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ideals.cc
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1 /****************************************
2 * Computer Algebra System SINGULAR *
3 ****************************************/
4 /*
5 * ABSTRACT - all basic methods to manipulate ideals
6 */
7 
8 /* includes */
9 
10 #include "kernel/mod2.h"
11 
12 #include "misc/options.h"
13 #include "misc/intvec.h"
14 
15 #include "coeffs/coeffs.h"
16 #include "coeffs/numbers.h"
17 // #include "coeffs/longrat.h"
18 
19 
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 #if 0
41 #include "Singular/ipprint.h" // ipPrint_MA0
42 #endif
43 
44 /* #define WITH_OLD_MINOR */
45 
46 /*0 implementation*/
47 
48 /*2
49 *returns a minimized set of generators of h1
50 */
51 ideal idMinBase (ideal h1)
52 {
53  ideal h2, h3,h4,e;
54  int j,k;
55  int i,l,ll;
56  intvec * wth;
57  BOOLEAN homog;
59  {
60  WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
61  e=idCopy(h1);
62  return e;
63  }
64  homog = idHomModule(h1,currRing->qideal,&wth);
66  {
67  if(!homog)
68  {
69  WarnS("minbase applies only to the local or homogeneous case over coefficient fields");
70  e=idCopy(h1);
71  return e;
72  }
73  else
74  {
75  ideal re=kMin_std(h1,currRing->qideal,(tHomog)homog,&wth,h2,NULL,0,3);
76  idDelete(&re);
77  return h2;
78  }
79  }
80  e=idInit(1,h1->rank);
81  if (idIs0(h1))
82  {
83  return e;
84  }
85  pEnlargeSet(&(e->m),IDELEMS(e),15);
86  IDELEMS(e) = 16;
87  h2 = kStd(h1,currRing->qideal,isNotHomog,NULL);
88  h3 = idMaxIdeal(1);
89  h4=idMult(h2,h3);
90  idDelete(&h3);
91  h3=kStd(h4,currRing->qideal,isNotHomog,NULL);
92  k = IDELEMS(h3);
93  while ((k > 0) && (h3->m[k-1] == NULL)) k--;
94  j = -1;
95  l = IDELEMS(h2);
96  while ((l > 0) && (h2->m[l-1] == NULL)) l--;
97  for (i=l-1; i>=0; i--)
98  {
99  if (h2->m[i] != NULL)
100  {
101  ll = 0;
102  while ((ll < k) && ((h3->m[ll] == NULL)
103  || !pDivisibleBy(h3->m[ll],h2->m[i])))
104  ll++;
105  if (ll >= k)
106  {
107  j++;
108  if (j > IDELEMS(e)-1)
109  {
110  pEnlargeSet(&(e->m),IDELEMS(e),16);
111  IDELEMS(e) += 16;
112  }
113  e->m[j] = pCopy(h2->m[i]);
114  }
115  }
116  }
117  idDelete(&h2);
118  idDelete(&h3);
119  idDelete(&h4);
120  if (currRing->qideal!=NULL)
121  {
122  h3=idInit(1,e->rank);
123  h2=kNF(h3,currRing->qideal,e);
124  idDelete(&h3);
125  idDelete(&e);
126  e=h2;
127  }
128  idSkipZeroes(e);
129  return e;
130 }
131 
132 
133 static ideal idSectWithElim (ideal h1,ideal h2, GbVariant alg)
134 // does not destroy h1,h2
135 {
136  if (TEST_OPT_PROT) PrintS("intersect by elimination method\n");
137  assume(!idIs0(h1));
138  assume(!idIs0(h2));
139  assume(IDELEMS(h1)<=IDELEMS(h2));
142  // add a new variable:
143  int j;
144  ring origRing=currRing;
145  ring r=rCopy0(origRing);
146  r->N++;
147  r->block0[0]=1;
148  r->block1[0]= r->N;
149  omFree(r->order);
150  r->order=(rRingOrder_t*)omAlloc0(3*sizeof(rRingOrder_t));
151  r->order[0]=ringorder_dp;
152  r->order[1]=ringorder_C;
153  char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr));
154  for (j=0;j<r->N-1;j++) names[j]=r->names[j];
155  names[r->N-1]=omStrDup("@");
156  omFree(r->names);
157  r->names=names;
158  rComplete(r,TRUE);
159  // fetch h1, h2
160  ideal h;
161  h1=idrCopyR(h1,origRing,r);
162  h2=idrCopyR(h2,origRing,r);
163  // switch to temp. ring r
164  rChangeCurrRing(r);
165  // create 1-t, t
166  poly omt=p_One(currRing);
167  p_SetExp(omt,r->N,1,currRing);
168  p_Setm(omt,currRing);
169  poly t=p_Copy(omt,currRing);
170  omt=p_Neg(omt,currRing);
171  omt=p_Add_q(omt,pOne(),currRing);
172  // compute (1-t)*h1
173  h1=(ideal)mp_MultP((matrix)h1,omt,currRing);
174  // compute t*h2
175  h2=(ideal)mp_MultP((matrix)h2,pCopy(t),currRing);
176  // (1-t)h1 + t*h2
177  h=idInit(IDELEMS(h1)+IDELEMS(h2),1);
178  int l;
179  for (l=IDELEMS(h1)-1; l>=0; l--)
180  {
181  h->m[l] = h1->m[l]; h1->m[l]=NULL;
182  }
183  j=IDELEMS(h1);
184  for (l=IDELEMS(h2)-1; l>=0; l--)
185  {
186  h->m[l+j] = h2->m[l]; h2->m[l]=NULL;
187  }
188  idDelete(&h1);
189  idDelete(&h2);
190  // eliminate t:
191  ideal res=idElimination(h,t,NULL,alg);
192  // cleanup
193  idDelete(&h);
194  pDelete(&t);
195  if (res!=NULL) res=idrMoveR(res,r,origRing);
196  rChangeCurrRing(origRing);
197  rDelete(r);
198  return res;
199 }
200 
201 static ideal idGroebner(ideal temp,int syzComp,GbVariant alg, intvec* hilb=NULL, intvec* w=NULL, tHomog hom=testHomog)
202 {
203  //Print("syz=%d\n",syzComp);
204  //PrintS(showOption());
205  //PrintLn();
206  ideal temp1;
207  if (w==NULL)
208  {
209  if (hom==testHomog)
210  hom=(tHomog)idHomModule(temp,currRing->qideal,&w); //sets w to weight vector or NULL
211  }
212  else
213  {
214  w=ivCopy(w);
215  hom=isHomog;
216  }
217 #ifdef HAVE_SHIFTBBA
218  if (rIsLPRing(currRing)) alg = GbStd;
219 #endif
220  if ((alg==GbStd)||(alg==GbDefault))
221  {
222  if (TEST_OPT_PROT &&(alg==GbStd)) { PrintS("std:"); mflush(); }
223  temp1 = kStd(temp,currRing->qideal,hom,&w,hilb,syzComp);
224  idDelete(&temp);
225  }
226  else if (alg==GbSlimgb)
227  {
228  if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); }
229  temp1 = t_rep_gb(currRing, temp, syzComp);
230  idDelete(&temp);
231  }
232  else if (alg==GbGroebner)
233  {
234  if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); }
235  BOOLEAN err;
236  temp1=(ideal)iiCallLibProc1("groebner",temp,MODUL_CMD,err);
237  if (err)
238  {
239  Werror("error %d in >>groebner<<",err);
240  temp1=idInit(1,1);
241  }
242  }
243  else if (alg==GbModstd)
244  {
245  if (TEST_OPT_PROT) { PrintS("modStd:"); mflush(); }
246  BOOLEAN err;
247  void *args[]={temp,(void*)1,NULL};
248  int arg_t[]={MODUL_CMD,INT_CMD,0};
249  leftv temp0=ii_CallLibProcM("modStd",args,arg_t,currRing,err);
250  temp1=(ideal)temp0->data;
251  omFreeBin((ADDRESS)temp0,sleftv_bin);
252  if (err)
253  {
254  Werror("error %d in >>modStd<<",err);
255  temp1=idInit(1,1);
256  }
257  }
258  else if (alg==GbSba)
259  {
260  if (TEST_OPT_PROT) { PrintS("sba:"); mflush(); }
261  temp1 = kSba(temp,currRing->qideal,hom,&w,1,0,NULL);
262  if (w!=NULL) delete w;
263  }
264  else if (alg==GbStdSat)
265  {
266  if (TEST_OPT_PROT) { PrintS("std:sat:"); mflush(); }
267  BOOLEAN err;
268  // search for 2nd block of vars
269  int i=0;
270  int block=-1;
271  loop
272  {
273  if ((currRing->order[i]!=ringorder_c)
274  && (currRing->order[i]!=ringorder_C)
275  && (currRing->order[i]!=ringorder_s))
276  {
277  if (currRing->order[i]==0) { err=TRUE;break;}
278  block++;
279  if (block==1) { block=i; break;}
280  }
281  i++;
282  }
283  if (block>0)
284  {
285  if (TEST_OPT_PROT)
286  {
287  Print("sat(%d..%d)\n",currRing->block0[block],currRing->block1[block]);
288  mflush();
289  }
290  ideal v=idInit(currRing->block1[block]-currRing->block0[block]+1,1);
291  for(i=currRing->block0[block];i<=currRing->block1[block];i++)
292  {
293  v->m[i-currRing->block0[block]]=pOne();
294  pSetExp(v->m[i-currRing->block0[block]],i,1);
295  pSetm(v->m[i-currRing->block0[block]]);
296  }
297  void *args[]={temp,v,NULL};
298  int arg_t[]={MODUL_CMD,IDEAL_CMD,0};
299  leftv temp0=ii_CallLibProcM("satstd",args,arg_t,currRing,err);
300  temp1=(ideal)temp0->data;
301  omFreeBin((ADDRESS)temp0, sleftv_bin);
302  }
303  if (err)
304  {
305  Werror("error %d in >>satstd<<",err);
306  temp1=idInit(1,1);
307  }
308  }
309  if (w!=NULL) delete w;
310  return temp1;
311 }
312 
313 /*2
314 * h3 := h1 intersect h2
315 */
316 ideal idSect (ideal h1,ideal h2, GbVariant alg)
317 {
318  int i,j,k;
319  unsigned length;
320  int flength = id_RankFreeModule(h1,currRing);
321  int slength = id_RankFreeModule(h2,currRing);
322  int rank=si_max(h1->rank,h2->rank);
323  if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank);
324 
325  BITSET save_opt;
326  SI_SAVE_OPT1(save_opt);
328 
329  ideal first,second,temp,temp1,result;
330  poly p,q;
331 
332  if (IDELEMS(h1)<IDELEMS(h2))
333  {
334  first = h1;
335  second = h2;
336  }
337  else
338  {
339  first = h2;
340  second = h1;
341  int t=flength; flength=slength; slength=t;
342  }
343  length = si_max(flength,slength);
344  if (length==0)
345  {
346  if ((currRing->qideal==NULL)
347  && (currRing->OrdSgn==1)
348  && (!rIsPluralRing(currRing))
350  return idSectWithElim(first,second,alg);
351  else length = 1;
352  }
353  if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n");
354  j = IDELEMS(first);
355 
356  ring orig_ring=currRing;
357  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
358  rSetSyzComp(length,syz_ring);
359  rChangeCurrRing(syz_ring);
360 
361  while ((j>0) && (first->m[j-1]==NULL)) j--;
362  temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j);
363  k = 0;
364  for (i=0;i<j;i++)
365  {
366  if (first->m[i]!=NULL)
367  {
368  if (syz_ring==orig_ring)
369  temp->m[k] = pCopy(first->m[i]);
370  else
371  temp->m[k] = prCopyR(first->m[i], orig_ring, syz_ring);
372  q = pOne();
373  pSetComp(q,i+1+length);
374  pSetmComp(q);
375  if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
376  p = temp->m[k];
377  while (pNext(p)!=NULL) pIter(p);
378  pNext(p) = q;
379  k++;
380  }
381  }
382  for (i=0;i<IDELEMS(second);i++)
383  {
384  if (second->m[i]!=NULL)
385  {
386  if (syz_ring==orig_ring)
387  temp->m[k] = pCopy(second->m[i]);
388  else
389  temp->m[k] = prCopyR(second->m[i], orig_ring,currRing);
390  if (slength==0) p_Shift(&(temp->m[k]),1,currRing);
391  k++;
392  }
393  }
394  intvec *w=NULL;
395 
396  if ((alg!=GbDefault)
397  && (alg!=GbGroebner)
398  && (alg!=GbModstd)
399  && (alg!=GbSlimgb)
400  && (alg!=GbStd))
401  {
402  WarnS("wrong algorithm for GB");
403  alg=GbDefault;
404  }
405  temp1=idGroebner(temp,length,alg);
406 
407  if(syz_ring!=orig_ring)
408  rChangeCurrRing(orig_ring);
409 
410  result = idInit(IDELEMS(temp1),rank);
411  j = 0;
412  for (i=0;i<IDELEMS(temp1);i++)
413  {
414  if ((temp1->m[i]!=NULL)
415  && (__p_GetComp(temp1->m[i],syz_ring)>length))
416  {
417  if(syz_ring==orig_ring)
418  {
419  p = temp1->m[i];
420  }
421  else
422  {
423  p = prMoveR(temp1->m[i], syz_ring,orig_ring);
424  }
425  temp1->m[i]=NULL;
426  while (p!=NULL)
427  {
428  q = pNext(p);
429  pNext(p) = NULL;
430  k = pGetComp(p)-1-length;
431  pSetComp(p,0);
432  pSetmComp(p);
433  /* Warning! multiply only from the left! it's very important for Plural */
434  result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k])));
435  p = q;
436  }
437  j++;
438  }
439  }
440  if(syz_ring!=orig_ring)
441  {
442  rChangeCurrRing(syz_ring);
443  idDelete(&temp1);
444  rChangeCurrRing(orig_ring);
445  rDelete(syz_ring);
446  }
447  else
448  {
449  idDelete(&temp1);
450  }
451 
453  SI_RESTORE_OPT1(save_opt);
454  if (TEST_OPT_RETURN_SB)
455  {
456  w=NULL;
457  temp1=kStd(result,currRing->qideal,testHomog,&w);
458  if (w!=NULL) delete w;
459  idDelete(&result);
460  idSkipZeroes(temp1);
