Context Navigation

source: git/kernel/GBEngine/kstd2.cc @ 3e5610

spielwiese

Last change on this file since 3e5610 was 3e5610, checked in by Hans Schoenemann <hannes@…>, 5 years ago
simplify delete lcm to kDeleteLcm (GBEngine)
Property mode set to `100644`
File size: 118.7 KB

Line
1	/****************************************
2	* Computer Algebra System SINGULAR *
3	****************************************/
4	/*
5	* ABSTRACT - Kernel: alg. of Buchberger
6	*/
7
8	// #define PDEBUG 2
9
10	#include "kernel/mod2.h"
11
12	#define GCD_SBA 1
13
14	// define if no buckets should be used
15	// #define NO_BUCKETS
16
17	#ifdef HAVE_PLURAL
18	#define PLURAL_INTERNAL_DECLARATIONS 1
19	#endif
20
21	/***********************************************
22	* SBA stuff -- start
23	***********************************************/
24	#define DEBUGF50 0
25	#define DEBUGF51 0
26
27	#ifdef DEBUGF5
28	#undef DEBUGF5
29	//#define DEBUGF5 1
30	#endif
31
32	#define F5C 1
33	#if F5C
34	#define F5CTAILRED 1
35	#endif
36
37	#define SBA_INTERRED_START 0
38	#define SBA_TAIL_RED 1
39	#define SBA_PRODUCT_CRITERION 0
40	#define SBA_PRINT_ZERO_REDUCTIONS 0
41	#define SBA_PRINT_REDUCTION_STEPS 0
42	#define SBA_PRINT_OPERATIONS 0
43	#define SBA_PRINT_SIZE_G 0
44	#define SBA_PRINT_SIZE_SYZ 0
45	#define SBA_PRINT_PRODUCT_CRITERION 0
46
47	// counts sba's reduction steps
48	#if SBA_PRINT_REDUCTION_STEPS
49	long sba_reduction_steps;
50	long sba_interreduction_steps;
51	#endif
52	#if SBA_PRINT_OPERATIONS
53	long sba_operations;
54	long sba_interreduction_operations;
55	#endif
56
57	/***********************************************
58	* SBA stuff -- done
59	***********************************************/
60
61	#include "kernel/GBEngine/kutil.h"
62	#include "misc/options.h"
63	#include "omalloc/omalloc.h"
64	#include "kernel/polys.h"
65	#include "kernel/ideals.h"
66	#include "kernel/GBEngine/kstd1.h"
67	#include "kernel/GBEngine/khstd.h"
68	#include "polys/kbuckets.h"
69	#include "polys/prCopy.h"
70	#include "polys/weight.h"
71	#include "misc/intvec.h"
72	#ifdef HAVE_PLURAL
73	#include "polys/nc/nc.h"
74	#endif
75	// #include "timer.h"
76
77	/* shiftgb stuff */
78	#include "kernel/GBEngine/shiftgb.h"
79
80	int (*test_PosInT)(const TSet T,const int tl,LObject &h);
81	int (*test_PosInL)(const LSet set, const int length,
82	LObject* L,const kStrategy strat);
83
84	// return -1 if no divisor is found
85	// number of first divisor, otherwise
86	int kFindDivisibleByInT(const kStrategy strat, const LObject* L, const int start)
87	{
88	unsigned long not_sev = ~L->sev;
89	int j = start;
90
91	const TSet T=strat->T;
92	const unsigned long* sevT=strat->sevT;
93	const ring r=currRing;
94	const BOOLEAN is_Ring=rField_is_Ring(r);
95	if (L->p!=NULL)
96	{
97	const poly p=L->p;
98
99	pAssume(~not_sev == p_GetShortExpVector(p, r));
100
101	if(is_Ring)
102	{
103	loop
104	{
105	if (j > strat->tl) return -1;
106	#if defined(PDEBUG) \|\| defined(PDIV_DEBUG)
107	if (p_LmShortDivisibleBy(T[j].p, sevT[j],p, not_sev, r))
108	{
109	if(n_DivBy(pGetCoeff(p), pGetCoeff(T[j].p), r->cf))
110	return j;
111	}
112	#else
113	if (!(sevT[j] & not_sev) &&
114	p_LmDivisibleBy(T[j].p, p, r))
115	{
116	if(n_DivBy(pGetCoeff(p), pGetCoeff(T[j].p), r->cf))
117	return j;
118	}
119	#endif
120	j++;
121	}
122	}
123	else
124	{
125	loop
126	{
127	if (j > strat->tl) return -1;
128	#if defined(PDEBUG) \|\| defined(PDIV_DEBUG)
129	if (p_LmShortDivisibleBy(T[j].p, sevT[j],p, not_sev, r))
130	{
131	return j;
132	}
133	#else
134	if (!(sevT[j] & not_sev) &&
135	p_LmDivisibleBy(T[j].p, p, r))
136	{
137	return j;
138	}
139	#endif
140	j++;
141	}
142	}
143	}
144	else
145	{
146	const poly p=L->t_p;
147	const ring r=strat->tailRing;
148	if(is_Ring)
149	{
150	loop
151	{
152	if (j > strat->tl) return -1;
153	#if defined(PDEBUG) \|\| defined(PDIV_DEBUG)
154	if (p_LmShortDivisibleBy(T[j].t_p, sevT[j],
155	p, not_sev, r))
156	{
157	if(n_DivBy(pGetCoeff(p), pGetCoeff(T[j].t_p), r->cf))
158	return j;
159	}
160	#else
161	if (!(sevT[j] & not_sev) &&
162	p_LmDivisibleBy(T[j].t_p, p, r))
163	{
164	if(n_DivBy(pGetCoeff(p), pGetCoeff(T[j].t_p), r->cf))
165	return j;
166	}
167	#endif
168	j++;
169	}
170	}
171	else
172	{
173	loop
174	{
175	if (j > strat->tl) return -1;
176	#if defined(PDEBUG) \|\| defined(PDIV_DEBUG)
177	if (p_LmShortDivisibleBy(T[j].t_p, sevT[j],
178	p, not_sev, r))
179	{
180	return j;
181	}
182	#else
183	if (!(sevT[j] & not_sev) &&
184	p_LmDivisibleBy(T[j].t_p, p, r))
185	{
186	return j;
187	}
188	#endif
189	j++;
190	}
191	}
192	}
193	}
194
195	// same as above, only with set S
196	int kFindDivisibleByInS(const kStrategy strat, int* max_ind, LObject* L)
197	{
198	unsigned long not_sev = ~L->sev;
199	poly p = L->GetLmCurrRing();
200	int j = 0;
201
202	pAssume(~not_sev == p_GetShortExpVector(p, currRing));
203
204	BOOLEAN is_Ring=rField_is_Ring(currRing);
205	#if 1
206	int ende;
207	if (is_Ring
208	\|\| (strat->ak>0)
209	\|\| currRing->pLexOrder)
210	ende=strat->sl;
211	else
212	{
213	ende=posInS(strat,*max_ind,p,0)+1;
214	if (ende>(max_ind)) ende=(max_ind);
215	}
216	#else
217	int ende=strat->sl;
218	#endif
219	if(is_Ring)
220	{
221	loop
222	{
223	if (j > ende) return -1;
224	#if defined(PDEBUG) \|\| defined(PDIV_DEBUG)
225	if (p_LmShortDivisibleBy(strat->S[j], strat->sevS[j],
226	p, not_sev, currRing))
227	{
228	if(n_DivBy(pGetCoeff(p), pGetCoeff(strat->S[j]), currRing->cf))
229	return j;
230	}
231	#else
232	if ( !(strat->sevS[j] & not_sev) &&
233	p_LmDivisibleBy(strat->S[j], p, currRing))
234	{
235	if(n_DivBy(pGetCoeff(p), pGetCoeff(strat->S[j]), currRing->cf))
236	return j;
237	}
238	#endif
239	j++;
240	}
241	}
242	else
243	{
244	loop
245	{
246	if (j > ende) return -1;
247	#if defined(PDEBUG) \|\| defined(PDIV_DEBUG)
248	if (p_LmShortDivisibleBy(strat->S[j], strat->sevS[j],
249	p, not_sev, currRing))
250	{
251	return j;
252	}
253	#else
254	if ( !(strat->sevS[j] & not_sev) &&
255	p_LmDivisibleBy(strat->S[j], p, currRing))
256	{
257	return j;
258	}
259	#endif
260	j++;
261	}
262	}
263	}
264
265	int kFindNextDivisibleByInS(const kStrategy strat, int start,int max_ind, LObject* L)
266	{
267	unsigned long not_sev = ~L->sev;
268	poly p = L->GetLmCurrRing();
269	int j = start;
270
271	pAssume(~not_sev == p_GetShortExpVector(p, currRing));
272	#if 1
273	int ende=max_ind;
274	#else
275	int ende=strat->sl;
276	#endif
277	if(rField_is_Ring(currRing))
278	{
279	loop
280	{
281	if (j > ende) return -1;
282	#if defined(PDEBUG) \|\| defined(PDIV_DEBUG)
283	if (p_LmShortDivisibleBy(strat->S[j], strat->sevS[j],
284	p, not_sev, currRing))
285	{
286	if(n_DivBy(pGetCoeff(p), pGetCoeff(strat->S[j]), currRing->cf))
287	return j;
288	}
289	#else
290	if ( !(strat->sevS[j] & not_sev) &&
291	p_LmDivisibleBy(strat->S[j], p, currRing))
292	{
293	if(n_DivBy(pGetCoeff(p), pGetCoeff(strat->S[j]), currRing->cf))
294	return j;
295	}
296	#endif
297	j++;
298	}
299	}
300	else
301	{
302	loop
303	{
304	if (j > ende) return -1;
305	#if defined(PDEBUG) \|\| defined(PDIV_DEBUG)
306	if (p_LmShortDivisibleBy(strat->S[j], strat->sevS[j],
307	p, not_sev, currRing))
308	{
309	return j;
310	}
311	#else
312	if ( !(strat->sevS[j] & not_sev) &&
313	p_LmDivisibleBy(strat->S[j], p, currRing))
314	{
315	return j;
316	}
317	#endif
318	j++;
319	}
320	}
321	}
322
323	#ifdef HAVE_RINGS
324	poly kFindZeroPoly(poly input_p, ring leadRing, ring tailRing)
325	{
326	// m = currRing->ch
327
328	if (input_p == NULL) return NULL;
329
330	poly p = input_p;
331	poly zeroPoly = NULL;
332	unsigned long a = (unsigned long) pGetCoeff(p);
333
334	int k_ind2 = 0;
335	int a_ind2 = ind2(a);
336
337	// unsigned long k = 1;
338	// of interest is only k_ind2, special routine for improvement ... TODO OLIVER
339	for (int i = 1; i <= leadRing->N; i++)
340	{
341	k_ind2 = k_ind2 + ind_fact_2(p_GetExp(p, i, leadRing));
342	}
343
344	a = (unsigned long) pGetCoeff(p);
345
346	number tmp1;
347	poly tmp2, tmp3;
348	poly lead_mult = p_ISet(1, tailRing);
349	if (n_GetChar(leadRing->cf) <= k_ind2 + a_ind2)
350	{
351	int too_much = k_ind2 + a_ind2 - n_GetChar(leadRing->cf);
352	int s_exp;
353	zeroPoly = p_ISet(a, tailRing);
354	for (int i = 1; i <= leadRing->N; i++)
355	{
356	s_exp = p_GetExp(p, i,leadRing);
357	if (s_exp % 2 != 0)
358	{
359	s_exp = s_exp - 1;
360	}
361	while ( (0 < ind2(s_exp)) && (ind2(s_exp) <= too_much) )
362	{
363	too_much = too_much - ind2(s_exp);
364	s_exp = s_exp - 2;
365	}
366	p_SetExp(lead_mult, i, p_GetExp(p, i,leadRing) - s_exp, tailRing);
367	for (int j = 1; j <= s_exp; j++)
368	{
369	tmp1 = nInit(j);
370	tmp2 = p_ISet(1, tailRing);
371	p_SetExp(tmp2, i, 1, tailRing);
372	p_Setm(tmp2, tailRing);
373	if (nIsZero(tmp1))
374	{ // should nowbe obsolet, test ! TODO OLIVER
375	zeroPoly = p_Mult_q(zeroPoly, tmp2, tailRing);
376	}
377	else
378	{
379	tmp3 = p_NSet(nCopy(tmp1), tailRing);
380	zeroPoly = p_Mult_q(zeroPoly, p_Add_q(tmp3, tmp2, tailRing), tailRing);
381	}
382	}
383	}
384	p_Setm(lead_mult, tailRing);
385	zeroPoly = p_Mult_mm(zeroPoly, lead_mult, tailRing);
386	tmp2 = p_NSet(nCopy(pGetCoeff(zeroPoly)), leadRing);
387	for (int i = 1; i <= leadRing->N; i++)
388	{
389	pSetExp(tmp2, i, p_GetExp(zeroPoly, i, tailRing));
390	}
391	p_Setm(tmp2, leadRing);
392	zeroPoly = p_LmDeleteAndNext(zeroPoly, tailRing);
393	pNext(tmp2) = zeroPoly;
394	return tmp2;
395	}
396	/* unsigned long alpha_k = twoPow(leadRing->ch - k_ind2);
397	if (1 == 0 && alpha_k <= a)
398	{ // Temporarly disabled, reducing coefficients not compatible with std TODO Oliver
399	zeroPoly = p_ISet((a / alpha_k)*alpha_k, tailRing);
400	for (int i = 1; i <= leadRing->N; i++)
401	{
402	for (unsigned long j = 1; j <= p_GetExp(p, i, leadRing); j++)
403	{
404	tmp1 = nInit(j);
405	tmp2 = p_ISet(1, tailRing);
406	p_SetExp(tmp2, i, 1, tailRing);
407	p_Setm(tmp2, tailRing);
408	if (nIsZero(tmp1))
409	{
410	zeroPoly = p_Mult_q(zeroPoly, tmp2, tailRing);
411	}
412	else
413	{
414	tmp3 = p_ISet((unsigned long) tmp1, tailRing);
415	zeroPoly = p_Mult_q(zeroPoly, p_Add_q(tmp2, tmp3, tailRing), tailRing);
416	}
417	}
418	}
419	tmp2 = p_ISet((unsigned long) pGetCoeff(zeroPoly), leadRing);
420	for (int i = 1; i <= leadRing->N; i++)
421	{
422	pSetExp(tmp2, i, p_GetExp(zeroPoly, i, tailRing));
423	}
424	p_Setm(tmp2, leadRing);
425	zeroPoly = p_LmDeleteAndNext(zeroPoly, tailRing);
426	pNext(tmp2) = zeroPoly;
427	return tmp2;
428	} */
429	return NULL;
430	}
431	#endif
432
433
434	#ifdef HAVE_RINGS
435	/*2
436	* reduction procedure for the ring Z/2^m
437	*/
438	int redRing (LObject* h,kStrategy strat)
439	{
440	if (h->IsNull()) return 0; // spoly is zero (can only occure with zero divisors)
441	if (strat->tl<0) return 1;
442
443	int at/,i/;
444	long d;
445	int j = 0;
446	int pass = 0;
447	// poly zeroPoly = NULL;
448
449	// TODO warum SetpFDeg notwendig?
