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syz3.cc
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1 /****************************************
2 * Computer Algebra System SINGULAR *
3 ****************************************/
4 /*
5 * ABSTRACT: resolutions
6 */
7 
8 #include "kernel/mod2.h"
9 
10 #include "misc/mylimits.h"
11 #include "misc/options.h"
12 #include "misc/intvec.h"
13 
14 #include "coeffs/numbers.h"
15 
16 #include "polys/monomials/ring.h"
17 #include "polys/kbuckets.h"
18 #include "polys/prCopy.h"
19 #include "polys/matpol.h"
20 
23 
24 #include "kernel/GBEngine/kstd1.h"
25 #include "kernel/GBEngine/kutil.h"
26 #include "kernel/GBEngine/syz.h"
27 
28 #include "kernel/ideals.h"
29 #include "kernel/polys.h"
30 
31 //#define SHOW_PROT
32 //#define SHOW_RED
33 //#define SHOW_Kosz
34 //#define SHOW_RESULT
35 //#define INVERT_PAIRS
36 //#define ONLY_STD
37 //#define EXPERIMENT1 //Hier stimmt was mit der Anzahl der Erzeuger in xyz11 nicht!!
38 #define EXPERIMENT2
39 #define EXPERIMENT3
40 #define WITH_BUCKET //Use of buckets in EXPERIMENT3 (Product criterion)
41 #define WITH_SCHREYER_ORD
42 #define USE_CHAINCRIT
43 #define USE_CHAINCRIT0
44 #define USE_PROD_CRIT
45 #define USE_REGULARITY
46 #define WITH_SORT
47 //#define FULL_TOTAKE
50 
51 /*3
52 * assumes the ideals old_ideal and new_ideal to be homogeneous
53 * tests whether the new_ideal is a regular extension of the old_ideal
54 */
55 static BOOLEAN syIsRegular(ideal old_ideal,ideal new_ideal,int deg)
56 {
57  intvec * old_hilbs=hFirstSeries(old_ideal,NULL,NULL,NULL);
58  intvec * new_hilbs=hFirstSeries(new_ideal,NULL,NULL,NULL);
59  int biggest_length=si_max(old_hilbs->length()+deg,new_hilbs->length());
60  intvec * shifted_old_hilbs=new intvec(biggest_length);
61  intvec * old_hilb1=new intvec(biggest_length);
62  intvec * new_hilb1=new intvec(biggest_length);
63  int i;
64  BOOLEAN isRegular=TRUE;
65 
66  for (i=old_hilbs->length()+deg-1;i>=deg;i--)
67  (*shifted_old_hilbs)[i] = (*old_hilbs)[i-deg];
68  for (i=old_hilbs->length()-1;i>=0;i--)
69  (*old_hilb1)[i] = (*old_hilbs)[i]-(*shifted_old_hilbs)[i];
70  for (i=old_hilbs->length()+deg-1;i>=old_hilbs->length();i--)
71  (*old_hilb1)[i] = -(*shifted_old_hilbs)[i];
72  for (i=new_hilbs->length()-1;i>=0;i--)
73  (*new_hilb1)[i] = (*new_hilbs)[i];
74  i = 0;
75  while ((i<biggest_length) && isRegular)
76  {
77  isRegular = isRegular && ((*old_hilb1)[i] == (*new_hilb1)[i]);
78  i++;
79  }
80  delete old_hilbs;
81  delete new_hilbs;
82  delete old_hilb1;
83  delete new_hilb1;
84  delete shifted_old_hilbs;
85  return isRegular;
86 }
87 
88 /*3
89 * shows the resolution stored in syzstr->orderedRes
90 */
91 #if 0 /* unused*/
92 static void syShowRes(syStrategy syzstr)
93 {
94  int i=0;
95 
96  while ((i<syzstr->length) && (!idIs0(syzstr->res[i])))
97  {
98  Print("aktueller hoechster index ist: %d\n",(*syzstr->Tl)[i]);
99  Print("der %d-te modul ist:\n",i);
100  idPrint(syzstr->res[i]);
101  PrintS("Seine Darstellung:\n");
102  idPrint(syzstr->orderedRes[i]);
103  i++;
104  }
105 }
106 #endif
107 
108 /*3
109 * produces the next subresolution for a regular extension
110 */
111 static void syCreateRegularExtension(syStrategy syzstr,ideal old_ideal,
112  ideal old_repr,int old_tl, poly next_generator,resolvente totake)
113 {
114  int index=syzstr->length-1,i,j,start,start_ttk/*,new_tl*/;
115  poly gen=pCopy(next_generator),p;
116  poly neg_gen=pCopy(next_generator);
117  ideal current_ideal,current_repr;
118  int current_tl;
119  poly w_gen=pHead(next_generator);
120  pSetComp(w_gen,0);
121  pSetmComp(w_gen);
122 
123  //syShowRes(syzstr);
124  neg_gen = pNeg(neg_gen);
125  if (pGetComp(gen)>0)
126  {
127  p_Shift(&gen,-1,currRing);
128  p_Shift(&neg_gen,-1,currRing);
129  }
130  while (index>0)
131  {
132  if (index%2==0)
133  p = gen;
134  else
135  p = neg_gen;
136  if (index>1)
137  {
138  current_ideal = syzstr->res[index-1];
139  current_repr = syzstr->orderedRes[index-1];
140  current_tl = (*syzstr->Tl)[index-1];
141  }
142  else
143  {
144  current_ideal = old_ideal;
145  current_repr = old_repr;
146  current_tl = old_tl;
147  }
148  if (!idIs0(current_ideal))
149  {
150  if (idIs0(syzstr->res[index]))
151  {
152  syzstr->res[index] = idInit(IDELEMS(current_ideal),
153  current_ideal->rank+current_tl);
154  syzstr->orderedRes[index] = idInit(IDELEMS(current_ideal),
155  current_ideal->rank);
156  start = 0;
157  }
158  else
159  {
160  start = IDELEMS(syzstr->res[index]);
161  while ((start>0) && (syzstr->res[index]->m[start-1]==NULL)) start--;
162  if (IDELEMS(syzstr->res[index])<start+IDELEMS(current_ideal))
163  {
164  pEnlargeSet(&syzstr->res[index]->m,IDELEMS(syzstr->res[index]),
165  IDELEMS(current_ideal));
166  IDELEMS(syzstr->res[index]) += IDELEMS(current_ideal);
167  pEnlargeSet(&syzstr->orderedRes[index]->m,IDELEMS(syzstr->orderedRes[index]),
168  IDELEMS(current_ideal));
169  IDELEMS(syzstr->orderedRes[index]) += IDELEMS(current_ideal);
170  }
171  }
172  if (idIs0(totake[index]))
173  {
174  totake[index] = idInit(IDELEMS(current_ideal),
175  current_ideal->rank+current_tl);
176  start_ttk = 0;
177  }
178  else
179  {
180  start_ttk = IDELEMS(totake[index]);
181  while ((start_ttk>0) && (totake[index]->m[start_ttk-1]==NULL)) start_ttk--;
182  if (IDELEMS(totake[index])<start_ttk+IDELEMS(current_ideal))
183  {
184  pEnlargeSet(&totake[index]->m,IDELEMS(totake[index]),
185  IDELEMS(current_ideal));
186  for (j=IDELEMS(totake[index]);j<IDELEMS(totake[index])+
187  IDELEMS(current_ideal);j++)
188  totake[index]->m[j] = NULL;
189  IDELEMS(totake[index]) += IDELEMS(current_ideal);
190  }
191  }
192  for (i=0;i<IDELEMS(current_ideal);i++)
193  {
194  if (current_ideal->m[i]!=NULL)
195  {
196  syzstr->res[index]->m[i+start] = pCopy(current_ideal->m[i]);
197  syzstr->res[index]->m[i+start] = pMult_mm(syzstr->res[index]->m[i+start],w_gen);
198  p_Shift(&syzstr->res[index]->m[i+start],current_tl,currRing);
199  syzstr->res[index]->m[i+start] = pAdd(syzstr->res[index]->m[i+start],
200  ppMult_qq(current_repr->m[i],p));
201  syzstr->orderedRes[index]->m[i+start] = pCopy(current_repr->m[i]);
202  syzstr->orderedRes[index]->m[i+start] =
203  pMult_mm(syzstr->orderedRes[index]->m[i+start],w_gen);
204  if ((*syzstr->Tl)[index]!=0)
205  p_Shift(&syzstr->orderedRes[index]->m[i+start],(*syzstr->Tl)[index],currRing);
206  }
207  }
208  for (i=0;i<IDELEMS(totake[index-1]);i++)
209  {
210  if (totake[index-1]->m[i]!=NULL)
211  {
212  if ((index==1) && ((i==IDELEMS(current_ideal) ||
213  (totake[index-1]->m[i+1]==NULL)))) break;
214  totake[index]->m[i+start_ttk] =
215  pMult_mm(pCopy(totake[index-1]->m[i]),w_gen);
216  p_Shift(&totake[index]->m[i+start_ttk],current_tl,currRing);
217 #ifdef FULL_TOTAKE
218  poly pp=pCopy(p);
219  p_Shift(&pp,i+1,currRing);
220  totake[index]->m[i+start_ttk] = pAdd(totake[index]->m[i+start_ttk],pp);
221 #endif
222  }
223  }
224  (*syzstr->Tl)[index] += current_tl;
225  }
226  index--;
227  }
228  pDelete(&gen);
229  pDelete(&neg_gen);
230  pDelete(&w_gen);
231  //syShowRes(syzstr);
232 }
233 
234 /*3
235 * proves the consistence of the pairset resPairs with the corresponding
236 * set of generators;
237 * only for tests
238 */
239 static void syTestPairs(SSet resPairs,int length,ideal old_generators)
240 {
241  int i=0;
242 
243  while (i<length)
244  {
245  if (resPairs[i].lcm!=NULL)
246  {
247  if (resPairs[i].p1!=NULL)
248  assume(resPairs[i].p1==old_generators->m[resPairs[i].ind1]);
249  if (resPairs[i].p2!=NULL)
250  assume(resPairs[i].p2==old_generators->m[resPairs[i].ind2]);
251  }
252  i++;
253  }
254 }
255 
256 /*3
257 * cancels the weight monomials given by the leading terms of totake
258 * from the resolution res;
259 * works in place on res, but reads only from totake
260 */
262 {
263  int length=syzstr->length;
264  int syzIndex=length-1,i,j;
265  resolvente res=syzstr->fullres;
266  poly p;
267 
268  while ((syzIndex!=0) && (res[syzIndex]==NULL)) syzIndex--;
269  while (syzIndex>0)
270  {
271  for(i=0;i<IDELEMS(res[syzIndex]);i++)
272  {
273 #ifdef USE_REGULARITY
274  if ((syzstr->regularity>0) && (res[syzIndex]->m[i]!=NULL))
275  {
276  if (p_FDeg(res[syzIndex]->m[i],currRing)>=syzstr->regularity+syzIndex)
277  pDelete(&res[syzIndex]->m[i]);
278  }
279 #endif
280  p = res[syzIndex]->m[i];
281  while (p!=NULL)
282  {
283  if (res[syzIndex-1]->m[pGetComp(p)-1]!=NULL)
284  {
285  for(j=1;j<=(currRing->N);j++)
286  {
287  pSetExp(p,j,pGetExp(p,j)
288  -pGetExp(res[syzIndex-1]->m[pGetComp(p)-1],j));
289  }
290  }
291  else
