ideals.cc
Go to the documentation of this file.
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 
20 #include "polys/monomials/ring.h"
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 
32 #include "kernel/GBEngine/kstd1.h"
33 #include "kernel/GBEngine/kutil.h"
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 /* #define WITH_OLD_MINOR */
41 
42 /*0 implementation*/
43 
44 /*2
45 *returns a minimized set of generators of h1
46 */
47 ideal idMinBase (ideal h1)
48 {
49  ideal h2, h3,h4,e;
50  int j,k;
51  int i,l,ll;
52  intvec * wth;
53  BOOLEAN homog;
55  {
56  WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
57  e=idCopy(h1);
58  return e;
59  }
60  homog = idHomModule(h1,currRing->qideal,&wth);
62  {
63  if(!homog)
64  {
65  WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
66  e=idCopy(h1);
67  return e;
68  }
69  else
70  {
71  ideal re=kMin_std(h1,currRing->qideal,(tHomog)homog,&wth,h2,NULL,0,3);
72  idDelete(&re);
73  return h2;
74  }
75  }
76  e=idInit(1,h1->rank);
77  if (idIs0(h1))
78  {
79  return e;
80  }
81  pEnlargeSet(&(e->m),IDELEMS(e),15);
82  IDELEMS(e) = 16;
83  h2 = kStd(h1,currRing->qideal,isNotHomog,NULL);
84  h3 = idMaxIdeal(1);
85  h4=idMult(h2,h3);
86  idDelete(&h3);
87  h3=kStd(h4,currRing->qideal,isNotHomog,NULL);
88  k = IDELEMS(h3);
89  while ((k > 0) && (h3->m[k-1] == NULL)) k--;
90  j = -1;
91  l = IDELEMS(h2);
92  while ((l > 0) && (h2->m[l-1] == NULL)) l--;
93  for (i=l-1; i>=0; i--)
94  {
95  if (h2->m[i] != NULL)
96  {
97  ll = 0;
98  while ((ll < k) && ((h3->m[ll] == NULL)
99  || !pDivisibleBy(h3->m[ll],h2->m[i])))
100  ll++;
101  if (ll >= k)
102  {
103  j++;
104  if (j > IDELEMS(e)-1)
105  {
106  pEnlargeSet(&(e->m),IDELEMS(e),16);
107  IDELEMS(e) += 16;
108  }
109  e->m[j] = pCopy(h2->m[i]);
110  }
111  }
112  }
113  idDelete(&h2);
114  idDelete(&h3);
115  idDelete(&h4);
116  if (currRing->qideal!=NULL)
117  {
118  h3=idInit(1,e->rank);
119  h2=kNF(h3,currRing->qideal,e);
120  idDelete(&h3);
121  idDelete(&e);
122  e=h2;
123  }
124  idSkipZeroes(e);
125  return e;
126 }
127 
128 
129 ideal idSectWithElim (ideal h1,ideal h2)
130 // does not destroy h1,h2
131 {
132  if (TEST_OPT_PROT) PrintS("intersect by elimination method\n");
133  assume(!idIs0(h1));
134  assume(!idIs0(h2));
135  assume(IDELEMS(h1)<=IDELEMS(h2));
138  // add a new variable:
139  int j;
140  ring origRing=currRing;
141  ring r=rCopy0(origRing);
142  r->N++;
143  r->block0[0]=1;
144  r->block1[0]= r->N;
145  omFree(r->order);
146  r->order=(rRingOrder_t*)omAlloc0(3*sizeof(rRingOrder_t));
147  r->order[0]=ringorder_dp;
148  r->order[1]=ringorder_C;
149  char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr));
150  for (j=0;j<r->N-1;j++) names[j]=r->names[j];
151  names[r->N-1]=omStrDup("@");
152  omFree(r->names);
153  r->names=names;
154  rComplete(r,TRUE);
155  // fetch h1, h2
156  ideal h;
157  h1=idrCopyR(h1,origRing,r);
158  h2=idrCopyR(h2,origRing,r);
159  // switch to temp. ring r
160  rChangeCurrRing(r);
161  // create 1-t, t
162  poly omt=p_One(currRing);
163  p_SetExp(omt,r->N,1,currRing);
164  p_Setm(omt,currRing);
165  poly t=p_Copy(omt,currRing);
166  omt=p_Neg(omt,currRing);
167  omt=p_Add_q(omt,pOne(),currRing);
168  // compute (1-t)*h1
169  h1=(ideal)mp_MultP((matrix)h1,omt,currRing);
170  // compute t*h2
171  h2=(ideal)mp_MultP((matrix)h2,pCopy(t),currRing);
172  // (1-t)h1 + t*h2
173  h=idInit(IDELEMS(h1)+IDELEMS(h2),1);
174  int l;
175  for (l=IDELEMS(h1)-1; l>=0; l--)
176  {
177  h->m[l] = h1->m[l]; h1->m[l]=NULL;
178  }
179  j=IDELEMS(h1);
180  for (l=IDELEMS(h2)-1; l>=0; l--)
181  {
182  h->m[l+j] = h2->m[l]; h2->m[l]=NULL;
183  }
184  idDelete(&h1);
185  idDelete(&h2);
186  // eliminate t:
187  ideal res=idElimination(h,t);
188  // cleanup
189  idDelete(&h);
190  pDelete(&t);
191  if (res!=NULL) res=idrMoveR(res,r,origRing);
192  rChangeCurrRing(origRing);
193  rDelete(r);
194  return res;
195 }
196 /*2
197 * h3 := h1 intersect h2
198 */
199 ideal idSect (ideal h1,ideal h2, GbVariant alg)
200 {
201  int i,j,k;
202  unsigned length;
203  int flength = id_RankFreeModule(h1,currRing);
204  int slength = id_RankFreeModule(h2,currRing);
205  int rank=si_max(h1->rank,h2->rank);
206  if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank);
207 
208  ideal first,second,temp,temp1,result;
209  poly p,q;
210 
211  if (IDELEMS(h1)<IDELEMS(h2))
212  {
213  first = h1;
214  second = h2;
215  }
216  else
217  {
218  first = h2;
219  second = h1;
220  int t=flength; flength=slength; slength=t;
221  }
222  length = si_max(flength,slength);
223  if (length==0)
224  {
225  if ((currRing->qideal==NULL)
226  && (currRing->OrdSgn==1)
227  && (!rIsPluralRing(currRing))
229  return idSectWithElim(first,second);
230  else length = 1;
231  }
232  if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n");
233  j = IDELEMS(first);
234 
235  ring orig_ring=currRing;
236  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
237  rSetSyzComp(length,syz_ring);
238  rChangeCurrRing(syz_ring);
239 
240  while ((j>0) && (first->m[j-1]==NULL)) j--;
241  temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j);
242  k = 0;
243  for (i=0;i<j;i++)
244  {
245  if (first->m[i]!=NULL)
246  {
247  if (syz_ring==orig_ring)
248  temp->m[k] = pCopy(first->m[i]);
249  else
250  temp->m[k] = prCopyR(first->m[i], orig_ring, syz_ring);
251  q = pOne();
252  pSetComp(q,i+1+length);
253  pSetmComp(q);
254  if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
255  p = temp->m[k];
256  while (pNext(p)!=NULL) pIter(p);
257  pNext(p) = q;
258  k++;
259  }
260  }
261  for (i=0;i<IDELEMS(second);i++)
262  {
263  if (second->m[i]!=NULL)
264  {
265  if (syz_ring==orig_ring)
266  temp->m[k] = pCopy(second->m[i]);
267  else
268  temp->m[k] = prCopyR(second->m[i], orig_ring,currRing);
269  if (slength==0) p_Shift(&(temp->m[k]),1,currRing);
270  k++;
271  }
272  }
273  intvec *w=NULL;
274  if (alg==GbDefault) alg=GbStd;
275  if (alg==GbStd)
276  {
277  if (TEST_OPT_PROT) { PrintS("std:"); mflush(); }
278  temp1 = kStd(temp,currRing->qideal,testHomog,&w,NULL,length);
279  if (w!=NULL) delete w;
280  idDelete(&temp);
281  }
282  else if (alg==GbSlimgb)
283  {
284  if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); }
285  temp1 = t_rep_gb(currRing, temp, temp->rank);
286  idDelete(&temp);
287  }
288  else if (alg==GbGroebner)
289  {
290  if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); }
291  BOOLEAN err;
292  temp1=(ideal)iiCallLibProc1("groebner",temp,MODUL_CMD,err);
293  if (err)
294  {
295  Werror("error %d in >>groebner<<",err);
296  temp1=idInit(1,1);
297  }
298  }
299  else if (alg==GbModstd)
300  {
301  if (TEST_OPT_PROT) { PrintS("modStd:"); mflush(); }
302  BOOLEAN err;
303  void *args[]={temp,(void*)1,NULL};
304  int arg_t[]={MODUL_CMD,INT_CMD,0};
305  temp1=(ideal)iiCallLibProcM("modStd",args,arg_t,err);
306  if (err)
307  {
308  Werror("error %d in >>modStd<<",err);
309  temp1=idInit(1,1);
310  }
311  }
312  else if (alg==GbStdSat)
313  {
314  if (TEST_OPT_PROT) { PrintS("std:sat:"); mflush(); }
315  BOOLEAN err;
316  // search for 2nd block of vars
317  int i=0;
318  int block=-1;
319  loop
320  {
321  if ((currRing->order[i]!=ringorder_c)
322  && (currRing->order[i]!=ringorder_C)
323  && (currRing->order[i]!=ringorder_s))
324  {
325  if (currRing->order[i]==0) { err=TRUE;break;}
326  block++;
327  if (block==1) { block=i; break;}
328  }
329  i++;
330  }
331  if (block>0)
332  {
333  if (TEST_OPT_PROT)
334  {
335  Print("sat(%d..%d)\n",currRing->block0[block],currRing->block1[block]);
336  mflush();
337  }
338  ideal v=idInit(currRing->block1[block]-currRing->block0[block]+1,1);
339  for(i=currRing->block0[block];i<=currRing->block1[block];i++)
340  {
341  v->m[i-currRing->block0[block]]=pOne();
342  pSetExp(v->m[i-currRing->block0[block]],i,1);
343  pSetm(v->m[i-currRing->block0[block]]);
344  }
345  void *args[]={temp,v,NULL};
346  int arg_t[]={MODUL_CMD,IDEAL_CMD,0};
347  temp1=(ideal)iiCallLibProcM("satstd",args,arg_t,err);
348  }
349  if (err)
350  {
351  Werror("error %d in >>satstd<<",err);
352  temp1=idInit(1,1);
353  }
354  }
355 
356  if(syz_ring!=orig_ring)
357  rChangeCurrRing(orig_ring);
358 
359  result = idInit(IDELEMS(temp1),rank);
360  j = 0;
361  for (i=0;i<IDELEMS(temp1);i++)
362  {
363  if ((temp1->m[i]!=NULL)
364  && (__p_GetComp(temp1->m[i],syz_ring)>length))
365  {
366  if(syz_ring==orig_ring)
367  {
368  p = temp1->m[i];
369  }
370  else
371  {
372  p = prMoveR(temp1->m[i], syz_ring,orig_ring);
373  }
374  temp1->m[i]=NULL;
375  while (p!=NULL)
376  {
377  q = pNext(p);
378  pNext(p) = NULL;
379  k = pGetComp(p)-1-length;
380  pSetComp(p,0);
381  pSetmComp(p);
382  /* Warning! multiply only from the left! it's very important for Plural */
383  result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k])));
384  p = q;
385  }
386  j++;
387  }
388  }
389  if(syz_ring!=orig_ring)
390  {
391  rChangeCurrRing(syz_ring);
392  idDelete(&temp1);
393  rChangeCurrRing(orig_ring);
394  rDelete(syz_ring);
395  }
396  else
397  {
398  idDelete(&temp1);
399  }
400 
401  idSkipZeroes(result);
402  if (TEST_OPT_RETURN_SB)
403  {
404  w=NULL;
405  temp1=kStd(result,currRing->qideal,testHomog,&w);
406  if (w!=NULL) delete w;
407  idDelete(&result);
408  idSkipZeroes(temp1);
409  return temp1;
410  }
411  else //temp1=kInterRed(result,currRing->qideal);
412  return result;
413 }
414 
415 /*2
416 * ideal/module intersection for a list of objects
417 * given as 'resolvente'
418 */
419 ideal idMultSect(resolvente arg, int length, GbVariant alg)
420 {
421  int i,j=0,k=0,l,maxrk=-1,realrki;
422  unsigned syzComp;
423  ideal bigmat,tempstd,result;
424  poly p;
425  int isIdeal=0;
426  intvec * w=NULL;
427 
428  /* find 0-ideals and max rank -----------------------------------*/
429  for (i=0;i<length;i++)
430  {
431  if (!idIs0(arg[i]))
432  {
433  realrki=id_RankFreeModule(arg[i],currRing);
434  k++;
435  j += IDELEMS(arg[i]);
436  if (realrki>maxrk) maxrk = realrki;
437  }
438  else
439  {
440  if (arg[i]!=NULL)
441  {
442  return idInit(1,arg[i]->rank);
443  }
444  }
445  }
446  if (maxrk == 0)
447  {
448  isIdeal = 1;
449  maxrk = 1;
450  }
451  /* init -----------------------------------------------------------*/
452  j += maxrk;
453  syzComp = k*maxrk;
454 
455  ring orig_ring=currRing;
456  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
457  rSetSyzComp(syzComp,syz_ring);
458  rChangeCurrRing(syz_ring);
459 
460  bigmat = idInit(j,(k+1)*maxrk);
461  /* create unit matrices ------------------------------------------*/
462  for (i=0;i<maxrk;i++)
463  {
464  for (j=0;j<=k;j++)
465  {
466  p = pOne();
467  pSetComp(p,i+1+j*maxrk);
468  pSetmComp(p);
469  bigmat->m[i] = pAdd(bigmat->m[i],p);
470  }
471  }
472  /* enter given ideals ------------------------------------------*/
473  i = maxrk;
474  k = 0;
475  for (j=0;j<length;j++)
476  {
477  if (arg[j]!=NULL)
478  {
479  for (l=0;l<IDELEMS(arg[j]);l++)
480  {
481  if (arg[j]->m[l]!=NULL)
482  {
483  if (syz_ring==orig_ring)
484  bigmat->m[i] = pCopy(arg[j]->m[l]);
485  else
486  bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring,currRing);
487  p_Shift(&(bigmat->m[i]),k*maxrk+isIdeal,currRing);
488  i++;
489  }
490  }
491  k++;
492  }
493  }
494  /* std computation --------------------------------------------*/
495  if (alg==GbDefault) alg=GbStd;
496  if (alg==GbStd)
497  {
498  if (TEST_OPT_PROT) { PrintS("std:"); mflush(); }
499  tempstd = kStd(bigmat,currRing->qideal,testHomog,&w,NULL,syzComp);
500  if (w!=NULL) delete w;
501  idDelete(&bigmat);
502  }
503  else if (alg==GbSlimgb)
504  {
505  if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); }
506  tempstd = t_rep_gb(currRing, bigmat, syzComp);
507  idDelete(&bigmat);
508  }
509  else if (alg==GbGroebner)
510  {
511  if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); }
512  BOOLEAN err;
513  tempstd=(ideal)iiCallLibProc1("groebner",bigmat,MODUL_CMD,err);
514  if (err)
515  {
516  Werror("error %d in >>groebner<<",err);
517  tempstd=idInit(1,1);
518  }
519  }
520 // else if (alg==GbModstd): requires ideal, not module
521 // {
522 // if (TEST_OPT_PROT) { PrintS("modstd:"); mflush(); }
523 // BOOLEAN err;
524 // tempstd=(ideal)iiCallLibProc1("modStd",bigmat,MODUL_CMD,err);
525 // if (err)
526 // {
527 // Werror("error %d in >>modStd<<",err);
528 // tempstd=idInit(1,1);
529 // }
530 // }
531  //else if (alg==GbSba): requires order C,...