461  return temp1;
462  }
463  //else
464  // temp1=kInterRed(result,currRing->qideal);
465  return result;
466 }
467 
468 /*2
469 * ideal/module intersection for a list of objects
470 * given as 'resolvente'
471 */
472 ideal idMultSect(resolvente arg, int length, GbVariant alg)
473 {
474  int i,j=0,k=0,l,maxrk=-1,realrki;
475  unsigned syzComp;
476  ideal bigmat,tempstd,result;
477  poly p;
478  int isIdeal=0;
479 
480  /* find 0-ideals and max rank -----------------------------------*/
481  for (i=0;i<length;i++)
482  {
483  if (!idIs0(arg[i]))
484  {
485  realrki=id_RankFreeModule(arg[i],currRing);
486  k++;
487  j += IDELEMS(arg[i]);
488  if (realrki>maxrk) maxrk = realrki;
489  }
490  else
491  {
492  if (arg[i]!=NULL)
493  {
494  return idInit(1,arg[i]->rank);
495  }
496  }
497  }
498  if (maxrk == 0)
499  {
500  isIdeal = 1;
501  maxrk = 1;
502  }
503  /* init -----------------------------------------------------------*/
504  j += maxrk;
505  syzComp = k*maxrk;
506 
507  ring orig_ring=currRing;
508  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
509  rSetSyzComp(syzComp,syz_ring);
510  rChangeCurrRing(syz_ring);
511 
512  bigmat = idInit(j,(k+1)*maxrk);
513  /* create unit matrices ------------------------------------------*/
514  for (i=0;i<maxrk;i++)
515  {
516  for (j=0;j<=k;j++)
517  {
518  p = pOne();
519  pSetComp(p,i+1+j*maxrk);
520  pSetmComp(p);
521  bigmat->m[i] = pAdd(bigmat->m[i],p);
522  }
523  }
524  /* enter given ideals ------------------------------------------*/
525  i = maxrk;
526  k = 0;
527  for (j=0;j<length;j++)
528  {
529  if (arg[j]!=NULL)
530  {
531  for (l=0;l<IDELEMS(arg[j]);l++)
532  {
533  if (arg[j]->m[l]!=NULL)
534  {
535  if (syz_ring==orig_ring)
536  bigmat->m[i] = pCopy(arg[j]->m[l]);
537  else
538  bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring,currRing);
539  p_Shift(&(bigmat->m[i]),k*maxrk+isIdeal,currRing);
540  i++;
541  }
542  }
543  k++;
544  }
545  }
546  /* std computation --------------------------------------------*/
547  if ((alg!=GbDefault)
548  && (alg!=GbGroebner)
549  && (alg!=GbModstd)
550  && (alg!=GbSlimgb)
551  && (alg!=GbStd))
552  {
553  WarnS("wrong algorithm for GB");
554  alg=GbDefault;
555  }
556  tempstd=idGroebner(bigmat,syzComp,alg);
557 
558  if(syz_ring!=orig_ring)
559  rChangeCurrRing(orig_ring);
560 
561  /* interpret result ----------------------------------------*/
562  result = idInit(IDELEMS(tempstd),maxrk);
563  k = 0;
564  for (j=0;j<IDELEMS(tempstd);j++)
565  {
566  if ((tempstd->m[j]!=NULL) && (__p_GetComp(tempstd->m[j],syz_ring)>syzComp))
567  {
568  if (syz_ring==orig_ring)
569  p = pCopy(tempstd->m[j]);
570  else
571  p = prCopyR(tempstd->m[j], syz_ring,currRing);
572  p_Shift(&p,-syzComp-isIdeal,currRing);
573  result->m[k] = p;
574  k++;
575  }
576  }
577  /* clean up ----------------------------------------------------*/
578  if(syz_ring!=orig_ring)
579  rChangeCurrRing(syz_ring);
580  idDelete(&tempstd);
581  if(syz_ring!=orig_ring)
582  {
583  rChangeCurrRing(orig_ring);
584  rDelete(syz_ring);
585  }
587  return result;
588 }
589 
590 /*2
591 *computes syzygies of h1,
592 *if quot != NULL it computes in the quotient ring modulo "quot"
593 *works always in a ring with ringorder_s
594 */
595 /* construct a "matrix" (h11 may be NULL)
596  * h1 h11
597  * E_n 0
598  * and compute a (column) GB of it, with a syzComp=rows(h1)=rows(h11)
599  * currRing must be a syz-ring with syzComp set
600  * result is a "matrix":
601  * G 0
602  * T S
603  * where G: GB of (h1+h11)
604  * T: G/h11=h1*T
605  * S: relative syzygies(h1) modulo h11
606  */
607 static ideal idPrepare (ideal h1, ideal h11, tHomog hom, int syzcomp, intvec **w, GbVariant alg)
608 {
609  ideal h2,h22;
610  int j,k;
611  poly p,q;
612 
613  if (idIs0(h1)) return NULL;
615  if (h11!=NULL)
616  {
617  k = si_max(k,(int)id_RankFreeModule(h11,currRing));
618  h22=idCopy(h11);
619  }
620  h2=idCopy(h1);
621  int i = IDELEMS(h2);
622  if (h11!=NULL) i+=IDELEMS(h22);
623  if (k == 0)
624  {
625  id_Shift(h2,1,currRing);
626  if (h11!=NULL) id_Shift(h22,1,currRing);
627  k = 1;
628  }
629  if (syzcomp<k)
630  {
631  Warn("syzcomp too low, should be %d instead of %d",k,syzcomp);
632  syzcomp = k;
634  }
635  h2->rank = syzcomp+i;
636 
637  //if (hom==testHomog)
638  //{
639  // if(idHomIdeal(h1,currRing->qideal))
640  // {
641  // hom=TRUE;
642  // }
643  //}
644 
645  for (j=0; j<IDELEMS(h2); j++)
646  {
647  p = h2->m[j];
648  q = pOne();
649 #ifdef HAVE_SHIFTBBA
650  // non multiplicative variable
651  if (rIsLPRing(currRing))
652  {
653  pSetExp(q, currRing->isLPring - currRing->LPncGenCount + j + 1, 1);
654  p_Setm(q, currRing);
655  }
656 #endif
657  pSetComp(q,syzcomp+1+j);
658  pSetmComp(q);
659  if (p!=NULL)
660  {
661 #ifdef HAVE_SHIFTBBA
662  if (rIsLPRing(currRing))
663  {
664  h2->m[j] = pAdd(p, q);
665  }
666  else
667 #endif
668  {
669  while (pNext(p)) pIter(p);
670  p->next = q;
671  }
672  }
673  else
674  h2->m[j]=q;
675  }
676  if (h11!=NULL)
677  {
678  ideal h=id_SimpleAdd(h2,h22,currRing);
679  id_Delete(&h2,currRing);
680  id_Delete(&h22,currRing);
681  h2=h;
682  }
683 
684  idTest(h2);
685  #if 0
687  PrintS(" --------------before std------------------------\n");
688  ipPrint_MA0(TT,"T");
689  PrintLn();
690  idDelete((ideal*)&TT);
691  #endif
692 
693  if ((alg!=GbDefault)
694  && (alg!=GbGroebner)
695  && (alg!=GbModstd)
696  && (alg!=GbSlimgb)
697  && (alg!=GbStd))
698  {
699  WarnS("wrong algorithm for GB");
700  alg=GbDefault;
701  }
702 
703  ideal h3;
704  if (w!=NULL) h3=idGroebner(h2,syzcomp,alg,NULL,*w,hom);
705  else h3=idGroebner(h2,syzcomp,alg,NULL,NULL,hom);
706  return h3;
707 }
708 
709 ideal idExtractG_T_S(ideal s_h3,matrix *T,ideal *S,long syzComp,
710  int h1_size,BOOLEAN inputIsIdeal,const ring oring, const ring sring)
711 {
712  // now sort the result, SB : leave in s_h3
713  // T: put in s_h2 (*T as a matrix)
714  // syz: put in *S
715  idSkipZeroes(s_h3);
716  ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank); // will become T
717 
718  #if 0
720  Print("after std: --------------syzComp=%d------------------------\n",syzComp);
721  ipPrint_MA0(TT,"T");
722  PrintLn();
723  idDelete((ideal*)&TT);
724  #endif
725 
726  int j, i=0;
727  for (j=0; j<IDELEMS(s_h3); j++)
728  {
729  if (s_h3->m[j] != NULL)
730  {
731  if (pGetComp(s_h3->m[j]) <= syzComp) // syz_ring == currRing
732  {
733  i++;
734  poly q = s_h3->m[j];
735  while (pNext(q) != NULL)
736  {
737  if (pGetComp(pNext(q)) > syzComp)
738  {
739  s_h2->m[i-1] = pNext(q);
740  pNext(q) = NULL;
741  }
742  else
743  {
744  pIter(q);
745  }
746  }
747  if (!inputIsIdeal) p_Shift(&(s_h3->m[j]), -1,currRing);
748  }
749  else
750  {
751  // we a syzygy here:
752  if (S!=NULL)
753  {
754  p_Shift(&s_h3->m[j], -syzComp,currRing);
755  (*S)->m[j]=s_h3->m[j];
756  s_h3->m[j]=NULL;
757  }
758  else
759  p_Delete(&(s_h3->m[j]),currRing);
760  }
761  }
762  }
763  idSkipZeroes(s_h3);
764 
765  #if 0
766  TT=id_Module2Matrix(idCopy(s_h2),currRing);
767  PrintS("T: ----------------------------------------\n");
768  ipPrint_MA0(TT,"T");
769  PrintLn();
770  idDelete((ideal*)&TT);
771  #endif
772 
773  if (S!=NULL) idSkipZeroes(*S);
774 
775  if (sring!=oring)
776  {
777  rChangeCurrRing(oring);
778  }
779 
780  if (T!=NULL)
781  {
782  *T = mpNew(h1_size,i);
783 
784  for (j=0; j<i; j++)
785  {
786  if (s_h2->m[j] != NULL)
787  {
788  poly q = prMoveR( s_h2->m[j], sring,oring);
789  s_h2->m[j] = NULL;
790 
791  if (q!=NULL)
792  {
793  q=pReverse(q);
794  while (q != NULL)
795  {
796  poly p = q;
797  pIter(q);
798  pNext(p) = NULL;
799  int t=pGetComp(p);
800  pSetComp(p,0);
801  pSetmComp(p);
802  MATELEM(*T,t-syzComp,j+1) = pAdd(MATELEM(*T,t-syzComp,j+1),p);
803  }
804  }
805  }
806  }
807  }
808  id_Delete(&s_h2,sring);
809 
810  for (i=0; i<IDELEMS(s_h3); i++)
811  {
812  s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], sring,oring);
813  }
814  if (S!=NULL)
815  {
816  for (i=0; i<IDELEMS(*S); i++)
817  {
818  (*S)->m[i] = prMoveR_NoSort((*S)->m[i], sring,oring);
819  }
820  }
821  return s_h3;
822 }
823 
824 /*2
825 * compute the syzygies of h1 in R/quot,
826 * weights of components are in w
827 * if setRegularity, return the regularity in deg
828 * do not change h1, w
829 */
830 ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp,
831  BOOLEAN setRegularity, int *deg, GbVariant alg)
832 {
833  ideal s_h1;
834  int j, k, length=0,reg;
835  BOOLEAN isMonomial=TRUE;
836  int ii, idElemens_h1;
837 
838  assume(h1 != NULL);
839 
840  idElemens_h1=IDELEMS(h1);
841 #ifdef PDEBUG
842  for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]);
843 #endif
844  if (idIs0(h1))
845  {
846  ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/);
847  return result;
848  }
849  int slength=(int)id_RankFreeModule(h1,currRing);
850  k=si_max(1,slength /*id_RankFreeModule(h1)*/);
851 
852  assume(currRing != NULL);
853  ring orig_ring=currRing;
854  ring syz_ring=rAssure_SyzComp(orig_ring,TRUE);
855  if (setSyzComp) rSetSyzComp(k,syz_ring);
856 
857  if (orig_ring != syz_ring)
858  {
859  rChangeCurrRing(syz_ring);
860  s_h1=idrCopyR_NoSort(h1,orig_ring,syz_ring);
861  }
862  else
863  {
864  s_h1 = h1;
865  }
866 
867  idTest(s_h1);
868 
869  BITSET save_opt;
870  SI_SAVE_OPT1(save_opt);
872 
873  ideal s_h3=idPrepare(s_h1,NULL,h,k,w,alg); // main (syz) GB computation
874 
875  SI_RESTORE_OPT1(save_opt);
876 
877  if (orig_ring != syz_ring)
878  {
879  idDelete(&s_h1);
880  for (j=0; j<IDELEMS(s_h3); j++)
881  {
882  if (s_h3->m[j] != NULL)
883  {
884  if (p_MinComp(s_h3->m[j],syz_ring) > k)
885  p_Shift(&s_h3->m[j], -k,syz_ring);
886  else
887  p_Delete(&s_h3->m[j],syz_ring);
888  }
889  }
890  idSkipZeroes(s_h3);
891  s_h3->rank -= k;
892  rChangeCurrRing(orig_ring);
893  s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
894  rDelete(syz_ring);
895  #ifdef HAVE_PLURAL
896  if (rIsPluralRing(orig_ring))
897  {
898  id_DelMultiples(s_h3,orig_ring);
899  idSkipZeroes(s_h3);
900  }
901  #endif
902  idTest(s_h3);
903  return s_h3;
904  }
905 
906  ideal e = idInit(IDELEMS(s_h3), s_h3->rank);
907 
908  for (j=IDELEMS(s_h3)-1; j>=0; j--)
909  {
910  if (s_h3->m[j] != NULL)
911  {
912  if (p_MinComp(s_h3->m[j],syz_ring) <= k)
913  {
914  e->m[j] = s_h3->m[j];
915  isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL);
916  p_Delete(&pNext(s_h3->m[j]),syz_ring);
917  s_h3->m[j] = NULL;
918  }
919  }
920  }
921 
922  idSkipZeroes(s_h3);
923  idSkipZeroes(e);
924 
925  if ((deg != NULL)
926  && (!isMonomial)
928  && (setRegularity)
929  && (h==isHomog)
930  && (!rIsPluralRing(currRing))
931  && (!rField_is_Ring(currRing))
932  )
933  {
934  assume(orig_ring==syz_ring);
935  ring dp_C_ring = rAssure_dp_C(syz_ring); // will do rChangeCurrRing later
936  if (dp_C_ring != syz_ring)
937  {
938  rChangeCurrRing(dp_C_ring);