292  PrintS("error in the resolvent\n");
293  pSetm(p);
294  pIter(p);
295  }
296  }
297  syzIndex--;
298  }
299 }
300 
301 /*3
302 * updates the pairset resPairs by generating all pairs including the
303 * new_generators in the 0-th modul;
304 * the new_generators are inserted in the old_generators;
305 * new_generators is empty after the procedure;
306 */
307 static void updatePairs(SSet *resPairs,int *l_pairs,syStrategy syzstr,
308  int index,ideal new_generators,ideal new_repr,int crit_comp)
309 {
310  if (idIs0(new_generators)) return;
311  ideal old_generators=syzstr->res[index];
312  ideal old_repr=syzstr->orderedRes[index];
313  int i=0,j,k,kk,og_elem=0,og_idel=IDELEMS(old_generators),l=*l_pairs,jj,ll,j1;
314  int og_ini=0;
315  ideal pairs=idInit(og_idel+IDELEMS(new_generators),old_generators->rank);
316  polyset prs=pairs->m;
317  poly p=NULL;
318  SObject tso;
319 
320  syInitializePair(&tso);
321  while ((og_elem<og_idel) && (old_generators->m[og_elem]!=NULL))
322  {
323  if ((index>0) && (pGetComp(old_generators->m[og_elem])<=crit_comp))
324  og_ini = og_elem;
325  og_elem++;
326  }
327  while ((l>0) && ((*resPairs)[l-1].lcm==NULL)) l--;
328  while ((i<IDELEMS(new_generators)) && (new_generators->m[i]!=NULL))
329  {
330  syTestPairs(*resPairs,*l_pairs,old_generators);
331  if (IDELEMS(old_generators)==og_elem)
332  {
333  pEnlargeSet(&old_generators->m,IDELEMS(old_generators),16);
334  IDELEMS(old_generators) += 16;
335  pEnlargeSet(&old_repr->m,IDELEMS(old_repr),16);
336  IDELEMS(old_repr) += 16;
337  }
338  k = p_FDeg(new_generators->m[i],currRing);
339  kk = pGetComp(new_generators->m[i]);
340  j = og_ini;
341  while ((j<og_elem) && (old_generators->m[j]!=NULL) &&
342  (pGetComp(old_generators->m[j])<kk)) j++;
343  while ((j<og_elem) && (old_generators->m[j]!=NULL) &&
344  (p_FDeg(old_generators->m[j],currRing)<=k)) j++;
345  for (jj=og_elem;jj>j;jj--)
346  {
347  old_generators->m[jj] = old_generators->m[jj-1];
348  old_repr->m[jj] = old_repr->m[jj-1];
349  }
350  old_generators->m[j] = new_generators->m[i];
351  new_generators->m[i] = NULL;
352  old_repr->m[j] = new_repr->m[i];
353  new_repr->m[i] = NULL;
354  og_elem++;
355  for (jj=0;jj<*l_pairs;jj++)
356  {
357  if ((*resPairs)[jj].lcm!=NULL)
358  {
359  if ((*resPairs)[jj].ind1>=j) (*resPairs)[jj].ind1++;
360  if ((*resPairs)[jj].ind2>=j) (*resPairs)[jj].ind2++;
361  }
362  }
363  syTestPairs(*resPairs,*l_pairs,old_generators);
364  for (jj=og_ini;jj<og_elem;jj++)
365  {
366  if ((j!=jj) && (pGetComp(old_generators->m[jj])==pGetComp(old_generators->m[j])))
367  {
368  p = pOne();
369  pLcm(old_generators->m[jj],old_generators->m[j],p);
370  pSetComp(p,j+1);
371  pSetm(p);
372  j1 = 0;
373  while (j1<jj)
374  {
375  if (prs[j1]!=NULL)
376  {
377  if (pLmDivisibleByNoComp(prs[j1],p))
378  {
379  pDelete(&p);
380  break;
381  }
382  else if (pLmDivisibleByNoComp(p,prs[j1]))
383  {
384  pDelete(&(prs[j1]));
385  }
386 #ifdef USE_CHAINCRIT0
387  else
388  {
389  poly p1,p2;
390  int ip=(currRing->N);
391  p1 = pMDivide(p,old_generators->m[jj]);
392  p2 = pMDivide(prs[j1],old_generators->m[j1]);
393  while ((ip>0) && (pGetExp(p1,ip)*pGetExp(p2,ip)==0)) ip--;
394  if (ip==0)
395  {
396  int ti=0;
397  while ((ti<l) && (((*resPairs)[ti].ind1!=j1)|| ((*resPairs)[ti].ind2!=jj))) ti++;
398  if (ti<l)
399  {
400  if (TEST_OPT_PROT) PrintS("cc");
401  syDeletePair(&(*resPairs)[ti]);
402  syCompactifyPairSet(*resPairs,*l_pairs,ti);
403  l--;
404  }
405  }
406  pDelete(&p1);
407  pDelete(&p2);
408  }
409 #endif
410  }
411  j1++;
412  }
413  if (p!=NULL)
414  prs[jj] = p;
415  }
416  }
417  for (jj=og_ini;jj<og_elem;jj++)
418  {
419  if (prs[jj] !=NULL)
420  {
421  if (l>=*l_pairs)
422  {
423  SSet temp = (SSet)omAlloc0((*l_pairs+16)*sizeof(SObject));
424  for (ll=0;ll<*l_pairs;ll++)
425  {
426  temp[ll].p = (*resPairs)[ll].p;
427  temp[ll].p1 = (*resPairs)[ll].p1;
428  temp[ll].p2 = (*resPairs)[ll].p2;
429  temp[ll].syz = (*resPairs)[ll].syz;
430  temp[ll].lcm = (*resPairs)[ll].lcm;
431  temp[ll].ind1 = (*resPairs)[ll].ind1;
432  temp[ll].ind2 = (*resPairs)[ll].ind2;
433  temp[ll].syzind = (*resPairs)[ll].syzind;
434  temp[ll].order = (*resPairs)[ll].order;
435  temp[ll].isNotMinimal = (*resPairs)[ll].isNotMinimal;
436  }
437  omFreeSize((ADDRESS)(*resPairs),*l_pairs*sizeof(SObject));
438  *l_pairs += 16;
439  (*resPairs) = temp;
440  }
441  tso.lcm = prs[jj];
442  prs[jj] = NULL;
443  tso.order = p_FDeg(tso.lcm,currRing);
444  tso.p1 = old_generators->m[jj];
445  tso.p2 = old_generators->m[j];
446  tso.ind1 = jj;
447  tso.ind2 = j;
448  tso.syzind = -1;
449  tso.isNotMinimal = NULL;
450  tso.p = NULL;
451  tso.syz = NULL;
452  SSet rP=*resPairs;
453 #ifdef SHOW_PROT
454 Print("erzeuge Paar im Modul %d,%d mit: \n",index,tso.order);
455 PrintS("poly1: ");pWrite(tso.p1);
456 PrintS("poly2: ");pWrite(tso.p2);
457 PrintS("syz: ");pWrite(tso.syz);
458 PrintS("sPoly: ");pWrite(tso.p);
459 PrintLn();
460 #endif
461  syEnterPair(rP,&tso,&l,index);
462  syInitializePair(&tso);
463  }
464  }
465  i++;
466  }
467  idDelete(&pairs);
468 }
469 
470 /*3
471 * performs the modification of a single reduction on the syzygy-level
472 */
473 inline void sySPRedSyz_Kosz(syStrategy syzstr,poly redWith,poly syz,poly q=NULL,int l_syz=-1)
474 {
475  poly p=pMDivide(q,redWith);
476  pSetCoeff(p,nDiv(pGetCoeff(q),pGetCoeff(redWith)));
477  kBucket_Minus_m_Mult_p(syzstr->syz_bucket,p,syz,&l_syz,NULL);
478  pDelete(&p);
479 }
480 
481 /*3
482 * normalizes the poly bucket by the ideal;
483 * stops the reduction whenever the leading component is less than the
484 * crit_comp;
485 * returns the changing status
486 */
487 static BOOLEAN syRedSyz(kBucket_pt bucket,ideal red,int crit_comp,int* g_l)
488 {
489  poly p = kBucketGetLm(bucket);
490  int j = 0,i=IDELEMS(red)-1;
491  number n;
492  BOOLEAN isChanged=FALSE;
493 
494  loop
495  {
496  if ((j>=i) || (p==NULL) || (pGetComp(p)<=crit_comp)) break;
497  if ((red->m[j]!=NULL) && (pDivisibleBy(red->m[j],p)))
498  {
499  n = kBucketPolyRed(bucket,red->m[j], g_l[j], NULL);
500  nDelete(&n);
501  p = kBucketGetLm(bucket);
502  isChanged = TRUE;
503  j = 0;
504  }
505  else
506  j++;
507  }
508  return isChanged;
509 }
510 
511 /*3
512 * a tail reduction for the syzygies yielding new generators
513 */
514 static poly syRedTailSyz(poly tored,ideal red,ideal sec_red,int crit_comp,syStrategy syzstr,
515  int * gen_length,int * secgen_length,int * tored_length)
516 {
517  int i=IDELEMS(red)-1,num_mon,num_tail;
518  poly h,hn;
519  // BOOLEAN dummy;
520 
521  while ((i>0) && (red->m[i-1]==NULL)) i--;
522  i--;
523  h = tored;
524  if ((h!=NULL) && (pGetComp(h)>crit_comp))
525  {
526  num_mon = 1;
527  hn = pNext(h);
528  num_tail = *tored_length-1;
529  while (hn!=NULL)
530  {
531  kBucketInit(syzstr->syz_bucket,hn,num_tail);
532  /*dummy =*/ (void) syRedSyz(syzstr->syz_bucket,red,crit_comp,gen_length);
533  kBucketClear(syzstr->syz_bucket,&hn,&num_tail);
534  pNext(h) = hn;
535  if ((hn==NULL) || (pGetComp(hn)<=crit_comp))
536  break;
537  else
538  {
539  pIter(h);
540  pIter(hn);
541  num_mon++;
542  num_tail--;
543  }
544  }
545  if (sec_red!=NULL)
546  {
547  while (hn!=NULL)
548  {
549  kBucketInit(syzstr->syz_bucket,hn,num_tail);
550  /*dummy =*/ (void) syRedSyz(syzstr->syz_bucket,sec_red,crit_comp,secgen_length);
551  kBucketClear(syzstr->syz_bucket,&hn,&num_tail);
552  pNext(h) = hn;
553  if (hn==NULL)
554  break;
555  else
556  {
557  pIter(h);
558  pIter(hn);
559  num_mon++;
560  num_tail--;
561  }
562  }
563  }
564  *tored_length = num_mon+num_tail;
565  }
566  assume(pLength(tored)==*tored_length);
567  return tored;
568 }
569 
570 #if 0
571 // unused
572 /*3
573 * the complete reduction of a single pair which is just stored
574 * in bucket and syz_bucket
575 */
576 static BOOLEAN syRedSyzPair(syStrategy syzstr,int index,int* g_l,int* orp_l)
577 {
578  kBucket_pt bucket=syzstr->bucket;
579  poly p = kBucketGetLm(bucket);
580  ideal red=syzstr->res[index],repr=syzstr->orderedRes[index];
581  int j = 0,i=IDELEMS(red)-1;
582  number n;
583  BOOLEAN isChanged=FALSE;
584 
585  loop
586  {
587  if ((j>=i) || (p==NULL)) break;
588  if ((red->m[j]!=NULL) && (pDivisibleBy(red->m[j],p)))
589  {
590  sySPRedSyz_Kosz(syzstr,red->m[j],repr->m[j],p,orp_l[j]);
591  n = kBucketPolyRed(bucket,red->m[j], g_l[j], NULL);
592  nDelete(&n);
593  p = kBucketGetLm(bucket);
594  isChanged = TRUE;
595  j = 0;
596  }
597  else
598  j++;
599  }
600  return isChanged;
601 }
602 #endif
603 
604 /*3
605 * the tailreduction for generators (which includes the correction of
