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 <omalloc/omalloc.h>
13 
14 #ifndef SING_NDEBUG
15 # define MYTEST 0
16 #else /* ifndef SING_NDEBUG */
17 # define MYTEST 0
18 #endif /* ifndef SING_NDEBUG */
19 
20 #include <omalloc/omalloc.h>
21 
22 #include <misc/options.h>
23 #include <misc/intvec.h>
24 
25 #include <coeffs/coeffs.h>
26 #include <coeffs/numbers.h>
27 // #include <coeffs/longrat.h>
28 
29 
30 #include <polys/monomials/ring.h>
31 #include <polys/matpol.h>
32 #include <polys/weight.h>
33 #include <polys/sparsmat.h>
34 #include <polys/prCopy.h>
35 #include <polys/nc/nc.h>
36 
37 
38 #include <kernel/ideals.h>
39 
40 #include <kernel/polys.h>
41 
42 #include <kernel/GBEngine/kstd1.h>
43 #include <kernel/GBEngine/syz.h>
44 
45 
46 /* #define WITH_OLD_MINOR */
47 
48 /*0 implementation*/
49 
50 /*2
51 *returns a minimized set of generators of h1
52 */
53 ideal idMinBase (ideal h1)
54 {
55  ideal h2, h3,h4,e;
56  int j,k;
57  int i,l,ll;
58  intvec * wth;
59  BOOLEAN homog;
60  #ifdef HAVE_RINGS
62  {
63  WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
64  e=idCopy(h1);
65  return e;
66  }
67  #endif
68  homog = idHomModule(h1,currRing->qideal,&wth);
70  {
71  if(!homog)
72  {
73  WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
74  e=idCopy(h1);
75  return e;
76  }
77  else
78  {
79  ideal re=kMin_std(h1,currRing->qideal,(tHomog)homog,&wth,h2,NULL,0,3);
80  idDelete(&re);
81  return h2;
82  }
83  }
84  e=idInit(1,h1->rank);
85  if (idIs0(h1))
86  {
87  return e;
88  }
89  pEnlargeSet(&(e->m),IDELEMS(e),15);
90  IDELEMS(e) = 16;
91  h2 = kStd(h1,currRing->qideal,isNotHomog,NULL);
92  h3 = idMaxIdeal(1);
93  h4=idMult(h2,h3);
94  idDelete(&h3);
95  h3=kStd(h4,currRing->qideal,isNotHomog,NULL);
96  k = IDELEMS(h3);
97  while ((k > 0) && (h3->m[k-1] == NULL)) k--;
98  j = -1;
99  l = IDELEMS(h2);
100  while ((l > 0) && (h2->m[l-1] == NULL)) l--;
101  for (i=l-1; i>=0; i--)
102  {
103  if (h2->m[i] != NULL)
104  {
105  ll = 0;
106  while ((ll < k) && ((h3->m[ll] == NULL)
107  || !pDivisibleBy(h3->m[ll],h2->m[i])))
108  ll++;
109  if (ll >= k)
110  {
111  j++;
112  if (j > IDELEMS(e)-1)
113  {
114  pEnlargeSet(&(e->m),IDELEMS(e),16);
115  IDELEMS(e) += 16;
116  }
117  e->m[j] = pCopy(h2->m[i]);
118  }
119  }
120  }
121  idDelete(&h2);
122  idDelete(&h3);
123  idDelete(&h4);
124  if (currRing->qideal!=NULL)
125  {
126  h3=idInit(1,e->rank);
127  h2=kNF(h3,currRing->qideal,e);
128  idDelete(&h3);
129  idDelete(&e);
130  e=h2;
131  }
132  idSkipZeroes(e);
133  return e;
134 }
135 
136 
137 /*2
138 *initialized a field with r numbers between beg and end for the
139 *procedure idNextChoise
140 */
141 ideal idSectWithElim (ideal h1,ideal h2)
142 // does not destroy h1,h2
143 {
144  if (TEST_OPT_PROT) PrintS("intersect by elimination method\n");
145  assume(!idIs0(h1));
146  assume(!idIs0(h2));
147  assume(IDELEMS(h1)<=IDELEMS(h2));
150  // add a new variable:
151  int j;
152  ring origRing=currRing;
153  ring r=rCopy0(origRing);
154  r->N++;
155  r->block0[0]=1;
156  r->block1[0]= r->N;
157  omFree(r->order);
158  r->order=(int*)omAlloc0(3*sizeof(int*));
159  r->order[0]=ringorder_dp;
160  r->order[1]=ringorder_C;
161  char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr));
162  for (j=0;j<r->N-1;j++) names[j]=r->names[j];
163  names[r->N-1]=omStrDup("@");
164  omFree(r->names);
165  r->names=names;
166  rComplete(r,TRUE);
167  // fetch h1, h2
168  ideal h;
169  h1=idrCopyR(h1,origRing,r);
170  h2=idrCopyR(h2,origRing,r);
171  // switch to temp. ring r
172  rChangeCurrRing(r);
173  // create 1-t, t
174  poly omt=p_One(currRing);
175  p_SetExp(omt,r->N,1,currRing);
176  poly t=p_Copy(omt,currRing);
177  p_Setm(omt,currRing);
178  omt=p_Neg(omt,currRing);
179  omt=p_Add_q(omt,pOne(),currRing);
180  // compute (1-t)*h1
181  h1=(ideal)mp_MultP((matrix)h1,omt,currRing);
182  // compute t*h2
183  h2=(ideal)mp_MultP((matrix)h2,pCopy(t),currRing);
184  // (1-t)h1 + t*h2
185  h=idInit(IDELEMS(h1)+IDELEMS(h2),1);
186  int l;
187  for (l=IDELEMS(h1)-1; l>=0; l--)
188  {
189  h->m[l] = h1->m[l]; h1->m[l]=NULL;
190  }
191  j=IDELEMS(h1);
192  for (l=IDELEMS(h2)-1; l>=0; l--)
193  {
194  h->m[l+j] = h2->m[l]; h2->m[l]=NULL;
195  }
196  idDelete(&h1);
197  idDelete(&h2);
198  // eliminate t:
199 
200  ideal res=idElimination(h,t);
201  // cleanup
202  idDelete(&h);
203  if (res!=NULL) res=idrMoveR(res,r,origRing);
204  rChangeCurrRing(origRing);
205  rDelete(r);
206  return res;
207 }
208 /*2
209 * h3 := h1 intersect h2
210 */
211 ideal idSect (ideal h1,ideal h2)
212 {
213  int i,j,k,length;
214  int flength = id_RankFreeModule(h1,currRing);
215  int slength = id_RankFreeModule(h2,currRing);
216  int rank=si_max(h1->rank,h2->rank);
217  if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank);
218 
219  ideal first,second,temp,temp1,result;
220  poly p,q;
221 
222  if (IDELEMS(h1)<IDELEMS(h2))
223  {
224  first = h1;
225  second = h2;
226  }
227  else
228  {
229  first = h2;
230  second = h1;
231  int t=flength; flength=slength; slength=t;
232  }
233  length = si_max(flength,slength);
234  if (length==0)
235  {
236  if ((currRing->qideal==NULL)
237  && (currRing->OrdSgn==1)
238  && (!rIsPluralRing(currRing))
240  return idSectWithElim(first,second);
241  else length = 1;
242  }
243  if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n");
244  j = IDELEMS(first);
245 
246  ring orig_ring=currRing;
247  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring);
248  rSetSyzComp(length, syz_ring);
249 
250  while ((j>0) && (first->m[j-1]==NULL)) j--;
251  temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j);
252  k = 0;
253  for (i=0;i<j;i++)
254  {
255  if (first->m[i]!=NULL)
256  {
257  if (syz_ring==orig_ring)
258  temp->m[k] = pCopy(first->m[i]);
259  else
260  temp->m[k] = prCopyR(first->m[i], orig_ring, syz_ring);
261  q = pOne();
262  pSetComp(q,i+1+length);
263  pSetmComp(q);
264  if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
265  p = temp->m[k];
266  while (pNext(p)!=NULL) pIter(p);
267  pNext(p) = q;
268  k++;
269  }
270  }
271  for (i=0;i<IDELEMS(second);i++)
272  {
273  if (second->m[i]!=NULL)
274  {
275  if (syz_ring==orig_ring)
276  temp->m[k] = pCopy(second->m[i]);
277  else
278  temp->m[k] = prCopyR(second->m[i], orig_ring,currRing);
279  if (slength==0) p_Shift(&(temp->m[k]),1,currRing);
280  k++;
281  }
282  }
283  intvec *w=NULL;
284  temp1 = kStd(temp,currRing->qideal,testHomog,&w,NULL,length);
285  if (w!=NULL) delete w;
286  idDelete(&temp);
287  if(syz_ring!=orig_ring)
288  rChangeCurrRing(orig_ring);
289 
290  result = idInit(IDELEMS(temp1),rank);
291  j = 0;
292  for (i=0;i<IDELEMS(temp1);i++)
293  {
294  if ((temp1->m[i]!=NULL)
295  && (p_GetComp(temp1->m[i],syz_ring)>length))
296  {
297  if(syz_ring==orig_ring)
298  {
299  p = temp1->m[i];
300  }
301  else
302  {
303  p = prMoveR(temp1->m[i], syz_ring,orig_ring);
304  }
305  temp1->m[i]=NULL;
306  while (p!=NULL)
307  {
308  q = pNext(p);
309  pNext(p) = NULL;
310  k = pGetComp(p)-1-length;
311  pSetComp(p,0);
312  pSetmComp(p);
313  /* Warning! multiply only from the left! it's very important for Plural */
314  result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k])));
315  p = q;
316  }
317  j++;
318  }
319  }
320  if(syz_ring!=orig_ring)
321  {
322  rChangeCurrRing(syz_ring);
323  idDelete(&temp1);
324  rChangeCurrRing(orig_ring);
325  rDelete(syz_ring);
326  }
327  else
328  {
329  idDelete(&temp1);
330  }
331 
332  idSkipZeroes(result);
333  if (TEST_OPT_RETURN_SB)
334  {
335  w=NULL;
336  temp1=kStd(result,currRing->qideal,testHomog,&w);
337  if (w!=NULL) delete w;
338  idDelete(&result);
339  idSkipZeroes(temp1);
340  return temp1;
341  }
342  else //temp1=kInterRed(result,currRing->qideal);
343  return result;
344 }
345 
346 /*2
347 * ideal/module intersection for a list of objects
348 * given as 'resolvente'
349 */
350 ideal idMultSect(resolvente arg, int length)
351 {
352  int i,j=0,k=0,syzComp,l,maxrk=-1,realrki;
353  ideal bigmat,tempstd,result;
354  poly p;
355  int isIdeal=0;
356  intvec * w=NULL;
357 
358  /* find 0-ideals and max rank -----------------------------------*/
359  for (i=0;i<length;i++)
360  {
361  if (!idIs0(arg[i]))
362  {
363  realrki=id_RankFreeModule(arg[i],currRing);
364  k++;
365  j += IDELEMS(arg[i]);
366  if (realrki>maxrk) maxrk = realrki;
367  }
368  else
369  {
370  if (arg[i]!=NULL)
371  {
372  return idInit(1,arg[i]->rank);
373  }
374  }
375  }
376  if (maxrk == 0)
377  {
378  isIdeal = 1;
379  maxrk = 1;
380  }
381  /* init -----------------------------------------------------------*/
382  j += maxrk;
383  syzComp = k*maxrk;
384 
385  ring orig_ring=currRing;
386  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring);
387  rSetSyzComp(syzComp, syz_ring);
388 
389  bigmat = idInit(j,(k+1)*maxrk);
390  /* create unit matrices ------------------------------------------*/
391  for (i=0;i<maxrk;i++)
392  {
393  for (j=0;j<=k;j++)
394  {
395  p = pOne();
396  pSetComp(p,i+1+j*maxrk);
397  pSetmComp(p);