532  //{
533  // if (TEST_OPT_PROT) { PrintS("sba:"); mflush(); }
534  // tempstd = kSba(bigmat,currRing->qideal,hom,w,1,0,NULL,syzComp);
535  // idDelete(&bigmat);
536  //}
537  else
538  {
539  tempstd=idInit(1,1);
540  Werror("wrong algorithm %d for SB",(int)alg);
541  }
542 
543  if(syz_ring!=orig_ring)
544  rChangeCurrRing(orig_ring);
545 
546  /* interprete result ----------------------------------------*/
547  result = idInit(IDELEMS(tempstd),maxrk);
548  k = 0;
549  for (j=0;j<IDELEMS(tempstd);j++)
550  {
551  if ((tempstd->m[j]!=NULL) && (__p_GetComp(tempstd->m[j],syz_ring)>syzComp))
552  {
553  if (syz_ring==orig_ring)
554  p = pCopy(tempstd->m[j]);
555  else
556  p = prCopyR(tempstd->m[j], syz_ring,currRing);
557  p_Shift(&p,-syzComp-isIdeal,currRing);
558  result->m[k] = p;
559  k++;
560  }
561  }
562  /* clean up ----------------------------------------------------*/
563  if(syz_ring!=orig_ring)
564  rChangeCurrRing(syz_ring);
565  idDelete(&tempstd);
566  if(syz_ring!=orig_ring)
567  {
568  rChangeCurrRing(orig_ring);
569  rDelete(syz_ring);
570  }
571  idSkipZeroes(result);
572  return result;
573 }
574 
575 /*2
576 *computes syzygies of h1,
577 *if quot != NULL it computes in the quotient ring modulo "quot"
578 *works always in a ring with ringorder_s
579 */
580 static ideal idPrepare (ideal h1, tHomog hom, int syzcomp, intvec **w, GbVariant alg)
581 {
582  ideal h2;
583  int j,k;
584  poly p,q;
585 
586  if (idIs0(h1)) return NULL;
587  k = id_RankFreeModule(h1,currRing);
588  h2=idCopy(h1);
589  int i = IDELEMS(h2);
590  if (k == 0)
591  {
592  id_Shift(h2,1,currRing);
593  k = 1;
594  }
595  if (syzcomp<k)
596  {
597  Warn("syzcomp too low, should be %d instead of %d",k,syzcomp);
598  syzcomp = k;
600  }
601  h2->rank = syzcomp+i;
602 
603  //if (hom==testHomog)
604  //{
605  // if(idHomIdeal(h1,currRing->qideal))
606  // {
607  // hom=TRUE;
608  // }
609  //}
610 
611  for (j=0; j<i; j++)
612  {
613  p = h2->m[j];
614  q = pOne();
615  pSetComp(q,syzcomp+1+j);
616  pSetmComp(q);
617  if (p!=NULL)
618  {
619  while (pNext(p)) pIter(p);
620  p->next = q;
621  }
622  else
623  h2->m[j]=q;
624  }
625 
626  idTest(h2);
627 
628  ideal h3=NULL;
629  if (alg==GbDefault) alg=GbStd;
630  if (alg==GbStd)
631  {
632  if (TEST_OPT_PROT) { PrintS("std:"); mflush(); }
633  h3 = kStd(h2,currRing->qideal,hom,w,NULL,syzcomp);
634  }
635  else if (alg==GbSlimgb)
636  {
637  if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); }
638  h3 = t_rep_gb(currRing, h2, syzcomp);
639  }
640  else if (alg==GbGroebner)
641  {
642  if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); }
643  BOOLEAN err;
644  h3=(ideal)iiCallLibProc1("groebner",idCopy(h2),MODUL_CMD,err);
645  if (err)
646  {
647  Werror("error %d in >>groebner<<",err);
648  h3=idInit(1,1);
649  }
650  }
651  else if (alg==GbModstd)
652  {
653  if (TEST_OPT_PROT) { PrintS("modstd:"); mflush(); }
654  BOOLEAN err;
655  void *args[]={idCopy(h2),(void*)1,NULL};
656  int arg_t[]={MODUL_CMD,INT_CMD,0};
657  h3=(ideal)iiCallLibProcM("modStd",args,arg_t,err);
658  if (err)
659  {
660  Werror("error %d in >>modStd<<",err);
661  h3=idInit(1,1);
662  }
663  }
664  else if (alg==GbStdSat)
665  {
666  if (TEST_OPT_PROT) { PrintS("std:sat:"); mflush(); }
667  BOOLEAN err;
668  // search for 2nd block of vars
669  int i=0;
670  int block=-1;
671  loop
672  {
673  if ((currRing->order[i]!=ringorder_c)
674  && (currRing->order[i]!=ringorder_C)
675  && (currRing->order[i]!=ringorder_s))
676  {
677  if (currRing->order[i]==0) { err=TRUE;break;}
678  block++;
679  if (block==1) { block=i; break;}
680  }
681  i++;
682  }
683  if (block>0)
684  {
685  if (TEST_OPT_PROT)
686  {
687  Print("sat(%d..%d)\n",currRing->block0[block],currRing->block1[block]);
688  mflush();
689  }
690  ideal v=idInit(currRing->block1[block]-currRing->block0[block]+1,1);
691  for(i=currRing->block0[block];i<=currRing->block1[block];i++)
692  {
693  v->m[i-currRing->block0[block]]=pOne();
694  pSetExp(v->m[i-currRing->block0[block]],i,1);
695  pSetm(v->m[i-currRing->block0[block]]);
696  }
697  void *args[]={idCopy(h2),v,NULL};
698  int arg_t[]={MODUL_CMD,IDEAL_CMD,0};
699  h3=(ideal)iiCallLibProcM("satstd",args,arg_t,err);
700  }
701  if (err)
702  {
703  Werror("error %d in >>satstd<<",err);
704  h3=idInit(1,1);
705  }
706  }
707  //else if (alg==GbSba): requires order C,...
708  //{
709  // if (TEST_OPT_PROT) { PrintS("sba:"); mflush(); }
710  // h3 = kSba(h2,currRing->qideal,hom,w,1,0,NULL,syzcomp);
711  //}
712  else
713  {
714  h3=idInit(1,1);
715  Werror("wrong algorithm %d for SB",(int)alg);
716  }
717 
718  idDelete(&h2);
719  return h3;
720 }
721 
722 /*2
723 * compute the syzygies of h1 in R/quot,
724 * weights of components are in w
725 * if setRegularity, return the regularity in deg
726 * do not change h1, w
727 */
728 ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp,
729  BOOLEAN setRegularity, int *deg, GbVariant alg)
730 {
731  ideal s_h1;
732  int j, k, length=0,reg;
733  BOOLEAN isMonomial=TRUE;
734  int ii, idElemens_h1;
735 
736  assume(h1 != NULL);
737 
738  idElemens_h1=IDELEMS(h1);
739 #ifdef PDEBUG
740  for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]);
741 #endif
742  if (idIs0(h1))
743  {
744  ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/);
745  return result;
746  }
747  int slength=(int)id_RankFreeModule(h1,currRing);
748  k=si_max(1,slength /*id_RankFreeModule(h1)*/);
749 
750  assume(currRing != NULL);
751  ring orig_ring=currRing;
752  ring syz_ring=rAssure_SyzComp(orig_ring,TRUE);
753  if (setSyzComp) rSetSyzComp(k,syz_ring);
754 
755  if (orig_ring != syz_ring)
756  {
757  rChangeCurrRing(syz_ring);
758  s_h1=idrCopyR_NoSort(h1,orig_ring,syz_ring);
759  }
760  else
761  {
762  s_h1 = h1;
763  }
764 
765  idTest(s_h1);
766 
767  ideal s_h3=idPrepare(s_h1,h,k,w,alg); // main (syz) GB computation
768 
769  if (s_h3==NULL)
770  {
771  if (orig_ring != syz_ring)
772  {
773  rChangeCurrRing(orig_ring);
774  rDelete(syz_ring);
775  }
776  return idFreeModule( idElemens_h1 /*IDELEMS(h1)*/);
777  }
778 
779  if (orig_ring != syz_ring)
780  {
781  idDelete(&s_h1);
782  for (j=0; j<IDELEMS(s_h3); j++)
783  {
784  if (s_h3->m[j] != NULL)
785  {
786  if (p_MinComp(s_h3->m[j],syz_ring) > k)
787  p_Shift(&s_h3->m[j], -k,syz_ring);
788  else
789  p_Delete(&s_h3->m[j],syz_ring);
790  }
791  }
792  idSkipZeroes(s_h3);
793  s_h3->rank -= k;
794  rChangeCurrRing(orig_ring);
795  s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
796  rDelete(syz_ring);
797  #ifdef HAVE_PLURAL
798  if (rIsPluralRing(orig_ring))
799  {
800  id_DelMultiples(s_h3,orig_ring);
801  idSkipZeroes(s_h3);
802  }
803  #endif
804  idTest(s_h3);
805  return s_h3;
806  }
807 
808  ideal e = idInit(IDELEMS(s_h3), s_h3->rank);
809 
810  for (j=IDELEMS(s_h3)-1; j>=0; j--)
811  {
812  if (s_h3->m[j] != NULL)
813  {
814  if (p_MinComp(s_h3->m[j],syz_ring) <= k)
815  {
816  e->m[j] = s_h3->m[j];
817  isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL);
818  p_Delete(&pNext(s_h3->m[j]),syz_ring);
819  s_h3->m[j] = NULL;
820  }
821  }
822  }
823 
824  idSkipZeroes(s_h3);
825  idSkipZeroes(e);
826 
827  if ((deg != NULL)
828  && (!isMonomial)
830  && (setRegularity)
831  && (h==isHomog)
832  && (!rIsPluralRing(currRing))
833  && (!rField_is_Ring(currRing))
834  )
835  {
836  assume(orig_ring==syz_ring);
837  ring dp_C_ring = rAssure_dp_C(syz_ring); // will do rChangeCurrRing later
838  if (dp_C_ring != syz_ring)
839  {
840  rChangeCurrRing(dp_C_ring);
841  e = idrMoveR_NoSort(e, syz_ring, dp_C_ring);
842  }
843  resolvente res = sySchreyerResolvente(e,-1,&length,TRUE, TRUE);
844  intvec * dummy = syBetti(res,length,&reg, *w);
845  *deg = reg+2;
846  delete dummy;
847  for (j=0;j<length;j++)
848  {
849  if (res[j]!=NULL) idDelete(&(res[j]));
850  }
851  omFreeSize((ADDRESS)res,length*sizeof(ideal));
852  idDelete(&e);
853  if (dp_C_ring != orig_ring)
854  {
855  rChangeCurrRing(orig_ring);
856  rDelete(dp_C_ring);
857  }
858  }
859  else
860  {
861  idDelete(&e);
862  }
863  assume(orig_ring==currRing);
864  idTest(s_h3);
865  if (currRing->qideal != NULL)
866  {
867  ideal ts_h3=kStd(s_h3,currRing->qideal,h,w);
868  idDelete(&s_h3);
869  s_h3 = ts_h3;
870  }
871  return s_h3;
872 }
873 
874 /*2
875 */
876 ideal idXXX (ideal h1, int k)
877 {
878  ideal s_h1;
879  intvec *w=NULL;
880 
881  assume(currRing != NULL);
882  ring orig_ring=currRing;
883  ring syz_ring=rAssure_SyzComp(orig_ring,TRUE);
884  rSetSyzComp(k,syz_ring);
885  rChangeCurrRing(syz_ring);
886 
887  if (orig_ring != syz_ring)
888  {
889  s_h1=idrCopyR_NoSort(h1,orig_ring, syz_ring);
890  }
891  else
892  {
893  s_h1 = h1;
894  }
895 
896  ideal s_h3=kStd(s_h1,NULL,testHomog,&w,NULL,k);
897 
898  if (s_h3==NULL)
899  {
900  return idFreeModule(IDELEMS(h1));
901  }
902 
903  if (orig_ring != syz_ring)
904  {
905  idDelete(&s_h1);
906  idSkipZeroes(s_h3);
907  rChangeCurrRing(orig_ring);
908  s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
909  rDelete(syz_ring);
910  idTest(s_h3);
911  return s_h3;
912  }
913 
914  idSkipZeroes(s_h3);
915  idTest(s_h3);
916  return s_h3;
917 }
918 
919 /*
920 *computes a standard basis for h1 and stores the transformation matrix
921 * in ma
922 */
923 ideal idLiftStd (ideal h1, matrix* ma, tHomog hi, ideal * syz, GbVariant alg)
924 {
925  int i, j, t, inputIsIdeal=id_RankFreeModule(h1,currRing);
926  long k;
927  poly p=NULL, q;
928  intvec *w=NULL;
929 
930  idDelete((ideal*)ma);
931  BOOLEAN lift3=FALSE;
932  if (syz!=NULL) { lift3=TRUE; idDelete(syz); }
933  if (idIs0(h1))
934  {
935  *ma=mpNew(1,0);
936  if (lift3)
937  {
938  *syz=idFreeModule(IDELEMS(h1));
939  }
940  return idInit(1,h1->rank);
941  }
942 
943  BITSET save2;
944  SI_SAVE_OPT2(save2);
945 
947 
948  if ((k==1) && (!lift3)) si_opt_2 |=Sy_bit(V_IDLIFT);
949 
