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1 /***************************************
2  * Computer Algebra System SINGULAR *
3  ***************************************/
4 /*
5  * ABSTRACT: resolutions
6  * reference: https://arxiv.org/abs/1502.01654
7  */
8 
9 #include "kernel/GBEngine/syz.h"
10 #include "coeffs/numbers.h"
11 #include "kernel/polys.h"
12 #include "kernel/ideals.h"
13 
14 #include <vector>
15 #include <map>
16 
17 /*
18  * set variables[i] to false if the i-th variable does not appear among the
19  * leading terms of L
20  */
21 static void update_variables(std::vector<bool> &variables, const ideal L)
22 {
23  const ring R = currRing;
24  const int l = L->ncols-1;
25  int k;
26  for (int j = R->N; j > 0; j--)
27  {
28  if (variables[j-1])
29  {
30  for (k = l; k >= 0; k--)
31  {
32  if (p_GetExp(L->m[k], j, R) > 0)
33  {
34  break;
35  }
36  }
37  if (k < 0)
38  { // no break
39  variables[j-1] = false;
40  }
41  }
42  }
43 }
44 
45 /*
46  * If the previous step in the resolution is reduced, then this check can be
47  * used to determine lower order terms.
48  */
49 static inline bool check_variables(const std::vector<bool> &variables,
50  const poly m)
51 {
52  const ring R = currRing;
53  // variables[R->N] is true iff index == 1, that is, for the first step in
54  // the resolution
55  if (UNLIKELY(variables[R->N]))
56  {
57  return true;
58  }
59  for (int j = R->N; j > 0; j--)
60  {
61  if (UNLIKELY(variables[j-1] && p_GetExp(m, j, R) > 0))
62  {
63  return true;
64  }
65  }
66  return false;
67 }
68 
69 /*
70  * For each step in the resolution, the following data is saved for each of the
71  * induced leading terms: the leading term itself, its short exponent vector,
72  * and its position in the ideal/module.
73  */
74 typedef struct {
75  poly lt;
76  unsigned long sev;
77  unsigned long comp;
78 } lt_struct;
79 
80 static void initialize_hash(lt_struct **C, const ideal L)
81 {
82  const ring R = currRing;
83  const unsigned long n_elems = L->ncols;
84  unsigned int *count
85  = (unsigned int *)omAlloc0((L->rank+1)*sizeof(unsigned int));
86  unsigned long k = 0;
87  while (k < n_elems)
88  {
89  count[__p_GetComp(L->m[k], R)]++;
90  k++;
91  }
92  for (int i = 0; i <= L->rank; i++)
93  {
94  // do ++count[i] and use C[i][0].comp to save count[i]
95  C[i] = (lt_struct *)omalloc0((++count[i])*sizeof(lt_struct));
96  C[i][0].comp = count[i];
97  }
98  k = n_elems;
99  // the order of the elements in each C[i] matters if check_variables() is
100  // to be used
101  while (k > 0)
102  {
103  const poly a = L->m[k-1];
104  const unsigned long comp = __p_GetComp(a, R);
105  C[comp][--count[comp]]
106  = (lt_struct){a, p_GetShortExpVector(a, R), k};
107  k--;
108  }
109  omFree(count);
110 }
111 
112 /*
113  * compute a new term in the resolution, that is, compute
114  * ( t * multiplier / f ) where f is an induced leading term from the previous
115  * module, or return NULL if no such f dividing t * multiplier exists, that is,
116  * if multiplier is a lower order term
117  */
118 static poly find_reducer(const poly multiplier, const poly t,
119  const lt_struct *const *const hash_previous_module)
120 {
121  const ring r = currRing;
122  const lt_struct *v = hash_previous_module[__p_GetComp(t, r)];
123  unsigned long count = v[0].comp;
124  if (UNLIKELY(count == 1))
125  {
126  return NULL;
127  }
128  const poly q = p_New(r);
129  pNext(q) = NULL;
130  p_MemSum_LengthGeneral(q->exp, multiplier->exp, t->exp, r->ExpL_Size);
131  const unsigned long q_not_sev = ~p_GetShortExpVector(q, r);
132  for(unsigned long i = 1; i < count; i++)
133  {
134  if (LIKELY(v[i].sev & q_not_sev)
135  || UNLIKELY(!(_p_LmDivisibleByNoComp(v[i].lt, q, r))))
136  {
137  continue;
138  }
140  p_ExpVectorDiff(q, q, v[i].lt, r);
141  p_SetComp(q, v[i].comp, r);
142  p_Setm(q, r);
143  number n = n_Div(p_GetCoeff(multiplier, r), p_GetCoeff(v[i].lt, r), r->cf);
144  n_InpMult(n, p_GetCoeff(t, r), r->cf);
145  p_SetCoeff0(q, n_InpNeg(n, r->cf), r);
146  return q;
147  }
148  p_LmFree(q, r);
149  return NULL;
150 }
151 