398  bigmat->m[i] = pAdd(bigmat->m[i],p);
399  }
400  }
401  /* enter given ideals ------------------------------------------*/
402  i = maxrk;
403  k = 0;
404  for (j=0;j<length;j++)
405  {
406  if (arg[j]!=NULL)
407  {
408  for (l=0;l<IDELEMS(arg[j]);l++)
409  {
410  if (arg[j]->m[l]!=NULL)
411  {
412  if (syz_ring==orig_ring)
413  bigmat->m[i] = pCopy(arg[j]->m[l]);
414  else
415  bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring,currRing);
416  p_Shift(&(bigmat->m[i]),k*maxrk+isIdeal,currRing);
417  i++;
418  }
419  }
420  k++;
421  }
422  }
423  /* std computation --------------------------------------------*/
424  tempstd = kStd(bigmat,currRing->qideal,testHomog,&w,NULL,syzComp);
425  if (w!=NULL) delete w;
426  idDelete(&bigmat);
427 
428  if(syz_ring!=orig_ring)
429  rChangeCurrRing(orig_ring);
430 
431  /* interprete result ----------------------------------------*/
432  result = idInit(IDELEMS(tempstd),maxrk);
433  k = 0;
434  for (j=0;j<IDELEMS(tempstd);j++)
435  {
436  if ((tempstd->m[j]!=NULL) && (p_GetComp(tempstd->m[j],syz_ring)>syzComp))
437  {
438  if (syz_ring==orig_ring)
439  p = pCopy(tempstd->m[j]);
440  else
441  p = prCopyR(tempstd->m[j], syz_ring,currRing);
442  p_Shift(&p,-syzComp-isIdeal,currRing);
443  result->m[k] = p;
444  k++;
445  }
446  }
447  /* clean up ----------------------------------------------------*/
448  if(syz_ring!=orig_ring)
449  rChangeCurrRing(syz_ring);
450  idDelete(&tempstd);
451  if(syz_ring!=orig_ring)
452  {
453  rChangeCurrRing(orig_ring);
454  rDelete(syz_ring);
455  }
456  idSkipZeroes(result);
457  return result;
458 }
459 
460 /*2
461 *computes syzygies of h1,
462 *if quot != NULL it computes in the quotient ring modulo "quot"
463 *works always in a ring with ringorder_s
464 */
465 static ideal idPrepare (ideal h1, tHomog hom, int syzcomp, intvec **w)
466 {
467  ideal h2, h3;
468  int i;
469  int j,k;
470  poly p,q;
471 
472  if (idIs0(h1)) return NULL;
473  k = id_RankFreeModule(h1,currRing);
474  h2=idCopy(h1);
475  i = IDELEMS(h2)-1;
476  if (k == 0)
477  {
478  id_Shift(h2,1,currRing);
479  k = 1;
480  }
481  if (syzcomp<k)
482  {
483  Warn("syzcomp too low, should be %d instead of %d",k,syzcomp);
484  syzcomp = k;
486  }
487  h2->rank = syzcomp+i+1;
488 
489  //if (hom==testHomog)
490  //{
491  // if(idHomIdeal(h1,currRing->qideal))
492  // {
493  // hom=TRUE;
494  // }
495  //}
496 
497 #if MYTEST
498 #ifdef RDEBUG
499  Print("Prepare::h2: ");
500  idPrint(h2);
501 
502  for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]);
503 
504 #endif
505 #endif
506 
507  for (j=0; j<=i; j++)
508  {
509  p = h2->m[j];
510  q = pOne();
511  pSetComp(q,syzcomp+1+j);
512  pSetmComp(q);
513  if (p!=NULL)
514  {
515  while (pNext(p)) pIter(p);
516  p->next = q;
517  }
518  else
519  h2->m[j]=q;
520  }
521 
522 #ifdef PDEBUG
523  for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]);
524 
525 #if MYTEST
526 #ifdef RDEBUG
527  Print("Prepare::Input: ");
528  idPrint(h2);
529 
530  Print("Prepare::currQuotient: ");
531  idPrint(currRing->qideal);
532 #endif
533 #endif
534 
535 #endif
536 
537  idTest(h2);
538 
539  h3 = kStd(h2,currRing->qideal,hom,w,NULL,syzcomp);
540 
541 #if MYTEST
542 #ifdef RDEBUG
543  Print("Prepare::Output: ");
544  idPrint(h3);
545  for(j=0;j<IDELEMS(h2);j++) pTest(h3->m[j]);
546 #endif
547 #endif
548 
549 
550  idDelete(&h2);
551  return h3;
552 }
553 
554 /*2
555 * compute the syzygies of h1 in R/quot,
556 * weights of components are in w
557 * if setRegularity, return the regularity in deg
558 * do not change h1, w
559 */
560 ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp,
561  BOOLEAN setRegularity, int *deg)
562 {
563  ideal s_h1;
564  int j, k, length=0,reg;
565  BOOLEAN isMonomial=TRUE;
566  int ii, idElemens_h1;
567 
568  assume(h1 != NULL);
569 
570  idElemens_h1=IDELEMS(h1);
571 #ifdef PDEBUG
572  for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]);
573 #endif
574  if (idIs0(h1))
575  {
576  ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/);
577  return result;
578  }
579  int slength=(int)id_RankFreeModule(h1,currRing);
580  k=si_max(1,slength /*id_RankFreeModule(h1)*/);
581 
582  assume(currRing != NULL);
583  ring orig_ring=currRing;
584  ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring);
585 
586  if (setSyzComp)
587  rSetSyzComp(k,syz_ring);
588 
589  if (orig_ring != syz_ring)
590  {
591  s_h1=idrCopyR_NoSort(h1,orig_ring,syz_ring);
592  }
593  else
594  {
595  s_h1 = h1;
596  }
597 
598  idTest(s_h1);
599 
600  ideal s_h3=idPrepare(s_h1,h,k,w); // main (syz) GB computation
601 
602  if (s_h3==NULL)
603  {
604  return idFreeModule( idElemens_h1 /*IDELEMS(h1)*/);
605  }
606 
607  if (orig_ring != syz_ring)
608  {
609  idDelete(&s_h1);
610  for (j=0; j<IDELEMS(s_h3); j++)
611  {
612  if (s_h3->m[j] != NULL)
613  {
614  if (p_MinComp(s_h3->m[j],syz_ring) > k)
615  p_Shift(&s_h3->m[j], -k,syz_ring);
616  else
617  p_Delete(&s_h3->m[j],syz_ring);
618  }
619  }
620  idSkipZeroes(s_h3);
621  s_h3->rank -= k;
622  rChangeCurrRing(orig_ring);
623  s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
624  rDelete(syz_ring);
625  #ifdef HAVE_PLURAL
626  if (rIsPluralRing(orig_ring))
627  {
628  id_DelMultiples(s_h3,orig_ring);
629  idSkipZeroes(s_h3);
630  }
631  #endif
632  idTest(s_h3);
633  return s_h3;
634  }
635 
636  ideal e = idInit(IDELEMS(s_h3), s_h3->rank);
637 
638  for (j=IDELEMS(s_h3)-1; j>=0; j--)
639  {
640  if (s_h3->m[j] != NULL)
641  {
642  if (p_MinComp(s_h3->m[j],syz_ring) <= k)
643  {
644  e->m[j] = s_h3->m[j];
645  isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL);
646  p_Delete(&pNext(s_h3->m[j]),syz_ring);
647  s_h3->m[j] = NULL;
648  }
649  }
650  }
651 
652  idSkipZeroes(s_h3);
653  idSkipZeroes(e);
654 
655  if ((deg != NULL)
656  && (!isMonomial)
658  && (setRegularity)
659  && (h==isHomog)
660  && (!rIsPluralRing(currRing))
661  #ifdef HAVE_RINGS
662  && (!rField_is_Ring(currRing))
663  #endif
664  )
665  {
666  ring dp_C_ring = rAssure_dp_C(syz_ring); // will do rChangeCurrRing later
667  if (dp_C_ring != syz_ring)
668  {
669  rChangeCurrRing(dp_C_ring);
670  e = idrMoveR_NoSort(e, syz_ring, dp_C_ring);
671  }
672  resolvente res = sySchreyerResolvente(e,-1,&length,TRUE, TRUE);
673  intvec * dummy = syBetti(res,length,&reg, *w);
674  *deg = reg+2;
675  delete dummy;
676  for (j=0;j<length;j++)
677  {
678  if (res[j]!=NULL) idDelete(&(res[j]));
679  }
680  omFreeSize((ADDRESS)res,length*sizeof(ideal));
681  idDelete(&e);
682  if (dp_C_ring != syz_ring)
683  {
684  rChangeCurrRing(syz_ring);
685  rDelete(dp_C_ring);
686  }
687  }
688  else
689  {
690  idDelete(&e);
691  }
692  idTest(s_h3);
693  if (currRing->qideal != NULL)
694  {
695  ideal ts_h3=kStd(s_h3,currRing->qideal,h,w);
696  idDelete(&s_h3);
697  s_h3 = ts_h3;
698  }
699  return s_h3;
700 }
701 
702 /*2
703 */
704 ideal idXXX (ideal h1, int k)
705 {
706  ideal s_h1;
707  intvec *w=NULL;
708 
709  assume(currRing != NULL);
710  ring orig_ring=currRing;
711  ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); rChangeCurrRing(syz_ring);
712 
713  rSetSyzComp(k,syz_ring);
714 
715  if (orig_ring != syz_ring)
716  {
717  s_h1=idrCopyR_NoSort(h1,orig_ring, syz_ring);
718  }
719  else
720  {
721  s_h1 = h1;
722  }
723 
724  ideal s_h3=kStd(s_h1,NULL,testHomog,&w,NULL,k);
725 
726  if (s_h3==NULL)
727  {
728  return idFreeModule(IDELEMS(h1));
729  }
730 
731  if (orig_ring != syz_ring)
732  {
733  idDelete(&s_h1);
734  idSkipZeroes(s_h3);
735  rChangeCurrRing(orig_ring);
736  s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
737  rDelete(syz_ring);
738  idTest(s_h3);
739  return s_h3;
740  }
741 
742  idSkipZeroes(s_h3);
743  idTest(s_h3);
744  return s_h3;
745 }
746 
747 /*
748 *computes a standard basis for h1 and stores the transformation matrix
749 * in ma
750 */
751 ideal idLiftStd (ideal h1, matrix* ma, tHomog hi, ideal * syz)
752 {
753  int i, j, t, inputIsIdeal=id_RankFreeModule(h1,currRing);
754  long k;
755  poly p=NULL, q;
756  intvec *w=NULL;
757 
758  idDelete((ideal*)ma);
759  BOOLEAN lift3=FALSE;
760  if (syz!=NULL) { lift3=TRUE; idDelete(syz); }
761  if (idIs0(h1))
762  {
763  *ma=mpNew(1,0);
764  if (lift3)
765  {
766  *syz=idFreeModule(IDELEMS(h1));
767  }
768  return idInit(1,h1->rank);
769  }
770 
771  BITSET save2;
772  SI_SAVE_OPT2(save2);
773 
774  k=si_max((long)1,id_RankFreeModule(h1,currRing));
775 
776  if ((k==1) && (!lift3)) si_opt_2 |=Sy_bit(V_IDLIFT);
777 
778  ring orig_ring = currRing;
779  ring syz_ring = rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring);
780  rSetSyzComp(k,syz_ring);
781 
782  ideal s_h1=h1;
783 
784  if (orig_ring != syz_ring)
785  s_h1 = idrCopyR_NoSort(h1,orig_ring,syz_ring);
786  else
787  s_h1 = h1;
788 
789  ideal s_h3=idPrepare(s_h1,hi,k,&w); // main (syz) GB computation
790 
791  ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank);
792 
793  if (lift3) (*syz)=idInit(IDELEMS(s_h3),IDELEMS(h1));
794 
795  if (w!=NULL) delete w;
796  i = 0;
797 
798  // now sort the result, SB : leave in s_h3