450	h->SetpFDeg();
451	assume(h->pFDeg() == h->FDeg);
452	long reddeg = h->GetpFDeg();
453
454	h->SetShortExpVector();
455	loop
456	{
457	j = kFindDivisibleByInT(strat, h);
458	if (j < 0)
459	{
460	// over ZZ: cleanup coefficients by complete reduction with monomials
461	postReduceByMon(h, strat);
462	if(h->p == NULL)
463	{
464	kDeleteLcm(h);
465	h->Clear();
466	return 0;
467	}
468	if(nIsZero(pGetCoeff(h->p))) return 2;
469	j = kFindDivisibleByInT(strat, h);
470	if(j < 0)
471	{
472	if(strat->tl >= 0)
473	h->i_r1 = strat->tl;
474	else
475	h->i_r1 = -1;
476	if (h->GetLmTailRing() == NULL)
477	{
478	kDeleteLcm(h);
479	h->Clear();
480	return 0;
481	}
482	return 1;
483	}
484	}
485	//printf("\nFound one: ");pWrite(strat->T[j].p);
486	//enterT(*h, strat);
487	ksReducePoly(h, &(strat->T[j]), NULL, NULL, strat); // with debug output
488	//printf("\nAfter small red: ");pWrite(h->p);
489	if (h->GetLmTailRing() == NULL)
490	{
491	kDeleteLcm(h);
492	h->Clear();
493	return 0;
494	}
495	h->SetShortExpVector();
496	d = h->SetpFDeg();
497	/- try to reduce the s-polynomial -/
498	pass++;
499	if (!TEST_OPT_REDTHROUGH &&
500	(strat->Ll >= 0) && ((d > reddeg) \|\| (pass > strat->LazyPass)))
501	{
502	h->SetLmCurrRing();
503	if (strat->posInLDependsOnLength)
504	h->SetLength(strat->length_pLength);
505	at = strat->posInL(strat->L,strat->Ll,h,strat);
506	if (at <= strat->Ll)
507	{
508	#ifdef KDEBUG
509	if (TEST_OPT_DEBUG) Print(" ->L[%d]\n",at);
510	#endif
511	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at); // NOT RING CHECKED OLIVER
512	h->Clear();
513	return -1;
514	}
515	}
516	if (d != reddeg)
517	{
518	if (d >= (long)strat->tailRing->bitmask)
519	{
520	if (h->pTotalDeg() >= (long)strat->tailRing->bitmask)
521	{
522	strat->overflow=TRUE;
523	//Print("OVERFLOW in redRing d=%ld, max=%ld\n",d,strat->tailRing->bitmask);
524	h->GetP();
525	at = strat->posInL(strat->L,strat->Ll,h,strat);
526	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
527	h->Clear();
528	return -1;
529	}
530	}
531	else if ((TEST_OPT_PROT) && (strat->Ll < 0))
532	{
533	Print(".%ld",d);mflush();
534	reddeg = d;
535	}
536	}
537	}
538	}
539	#endif
540
541	/*2
542	* reduction procedure for the homogeneous case
543	* and the case of a degree-ordering
544	*/
545	int redHomog (LObject* h,kStrategy strat)
546	{
547	if (strat->tl<0) return 1;
548	//if (h->GetLmTailRing()==NULL) return 0; // HS: SHOULD NOT BE NEEDED!
549	assume(h->FDeg == h->pFDeg());
550
551	poly h_p;
552	int i,j,at,pass, ii;
553	unsigned long not_sev;
554	// long reddeg,d;
555
556	pass = j = 0;
557	// d = reddeg = h->GetpFDeg();
558	h->SetShortExpVector();
559	int li;
560	h_p = h->GetLmTailRing();
561	not_sev = ~ h->sev;
562	loop
563	{
564	j = kFindDivisibleByInT(strat, h);
565	if (j < 0) return 1;
566
567	li = strat->T[j].pLength;
568	if (li<=0) li=strat->T[j].GetpLength();
569	ii = j;
570	/*
571	* the polynomial to reduce with (up to the moment) is;
572	* pi with length li
573	*/
574	i = j;
575	#if 1
576	if (TEST_OPT_LENGTH)
577	loop
578	{
579	/- search the shortest possible with respect to length -/
580	i++;
581	if (i > strat->tl)
582	break;
583	if (li==1)
584	break;
585	if ((strat->T[i].pLength < li)
586	&&
587	p_LmShortDivisibleBy(strat->T[i].GetLmTailRing(), strat->sevT[i],
588	h_p, not_sev, strat->tailRing))
589	{
590	/*
591	* the polynomial to reduce with is now;
592	*/
593	li = strat->T[i].pLength;
594	if (li<=0) li=strat->T[i].GetpLength();
595	ii = i;
596	}
597	}
598	#endif
599
600	/*
601	* end of search: have to reduce with pi
602	*/
603	#ifdef KDEBUG
604	if (TEST_OPT_DEBUG)
605	{
606	PrintS("red:");
607	h->wrp();
608	PrintS(" with ");
609	strat->T[ii].wrp();
610	}
611	#endif
612	assume(strat->fromT == FALSE);
613
614	ksReducePoly(h, &(strat->T[ii]), NULL, NULL, strat);
615	#if SBA_PRINT_REDUCTION_STEPS
616	sba_interreduction_steps++;
617	#endif
618	#if SBA_PRINT_OPERATIONS
619	sba_interreduction_operations += pLength(strat->T[ii].p);
620	#endif
621
622	#ifdef KDEBUG
623	if (TEST_OPT_DEBUG)
624	{
625	PrintS("\nto ");
626	h->wrp();
627	PrintLn();
628	}
629	#endif
630
631	h_p = h->GetLmTailRing();
632	if (h_p == NULL)
633	{
634	kDeleteLcm(h);
635	return 0;
636	}
637	h->SetShortExpVector();
638	not_sev = ~ h->sev;
639	/*
640	* try to reduce the s-polynomial h
641	*test first whether h should go to the lazyset L
642	*-if the degree jumps
643	*-if the number of pre-defined reductions jumps
644	*/
645	pass++;
646	if (!TEST_OPT_REDTHROUGH && (strat->Ll >= 0) && (pass > strat->LazyPass))
647	{
648	h->SetLmCurrRing();
649	at = strat->posInL(strat->L,strat->Ll,h,strat);
650	if (at <= strat->Ll)
651	{
652	int dummy=strat->sl;
653	if (kFindDivisibleByInS(strat, &dummy, h) < 0)
654	return 1;
655	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
656	#ifdef KDEBUG
657	if (TEST_OPT_DEBUG)
658	Print(" lazy: -> L%d\n",at);
659	#endif
660	h->Clear();
661	return -1;
662	}
663	}
664	}
665	}
666
667	KINLINE int ksReducePolyTailSig(LObject* PR, TObject* PW, LObject* Red, kStrategy strat)
668	{
669	BOOLEAN ret;
670	number coef;
671	assume(PR->GetLmCurrRing() != PW->GetLmCurrRing());
672	if(!rField_is_Ring(currRing))
673	Red->HeadNormalize();
674	/*
675	printf("------------------------\n");
676	pWrite(Red->GetLmCurrRing());
677	*/
678	if(rField_is_Ring(currRing))
679	ret = ksReducePolySigRing(Red, PW, 1, NULL, &coef, strat);
680	else
681	ret = ksReducePolySig(Red, PW, 1, NULL, &coef, strat);
682	if (!ret)
683	{
684	if (! n_IsOne(coef, currRing->cf) && !rField_is_Ring(currRing))
685	{
686	PR->Mult_nn(coef);
687	// HANNES: mark for Normalize
688	}
689	n_Delete(&coef, currRing->cf);
690	}
691	return ret;
692	}
693
694	/*2
695	* reduction procedure for signature-based standard
696	* basis algorithms:
697	* all reductions have to be sig-safe!
698	*
699	* 2 is returned if and only if the pair is rejected by the rewritten criterion
700	* at exactly this point of the computations. This is the last possible point
701	* such a check can be done => checks with the biggest set of available
702	* signatures
703	*/
704
705	int redSig (LObject* h,kStrategy strat)
706	{
707	if (strat->tl<0) return 1;
708	//if (h->GetLmTailRing()==NULL) return 0; // HS: SHOULD NOT BE NEEDED!
709	//printf("FDEGS: %ld -- %ld\n",h->FDeg, h->pFDeg());
710	assume(h->FDeg == h->pFDeg());
711	//#if 1
712	#ifdef DEBUGF5
713	PrintS("------- IN REDSIG -------\n");
714	Print("p: ");
715	pWrite(pHead(h->p));
716	PrintS("p1: ");
717	pWrite(pHead(h->p1));
718	PrintS("p2: ");
719	pWrite(pHead(h->p2));
720	PrintS("---------------------------\n");
721	#endif
722	poly h_p;
723	int i,j,at,pass, ii;
724	int start=0;
725	int sigSafe;
726	unsigned long not_sev;
727	// long reddeg,d;
728
729	pass = j = 0;
730	// d = reddeg = h->GetpFDeg();
731	h->SetShortExpVector();
732	int li;
733	h_p = h->GetLmTailRing();
734	not_sev = ~ h->sev;
735	loop
736	{
737	j = kFindDivisibleByInT(strat, h, start);
738	if (j < 0)
739	{
740	return 1;
741	}
742
743	li = strat->T[j].pLength;
744	if (li<=0) li=strat->T[j].GetpLength();
745	ii = j;
746	/*
747	* the polynomial to reduce with (up to the moment) is;
748	* pi with length li
749	*/
750	i = j;
751	#if 1
752	if (TEST_OPT_LENGTH)
753	loop
754	{
755	/- search the shortest possible with respect to length -/
756	i++;
757	if (i > strat->tl)
758	break;
759	if (li==1)
760	break;
761	if ((strat->T[i].pLength < li)
762	&&
763	p_LmShortDivisibleBy(strat->T[i].GetLmTailRing(), strat->sevT[i],
764	h_p, not_sev, strat->tailRing))
765	{
766	/*
767	* the polynomial to reduce with is now;
768	*/
769	li = strat->T[i].pLength;
770	if (li<=0) li=strat->T[i].GetpLength();
771	ii = i;
772	}
773	}
774	start = ii+1;
775	#endif
776
777	/*
778	* end of search: have to reduce with pi
779	*/
780	#ifdef KDEBUG
781	if (TEST_OPT_DEBUG)
782	{
783	PrintS("red:");
784	h->wrp();
785	PrintS(" with ");
786	strat->T[ii].wrp();
787	}
788	#endif
789	assume(strat->fromT == FALSE);
790	//#if 1
791	#ifdef DEBUGF5
792	Print("BEFORE REDUCTION WITH %d:\n",ii);
793	PrintS("--------------------------------\n");
794	pWrite(h->sig);
795	pWrite(strat->T[ii].sig);
796	pWrite(h->GetLmCurrRing());
797	pWrite(pHead(h->p1));
798	pWrite(pHead(h->p2));
799	pWrite(pHead(strat->T[ii].p));
800	PrintS("--------------------------------\n");
801	printf("INDEX OF REDUCER T: %d\n",ii);
802	#endif
803	sigSafe = ksReducePolySig(h, &(strat->T[ii]), strat->S_2_R[ii], NULL, NULL, strat);
804	#if SBA_PRINT_REDUCTION_STEPS
805	if (sigSafe != 3)
806	sba_reduction_steps++;
807	#endif
808	#if SBA_PRINT_OPERATIONS
809	if (sigSafe != 3)
810	sba_operations += pLength(strat->T[ii].p);
811	#endif
812	// if reduction has taken place, i.e. the reduction was sig-safe
813	// otherwise start is already at the next position and the loop
814	// searching reducers in T goes on from index start
815	//#if 1
816	#ifdef DEBUGF5
817	Print("SigSAFE: %d\n",sigSafe);
818	#endif
819	if (sigSafe != 3)
820	{
821	// start the next search for reducers in T from the beginning
822	start = 0;
823	#ifdef KDEBUG
824	if (TEST_OPT_DEBUG)
825	{
826	PrintS("\nto ");
827	h->wrp();
828	PrintLn();
829	}
830	#endif
831
832	h_p = h->GetLmTailRing();
833	if (h_p == NULL)
834	{
835	kDeleteLcm(h);
836	return 0;
837	}
838	h->SetShortExpVector();
839	not_sev = ~ h->sev;
840	/*
841	* try to reduce the s-polynomial h
842	*test first whether h should go to the lazyset L
843	*-if the degree jumps
844	*-if the number of pre-defined reductions jumps
845	*/
846	pass++;
847	if (!TEST_OPT_REDTHROUGH && (strat->Ll >= 0) && (pass > strat->LazyPass))
848	{
849	h->SetLmCurrRing();
850	at = strat->posInL(strat->L,strat->Ll,h,strat);
851	if (at <= strat->Ll)
852	{
853	int dummy=strat->sl;
854	if (kFindDivisibleByInS(strat, &dummy, h) < 0)
855	{
856	return 1;
857	}
858	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
859	#ifdef KDEBUG
860	if (TEST_OPT_DEBUG)
861	Print(" lazy: -> L%d\n",at);
862	#endif
863	h->Clear();
864	return -1;
865	}
866	}
867	}
868	}
869	}
870
871
872	int redSigRing (LObject* h,kStrategy strat)
873	{
874	//Since reduce is really bad for SBA we use the following idea:
875	// We first check if we can build a gcd pair between h and S
876	//where the sig remains the same and replace h by this gcd poly
877	assume(rField_is_Ring(currRing));
878	#if GCD_SBA
879	while(sbaCheckGcdPair(h,strat))
880	{
881	h->sev = pGetShortExpVector(h->p);
882	}
883	#endif
884	poly beforeredsig;
885	beforeredsig = pCopy(h->sig);
886
887	if (strat->tl<0) return 1;
888	//if (h->GetLmTailRing()==NULL) return 0; // HS: SHOULD NOT BE NEEDED!