950  ring orig_ring = currRing;
951  ring syz_ring = rAssure_SyzOrder(orig_ring,TRUE);
952  rSetSyzComp(k,syz_ring);
953  rChangeCurrRing(syz_ring);
954 
955  ideal s_h1=h1;
956 
957  if (orig_ring != syz_ring)
958  s_h1 = idrCopyR_NoSort(h1,orig_ring,syz_ring);
959  else
960  s_h1 = h1;
961 
962  ideal s_h3=idPrepare(s_h1,hi,k,&w,alg); // main (syz) GB computation
963 
964  ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank);
965 
966  if (lift3) (*syz)=idInit(IDELEMS(s_h3),IDELEMS(h1));
967 
968  if (w!=NULL) delete w;
969  i = 0;
970 
971  // now sort the result, SB : leave in s_h3
972  // T: put in s_h2
973  // syz: put in *syz
974  for (j=0; j<IDELEMS(s_h3); j++)
975  {
976  if (s_h3->m[j] != NULL)
977  {
978  //if (p_MinComp(s_h3->m[j],syz_ring) <= k)
979  if (pGetComp(s_h3->m[j]) <= k) // syz_ring == currRing
980  {
981  i++;
982  q = s_h3->m[j];
983  while (pNext(q) != NULL)
984  {
985  if (pGetComp(pNext(q)) > k)
986  {
987  s_h2->m[j] = pNext(q);
988  pNext(q) = NULL;
989  }
990  else
991  {
992  pIter(q);
993  }
994  }
995  if (!inputIsIdeal) p_Shift(&(s_h3->m[j]), -1,currRing);
996  }
997  else
998  {
999  // we a syzygy here:
1000  if (lift3)
1001  {
1002  p_Shift(&s_h3->m[j], -k,currRing);
1003  (*syz)->m[j]=s_h3->m[j];
1004  s_h3->m[j]=NULL;
1005  }
1006  else
1007  p_Delete(&(s_h3->m[j]),currRing);
1008  }
1009  }
1010  }
1011  idSkipZeroes(s_h3);
1012  //extern char * iiStringMatrix(matrix im, int dim,char ch);
1013  //PrintS("SB: ----------------------------------------\n");
1014  //PrintS(iiStringMatrix((matrix)s_h3,k,'\n'));
1015  //PrintLn();
1016  //PrintS("T: ----------------------------------------\n");
1017  //PrintS(iiStringMatrix((matrix)s_h2,h1->rank,'\n'));
1018  //PrintLn();
1019 
1020  if (lift3) idSkipZeroes(*syz);
1021 
1022  j = IDELEMS(s_h1);
1023 
1024 
1025  if (syz_ring!=orig_ring)
1026  {
1027  idDelete(&s_h1);
1028  rChangeCurrRing(orig_ring);
1029  }
1030 
1031  *ma = mpNew(j,i);
1032 
1033  i = 1;
1034  for (j=0; j<IDELEMS(s_h2); j++)
1035  {
1036  if (s_h2->m[j] != NULL)
1037  {
1038  q = prMoveR( s_h2->m[j], syz_ring,orig_ring);
1039  s_h2->m[j] = NULL;
1040 
1041  if (q!=NULL)
1042  {
1043  q=pReverse(q);
1044  while (q != NULL)
1045  {
1046  p = q;
1047  pIter(q);
1048  pNext(p) = NULL;
1049  t=pGetComp(p);
1050  pSetComp(p,0);
1051  pSetmComp(p);
1052  MATELEM(*ma,t-k,i) = pAdd(MATELEM(*ma,t-k,i),p);
1053  }
1054  }
1055  i++;
1056  }
1057  }
1058  idDelete(&s_h2);
1059 
1060  for (i=0; i<IDELEMS(s_h3); i++)
1061  {
1062  s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], syz_ring,orig_ring);
1063  }
1064  if (lift3)
1065  {
1066  for (i=0; i<IDELEMS(*syz); i++)
1067  {
1068  (*syz)->m[i] = prMoveR_NoSort((*syz)->m[i], syz_ring,orig_ring);
1069  }
1070  }
1071 
1072  if (syz_ring!=orig_ring) rDelete(syz_ring);
1073  SI_RESTORE_OPT2(save2);
1074  return s_h3;
1075 }
1076 
1077 static void idPrepareStd(ideal s_temp, int k)
1078 {
1079  int j,rk=id_RankFreeModule(s_temp,currRing);
1080  poly p,q;
1081 
1082  if (rk == 0)
1083  {
1084  for (j=0; j<IDELEMS(s_temp); j++)
1085  {
1086  if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1);
1087  }
1088  k = si_max(k,1);
1089  }
1090  for (j=0; j<IDELEMS(s_temp); j++)
1091  {
1092  if (s_temp->m[j]!=NULL)
1093  {
1094  p = s_temp->m[j];
1095  q = pOne();
1096  //pGetCoeff(q)=nInpNeg(pGetCoeff(q)); //set q to -1
1097  pSetComp(q,k+1+j);
1098  pSetmComp(q);
1099  while (pNext(p)) pIter(p);
1100  pNext(p) = q;
1101  }
1102  }
1103  s_temp->rank = k+IDELEMS(s_temp);
1104 }
1105 
1106 /*2
1107 *computes a representation of the generators of submod with respect to those
1108 * of mod
1109 */
1110 
1111 ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape,
1112  BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
1113 {
1114  int lsmod =id_RankFreeModule(submod,currRing), j, k;
1115  int comps_to_add=0;
1116  poly p;
1117 
1118  if (idIs0(submod))
1119  {
1120  if (unit!=NULL)
1121  {
1122  *unit=mpNew(1,1);
1123  MATELEM(*unit,1,1)=pOne();
1124  }
1125  if (rest!=NULL)
1126  {
1127  *rest=idInit(1,mod->rank);
1128  }
1129  return idInit(1,mod->rank);
1130  }
1131  if (idIs0(mod)) /* and not idIs0(submod) */
1132  {
1133  WerrorS("2nd module does not lie in the first");
1134  return NULL;
1135  }
1136  if (unit!=NULL)
1137  {
1138  comps_to_add = IDELEMS(submod);
1139  while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL))
1140  comps_to_add--;
1141  }
1143  if ((k!=0) && (lsmod==0)) lsmod=1;
1144  k=si_max(k,(int)mod->rank);
1145  if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; }
1146 
1147  ring orig_ring=currRing;
1148  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
1149  rSetSyzComp(k,syz_ring);
1150  rChangeCurrRing(syz_ring);
1151 
1152  ideal s_mod, s_temp;
1153  if (orig_ring != syz_ring)
1154  {
1155  s_mod = idrCopyR_NoSort(mod,orig_ring,syz_ring);
1156  s_temp = idrCopyR_NoSort(submod,orig_ring,syz_ring);
1157  }
1158  else
1159  {
1160  s_mod = mod;
1161  s_temp = idCopy(submod);
1162  }
1163  ideal s_h3;
1164  if (isSB)
1165  {
1166  s_h3 = idCopy(s_mod);
1167  idPrepareStd(s_h3, k+comps_to_add);
1168  }
1169  else
1170  {
1171  s_h3 = idPrepare(s_mod,(tHomog)FALSE,k+comps_to_add,NULL,alg);
1172  }
1173  if (!goodShape)
1174  {
1175  for (j=0;j<IDELEMS(s_h3);j++)
1176  {
1177  if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k))
1178  p_Delete(&(s_h3->m[j]),currRing);
1179  }
1180  }
1181  idSkipZeroes(s_h3);
1182  if (lsmod==0)
1183  {
1184  id_Shift(s_temp,1,currRing);
1185  }
1186  if (unit!=NULL)
1187  {
1188  for(j = 0;j<comps_to_add;j++)
1189  {
1190  p = s_temp->m[j];
1191  if (p!=NULL)
1192  {
1193  while (pNext(p)!=NULL) pIter(p);
1194  pNext(p) = pOne();
1195  pIter(p);
1196  pSetComp(p,1+j+k);
1197  pSetmComp(p);
1198  p = pNeg(p);
1199  }
1200  }
1201  s_temp->rank += (k+comps_to_add);
1202  }
1203  ideal s_result = kNF(s_h3,currRing->qideal,s_temp,k);
1204  s_result->rank = s_h3->rank;
1205  ideal s_rest = idInit(IDELEMS(s_result),k);
1206  idDelete(&s_h3);
1207  idDelete(&s_temp);
1208 
1209  for (j=0;j<IDELEMS(s_result);j++)
1210  {
1211  if (s_result->m[j]!=NULL)
1212  {
1213  if (pGetComp(s_result->m[j])<=k)
1214  {
1215  if (!divide)
1216  {
1217  if (isSB)
1218  {
1219  WarnS("first module not a standardbasis\n"
1220  "// ** or second not a proper submodule");
1221  }
1222  else
1223  WerrorS("2nd module does not lie in the first");
1224  idDelete(&s_result);
1225  idDelete(&s_rest);
1226  s_result=idInit(IDELEMS(submod),submod->rank);
1227  break;
1228  }
1229  else
1230  {
1231  p = s_rest->m[j] = s_result->m[j];
1232  while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p);
1233  s_result->m[j] = pNext(p);
1234  pNext(p) = NULL;
1235  }
1236  }
1237  p_Shift(&(s_result->m[j]),-k,currRing);
1238  pNeg(s_result->m[j]);
1239  }
1240  }
1241  if ((lsmod==0) && (s_rest!=NULL))
1242  {
1243  for (j=IDELEMS(s_rest);j>0;j--)
1244  {
1245  if (s_rest->m[j-1]!=NULL)
1246  {
1247  p_Shift(&(s_rest->m[j-1]),-1,currRing);
1248  s_rest->m[j-1] = s_rest->m[j-1];
1249  }
1250  }
1251  }
1252  if(syz_ring!=orig_ring)
1253  {
1254  idDelete(&s_mod);
1255  rChangeCurrRing(orig_ring);
1256  s_result = idrMoveR_NoSort(s_result, syz_ring, orig_ring);
1257  s_rest = idrMoveR_NoSort(s_rest, syz_ring, orig_ring);
1258  rDelete(syz_ring);
1259  }
1260  if (rest!=NULL)
1261  *rest = s_rest;
1262  else
1263  idDelete(&s_rest);
1264 //idPrint(s_result);
1265  if (unit!=NULL)
1266  {
1267  *unit=mpNew(comps_to_add,comps_to_add);
1268  int i;
1269  for(i=0;i<IDELEMS(s_result);i++)
1270  {
1271  poly p=s_result->m[i];
1272  poly q=NULL;
1273  while(p!=NULL)
1274  {
1275  if(pGetComp(p)<=comps_to_add)
1276  {
1277  pSetComp(p,0);
1278  if (q!=NULL)
1279  {
1280  pNext(q)=pNext(p);
1281  }
1282  else
1283  {
1284  pIter(s_result->m[i]);
1285  }
1286  pNext(p)=NULL;
1287  MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p);
1288  if(q!=NULL) p=pNext(q);
1289  else p=s_result->m[i];
1290  }
1291  else
1292  {
1293  q=p;
1294  pIter(p);
1295  }
1296  }
1297  p_Shift(&s_result->m[i],-comps_to_add,currRing);
1298  }
1299  }
1300  return s_result;
1301 }
1302 
1303 /*2
1304 *computes division of P by Q with remainder up to (w-weighted) degree n
1305 *P, Q, and w are not changed
1306 */
1307 void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,short *w)
1308 {
1309  long N=0;
1310  int i;
1311  for(i=IDELEMS(Q)-1;i>=0;i--)
1312  if(w==NULL)
1313  N=si_max(N,p_Deg(Q->m[i],currRing));
1314  else
1315  N=si_max(N,p_DegW(Q->m[i],w,currRing));
1316  N+=n;
1317 
1318  T=mpNew(IDELEMS(Q),IDELEMS(P));
1319  R=idInit(IDELEMS(P),P->rank);
1320 
1321  for(i=IDELEMS(P)-1;i>=0;i--)
1322  {
1323  poly p;
1324  if(w==NULL)
1325  p=ppJet(P->m[i],N);
1326  else
1327  p=ppJetW(P->m[i],N,w);
1328 
1329  int j=IDELEMS(Q)-1;
1330  while(p!=NULL)
1331  {
1332  if(pDivisibleBy(Q->m[j],p))
1333  {
1334  poly p0=p_DivideM(pHead(p),pHead(Q->m[j]),currRing);
1335  if(w==NULL)
1336  p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N);
1337  else
1338  p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w);
1339  pNormalize(p);
1340  if(((w==NULL)&&(p_Deg(p0,currRing)>n))||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
1341  p_Delete(&p0,currRing);
1342  else
1343  MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0);
1344  j=IDELEMS(Q)-1;
1345  }
1346  else
1347  {
1348  if(j==0)
1349  {
1350  poly p0=p;
1351  pIter(p);
1352  pNext(p0)=NULL;
1353  if(((w==NULL)&&(p_Deg(p0,currRing)>n))
1354  ||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
1355  p_Delete(&p0,currRing);
1356  else
1357  R->m[i]=pAdd(R->m[i],p0);
1358  j=IDELEMS(Q)-1;
1359  }
1360  else
1361  j--;
1362  }
1363  }
1364  }
1365 }
1366 
1367 /*2
1368 *computes the quotient of h1,h2 : internal routine for idQuot
1369 *BEWARE: the returned ideals may contain incorrectly ordered polys !