152 static poly traverse_tail(const poly multiplier, const int comp,
153  const ideal previous_module, const std::vector<bool> &variables,
154  const lt_struct *const *const hash_previous_module);
155 
156 static poly compute_image(const poly multiplier, const int comp,
157  const ideal previous_module, const std::vector<bool> &variables,
158  const lt_struct *const *const hash_previous_module,
159  const bool use_cache);
160 
161 /*
162  * recursively call traverse_tail() for each new term found by find_reducer()
163  */
164 static poly reduce_term(const poly multiplier, const poly term,
165  const ideal previous_module, const std::vector<bool> &variables,
166  const lt_struct *const *const hash_previous_module,
167  const bool use_cache)
168 {
169  poly s = find_reducer(multiplier, term, hash_previous_module);
170  if (s == NULL)
171  {
172  return NULL;
173  }
174  const ring r = currRing;
175  const int c = __p_GetComp(s, r) - 1;
176  poly t;
177  if (use_cache)
178  {
179  t = traverse_tail(s, c, previous_module, variables,
180  hash_previous_module);
181  } else {
182  t = compute_image(s, c, previous_module, variables,
183  hash_previous_module, false);
184  }
185  return p_Add_q(s, t, r);
186 }
187 
188 /*
189  * iterating over tail, call reduce_term(multiplier, p, ...) for each term p in
190  * tail and sum up the results
191  */
192 static poly compute_image(const poly multiplier, const int comp,
193  const ideal previous_module, const std::vector<bool> &variables,
194  const lt_struct *const *const hash_previous_module,
195  const bool use_cache)
196 {
197  const poly tail = previous_module->m[comp]->next;
198  if (UNLIKELY(tail == NULL) || !check_variables(variables, multiplier))
199  {
200  return NULL;
201  }
203  for (poly p = tail; p != NULL; p = pNext(p))
204  {
205  const poly rt = reduce_term(multiplier, p, previous_module, variables,
206  hash_previous_module, use_cache);
207  sBucket_Add_p(sum, rt, pLength(rt));
208  }
209  poly s;
210  int l;
211  sBucketClearAdd(sum, &s, &l);
212  sBucketDestroy(&sum);
213  return s;
214 }
215 
217 {
218  inline bool operator() (const poly& l, const poly& r) const
219  {
220  return (p_LmCmp(l, r, currRing) == -1);
221  /* For expensive orderings, consider:
222  * return (memcmp(l->exp, r->exp,
223  * (currRing->CmpL_Size)*sizeof(unsigned long)) < 0);
224  */
225  }
226 };
227 
228 typedef std::map<poly, poly, cache_compare> cache_term;
229 
231 
232 static void initialize_cache(const int size)
233 {
234  Cache = new cache_term[size];
235 }
236 
237 static void delete_cache(const int size)
238 {
239  const ring r = currRing;
240  for (int i = 0; i < size; i++)
241  {
242  cache_term *T = &(Cache[i]);
243  for (cache_term::iterator itr = T->begin(); itr != T->end(); ++itr)
244  {
245  p_Delete(&(itr->second), r);
246  p_Delete(const_cast<poly*>(&(itr->first)), r);
247  }
248  T->clear();
249  }
250  delete[](Cache);
251 }
252 
253 static void insert_into_cache_term(cache_term *T, const poly multiplier,
254  const poly p)
255 {
256  const ring r = currRing;
257  T->insert(cache_term::value_type(p_Head(multiplier, r), p_Copy(p, r)));
258 }
259 
260 static poly get_from_cache_term(const cache_term::const_iterator itr,
261  const poly multiplier)
262 {
263  if (LIKELY(itr->second == NULL))
264  {
265  return NULL;
266  }
267  const ring r = currRing;
268  poly p = p_Copy(itr->second, r);
269  if (LIKELY(!n_Equal(pGetCoeff(multiplier), pGetCoeff(itr->first), r->cf)))
270  {
271  number n = n_Div(pGetCoeff(multiplier), pGetCoeff(itr->first), r->cf);
272  p = p_Mult_nn(p, n, r);
273  n_Delete(&n, r->cf);
274  }
275  return p;
276 }
277 
278 static poly traverse_tail(const poly multiplier, const int comp,
279  const ideal previous_module, const std::vector<bool> &variables,
280  const lt_struct *const *const hash_previous_module)
281 {
282  cache_term *T = &(Cache[comp]);
283  cache_term::const_iterator itr = T->find(multiplier);
284  if (LIKELY(itr != T->end()))
285  {
286  return get_from_cache_term(itr, multiplier);
287  }
288  poly p = compute_image(multiplier, comp, previous_module, variables,