889	//printf("FDEGS: %ld -- %ld\n",h->FDeg, h->pFDeg());
890	assume(h->FDeg == h->pFDeg());
891	//#if 1
892	#ifdef DEBUGF5
893	Print("------- IN REDSIG -------\n");
894	Print("p: ");
895	pWrite(pHead(h->p));
896	Print("p1: ");
897	pWrite(pHead(h->p1));
898	Print("p2: ");
899	pWrite(pHead(h->p2));
900	Print("---------------------------\n");
901	#endif
902	poly h_p;
903	int i,j,at,pass, ii;
904	int start=0;
905	int sigSafe;
906	unsigned long not_sev;
907	// long reddeg,d;
908
909	pass = j = 0;
910	// d = reddeg = h->GetpFDeg();
911	h->SetShortExpVector();
912	int li;
913	h_p = h->GetLmTailRing();
914	not_sev = ~ h->sev;
915	loop
916	{
917	j = kFindDivisibleByInT(strat, h, start);
918	if (j < 0)
919	{
920	#if GCD_SBA
921	while(sbaCheckGcdPair(h,strat))
922	{
923	h->sev = pGetShortExpVector(h->p);
924	h->is_redundant = FALSE;
925	start = 0;
926	}
927	#endif
928	// over ZZ: cleanup coefficients by complete reduction with monomials
929	postReduceByMonSig(h, strat);
930	if(h->p == NULL \|\| nIsZero(pGetCoeff(h->p))) return 2;
931	j = kFindDivisibleByInT(strat, h,start);
932	if(j < 0)
933	{
934	if(strat->tl >= 0)
935	h->i_r1 = strat->tl;
936	else
937	h->i_r1 = -1;
938	if (h->GetLmTailRing() == NULL)
939	{
940	kDeleteLcm(h);
941	h->Clear();
942	return 0;
943	}
944	//Check for sigdrop after reduction
945	if(pLtCmp(beforeredsig,h->sig) == 1)
946	{
947	strat->sigdrop = TRUE;
948	//Reduce it as much as you can
949	int red_result = redRing(h,strat);
950	if(red_result == 0)
951	{
952	//It reduced to 0, cancel the sigdrop
953	strat->sigdrop = FALSE;
954	p_Delete(&h->sig,currRing);h->sig = NULL;
955	return 0;
956	}
957	else
958	{
959	//strat->enterS(*h, strat->sl+1, strat, strat->tl);
960	return 0;
961	}
962	}
963	p_Delete(&beforeredsig,currRing);
964	return 1;
965	}
966	}
967
968	li = strat->T[j].pLength;
969	if (li<=0) li=strat->T[j].GetpLength();
970	ii = j;
971	/*
972	* the polynomial to reduce with (up to the moment) is;
973	* pi with length li
974	*/
975	i = j;
976	if (TEST_OPT_LENGTH)
977	loop
978	{
979	/- search the shortest possible with respect to length -/
980	i++;
981	if (i > strat->tl)
982	break;
983	if (li==1)
984	break;
985	if ((strat->T[i].pLength < li)
986	&& n_DivBy(pGetCoeff(h_p),pGetCoeff(strat->T[i].p),currRing->cf)
987	&& p_LmShortDivisibleBy(strat->T[i].GetLmTailRing(), strat->sevT[i],
988	h_p, not_sev, strat->tailRing))
989	{
990	/*
991	* the polynomial to reduce with is now;
992	*/
993	li = strat->T[i].pLength;
994	if (li<=0) li=strat->T[i].GetpLength();
995	ii = i;
996	}
997	}
998
999	start = ii+1;
1000
1001	/*
1002	* end of search: have to reduce with pi
1003	*/
1004	#ifdef KDEBUG
1005	if (TEST_OPT_DEBUG)
1006	{
1007	PrintS("red:");
1008	h->wrp();
1009	PrintS(" with ");
1010	strat->T[ii].wrp();
1011	}
1012	#endif
1013	assume(strat->fromT == FALSE);
1014	//#if 1
1015	#ifdef DEBUGF5
1016	Print("BEFORE REDUCTION WITH %d:\n",ii);
1017	Print("--------------------------------\n");
1018	pWrite(h->sig);
1019	pWrite(strat->T[ii].sig);
1020	pWrite(h->GetLmCurrRing());
1021	pWrite(pHead(h->p1));
1022	pWrite(pHead(h->p2));
1023	pWrite(pHead(strat->T[ii].p));
1024	Print("--------------------------------\n");
1025	printf("INDEX OF REDUCER T: %d\n",ii);
1026	#endif
1027	sigSafe = ksReducePolySigRing(h, &(strat->T[ii]), strat->S_2_R[ii], NULL, NULL, strat);
1028	if(h->p == NULL && h->sig == NULL)
1029	{
1030	//Trivial case catch
1031	strat->sigdrop = FALSE;
1032	}
1033	#if 0
1034	//If the reducer has the same lt (+ or -) as the other one, reduce it via redRing
1035	//In some cases this proves to be very bad
1036	if(rField_is_Ring(currRing) && h->p != NULL && pLmCmp(h->p,strat->T[ii].p)==0)
1037	{
1038	int red_result = redRing(h,strat);
1039	if(red_result == 0)
1040	{
1041	pDelete(&h->sig);h->sig = NULL;
1042	return 0;
1043	}
1044	else
1045	{
1046	strat->sigdrop = TRUE;
1047	return 1;
1048	}
1049	}
1050	#endif
1051	if(strat->sigdrop)
1052	return 1;
1053	#if SBA_PRINT_REDUCTION_STEPS
1054	if (sigSafe != 3)
1055	sba_reduction_steps++;
1056	#endif
1057	#if SBA_PRINT_OPERATIONS
1058	if (sigSafe != 3)
1059	sba_operations += pLength(strat->T[ii].p);
1060	#endif
1061	// if reduction has taken place, i.e. the reduction was sig-safe
1062	// otherwise start is already at the next position and the loop
1063	// searching reducers in T goes on from index start
1064	//#if 1
1065	#ifdef DEBUGF5
1066	Print("SigSAFE: %d\n",sigSafe);
1067	#endif
1068	if (sigSafe != 3)
1069	{
1070	// start the next search for reducers in T from the beginning
1071	start = 0;
1072	#ifdef KDEBUG
1073	if (TEST_OPT_DEBUG)
1074	{
1075	PrintS("\nto ");
1076	h->wrp();
1077	PrintLn();
1078	}
1079	#endif
1080
1081	h_p = h->GetLmTailRing();
1082	if (h_p == NULL)
1083	{
1084	kDeleteLcm(h);
1085	return 0;
1086	}
1087	h->SetShortExpVector();
1088	not_sev = ~ h->sev;
1089	/*
1090	* try to reduce the s-polynomial h
1091	*test first whether h should go to the lazyset L
1092	*-if the degree jumps
1093	*-if the number of pre-defined reductions jumps
1094	*/
1095	pass++;
1096	if (!TEST_OPT_REDTHROUGH && (strat->Ll >= 0) && (pass > strat->LazyPass))
1097	{
1098	h->SetLmCurrRing();
1099	at = strat->posInL(strat->L,strat->Ll,h,strat);
1100	if (at <= strat->Ll)
1101	{
1102	int dummy=strat->sl;
1103	if (kFindDivisibleByInS(strat, &dummy, h) < 0)
1104	{
1105	return 1;
1106	}
1107	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
1108	#ifdef KDEBUG
1109	if (TEST_OPT_DEBUG)
1110	Print(" lazy: -> L%d\n",at);
1111	#endif
1112	h->Clear();
1113	return -1;
1114	}
1115	}
1116	}
1117	}
1118	}
1119
1120	// tail reduction for SBA
1121	poly redtailSba (LObject* L, int pos, kStrategy strat, BOOLEAN withT, BOOLEAN normalize)
1122	{
1123	#define REDTAIL_CANONICALIZE 100
1124	strat->redTailChange=FALSE;
1125	if (strat->noTailReduction) return L->GetLmCurrRing();
1126	poly h, p;
1127	p = h = L->GetLmTailRing();
1128	if ((h==NULL) \|\| (pNext(h)==NULL))
1129	return L->GetLmCurrRing();
1130
1131	TObject* With;
1132	// placeholder in case strat->tl < 0
1133	TObject With_s(strat->tailRing);
1134
1135	LObject Ln(pNext(h), strat->tailRing);
1136	Ln.sig = L->sig;
1137	Ln.sevSig = L->sevSig;
1138	Ln.pLength = L->GetpLength() - 1;
1139
1140	pNext(h) = NULL;
1141	if (L->p != NULL) pNext(L->p) = NULL;
1142	L->pLength = 1;
1143
1144	Ln.PrepareRed(strat->use_buckets);
1145
1146	int cnt=REDTAIL_CANONICALIZE;
1147	while(!Ln.IsNull())
1148	{
1149	loop
1150	{
1151	if(rField_is_Ring(currRing) && strat->sigdrop)
1152	break;
1153	Ln.SetShortExpVector();
1154	if (withT)
1155	{
1156	int j;
1157	j = kFindDivisibleByInT(strat, &Ln);
1158	if (j < 0) break;
1159	With = &(strat->T[j]);
1160	}
1161	else
1162	{
1163	With = kFindDivisibleByInS_T(strat, pos, &Ln, &With_s);
1164	if (With == NULL) break;
1165	}
1166	cnt--;
1167	if (cnt==0)
1168	{
1169	cnt=REDTAIL_CANONICALIZE;
1170	/poly tmp=/Ln.CanonicalizeP();
1171	if (normalize && !rField_is_Ring(currRing))
1172	{
1173	Ln.Normalize();
1174	//pNormalize(tmp);
1175	//if (TEST_OPT_PROT) { PrintS("n"); mflush(); }
1176	}
1177	}
1178	if (normalize && (!TEST_OPT_INTSTRATEGY) && !rField_is_Ring(currRing) && (!nIsOne(pGetCoeff(With->p))))
1179	{
1180	With->pNorm();
1181	}
1182	strat->redTailChange=TRUE;
1183	int ret = ksReducePolyTailSig(L, With, &Ln, strat);
1184	if(rField_is_Ring(currRing))
1185	L->sig = Ln.sig;
1186	//Because Ln.sig is set to L->sig, but in ksReducePolyTailSig -> ksReducePolySig
1187	// I delete it an then set Ln.sig. Hence L->sig is lost
1188	#if SBA_PRINT_REDUCTION_STEPS
1189	if (ret != 3)
1190	sba_reduction_steps++;
1191	#endif
1192	#if SBA_PRINT_OPERATIONS
1193	if (ret != 3)
1194	sba_operations += pLength(With->p);
1195	#endif
1196	if (ret)
1197	{
1198	// reducing the tail would violate the exp bound
1199	// set a flag and hope for a retry (in bba)
1200	strat->completeReduce_retry=TRUE;
1201	if ((Ln.p != NULL) && (Ln.t_p != NULL)) Ln.p=NULL;
1202	do
1203	{
1204	pNext(h) = Ln.LmExtractAndIter();
1205	pIter(h);
1206	L->pLength++;
1207	} while (!Ln.IsNull());
1208	goto all_done;
1209	}
1210	if (Ln.IsNull()) goto all_done;
1211	if (! withT) With_s.Init(currRing);
1212	if(rField_is_Ring(currRing) && strat->sigdrop)
1213	{
1214	//Cannot break the loop here so easily
1215	break;
1216	}
1217	}
1218	pNext(h) = Ln.LmExtractAndIter();
1219	pIter(h);
1220	if(!rField_is_Ring(currRing))
1221	pNormalize(h);
1222	L->pLength++;
1223	}
1224	all_done:
1225	Ln.Delete();
1226	if (L->p != NULL) pNext(L->p) = pNext(p);
1227
1228	if (strat->redTailChange)
1229	{
1230	L->length = 0;
1231	}
1232	//if (TEST_OPT_PROT) { PrintS("N"); mflush(); }
1233	//L->Normalize(); // HANNES: should have a test
1234	kTest_L(L);
1235	return L->GetLmCurrRing();
1236	}
1237
1238	/*2
1239	* reduction procedure for the inhomogeneous case
1240	* and not a degree-ordering
1241	*/
1242	int redLazy (LObject* h,kStrategy strat)
1243	{
1244	if (strat->tl<0) return 1;
1245	int at,i,ii,li;
1246	int j = 0;
1247	int pass = 0;
1248	assume(h->pFDeg() == h->FDeg);
1249	long reddeg = h->GetpFDeg();
1250	long d;
1251	unsigned long not_sev;
1252
1253	h->SetShortExpVector();
1254	poly h_p = h->GetLmTailRing();
1255	not_sev = ~ h->sev;
1256	loop
1257	{
1258	j = kFindDivisibleByInT(strat, h);
1259	if (j < 0) return 1;
1260
1261	li = strat->T[j].pLength;
1262	if (li<=0) li=strat->T[j].GetpLength();
1263	ii = j;
1264	/*
1265	* the polynomial to reduce with (up to the moment) is;
1266	* pi with length li
1267	*/
1268
1269	i = j;
1270	#if 1
1271	if (TEST_OPT_LENGTH)
1272	loop
1273	{
1274	/- search the shortest possible with respect to length -/
1275	i++;
1276	if (i > strat->tl)
1277	break;
1278	if (li==1)
1279	break;
1280	if ((strat->T[i].pLength < li)
1281	&&
1282	p_LmShortDivisibleBy(strat->T[i].GetLmTailRing(), strat->sevT[i],
1283	h_p, not_sev, strat->tailRing))
1284	{
1285	/*
1286	* the polynomial to reduce with is now;
1287	*/
1288	li = strat->T[i].pLength;
1289	if (li<=0) li=strat->T[i].GetpLength();
1290	ii = i;
1291	}
1292	}
1293	#endif
1294
1295	/*
1296	* end of search: have to reduce with pi
1297	*/
1298
1299
1300	#ifdef KDEBUG
1301	if (TEST_OPT_DEBUG)
1302	{
1303	PrintS("red:");
1304	h->wrp();
1305	PrintS(" with ");
1306	strat->T[ii].wrp();
1307	}
1308	#endif
1309
1310	ksReducePoly(h, &(strat->T[ii]), NULL, NULL, strat);
1311	#if SBA_PRINT_REDUCTION_STEPS
1312	sba_interreduction_steps++;
1313	#endif
1314	#if SBA_PRINT_OPERATIONS
1315	sba_interreduction_operations += pLength(strat->T[ii].p);
1316	#endif
1317
1318	#ifdef KDEBUG
1319	if (TEST_OPT_DEBUG)
1320	{
1321	PrintS("\nto ");
1322	h->wrp();
1323	PrintLn();
1324	}
1325	#endif
1326
1327	h_p=h->GetLmTailRing();
1328
1329	if (h_p == NULL)
1330	{
1331	kDeleteLcm(h);
1332	return 0;
1333	}
1334	h->SetShortExpVector();
1335	not_sev = ~ h->sev;
1336	d = h->SetpFDeg();
1337	/- try to reduce the s-polynomial -/
1338	pass++;
1339	if (//!TEST_OPT_REDTHROUGH &&
1340	(strat->Ll >= 0) && ((d > reddeg) \|\| (pass > strat->LazyPass)))
1341	{
1342	h->SetLmCurrRing();
1343	at = strat->posInL(strat->L,strat->Ll,h,strat);
1344	if (at <= strat->Ll)
1345	{
1346	#if 1
1347	int dummy=strat->sl;
1348	if (kFindDivisibleByInS(strat, &dummy, h) < 0)
1349	return 1;
1350	#endif
1351	#ifdef KDEBUG
1352	if (TEST_OPT_DEBUG) Print(" ->L[%d]\n",at);
1353	#endif
1354	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
1355	h->Clear();
1356	return -1;
1357	}
1358	}
1359	else if (d != reddeg)
1360	{
1361	if (d>=(long)strat->tailRing->bitmask)
1362	{
1363	if (h->pTotalDeg() >= (long)strat->tailRing->bitmask)
1364	{
1365	strat->overflow=TRUE;
1366	//Print("OVERFLOW in redLazy d=%ld, max=%ld\n",d,strat->tailRing->bitmask);
1367	h->GetP();
1368	at = strat->posInL(strat->L,strat->Ll,h,strat);
1369	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
1370	h->Clear();
1371	return -1;
1372	}
1373	}
1374	else if ((TEST_OPT_PROT) && (strat->Ll < 0))
1375	{
1376	Print(".%ld",d);mflush();
1377	reddeg = d;
1378	}
1379	}
1380	}
1381	}
1382	/*2
1383	* reduction procedure for the sugar-strategy (honey)
1384	* reduces h with elements from T choosing first possible
1385	* element in T with respect to the given ecart
1386	*/
1387	int redHoney (LObject* h, kStrategy strat)
1388	{
1389	if (strat->tl<0) return 1;
1390	//if (h->GetLmTailRing()==NULL) return 0; // HS: SHOULD NOT BE NEEDED!