606 * the corresponding representation)
607 */
608 #if 0 /*unused*/
609 static void syRedTailSyzPair(SObject tso,syStrategy syzstr,int index,
610  int * gen_length,int* orp_l,int * tored_l,int * syzred_l)
611 {
612  int num_mon,num_tail,syz_l;
613  poly h,hn;
614  BOOLEAN dummy;
615 
616  h = tso.p;
617  kBucketInit(syzstr->syz_bucket,tso.syz,*syzred_l);
618  if (h!=NULL)
619  {
620  num_mon = 1;
621  hn = pNext(h);
622  num_tail = *tored_l-1;
623  while (hn!=NULL)
624  {
625  kBucketInit(syzstr->bucket,hn,num_tail);
626  dummy = syRedSyzPair(syzstr,index,gen_length,orp_l);
627  kBucketClear(syzstr->bucket,&hn,&num_tail);
628  pNext(h) = hn;
629  if (hn==NULL)
630  break;
631  else
632  {
633  pIter(h);
634  pIter(hn);
635  num_mon++;
636  num_tail--;
637  }
638  }
639  *tored_l = num_mon+num_tail;
640  }
641  kBucketClear(syzstr->syz_bucket,&tso.syz,&syz_l);
642  assume(pLength(tso.syz)==syz_l);
643  assume(pLength(tso.p)==*tored_l);
644 }
645 #endif
646 
647 /*3
648 * the reduction of a pair in the 0-th module
649 */
650 static void redOnePair(SSet resPairs,int itso,int l, ideal syzygies,
651  int crit_comp, syStrategy syzstr,int index,ideal new_generators,
652  ideal new_repr,int * ogm_l,int * orp_l)
653 {
654  SObject tso = resPairs[itso];
655  assume (tso.lcm!=NULL);
656  ideal old_generators=syzstr->res[index];
657  ideal old_repr=syzstr->orderedRes[index];
658  int og_idel=IDELEMS(old_generators),ng_place=IDELEMS(new_generators);
659  int toReplace=0;
660  int i,j,syz_l;
661  number /*coefgcd,*/n;
662  polyset ogm=old_generators->m;
663  poly p;
664  BOOLEAN deleteP=FALSE;
665 #ifdef EXPERIMENT1
666  poly syzp;
667 #endif
668  int syz_place=IDELEMS(syzygies);
669 
670  while ((syz_place>0) && (syzygies->m[syz_place-1]==NULL)) syz_place--;
671  while ((ng_place>0) && (new_generators->m[ng_place-1]==NULL)) ng_place--;
672  while ((og_idel>0) && (old_generators->m[og_idel-1]==NULL)) og_idel--;
673  assume (tso.ind1<og_idel);
674  assume (tso.ind2<og_idel);
675  assume (tso.ind1!=tso.ind2);
676  assume (tso.p1 == old_generators->m[tso.ind1]);
677  assume (tso.p2 == old_generators->m[tso.ind2]);
678  tso.p1 = old_generators->m[tso.ind1];
679  tso.p2 = old_generators->m[tso.ind2];
680  if ((tso.p1!=NULL) && (tso.p2!=NULL))
681  {
682  if (TEST_OPT_PROT)
683  PrintS(".");
684  if (index==0)
685  {
686 /*--- tests whether a generator must be replaced (lt(f1)|lt(f2)!)--*/
687  if (p_FDeg(tso.p1,currRing)==p_FDeg(tso.lcm,currRing))
688  toReplace = tso.ind1+1;
689  else if (p_FDeg(tso.p2,currRing)==p_FDeg(tso.lcm,currRing))
690  toReplace = tso.ind2+1;
691  }
692 #ifdef EXPERIMENT3
693 /*--- tests whether the product criterion applies --------------*/
694  if ((index==0) && (old_generators->rank==1) &&
695  (p_FDeg(tso.p1,currRing)+p_FDeg(tso.p2,currRing)==tso.order))
696  {
697  tso.p = NULL;
698  p = pCopy(tso.p1);
699  p_Shift(&p,-1,currRing);
700 #ifdef WITH_BUCKET
701  poly pp;
702  pp = pMult_mm(pCopy(old_repr->m[tso.ind2]),p);
703  kBucketInit(syzstr->syz_bucket,pp,-1);
704  pLmDelete(&p);
705  p = pNeg(p);
706  pp = pCopy(old_repr->m[tso.ind2]);
707  int il=-1;
708  while (p!=NULL)
709  {
711  pLmDelete(&p);
712  }
713  pDelete(&pp);
714  p = pCopy(tso.p2);
715  p_Shift(&p,-1,currRing);
716  pp = pCopy(old_repr->m[tso.ind1]);
717  il=-1;
718  while (p!=NULL)
719  {
721  pLmDelete(&p);
722  }
723  pDelete(&pp);
724  kBucketClear(syzstr->syz_bucket,&tso.syz,&j);
725 #else
726  tso.syz = pMult(p,pCopy(old_repr->m[tso.ind2]));
727  p = pCopy(tso.p2);
728  p_Shift(&p,-1,currRing);
729  tso.syz = pSub(tso.syz,pMult(p,pCopy(old_repr->m[tso.ind1])));
730 #endif
731  }
732  else
733 #endif
734 /*--- the product criterion does not apply --------------------*/
735  {
736  tso.p = ksOldCreateSpoly(tso.p2,tso.p1);
737  number coefgcd = n_Gcd(pGetCoeff(tso.p1),pGetCoeff(tso.p2),currRing->cf);
738  assume (old_repr->m[tso.ind1]!=NULL);
739  tso.syz = pCopy(old_repr->m[tso.ind1]);
740  poly tt = pMDivide(tso.lcm,tso.p1);
741  pSetComp(tt,0);
742  pSetmComp(tt);
743  pSetCoeff(tt,nDiv(pGetCoeff(tso.p1),coefgcd));
744  tso.syz = pMult_mm(tso.syz,tt);
745  pDelete(&tt);
746  coefgcd = nInpNeg(coefgcd);
747  assume (old_repr->m[tso.ind2]!=NULL);
748  p = pCopy(old_repr->m[tso.ind2]);
749  tt = pMDivide(tso.lcm,tso.p2);
750  pSetComp(tt,0);
751  pSetmComp(tt);
752  pSetCoeff(tt,nDiv(pGetCoeff(tso.p2),coefgcd));
753  p = pMult_mm(p,tt);
754  pDelete(&tt);
755  tso.syz = pAdd(p,tso.syz);
756 #ifdef EXPERIMENT2
757  if ((tso.syz!=NULL) && (pGetComp(tso.syz)<=crit_comp))
758  {
759 /*--- breaks when the leading component is less than crit_comp ------*/
760  deleteP = TRUE;
761  discard_pairs++;
762  }
763 #endif
764  nDelete(&coefgcd);
765  } //End of the else-part of EXPERIMENT3
766 #ifdef SHOW_PROT
767 Print("reduziere Paar im Module %d mit: \n",index);
768 PrintS("poly1: ");pWrite(tso.p1);
769 PrintS("poly2: ");pWrite(tso.p2);
770 PrintS("syz: ");pWrite(tso.syz);
771 PrintS("sPoly: ");pWrite(tso.p);
772 #endif
773  assume(tso.syz!=NULL);
774  kBucketInit(syzstr->syz_bucket,tso.syz,-1);
775  if ((tso.p!=NULL) && (!deleteP))
776  {
777  kBucketInit(syzstr->bucket,tso.p,-1);
778  p = kBucketGetLm(syzstr->bucket);
779  j = 0;
780  loop
781  {
782  if (j>=og_idel)
783  {
784 /*--- reduction with generators computed in this procedure ---*/
785  j = 0;
786  while ((j<ng_place) && (!pDivisibleBy(new_generators->m[j],p))) j++;
787  if (j>=ng_place) break;
788  assume (new_repr->m[j]!=NULL);
789  sySPRedSyz_Kosz(syzstr,new_generators->m[j],new_repr->m[j],p);
790  n = kBucketPolyRed(syzstr->bucket,new_generators->m[j],
791  pLength(new_generators->m[j]), NULL);
792  p = kBucketGetLm(syzstr->bucket);
793 #ifdef EXPERIMENT1
794  syzp = kBucketGetLm(syzstr->syz_bucket);
795  if ((syzp!=NULL) && (pGetComp(syzp)<=crit_comp))
796  {
797  deleteP =TRUE;
798  break;
799  }
800  //if (syzp==NULL)
801  //assume(p==NULL);
802  //else
803  //if (pGetComp(syzp)<=crit_comp) short_pairs++;
804 #endif
805  if (p==NULL) break;
806  j = 0;
807  }
808  if (pDivisibleBy(ogm[j],p))
809  {
810 /*--- reduction with general old generators ---------------------*/
811  assume (old_repr->m[j]!=NULL);
812  sySPRedSyz_Kosz(syzstr,ogm[j],old_repr->m[j],p,orp_l[j]);
813  n = kBucketPolyRed(syzstr->bucket,ogm[j],ogm_l[j], NULL);
814  p = kBucketGetLm(syzstr->bucket);
815 #ifdef EXPERIMENT1
816  syzp = kBucketGetLm(syzstr->syz_bucket);
817  if ((syzp!=NULL) && (pGetComp(syzp)<=crit_comp))
818  {
819  break;
820  deleteP =TRUE;
821  }
822  //if (syzp==NULL)
823  //assume(p==NULL);
824  //else
825  //if ((pGetComp(syzp)<=crit_comp) && (p!=NULL)) short_pairs++;
826 #endif
827  if (p==NULL) break;
828  j = 0;
829  }
830  else
831  j++;
832  }
833  kBucketClear(syzstr->bucket,&tso.p,&tso.length);
834  }
835  kBucketClear(syzstr->syz_bucket,&tso.syz,&syz_l);
836  if (deleteP)
837  {
838  pDelete(&tso.p);
839  pDelete(&tso.syz);
840  }
841  }
842  else
843  {
844  PrintS("Shit happens!\n");
845  }
846 #ifdef SHOW_PROT
847 Print("erhalte Paar im Module %d mit: \n",index);
848 PrintS("syz: ");pWrite(tso.syz);
849 PrintS("sPoly: ");pWrite(tso.p);
850 PrintLn();
851 #endif
852  if (toReplace)
853  {
854 /*-- replaces the generator if necessary ------------------*/
855  pDelete(&old_generators->m[toReplace-1]);
856  pDelete(&old_repr->m[toReplace-1]);
857  for (i=toReplace-1;i<og_idel-1;i++)
858  {
859  old_generators->m[i] = old_generators->m[i+1];
860  old_repr->m[i] = old_repr->m[i+1];
861  }
862  old_generators->m[og_idel-1] = NULL;
863  old_repr->m[og_idel-1] = NULL;
864  for (i=itso+1;i<l;i++)
865  {
866  if (resPairs[i].lcm!=NULL)
867  {
868  if ((resPairs[i].ind1==toReplace-1)||(resPairs[i].ind2==toReplace-1))
869  syDeletePair(&resPairs[i]);
870  else
871  {
872  if (resPairs[i].ind1>=toReplace)
873  (resPairs[i].ind1)--;
874  if (resPairs[i].ind2>=toReplace)
875  (resPairs[i].ind2)--;
876  }
877  }
878  }
879  syCompactifyPairSet(resPairs,l,itso+1);
880  }
881  if (tso.p!=NULL)
882  {
883 /*-- stores the new generator ---------------------------------*/
884  //syRedTailSyzPair(tso,syzstr,index,ogm_l,orp_l,&tso.length,&syz_l);
885  if (ng_place>=IDELEMS(new_generators))
886  {
887  pEnlargeSet(&new_generators->m,IDELEMS(new_generators),16);
888  IDELEMS(new_generators) += 16;
889  pEnlargeSet(&new_repr->m,IDELEMS(new_repr),16);
890  IDELEMS(new_repr) += 16;
891  }
892  if (!nIsOne(pGetCoeff(tso.p)))
893  {
894  n=nInvers(pGetCoeff(tso.p));
895  pNorm(tso.p);
896  tso.syz=__p_Mult_nn(tso.syz,n,currRing);
897  nDelete(&n);
898  }