799  // T: put in s_h2
800  // syz: put in *syz
801  for (j=0; j<IDELEMS(s_h3); j++)
802  {
803  if (s_h3->m[j] != NULL)
804  {
805  //if (p_MinComp(s_h3->m[j],syz_ring) <= k)
806  if (pGetComp(s_h3->m[j]) <= k) // syz_ring == currRing
807  {
808  i++;
809  q = s_h3->m[j];
810  while (pNext(q) != NULL)
811  {
812  if (pGetComp(pNext(q)) > k)
813  {
814  s_h2->m[j] = pNext(q);
815  pNext(q) = NULL;
816  }
817  else
818  {
819  pIter(q);
820  }
821  }
822  if (!inputIsIdeal) p_Shift(&(s_h3->m[j]), -1,currRing);
823  }
824  else
825  {
826  // we a syzygy here:
827  if (lift3)
828  {
829  p_Shift(&s_h3->m[j], -k,currRing);
830  (*syz)->m[j]=s_h3->m[j];
831  s_h3->m[j]=NULL;
832  }
833  else
834  p_Delete(&(s_h3->m[j]),currRing);
835  }
836  }
837  }
838  idSkipZeroes(s_h3);
839  //extern char * iiStringMatrix(matrix im, int dim,char ch);
840  //PrintS("SB: ----------------------------------------\n");
841  //PrintS(iiStringMatrix((matrix)s_h3,k,'\n'));
842  //PrintLn();
843  //PrintS("T: ----------------------------------------\n");
844  //PrintS(iiStringMatrix((matrix)s_h2,h1->rank,'\n'));
845  //PrintLn();
846 
847  if (lift3) idSkipZeroes(*syz);
848 
849  j = IDELEMS(s_h1);
850 
851 
852  if (syz_ring!=orig_ring)
853  {
854  idDelete(&s_h1);
855  rChangeCurrRing(orig_ring);
856  }
857 
858  *ma = mpNew(j,i);
859 
860  i = 1;
861  for (j=0; j<IDELEMS(s_h2); j++)
862  {
863  if (s_h2->m[j] != NULL)
864  {
865  q = prMoveR( s_h2->m[j], syz_ring,orig_ring);
866  s_h2->m[j] = NULL;
867 
868  if (q!=NULL)
869  {
870  q=pReverse(q);
871  while (q != NULL)
872  {
873  p = q;
874  pIter(q);
875  pNext(p) = NULL;
876  t=pGetComp(p);
877  pSetComp(p,0);
878  pSetmComp(p);
879  MATELEM(*ma,t-k,i) = pAdd(MATELEM(*ma,t-k,i),p);
880  }
881  }
882  i++;
883  }
884  }
885  idDelete(&s_h2);
886 
887  for (i=0; i<IDELEMS(s_h3); i++)
888  {
889  s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], syz_ring,orig_ring);
890  }
891  if (lift3)
892  {
893  for (i=0; i<IDELEMS(*syz); i++)
894  {
895  (*syz)->m[i] = prMoveR_NoSort((*syz)->m[i], syz_ring,orig_ring);
896  }
897  }
898 
899  if (syz_ring!=orig_ring) rDelete(syz_ring);
900  SI_RESTORE_OPT2(save2);
901  return s_h3;
902 }
903 
904 static void idPrepareStd(ideal s_temp, int k)
905 {
906  int j,rk=id_RankFreeModule(s_temp,currRing);
907  poly p,q;
908 
909  if (rk == 0)
910  {
911  for (j=0; j<IDELEMS(s_temp); j++)
912  {
913  if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1);
914  }
915  k = si_max(k,1);
916  }
917  for (j=0; j<IDELEMS(s_temp); j++)
918  {
919  if (s_temp->m[j]!=NULL)
920  {
921  p = s_temp->m[j];
922  q = pOne();
923  //pGetCoeff(q)=nInpNeg(pGetCoeff(q)); //set q to -1
924  pSetComp(q,k+1+j);
925  pSetmComp(q);
926  while (pNext(p)) pIter(p);
927  pNext(p) = q;
928  }
929  }
930  s_temp->rank += k;
931 }
932 
933 /*2
934 *computes a representation of the generators of submod with respect to those
935 * of mod
936 */
937 
938 ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape,
939  BOOLEAN isSB, BOOLEAN divide, matrix *unit)
940 {
941  int lsmod =id_RankFreeModule(submod,currRing), j, k;
942  int comps_to_add=0;
943  poly p;
944 
945  if (idIs0(submod))
946  {
947  if (unit!=NULL)
948  {
949  *unit=mpNew(1,1);
950  MATELEM(*unit,1,1)=pOne();
951  }
952  if (rest!=NULL)
953  {
954  *rest=idInit(1,mod->rank);
955  }
956  return idInit(1,mod->rank);
957  }
958  if (idIs0(mod)) /* and not idIs0(submod) */
959  {
960  WerrorS("2nd module does not lie in the first");
961  return NULL;
962  }
963  if (unit!=NULL)
964  {
965  comps_to_add = IDELEMS(submod);
966  while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL))
967  comps_to_add--;
968  }
970  if ((k!=0) && (lsmod==0)) lsmod=1;
971  k=si_max(k,(int)mod->rank);
972  if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; }
973 
974  ring orig_ring=currRing;
975  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring);
976  rSetSyzComp(k,syz_ring);
977 
978  ideal s_mod, s_temp;
979  if (orig_ring != syz_ring)
980  {
981  s_mod = idrCopyR_NoSort(mod,orig_ring,syz_ring);
982  s_temp = idrCopyR_NoSort(submod,orig_ring,syz_ring);
983  }
984  else
985  {
986  s_mod = mod;
987  s_temp = idCopy(submod);
988  }
989  ideal s_h3;
990  if (isSB)
991  {
992  s_h3 = idCopy(s_mod);
993  idPrepareStd(s_h3, k+comps_to_add);
994  }
995  else
996  {
997  s_h3 = idPrepare(s_mod,(tHomog)FALSE,k+comps_to_add,NULL);
998  }
999  if (!goodShape)
1000  {
1001  for (j=0;j<IDELEMS(s_h3);j++)
1002  {
1003  if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k))
1004  p_Delete(&(s_h3->m[j]),currRing);
1005  }
1006  }
1007  idSkipZeroes(s_h3);
1008  if (lsmod==0)
1009  {
1010  id_Shift(s_temp,1,currRing);
1011  }
1012  if (unit!=NULL)
1013  {
1014  for(j = 0;j<comps_to_add;j++)
1015  {
1016  p = s_temp->m[j];
1017  if (p!=NULL)
1018  {
1019  while (pNext(p)!=NULL) pIter(p);
1020  pNext(p) = pOne();
1021  pIter(p);
1022  pSetComp(p,1+j+k);
1023  pSetmComp(p);
1024  p = pNeg(p);
1025  }
1026  }
1027  s_temp->rank += k;
1028  }
1029  ideal s_result = kNF(s_h3,currRing->qideal,s_temp,k);
1030  s_result->rank = s_h3->rank;
1031  ideal s_rest = idInit(IDELEMS(s_result),k);
1032  idDelete(&s_h3);
1033  idDelete(&s_temp);
1034 
1035  for (j=0;j<IDELEMS(s_result);j++)
1036  {
1037  if (s_result->m[j]!=NULL)
1038  {
1039  if (pGetComp(s_result->m[j])<=k)
1040  {
1041  if (!divide)
1042  {
1043  if (isSB)
1044  {
1045  WarnS("first module not a standardbasis\n"
1046  "// ** or second not a proper submodule");
1047  }
1048  else
1049  WerrorS("2nd module does not lie in the first");
1050  idDelete(&s_result);
1051  idDelete(&s_rest);
1052  s_result=idInit(IDELEMS(submod),submod->rank);
1053  break;
1054  }
1055  else
1056  {
1057  p = s_rest->m[j] = s_result->m[j];
1058  while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p);
1059  s_result->m[j] = pNext(p);
1060  pNext(p) = NULL;
1061  }
1062  }
1063  p_Shift(&(s_result->m[j]),-k,currRing);
1064  pNeg(s_result->m[j]);
1065  }
1066  }
1067  if ((lsmod==0) && (s_rest!=NULL))
1068  {
1069  for (j=IDELEMS(s_rest);j>0;j--)
1070  {
1071  if (s_rest->m[j-1]!=NULL)
1072  {
1073  p_Shift(&(s_rest->m[j-1]),-1,currRing);
1074  s_rest->m[j-1] = s_rest->m[j-1];
1075  }
1076  }
1077  }
1078  if(syz_ring!=orig_ring)
1079  {
1080  idDelete(&s_mod);
1081  rChangeCurrRing(orig_ring);
1082  s_result = idrMoveR_NoSort(s_result, syz_ring, orig_ring);
1083  s_rest = idrMoveR_NoSort(s_rest, syz_ring, orig_ring);
1084  rDelete(syz_ring);
1085  }
1086  if (rest!=NULL)
1087  *rest = s_rest;
1088  else
1089  idDelete(&s_rest);
1090 //idPrint(s_result);
1091  if (unit!=NULL)
1092  {
1093  *unit=mpNew(comps_to_add,comps_to_add);
1094  int i;
1095  for(i=0;i<IDELEMS(s_result);i++)
1096  {
1097  poly p=s_result->m[i];
1098  poly q=NULL;
1099  while(p!=NULL)
1100  {
1101  if(pGetComp(p)<=comps_to_add)
1102  {
1103  pSetComp(p,0);
1104  if (q!=NULL)
1105  {
1106  pNext(q)=pNext(p);
1107  }
1108  else
1109  {
1110  pIter(s_result->m[i]);
1111  }
1112  pNext(p)=NULL;
1113  MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p);
1114  if(q!=NULL) p=pNext(q);
1115  else p=s_result->m[i];
1116  }
1117  else
1118  {
1119  q=p;
1120  pIter(p);
1121  }
1122  }
1123  p_Shift(&s_result->m[i],-comps_to_add,currRing);
1124  }
1125  }
1126  return s_result;
1127 }
1128 
1129 /*2
1130 *computes division of P by Q with remainder up to (w-weighted) degree n
1131 *P, Q, and w are not changed
1132 */
1133 void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,short *w)
1134 {
1135  long N=0;
1136  int i;
1137  for(i=IDELEMS(Q)-1;i>=0;i--)
1138  if(w==NULL)
1139  N=si_max(N,p_Deg(Q->m[i],currRing));
1140  else
1141  N=si_max(N,p_DegW(Q->m[i],w,currRing));
1142  N+=n;
1143 
1144  T=mpNew(IDELEMS(Q),IDELEMS(P));
1145  R=idInit(IDELEMS(P),P->rank);
1146 
1147  for(i=IDELEMS(P)-1;i>=0;i--)
1148  {
1149  poly p;
1150  if(w==NULL)
1151  p=ppJet(P->m[i],N);
1152  else
1153  p=ppJetW(P->m[i],N,w);
1154 
1155  int j=IDELEMS(Q)-1;
1156  while(p!=NULL)
1157  {
1158  if(pDivisibleBy(Q->m[j],p))
1159  {
1160  poly p0=p_DivideM(pHead(p),pHead(Q->m[j]),currRing);
1161  if(w==NULL)
1162  p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N);
1163  else
1164  p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w);
1165  pNormalize(p);
1166  if(((w==NULL)&&(p_Deg(p0,currRing)>n))||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
1167  p_Delete(&p0,currRing);
1168  else
1169  MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0);
1170  j=IDELEMS(Q)-1;
1171  }
1172  else
1173  {
1174  if(j==0)
1175  {
1176  poly p0=p;
1177  pIter(p);
1178  pNext(p0)=NULL;
1179  if(((w==NULL)&&(p_Deg(p0,currRing)>n))
1180  ||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
1181  p_Delete(&p0,currRing);
1182  else
1183  R->m[i]=pAdd(R->m[i],p0);
1184  j=IDELEMS(Q)-1;
1185  }
1186  else
1187  j--;
1188  }
1189  }
1190  }
1191 }
1192 
1193 /*2
1194 *computes the quotient of h1,h2 : internal routine for idQuot
1195 *BEWARE: the returned ideals may contain incorrectly ordered polys !