1391	assume(h->FDeg == h->pFDeg());
1392	poly h_p;
1393	int i,j,at,pass,ei, ii, h_d;
1394	unsigned long not_sev;
1395	long reddeg,d;
1396
1397	pass = j = 0;
1398	d = reddeg = h->GetpFDeg() + h->ecart;
1399	h->SetShortExpVector();
1400	int li;
1401	h_p = h->GetLmTailRing();
1402	not_sev = ~ h->sev;
1403
1404	h->PrepareRed(strat->use_buckets);
1405	loop
1406	{
1407	j=kFindDivisibleByInT(strat, h);
1408	if (j < 0) return 1;
1409
1410	ei = strat->T[j].ecart;
1411	li = strat->T[j].pLength;
1412	if (li<=0) li=strat->T[j].GetpLength();
1413	ii = j;
1414	/*
1415	* the polynomial to reduce with (up to the moment) is;
1416	* pi with ecart ei (T[ii])
1417	*/
1418	i = j;
1419	if (TEST_OPT_LENGTH)
1420	loop
1421	{
1422	/- takes the first possible with respect to ecart -/
1423	i++;
1424	if (i > strat->tl)
1425	break;
1426	//if (ei < h->ecart)
1427	// break;
1428	if (li==1)
1429	break;
1430	if ((((strat->T[i].ecart < ei) && (ei> h->ecart))
1431	\|\| ((strat->T[i].ecart <= h->ecart) && (strat->T[i].pLength < li)))
1432	&&
1433	p_LmShortDivisibleBy(strat->T[i].GetLmTailRing(), strat->sevT[i],
1434	h_p, not_sev, strat->tailRing))
1435	{
1436	/*
1437	* the polynomial to reduce with is now;
1438	*/
1439	ei = strat->T[i].ecart;
1440	li = strat->T[i].pLength;
1441	if (li<=0) li=strat->T[i].GetpLength();
1442	ii = i;
1443	}
1444	}
1445
1446	/*
1447	* end of search: have to reduce with pi
1448	*/
1449	if (!TEST_OPT_REDTHROUGH && (pass!=0) && (ei > h->ecart))
1450	{
1451	h->GetTP(); // clears bucket
1452	h->SetLmCurrRing();
1453	/*
1454	* It is not possible to reduce h with smaller ecart;
1455	* if possible h goes to the lazy-set L,i.e
1456	* if its position in L would be not the last one
1457	*/
1458	if (strat->Ll >= 0) /* L is not empty */
1459	{
1460	at = strat->posInL(strat->L,strat->Ll,h,strat);
1461	if(at <= strat->Ll)
1462	/- h will not become the next element to reduce -/
1463	{
1464	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
1465	#ifdef KDEBUG
1466	if (TEST_OPT_DEBUG) Print(" ecart too big: -> L%d\n",at);
1467	#endif
1468	h->Clear();
1469	return -1;
1470	}
1471	}
1472	}
1473	#ifdef KDEBUG
1474	if (TEST_OPT_DEBUG)
1475	{
1476	PrintS("red:");
1477	h->wrp();
1478	Print("\nwith T[%d]:",ii);
1479	strat->T[ii].wrp();
1480	}
1481	#endif
1482	assume(strat->fromT == FALSE);
1483
1484	ksReducePoly(h,&(strat->T[ii]),strat->kNoetherTail(),NULL,strat);
1485	#if SBA_PRINT_REDUCTION_STEPS
1486	sba_interreduction_steps++;
1487	#endif
1488	#if SBA_PRINT_OPERATIONS
1489	sba_interreduction_operations += pLength(strat->T[ii].p);
1490	#endif
1491	#ifdef KDEBUG
1492	if (TEST_OPT_DEBUG)
1493	{
1494	PrintS("\nto:");
1495	h->wrp();
1496	PrintLn();
1497	}
1498	#endif
1499	if(h->IsNull())
1500	{
1501	kDeleteLcm(h);
1502	h->Clear();
1503	return 0;
1504	}
1505	if (TEST_OPT_IDLIFT)
1506	{
1507	if (h->p!=NULL)
1508	{
1509	if(p_GetComp(h->p,currRing)>strat->syzComp)
1510	{
1511	h->Delete();
1512	return 0;
1513	}
1514	}
1515	else if (h->t_p!=NULL)
1516	{
1517	if(p_GetComp(h->t_p,strat->tailRing)>strat->syzComp)
1518	{
1519	h->Delete();
1520	return 0;
1521	}
1522	}
1523	}
1524	h->SetShortExpVector();
1525	not_sev = ~ h->sev;
1526	h_d = h->SetpFDeg();
1527	/* compute the ecart */
1528	if (ei <= h->ecart)
1529	h->ecart = d-h_d;
1530	else
1531	h->ecart = d-h_d+ei-h->ecart;
1532
1533	/*
1534	* try to reduce the s-polynomial h
1535	*test first whether h should go to the lazyset L
1536	*-if the degree jumps
1537	*-if the number of pre-defined reductions jumps
1538	*/
1539	pass++;
1540	d = h_d + h->ecart;
1541	if (!TEST_OPT_REDTHROUGH && (strat->Ll >= 0) && ((d > reddeg) \|\| (pass > strat->LazyPass)))
1542	{
1543	h->GetTP(); // clear bucket
1544	h->SetLmCurrRing();
1545	at = strat->posInL(strat->L,strat->Ll,h,strat);
1546	if (at <= strat->Ll)
1547	{
1548	int dummy=strat->sl;
1549	if (kFindDivisibleByInS(strat, &dummy, h) < 0)
1550	return 1;
1551	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
1552	#ifdef KDEBUG
1553	if (TEST_OPT_DEBUG)
1554	Print(" degree jumped: -> L%d\n",at);
1555	#endif
1556	h->Clear();
1557	return -1;
1558	}
1559	}
1560	else if (d > reddeg)
1561	{
1562	if (d>=(long)strat->tailRing->bitmask)
1563	{
1564	if (h->pTotalDeg()+h->ecart >= (long)strat->tailRing->bitmask)
1565	{
1566	strat->overflow=TRUE;
1567	//Print("OVERFLOW in redHoney d=%ld, max=%ld\n",d,strat->tailRing->bitmask);
1568	h->GetP();
1569	at = strat->posInL(strat->L,strat->Ll,h,strat);
1570	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
1571	h->Clear();
1572	return -1;
1573	}
1574	}
1575	else if (TEST_OPT_PROT && (strat->Ll < 0) )
1576	{
1577	//h->wrp(); Print("<%d>\n",h->GetpLength());
1578	reddeg = d;
1579	Print(".%ld",d); mflush();
1580	}
1581	}
1582	}
1583	}
1584
1585	/*2
1586	* reduction procedure for the normal form
1587	*/
1588
1589	poly redNF (poly h,int &max_ind,int nonorm,kStrategy strat)
1590	{
1591	#define REDNF_CANONICALIZE 60
1592	if (h==NULL) return NULL;
1593	int j;
1594	int cnt=REDNF_CANONICALIZE;
1595	max_ind=strat->sl;
1596
1597	if (0 > strat->sl)
1598	{
1599	return h;
1600	}
1601	LObject P(h);
1602	P.SetShortExpVector();
1603	P.bucket = kBucketCreate(currRing);
1604	kBucketInit(P.bucket,P.p,pLength(P.p));
1605	kbTest(P.bucket);
1606	#ifdef HAVE_RINGS
1607	BOOLEAN is_ring = rField_is_Ring(currRing);
1608	#endif
1609	#ifdef KDEBUG
1610	// if (TEST_OPT_DEBUG)
1611	// {
1612	// PrintS("redNF: starting S:\n");
1613	// for( j = 0; j <= max_ind; j++ )
1614	// {
1615	// Print("S[%d] (of size: %d): ", j, pSize(strat->S[j]));
1616	// pWrite(strat->S[j]);
1617	// }
1618	// };
1619	#endif
1620
1621	loop
1622	{
1623	j=kFindDivisibleByInS(strat,&max_ind,&P);
1624	if (j>=0)
1625	{
1626	#ifdef HAVE_RINGS
1627	if (!is_ring)
1628	{
1629	#endif
1630	int sl=pSize(strat->S[j]);
1631	int jj=j;
1632	loop
1633	{
1634	int sll;
1635	jj=kFindNextDivisibleByInS(strat,jj+1,max_ind,&P);
1636	if (jj<0) break;
1637	sll=pSize(strat->S[jj]);
1638	if (sll<sl)
1639	{
1640	#ifdef KDEBUG
1641	if (TEST_OPT_DEBUG) Print("better(S%d:%d -> S%d:%d)\n",j,sl,jj,sll);
1642	#endif
1643	//else if (TEST_OPT_PROT) { PrintS("b"); mflush(); }
1644	j=jj;
1645	sl=sll;
1646	}
1647	}
1648	if ((nonorm==0) && (!nIsOne(pGetCoeff(strat->S[j]))))
1649	{
1650	pNorm(strat->S[j]);
1651	//if (TEST_OPT_PROT) { PrintS("n"); mflush(); }
1652	}
1653	#ifdef HAVE_RINGS
1654	}
1655	#endif
1656	nNormalize(pGetCoeff(P.p));
1657	#ifdef KDEBUG
1658	if (TEST_OPT_DEBUG)
1659	{
1660	PrintS("red:");
1661	wrp(h);
1662	PrintS(" with ");
1663	wrp(strat->S[j]);
1664	}
1665	#endif
1666	#ifdef HAVE_PLURAL
1667	if (rIsPluralRing(currRing))
1668	{
1669	number coef;
1670	nc_kBucketPolyRed_NF(P.bucket,strat->S[j],&coef);
1671	nDelete(&coef);
1672	}
1673	else
1674	#endif
1675	{
1676	number coef;
1677	coef=kBucketPolyRed(P.bucket,strat->S[j],pLength(strat->S[j]),strat->kNoether);
1678	nDelete(&coef);
1679	}
1680	cnt--;
1681	if (cnt==0)
1682	{
1683	kBucketCanonicalize(P.bucket);
1684	cnt=REDNF_CANONICALIZE;
1685	}
1686	h = kBucketGetLm(P.bucket); // FRAGE OLIVER
1687	if (h==NULL)
1688	{
1689	kBucketDestroy(&P.bucket);
1690
1691	#ifdef KDEBUG
1692	// if (TEST_OPT_DEBUG)
1693	// {
1694	// PrintS("redNF: starting S:\n");
1695	// for( j = 0; j <= max_ind; j++ )
1696	// {
1697	// Print("S[%d] (of size: %d): ", j, pSize(strat->S[j]));
1698	// pWrite(strat->S[j]);
1699	// }
1700	// };
1701	#endif
1702
1703	return NULL;
1704	}
1705	kbTest(P.bucket);
1706	P.p=h;
1707	P.t_p=NULL;
1708	P.SetShortExpVector();
1709	#ifdef KDEBUG
1710	if (TEST_OPT_DEBUG)
1711	{
1712	PrintS("\nto:");
1713	wrp(h);
1714	PrintLn();
1715	}
1716	#endif
1717	}
1718	else
1719	{
1720	P.p=kBucketClear(P.bucket);
1721	kBucketDestroy(&P.bucket);
1722	pNormalize(P.p);
1723
1724	#ifdef KDEBUG
1725	// if (TEST_OPT_DEBUG)
1726	// {
1727	// PrintS("redNF: starting S:\n");
1728	// for( j = 0; j <= max_ind; j++ )
1729	// {
1730	// Print("S[%d] (of size: %d): ", j, pSize(strat->S[j]));
1731	// pWrite(strat->S[j]);
1732	// }
1733	// };
1734	#endif
1735
1736	return P.p;
1737	}
1738	}
1739	}
1740
1741	/*2
1742	* reduction procedure from global case but with jet bound
1743	*/
1744
1745	poly redNFBound (poly h,int &max_ind,int nonorm,kStrategy strat,int bound)
1746	{
1747	h = pJet(h,bound);
1748	if (h==NULL) return NULL;
1749	int j;
1750	max_ind=strat->sl;
1751
1752	if (0 > strat->sl)
1753	{
1754	return h;
1755	}
1756	LObject P(h);
1757	P.SetShortExpVector();
1758	P.bucket = kBucketCreate(currRing);
1759	kBucketInit(P.bucket,P.p,pLength(P.p));
1760	kbTest(P.bucket);
1761	#ifdef HAVE_RINGS
1762	BOOLEAN is_ring = rField_is_Ring(currRing);
1763	#endif
1764	#ifdef KDEBUG
1765	// if (TEST_OPT_DEBUG)
1766	// {
1767	// PrintS("redNF: starting S:\n");
1768	// for( j = 0; j <= max_ind; j++ )
1769	// {
1770	// Print("S[%d] (of size: %d): ", j, pSize(strat->S[j]));
1771	// pWrite(strat->S[j]);
1772	// }
1773	// };
1774	#endif
1775
1776	loop
1777	{
1778	j=kFindDivisibleByInS(strat,&max_ind,&P);
1779	if (j>=0)
1780	{
1781	#ifdef HAVE_RINGS
1782	if (!is_ring)
1783	{
1784	#endif
1785	int sl=pSize(strat->S[j]);
1786	int jj=j;
1787	loop
1788	{
1789	int sll;
1790	jj=kFindNextDivisibleByInS(strat,jj+1,max_ind,&P);
1791	if (jj<0) break;
1792	sll=pSize(strat->S[jj]);
1793	if (sll<sl)
1794	{
1795	#ifdef KDEBUG
1796	if (TEST_OPT_DEBUG) Print("better(S%d:%d -> S%d:%d)\n",j,sl,jj,sll);
1797	#endif
1798	//else if (TEST_OPT_PROT) { PrintS("b"); mflush(); }
1799	j=jj;
1800	sl=sll;
1801	}
1802	}
1803	if ((nonorm==0) && (!nIsOne(pGetCoeff(strat->S[j]))))
1804	{
1805	pNorm(strat->S[j]);
1806	//if (TEST_OPT_PROT) { PrintS("n"); mflush(); }
1807	}
1808	#ifdef HAVE_RINGS
1809	}
1810	#endif
1811	nNormalize(pGetCoeff(P.p));
1812	#ifdef KDEBUG
1813	if (TEST_OPT_DEBUG)
1814	{
1815	PrintS("red:");
1816	wrp(h);
1817	PrintS(" with ");
1818	wrp(strat->S[j]);
1819	}
1820	#endif
1821	#ifdef HAVE_PLURAL
1822	if (rIsPluralRing(currRing))
1823	{
1824	number coef;