899  new_generators->m[ng_place] = tso.p;
900  tso.p = NULL;
901  new_repr->m[ng_place] = tso.syz;
902  tso.syz = NULL;
903  }
904  else
905  {
906 /*--- takes the syzygy as new generator of the next module ---*/
907  if (tso.syz==NULL)
908  {
909 #ifndef EXPERIMENT2
910 #ifdef EXPERIMENT3
911  short_pairs++;
912 #endif
913 #endif
914  }
915  else if (pGetComp(tso.syz)<=crit_comp)
916  {
917  pDelete(&tso.syz);
918  }
919  else
920  {
921  if (syz_place>=IDELEMS(syzygies))
922  {
923  pEnlargeSet(&syzygies->m,IDELEMS(syzygies),16);
924  IDELEMS(syzygies) += 16;
925  }
926  syzygies->m[syz_place] = tso.syz;
927  tso.syz = NULL;
928  pNorm(syzygies->m[syz_place]);
929  }
930  }
931  resPairs[itso] = tso;
932  syDeletePair(&resPairs[itso]);
933  syTestPairs(resPairs,l,old_generators);
934 }
935 
936 /*3
937 * reduction of all pairs of a fixed degree of the 0-th module
938 */
939 static BOOLEAN redPairs(SSet resPairs,int l_pairs, ideal syzygies,
940  ideal new_generators,ideal new_repr, int crit_comp,syStrategy syzstr,
941  int index)
942 {
943  if (resPairs[0].lcm==NULL) return TRUE;
944  int i,j,actdeg=resPairs[0].order;
945  int * ogm_l=(int*)omAlloc0(IDELEMS(syzstr->res[index])*sizeof(int));
946  int * orp_l=(int*)omAlloc0(IDELEMS(syzstr->orderedRes[index])*sizeof(int));
947  // int t1=IDELEMS(syzstr->res[index]),t2=IDELEMS(syzstr->orderedRes[index]);
948 
949  for (j=IDELEMS(syzstr->res[index])-1;j>=0;j--)
950  {
951  if (syzstr->res[index]->m[j]!=NULL)
952  ogm_l[j] = pLength(syzstr->res[index]->m[j]);
953  }
954  for (j=IDELEMS(syzstr->orderedRes[index])-1;j>=0;j--)
955  {
956  if (syzstr->orderedRes[index]->m[j]!=NULL)
957  orp_l[j] = pLength(syzstr->orderedRes[index]->m[j]);
958  }
959  loop
960  {
961  i = 0;
962  if (TEST_OPT_PROT)
963  Print("(%d,%d)",index,resPairs[0].order);
964  while (resPairs[i].order==actdeg)
965  {
966  syTestPairs(resPairs,l_pairs,syzstr->res[index]);
967  redOnePair(resPairs,i,l_pairs,syzygies,crit_comp,syzstr,index,
968  new_generators, new_repr,ogm_l,orp_l);
969  i++;
970  syTestPairs(resPairs,l_pairs,syzstr->res[index]);
971  }
972  syTestPairs(resPairs,l_pairs,syzstr->res[index]);
973  syCompactifyPairSet(resPairs,l_pairs,0);
974  syTestPairs(resPairs,l_pairs,syzstr->res[index]);
975  if (!idIs0(new_generators))
976  break;
977  else if (resPairs[0].lcm==NULL) //there are no pairs left and no new_gens
978  {
979  omFreeSize((ADDRESS)ogm_l,IDELEMS(syzstr->res[index])*sizeof(int));
980  omFreeSize((ADDRESS)orp_l,IDELEMS(syzstr->orderedRes[index])*sizeof(int));
981  return TRUE;
982  }
983  else
984  actdeg = resPairs[0].order;
985  }
986  syTestPairs(resPairs,l_pairs,syzstr->res[index]);
987  omFreeSize((ADDRESS)ogm_l,IDELEMS(syzstr->res[index])*sizeof(int));
988  omFreeSize((ADDRESS)orp_l,IDELEMS(syzstr->orderedRes[index])*sizeof(int));
989  return FALSE;
990 }
991 
992 /*3
993 * extends the standard basis old_generators with new_generators;
994 * returns the syzygies which involve the new elements;
995 * assumes that the components of the new_generators are sperated
996 * from those of old_generators, i.e. whenever the leading term
997 * of a syzygy lies in the part of the old_generators, the syzygy
998 * lie just in the module old_generators
999 * assumes that the new_generators are reduced w.r.t. old_generators
1000 */
1001 static ideal kosz_std(ideal new_generators,ideal new_repr,syStrategy syzstr,
1002  int index,int next_comp)
1003 {
1004  int og_idel=IDELEMS(syzstr->res[index]);
1005  int l_pairs=2*og_idel;
1006  ideal syzygies=idInit(16,syzstr->res[index]->rank+1);
1007  if ((idIs0(new_generators)) || (new_generators->m[0]==NULL))
1008  {
1009  WerrorS("Hier ist was faul!\n");
1010  return NULL;
1011  }
1012  SSet resPairs=(SSet)omAlloc0(l_pairs*sizeof(SObject));
1013  loop
1014  {
1015  updatePairs(&resPairs,&l_pairs,syzstr,index,
1016  new_generators,new_repr,next_comp);
1017  if (redPairs(resPairs,l_pairs,syzygies, new_generators,new_repr,
1018  next_comp,syzstr,index)) break;
1019  }
1020  omFreeSize((SSet)resPairs,l_pairs*sizeof(SObject));
1021  return syzygies;
1022 }
1023 
1024 /*3
1025 * normalizes the incoming generators
1026 */
1027 static poly normalize(poly next_p,ideal add_generators, syStrategy syzstr,
1028  int * g_l,int * p_l,int crit_comp)
1029 {
1030  int j=0,i=IDELEMS(add_generators);
1031  kBucketInit(syzstr->bucket,next_p,pLength(next_p));
1032  poly p = kBucketGetLm(syzstr->bucket),result;
1033  number n;
1034 
1035  loop
1036  {
1037  if ((j>=i) || (p==NULL) || (pGetComp(p)<=crit_comp)) break;
1038  if ((add_generators->m[j]!=NULL) && (pDivisibleBy(add_generators->m[j],p)))
1039  {
1040  n = kBucketPolyRed(syzstr->bucket,add_generators->m[j], g_l[j],
1041  NULL);
1042  nDelete(&n);
1043  p = kBucketGetLm(syzstr->bucket);
1044  j = 0;
1045  }
1046  else
1047  j++;
1048  }
1049  kBucketClear(syzstr->bucket,&result,p_l);
1050  return result;
1051 }
1052 
1053 /*3
1054 * updates the pairs in the higher modules
1055 */
1056 static void updatePairsHIndex(SSet *resPairs,int *l_pairs,syStrategy /*syzstr*/,
1057  int index,ideal add_generators,ideal /*add_repr*/,ideal /*new_generators*/,
1058  ideal /*new_repr*/,int /*crit_comp*/,int* first_new)
1059 {
1060  int i=*first_new,l=*l_pairs,j,ll,j1,add_idel=IDELEMS(add_generators);
1061  ideal pairs=idInit(add_idel,add_generators->rank);
1062  polyset prs=pairs->m;
1063  poly p=NULL;
1064  SObject tso;
1065 
1066  syInitializePair(&tso);
1067  while ((l>0) && ((*resPairs)[l-1].lcm==NULL)) l--;
1068  while ((i<add_idel) && (add_generators->m[i]!=NULL))
1069  {
1070  for (j=0;j<i;j++)
1071  {
1072  if (pGetComp(add_generators->m[j]) == pGetComp(add_generators->m[i]))
1073  {
1074  p = pOne();
1075  pLcm(add_generators->m[j],add_generators->m[i],p);
1076  pSetComp(p,i+1);
1077  pSetm(p);
1078  j1 = 0;
1079  while (j1<j)
1080  {
1081  if (prs[j1]!=NULL)
1082  {
1083  if (pLmDivisibleByNoComp(prs[j1],p))
1084  {
1085  pDelete(&p);
1086  break;
1087  }
1088  else if (pLmDivisibleByNoComp(p,prs[j1]))
1089  {
1090  pDelete(&(prs[j1]));
1091  }
1092 #ifdef USE_CHAINCRIT
1093  else
1094  {
1095  poly p1,p2;
1096  int ip=(currRing->N);
1097  p1 = pMDivide(p,add_generators->m[j]);
1098  p2 = pMDivide(prs[j1],add_generators->m[j1]);
1099  while ((ip>0) && (pGetExp(p1,ip)*pGetExp(p2,ip)==0)) ip--;
1100  if (ip==0)
1101  {
1102  int ti=0;
1103  while ((ti<l) && (((*resPairs)[ti].ind1!=j1)|| ((*resPairs)[ti].ind2!=j))) ti++;
1104  if (ti<l)
1105  {
1106  if (TEST_OPT_PROT) PrintS("cc");
1107  syDeletePair(&(*resPairs)[ti]);
1108  syCompactifyPairSet(*resPairs,*l_pairs,ti);
1109  l--;
1110  }
1111  }
1112  pDelete(&p1);
1113  pDelete(&p2);
1114  }
1115 #endif
1116  }
1117  j1++;
1118  }
1119  if (p!=NULL)
1120  prs[j] = p;
1121  }
1122  }
1123  for (j=0;j<i;j++)
1124  {
1125  if (prs[j] !=NULL)
1126  {
1127  if (l>=*l_pairs)
1128  {
1129  SSet temp = (SSet)omAlloc0((*l_pairs+16)*sizeof(SObject));
1130  for (ll=0;ll<*l_pairs;ll++)
1131  {
1132  temp[ll].p = (*resPairs)[ll].p;
1133  temp[ll].p1 = (*resPairs)[ll].p1;
1134  temp[ll].p2 = (*resPairs)[ll].p2;
1135  temp[ll].syz = (*resPairs)[ll].syz;
1136  temp[ll].lcm = (*resPairs)[ll].lcm;
1137  temp[ll].ind1 = (*resPairs)[ll].ind1;
1138  temp[ll].ind2 = (*resPairs)[ll].ind2;
1139  temp[ll].syzind = (*resPairs)[ll].syzind;
1140  temp[ll].order = (*resPairs)[ll].order;
1141  temp[ll].isNotMinimal = (*resPairs)[ll].isNotMinimal;
1142  }
1143  omFreeSize((ADDRESS)(*resPairs),*l_pairs*sizeof(SObject));
1144  *l_pairs += 16;
1145  (*resPairs) = temp;
1146  }
1147  tso.lcm = prs[j];
1148  prs[j] = NULL;
1149  tso.order = p_FDeg(tso.lcm,currRing);
1150  tso.p1 = add_generators->m[j];
1151  tso.p2 = add_generators->m[i];
1152  tso.ind1 = j;
1153  tso.ind2 = i;
1154  tso.syzind = -1;
1155  tso.isNotMinimal = NULL;
1156  tso.p = NULL;
1157  tso.syz = NULL;
1158  SSet rP=*resPairs;
1159 #ifdef SHOW_PROT
1160 Print("erzeuge Paar im Modul %d,%d mit: \n",index,tso.order);
1161 PrintS("poly1: ");pWrite(tso.p1);
1162 PrintS("poly2: ");pWrite(tso.p2);
1163 PrintS("syz: ");pWrite(tso.syz);
1164 PrintS("sPoly: ");pWrite(tso.p);
1165 PrintLn();
1166 #endif
1167  syEnterPair(rP,&tso,&l,index);
1168  syInitializePair(&tso);
1169  }
1170  }
1171  i++;
1172  }
1173  *first_new = i;
1174  idDelete(&pairs);
1175 }
1176 
1177 /*3
1178 * reduction of a single pair in the higher moduls
1179 */
1180 #ifdef SHOW_PROT
1181 static void redOnePairHIndex(SSet resPairs,int itso, int crit_comp,
1182  syStrategy syzstr,int index,ideal add_generators, ideal add_repr,
