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ideals.cc
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1/****************************************
2* Computer Algebra System SINGULAR *
3****************************************/
4/*
5* ABSTRACT - all basic methods to manipulate ideals
6*/
7
8/* includes */
9
10#include "kernel/mod2.h"
11
12#include "misc/options.h"
13#include "misc/intvec.h"
14
15#include "coeffs/coeffs.h"
16#include "coeffs/numbers.h"
17// #include "coeffs/longrat.h"
18
19
21#include "polys/matpol.h"
22#include "polys/weight.h"
23#include "polys/sparsmat.h"
24#include "polys/prCopy.h"
25#include "polys/nc/nc.h"
26
27
28#include "kernel/ideals.h"
29
30#include "kernel/polys.h"
31
34#include "kernel/GBEngine/tgb.h"
35#include "kernel/GBEngine/syz.h"
36#include "Singular/ipshell.h" // iiCallLibProc1
37#include "Singular/ipid.h" // ggetid
38
39
40#if 0
41#include "Singular/ipprint.h" // ipPrint_MA0
42#endif
43
44/* #define WITH_OLD_MINOR */
45
46/*0 implementation*/
47
48/*2
49*returns a minimized set of generators of h1
50*/
52{
53 ideal h2, h3,h4,e;
54 int j,k;
55 int i,l,ll;
56 intvec * wth;
57 BOOLEAN homog;
59 {
60 WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
61 e=idCopy(h1);
62 return e;
63 }
64 homog = idHomModule(h1,currRing->qideal,&wth);
66 {
67 if(!homog)
68 {
69 WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
70 e=idCopy(h1);
71 return e;
72 }
73 else
74 {
75 ideal re=kMin_std(h1,currRing->qideal,(tHomog)homog,&wth,h2,NULL,0,3);
76 idDelete(&re);
77 return h2;
78 }
79 }
80 e=idInit(1,h1->rank);
81 if (idIs0(h1))
82 {
83 return e;
84 }
85 h2 = kStd(h1,currRing->qideal,isNotHomog,NULL);
86 if (SB!=NULL) *SB=h2;
87 h3 = idMaxIdeal(1);
88 h4=idMult(h2,h3);
89 idDelete(&h3);
91 k = IDELEMS(h3);
92 while ((k > 0) && (h3->m[k-1] == NULL)) k--;
93 j = -1;
94 l = IDELEMS(h2);
95 while ((l > 0) && (h2->m[l-1] == NULL)) l--;
96 for (i=l-1; i>=0; i--)
97 {
98 if (h2->m[i] != NULL)
99 {
100 ll = 0;
101 while ((ll < k) && ((h3->m[ll] == NULL)
102 || !pDivisibleBy(h3->m[ll],h2->m[i])))
103 ll++;
104 if (ll >= k)
105 {
106 j++;
107 if (j > IDELEMS(e)-1)
108 {
109 pEnlargeSet(&(e->m),IDELEMS(e),16);
110 IDELEMS(e) += 16;
111 }
112 e->m[j] = pCopy(h2->m[i]);
113 }
114 }
115 }
116 if (SB==NULL) idDelete(&h2);
117 idDelete(&h3);
118 idDelete(&h4);
119 if (currRing->qideal!=NULL)
120 {
121 h3=idInit(1,e->rank);
122 h2=kNF(h3,currRing->qideal,e);
123 idDelete(&h3);
124 idDelete(&e);
125 e=h2;
126 }
127 idSkipZeroes(e);
128 return e;
129}
130
131
133// does not destroy h1,h2
134{
135 if (TEST_OPT_PROT) PrintS("intersect by elimination method\n");
136 assume(!idIs0(h1));
137 assume(!idIs0(h2));
141 // add a new variable:
142 int j;
145 r->N++;
146 r->block0[0]=1;
147 r->block1[0]= r->N;
148 omFree(r->order);
149 r->order=(rRingOrder_t*)omAlloc0(3*sizeof(rRingOrder_t));
150 r->order[0]=ringorder_dp;
151 r->order[1]=ringorder_C;
152 char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr));
153 for (j=0;j<r->N-1;j++) names[j]=r->names[j];
154 names[r->N-1]=omStrDup("@");
155 omFree(r->names);
156 r->names=names;
157 rComplete(r,TRUE);
158 // fetch h1, h2
159 ideal h;
162 // switch to temp. ring r
164 // create 1-t, t
165 poly omt=p_One(currRing);
166 p_SetExp(omt,r->N,1,currRing);
168 poly t=p_Copy(omt,currRing);
171 // compute (1-t)*h1
173 // compute t*h2
175 // (1-t)h1 + t*h2
177 int l;
178 for (l=IDELEMS(h1)-1; l>=0; l--)
179 {
180 h->m[l] = h1->m[l]; h1->m[l]=NULL;
181 }
182 j=IDELEMS(h1);
183 for (l=IDELEMS(h2)-1; l>=0; l--)
184 {
185 h->m[l+j] = h2->m[l]; h2->m[l]=NULL;
186 }
187 idDelete(&h1);
188 idDelete(&h2);
189 // eliminate t:
191 // cleanup
192 idDelete(&h);
193 pDelete(&t);
194 if (res!=NULL) res=idrMoveR(res,r,origRing);
196 rDelete(r);
197 return res;
198}
199
201{
202 //Print("syz=%d\n",syzComp);
203 //PrintS(showOption());
204 //PrintLn();
205 ideal res=NULL;
206 if (w==NULL)
207 {
208 if (hom==testHomog)
209 hom=(tHomog)idHomModule(temp,currRing->qideal,&w); //sets w to weight vector or NULL
210 }
211 else
212 {
213 w=ivCopy(w);
214 hom=isHomog;
215 }
216#ifdef HAVE_SHIFTBBA
217 if (rIsLPRing(currRing)) alg = GbStd;
218#endif
219 if ((alg==GbStd)||(alg==GbDefault))
220 {
221 if (TEST_OPT_PROT &&(alg==GbStd)) { PrintS("std:"); mflush(); }
222 res = kStd(temp,currRing->qideal,hom,&w,hilb,syzComp);
223 idDelete(&temp);
224 }
225 else if (alg==GbSlimgb)
226 {
227 if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); }
228 res = t_rep_gb(currRing, temp, syzComp);
229 idDelete(&temp);
230 }
231 else if (alg==GbGroebner)
232 {
233 if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); }
234 BOOLEAN err;
235 res=(ideal)iiCallLibProc1("groebner",temp,MODUL_CMD,err);
236 if (err)
237 {
238 Werror("error %d in >>groebner<<",err);
239 res=idInit(1,1);
240 }
241 }
242 else if (alg==GbModstd)
243 {
244 if (TEST_OPT_PROT) { PrintS("modStd:"); mflush(); }
245 BOOLEAN err;
246 void *args[]={temp,(void*)1,NULL};
247 int arg_t[]={MODUL_CMD,INT_CMD,0};
248 leftv temp0=ii_CallLibProcM("modStd",args,arg_t,currRing,err);
249 res=(ideal)temp0->data;
251 if (err)
252 {
253 Werror("error %d in >>modStd<<",err);
254 res=idInit(1,1);
255 }
256 }
257 else if (alg==GbSba)
258 {
259 if (TEST_OPT_PROT) { PrintS("sba:"); mflush(); }
260 res = kSba(temp,currRing->qideal,hom,&w,1,0,NULL);
261 if (w!=NULL) delete w;
262 }
263 else if (alg==GbStdSat)
264 {
265 if (TEST_OPT_PROT) { PrintS("std:sat:"); mflush(); }
266 BOOLEAN err;
267 // search for 2nd block of vars
268 int i=0;
269 int block=-1;
270 loop
271 {
272 if ((currRing->order[i]!=ringorder_c)
273 && (currRing->order[i]!=ringorder_C)
274 && (currRing->order[i]!=ringorder_s))
275 {
276 if (currRing->order[i]==0) { err=TRUE;break;}
277 block++;
278 if (block==1) { block=i; break;}
279 }
280 i++;
281 }
282 if (block>0)
283 {
284 if (TEST_OPT_PROT)
285 {
286 Print("sat(%d..%d)\n",currRing->block0[block],currRing->block1[block]);
287 mflush();
288 }
289 ideal v=idInit(currRing->block1[block]-currRing->block0[block]+1,1);
290 for(i=currRing->block0[block];i<=currRing->block1[block];i++)
291 {
292 v->m[i-currRing->block0[block]]=pOne();
293 pSetExp(v->m[i-currRing->block0[block]],i,1);
294 pSetm(v->m[i-currRing->block0[block]]);
295 }
296 void *args[]={temp,v,NULL};
297 int arg_t[]={MODUL_CMD,IDEAL_CMD,0};
298 leftv temp0=ii_CallLibProcM("satstd",args,arg_t,currRing,err);
299 res=(ideal)temp0->data;
301 }
302 if (err)
303 {
304 Werror("error %d in >>satstd<<",err);
305 res=idInit(1,1);
306 }
307 }
308 if (w!=NULL) delete w;
309 return res;
310}
311
312/*2
313* h3 := h1 intersect h2
314*/
316{
317 int i,j,k;
318 unsigned length;
321 int rank=si_max(h1->rank,h2->rank);
322 if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank);
323
327
329 poly p,q;
330
331 if (IDELEMS(h1)<IDELEMS(h2))
332 {
333 first = h1;
334 second = h2;
335 }
336 else
337 {
338 first = h2;
339 second = h1;
340 int t=flength; flength=slength; slength=t;
341 }
343 if (length==0)
344 {
345 if ((currRing->qideal==NULL)
346 && (currRing->OrdSgn==1)
349 return idSectWithElim(first,second,alg);
350 else length = 1;
351 }
352 if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n");
353 j = IDELEMS(first);
354
360
361 while ((j>0) && (first->m[j-1]==NULL)) j--;
362 temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j);
363 k = 0;
364 for (i=0;i<j;i++)
365 {
366 if (first->m[i]!=NULL)
367 {
368 if (syz_ring==orig_ring)
369 temp->m[k] = pCopy(first->m[i]);
370 else
371 temp->m[k] = prCopyR(first->m[i], orig_ring, syz_ring);
372 q = pOne();
373 pSetComp(q,i+1+length);
374 pSetmComp(q);
375 if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
376 p = temp->m[k];
377 while (pNext(p)!=NULL) pIter(p);
378 pNext(p) = q;
379 k++;
380 }
381 }
382 for (i=0;i<IDELEMS(second);i++)
383 {
384 if (second->m[i]!=NULL)
385 {
386 if (syz_ring==orig_ring)
387 temp->m[k] = pCopy(second->m[i]);
388 else
389 temp->m[k] = prCopyR(second->m[i], orig_ring,currRing);
390 if (slength==0) p_Shift(&(temp->m[k]),1,currRing);
391 k++;
392 }
393 }
394 intvec *w=NULL;
395
396 if ((alg!=GbDefault)
397 && (alg!=GbGroebner)
398 && (alg!=GbModstd)
399 && (alg!=GbSlimgb)
400 && (alg!=GbStd))
401 {
402 WarnS("wrong algorithm for GB");
404 }
406
409
410 result = idInit(IDELEMS(temp1),rank);
411 j = 0;
412 for (i=0;i<IDELEMS(temp1);i++)
413 {
414 if ((temp1->m[i]!=NULL)
416 {
418 {
419 p = temp1->m[i];
420 }
421 else
422 {
424 }
425 temp1->m[i]=NULL;
426 while (p!=NULL)
427 {
428 q = pNext(p);
429 pNext(p) = NULL;
430 k = pGetComp(p)-1-length;
431 pSetComp(p,0);
432 pSetmComp(p);
433 /* Warning! multiply only from the left! it's very important for Plural */
434 result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k])));
435 p = q;
436 }
437 j++;
438 }
439 }
441 {
443 idDelete(&temp1);
446 }
447 else
448 {
449 idDelete(&temp1);
450 }
451
455 {
456 w=NULL;
458 if (w!=NULL) delete w;
461 return temp1;
462 }
463 //else
464 // temp1=kInterRed(result,currRing->qideal);
465 return result;
466}
467
468/*2
469* ideal/module intersection for a list of objects
470* given as 'resolvente'
471*/
473{
474 int i,j=0,k=0,l,maxrk=-1,realrki;
475 unsigned syzComp;
477 poly p;
478 int isIdeal=0;
479
480 /* find 0-ideals and max rank -----------------------------------*/
481 for (i=0;i<length;i++)
482 {
483 if (!idIs0(arg[i]))
484 {
486 k++;
487 j += IDELEMS(arg[i]);
488 if (realrki>maxrk) maxrk = realrki;
489 }
490 else
491 {
492 if (arg[i]!=NULL)
493 {
494 return idInit(1,arg[i]->rank);
495 }
496 }
497 }
498 if (maxrk == 0)
499 {
500 isIdeal = 1;
501 maxrk = 1;
502 }
503 /* init -----------------------------------------------------------*/
504 j += maxrk;
505 syzComp = k*maxrk;
506
510
513 rSetSyzComp(syzComp,syz_ring);
515
516 bigmat = idInit(j,(k+1)*maxrk);
517 /* create unit matrices ------------------------------------------*/
518 for (i=0;i<maxrk;i++)
519 {
520 for (j=0;j<=k;j++)
521 {
522 p = pOne();
523 pSetComp(p,i+1+j*maxrk);
524 pSetmComp(p);
525 bigmat->m[i] = pAdd(bigmat->m[i],p);
526 }
527 }
528 /* enter given ideals ------------------------------------------*/
529 i = maxrk;
530 k = 0;
531 for (j=0;j<length;j++)
532 {
533 if (arg[j]!=NULL)
534 {
535 for (l=0;l<IDELEMS(arg[j]);l++)
536 {
537 if (arg[j]->m[l]!=NULL)
538 {
539 if (syz_ring==orig_ring)
540 bigmat->m[i] = pCopy(arg[j]->m[l]);
541 else
542 bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring,currRing);
544 i++;
545 }
546 }
547 k++;
548 }
549 }
550 /* std computation --------------------------------------------*/
551 if ((alg!=GbDefault)
552 && (alg!=GbGroebner)
553 && (alg!=GbModstd)
554 && (alg!=GbSlimgb)
555 && (alg!=GbStd))
556 {
557 WarnS("wrong algorithm for GB");
559 }
560 tempstd=idGroebner(bigmat,syzComp,alg);
561
564
565 /* interpret result ----------------------------------------*/
567 k = 0;
568 for (j=0;j<IDELEMS(tempstd);j++)
569 {
570 if ((tempstd->m[j]!=NULL) && (__p_GetComp(tempstd->m[j],syz_ring)>syzComp))
571 {
572 if (syz_ring==orig_ring)
573 p = pCopy(tempstd->m[j]);
574 else
576 p_Shift(&p,-syzComp-isIdeal,currRing);
577 result->m[k] = p;
578 k++;
579 }
580 }
581 /* clean up ----------------------------------------------------*/
586 {
589 }
592 return result;
593}
594
595/*2
596*computes syzygies of h1,
597*if quot != NULL it computes in the quotient ring modulo "quot"
598*works always in a ring with ringorder_s
599*/
600/* construct a "matrix" (h11 may be NULL)
601 * h1 h11
602 * E_n 0
603 * and compute a (column) GB of it, with a syzComp=rows(h1)=rows(h11)
604 * currRing must be a syz-ring with syzComp set
605 * result is a "matrix":
606 * G 0
607 * T S
608 * where G: GB of (h1+h11)
609 * T: G/h11=h1*T
610 * S: relative syzygies(h1) modulo h11
611 * if V_IDLIFT is set, ignore/do not return S
612 */
614{
615 ideal h2,h22;
616 int j,k;
617 poly p,q;
618
619 assume(!idIs0(h1));
621 if (h11!=NULL)
622 {
624 h22=idCopy(h11);
625 }
626 h2=idCopy(h1);
627 int i = IDELEMS(h2);
628 if (h11!=NULL) i+=IDELEMS(h22);
629 if (k == 0)
630 {
632 if (h11!=NULL) id_Shift(h22,1,currRing);
633 k = 1;
634 }
635 if (syzcomp<k)
636 {
637 Warn("syzcomp too low, should be %d instead of %d",k,syzcomp);
638 syzcomp = k;
640 }
641 h2->rank = syzcomp+i;
642
643 //if (hom==testHomog)
644 //{
645 // if(idHomIdeal(h1,currRing->qideal))
646 // {
647 // hom=TRUE;
648 // }
649 //}
650
651 for (j=0; j<IDELEMS(h2); j++)
652 {
653 p = h2->m[j];
654 q = pOne();
655#ifdef HAVE_SHIFTBBA
656 // non multiplicative variable
657 if (rIsLPRing(currRing))
658 {
659 pSetExp(q, currRing->isLPring - currRing->LPncGenCount + j + 1, 1);
660 p_Setm(q, currRing);
661 }
662#endif
663 pSetComp(q,syzcomp+1+j);