289  hash_previous_module, true);
290  insert_into_cache_term(T, multiplier, p);
291  return p;
292 }
293 
294 /*
295  * lift the extended induced leading term a to a syzygy
296  */
297 static poly lift_ext_LT(const poly a, const ideal previous_module,
298  const std::vector<bool> &variables,
299  const lt_struct *const *const hash_previous_module,
300  const bool use_cache)
301 {
302  const ring R = currRing;
303  // the leading term does not need to be cached
304  poly t1 = compute_image(a, __p_GetComp(a, R)-1, previous_module, variables,
305  hash_previous_module, use_cache);
306  poly t2;
307  if (use_cache)
308  {
309  t2 = traverse_tail(a->next, __p_GetComp(a->next, R)-1,
310  previous_module, variables, hash_previous_module);
311  } else {
312  t2 = compute_image(a->next, __p_GetComp(a->next, R)-1,
313  previous_module, variables, hash_previous_module, false);
314  }
315  t1 = p_Add_q(t1, t2, R);
316  return t1;
317 }
318 
319 /*****************************************************************************/
320 
321 typedef poly syzHeadFunction(ideal, int, int);
322 
323 /*
324  * compute the induced leading term corresponding to the index pair (i, j)
325  */
326 static poly syzHeadFrame(const ideal G, const int i, const int j)
327 {
328  const ring r = currRing;
329  const poly f_i = G->m[i];
330  const poly f_j = G->m[j];
331  poly head = p_Init(r);
332  pSetCoeff0(head, n_Init(1, r->cf));
333  long exp_i, exp_j, lcm;
334  for (int k = (int)r->N; k > 0; k--)
335  {
336  exp_i = p_GetExp(f_i, k, r);
337  exp_j = p_GetExp(f_j, k, r);
338  lcm = si_max(exp_i, exp_j);
339  p_SetExp(head, k, lcm-exp_i, r);
340  }
341  p_SetComp(head, i+1, r);
342  p_Setm(head, r);
343  return head;
344 }
345 
346 /*
347  * compute the _extended_ induced leading term corresponding to the index pair
348  * (i, j), that is, the first two terms w.r.t. the induced order
349  */
350 static poly syzHeadExtFrame(const ideal G, const int i, const int j)
351 {
352  const ring r = currRing;
353  const poly f_i = G->m[i];
354  const poly f_j = G->m[j];
355  poly head = p_Init(r);
356  pSetCoeff0(head, n_Init(1, r->cf));
357  poly head_ext = p_Init(r);
358  pSetCoeff0(head_ext, n_InpNeg(n_Div(pGetCoeff(f_i), pGetCoeff(f_j), r->cf),
359  r->cf));
360  long exp_i, exp_j, lcm;
361  for (int k = (int)r->N; k > 0; k--)
362  {
363  exp_i = p_GetExp(f_i, k, r);
364  exp_j = p_GetExp(f_j, k, r);
365  lcm = si_max(exp_i, exp_j);
366  p_SetExp(head, k, lcm-exp_i, r);
367  p_SetExp(head_ext, k, lcm-exp_j, r);
368  }
369  p_SetComp(head, i+1, r);
370  p_Setm(head, r);
371  p_SetComp(head_ext, j+1, r);
372  p_Setm(head_ext, r);
373  head->next = head_ext;
374  return head;
375 }
376 
377 typedef ideal syzM_i_Function(ideal, int, syzHeadFunction);
378 
379 /*
380  * compute the monomial ideal M_i, see reference;
381  * in the first step, we cannot assume that all leading terms which lie in the
382  * component are adjacent to each other
383  */
384 static ideal syzM_i_unsorted(const ideal G, const int i,
385  syzHeadFunction *syzHead)
386 {
387  const ring r = currRing;
388  ideal M_i = NULL;
389  unsigned long comp = __p_GetComp(G->m[i], r);
390  int ncols = 0;
391  for (int j = i-1; j >= 0; j--)
392  {
393  if (__p_GetComp(G->m[j], r) == comp) ncols++;
394  }
395  if (ncols > 0)
396  {
397  M_i = idInit(ncols, G->ncols);
398  int k = ncols-1;
399  for (int j = i-1; j >= 0; j--)
400  {
401  if (__p_GetComp(G->m[j], r) == comp)
402  {
403  M_i->m[k] = syzHead(G, i, j);
404  k--;
405  }
406  }
407  id_DelDiv(M_i, currRing);
408  idSkipZeroes(M_i);
409  }
410  return M_i;
411 }
412 
413 /*
414  * compute the monomial ideal M_i, see reference;
415  * from step two on, we can assume that all leading terms which lie in the same
416  * component are adjacent to each other
417  */
418 static ideal syzM_i_sorted(const ideal G, const int i,
419  syzHeadFunction *syzHead)
420 {
421  const ring r = currRing;
422  ideal M_i = NULL;
423  unsigned long comp = __p_GetComp(G->m[i], r);
424  int index = i-1;
425  while (__p_GetComp(G->m[index], r) == comp) index--;