939  e = idrMoveR_NoSort(e, syz_ring, dp_C_ring);
940  }
942  intvec * dummy = syBetti(res,length,&reg, *w);
943  *deg = reg+2;
944  delete dummy;
945  for (j=0;j<length;j++)
946  {
947  if (res[j]!=NULL) idDelete(&(res[j]));
948  }
949  omFreeSize((ADDRESS)res,length*sizeof(ideal));
950  idDelete(&e);
951  if (dp_C_ring != orig_ring)
952  {
953  rChangeCurrRing(orig_ring);
954  rDelete(dp_C_ring);
955  }
956  }
957  else
958  {
959  idDelete(&e);
960  }
961  assume(orig_ring==currRing);
962  idTest(s_h3);
963  if (currRing->qideal != NULL)
964  {
965  ideal ts_h3=kStd(s_h3,currRing->qideal,h,w);
966  idDelete(&s_h3);
967  s_h3 = ts_h3;
968  }
969  return s_h3;
970 }
971 
972 /*
973 *computes a standard basis for h1 and stores the transformation matrix
974 * in ma
975 */
976 ideal idLiftStd (ideal h1, matrix* T, tHomog hi, ideal * S, GbVariant alg,
977  ideal h11)
978 {
979  int inputIsIdeal=id_RankFreeModule(h1,currRing);
980  long k;
981  intvec *w=NULL;
982 
983  idDelete((ideal*)T);
984  BOOLEAN lift3=FALSE;
985  if (S!=NULL) { lift3=TRUE; idDelete(S); }
986  if (idIs0(h1))
987  {
988  *T=mpNew(1,IDELEMS(h1));
989  if (lift3)
990  {
991  *S=idFreeModule(IDELEMS(h1));
992  }
993  return idInit(1,h1->rank);
994  }
995 
996  BITSET save2;
997  SI_SAVE_OPT2(save2);
998 
999  k=si_max(1,inputIsIdeal);
1000 
1001  if ((!lift3)&&(!TEST_OPT_RETURN_SB)) si_opt_2 |=Sy_bit(V_IDLIFT);
1002 
1003  ring orig_ring = currRing;
1004  ring syz_ring = rAssure_SyzOrder(orig_ring,TRUE);
1005  rSetSyzComp(k,syz_ring);
1006  rChangeCurrRing(syz_ring);
1007 
1008  ideal s_h1;
1009 
1010  if (orig_ring != syz_ring)
1011  s_h1 = idrCopyR_NoSort(h1,orig_ring,syz_ring);
1012  else
1013  s_h1 = h1;
1014  ideal s_h11=NULL;
1015  if (h11!=NULL)
1016  {
1017  s_h11=idrCopyR_NoSort(h11,orig_ring,syz_ring);
1018  }
1019 
1020 
1021  ideal s_h3=idPrepare(s_h1,s_h11,hi,k,&w,alg); // main (syz) GB computation
1022 
1023 
1024  if (w!=NULL) delete w;
1025  if (syz_ring!=orig_ring)
1026  {
1027  idDelete(&s_h1);
1028  if (s_h11!=NULL) idDelete(&s_h11);
1029  }
1030 
1031  if (S!=NULL) (*S)=idInit(IDELEMS(s_h3),IDELEMS(h1));
1032 
1033  s_h3=idExtractG_T_S(s_h3,T,S,k,IDELEMS(h1),inputIsIdeal,orig_ring,syz_ring);
1034 
1035  if (syz_ring!=orig_ring) rDelete(syz_ring);
1036  s_h3->rank=h1->rank;
1037  SI_RESTORE_OPT2(save2);
1038  return s_h3;
1039 }
1040 
1041 static void idPrepareStd(ideal s_temp, int k)
1042 {
1043  int j,rk=id_RankFreeModule(s_temp,currRing);
1044  poly p,q;
1045 
1046  if (rk == 0)
1047  {
1048  for (j=0; j<IDELEMS(s_temp); j++)
1049  {
1050  if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1);
1051  }
1052  k = si_max(k,1);
1053  }
1054  for (j=0; j<IDELEMS(s_temp); j++)
1055  {
1056  if (s_temp->m[j]!=NULL)
1057  {
1058  p = s_temp->m[j];
1059  q = pOne();
1060  //pGetCoeff(q)=nInpNeg(pGetCoeff(q)); //set q to -1
1061  pSetComp(q,k+1+j);
1062  pSetmComp(q);
1063 #ifdef HAVE_SHIFTBBA
1064  // non multiplicative variable
1065  if (rIsLPRing(currRing))
1066  {
1067  pSetExp(q, currRing->isLPring - currRing->LPncGenCount + j + 1, 1);
1068  p_Setm(q, currRing);
1069  s_temp->m[j] = pAdd(p, q);
1070  }
1071  else
1072 #endif
1073  {
1074  while (pNext(p)) pIter(p);
1075  pNext(p) = q;
1076  }
1077  }
1078  }
1079  s_temp->rank = k+IDELEMS(s_temp);
1080 }
1081 
1082 static void idLift_setUnit(int e_mod, matrix *unit)
1083 {
1084  if (unit!=NULL)
1085  {
1086  *unit=mpNew(e_mod,e_mod);
1087  // make sure that U is a diagonal matrix of units
1088  for(int i=e_mod;i>0;i--)
1089  {
1090  MATELEM(*unit,i,i)=pOne();
1091  }
1092  }
1093 }
1094 /*2
1095 *computes a representation of the generators of submod with respect to those
1096 * of mod
1097 */
1098 /// represents the generators of submod in terms of the generators of mod
1099 /// (Matrix(SM)*U-Matrix(rest)) = Matrix(M)*Matrix(result)
1100 /// goodShape: maximal non-zero index in generators of SM <= that of M
1101 /// isSB: generators of M form a Groebner basis
1102 /// divide: allow SM not to be a submodule of M
1103 /// U is an diagonal matrix of units (non-constant only in local rings)
1104 /// rest is: 0 if SM in M, SM if not divide, NF(SM,std(M)) if divide
1105 ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape,
1106  BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
1107 {
1108  int lsmod =id_RankFreeModule(submod,currRing), j, k;
1109  int comps_to_add=0;
1110  int idelems_mod=IDELEMS(mod);
1111  int idelems_submod=IDELEMS(submod);
1112  poly p;
1113 
1114  if (idIs0(submod))
1115  {
1116  if (rest!=NULL)
1117  {
1118  *rest=idInit(1,mod->rank);
1119  }
1120  idLift_setUnit(idelems_submod,unit);
1121  return idInit(1,idelems_mod);
1122  }
1123  if (idIs0(mod)) /* and not idIs0(submod) */
1124  {
1125  if (rest!=NULL)
1126  {
1127  *rest=idCopy(submod);
1128  idLift_setUnit(idelems_submod,unit);
1129  return idInit(1,idelems_mod);
1130  }
1131  else
1132  {
1133  WerrorS("2nd module does not lie in the first");
1134  return NULL;
1135  }
1136  }
1137  if (unit!=NULL)
1138  {
1139  comps_to_add = idelems_submod;
1140  while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL))
1141  comps_to_add--;
1142  }
1144  if ((k!=0) && (lsmod==0)) lsmod=1;
1145  k=si_max(k,(int)mod->rank);
1146  if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; }
1147 
1148  ring orig_ring=currRing;
1149  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
1150  rSetSyzComp(k,syz_ring);
1151  rChangeCurrRing(syz_ring);
1152 
1153  ideal s_mod, s_temp;
1154  if (orig_ring != syz_ring)
1155  {
1156  s_mod = idrCopyR_NoSort(mod,orig_ring,syz_ring);
1157  s_temp = idrCopyR_NoSort(submod,orig_ring,syz_ring);
1158  }
1159  else
1160  {
1161  s_mod = mod;
1162  s_temp = idCopy(submod);
1163  }
1164  ideal s_h3;
1165  if (isSB)
1166  {
1167  s_h3 = idCopy(s_mod);
1168  idPrepareStd(s_h3, k+comps_to_add);
1169  }
1170  else
1171  {
1172  s_h3 = idPrepare(s_mod,NULL,(tHomog)FALSE,k+comps_to_add,NULL,alg);
1173  }
1174  if (!goodShape)
1175  {
1176  for (j=0;j<IDELEMS(s_h3);j++)
1177  {
1178  if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k))
1179  p_Delete(&(s_h3->m[j]),currRing);
1180  }
1181  }
1182  idSkipZeroes(s_h3);
1183  if (lsmod==0)
1184  {
1185  id_Shift(s_temp,1,currRing);
1186  }
1187  if (unit!=NULL)
1188  {
1189  for(j = 0;j<comps_to_add;j++)
1190  {
1191  p = s_temp->m[j];
1192  if (p!=NULL)
1193  {
1194  while (pNext(p)!=NULL) pIter(p);
1195  pNext(p) = pOne();
1196  pIter(p);
1197  pSetComp(p,1+j+k);
1198  pSetmComp(p);
1199  p = pNeg(p);
1200  }
1201  }
1202  s_temp->rank += (k+comps_to_add);
1203  }
1204  ideal s_result = kNF(s_h3,currRing->qideal,s_temp,k);
1205  s_result->rank = s_h3->rank;
1206  ideal s_rest = idInit(IDELEMS(s_result),k);
1207  idDelete(&s_h3);
1208  idDelete(&s_temp);
1209 
1210  for (j=0;j<IDELEMS(s_result);j++)
1211  {
1212  if (s_result->m[j]!=NULL)
1213  {
1214  if (pGetComp(s_result->m[j])<=k)
1215  {
1216  if (!divide)
1217  {
1218  if (rest==NULL)
1219  {
1220  if (isSB)
1221  {
1222  WarnS("first module not a standardbasis\n"
1223  "// ** or second not a proper submodule");
1224  }
1225  else
1226  WerrorS("2nd module does not lie in the first");
1227  }
1228  idDelete(&s_result);
1229  idDelete(&s_rest);
1230  if(syz_ring!=orig_ring)
1231  {
1232  idDelete(&s_mod);
1233  rChangeCurrRing(orig_ring);
1234  rDelete(syz_ring);
1235  }
1236  if (unit!=NULL)
1237  {
1238  idLift_setUnit(idelems_submod,unit);
1239  }
1240  if (rest!=NULL) *rest=idCopy(submod);
1241  s_result=idInit(idelems_submod,idelems_mod);
1242  return s_result;
1243  }
1244  else
1245  {
1246  p = s_rest->m[j] = s_result->m[j];
1247  while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p);
1248  s_result->m[j] = pNext(p);
1249  pNext(p) = NULL;
1250  }
1251  }
1252  p_Shift(&(s_result->m[j]),-k,currRing);
1253  pNeg(s_result->m[j]);
1254  }
1255  }
1256  if ((lsmod==0) && (s_rest!=NULL))
1257  {
1258  for (j=IDELEMS(s_rest);j>0;j--)
1259  {
1260  if (s_rest->m[j-1]!=NULL)
1261  {
1262  p_Shift(&(s_rest->m[j-1]),-1,currRing);
1263  }
1264  }
1265  }
1266  if(syz_ring!=orig_ring)
1267  {
1268  idDelete(&s_mod);
1269  rChangeCurrRing(orig_ring);
1270  s_result = idrMoveR_NoSort(s_result, syz_ring, orig_ring);
1271  s_rest = idrMoveR_NoSort(s_rest, syz_ring, orig_ring);
1272  rDelete(syz_ring);
1273  }
1274  if (rest!=NULL)
1275  {
1276  s_rest->rank=mod->rank;
1277  *rest = s_rest;
1278  }
1279  else
1280  idDelete(&s_rest);
1281  if (unit!=NULL)
1282  {
1283  *unit=mpNew(idelems_submod,idelems_submod);
1284  int i;
1285  for(i=0;i<IDELEMS(s_result);i++)
1286  {
1287  poly p=s_result->m[i];
1288  poly q=NULL;
1289  while(p!=NULL)
1290  {
1291  if(pGetComp(p)<=comps_to_add)
1292  {
1293  pSetComp(p,0);
1294  if (q!=NULL)
1295  {
1296  pNext(q)=pNext(p);
1297  }
1298  else
1299  {
1300  pIter(s_result->m[i]);
1301  }
1302  pNext(p)=NULL;
1303  MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p);
1304  if(q!=NULL) p=pNext(q);
1305  else p=s_result->m[i];
1306  }
1307  else
1308  {
1309  q=p;
1310  pIter(p);
1311  }
1312  }
1313  p_Shift(&s_result->m[i],-comps_to_add,currRing);
1314  }
1315  }
1316  s_result->rank=idelems_mod;
1317  return s_result;
1318 }
1319 
1320 /*2
1321 *computes division of P by Q with remainder up to (w-weighted) degree n
1322 *P, Q, and w are not changed
1323 */
1324 void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,int *w)
1325 {
1326  long N=0;
1327  int i;
1328  for(i=IDELEMS(Q)-1;i>=0;i--)
1329  if(w==NULL)
1330  N=si_max(N,p_Deg(Q->m[i],currRing));
1331  else
1332  N=si_max(N,p_DegW(Q->m[i],w,currRing));
1333  N+=n;
1334 
1335  T=mpNew(IDELEMS(Q),IDELEMS(P));
1336  R=idInit(IDELEMS(P),P->rank);
1337 
1338  for(i=IDELEMS(P)-1;i>=0;i--)
1339  {
1340  poly p;
1341  if(w==NULL)
1342  p=ppJet(P->m[i],N);
1343  else
1344  p=ppJetW(P->m[i],N,w);
1345 
1346  int j=IDELEMS(Q)-1;
1347  while(p!=NULL)
1348  {
1349  if(pDivisibleBy(Q->m[j],p))
1350  {
1351  poly p0=p_DivideM(pHead(p),pHead(Q->m[j]),currRing);
1352  if(w==NULL)
1353  p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N);
1354  else
1355  p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w);
1356  pNormalize(p);
1357  if(((w==NULL)&&(p_Deg(p0,currRing)>n))||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
1358  p_Delete(&p0,currRing);
1359  else
1360  MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0);
1361  j=IDELEMS(Q)-1;
1362  }
1363  else
1364  {
1365  if(j==0)
1366  {
1367  poly p0=p;
1368  pIter(p);
1369  pNext(p0)=NULL;
1370  if(((w==NULL)&&(p_Deg(p0,currRing)>n))
1371  ||((w!=NULL)&&(p_DegW(p0,w,currRing)>n)))
1372  p_Delete(&p0,currRing);
1373  else
1374  R->m[i]=pAdd(R->m[i],p0);
1375  j=IDELEMS(Q)-1;
1376  }
1377  else
1378  j--;
1379  }
1380  }
1381  }
1382 }
1383 
1384 /*2
1385 *computes the quotient of h1,h2 : internal routine for idQuot
1386 *BEWARE: the returned ideals may contain incorrectly ordered polys !