1183  ideal new_generators, ideal new_repr,int * next_place_add,int ** g_l,
1184  poly deg_soc)
1185 #else
1186 static void redOnePairHIndex(SSet resPairs,int itso, int crit_comp,
1187  syStrategy syzstr,int /*index*/,ideal add_generators, ideal add_repr,
1188  ideal new_generators, ideal new_repr,int * next_place_add,int ** g_l,
1189  poly deg_soc)
1190 #endif
1191 {
1192  SObject tso = resPairs[itso];
1193  assume (tso.lcm!=NULL);
1194  int ng_place=IDELEMS(new_generators);
1195  int i,j;
1196  number n;
1197  poly p;
1198 #ifdef EXPERIMENT1
1199  poly syzp;
1200 #endif
1201 
1202  assume (tso.ind1<*next_place_add);
1203  assume (tso.ind2<*next_place_add);
1204  assume (tso.ind1!=tso.ind2);
1205  assume (tso.p1 == add_generators->m[tso.ind1]);
1206  assume (tso.p2 == add_generators->m[tso.ind2]);
1207  tso.p1 = add_generators->m[tso.ind1];
1208  tso.p2 = add_generators->m[tso.ind2];
1209  if ((tso.p1!=NULL) && (tso.p2!=NULL))
1210  {
1211  if (TEST_OPT_PROT)
1212  PrintS(".");
1213 #ifdef USE_PROD_CRIT
1214  if (p_FDeg(tso.p1,currRing)+p_FDeg(tso.p2,currRing)==tso.order+p_FDeg(deg_soc,currRing))
1215  {
1216  if (TEST_OPT_PROT) PrintS("pc");
1217  int ac=pGetComp(tso.p1);
1218  assume(ac=pGetComp(tso.p2));
1219  poly p1=pCopy(tso.p1);
1220  poly p2=pCopy(tso.p2);
1221  poly pp1,pp2,tp1,tp2;
1222  poly sp1=pCopy(add_repr->m[tso.ind1]),sp2=pCopy(add_repr->m[tso.ind2]);
1223  pp1 = p1;
1224  pp2 = p2;
1225  loop
1226  {
1227  assume(pp1!=NULL);
1228  for(i=(int)(currRing->N); i; i--)
1229  pSetExp(pp1,i, pGetExp(pp1,i)- pGetExp(deg_soc,i));
1230  pSetComp(pp1, 0);
1231  pSetm(pp1);
1232  if ((pNext(pp1)!=NULL) && (pGetComp(pNext(pp1))!=ac)) break;
1233  pIter(pp1);
1234  }
1235  loop
1236  {
1237  assume(pp2!=NULL);
1238  for(i=(int)(currRing->N); i; i--)
1239  pSetExp(pp2,i, pGetExp(pp2,i)- pGetExp(deg_soc,i));
1240  pSetComp(pp2, 0);
1241  pSetm(pp2);
1242  if ((pNext(pp2)!=NULL) && (pGetComp(pNext(pp2))!=ac)) break;
1243  pIter(pp2);
1244  }
1245  tp1 = pNext(pp1);
1246  tp2 = pNext(pp2);
1247  pNext(pp1) = NULL;
1248  pNext(pp2) = NULL;
1249  //p_Shift(&p1,-ac,currRing);
1250  //p_Shift(&p2,-ac,currRing);
1251  tp1 = pMult(tp1,pCopy(p2));
1252  tp2 = pMult(tp2,pCopy(p1));
1253  sp1 = pMult(p2,sp1);
1254  sp2 = pMult(p1,sp2);
1255  tso.p = pSub(tp1,tp2);
1256  tso.syz = pSub(sp1,sp2);
1257  }
1258  else
1259 #endif
1260  {
1261  tso.p = ksOldCreateSpoly(tso.p2,tso.p1);
1262  number coefgcd = n_Gcd(pGetCoeff(tso.p1),pGetCoeff(tso.p2),currRing->cf);
1263  assume (add_repr->m[tso.ind1]!=NULL);
1264  tso.syz = pCopy(add_repr->m[tso.ind1]);
1265  poly tt = pMDivide(tso.lcm,tso.p1);
1266  pSetComp(tt,0);
1267  pSetmComp(tt);
1268  pSetCoeff(tt,nDiv(pGetCoeff(tso.p1),coefgcd));
1269  tso.syz = pMult_mm(tso.syz,tt);
1270  pDelete(&tt);
1271  coefgcd = nInpNeg(coefgcd);
1272  assume (add_repr->m[tso.ind2]!=NULL);
1273  p = pCopy(add_repr->m[tso.ind2]);
1274  tt = pMDivide(tso.lcm,tso.p2);
1275  pSetComp(tt,0);
1276  pSetmComp(tt);
1277  pSetCoeff(tt,nDiv(pGetCoeff(tso.p2),coefgcd));
1278  p = pMult_mm(p,tt);
1279  pDelete(&tt);
1280  tso.syz = pAdd(p,tso.syz);
1281  nDelete(&coefgcd);
1282  }
1283 #ifdef SHOW_PROT
1284 Print("reduziere Paar im Module %d mit: \n",index);
1285 PrintS("poly1: ");pWrite(tso.p1);
1286 PrintS("poly2: ");pWrite(tso.p2);
1287 PrintS("syz: ");pWrite(tso.syz);
1288 PrintS("sPoly: ");pWrite(tso.p);
1289 #endif
1290  assume(tso.syz!=NULL);
1291  kBucketInit(syzstr->syz_bucket,tso.syz,-1);
1292  if (tso.p!=NULL)
1293  {
1294  kBucketInit(syzstr->bucket,tso.p,-1);
1295  p = kBucketGetLm(syzstr->bucket);
1296  j = 0;
1297  loop
1298  {
1299  if (j>=*next_place_add) break;
1300  if (pDivisibleBy(add_generators->m[j],p))
1301  {
1302  assume (add_repr->m[j]!=NULL);
1303  sySPRedSyz_Kosz(syzstr,add_generators->m[j],add_repr->m[j],p);
1304  n = kBucketPolyRed(syzstr->bucket,add_generators->m[j],
1305  pLength(add_generators->m[j]), NULL);
1306  p = kBucketGetLm(syzstr->bucket);
1307  if ((p==NULL) || (pGetComp(p)<=crit_comp)) break;
1308  j = 0;
1309  }
1310  else
1311  j++;
1312  }
1313  kBucketClear(syzstr->bucket,&tso.p,&tso.length);
1314  }
1315  kBucketClear(syzstr->syz_bucket,&tso.syz,&j);
1316  }
1317  else
1318  {
1319  PrintS("Shit happens!\n");
1320  }
1321 #ifdef SHOW_PROT
1322 Print("erhalte Paar im Module %d mit: \n",index);
1323 PrintS("syz: ");pWrite(tso.syz);
1324 PrintS("sPoly: ");pWrite(tso.p);
1325 PrintLn();
1326 #endif
1327  if (tso.p!=NULL)
1328  {
1329  if (!nIsOne(pGetCoeff(tso.p)))
1330  {
1331  n=nInvers(pGetCoeff(tso.p));
1332  pNorm(tso.p);
1333  tso.syz=__p_Mult_nn(tso.syz,n,currRing);
1334  nDelete(&n);
1335  }
1336  }
1337  if ((TEST_OPT_PROT) && (tso.syz==NULL)) PrintS("null");
1338  if ((tso.p!=NULL) && (pGetComp(tso.p)>crit_comp))
1339  {
1340  if (*next_place_add>=IDELEMS(add_generators))
1341  {
1342  pEnlargeSet(&add_generators->m,IDELEMS(add_generators),16);
1343  pEnlargeSet(&add_repr->m,IDELEMS(add_repr),16);
1344  *g_l = (int*)omRealloc0Size((ADDRESS)*g_l, IDELEMS(add_generators)*sizeof(int),
1345  (IDELEMS(add_generators)+16)*sizeof(int));
1346  IDELEMS(add_generators) += 16;
1347  IDELEMS(add_repr) += 16;
1348  }
1349  assume(add_repr->m[*next_place_add]==NULL);
1350  add_generators->m[*next_place_add] = tso.p;
1351  add_repr->m[*next_place_add] = tso.syz;
1352  (*g_l)[*next_place_add] = tso.length;
1353  (*next_place_add)++;
1354  }
1355  else
1356  {
1357  while ((ng_place>0) && (new_generators->m[ng_place-1]==NULL) &&
1358  (new_repr->m[ng_place-1]==NULL)) ng_place--;
1359  if (ng_place>=IDELEMS(new_generators))
1360  {
1361  pEnlargeSet(&new_generators->m,IDELEMS(new_generators),16);
1362  IDELEMS(new_generators) += 16;
1363  pEnlargeSet(&new_repr->m,IDELEMS(new_repr),16);
1364  IDELEMS(new_repr) += 16;
1365  }
1366  new_generators->m[ng_place] = tso.p;
1367  new_repr->m[ng_place] = tso.syz;
1368  }
1369  tso.p = NULL;
1370  tso.syz = NULL;
1371  resPairs[itso] = tso;
1372  syDeletePair(&resPairs[itso]);
1373 }
1374 
1375 /*3
1376 * reduction of all pairs of a fixed degree of a fixed module
1377 */
1378 static BOOLEAN reducePairsHIndex(SSet resPairs,int l_pairs,syStrategy syzstr,
1379  int index,ideal add_generators,ideal add_repr,ideal new_generators,
1380  ideal new_repr,int crit_comp,int * red_deg,int * next_place_add,int **g_l,
1381  resolvente totake)
1382 {
1383  if (resPairs[0].lcm==NULL) return FALSE;
1384  int i=0;
1385  poly deg_soc;
1386 
1387  if (TEST_OPT_PROT)
1388  Print("(%d,%d)",index,resPairs[0].order);
1389  while ((i<l_pairs) && (resPairs[i].order==*red_deg))
1390  {
1391  assume(totake[index-1]!=NULL);
1392  assume(pGetComp(resPairs[i].p1)<=IDELEMS(totake[index-1]));
1393  assume(totake[index-1]->m[pGetComp(resPairs[i].p1)-1]!=NULL);
1394  deg_soc = totake[index-1]->m[pGetComp(resPairs[i].p1)-1];
1395  redOnePairHIndex(resPairs,i,crit_comp,syzstr,index, add_generators,add_repr,
1396  new_generators, new_repr,next_place_add,g_l,deg_soc);
1397  i++;
1398  }
1399  syCompactifyPairSet(resPairs,l_pairs,0);
1400  if (resPairs[0].lcm==NULL) //there are no pairs left and no new_gens
1401  return FALSE;
1402  else
1403  *red_deg = resPairs[0].order;
1404  return TRUE;
1405 }
1406 
1407 /*3
1408 * we proceed the generators of the next module;
1409 * they are stored in add_generators and add_repr;
1410 * if the normal form of a new generators w.r.t. add_generators has
1411 * pGetComp<crit_comp it is skipped from the reduction;
1412 * new_generators and new_repr (which are empty) stores the result of the
1413 * reduction which is normalized afterwards
1414 */
1415 static void procedeNextGenerators(ideal temp_generators,ideal /*temp_repr*/,
1416  ideal new_generators, ideal new_repr, ideal add_generators,
1417  ideal add_repr, syStrategy syzstr,int index, int crit_comp,
1418  resolvente totake)
1419 {
1420  int i=0,j,next_new_el;
1421  int idel_temp=IDELEMS(temp_generators);
1422  int next_place_add;
1423  int p_length,red_deg,l_pairs=IDELEMS(add_generators);
1424  poly next_p;
1425  int * gen_length=(int*)omAlloc0(IDELEMS(add_generators)*sizeof(int));
1426  int * secgen_length=(int*)omAlloc0(IDELEMS(syzstr->res[index])*sizeof(int));
1427  BOOLEAN pairs_left;
1428  SSet resPairs=(SSet)omAlloc0(l_pairs*sizeof(SObject));
1429 
1430  for (j=IDELEMS(syzstr->res[index])-1;j>=0;j--)
1431  {
1432  if (syzstr->res[index]->m[j]!=NULL)
1433  secgen_length[j] = pLength(syzstr->res[index]->m[j]);
1434  }
1435  assume(idIs0(new_generators));
1436  next_place_add = IDELEMS(add_generators);
1437  while ((next_place_add>0) && (add_generators->m[next_place_add-1]==NULL))