426  index++;
427  int ncols = i-index;
428  if (ncols > 0)
429  {
430  M_i = idInit(ncols, G->ncols);
431  for (int j = ncols-1; j >= 0; j--)
432  {
433  M_i->m[j] = syzHead(G, i, j+index);
434  }
435  id_DelDiv(M_i, currRing);
436  idSkipZeroes(M_i);
437  }
438  return M_i;
439 }
440 
441 /*
442  * concatenate the ideals in M[]
443  */
444 static ideal idConcat(const ideal *M, const int size, const int rank)
445 {
446  int ncols = 0;
447  for (int i = size-1; i >= 0; i--)
448  {
449  if (M[i] != NULL)
450  {
451  ncols += M[i]->ncols;
452  }
453  }
454  if (ncols == 0) return idInit(1, rank);
455  ideal result = idInit(ncols, rank);
456  int k = ncols-1;
457  for (int i = size-1; i >= 0; i--)
458  {
459  if (M[i] != NULL)
460  {
461  for (int j = M[i]->ncols-1; j >= 0; j--)
462  {
463  result->m[k] = M[i]->m[j];
464  k--;
465  }
466  }
467  }
468  return result;
469 }
470 
471 static int compare_comp(const poly p_a, const poly p_b)
472 {
473  const ring r = currRing;
474  long comp_a = __p_GetComp(p_a, r);
475  long comp_b = __p_GetComp(p_b, r);
476  return (comp_a > comp_b) - (comp_a < comp_b);
477 }
478 
479 static int compare_deg(const poly p_a, const poly p_b)
480 {
481  const ring r = currRing;
482  long deg_a = p_Deg(p_a, r);
483  long deg_b = p_Deg(p_b, r);
484  return (deg_a > deg_b) - (deg_a < deg_b);
485 }
486 
487 static int compare_lex(const poly p_a, const poly p_b)
488 {
489  int cmp;
490  const ring r = currRing;
491  int exp_a[r->N+1];
492  int exp_b[r->N+1];
493  p_GetExpV(p_a, exp_a, r);
494  p_GetExpV(p_b, exp_b, r);
495  for (int i = r->N; i > 0; i--)
496  {
497  cmp = (exp_a[i] > exp_b[i]) - (exp_a[i] < exp_b[i]);
498  if (cmp != 0)
499  {
500  return cmp;
501  }
502  }
503  return 0;
504 }
505 
506 static int compare_Mi(const void* a, const void *b)
507 {
508  poly p_a = *((poly *)a);
509  poly p_b = *((poly *)b);
510  int cmp;
511  if ((cmp = compare_comp(p_a, p_b))
512  || (cmp = compare_deg(p_a, p_b))
513  || (cmp = compare_lex(p_a, p_b)))
514  {
515  return cmp;
516  }
517  return 0;
518 }
519 
520 /*
521  * compute the frame, that is, the induced leading terms for the next step in
522  * the resolution
523  */
524 static ideal computeFrame(const ideal G, syzM_i_Function syzM_i,
525  syzHeadFunction *syzHead)
526 {
527  ideal *M = (ideal *)omalloc((G->ncols-1)*sizeof(ideal));
528  for (int i = G->ncols-2; i >= 0; i--)
529  {
530  M[i] = syzM_i(G, i+1, syzHead);
531  }
532  ideal frame = idConcat(M, G->ncols-1, G->ncols);
533  for (int i = G->ncols-2; i >= 0; i--)
534  {
535  if (M[i] != NULL)
536  {
537  omFreeSize(M[i]->m, M[i]->ncols*sizeof(poly));
539  }
540  }
541  omfree(M);
542  qsort(frame->m, frame->ncols, sizeof(poly), compare_Mi);
543  return frame;
544 }
545 
546 /*
547  * lift each (extended) induced leading term to a syzygy
548  */
549 static void computeLiftings(const resolvente res, const int index,
550  const std::vector<bool> &variables, const bool use_cache)
551 {
552  if (use_cache)
553  {
555  }
556  lt_struct **hash_previous_module
557  = (lt_struct **)omAlloc((res[index-1]->rank+1)*sizeof(lt_struct *));
558  initialize_hash(hash_previous_module, res[index-1]);
559  for (int j = res[index]->ncols-1; j >= 0; j--)
560  {
561  res[index]->m[j]->next->next = lift_ext_LT(res[index]->m[j],
562  res[index-1], variables, hash_previous_module, use_cache);
563  }
564  for (int i = 0; i <= res[index-1]->rank; i++)
565  {
566  omfree(hash_previous_module[i]);
567  }
568  omFree(hash_previous_module);
569  if (use_cache)
570  {
572  }
573 }
574 
575 /*
576  * check if the monomial m contains any of the variables set to false
577  */
578 static inline bool contains_unused_variable(const poly m,
579  const std::vector<bool> &variables)
580 {
581  const ring R = currRing;
582  for (int j = R->N; j > 0; j--)
583  {
584  if (!variables[j-1] && p_GetExp(m, j, R) > 0)
585  {
586  return true;
587  }
588  }
589  return false;
590 }
591 
592 /*
593  * delete any term in res[index] which contains any of the variables set to
594  * false
595  */
596 static void delete_variables(resolvente res, const int index,