1387 *
1388 */
1389 static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
1390 {
1391  idTest(h1);
1392  idTest(h2);
1393 
1394  ideal temph1;
1395  poly p,q = NULL;
1396  int i,l,ll,k,kkk,kmax;
1397  int j = 0;
1398  int k1 = id_RankFreeModule(h1,currRing);
1399  int k2 = id_RankFreeModule(h2,currRing);
1400  tHomog hom=isNotHomog;
1401  k=si_max(k1,k2);
1402  if (k==0)
1403  k = 1;
1404  if ((k2==0) && (k>1)) *addOnlyOne = FALSE;
1405  intvec * weights;
1406  hom = (tHomog)idHomModule(h1,currRing->qideal,&weights);
1407  if /**addOnlyOne &&*/ (/*(*/ !h1IsStb /*)*/)
1408  temph1 = kStd(h1,currRing->qideal,hom,&weights,NULL);
1409  else
1410  temph1 = idCopy(h1);
1411  if (weights!=NULL) delete weights;
1412  idTest(temph1);
1413 /*--- making a single vector from h2 ---------------------*/
1414  for (i=0; i<IDELEMS(h2); i++)
1415  {
1416  if (h2->m[i] != NULL)
1417  {
1418  p = pCopy(h2->m[i]);
1419  if (k2 == 0)
1420  p_Shift(&p,j*k+1,currRing);
1421  else
1422  p_Shift(&p,j*k,currRing);
1423  q = pAdd(q,p);
1424  j++;
1425  }
1426  }
1427  *kkmax = kmax = j*k+1;
1428 /*--- adding a monomial for the result (syzygy) ----------*/
1429  p = q;
1430  while (pNext(p)!=NULL) pIter(p);
1431  pNext(p) = pOne();
1432  pIter(p);
1433  pSetComp(p,kmax);
1434  pSetmComp(p);
1435 /*--- constructing the big matrix ------------------------*/
1436  ideal h4 = idInit(k,kmax+k-1);
1437  h4->m[0] = q;
1438  if (k2 == 0)
1439  {
1440  for (i=1; i<k; i++)
1441  {
1442  if (h4->m[i-1]!=NULL)
1443  {
1444  p = p_Copy_noCheck(h4->m[i-1], currRing); /*h4->m[i-1]!=NULL*/
1445  p_Shift(&p,1,currRing);
1446  h4->m[i] = p;
1447  }
1448  else break;
1449  }
1450  }
1451  idSkipZeroes(h4);
1452  kkk = IDELEMS(h4);
1453  i = IDELEMS(temph1);
1454  for (l=0; l<i; l++)
1455  {
1456  if(temph1->m[l]!=NULL)
1457  {
1458  for (ll=0; ll<j; ll++)
1459  {
1460  p = pCopy(temph1->m[l]);
1461  if (k1 == 0)
1462  p_Shift(&p,ll*k+1,currRing);
1463  else
1464  p_Shift(&p,ll*k,currRing);
1465  if (kkk >= IDELEMS(h4))
1466  {
1467  pEnlargeSet(&(h4->m),IDELEMS(h4),16);
1468  IDELEMS(h4) += 16;
1469  }
1470  h4->m[kkk] = p;
1471  kkk++;
1472  }
1473  }
1474  }
1475 /*--- if h2 goes in as single vector - the h1-part is just SB ---*/
1476  if (*addOnlyOne)
1477  {
1478  idSkipZeroes(h4);
1479  p = h4->m[0];
1480  for (i=0;i<IDELEMS(h4)-1;i++)
1481  {
1482  h4->m[i] = h4->m[i+1];
1483  }
1484  h4->m[IDELEMS(h4)-1] = p;
1485  }
1486  idDelete(&temph1);
1487  //idTest(h4);//see remark at the beginning
1488  return h4;
1489 }
1490 
1491 /*2
1492 *computes the quotient of h1,h2
1493 */
1494 ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
1495 {
1496  // first check for special case h1:(0)
1497  if (idIs0(h2))
1498  {
1499  ideal res;
1500  if (resultIsIdeal)
1501  {
1502  res = idInit(1,1);
1503  res->m[0] = pOne();
1504  }
1505  else
1506  res = idFreeModule(h1->rank);
1507  return res;
1508  }
1509  int i, kmax;
1510  BOOLEAN addOnlyOne=TRUE;
1511  tHomog hom=isNotHomog;
1512  intvec * weights1;
1513 
1514  ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax);
1515 
1516  hom = (tHomog)idHomModule(s_h4,currRing->qideal,&weights1);
1517 
1518  ring orig_ring=currRing;
1519  ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE);
1520  rSetSyzComp(kmax-1,syz_ring);
1521  rChangeCurrRing(syz_ring);
1522  if (orig_ring!=syz_ring)
1523  // s_h4 = idrMoveR_NoSort(s_h4,orig_ring, syz_ring);
1524  s_h4 = idrMoveR(s_h4,orig_ring, syz_ring);
1525  idTest(s_h4);
1526 
1527  #if 0
1528  matrix m=idModule2Matrix(idCopy(s_h4));
1529  PrintS("start:\n");
1530  ipPrint_MA0(m,"Q");
1531  idDelete((ideal *)&m);
1532  PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn();
1533  #endif
1534 
1535  ideal s_h3;
1536  BITSET old_test1;
1537  SI_SAVE_OPT1(old_test1);
1539  if (addOnlyOne)
1540  {
1542  s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,0/*kmax-1*/,IDELEMS(s_h4)-1);
1543  }
1544  else
1545  {
1546  s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,kmax-1);
1547  }
1548  SI_RESTORE_OPT1(old_test1);
1549 
1550  #if 0
1551  // only together with the above debug stuff
1552  idSkipZeroes(s_h3);
1553  m=idModule2Matrix(idCopy(s_h3));
1554  Print("result, kmax=%d:\n",kmax);
1555  ipPrint_MA0(m,"S");
1556  idDelete((ideal *)&m);
1557  #endif
1558 
1559  idTest(s_h3);
1560  if (weights1!=NULL) delete weights1;
1561  idDelete(&s_h4);
1562 
1563  for (i=0;i<IDELEMS(s_h3);i++)
1564  {
1565  if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax))
1566  {
1567  if (resultIsIdeal)
1568  p_Shift(&s_h3->m[i],-kmax,currRing);
1569  else
1570  p_Shift(&s_h3->m[i],-kmax+1,currRing);
1571  }
1572  else
1573  p_Delete(&s_h3->m[i],currRing);
1574  }
1575  if (resultIsIdeal)
1576  s_h3->rank = 1;
1577  else
1578  s_h3->rank = h1->rank;
1579  if(syz_ring!=orig_ring)
1580  {
1581  rChangeCurrRing(orig_ring);
1582  s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring);
1583  rDelete(syz_ring);
1584  }
1585  idSkipZeroes(s_h3);
1586  idTest(s_h3);
1587  return s_h3;
1588 }
1589 
1590 /*2
1591 * eliminate delVar (product of vars) in h1
1592 */
1593 ideal idElimination (ideal h1,poly delVar,intvec *hilb, GbVariant alg)
1594 {
1595  int i,j=0,k,l;
1596  ideal h,hh, h3;
1597  rRingOrder_t *ord;
1598  int *block0,*block1;
1599  int ordersize=2;
1600  int **wv;
1601  tHomog hom;
1602  intvec * w;
1603  ring tmpR;
1604  ring origR = currRing;
1605 
1606  if (delVar==NULL)
1607  {
1608  return idCopy(h1);
1609  }
1610  if ((currRing->qideal!=NULL) && rIsPluralRing(origR))
1611  {
1612  WerrorS("cannot eliminate in a qring");
1613  return NULL;
1614  }
1615  if (idIs0(h1)) return idInit(1,h1->rank);
1616 #ifdef HAVE_PLURAL
1617  if (rIsPluralRing(origR))
1618  /* in the NC case, we have to check the admissibility of */
1619  /* the subalgebra to be intersected with */
1620  {
1621  if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */
1622  {
1623  if (nc_CheckSubalgebra(delVar,origR))
1624  {
1625  WerrorS("no elimination is possible: subalgebra is not admissible");
1626  return NULL;
1627  }
1628  }
1629  }
1630 #endif
1631  hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL
1632  h3=idInit(16,h1->rank);
1633  ordersize=rBlocks(origR)+1;
1634 #if 0
1635  if (rIsPluralRing(origR)) // we have too keep the odering: it may be needed
1636  // for G-algebra
1637  {
1638  for (k=0;k<ordersize-1; k++)
1639  {
1640  block0[k+1] = origR->block0[k];
1641  block1[k+1] = origR->block1[k];
1642  ord[k+1] = origR->order[k];
1643  if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
1644  }
1645  }
1646  else
1647  {
1648  block0[1] = 1;
1649  block1[1] = (currRing->N);
1650  if (origR->OrdSgn==1) ord[1] = ringorder_wp;
1651  else ord[1] = ringorder_ws;
1652  wv[1]=(int*)omAlloc0((currRing->N)*sizeof(int));
1653  double wNsqr = (double)2.0 / (double)(currRing->N);
1655  int *x= (int * )omAlloc(2 * ((currRing->N) + 1) * sizeof(int));
1656  int sl=IDELEMS(h1) - 1;
1657  wCall(h1->m, sl, x, wNsqr);
1658  for (sl = (currRing->N); sl!=0; sl--)
1659  wv[1][sl-1] = x[sl + (currRing->N) + 1];
1660  omFreeSize((ADDRESS)x, 2 * ((currRing->N) + 1) * sizeof(int));
1661 
1662  ord[2]=ringorder_C;
1663  ord[3]=0;
1664  }
1665 #else
1666 #endif
1667  if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR)))
1668  {
1669  #if 1
1670  // we change to an ordering:
1671  // aa(1,1,1,...,0,0,0),wp(...),C
1672  // this seems to be better than version 2 below,
1673  // according to Tst/../elimiate_[3568].tat (- 17 %)
1674  ord=(rRingOrder_t*)omAlloc0(4*sizeof(rRingOrder_t));
1675  block0=(int*)omAlloc0(4*sizeof(int));
1676  block1=(int*)omAlloc0(4*sizeof(int));
1677  wv=(int**) omAlloc0(4*sizeof(int**));
1678  block0[0] = block0[1] = 1;
1679  block1[0] = block1[1] = rVar(origR);
1680  wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1681  // use this special ordering: like ringorder_a, except that pFDeg, pWeights
1682  // ignore it
1683  ord[0] = ringorder_aa;
1684  for (j=0;j<rVar(origR);j++)
1685  if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
1686  BOOLEAN wp=FALSE;
1687  for (j=0;j<rVar(origR);j++)
1688  if (p_Weight(j+1,origR)!=1) { wp=TRUE;break; }
1689  if (wp)
1690  {
1691  wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1692  for (j=0;j<rVar(origR);j++)
1693  wv[1][j]=p_Weight(j+1,origR);
1694  ord[1] = ringorder_wp;
1695  }
1696  else
1697  ord[1] = ringorder_dp;
1698  #else
1699  // we change to an ordering:
1700  // a(w1,...wn),wp(1,...0.....),C
1701  ord=(int*)omAlloc0(4*sizeof(int));
1702  block0=(int*)omAlloc0(4*sizeof(int));
1703  block1=(int*)omAlloc0(4*sizeof(int));
1704  wv=(int**) omAlloc0(4*sizeof(int**));
1705  block0[0] = block0[1] = 1;
1706  block1[0] = block1[1] = rVar(origR);
1707  wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1708  wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1709  ord[0] = ringorder_a;
1710  for (j=0;j<rVar(origR);j++)
1711  wv[0][j]=pWeight(j+1,origR);
1712  ord[1] = ringorder_wp;
1713  for (j=0;j<rVar(origR);j++)
1714  if (pGetExp(delVar,j+1)!=0) wv[1][j]=1;
1715  #endif
1716  ord[2] = ringorder_C;
1717  ord[3] = (rRingOrder_t)0;
1718  }
1719  else
1720  {
1721  // we change to an ordering:
1722  // aa(....),orig_ordering
1723  ord=(rRingOrder_t*)omAlloc0(ordersize*sizeof(rRingOrder_t));
1724  block0=(int*)omAlloc0(ordersize*sizeof(int));
1725  block1=(int*)omAlloc0(ordersize*sizeof(int));
1726  wv=(int**) omAlloc0(ordersize*sizeof(int**));
1727  for (k=0;k<ordersize-1; k++)
1728  {
1729  block0[k+1] = origR->block0[k];
1730  block1[k+1] = origR->block1[k];
1731  ord[k+1] = origR->order[k];
1732  if (origR->wvhdl[k]!=NULL)
1733  #ifdef HAVE_OMALLOC
1734  wv[k+1] = (int*) omMemDup(origR->wvhdl[k]);
1735  #else
1736  {
1737  int l=(origR->block1[k]-origR->block0[k]+1)*sizeof(int);
1738  if (origR->order[k]==ringorder_a64) l*=2;
1739  wv[k+1]=(int*)omalloc(l);
1740  memcpy(wv[k+1],origR->wvhdl[k],l);
1741  }
1742  #endif
1743  }
1744  block0[0] = 1;
1745  block1[0] = rVar(origR);
1746  wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int));
1747  for (j=0;j<rVar(origR);j++)
1748  if (pGetExp(delVar,j+1)!=0) wv[0][j]=1;
1749  // use this special ordering: like ringorder_a, except that pFDeg, pWeights
1750  // ignore it
1751  ord[0] = ringorder_aa;
1752  }
1753  // fill in tmp ring to get back the data later on
1754  tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL
1755  //rUnComplete(tmpR);
1756  tmpR->p_Procs=NULL;
1757  tmpR->order = ord;
1758  tmpR->block0 = block0;
1759  tmpR->block1 = block1;
1760  tmpR->wvhdl = wv;
1761  rComplete(tmpR, 1);
1762 
1763 #ifdef HAVE_PLURAL
1764  /* update nc structure on tmpR */
1765  if (rIsPluralRing(origR))
1766  {
1767  if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal!
1768  {
1769  WerrorS("no elimination is possible: ordering condition is violated");
1770  // cleanup
1771  rDelete(tmpR);
1772  if (w!=NULL)
1773  delete w;
1774  return NULL;
1775  }
1776  }
1777 #endif
1778  // change into the new ring
1779  //pChangeRing((currRing->N),currRing->OrdSgn,ord,block0,block1,wv);
1780  rChangeCurrRing(tmpR);
1781 
1782  //h = idInit(IDELEMS(h1),h1->rank);
1783  // fetch data from the old ring
1784  //for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR);
1785  h=idrCopyR(h1,origR,currRing);
1786  if (origR->qideal!=NULL)
1787  {
1788  WarnS("eliminate in q-ring: experimental");
1789  ideal q=idrCopyR(origR->qideal,origR,currRing);
1790  ideal s=idSimpleAdd(h,q);
1791  idDelete(&h);
1792  idDelete(&q);
1793  h=s;
1794  }
1795  // compute GB
1796  if ((alg!=GbDefault)
1797  && (alg!=GbGroebner)
1798  && (alg!=GbModstd)
1799  && (alg!=GbSlimgb)
1800  && (alg!=GbSba)
1801  && (alg!=GbStd))
1802  {
1803  WarnS("wrong algorithm for GB");
1804  alg=GbDefault;
1805  }
1806  BITSET save2;
1807  SI_SAVE_OPT2(save2);
1809  hh=idGroebner(h,0,alg,hilb);
1810  SI_RESTORE_OPT2(save2);
1811  // go back to the original ring
1812  rChangeCurrRing(origR);
1813  i = IDELEMS(hh)-1;
1814  while ((i >= 0) && (hh->m[i] == NULL)) i--;
1815  j = -1;
1816  // fetch data from temp ring
1817  for (k=0; k<=i; k++)
1818  {
1819  l=(currRing->N);
1820  while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--;
1821  if (l==0)
1822  {
1823  j++;
1824  if (j >= IDELEMS(h3))
1825  {
1826  pEnlargeSet(&(h3->m),IDELEMS(h3),16);
1827  IDELEMS(h3) += 16;
1828  }
1829  h3->m[j] = prMoveR( hh->m[k], tmpR,origR);
1830  hh->m[k] = NULL;
1831  }
1832  }
1833  id_Delete(&hh, tmpR);
1834  idSkipZeroes(h3);
1835  rDelete(tmpR);
1836  if (w!=NULL)
1837  delete w;
1838  return h3;
1839 }
1840 
1841 #ifdef WITH_OLD_MINOR
1842 /*2
1843 * compute the which-th ar-minor of the matrix a
1844 */
1845 poly idMinor(matrix a, int ar, unsigned long which, ideal R)
1846 {
1847  int i,j/*,k,size*/;
1848  unsigned long curr;
1849  int *rowchoise,*colchoise;
1850  BOOLEAN rowch,colch;
1851  // ideal result;
1852  matrix tmp;
1853  poly p,q;
1854 
1855  rowchoise=(int *)omAlloc(ar*sizeof(int));
1856  colchoise=(int *)omAlloc(ar*sizeof(int));
1857  tmp=mpNew(ar,ar);
1858  curr = 0; /* index of current minor */
1859  idInitChoise(ar,1,a->rows(),&rowch,rowchoise);
1860  while (!rowch)
1861  {
1862  idInitChoise(ar,1,a->cols(),&colch,colchoise);
1863  while (!colch)
1864  {
1865  if (curr == which)
1866  {
1867  for (i=1; i<=ar; i++)
1868  {
1869  for (j=1; j<=ar; j++)
1870  {
1871  MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
1872  }
1873  }
1874  p = mp_DetBareiss(tmp,currRing);
1875  if (p!=NULL)
1876  {
1877  if (R!=NULL)
1878  {
1879  q = p;
1880  p = kNF(R,currRing->qideal,q);
1881  p_Delete(&q,currRing);
1882  }
1883  }
1884  /*delete the matrix tmp*/
1885  for (i=1; i<=ar; i++)
1886  {
1887  for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
1888  }
1889  idDelete((ideal*)&tmp);
1890  omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
1891  omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
1892  return (p);
1893  }
1894  curr++;
1895  idGetNextChoise(ar,a->cols(),&colch,colchoise);
1896  }
1897  idGetNextChoise(ar,a->rows(),&rowch,rowchoise);
1898  }
1899  return (poly) 1;
1900 }
1901 
1902 /*2
1903 * compute all ar-minors of the matrix a
1904 */
1905 ideal idMinors(matrix a, int ar, ideal R)
1906 {
1907  int i,j,/*k,*/size;
1908  int *rowchoise,*colchoise;
1909  BOOLEAN rowch,colch;
1910  ideal result;
1911  matrix tmp;
1912  poly p,q;
1913 
1914  i = binom(a->rows(),ar);
1915  j = binom(a->cols(),ar);
1916  size=i*j;
1917 
1918  rowchoise=(int *)omAlloc(ar*sizeof(int));
1919  colchoise=(int *)omAlloc(ar*sizeof(int));
1920  result=idInit(size,1);
1921  tmp=mpNew(ar,ar);
1922  // k = 0; /* the index in result*/
1923  idInitChoise(ar,1,a->rows(),&rowch,rowchoise);
1924  while (!rowch)
1925  {
1926  idInitChoise(ar,1,a->cols(),&colch,colchoise);
1927  while (!colch)
1928  {
1929  for (i=1; i<=ar; i++)
1930  {
1931  for (j=1; j<=ar; j++)
1932  {
1933  MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]);
1934  }
1935  }
1936  p = mp_DetBareiss(tmp,currRing);
1937  if (p!=NULL)
1938  {
1939  if (R!=NULL)
1940  {
1941  q = p;
1942  p = kNF(R,currRing->qideal,q);
1943  p_Delete(&q,currRing);
1944  }
1945  }
1946  if (k>=size)
1947  {
1948  pEnlargeSet(&result->m,size,32);
1949  size += 32;
1950  }
1951  result->m[k] = p;
1952  k++;
1953  idGetNextChoise(ar,a->cols(),&colch,colchoise);
1954  }
1955  idGetNextChoise(ar,a->rows(),&rowch,rowchoise);
1956  }
1957  /*delete the matrix tmp*/
1958  for (i=1; i<=ar; i++)
1959  {
1960  for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL;
1961  }
1962  idDelete((ideal*)&tmp);
1963  if (k==0)
1964  {
1965  k=1;
1966  result->m[0]=NULL;
1967  }
1968  omFreeSize((ADDRESS)rowchoise,ar*sizeof(int));
1969  omFreeSize((ADDRESS)colchoise,ar*sizeof(int));
1970  pEnlargeSet(&result->m,size,k-size);
1971  IDELEMS(result) = k;
1972  return (result);
1973 }
1974 #else
1975 
1976 
1977 /// compute all ar-minors of the matrix a
1978 /// the caller of mpRecMin
1979 /// the elements of the result are not in R (if R!=NULL)
1980 ideal idMinors(matrix a, int ar, ideal R)
1981 {
1982 
1983  const ring origR=currRing;
1984  id_Test((ideal)a, origR);
1985 
1986  const int r = a->nrows;
1987  const int c = a->ncols;
1988 
1989  if((ar<=0) || (ar>r) || (ar>c))
1990  {
1991  Werror("%d-th minor, matrix is %dx%d",ar,r,c);
1992  return NULL;
1993  }
1994 
1995  ideal h = id_Matrix2Module(mp_Copy(a,origR),origR);
1996  long bound = sm_ExpBound(h,c,r,ar,origR);
1997  id_Delete(&h, origR);
1998 
1999  ring tmpR = sm_RingChange(origR,bound);
2000 
2001  matrix b = mpNew(r,c);
2002 
2003  for (int i=r*c-1;i>=0;i--)
2004  if (a->m[i] != NULL)
2005  b->m[i] = prCopyR(a->m[i],origR,tmpR);
2006 
2007  id_Test( (ideal)b, tmpR);
2008 
2009  if (R!=NULL)