1370 *
1371 */
1372 static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
1373 {
1374  idTest(h1);
1375  idTest(h2);
1376 
1377  ideal temph1;
1378  poly p,q = NULL;
1379  int i,l,ll,k,kkk,kmax;
1380  int j = 0;
1381  int k1 = id_RankFreeModule(h1,currRing);
1382  int k2 = id_RankFreeModule(h2,currRing);
1383  tHomog hom=isNotHomog;
1384  k=si_max(k1,k2);
1385  if (k==0)
1386  k = 1;
1387  if ((k2==0) && (k>1)) *addOnlyOne = FALSE;
1388  intvec * weights;
1389  hom = (tHomog)idHomModule(h1,currRing->qideal,&weights);
1390  if /**addOnlyOne &&*/ (/*(*/ !h1IsStb /*)*/)
1391  temph1 = kStd(h1,currRing->qideal,hom,&weights,NULL);
1392  else
1393  temph1 = idCopy(h1);
1394  if (weights!=NULL) delete weights;
1395  idTest(temph1);
1396 /*--- making a single vector from h2 ---------------------*/
1397  for (i=0; i<IDELEMS(h2); i++)
1398  {
1399  if (h2->m[i] != NULL)
1400  {
1401  p = pCopy(h2->m[i]);
1402  if (k2 == 0)
1403  p_Shift(&p,j*k+1,currRing);
1404  else
1405  p_Shift(&p,j*k,currRing);
1406  q = pAdd(q,p);
1407  j++;
1408  }
1409  }
1410  *kkmax = kmax = j*k+1;
1411 /*--- adding a monomial for the result (syzygy) ----------*/
1412  p = q;
1413  while (pNext(p)!=NULL) pIter(p);
1414  pNext(p) = pOne();
1415  pIter(p);
1416  pSetComp(p,kmax);
1417  pSetmComp(p);
1418 /*--- constructing the big matrix ------------------------*/
1419  ideal h4 = idInit(k,kmax+k-1);
1420  h4->m[0] = q;
1421  if (k2 == 0)
1422  {
1423  for (i=1; i<k; i++)
1424  {
1425  if (h4->m[i-1]!=NULL)
1426  {
1427  p = p_Copy_noCheck(h4->m[i-1], currRing); /*h4->m[i-1]!=NULL*/
1428  p_Shift(&p,1,currRing);
1429  h4->m[i] = p;
1430  }
1431  else break;
1432  }
1433  }
1434  idSkipZeroes(h4);
1435  kkk = IDELEMS(h4);
1436  i = IDELEMS(temph1);
1437  for (l=0; l<i; l++)
1438  {
1439  if(temph1->m[l]!=NULL)
1440  {
1441  for (ll=0; ll<j; ll++)
1442  {
1443  p = pCopy(temph1->m[l]);
1444  if (k1 == 0)
1445  p_Shift(&p,ll*k+1,currRing);
1446  else
1447  p_Shift(&p,ll*k,currRing);
1448  if (kkk >= IDELEMS(h4))
1449  {
1450  pEnlargeSet(&(h4->m),IDELEMS(h4),16);
1451  IDELEMS(h4) += 16;
1452  }
1453  h4->m[kkk] = p;
1454  kkk++;
1455  }
1456  }
1457  }
1458 /*--- if h2 goes in as single vector - the h1-part is just SB ---*/
1459  if (*addOnlyOne)
1460  {
1461  idSkipZeroes(h4);
1462  p = h4->m[0];
1463  for (i=0;i<IDELEMS(h4)-1;i++)
1464  {
1465  h4->m[i] = h4->m[i+1];
1466  }
1467  h4->m[IDELEMS(h4)-1] = p;
1468  }
1469  idDelete(&temph1);
1470  //idTest(h4);//see remark at the beginning
1471  return h4;
1472 }
1473 
1474 /*2
1475 *computes the quotient of h1,h2
1476 */
1477 ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
1478 {
1479  // first check for special case h1:(0)
1480  if (idIs0(h2))
1481  {
1482  ideal res;
1483  if (resultIsIdeal)
1484  {
1485  res = idInit(1,1);
1486  res->m[0] = pOne();
1487  }
1488  else
1489  res = idFreeModule(h1->rank);
1490  return res;
1491  }
1492  int i, kmax;
1493  BOOLEAN addOnlyOne=TRUE;
1494  tHomog hom=isNotHomog;
1495  intvec * weights1;
1496 
1497  ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax);
1498 
1499  hom = (tHomog)idHomModule(s_h4,currRing->qideal,&weights1);
1500 
1501  ring orig_ring=currRing;
1502  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
1503  rSetSyzComp(kmax-1,syz_ring);
1504  rChangeCurrRing(syz_ring);
1505  if (orig_ring!=syz_ring)
1506  // s_h4 = idrMoveR_NoSort(s_h4,orig_ring, syz_ring);
1507  s_h4 = idrMoveR(s_h4,orig_ring, syz_ring);
1508  idTest(s_h4);
1509  #if 0
1510  void ipPrint_MA0(matrix m, const char *name);
1511  matrix m=idModule2Matrix(idCopy(s_h4));
1512  PrintS("start:\n");
1513  ipPrint_MA0(m,"Q");
1514  idDelete((ideal *)&m);
1515  PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn();
1516  #endif
1517  ideal s_h3;
1518  if (addOnlyOne)
1519  {
1520  BITSET old_test1;
1521  SI_SAVE_OPT1(old_test1);
1523  s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,0/*kmax-1*/,IDELEMS(s_h4)-1);
1524  SI_RESTORE_OPT1(old_test1);
1525  }
1526  else
1527  {
1528  s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,kmax-1);
1529  }
1530  #if 0
1531  // only together with the above debug stuff
1532  idSkipZeroes(s_h3);
1533  m=idModule2Matrix(idCopy(s_h3));
1534  Print("result, kmax=%d:\n",kmax);
1535  ipPrint_MA0(m,"S");
1536  idDelete((ideal *)&m);
1537  #endif
1538  idTest(s_h3);
1539  if (weights1!=NULL) delete weights1;
1540  idDelete(&s_h4);
1541 
1542  for (i=0;i<IDELEMS(s_h3);i++)
1543  {
1544  if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax))
1545  {
1546  if (resultIsIdeal)
1547  p_Shift(&s_h3->m[i],-kmax,currRing);
1548  else
1549  p_Shift(&s_h3->m[i],-kmax+1,currRing);
1550  }
1551  else
1552  p_Delete(&s_h3->m[i],currRing);
1553  }
1554  if (resultIsIdeal)
1555  s_h3->rank = 1;
1556  else
1557  s_h3->rank = h1->rank;
1558  if(syz_ring!=orig_ring)
1559  {
1560  rChangeCurrRing(orig_ring);
1561  s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
1562  rDelete(syz_ring);
1563  }
1564  idSkipZeroes(s_h3);
1565  idTest(s_h3);
1566  return s_h3;
1567 }
1568 
1569 /*2
1570 * eliminate delVar (product of vars) in h1
1571 */
1572 ideal idElimination (ideal h1,poly delVar,intvec *hilb, GbVariant alg)
1573 {
1574  int i,j=0,k,l;
1575  ideal h,hh, h3;
1576  rRingOrder_t *ord;
1577  int *block0,*block1;
1578  int ordersize=2;
1579  int **wv;
1580  tHomog hom;
1581  intvec * w;
1582  ring tmpR;
1583  ring origR = currRing;
1584 
1585  if (delVar==NULL)
1586  {
1587  return idCopy(h1);
1588  }
1589  if ((currRing->qideal!=NULL) && rIsPluralRing(origR))
1590  {
1591  WerrorS("cannot eliminate in a qring");
1592  return NULL;
1593  }
1594  if (idIs0(h1)) return idInit(1,h1->rank);
1595 #ifdef HAVE_PLURAL
1596  if (rIsPluralRing(origR))
1597  /* in the NC case, we have to check the admissibility of */
1598  /* the subalgebra to be intersected with */
1599  {
1600  if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */
1601  {
1602  if (nc_CheckSubalgebra(delVar,origR))
1603  {
1604  WerrorS("no elimination is possible: subalgebra is not admissible");
1605  return NULL;
1606  }
1607  }
1608  }
1609 #endif
1610  hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL
1611  h3=idInit(16,h1->rank);
1612  for (k=0;; k++)
1613  {
1614  if (origR->order[k]!=0) ordersize++;
1615  else break;
1616  }
1617 #if 0
1618  if (rIsPluralRing(origR)) // we have too keep the odering: it may be needed
1619  // for G-algebra
1620  {
1621  for (k=0;k<ordersize-1; k++)
1622  {
1623  block0[k+1] = origR->block0[k];
1624  block1[k+1] = origR->block1[k];
1625  ord[k+1] = origR->order[k];
1626  if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
1627  }
1628  }
1629  else
1630  {
1631  block0[1] = 1;
1632  block1[1] = (currRing->N);
1633  if (origR->OrdSgn==1) ord[1] = ringorder_wp;
1634  else ord[1] = ringorder_ws;
1635  wv[1]=(int*)omAlloc0((currRing->N)*sizeof(int));
1636  double wNsqr = (double)2.0 / (double)(currRing->N);
1638  int *x= (int * )omAlloc(2 * ((currRing->N) + 1) * sizeof(int));
1639  int sl=IDELEMS(h1) - 1;
1640  wCall(h1->m, sl, x, wNsqr);
1641  for (sl = (currRing->N); sl!=0; sl--)
1642  wv[1][sl-1] = x[sl + (currRing->N) + 1];
1643  omFreeSize((ADDRESS)x, 2 * ((currRing->N) + 1) * sizeof(int));
1644 
1645  ord[2]=ringorder_C;
1646  ord[3]=0;
1647  }
1648 #else
1649 #endif
1650  if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR)))
1651  {
1652  #if 1
1653  // we change to an ordering:
1654  // aa(1,1,1,...,0,0,0),wp(...),C
1655  // this seems to be better than version 2 below,
1656  // according to Tst/../elimiate_[3568].tat (- 17 %)
1657  ord=(rRingOrder_t*)omAlloc0(4*sizeof(rRingOrder_t));
1658  block0=(int*)omAlloc0(4*sizeof(int));
1659  block1=(int*)omAlloc0(4*sizeof(int));
1660  wv=(int**) omAlloc0(4*sizeof(int**));
1661  block0[0] = block0[1] = 1;
1662  block1[0] = block1[1] = rVar(origR);
1663  wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1664  // use this special ordering: like ringorder_a, except that pFDeg, pWeights
1665  // ignore it
1666  ord[0] = ringorder_aa;
1667  for (j=0;j<rVar(origR);j++)
1668  if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
1669  BOOLEAN wp=FALSE;
1670  for (j=0;j<rVar(origR);j++)
1671  if (p_Weight(j+1,origR)!=1) { wp=TRUE;break; }
1672  if (wp)
1673  {
1674  wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1675  for (j=0;j<rVar(origR);j++)
1676  wv[1][j]=p_Weight(j+1,origR);
1677  ord[1] = ringorder_wp;
1678  }
1679  else
1680  ord[1] = ringorder_dp;
1681  #else
1682  // we change to an ordering:
1683  // a(w1,...wn),wp(1,...0.....),C
1684  ord=(int*)omAlloc0(4*sizeof(int));
1685  block0=(int*)omAlloc0(4*sizeof(int));
1686  block1=(int*)omAlloc0(4*sizeof(int));
1687  wv=(int**) omAlloc0(4*sizeof(int**));
1688  block0[0] = block0[1] = 1;
1689  block1[0] = block1[1] = rVar(origR);
1690  wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1691  wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1692  ord[0] = ringorder_a;
1693  for (j=0;j<rVar(origR);j++)
1694  wv[0][j]=pWeight(j+1,origR);
1695  ord[1] = ringorder_wp;
1696  for (j=0;j<rVar(origR);j++)
1697  if (pGetExp(delVar,j+1)!=0) wv[1][j]=1;
1698  #endif
1699  ord[2] = ringorder_C;
1700  ord[3] = (rRingOrder_t)0;
1701  }
1702  else
1703  {
1704  // we change to an ordering:
1705  // aa(....),orig_ordering
1706  ord=(rRingOrder_t*)omAlloc0(ordersize*sizeof(rRingOrder_t));
1707  block0=(int*)omAlloc0(ordersize*sizeof(int));
1708  block1=(int*)omAlloc0(ordersize*sizeof(int));
1709  wv=(int**) omAlloc0(ordersize*sizeof(int**));
1710  for (k=0;k<ordersize-1; k++)
1711  {
1712  block0[k+1] = origR->block0[k];
1713  block1[k+1] = origR->block1[k];
1714  ord[k+1] = origR->order[k];
1715  if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
1716  }
1717  block0[0] = 1;
1718  block1[0] = rVar(origR);
1719  wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1720  for (j=0;j<rVar(origR);j++)
1721  if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
1722  // use this special ordering: like ringorder_a, except that pFDeg, pWeights
1723  // ignore it
1724  ord[0] = ringorder_aa;
1725  }
1726  // fill in tmp ring to get back the data later on
1727  tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL
1728  //rUnComplete(tmpR);
1729  tmpR->p_Procs=NULL;
1730  tmpR->order = ord;
1731  tmpR->block0 = block0;
1732  tmpR->block1 = block1;
1733  tmpR->wvhdl = wv;
1734  rComplete(tmpR, 1);
1735 
1736 #ifdef HAVE_PLURAL
1737  /* update nc structure on tmpR */
1738  if (rIsPluralRing(origR))
1739  {
1740  if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal!