1196 *
1197 */
1198 static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
1199 {
1200  idTest(h1);
1201  idTest(h2);
1202 
1203  ideal temph1;
1204  poly p,q = NULL;
1205  int i,l,ll,k,kkk,kmax;
1206  int j = 0;
1207  int k1 = id_RankFreeModule(h1,currRing);
1208  int k2 = id_RankFreeModule(h2,currRing);
1209  tHomog hom=isNotHomog;
1210  k=si_max(k1,k2);
1211  if (k==0)
1212  k = 1;
1213  if ((k2==0) && (k>1)) *addOnlyOne = FALSE;
1214  intvec * weights;
1215  hom = (tHomog)idHomModule(h1,currRing->qideal,&weights);
1216  if /**addOnlyOne &&*/ (/*(*/ !h1IsStb /*)*/)
1217  temph1 = kStd(h1,currRing->qideal,hom,&weights,NULL);
1218  else
1219  temph1 = idCopy(h1);
1220  if (weights!=NULL) delete weights;
1221  idTest(temph1);
1222 /*--- making a single vector from h2 ---------------------*/
1223  for (i=0; i<IDELEMS(h2); i++)
1224  {
1225  if (h2->m[i] != NULL)
1226  {
1227  p = pCopy(h2->m[i]);
1228  if (k2 == 0)
1229  p_Shift(&p,j*k+1,currRing);
1230  else
1231  p_Shift(&p,j*k,currRing);
1232  q = pAdd(q,p);
1233  j++;
1234  }
1235  }
1236  *kkmax = kmax = j*k+1;
1237 /*--- adding a monomial for the result (syzygy) ----------*/
1238  p = q;
1239  while (pNext(p)!=NULL) pIter(p);
1240  pNext(p) = pOne();
1241  pIter(p);
1242  pSetComp(p,kmax);
1243  pSetmComp(p);
1244 /*--- constructing the big matrix ------------------------*/
1245  ideal h4 = idInit(16,kmax+k-1);
1246  h4->m[0] = q;
1247  if (k2 == 0)
1248  {
1249  if (k > IDELEMS(h4))
1250  {
1251  pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4));
1252  IDELEMS(h4) = k;
1253  }
1254  for (i=1; i<k; i++)
1255  {
1256  if (h4->m[i-1]!=NULL)
1257  {
1258  p = p_Copy_noCheck(h4->m[i-1], currRing); p_Shift(&p,1,currRing);
1259  // pTest(p);
1260  h4->m[i] = p;
1261  }
1262  }
1263  }
1264  idSkipZeroes(h4);
1265  kkk = IDELEMS(h4);
1266  i = IDELEMS(temph1);
1267  for (l=0; l<i; l++)
1268  {
1269  if(temph1->m[l]!=NULL)
1270  {
1271  for (ll=0; ll<j; ll++)
1272  {
1273  p = pCopy(temph1->m[l]);
1274  if (k1 == 0)
1275  p_Shift(&p,ll*k+1,currRing);
1276  else
1277  p_Shift(&p,ll*k,currRing);
1278  if (kkk >= IDELEMS(h4))
1279  {
1280  pEnlargeSet(&(h4->m),IDELEMS(h4),16);
1281  IDELEMS(h4) += 16;
1282  }
1283  h4->m[kkk] = p;
1284  kkk++;
1285  }
1286  }
1287  }
1288 /*--- if h2 goes in as single vector - the h1-part is just SB ---*/
1289  if (*addOnlyOne)
1290  {
1291  idSkipZeroes(h4);
1292  p = h4->m[0];
1293  for (i=0;i<IDELEMS(h4)-1;i++)
1294  {
1295  h4->m[i] = h4->m[i+1];
1296  }
1297  h4->m[IDELEMS(h4)-1] = p;
1298  #ifdef HAVE_RINGS
1299  if(!rField_is_Ring(currRing))
1300  #endif
1301  si_opt_1 |= Sy_bit(OPT_SB_1);
1302  }
1303  idDelete(&temph1);
1304  //idTest(h4);//see remark at the beginning
1305  return h4;
1306 }
1307 /*2
1308 *computes the quotient of h1,h2
1309 */
1310 ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
1311 {
1312  // first check for special case h1:(0)
1313  if (idIs0(h2))
1314  {
1315  ideal res;
1316  if (resultIsIdeal)
1317  {
1318  res = idInit(1,1);
1319  res->m[0] = pOne();
1320  }
1321  else
1322  res = idFreeModule(h1->rank);
1323  return res;
1324  }
1325  BITSET old_test1;
1326  SI_SAVE_OPT1(old_test1);
1327  int i, kmax;
1328  BOOLEAN addOnlyOne=TRUE;
1329  tHomog hom=isNotHomog;
1330  intvec * weights1;
1331 
1332  ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax);
1333 
1334  hom = (tHomog)idHomModule(s_h4,currRing->qideal,&weights1);
1335 
1336  ring orig_ring=currRing;
1337  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); rChangeCurrRing(syz_ring);
1338  rSetSyzComp(kmax-1,syz_ring);
1339  if (orig_ring!=syz_ring)
1340  // s_h4 = idrMoveR_NoSort(s_h4,orig_ring, syz_ring);
1341  s_h4 = idrMoveR(s_h4,orig_ring, syz_ring);
1342  idTest(s_h4);
1343  #if 0
1344  void ipPrint_MA0(matrix m, const char *name);
1345  matrix m=idModule2Matrix(idCopy(s_h4));
1346  PrintS("start:\n");
1347  ipPrint_MA0(m,"Q");
1348  idDelete((ideal *)&m);
1349  PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn();
1350  #endif
1351  ideal s_h3;
1352  if (addOnlyOne)
1353  {
1354  s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,0/*kmax-1*/,IDELEMS(s_h4)-1);
1355  }
1356  else
1357  {
1358  s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,kmax-1);
1359  }
1360  SI_RESTORE_OPT1(old_test1);
1361  #if 0
1362  // only together with the above debug stuff
1363  idSkipZeroes(s_h3);
1364  m=idModule2Matrix(idCopy(s_h3));
1365  Print("result, kmax=%d:\n",kmax);
1366  ipPrint_MA0(m,"S");
1367  idDelete((ideal *)&m);
1368  #endif
1369  idTest(s_h3);
1370  if (weights1!=NULL) delete weights1;
1371  idDelete(&s_h4);
1372 
1373  for (i=0;i<IDELEMS(s_h3);i++)
1374  {
1375  if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax))
1376  {
1377  if (resultIsIdeal)
1378  p_Shift(&s_h3->m[i],-kmax,currRing);
1379  else
1380  p_Shift(&s_h3->m[i],-kmax+1,currRing);
1381  }
1382  else
1383  p_Delete(&s_h3->m[i],currRing);
1384  }
1385  if (resultIsIdeal)
1386  s_h3->rank = 1;
1387  else
1388  s_h3->rank = h1->rank;
1389  if(syz_ring!=orig_ring)
1390  {
1391  rChangeCurrRing(orig_ring);
1392  s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
1393  rDelete(syz_ring);
1394  }
1395  idSkipZeroes(s_h3);
1396  idTest(s_h3);
1397  return s_h3;
1398 }
1399 
1400 /*2
1401 * eliminate delVar (product of vars) in h1
1402 */
1403 ideal idElimination (ideal h1,poly delVar,intvec *hilb)
1404 {
1405  int i,j=0,k,l;
1406  ideal h,hh, h3;
1407  int *ord,*block0,*block1;
1408  int ordersize=2;
1409  int **wv;
1410  tHomog hom;
1411  intvec * w;
1412  ring tmpR;
1413  ring origR = currRing;
1414 
1415  if (delVar==NULL)
1416  {
1417  return idCopy(h1);
1418  }
1419  if ((currRing->qideal!=NULL) && rIsPluralRing(origR))
1420  {
1421  WerrorS("cannot eliminate in a qring");
1422  return NULL;
1423  }
1424  if (idIs0(h1)) return idInit(1,h1->rank);
1425 #ifdef HAVE_PLURAL
1426  if (rIsPluralRing(origR))
1427  /* in the NC case, we have to check the admissibility of */
1428  /* the subalgebra to be intersected with */
1429  {
1430  if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */
1431  {
1432  if (nc_CheckSubalgebra(delVar,origR))
1433  {
1434  WerrorS("no elimination is possible: subalgebra is not admissible");
1435  return NULL;
1436  }
1437  }
1438  }
1439 #endif
1440  hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL
1441  h3=idInit(16,h1->rank);
1442  for (k=0;; k++)
1443  {
1444  if (origR->order[k]!=0) ordersize++;
1445  else break;
1446  }
1447 #if 0
1448  if (rIsPluralRing(origR)) // we have too keep the odering: it may be needed
1449  // for G-algebra
1450  {
1451  for (k=0;k<ordersize-1; k++)
1452  {
1453  block0[k+1] = origR->block0[k];
1454  block1[k+1] = origR->block1[k];
1455  ord[k+1] = origR->order[k];
1456  if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
1457  }
1458  }
1459  else
1460  {
1461  block0[1] = 1;
1462  block1[1] = (currRing->N);
1463  if (origR->OrdSgn==1) ord[1] = ringorder_wp;
1464  else ord[1] = ringorder_ws;
1465  wv[1]=(int*)omAlloc0((currRing->N)*sizeof(int));
1466  double wNsqr = (double)2.0 / (double)(currRing->N);
1468  int *x= (int * )omAlloc(2 * ((currRing->N) + 1) * sizeof(int));
1469  int sl=IDELEMS(h1) - 1;
1470  wCall(h1->m, sl, x, wNsqr);
1471  for (sl = (currRing->N); sl!=0; sl--)
1472  wv[1][sl-1] = x[sl + (currRing->N) + 1];
1473  omFreeSize((ADDRESS)x, 2 * ((currRing->N) + 1) * sizeof(int));
1474 
1475  ord[2]=ringorder_C;
1476  ord[3]=0;
1477  }
1478 #else
1479 #endif
1480  if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR)))
1481  {
1482  #if 1
1483  // we change to an ordering:
1484  // aa(1,1,1,...,0,0,0),wp(...),C
1485  // this seems to be better than version 2 below,
1486  // according to Tst/../elimiate_[3568].tat (- 17 %)
1487  ord=(int*)omAlloc0(4*sizeof(int));
1488  block0=(int*)omAlloc0(4*sizeof(int));
1489  block1=(int*)omAlloc0(4*sizeof(int));
1490  wv=(int**) omAlloc0(4*sizeof(int**));
1491  block0[0] = block0[1] = 1;
1492  block1[0] = block1[1] = rVar(origR);
1493  wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1494  // use this special ordering: like ringorder_a, except that pFDeg, pWeights
1495  // ignore it
1496  ord[0] = ringorder_aa;
1497  for (j=0;j<rVar(origR);j++)
1498  if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
1499  BOOLEAN wp=FALSE;
1500  for (j=0;j<rVar(origR);j++)
1501  if (pWeight(j+1,origR)!=1) { wp=TRUE;break; }
1502  if (wp)
1503  {
1504  wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1505  for (j=0;j<rVar(origR);j++)
1506  wv[1][j]=pWeight(j+1,origR);
1507  ord[1] = ringorder_wp;
1508  }
1509  else
1510  ord[1] = ringorder_dp;
1511  #else
1512  // we change to an ordering:
1513  // a(w1,...wn),wp(1,...0.....),C
1514  ord=(int*)omAlloc0(4*sizeof(int));
1515  block0=(int*)omAlloc0(4*sizeof(int));
1516  block1=(int*)omAlloc0(4*sizeof(int));
1517  wv=(int**) omAlloc0(4*sizeof(int**));
1518  block0[0] = block0[1] = 1;
1519  block1[0] = block1[1] = rVar(origR);
1520  wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1521  wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1522  ord[0] = ringorder_a;
1523  for (j=0;j<rVar(origR);j++)
1524  wv[0][j]=pWeight(j+1,origR);
1525  ord[1] = ringorder_wp;
1526  for (j=0;j<rVar(origR);j++)
1527  if (pGetExp(delVar,j+1)!=0) wv[1][j]=1;
1528  #endif
1529  ord[2] = ringorder_C;
1530  ord[3] = 0;
1531  }
1532  else
1533  {
1534  // we change to an ordering:
1535  // aa(....),orig_ordering
1536  ord=(int*)omAlloc0(ordersize*sizeof(int));
1537  block0=(int*)omAlloc0(ordersize*sizeof(int));
1538  block1=(int*)omAlloc0(ordersize*sizeof(int));
1539  wv=(int**) omAlloc0(ordersize*sizeof(int**));
1540  for (k=0;k<ordersize-1; k++)
1541  {
1542  block0[k+1] = origR->block0[k];
1543  block1[k+1] = origR->block1[k];
1544  ord[k+1] = origR->order[k];
1545  if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
1546  }
1547  block0[0] = 1;
1548  block1[0] = rVar(origR);
1549  wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1550  for (j=0;j<rVar(origR);j++)
1551  if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
1552  // use this special ordering: like ringorder_a, except that pFDeg, pWeights
1553  // ignore it
1554  ord[0] = ringorder_aa;
1555  }
1556  // fill in tmp ring to get back the data later on
1557  tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL
1558  //rUnComplete(tmpR);
1559  tmpR->p_Procs=NULL;
1560  tmpR->order = ord;
1561  tmpR->block0 = block0;
1562  tmpR->block1 = block1;
1563  tmpR->wvhdl = wv;
1564  rComplete(tmpR, 1);
1565 
1566 #ifdef HAVE_PLURAL
1567  /* update nc structure on tmpR */
1568  if (rIsPluralRing(origR))
1569  {
1570  if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal!