1438  next_place_add--;
1439  int next_deg = p_FDeg(temp_generators->m[i],currRing);
1440  next_new_el = next_place_add;
1441 /*--- loop about all all elements-----------------------------------*/
1442  while ((i<idel_temp) && (temp_generators->m[i]!=NULL))
1443  {
1444 /*--- separates elements of equal degree----------------------------*/
1445 #ifdef USE_REGULARITY
1446  if (syzstr->regularity>0)
1447  {
1448  if (next_deg >= syzstr->regularity+index)
1449  {
1450  while ((i<idel_temp) && (temp_generators->m[i]!=NULL))
1451  {
1452  pDelete(&temp_generators->m[i]);
1453  i++;
1454  }
1455  break;
1456  }
1457  }
1458 #endif
1459  while ((i<idel_temp) && (p_FDeg(temp_generators->m[i],currRing)==next_deg))
1460  {
1461  next_p = temp_generators->m[i];
1462  temp_generators->m[i] = NULL;
1463  next_p = normalize(next_p,add_generators,syzstr,gen_length,&p_length,
1464  crit_comp);
1465  if (next_p!=NULL)
1466  {
1467  if (pGetComp(next_p)<=crit_comp)
1468  {
1469  pDelete(&next_p);
1470  //if (TEST_OPT_PROT) Print("u(%d)",index);
1471  }
1472  else
1473  {
1474  next_p = syRedTailSyz(next_p,add_generators,syzstr->res[index],crit_comp,syzstr,
1475  gen_length,secgen_length,&p_length);
1476  if (!nIsOne(pGetCoeff(next_p)))
1477  pNorm(next_p);
1478  if (next_place_add>=IDELEMS(add_generators))
1479  {
1480  pEnlargeSet(&add_generators->m,IDELEMS(add_generators),16);
1481  pEnlargeSet(&add_repr->m,IDELEMS(add_repr),16);
1482  gen_length = (int*)omRealloc0Size((ADDRESS)gen_length, IDELEMS(add_generators)*sizeof(int),
1483  (IDELEMS(add_generators)+16)*sizeof(int));
1484  IDELEMS(add_generators) += 16;
1485  IDELEMS(add_repr) += 16;
1486  }
1487  add_generators->m[next_place_add] = next_p;
1488  if (totake[index]==NULL)
1489  totake[index] = idInit(16,new_generators->rank);
1490  if ((*syzstr->Tl)[index]==IDELEMS(totake[index]))
1491  {
1492  pEnlargeSet(&totake[index]->m,IDELEMS(totake[index]),
1493  (*syzstr->Tl)[index]+16-IDELEMS(totake[index]));
1494  for (j=IDELEMS(totake[index]);j<(*syzstr->Tl)[index]+16;j++)
1495  totake[index]->m[j] = NULL;
1496  IDELEMS(totake[index]) = (*syzstr->Tl)[index]+16;
1497  }
1498 #ifdef FULL_TOTAKE
1499  totake[index]->m[(*syzstr->Tl)[index]] = pCopy(next_p);
1500 #else
1501  totake[index]->m[(*syzstr->Tl)[index]] = pHead(next_p);
1502 #endif
1503  assume(add_repr->m[next_place_add]==NULL);
1504 #ifdef WITH_SCHREYER_ORD
1505  add_repr->m[next_place_add] = pHead(add_generators->m[next_place_add]);
1506 #else
1507  add_repr->m[next_place_add] = pOne();
1508 #endif
1509  ((*syzstr->Tl)[index])++;
1510  pSetComp(add_repr->m[next_place_add],(*syzstr->Tl)[index]);
1511  pSetmComp(add_repr->m[next_place_add]);
1512  gen_length[next_place_add] = p_length;
1513  next_place_add++;
1514  }
1515  }
1516  i++;
1517  } //end inner loop
1518  red_deg = next_deg;
1519  if (i<idel_temp)
1520  next_deg = p_FDeg(temp_generators->m[i],currRing);
1521  else
1522  next_deg = -1;
1523  if ((next_place_add>next_new_el) || (next_deg<0)) //there are new generators or pairs
1524  {
1525 /*-reducing and generating pairs until the degree of the next generators-*/
1526  pairs_left = TRUE;
1527  while (pairs_left && ((next_deg<0) || (red_deg<= next_deg)))
1528  {
1529  updatePairsHIndex(&resPairs,&l_pairs,syzstr,index,add_generators,
1530  add_repr,new_generators,new_repr,crit_comp,&next_new_el);
1531  pairs_left = reducePairsHIndex(resPairs,l_pairs,syzstr,index,add_generators,
1532  add_repr,new_generators,new_repr,crit_comp,&red_deg,&next_place_add,&gen_length,
1533  totake);
1534  }
1535  }
1536  }
1537  omFreeSize((SSet)resPairs,l_pairs*sizeof(SObject));
1538  omFreeSize((ADDRESS)gen_length,IDELEMS(add_generators)*sizeof(int));
1539  omFreeSize((ADDRESS)secgen_length,IDELEMS(syzstr->res[index])*sizeof(int));
1540 }
1541 
1542 /*3
1543 * normalizes the part of the next reduction lying within the block
1544 * of former generators (old_generators);
1545 */
1546 static ideal normalizeOldPart(ideal new_generators,ideal new_repr,
1547  syStrategy syzstr,int index,int /*crit_comp*/)
1548 {
1549  ideal old_generators= syzstr->res[index];
1550  ideal old_repr= syzstr->orderedRes[index];
1551  int i,j=0,ii=IDELEMS(old_generators)-1,dummy;
1552  poly p;
1553  number n;
1554  int * g_l=(int*)omAlloc0(IDELEMS(old_generators)*sizeof(int));
1555 
1556  for (i=0;i<IDELEMS(old_generators);i++)
1557  {
1558  if (old_generators->m[i]!=NULL)
1559  {
1560  g_l[i] = pLength(old_generators->m[i]);
1561  }
1562  }
1563  for (i=IDELEMS(new_generators)-1;i>=0;i--)
1564  {
1565  if (new_generators->m[i]!=NULL)
1566  {
1567  kBucketInit(syzstr->bucket,new_generators->m[i],
1568  pLength(new_generators->m[i]));
1569  kBucketInit(syzstr->syz_bucket,new_repr->m[i],
1570  pLength(new_repr->m[i]));
1571  p = kBucketGetLm(syzstr->bucket);
1572  loop
1573  {
1574  if ((j>=ii) || (p==NULL)) break;
1575  if ((old_generators->m[j]!=NULL) &&
1576  (pDivisibleBy(old_generators->m[j],p)))
1577  {
1578  sySPRedSyz_Kosz(syzstr,old_generators->m[j],old_repr->m[j],p);
1579  n = kBucketPolyRed(syzstr->bucket,old_generators->m[j], g_l[j],
1580  NULL);
1581  nDelete(&n);
1582  p = kBucketGetLm(syzstr->bucket);
1583  j = 0;
1584  }
1585  else
1586  j++;
1587  }
1588  assume (p==NULL);
1589  kBucketClear(syzstr->bucket,&new_generators->m[i],&dummy);
1590  kBucketClear(syzstr->syz_bucket,&new_repr->m[i],&dummy);
1591  }
1592  }
1593  ideal result=idInit(IDELEMS(new_repr),new_repr->rank);
1594  for (j=IDELEMS(new_repr)-1;j>=0;j--)
1595  {
1596  result->m[j] = new_repr->m[j];
1597  if ((result->m[j]!=NULL) && (!nIsOne(pGetCoeff(result->m[j]))))
1598  pNorm(result->m[j]);
1599  new_repr->m[j] = NULL;
1600  }
1601  omFreeSize((ADDRESS)g_l,IDELEMS(old_generators)*sizeof(int));
1602  return result;
1603 }
1604 
1605 /*3
1606 * constructs the new subresolution for a nonregular extension
1607 */
1608 static ideal kosz_ext(ideal new_generators,ideal new_repr,syStrategy syzstr,
1609  int index,int next_comp,resolvente totake)
1610 {
1611  ideal temp_generators =idInit(IDELEMS(new_generators),new_generators->rank);
1612  ideal temp_repr=idInit(IDELEMS(new_repr),new_repr->rank);
1613  ideal add_generators =idInit(IDELEMS(new_generators),new_generators->rank);
1614  ideal add_repr=idInit(IDELEMS(new_repr),new_repr->rank);
1615  int min_deg=-1;
1616  int j,jj,k,deg_p,idel_temp=IDELEMS(temp_generators);
1617  poly p;
1618 /*--reorder w.r.t. the degree----------------------------------------*/
1619  for (j=IDELEMS(new_generators)-1;j>=0;j--)
1620  {
1621  if (new_generators->m[j]!=NULL)
1622  {
1623  p = new_generators->m[j];
1624  new_generators->m[j] = NULL;
1625  deg_p = p_FDeg(p,currRing);
1626  if (min_deg<0)
1627  {
1628  min_deg = deg_p;
1629  }
1630  else
1631  {
1632  if (deg_p<min_deg) min_deg = deg_p;
1633  }
1634  k = 0;
1635  while ((k<idel_temp) && (temp_generators->m[k]!=NULL) &&
1636  (p_FDeg(temp_generators->m[k],currRing)<=deg_p)) k++;
1637  for (jj=idel_temp-1;jj>k;jj--)
1638  {
1639  temp_generators->m[jj] = temp_generators->m[jj-1];
1640  }
1641  temp_generators->m[k] = p;
1642  }
1643  }
1644 /*--- computing the standard basis in the resolution of the extension -*/
1645  procedeNextGenerators(temp_generators,temp_repr,new_generators,new_repr,
1646  add_generators,add_repr,syzstr,index,next_comp,totake);
1647  j = IDELEMS(syzstr->res[index]);
1648  while ((j>0) && (syzstr->res[index]->m[j-1]==NULL)) j--;
1649  jj = IDELEMS(add_generators);
1650  while ((jj>0) && (add_generators->m[jj-1]==NULL)) jj--;
1651  if (j+jj>=IDELEMS(syzstr->res[index]))
1652  {
1653  pEnlargeSet(&syzstr->res[index]->m,IDELEMS(syzstr->res[index]),
1654  j+jj+1-IDELEMS(syzstr->res[index]));
1655  IDELEMS(syzstr->res[index]) = j+jj+1;
1656  pEnlargeSet(&syzstr->orderedRes[index]->m,IDELEMS(syzstr->orderedRes[index]),
1657  j+jj+1-IDELEMS(syzstr->orderedRes[index]));
1658  IDELEMS(syzstr->orderedRes[index]) = j+jj+1;
1659  }
1660  for (k=0;k<jj;k++)
1661  {
1662  syzstr->res[index]->m[j+k] = add_generators->m[k];
1663  syzstr->orderedRes[index]->m[j+k] = add_repr->m[k];
1664  add_generators->m[k] = NULL;
1665  add_repr->m[k] = NULL;
1666  }
1667  assume(idIs0(add_generators));
1668  assume(idIs0(add_repr));
1669  idDelete(&add_generators);
1670  idDelete(&add_repr);
1671  idDelete(&temp_generators);
1672  idDelete(&temp_repr);
1673 /*--- normalizing the rest to get the syzygies ------------------------*/
1674  return normalizeOldPart(new_generators,new_repr,syzstr,index,next_comp);
1675 }
1676 
1677 /*
1678 * this procedure assumes that the first order is C !!!