1741  {
1742  WerrorS("no elimination is possible: ordering condition is violated");
1743  // cleanup
1744  rDelete(tmpR);
1745  if (w!=NULL)
1746  delete w;
1747  return NULL;
1748  }
1749  }
1750 #endif
1751  // change into the new ring
1752  //pChangeRing((currRing->N),currRing->OrdSgn,ord,block0,block1,wv);
1753  rChangeCurrRing(tmpR);
1754 
1755  //h = idInit(IDELEMS(h1),h1->rank);
1756  // fetch data from the old ring
1757  //for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR);
1758  h=idrCopyR(h1,origR,currRing);
1759  if (origR->qideal!=NULL)
1760  {
1761  WarnS("eliminate in q-ring: experimental");
1762  ideal q=idrCopyR(origR->qideal,origR,currRing);
1763  ideal s=idSimpleAdd(h,q);
1764  idDelete(&h);
1765  idDelete(&q);
1766  h=s;
1767  }
1768  // compute kStd
1769 #if 1
1770  //rWrite(tmpR);PrintLn();
1771  //BITSET save1;
1772  //SI_SAVE_OPT1(save1);
1773  //si_opt_1 |=1;
1774  //Print("h: %d gen, rk=%d\n",IDELEMS(h),h->rank);
1775  //extern char * showOption();
1776  //Print("%s\n",showOption());
1777  if (alg==GbDefault) alg=GbStd;
1778  if (alg==GbStd)
1779  {
1780  if (TEST_OPT_PROT) { PrintS("std:"); mflush(); }
1781  hh = kStd(h,NULL,hom,&w,hilb);
1782  }
1783  else if (alg==GbSlimgb)
1784  {
1785  if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); }
1786  hh = t_rep_gb(currRing, h, 0);
1787  }
1788  else if (alg==GbGroebner)
1789  {
1790  if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); }
1791  BOOLEAN err;
1792  hh=(ideal)iiCallLibProc1("groebner",idCopy(h),MODUL_CMD,err);
1793  if (err)
1794  {
1795  Werror("error %d in >>groebner<<",err);
1796  hh=idInit(1,1);
1797  }
1798  }
1799  else if (alg==GbModstd)
1800  {
1801  if (TEST_OPT_PROT) { PrintS("modstd:"); mflush(); }
1802  BOOLEAN err;
1803  void *args[]={idCopy(h),(void*)1,NULL};
1804  int arg_t[]={IDEAL_CMD,INT_CMD,0};
1805  hh=(ideal)iiCallLibProcM("modStd",args,arg_t,err);
1806  if (err)
1807  {
1808  Werror("error %d in >>modStd<<",err);
1809  hh=idInit(1,1);
1810  }
1811  }
1812  else if (alg==GbSba)
1813  {
1814  if (TEST_OPT_PROT) { PrintS("sba:"); mflush(); }
1815  hh = kSba(h,currRing->qideal,hom,&w,1,0,NULL);
1816  }
1817  else
1818  {
1819  hh=idInit(1,1);
1820  Werror("wrong algorithm %d for SB",(int)alg);
1821  }
1822  //SI_RESTORE_OPT1(save1);
1823  idDelete(&h);
1824 #else
1825  extern ideal kGroebner(ideal F, ideal Q);
1826  hh=kGroebner(h,NULL);
1827 #endif
1828  // go back to the original ring
1829  rChangeCurrRing(origR);
1830  i = IDELEMS(hh)-1;
1831  while ((i >= 0) && (hh->m[i] == NULL)) i--;
1832  j = -1;
1833  // fetch data from temp ring
1834  for (k=0; k<=i; k++)
1835  {
1836  l=(currRing->N);
1837  while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--;
1838  if (l==0)
1839  {
1840  j++;
1841  if (j >= IDELEMS(h3))
1842  {
1843  pEnlargeSet(&(h3->m),IDELEMS(h3),16);
1844  IDELEMS(h3) += 16;
1845  }
1846  h3->m[j] = prMoveR( hh->m[k], tmpR,origR);
1847  hh->m[k] = NULL;
1848  }
1849  }
1850  id_Delete(&hh, tmpR);
1851  idSkipZeroes(h3);
1852  rDelete(tmpR);
1853  if (w!=NULL)
1854  delete w;
1855  return h3;
1856 }
1857 
1858 #ifdef WITH_OLD_MINOR
1859 /*2
1860 * compute the which-th ar-minor of the matrix a
1861 */
1862 poly idMinor(matrix a, int ar, unsigned long which, ideal R)
1863 {
1864  int i,j/*,k,size*/;
1865  unsigned long curr;
1866  int *rowchoise,*colchoise;
1867  BOOLEAN rowch,colch;
1868  // ideal result;
1869  matrix tmp;
1870  poly p,q;
1871 
1872  i = binom(a->rows(),ar);
1873  j = binom(a->cols(),ar);
1874 
1875  rowchoise=(int *)omAlloc(ar*sizeof(int));
1876  colchoise=(int *)omAlloc(ar*sizeof(int));
1877  // if ((i>512) || (j>512) || (i*j >512)) size=512;
1878  // else size=i*j;
1879  // result=idInit(size,1);
1880  tmp=mpNew(ar,ar);
1881  // k = 0; /* the index in result*/
1882  curr = 0; /* index of current minor */
1883  idInitChoise(ar,1,a->rows(),&rowch,rowchoise);
1884  while (!rowch)
1885  {
1886  idInitChoise(ar,1,a->cols(),&colch,colchoise);
1887  while (!colch)
1888  {
1889  if (curr == which)
1890  {
1891  for (i=1; i<=ar; i++)
1892  {
1893  for (j=1; j<=ar; j++)
1894  {
1895  MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
1896  }
1897  }
1898  p = mp_DetBareiss(tmp,currRing);
1899  if (p!=NULL)
1900  {
1901  if (R!=NULL)
1902  {
1903  q = p;
1904  p = kNF(R,currRing->qideal,q);
1905  p_Delete(&q,currRing);
1906  }
1907  /*delete the matrix tmp*/
1908  for (i=1; i<=ar; i++)
1909  {
1910  for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
1911  }
1912  idDelete((ideal*)&tmp);
1913  omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
1914  omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
1915  return (p);
1916  }
1917  }
1918  curr++;
1919  idGetNextChoise(ar,a->cols(),&colch,colchoise);
1920  }
1921  idGetNextChoise(ar,a->rows(),&rowch,rowchoise);
1922  }
1923  return (poly) 1;
1924 }
1925 
1926 /*2
1927 * compute all ar-minors of the matrix a
1928 */
1929 ideal idMinors(matrix a, int ar, ideal R)
1930 {
1931  int i,j,/*k,*/size;
1932  int *rowchoise,*colchoise;
1933  BOOLEAN rowch,colch;
1934  ideal result;
1935  matrix tmp;
1936  poly p,q;
1937 
1938  i = binom(a->rows(),ar);
1939  j = binom(a->cols(),ar);
1940 
1941  rowchoise=(int *)omAlloc(ar*sizeof(int));
1942  colchoise=(int *)omAlloc(ar*sizeof(int));
1943  if ((i>512) || (j>512) || (i*j >512)) size=512;
1944  else size=i*j;
1945  result=idInit(size,1);
1946  tmp=mpNew(ar,ar);
1947  // k = 0; /* the index in result*/
1948  idInitChoise(ar,1,a->rows(),&rowch,rowchoise);
1949  while (!rowch)
1950  {
1951  idInitChoise(ar,1,a->cols(),&colch,colchoise);
1952  while (!colch)
1953  {
1954  for (i=1; i<=ar; i++)
1955  {
1956  for (j=1; j<=ar; j++)
1957  {
1958  MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
1959  }
1960  }
1961  p = mp_DetBareiss(tmp,currRing);
1962  if (p!=NULL)
1963  {
1964  if (R!=NULL)
1965  {
1966  q = p;
1967  p = kNF(R,currRing->qideal,q);
1968  p_Delete(&q,currRing);
1969  }
1970  if (p!=NULL)
1971  {
1972  if (k>=size)
1973  {
1974  pEnlargeSet(&result->m,size,32);
1975  size += 32;
1976  }
1977  result->m[k] = p;
1978  k++;
1979  }
1980  }
1981  idGetNextChoise(ar,a->cols(),&colch,colchoise);
1982  }
1983  idGetNextChoise(ar,a->rows(),&rowch,rowchoise);
1984  }
1985  /*delete the matrix tmp*/
1986  for (i=1; i<=ar; i++)
1987  {
1988  for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
1989  }
1990  idDelete((ideal*)&tmp);
1991  if (k==0)
1992  {
1993  k=1;
1994  result->m[0]=NULL;
1995  }
1996  omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
1997  omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
1998  pEnlargeSet(&result->m,size,k-size);
1999  IDELEMS(result) = k;
2000  return (result);
2001 }
2002 #else
2003 
2004 
2005 /// compute all ar-minors of the matrix a
2006 /// the caller of mpRecMin
2007 /// the elements of the result are not in R (if R!=NULL)
2008 ideal idMinors(matrix a, int ar, ideal R)
2009 {
2010 
2011  const ring origR=currRing;
2012  id_Test((ideal)a, origR);
2013 
2014  const int r = a->nrows;
2015  const int c = a->ncols;
2016 
2017  if((ar<=0) || (ar>r) || (ar>c))
2018  {
2019  Werror("%d-th minor, matrix is %dx%d",ar,r,c);
2020  return NULL;
2021  }
2022 
2023  ideal h = id_Matrix2Module(mp_Copy(a,origR),origR);
2024  long bound = sm_ExpBound(h,c,r,ar,origR);
2025  id_Delete(&h, origR);
2026 
2027  ring tmpR = sm_RingChange(origR,bound);
2028 
2029  matrix b = mpNew(r,c);
2030 
2031  for (int i=r*c-1;i>=0;i--)
2032  if (a->m[i] != NULL)
2033  b->m[i] = prCopyR(a->m[i],origR,tmpR);
2034 
2035  id_Test( (ideal)b, tmpR);
2036 
2037  if (R!=NULL)
2038  {
2039  R = idrCopyR(R,origR,tmpR); // TODO: overwrites R? memory leak?
2040  //if (ar>1) // otherwise done in mpMinorToResult
2041  //{
2042  // matrix bb=(matrix)kNF(R,currRing->qideal,(ideal)b);
2043  // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols;
2044  // idDelete((ideal*)&b); b=bb;
2045  //}
2046  id_Test( R, tmpR);
2047  }
2048 
2049 
2050  ideal result = idInit(32,1);
2051 
2052  int elems = 0;
2053 
2054  if(ar>1)
2055  mp_RecMin(ar-1,result,elems,b,r,c,NULL,R,tmpR);
2056  else
2057  mp_MinorToResult(result,elems,b,r,c,R,tmpR);
2058 
2059  id_Test( (ideal)b, tmpR);
2060 
2061  id_Delete((ideal *)&b, tmpR);
2062 
2063  if (R!=NULL) id_Delete(&R,tmpR);
2064 
2065  idSkipZeroes(result);
2066  rChangeCurrRing(origR);
2067  result = idrMoveR(result,tmpR,origR);
2068  sm_KillModifiedRing(tmpR);
2069  idTest(result);
2070  return result;
2071 }
2072 #endif
2073 
2074 /*2
2075 *returns TRUE if id1 is a submodule of id2
2076 */
2077 BOOLEAN idIsSubModule(ideal id1,ideal id2)
2078 {
2079  int i;
2080  poly p;
2081 
2082  if (idIs0(id1)) return TRUE;
2083  for (i=0;i<IDELEMS(id1);i++)
2084  {
2085  if (id1->m[i] != NULL)
2086  {
2087  p = kNF(id2,currRing->qideal,id1->m[i]);
2088  if (p != NULL)
2089  {
2090  p_Delete(&p,currRing);
2091  return FALSE;
2092  }
2093  }
2094  }
2095  return TRUE;
2096 }
2097 
2099 {
2100  if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
2101  if (idIs0(m)) return TRUE;
2102 
2103  int cmax=-1;
2104  int i;
2105  poly p=NULL;
2106  int length=IDELEMS(m);
2107  polyset P=m->m;
2108  for (i=length-1;i>=0;i--)
2109  {
2110  p=P[i];
2111  if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
2112  }
2113  if (w != NULL)
2114  if (w->length()+1 < cmax)
2115  {
2116  // Print("length: %d - %d \n", w->length(),cmax);
2117  return FALSE;
2118  }
2119 
2120  if(w!=NULL)
2121  p_SetModDeg(w, currRing);
2122 
2123  for (i=length-1;i>=0;i--)
2124  {
2125  p=P[i];
2126  if (p!=NULL)
2127  {
2128  int d=currRing->pFDeg(p,currRing);
2129  loop
2130  {
2131  pIter(p);
2132  if (p==NULL) break;
2133  if (d!=currRing->pFDeg(p,currRing))
2134  {
2135  //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
2136  if(w!=NULL)
2138  return FALSE;
2139  }
2140  }
2141  }
2142  }
2143 
2144  if(w!=NULL)
2146 
2147  return TRUE;
2148 }
2149 
2150 ideal idSeries(int n,ideal M,matrix U,intvec *w)
2151 {
2152  for(int i=IDELEMS(M)-1;i>=0;i--)
2153  {
2154  if(U==NULL)
2155  M->m[i]=pSeries(n,M->m[i],NULL,w);
2156  else
2157  {
2158  M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w);
2159  MATELEM(U,i+1,i+1)=NULL;
2160  }
2161  }
2162  if(U!=NULL)
2163  idDelete((ideal*)&U);
2164  return M;
2165 }
2166 
2168 {
2169  int e=MATCOLS(i)*MATROWS(i);
2170  matrix r=mpNew(MATROWS(i),MATCOLS(i));
2171  r->rank=i->rank;
2172  int j;
2173  for(j=0; j<e; j++)
2174  {
2175  r->m[j]=pDiff(i->m[j],k);
2176  }
2177  return r;
2178 }
2179 
2180 matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply)
2181 {
2182  matrix r=mpNew(IDELEMS(I),IDELEMS(J));
2183  int i,j;
2184  for(i=0; i<IDELEMS(I); i++)
2185  {
2186  for(j=0; j<IDELEMS(J); j++)
2187  {
2188  MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply);
2189  }
2190  }
2191  return r;
2192 }
2193 
2194 /*3
2195 *handles for some ideal operations the ring/syzcomp managment
2196 *returns all syzygies (componentwise-)shifted by -syzcomp
2197 *or -syzcomp-1 (in case of ideals as input)
2198 static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE)
2199 {
2200  ring orig_ring=currRing;
2201  ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); rChangeCurrRing(syz_ring);
2202  rSetSyzComp(length, syz_ring);
2203 
2204  ideal s_temp;
2205  if (orig_ring!=syz_ring)
2206  s_temp=idrMoveR_NoSort(arg,orig_ring, syz_ring);
2207  else
2208  s_temp=arg;
2209 
2210  ideal s_temp1 = kStd(s_temp,currRing->qideal,testHomog,&w,NULL,length);
2211  if (w!=NULL) delete w;
2212 
2213  if (syz_ring!=orig_ring)
2214  {
2215  idDelete(&s_temp);
2216  rChangeCurrRing(orig_ring);
2217  }
2218 
2219  idDelete(&temp);
2220  ideal temp1=idRingCopy(s_temp1,syz_ring);
2221 
2222  if (syz_ring!=orig_ring)
2223  {
2224  rChangeCurrRing(syz_ring);
2225  idDelete(&s_temp1);
2226  rChangeCurrRing(orig_ring);
2227  rDelete(syz_ring);
2228  }
2229 
2230  for (i=0;i<IDELEMS(temp1);i++)
2231  {
2232  if ((temp1->m[i]!=NULL)
2233  && (pGetComp(temp1->m[i])<=length))
2234  {
2235  pDelete(&(temp1->m[i]));
2236  }
2237  else
2238  {
2239  p_Shift(&(temp1->m[i]),-length,currRing);
2240  }
2241  }
2242  temp1->rank = rk;
2243  idSkipZeroes(temp1);
2244 
2245  return temp1;
2246 }
2247 */
2248 /*2
2249 * represents (h1+h2)/h2=h1/(h1 intersect h2)
2250 */
2251 //ideal idModulo (ideal h2,ideal h1)
2252 ideal idModulo (ideal h2,ideal h1, tHomog hom, intvec ** w)
2253 {
2254  intvec *wtmp=NULL;
2255 
2256  int i,k,rk,flength=0,slength,length;
2257  poly p,q;
2258 
2259  if (idIs0(h2))
2260  return idFreeModule(si_max(1,h2->ncols));
2261  if (!idIs0(h1))
2262  flength = id_RankFreeModule(h1,currRing);
2263  slength = id_RankFreeModule(h2,currRing);
2264  length = si_max(flength,slength);
2265  if (length==0)
2266  {
2267  length = 1;
2268  }
2269  ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2));
2270  if ((w!=NULL)&&((*w)!=NULL))
2271  {
2272  //Print("input weights:");(*w)->show(1);PrintLn();
2273  int d;
2274  int k;