1825	nc_kBucketPolyRed_NF(P.bucket,strat->S[j],&coef);
1826	nDelete(&coef);
1827	}
1828	else
1829	#endif
1830	{
1831	number coef;
1832	coef=kBucketPolyRed(P.bucket,strat->S[j],pLength(strat->S[j]),strat->kNoether);
1833	P.p = kBucketClear(P.bucket);
1834	P.p = pJet(P.p,bound);
1835	if(!P.IsNull())
1836	{
1837	kBucketDestroy(&P.bucket);
1838	P.SetShortExpVector();
1839	P.bucket = kBucketCreate(currRing);
1840	kBucketInit(P.bucket,P.p,pLength(P.p));
1841	}
1842	nDelete(&coef);
1843	}
1844	h = kBucketGetLm(P.bucket); // FRAGE OLIVER
1845	if (h==NULL)
1846	{
1847	kBucketDestroy(&P.bucket);
1848
1849	#ifdef KDEBUG
1850	// if (TEST_OPT_DEBUG)
1851	// {
1852	// PrintS("redNF: starting S:\n");
1853	// for( j = 0; j <= max_ind; j++ )
1854	// {
1855	// Print("S[%d] (of size: %d): ", j, pSize(strat->S[j]));
1856	// pWrite(strat->S[j]);
1857	// }
1858	// };
1859	#endif
1860
1861	return NULL;
1862	}
1863	kbTest(P.bucket);
1864	P.p=h;
1865	P.t_p=NULL;
1866	P.SetShortExpVector();
1867	#ifdef KDEBUG
1868	if (TEST_OPT_DEBUG)
1869	{
1870	PrintS("\nto:");
1871	wrp(h);
1872	PrintLn();
1873	}
1874	#endif
1875	}
1876	else
1877	{
1878	P.p=kBucketClear(P.bucket);
1879	kBucketDestroy(&P.bucket);
1880	pNormalize(P.p);
1881
1882	#ifdef KDEBUG
1883	// if (TEST_OPT_DEBUG)
1884	// {
1885	// PrintS("redNF: starting S:\n");
1886	// for( j = 0; j <= max_ind; j++ )
1887	// {
1888	// Print("S[%d] (of size: %d): ", j, pSize(strat->S[j]));
1889	// pWrite(strat->S[j]);
1890	// }
1891	// };
1892	#endif
1893
1894	return P.p;
1895	}
1896	}
1897	}
1898
1899	void kDebugPrint(kStrategy strat);
1900
1901	ideal bba (ideal F, ideal Q,intvec w,intvec hilb,kStrategy strat)
1902	{
1903	int red_result = 1;
1904	int olddeg,reduc;
1905	int hilbeledeg=1,hilbcount=0,minimcnt=0;
1906	BOOLEAN withT = FALSE;
1907	BITSET save;
1908	SI_SAVE_OPT1(save);
1909
1910	initBuchMoraCrit(strat); /set Gebauer, honey, sugarCrit/
1911	if(rField_is_Ring(currRing))
1912	initBuchMoraPosRing(strat);
1913	else
1914	initBuchMoraPos(strat);
1915	initHilbCrit(F,Q,&hilb,strat);
1916	initBba(strat);
1917	/set enterS, spSpolyShort, reduce, red, initEcart, initEcartPair/
1918	/Shdl=/initBuchMora(F, Q,strat);
1919	if (strat->minim>0) strat->M=idInit(IDELEMS(F),F->rank);
1920	reduc = olddeg = 0;
1921
1922	#ifndef NO_BUCKETS
1923	if (!TEST_OPT_NOT_BUCKETS)
1924	strat->use_buckets = 1;
1925	#endif
1926	// redtailBBa against T for inhomogenous input
1927	if (!TEST_OPT_OLDSTD)
1928	withT = ! strat->homog;
1929
1930	// strat->posInT = posInT_pLength;
1931	kTest_TS(strat);
1932
1933	#ifdef HAVE_TAIL_RING
1934	if(!idIs0(F) &&(!rField_is_Ring(currRing))) // create strong gcd poly computes with tailring and S[i] ->to be fixed
1935	kStratInitChangeTailRing(strat);
1936	#endif
1937	if (BVERBOSE(23))
1938	{
1939	if (test_PosInT!=NULL) strat->posInT=test_PosInT;
1940	if (test_PosInL!=NULL) strat->posInL=test_PosInL;
1941	kDebugPrint(strat);
1942	}
1943
1944
1945	#ifdef KDEBUG
1946	//kDebugPrint(strat);
1947	#endif
1948	/* compute------------------------------------------------------- */
1949	while (strat->Ll >= 0)
1950	{
1951	#ifdef KDEBUG
1952	if (TEST_OPT_DEBUG) messageSets(strat);
1953	#endif
1954	if (siCntrlc)
1955	{
1956	while (strat->Ll >= 0)
1957	deleteInL(strat->L,&strat->Ll,strat->Ll,strat);
1958	strat->noClearS=TRUE;
1959	}
1960	if (TEST_OPT_DEGBOUND
1961	&& ((strat->honey && (strat->L[strat->Ll].ecart+currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))
1962	\|\| ((!strat->honey) && (currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))))
1963	{
1964	/*
1965	*stops computation if
1966	* 24 IN test and the degree +ecart of L[strat->Ll] is bigger then
1967	*a predefined number Kstd1_deg
1968	*/
1969	while ((strat->Ll >= 0)
1970	&& (strat->L[strat->Ll].p1!=NULL) && (strat->L[strat->Ll].p2!=NULL)
1971	&& ((strat->honey && (strat->L[strat->Ll].ecart+currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))
1972	\|\| ((!strat->honey) && (currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg)))
1973	)
1974	deleteInL(strat->L,&strat->Ll,strat->Ll,strat);
1975	if (strat->Ll<0) break;
1976	else strat->noClearS=TRUE;
1977	}
1978	if (strat->Ll== 0) strat->interpt=TRUE;
1979	/* picks the last element from the lazyset L */
1980	strat->P = strat->L[strat->Ll];
1981	strat->Ll--;
1982
1983	if (pNext(strat->P.p) == strat->tail)
1984	{
1985	// deletes the short spoly
1986	if (rField_is_Ring(currRing))
1987	pLmDelete(strat->P.p);
1988	else
1989	pLmFree(strat->P.p);
1990	strat->P.p = NULL;
1991	poly m1 = NULL, m2 = NULL;
1992
1993	// check that spoly creation is ok
1994	while (strat->tailRing != currRing &&
1995	!kCheckSpolyCreation(&(strat->P), strat, m1, m2))
1996	{
1997	assume(m1 == NULL && m2 == NULL);
1998	// if not, change to a ring where exponents are at least
1999	// large enough
2000	if (!kStratChangeTailRing(strat))
2001	{
2002	WerrorS("OVERFLOW...");
2003	break;
2004	}
2005	}
2006	// create the real one
2007	ksCreateSpoly(&(strat->P), NULL, strat->use_buckets,
2008	strat->tailRing, m1, m2, strat->R);
2009	}
2010	else if (strat->P.p1 == NULL)
2011	{
2012	if (strat->minim > 0)
2013	strat->P.p2=p_Copy(strat->P.p, currRing, strat->tailRing);
2014	// for input polys, prepare reduction
2015	strat->P.PrepareRed(strat->use_buckets);
2016	}
2017
2018	if (strat->P.p == NULL && strat->P.t_p == NULL)
2019	{
2020	red_result = 0;
2021	}
2022	else
2023	{
2024	if (TEST_OPT_PROT)
2025	message((strat->honey ? strat->P.ecart : 0) + strat->P.pFDeg(),
2026	&olddeg,&reduc,strat, red_result);
2027
2028	/* reduction of the element chosen from L */
2029	red_result = strat->red(&strat->P,strat);
2030	if (errorreported) break;
2031	}
2032
2033	if (strat->overflow)
2034	{
2035	if (!kStratChangeTailRing(strat)) { WerrorS("OVERFLOW.."); break;}
2036	}
2037
2038	// reduction to non-zero new poly
2039	if (red_result == 1)
2040	{
2041	// get the polynomial (canonicalize bucket, make sure P.p is set)
2042	strat->P.GetP(strat->lmBin);
2043	// in the homogeneous case FDeg >= pFDeg (sugar/honey)
2044	// but now, for entering S, T, we reset it
2045	// in the inhomogeneous case: FDeg == pFDeg
2046	if (strat->homog) strat->initEcart(&(strat->P));
2047
2048	/* statistic */
2049	if (TEST_OPT_PROT) PrintS("s");
2050
2051	int pos=posInS(strat,strat->sl,strat->P.p,strat->P.ecart);
2052
2053	// reduce the tail and normalize poly
2054	// in the ring case we cannot expect LC(f) = 1,
2055	// therefore we call pCleardenom instead of pNorm
2056	strat->redTailChange=FALSE;
2057	if ((TEST_OPT_INTSTRATEGY) \|\| (rField_is_Ring(currRing)))
2058	{
2059	strat->P.pCleardenom();
2060	if ((TEST_OPT_REDSB)\|\|(TEST_OPT_REDTAIL))
2061	{
2062	strat->P.p = redtailBba(&(strat->P),pos-1,strat, withT,!TEST_OPT_CONTENTSB);
2063	strat->P.pCleardenom();
2064	if (strat->redTailChange) { strat->P.t_p=NULL; }
2065	}
2066	}
2067	else
2068	{
2069	strat->P.pNorm();
2070	if ((TEST_OPT_REDSB)\|\|(TEST_OPT_REDTAIL))
2071	{
2072	strat->P.p = redtailBba(&(strat->P),pos-1,strat, withT);
2073	if (strat->redTailChange) { strat->P.t_p=NULL; }
2074	}
2075	}
2076
2077	#ifdef KDEBUG
2078	if (TEST_OPT_DEBUG){PrintS("new s:");strat->P.wrp();PrintLn();}
2079	#endif /* KDEBUG */
2080
2081	// min_std stuff
2082	if ((strat->P.p1==NULL) && (strat->minim>0))
2083	{
2084	if (strat->minim==1)
2085	{
2086	strat->M->m[minimcnt]=p_Copy(strat->P.p,currRing,strat->tailRing);
2087	p_Delete(&strat->P.p2, currRing, strat->tailRing);
2088	}
2089	else
2090	{
2091	strat->M->m[minimcnt]=strat->P.p2;
2092	strat->P.p2=NULL;
2093	}
2094	if (strat->tailRing!=currRing && pNext(strat->M->m[minimcnt])!=NULL)
2095	pNext(strat->M->m[minimcnt])
2096	= strat->p_shallow_copy_delete(pNext(strat->M->m[minimcnt]),
2097	strat->tailRing, currRing,
2098	currRing->PolyBin);
2099	minimcnt++;
2100	}
2101
2102	// enter into S, L, and T
2103	if ((!TEST_OPT_IDLIFT) \|\| (pGetComp(strat->P.p) <= strat->syzComp))
2104	{
2105	enterT(strat->P, strat);
2106	if (rField_is_Ring(currRing))
2107	superenterpairs(strat->P.p,strat->sl,strat->P.ecart,pos,strat, strat->tl);
2108	else
2109	enterpairs(strat->P.p,strat->sl,strat->P.ecart,pos,strat, strat->tl);
2110	// posInS only depends on the leading term
2111	strat->enterS(strat->P, pos, strat, strat->tl);
2112	#if 0
2113	int pl=pLength(strat->P.p);
2114	if (pl==1)
2115	{
2116	//if (TEST_OPT_PROT)
2117	//PrintS("<1>");
2118	}
2119	else if (pl==2)
2120	{
2121	//if (TEST_OPT_PROT)
2122	//PrintS("<2>");
2123	}
2124	#endif
2125	}
2126	if (hilb!=NULL) khCheck(Q,w,hilb,hilbeledeg,hilbcount,strat);
2127	// Print("[%d]",hilbeledeg);
2128	kDeleteLcm(&strat->P);
2129	if (strat->s_poly!=NULL)
2130	{
2131	// the only valid entries are: strat->P.p,
2132	// strat->tailRing (read-only, keep it)
2133	// (and P->p1, P->p2 (read-only, must set to NULL if P.p is changed)
2134	if (strat->s_poly(strat))
2135	{
2136	// we are called AFTER enterS, i.e. if we change P
2137	// we have to add it also to S/T
2138	// and add pairs
2139	int pos=posInS(strat,strat->sl,strat->P.p,strat->P.ecart);
2140	enterT(strat->P, strat);
2141	if (rField_is_Ring(currRing))
2142	superenterpairs(strat->P.p,strat->sl,strat->P.ecart,pos,strat, strat->tl);
2143	else
2144	enterpairs(strat->P.p,strat->sl,strat->P.ecart,pos,strat, strat->tl);
2145	strat->enterS(strat->P, pos, strat, strat->tl);
2146	}
2147	}
2148	}
2149	else if (strat->P.p1 == NULL && strat->minim > 0)
2150	{
2151	p_Delete(&strat->P.p2, currRing, strat->tailRing);
2152	}
2153
2154	#ifdef KDEBUG
2155	memset(&(strat->P), 0, sizeof(strat->P));
2156	#endif /* KDEBUG */
2157	kTest_TS(strat);
2158	}
2159	#ifdef KDEBUG
2160	if (TEST_OPT_DEBUG) messageSets(strat);
2161	#endif /* KDEBUG */
2162
2163	if (TEST_OPT_SB_1)
2164	{
2165	if(!rField_is_Ring(currRing))
2166	{
2167	int k=1;
2168	int j;
2169	while(k<=strat->sl)
2170	{
2171	j=0;
2172	loop
2173	{
2174	if (j>=k) break;
2175	clearS(strat->S[j],strat->sevS[j],&k,&j,strat);
2176	j++;
2177	}
2178	k++;