664 pSetmComp(q);
665 if (p!=NULL)
666 {
667#ifdef HAVE_SHIFTBBA
668 if (rIsLPRing(currRing))
669 {
670 h2->m[j] = pAdd(p, q);
671 }
672 else
673#endif
674 {
675 while (pNext(p)) pIter(p);
676 p->next = q;
677 }
678 }
679 else
680 h2->m[j]=q;
681 }
682 if (h11!=NULL)
683 {
687 h2=h;
688 }
689
690 idTest(h2);
691 #if 0
693 PrintS(" --------------before std------------------------\n");
694 ipPrint_MA0(TT,"T");
695 PrintLn();
696 idDelete((ideal*)&TT);
697 #endif
698
699 if ((alg!=GbDefault)
700 && (alg!=GbGroebner)
701 && (alg!=GbModstd)
702 && (alg!=GbSlimgb)
703 && (alg!=GbStd))
704 {
705 WarnS("wrong algorithm for GB");
707 }
708
709 ideal h3;
710 if (w!=NULL) h3=idGroebner(h2,syzcomp,alg,NULL,*w,hom);
711 else h3=idGroebner(h2,syzcomp,alg,NULL,NULL,hom);
712 return h3;
713}
714
717{
718 // now sort the result, SB : leave in s_h3
719 // T: put in s_h2 (*T as a matrix)
720 // syz: put in *S
722 ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank); // will become T
723
724 #if 0
726 Print("after std: --------------syzComp=%d------------------------\n",syzComp);
727 ipPrint_MA0(TT,"T");
728 PrintLn();
729 idDelete((ideal*)&TT);
730 #endif
731
732 int j, i=0;
733 for (j=0; j<IDELEMS(s_h3); j++)
734 {
735 if (s_h3->m[j] != NULL)
736 {
737 if (pGetComp(s_h3->m[j]) <= syzComp) // syz_ring == currRing
738 {
739 i++;
740 poly q = s_h3->m[j];
741 while (pNext(q) != NULL)
742 {
743 if (pGetComp(pNext(q)) > syzComp)
744 {
745 s_h2->m[i-1] = pNext(q);
746 pNext(q) = NULL;
747 }
748 else
749 {
750 pIter(q);
751 }
752 }
753 if (!inputIsIdeal) p_Shift(&(s_h3->m[j]), -1,currRing);
754 }
755 else
756 {
757 // we a syzygy here:
758 if (S!=NULL)
759 {
760 p_Shift(&s_h3->m[j], -syzComp,currRing);
761 (*S)->m[j]=s_h3->m[j];
762 s_h3->m[j]=NULL;
763 }
764 else
765 p_Delete(&(s_h3->m[j]),currRing);
766 }
767 }
768 }
770
771 #if 0
773 PrintS("T: ----------------------------------------\n");
774 ipPrint_MA0(TT,"T");
775 PrintLn();
776 idDelete((ideal*)&TT);
777 #endif
778
779 if (S!=NULL) idSkipZeroes(*S);
780
781 if (sring!=oring)
782 {
784 }
785
786 if (T!=NULL)
787 {
788 *T = mpNew(h1_size,i);
789
790 for (j=0; j<i; j++)
791 {
792 if (s_h2->m[j] != NULL)
793 {
794 poly q = prMoveR( s_h2->m[j], sring,oring);
795 s_h2->m[j] = NULL;
796
797 if (q!=NULL)
798 {
799 q=pReverse(q);
800 while (q != NULL)
801 {
802 poly p = q;
803 pIter(q);
804 pNext(p) = NULL;
805 int t=pGetComp(p);
806 pSetComp(p,0);
807 pSetmComp(p);
808 MATELEM(*T,t-syzComp,j+1) = pAdd(MATELEM(*T,t-syzComp,j+1),p);
809 }
810 }
811 }
812 }
813 }
815
816 for (i=0; i<IDELEMS(s_h3); i++)
817 {
818 s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], sring,oring);
819 }
820 if (S!=NULL)
821 {
822 for (i=0; i<IDELEMS(*S); i++)
823 {
824 (*S)->m[i] = prMoveR_NoSort((*S)->m[i], sring,oring);
825 }
826 }
827 return s_h3;
828}
829
830/*2
831* compute the syzygies of h1 in R/quot,
832* weights of components are in w
833* if setRegularity, return the regularity in deg
834* do not change h1, w
835*/
838{
839 ideal s_h1;
840 int j, k, length=0,reg;
842 int ii, idElemens_h1;
843
844 assume(h1 != NULL);
845
847#ifdef PDEBUG
848 for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]);
849#endif
850 if (idIs0(h1))
851 {
852 ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/);
853 return result;
854 }
856 k=si_max(1,slength /*id_RankFreeModule(h1)*/);
857
858 assume(currRing != NULL);
862
863 if (orig_ring != syz_ring)
864 {
867 }
868 else
869 {
870 s_h1 = h1;
871 }
872
873 idTest(s_h1);
874
878
879 ideal s_h3=idPrepare(s_h1,NULL,h,k,w,alg); // main (syz) GB computation
880
882
883 if (orig_ring != syz_ring)
884 {
885 idDelete(&s_h1);
886 for (j=0; j<IDELEMS(s_h3); j++)
887 {
888 if (s_h3->m[j] != NULL)
889 {
890 if (p_MinComp(s_h3->m[j],syz_ring) > k)
891 p_Shift(&s_h3->m[j], -k,syz_ring);
892 else
893 p_Delete(&s_h3->m[j],syz_ring);
894 }
895 }
897 s_h3->rank -= k;
901 #ifdef HAVE_PLURAL
903 {
906 }
907 #endif
908 idTest(s_h3);
909 return s_h3;
910 }
911
912 ideal e = idInit(IDELEMS(s_h3), s_h3->rank);
913
914 for (j=IDELEMS(s_h3)-1; j>=0; j--)
915 {
916 if (s_h3->m[j] != NULL)
917 {
918 if (p_MinComp(s_h3->m[j],syz_ring) <= k)
919 {
920 e->m[j] = s_h3->m[j];
923 s_h3->m[j] = NULL;
924 }
925 }
926 }
927
929 idSkipZeroes(e);
930
931 if ((deg != NULL)
932 && (!isMonomial)
934 && (setRegularity)
935 && (h==isHomog)
938 )
939 {
941 ring dp_C_ring = rAssure_dp_C(syz_ring); // will do rChangeCurrRing later
942 if (dp_C_ring != syz_ring)
943 {
946 }
949 *deg = reg+2;
950 delete dummy;
951 for (j=0;j<length;j++)
952 {
953 if (res[j]!=NULL) idDelete(&(res[j]));
954 }
956 idDelete(&e);
957 if (dp_C_ring != orig_ring)
958 {
961 }
962 }
963 else
964 {
965 idDelete(&e);
966 }
968 idTest(s_h3);
969 if (currRing->qideal != NULL)
970 {
971 ideal ts_h3=kStd(s_h3,currRing->qideal,h,w);
972 idDelete(&s_h3);
973 s_h3 = ts_h3;
974 }
975 return s_h3;
976}
977
978/*
979*computes a standard basis for h1 and stores the transformation matrix
980* in ma
981*/
983 ideal h11)
984{
986 long k;
987 intvec *w=NULL;
988
989 idDelete((ideal*)T);
991 if (S!=NULL) { lift3=TRUE; idDelete(S); }
992 if (idIs0(h1))
993 {
994 *T=mpNew(1,IDELEMS(h1));
995 if (lift3)
996 {
998 }
999 return idInit(1,h1->rank);
1000 }
1001
1006
1008
1013
1014 ideal s_h1;
1015
1016 if (orig_ring != syz_ring)
1018 else
1019 s_h1 = h1;
1021 if (h11!=NULL)
1022 {
1024 }
1025
1026
1027 ideal s_h3=idPrepare(s_h1,s_h11,hi,k,&w,alg); // main (syz) GB computation
1028
1029
1030 if (w!=NULL) delete w;
1031 if (syz_ring!=orig_ring)
1032 {
1033 idDelete(&s_h1);
1034 if (s_h11!=NULL) idDelete(&s_h11);
1035 }
1036
1037 if (S!=NULL) (*S)=idInit(IDELEMS(s_h3),IDELEMS(h1));
1038
1040
1042 s_h3->rank=h1->rank;
1044 return s_h3;
1045}
1046
1047static void idPrepareStd(ideal s_temp, int k)
1048{
1050 poly p,q;
1051
1052 if (rk == 0)
1053 {
1054 for (j=0; j<IDELEMS(s_temp); j++)
1055 {
1056 if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1);
1057 }
1058 k = si_max(k,1);
1059 }
1060 for (j=0; j<IDELEMS(s_temp); j++)
1061 {
1062 if (s_temp->m[j]!=NULL)
1063 {
1064 p = s_temp->m[j];
1065 q = pOne();
1066 //pGetCoeff(q)=nInpNeg(pGetCoeff(q)); //set q to -1
1067 pSetComp(q,k+1+j);
1068 pSetmComp(q);
1069#ifdef HAVE_SHIFTBBA
1070 // non multiplicative variable
1071 if (rIsLPRing(currRing))
1072 {
1073 pSetExp(q, currRing->isLPring - currRing->LPncGenCount + j + 1, 1);
1074 p_Setm(q, currRing);
1075 s_temp->m[j] = pAdd(p, q);
1076 }
1077 else
1078#endif
1079 {
1080 while (pNext(p)) pIter(p);
1081 pNext(p) = q;
1082 }
1083 }
1084 }
1085 s_temp->rank = k+IDELEMS(s_temp);
1086}
1087
1089{
1090 if (unit!=NULL)
1091 {
1093 // make sure that U is a diagonal matrix of units
1094 for(int i=e_mod;i>0;i--)
1095 {
1096 MATELEM(*unit,i,i)=pOne();
1097 }
1098 }
1099}
1100/*2
1101*computes a representation of the generators of submod with respect to those
1102* of mod
1103*/
1104/// represents the generators of submod in terms of the generators of mod
1105/// (Matrix(SM)*U-Matrix(rest)) = Matrix(M)*Matrix(result)
1106/// goodShape: maximal non-zero index in generators of SM <= that of M
1107/// isSB: generators of M form a Groebner basis
1108/// divide: allow SM not to be a submodule of M
1109/// U is an diagonal matrix of units (non-constant only in local rings)
1110/// rest is: 0 if SM in M, SM if not divide, NF(SM,std(M)) if divide
1113{
1115 int comps_to_add=0;
1116 int idelems_mod=IDELEMS(mod);
1118 poly p;
1119
1120 if (idIs0(submod))
1121 {
1122 if (rest!=NULL)
1123 {
1124 *rest=idInit(1,mod->rank);
1125 }
1127 return idInit(1,idelems_mod);
1128 }
1129 if (idIs0(mod)) /* and not idIs0(submod) */
1130 {
1131 if (rest!=NULL)
1132 {
1133 *rest=idCopy(submod);
1135 return idInit(1,idelems_mod);
1136 }
1137 else
1138 {
1139 WerrorS("2nd module does not lie in the first");
1140 return NULL;
1141 }
1142 }
1143 if (unit!=NULL)
1144 {
1146 while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL))
1147 comps_to_add--;
1148 }
1150 if ((k!=0) && (lsmod==0)) lsmod=1;
1151 k=si_max(k,(int)mod->rank);
1152 if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; }
1153
1158
1160 if (orig_ring != syz_ring)
1161 {
1164 }
1165 else
1166 {
1167 s_mod = mod;
1168 s_temp = idCopy(submod);
1169 }
1170 BITSET save2;
1172
1173 if ((rest==NULL)
1175 && (!rIsNCRing(currRing))
1176 && (!TEST_OPT_RETURN_SB))
1178 else
1179 si_opt_2 &=~Sy_bit(V_IDLIFT);
1180 ideal s_h3;
1181 if (isSB && !TEST_OPT_IDLIFT)
1182 {
1183 s_h3 = idCopy(s_mod);
1185 }
1186 else
1187 {
1189 }
1191
1192 if (!goodShape)
1193 {
1194 for (j=0;j<IDELEMS(s_h3);j++)
1195 {
1196 if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k))
1197 p_Delete(&(s_h3->m[j]),currRing);
1198 }
1199 }
1201 if (lsmod==0)
1202 {
1204 }
1205 if (unit!=NULL)
1206 {
1207 for(j = 0;j<comps_to_add;j++)
1208 {
1209 p = s_temp->m[j];
1210 if (p!=NULL)
1211 {
1212 while (pNext(p)!=NULL) pIter(p);
1213 pNext(p) = pOne();
1214 pIter(p);
1215 pSetComp(p,1+j+k);
1216 pSetmComp(p);
1217 p = pNeg(p);
1218 }
1219 }
1220 s_temp->rank += (k+comps_to_add);
1221 }
1222 ideal s_result = kNF(s_h3,currRing->qideal,s_temp,k);
1223 s_result->rank = s_h3->rank;
1225 idDelete(&s_h3);
1226 idDelete(&s_temp);
1227
1228 for (j=0;j<IDELEMS(s_result);j++)
1229 {
1230 if (s_result->m[j]!=NULL)
1231 {
1232 if (pGetComp(s_result->m[j])<=k)
1233 {
1234 if (!divide)
1235 {
1236 if (rest==NULL)
1237 {
1238 if (isSB)
1239 {
1240 WarnS("first module not a standardbasis\n"
1241 "// ** or second not a proper submodule");
1242 }
1243 else
1244 WerrorS("2nd module does not lie in the first");
1245 }
1247 idDelete(&s_rest);
1248 if(syz_ring!=orig_ring)
1249 {
1250 idDelete(&s_mod);
1253 }
1254 if (unit!=NULL)
1255 {
1257 }
1258 if (rest!=NULL) *rest=idCopy(submod);
1260 return s_result;
1261 }
1262 else
1263 {
1264 p = s_rest->m[j] = s_result->m[j];
1265 while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p);
1266 s_result->m[j] = pNext(p);
1267 pNext(p) = NULL;
1268 }
1269 }
1270 p_Shift(&(s_result->m[j]),-k,currRing);
1271 pNeg(s_result->m[j]);
1272 }
1273 }
1274 if ((lsmod==0) && (s_rest!=NULL))
1275 {
1276 for (j=IDELEMS(s_rest);j>0;j--)
1277 {
1278 if (s_rest->m[j-1]!=NULL)
1279 {
1280 p_Shift(&(s_rest->m[j-1]),-1,currRing);
1281 }
1282 }
1283 }
1284 if(syz_ring!=orig_ring)
1285 {
1286 idDelete(&s_mod);
1291 }
1292 if (rest!=NULL)
1293 {
1294 s_rest->rank=mod->rank;
1295 *rest = s_rest;
1296 }
1297 else
1298 idDelete(&s_rest);
1299 if (unit!=NULL)
1300 {
1302 int i;
1303 for(i=0;i<IDELEMS(s_result);i++)
1304 {
1305 poly p=s_result->m[i];
1306 poly q=NULL;
1307 while(p!=NULL)
1308 {
1309 if(pGetComp(p)<=comps_to_add)
1310 {
1311 pSetComp(p,0);
1312 if (q!=NULL)
1313 {
1314 pNext(q)=pNext(p);
1315 }
1316 else
1317 {
1318 pIter(s_result->m[i]);
1319 }
1320 pNext(p)=NULL;
1321 MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p);
1322 if(q!=NULL) p=pNext(q);
1323 else p=s_result->m[i];
1324 }
1325 else
1326 {
1327 q=p;
1328 pIter(p);
1329 }
1330 }
1332 }
1333 }
1334 s_result->rank=idelems_mod;
1335 return s_result;
1336}
1337
1338/*2
1339*computes division of P by Q with remainder up to (w-weighted) degree n
1340*P, Q, and w are not changed
1341*/
1342void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,int *w)
1343{
1344 long N=0;
1345 int i;
1346 for(i=IDELEMS(Q)-1;i>=0;i--)
1347 if(w==NULL)
1348 N=si_max(N,p_Deg(Q->m[i],currRing));
1349 else
1350 N=si_max(N,p_DegW(Q->m[i],w,currRing));
1351 N+=n;
1352
1353 T=mpNew(IDELEMS(Q),IDELEMS(P));
1354 R=idInit(IDELEMS(P),P->rank);
1355
1356 for(i=IDELEMS(P)-1;i>=0;i--)
1357 {
1358 poly p;
1359 if(w==NULL)
1360 p=ppJet(P->m[i],N);
1361 else
1362 p=ppJetW(P->m[i],N,w);
1363
1364 int j=IDELEMS(Q)-1;
1365 while(p!=NULL)
1366 {
1367 if(pDivisibleBy(Q->m[j],p))
1368 {
1369 poly p0=p_DivideM(pHead(p),pHead(Q->m[j]),currRing);
1370 if(w==NULL)
1371 p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N);
1372 else
1373 p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w);
1374 pNormalize(p);
1375 if(((w==NULL)&&(p_Deg(p0,currRing)>n))||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
1377 else
1378 MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0);
1379 j=IDELEMS(Q)-1;
1380 }
1381 else
1382 {
1383 if(j==0)
1384 {
1385 poly p0=p;
1386 pIter(p);
1387 pNext(p0)=NULL;
1388 if(((w==NULL)&&(p_Deg(p0,currRing)>n))
1389 ||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
1391 else
1392 R->m[i]=pAdd(R->m[i],p0);
1393 j=IDELEMS(Q)-1;
1394 }
1395 else
1396 j--;
1397 }
1398 }
1399 }
1400}
1401
1402/*2
1403*computes the quotient of h1,h2 : internal routine for idQuot
1404*BEWARE: the returned ideals may contain incorrectly ordered polys !