2275  wtmp=new intvec(length+IDELEMS(h2));
2276  for (i=0;i<length;i++)
2277  ((*wtmp)[i])=(**w)[i];
2278  for (i=0;i<IDELEMS(h2);i++)
2279  {
2280  poly p=h2->m[i];
2281  if (p!=NULL)
2282  {
2283  d = p_Deg(p,currRing);
2284  k= pGetComp(p);
2285  if (slength>0) k--;
2286  d +=((**w)[k]);
2287  ((*wtmp)[i+length]) = d;
2288  }
2289  }
2290  //Print("weights:");wtmp->show(1);PrintLn();
2291  }
2292  for (i=0;i<IDELEMS(h2);i++)
2293  {
2294  temp->m[i] = pCopy(h2->m[i]);
2295  q = pOne();
2296  pSetComp(q,i+1+length);
2297  pSetmComp(q);
2298  if(temp->m[i]!=NULL)
2299  {
2300  if (slength==0) p_Shift(&(temp->m[i]),1,currRing);
2301  p = temp->m[i];
2302  while (pNext(p)!=NULL) pIter(p);
2303  pNext(p) = q; // will be sorted later correctly
2304  }
2305  else
2306  temp->m[i]=q;
2307  }
2308  rk = k = IDELEMS(h2);
2309  if (!idIs0(h1))
2310  {
2311  pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1));
2312  IDELEMS(temp) += IDELEMS(h1);
2313  for (i=0;i<IDELEMS(h1);i++)
2314  {
2315  if (h1->m[i]!=NULL)
2316  {
2317  temp->m[k] = pCopy(h1->m[i]);
2318  if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
2319  k++;
2320  }
2321  }
2322  }
2323 
2324  ring orig_ring=currRing;
2325  ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE);
2326  rSetSyzComp(length,syz_ring);
2327  rChangeCurrRing(syz_ring);
2328  // we can use OPT_RETURN_SB only, if syz_ring==orig_ring,
2329  // therefore we disable OPT_RETURN_SB for modulo:
2330  // (see tr. #701)
2331  //if (TEST_OPT_RETURN_SB)
2332  // rSetSyzComp(IDELEMS(h2)+length, syz_ring);
2333  //else
2334  // rSetSyzComp(length, syz_ring);
2335  ideal s_temp;
2336 
2337  if (syz_ring != orig_ring)
2338  {
2339  s_temp = idrMoveR_NoSort(temp, orig_ring, syz_ring);
2340  }
2341  else
2342  {
2343  s_temp = temp;
2344  }
2345 
2346  idTest(s_temp);
2347  ideal s_temp1 = kStd(s_temp,currRing->qideal,hom,&wtmp,NULL,length);
2348 
2349  //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn();
2350  if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL))
2351  {
2352  delete *w;
2353  *w=new intvec(IDELEMS(h2));
2354  for (i=0;i<IDELEMS(h2);i++)
2355  ((**w)[i])=(*wtmp)[i+length];
2356  }
2357  if (wtmp!=NULL) delete wtmp;
2358 
2359  for (i=0;i<IDELEMS(s_temp1);i++)
2360  {
2361  if ((s_temp1->m[i]!=NULL)
2362  && (((int)pGetComp(s_temp1->m[i]))<=length))
2363  {
2364  p_Delete(&(s_temp1->m[i]),currRing);
2365  }
2366  else
2367  {
2368  p_Shift(&(s_temp1->m[i]),-length,currRing);
2369  }
2370  }
2371  s_temp1->rank = rk;
2372  idSkipZeroes(s_temp1);
2373 
2374  if (syz_ring!=orig_ring)
2375  {
2376  rChangeCurrRing(orig_ring);
2377  s_temp1 = idrMoveR_NoSort(s_temp1, syz_ring, orig_ring);
2378  rDelete(syz_ring);
2379  // Hmm ... here seems to be a memory leak
2380  // However, simply deleting it causes memory trouble
2381  // idDelete(&s_temp);
2382  }
2383  else
2384  {
2385  idDelete(&temp);
2386  }
2387  idTest(s_temp1);
2388  return s_temp1;
2389 }
2390 
2391 /*
2392 *computes module-weights for liftings of homogeneous modules
2393 */
2394 intvec * idMWLift(ideal mod,intvec * weights)
2395 {
2396  if (idIs0(mod)) return new intvec(2);
2397  int i=IDELEMS(mod);
2398  while ((i>0) && (mod->m[i-1]==NULL)) i--;
2399  intvec *result = new intvec(i+1);
2400  while (i>0)
2401  {
2402  (*result)[i]=currRing->pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])];
2403  }
2404  return result;
2405 }
2406 
2407 /*2
2408 *sorts the kbase for idCoef* in a special way (lexicographically
2409 *with x_max,...,x_1)
2410 */
2411 ideal idCreateSpecialKbase(ideal kBase,intvec ** convert)
2412 {
2413  int i;
2414  ideal result;
2415 
2416  if (idIs0(kBase)) return NULL;
2417  result = idInit(IDELEMS(kBase),kBase->rank);
2418  *convert = idSort(kBase,FALSE);
2419  for (i=0;i<(*convert)->length();i++)
2420  {
2421  result->m[i] = pCopy(kBase->m[(**convert)[i]-1]);
2422  }
2423  return result;
2424 }
2425 
2426 /*2
2427 *returns the index of a given monom in the list of the special kbase
2428 */
2429 int idIndexOfKBase(poly monom, ideal kbase)
2430 {
2431  int j=IDELEMS(kbase);
2432 
2433  while ((j>0) && (kbase->m[j-1]==NULL)) j--;
2434  if (j==0) return -1;
2435  int i=(currRing->N);
2436  while (i>0)
2437  {
2438  loop
2439  {
2440  if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1;
2441  if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break;
2442  j--;
2443  if (j==0) return -1;
2444  }
2445  if (i==1)
2446  {
2447  while(j>0)
2448  {
2449  if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1;
2450  if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1;
2451  j--;
2452  }
2453  }
2454  i--;
2455  }
2456  return -1;
2457 }
2458 
2459 /*2
2460 *decomposes the monom in a part of coefficients described by the
2461 *complement of how and a monom in variables occuring in how, the
2462 *index of which in kbase is returned as integer pos (-1 if it don't
2463 *exists)
2464 */
2465 poly idDecompose(poly monom, poly how, ideal kbase, int * pos)
2466 {
2467  int i;
2468  poly coeff=pOne(), base=pOne();
2469 
2470  for (i=1;i<=(currRing->N);i++)
2471  {
2472  if (pGetExp(how,i)>0)
2473  {
2474  pSetExp(base,i,pGetExp(monom,i));
2475  }
2476  else
2477  {
2478  pSetExp(coeff,i,pGetExp(monom,i));
2479  }
2480  }
2481  pSetComp(base,pGetComp(monom));
2482  pSetm(base);
2483  pSetCoeff(coeff,nCopy(pGetCoeff(monom)));
2484  pSetm(coeff);
2485  *pos = idIndexOfKBase(base,kbase);
2486  if (*pos<0)
2487  p_Delete(&coeff,currRing);
2489  return coeff;
2490 }
2491 
2492 /*2
2493 *returns a matrix A of coefficients with kbase*A=arg
2494 *if all monomials in variables of how occur in kbase
2495 *the other are deleted
2496 */
2497 matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
2498 {
2499  matrix result;
2500  ideal tempKbase;
2501  poly p,q;
2502  intvec * convert;
2503  int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos;
2504 #if 0
2505  while ((i>0) && (kbase->m[i-1]==NULL)) i--;
2506  if (idIs0(arg))
2507  return mpNew(i,1);
2508  while ((j>0) && (arg->m[j-1]==NULL)) j--;
2509  result = mpNew(i,j);
2510 #else
2511  result = mpNew(i, j);
2512  while ((j>0) && (arg->m[j-1]==NULL)) j--;
2513 #endif
2514 
2515  tempKbase = idCreateSpecialKbase(kbase,&convert);
2516  for (k=0;k<j;k++)
2517  {
2518  p = arg->m[k];
2519  while (p!=NULL)
2520  {
2521  q = idDecompose(p,how,tempKbase,&pos);
2522  if (pos>=0)
2523  {
2524  MATELEM(result,(*convert)[pos],k+1) =
2525  pAdd(MATELEM(result,(*convert)[pos],k+1),q);
2526  }
2527  else
2528  p_Delete(&q,currRing);
2529  pIter(p);
2530  }
2531  }
2532  idDelete(&tempKbase);
2533  return result;
2534 }
2535 
2536 static void idDeleteComps(ideal arg,int* red_comp,int del)
2537 // red_comp is an array [0..args->rank]
2538 {
2539  int i,j;
2540  poly p;
2541 
2542  for (i=IDELEMS(arg)-1;i>=0;i--)
2543  {
2544  p = arg->m[i];
2545  while (p!=NULL)
2546  {
2547  j = pGetComp(p);
2548  if (red_comp[j]!=j)
2549  {
2550  pSetComp(p,red_comp[j]);
2551  pSetmComp(p);
2552  }
2553  pIter(p);
2554  }
2555  }
2556  (arg->rank) -= del;
2557 }
2558 
2559 /*2
2560 * returns the presentation of an isomorphic, minimally
2561 * embedded module (arg represents the quotient!)
2562 */
2563 ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w)
2564 {
2565  if (idIs0(arg)) return idInit(1,arg->rank);
2566  int i,next_gen,next_comp;
2567  ideal res=arg;
2568  if (!inPlace) res = idCopy(arg);
2569  res->rank=si_max(res->rank,id_RankFreeModule(res,currRing));
2570  int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int));
2571  for (i=res->rank;i>=0;i--) red_comp[i]=i;
2572 
2573  int del=0;
2574  loop
2575  {
2576  next_gen = id_ReadOutPivot(res, &next_comp, currRing);
2577  if (next_gen<0) break;
2578  del++;
2579  syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res));
2580  for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--;
2581  if ((w !=NULL)&&(*w!=NULL))
2582  {
2583  for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i];
2584  }
2585  }
2586 
2587  idDeleteComps(res,red_comp,del);
2588  idSkipZeroes(res);
2589  omFree(red_comp);
2590 
2591  if ((w !=NULL)&&(*w!=NULL) &&(del>0))
2592  {
2593  int nl=si_max((*w)->length()-del,1);
2594  intvec *wtmp=new intvec(nl);
2595  for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i];
2596  delete *w;
2597  *w=wtmp;
2598  }
2599  return res;
2600 }
2601 
2602 #include "polys/clapsing.h"
2603 
2604 #if 0
2605 poly id_GCD(poly f, poly g, const ring r)
2606 {
2607  ring save_r=currRing;
2608  rChangeCurrRing(r);
2609  ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
2610  intvec *w = NULL;
2611  ideal S=idSyzygies(I,testHomog,&w);
2612  if (w!=NULL) delete w;
2613  poly gg=pTakeOutComp(&(S->m[0]),2);
2614  idDelete(&S);
2615  poly gcd_p=singclap_pdivide(f,gg,r);
2616  p_Delete(&gg,r);
2617  rChangeCurrRing(save_r);
2618  return gcd_p;
2619 }
2620 #else
2621 poly id_GCD(poly f, poly g, const ring r)
2622 {
2623  ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
2624  intvec *w = NULL;
2625 
2626  ring save_r = currRing;
2627  rChangeCurrRing(r);
2628  ideal S=idSyzygies(I,testHomog,&w);
2629  rChangeCurrRing(save_r);
2630 
2631  if (w!=NULL) delete w;
2632  poly gg=p_TakeOutComp(&(S->m[0]), 2, r);
2633  id_Delete(&S, r);
2634  poly gcd_p=singclap_pdivide(f,gg, r);
2635  p_Delete(&gg, r);
2636 
2637  return gcd_p;
2638 }
2639 #endif
2640 
2641 #if 0
2642 /*2
2643 * xx,q: arrays of length 0..rl-1
2644 * xx[i]: SB mod q[i]
2645 * assume: char=0
2646 * assume: q[i]!=0
2647 * destroys xx
2648 */
2649 ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring R)
2650 {
2651  int cnt=IDELEMS(xx[0])*xx[0]->nrows;
2652  ideal result=idInit(cnt,xx[0]->rank);
2653  result->nrows=xx[0]->nrows; // for lifting matrices
2654  result->ncols=xx[0]->ncols; // for lifting matrices
2655  int i,j;
2656  poly r,h,hh,res_p;
2657  number *x=(number *)omAlloc(rl*sizeof(number));
2658  for(i=cnt-1;i>=0;i--)
2659  {
2660  res_p=NULL;
2661  loop
2662  {
2663  r=NULL;
2664  for(j=rl-1;j>=0;j--)
2665  {
2666  h=xx[j]->m[i];
2667  if ((h!=NULL)
2668  &&((r==NULL)||(p_LmCmp(r,h,R)==-1)))
2669  r=h;
2670  }
2671  if (r==NULL) break;
2672  h=p_Head(r, R);
2673  for(j=rl-1;j>=0;j--)
2674  {
2675  hh=xx[j]->m[i];
2676  if ((hh!=NULL) && (p_LmCmp(r,hh, R)==0))
2677  {
2678  x[j]=p_GetCoeff(hh, R);
2679  hh=p_LmFreeAndNext(hh, R);
2680  xx[j]->m[i]=hh;
2681  }
2682  else
2683  x[j]=n_Init(0, R->cf); // is R->cf really n_Q???, yes!
2684  }
2685 
2686  number n=n_ChineseRemainder(x,q,rl, R->cf);
2687 
2688  for(j=rl-1;j>=0;j--)
2689  {
2690  x[j]=NULL; // nlInit(0...) takes no memory
2691  }
2692  if (n_IsZero(n, R->cf)) p_Delete(&h, R);
2693  else
2694  {
2695  p_SetCoeff(h,n, R);
2696  //Print("new mon:");pWrite(h);
2697  res_p=p_Add_q(res_p, h, R);
2698  }
2699  }
2700  result->m[i]=res_p;
2701  }
2702  omFree(x);
2703  for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]), R);
2704  omFree(xx);
2705  return result;
2706 }
2707 #endif
2708 /* currently unsed:
2709 ideal idChineseRemainder(ideal *xx, intvec *iv)
2710 {
2711  int rl=iv->length();
2712  number *q=(number *)omAlloc(rl*sizeof(number));
2713  int i;
2714  for(i=0; i<rl; i++)
2715  {
2716  q[i]=nInit((*iv)[i]);
2717  }
2718  return idChineseRemainder(xx,q,rl);
2719 }
2720 */
2721 /*
2722  * lift ideal with coeffs over Z (mod N) to Q via Farey
2723  */
2724 ideal id_Farey(ideal x, number N, const ring r)
2725 {
2726  int cnt=IDELEMS(x)*x->nrows;
2727  ideal result=idInit(cnt,x->rank);
2728  result->nrows=x->nrows; // for lifting matrices
2729  result->ncols=x->ncols; // for lifting matrices
2730 
2731  int i;
2732  for(i=cnt-1;i>=0;i--)
2733  {
2734  result->m[i]=p_Farey(x->m[i],N,r);
2735  }
2736  return result;
2737 }
2738 
2739 
2740 
2741 
2742 // uses glabl vars via pSetModDeg
2743 /*
2744 BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
2745 {
2746  if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
2747  if (idIs0(m)) return TRUE;
2748 
2749  int cmax=-1;
2750  int i;
2751  poly p=NULL;
2752  int length=IDELEMS(m);
2753  poly* P=m->m;
2754  for (i=length-1;i>=0;i--)
2755  {
2756  p=P[i];
2757  if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
2758  }
2759  if (w != NULL)
2760  if (w->length()+1 < cmax)
2761  {
2762  // Print("length: %d - %d \n", w->length(),cmax);
2763  return FALSE;
2764  }
2765 
2766  if(w!=NULL)
2767  p_SetModDeg(w, currRing);
2768 
2769  for (i=length-1;i>=0;i--)
2770  {
2771  p=P[i];
2772  poly q=p;
2773  if (p!=NULL)
2774  {
2775  int d=p_FDeg(p,currRing);
2776  loop
2777  {
2778  pIter(p);
2779  if (p==NULL) break;
2780  if (d!=p_FDeg(p,currRing))
2781  {
2782  //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
2783  if(w!=NULL)
2784  p_SetModDeg(NULL, currRing);
2785  return FALSE;
2786  }
2787  }
2788  }
2789  }
2790 
2791  if(w!=NULL)
2792  p_SetModDeg(NULL, currRing);
2793 
2794  return TRUE;
2795 }
2796 */
2797 
2798 /// keeps the first k (>= 1) entries of the given ideal
2799 /// (Note that the kept polynomials may be zero.)