2179	}
2180	}
2181	}
2182	/* complete reduction of the standard basis--------- */
2183	if (TEST_OPT_REDSB)
2184	{
2185	completeReduce(strat);
2186	if (strat->completeReduce_retry)
2187	{
2188	// completeReduce needed larger exponents, retry
2189	// to reduce with S (instead of T)
2190	// and in currRing (instead of strat->tailRing)
2191	#ifdef HAVE_TAIL_RING
2192	if(currRing->bitmask>strat->tailRing->bitmask)
2193	{
2194	strat->completeReduce_retry=FALSE;
2195	cleanT(strat);strat->tailRing=currRing;
2196	int i;
2197	for(i=strat->sl;i>=0;i--) strat->S_2_R[i]=-1;
2198	completeReduce(strat);
2199	}
2200	if (strat->completeReduce_retry)
2201	#endif
2202	Werror("exponent bound is %ld",currRing->bitmask);
2203	}
2204	}
2205	else if (TEST_OPT_PROT) PrintLn();
2206	/* release temp data-------------------------------- */
2207	exitBuchMora(strat);
2208	/* postprocessing for GB over ZZ --------------------*/
2209	if (!errorreported)
2210	{
2211	if(rField_is_Ring_Z(currRing))
2212	{
2213	for(int i = 0;i<=strat->sl;i++)
2214	{
2215	if(!nGreaterZero(pGetCoeff(strat->S[i])))
2216	{
2217	strat->S[i] = pNeg(strat->S[i]);
2218	}
2219	}
2220	finalReduceByMon(strat);
2221	for(int i = 0;i<IDELEMS(strat->Shdl);i++)
2222	{
2223	if(!nGreaterZero(pGetCoeff(strat->Shdl->m[i])))
2224	{
2225	strat->S[i] = pNeg(strat->Shdl->m[i]);
2226	}
2227	}
2228	}
2229	//else if (rField_is_Ring(currRing))
2230	// finalReduceByMon(strat);
2231	}
2232	// if (TEST_OPT_WEIGHTM)
2233	// {
2234	// pRestoreDegProcs(currRing,pFDegOld, pLDegOld);
2235	// if (ecartWeights)
2236	// {
2237	// omFreeSize((ADDRESS)ecartWeights,((currRing->N)+1)*sizeof(short));
2238	// ecartWeights=NULL;
2239	// }
2240	// }
2241	if ((TEST_OPT_PROT) \|\| (TEST_OPT_DEBUG)) messageStat(hilbcount,strat);
2242	SI_RESTORE_OPT1(save);
2243	/* postprocessing for GB over Q-rings ------------------*/
2244	if ((Q!=NULL)&&(!errorreported)) updateResult(strat->Shdl,Q,strat);
2245
2246	idTest(strat->Shdl);
2247
2248	return (strat->Shdl);
2249	}
2250
2251	ideal sba (ideal F0, ideal Q,intvec w,intvec hilb,kStrategy strat)
2252	{
2253	// ring order stuff:
2254	// in sba we have (until now) two possibilities:
2255	// 1. an incremental computation w.r.t. (C,monomial order)
2256	// 2. a (possibly non-incremental) computation w.r.t. the
2257	// induced Schreyer order.
2258	// The corresponding orders are computed in sbaRing(), depending
2259	// on the flag strat->sbaOrder
2260	#if SBA_PRINT_ZERO_REDUCTIONS
2261	long zeroreductions = 0;
2262	#endif
2263	#if SBA_PRINT_PRODUCT_CRITERION
2264	long product_criterion = 0;
2265	#endif
2266	#if SBA_PRINT_SIZE_G
2267	int size_g = 0;
2268	int size_g_non_red = 0;
2269	#endif
2270	#if SBA_PRINT_SIZE_SYZ
2271	long size_syz = 0;
2272	#endif
2273	// global variable
2274	#if SBA_PRINT_REDUCTION_STEPS
2275	sba_reduction_steps = 0;
2276	sba_interreduction_steps = 0;
2277	#endif
2278	#if SBA_PRINT_OPERATIONS
2279	sba_operations = 0;
2280	sba_interreduction_operations = 0;
2281	#endif
2282
2283	ideal F1 = F0;
2284	ring sRing, currRingOld;
2285	currRingOld = currRing;
2286	if (strat->sbaOrder == 1 \|\| strat->sbaOrder == 3)
2287	{
2288	sRing = sbaRing(strat);
2289	if (sRing!=currRingOld)
2290	{
2291	rChangeCurrRing (sRing);
2292	F1 = idrMoveR (F0, currRingOld, currRing);
2293	}
2294	}
2295	ideal F;
2296	// sort ideal F
2297	//Put the SigDrop element on the correct position (think of sbaEnterS)
2298	//We also sort them
2299	if(rField_is_Ring(currRing) && strat->sigdrop)
2300	{
2301	#if 1
2302	F = idInit(IDELEMS(F1),F1->rank);
2303	for (int i=0; i<IDELEMS(F1);++i)
2304	F->m[i] = F1->m[i];
2305	if(strat->sbaEnterS >= 0)
2306	{
2307	poly dummy;
2308	dummy = pCopy(F->m[0]); //the sigdrop element
2309	for(int i = 0;i<strat->sbaEnterS;i++)
2310	F->m[i] = F->m[i+1];
2311	F->m[strat->sbaEnterS] = dummy;
2312	}
2313	#else
2314	F = idInit(1,F1->rank);
2315	//printf("\nBefore the initial block sorting:\n");idPrint(F1);
2316	F->m[0] = F1->m[0];
2317	int pos;
2318	if(strat->sbaEnterS >= 0)
2319	{
2320	for(int i=1;i<=strat->sbaEnterS;i++)
2321	{
2322	pos = posInIdealMonFirst(F,F1->m[i],1,strat->sbaEnterS);
2323	idInsertPolyOnPos(F,F1->m[i],pos);
2324	}
2325	for(int i=strat->sbaEnterS+1;i<IDELEMS(F1);i++)
2326	{
2327	pos = posInIdealMonFirst(F,F1->m[i],strat->sbaEnterS+1,IDELEMS(F));
2328	idInsertPolyOnPos(F,F1->m[i],pos);
2329	}
2330	poly dummy;
2331	dummy = pCopy(F->m[0]); //the sigdrop element
2332	for(int i = 0;i<strat->sbaEnterS;i++)
2333	F->m[i] = F->m[i+1];
2334	F->m[strat->sbaEnterS] = dummy;
2335	}
2336	else
2337	{
2338	for(int i=1;i<IDELEMS(F1);i++)
2339	{
2340	pos = posInIdealMonFirst(F,F1->m[i],1,IDELEMS(F));
2341	idInsertPolyOnPos(F,F1->m[i],pos);
2342	}
2343	}
2344	#endif
2345	//printf("\nAfter the initial block sorting:\n");idPrint(F);getchar();
2346	}
2347	else
2348	{
2349	F = idInit(IDELEMS(F1),F1->rank);
2350	intvec *sort = idSort(F1);
2351	for (int i=0; i<sort->length();++i)
2352	F->m[i] = F1->m[(*sort)[i]-1];
2353	if(rField_is_Ring(currRing))
2354	{
2355	// put the monomials after the sbaEnterS polynomials
2356	//printf("\nThis is the ideal before sorting (sbaEnterS = %i)\n",strat->sbaEnterS);idPrint(F);
2357	int nrmon = 0;
2358	for(int i = IDELEMS(F)-1,j;i>strat->sbaEnterS+nrmon+1 ;i--)
2359	{
2360	//pWrite(F->m[i]);
2361	if(F->m[i] != NULL && pNext(F->m[i]) == NULL)
2362	{
2363	poly mon = F->m[i];
2364	for(j = i;j>strat->sbaEnterS+nrmon+1;j--)
2365	{
2366	F->m[j] = F->m[j-1];
2367	}
2368	F->m[j] = mon;
2369	nrmon++;
2370	}
2371	//idPrint(F);
2372	}
2373	}
2374	}
2375	//printf("\nThis is the ideal after sorting\n");idPrint(F);getchar();
2376	if(rField_is_Ring(currRing))
2377	strat->sigdrop = FALSE;
2378	strat->nrsyzcrit = 0;
2379	strat->nrrewcrit = 0;
2380	#if SBA_INTERRED_START
2381	F = kInterRed(F,NULL);
2382	#endif
2383	#if F5DEBUG
2384	printf("SBA COMPUTATIONS DONE IN THE FOLLOWING RING:\n");
2385	rWrite (currRing);
2386	printf("ordSgn = %d\n",currRing->OrdSgn);
2387	printf("\n");
2388	#endif
2389	int srmax,lrmax, red_result = 1;
2390	int olddeg,reduc;
2391	int hilbeledeg=1,hilbcount=0,minimcnt=0;
2392	LObject L;
2393	BOOLEAN withT = TRUE;
2394	strat->max_lower_index = 0;
2395	//initBuchMoraCrit(strat); /set Gebauer, honey, sugarCrit/
2396	initSbaCrit(strat); /set Gebauer, honey, sugarCrit/
2397	initSbaPos(strat);
2398	initHilbCrit(F,Q,&hilb,strat);
2399	initSba(F,strat);
2400	/set enterS, spSpolyShort, reduce, red, initEcart, initEcartPair/
2401	/Shdl=/initSbaBuchMora(F, Q,strat);
2402	idTest(strat->Shdl);
2403	if (strat->minim>0) strat->M=idInit(IDELEMS(F),F->rank);
2404	srmax = strat->sl;
2405	reduc = olddeg = lrmax = 0;
2406	#ifndef NO_BUCKETS
2407	if (!TEST_OPT_NOT_BUCKETS)
2408	strat->use_buckets = 1;
2409	#endif
2410
2411	// redtailBBa against T for inhomogenous input
2412	// if (!TEST_OPT_OLDSTD)
2413	// withT = ! strat->homog;
2414
2415	// strat->posInT = posInT_pLength;
2416	kTest_TS(strat);
2417
2418	#ifdef HAVE_TAIL_RING
2419	if(!idIs0(F) &&(!rField_is_Ring(currRing))) // create strong gcd poly computes with tailring and S[i] ->to be fixed
2420	kStratInitChangeTailRing(strat);
2421	#endif
2422	if (BVERBOSE(23))
2423	{
2424	if (test_PosInT!=NULL) strat->posInT=test_PosInT;
2425	if (test_PosInL!=NULL) strat->posInL=test_PosInL;
2426	kDebugPrint(strat);
2427	}
2428	// We add the elements directly in S from the previous loop
2429	if(rField_is_Ring(currRing) && strat->sbaEnterS >= 0)
2430	{
2431	for(int i = 0;i<strat->sbaEnterS;i++)
2432	{
2433	//Update: now the element is at the corect place
2434	//i+1 because on the 0 position is the sigdrop element
2435	enterT(strat->L[strat->Ll-(i)],strat);
2436	strat->enterS(strat->L[strat->Ll-(i)], strat->sl+1, strat, strat->tl);
2437	}
2438	strat->Ll = strat->Ll - strat->sbaEnterS;
2439	strat->sbaEnterS = -1;
2440	}
2441	kTest_TS(strat);
2442	#ifdef KDEBUG
2443	//kDebugPrint(strat);
2444	#endif
2445	/* compute------------------------------------------------------- */
2446	while (strat->Ll >= 0)
2447	{
2448	if (strat->Ll > lrmax) lrmax =strat->Ll;/stat./
2449	#ifdef KDEBUG
2450	if (TEST_OPT_DEBUG) messageSets(strat);
2451	#endif
2452	if (strat->Ll== 0) strat->interpt=TRUE;
2453	/*
2454	if (TEST_OPT_DEGBOUND
2455	&& ((strat->honey && (strat->L[strat->Ll].ecart+currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))
2456	\|\| ((!strat->honey) && (currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))))
2457	{
2458
2459	//stops computation if
2460	// 24 IN test and the degree +ecart of L[strat->Ll] is bigger then
2461	//a predefined number Kstd1_deg
2462	while ((strat->Ll >= 0)
2463	&& (strat->L[strat->Ll].p1!=NULL) && (strat->L[strat->Ll].p2!=NULL)
2464	&& ((strat->honey && (strat->L[strat->Ll].ecart+currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))
2465	\|\| ((!strat->honey) && (currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg)))
2466	)
2467	deleteInL(strat->L,&strat->Ll,strat->Ll,strat);
2468	if (strat->Ll<0) break;
2469	else strat->noClearS=TRUE;
2470	}
2471	*/
2472	if (strat->sbaOrder == 1 && pGetComp(strat->L[strat->Ll].sig) != strat->currIdx)
2473	{
2474	strat->currIdx = pGetComp(strat->L[strat->Ll].sig);
2475	#if F5C
2476	// 1. interreduction of the current standard basis
2477	// 2. generation of new principal syzygy rules for syzCriterion
2478	f5c ( strat, olddeg, minimcnt, hilbeledeg, hilbcount, srmax,
2479	lrmax, reduc, Q, w, hilb );
2480	#endif
2481	// initialize new syzygy rules for the next iteration step
2482	initSyzRules(strat);
2483	}
2484	/*********************************************************************
2485	* interrreduction step is done, we can go on with the next iteration
2486	* step of the signature-based algorithm
2487	********************************************************************/
2488	/* picks the last element from the lazyset L */
2489	strat->P = strat->L[strat->Ll];
2490	strat->Ll--;
2491
2492	if(rField_is_Ring(currRing))