597  const std::vector<bool> &variables)
598 {
599  for (int i = 0; i < res[index]->ncols; i++)
600  {
601  poly p_iter = res[index]->m[i]->next;
602  if (p_iter != NULL)
603  {
604  while (p_iter->next != NULL)
605  {
606  if (contains_unused_variable(p_iter->next, variables))
607  {
608  pLmDelete(&p_iter->next);
609  } else {
610  pIter(p_iter);
611  }
612  }
613  }
614  }
615 }
616 
617 static void delete_tails(resolvente res, const int index)
618 {
619  const ring r = currRing;
620  for (int i = 0; i < res[index]->ncols; i++)
621  {
622  if (res[index]->m[i] != NULL)
623  {
624  p_Delete(&(res[index]->m[i]->next), r);
625  }
626  }
627 }
628 
629 /*
630  * for each step in the resolution, compute the corresponding module until
631  * either index == max_index is reached or res[index] is the zero module
632  */
633 static int computeResolution_iteration(resolvente res, const int max_index,
634  syzHeadFunction *syzHead, const bool do_lifting,
635  const bool single_module, const bool use_cache,
636  const bool use_tensor_trick, std::vector<bool> &variables)
637 {
638  int index = 1;
639  while (!idIs0(res[index]))
640  {
641  if (do_lifting)
642  {
643  computeLiftings(res, index, variables, use_cache);
644  if (single_module)
645  {
646  delete_tails(res, index-1);
647  }
648  // we don't know if the input is a reduced SB:
649  if (index == 1)
650  {
651  variables[currRing->N] = false;
652  }
654  if (use_tensor_trick)
655  {
657  }
658  }
659  if (index >= max_index) { break; }
660  index++;
661  res[index] = computeFrame(res[index-1], syzM_i_sorted, syzHead);
662  }
663  return index;
664 }
665 
666 /*
667  * compute the frame of the first syzygy module and set variables, then call
668  * computeResolution_iteration() for the remaining steps
669  */
670 static int computeResolution(resolvente res, const int max_index,
671  syzHeadFunction *syzHead, const bool do_lifting,
672  const bool single_module, const bool use_cache,
673  const bool use_tensor_trick)
674 {
675  if (idIs0(res[0]))
676  {
677  return 1;
678  }
679  std::vector<bool> variables;
680  variables.resize(currRing->N+1, true);
681  if (do_lifting)
682  {
684  if (use_tensor_trick)
685  {
687  }
688  }
689  int index = 0;
690  if (max_index > 0)
691  {
692  res[1] = computeFrame(res[0], syzM_i_unsorted, syzHead);
693  index = computeResolution_iteration(res, max_index, syzHead,
694  do_lifting, single_module, use_cache, use_tensor_trick,
695  variables);
696  }
697  variables.clear();
698  return index+1;
699 }
700 
701 static void set_options(syzHeadFunction **syzHead_ptr, bool *do_lifting_ptr,
702  bool *single_module_ptr, const char *method)
703 {
704  if (strcmp(method, "complete") == 0)
705  { // default
706  *syzHead_ptr = syzHeadExtFrame;
707  *do_lifting_ptr = true;
708  *single_module_ptr = false;
709  }
710  else if (strcmp(method, "frame") == 0)
711  {
712  *syzHead_ptr = syzHeadFrame;
713  *do_lifting_ptr = false;
714  *single_module_ptr = false;
715  }
716  else if (strcmp(method, "extended frame") == 0)
717  {
718  *syzHead_ptr = syzHeadExtFrame;
719  *do_lifting_ptr = false;
720  *single_module_ptr = false;
721  }
722  else if (strcmp(method, "single module") == 0)
723  {
724  *syzHead_ptr = syzHeadExtFrame;
725  *do_lifting_ptr = true;
726  *single_module_ptr = true;
727  }
728  else { // "linear strand" (not yet implemented)
729  *syzHead_ptr = syzHeadExtFrame;
730  *do_lifting_ptr = true;
731  *single_module_ptr = false;
732  }
733 }
734 
735 /*
736  * insert the first term of r at the right place
737  */
738 #define insert_first_term(r, p, q, R) \
739 do \
740 { \
741  p = r; \
742  q = p->next; \
743  if (q != NULL && p_LmCmp(p, q, R) != 1) { \
744  while (q->next != NULL && p_LmCmp(p, q->next, R) == -1) { \
745  pIter(q); \
746  } \
747  r = p->next; \
748  p->next = q->next; \
749  q->next = p; \
750  } \
751 } \
752 while (0)
753 
754 /*
755  * For each poly in the resolution, insert the first two terms at their right
756  * places. If single_module is true, then only consider the last module.