2800 void idKeepFirstK(ideal id, const int k)
2801 {
2802  for (int i = IDELEMS(id)-1; i >= k; i--)
2803  {
2804  if (id->m[i] != NULL) pDelete(&id->m[i]);
2805  }
2806  int kk=k;
2807  if (k==0) kk=1; /* ideals must have at least one element(0)*/
2808  pEnlargeSet(&(id->m), IDELEMS(id), kk-IDELEMS(id));
2809  IDELEMS(id) = kk;
2810 }
2811 
2812 typedef struct
2813 {
2814  poly p;
2815  int index;
2816 } poly_sort;
2817 
2818 int pCompare_qsort(const void *a, const void *b)
2819 {
2820  return (p_Compare(((poly_sort *)a)->p, ((poly_sort *)b)->p,currRing));
2821 }
2822 
2823 void idSort_qsort(poly_sort *id_sort, int idsize)
2824 {
2825  qsort(id_sort, idsize, sizeof(poly_sort), pCompare_qsort);
2826 }
2827 
2828 /*2
2829 * ideal id = (id[i])
2830 * if id[i] = id[j] then id[j] is deleted for j > i
2831 */
2832 void idDelEquals(ideal id)
2833 {
2834  int idsize = IDELEMS(id);
2835  poly_sort *id_sort = (poly_sort *)omAlloc0(idsize*sizeof(poly_sort));
2836  for (int i = 0; i < idsize; i++)
2837  {
2838  id_sort[i].p = id->m[i];
2839  id_sort[i].index = i;
2840  }
2841  idSort_qsort(id_sort, idsize);
2842  int index, index_i, index_j;
2843  int i = 0;
2844  for (int j = 1; j < idsize; j++)
2845  {
2846  if (id_sort[i].p != NULL && pEqualPolys(id_sort[i].p, id_sort[j].p))
2847  {
2848  index_i = id_sort[i].index;
2849  index_j = id_sort[j].index;
2850  if (index_j > index_i)
2851  {
2852  index = index_j;
2853  }
2854  else
2855  {
2856  index = index_i;
2857  i = j;
2858  }
2859  pDelete(&id->m[index]);
2860  }
2861  else
2862  {
2863  i = j;
2864  }
2865  }
2866  omFreeSize((ADDRESS)(id_sort), idsize*sizeof(poly_sort));
2867 }
2868 
2870 
2872 {
2873  BOOLEAN b = FALSE; // set b to TRUE, if spoly was changed,
2874  // let it remain FALSE otherwise
2875  if (strat->P.t_p==NULL)
2876  {
2877  poly p=strat->P.p;
2878 
2879  // iterate over all terms of p and
2880  // compute the minimum mm of all exponent vectors
2881  int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int));
2882  int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
2883  p_GetExpV(p,mm,currRing);
2884  bool nonTrivialSaturationToBeDone=true;
2885  for (p=pNext(p); p!=NULL; pIter(p))
2886  {
2887  nonTrivialSaturationToBeDone=false;
2888  p_GetExpV(p,m0,currRing);
2889  for (int i=rVar(currRing); i>0; i--)
2890  {
2892  {
2893  mm[i]=si_min(mm[i],m0[i]);
2894  if (mm[i]>0) nonTrivialSaturationToBeDone=true;
2895  }
2896  else mm[i]=0;
2897  }
2898  // abort if the minimum is zero in each component
2899  if (!nonTrivialSaturationToBeDone) break;
2900  }
2901  if (nonTrivialSaturationToBeDone)
2902  {
2903  // std::cout << "simplifying!" << std::endl;
2904  if (TEST_OPT_PROT) { PrintS("S"); mflush(); }
2905  p=p_Copy(strat->P.p,currRing);
2906  //pWrite(p);
2907  // for (int i=rVar(currRing); i>0; i--)
2908  // if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]);
2909  //PrintLn();
2910  memset(&strat->P,0,sizeof(strat->P));
2911  strat->P.tailRing = strat->tailRing;
2912  strat->P.p=p;
2913  while(p!=NULL)
2914  {
2915  for (int i=rVar(currRing); i>0; i--)
2916  {
2917  p_SubExp(p,i,mm[i],currRing);
2918  }
2919  p_Setm(p,currRing);
2920  pIter(p);
2921  }
2922  b = TRUE;
2923  }
2924  omFree(mm);
2925  omFree(m0);
2926  }
2927  else
2928  {
2929  poly p=strat->P.t_p;
2930 
2931  // iterate over all terms of p and
2932  // compute the minimum mm of all exponent vectors
2933  int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int));
2934  int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
2935  p_GetExpV(p,mm,strat->tailRing);
2936  bool nonTrivialSaturationToBeDone=true;
2937  for (p = pNext(p); p!=NULL; pIter(p))
2938  {
2939  nonTrivialSaturationToBeDone=false;
2940  p_GetExpV(p,m0,strat->tailRing);
2941  for(int i=rVar(currRing); i>0; i--)
2942  {
2944  {
2945  mm[i]=si_min(mm[i],m0[i]);
2946  if (mm[i]>0) nonTrivialSaturationToBeDone = true;
2947  }
2948  else mm[i]=0;
2949  }
2950  // abort if the minimum is zero in each component
2951  if (!nonTrivialSaturationToBeDone) break;
2952  }
2953  if (nonTrivialSaturationToBeDone)
2954  {
2955  if (TEST_OPT_PROT) { PrintS("S"); mflush(); }
2956  p=p_Copy(strat->P.t_p,strat->tailRing);
2957  //p_Write(p,strat->tailRing);
2958  // for (int i=rVar(currRing); i>0; i--)
2959  // if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]);
2960  //PrintLn();
2961  memset(&strat->P,0,sizeof(strat->P));
2962  strat->P.tailRing = strat->tailRing;
2963  strat->P.t_p=p;
2964  while(p!=NULL)
2965  {
2966  for(int i=rVar(currRing); i>0; i--)
2967  {
2968  p_SubExp(p,i,mm[i],strat->tailRing);
2969  }
2970  p_Setm(p,strat->tailRing);
2971  pIter(p);
2972  }
2973  strat->P.GetP();
2974  b = TRUE;
2975  }
2976  omFree(mm);
2977  omFree(m0);
2978  }
2979  return b; // return TRUE if sp was changed, FALSE if not
2980 }
2981 
2982 ideal id_Satstd(const ideal I, ideal J, const ring r)
2983 {
2984  ring save=currRing;
2985  if (currRing!=r) rChangeCurrRing(r);
2986  idSkipZeroes(J);
2987  id_satstdSaturatingVariables=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
2988  int k=IDELEMS(J);
2989  if (k>1)
2990  {
2991  for (int i=0; i<k; i++)
2992  {
2993  poly x = J->m[i];
2994  int li = p_Var(x,r);
2995  if (li>0)
2997  else
2998  {
2999  if (currRing!=save) rChangeCurrRing(save);
3000  WerrorS("ideal generators must be variables");
3001  return NULL;
3002  }
3003  }
3004  }
3005  else
3006  {
3007  poly x = J->m[0];
3008  for (int i=1; i<=r->N; i++)
3009  {
3010  int li = p_GetExp(x,i,r);
3011  if (li==1)
3013  else if (li>1)
3014  {
3015  if (currRing!=save) rChangeCurrRing(save);
3016  Werror("exponent(x(%d)^%d) must be 0 or 1",i,li);
3017  return NULL;
3018  }
3019  }
3020  }
3021  ideal res=kStd(I,r->qideal,testHomog,NULL,NULL,0,0,NULL,id_sat_vars_sp);
3024  if (currRing!=save) rChangeCurrRing(save);
3025  return res;
3026 }
3027 
3028 GbVariant syGetAlgorithm(char *n, const ring r, const ideal /*M*/)
3029 {
3030  GbVariant alg=GbDefault;
3031  if (strcmp(n,"slimgb")==0) alg=GbSlimgb;
3032  else if (strcmp(n,"std")==0) alg=GbStd;
3033  else if (strcmp(n,"sba")==0) alg=GbSba;
3034  else if (strcmp(n,"singmatic")==0) alg=GbSingmatic;
3035  else if (strcmp(n,"groebner")==0) alg=GbGroebner;
3036  else if (strcmp(n,"modstd")==0) alg=GbModstd;
3037  else if (strcmp(n,"ffmod")==0) alg=GbFfmod;
3038  else if (strcmp(n,"nfmod")==0) alg=GbNfmod;
3039  else if (strcmp(n,"std:sat")==0) alg=GbStdSat;
3040  else Warn(">>%s<< is an unknown algorithm",n);
3041 
3042  if (alg==GbSlimgb) // test conditions for slimgb
3043  {
3044  if(rHasGlobalOrdering(r)
3045  &&(!rIsPluralRing(r))
3046  &&(r->qideal==NULL)
3047  &&(!rField_is_Ring(r)))
3048  {
3049  return GbSlimgb;
3050  }
3051  if (TEST_OPT_PROT)
3052  WarnS("requires: coef:field, commutative, global ordering, not qring");
3053  }
3054  else if (alg==GbSba) // cond. for sba
3055  {
3056  if(rField_is_Domain(r)
3057  &&(!rIsPluralRing(r))
3058  &&(rHasGlobalOrdering(r)))
3059  {
3060  return GbSba;
3061  }
3062  if (TEST_OPT_PROT)
3063  WarnS("requires: coef:domain, commutative, global ordering");
3064  }
3065  else if (alg==GbGroebner) // cond. for groebner
3066  {
3067  return GbGroebner;
3068  }
3069  else if(alg==GbModstd) // cond for modstd: Q or Q(a)
3070  {
3071  if(ggetid("modStd")==NULL)
3072  {
3073  WarnS(">>modStd<< not found");
3074  }
3075  else if(rField_is_Q(r)
3076  &&(!rIsPluralRing(r))
3077  &&(rHasGlobalOrdering(r)))
3078  {
3079  return GbModstd;
3080  }
3081  if (TEST_OPT_PROT)
3082  WarnS("requires: coef:QQ, commutative, global ordering");
3083  }
3084  else if(alg==GbStdSat) // cond for std:sat: 2 blocks of variables
3085  {
3086  if(ggetid("satstd")==NULL)
3087  {
3088  WarnS(">>satstd<< not found");
3089  }
3090  else
3091  {
3092  return GbStdSat;
3093  }
3094  }
3095 
3096  return GbStd; // no conditions for std
3097 }
3098 //----------------------------------------------------------------------------
3099 // GB-algorithms and their pre-conditions
3100 // std slimgb sba singmatic modstd ffmod nfmod groebner
3101 // + + + - + - - + coeffs: QQ
3102 // + + + + - - - + coeffs: ZZ/p
3103 // + + + - ? - + + coeffs: K[a]/f
3104 // + + + - ? + - + coeffs: K(a)
3105 // + - + - - - - + coeffs: domain, not field
3106 // + - - - - - - + coeffs: zero-divisors
3107 // + + + + - ? ? + also for modules: C
3108 // + + - + - ? ? + also for modules: all orderings
3109 // + + - - - - - + exterior algebra
3110 // + + - - - - - + G-algebra
3111 // + + + + + + + + degree ordering
3112 // + - + + + + + + non-degree ordering
3113 // - - - + + + + + parallel
#define TEST_OPT_NOTREGULARITY
Definition: options.h:118
int & rows()
Definition: matpol.h:23
matrix idDiff(matrix i, int k)
Definition: ideals.cc:2167
#define __p_GetComp(p, r)
Definition: monomials.h:63
#define pSetmComp(p)
TODO:
Definition: polys.h:268
void p_SetModDeg(intvec *w, ring r)
Definition: p_polys.cc:3633
for idElimination, like a, except pFDeg, pWeigths ignore it
Definition: ring.h:91
ideal id_Satstd(const ideal I, ideal J, const ring r)
Definition: ideals.cc:2982
#define idMaxIdeal(D)
initialise the maximal ideal (at 0)
Definition: ideals.h:33
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:258
idhdl ggetid(const char *n)
Definition: ipid.cc:521
int j
Definition: facHensel.cc:105
void idDelEquals(ideal id)
Definition: ideals.cc:2832
#define omMemDup(s)
Definition: omAllocDecl.h:264
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
Definition: kstd1.cc:2822
#define pSetm(p)
Definition: polys.h:266
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:2800
static ideal idPrepare(ideal h1, tHomog hom, int syzcomp, intvec **w, GbVariant alg)
Definition: ideals.cc:580
ideal idMultSect(resolvente arg, int length, GbVariant alg)
Definition: ideals.cc:419
static void idPrepareStd(ideal s_temp, int k)
Definition: ideals.cc:1077
void PrintLn()
Definition: reporter.cc:310
static CanonicalForm bound(const CFMatrix &M)
Definition: cf_linsys.cc:460
#define Print
Definition: emacs.cc:80
Definition: tok.h:96
#define pAdd(p, q)
Definition: polys.h:198
#define block
Definition: scanner.cc:665
poly idDecompose(poly monom, poly how, ideal kbase, int *pos)
Definition: ideals.cc:2465
CF_NO_INLINE CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
Definition: cf_inline.cc:564
static BOOLEAN idHomIdeal(ideal id, ideal Q=NULL)
Definition: ideals.h:91
poly prCopyR(poly p, ring src_r, ring dest_r)
Definition: prCopy.cc:34
#define idDelete(H)
delete an ideal
Definition: ideals.h:29
void idLiftW(ideal P, ideal Q, int n, matrix &T, ideal &R, short *w)
Definition: ideals.cc:1307
#define TEST_OPT_PROT
Definition: options.h:102
#define pMaxComp(p)
Definition: polys.h:294
#define pSetExp(p, i, v)
Definition: polys.h:42
static int si_min(const int a, const int b)
Definition: auxiliary.h:139
#define FALSE
Definition: auxiliary.h:94
Compatiblity layer for legacy polynomial operations (over currRing)
int idIndexOfKBase(poly monom, ideal kbase)
Definition: ideals.cc:2429
ideal kSba(ideal F, ideal Q, tHomog h, intvec **w, int sbaOrder, int arri, intvec *hilb, int syzComp, int newIdeal, intvec *vw)
Definition: kstd1.cc:2273
#define ppJet(p, m)
Definition: polys.h:362
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition: p_polys.cc:3455
BOOLEAN nc_rComplete(const ring src, ring dest, bool bSetupQuotient)
Definition: ring.cc:5563
#define id_Test(A, lR)
Definition: simpleideals.h:79
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
Definition: ideals.cc:2098
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
poly prMoveR(poly &p, ring src_r, ring dest_r)
Definition: prCopy.cc:89
#define pTest(p)
Definition: polys.h:410
GbVariant
Definition: ideals.h:118
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:1603
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:538
#define ppMult_mm(p, m)
Definition: polys.h:196
static void p_GetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1455
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define idSimpleAdd(A, B)
Definition: ideals.h:42
matrix idDiffOp(ideal I, ideal J, BOOLEAN multiply)
Definition: ideals.cc:2180
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition: ring.h:586
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
#define pNeg(p)
Definition: polys.h:193
int pCompare_qsort(const void *a, const void *b)
Definition: ideals.cc:2818
char N base
Definition: ValueTraits.h:144
CanonicalForm divide(const CanonicalForm &ff, const CanonicalForm &f, const CFList &as)
#define TRUE
Definition: auxiliary.h:98
ring rAssure_SyzOrder(const ring r, BOOLEAN complete)
Definition: ring.cc:4387
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:2088
static BOOLEAN rField_is_Domain(const ring r)
Definition: ring.h:482
void * ADDRESS
Definition: auxiliary.h:133
#define SI_SAVE_OPT1(A)
Definition: options.h:22
g
Definition: cfModGcd.cc:4031
void WerrorS(const char *s)
Definition: feFopen.cc:24
int k
Definition: cfEzgcd.cc:92
ideal idModulo(ideal h2, ideal h1, tHomog hom, intvec **w)
Definition: ideals.cc:2252
static intvec * idSort(ideal id, BOOLEAN nolex=TRUE)
Definition: ideals.h:186
#define Q
Definition: sirandom.c:25
#define TEST_V_INTERSECT_ELIM
Definition: options.h:141
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:1507
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 loop
Definition: structs.h:80
#define pEqualPolys(p1, p2)
Definition: polys.h:395
#define WarnS
Definition: emacs.cc:78
#define pMinComp(p)
Definition: polys.h:295
#define pJetW(p, m, iv)
Definition: polys.h:365
ideal idMinEmbedding(ideal arg, BOOLEAN inPlace, intvec **w)
Definition: ideals.cc:2563
#define BITSET
Definition: structs.h:20
poly singclap_pdivide(poly f, poly g, const ring r)
Definition: clapsing.cc:556
#define omAlloc(size)
Definition: omAllocDecl.h:210
long sm_ExpBound(ideal m, int di, int ra, int t, const ring currRing)
Definition: sparsmat.cc:188
ideal idQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
Definition: ideals.cc:1477
#define Sy_bit(x)
Definition: options.h:32
static number p_SetCoeff(poly p, number n, ring r)
Definition: p_polys.h:411
#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:2815
void * iiCallLibProc1(const char *n, void *arg, int arg_type, BOOLEAN &err)
Definition: iplib.cc:612
ideal idMinBase(ideal h1)
Definition: ideals.cc:47
static long p_SubExp(poly p, int v, long ee, ring r)
Definition: p_polys.h:612
matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
Definition: ideals.cc:2497
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
Definition: p_polys.h:801
#define mflush()
Definition: reporter.h:57
#define pIter(p)
Definition: monomials.h:37
static BOOLEAN idHomModule(ideal m, ideal Q, intvec **w)
Definition: ideals.h:96
int p_Weight(int i, const ring r)
Definition: p_polys.cc:695
#define M
Definition: sirandom.c:24
#define pGetExp(p, i)
Exponent.