2010  {
2011  R = idrCopyR(R,origR,tmpR); // TODO: overwrites R? memory leak?
2012  //if (ar>1) // otherwise done in mpMinorToResult
2013  //{
2014  // matrix bb=(matrix)kNF(R,currRing->qideal,(ideal)b);
2015  // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols;
2016  // idDelete((ideal*)&b); b=bb;
2017  //}
2018  id_Test( R, tmpR);
2019  }
2020 
2021  int size=binom(r,ar)*binom(c,ar);
2022  ideal result = idInit(size,1);
2023 
2024  int elems = 0;
2025 
2026  if(ar>1)
2027  mp_RecMin(ar-1,result,elems,b,r,c,NULL,R,tmpR);
2028  else
2029  mp_MinorToResult(result,elems,b,r,c,R,tmpR);
2030 
2031  id_Test( (ideal)b, tmpR);
2032 
2033  id_Delete((ideal *)&b, tmpR);
2034 
2035  if (R!=NULL) id_Delete(&R,tmpR);
2036 
2037  rChangeCurrRing(origR);
2038  result = idrMoveR(result,tmpR,origR);
2039  sm_KillModifiedRing(tmpR);
2040  idTest(result);
2041  return result;
2042 }
2043 #endif
2044 
2045 /*2
2046 *returns TRUE if id1 is a submodule of id2
2047 */
2048 BOOLEAN idIsSubModule(ideal id1,ideal id2)
2049 {
2050  int i;
2051  poly p;
2052 
2053  if (idIs0(id1)) return TRUE;
2054  for (i=0;i<IDELEMS(id1);i++)
2055  {
2056  if (id1->m[i] != NULL)
2057  {
2058  p = kNF(id2,currRing->qideal,id1->m[i]);
2059  if (p != NULL)
2060  {
2061  p_Delete(&p,currRing);
2062  return FALSE;
2063  }
2064  }
2065  }
2066  return TRUE;
2067 }
2068 
2070 {
2071  if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
2072  if (idIs0(m)) return TRUE;
2073 
2074  int cmax=-1;
2075  int i;
2076  poly p=NULL;
2077  int length=IDELEMS(m);
2078  polyset P=m->m;
2079  for (i=length-1;i>=0;i--)
2080  {
2081  p=P[i];
2082  if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
2083  }
2084  if (w != NULL)
2085  if (w->length()+1 < cmax)
2086  {
2087  // Print("length: %d - %d \n", w->length(),cmax);
2088  return FALSE;
2089  }
2090 
2091  if(w!=NULL)
2093 
2094  for (i=length-1;i>=0;i--)
2095  {
2096  p=P[i];
2097  if (p!=NULL)
2098  {
2099  int d=currRing->pFDeg(p,currRing);
2100  loop
2101  {
2102  pIter(p);
2103  if (p==NULL) break;
2104  if (d!=currRing->pFDeg(p,currRing))
2105  {
2106  //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
2107  if(w!=NULL)
2109  return FALSE;
2110  }
2111  }
2112  }
2113  }
2114 
2115  if(w!=NULL)
2117 
2118  return TRUE;
2119 }
2120 
2121 ideal idSeries(int n,ideal M,matrix U,intvec *w)
2122 {
2123  for(int i=IDELEMS(M)-1;i>=0;i--)
2124  {
2125  if(U==NULL)
2126  M->m[i]=pSeries(n,M->m[i],NULL,w);
2127  else
2128  {
2129  M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w);
2130  MATELEM(U,i+1,i+1)=NULL;
2131  }
2132  }
2133  if(U!=NULL)
2134  idDelete((ideal*)&U);
2135  return M;
2136 }
2137 
2139 {
2140  int e=MATCOLS(i)*MATROWS(i);
2141  matrix r=mpNew(MATROWS(i),MATCOLS(i));
2142  r->rank=i->rank;
2143  int j;
2144  for(j=0; j<e; j++)
2145  {
2146  r->m[j]=pDiff(i->m[j],k);
2147  }
2148  return r;
2149 }
2150 
2151 matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply)
2152 {
2153  matrix r=mpNew(IDELEMS(I),IDELEMS(J));
2154  int i,j;
2155  for(i=0; i<IDELEMS(I); i++)
2156  {
2157  for(j=0; j<IDELEMS(J); j++)
2158  {
2159  MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply);
2160  }
2161  }
2162  return r;
2163 }
2164 
2165 /*3
2166 *handles for some ideal operations the ring/syzcomp management
2167 *returns all syzygies (componentwise-)shifted by -syzcomp
2168 *or -syzcomp-1 (in case of ideals as input)
2169 static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE)
2170 {
2171  ring orig_ring=currRing;
2172  ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); rChangeCurrRing(syz_ring);
2173  rSetSyzComp(length, syz_ring);
2174 
2175  ideal s_temp;
2176  if (orig_ring!=syz_ring)
2177  s_temp=idrMoveR_NoSort(arg,orig_ring, syz_ring);
2178  else
2179  s_temp=arg;
2180 
2181  ideal s_temp1 = kStd(s_temp,currRing->qideal,testHomog,&w,NULL,length);
2182  if (w!=NULL) delete w;
2183 
2184  if (syz_ring!=orig_ring)
2185  {
2186  idDelete(&s_temp);
2187  rChangeCurrRing(orig_ring);
2188  }
2189 
2190  idDelete(&temp);
2191  ideal temp1=idRingCopy(s_temp1,syz_ring);
2192 
2193  if (syz_ring!=orig_ring)
2194  {
2195  rChangeCurrRing(syz_ring);
2196  idDelete(&s_temp1);
2197  rChangeCurrRing(orig_ring);
2198  rDelete(syz_ring);
2199  }
2200 
2201  for (i=0;i<IDELEMS(temp1);i++)
2202  {
2203  if ((temp1->m[i]!=NULL)
2204  && (pGetComp(temp1->m[i])<=length))
2205  {
2206  pDelete(&(temp1->m[i]));
2207  }
2208  else
2209  {
2210  p_Shift(&(temp1->m[i]),-length,currRing);
2211  }
2212  }
2213  temp1->rank = rk;
2214  idSkipZeroes(temp1);
2215 
2216  return temp1;
2217 }
2218 */
2219 
2220 #ifdef HAVE_SHIFTBBA
2221 ideal idModuloLP (ideal h2,ideal h1, tHomog, intvec ** w, matrix *T, GbVariant alg)
2222 {
2223  intvec *wtmp=NULL;
2224  if (T!=NULL) idDelete((ideal*)T);
2225 
2226  int i,k,rk,flength=0,slength,length;
2227  poly p,q;
2228 
2229  if (idIs0(h2))
2230  return idFreeModule(si_max(1,h2->ncols));
2231  if (!idIs0(h1))
2232  flength = id_RankFreeModule(h1,currRing);
2233  slength = id_RankFreeModule(h2,currRing);
2234  length = si_max(flength,slength);
2235  if (length==0)
2236  {
2237  length = 1;
2238  }
2239  ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2));
2240  if ((w!=NULL)&&((*w)!=NULL))
2241  {
2242  //Print("input weights:");(*w)->show(1);PrintLn();
2243  int d;
2244  int k;
2245  wtmp=new intvec(length+IDELEMS(h2));
2246  for (i=0;i<length;i++)
2247  ((*wtmp)[i])=(**w)[i];
2248  for (i=0;i<IDELEMS(h2);i++)
2249  {
2250  poly p=h2->m[i];
2251  if (p!=NULL)
2252  {
2253  d = p_Deg(p,currRing);
2254  k= pGetComp(p);
2255  if (slength>0) k--;
2256  d +=((**w)[k]);
2257  ((*wtmp)[i+length]) = d;
2258  }
2259  }
2260  //Print("weights:");wtmp->show(1);PrintLn();
2261  }
2262  for (i=0;i<IDELEMS(h2);i++)
2263  {
2264  temp->m[i] = pCopy(h2->m[i]);
2265  q = pOne();
2266  // non multiplicative variable
2267  pSetExp(q, currRing->isLPring - currRing->LPncGenCount + i + 1, 1);
2268  p_Setm(q, currRing);
2269  pSetComp(q,i+1+length);
2270  pSetmComp(q);
2271  if(temp->m[i]!=NULL)
2272  {
2273  if (slength==0) p_Shift(&(temp->m[i]),1,currRing);
2274  p = temp->m[i];
2275  temp->m[i] = pAdd(p, q);
2276  }
2277  else
2278  temp->m[i]=q;
2279  }
2280  rk = k = IDELEMS(h2);
2281  if (!idIs0(h1))
2282  {
2283  pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1));
2284  IDELEMS(temp) += IDELEMS(h1);
2285  for (i=0;i<IDELEMS(h1);i++)
2286  {
2287  if (h1->m[i]!=NULL)
2288  {
2289  temp->m[k] = pCopy(h1->m[i]);
2290  if (flength==0) p_Shift(&(temp->m[k]),1,currRing);
2291  k++;
2292  }
2293  }
2294  }
2295 
2296  ring orig_ring=currRing;
2297  ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE);
2298  rSetSyzComp(length,syz_ring);
2299  rChangeCurrRing(syz_ring);
2300  // we can use OPT_RETURN_SB only, if syz_ring==orig_ring,
2301  // therefore we disable OPT_RETURN_SB for modulo:
2302  // (see tr. #701)
2303  //if (TEST_OPT_RETURN_SB)
2304  // rSetSyzComp(IDELEMS(h2)+length, syz_ring);
2305  //else
2306  // rSetSyzComp(length, syz_ring);
2307  ideal s_temp;
2308 
2309  if (syz_ring != orig_ring)
2310  {
2311  s_temp = idrMoveR_NoSort(temp, orig_ring, syz_ring);
2312  }
2313  else
2314  {
2315  s_temp = temp;
2316  }
2317 
2318  idTest(s_temp);
2319  unsigned save_opt,save_opt2;
2320  SI_SAVE_OPT1(save_opt);
2321  SI_SAVE_OPT2(save_opt2);
2322  if (T==NULL) si_opt_1 |= Sy_bit(OPT_REDTAIL_SYZ);
2324  ideal s_temp1 = idGroebner(s_temp,length,alg);
2325  SI_RESTORE_OPT1(save_opt);
2326  SI_RESTORE_OPT2(save_opt2);
2327 
2328  //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn();
2329  if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL))
2330  {
2331  delete *w;
2332  *w=new intvec(IDELEMS(h2));
2333  for (i=0;i<IDELEMS(h2);i++)
2334  ((**w)[i])=(*wtmp)[i+length];
2335  }
2336  if (wtmp!=NULL) delete wtmp;
2337 
2338  if (T==NULL)
2339  {
2340  for (i=0;i<IDELEMS(s_temp1);i++)
2341  {
2342  if (s_temp1->m[i]!=NULL)
2343  {
2344  if (((int)pGetComp(s_temp1->m[i]))<=length)
2345  {
2346  p_Delete(&(s_temp1->m[i]),currRing);
2347  }
2348  else
2349  {
2350  p_Shift(&(s_temp1->m[i]),-length,currRing);
2351  }
2352  }
2353  }
2354  }
2355  else
2356  {
2357  *T=mpNew(IDELEMS(s_temp1),IDELEMS(h2));
2358  for (i=0;i<IDELEMS(s_temp1);i++)
2359  {
2360  if (s_temp1->m[i]!=NULL)
2361  {
2362  if (((int)pGetComp(s_temp1->m[i]))<=length)
2363  {
2364  do
2365  {
2366  p_LmDelete(&(s_temp1->m[i]),currRing);
2367  } while((int)pGetComp(s_temp1->m[i])<=length);
2368  poly q = prMoveR( s_temp1->m[i], syz_ring,orig_ring);
2369  s_temp1->m[i] = NULL;
2370  if (q!=NULL)
2371  {
2372  q=pReverse(q);
2373  do
2374  {
2375  poly p = q;
2376  long t=pGetComp(p);
2377  pIter(q);
2378  pNext(p) = NULL;
2379  pSetComp(p,0);
2380  pSetmComp(p);
2381  pTest(p);
2382  MATELEM(*T,(int)t-length,i) = pAdd(MATELEM(*T,(int)t-length,i),p);
2383  } while (q != NULL);
2384  }
2385  }
2386  else
2387  {
2388  p_Shift(&(s_temp1->m[i]),-length,currRing);
2389  }
2390  }
2391  }
2392  }
2393  s_temp1->rank = rk;
2394  idSkipZeroes(s_temp1);
2395 
2396  if (syz_ring!=orig_ring)
2397  {
2398  rChangeCurrRing(orig_ring);
2399  s_temp1 = idrMoveR_NoSort(s_temp1, syz_ring, orig_ring);
2400  rDelete(syz_ring);
2401  // Hmm ... here seems to be a memory leak
2402  // However, simply deleting it causes memory trouble
2403  // idDelete(&s_temp);
2404  }
2405  idTest(s_temp1);
2406  return s_temp1;
2407 }
2408 #endif
2409 
2410 /*2
2411 * represents (h1+h2)/h2=h1/(h1 intersect h2)
2412 */
2413 //ideal idModulo (ideal h2,ideal h1)
2414 ideal idModulo (ideal h2,ideal h1, tHomog hom, intvec ** w, matrix *T, GbVariant alg)
2415 {
2416 #ifdef HAVE_SHIFTBBA
2417  if (rIsLPRing(currRing))
2418  return idModuloLP(h2,h1,hom,w,T,alg);
2419 #endif
2420  intvec *wtmp=NULL;
2421  if (T!=NULL) idDelete((ideal*)T);
2422 
2423  int i,flength=0,slength,length;
2424 
2425  if (idIs0(h2))
2426  return idFreeModule(si_max(1,h2->ncols));
2427  if (!idIs0(h1))
2428  flength = id_RankFreeModule(h1,currRing);
2429  slength = id_RankFreeModule(h2,currRing);
2430  length = si_max(flength,slength);
2431  BOOLEAN inputIsIdeal=FALSE;
2432  if (length==0)
2433  {
2434  length = 1;
2435  inputIsIdeal=TRUE;
2436  }
2437  if ((w!=NULL)&&((*w)!=NULL))
2438  {
2439  //Print("input weights:");(*w)->show(1);PrintLn();
2440  int d;
2441  int k;
2442  wtmp=new intvec(length+IDELEMS(h2));
2443  for (i=0;i<length;i++)
2444  ((*wtmp)[i])=(**w)[i];
2445  for (i=0;i<IDELEMS(h2);i++)
2446  {
2447  poly p=h2->m[i];
2448  if (p!=NULL)
2449  {
2450  d = p_Deg(p,currRing);
2451  k= pGetComp(p);
2452  if (slength>0) k--;
2453  d +=((**w)[k]);
2454  ((*wtmp)[i+length]) = d;
2455  }
2456  }
2457  //Print("weights:");wtmp->show(1);PrintLn();
2458  }
2459  ideal s_temp1;
2460  ring orig_ring=currRing;
2461  ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE);
2462  rSetSyzComp(length,syz_ring);
2463  {
2464  rChangeCurrRing(syz_ring);
2465  ideal s1,s2;
2466 
2467  if (syz_ring != orig_ring)
2468  {
2469  s1 = idrCopyR_NoSort(h1, orig_ring, syz_ring);
2470  s2 = idrCopyR_NoSort(h2, orig_ring, syz_ring);
2471  }
2472  else
2473  {
2474  s1=idCopy(h1);
