iff LT(f) divides LT(g),...
Definition p_polys.cc:1648
poly p_Homogen(poly p, int varnum, const ring r)
Definition p_polys.cc:3276
poly p_Subst(poly p, int n, poly e, const ring r)
Definition p_polys.cc:3980
void p_Vec2Polys(poly v, poly **p, int *len, const ring r)
Definition p_polys.cc:3647
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
Definition p_polys.cc:4756
poly p_PermPoly(poly p, const int *perm, const ring oldRing, const ring dst, nMapFunc nMap, const int *par_perm, int OldPar, BOOLEAN use_mult)
Definition p_polys.cc:4152
poly p_Power(poly p, int i, const ring r)
Definition p_polys.cc:2203
void p_Normalize(poly p, const ring r)
Definition p_polys.cc:3835
void p_Norm(poly p1, const ring r)
Definition p_polys.cc:3741
poly pp_Jet0(poly p, const ring R)
Definition p_polys.cc:4408
int p_MinDeg(poly p, intvec *w, const ring R)
Definition p_polys.cc:4498
unsigned long p_GetShortExpVector(const poly p, const ring r)
Definition p_polys.cc:4830
BOOLEAN p_IsHomogeneousW(poly p, const intvec *w, const ring r)
Definition p_polys.cc:3349
poly p_One(const ring r)
Definition p_polys.cc:1316
void pEnlargeSet(poly **p, int l, int increment)
Definition p_polys.cc:3718
BOOLEAN p_IsHomogeneous(poly p, const ring r)
Definition p_polys.cc:3325
poly pp_JetW(poly p, int m, int *w, const ring R)
Definition p_polys.cc:4453
poly p_CopyPowerProduct0(const poly p, number n, const ring r)
like p_Head, but with coefficient n
Definition p_polys.cc:5018
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
Definition p_polys.cc:4562
static int pLength(poly a)
Definition p_polys.h:190
static long p_GetExpDiff(poly p1, poly p2, int i, ring r)
Definition p_polys.h:635
static poly p_Add_q(poly p, poly q, const ring r)
Definition p_polys.h:936
static poly p_Mult_q(poly p, poly q, const ring r)
Definition p_polys.h:1114
#define p_LmEqual(p1, p2, r)
Definition p_polys.h:1723
BOOLEAN _p_LmTest(poly p, ring r, int level)
Definition pDebug.cc:326
void p_ShallowDelete(poly *p, const ring r)
static void p_SetCompP(poly p, int i, ring r)
Definition p_polys.h:254
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
Definition p_polys.h:488
#define pp_Test(p, lmRing, tailRing)
Definition p_polys.h:163
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
Definition p_polys.h:247
static long p_IncrExp(poly p, int v, ring r)
Definition p_polys.h:591
static void p_Setm(poly p, const ring r)
Definition p_polys.h:233
#define p_SetmComp
Definition p_polys.h:244
static poly p_SortMerge(poly p, const ring r, BOOLEAN revert=FALSE)
Definition p_polys.h:1229
static poly pReverse(poly p)
Definition p_polys.h:335
static int p_LtCmp(poly p, poly q, const ring r)
Definition p_polys.h:1621
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
Definition p_polys.h:1006
static poly p_Head(const poly p, const ring r)
copy the (leading) term of p
Definition p_polys.h:860
static BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, poly b, unsigned long not_sev_b, const ring r)
Definition p_polys.h:1910
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
Definition p_polys.h:469
static BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
Definition p_polys.h:1891
static long p_MaxComp(poly p, ring lmRing, ring tailRing)
Definition p_polys.h:292
static void p_Delete(poly *p, const ring r)
Definition p_polys.h:901
static poly pp_Mult_qq(poly p, poly q, const ring r)
Definition p_polys.h:1151
static void p_LmFree(poly p, ring)
Definition p_polys.h:683
static BOOLEAN p_IsUnit(const poly p, const ring r)
Definition p_polys.h:1991
static poly p_LmDeleteAndNext(poly p, const ring r)
Definition p_polys.h:755
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition p_polys.h:846
static long p_Totaldegree(poly p, const ring r)
Definition p_polys.h:1507
BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level)
Definition pDebug.cc:336
#define p_Test(p, r)
Definition p_polys.h:161
static BOOLEAN p_IsConstantPoly(const poly p, const ring r)
Definition p_polys.h:1978
void p_wrp(poly p, ring lmRing, ring tailRing)
Definition polys0.cc:373
#define pSetm(p)
Definition polys.h:271
#define pGetComp(p)
Component.