1679 * INPUT: old_generators - the generators of the actual module
1680 * computed so far (they are mixed vectors)
1681 * old_repr - the representations of the old generators
1682 * new_generators - generators coming from reductions below,
1683 * they must have leading terms in new components
1684 * (they live only in the module part)
1685 * (*syzstr->Tl)[index] - the last used component in the syzygy
1686 * OUTPUT: old_generators is updated
1687 * new_generators is empty
1688 * the return value is a set of new generators for the syzygies,
1689 */
1690 static ideal syAppendSyz(ideal new_generators, syStrategy syzstr,int index,int crit_comp,
1691  resolvente totake)
1692 {
1693  int i,j;
1694  ideal result;
1695  int rk_new_gens = id_RankFreeModule(new_generators,currRing);
1696  if (syzstr->res[index]==NULL)
1697  {
1698  syzstr->res[index] = idInit(1,si_max(rk_new_gens,1));
1699  syzstr->orderedRes[index] = idInit(1,si_max(rk_new_gens,1));
1700  }
1701  int ng_idel=IDELEMS(new_generators);
1702  ideal new_repr =idInit(ng_idel, crit_comp+ng_idel);
1703 
1704  if (index==0)
1705  {
1706  //int * og_l=(int*)omAlloc0(IDELEMS(syzstr->res[0])*sizeof(int));
1707  //for (i=IDELEMS(syzstr->res[0])-1;i>=0;i--)
1708  //{
1709  //if (syzstr->res[0]->m[i]!=NULL)
1710  //og_l[i] = pLength(syzstr->res[0]->m[i]);
1711  //}
1712  for (i=0;i<ng_idel;i++)
1713  {
1714  if (new_generators->m[i]!=NULL)
1715  {
1716  //int ng_l=pLength(new_generators->m[i]);
1717  //new_generators->m[i] = syRedTailSyz(new_generators->m[i],syzstr->res[0],NULL,0,syzstr,
1718  //og_l,NULL,&ng_l);
1719  if (totake[index]==NULL)
1720  totake[index] = idInit(16,new_generators->rank);
1721  if ((*syzstr->Tl)[index]>=IDELEMS(totake[index]))
1722  {
1723  pEnlargeSet(&totake[index]->m,IDELEMS(totake[index]),
1724  (*syzstr->Tl)[index]+16-IDELEMS(totake[index]));
1725  for (j=IDELEMS(totake[index]);j<(*syzstr->Tl)[index]+16;j++)
1726  totake[index]->m[j] = NULL;
1727  IDELEMS(totake[index]) = (*syzstr->Tl)[index]+16;
1728  }
1729 #ifdef FULL_TOTAKE
1730  totake[index]->m[(*syzstr->Tl)[index]] = pCopy(new_generators->m[i]);
1731 #else
1732  totake[index]->m[(*syzstr->Tl)[index]] = pHead(new_generators->m[i]);
1733 #endif
1734 #ifdef WITH_SCHREYER_ORD
1735  new_repr->m[i] = pHead(new_generators->m[i]);
1736 #else
1737  new_repr->m[i] = pOne();
1738 #endif
1739  ((*syzstr->Tl)[index])++;
1740  pSetComp(new_repr->m[i],(*syzstr->Tl)[index]);
1741  pSetmComp(new_repr->m[i]);
1742  }
1743  }
1744  //omFreeSize((ADDRESS)og_l,IDELEMS(syzstr->res[0])*sizeof(int));
1745 #ifdef SHOW_PROT
1746 PrintS("Add new generators:\n");
1747 idPrint(new_generators);
1748 PrintS("with representations:\n");
1749 idPrint(new_repr);
1750 #endif
1751  result = kosz_std(new_generators,new_repr,syzstr,index,crit_comp);
1752  }
1753  else
1754  {
1755  result = kosz_ext(new_generators,new_repr,syzstr,index,crit_comp,totake);
1756  }
1758  assume(idIs0(new_repr));
1759  idDelete(&new_repr);
1760  return result;
1761 }
1762 
1763 /*
1764 * main call of the extended Koszul-resolution
1765 */
1766 syStrategy syKosz(ideal arg,int * length)
1767 {
1768  int i,j,jj,k=0,index=0,rk_arg/*,next_syz=0*/;
1769  int crit_comp,t_comp,next_deg,old_tl;
1770  ideal temp=NULL,old_ideal,old_repr;
1771  ring origR = currRing;
1772  poly next_gen;
1773  BOOLEAN isRegular;
1774 
1775  discard_pairs = 0;
1776  short_pairs = 0;
1777  if (idIs0(arg)) return NULL;
1778  rk_arg = id_RankFreeModule(arg,currRing);
1779  syStrategy syzstr=(syStrategy)omAlloc0(sizeof(ssyStrategy));
1780 /*--- changes to a Cdp-ring ----------------------------*/
1781  syzstr->syRing = rAssure_C_dp(origR); rChangeCurrRing(syzstr->syRing);
1782 /*--- initializes the data structures---------------*/
1783  syzstr->length = *length = (syzstr->syRing->N)+2;
1784  syzstr->regularity = -1;
1785  if (origR!=syzstr->syRing)
1786  temp = idrCopyR(arg, origR, syzstr->syRing);
1787  else
1788  temp = idCopy(arg);
1789  if (rk_arg==0)
1790  {
1791  id_Shift(temp,1,currRing);
1792  }
1793  idSkipZeroes(temp);
1794 #ifdef WITH_SORT
1795  if (temp->m[0]!=NULL)
1796  {
1797  int md;
1798  int maxdeg=p_FDeg(temp->m[IDELEMS(temp)-1],currRing);
1799  ideal temp1=idInit(IDELEMS(temp),temp->rank);
1800  for (j=IDELEMS(temp)-2;j>=0;j--)
1801  {
1802  jj = p_FDeg(temp->m[j],currRing);
1803  if (jj>maxdeg) maxdeg = jj;
1804  }
1805  while (!idIs0(temp))
1806  {
1807  md = maxdeg;
1808  for (j=IDELEMS(temp)-1;j>=0;j--)
1809  {
1810  if (temp->m[j]!=NULL)
1811  {
1812  jj = p_FDeg(temp->m[j],currRing);
1813  if (jj<md) md = jj;
1814  }
1815  }
1816  for (j=0;j<IDELEMS(temp);j++)
1817  {
1818  if ((temp->m[j]!=NULL) && (p_FDeg(temp->m[j],currRing)==md))
1819  {
1820  temp1->m[k] = temp->m[j];
1821  temp->m[j] = NULL;
1822  k++;
1823  }
1824  }
1825  }
1826  idDelete(&temp);
1827  temp = temp1;
1828  temp1 = NULL;
1829  }
1830 #endif
1831 #ifdef USE_REGULARITY
1832  int last_generator=IDELEMS(temp)-1;
1833  while ((last_generator>=0) && (temp->m[last_generator]==NULL))
1834  last_generator--;
1835 #endif
1836  syzstr->res = (resolvente)omAlloc0((*length+1)*sizeof(ideal));
1837  syzstr->orderedRes = (resolvente)omAlloc0((*length+1)*sizeof(ideal));
1838  resolvente totake=(resolvente)omAlloc0((*length+1)*sizeof(ideal));
1839  syzstr->Tl = new intvec(*length+1);
1840  syzstr->bucket = kBucketCreate(currRing);
1841  syzstr->syz_bucket = kBucketCreate(currRing);
1842  ideal new_generators=idInit(1,si_max(rk_arg,1));
1843  ideal temp_gens,old_std;
1844  syzstr->res[0] = idInit(1,1);
1845  if (rk_arg>1) syzstr->res[0]->rank = rk_arg;
1846  syzstr->orderedRes[0] = idInit(1,1);
1847 /*--- computes the resolution ----------------------*/
1848  i = 0;
1849  while (i<IDELEMS(temp))
1850  {
1851  if (temp->m[i]!=NULL)
1852  {
1853  new_generators->m[0] = kNF(syzstr->res[0],currRing->qideal,temp->m[i]);
1854  if (!nIsOne(pGetCoeff(new_generators->m[0])))
1855  pNorm(new_generators->m[0]);
1856  next_deg = p_FDeg(new_generators->m[0],currRing);
1857  next_gen = pCopy(new_generators->m[0]);
1858  }
1859  if (!idIs0(new_generators))
1860  {
1861  index = 0;
1862  while (index<=*length)
1863  {
1864  if (index==0)
1865  {
1866  old_ideal = idCopy(syzstr->res[0]);
1867  old_repr = idCopy(syzstr->orderedRes[0]);
1868  old_tl = (*syzstr->Tl)[0];
1869  old_std = id_Head(syzstr->res[0],currRing);
1870  }
1871  t_comp = (*syzstr->Tl)[index];
1872  if (index==0) crit_comp = t_comp;
1873  temp_gens = syAppendSyz(new_generators,syzstr, index,crit_comp,totake);
1874  crit_comp = t_comp;
1875  if (index==0)
1876  {
1877  isRegular = syIsRegular(old_std,syzstr->res[0],next_deg);
1878 #ifndef ONLY_STD
1879  if (isRegular)
1880  syCreateRegularExtension(syzstr,old_ideal,old_repr,old_tl,next_gen,
1881  totake);
1882 #ifdef USE_REGULARITY
1883  if ((index==0) && (!isRegular) && (i==last_generator))
1884  {
1885 /*----------- we are computing the regularity -----------------------*/
1886  ideal initial=id_Head(syzstr->res[0],currRing);
1887  int len=0,reg=0;
1888  intvec *w=NULL;
1889  ring dp_C_ring = rAssure_dp_C(currRing); rChangeCurrRing(dp_C_ring);
1890  initial = idrMoveR_NoSort(initial, syzstr->syRing, dp_C_ring);
1892  intvec * dummy = syBetti(res,len,&reg, w);
1893  syzstr->regularity = reg+2;
1894  delete dummy;
1895  delete w;
1896  for (j=0;j<len;j++)
1897  {
1898  if (res[j]!=NULL) idDelete(&(res[j]));
1899  }
1900  omFreeSize((ADDRESS)res,len*sizeof(ideal));
1901  idDelete(&initial);
1902  rChangeCurrRing(syzstr->syRing);
1903  rDelete(dp_C_ring);
1904  }
1905 #endif
1906 #endif
1907  idDelete(&old_ideal);
1908  idDelete(&old_repr);
1909  idDelete(&old_std);
1910  if (TEST_OPT_PROT)
1911  {
1912  if (isRegular)
1913  PrintS("\n regular\n");
1914  else
1915  PrintS("\n not regular\n");
1916  }
1917  if (next_gen!=NULL)
1918  pDelete(&next_gen);
1919  if (isRegular)
1920  {
1921  idDelete(&temp_gens);
1922  break;
1923  }
1924  }
1925  idDelete(&new_generators);
1926  new_generators = temp_gens;
1927 #ifdef ONLY_STD
1928  break;
1929 #endif
1930  if (idIs0(new_generators)) break;
1931  index++;
1932  }
1933  if (!idIs0(new_generators))
1934  {
1935  for (j=0;j<IDELEMS(new_generators);j++)
1936  {
1937  if (new_generators->m[j]!=NULL)
1938  {
1939  pDelete(&new_generators->m[j]);
1940  new_generators->m[j] = NULL;
1941  }
1942  }
1943  }
1944  }
1945  i++;
1946  }
1947  if (idIs0(new_generators) && new_generators!=NULL) idDelete(&new_generators);
1948  if (temp!=NULL) idDelete(&temp);
1949  kBucketDestroy(&(syzstr->bucket));
1950  kBucketDestroy(&(syzstr->syz_bucket));
1951  index = 0;
1952  syzstr->fullres = syzstr->res;
1953  syzstr->res = NULL;
1954  index = 0;
1955  while ((index<=*length) && (syzstr->fullres[index]!=NULL))
1956  {
1957 #ifdef SHOW_RESULT
1958  Print("The %d-th syzygy-module is now:\n",index);
1959  ideal ttt=id_Head(syzstr->fullres[index],currRing);
1960  idShow(ttt);
1961  idDelete(&ttt);
1962  //if (index>0)
1963  //{
1964  //Print("The related module is: \n");
1965  //idPrint(totake[index-1]);
1966  //}
1967  //Print("The %d-th module of the minimal resolution is:\n",index);
1968  if (!idIs0(totake[index]))
1969  idShow(totake[index]);
1970  //Print("with standard basis:\n");
1971  //idPrint(syzstr->fullres[index]);
1972  //if ((index<*length) && (totake[index+1]!=NULL))
1973  //{
1974  //Print("The %d-th syzygy-module is now:\n",index+1);
1975  //idPrint(totake[index+1]);
1976  //matrix m1=idModule2Matrix(totake[index]);
1977  //matrix m2=idModule2Matrix(totake[index+1]);
1978  //matrix m3=mpMult(m1,m2);
1979  //idPrint((ideal)m3);
1980  //}
1981 #endif
1982  if (!idIs0(totake[index]))
1983  {
1984  for(i=0;i<IDELEMS(totake[index]);i++)
1985  {
1986  if (totake[index]->m[i]!=NULL)
1987  {
1988  j=0;
1989  while ((j<IDELEMS(syzstr->fullres[index])) &&
1990  ((syzstr->fullres[index]->m[j]==NULL) ||
1991  (!pLmEqual(syzstr->fullres[index]->m[j],totake[index]->m[i])))) j++;
1992  if (j<IDELEMS(syzstr->fullres[index]))
1993  {
1994  pDelete(&totake[index]->m[i]);
1995  totake[index]->m[i] = syzstr->fullres[index]->m[j];
1996  syzstr->fullres[index]->m[j] = NULL;
1997  }
1998  else
1999  {
2000  PrintS("Da ist was faul!!!\n");
2001  Print("Aber: Regularitaet %d, Grad %ld\n",
2002  syzstr->regularity,p_FDeg(totake[index]->m[i],currRing));
2003  }
2004  }
2005  }
2006  idDelete(&syzstr->fullres[index]);
2007  syzstr->fullres[index] = totake[index];
2008  }
2009 #ifdef SHOW_RESULT
2010  idShow(syzstr->fullres[index]);
2011 #endif
2012  index++;
2013  }
2014  syReorder_Kosz(syzstr);
2015  index = 0;
2016  while ((index<=*length) && (syzstr->orderedRes[index]!=NULL))
2017  {
2018  idDelete(&(syzstr->orderedRes[index]));
2019  index++;
2020  }
2021  if (origR!=syzstr->syRing)
2022  {
2023  rChangeCurrRing(origR);
2024  index = 0;
2025  while ((index<=*length) && (syzstr->fullres[index]!=NULL))
2026  {
2027  syzstr->fullres[index] = idrMoveR(syzstr->fullres[index],syzstr->syRing, origR);
2028  index++;
2029  }
2030  }
2031  delete syzstr->Tl;
2032  syzstr->Tl = NULL;
2033  rDelete(syzstr->syRing);
2034  syzstr->syRing = NULL;
2035  omFreeSize((ADDRESS)totake,(*length+1)*sizeof(ideal));
2036  omFreeSize((ADDRESS)syzstr->orderedRes,(*length+1)*sizeof(ideal));
2037 //Print("Pairs to discard: %d\n",discard_pairs);
2038 //Print("Pairs shorter reduced: %d\n",short_pairs);
2039 //discard_pairs = 0;
2040 //short_pairs = 0;
2041  return syzstr;
2042 }
2043 
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
CanonicalForm FACTORY_PUBLIC pp(const CanonicalForm &)
CanonicalForm pp ( const CanonicalForm & f )
Definition: cf_gcd.cc:676
int l
Definition: cfEzgcd.cc:100
int m
Definition: cfEzgcd.cc:128
int i
Definition: cfEzgcd.cc:132
int k
Definition: cfEzgcd.cc:99
int p
Definition: cfModGcd.cc:4078
Definition: intvec.h:23
int length() const
Definition: intvec.h:94
static FORCE_INLINE number n_Gcd(number a, number b, const coeffs r)
in Z: return the gcd of 'a' and 'b' in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ,...