1405*
1406*/
1408{
1409 idTest(h1);
1410 idTest(h2);
1411
1412 ideal temph1;
1413 poly p,q = NULL;
1414 int i,l,ll,k,kkk,kmax;
1415 int j = 0;
1419 k=si_max(k1,k2);
1420 if (k==0)
1421 k = 1;
1422 if ((k2==0) && (k>1)) *addOnlyOne = FALSE;
1423 intvec * weights;
1424 hom = (tHomog)idHomModule(h1,currRing->qideal,&weights);
1425 if /**addOnlyOne &&*/ (/*(*/ !h1IsStb /*)*/)
1426 temph1 = kStd(h1,currRing->qideal,hom,&weights,NULL);
1427 else
1428 temph1 = idCopy(h1);
1429 if (weights!=NULL) delete weights;
1430 idTest(temph1);
1431/*--- making a single vector from h2 ---------------------*/
1432 for (i=0; i<IDELEMS(h2); i++)
1433 {
1434 if (h2->m[i] != NULL)
1435 {
1436 p = pCopy(h2->m[i]);
1437 if (k2 == 0)
1438 p_Shift(&p,j*k+1,currRing);
1439 else
1440 p_Shift(&p,j*k,currRing);
1441 q = pAdd(q,p);
1442 j++;
1443 }
1444 }
1445 *kkmax = kmax = j*k+1;
1446/*--- adding a monomial for the result (syzygy) ----------*/
1447 p = q;
1448 while (pNext(p)!=NULL) pIter(p);
1449 pNext(p) = pOne();
1450 pIter(p);
1451 pSetComp(p,kmax);
1452 pSetmComp(p);
1453/*--- constructing the big matrix ------------------------*/
1454 ideal h4 = idInit(k,kmax+k-1);
1455 h4->m[0] = q;
1456 if (k2 == 0)
1457 {
1458 for (i=1; i<k; i++)
1459 {
1460 if (h4->m[i-1]!=NULL)
1461 {
1462 p = p_Copy_noCheck(h4->m[i-1], currRing); /*h4->m[i-1]!=NULL*/
1463 p_Shift(&p,1,currRing);
1464 h4->m[i] = p;
1465 }
1466 else break;
1467 }
1468 }
1470 kkk = IDELEMS(h4);
1471 i = IDELEMS(temph1);
1472 for (l=0; l<i; l++)
1473 {
1474 if(temph1->m[l]!=NULL)
1475 {
1476 for (ll=0; ll<j; ll++)
1477 {
1478 p = pCopy(temph1->m[l]);
1479 if (k1 == 0)
1480 p_Shift(&p,ll*k+1,currRing);
1481 else
1482 p_Shift(&p,ll*k,currRing);
1483 if (kkk >= IDELEMS(h4))
1484 {
1485 pEnlargeSet(&(h4->m),IDELEMS(h4),16);
1486 IDELEMS(h4) += 16;
1487 }
1488 h4->m[kkk] = p;
1489 kkk++;
1490 }
1491 }
1492 }
1493/*--- if h2 goes in as single vector - the h1-part is just SB ---*/
1494 if (*addOnlyOne)
1495 {
1497 p = h4->m[0];
1498 for (i=0;i<IDELEMS(h4)-1;i++)
1499 {
1500 h4->m[i] = h4->m[i+1];
1501 }
1502 h4->m[IDELEMS(h4)-1] = p;
1503 }
1504 idDelete(&temph1);
1505 //idTest(h4);//see remark at the beginning
1506 return h4;
1507}
1508
1509/*2
1510*computes the quotient of h1,h2
1511*/
1513{
1514 // first check for special case h1:(0)
1515 if (idIs0(h2))
1516 {
1517 ideal res;
1518 if (resultIsIdeal)
1519 {
1520 res = idInit(1,1);
1521 res->m[0] = pOne();
1522 }
1523 else
1524 res = idFreeModule(h1->rank);
1525 return res;
1526 }
1527 int i, kmax;
1530 intvec * weights1;
1531
1533
1535
1540 if (orig_ring!=syz_ring)
1541 // s_h4 = idrMoveR_NoSort(s_h4,orig_ring, syz_ring);
1543 idTest(s_h4);
1544
1545 #if 0
1547 PrintS("start:\n");
1548 ipPrint_MA0(m,"Q");
1549 idDelete((ideal *)&m);
1550 PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn();
1551 #endif
1552
1553 ideal s_h3;
1557 if (addOnlyOne)
1558 {
1560 s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,0/*kmax-1*/,IDELEMS(s_h4)-1);
1561 }
1562 else
1563 {
1564 s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,kmax-1);
1565 }
1567
1568 #if 0
1569 // only together with the above debug stuff
1572 Print("result, kmax=%d:\n",kmax);
1573 ipPrint_MA0(m,"S");
1574 idDelete((ideal *)&m);
1575 #endif
1576
1577 idTest(s_h3);
1578 if (weights1!=NULL) delete weights1;
1579 idDelete(&s_h4);
1580
1581 for (i=0;i<IDELEMS(s_h3);i++)
1582 {
1583 if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax))
1584 {
1585 if (resultIsIdeal)
1586 p_Shift(&s_h3->m[i],-kmax,currRing);
1587 else
1588 p_Shift(&s_h3->m[i],-kmax+1,currRing);
1589 }
1590 else
1591 p_Delete(&s_h3->m[i],currRing);
1592 }
1593 if (resultIsIdeal)
1594 s_h3->rank = 1;
1595 else
1596 s_h3->rank = h1->rank;
1597 if(syz_ring!=orig_ring)
1598 {
1602 }
1604 idTest(s_h3);
1605 return s_h3;
1606}
1607
1608/*2
1609* eliminate delVar (product of vars) in h1
1610*/
1612{
1613 int i,j=0,k,l;
1614 ideal h,hh, h3;
1615 rRingOrder_t *ord;
1616 int *block0,*block1;
1617 int ordersize=2;
1618 int **wv;
1619 tHomog hom;
1620 intvec * w;
1621 ring tmpR;
1623
1624 if (delVar==NULL)
1625 {
1626 return idCopy(h1);
1627 }
1628 if ((currRing->qideal!=NULL) && rIsPluralRing(origR))
1629 {
1630 WerrorS("cannot eliminate in a qring");
1631 return NULL;
1632 }
1633 if (idIs0(h1)) return idInit(1,h1->rank);
1634#ifdef HAVE_PLURAL
1635 if (rIsPluralRing(origR))
1636 /* in the NC case, we have to check the admissibility of */
1637 /* the subalgebra to be intersected with */
1638 {
1639 if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */
1640 {
1642 {
1643 WerrorS("no elimination is possible: subalgebra is not admissible");
1644 return NULL;
1645 }
1646 }
1647 }
1648#endif
1649 hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL
1650 h3=idInit(16,h1->rank);
1652#if 0
1653 if (rIsPluralRing(origR)) // we have too keep the odering: it may be needed
1654 // for G-algebra
1655 {
1656 for (k=0;k<ordersize-1; k++)
1657 {
1658 block0[k+1] = origR->block0[k];
1659 block1[k+1] = origR->block1[k];
1660 ord[k+1] = origR->order[k];
1661 if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
1662 }
1663 }
1664 else
1665 {
1666 block0[1] = 1;
1667 block1[1] = (currRing->N);
1668 if (origR->OrdSgn==1) ord[1] = ringorder_wp;
1669 else ord[1] = ringorder_ws;
1670 wv[1]=(int*)omAlloc0((currRing->N)*sizeof(int));
1671 double wNsqr = (double)2.0 / (double)(currRing->N);
1673 int *x= (int * )omAlloc(2 * ((currRing->N) + 1) * sizeof(int));
1674 int sl=IDELEMS(h1) - 1;
1675 wCall(h1->m, sl, x, wNsqr);
1676 for (sl = (currRing->N); sl!=0; sl--)
1677 wv[1][sl-1] = x[sl + (currRing->N) + 1];
1678 omFreeSize((ADDRESS)x, 2 * ((currRing->N) + 1) * sizeof(int));
1679
1680 ord[2]=ringorder_C;
1681 ord[3]=0;
1682 }
1683#else
1684#endif
1685 if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR)))
1686 {
1687 #if 1
1688 // we change to an ordering:
1689 // aa(1,1,1,...,0,0,0),wp(...),C
1690 // this seems to be better than version 2 below,
1691 // according to Tst/../elimiate_[3568].tat (- 17 %)
1692 ord=(rRingOrder_t*)omAlloc0(4*sizeof(rRingOrder_t));
1693 block0=(int*)omAlloc0(4*sizeof(int));
1694 block1=(int*)omAlloc0(4*sizeof(int));
1695 wv=(int**) omAlloc0(4*sizeof(int**));
1696 block0[0] = block0[1] = 1;
1697 block1[0] = block1[1] = rVar(origR);
1698 wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1699 // use this special ordering: like ringorder_a, except that pFDeg, pWeights
1700 // ignore it
1701 ord[0] = ringorder_aa;
1702 for (j=0;j<rVar(origR);j++)
1703 if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
1704 BOOLEAN wp=FALSE;
1705 for (j=0;j<rVar(origR);j++)
1706 if (p_Weight(j+1,origR)!=1) { wp=TRUE;break; }
1707 if (wp)
1708 {
1709 wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1710 for (j=0;j<rVar(origR);j++)
1711 wv[1][j]=p_Weight(j+1,origR);
1712 ord[1] = ringorder_wp;
1713 }
1714 else
1715 ord[1] = ringorder_dp;
1716 #else
1717 // we change to an ordering:
1718 // a(w1,...wn),wp(1,...0.....),C
1719 ord=(int*)omAlloc0(4*sizeof(int));
1720 block0=(int*)omAlloc0(4*sizeof(int));
1721 block1=(int*)omAlloc0(4*sizeof(int));
1722 wv=(int**) omAlloc0(4*sizeof(int**));
1723 block0[0] = block0[1] = 1;
1724 block1[0] = block1[1] = rVar(origR);
1725 wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1726 wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1727 ord[0] = ringorder_a;
1728 for (j=0;j<rVar(origR);j++)
1729 wv[0][j]=pWeight(j+1,origR);
1730 ord[1] = ringorder_wp;
1731 for (j=0;j<rVar(origR);j++)
1732 if (pGetExp(delVar,j+1)!=0) wv[1][j]=1;
1733 #endif
1734 ord[2] = ringorder_C;
1735 ord[3] = (rRingOrder_t)0;
1736 }
1737 else
1738 {
1739 // we change to an ordering:
1740 // aa(....),orig_ordering
1742 block0=(int*)omAlloc0(ordersize*sizeof(int));
1743 block1=(int*)omAlloc0(ordersize*sizeof(int));
1744 wv=(int**) omAlloc0(ordersize*sizeof(int**));
1745 for (k=0;k<ordersize-1; k++)
1746 {
1747 block0[k+1] = origR->block0[k];
1748 block1[k+1] = origR->block1[k];
1749 ord[k+1] = origR->order[k];
1750 if (origR->wvhdl[k]!=NULL)
1751 #ifdef HAVE_OMALLOC
1752 wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
1753 #else
1754 {
1755 int l=(origR->block1[k]-origR->block0[k]+1)*sizeof(int);
1756 if (origR->order[k]==ringorder_a64) l*=2;
1757 wv[k+1]=(int*)omalloc(l);
1758 memcpy(wv[k+1],origR->wvhdl[k],l);
1759 }
1760 #endif
1761 }
1762 block0[0] = 1;
1763 block1[0] = rVar(origR);
1764 wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1765 for (j=0;j<rVar(origR);j++)
1766 if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
1767 // use this special ordering: like ringorder_a, except that pFDeg, pWeights
1768 // ignore it
1769 ord[0] = ringorder_aa;
1770 }
1771 // fill in tmp ring to get back the data later on
1772 tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL
1773 //rUnComplete(tmpR);
1774 tmpR->p_Procs=NULL;
1775 tmpR->order = ord;
1776 tmpR->block0 = block0;
1777 tmpR->block1 = block1;
1778 tmpR->wvhdl = wv;
1779 rComplete(tmpR, 1);
1780
1781#ifdef HAVE_PLURAL
1782 /* update nc structure on tmpR */
1783 if (rIsPluralRing(origR))
1784 {
1785 if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal!