757  */
758 static void insert_ext_induced_LTs(const resolvente res, const int length,
759  const bool single_module)
760 {
761  const ring R = currRing;
762  poly p, q;
763  int index = (single_module ? length-1 : 1);
764  while (index < length && !idIs0(res[index]))
765  {
766  for (int j = res[index]->ncols-1; j >= 0; j--)
767  {
768  insert_first_term(res[index]->m[j]->next, p, q, R);
769  insert_first_term(res[index]->m[j], p, q, R);
770  }
771  index++;
772  }
773 }
774 
775 /*
776  * Compute the Schreyer resolution of arg, see reference at the beginning of
777  * this file.
778  *
779  * If use_cache == true (default), the result of compute_image() is cached for
780  * _every_ term in the current step of the resolution. This corresponds to the
781  * subtree attached to the node which represents this term, see reference.
782  *
783  * If use_tensor_trick == true, the current module is modified after each
784  * lifting step in the resolution: any term which contains a variable which
785  * does not appear among the (induced) leading terms is deleted. Note that the
786  * resulting object is not necessarily a complex anymore. However, constant
787  * entries remain exactly the same. This option does not apply for
788  * method == "frame" and method "extended frame".
789  *
790  * These two options are used in PrymGreen.jl; do not delete!
791  */
792 syStrategy syFrank(const ideal arg, const int length, const char *method,
793  const bool use_cache, const bool use_tensor_trick)
794 {
796  resolvente res = (resolvente)omAlloc0((length+1)*sizeof(ideal));
797  if (strcmp(method, "frame") != 0)
798  {
799  res[0] = id_Copy(arg, currRing);
800  }
801  else
802  {
803  res[0] = id_Head(arg, currRing);
804  }
805  syzHeadFunction *syzHead;
806  bool do_lifting;
807  bool single_module;
808  set_options(&syzHead, &do_lifting, &single_module, method);
809  int new_length = computeResolution(res, length-1, syzHead, do_lifting,
810  single_module, use_cache, use_tensor_trick);
811  if (new_length < length)
812  {
813  res = (resolvente)omReallocSize(res, (length+1)*sizeof(ideal),
814  (new_length+1)*sizeof(ideal));
815  }
816  if (strcmp(method, "frame") != 0)
817  {
818  insert_ext_induced_LTs(res, new_length, single_module);
819  }
820  result->fullres = res;
821  result->length = new_length;
822  result->list_length = new_length;
823  return result;
824 }
825 
static int si_max(const int a, const int b)
Definition: auxiliary.h:124
#define UNLIKELY(X)
Definition: auxiliary.h:404
#define LIKELY(X)
Definition: auxiliary.h:403
int size(const CanonicalForm &f, const Variable &v)
int size ( const CanonicalForm & f, const Variable & v )
Definition: cf_ops.cc:600
CanonicalForm head(const CanonicalForm &f)
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
CanonicalForm b
Definition: cfModGcd.cc:4103
int int ncols
Definition: cf_linsys.cc:32
Class Cache is a template-implementation of a cache with arbitrary classes for representing keys and ...
Definition: Cache.h:69
Definition: int_poly.h:33
static FORCE_INLINE number n_InpNeg(number n, const coeffs r)
in-place negation of n MUST BE USED: n = n_InpNeg(n) (no copy is returned)
Definition: coeffs.h:554
static FORCE_INLINE number n_Div(number a, number b, const coeffs r)
return the quotient of 'a' and 'b', i.e., a/b; raises an error if 'b' is not invertible in r exceptio...