1571  {
1572  Werror("no elimination is possible: ordering condition is violated");
1573  // cleanup
1574  rDelete(tmpR);
1575  if (w!=NULL)
1576  delete w;
1577  return NULL;
1578  }
1579  }
1580 #endif
1581  // change into the new ring
1582  //pChangeRing((currRing->N),currRing->OrdSgn,ord,block0,block1,wv);
1583  rChangeCurrRing(tmpR);
1584 
1585  //h = idInit(IDELEMS(h1),h1->rank);
1586  // fetch data from the old ring
1587  //for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR);
1588  h=idrCopyR(h1,origR,currRing);
1589  if (origR->qideal!=NULL)
1590  {
1591  WarnS("eliminate in q-ring: experimental");
1592  ideal q=idrCopyR(origR->qideal,origR,currRing);
1593  ideal s=idSimpleAdd(h,q);
1594  idDelete(&h);
1595  idDelete(&q);
1596  h=s;
1597  }
1598  // compute kStd
1599 #if 1
1600  //rWrite(tmpR);PrintLn();
1601  //BITSET save1;
1602  //SI_SAVE_OPT1(save1);
1603  //si_opt_1 |=1;
1604  //Print("h: %d gen, rk=%d\n",IDELEMS(h),h->rank);
1605  //extern char * showOption();
1606  //Print("%s\n",showOption());
1607  hh = kStd(h,NULL,hom,&w,hilb);
1608  //SI_RESTORE_OPT1(save1);
1609  idDelete(&h);
1610 #else
1611  extern ideal kGroebner(ideal F, ideal Q);
1612  hh=kGroebner(h,NULL);
1613 #endif
1614  // go back to the original ring
1615  rChangeCurrRing(origR);
1616  i = IDELEMS(hh)-1;
1617  while ((i >= 0) && (hh->m[i] == NULL)) i--;
1618  j = -1;
1619  // fetch data from temp ring
1620  for (k=0; k<=i; k++)
1621  {
1622  l=(currRing->N);
1623  while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--;
1624  if (l==0)
1625  {
1626  j++;
1627  if (j >= IDELEMS(h3))
1628  {
1629  pEnlargeSet(&(h3->m),IDELEMS(h3),16);
1630  IDELEMS(h3) += 16;
1631  }
1632  h3->m[j] = prMoveR( hh->m[k], tmpR,origR);
1633  hh->m[k] = NULL;
1634  }
1635  }
1636  id_Delete(&hh, tmpR);
1637  idSkipZeroes(h3);
1638  rDelete(tmpR);
1639  if (w!=NULL)
1640  delete w;
1641  return h3;
1642 }
1643 
1644 #ifdef WITH_OLD_MINOR
1645 /*2
1646 * compute the which-th ar-minor of the matrix a
1647 */
1648 poly idMinor(matrix a, int ar, unsigned long which, ideal R)
1649 {
1650  int i,j/*,k,size*/;
1651  unsigned long curr;
1652  int *rowchoise,*colchoise;
1653  BOOLEAN rowch,colch;
1654  // ideal result;
1655  matrix tmp;
1656  poly p,q;
1657 
1658  i = binom(a->rows(),ar);
1659  j = binom(a->cols(),ar);
1660 
1661  rowchoise=(int *)omAlloc(ar*sizeof(int));
1662  colchoise=(int *)omAlloc(ar*sizeof(int));
1663  // if ((i>512) || (j>512) || (i*j >512)) size=512;
1664  // else size=i*j;
1665  // result=idInit(size,1);
1666  tmp=mpNew(ar,ar);
1667  // k = 0; /* the index in result*/
1668  curr = 0; /* index of current minor */
1669  idInitChoise(ar,1,a->rows(),&rowch,rowchoise);
1670  while (!rowch)
1671  {
1672  idInitChoise(ar,1,a->cols(),&colch,colchoise);
1673  while (!colch)
1674  {
1675  if (curr == which)
1676  {
1677  for (i=1; i<=ar; i++)
1678  {
1679  for (j=1; j<=ar; j++)
1680  {
1681  MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
1682  }
1683  }
1684  p = mp_DetBareiss(tmp,currRing);
1685  if (p!=NULL)
1686  {
1687  if (R!=NULL)
1688  {
1689  q = p;
1690  p = kNF(R,currRing->qideal,q);
1691  p_Delete(&q,currRing);
1692  }
1693  /*delete the matrix tmp*/
1694  for (i=1; i<=ar; i++)
1695  {
1696  for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
1697  }
1698  idDelete((ideal*)&tmp);
1699  omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
1700  omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
1701  return (p);
1702  }
1703  }
1704  curr++;
1705  idGetNextChoise(ar,a->cols(),&colch,colchoise);
1706  }
1707  idGetNextChoise(ar,a->rows(),&rowch,rowchoise);
1708  }
1709  return (poly) 1;
1710 }
1711 
1712 /*2
1713 * compute all ar-minors of the matrix a
1714 */
1715 ideal idMinors(matrix a, int ar, ideal R)
1716 {
1717  int i,j,/*k,*/size;
1718  int *rowchoise,*colchoise;
1719  BOOLEAN rowch,colch;
1720  ideal result;
1721  matrix tmp;
1722  poly p,q;
1723 
1724  i = binom(a->rows(),ar);
1725  j = binom(a->cols(),ar);
1726 
1727  rowchoise=(int *)omAlloc(ar*sizeof(int));
1728  colchoise=(int *)omAlloc(ar*sizeof(int));
1729  if ((i>512) || (j>512) || (i*j >512)) size=512;
1730  else size=i*j;
1731  result=idInit(size,1);
1732  tmp=mpNew(ar,ar);
1733  // k = 0; /* the index in result*/
1734  idInitChoise(ar,1,a->rows(),&rowch,rowchoise);
1735  while (!rowch)
1736  {
1737  idInitChoise(ar,1,a->cols(),&colch,colchoise);
1738  while (!colch)
1739  {
1740  for (i=1; i<=ar; i++)
1741  {
1742  for (j=1; j<=ar; j++)
1743  {
1744  MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
1745  }
1746  }
1747  p = mp_DetBareiss(tmp,vcurrRing);
1748  if (p!=NULL)
1749  {
1750  if (R!=NULL)
1751  {
1752  q = p;
1753  p = kNF(R,currRing->qideal,q);
1754  p_Delete(&q,currRing);
1755  }
1756  if (p!=NULL)
1757  {
1758  if (k>=size)
1759  {
1760  pEnlargeSet(&result->m,size,32);
1761  size += 32;
1762  }
1763  result->m[k] = p;
1764  k++;
1765  }
1766  }
1767  idGetNextChoise(ar,a->cols(),&colch,colchoise);
1768  }
1769  idGetNextChoise(ar,a->rows(),&rowch,rowchoise);
1770  }
1771  /*delete the matrix tmp*/
1772  for (i=1; i<=ar; i++)
1773  {
1774  for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
1775  }
1776  idDelete((ideal*)&tmp);
1777  if (k==0)
1778  {
1779  k=1;
1780  result->m[0]=NULL;
1781  }
1782  omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
1783  omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
1784  pEnlargeSet(&result->m,size,k-size);
1785  IDELEMS(result) = k;
1786  return (result);
1787 }
1788 #else
1789 
1790 
1791 /// compute all ar-minors of the matrix a
1792 /// the caller of mpRecMin
1793 /// the elements of the result are not in R (if R!=NULL)
1794 ideal idMinors(matrix a, int ar, ideal R)
1795 {
1796 
1797  const ring origR=currRing;
1798  id_Test((ideal)a, origR);
1799 
1800  const int r = a->nrows;
1801  const int c = a->ncols;
1802 
1803  if((ar<=0) || (ar>r) || (ar>c))
1804  {
1805  Werror("%d-th minor, matrix is %dx%d",ar,r,c);
1806  return NULL;
1807  }
1808 
1809  ideal h = id_Matrix2Module(mp_Copy(a,origR),origR);
1810  long bound = sm_ExpBound(h,c,r,ar,origR);
1811  id_Delete(&h, origR);
1812 
1813  ring tmpR = sm_RingChange(origR,bound);
1814 
1815  matrix b = mpNew(r,c);
1816 
1817  for (int i=r*c-1;i>=0;i--)
1818  if (a->m[i] != NULL)
1819  b->m[i] = prCopyR(a->m[i],origR,tmpR);
1820 
1821  id_Test( (ideal)b, tmpR);
1822 
1823  if (R!=NULL)
1824  {
1825  R = idrCopyR(R,origR,tmpR); // TODO: overwrites R? memory leak?
1826  //if (ar>1) // otherwise done in mpMinorToResult
1827  //{
1828  // matrix bb=(matrix)kNF(R,currRing->qideal,(ideal)b);
1829  // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols;
1830  // idDelete((ideal*)&b); b=bb;
1831  //}
1832  id_Test( R, tmpR);
1833  }
1834 
1835 
1836  ideal result = idInit(32,1);
1837 
1838  int elems = 0;
1839 
1840  if(ar>1)
1841  mp_RecMin(ar-1,result,elems,b,r,c,NULL,R,tmpR);
1842  else
1843  mp_MinorToResult(result,elems,b,r,c,R,tmpR);
1844 
1845  id_Test( (ideal)b, tmpR);
1846 
1847  id_Delete((ideal *)&b, tmpR);
1848 
1849  if (R!=NULL) idDelete(&R);
1850 
1851  idSkipZeroes(result);
1852  rChangeCurrRing(origR);
1853  result = idrMoveR(result,tmpR,origR);
1854  sm_KillModifiedRing(tmpR);
1855  idTest(result);
1856  return result;
1857 }
1858 #endif
1859 
1860 /*2
1861 *returns TRUE if id1 is a submodule of id2
1862 */
1863 BOOLEAN idIsSubModule(ideal id1,ideal id2)
1864 {
1865  int i;
1866  poly p;
1867 
1868  if (idIs0(id1)) return TRUE;
1869  for (i=0;i<IDELEMS(id1);i++)
1870  {
1871  if (id1->m[i] != NULL)
1872  {
1873  p = kNF(id2,currRing->qideal,id1->m[i]);
1874  if (p != NULL)
1875  {
1876  p_Delete(&p,currRing);
1877  return FALSE;
1878  }
1879  }
1880  }
1881  return TRUE;
1882 }
1883 
1885 {
1886  if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
1887  if (idIs0(m)) return TRUE;
1888 
1889  int cmax=-1;
1890  int i;
1891  poly p=NULL;
1892  int length=IDELEMS(m);
1893  polyset P=m->m;
1894  for (i=length-1;i>=0;i--)
1895  {
1896  p=P[i];
1897  if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
1898  }
1899  if (w != NULL)
1900  if (w->length()+1 < cmax)
1901  {
1902  // Print("length: %d - %d \n", w->length(),cmax);
1903  return FALSE;
1904  }
1905 
1906  if(w!=NULL)
1907  p_SetModDeg(w, currRing);
1908 
1909  for (i=length-1;i>=0;i--)
1910  {
1911  p=P[i];
1912  if (p!=NULL)
1913  {
1914  int d=currRing->pFDeg(p,currRing);
1915  loop
1916  {
1917  pIter(p);
1918  if (p==NULL) break;
1919  if (d!=currRing->pFDeg(p,currRing))
1920  {
1921  //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
1922  if(w!=NULL)
1924  return FALSE;
1925  }
1926  }
1927  }
1928  }
1929 
1930  if(w!=NULL)
1932 
1933  return TRUE;
1934 }
1935 
1936 ideal idSeries(int n,ideal M,matrix U,intvec *w)
1937 {
1938  for(int i=IDELEMS(M)-1;i>=0;i--)
1939  {
1940  if(U==NULL)
1941  M->m[i]=pSeries(n,M->m[i],NULL,w);
1942  else
1943  {
1944  M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w);
1945  MATELEM(U,i+1,i+1)=NULL;
1946  }
1947  }
1948  if(U!=NULL)
1949  idDelete((ideal*)&U);
1950  return M;
1951 }
1952 
1954 {
1955  int e=MATCOLS(i)*MATROWS(i);
1956  matrix r=mpNew(MATROWS(i),MATCOLS(i));
1957  r->rank=i->rank;
1958  int j;
1959  for(j=0; j<e; j++)
1960  {
1961  r->m[j]=pDiff(i->m[j],k);
1962  }
1963  return r;
1964 }
1965 
1966 matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply)
1967 {
1968  matrix r=mpNew(IDELEMS(I),IDELEMS(J));
1969  int i,j;
1970  for(i=0; i<IDELEMS(I); i++)
1971  {
1972  for(j=0; j<IDELEMS(J); j++)
1973  {
1974  MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply);
1975  }
1976  }
1977  return r;
1978 }
1979 
1980 /*3
1981 *handles for some ideal operations the ring/syzcomp managment
1982 *returns all syzygies (componentwise-)shifted by -syzcomp
1983 *or -syzcomp-1 (in case of ideals as input)
1984 static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE)
1985 {
1986  ring orig_ring=currRing;
1987  ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); rChangeCurrRing(syz_ring);
1988  rSetSyzComp(length, syz_ring);
1989 
1990  ideal s_temp;
1991  if (orig_ring!=syz_ring)
1992  s_temp=idrMoveR_NoSort(arg,orig_ring, syz_ring);
1993  else
1994  s_temp=arg;
1995 
1996  ideal s_temp1 = kStd(s_temp,currRing->qideal,testHomog,&w,NULL,length);
1997  if (w!=NULL) delete w;
1998 
1999  if (syz_ring!=orig_ring)
2000  {
2001  idDelete(&s_temp);
2002  rChangeCurrRing(orig_ring);
2003  }
2004 
2005  idDelete(&temp);
2006  ideal temp1=idRingCopy(s_temp1,syz_ring);
2007 
2008  if (syz_ring!=orig_ring)
2009  {
2010  rChangeCurrRing(syz_ring);
2011  idDelete(&s_temp1);
2012  rChangeCurrRing(orig_ring);
2013  rDelete(syz_ring);
2014  }
2015 
2016  for (i=0;i<IDELEMS(temp1);i++)
2017  {
2018  if ((temp1->m[i]!=NULL)
2019  && (pGetComp(temp1->m[i])<=length))
2020  {
2021  pDelete(&(temp1->m[i]));
2022  }
2023  else
2024  {
2025  p_Shift(&(temp1->m[i]),-length,currRing);
2026  }
2027  }
2028  temp1->rank = rk;
2029  idSkipZeroes(temp1);
2030 
2031  return temp1;
2032 }
2033 */
2034 /*2
2035 * represents (h1+h2)/h2=h1/(h1 intersect h2)