Definition: polys.h:41
char * char_ptr
Definition: structs.h:58
poly * m
Definition: matpol.h:18
CanonicalForm b
Definition: cfModGcd.cc:4044
void id_Shift(ideal M, int s, const ring r)
static poly p_Head(poly p, const ring r)
Definition: p_polys.h:824
long p_DegW(poly p, const short *w, const ring R)
Definition: p_polys.cc:680
static ideal idInitializeQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
Definition: ideals.cc:1372
long p_Deg(poly a, const ring r)
Definition: p_polys.cc:577
Coefficient rings, fields and other domains suitable for Singular polynomials.
ideal idSeries(int n, ideal M, matrix U, intvec *w)
Definition: ideals.cc:2150
poly p_Farey(poly p, number N, const ring r)
Definition: p_polys.cc:50
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:19
#define pSub(a, b)
Definition: polys.h:282
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:2394
CanonicalForm res
Definition: facAbsFact.cc:64
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:48
poly p_One(const ring r)
Definition: p_polys.cc:1303
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:3394
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:468
tHomog
Definition: structs.h:39
#define pSetCompP(a, i)
Definition: polys.h:298
#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:2008
ideal idFreeModule(int i)
Definition: ideals.h:111
#define assume(x)
Definition: mod2.h:390
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition: ring.h:397
double(* wFunctional)(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition: weight.cc:20
ring rCopy0(const ring r, BOOLEAN copy_qideal, BOOLEAN copy_ordering)
Definition: ring.cc:1365
ideal idSectWithElim(ideal h1, ideal h2)
Definition: ideals.cc:129
ring rAssure_SyzComp(const ring r, BOOLEAN complete)
Definition: ring.cc:4392
ring rAssure_dp_C(const ring r)
Definition: ring.cc:4910
void idSort_qsort(poly_sort *id_sort, int idsize)
Definition: ideals.cc:2823
static BOOLEAN id_sat_vars_sp(kStrategy strat)
Definition: ideals.cc:2871
ideal t_rep_gb(const ring r, ideal arg_I, int syz_comp, BOOLEAN F4_mode)
Definition: tgb.cc:3520
rRingOrder_t
order stuff
Definition: ring.h:67
void ipPrint_MA0(matrix m, const char *name)
Definition: ipprint.cc:57
ideal idrMoveR(ideal &id, ring src_r, ring dest_r)
Definition: prCopy.cc:247
#define pSetComp(p, v)
Definition: polys.h:38
static int p_LmCmp(poly p, poly q, const ring r)
Definition: p_polys.h:1496
#define pJet(p, m)
Definition: polys.h:363
int m
Definition: cfEzgcd.cc:121
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
LObject P
Definition: kutil.h:298
static int si_max(const int a, const int b)
Definition: auxiliary.h:138
poly * polyset
Definition: polys.h:254
FILE * f
Definition: checklibs.c:9
int p_Compare(const poly a, const poly b, const ring R)
Definition: p_polys.cc:4812
int i
Definition: cfEzgcd.cc:125
Definition: nc.h:16
void PrintS(const char *s)
Definition: reporter.cc:284
static BOOLEAN rField_is_Q(const ring r)
Definition: ring.h:501
static long p_MinComp(poly p, ring lmRing, ring tailRing)
Definition: p_polys.h:312
#define pOne()
Definition: polys.h:310
char name(const Variable &v)
Definition: factory.h:180
ideal idCreateSpecialKbase(ideal kBase, intvec **convert)
Definition: ideals.cc:2411
Definition: ideals.h:124
static poly p_LmFreeAndNext(poly p, ring)
Definition: p_polys.h:702
BOOLEAN idIsSubModule(ideal id1, ideal id2)
Definition: ideals.cc:2077
resolvente sySchreyerResolvente(ideal arg, int maxlength, int *length, BOOLEAN isMonomial=FALSE, BOOLEAN notReplace=FALSE)
Definition: syz0.cc:855
#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:23
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff &#39;n&#39; represents the zero element.
Definition: coeffs.h:464
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
static poly pReverse(poly p)
Definition: p_polys.h:334
ideal idCopy(ideal A)
Definition: ideals.h:60
ideal idLiftStd(ideal h1, matrix *ma, tHomog hi, ideal *syz, GbVariant alg)
Definition: ideals.cc:923
static int index(p_Length length, p_Ord ord)
Definition: p_Procs_Impl.h:592
void rSetSyzComp(int k, const ring r)
Definition: ring.cc:5016
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
ideal idSyzygies(ideal h1, tHomog h, intvec **w, BOOLEAN setSyzComp, BOOLEAN setRegularity, int *deg, GbVariant alg)
Definition: ideals.cc:728
poly id_GCD(poly f, poly g, const ring r)
Definition: ideals.cc:2621
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
Definition: p_polys.cc:4612
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition: matpol.cc:37
#define TEST_OPT_RETURN_SB
Definition: options.h:111
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:856
matrix mp_MultP(matrix a, poly p, const ring R)
multiply a matrix &#39;a&#39; by a poly &#39;p&#39;, destroy the args
Definition: matpol.cc:148
#define SI_RESTORE_OPT2(A)
Definition: options.h:26
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition: simpleideals.cc:35
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:37
#define pSeries(n, p, u, w)
Definition: polys.h:367
ideal idElimination(ideal h1, poly delVar, intvec *hilb, GbVariant alg)
Definition: ideals.cc:1572
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:487
poly p_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1560
int & cols()
Definition: matpol.h:24
Definition: nc.h:21
void * iiCallLibProcM(const char *n, void **args, int *arg_types, BOOLEAN &err)
args: NULL terminated arry of arguments arg_types: 0 terminated array of corresponding types ...
Definition: iplib.cc:646
#define MATCOLS(i)
Definition: matpol.h:27
poly p
Definition: ideals.cc:2814
static BOOLEAN rField_is_Ring(const ring r)
Definition: ring.h:479
#define NULL
Definition: omList.c:12
#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:138
ideal id_Farey(ideal x, number N, const ring r)
Definition: ideals.cc:2724
void pEnlargeSet(poly **p, int l, int increment)
Definition: p_polys.cc:3656
int length() const
Definition: intvec.h:94
void wCall(poly *s, int sl, int *x, double wNsqr, const ring R)
Definition: weight.cc:108
BOOLEAN rHasGlobalOrdering(const ring r)
Definition: ring.h:754
void rDelete(ring r)
unconditionally deletes fields in r
Definition: ring.cc:448
GbVariant syGetAlgorithm(char *n, const ring r, const ideal)
Definition: ideals.cc:3028
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:334
void sm_KillModifiedRing(ring r)
Definition: sparsmat.cc:289
static void idDeleteComps(ideal arg, int *red_comp, int del)
Definition: ideals.cc:2536
ring tailRing
Definition: kutil.h:341
#define pMult(p, q)
Definition: polys.h:202
ideal kMin_std(ideal F, ideal Q, tHomog h, intvec **w, ideal &M, intvec *hilb, int syzComp, int reduced)
Definition: kstd1.cc:2673
static int * id_satstdSaturatingVariables
Definition: ideals.cc:2869
#define R
Definition: sirandom.c:26
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
static BOOLEAN length(leftv result, leftv arg)
Definition: interval.cc:263
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:1676
#define pDelete(p_ptr)
Definition: polys.h:181
Variable x
Definition: cfModGcd.cc:4023
#define nCopy(n)
Definition: numbers.h:15
#define pNext(p)
Definition: monomials.h:36
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:12
ideal idrCopyR(ideal id, ring src_r, ring dest_r)
Definition: prCopy.cc:191
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:232
void syGaussForOne(ideal syz, int elnum, int ModComp, int from, int till)
Definition: syz.cc:218
#define p_GetCoeff(p, r)
Definition: monomials.h:50
matrix mp_Copy(matrix a, const ring r)
copies matrix a (from ring r to r)
Definition: matpol.cc:64
ideal * resolvente
Definition: ideals.h:18
static nc_type & ncRingType(nc_struct *p)
Definition: nc.h:159
ideal idXXX(ideal h1, int k)
Definition: ideals.cc:876
#define TEST_V_INTERSECT_SYZ
Definition: options.h:142
poly prMoveR_NoSort(poly &p, ring src_r, ring dest_r)
Definition: prCopy.cc:100
static poly p_Neg(poly p, const ring r)
Definition: p_polys.h:1042
intvec * syBetti(resolvente res, int length, int *regularity, intvec *weights, BOOLEAN tomin, int *row_shift)
Definition: syz.cc:770
int id_ReadOutPivot(ideal arg, int *comp, const ring r)
#define pDiff(a, b)
Definition: polys.h:291
#define OPT_SB_1
Definition: options.h:94
#define pDiffOp(a, b, m)
Definition: polys.h:292
ideal idLift(ideal mod, ideal submod, ideal *rest, BOOLEAN goodShape, BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
Definition: ideals.cc:1111
#define MATROWS(i)
Definition: matpol.h:26
int p
Definition: cfModGcd.cc:4019
void wrp(poly p)
Definition: polys.h:305
static jList * T
Definition: janet.cc:30
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:891
BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r)
Definition: old.gring.cc:2568
unsigned si_opt_2
Definition: options.c:6
static Poly * h
Definition: janet.cc:971
s?
Definition: ring.h:76
int BOOLEAN
Definition: auxiliary.h:85
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition: polys.h:31
int p_Var(poly m, const ring r)
Definition: p_polys.cc:4562
#define SI_RESTORE_OPT1(A)
Definition: options.h:25
#define ppJetW(p, m, iv)
Definition: polys.h:364
ideal idrCopyR_NoSort(ideal id, ring src_r, ring dest_r)
Definition: prCopy.cc:204
#define V_IDLIFT
Definition: options.h:62
ideal id_Matrix2Module(matrix mat, const ring R)
converts mat to module, destroys mat
static ideal idMult(ideal h1, ideal h2)
hh := h1 * h2
Definition: ideals.h:84
int binom(int n, int r)
void Werror(const char *fmt,...)
Definition: reporter.cc:189
ideal kGroebner(ideal F, ideal Q)
Definition: ipshell.cc:6231
Definition: ideals.h:122
#define omAlloc0(size)
Definition: omAllocDecl.h:211
return result
Definition: facAbsBiFact.cc:76
int l
Definition: cfEzgcd.cc:93
double wFunctionalBuch(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition: weight0.c:78
ideal idSect(ideal h1, ideal h2, GbVariant alg)
Definition: ideals.cc:199
ideal idrMoveR_NoSort(ideal &id, ring src_r, ring dest_r)
Definition: prCopy.cc:260
long rank
Definition: matpol.h:19
#define pWeight(i)
Definition: polys.h:275
#define pCopy(p)
return a copy of the poly
Definition: polys.h:180
#define MATELEM(mat, i, j)
1-based access to matrix
Definition: matpol.h:29
#define idTest(id)
Definition: ideals.h:47
#define SI_SAVE_OPT2(A)
Definition: options.h:23
#define pNormalize(p)
Definition: polys.h:312
#define Warn
Definition: emacs.cc:77
#define omStrDup(s)
Definition: omAllocDecl.h:263