1786 {
1787 WerrorS("no elimination is possible: ordering condition is violated");
1788 // cleanup
1789 rDelete(tmpR);
1790 if (w!=NULL)
1791 delete w;
1792 return NULL;
1793 }
1794 }
1795#endif
1796 // change into the new ring
1797 //pChangeRing((currRing->N),currRing->OrdSgn,ord,block0,block1,wv);
1799
1800 //h = idInit(IDELEMS(h1),h1->rank);
1801 // fetch data from the old ring
1802 //for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR);
1804 if (origR->qideal!=NULL)
1805 {
1806 WarnS("eliminate in q-ring: experimental");
1807 ideal q=idrCopyR(origR->qideal,origR,currRing);
1808 ideal s=idSimpleAdd(h,q);
1809 idDelete(&h);
1810 idDelete(&q);
1811 h=s;
1812 }
1813 // compute GB
1814 if ((alg!=GbDefault)
1815 && (alg!=GbGroebner)
1816 && (alg!=GbModstd)
1817 && (alg!=GbSlimgb)
1818 && (alg!=GbSba)
1819 && (alg!=GbStd))
1820 {
1821 WarnS("wrong algorithm for GB");
1822 alg=GbDefault;
1823 }
1824 hh=idGroebner(h,0,alg,hilb);
1825 // go back to the original ring
1827 i = IDELEMS(hh)-1;
1828 while ((i >= 0) && (hh->m[i] == NULL)) i--;
1829 j = -1;
1830 // fetch data from temp ring
1831 for (k=0; k<=i; k++)
1832 {
1833 l=(currRing->N);
1834 while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--;
1835 if (l==0)
1836 {
1837 j++;
1838 if (j >= IDELEMS(h3))
1839 {
1840 pEnlargeSet(&(h3->m),IDELEMS(h3),16);
1841 IDELEMS(h3) += 16;
1842 }
1843 h3->m[j] = prMoveR( hh->m[k], tmpR,origR);
1844 hh->m[k] = NULL;
1845 }
1846 }
1847 id_Delete(&hh, tmpR);
1849 rDelete(tmpR);
1850 if (w!=NULL)
1851 delete w;
1852 return h3;
1853}
1854
1855#ifdef WITH_OLD_MINOR
1856/*2
1857* compute the which-th ar-minor of the matrix a
1858*/
1859poly idMinor(matrix a, int ar, unsigned long which, ideal R)
1860{
1861 int i,j/*,k,size*/;
1862 unsigned long curr;
1863 int *rowchoise,*colchoise;
1865 // ideal result;
1866 matrix tmp;
1867 poly p,q;
1868
1869 rowchoise=(int *)omAlloc(ar*sizeof(int));
1870 colchoise=(int *)omAlloc(ar*sizeof(int));
1871 tmp=mpNew(ar,ar);
1872 curr = 0; /* index of current minor */
1874 while (!rowch)
1875 {
1877 while (!colch)
1878 {
1879 if (curr == which)
1880 {
1881 for (i=1; i<=ar; i++)
1882 {
1883 for (j=1; j<=ar; j++)
1884 {
1885 MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
1886 }
1887 }
1889 if (p!=NULL)
1890 {
1891 if (R!=NULL)
1892 {
1893 q = p;
1894 p = kNF(R,currRing->qideal,q);
1895 p_Delete(&q,currRing);
1896 }
1897 }
1898 /*delete the matrix tmp*/
1899 for (i=1; i<=ar; i++)
1900 {
1901 for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
1902 }
1903 idDelete((ideal*)&tmp);
1904 omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
1905 omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
1906 return (p);
1907 }
1908 curr++;
1910 }
1912 }
1913 return (poly) 1;
1914}
1915
1916/*2
1917* compute all ar-minors of the matrix a
1918*/
1919ideal idMinors(matrix a, int ar, ideal R)
1920{
1921 int i,j,/*k,*/size;
1922 int *rowchoise,*colchoise;
1924 ideal result;
1925 matrix tmp;
1926 poly p,q;
1927
1928 i = binom(a->rows(),ar);
1929 j = binom(a->cols(),ar);
1930 size=i*j;
1931
1932 rowchoise=(int *)omAlloc(ar*sizeof(int));
1933 colchoise=(int *)omAlloc(ar*sizeof(int));
1934 result=idInit(size,1);
1935 tmp=mpNew(ar,ar);
1936 // k = 0; /* the index in result*/
1938 while (!rowch)
1939 {
1941 while (!colch)
1942 {
1943 for (i=1; i<=ar; i++)
1944 {
1945 for (j=1; j<=ar; j++)
1946 {
1947 MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
1948 }
1949 }
1951 if (p!=NULL)
1952 {
1953 if (R!=NULL)
1954 {
1955 q = p;
1956 p = kNF(R,currRing->qideal,q);
1957 p_Delete(&q,currRing);
1958 }
1959 }
1960 if (k>=size)
1961 {
1962 pEnlargeSet(&result->m,size,32);
1963 size += 32;
1964 }
1965 result->m[k] = p;
1966 k++;
1968 }
1970 }
1971 /*delete the matrix tmp*/
1972 for (i=1; i<=ar; i++)
1973 {
1974 for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
1975 }
1976 idDelete((ideal*)&tmp);
1977 if (k==0)
1978 {
1979 k=1;
1980 result->m[0]=NULL;
1981 }
1982 omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
1983 omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
1985 IDELEMS(result) = k;
1986 return (result);
1987}
1988#else
1989
1990
1991/// compute all ar-minors of the matrix a
1992/// the caller of mpRecMin
1993/// the elements of the result are not in R (if R!=NULL)
1995{
1996
1997 const ring origR=currRing;
1998 id_Test((ideal)a, origR);
1999
2000 const int r = a->nrows;
2001 const int c = a->ncols;
2002
2003 if((ar<=0) || (ar>r) || (ar>c))
2004 {
2005 Werror("%d-th minor, matrix is %dx%d",ar,r,c);
2006 return NULL;
2007 }
2008
2010 long bound = sm_ExpBound(h,c,r,ar,origR);
2011 id_Delete(&h, origR);
2012
2014
2015 matrix b = mpNew(r,c);
2016
2017 for (int i=r*c-1;i>=0;i--)
2018 if (a->m[i] != NULL)
2019 b->m[i] = prCopyR(a->m[i],origR,tmpR);
2020
2021 id_Test( (ideal)b, tmpR);
2022
2023 if (R!=NULL)
2024 {
2025 R = idrCopyR(R,origR,tmpR); // TODO: overwrites R? memory leak?
2026 //if (ar>1) // otherwise done in mpMinorToResult
2027 //{
2028 // matrix bb=(matrix)kNF(R,currRing->qideal,(ideal)b);
2029 // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols;
2030 // idDelete((ideal*)&b); b=bb;
2031 //}
2032 id_Test( R, tmpR);
2033 }
2034
2035 int size=binom(r,ar)*binom(c,ar);
2036 ideal result = idInit(size,1);
2037
2038 int elems = 0;
2039
2040 if(ar>1)
2041 mp_RecMin(ar-1,result,elems,b,r,c,NULL,R,tmpR);
2042 else
2043 mp_MinorToResult(result,elems,b,r,c,R,tmpR);
2044
2045 id_Test( (ideal)b, tmpR);
2046
2047 id_Delete((ideal *)&b, tmpR);
2048
2049 if (R!=NULL) id_Delete(&R,tmpR);
2050
2054 idTest(result);
2055 return result;
2056}
2057#endif
2058
2059/*2
2060*returns TRUE if id1 is a submodule of id2
2061*/
2063{
2064 int i;
2065 poly p;
2066
2067 if (idIs0(id1)) return TRUE;
2068 for (i=0;i<IDELEMS(id1);i++)
2069 {
2070 if (id1->m[i] != NULL)
2071 {
2072 p = kNF(id2,currRing->qideal,id1->m[i]);
2073 if (p != NULL)
2074 {
2076 return FALSE;
2077 }
2078 }
2079 }
2080 return TRUE;
2081}
2082
2084{
2085 if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
2086 if (idIs0(m)) return TRUE;
2087
2088 int cmax=-1;
2089 int i;
2090 poly p=NULL;
2091 int length=IDELEMS(m);
2092 polyset P=m->m;
2093 for (i=length-1;i>=0;i--)
2094 {
2095 p=P[i];
2096 if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
2097 }
2098 if (w != NULL)
2099 if (w->length()+1 < cmax)
2100 {
2101 // Print("length: %d - %d \n", w->length(),cmax);
2102 return FALSE;
2103 }
2104
2105 if(w!=NULL)
2107
2108 for (i=length-1;i>=0;i--)
2109 {
2110 p=P[i];
2111 if (p!=NULL)
2112 {
2113 int d=currRing->pFDeg(p,currRing);
2114 loop
2115 {
2116 pIter(p);
2117 if (p==NULL) break;
2118 if (d!=currRing->pFDeg(p,currRing))
2119 {
2120 //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
2121 if(w!=NULL)
2123 return FALSE;
2124 }
2125 }
2126 }
2127 }
2128
2129 if(w!=NULL)
2131
2132 return TRUE;
2133}
2134
2136{
2137 for(int i=IDELEMS(M)-1;i>=0;i--)
2138 {
2139 if(U==NULL)
2140 M->m[i]=pSeries(n,M->m[i],NULL,w);
2141 else
2142 {
2143 M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w);
2144 MATELEM(U,i+1,i+1)=NULL;
2145 }
2146 }
2147 if(U!=NULL)
2148 idDelete((ideal*)&U);
2149 return M;
2150}
2151
2153{
2154 int e=MATCOLS(i)*MATROWS(i);
2156 r->rank=i->rank;
2157 int j;
2158 for(j=0; j<e; j++)
2159 {
2160 r->m[j]=pDiff(i->m[j],k);
2161 }
2162 return r;
2163}
2164
2166{
2168 int i,j;
2169 for(i=0; i<IDELEMS(I); i++)
2170 {
2171 for(j=0; j<IDELEMS(J); j++)
2172 {
2173 MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply);
2174 }
2175 }
2176 return r;
2177}
2178
2179/*3
2180*handles for some ideal operations the ring/syzcomp management
2181*returns all syzygies (componentwise-)shifted by -syzcomp
2182*or -syzcomp-1 (in case of ideals as input)
2183static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE)
2184{
2185 ring orig_ring=currRing;
2186 ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); rChangeCurrRing(syz_ring);
2187 rSetSyzComp(length, syz_ring);
2188
2189 ideal s_temp;
2190 if (orig_ring!=syz_ring)
2191 s_temp=idrMoveR_NoSort(arg,orig_ring, syz_ring);
2192 else
2193 s_temp=arg;
2194
2195 ideal s_temp1 = kStd(s_temp,currRing->qideal,testHomog,&w,NULL,length);
2196 if (w!=NULL) delete w;
2197
2198 if (syz_ring!=orig_ring)
2199 {
2200 idDelete(&s_temp);
2201 rChangeCurrRing(orig_ring);
2202 }
2203
2204 idDelete(&temp);
2205 ideal temp1=idRingCopy(s_temp1,syz_ring);
2206
2207 if (syz_ring!=orig_ring)
2208 {
2209 rChangeCurrRing(syz_ring);
2210 idDelete(&s_temp1);
2211 rChangeCurrRing(orig_ring);
2212 rDelete(syz_ring);
2213 }
2214
2215 for (i=0;i<IDELEMS(temp1);i++)
2216 {
2217 if ((temp1->m[i]!=NULL)
2218 && (pGetComp(temp1->m[i])<=length))
2219 {
2220 pDelete(&(temp1->m[i]));
2221 }
2222 else
2223 {
2224 p_Shift(&(temp1->m[i]),-length,currRing);
2225 }
2226 }
2227 temp1->rank = rk;
2228 idSkipZeroes(temp1);
2229
2230 return temp1;
2231}
2232*/
2233
2234#ifdef HAVE_SHIFTBBA
2236{
2237 intvec *wtmp=NULL;
2238 if (T!=NULL) idDelete((ideal*)T);
2239
2240 int i,k,rk,flength=0,slength,length;
2241 poly p,q;
2242
2243 if (idIs0(h2))
2244 return idFreeModule(si_max(1,h2->ncols));
2245 if (!idIs0(h1))
2249 if (length==0)
2250 {
2251 length = 1;
2252 }
2254 if ((w!=NULL)&&((*w)!=NULL))
2255 {
2256 //Print("input weights:");(*w)->show(1);PrintLn();
2257 int d;
2258 int k;
2259 wtmp=new intvec(length+IDELEMS(h2));
2260 for (i=0;i<length;i++)
2261 ((*wtmp)[i])=(**w)[i];
2262 for (i=0;i<IDELEMS(h2);i++)
2263 {
2264 poly p=h2->m[i];
2265 if (p!=NULL)
2266 {
2267 d = p_Deg(p,currRing);
2268 k= pGetComp(p);
2269 if (slength>0) k--;
2270 d +=((**w)[k]);
2271 ((*wtmp)[i+length]) = d;
2272 }
2273 }
2274 //Print("weights:");wtmp->show(1);PrintLn();
2275 }
2276 for (i=0;i<IDELEMS(h2);i++)
2277 {
2278 temp->m[i] = pCopy(h2->m[i]);
2279 q = pOne();
2280 // non multiplicative variable
2281 pSetExp(q, currRing->isLPring - currRing->LPncGenCount + i + 1, 1);
2282 p_Setm(q, currRing);
2283 pSetComp(q,i+1+length);
2284 pSetmComp(q);
2285 if(temp->m[i]!=NULL)
2286 {
2287 if (slength==0) p_Shift(&(temp->m[i]),1,currRing);
2288 p = temp->m[i];
2289 temp->m[i] = pAdd(p, q);
2290 }
2291 else
2292 temp->m[i]=q;
2293 }
2294 rk = k = IDELEMS(h2);
2295 if (!idIs0(h1))
2296 {
2298 IDELEMS(temp) += IDELEMS(h1);
2299 for (i=0;i<IDELEMS(h1);i++)
2300 {
2301 if (h1->m[i]!=NULL)
2302 {
2303 temp->m[k] = pCopy(h1->m[i]);
2304 if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
2305 k++;
2306 }
2307 }
2308 }
2309
2314 // we can use OPT_RETURN_SB only, if syz_ring==orig_ring,
2315 // therefore we disable OPT_RETURN_SB for modulo:
2316 // (see tr. #701)
2317 //if (TEST_OPT_RETURN_SB)
2318 // rSetSyzComp(IDELEMS(h2)+length, syz_ring);
2319 //else
2320 // rSetSyzComp(length, syz_ring);
2321 ideal s_temp;
2322
2323 if (syz_ring != orig_ring)
2324 {
2326 }
2327 else
2328 {
2329 s_temp = temp;
2330 }
2331
2332 idTest(s_temp);
2339
2340 //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn();
2341 if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL))
2342 {
2343 delete *w;
2344 *w=new intvec(IDELEMS(h2));
2345 for (i=0;i<IDELEMS(h2);i++)
2346 ((**w)[i])=(*wtmp)[i+length];
2347 }
2348 if (wtmp!=NULL) delete wtmp;
2349
2350 if (T==NULL)
2351 {
2352 for (i=0;i<IDELEMS(s_temp1);i++)
2353 {
2354 if (s_temp1->m[i]!=NULL)
2355 {
2356 if (((int)pGetComp(s_temp1->m[i]))<=length)
2357 {
2358 p_Delete(&(s_temp1->m[i]),currRing);
2359 }
2360 else
2361 {
2362 p_Shift(&(s_temp1->m[i]),-length,currRing);
2363 }
2364 }
2365 }
2366 }
2367 else
2368 {
2370 for (i=0;i<IDELEMS(s_temp1);i++)
2371 {
2372 if (s_temp1->m[i]!=NULL)
2373 {
2374 if (((int)pGetComp(s_temp1->m[i]))<=length)
2375 {
2376 do
2377 {
2378 p_LmDelete(&(s_temp1->m[i]),currRing);
2379 } while((int)pGetComp(s_temp1->m[i])<=length);
2380 poly q = prMoveR( s_temp1->m[i], syz_ring,orig_ring);
2381 s_temp1->m[i] = NULL;
2382 if (q!=NULL)
2383 {
2384 q=pReverse(q);
2385 do
2386 {
2387 poly p = q;
2388 long t=pGetComp(p);
2389 pIter(q);
2390 pNext(p) = NULL;
2391 pSetComp(p,0);
2392 pSetmComp(p);
2393 pTest(p);
2394 MATELEM(*T,(int)t-length,i) = pAdd(MATELEM(*T,(int)t-length,i),p);
2395 } while (q != NULL);
2396 }
2397 }
2398 else
2399 {
2400 p_Shift(&(s_temp1->m[i]),-length,currRing);
2401 }
2402 }
2403 }
2404 }
2405 s_temp1->rank = rk;
2407
2408 if (syz_ring!=orig_ring)
2409 {