2036 */
2037 //ideal idModulo (ideal h2,ideal h1)
2038 ideal idModulo (ideal h2,ideal h1, tHomog hom, intvec ** w)
2039 {
2040  intvec *wtmp=NULL;
2041 
2042  int i,k,rk,flength=0,slength,length;
2043  poly p,q;
2044 
2045  if (idIs0(h2))
2046  return idFreeModule(si_max(1,h2->ncols));
2047  if (!idIs0(h1))
2048  flength = id_RankFreeModule(h1,currRing);
2049  slength = id_RankFreeModule(h2,currRing);
2050  length = si_max(flength,slength);
2051  if (length==0)
2052  {
2053  length = 1;
2054  }
2055  ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2));
2056  if ((w!=NULL)&&((*w)!=NULL))
2057  {
2058  //Print("input weights:");(*w)->show(1);PrintLn();
2059  int d;
2060  int k;
2061  wtmp=new intvec(length+IDELEMS(h2));
2062  for (i=0;i<length;i++)
2063  ((*wtmp)[i])=(**w)[i];
2064  for (i=0;i<IDELEMS(h2);i++)
2065  {
2066  poly p=h2->m[i];
2067  if (p!=NULL)
2068  {
2069  d = p_Deg(p,currRing);
2070  k= pGetComp(p);
2071  if (slength>0) k--;
2072  d +=((**w)[k]);
2073  ((*wtmp)[i+length]) = d;
2074  }
2075  }
2076  //Print("weights:");wtmp->show(1);PrintLn();
2077  }
2078  for (i=0;i<IDELEMS(h2);i++)
2079  {
2080  temp->m[i] = pCopy(h2->m[i]);
2081  q = pOne();
2082  pSetComp(q,i+1+length);
2083  pSetmComp(q);
2084  if(temp->m[i]!=NULL)
2085  {
2086  if (slength==0) p_Shift(&(temp->m[i]),1,currRing);
2087  p = temp->m[i];
2088  while (pNext(p)!=NULL) pIter(p);
2089  pNext(p) = q; // will be sorted later correctly
2090  }
2091  else
2092  temp->m[i]=q;
2093  }
2094  rk = k = IDELEMS(h2);
2095  if (!idIs0(h1))
2096  {
2097  pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1));
2098  IDELEMS(temp) += IDELEMS(h1);
2099  for (i=0;i<IDELEMS(h1);i++)
2100  {
2101  if (h1->m[i]!=NULL)
2102  {
2103  temp->m[k] = pCopy(h1->m[i]);
2104  if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
2105  k++;
2106  }
2107  }
2108  }
2109 
2110  ring orig_ring=currRing;
2111  ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); rChangeCurrRing(syz_ring);
2112  // we can use OPT_RETURN_SB only, if syz_ring==orig_ring,
2113  // therefore we disable OPT_RETURN_SB for modulo:
2114  // (see tr. #701)
2115  //if (TEST_OPT_RETURN_SB)
2116  // rSetSyzComp(IDELEMS(h2)+length, syz_ring);
2117  //else
2118  rSetSyzComp(length, syz_ring);
2119  ideal s_temp;
2120 
2121  if (syz_ring != orig_ring)
2122  {
2123  s_temp = idrMoveR_NoSort(temp, orig_ring, syz_ring);
2124  }
2125  else
2126  {
2127  s_temp = temp;
2128  }
2129 
2130  idTest(s_temp);
2131  ideal s_temp1 = kStd(s_temp,currRing->qideal,hom,&wtmp,NULL,length);
2132 
2133  //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn();
2134  if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL))
2135  {
2136  delete *w;
2137  *w=new intvec(IDELEMS(h2));
2138  for (i=0;i<IDELEMS(h2);i++)
2139  ((**w)[i])=(*wtmp)[i+length];
2140  }
2141  if (wtmp!=NULL) delete wtmp;
2142 
2143  for (i=0;i<IDELEMS(s_temp1);i++)
2144  {
2145  if ((s_temp1->m[i]!=NULL)
2146  && (((int)pGetComp(s_temp1->m[i]))<=length))
2147  {
2148  p_Delete(&(s_temp1->m[i]),currRing);
2149  }
2150  else
2151  {
2152  p_Shift(&(s_temp1->m[i]),-length,currRing);
2153  }
2154  }
2155  s_temp1->rank = rk;
2156  idSkipZeroes(s_temp1);
2157 
2158  if (syz_ring!=orig_ring)
2159  {
2160  rChangeCurrRing(orig_ring);
2161  s_temp1 = idrMoveR_NoSort(s_temp1, syz_ring, orig_ring);
2162  rDelete(syz_ring);
2163  // Hmm ... here seems to be a memory leak
2164  // However, simply deleting it causes memory trouble
2165  // idDelete(&s_temp);
2166  }
2167  else
2168  {
2169  idDelete(&temp);
2170  }
2171  idTest(s_temp1);
2172  return s_temp1;
2173 }
2174 
2175 /*
2176 *computes module-weights for liftings of homogeneous modules
2177 */
2178 intvec * idMWLift(ideal mod,intvec * weights)
2179 {
2180  if (idIs0(mod)) return new intvec(2);
2181  int i=IDELEMS(mod);
2182  while ((i>0) && (mod->m[i-1]==NULL)) i--;
2183  intvec *result = new intvec(i+1);
2184  while (i>0)
2185  {
2186  (*result)[i]=currRing->pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])];
2187  }
2188  return result;
2189 }
2190 
2191 /*2
2192 *sorts the kbase for idCoef* in a special way (lexicographically
2193 *with x_max,...,x_1)
2194 */
2195 ideal idCreateSpecialKbase(ideal kBase,intvec ** convert)
2196 {
2197  int i;
2198  ideal result;
2199 
2200  if (idIs0(kBase)) return NULL;
2201  result = idInit(IDELEMS(kBase),kBase->rank);
2202  *convert = idSort(kBase,FALSE);
2203  for (i=0;i<(*convert)->length();i++)
2204  {
2205  result->m[i] = pCopy(kBase->m[(**convert)[i]-1]);
2206  }
2207  return result;
2208 }
2209 
2210 /*2
2211 *returns the index of a given monom in the list of the special kbase
2212 */
2213 int idIndexOfKBase(poly monom, ideal kbase)
2214 {
2215  int j=IDELEMS(kbase);
2216 
2217  while ((j>0) && (kbase->m[j-1]==NULL)) j--;
2218  if (j==0) return -1;
2219  int i=(currRing->N);
2220  while (i>0)
2221  {
2222  loop
2223  {
2224  if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1;
2225  if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break;
2226  j--;
2227  if (j==0) return -1;
2228  }
2229  if (i==1)
2230  {
2231  while(j>0)
2232  {
2233  if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1;
2234  if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1;
2235  j--;
2236  }
2237  }
2238  i--;
2239  }
2240  return -1;
2241 }
2242 
2243 /*2
2244 *decomposes the monom in a part of coefficients described by the
2245 *complement of how and a monom in variables occuring in how, the
2246 *index of which in kbase is returned as integer pos (-1 if it don't
2247 *exists)
2248 */
2249 poly idDecompose(poly monom, poly how, ideal kbase, int * pos)
2250 {
2251  int i;
2252  poly coeff=pOne(), base=pOne();
2253 
2254  for (i=1;i<=(currRing->N);i++)
2255  {
2256  if (pGetExp(how,i)>0)
2257  {
2258  pSetExp(base,i,pGetExp(monom,i));
2259  }
2260  else
2261  {
2262  pSetExp(coeff,i,pGetExp(monom,i));
2263  }
2264  }
2265  pSetComp(base,pGetComp(monom));
2266  pSetm(base);
2267  pSetCoeff(coeff,nCopy(pGetCoeff(monom)));
2268  pSetm(coeff);
2269  *pos = idIndexOfKBase(base,kbase);
2270  if (*pos<0)
2271  p_Delete(&coeff,currRing);
2273  return coeff;
2274 }
2275 
2276 /*2
2277 *returns a matrix A of coefficients with kbase*A=arg
2278 *if all monomials in variables of how occur in kbase
2279 *the other are deleted
2280 */
2281 matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
2282 {
2283  matrix result;
2284  ideal tempKbase;
2285  poly p,q;
2286  intvec * convert;
2287  int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos;
2288 #if 0
2289  while ((i>0) && (kbase->m[i-1]==NULL)) i--;
2290  if (idIs0(arg))
2291  return mpNew(i,1);
2292  while ((j>0) && (arg->m[j-1]==NULL)) j--;
2293  result = mpNew(i,j);
2294 #else
2295  result = mpNew(i, j);
2296  while ((j>0) && (arg->m[j-1]==NULL)) j--;
2297 #endif
2298 
2299  tempKbase = idCreateSpecialKbase(kbase,&convert);
2300  for (k=0;k<j;k++)
2301  {
2302  p = arg->m[k];
2303  while (p!=NULL)
2304  {
2305  q = idDecompose(p,how,tempKbase,&pos);
2306  if (pos>=0)
2307  {
2308  MATELEM(result,(*convert)[pos],k+1) =
2309  pAdd(MATELEM(result,(*convert)[pos],k+1),q);
2310  }
2311  else
2312  p_Delete(&q,currRing);
2313  pIter(p);
2314  }
2315  }
2316  idDelete(&tempKbase);
2317  return result;
2318 }
2319 
2320 static void idDeleteComps(ideal arg,int* red_comp,int del)
2321 // red_comp is an array [0..args->rank]
2322 {
2323  int i,j;
2324  poly p;
2325 
2326  for (i=IDELEMS(arg)-1;i>=0;i--)
2327  {
2328  p = arg->m[i];
2329  while (p!=NULL)
2330  {
2331  j = pGetComp(p);
2332  if (red_comp[j]!=j)
2333  {
2334  pSetComp(p,red_comp[j]);
2335  pSetmComp(p);
2336  }
2337  pIter(p);
2338  }
2339  }
2340  (arg->rank) -= del;
2341 }
2342 
2343 /*2
2344 * returns the presentation of an isomorphic, minimally
2345 * embedded module (arg represents the quotient!)
2346 */
2347 ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w)
2348 {
2349  if (idIs0(arg)) return idInit(1,arg->rank);
2350  int i,next_gen,next_comp;
2351  ideal res=arg;
2352  if (!inPlace) res = idCopy(arg);
2353  res->rank=si_max(res->rank,id_RankFreeModule(res,currRing));
2354  int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int));
2355  for (i=res->rank;i>=0;i--) red_comp[i]=i;
2356 
2357  int del=0;
2358  loop
2359  {
2360  next_gen = id_ReadOutPivot(res, &next_comp, currRing);
2361  if (next_gen<0) break;
2362  del++;
2363  syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res));
2364  for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--;
2365  if ((w !=NULL)&&(*w!=NULL))
2366  {
2367  for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i];
2368  }
2369  }
2370 
2371  idDeleteComps(res,red_comp,del);
2372  idSkipZeroes(res);
2373  omFree(red_comp);
2374 
2375  if ((w !=NULL)&&(*w!=NULL) &&(del>0))
2376  {
2377  int nl=si_max((*w)->length()-del,1);
2378  intvec *wtmp=new intvec(nl);
2379  for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i];
2380  delete *w;
2381  *w=wtmp;
2382  }
2383  return res;
2384 }
2385 
2386 #include <polys/clapsing.h>
2387 
2388 #if 0
2389 poly id_GCD(poly f, poly g, const ring r)
2390 {
2391  ring save_r=currRing;
2392  rChangeCurrRing(r);
2393  ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
2394  intvec *w = NULL;
2395  ideal S=idSyzygies(I,testHomog,&w);
2396  if (w!=NULL) delete w;
2397  poly gg=pTakeOutComp(&(S->m[0]),2);
2398  idDelete(&S);
2399  poly gcd_p=singclap_pdivide(f,gg,r);
2400  p_Delete(&gg,r);
2401  rChangeCurrRing(save_r);
2402  return gcd_p;
2403 }
2404 #else
2405 poly id_GCD(poly f, poly g, const ring r)
2406 {
2407  ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
2408  intvec *w = NULL;
2409 
2410  ring save_r = currRing; rChangeCurrRing(r); ideal S=idSyzygies(I,testHomog,&w); rChangeCurrRing(save_r);
2411 
2412  if (w!=NULL) delete w;
2413  poly gg=p_TakeOutComp(&(S->m[0]), 2, r);
2414  id_Delete(&S, r);
2415  poly gcd_p=singclap_pdivide(f,gg, r);
2416  p_Delete(&gg, r);
2417 
2418  return gcd_p;
2419 }
2420 #endif
2421 
2422 #if 0
2423 /*2
2424 * xx,q: arrays of length 0..rl-1
2425 * xx[i]: SB mod q[i]
2426 * assume: char=0
2427 * assume: q[i]!=0
2428 * destroys xx
2429 */
2430 ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring R)
2431 {
2432  int cnt=IDELEMS(xx[0])*xx[0]->nrows;
2433  ideal result=idInit(cnt,xx[0]->rank);
2434  result->nrows=xx[0]->nrows; // for lifting matrices
2435  result->ncols=xx[0]->ncols; // for lifting matrices
2436  int i,j;
2437  poly r,h,hh,res_p;
2438  number *x=(number *)omAlloc(rl*sizeof(number));
2439  for(i=cnt-1;i>=0;i--)
2440  {
2441  res_p=NULL;
2442  loop
2443  {
2444  r=NULL;
2445  for(j=rl-1;j>=0;j--)
2446  {
2447  h=xx[j]->m[i];
2448  if ((h!=NULL)
2449  &&((r==NULL)||(p_LmCmp(r,h,R)==-1)))
2450  r=h;
2451  }
2452  if (r==NULL) break;
2453  h=p_Head(r, R);
2454  for(j=rl-1;j>=0;j--)
2455  {
2456  hh=xx[j]->m[i];
2457  if ((hh!=NULL) && (p_LmCmp(r,hh, R)==0))
2458  {
2459  x[j]=p_GetCoeff(hh, R);
2460  hh=p_LmFreeAndNext(hh, R);
2461  xx[j]->m[i]=hh;
2462  }
2463  else
2464  x[j]=n_Init(0, R->cf); // is R->cf really n_Q???, yes!