2493	strat->sbaEnterS = pGetComp(strat->P.sig) - 1;
2494	/* reduction of the element chosen from L */
2495	if (!strat->rewCrit2(strat->P.sig, ~strat->P.sevSig, strat->P.GetLmCurrRing(), strat, strat->P.checked+1))
2496	{
2497	//#if 1
2498	#ifdef DEBUGF5
2499	PrintS("SIG OF NEXT PAIR TO HANDLE IN SIG-BASED ALGORITHM\n");
2500	PrintS("-------------------------------------------------\n");
2501	pWrite(strat->P.sig);
2502	pWrite(pHead(strat->P.p));
2503	pWrite(pHead(strat->P.p1));
2504	pWrite(pHead(strat->P.p2));
2505	PrintS("-------------------------------------------------\n");
2506	#endif
2507	if (pNext(strat->P.p) == strat->tail)
2508	{
2509	// deletes the short spoly
2510	/*
2511	if (rField_is_Ring(currRing))
2512	pLmDelete(strat->P.p);
2513	else
2514	pLmFree(strat->P.p);
2515	*/
2516	// TODO: needs some masking
2517	// TODO: masking needs to vanish once the signature
2518	// sutff is completely implemented
2519	strat->P.p = NULL;
2520	poly m1 = NULL, m2 = NULL;
2521
2522	// check that spoly creation is ok
2523	while (strat->tailRing != currRing &&
2524	!kCheckSpolyCreation(&(strat->P), strat, m1, m2))
2525	{
2526	assume(m1 == NULL && m2 == NULL);
2527	// if not, change to a ring where exponents are at least
2528	// large enough
2529	if (!kStratChangeTailRing(strat))
2530	{
2531	WerrorS("OVERFLOW...");
2532	break;
2533	}
2534	}
2535	// create the real one
2536	ksCreateSpoly(&(strat->P), NULL, strat->use_buckets,
2537	strat->tailRing, m1, m2, strat->R);
2538
2539	}
2540	else if (strat->P.p1 == NULL)
2541	{
2542	if (strat->minim > 0)
2543	strat->P.p2=p_Copy(strat->P.p, currRing, strat->tailRing);
2544	// for input polys, prepare reduction
2545	if(!rField_is_Ring(currRing))
2546	strat->P.PrepareRed(strat->use_buckets);
2547	}
2548	if (strat->P.p == NULL && strat->P.t_p == NULL)
2549	{
2550	red_result = 0;
2551	}
2552	else
2553	{
2554	//#if 1
2555	#ifdef DEBUGF5
2556	PrintS("Poly before red: ");
2557	pWrite(pHead(strat->P.p));
2558	pWrite(strat->P.sig);
2559	#endif
2560	#if SBA_PRODUCT_CRITERION
2561	if (strat->P.prod_crit)
2562	{
2563	#if SBA_PRINT_PRODUCT_CRITERION
2564	product_criterion++;
2565	#endif
2566	int pos = posInSyz(strat, strat->P.sig);
2567	enterSyz(strat->P, strat, pos);
2568	kDeleteLcm(&strat->P);
2569	red_result = 2;
2570	}
2571	else
2572	{
2573	red_result = strat->red(&strat->P,strat);
2574	}
2575	#else
2576	red_result = strat->red(&strat->P,strat);
2577	#endif
2578	}
2579	}
2580	else
2581	{
2582	/*
2583	if (strat->P.lcm != NULL)
2584	pLmFree(strat->P.lcm);
2585	*/
2586	red_result = 2;
2587	}
2588	if(rField_is_Ring(currRing))
2589	{
2590	if(strat->P.sig!= NULL && !nGreaterZero(pGetCoeff(strat->P.sig)))
2591	{
2592	strat->P.p = pNeg(strat->P.p);
2593	strat->P.sig = pNeg(strat->P.sig);
2594	}
2595	strat->P.pLength = pLength(strat->P.p);
2596	if(strat->P.sig != NULL)
2597	strat->P.sevSig = pGetShortExpVector(strat->P.sig);
2598	if(strat->P.p != NULL)
2599	strat->P.sev = pGetShortExpVector(strat->P.p);
2600	}
2601	//sigdrop case
2602	if(rField_is_Ring(currRing) && strat->sigdrop)
2603	{
2604	//First reduce it as much as one can
2605	red_result = redRing(&strat->P,strat);
2606	if(red_result == 0)
2607	{
2608	strat->sigdrop = FALSE;
2609	pDelete(&strat->P.sig);
2610	strat->P.sig = NULL;
2611	}
2612	else
2613	{
2614	strat->enterS(strat->P, 0, strat, strat->tl);
2615	if (TEST_OPT_PROT)
2616	PrintS("-");
2617	break;
2618	}
2619	}
2620	if(rField_is_Ring(currRing) && strat->blockred > strat->blockredmax)
2621	{
2622	strat->sigdrop = TRUE;
2623	break;
2624	}
2625
2626	if (errorreported) break;
2627
2628	//#if 1
2629	#ifdef DEBUGF5
2630	if (red_result != 0)
2631	{
2632	PrintS("Poly after red: ");
2633	pWrite(pHead(strat->P.p));
2634	pWrite(strat->P.GetLmCurrRing());
2635	pWrite(strat->P.sig);
2636	printf("%d\n",red_result);
2637	}
2638	#endif
2639	if (TEST_OPT_PROT)
2640	{
2641	if(strat->P.p != NULL)
2642	message((strat->honey ? strat->P.ecart : 0) + strat->P.pFDeg(),
2643	&olddeg,&reduc,strat, red_result);
2644	else
2645	message((strat->honey ? strat->P.ecart : 0),
2646	&olddeg,&reduc,strat, red_result);
2647	}
2648
2649	if (strat->overflow)
2650	{
2651	if (!kStratChangeTailRing(strat)) { WerrorS("OVERFLOW.."); break;}
2652	}
2653	// reduction to non-zero new poly
2654	if (red_result == 1)
2655	{
2656	// get the polynomial (canonicalize bucket, make sure P.p is set)
2657	strat->P.GetP(strat->lmBin);
2658
2659	// sig-safe computations may lead to wrong FDeg computation, thus we need
2660	// to recompute it to make sure everything is alright
2661	(strat->P).FDeg = (strat->P).pFDeg();
2662	// in the homogeneous case FDeg >= pFDeg (sugar/honey)
2663	// but now, for entering S, T, we reset it
2664	// in the inhomogeneous case: FDeg == pFDeg
2665	if (strat->homog) strat->initEcart(&(strat->P));
2666
2667	/* statistic */
2668	if (TEST_OPT_PROT) PrintS("s");
2669
2670	//int pos=posInS(strat,strat->sl,strat->P.p,strat->P.ecart);
2671	// in F5E we know that the last reduced element is already the
2672	// the one with highest signature
2673	int pos = strat->sl+1;
2674
2675	// reduce the tail and normalize poly
2676	// in the ring case we cannot expect LC(f) = 1,
2677	// therefore we call pCleardenom instead of pNorm
2678	#ifdef HAVE_RINGS
2679	poly beforetailred;
2680	if(rField_is_Ring(currRing))
2681	beforetailred = pCopy(strat->P.sig);
2682	#endif
2683	#if SBA_TAIL_RED
2684	if(rField_is_Ring(currRing))
2685	{
2686	if ((TEST_OPT_REDSB)\|\|(TEST_OPT_REDTAIL))
2687	strat->P.p = redtailSba(&(strat->P),pos-1,strat, withT);
2688	}
2689	else
2690	{
2691	if (strat->sbaOrder != 2)
2692	{
2693	if (TEST_OPT_INTSTRATEGY)
2694	{
2695	strat->P.pCleardenom();
2696	if ((TEST_OPT_REDSB)\|\|(TEST_OPT_REDTAIL))
2697	{
2698	strat->P.p = redtailSba(&(strat->P),pos-1,strat, withT);
2699	strat->P.pCleardenom();
2700	}
2701	}
2702	else
2703	{
2704	strat->P.pNorm();
2705	if ((TEST_OPT_REDSB)\|\|(TEST_OPT_REDTAIL))
2706	strat->P.p = redtailSba(&(strat->P),pos-1,strat, withT);
2707	}
2708	}
2709	}
2710	// It may happen that we have lost the sig in redtailsba
2711	// It cannot reduce to 0 since here we are doing just tail reduction.
2712	// Best case scenerio: remains the leading term
2713	if(rField_is_Ring(currRing) && strat->sigdrop)
2714	{
2715	strat->enterS(strat->P, 0, strat, strat->tl);
2716	break;
2717	}
2718	#endif
2719	if(rField_is_Ring(currRing))
2720	{
2721	if(strat->P.sig == NULL \|\| pLtCmp(beforetailred,strat->P.sig) == 1)
2722	{
2723	strat->sigdrop = TRUE;
2724	//Reduce it as much as you can
2725	red_result = redRing(&strat->P,strat);
2726	if(red_result == 0)
2727	{
2728	//It reduced to 0, cancel the sigdrop
2729	strat->sigdrop = FALSE;
2730	p_Delete(&strat->P.sig,currRing);strat->P.sig = NULL;
2731	}
2732	else
2733	{
2734	strat->enterS(strat->P, 0, strat, strat->tl);
2735	break;
2736	}
2737	}
2738	p_Delete(&beforetailred,currRing);
2739	// strat->P.p = NULL may appear if we had a sigdrop above and reduced to 0 via redRing
2740	if(strat->P.p == NULL)
2741	goto case_when_red_result_changed;
2742	}
2743	// remove sigsafe label since it is no longer valid for the next element to
2744	// be reduced
2745	if (strat->sbaOrder == 1)
2746	{
2747	for (int jj = 0; jj<strat->tl+1; jj++)
2748	{
2749	if (pGetComp(strat->T[jj].sig) == strat->currIdx)
2750	{
2751	strat->T[jj].is_sigsafe = FALSE;
2752	}
2753	}
2754	}
2755	else
2756	{
2757	for (int jj = 0; jj<strat->tl+1; jj++)
2758	{
2759	strat->T[jj].is_sigsafe = FALSE;
2760	}
2761	}
2762	#ifdef KDEBUG
2763	if (TEST_OPT_DEBUG){PrintS("new s:");strat->P.wrp();PrintLn();}
2764	#endif /* KDEBUG */
2765
2766	// min_std stuff
2767	if ((strat->P.p1==NULL) && (strat->minim>0))
2768	{
2769	if (strat->minim==1)
2770	{
2771	strat->M->m[minimcnt]=p_Copy(strat->P.p,currRing,strat->tailRing);
2772	p_Delete(&strat->P.p2, currRing, strat->tailRing);
2773	}
2774	else
2775	{
2776	strat->M->m[minimcnt]=strat->P.p2;
2777	strat->P.p2=NULL;
2778	}
2779	if (strat->tailRing!=currRing && pNext(strat->M->m[minimcnt])!=NULL)
2780	pNext(strat->M->m[minimcnt])
2781	= strat->p_shallow_copy_delete(pNext(strat->M->m[minimcnt]),
2782	strat->tailRing, currRing,
2783	currRing->PolyBin);
2784	minimcnt++;
2785	}
2786
2787	// enter into S, L, and T
2788	//if ((!TEST_OPT_IDLIFT) \|\| (pGetComp(strat->P.p) <= strat->syzComp))
2789	enterT(strat->P, strat);
2790	strat->T[strat->tl].is_sigsafe = FALSE;
2791	/*
2792	printf("hier\n");
2793	pWrite(strat->P.GetLmCurrRing());
2794	pWrite(strat->P.sig);
2795	*/
2796	if (rField_is_Ring(currRing))
2797	superenterpairsSig(strat->P.p,strat->P.sig,strat->sl+1,strat->sl,strat->P.ecart,pos,strat, strat->tl);
2798	else
2799	enterpairsSig(strat->P.p,strat->P.sig,strat->sl+1,strat->sl,strat->P.ecart,pos,strat, strat->tl);
2800	if(rField_is_Ring(currRing) && strat->sigdrop)
2801	break;
2802	if(rField_is_Ring(currRing))
2803	strat->P.sevSig = p_GetShortExpVector(strat->P.sig,currRing);
2804	strat->enterS(strat->P, pos, strat, strat->tl);
2805	if(strat->sbaOrder != 1)
2806	{
2807	BOOLEAN overwrite = FALSE;
2808	for (int tk=0; tk<strat->sl+1; tk++)
2809	{
2810	if (pGetComp(strat->sig[tk]) == pGetComp(strat->P.sig))
2811	{
2812	//printf("TK %d / %d\n",tk,strat->sl);
2813	overwrite = FALSE;
2814	break;
2815	}
2816	}
2817	//printf("OVERWRITE %d\n",overwrite);
2818	if (overwrite)
2819	{
2820	int cmp = pGetComp(strat->P.sig);
2821	int* vv = (int)omAlloc((currRing->N+1)sizeof(int));
2822	p_GetExpV (strat->P.p,vv,currRing);
2823	p_SetExpV (strat->P.sig, vv,currRing);
2824	p_SetComp (strat->P.sig,cmp,currRing);
2825
2826	strat->P.sevSig = pGetShortExpVector (strat->P.sig);
2827	int i;
2828	LObject Q;
2829	for(int ps=0;ps<strat->sl+1;ps++)
2830	{
2831
2832	strat->newt = TRUE;
2833	if (strat->syzl == strat->syzmax)
2834	{
2835	pEnlargeSet(&strat->syz,strat->syzmax,setmaxTinc);
2836	strat->sevSyz = (unsigned long*) omRealloc0Size(strat->sevSyz,