2413 // Hmm ... here seems to be a memory leak
2414 // However, simply deleting it causes memory trouble
2415 // idDelete(&s_temp);
2416 }
2417 idTest(s_temp1);
2418 return s_temp1;
2419}
2420#endif
2421
2422/*2
2423* represents (h1+h2)/h2=h1/(h1 intersect h2)
2424*/
2425//ideal idModulo (ideal h2,ideal h1)
2427{
2428#ifdef HAVE_SHIFTBBA
2429 if (rIsLPRing(currRing))
2430 return idModuloLP(h2,h1,hom,w,T,alg);
2431#endif
2432 intvec *wtmp=NULL;
2433 if (T!=NULL) idDelete((ideal*)T);
2434
2435 int i,flength=0,slength,length;
2436
2437 if (idIs0(h2))
2438 return idFreeModule(si_max(1,h2->ncols));
2439 if (!idIs0(h1))
2444 if (length==0)
2445 {
2446 length = 1;
2448 }
2449 if ((w!=NULL)&&((*w)!=NULL))
2450 {
2451 //Print("input weights:");(*w)->show(1);PrintLn();
2452 int d;
2453 int k;
2454 wtmp=new intvec(length+IDELEMS(h2));
2455 for (i=0;i<length;i++)
2456 ((*wtmp)[i])=(**w)[i];
2457 for (i=0;i<IDELEMS(h2);i++)
2458 {
2459 poly p=h2->m[i];
2460 if (p!=NULL)
2461 {
2462 d = p_Deg(p,currRing);
2463 k= pGetComp(p);
2464 if (slength>0) k--;
2465 d +=((**w)[k]);
2466 ((*wtmp)[i+length]) = d;
2467 }
2468 }
2469 //Print("weights:");wtmp->show(1);PrintLn();
2470 }
2471 ideal s_temp1;
2475 {
2477 ideal s1,s2;
2478
2479 if (syz_ring != orig_ring)
2480 {
2483 }
2484 else
2485 {
2486 s1=idCopy(h1);
2487 s2=idCopy(h2);
2488 }
2489
2492 if (T==NULL) si_opt_1 |= Sy_bit(OPT_REDTAIL);
2496 }
2497
2498 //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn();
2499 if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL))
2500 {
2501 delete *w;
2502 *w=new intvec(IDELEMS(h2));
2503 for (i=0;i<IDELEMS(h2);i++)
2504 ((**w)[i])=(*wtmp)[i+length];
2505 }
2506 if (wtmp!=NULL) delete wtmp;
2507
2510
2511 idDelete(&s_temp1);
2512 if (syz_ring!=orig_ring)
2513 {
2515 }
2516 idTest(h2);
2517 idTest(h1);
2518 idTest(result);
2519 if (T!=NULL) idTest((ideal)*T);
2520 return result;
2521}
2522
2523/*
2524*computes module-weights for liftings of homogeneous modules
2525*/
2526#if 0
2527static intvec * idMWLift(ideal mod,intvec * weights)
2528{
2529 if (idIs0(mod)) return new intvec(2);
2530 int i=IDELEMS(mod);
2531 while ((i>0) && (mod->m[i-1]==NULL)) i--;
2532 intvec *result = new intvec(i+1);
2533 while (i>0)
2534 {
2535 (*result)[i]=currRing->pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])];
2536 }
2537 return result;
2538}
2539#endif
2540
2541/*2
2542*sorts the kbase for idCoef* in a special way (lexicographically
2543*with x_max,...,x_1)
2544*/
2546{
2547 int i;
2548 ideal result;
2549
2550 if (idIs0(kBase)) return NULL;
2551 result = idInit(IDELEMS(kBase),kBase->rank);
2552 *convert = idSort(kBase,FALSE);
2553 for (i=0;i<(*convert)->length();i++)
2554 {
2555 result->m[i] = pCopy(kBase->m[(**convert)[i]-1]);
2556 }
2557 return result;
2558}
2559
2560/*2
2561*returns the index of a given monom in the list of the special kbase
2562*/
2564{
2565 int j=IDELEMS(kbase);
2566
2567 while ((j>0) && (kbase->m[j-1]==NULL)) j--;
2568 if (j==0) return -1;
2569 int i=(currRing->N);
2570 while (i>0)
2571 {
2572 loop
2573 {
2574 if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1;
2575 if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break;
2576 j--;
2577 if (j==0) return -1;
2578 }
2579 if (i==1)
2580 {
2581 while(j>0)
2582 {
2583 if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1;
2584 if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1;
2585 j--;
2586 }
2587 }
2588 i--;
2589 }
2590 return -1;
2591}
2592
2593/*2
2594*decomposes the monom in a part of coefficients described by the
2595*complement of how and a monom in variables occurring in how, the
2596*index of which in kbase is returned as integer pos (-1 if it don't
2597*exists)
2598*/
2599poly idDecompose(poly monom, poly how, ideal kbase, int * pos)
2600{
2601 int i;
2602 poly coeff=pOne(), base=pOne();
2603
2604 for (i=1;i<=(currRing->N);i++)
2605 {
2606 if (pGetExp(how,i)>0)
2607 {
2608 pSetExp(base,i,pGetExp(monom,i));
2609 }
2610 else
2611 {
2612 pSetExp(coeff,i,pGetExp(monom,i));
2613 }
2614 }
2615 pSetComp(base,pGetComp(monom));
2616 pSetm(base);
2617 pSetCoeff(coeff,nCopy(pGetCoeff(monom)));
2618 pSetm(coeff);
2619 *pos = idIndexOfKBase(base,kbase);
2620 if (*pos<0)
2621 p_Delete(&coeff,currRing);
2622 p_Delete(&base,currRing);
2623 return coeff;
2624}
2625
2626/*2
2627*returns a matrix A of coefficients with kbase*A=arg
2628*if all monomials in variables of how occur in kbase
2629*the other are deleted
2630*/
2632{
2633 matrix result;
2635 poly p,q;
2636 intvec * convert;
2637 int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos;
2638#if 0
2639 while ((i>0) && (kbase->m[i-1]==NULL)) i--;
2640 if (idIs0(arg))
2641 return mpNew(i,1);
2642 while ((j>0) && (arg->m[j-1]==NULL)) j--;
2643 result = mpNew(i,j);
2644#else
2645 result = mpNew(i, j);
2646 while ((j>0) && (arg->m[j-1]==NULL)) j--;
2647#endif
2648
2650 for (k=0;k<j;k++)
2651 {
2652 p = arg->m[k];
2653 while (p!=NULL)
2654 {
2655 q = idDecompose(p,how,tempKbase,&pos);
2656 if (pos>=0)
2657 {
2658 MATELEM(result,(*convert)[pos],k+1) =
2659 pAdd(MATELEM(result,(*convert)[pos],k+1),q);
2660 }
2661 else
2662 p_Delete(&q,currRing);
2663 pIter(p);
2664 }
2665 }
2667 return result;
2668}
2669
2670static void idDeleteComps(ideal arg,int* red_comp,int del)
2671// red_comp is an array [0..args->rank]
2672{
2673 int i,j;
2674 poly p;
2675
2676 for (i=IDELEMS(arg)-1;i>=0;i--)
2677 {
2678 p = arg->m[i];
2679 while (p!=NULL)
2680 {
2681 j = pGetComp(p);
2682 if (red_comp[j]!=j)
2683 {
2684 pSetComp(p,red_comp[j]);
2685 pSetmComp(p);
2686 }
2687 pIter(p);
2688 }
2689 }
2690 (arg->rank) -= del;
2691}
2692
2693/*3
2694* searches for the next unit in the components of the module arg and
2695* returns the first one;
2696*/
2697static int id_ReadOutPivot(ideal arg,int* comp, const ring r)
2698{
2699 int i=0,j, generator=-1;
2700 int rk_arg=arg->rank; //idRankFreeModule(arg);
2701 int * componentIsUsed =(int *)omAlloc((rk_arg+1)*sizeof(int));
2702 poly p;
2703
2704 while ((generator<0) && (i<IDELEMS(arg)))
2705 {
2706 memset(componentIsUsed,0,(rk_arg+1)*sizeof(int));
2707 p = arg->m[i];
2708 if (rField_is_Ring(r))
2709 {
2710 while (p!=NULL)
2711 {
2712 j = __p_GetComp(p,r);
2713 if (componentIsUsed[j]==0)
2714 {
2715 if (p_LmIsConstantComp(p,r) &&
2716 n_IsUnit(pGetCoeff(p),r->cf))
2717 {
2718 generator = i;
2719 componentIsUsed[j] = 1;
2720 }
2721 else
2722 {
2723 componentIsUsed[j] = -1;
2724 }
2725 }
2726 else if (componentIsUsed[j]>0)
2727 {
2728 (componentIsUsed[j])++;
2729 }
2730 pIter(p);
2731 }
2732 }
2733 else
2734 {
2735 while (p!=NULL)
2736 {
2737 j = __p_GetComp(p,r);
2738 if (componentIsUsed[j]==0)
2739 {
2740 if (p_LmIsConstantComp(p,r))
2741 {
2742 generator = i;
2743 componentIsUsed[j] = 1;
2744 }
2745 else
2746 {
2747 componentIsUsed[j] = -1;
2748 }
2749 }
2750 else if (componentIsUsed[j]>0)
2751 {
2752 (componentIsUsed[j])++;
2753 }
2754 pIter(p);
2755 }
2756 }
2757 i++;
2758 }
2759 i = 0;
2760 *comp = -1;
2761 for (j=0;j<=rk_arg;j++)
2762 {
2763 if (componentIsUsed[j]>0)
2764 {
2765 if ((*comp==-1) || (componentIsUsed[j]<i))
2766 {
2767 *comp = j;
2769 }
2770 }
2771 }
2773 return generator;
2774}
2775
2776/*2
2777* returns the presentation of an isomorphic, minimally
2778* embedded module (arg represents the quotient!)
2779*/
2781 int* red_comp, int &del)
2782{
2783 if (idIs0(arg)) return idInit(1,arg->rank);
2784 int i,next_gen,next_comp;
2785 ideal res=arg;
2786 if (!inPlace) res = idCopy(arg);
2788 for (i=res->rank;i>=0;i--) red_comp[i]=i;
2789
2790 loop
2791 {
2793 if (next_gen<0) break;
2794 del++;
2796 for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--;
2797 if ((w !=NULL)&&(*w!=NULL))
2798 {
2799 for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i];
2800 }
2801 }
2802
2804
2805 if ((w !=NULL)&&(*w!=NULL) &&(del>0))
2806 {
2807 int nl=si_max((*w)->length()-del,1);
2808 intvec *wtmp=new intvec(nl);
2809 for(i=0;i<nl;i++) (*wtmp)[i]=(**w)[i];
2810 delete *w;
2811 *w=wtmp;
2812 }
2813 return res;
2814}
2815
2817{
2818 int *red_comp=(int*)omAlloc((arg->rank+1)*sizeof(int));
2819 int del=0;
2823 return res;
2824}
2825
2827{
2828 int *red_comp=(int*)omAlloc((arg->rank+1)*sizeof(int));
2829 int del=0;
2832 //idDeleteComps(res,red_comp,del);
2834 return res;
2835}
2836
2838{
2839 if (idIs0(arg))
2840 {
2841 trans=idFreeModule(arg->rank);
2842 if (g!=NULL)
2843 {
2844 for(int i=0;i<arg->rank;i++) g[i]=i+1;
2845 }
2846 return arg;
2847 }
2848 int *red_comp=(int*)omAlloc((arg->rank+1)*sizeof(int));
2849 int del=0;
2852 for(int i=1;i<=arg->rank;i++)
2853 {
2854 g[i-1]=red_comp[i];
2855 }
2857 return res;
2858}
2859
2860extern void ipPrint_MA0(matrix m, const char *name);
2861#if 0 // unused
2863{
2864 ideal a=idCopy(arg);
2865 // add unit matrix to a
2866 int k=a->rank+1;
2867 const int rk=a->rank;
2868 poly p;
2869 int i;
2870 for(i=0;i<IDELEMS(a);i++,k++)
2871 {
2872 p=pOne();
2874 a->m[i]=p_Add_q(a->m[i],p,currRing);
2875 }
2876 // search a unit in orig part of a
2877 // and subtract, start at start
2878 int start=0;
2879 loop
2880 {
2881 PrintS("matrix:\n");
2882 ipPrint_MA0((matrix)a,"a");
2883 i=start;
2884 if (i>=IDELEMS(a)) break;
2885 p=a->m[i];
2886 start=IDELEMS(a);
2887 while((p!=NULL)&&(pGetComp(p)<=rk)&&(p_Totaldegree(p,currRing)>0)) pIter(p);
2888 if ((p!=NULL)&&(pGetComp(p)<=rk)&&(p_Totaldegree(p,currRing)==0))
2889 { // found const in vector i, comp k
2890 k=pGetComp(p);
2891 // normalize:
2892 number n=nCopy(pGetCoeff(p));
2893 n=nInpNeg(n);
2894 a->m[i]=p_Div_nn(p,n,currRing);
2895 // subtract
2896 BOOLEAN changed=FALSE;
2897 for(int j=IDELEMS(a)-1;j>=0;j--)
2898 {
2899 if (j!=i)
2900 {
2901 poly q=p_Vec2Poly(a->m[j],k,currRing);
2902 if (q!=NULL)
2903 {
2904 start=j; // changed entries start at j
2905 changed=TRUE;
2906 poly s=p_Mult_q(a->m[i],q,currRing);
2907 a->m[j]=p_Add_q(a->m[j],s,currRing);
2908 }
2909 }
2910 }
2911 if(changed) continue;
2912 }
2913 else i++;
2914 }
2915 // a -> result,trans
2916 trans=idInit(IDELEMS(a),IDELEMS(a));
2918 for(i=0;i<IDELEMS(a);i++)
2919 {
2920 while(a->m[i]!=NULL)
2921 {
2922 poly p=a->m[i];
2923 a->m[i]=p->next;
2924 p->next=NULL;
2925 if(pGetComp(p)<=rk)
2926 {
2927 result->m[i]=p_Add_q(result->m[i],p,currRing);
2928 }
2929 else
2930 {
2931 p_Shift(&p,-rk,currRing);
2932 trans->m[i]=p_Add_q(trans->m[i],p,currRing);
2933 }
2934 }
2935 }
2936 PrintS("prune:\n");
2938 PrintS("trans:\n");
2939 ipPrint_MA0((matrix)trans,"T");
2940 idDelete(&a);
2941 return result;
2942}
2943#endif
2944#include "polys/clapsing.h"
2945
2946#if 0
2947poly id_GCD(poly f, poly g, const ring r)
2948{
2950 rChangeCurrRing(r);
2951 ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
2952 intvec *w = NULL;
2954 if (w!=NULL) delete w;
2955 poly gg=pTakeOutComp(&(S->m[0]),2);
2956 idDelete(&S);
2957 poly gcd_p=singclap_pdivide(f,gg,r);
2958 p_Delete(&gg,r);
2960 return gcd_p;
2961}
2962#else
2963poly id_GCD(poly f, poly g, const ring r)
2964{
2965 ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
2966 intvec *w = NULL;
2967
2969 rChangeCurrRing(r);
2972
2973 if (w!=NULL) delete w;
2974 poly gg=p_TakeOutComp(&(S->m[0]), 2, r);
2975 id_Delete(&S, r);
2976 poly gcd_p=singclap_pdivide(f,gg, r);
2977 p_Delete(&gg, r);
2978
2979 return gcd_p;
2980}
2981#endif
2982
2983#if 0
2984/*2
2985* xx,q: arrays of length 0..rl-1
2986* xx[i]: SB mod q[i]
2987* assume: char=0
2988* assume: q[i]!=0
2989* destroys xx
2990*/
2991ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring R)
2992{
2993 int cnt=IDELEMS(xx[0])*xx[0]->nrows;
2994 ideal result=idInit(cnt,xx[0]->rank);
2995 result->nrows=xx[0]->nrows; // for lifting matrices
2996 result->ncols=xx[0]->ncols; // for lifting matrices
2997 int i,j;
2998 poly r,h,hh,res_p;
2999 number *x=(number *)omAlloc(rl*sizeof(number));
3000 for(i=cnt-1;i>=0;i--)
3001 {
3002 res_p=NULL;
3003 loop
3004 {
3005 r=NULL;
3006 for(j=rl-1;j>=0;j--)
3007 {
3008 h=xx[j]->m[i];
3009 if ((h!=NULL)
3010 &&((r==NULL)||(p_LmCmp(r,h,R)==-1)))
3011 r=h;
3012 }
3013 if (r==NULL) break;
3014 h=p_Head(r, R);
3015 for(j=rl-1;j>=0;j--)
3016 {
3017 hh=xx[j]->m[i];
3018 if ((hh!=NULL) && (p_LmCmp(r,hh, R)==0))
3019 {
3020 x[j]=p_GetCoeff(hh, R);
3022 xx[j]->m[i]=hh;
3023 }
3024 else
3025 x[j]=n_Init(0, R->cf); // is R->cf really n_Q???, yes!