2465  }
2466 
2467  number n=n_ChineseRemainder(x,q,rl, R->cf);
2468 
2469  for(j=rl-1;j>=0;j--)
2470  {
2471  x[j]=NULL; // nlInit(0...) takes no memory
2472  }
2473  if (n_IsZero(n, R->cf)) p_Delete(&h, R);
2474  else
2475  {
2476  p_SetCoeff(h,n, R);
2477  //Print("new mon:");pWrite(h);
2478  res_p=p_Add_q(res_p, h, R);
2479  }
2480  }
2481  result->m[i]=res_p;
2482  }
2483  omFree(x);
2484  for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]), R);
2485  omFree(xx);
2486  return result;
2487 }
2488 #endif
2489 /* currently unsed:
2490 ideal idChineseRemainder(ideal *xx, intvec *iv)
2491 {
2492  int rl=iv->length();
2493  number *q=(number *)omAlloc(rl*sizeof(number));
2494  int i;
2495  for(i=0; i<rl; i++)
2496  {
2497  q[i]=nInit((*iv)[i]);
2498  }
2499  return idChineseRemainder(xx,q,rl);
2500 }
2501 */
2502 /*
2503  * lift ideal with coeffs over Z (mod N) to Q via Farey
2504  */
2505 ideal id_Farey(ideal x, number N, const ring r)
2506 {
2507  int cnt=IDELEMS(x)*x->nrows;
2508  ideal result=idInit(cnt,x->rank);
2509  result->nrows=x->nrows; // for lifting matrices
2510  result->ncols=x->ncols; // for lifting matrices
2511 
2512  int i;
2513  for(i=cnt-1;i>=0;i--)
2514  {
2515  result->m[i]=p_Farey(x->m[i],N,r);
2516  }
2517  return result;
2518 }
2519 
2520 
2521 
2522 
2523 // uses glabl vars via pSetModDeg
2524 /*
2525 BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
2526 {
2527  if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
2528  if (idIs0(m)) return TRUE;
2529 
2530  int cmax=-1;
2531  int i;
2532  poly p=NULL;
2533  int length=IDELEMS(m);
2534  poly* P=m->m;
2535  for (i=length-1;i>=0;i--)
2536  {
2537  p=P[i];
2538  if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
2539  }
2540  if (w != NULL)
2541  if (w->length()+1 < cmax)
2542  {
2543  // Print("length: %d - %d \n", w->length(),cmax);
2544  return FALSE;
2545  }
2546 
2547  if(w!=NULL)
2548  p_SetModDeg(w, currRing);
2549 
2550  for (i=length-1;i>=0;i--)
2551  {
2552  p=P[i];
2553  poly q=p;
2554  if (p!=NULL)
2555  {
2556  int d=p_FDeg(p,currRing);
2557  loop
2558  {
2559  pIter(p);
2560  if (p==NULL) break;
2561  if (d!=p_FDeg(p,currRing))
2562  {
2563  //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
2564  if(w!=NULL)
2565  p_SetModDeg(NULL, currRing);
2566  return FALSE;
2567  }
2568  }
2569  }
2570  }
2571 
2572  if(w!=NULL)
2573  p_SetModDeg(NULL, currRing);
2574 
2575  return TRUE;
2576 }
2577 */
2578 
2579 /// keeps the first k (>= 1) entries of the given ideal
2580 /// (Note that the kept polynomials may be zero.)
2581 void idKeepFirstK(ideal id, const int k)
2582 {
2583  for (int i = IDELEMS(id)-1; i >= k; i--)
2584  {
2585  if (id->m[i] != NULL) pDelete(&id->m[i]);
2586  }
2587  int kk=k;
2588  if (k==0) kk=1; /* ideals must have at least one element(0)*/
2589  pEnlargeSet(&(id->m), IDELEMS(id), kk-IDELEMS(id));
2590  IDELEMS(id) = kk;
2591 }
2592 
2593 /*
2594 * compare the leading terms of a and b
2595 */
2596 static int tCompare(const poly a, const poly b)
2597 {
2598  if (b == NULL) return(a != NULL);
2599  if (a == NULL) return(-1);
2600 
2601  /* a != NULL && b != NULL */
2602  int r = pLmCmp(a, b);
2603  if (r != 0) return(r);
2604  number h = nSub(pGetCoeff(a), pGetCoeff(b));
2605  r = -1 + nIsZero(h) + 2*nGreaterZero(h); /* -1: <, 0:==, 1: > */
2606  nDelete(&h);
2607  return(r);
2608 }
2609 
2610 /*
2611 * compare a and b (rev-lex on terms)
2612 */
2613 static int pCompare(const poly a, const poly b)
2614 {
2615  int r = tCompare(a, b);
2616  if (r != 0) return(r);
2617 
2618  poly aa = a;
2619  poly bb = b;
2620  while (r == 0 && aa != NULL && bb != NULL)
2621  {
2622  pIter(aa);
2623  pIter(bb);
2624  r = tCompare(aa, bb);
2625  }
2626  return(r);
2627 }
2628 
2629 typedef struct
2630 {
2632  int index;
2633 } poly_sort;
2634 
2635 int pCompare_qsort(const void *a, const void *b)
2636 {
2637  int res = pCompare(((poly_sort *)a)->p, ((poly_sort *)b)->p);
2638  return(res);
2639 }
2640 
2641 void idSort_qsort(poly_sort *id_sort, int idsize)
2642 {
2643  qsort(id_sort, idsize, sizeof(poly_sort), pCompare_qsort);
2644 }
2645 
2646 /*2
2647 * ideal id = (id[i])
2648 * if id[i] = id[j] then id[j] is deleted for j > i
2649 */
2650 void idDelEquals(ideal id)
2651 {
2652  int idsize = IDELEMS(id);
2653  poly_sort *id_sort = (poly_sort *)omAlloc0(idsize*sizeof(poly_sort));
2654  for (int i = 0; i < idsize; i++)
2655  {
2656  id_sort[i].p = id->m[i];
2657  id_sort[i].index = i;
2658  }
2659  idSort_qsort(id_sort, idsize);
2660  int index, index_i, index_j;
2661  int i = 0;
2662  for (int j = 1; j < idsize; j++)
2663  {
2664  if (id_sort[i].p != NULL && pEqualPolys(id_sort[i].p, id_sort[j].p))
2665  {
2666  index_i = id_sort[i].index;
2667  index_j = id_sort[j].index;
2668  if (index_j > index_i)
2669  {
2670  index = index_j;
2671  }
2672  else
2673  {
2674  index = index_i;
2675  i = j;
2676  }
2677  pDelete(&id->m[index]);
2678  }
2679  else
2680  {
2681  i = j;
2682  }
2683  }
2684  omFreeSize((ADDRESS)(id_sort), idsize*sizeof(poly_sort));
2685 }
#define TEST_OPT_NOTREGULARITY
Definition: options.h:114
int & rows()
Definition: matpol.h:24
matrix idDiff(matrix i, int k)
Definition: ideals.cc:1953
#define pSetmComp(p)
TODO:
Definition: polys.h:243
void p_SetModDeg(intvec *w, ring r)
Definition: p_polys.cc:3517
for idElimination, like a, except pFDeg, pWeigths ignore it
Definition: ring.h:693
#define idMaxIdeal(D)
initialise the maximal ideal (at 0)
Definition: ideals.h:38
const CanonicalForm int s
Definition: facAbsFact.cc:55
unsigned si_opt_1
Definition: options.c:5
ring sm_RingChange(const ring origR, long bound)
Definition: sparsmat.cc:263
void idDelEquals(ideal id)
Definition: ideals.cc:2650
#define omMemDup(s)
Definition: omAllocDecl.h:264
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
Definition: kstd1.cc:2815
#define pSetm(p)
Definition: polys.h:241
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:2581
static void idPrepareStd(ideal s_temp, int k)
Definition: ideals.cc:904
const poly a
Definition: syzextra.cc:212
void PrintLn()
Definition: reporter.cc:322
static CanonicalForm bound(const CFMatrix &M)
Definition: cf_linsys.cc:460
#define Print
Definition: emacs.cc:83
#define pAdd(p, q)
Definition: polys.h:174
poly idDecompose(poly monom, poly how, ideal kbase, int *pos)
Definition: ideals.cc:2249
CF_NO_INLINE CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
Definition: cf_inline.cc:564
poly prCopyR(poly p, ring src_r, ring dest_r)
Definition: prCopy.cc:36
void idLiftW(ideal P, ideal Q, int n, matrix &T, ideal &R, short *w)
Definition: ideals.cc:1133
#define TEST_OPT_PROT
Definition: options.h:98
#define pMaxComp(p)
Definition: polys.h:270
loop
Definition: myNF.cc:98
#define pSetExp(p, i, v)
Definition: polys.h:42
#define FALSE
Definition: auxiliary.h:140
Compatiblity layer for legacy polynomial operations (over currRing)
int idIndexOfKBase(poly monom, ideal kbase)
Definition: ideals.cc:2213
#define ppJet(p, m)
Definition: polys.h:338
return P p
Definition: myNF.cc:203
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition: p_polys.cc:3378
BOOLEAN nc_rComplete(const ring src, ring dest, bool bSetupQuotient)
Definition: ring.cc:5531
#define id_Test(A, lR)
Definition: simpleideals.h:80
#define pLmCmp(p, q)
returns 0|1|-1 if p=q|p>q|p
Definition: polys.h:105
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
Definition: ideals.cc:1884
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
#define p_GetComp(p, r)
Definition: monomials.h:72
poly prMoveR(poly &p, ring src_r, ring dest_r)
Definition: prCopy.cc:91
#define pTest(p)
Definition: polys.h:387
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:1508
static int tCompare(const poly a, const poly b)
Definition: ideals.cc:2596
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 ppMult_mm(p, m)
Definition: polys.h:172
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define idSimpleAdd(A, B)
Definition: ideals.h:58
matrix idDiffOp(ideal I, ideal J, BOOLEAN multiply)
Definition: ideals.cc:1966
const CanonicalForm CFMap CFMap int &both_non_zero int n
Definition: cfEzgcd.cc:52
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition: ring.h:540
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
#define pNeg(p)
Definition: polys.h:169
int pCompare_qsort(const void *a, const void *b)
Definition: ideals.cc:2635
char N base
Definition: ValueTraits.h:144
CanonicalForm divide(const CanonicalForm &ff, const CanonicalForm &f, const CFList &as)
#define TRUE
Definition: auxiliary.h:144
ring rAssure_SyzOrder(const ring r, BOOLEAN complete)
Definition: ring.cc:4381
ideal kStd(ideal F, ideal Q, tHomog h, intvec **w, intvec *hilb, int syzComp, int newIdeal, intvec *vw, s_poly_proc_t sp)
Definition: kstd1.cc:2221
int length() const
Definition: intvec.h:86
ideal idMultSect(resolvente arg, int length)
Definition: ideals.cc:350
static void ipPrint_MA0(matrix m, const char *name)
Definition: ipprint.cc:63
void * ADDRESS
Definition: auxiliary.h:161
#define SI_SAVE_OPT1(A)
Definition: options.h:20
g
Definition: cfModGcd.cc:4031
void WerrorS(const char *s)
Definition: feFopen.cc:23
int k
Definition: cfEzgcd.cc:93
ideal idModulo(ideal h2, ideal h1, tHomog hom, intvec **w)
Definition: ideals.cc:2038
#define Q
Definition: sirandom.c:25
#define TEST_V_INTERSECT_ELIM
Definition: options.h:136
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:1412
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy ...