Definition polys.h:37
#define pSetComp(p, v)
Definition polys.h:38
void PrintS(const char *s)
Definition reporter.cc:284
void PrintLn()
Definition reporter.cc:310
long(* pFDegProc)(poly p, ring r)
Definition ring.h:38
@ ringorder_lp
Definition ring.h:77
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition ring.h:597
static BOOLEAN rField_has_simple_inverse(const ring r)
Definition ring.h:553
#define rField_is_Ring(R)
Definition ring.h:490
void sBucketClearMerge(sBucket_pt bucket, poly *p, int *length)
Definition sbuckets.cc:237
void sBucket_Merge_p(sBucket_pt bucket, poly p, int length)
Merges p into Spoly: assumes Bpoly and p have no common monoms destroys p!
Definition sbuckets.cc:148
void sBucketDestroy(sBucket_pt *bucket)
Definition sbuckets.cc:103
sBucket_pt sBucketCreate(const ring r)
Definition sbuckets.cc:96
void id_DBLmTest(ideal h1, int level, const char *f, const int l, const ring r)
Internal verification for ideals/modules and dense matrices!
ideal id_Add(ideal h1, ideal h2, const ring r)
h1 + h2
STATIC_VAR int idpowerpoint
ideal id_Vec2Ideal(poly vec, const ring R)
ideal idInit(int idsize, int rank)
initialise an ideal / module
int id_PosConstant(ideal id, const ring r)
index of generator with leading term in ground ring (if any); otherwise -1
int binom(int n, int r)
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
int idSkipZeroes0(ideal ide)
void id_DBTest(ideal h1, int level, const char *f, const int l, const ring r, const ring tailRing)
Internal verification for ideals/modules and dense matrices!
poly id_Array2Vector(poly *m, unsigned n, const ring R)
for julia: convert an array of poly to vector
static void id_NextPotence(ideal given, ideal result, int begin, int end, int deg, int restdeg, poly ap, const ring r)
intvec * id_Sort(const ideal id, const BOOLEAN nolex, const ring r)
sorts the ideal w.r.t. the actual ringordering uses lex-ordering when nolex = FALSE
intvec * id_QHomWeight(ideal id, const ring r)
void id_Norm(ideal id, const ring r)
ideal id = (id[i]), result is leadcoeff(id[i]) = 1
BOOLEAN id_HomIdeal(ideal id, ideal Q, const ring r)
STATIC_VAR poly * idpower
static void makemonoms(int vars, int actvar, int deg, int monomdeg, const ring r)
BOOLEAN id_HomModuleW(ideal id, ideal Q, const intvec *w, const intvec *module_w, const ring r)
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
void id_Normalize(ideal I, const ring r)
normialize all polys in id
ideal id_Transp(ideal a, const ring rRing)
transpose a module
void id_Delete0(ideal *h, ring r)
ideal id_FreeModule(int i, const ring r)
the free module of rank i
BOOLEAN id_IsZeroDim(ideal I, const ring r)
ideal id_Homogen(ideal h, int varnum, const ring r)
ideal id_Power(ideal given, int exp, const ring r)
matrix id_Module2Matrix(ideal mod, const ring R)
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
BOOLEAN idInsertPoly(ideal h1, poly h2)
insert h2 into h1 (if h2 is not the zero polynomial) return TRUE iff h2 was indeed inserted
ideal id_Copy(ideal h1, const ring r)
copy an ideal
BOOLEAN id_IsConstant(ideal id, const ring r)
test if the ideal has only constant polynomials NOTE: zero ideal/module is also constant
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
BOOLEAN id_HomIdealW(ideal id, ideal Q, const intvec *w, const ring r)
ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing)
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
BOOLEAN idInsertPolyOnPos(ideal I, poly p, int pos)
insert p into I on position pos
ideal id_Jet0(const ideal i, const ring R)
ideal id_MaxIdeal(const ring r)
initialise the maximal ideal (at 0)
void id_DelDiv(ideal id, const ring r)
delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., delete id[i], if LT(i) == coeff*mon*L...