3026 }
3027
3028 number n=n_ChineseRemainder(x,q,rl, R->cf);
3029
3030 for(j=rl-1;j>=0;j--)
3031 {
3032 x[j]=NULL; // nlInit(0...) takes no memory
3033 }
3034 if (n_IsZero(n, R->cf)) p_Delete(&h, R);
3035 else
3036 {
3037 p_SetCoeff(h,n, R);
3038 //Print("new mon:");pWrite(h);
3039 res_p=p_Add_q(res_p, h, R);
3040 }
3041 }
3042 result->m[i]=res_p;
3043 }
3044 omFree(x);
3045 for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]), R);
3046 omFree(xx);
3047 return result;
3048}
3049#endif
3050/* currently unused:
3051ideal idChineseRemainder(ideal *xx, intvec *iv)
3052{
3053 int rl=iv->length();
3054 number *q=(number *)omAlloc(rl*sizeof(number));
3055 int i;
3056 for(i=0; i<rl; i++)
3057 {
3058 q[i]=nInit((*iv)[i]);
3059 }
3060 return idChineseRemainder(xx,q,rl);
3061}
3062*/
3063/*
3064 * lift ideal with coeffs over Z (mod N) to Q via Farey
3065 */
3067{
3068 int cnt=IDELEMS(x)*x->nrows;
3069 ideal result=idInit(cnt,x->rank);
3070 result->nrows=x->nrows; // for lifting matrices
3071 result->ncols=x->ncols; // for lifting matrices
3072
3073 int i;
3074 for(i=cnt-1;i>=0;i--)
3075 {
3076 result->m[i]=p_Farey(x->m[i],N,r);
3077 }
3078 return result;
3079}
3080
3081
3082
3083
3084// uses glabl vars via pSetModDeg
3085/*
3086BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
3087{
3088 if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
3089 if (idIs0(m)) return TRUE;
3090
3091 int cmax=-1;
3092 int i;
3093 poly p=NULL;
3094 int length=IDELEMS(m);
3095 poly* P=m->m;
3096 for (i=length-1;i>=0;i--)
3097 {
3098 p=P[i];
3099 if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
3100 }
3101 if (w != NULL)
3102 if (w->length()+1 < cmax)
3103 {
3104 // Print("length: %d - %d \n", w->length(),cmax);
3105 return FALSE;
3106 }
3107
3108 if(w!=NULL)
3109 p_SetModDeg(w, currRing);
3110
3111 for (i=length-1;i>=0;i--)
3112 {
3113 p=P[i];
3114 poly q=p;
3115 if (p!=NULL)
3116 {
3117 int d=p_FDeg(p,currRing);
3118 loop
3119 {
3120 pIter(p);
3121 if (p==NULL) break;
3122 if (d!=p_FDeg(p,currRing))
3123 {
3124 //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
3125 if(w!=NULL)
3126 p_SetModDeg(NULL, currRing);
3127 return FALSE;
3128 }
3129 }
3130 }
3131 }
3132
3133 if(w!=NULL)
3134 p_SetModDeg(NULL, currRing);
3135
3136 return TRUE;
3137}
3138*/
3139
3140/// keeps the first k (>= 1) entries of the given ideal
3141/// (Note that the kept polynomials may be zero.)
3142void idKeepFirstK(ideal id, const int k)
3143{
3144 for (int i = IDELEMS(id)-1; i >= k; i--)
3145 {
3146 if (id->m[i] != NULL) pDelete(&id->m[i]);
3147 }
3148 int kk=k;
3149 if (k==0) kk=1; /* ideals must have at least one element(0)*/
3150 pEnlargeSet(&(id->m), IDELEMS(id), kk-IDELEMS(id));
3151 IDELEMS(id) = kk;
3152}
3153
3154typedef struct
3155{
3156 poly p;
3158} poly_sort;
3159
3160int pCompare_qsort(const void *a, const void *b)
3161{
3162 return (p_Compare(((poly_sort *)a)->p, ((poly_sort *)b)->p,currRing));
3163}
3164
3169
3170/*2
3171* ideal id = (id[i])
3172* if id[i] = id[j] then id[j] is deleted for j > i
3173*/
3175{
3176 int idsize = IDELEMS(id);
3178 for (int i = 0; i < idsize; i++)
3179 {
3180 id_sort[i].p = id->m[i];
3181 id_sort[i].index = i;
3182 }
3184 int index, index_i, index_j;
3185 int i = 0;
3186 for (int j = 1; j < idsize; j++)
3187 {
3188 if (id_sort[i].p != NULL && pEqualPolys(id_sort[i].p, id_sort[j].p))
3189 {
3190 index_i = id_sort[i].index;
3191 index_j = id_sort[j].index;
3192 if (index_j > index_i)
3193 {
3194 index = index_j;
3195 }
3196 else
3197 {
3198 index = index_i;
3199 i = j;
3200 }
3201 pDelete(&id->m[index]);
3202 }
3203 else
3204 {
3205 i = j;
3206 }
3207 }
3209}
3210
3212
3214{
3215 BOOLEAN b = FALSE; // set b to TRUE, if spoly was changed,
3216 // let it remain FALSE otherwise
3217 if (strat->P.t_p==NULL)
3218 {
3219 poly p=strat->P.p;
3220
3221 // iterate over all terms of p and
3222 // compute the minimum mm of all exponent vectors
3223 int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int));
3224 int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
3227 for (; p!=NULL; pIter(p))
3228 {
3231 for (int i=rVar(currRing); i>0; i--)
3232 {
3234 {
3235 mm[i]=si_min(mm[i],m0[i]);
3236 if (mm[i]>0) nonTrivialSaturationToBeDone=true;
3237 }
3238 else mm[i]=0;
3239 }
3240 // abort if the minimum is zero in each component
3241 if (!nonTrivialSaturationToBeDone) break;
3242 }
3244 {
3245 // std::cout << "simplifying!" << std::endl;
3246 if (TEST_OPT_PROT) { PrintS("S"); mflush(); }
3247 p=p_Copy(strat->P.p,currRing);
3248 //pWrite(p);
3249 // for (int i=rVar(currRing); i>0; i--)
3250 // if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]);
3251 //PrintLn();
3252 strat->P.Init(strat->tailRing);
3253 //memset(&strat->P,0,sizeof(strat->P));
3254 //strat->P.tailRing = strat->tailRing; // done by Init
3255 strat->P.p=p;
3256 while(p!=NULL)
3257 {
3258 for (int i=rVar(currRing); i>0; i--)
3259 {
3260 p_SubExp(p,i,mm[i],currRing);
3261 }
3262 p_Setm(p,currRing);
3263 pIter(p);
3264 }
3265 b = TRUE;
3266 }
3267 omFree(mm);
3268 omFree(m0);
3269 }
3270 else
3271 {
3272 poly p=strat->P.t_p;
3273
3274 // iterate over all terms of p and
3275 // compute the minimum mm of all exponent vectors
3276 int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int));
3277 int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
3278 p_GetExpV(p,mm,strat->tailRing);
3280 for (; p!=NULL; pIter(p))
3281 {
3283 p_GetExpV(p,m0,strat->tailRing);
3284 for(int i=rVar(currRing); i>0; i--)
3285 {
3287 {
3288 mm[i]=si_min(mm[i],m0[i]);
3289 if (mm[i]>0) nonTrivialSaturationToBeDone = true;
3290 }
3291 else mm[i]=0;
3292 }
3293 // abort if the minimum is zero in each component
3294 if (!nonTrivialSaturationToBeDone) break;
3295 }
3297 {
3298 if (TEST_OPT_PROT) { PrintS("S"); mflush(); }
3299 p=p_Copy(strat->P.t_p,strat->tailRing);
3300 //p_Write(p,strat->tailRing);
3301 // for (int i=rVar(currRing); i>0; i--)
3302 // if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]);
3303 //PrintLn();
3304 strat->P.Init(strat->tailRing);
3305 //memset(&strat->P,0,sizeof(strat->P));
3306 //strat->P.tailRing = strat->tailRing;// done by Init
3307 strat->P.t_p=p;
3308 while(p!=NULL)
3309 {
3310 for(int i=rVar(currRing); i>0; i--)
3311 {
3312 p_SubExp(p,i,mm[i],strat->tailRing);
3313 }
3314 p_Setm(p,strat->tailRing);
3315 pIter(p);
3316 }
3317 strat->P.GetP();
3318 b = TRUE;
3319 }
3320 omFree(mm);
3321 omFree(m0);
3322 }
3323 return b; // return TRUE if sp was changed, FALSE if not
3324}
3325
3327{
3329 if (currRing!=r) rChangeCurrRing(r);
3330 idSkipZeroes(J);
3332 int k=IDELEMS(J);
3333 if (k>1)
3334 {
3335 for (int i=0; i<k; i++)
3336 {
3337 poly x = J->m[i];
3338 int li = p_Var(x,r);
3339 if (li>0)
3341 else
3342 {
3344 WerrorS("ideal generators must be variables");
3345 return NULL;
3346 }
3347 }
3348 }
3349 else
3350 {
3351 poly x = J->m[0];
3352 if (pNext(x)!=NULL)
3353 {
3354 Werror("generator must be a monomial");
3356 return NULL;
3357 }
3358 for (int i=1; i<=r->N; i++)
3359 {
3360 int li = p_GetExp(x,i,r);
3361 if (li==1)
3363 else if (li>1)
3364 {
3366 Werror("exponent(x(%d)^%d) must be 0 or 1",i,li);
3367 return NULL;
3368 }
3369 }
3370 }
3375 return res;
3376}
3377
3379{
3380 rRingOrder_t *ord;
3381 int *block0,*block1;
3382 int **wv;
3383
3384 // construction extension ring
3385 ord=(rRingOrder_t*)omAlloc0(4*sizeof(rRingOrder_t));
3386 block0=(int*)omAlloc0(4*sizeof(int));
3387 block1=(int*)omAlloc0(4*sizeof(int));
3388 wv=(int**) omAlloc0(4*sizeof(int**));
3389 wv[0]=(int*)omAlloc0((rVar(origR) + 2)*sizeof(int));
3390 block0[0] = block0[1] = 1;
3391 block1[0] = block1[1] = rVar(origR)+1;
3392 // use this special ordering: like ringorder_a, except that pFDeg, pWeights
3393 // ignore it
3394 ord[0] = ringorder_aa;
3395 wv[0][rVar(origR)]=1;
3396 BOOLEAN wp=FALSE;
3397 for (int j=0;j<rVar(origR);j++)
3398 if (p_Weight(j+1,origR)!=1) { wp=TRUE;break; }
3399 if (wp)
3400 {
3401 wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
3402 for (int j=0;j<rVar(origR);j++)
3403 wv[1][j]=p_Weight(j+1,origR);
3404 ord[1] = ringorder_wp;
3405 }
3406 else
3407 ord[1] = ringorder_dp;
3408 ord[2] = ringorder_C;
3409 ord[3] = (rRingOrder_t)0;
3410 char **names=(char**)omAlloc0((origR->N+1) * sizeof(char *));
3411 for (int j=0;j<rVar(origR);j++)
3412 names[j]=origR->names[j];
3413 names[rVar(origR)]=(char*)"@";
3414 ring tmpR=rDefault(nCopyCoeff(origR->cf),rVar(origR)+1,names,4,ord,block0,block1,wv);
3415 omFree(names);
3416 rComplete(tmpR, 1);
3418 // map I
3420 // map J
3422 // J[1]*t-1
3423 poly t=pOne();
3424 p_SetExp(t,rVar(tmpR),1,tmpR);
3425 p_Setm(t,tmpR);
3426 poly p=JJ->m[0];
3427 p_Norm(p,currRing);
3428 p=p_Mult_q(p,t,tmpR);
3429 p=p_Sub(p,pOne(),tmpR);
3430 JJ->m[0]=p;
3432 idTest(T);
3433 id_Delete(&II,tmpR);
3434 id_Delete(&JJ,tmpR);
3435 // elimination
3436 t=pOne();
3437 p_SetExp(t,rVar(tmpR),1,tmpR);
3438 p_Setm(t,tmpR);
3440 p_Delete(&t,tmpR);
3441 for(int j=0;j<IDELEMS(TT);j++)
3442 {
3443 if ((TT->m[j]!=NULL)
3444 && (p_GetExp(TT->m[j],rVar(tmpR),tmpR)>0))
3445 {
3446 p_Delete(&TT->m[j],tmpR);
3447 }
3448 }
3449 // map back
3451 id_Delete(&TT,tmpR);
3453 rDelete(tmpR);
3455 return TTT;
3456}
3457
3459{
3460 if(idIs0(J))
3461 {
3462 ideal res;
3463 if(isIdeal)
3464 {
3465 res=idInit(1,1);
3466 res->m[0]=pOne();
3467 }
3468 else
3469 {
3470 res=idFreeModule(I->rank);
3471 }
3472 k=1;
3473 return(res);
3474 }
3476 //if (idElem(J)==1)
3477 //{
3478 // idSkipZeroes(J);
3479 // return id_Sat_principal(I,J,currRing);
3480 //}
3481 //---------------------------------------------------
3482 BOOLEAN only_vars=TRUE; // enabled for I:x_i
3483 if (idElem(J)==1)
3484 {
3485 for(int j=IDELEMS(J)-1;j>=0;j--)
3486 {
3487 poly p=J->m[j];
3488 if (p!=NULL)
3489 {
3490 if (pVar(p)==0)
3491 {
3493 break;
3494 }
3495 }
3496 }
3497 }
3499 && (idElem(J)==1))
3500 {
3502 intvec *w=NULL;
3505 k=0;
3506 loop
3507 {
3508 k++;
3510 ideal tmp=kNF(Istd,currRing->qideal,Iquot,5);
3511 int elem=idElem(tmp);
3514 Istd=Iquot;
3515 w=NULL;
3516 Istd=kStd(Iquot,currRing->qideal,testHomog,&w);
3517 if (w!=NULL) delete w;
3519 if (elem==0) break;
3520 }
3521 k--;
3523 //PrintS("\nSatstd:\n");
3524 //iiWriteMatrix((matrix)I,"I",1,currRing,0); PrintLn();
3525 //iiWriteMatrix((matrix)J,"J",1,currRing,0); PrintLn();
3526 //iiWriteMatrix((matrix)Istd,"res",1,currRing,0);PrintLn();
3527 //id_Delete(&Istd,currRing);
3529 return Istd;
3530 }
3531 //--------------------------------------------------
3533 intvec *w=NULL;
3534 Istd=idCopy(I);
3535 k=0;
3536 loop
3537 {
3538 k++;
3540 isSB=FALSE;
3541 si_opt_2|=Sy_bit(V_NOT_TRICKS); // used from 2nd loop on
3542 ideal tmp=kNF(Istd,currRing->qideal,Iquot,5);
3543 int elem=idElem(tmp);
3546 Istd=Iquot;
3547 if (elem==0) break;