Definition: coeffs.h:612
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:452
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
static FORCE_INLINE void n_InpMult(number &a, number b, const coeffs r)
multiplication of 'a' and 'b'; replacement of 'a' by the product a*b
Definition: coeffs.h:638
static FORCE_INLINE BOOLEAN n_Equal(number a, number b, const coeffs r)
TRUE iff 'a' and 'b' represent the same number; they may have different representations.
Definition: coeffs.h:457
static ideal p_a(ideal h)
Definition: cohomo.cc:1335
static ideal p_b(ideal h, poly a)
Definition: cohomo.cc:1427
return result
Definition: facAbsBiFact.cc:75
const CanonicalForm int s
Definition: facAbsFact.cc:51
CanonicalForm res
Definition: facAbsFact.cc:60
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
int j
Definition: facHensel.cc:110
int comp(const CanonicalForm &A, const CanonicalForm &B)
compare polynomials
#define STATIC_VAR
Definition: globaldefs.h:7
ideal id_Copy(ideal h1, const ring r)
copy an ideal
BOOLEAN idIs0(ideal h)
returns true if h is the zero ideal
ideal * resolvente
Definition: ideals.h:18
STATIC_VAR int variables
static BOOLEAN length(leftv result, leftv arg)
Definition: interval.cc:257
STATIC_VAR jList * T
Definition: janet.cc:30
STATIC_VAR TreeM * G
Definition: janet.cc:31
ListNode * next
Definition: janet.h:31
int lcm(unsigned long *l, unsigned long *a, unsigned long *b, unsigned long p, int dega, int degb)
Definition: minpoly.cc:709
#define p_SetCoeff0(p, n, r)
Definition: monomials.h:60
#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 pSetCoeff0(p, n)
Definition: monomials.h:59
#define p_GetCoeff(p, r)
Definition: monomials.h:50
#define __p_GetComp(p, r)
Definition: monomials.h:63
#define omfree(addr)
Definition: omAllocDecl.h:237
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc(size)
Definition: omAllocDecl.h:210
#define omReallocSize(addr, o_size, size)
Definition: omAllocDecl.h:220
#define omalloc0(size)
Definition: omAllocDecl.h:229
#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 NULL
Definition: omList.c:12
#define p_MemSum_LengthGeneral(r, s1, s2, length)
Definition: p_MemAdd.h:86
static int index(p_Length length, p_Ord ord)
Definition: p_Procs_Impl.h:592
unsigned long p_GetShortExpVector(const poly p, const ring r)
Definition: p_polys.cc:4776
long p_Deg(poly a, const ring r)
Definition: p_polys.cc:587
static int pLength(poly a)
Definition: p_polys.h:188
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:934
static void p_MemAdd_NegWeightAdjust(poly p, const ring r)
Definition: p_polys.h:1290
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 void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r)
Definition: p_polys.h:1472
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
Definition: p_polys.h:245
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:231
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 poly p_New(const ring, omBin bin)
Definition: p_polys.h:662
static poly p_Mult_nn(poly p, number n, const ring r)
Definition: p_polys.h:956
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:899
static BOOLEAN _p_LmDivisibleByNoComp(poly a, poly b, const ring r)
return: FALSE, if there exists i, such that a->exp[i] > b->exp[i] TRUE, otherwise (1) Consider long v...
Definition: p_polys.h:1763
static void p_GetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1518
static void p_LmFree(poly p, ring)
Definition: p_polys.h:681
static poly p_Init(const ring r, omBin bin)
Definition: p_polys.h:1318
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:844
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 pLmDelete(p)
assume p != NULL, deletes Lm(p)->coef and Lm(p)
Definition: polys.h:76
void sBucket_Add_p(sBucket_pt bucket, poly p, int length)
adds poly p to bucket destroys p!
Definition: sbuckets.cc:203
void sBucketDestroy(sBucket_pt *bucket)
Definition: sbuckets.cc:103
sBucket_pt sBucketCreate(const ring r)
Definition: sbuckets.cc:96
void sBucketClearAdd(sBucket_pt bucket, poly *p, int *length)
Definition: sbuckets.cc:275
int status int void size_t count
Definition: si_signals.h:59
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
void id_DelDiv(ideal id, const ring r)
delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., delete id[i], if LT(i) == coeff*mon*L...