2475  s2=idCopy(h2);
2476  }
2477 
2478  unsigned save_opt,save_opt2;
2479  SI_SAVE_OPT1(save_opt);
2480  SI_SAVE_OPT2(save_opt2);
2481  if (T==NULL) si_opt_1 |= Sy_bit(OPT_REDTAIL);
2483  s_temp1 = idPrepare(s2,s1,testHomog,length,w,alg);
2484  SI_RESTORE_OPT1(save_opt);
2485  SI_RESTORE_OPT2(save_opt2);
2486  }
2487 
2488  //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn();
2489  if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL))
2490  {
2491  delete *w;
2492  *w=new intvec(IDELEMS(h2));
2493  for (i=0;i<IDELEMS(h2);i++)
2494  ((**w)[i])=(*wtmp)[i+length];
2495  }
2496  if (wtmp!=NULL) delete wtmp;
2497 
2498  ideal result=idInit(IDELEMS(s_temp1),IDELEMS(h2));
2499  s_temp1=idExtractG_T_S(s_temp1,T,&result,length,IDELEMS(h2),inputIsIdeal,orig_ring,syz_ring);
2500 
2501  idDelete(&s_temp1);
2502  if (syz_ring!=orig_ring)
2503  {
2504  rDelete(syz_ring);
2505  }
2506  idTest(h2);
2507  idTest(h1);
2508  idTest(result);
2509  if (T!=NULL) idTest((ideal)*T);
2510  return result;
2511 }
2512 
2513 /*
2514 *computes module-weights for liftings of homogeneous modules
2515 */
2516 #if 0
2517 static intvec * idMWLift(ideal mod,intvec * weights)
2518 {
2519  if (idIs0(mod)) return new intvec(2);
2520  int i=IDELEMS(mod);
2521  while ((i>0) && (mod->m[i-1]==NULL)) i--;
2522  intvec *result = new intvec(i+1);
2523  while (i>0)
2524  {
2525  (*result)[i]=currRing->pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])];
2526  }
2527  return result;
2528 }
2529 #endif
2530 
2531 /*2
2532 *sorts the kbase for idCoef* in a special way (lexicographically
2533 *with x_max,...,x_1)
2534 */
2535 ideal idCreateSpecialKbase(ideal kBase,intvec ** convert)
2536 {
2537  int i;
2538  ideal result;
2539 
2540  if (idIs0(kBase)) return NULL;
2541  result = idInit(IDELEMS(kBase),kBase->rank);
2542  *convert = idSort(kBase,FALSE);
2543  for (i=0;i<(*convert)->length();i++)
2544  {
2545  result->m[i] = pCopy(kBase->m[(**convert)[i]-1]);
2546  }
2547  return result;
2548 }
2549 
2550 /*2
2551 *returns the index of a given monom in the list of the special kbase
2552 */
2553 int idIndexOfKBase(poly monom, ideal kbase)
2554 {
2555  int j=IDELEMS(kbase);
2556 
2557  while ((j>0) && (kbase->m[j-1]==NULL)) j--;
2558  if (j==0) return -1;
2559  int i=(currRing->N);
2560  while (i>0)
2561  {
2562  loop
2563  {
2564  if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1;
2565  if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break;
2566  j--;
2567  if (j==0) return -1;
2568  }
2569  if (i==1)
2570  {
2571  while(j>0)
2572  {
2573  if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1;
2574  if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1;
2575  j--;
2576  }
2577  }
2578  i--;
2579  }
2580  return -1;
2581 }
2582 
2583 /*2
2584 *decomposes the monom in a part of coefficients described by the
2585 *complement of how and a monom in variables occurring in how, the
2586 *index of which in kbase is returned as integer pos (-1 if it don't
2587 *exists)
2588 */
2589 poly idDecompose(poly monom, poly how, ideal kbase, int * pos)
2590 {
2591  int i;
2592  poly coeff=pOne(), base=pOne();
2593 
2594  for (i=1;i<=(currRing->N);i++)
2595  {
2596  if (pGetExp(how,i)>0)
2597  {
2598  pSetExp(base,i,pGetExp(monom,i));
2599  }
2600  else
2601  {
2602  pSetExp(coeff,i,pGetExp(monom,i));
2603  }
2604  }
2605  pSetComp(base,pGetComp(monom));
2606  pSetm(base);
2607  pSetCoeff(coeff,nCopy(pGetCoeff(monom)));
2608  pSetm(coeff);
2609  *pos = idIndexOfKBase(base,kbase);
2610  if (*pos<0)
2611  p_Delete(&coeff,currRing);
2613  return coeff;
2614 }
2615 
2616 /*2
2617 *returns a matrix A of coefficients with kbase*A=arg
2618 *if all monomials in variables of how occur in kbase
2619 *the other are deleted
2620 */
2621 matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
2622 {
2623  matrix result;
2624  ideal tempKbase;
2625  poly p,q;
2626  intvec * convert;
2627  int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos;
2628 #if 0
2629  while ((i>0) && (kbase->m[i-1]==NULL)) i--;
2630  if (idIs0(arg))
2631  return mpNew(i,1);
2632  while ((j>0) && (arg->m[j-1]==NULL)) j--;
2633  result = mpNew(i,j);
2634 #else
2635  result = mpNew(i, j);
2636  while ((j>0) && (arg->m[j-1]==NULL)) j--;
2637 #endif
2638 
2639  tempKbase = idCreateSpecialKbase(kbase,&convert);
2640  for (k=0;k<j;k++)
2641  {
2642  p = arg->m[k];
2643  while (p!=NULL)
2644  {
2645  q = idDecompose(p,how,tempKbase,&pos);
2646  if (pos>=0)
2647  {
2648  MATELEM(result,(*convert)[pos],k+1) =
2649  pAdd(MATELEM(result,(*convert)[pos],k+1),q);
2650  }
2651  else
2652  p_Delete(&q,currRing);
2653  pIter(p);
2654  }
2655  }
2656  idDelete(&tempKbase);
2657  return result;
2658 }
2659 
2660 static void idDeleteComps(ideal arg,int* red_comp,int del)
2661 // red_comp is an array [0..args->rank]
2662 {
2663  int i,j;
2664  poly p;
2665 
2666  for (i=IDELEMS(arg)-1;i>=0;i--)
2667  {
2668  p = arg->m[i];
2669  while (p!=NULL)
2670  {
2671  j = pGetComp(p);
2672  if (red_comp[j]!=j)
2673  {
2674  pSetComp(p,red_comp[j]);
2675  pSetmComp(p);
2676  }
2677  pIter(p);
2678  }
2679  }
2680  (arg->rank) -= del;
2681 }
2682 
2683 /*2
2684 * returns the presentation of an isomorphic, minimally
2685 * embedded module (arg represents the quotient!)
2686 */
2687 ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w)
2688 {
2689  if (idIs0(arg)) return idInit(1,arg->rank);
2690  int i,next_gen,next_comp;
2691  ideal res=arg;
2692  if (!inPlace) res = idCopy(arg);
2693  res->rank=si_max(res->rank,id_RankFreeModule(res,currRing));
2694  int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int));
2695  for (i=res->rank;i>=0;i--) red_comp[i]=i;
2696 
2697  int del=0;
2698  loop
2699  {
2700  next_gen = id_ReadOutPivot(res, &next_comp, currRing);
2701  if (next_gen<0) break;
2702  del++;
2703  syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res));
2704  for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--;
2705  if ((w !=NULL)&&(*w!=NULL))
2706  {
2707  for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i];
2708  }
2709  }
2710 
2711  idDeleteComps(res,red_comp,del);
2712  idSkipZeroes(res);
2713  omFree(red_comp);
2714 
2715  if ((w !=NULL)&&(*w!=NULL) &&(del>0))
2716  {
2717  int nl=si_max((*w)->length()-del,1);
2718  intvec *wtmp=new intvec(nl);
2719  for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i];
2720  delete *w;
2721  *w=wtmp;
2722  }
2723  return res;
2724 }
2725 
2726 #include "polys/clapsing.h"
2727 
2728 #if 0
2729 poly id_GCD(poly f, poly g, const ring r)
2730 {
2731  ring save_r=currRing;
2732  rChangeCurrRing(r);
2733  ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
2734  intvec *w = NULL;
2735  ideal S=idSyzygies(I,testHomog,&w);
2736  if (w!=NULL) delete w;
2737  poly gg=pTakeOutComp(&(S->m[0]),2);
2738  idDelete(&S);
2739  poly gcd_p=singclap_pdivide(f,gg,r);
2740  p_Delete(&gg,r);
2741  rChangeCurrRing(save_r);
2742  return gcd_p;
2743 }
2744 #else
2745 poly id_GCD(poly f, poly g, const ring r)
2746 {
2747  ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g;
2748  intvec *w = NULL;
2749 
2750  ring save_r = currRing;
2751  rChangeCurrRing(r);
2752  ideal S=idSyzygies(I,testHomog,&w);
2753  rChangeCurrRing(save_r);
2754 
2755  if (w!=NULL) delete w;
2756  poly gg=p_TakeOutComp(&(S->m[0]), 2, r);
2757  id_Delete(&S, r);
2758  poly gcd_p=singclap_pdivide(f,gg, r);
2759  p_Delete(&gg, r);
2760 
2761  return gcd_p;
2762 }
2763 #endif
2764 
2765 #if 0
2766 /*2
2767 * xx,q: arrays of length 0..rl-1
2768 * xx[i]: SB mod q[i]
2769 * assume: char=0
2770 * assume: q[i]!=0
2771 * destroys xx
2772 */
2773 ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring R)
2774 {
2775  int cnt=IDELEMS(xx[0])*xx[0]->nrows;
2776  ideal result=idInit(cnt,xx[0]->rank);
2777  result->nrows=xx[0]->nrows; // for lifting matrices
2778  result->ncols=xx[0]->ncols; // for lifting matrices
2779  int i,j;
2780  poly r,h,hh,res_p;
2781  number *x=(number *)omAlloc(rl*sizeof(number));
2782  for(i=cnt-1;i>=0;i--)
2783  {
2784  res_p=NULL;
2785  loop
2786  {
2787  r=NULL;
2788  for(j=rl-1;j>=0;j--)
2789  {
2790  h=xx[j]->m[i];
2791  if ((h!=NULL)
2792  &&((r==NULL)||(p_LmCmp(r,h,R)==-1)))
2793  r=h;
2794  }
2795  if (r==NULL) break;
2796  h=p_Head(r, R);
2797  for(j=rl-1;j>=0;j--)
2798  {
2799  hh=xx[j]->m[i];
2800  if ((hh!=NULL) && (p_LmCmp(r,hh, R)==0))
2801  {
2802  x[j]=p_GetCoeff(hh, R);
2803  hh=p_LmFreeAndNext(hh, R);
2804  xx[j]->m[i]=hh;
2805  }
2806  else
2807  x[j]=n_Init(0, R->cf); // is R->cf really n_Q???, yes!
2808  }
2809 
2810  number n=n_ChineseRemainder(x,q,rl, R->cf);
2811 
2812  for(j=rl-1;j>=0;j--)
2813  {
2814  x[j]=NULL; // nlInit(0...) takes no memory
2815  }
2816  if (n_IsZero(n, R->cf)) p_Delete(&h, R);
2817  else
2818  {
2819  p_SetCoeff(h,n, R);
2820  //Print("new mon:");pWrite(h);
2821  res_p=p_Add_q(res_p, h, R);
2822  }
2823  }
2824  result->m[i]=res_p;
2825  }
2826  omFree(x);
2827  for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]), R);
2828  omFree(xx);
2829  return result;
2830 }
2831 #endif
2832 /* currently unused:
2833 ideal idChineseRemainder(ideal *xx, intvec *iv)
2834 {
2835  int rl=iv->length();
2836  number *q=(number *)omAlloc(rl*sizeof(number));
2837  int i;
2838  for(i=0; i<rl; i++)
2839  {
2840  q[i]=nInit((*iv)[i]);
2841  }
2842  return idChineseRemainder(xx,q,rl);
2843 }
2844 */
2845 /*
2846  * lift ideal with coeffs over Z (mod N) to Q via Farey
2847  */
2848 ideal id_Farey(ideal x, number N, const ring r)
2849 {
2850  int cnt=IDELEMS(x)*x->nrows;
2851  ideal result=idInit(cnt,x->rank);
2852  result->nrows=x->nrows; // for lifting matrices
2853  result->ncols=x->ncols; // for lifting matrices
2854 
2855  int i;
2856  for(i=cnt-1;i>=0;i--)
2857  {
2858  result->m[i]=p_Farey(x->m[i],N,r);
2859  }
2860  return result;
2861 }
2862 
2863 
2864 
2865 
2866 // uses glabl vars via pSetModDeg
2867 /*
2868 BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
2869 {
2870  if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;}
2871  if (idIs0(m)) return TRUE;
2872 
2873  int cmax=-1;
2874  int i;
2875  poly p=NULL;
2876  int length=IDELEMS(m);
2877  poly* P=m->m;
2878  for (i=length-1;i>=0;i--)
2879  {
2880  p=P[i];
2881  if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1);
2882  }
2883  if (w != NULL)
2884  if (w->length()+1 < cmax)
2885  {
2886  // Print("length: %d - %d \n", w->length(),cmax);
2887  return FALSE;
2888  }
2889 
2890  if(w!=NULL)
2891  p_SetModDeg(w, currRing);
2892 
2893  for (i=length-1;i>=0;i--)
2894  {
2895  p=P[i];
2896  poly q=p;
2897  if (p!=NULL)
2898  {
2899  int d=p_FDeg(p,currRing);
2900  loop
2901  {
2902  pIter(p);
2903  if (p==NULL) break;
2904  if (d!=p_FDeg(p,currRing))
2905  {
2906  //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing));
2907  if(w!=NULL)
2908  p_SetModDeg(NULL, currRing);
2909  return FALSE;
2910  }
2911  }
2912  }
2913  }
2914 
2915  if(w!=NULL)
2916  p_SetModDeg(NULL, currRing);
2917 
2918  return TRUE;
2919 }
2920 */
2921 
2922 /// keeps the first k (>= 1) entries of the given ideal
2923 /// (Note that the kept polynomials may be zero.)