3548 }
3549 k--;
3550 Istd=kStd(Iquot,currRing->qideal,testHomog,&w);
3553 //if (only_vars)
3554 //{
3555 // iiWriteMatrix((matrix)Istd,"org",1,currRing,0);
3556 //}
3557 return Istd;
3558}
3567
3569{
3570 ideal II=id_Copy(I,r);
3571 if (var_num==1)
3572 {
3574 if (tmpR!=r)
3575 {
3577 II=idrMoveR(II,r,tmpR);
3578 }
3580 id_Delete(&II,tmpR);
3581 intvec *ww=NULL;
3582 II=kStd(III,currRing->qideal,(tHomog)TRUE,&ww);
3583 if (ww!=NULL) delete ww;
3584 id_Delete(&III,tmpR);
3585 if (tmpR!=r)
3586 {
3587 rChangeCurrRing(r);
3588 II=idrMoveR(II,tmpR,r);
3589 }
3590 return II;
3591 }
3593 int *perm=(int*)omAlloc0((rVar(r)+1)*sizeof(int));
3594 for(int i=rVar(r)-1; i>0; i--) perm[i]=i;
3595 perm[var_num]=1;
3596 perm[1]=var_num;
3597 for(int i=IDELEMS(II)-1; i>=0;i--)
3598 {
3599 III->m[i]=p_PermPoly(II->m[i],perm,r,r,ndCopyMap,NULL,0,FALSE);
3600 }
3601 id_Delete(&II,r);
3602 II=id_Homogenize(III,1,r);
3603 id_Delete(&III,r);
3604 III=idInit(IDELEMS(II),1);
3605 for(int i=IDELEMS(II)-1; i>=0;i--)
3606 {
3607 III->m[i]=p_PermPoly(II->m[i],perm,r,r,ndCopyMap,NULL,0,FALSE);
3608 }
3609 id_Delete(&II,r);
3610 return III;
3611}
3612
3614{
3615 ideal II=id_Copy(I,r);
3616 if (var_num==1)
3617 {
3619 if (tmpR!=r)
3620 {
3622 II=idrMoveR(II,r,tmpR);
3623 }
3625 id_Delete(&II,tmpR);
3626 intvec *ww=NULL;
3627 II=kStd(III,currRing->qideal,(tHomog)TRUE,&ww);
3628 if (ww!=NULL) delete ww;
3629 id_Delete(&III,tmpR);
3630 if (tmpR!=r)
3631 {
3632 rChangeCurrRing(r);
3633 II=idrMoveR(II,tmpR,r);
3634 }
3635 return II;
3636 }
3638 int *perm=(int*)omAlloc0((rVar(r)+1)*sizeof(int));
3639 for(int i=rVar(r)-1; i>0; i--) perm[i]=i;
3640 perm[var_num]=1;
3641 perm[1]=var_num;
3642 for(int i=IDELEMS(II)-1; i>=0;i--)
3643 {
3644 III->m[i]=p_PermPoly(II->m[i],perm,r,r,ndCopyMap,NULL,0,FALSE);
3645 }
3646 id_Delete(&II,r);
3647 II=id_HomogenizeW(III,1,w,r);
3648 id_Delete(&III,r);
3649 III=idInit(IDELEMS(II),1);
3650 for(int i=IDELEMS(II)-1; i>=0;i--)
3651 {
3652 III->m[i]=p_PermPoly(II->m[i],perm,r,r,ndCopyMap,NULL,0,FALSE);
3653 }
3654 id_Delete(&II,r);
3655 return III;
3656}
3657
3658GbVariant syGetAlgorithm(char *n, const ring r, const ideal /*M*/)
3659{
3661 if (strcmp(n,"default")==0) alg=GbDefault;
3662 else if (strcmp(n,"slimgb")==0) alg=GbSlimgb;
3663 else if (strcmp(n,"std")==0) alg=GbStd;
3664 else if (strcmp(n,"sba")==0) alg=GbSba;
3665 else if (strcmp(n,"singmatic")==0) alg=GbSingmatic;
3666 else if (strcmp(n,"groebner")==0) alg=GbGroebner;
3667 else if (strcmp(n,"modstd")==0) alg=GbModstd;
3668 else if (strcmp(n,"ffmod")==0) alg=GbFfmod;
3669 else if (strcmp(n,"nfmod")==0) alg=GbNfmod;
3670 else if (strcmp(n,"std:sat")==0) alg=GbStdSat;
3671 else Warn(">>%s<< is an unknown algorithm",n);
3672
3673 if (alg==GbSlimgb) // test conditions for slimgb
3674 {
3675 if(rHasGlobalOrdering(r)
3676 &&(!rIsNCRing(r))
3677 &&(r->qideal==NULL)
3678 &&(!rField_is_Ring(r)))
3679 {
3680 return GbSlimgb;
3681 }
3682 if (TEST_OPT_PROT)
3683 WarnS("requires: coef:field, commutative, global ordering, not qring");
3684 }
3685 else if (alg==GbSba) // cond. for sba
3686 {
3687 if(rField_is_Domain(r)
3688 &&(!rIsNCRing(r))
3689 &&(rHasGlobalOrdering(r)))
3690 {
3691 return GbSba;
3692 }
3693 if (TEST_OPT_PROT)
3694 WarnS("requires: coef:domain, commutative, global ordering");
3695 }
3696 else if (alg==GbGroebner) // cond. for groebner
3697 {
3698 return GbGroebner;
3699 }
3700 else if(alg==GbModstd) // cond for modstd: Q or Q(a)
3701 {
3702 if(ggetid("modStd")==NULL)
3703 {
3704 WarnS(">>modStd<< not found");
3705 }
3706 else if(rField_is_Q(r)
3707 &&(!rIsNCRing(r))
3708 &&(rHasGlobalOrdering(r)))
3709 {
3710 return GbModstd;
3711 }
3712 if (TEST_OPT_PROT)
3713 WarnS("requires: coef:QQ, commutative, global ordering");
3714 }
3715 else if(alg==GbStdSat) // cond for std:sat: 2 blocks of variables
3716 {
3717 if(ggetid("satstd")==NULL)
3718 {
3719 WarnS(">>satstd<< not found");
3720 }
3721 else
3722 {
3723 return GbStdSat;
3724 }
3725 }
3726
3727 return GbStd; // no conditions for std
3728}
3729//----------------------------------------------------------------------------
3730// GB-algorithms and their pre-conditions
3731// std slimgb sba singmatic modstd ffmod nfmod groebner
3732// + + + - + - - + coeffs: QQ
3733// + + + + - - - + coeffs: ZZ/p
3734// + + + - ? - + + coeffs: K[a]/f
3735// + + + - ? + - + coeffs: K(a)
3736// + - + - - - - + coeffs: domain, not field
3737// + - - - - - - + coeffs: zero-divisors
3738// + + + + - ? ? + also for modules: C
3739// + + - + - ? ? + also for modules: all orderings
3740// + + - - - - - + exterior algebra
3741// + + - - - - - + G-algebra
3742// + + + + + + + + degree ordering
3743// + - + + + + + + non-degree ordering
3744// - - - + + + + + parallel
#define BITSET
Definition auxiliary.h:85
static int si_max(const int a, const int b)
Definition auxiliary.h:125
int BOOLEAN
Definition auxiliary.h:88
#define TRUE
Definition auxiliary.h:101
#define FALSE
Definition auxiliary.h:97
static int si_min(const int a, const int b)
Definition auxiliary.h:126
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 &)
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
g
Definition cfModGcd.cc:4098
CanonicalForm b
Definition cfModGcd.cc:4111
static CanonicalForm bound(const CFMatrix &M)
Definition cf_linsys.cc:460
FILE * f
Definition checklibs.c:9
poly singclap_pdivide(poly f, poly g, const ring r)
Definition clapsing.cc:624
int length() const
Matrices of numbers.
Definition bigintmat.h:51
int nrows
Definition matpol.h:20
long rank
Definition matpol.h:19
int ncols
Definition matpol.h:21
poly * m
Definition matpol.h:18
int & cols()
Definition matpol.h:24
int & rows()
Definition matpol.h:23
ring tailRing
Definition kutil.h:344
LObject P
Definition kutil.h:303
Class used for (list of) interpreter objects.
Definition subexpr.h:83
Coefficient rings, fields and other domains suitable for Singular polynomials.
number ndCopyMap(number a, const coeffs src, const coeffs dst)
Definition numbers.cc:287
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_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition coeffs.h:468
static FORCE_INLINE coeffs nCopyCoeff(const coeffs r)
"copy" coeffs, i.e. increment ref
Definition coeffs.h:437
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
Definition coeffs.h:539
#define Print
Definition emacs.cc:80
#define Warn
Definition emacs.cc:77
#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
CanonicalForm divide(const CanonicalForm &ff, const CanonicalForm &f, const CFList &as)
const Variable & v
< [in] a sqrfree bivariate poly
Definition facBivar.h:39
int j
Definition facHensel.cc:110
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
char name(const Variable &v)
Definition factory.h:189
void WerrorS(const char *s)
Definition feFopen.cc:24
#define STATIC_VAR
Definition globaldefs.h:7
@ IDEAL_CMD
Definition grammar.cc:285
@ MODUL_CMD
Definition grammar.cc:288
GbVariant syGetAlgorithm(char *n, const ring r, const ideal)
Definition ideals.cc:3658
static ideal idMinEmbedding1(ideal arg, BOOLEAN inPlace, intvec **w, int *red_comp, int &del)
Definition ideals.cc:2780
int index
Definition ideals.cc:3157
static void idPrepareStd(ideal s_temp, int k)
Definition ideals.cc:1047
matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
Definition ideals.cc:2631
void idLiftW(ideal P, ideal Q, int n, matrix &T, ideal &R, int *w)
Definition ideals.cc:1342
static void idLift_setUnit(int e_mod, matrix *unit)
Definition ideals.cc:1088
ideal idSyzygies(ideal h1, tHomog h, intvec **w, BOOLEAN setSyzComp, BOOLEAN setRegularity, int *deg, GbVariant alg)
Definition ideals.cc:836
matrix idDiff(matrix i, int k)
Definition ideals.cc:2152
ideal id_Sat_principal(ideal I, ideal J, const ring origR)
Definition ideals.cc:3378
ideal idSaturateGB(ideal I, ideal J, int &k, BOOLEAN isIdeal)
Definition ideals.cc:3563
static ideal idGroebner(ideal temp, int syzComp, GbVariant alg, bigintmat *hilb=NULL, intvec *w=NULL, tHomog hom=testHomog)
Definition ideals.cc:200
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
Definition ideals.cc:2083
ideal id_Homogenize(ideal I, int var_num, const ring r)
Definition ideals.cc:3568
ideal idLiftStd(ideal h1, matrix *T, tHomog hi, ideal *S, GbVariant alg, ideal h11)
Definition ideals.cc:982
void idDelEquals(ideal id)
Definition ideals.cc:3174
int pCompare_qsort(const void *a, const void *b)
Definition ideals.cc:3160
ideal idQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
Definition ideals.cc:1512
ideal id_HomogenizeW(ideal I, int var_num, intvec *w, const ring r)
Definition ideals.cc:3613
ideal idMinors(matrix a, int ar, ideal R)
compute all ar-minors of the matrix a the caller of mpRecMin the elements of the result are not in R ...
Definition ideals.cc:1994
ideal idSaturate(ideal I, ideal J, int &k, BOOLEAN isIdeal)
Definition ideals.cc:3559
void ipPrint_MA0(matrix m, const char *name)
Definition ipprint.cc:57
BOOLEAN idIsSubModule(ideal id1, ideal id2)
Definition ideals.cc:2062
ideal idSeries(int n, ideal M, matrix U, intvec *w)
Definition ideals.cc:2135
ideal idMinEmbedding_with_map_v(ideal arg, intvec **w, ideal &trans, int *g)
Definition ideals.cc:2837
ideal idCreateSpecialKbase(ideal kBase, intvec **convert)
Definition ideals.cc:2545
static ideal idPrepare(ideal h1, ideal h11, tHomog hom, int syzcomp, intvec **w, GbVariant alg)
Definition ideals.cc:613
poly id_GCD(poly f, poly g, const ring r)
Definition ideals.cc:2963
int idIndexOfKBase(poly monom, ideal kbase)
Definition ideals.cc:2563
poly idDecompose(poly monom, poly how, ideal kbase, int *pos)
Definition ideals.cc:2599
ideal idSaturate_intern(ideal I, ideal J, int &k, BOOLEAN isIdeal, BOOLEAN isSB)
Definition ideals.cc:3458
matrix idDiffOp(ideal I, ideal J, BOOLEAN multiply)
Definition ideals.cc:2165
ideal idElimination(ideal h1, poly delVar, bigintmat *hilb, GbVariant alg)
Definition ideals.cc:1611
void idSort_qsort(poly_sort *id_sort, int idsize)
Definition ideals.cc:3165
static ideal idInitializeQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
Definition ideals.cc:1407
static ideal idSectWithElim(ideal h1, ideal h2, GbVariant alg)
Definition ideals.cc:132
ideal idSect(ideal h1, ideal h2, GbVariant alg)
Definition ideals.cc:315
ideal idMultSect(resolvente arg, int length, GbVariant alg)
Definition ideals.cc:472
void idKeepFirstK(ideal id, const int k)
keeps the first k (>= 1) entries of the given ideal (Note that the kept polynomials may be zero....
Definition ideals.cc:3142
ideal idLift(ideal mod, ideal submod, ideal *rest, BOOLEAN goodShape, BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
represents the generators of submod in terms of the generators of mod (Matrix(SM)*U-Matrix(rest)) = M...