Definition: monomials.h:51
#define pEqualPolys(p1, p2)
Definition: polys.h:372
#define WarnS
Definition: emacs.cc:81
#define pMinComp(p)
Definition: polys.h:271
#define pJetW(p, m, iv)
Definition: polys.h:341
ideal idMinEmbedding(ideal arg, BOOLEAN inPlace, intvec **w)
Definition: ideals.cc:2347
#define BITSET
Definition: structs.h:17
poly singclap_pdivide(poly f, poly g, const ring r)
Definition: clapsing.cc:547
#define omAlloc(size)
Definition: omAllocDecl.h:210
static bool rIsPluralRing(const ring r)
we must always have this test!
Definition: ring.h:361
long sm_ExpBound(ideal m, int di, int ra, int t, const ring currRing)
Definition: sparsmat.cc:194
ideal idQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
Definition: ideals.cc:1310
#define Sy_bit(x)
Definition: options.h:30
static number p_SetCoeff(poly p, number n, ring r)
Definition: p_polys.h:401
intvec * idSort(ideal id, BOOLEAN nolex=TRUE)
Definition: ideals.h:184
#define pGetComp(p)
Component.
Definition: polys.h:37
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:811
int index
Definition: ideals.cc:2632
ideal idMinBase(ideal h1)
Definition: ideals.cc:53
matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
Definition: ideals.cc:2281
int pWeight(int i, const ring R=currRing)
Definition: polys.h:250
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
Definition: p_polys.h:804
#define pIter(p)
Definition: monomials.h:44
poly res
Definition: myNF.cc:322
#define M
Definition: sirandom.c:24
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:12
#define pGetExp(p, i)
Exponent.
Definition: polys.h:41
char * char_ptr
Definition: structs.h:56
poly * m
Definition: matpol.h:19
void id_Shift(ideal M, int s, const ring r)
static poly p_Head(poly p, const ring r)
Definition: p_polys.h:819
#define idPrint(id)
Definition: ideals.h:62
long p_DegW(poly p, const short *w, const ring R)
Definition: p_polys.cc:689
static ideal idInitializeQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
Definition: ideals.cc:1198
ideal idSect(ideal h1, ideal h2)
Definition: ideals.cc:211
long p_Deg(poly a, const ring r)
Definition: p_polys.cc:586
const ring r
Definition: syzextra.cc:208
Coefficient rings, fields and other domains suitable for Singular polynomials.
ideal idSeries(int n, ideal M, matrix U, intvec *w)
Definition: ideals.cc:1936
ideal idElimination(ideal h1, poly delVar, intvec *hilb)
Definition: ideals.cc:1403
poly p_Farey(poly p, number N, const ring r)
Definition: p_polys.cc:61
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 ...
Definition: intvec.h:16
#define pSub(a, b)
Definition: polys.h:258
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
intvec * idMWLift(ideal mod, intvec *weights)
Definition: ideals.cc:2178
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:49
poly p_One(const ring r)
Definition: p_polys.cc:1318
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:3435
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent : the integer VarOffset encodes:
Definition: p_polys.h:465
tHomog
Definition: structs.h:37
int j
Definition: myNF.cc:70
END_NAMESPACE BEGIN_NAMESPACE_SINGULARXX ideal poly int syzComp
Definition: myNF.cc:291
#define nGreaterZero(n)
Definition: numbers.h:27
#define pSetCompP(a, i)
Definition: polys.h:274
#define omFree(addr)
Definition: omAllocDecl.h:261
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:1794
ideal idFreeModule(int i)
Definition: ideals.h:126
#define assume(x)
Definition: mod2.h:405
double(* wFunctional)(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition: weight.cc:28
ring rCopy0(const ring r, BOOLEAN copy_qideal, BOOLEAN copy_ordering)
Definition: ring.cc:1318
ideal idSectWithElim(ideal h1, ideal h2)
Definition: ideals.cc:141
ring rAssure_SyzComp(const ring r, BOOLEAN complete)
Definition: ring.cc:4386
pNormalize(P.p)
ring rAssure_dp_C(const ring r)
Definition: ring.cc:4885
static int pCompare(const poly a, const poly b)
Definition: ideals.cc:2613
void idSort_qsort(poly_sort *id_sort, int idsize)
Definition: ideals.cc:2641
ideal idrMoveR(ideal &id, ring src_r, ring dest_r)
Definition: prCopy.cc:249
#define pSetComp(p, v)
Definition: polys.h:38
static int p_LmCmp(poly p, poly q, const ring r)
Definition: p_polys.h:1472
#define pJet(p, m)
Definition: polys.h:339
int m
Definition: cfEzgcd.cc:119
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
#define nSub(n1, n2)
Definition: numbers.h:22
static int si_max(const int a, const int b)
Definition: auxiliary.h:166
FILE * f
Definition: checklibs.c:7
int i
Definition: cfEzgcd.cc:123
Definition: nc.h:24
void PrintS(const char *s)
Definition: reporter.cc:294
static long p_MinComp(poly p, ring lmRing, ring tailRing)
Definition: p_polys.h:302
#define pOne()
Definition: polys.h:286
ideal idCreateSpecialKbase(ideal kBase, intvec **convert)
Definition: ideals.cc:2195
static poly p_LmFreeAndNext(poly p, ring)
Definition: p_polys.h:699
BOOLEAN idIsSubModule(ideal id1, ideal id2)
Definition: ideals.cc:1863
resolvente sySchreyerResolvente(ideal arg, int maxlength, int *length, BOOLEAN isMonomial=FALSE, BOOLEAN notReplace=FALSE)
Definition: syz0.cc:861
#define pHead(p)
returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL ...
Definition: polys.h:67
#define IDELEMS(i)
Definition: simpleideals.h:24
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition: coeffs.h:465
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
static poly pReverse(poly p)
Definition: p_polys.h:324
#define nDelete(n)
Definition: numbers.h:16
ideal idCopy(ideal A)
Definition: ideals.h:76
static int index(p_Length length, p_Ord ord)
Definition: p_Procs_Impl.h:597
void rSetSyzComp(int k, const ring r)
Definition: ring.cc:4991
void rChangeCurrRing(ring r)
Definition: polys.cc:14
int size(const CanonicalForm &f, const Variable &v)
int size ( const CanonicalForm & f, const Variable & v )
Definition: cf_ops.cc:600
poly id_GCD(poly f, poly g, const ring r)
Definition: ideals.cc:2405
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
Definition: p_polys.cc:4485
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition: matpol.cc:48
#define TEST_OPT_RETURN_SB
Definition: options.h:107
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:850
ideal idMult(ideal h1, ideal h2)
hh := h1 * h2
Definition: ideals.h:99
matrix mp_MultP(matrix a, poly p, const ring R)
multiply a matrix 'a' by a poly 'p', destroy the args
Definition: matpol.cc:159
#define SI_RESTORE_OPT2(A)
Definition: options.h:24
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition: simpleideals.cc:38
#define pSeries(n, p, u, w)
Definition: polys.h:343
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent : VarOffset encodes the position in p->exp
Definition: p_polys.h:484
poly p_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1501
int & cols()
Definition: matpol.h:25
Definition: nc.h:29
char name(const Variable &v)
Definition: variable.h:95
#define MATCOLS(i)
Definition: matpol.h:28
poly p
Definition: ideals.cc:2631
#define nIsZero(n)
Definition: numbers.h:19
static BOOLEAN rField_is_Ring(const ring r)
Definition: ring.h:437
#define NULL
Definition: omList.c:10
BOOLEAN idHomIdeal(ideal id, ideal Q=NULL)
Definition: ideals.h:106
static ideal idPrepare(ideal h1, tHomog hom, int syzcomp, intvec **w)
Definition: ideals.cc:465
poly * polyset
Definition: hutil.h:17
#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:126
ideal id_Farey(ideal x, number N, const ring r)
Definition: ideals.cc:2505
void pEnlargeSet(poly **p, int l, int increment)
Definition: p_polys.cc:3540
void wCall(poly *s, int sl, int *x, double wNsqr, const ring R)
Definition: weight.cc:116
BOOLEAN rHasGlobalOrdering(const ring r)
Definition: ring.h:752
void rDelete(ring r)
unconditionally deletes fields in r
Definition: ring.cc:448
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:310
void sm_KillModifiedRing(ring r)
Definition: sparsmat.cc:294
static void idDeleteComps(ideal arg, int *red_comp, int del)
Definition: ideals.cc:2320
#define pMult(p, q)
Definition: polys.h:178
ideal kMin_std(ideal F, ideal Q, tHomog h, intvec **w, ideal &M, intvec *hilb, int syzComp, int reduced)
Definition: kstd1.cc:2664
#define R
Definition: sirandom.c:26
ideal idLiftStd(ideal h1, matrix *ma, tHomog hi, ideal *syz)
Definition: ideals.cc:751
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
const CanonicalForm & w
Definition: facAbsFact.cc:55
poly mp_DetBareiss(matrix a, const ring r)
returns the determinant of the matrix m; uses Bareiss algorithm
Definition: matpol.cc:1581
#define pDelete(p_ptr)
Definition: polys.h:157
Variable x
Definition: cfModGcd.cc:4023
#define nCopy(n)
Definition: numbers.h:15
#define pNext(p)
Definition: monomials.h:43
ideal idrCopyR(ideal id, ring src_r, ring dest_r)
Definition: prCopy.cc:193
ideal idLift(ideal mod, ideal submod, ideal *rest, BOOLEAN goodShape, BOOLEAN isSB, BOOLEAN divide, matrix *unit)
Definition: ideals.cc:938
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:436
void syGaussForOne(ideal syz, int elnum, int ModComp, int from, int till)
Definition: syz.cc:223
#define p_GetCoeff(p, r)
Definition: monomials.h:57
matrix mp_Copy(matrix a, const ring r)
copies matrix a (from ring r to r)
Definition: matpol.cc:75
ideal * resolvente
Definition: ideals.h:20
static nc_type & ncRingType(nc_struct *p)
Definition: nc.h:175
ideal idXXX(ideal h1, int k)
Definition: ideals.cc:704
#define TEST_V_INTERSECT_SYZ
Definition: options.h:137
poly prMoveR_NoSort(poly &p, ring src_r, ring dest_r)
Definition: prCopy.cc:102
static poly p_Neg(poly p, const ring r)
Definition: p_polys.h:1018
intvec * syBetti(resolvente res, int length, int *regularity, intvec *weights, BOOLEAN tomin, int *row_shift)
Definition: syz.cc:793
int id_ReadOutPivot(ideal arg, int *comp, const ring r)
#define pDiff(a, b)
Definition: polys.h:267
#define OPT_SB_1
Definition: options.h:90
#define pDiffOp(a, b, m)
Definition: polys.h:268
#define MATROWS(i)
Definition: matpol.h:27
void wrp(poly p)
Definition: polys.h:281
kBucketDestroy & P
Definition: myNF.cc:191
static jList * T
Definition: janet.cc:37
polyrec * poly
Definition: hilb.h:10
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:884
BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r)
Definition: old.gring.cc:2633
unsigned si_opt_2
Definition: options.c:6
static Poly * h
Definition: janet.cc:978
int BOOLEAN
Definition: auxiliary.h:131
ideal idSyzygies(ideal h1, tHomog h, intvec **w, BOOLEAN setSyzComp, BOOLEAN setRegularity, int *deg)
Definition: ideals.cc:560
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
const poly b
Definition: syzextra.cc:213
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition: polys.h:31
#define SI_RESTORE_OPT1(A)
Definition: options.h:23
#define ppJetW(p, m, iv)
Definition: polys.h:340
ideal idrCopyR_NoSort(ideal id, ring src_r, ring dest_r)
Definition: prCopy.cc:206
#define V_IDLIFT
Definition: options.h:60
ideal id_Matrix2Module(matrix mat, const ring R)
BOOLEAN idHomModule(ideal m, ideal Q, intvec **w)
Definition: ideals.h:111
int binom(int n, int r)
void Werror(const char *fmt,...)
Definition: reporter.cc:199
void idDelete(ideal *h)
delete an ideal
Definition: ideals.h:31
ideal kGroebner(ideal F, ideal Q)
Definition: ipshell.cc:5804
#define omAlloc0(size)
Definition: omAllocDecl.h:211
return result
Definition: facAbsBiFact.cc:76
int l
Definition: cfEzgcd.cc:94
double wFunctionalBuch(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition: weight0.c:82
ideal idrMoveR_NoSort(ideal &id, ring src_r, ring dest_r)
Definition: prCopy.cc:262
long rank
Definition: matpol.h:20
#define pCopy(p)
return a copy of the poly
Definition: polys.h:156
#define MATELEM(mat, i, j)
Definition: matpol.h:29
#define idTest(id)
Definition: ideals.h:63
#define SI_SAVE_OPT2(A)
Definition: options.h:21
#define Warn
Definition: emacs.cc:80
#define omStrDup(s)
Definition: omAllocDecl.h:263