2924 void idKeepFirstK(ideal id, const int k)
2925 {
2926  for (int i = IDELEMS(id)-1; i >= k; i--)
2927  {
2928  if (id->m[i] != NULL) pDelete(&id->m[i]);
2929  }
2930  int kk=k;
2931  if (k==0) kk=1; /* ideals must have at least one element(0)*/
2932  pEnlargeSet(&(id->m), IDELEMS(id), kk-IDELEMS(id));
2933  IDELEMS(id) = kk;
2934 }
2935 
2936 typedef struct
2937 {
2938  poly p;
2939  int index;
2940 } poly_sort;
2941 
2942 int pCompare_qsort(const void *a, const void *b)
2943 {
2944  return (p_Compare(((poly_sort *)a)->p, ((poly_sort *)b)->p,currRing));
2945 }
2946 
2947 void idSort_qsort(poly_sort *id_sort, int idsize)
2948 {
2949  qsort(id_sort, idsize, sizeof(poly_sort), pCompare_qsort);
2950 }
2951 
2952 /*2
2953 * ideal id = (id[i])
2954 * if id[i] = id[j] then id[j] is deleted for j > i
2955 */
2956 void idDelEquals(ideal id)
2957 {
2958  int idsize = IDELEMS(id);
2959  poly_sort *id_sort = (poly_sort *)omAlloc0(idsize*sizeof(poly_sort));
2960  for (int i = 0; i < idsize; i++)
2961  {
2962  id_sort[i].p = id->m[i];
2963  id_sort[i].index = i;
2964  }
2965  idSort_qsort(id_sort, idsize);
2966  int index, index_i, index_j;
2967  int i = 0;
2968  for (int j = 1; j < idsize; j++)
2969  {
2970  if (id_sort[i].p != NULL && pEqualPolys(id_sort[i].p, id_sort[j].p))
2971  {
2972  index_i = id_sort[i].index;
2973  index_j = id_sort[j].index;
2974  if (index_j > index_i)
2975  {
2976  index = index_j;
2977  }
2978  else
2979  {
2980  index = index_i;
2981  i = j;
2982  }
2983  pDelete(&id->m[index]);
2984  }
2985  else
2986  {
2987  i = j;
2988  }
2989  }
2990  omFreeSize((ADDRESS)(id_sort), idsize*sizeof(poly_sort));
2991 }
2992 
2994 
2996 {
2997  BOOLEAN b = FALSE; // set b to TRUE, if spoly was changed,
2998  // let it remain FALSE otherwise
2999  if (strat->P.t_p==NULL)
3000  {
3001  poly p=strat->P.p;
3002 
3003  // iterate over all terms of p and
3004  // compute the minimum mm of all exponent vectors
3005  int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int));
3006  int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
3007  p_GetExpV(p,mm,currRing);
3008  bool nonTrivialSaturationToBeDone=true;
3009  for (p=pNext(p); p!=NULL; pIter(p))
3010  {
3011  nonTrivialSaturationToBeDone=false;
3012  p_GetExpV(p,m0,currRing);
3013  for (int i=rVar(currRing); i>0; i--)
3014  {
3016  {
3017  mm[i]=si_min(mm[i],m0[i]);
3018  if (mm[i]>0) nonTrivialSaturationToBeDone=true;
3019  }
3020  else mm[i]=0;
3021  }
3022  // abort if the minimum is zero in each component
3023  if (!nonTrivialSaturationToBeDone) break;
3024  }
3025  if (nonTrivialSaturationToBeDone)
3026  {
3027  // std::cout << "simplifying!" << std::endl;
3028  if (TEST_OPT_PROT) { PrintS("S"); mflush(); }
3029  p=p_Copy(strat->P.p,currRing);
3030  //pWrite(p);
3031  // for (int i=rVar(currRing); i>0; i--)
3032  // if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]);
3033  //PrintLn();
3034  strat->P.Init(currRing);
3035  //memset(&strat->P,0,sizeof(strat->P));
3036  strat->P.tailRing = strat->tailRing;
3037  strat->P.p=p;
3038  while(p!=NULL)
3039  {
3040  for (int i=rVar(currRing); i>0; i--)
3041  {
3042  p_SubExp(p,i,mm[i],currRing);
3043  }
3044  p_Setm(p,currRing);
3045  pIter(p);
3046  }
3047  b = TRUE;
3048  }
3049  omFree(mm);
3050  omFree(m0);
3051  }
3052  else
3053  {
3054  poly p=strat->P.t_p;
3055 
3056  // iterate over all terms of p and
3057  // compute the minimum mm of all exponent vectors
3058  int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int));
3059  int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
3060  p_GetExpV(p,mm,strat->tailRing);
3061  bool nonTrivialSaturationToBeDone=true;
3062  for (p = pNext(p); p!=NULL; pIter(p))
3063  {
3064  nonTrivialSaturationToBeDone=false;
3065  p_GetExpV(p,m0,strat->tailRing);
3066  for(int i=rVar(currRing); i>0; i--)
3067  {
3069  {
3070  mm[i]=si_min(mm[i],m0[i]);
3071  if (mm[i]>0) nonTrivialSaturationToBeDone = true;
3072  }
3073  else mm[i]=0;
3074  }
3075  // abort if the minimum is zero in each component
3076  if (!nonTrivialSaturationToBeDone) break;
3077  }
3078  if (nonTrivialSaturationToBeDone)
3079  {
3080  if (TEST_OPT_PROT) { PrintS("S"); mflush(); }
3081  p=p_Copy(strat->P.t_p,strat->tailRing);
3082  //p_Write(p,strat->tailRing);
3083  // for (int i=rVar(currRing); i>0; i--)
3084  // if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]);
3085  //PrintLn();
3086  strat->P.Init(currRing);
3087  //memset(&strat->P,0,sizeof(strat->P));
3088  strat->P.tailRing = strat->tailRing;
3089  strat->P.t_p=p;
3090  while(p!=NULL)
3091  {
3092  for(int i=rVar(currRing); i>0; i--)
3093  {
3094  p_SubExp(p,i,mm[i],strat->tailRing);
3095  }
3096  p_Setm(p,strat->tailRing);
3097  pIter(p);
3098  }
3099  strat->P.GetP();
3100  b = TRUE;
3101  }
3102  omFree(mm);
3103  omFree(m0);
3104  }
3105  return b; // return TRUE if sp was changed, FALSE if not
3106 }
3107 
3108 ideal id_Satstd(const ideal I, ideal J, const ring r)
3109 {
3110  ring save=currRing;
3111  if (currRing!=r) rChangeCurrRing(r);
3112  idSkipZeroes(J);
3113  id_satstdSaturatingVariables=(int*)omAlloc0((1+rVar(currRing))*sizeof(int));
3114  int k=IDELEMS(J);
3115  if (k>1)
3116  {
3117  for (int i=0; i<k; i++)
3118  {
3119  poly x = J->m[i];
3120  int li = p_Var(x,r);
3121  if (li>0)
3123  else
3124  {
3125  if (currRing!=save) rChangeCurrRing(save);
3126  WerrorS("ideal generators must be variables");
3127  return NULL;
3128  }
3129  }
3130  }
3131  else
3132  {
3133  poly x = J->m[0];
3134  for (int i=1; i<=r->N; i++)
3135  {
3136  int li = p_GetExp(x,i,r);
3137  if (li==1)
3139  else if (li>1)
3140  {
3141  if (currRing!=save) rChangeCurrRing(save);
3142  Werror("exponent(x(%d)^%d) must be 0 or 1",i,li);
3143  return NULL;
3144  }
3145  }
3146  }
3147  ideal res=kStd(I,r->qideal,testHomog,NULL,NULL,0,0,NULL,id_sat_vars_sp);
3150  if (currRing!=save) rChangeCurrRing(save);
3151  return res;
3152 }
3153 
3154 GbVariant syGetAlgorithm(char *n, const ring r, const ideal /*M*/)
3155 {
3156  GbVariant alg=GbDefault;
3157  if (strcmp(n,"default")==0) alg=GbDefault;
3158  else if (strcmp(n,"slimgb")==0) alg=GbSlimgb;
3159  else if (strcmp(n,"std")==0) alg=GbStd;
3160  else if (strcmp(n,"sba")==0) alg=GbSba;
3161  else if (strcmp(n,"singmatic")==0) alg=GbSingmatic;
3162  else if (strcmp(n,"groebner")==0) alg=GbGroebner;
3163  else if (strcmp(n,"modstd")==0) alg=GbModstd;
3164  else if (strcmp(n,"ffmod")==0) alg=GbFfmod;
3165  else if (strcmp(n,"nfmod")==0) alg=GbNfmod;
3166  else if (strcmp(n,"std:sat")==0) alg=GbStdSat;
3167  else Warn(">>%s<< is an unknown algorithm",n);
3168 
3169  if (alg==GbSlimgb) // test conditions for slimgb
3170  {
3171  if(rHasGlobalOrdering(r)
3172  &&(!rIsNCRing(r))
3173  &&(r->qideal==NULL)
3174  &&(!rField_is_Ring(r)))
3175  {
3176  return GbSlimgb;
3177  }
3178  if (TEST_OPT_PROT)
3179  WarnS("requires: coef:field, commutative, global ordering, not qring");
3180  }
3181  else if (alg==GbSba) // cond. for sba
3182  {
3183  if(rField_is_Domain(r)
3184  &&(!rIsNCRing(r))
3185  &&(rHasGlobalOrdering(r)))
3186  {
3187  return GbSba;
3188  }
3189  if (TEST_OPT_PROT)
3190  WarnS("requires: coef:domain, commutative, global ordering");
3191  }
3192  else if (alg==GbGroebner) // cond. for groebner
3193  {
3194  return GbGroebner;
3195  }
3196  else if(alg==GbModstd) // cond for modstd: Q or Q(a)
3197  {
3198  if(ggetid("modStd")==NULL)
3199  {
3200  WarnS(">>modStd<< not found");
3201  }
3202  else if(rField_is_Q(r)
3203  &&(!rIsNCRing(r))
3204  &&(rHasGlobalOrdering(r)))
3205  {
3206  return GbModstd;
3207  }
3208  if (TEST_OPT_PROT)
3209  WarnS("requires: coef:QQ, commutative, global ordering");
3210  }
3211  else if(alg==GbStdSat) // cond for std:sat: 2 blocks of variables
3212  {
3213  if(ggetid("satstd")==NULL)
3214  {
3215  WarnS(">>satstd<< not found");
3216  }
3217  else
3218  {
3219  return GbStdSat;
3220  }
3221  }
3222 
3223  return GbStd; // no conditions for std
3224 }
3225 //----------------------------------------------------------------------------
3226 // GB-algorithms and their pre-conditions
3227 // std slimgb sba singmatic modstd ffmod nfmod groebner
3228 // + + + - + - - + coeffs: QQ
3229 // + + + + - - - + coeffs: ZZ/p
3230 // + + + - ? - + + coeffs: K[a]/f
3231 // + + + - ? + - + coeffs: K(a)
3232 // + - + - - - - + coeffs: domain, not field
3233 // + - - - - - - + coeffs: zero-divisors
3234 // + + + + - ? ? + also for modules: C
3235 // + + - + - ? ? + also for modules: all orderings
3236 // + + - - - - - + exterior algebra
3237 // + + - - - - - + G-algebra
3238 // + + + + + + + + degree ordering
3239 // + - + + + + + + non-degree ordering
3240 // - - - + + + + + parallel
static int si_max(const int a, const int b)
Definition: auxiliary.h:124
int BOOLEAN
Definition: auxiliary.h:87
#define TRUE
Definition: auxiliary.h:100
#define FALSE
Definition: auxiliary.h:96
void * ADDRESS
Definition: auxiliary.h:119
static int si_min(const int a, const int b)
Definition: auxiliary.h:125
int size(const CanonicalForm &f, const Variable &v)
int size ( const CanonicalForm & f, const Variable & v )
Definition: cf_ops.cc:600
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:56
int l
Definition: cfEzgcd.cc:100
int m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
int k
Definition: cfEzgcd.cc:99
Variable x
Definition: cfModGcd.cc:4082
int p
Definition: cfModGcd.cc:4078
g
Definition: cfModGcd.cc:4090
CanonicalForm b
Definition: cfModGcd.cc:4103
static CanonicalForm bound(const CFMatrix &M)
Definition: cf_linsys.cc:460
FILE * f
Definition: checklibs.c:9
poly singclap_pdivide(poly f, poly g, const ring r)
Definition: clapsing.cc:624
Definition: intvec.h:23
int nrows
Definition: matpol.h:20
long rank
Definition: matpol.h:19
int & rows()
Definition: matpol.h:23
int ncols
Definition: matpol.h:21
int & cols()
Definition: matpol.h:24
poly * m
Definition: matpol.h:18
ring tailRing
Definition: kutil.h:343
LObject P
Definition: kutil.h:302
Class used for (list of) interpreter objects.
Definition: subexpr.h:83
void * data
Definition: subexpr.h:88
Coefficient rings, fields and other domains suitable for Singular polynomials.
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition: coeffs.h:461
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:535
#define Print
Definition: emacs.cc:80
#define Warn
Definition: emacs.cc:77
#define WarnS
Definition: emacs.cc:78
return result
Definition: facAbsBiFact.cc:75
const CanonicalForm int s
Definition: facAbsFact.cc:51
CanonicalForm res
Definition: facAbsFact.cc:60
const CanonicalForm & w
Definition: facAbsFact.cc:51
CanonicalForm divide(const CanonicalForm &ff, const CanonicalForm &f, const CFList &as)
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
int j
Definition: facHensel.cc:110
void WerrorS(const char *s)
Definition: feFopen.cc:24
#define STATIC_VAR
Definition: globaldefs.h:7
@ IDEAL_CMD
Definition: grammar.cc:284
@ MODUL_CMD
Definition: grammar.cc:287
GbVariant syGetAlgorithm(char *n, const ring r, const ideal)
Definition: ideals.cc:3154
int index
Definition: ideals.cc:2939
static void idPrepareStd(ideal s_temp, int k)
Definition: ideals.cc:1041
matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how)
Definition: ideals.cc:2621
void idLiftW(ideal P, ideal Q, int n, matrix &T, ideal &R, int *w)
Definition: ideals.cc:1324
static void idLift_setUnit(int e_mod, matrix *unit)
Definition: ideals.cc:1082
ideal idSyzygies(ideal h1, tHomog h, intvec **w, BOOLEAN setSyzComp, BOOLEAN setRegularity, int *deg, GbVariant alg)
Definition: ideals.cc:830
poly p
Definition: ideals.cc:2938
matrix idDiff(matrix i, int k)
Definition: ideals.cc:2138
BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w)
Definition: ideals.cc:2069
ideal idLiftStd(ideal h1, matrix *T, tHomog hi, ideal *S, GbVariant alg, ideal h11)
Definition: ideals.cc:976
void idDelEquals(ideal id)
Definition: ideals.cc:2956
int pCompare_qsort(const void *a, const void *b)
Definition: ideals.cc:2942
ideal idQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal)
Definition: ideals.cc:1494
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:1980
BOOLEAN idIsSubModule(ideal id1, ideal id2)
Definition: ideals.cc:2048
ideal idSeries(int n, ideal M, matrix U, intvec *w)
Definition: ideals.cc:2121
static ideal idGroebner(ideal temp, int syzComp, GbVariant alg, intvec *hilb=NULL, intvec *w=NULL, tHomog hom=testHomog)
Definition: ideals.cc:201
ideal idCreateSpecialKbase(ideal kBase, intvec **convert)
Definition: ideals.cc:2535
static ideal idPrepare(ideal h1, ideal h11, tHomog hom, int syzcomp, intvec **w, GbVariant alg)
Definition: ideals.cc:607
poly id_GCD(poly f, poly g, const ring r)
Definition: ideals.cc:2745
int idIndexOfKBase(poly monom, ideal kbase)
Definition: ideals.cc:2553
poly idDecompose(poly monom, poly how, ideal kbase, int *pos)
Definition: ideals.cc:2589
matrix idDiffOp(ideal I, ideal J, BOOLEAN multiply)
Definition: ideals.cc:2151
void idSort_qsort(poly_sort *id_sort, int idsize)
Definition: ideals.cc:2947
static ideal idInitializeQuot(ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax)
Definition: ideals.cc:1389
ideal idElimination(ideal h1, poly delVar, intvec *hilb, GbVariant alg)
Definition: ideals.cc:1593
static ideal idSectWithElim(ideal h1, ideal h2, GbVariant alg)
Definition: ideals.cc:133
ideal idMinBase(ideal h1)
Definition: ideals.cc:51
ideal idSect(ideal h1, ideal h2, GbVariant alg)
Definition: ideals.cc:316
ideal idMultSect(resolvente arg, int length, GbVariant alg)
Definition: ideals.cc:472
void idKeepFirstK(ideal id, const int k)
keeps the first k (>= 1) entries of the given ideal (Note that the kept polynomials may be zero....
Definition: ideals.cc:2924
ideal idLift(ideal mod, ideal submod, ideal *rest, BOOLEAN goodShape, BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg)
represents the generators of submod in terms of the generators of mod (Matrix(SM)*U-Matrix(rest)) = M...