VAR omBin sip_sideal_bin
Definition: simpleideals.cc:27
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
#define R
Definition: sirandom.c:27
#define M
Definition: sirandom.c:25
bool operator()(const poly &l, const poly &r) const
Definition: syz4.cc:218
static bool check_variables(const std::vector< bool > &variables, const poly m)
Definition: syz4.cc:49
static int compare_deg(const poly p_a, const poly p_b)
Definition: syz4.cc:479
static ideal syzM_i_sorted(const ideal G, const int i, syzHeadFunction *syzHead)
Definition: syz4.cc:418
static void update_variables(std::vector< bool > &variables, const ideal L)
Definition: syz4.cc:21
std::map< poly, poly, cache_compare > cache_term
Definition: syz4.cc:228
static ideal computeFrame(const ideal G, syzM_i_Function syzM_i, syzHeadFunction *syzHead)
Definition: syz4.cc:524
static int compare_comp(const poly p_a, const poly p_b)
Definition: syz4.cc:471
static ideal idConcat(const ideal *M, const int size, const int rank)
Definition: syz4.cc:444
static poly lift_ext_LT(const poly a, const ideal previous_module, const std::vector< bool > &variables, const lt_struct *const *const hash_previous_module, const bool use_cache)
Definition: syz4.cc:297
static void initialize_hash(lt_struct **C, const ideal L)
Definition: syz4.cc:80
static poly get_from_cache_term(const cache_term::const_iterator itr, const poly multiplier)
Definition: syz4.cc:260
static poly syzHeadExtFrame(const ideal G, const int i, const int j)
Definition: syz4.cc:350
static poly traverse_tail(const poly multiplier, const int comp, const ideal previous_module, const std::vector< bool > &variables, const lt_struct *const *const hash_previous_module)
Definition: syz4.cc:278
poly lt
Definition: syz4.cc:75
static void computeLiftings(const resolvente res, const int index, const std::vector< bool > &variables, const bool use_cache)
Definition: syz4.cc:549
static bool contains_unused_variable(const poly m, const std::vector< bool > &variables)
Definition: syz4.cc:578
static int compare_lex(const poly p_a, const poly p_b)
Definition: syz4.cc:487
unsigned long comp
Definition: syz4.cc:77
ideal syzM_i_Function(ideal, int, syzHeadFunction)
Definition: syz4.cc:377
static void set_options(syzHeadFunction **syzHead_ptr, bool *do_lifting_ptr, bool *single_module_ptr, const char *method)
Definition: syz4.cc:701
static void initialize_cache(const int size)
Definition: syz4.cc:232
static poly compute_image(const poly multiplier, const int comp, const ideal previous_module, const std::vector< bool > &variables, const lt_struct *const *const hash_previous_module, const bool use_cache)
Definition: syz4.cc:192
unsigned long sev
Definition: syz4.cc:76
#define insert_first_term(r, p, q, R)
Definition: syz4.cc:738
static poly find_reducer(const poly multiplier, const poly t, const lt_struct *const *const hash_previous_module)
Definition: syz4.cc:118
static void delete_tails(resolvente res, const int index)
Definition: syz4.cc:617
static int computeResolution(resolvente res, const int max_index, syzHeadFunction *syzHead, const bool do_lifting, const bool single_module, const bool use_cache, const bool use_tensor_trick)
Definition: syz4.cc:670
syStrategy syFrank(const ideal arg, const int length, const char *method, const bool use_cache, const bool use_tensor_trick)
Definition: syz4.cc:792
STATIC_VAR cache_term * Cache
Definition: syz4.cc:230
static void insert_into_cache_term(cache_term *T, const poly multiplier, const poly p)
Definition: syz4.cc:253
static void delete_cache(const int size)
Definition: syz4.cc:237
static poly syzHeadFrame(const ideal G, const int i, const int j)
Definition: syz4.cc:326
static void insert_ext_induced_LTs(const resolvente res, const int length, const bool single_module)
Definition: syz4.cc:758
static poly reduce_term(const poly multiplier, const poly term, const ideal previous_module, const std::vector< bool > &variables, const lt_struct *const *const hash_previous_module, const bool use_cache)
Definition: syz4.cc:164
static int computeResolution_iteration(resolvente res, const int max_index, syzHeadFunction *syzHead, const bool do_lifting, const bool single_module, const bool use_cache, const bool use_tensor_trick, std::vector< bool > &variables)
Definition: syz4.cc:633
static ideal syzM_i_unsorted(const ideal G, const int i, syzHeadFunction *syzHead)
Definition: syz4.cc:384
static int compare_Mi(const void *a, const void *b)
Definition: syz4.cc:506
static void delete_variables(resolvente res, const int index, const std::vector< bool > &variables)
Definition: syz4.cc:596
poly syzHeadFunction(ideal, int, int)
Definition: syz4.cc:321
ssyStrategy * syStrategy
Definition: syz.h:35