Definition ideals.cc:1111
STATIC_VAR int * id_satstdSaturatingVariables
Definition ideals.cc:3211
ideal idExtractG_T_S(ideal s_h3, matrix *T, ideal *S, long syzComp, int h1_size, BOOLEAN inputIsIdeal, const ring oring, const ring sring)
Definition ideals.cc:715
static void idDeleteComps(ideal arg, int *red_comp, int del)
Definition ideals.cc:2670
ideal idModulo(ideal h2, ideal h1, tHomog hom, intvec **w, matrix *T, GbVariant alg)
Definition ideals.cc:2426
ideal idMinEmbedding_with_map(ideal arg, intvec **w, ideal &trans)
Definition ideals.cc:2826
ideal idMinBase(ideal h1, ideal *SB)
Definition ideals.cc:51
ideal id_Farey(ideal x, number N, const ring r)
Definition ideals.cc:3066
ideal id_Satstd(const ideal I, ideal J, const ring r)
Definition ideals.cc:3326
static int id_ReadOutPivot(ideal arg, int *comp, const ring r)
Definition ideals.cc:2697
ideal idModuloLP(ideal h2, ideal h1, tHomog, intvec **w, matrix *T, GbVariant alg)
Definition ideals.cc:2235
static BOOLEAN id_sat_vars_sp(kStrategy strat)
Definition ideals.cc:3213
ideal idMinEmbedding(ideal arg, BOOLEAN inPlace, intvec **w)
Definition ideals.cc:2816
int binom(int n, int r)
GbVariant
Definition ideals.h:119
@ GbGroebner
Definition ideals.h:126
@ GbModstd
Definition ideals.h:127
@ GbStdSat
Definition ideals.h:130
@ GbSlimgb
Definition ideals.h:123
@ GbFfmod
Definition ideals.h:128
@ GbNfmod
Definition ideals.h:129
@ GbDefault
Definition ideals.h:120
@ GbStd
Definition ideals.h:122
@ GbSingmatic
Definition ideals.h:131
@ GbSba
Definition ideals.h:124
#define idDelete(H)
delete an ideal
Definition ideals.h:29
#define idSimpleAdd(A, B)
Definition ideals.h:42
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
ideal id_Copy(ideal h1, const ring r)
copy an ideal
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
static BOOLEAN idHomModule(ideal m, ideal Q, intvec **w)
Definition ideals.h:96
#define idTest(id)
Definition ideals.h:47
static BOOLEAN idHomIdeal(ideal id, ideal Q=NULL)
Definition ideals.h:91
static ideal idMult(ideal h1, ideal h2)
hh := h1 * h2
Definition ideals.h:84
ideal idCopy(ideal A)
Definition ideals.h:60
#define idMaxIdeal(D)
initialise the maximal ideal (at 0)
Definition ideals.h:33
ideal * resolvente
Definition ideals.h:18
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
static intvec * idSort(ideal id, BOOLEAN nolex=TRUE)
Definition ideals.h:187
ideal idFreeModule(int i)
Definition ideals.h:111
static BOOLEAN length(leftv result, leftv arg)
Definition interval.cc:257
intvec * ivCopy(const intvec *o)
Definition intvec.h:145
idhdl ggetid(const char *n)
Definition ipid.cc:581
EXTERN_VAR omBin sleftv_bin
Definition ipid.h:145
leftv ii_CallLibProcM(const char *n, void **args, int *arg_types, const ring R, BOOLEAN &err)
args: NULL terminated array of arguments arg_types: 0 terminated array of corresponding types
Definition iplib.cc:710
void * iiCallLibProc1(const char *n, void *arg, int arg_type, BOOLEAN &err)
Definition iplib.cc:636
STATIC_VAR jList * T
Definition janet.cc:30
STATIC_VAR Poly * h
Definition janet.cc:971
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition p_polys.cc:3575
ideal kStd(ideal F, ideal Q, tHomog h, intvec **w, bigintmat *hilb, int syzComp, int newIdeal, intvec *vw, s_poly_proc_t sp)
Definition kstd1.cc:2603
ideal kMin_std(ideal F, ideal Q, tHomog h, intvec **w, ideal &M, bigintmat *hilb, int syzComp, int reduced)
Definition kstd1.cc:3057
ideal kSba(ideal F, ideal Q, tHomog h, intvec **w, int sbaOrder, int arri, bigintmat *hilb, int syzComp, int newIdeal, intvec *vw)
Definition kstd1.cc:2656
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
Definition kstd1.cc:3209
@ nc_skew
Definition nc.h:16
@ nc_exterior
Definition nc.h:21
static nc_type & ncRingType(nc_struct *p)
Definition nc.h:159
BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r)
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition matpol.cc:37
matrix mp_MultP(matrix a, poly p, const ring R)
multiply a matrix 'a' by a poly 'p', destroy the args
Definition matpol.cc:141
matrix mp_Copy(matrix a, const ring r)
copies matrix a (from ring r to r)
Definition matpol.cc:57
void mp_MinorToResult(ideal result, int &elems, matrix a, int r, int c, ideal R, const ring)
entries of a are minors and go to result (only if not in R)
Definition matpol.cc:1501
void mp_RecMin(int ar, ideal result, int &elems, matrix a, int lr, int lc, poly barDiv, ideal R, const ring r)
produces recursively the ideal of all arxar-minors of a
Definition matpol.cc:1597
poly mp_DetBareiss(matrix a, const ring r)
returns the determinant of the matrix m; uses Bareiss algorithm
Definition matpol.cc:1670
#define MATELEM(mat, i, j)
1-based access to matrix
Definition matpol.h:29
#define MATROWS(i)
Definition matpol.h:26
#define MATCOLS(i)
Definition matpol.h:27
#define assume(x)
Definition mod2.h:389
#define pIter(p)
Definition monomials.h:37
#define pNext(p)
Definition monomials.h:36
#define p_GetCoeff(p, r)
Definition monomials.h:50
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 nInpNeg(n)
Definition numbers.h:21
#define nCopy(n)
Definition numbers.h:15
#define omStrDup(s)
#define omFreeSize(addr, size)
#define omAlloc(size)
#define omalloc(size)
#define omFree(addr)
#define omAlloc0(size)
#define omFreeBin(addr, bin)
#define omMemDup(s)
#define NULL
Definition omList.c:12
VAR unsigned si_opt_2
Definition options.c:6
VAR unsigned si_opt_1
Definition options.c:5
#define SI_SAVE_OPT(A, B)
Definition options.h:20
#define TEST_OPT_IDLIFT
Definition options.h:131
#define SI_SAVE_OPT2(A)
Definition options.h:22
#define OPT_REDTAIL_SYZ
Definition options.h:88
#define OPT_REDTAIL
Definition options.h:92
#define OPT_SB_1
Definition options.h:96
#define SI_SAVE_OPT1(A)
Definition options.h:21
#define SI_RESTORE_OPT1(A)
Definition options.h:24
#define SI_RESTORE_OPT2(A)
Definition options.h:25
#define Sy_bit(x)
Definition options.h:31
#define TEST_OPT_RETURN_SB
Definition options.h:114
#define V_NOT_TRICKS
Definition options.h:71
#define TEST_V_INTERSECT_ELIM
Definition options.h:146
#define TEST_V_INTERSECT_SYZ
Definition options.h:147
#define TEST_OPT_NOTREGULARITY
Definition options.h:122
#define TEST_OPT_PROT
Definition options.h:105
#define V_IDLIFT
Definition options.h:63
#define SI_RESTORE_OPT(A, B)
Definition options.h:23
static int index(p_Length length, p_Ord ord)
poly p_DivideM(poly a, poly b, const ring r)
Definition p_polys.cc:1582
poly p_Farey(poly p, number N, const ring r)
Definition p_polys.cc:54
int p_Weight(int i, const ring r)
Definition p_polys.cc:706
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
Definition p_polys.cc:4815
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:4211
poly p_Div_nn(poly p, const number n, const ring r)
Definition p_polys.cc:1506
void p_Norm(poly p1, const ring r)
Definition p_polys.cc:3799
int p_Compare(const poly a, const poly b, const ring R)
Definition p_polys.cc:5005
long p_DegW(poly p, const int *w, const ring R)
Definition p_polys.cc:691
poly p_Vec2Poly(poly v, int k, const ring r)
Definition p_polys.cc:3653
void p_SetModDeg(intvec *w, ring r)
Definition p_polys.cc:3753
int p_Var(poly m, const ring r)
Definition p_polys.cc:4765
poly p_One(const ring r)
Definition p_polys.cc:1314
poly p_Sub(poly p1, poly p2, const ring r)
Definition p_polys.cc:1994
void pEnlargeSet(poly **p, int l, int increment)
Definition p_polys.cc:3776
long p_Deg(poly a, const ring r)
Definition p_polys.cc:586
static poly p_Neg(poly p, const ring r)
Definition p_polys.h:1109
static poly p_Add_q(poly p, poly q, const ring r)
Definition p_polys.h:938
static void p_LmDelete(poly p, const ring r)
Definition p_polys.h:725
static poly p_Mult_q(poly p, poly q, const ring r)
Definition p_polys.h:1120
static long p_SubExp(poly p, int v, long ee, ring r)
Definition p_polys.h:615
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:490
static long p_MinComp(poly p, ring lmRing, ring tailRing)
Definition p_polys.h:315
static void p_Setm(poly p, const ring r)
Definition p_polys.h:235
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
Definition p_polys.h:838
static number p_SetCoeff(poly p, number n, ring r)
Definition p_polys.h:414
static poly pReverse(poly p)
Definition p_polys.h:337
static BOOLEAN p_LmIsConstantComp(const poly p, const ring r)
Definition p_polys.h:1008
static poly p_Head(const poly p, const ring r)
copy the (leading) term of p
Definition p_polys.h:862
static int p_LmCmp(poly p, poly q, const ring r)
Definition p_polys.h:1596
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:471
static void p_Delete(poly *p, const ring r)
Definition p_polys.h:903
static void p_GetExpV(poly p, int *ev, const ring r)
Definition p_polys.h:1536
static poly p_LmFreeAndNext(poly p, ring)
Definition p_polys.h:713
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition p_polys.h:848
static long p_Totaldegree(poly p, const ring r)
Definition p_polys.h:1523
void rChangeCurrRing(ring r)
Definition polys.cc:16
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition polys.cc:13
Compatibility layer for legacy polynomial operations (over currRing)
#define pAdd(p, q)
Definition polys.h:204
#define pTest(p)
Definition polys.h:415
#define pDelete(p_ptr)
Definition polys.h:187
#define ppJet(p, m)
Definition polys.h:367
#define pHead(p)
returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL
Definition polys.h:68
#define pSetm(p)
Definition polys.h:272
#define pNeg(p)
Definition polys.h:199
#define ppMult_mm(p, m)
Definition polys.h:202
#define pSetCompP(a, i)
Definition polys.h:304
#define pGetComp(p)
Component.
Definition polys.h:38
#define pDiff(a, b)
Definition polys.h:297
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition polys.h:32
#define pVar(m)
Definition polys.h:381
#define pJet(p, m)
Definition polys.h:368
#define pSub(a, b)
Definition polys.h:288
#define pWeight(i)
Definition polys.h:281
#define ppJetW(p, m, iv)
Definition polys.h:369
#define pMaxComp(p)
Definition polys.h:300
#define pSetComp(p, v)
Definition polys.h:39
void wrp(poly p)
Definition polys.h:311
#define pMult(p, q)
Definition polys.h:208
#define pJetW(p, m, iv)
Definition polys.h:370
#define pDiffOp(a, b, m)
Definition polys.h:298
#define pSeries(n, p, u, w)
Definition polys.h:372
#define pGetExp(p, i)
Exponent.
Definition polys.h:42
#define pSetmComp(p)
TODO:
Definition polys.h:274
#define pNormalize(p)
Definition polys.h:318
#define pEqualPolys(p1, p2)
Definition polys.h:400
#define pDivisibleBy(a, b)
returns TRUE, if leading monom of a divides leading monom of b i.e., if there exists a expvector c > ...
Definition polys.h:139
#define pSetExp(p, i, v)
Definition polys.h:43
void pTakeOutComp(poly *p, long comp, poly *q, int *lq, const ring R=currRing)
Splits *p into two polys: *q which consists of all monoms with component == comp and *p of all other ...
Definition polys.h:339
#define pCopy(p)
return a copy of the poly
Definition polys.h:186
#define pOne()
Definition polys.h:316
#define pMinComp(p)
Definition polys.h:301
poly * polyset
Definition polys.h:260
poly prMoveR(poly &p, ring src_r, ring dest_r)
Definition prCopy.cc:90
ideal idrMoveR(ideal &id, ring src_r, ring dest_r)
Definition prCopy.cc:248
poly prCopyR(poly p, ring src_r, ring dest_r)
Definition prCopy.cc:34
ideal idrCopyR(ideal id, ring src_r, ring dest_r)
Definition prCopy.cc:192
ideal idrMoveR_NoSort(ideal &id, ring src_r, ring dest_r)
Definition prCopy.cc:261
poly prMoveR_NoSort(poly &p, ring src_r, ring dest_r)
Definition prCopy.cc:101
ideal idrCopyR_NoSort(ideal id, ring src_r, ring dest_r)
Definition prCopy.cc:205
void PrintS(const char *s)
Definition reporter.cc:284
void PrintLn()
Definition reporter.cc:310
void Werror(const char *fmt,...)
Definition reporter.cc:189
#define mflush()
Definition reporter.h:58
BOOLEAN rComplete(ring r, int force)
this needs to be called whenever a new ring is created: new fields in ring are created (like VarOffse...
Definition ring.cc:3518
ring rAssure_SyzComp(const ring r, BOOLEAN complete)
Definition ring.cc:4519
BOOLEAN nc_rComplete(const ring src, ring dest, bool bSetupQuotient)
Definition ring.cc:5825
ring rAssure_Wp_C(const ring r, intvec *w)
Definition ring.cc:4934
ring rAssure_Dp_C(const ring r)
Definition ring.cc:5116
BOOLEAN rOrd_is_Totaldegree_Ordering(const ring r)
Definition ring.cc:2034
ring rAssure_SyzOrder(const ring r, BOOLEAN complete)
Definition ring.cc:4514
ring rCopy0(const ring r, BOOLEAN copy_qideal, BOOLEAN copy_ordering)
Definition ring.cc:1424
void rDelete(ring r)
unconditionally deletes fields in r
Definition ring.cc:452
ring rDefault(const coeffs cf, int N, char **n, int ord_size, rRingOrder_t *ord, int *block0, int *block1, int **wvhdl, unsigned long bitmask)
Definition ring.cc:103
void rSetSyzComp(int k, const ring r)
Definition ring.cc:5222
ring rAssure_dp_C(const ring r)
Definition ring.cc:5111
static BOOLEAN rHasGlobalOrdering(const ring r)
Definition ring.h:768
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition ring.h:406
static int rBlocks(const ring r)
Definition ring.h:574
static BOOLEAN rField_is_Domain(const ring r)
Definition ring.h:493
static BOOLEAN rIsLPRing(const ring r)
Definition ring.h:417
rRingOrder_t
order stuff
Definition ring.h:69
@ ringorder_a
Definition ring.h:71
@ ringorder_a64
for int64 weights
Definition ring.h:72
@ ringorder_C
Definition ring.h:74
@ ringorder_dp
Definition ring.h:79
@ ringorder_c
Definition ring.h:73
@ ringorder_aa
for idElimination, like a, except pFDeg, pWeigths ignore it
Definition ring.h:93
@ ringorder_ws
Definition ring.h:88
@ ringorder_s
s?
Definition ring.h:77
@ ringorder_wp
Definition ring.h:82
static BOOLEAN rField_is_Q(const ring r)
Definition ring.h:512
static BOOLEAN rIsNCRing(const ring r)
Definition ring.h:427
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition ring.h:598
#define rField_is_Ring(R)
Definition ring.h:491
#define block
Definition scanner.cc:646
ideal idInit(int idsize, int rank)
initialise an ideal / module
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
ideal id_Homogen(ideal h, int varnum, const ring r)
matrix id_Module2Matrix(ideal mod, const ring R)
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
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
ideal id_Matrix2Module(matrix mat, const ring R)
converts mat to module, destroys mat
ideal id_SimpleAdd(ideal h1, ideal h2, const ring R)
concat the lists h1 and h2 without zeros
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
void id_Shift(ideal M, int s, const ring r)
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
#define IDELEMS(i)
#define id_Test(A, lR)
static int idElem(const ideal F)
number of non-zero polys in F
#define R
Definition sirandom.c:27
#define M
Definition sirandom.c:25
#define Q
Definition sirandom.c:26
long sm_ExpBound(ideal m, int di, int ra, int t, const ring currRing)
Definition sparsmat.cc:188
ring sm_RingChange(const ring origR, long bound)
Definition sparsmat.cc:258
void sm_KillModifiedRing(ring r)
Definition sparsmat.cc:289
char * char_ptr
Definition structs.h:49
tHomog
Definition structs.h:31
@ isHomog
Definition structs.h:33
@ testHomog
Definition structs.h:34
@ isNotHomog
Definition structs.h:32
#define loop
Definition structs.h:71
void syGaussForOne(ideal syz, int elnum, int ModComp, int from, int till)
Definition syz.cc:218
intvec * syBetti(resolvente res, int length, int *regularity, intvec *weights, BOOLEAN tomin, int *row_shift)
Definition syz.cc:783
resolvente sySchreyerResolvente(ideal arg, int maxlength, int *length, BOOLEAN isMonomial=FALSE, BOOLEAN notReplace=FALSE)
Definition syz0.cc:855
ideal t_rep_gb(const ring r, ideal arg_I, int syz_comp, BOOLEAN F4_mode)
Definition tgb.cc:3581
@ INT_CMD
Definition tok.h:96
THREAD_VAR double(* wFunctional)(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition weight.cc:20
void wCall(poly *s, int sl, int *x, double wNsqr, const ring R)
Definition weight.cc:108
double wFunctionalBuch(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition weight0.cc:78