Definition: ideals.cc:1105
STATIC_VAR int * id_satstdSaturatingVariables
Definition: ideals.cc:2993
ideal idExtractG_T_S(ideal s_h3, matrix *T, ideal *S, long syzComp, int h1_size, BOOLEAN inputIsIdeal, const ring oring, const ring sring)
Definition: ideals.cc:709
static void idDeleteComps(ideal arg, int *red_comp, int del)
Definition: ideals.cc:2660
ideal idModulo(ideal h2, ideal h1, tHomog hom, intvec **w, matrix *T, GbVariant alg)
Definition: ideals.cc:2414
ideal id_Farey(ideal x, number N, const ring r)
Definition: ideals.cc:2848
ideal id_Satstd(const ideal I, ideal J, const ring r)
Definition: ideals.cc:3108
ideal idModuloLP(ideal h2, ideal h1, tHomog, intvec **w, matrix *T, GbVariant alg)
Definition: ideals.cc:2221
static BOOLEAN id_sat_vars_sp(kStrategy strat)
Definition: ideals.cc:2995
ideal idMinEmbedding(ideal arg, BOOLEAN inPlace, intvec **w)
Definition: ideals.cc:2687
int binom(int n, int r)
GbVariant
Definition: ideals.h:119
@ GbGroebner
Definition: ideals.h:126
@ GbModstd
Definition: ideals.h:127
@ GbStdSat
Definition: ideals.h:130
@ GbSlimgb
Definition: ideals.h:123
@ GbFfmod
Definition: ideals.h:128
@ GbNfmod
Definition: ideals.h:129
@ GbDefault
Definition: ideals.h:120
@ GbStd
Definition: ideals.h:122
@ GbSingmatic
Definition: ideals.h:131
@ GbSba
Definition: ideals.h:124
#define idDelete(H)
delete an ideal
Definition: ideals.h:29
#define idSimpleAdd(A, B)
Definition: ideals.h:42
void idGetNextChoise(int r, int end, BOOLEAN *endch, int *choise)
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
static BOOLEAN idHomModule(ideal m, ideal Q, intvec **w)
Definition: ideals.h:96
static intvec * idSort(ideal id, BOOLEAN nolex=TRUE)
Definition: ideals.h:184
#define idTest(id)
Definition: ideals.h:47
static BOOLEAN idHomIdeal(ideal id, ideal Q=NULL)
Definition: ideals.h:91
static ideal idMult(ideal h1, ideal h2)
hh := h1 * h2
Definition: ideals.h:84
ideal idCopy(ideal A)
Definition: ideals.h:60
#define idMaxIdeal(D)
initialise the maximal ideal (at 0)
Definition: ideals.h:33
ideal * resolvente
Definition: ideals.h:18
void idInitChoise(int r, int beg, int end, BOOLEAN *endch, int *choise)
ideal idFreeModule(int i)
Definition: ideals.h:111
static BOOLEAN length(leftv result, leftv arg)
Definition: interval.cc:257
intvec * ivCopy(const intvec *o)
Definition: intvec.h:145
idhdl ggetid(const char *n)
Definition: ipid.cc:581
EXTERN_VAR omBin sleftv_bin
Definition: ipid.h:145
void * iiCallLibProc1(const char *n, void *arg, int arg_type, BOOLEAN &err)
Definition: iplib.cc:627
leftv ii_CallLibProcM(const char *n, void **args, int *arg_types, const ring R, BOOLEAN &err)
args: NULL terminated array of arguments arg_types: 0 terminated array of corresponding types
Definition: iplib.cc:701
void ipPrint_MA0(matrix m, const char *name)
Definition: ipprint.cc:57
STATIC_VAR jList * T
Definition: janet.cc:30
STATIC_VAR Poly * h
Definition: janet.cc:971
STATIC_VAR jList * Q
Definition: janet.cc:30
void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r)
Definition: p_polys.cc:3492
ideal kMin_std(ideal F, ideal Q, tHomog h, intvec **w, ideal &M, intvec *hilb, int syzComp, int reduced)
Definition: kstd1.cc:3034
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
Definition: kstd1.cc:3182
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:2632
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:2447
@ nc_skew
Definition: nc.h:16
@ nc_exterior
Definition: nc.h:21
BOOLEAN nc_CheckSubalgebra(poly PolyVar, ring r)
Definition: old.gring.cc:2576
static nc_type & ncRingType(nc_struct *p)
Definition: nc.h:159
matrix mpNew(int r, int c)
create a r x c zero-matrix
Definition: matpol.cc:37
matrix mp_MultP(matrix a, poly p, const ring R)
multiply a matrix 'a' by a poly 'p', destroy the args
Definition: matpol.cc:148
matrix mp_Copy(matrix a, const ring r)
copies matrix a (from ring r to r)
Definition: matpol.cc:64
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
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
poly mp_DetBareiss(matrix a, const ring r)
returns the determinant of the matrix m; uses Bareiss algorithm
Definition: matpol.cc:1676
#define MATELEM(mat, i, j)
1-based access to matrix
Definition: matpol.h:29
#define MATROWS(i)
Definition: matpol.h:26
#define MATCOLS(i)
Definition: matpol.h:27
#define assume(x)
Definition: mod2.h:389
#define pIter(p)
Definition: monomials.h:37
#define pNext(p)
Definition: monomials.h:36
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:44
#define p_GetCoeff(p, r)
Definition: monomials.h:50
#define __p_GetComp(p, r)
Definition: monomials.h:63
char N base
Definition: ValueTraits.h:144
#define nCopy(n)
Definition: numbers.h:15
#define omStrDup(s)
Definition: omAllocDecl.h:263
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc(size)
Definition: omAllocDecl.h:210
#define omalloc(size)
Definition: omAllocDecl.h:228
#define omFree(addr)
Definition: omAllocDecl.h:261
#define omAlloc0(size)
Definition: omAllocDecl.h:211
#define omFreeBin(addr, bin)
Definition: omAllocDecl.h:259
#define omMemDup(s)
Definition: omAllocDecl.h:264
#define NULL
Definition: omList.c:12
VAR unsigned si_opt_2
Definition: options.c:6
VAR unsigned si_opt_1
Definition: options.c:5
#define SI_SAVE_OPT2(A)
Definition: options.h:22
#define OPT_REDTAIL_SYZ
Definition: options.h:88
#define OPT_REDTAIL
Definition: options.h:92
#define OPT_SB_1
Definition: options.h:96
#define SI_SAVE_OPT1(A)
Definition: options.h:21
#define SI_RESTORE_OPT1(A)
Definition: options.h:24
#define SI_RESTORE_OPT2(A)
Definition: options.h:25
#define Sy_bit(x)
Definition: options.h:31
#define TEST_OPT_RETURN_SB
Definition: options.h:113
#define TEST_V_INTERSECT_ELIM
Definition: options.h:145
#define TEST_V_INTERSECT_SYZ
Definition: options.h:146
#define TEST_OPT_NOTREGULARITY
Definition: options.h:121
#define TEST_OPT_PROT
Definition: options.h:104
#define V_IDLIFT
Definition: options.h:63
#define V_IDELIM
Definition: options.h:71
static int index(p_Length length, p_Ord ord)
Definition: p_Procs_Impl.h:592
poly p_DivideM(poly a, poly b, const ring r)
Definition: p_polys.cc:1574
poly p_Farey(poly p, number N, const ring r)
Definition: p_polys.cc:54
int p_Weight(int i, const ring r)
Definition: p_polys.cc:705
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
Definition: p_polys.cc:4702
int p_Compare(const poly a, const poly b, const ring R)
Definition: p_polys.cc:4845
long p_DegW(poly p, const int *w, const ring R)
Definition: p_polys.cc:690
void p_SetModDeg(intvec *w, ring r)
Definition: p_polys.cc:3669
int p_Var(poly m, const ring r)
Definition: p_polys.cc:4652
poly p_One(const ring r)
Definition: p_polys.cc:1313
void pEnlargeSet(poly **p, int l, int increment)
Definition: p_polys.cc:3692
long p_Deg(poly a, const ring r)
Definition: p_polys.cc:587
static poly p_Neg(poly p, const ring r)
Definition: p_polys.h:1105
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:934
static void p_LmDelete(poly p, const ring r)
Definition: p_polys.h:721
static long p_SubExp(poly p, int v, long ee, ring r)
Definition: p_polys.h:611
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
Definition: p_polys.h:486
static long p_MinComp(poly p, ring lmRing, ring tailRing)
Definition: p_polys.h:311
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:231
static poly p_Copy_noCheck(poly p, const ring r)
returns a copy of p (without any additional testing)
Definition: p_polys.h:834
static number p_SetCoeff(poly p, number n, ring r)
Definition: p_polys.h:410
static poly pReverse(poly p)
Definition: p_polys.h:333
static poly p_Head(const poly p, const ring r)
copy the (leading) term of p
Definition: p_polys.h:858
static int p_LmCmp(poly p, poly q, const ring r)
Definition: p_polys.h:1578
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
Definition: p_polys.h:467
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:899
static void p_GetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1518
static poly p_LmFreeAndNext(poly p, ring)
Definition: p_polys.h:709
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:844
void rChangeCurrRing(ring r)
Definition: polys.cc:15
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
Compatibility layer for legacy polynomial operations (over currRing)
#define pAdd(p, q)
Definition: polys.h:203
#define pTest(p)
Definition: polys.h:414
#define pDelete(p_ptr)
Definition: polys.h:186
#define ppJet(p, m)
Definition: polys.h:366
#define pHead(p)
returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL
Definition: polys.h:67
#define pSetm(p)
Definition: polys.h:271
#define pNeg(p)
Definition: polys.h:198
#define ppMult_mm(p, m)
Definition: polys.h:201
#define pSetCompP(a, i)
Definition: polys.h:303
#define pGetComp(p)
Component.
Definition: polys.h:37
#define pDiff(a, b)
Definition: polys.h:296
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition: polys.h:31
#define pJet(p, m)
Definition: polys.h:367
#define pSub(a, b)
Definition: polys.h:287
#define pWeight(i)
Definition: polys.h:280
#define ppJetW(p, m, iv)
Definition: polys.h:368
#define pMaxComp(p)
Definition: polys.h:299
#define pSetComp(p, v)
Definition: polys.h:38
void wrp(poly p)
Definition: polys.h:310
#define pMult(p, q)
Definition: polys.h:207
#define pJetW(p, m, iv)
Definition: polys.h:369
#define pDiffOp(a, b, m)
Definition: polys.h:297
#define pSeries(n, p, u, w)
Definition: polys.h:371
#define pGetExp(p, i)
Exponent.
Definition: polys.h:41
#define pSetmComp(p)
TODO:
Definition: polys.h:273
#define pNormalize(p)
Definition: polys.h:317
#define pEqualPolys(p1, p2)
Definition: polys.h:399
#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
#define pSetExp(p, i, v)
Definition: polys.h:42
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:338
#define pCopy(p)
return a copy of the poly
Definition: polys.h:185
#define pOne()
Definition: polys.h:315
#define pMinComp(p)
Definition: polys.h:300
poly * polyset
Definition: polys.h:259
poly prMoveR(poly &p, ring src_r, ring dest_r)
Definition: prCopy.cc:90
ideal idrMoveR(ideal &id, ring src_r, ring dest_r)
Definition: prCopy.cc:248
poly prCopyR(poly p, ring src_r, ring dest_r)
Definition: prCopy.cc:34
ideal idrCopyR(ideal id, ring src_r, ring dest_r)
Definition: prCopy.cc:192
ideal idrMoveR_NoSort(ideal &id, ring src_r, ring dest_r)
Definition: prCopy.cc:261
poly prMoveR_NoSort(poly &p, ring src_r, ring dest_r)
Definition: prCopy.cc:101
ideal idrCopyR_NoSort(ideal id, ring src_r, ring dest_r)
Definition: prCopy.cc:205
void PrintS(const char *s)
Definition: reporter.cc:284
void PrintLn()
Definition: reporter.cc:310
void Werror(const char *fmt,...)
Definition: reporter.cc:189
#define mflush()
Definition: reporter.h:58
BOOLEAN rComplete(ring r, int force)
this needs to be called whenever a new ring is created: new fields in ring are created (like VarOffse...
Definition: ring.cc:3450
ring rAssure_SyzComp(const ring r, BOOLEAN complete)
Definition: ring.cc:4435
BOOLEAN nc_rComplete(const ring src, ring dest, bool bSetupQuotient)
Definition: ring.cc:5685
ring rAssure_SyzOrder(const ring r, BOOLEAN complete)
Definition: ring.cc:4430
ring rCopy0(const ring r, BOOLEAN copy_qideal, BOOLEAN copy_ordering)
Definition: ring.cc:1421
void rDelete(ring r)
unconditionally deletes fields in r
Definition: ring.cc:450
void rSetSyzComp(int k, const ring r)
Definition: ring.cc:5086
ring rAssure_dp_C(const ring r)
Definition: ring.cc:4980
static BOOLEAN rIsPluralRing(const ring r)
we must always have this test!
Definition: ring.h:400
static int rBlocks(const ring r)
Definition: ring.h:568
static BOOLEAN rField_is_Domain(const ring r)
Definition: ring.h:487
static BOOLEAN rIsLPRing(const ring r)
Definition: ring.h:411
rRingOrder_t
order stuff
Definition: ring.h:68
@ ringorder_a
Definition: ring.h:70
@ ringorder_a64
for int64 weights
Definition: ring.h:71
@ ringorder_C
Definition: ring.h:73
@ ringorder_dp
Definition: ring.h:78
@ ringorder_c
Definition: ring.h:72
@ ringorder_aa
for idElimination, like a, except pFDeg, pWeigths ignore it
Definition: ring.h:91
@ ringorder_ws
Definition: ring.h:86
@ ringorder_s
s?
Definition: ring.h:76
@ ringorder_wp
Definition: ring.h:81
static BOOLEAN rField_is_Q(const ring r)
Definition: ring.h:506
static BOOLEAN rIsNCRing(const ring r)
Definition: ring.h:421
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition: ring.h:592
BOOLEAN rHasGlobalOrdering(const ring r)
Definition: ring.h:759
#define rField_is_Ring(R)
Definition: ring.h:485
#define block
Definition: scanner.cc:646
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition: simpleideals.cc:35
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
matrix id_Module2Matrix(ideal mod, const ring R)
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
int id_ReadOutPivot(ideal arg, int *comp, const ring r)
void id_DelMultiples(ideal id, const ring r)
ideal id = (id[i]), c any unit if id[i] = c*id[j] then id[j] is deleted for j > i
ideal id_Matrix2Module(matrix mat, const ring R)
converts mat to module, destroys mat
ideal id_SimpleAdd(ideal h1, ideal h2, const ring R)
concat the lists h1 and h2 without zeros
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
void id_Shift(ideal M, int s, const ring r)
ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r)
#define IDELEMS(i)
Definition: simpleideals.h:23
#define id_Test(A, lR)
Definition: simpleideals.h:87
#define R
Definition: sirandom.c:27
#define M
Definition: sirandom.c:25
long sm_ExpBound(ideal m, int di, int ra, int t, const ring currRing)
Definition: sparsmat.cc:188
ring sm_RingChange(const ring origR, long bound)
Definition: sparsmat.cc:258
void sm_KillModifiedRing(ring r)
Definition: sparsmat.cc:289
char * char_ptr
Definition: structs.h:53
tHomog
Definition: structs.h:35
@ isHomog
Definition: structs.h:37
@ testHomog
Definition: structs.h:38
@ isNotHomog
Definition: structs.h:36
#define BITSET
Definition: structs.h:16
#define loop
Definition: structs.h:75
intvec * syBetti(resolvente res, int length, int *regularity, intvec *weights, BOOLEAN tomin, int *row_shift)
Definition: syz.cc:770
void syGaussForOne(ideal syz, int elnum, int ModComp, int from, int till)
Definition: syz.cc:218
resolvente sySchreyerResolvente(ideal arg, int maxlength, int *length, BOOLEAN isMonomial=FALSE, BOOLEAN notReplace=FALSE)
Definition: syz0.cc:855
ideal t_rep_gb(const ring r, ideal arg_I, int syz_comp, BOOLEAN F4_mode)
Definition: tgb.cc:3571
@ INT_CMD
Definition: tok.h:96
THREAD_VAR double(* wFunctional)(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition: weight.cc:20
void wCall(poly *s, int sl, int *x, double wNsqr, const ring R)
Definition: weight.cc:108
double wFunctionalBuch(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
Definition: weight0.cc:78