Definition: coeffs.h:661
#define Print
Definition: emacs.cc:80
return result
Definition: facAbsBiFact.cc:75
CanonicalForm res
Definition: facAbsFact.cc:60
const CanonicalForm & w
Definition: facAbsFact.cc:51
int j
Definition: facHensel.cc:110
void WerrorS(const char *s)
Definition: feFopen.cc:24
#define VAR
Definition: globaldefs.h:5
intvec * hFirstSeries(ideal A, intvec *module_w, ideal Q, intvec *wdegree)
Definition: hilb.cc:2036
#define idDelete(H)
delete an ideal
Definition: ideals.h:29
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
#define idPrint(id)
Definition: ideals.h:46
ideal idCopy(ideal A)
Definition: ideals.h:60
ideal * resolvente
Definition: ideals.h:18
poly initial(const poly p, const ring r, const gfan::ZVector &w)
Returns the initial form of p with respect to w.
Definition: initial.cc:30
static BOOLEAN length(leftv result, leftv arg)
Definition: interval.cc:257
STATIC_VAR Poly * h
Definition: janet.cc:971
KINLINE poly ksOldCreateSpoly(poly p1, poly p2, poly spNoether, ring r)
Definition: kInline.h:1196
void kBucketClear(kBucket_pt bucket, poly *p, int *length)
Definition: kbuckets.cc:521
void kBucket_Minus_m_Mult_p(kBucket_pt bucket, poly m, poly p, int *l, poly spNoether)
Bpoly == Bpoly - m*p; where m is a monom Does not destroy p and m assume (*l <= 0 || pLength(p) == *l...
Definition: kbuckets.cc:722
void kBucketDestroy(kBucket_pt *bucket_pt)
Definition: kbuckets.cc:216
void kBucketInit(kBucket_pt bucket, poly lm, int length)
Definition: kbuckets.cc:493
kBucket_pt kBucketCreate(const ring bucket_ring)
Creation/Destruction of buckets.
Definition: kbuckets.cc:209
number kBucketPolyRed(kBucket_pt bucket, poly p1, int l1, poly spNoether)
Definition: kbuckets.cc:1071
const poly kBucketGetLm(kBucket_pt bucket)
Definition: kbuckets.cc:506
poly p
Definition: kbuckets.h:186
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
Definition: kstd1.cc:3182
void pairs()
int lcm(unsigned long *l, unsigned long *a, unsigned long *b, unsigned long p, int dega, int degb)
Definition: minpoly.cc:709
#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 nDiv(a, b)
Definition: numbers.h:32
#define nDelete(n)
Definition: numbers.h:16
#define nInpNeg(n)
Definition: numbers.h:21
#define nInvers(a)
Definition: numbers.h:33
#define nIsOne(n)
Definition: numbers.h:25
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc0(size)
Definition: omAllocDecl.h:211
#define omRealloc0Size(addr, o_size, size)
Definition: omAllocDecl.h:221
#define NULL
Definition: omList.c:12
#define TEST_OPT_PROT
Definition: options.h:104
static int index(p_Length length, p_Ord ord)
Definition: p_Procs_Impl.h:592
void p_Shift(poly *p, int i, const ring r)
shifts components of the vector p by i
Definition: p_polys.cc:4702
void pEnlargeSet(poly **p, int l, int increment)
Definition: p_polys.cc:3692
static int pLength(poly a)
Definition: p_polys.h:188
static long p_FDeg(const poly p, const ring r)
Definition: p_polys.h:378
#define __p_Mult_nn(p, n, r)
Definition: p_polys.h:969
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 pDelete(p_ptr)
Definition: polys.h:186
#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 pLmEqual(p1, p2)
Definition: polys.h:111
#define pGetComp(p)
Component.
Definition: polys.h:37
#define pSetCoeff(p, n)
deletes old coeff before setting the new one
Definition: polys.h:31
void pNorm(poly p)
Definition: polys.h:362
#define pSub(a, b)
Definition: polys.h:287
#define ppMult_qq(p, q)
Definition: polys.h:208
#define pSetComp(p, v)
Definition: polys.h:38
#define pLmDelete(p)
assume p != NULL, deletes Lm(p)->coef and Lm(p)
Definition: polys.h:76
#define pMult(p, q)
Definition: polys.h:207
void pWrite(poly p)
Definition: polys.h:308
#define pGetExp(p, i)
Exponent.
Definition: polys.h:41
#define pSetmComp(p)
TODO:
Definition: polys.h:273
#define pMult_mm(p, m)
Definition: polys.h:202
#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
#define pMDivide(a, b)
Definition: polys.h:293
#define pCopy(p)
return a copy of the poly
Definition: polys.h:185
#define pOne()
Definition: polys.h:315
poly * polyset
Definition: polys.h:259
#define pLcm(a, b, m)
Definition: polys.h:295
#define pLmDivisibleByNoComp(a, b)
like pLmDivisibleBy, does not check components
Definition: polys.h:142
ideal idrMoveR(ideal &id, ring src_r, ring dest_r)
Definition: prCopy.cc:248
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
void PrintS(const char *s)
Definition: reporter.cc:284
void PrintLn()
Definition: reporter.cc:310
ring rAssure_C_dp(const ring r)
Definition: ring.cc:4985
void rDelete(ring r)
unconditionally deletes fields in r
Definition: ring.cc:450
ring rAssure_dp_C(const ring r)
Definition: ring.cc:4980
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition: simpleideals.cc:35
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
long id_RankFreeModule(ideal s, ring lmRing, ring tailRing)
return the maximal component number found in any polynomial in s
void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint)
Definition: simpleideals.cc:57
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
void id_Shift(ideal M, int s, const ring r)
#define IDELEMS(i)
Definition: simpleideals.h:23
#define loop
Definition: structs.h:75
static poly normalize(poly next_p, ideal add_generators, syStrategy syzstr, int *g_l, int *p_l, int crit_comp)
Definition: syz3.cc:1027
static ideal syAppendSyz(ideal new_generators, syStrategy syzstr, int index, int crit_comp, resolvente totake)
Definition: syz3.cc:1690
static void syCreateRegularExtension(syStrategy syzstr, ideal old_ideal, ideal old_repr, int old_tl, poly next_generator, resolvente totake)
Definition: syz3.cc:111
void syReorder_Kosz(syStrategy syzstr)
Definition: syz3.cc:261
static BOOLEAN syRedSyz(kBucket_pt bucket, ideal red, int crit_comp, int *g_l)
Definition: syz3.cc:487
static ideal normalizeOldPart(ideal new_generators, ideal new_repr, syStrategy syzstr, int index, int)
Definition: syz3.cc:1546
static void redOnePairHIndex(SSet resPairs, int itso, int crit_comp, syStrategy syzstr, int, ideal add_generators, ideal add_repr, ideal new_generators, ideal new_repr, int *next_place_add, int **g_l, poly deg_soc)
Definition: syz3.cc:1186
syStrategy syKosz(ideal arg, int *length)
Definition: syz3.cc:1766
static void syTestPairs(SSet resPairs, int length, ideal old_generators)
Definition: syz3.cc:239
static void redOnePair(SSet resPairs, int itso, int l, ideal syzygies, int crit_comp, syStrategy syzstr, int index, ideal new_generators, ideal new_repr, int *ogm_l, int *orp_l)
Definition: syz3.cc:650
static BOOLEAN reducePairsHIndex(SSet resPairs, int l_pairs, syStrategy syzstr, int index, ideal add_generators, ideal add_repr, ideal new_generators, ideal new_repr, int crit_comp, int *red_deg, int *next_place_add, int **g_l, resolvente totake)
Definition: syz3.cc:1378
static BOOLEAN redPairs(SSet resPairs, int l_pairs, ideal syzygies, ideal new_generators, ideal new_repr, int crit_comp, syStrategy syzstr, int index)
Definition: syz3.cc:939
VAR int short_pairs
Definition: syz3.cc:49
static void updatePairs(SSet *resPairs, int *l_pairs, syStrategy syzstr, int index, ideal new_generators, ideal new_repr, int crit_comp)
Definition: syz3.cc:307
static void updatePairsHIndex(SSet *resPairs, int *l_pairs, syStrategy, int index, ideal add_generators, ideal, ideal, ideal, int, int *first_new)
Definition: syz3.cc:1056
static void procedeNextGenerators(ideal temp_generators, ideal, ideal new_generators, ideal new_repr, ideal add_generators, ideal add_repr, syStrategy syzstr, int index, int crit_comp, resolvente totake)
Definition: syz3.cc:1415
void sySPRedSyz_Kosz(syStrategy syzstr, poly redWith, poly syz, poly q=NULL, int l_syz=-1)
Definition: syz3.cc:473
static ideal kosz_std(ideal new_generators, ideal new_repr, syStrategy syzstr, int index, int next_comp)
Definition: syz3.cc:1001
static poly syRedTailSyz(poly tored, ideal red, ideal sec_red, int crit_comp, syStrategy syzstr, int *gen_length, int *secgen_length, int *tored_length)
Definition: syz3.cc:514
VAR int discard_pairs
Definition: syz3.cc:48
static BOOLEAN syIsRegular(ideal old_ideal, ideal new_ideal, int deg)
Definition: syz3.cc:55
static ideal kosz_ext(ideal new_generators, ideal new_repr, syStrategy syzstr, int index, int next_comp, resolvente totake)
Definition: syz3.cc:1608
intvec * syBetti(resolvente res, int length, int *regularity, intvec *weights, BOOLEAN tomin, int *row_shift)
Definition: syz.cc:770
resolvente sySchreyerResolvente(ideal arg, int maxlength, int *length, BOOLEAN isMonomial=FALSE, BOOLEAN notReplace=FALSE)
Definition: syz0.cc:855
ring syRing
Definition: syz.h:56
void syCompactifyPairSet(SSet sPairs, int sPlength, int first)
Definition: syz1.cc:104
kBucket_pt syz_bucket
Definition: syz.h:55
resolvente res
Definition: syz.h:47
resolvente fullres
Definition: syz.h:57
intvec * Tl
Definition: syz.h:50
ssyStrategy * syStrategy
Definition: syz.h:35
resolvente orderedRes
Definition: syz.h:48
void syEnterPair(syStrategy syzstr, SObject *so, int *sPlength, int index)
Definition: syz1.cc:1035
void syInitializePair(SObject *so)
Definition: syz1.cc:63
int length
Definition: syz.h:60
int regularity
Definition: syz.h:61
kBucket_pt bucket
Definition: syz.h:54
void syDeletePair(SObject *so)
Definition: syz1.cc:44
SObject * SSet
Definition: syz.h:32