int id_MinDegW(ideal M, intvec *w, const ring r)
void id_DelMultiples(ideal id, const ring r)
ideal id = (id[i]), c any unit if id[i] = c*id[j] then id[j] is deleted for j > i
void id_ShallowDelete(ideal *h, ring r)
Shallowdeletes an ideal/matrix.
BOOLEAN id_InsertPolyWithTests(ideal h1, const int validEntries, const poly h2, const bool zeroOk, const bool duplicateOk, const ring r)
insert h2 into h1 depending on the two boolean parameters:
ideal id_Mult(ideal h1, ideal h2, const ring R)
h1 * h2 one h_i must be an ideal (with at least one column) the other h_i may be a module (with no co...
ideal id_CopyFirstK(const ideal ide, const int k, const ring r)
copies the first k (>= 1) entries of the given ideal/module and returns these as a new ideal/module (...
matrix id_Module2formatedMatrix(ideal mod, int rows, int cols, const ring R)
void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint)
ideal id_Matrix2Module(matrix mat, const ring R)
converts mat to module, destroys mat
ideal id_ResizeModule(ideal mod, int rows, int cols, const ring R)
ideal id_Delete_Pos(const ideal I, const int p, const ring r)
static int p_Comp_RevLex(poly a, poly b, BOOLEAN nolex, const ring R)
for idSort: compare a and b revlex inclusive module comp.
void id_DelEquals(ideal id, const ring r)
ideal id = (id[i]) if id[i] = id[j] then id[j] is deleted for j > i
VAR omBin sip_sideal_bin
ideal id_Jet(const ideal i, int d, const ring R)
static void id_DelDiv_SEV(ideal id, int k, const ring r)
delete id[j], if LT(j) == coeff*mon*LT(i)
ideal id_SimpleAdd(ideal h1, ideal h2, const ring R)
concat the lists h1 and h2 without zeros
void id_DelLmEquals(ideal id, const ring r)
Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i.
ideal id_JetW(const ideal i, int d, intvec *iv, const ring R)
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
void id_Shift(ideal M, int s, const ring r)
int idGetNumberOfChoise(int t, int d, int begin, int end, int *choise)
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
ideal id_PermIdeal(ideal I, int R, int C, const int *perm, const ring src, const ring dst, nMapFunc nMap, const int *par_perm, int P, BOOLEAN use_mult)
mapping ideals/matrices to other rings
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
static void lpmakemonoms(int vars, int deg, const ring r)
void id_Compactify(ideal id, const ring r)
BOOLEAN id_HomModule(ideal m, ideal Q, intvec **w, const ring R)
ideal id_Subst(ideal id, int n, poly e, const ring r)
#define IDELEMS(i)
#define id_Test(A, lR)
The following sip_sideal structure has many different uses thoughout Singular. Basic use-cases for it...
#define R
Definition sirandom.c:27
#define M
Definition sirandom.c:25
#define Q
Definition sirandom.c:26
int * iv2array(intvec *iv, const ring R)
Definition weight.cc:200
EXTERN_VAR short * ecartWeights
Definition weight.h:12
#define omPrintAddrInfo(A, B, C)
Definition xalloc.h:270