2837	(strat->syzmax)*sizeof(unsigned long),
2838	((strat->syzmax)+setmaxTinc)
2839	*sizeof(unsigned long));
2840	strat->syzmax += setmaxTinc;
2841	}
2842	Q.sig = pCopy(strat->P.sig);
2843	// add LM(F->m[i]) to the signature to get a Schreyer order
2844	// without changing the underlying polynomial ring at all
2845	if (strat->sbaOrder == 0)
2846	p_ExpVectorAdd (Q.sig,strat->S[ps],currRing);
2847	// since p_Add_q() destroys all input
2848	// data we need to recreate help
2849	// each time
2850	// ----------------------------------------------------------
2851	// in the Schreyer order we always know that the multiplied
2852	// module monomial strat->P.sig gives the leading monomial of
2853	// the corresponding principal syzygy
2854	// => we do not need to compute the "real" syzygy completely
2855	poly help = p_Copy(strat->sig[ps],currRing);
2856	p_ExpVectorAdd (help,strat->P.p,currRing);
2857	Q.sig = p_Add_q(Q.sig,help,currRing);
2858	//printf("%d. SYZ ",i+1);
2859	//pWrite(strat->syz[i]);
2860	Q.sevSig = p_GetShortExpVector(Q.sig,currRing);
2861	i = posInSyz(strat, Q.sig);
2862	enterSyz(Q, strat, i);
2863	}
2864	}
2865	}
2866	// deg - idx - lp/rp
2867	// => we need to add syzygies with indices > pGetComp(strat->P.sig)
2868	if(strat->sbaOrder == 0 \|\| strat->sbaOrder == 3)
2869	{
2870	int cmp = pGetComp(strat->P.sig);
2871	int max_cmp = IDELEMS(F);
2872	int* vv = (int)omAlloc((currRing->N+1)sizeof(int));
2873	p_GetExpV (strat->P.p,vv,currRing);
2874	LObject Q;
2875	int pos;
2876	int idx = __p_GetComp(strat->P.sig,currRing);
2877	//printf("++ -- adding syzygies -- ++\n");
2878	// if new element is the first one in this index
2879	if (strat->currIdx < idx)
2880	{
2881	for (int i=0; i<strat->sl; ++i)
2882	{
2883	Q.sig = p_Copy(strat->P.sig,currRing);
2884	p_ExpVectorAdd(Q.sig,strat->S[i],currRing);
2885	poly help = p_Copy(strat->sig[i],currRing);
2886	p_ExpVectorAdd(help,strat->P.p,currRing);
2887	Q.sig = p_Add_q(Q.sig,help,currRing);
2888	//pWrite(Q.sig);
2889	pos = posInSyz(strat, Q.sig);
2890	enterSyz(Q, strat, pos);
2891	}
2892	strat->currIdx = idx;
2893	}
2894	else
2895	{
2896	// if the element is not the first one in the given index we build all
2897	// possible syzygies with elements of higher index
2898	for (int i=cmp+1; i<=max_cmp; ++i)
2899	{
2900	pos = -1;
2901	for (int j=0; j<strat->sl; ++j)
2902	{
2903	if (__p_GetComp(strat->sig[j],currRing) == i)
2904	{
2905	pos = j;
2906	break;
2907	}
2908	}
2909	if (pos != -1)
2910	{
2911	Q.sig = p_One(currRing);
2912	p_SetExpV(Q.sig, vv, currRing);
2913	// F->m[i-1] corresponds to index i
2914	p_ExpVectorAdd(Q.sig,F->m[i-1],currRing);
2915	p_SetComp(Q.sig, i, currRing);
2916	poly help = p_Copy(strat->P.sig,currRing);
2917	p_ExpVectorAdd(help,strat->S[pos],currRing);
2918	Q.sig = p_Add_q(Q.sig,help,currRing);
2919	if (strat->sbaOrder == 0)
2920	{
2921	if (p_LmCmp(Q.sig,strat->syz[strat->syzl-1],currRing) == -currRing->OrdSgn)
2922	{
2923	pos = posInSyz(strat, Q.sig);
2924	enterSyz(Q, strat, pos);
2925	}
2926	}
2927	else
2928	{
2929	pos = posInSyz(strat, Q.sig);
2930	enterSyz(Q, strat, pos);
2931	}
2932	}
2933	}
2934	//printf("++ -- done adding syzygies -- ++\n");
2935	}
2936	}
2937	//#if 1
2938	#if DEBUGF50
2939	printf("---------------------------\n");
2940	Print(" %d. ELEMENT ADDED TO GCURR:\n",strat->sl+1);
2941	PrintS("LEAD POLY: "); pWrite(pHead(strat->S[strat->sl]));
2942	PrintS("SIGNATURE: "); pWrite(strat->sig[strat->sl]);
2943	#endif
2944	/*
2945	if (newrules)
2946	{
2947	newrules = FALSE;
2948	}
2949	*/
2950	#if 0
2951	int pl=pLength(strat->P.p);
2952	if (pl==1)
2953	{
2954	//if (TEST_OPT_PROT)
2955	//PrintS("<1>");
2956	}
2957	else if (pl==2)
2958	{
2959	//if (TEST_OPT_PROT)
2960	//PrintS("<2>");
2961	}
2962	#endif
2963	if (hilb!=NULL) khCheck(Q,w,hilb,hilbeledeg,hilbcount,strat);
2964	// Print("[%d]",hilbeledeg);
2965	kDeleteLcm(&strat->P);
2966	if (strat->sl>srmax) srmax = strat->sl;
2967	}
2968	else
2969	{
2970	case_when_red_result_changed:
2971	// adds signature of the zero reduction to
2972	// strat->syz. This is the leading term of
2973	// syzygy and can be used in syzCriterion()
2974	// the signature is added if and only if the
2975	// pair was not detected by the rewritten criterion in strat->red = redSig
2976	if (red_result!=2)
2977	{
2978	#if SBA_PRINT_ZERO_REDUCTIONS
2979	zeroreductions++;
2980	#endif
2981	if(rField_is_Ring(currRing) && strat->P.p == NULL && strat->P.sig == NULL)
2982	{
2983	//Catch the case when p = 0, sig = 0
2984	}
2985	else
2986	{
2987	int pos = posInSyz(strat, strat->P.sig);
2988	enterSyz(strat->P, strat, pos);
2989	//#if 1
2990	#ifdef DEBUGF5
2991	Print("ADDING STUFF TO SYZ : ");
2992	//pWrite(strat->P.p);
2993	pWrite(strat->P.sig);
2994	#endif
2995	}
2996	}
2997	if (strat->P.p1 == NULL && strat->minim > 0)
2998	{
2999	p_Delete(&strat->P.p2, currRing, strat->tailRing);
3000	}
3001	}
3002
3003	#ifdef KDEBUG
3004	memset(&(strat->P), 0, sizeof(strat->P));
3005	#endif /* KDEBUG */
3006	kTest_TS(strat);
3007	}
3008	#if 0
3009	if(strat->sigdrop)
3010	printf("\nSigDrop!\n");
3011	else
3012	printf("\nEnded with no SigDrop\n");
3013	#endif
3014	// Clean strat->P for the next sba call
3015	if(rField_is_Ring(currRing) && strat->sigdrop)
3016	{
3017	//This is used to know how many elements can we directly add to S in the next run
3018	if(strat->P.sig != NULL)
3019	strat->sbaEnterS = pGetComp(strat->P.sig)-1;
3020	//else we already set it at the beggining of the loop
3021	#ifdef KDEBUG
3022	memset(&(strat->P), 0, sizeof(strat->P));
3023	#endif /* KDEBUG */
3024	}
3025	#ifdef KDEBUG
3026	if (TEST_OPT_DEBUG) messageSets(strat);
3027	#endif /* KDEBUG */
3028
3029	if (TEST_OPT_SB_1)
3030	{
3031	if(!rField_is_Ring(currRing))
3032	{
3033	int k=1;
3034	int j;
3035	while(k<=strat->sl)
3036	{
3037	j=0;
3038	loop
3039	{
3040	if (j>=k) break;
3041	clearS(strat->S[j],strat->sevS[j],&k,&j,strat);
3042	j++;
3043	}
3044	k++;
3045	}
3046	}
3047	}
3048	/* complete reduction of the standard basis--------- */
3049	if (TEST_OPT_REDSB)
3050	{
3051	completeReduce(strat);
3052	if (strat->completeReduce_retry)
3053	{
3054	// completeReduce needed larger exponents, retry
3055	// to reduce with S (instead of T)
3056	// and in currRing (instead of strat->tailRing)
3057	#ifdef HAVE_TAIL_RING
3058	if(currRing->bitmask>strat->tailRing->bitmask)
3059	{
3060	strat->completeReduce_retry=FALSE;
3061	cleanT(strat);strat->tailRing=currRing;
3062	int i;
3063	for(i=strat->sl;i>=0;i--) strat->S_2_R[i]=-1;
3064	completeReduce(strat);
3065	}
3066	if (strat->completeReduce_retry)
3067	#endif
3068	Werror("exponent bound is %ld",currRing->bitmask);
3069	}
3070	}
3071	else if (TEST_OPT_PROT) PrintLn();
3072
3073	#if SBA_PRINT_SIZE_SYZ
3074	// that is correct, syzl is counting one too far
3075	size_syz = strat->syzl;
3076	#endif
3077	// if (TEST_OPT_WEIGHTM)
3078	// {
3079	// pRestoreDegProcs(pFDegOld, pLDegOld);
3080	// if (ecartWeights)
3081	// {
3082	// omFreeSize((ADDRESS)ecartWeights,(pVariables+1)*sizeof(short));
3083	// ecartWeights=NULL;
3084	// }
3085	// }
3086	if (TEST_OPT_PROT) messageStatSBA(hilbcount,strat);
3087	if (Q!=NULL) updateResult(strat->Shdl,Q,strat);
3088	#if SBA_PRINT_SIZE_G
3089	size_g_non_red = IDELEMS(strat->Shdl);
3090	#endif
3091	if(!rField_is_Ring(currRing))
3092	exitSba(strat);
3093	// I have to add the initial input polynomials which where not used (p1 and p2 = NULL)
3094	#ifdef HAVE_RINGS
3095	int k;
3096	if(rField_is_Ring(currRing))
3097	{
3098	//for(k = strat->sl;k>=0;k--)
3099	// {printf("\nS[%i] = %p\n",k,strat->Shdl->m[k]);pWrite(strat->Shdl->m[k]);}
3100	k = strat->Ll;
3101	#if 1
3102	// 1 - adds just the unused ones, 0 - adds everthing
3103	for(;k>=0 && (strat->L[k].p1 != NULL \|\| strat->L[k].p2 != NULL);k--)
3104	{
3105	//printf("\nDeleted k = %i, %p\n",k,strat->L[k].p);pWrite(strat->L[k].p);pWrite(strat->L[k].p1);pWrite(strat->L[k].p2);
3106	deleteInL(strat->L,&strat->Ll,k,strat);
3107	}
3108	#endif
3109	//for(int kk = strat->sl;kk>=0;kk--)
3110	// {printf("\nS[%i] = %p\n",kk,strat->Shdl->m[kk]);pWrite(strat->Shdl->m[kk]);}
3111	//idPrint(strat->Shdl);
3112	//printf("\nk = %i\n",k);
3113	for(;k>=0 && strat->L[k].p1 == NULL && strat->L[k].p2 == NULL;k--)
3114	{
3115	//printf("\nAdded k = %i\n",k);
3116	strat->enterS(strat->L[k], strat->sl+1, strat, strat->tl);
3117	//printf("\nThis elements was added from L on pos %i\n",strat->sl);pWrite(strat->S[strat->sl]);pWrite(strat->sig[strat->sl]);
3118	}
3119	}
3120	// Find the "sigdrop element" and put the same signature as the previous one - do we really need this?? - now i put it on the 0 position - no more comparing needed
3121	#if 0
3122	if(strat->sigdrop && rField_is_Ring(currRing))
3123	{
3124	for(k=strat->sl;k>=0;k--)
3125	{
3126	printf("\nsig[%i] = ",i);pWrite(strat->sig[k]);
3127	if(strat->sig[k] == NULL)
3128	strat->sig[k] = pCopy(strat->sig[k-1]);
3129	}
3130	}
3131	#endif
3132	#endif
3133	//Never do this - you will damage S
3134	//idSkipZeroes(strat->Shdl);
3135	//idPrint(strat->Shdl);
3136
3137	if ((strat->sbaOrder == 1 \|\| strat->sbaOrder == 3) && sRing!=currRingOld)
3138	{
3139	rChangeCurrRing (currRingOld);
3140	F0 = idrMoveR (F1, sRing, currRing);
3141	strat->Shdl = idrMoveR_NoSort (strat->Shdl, sRing, currRing);
3142	rChangeCurrRing (sRing);
3143	if(rField_is_Ring(currRing))
3144	exitSba(strat);
3145	rChangeCurrRing (currRingOld);
3146	if(strat->tailRing == sRing)
3147	strat->tailRing = currRing;
3148	rDelete (sRing);
3149	}
3150	if(rField_is_Ring(currRing) && !strat->sigdrop)
3151	id_DelDiv(strat->Shdl, currRing);
3152	if(!rField_is_Ring(currRing))
3153	id_DelDiv(strat->Shdl, currRing);
3154	idSkipZeroes(strat->Shdl);
3155	idTest(strat->Shdl);
3156
3157	#if SBA_PRINT_SIZE_G
3158	size_g = IDELEMS(strat->Shdl);
3159	#endif
3160	#ifdef DEBUGF5
3161	printf("SIZE OF SHDL: %d\n",IDELEMS(strat->Shdl));
3162	int oo = 0;
3163	while (oo<IDELEMS(strat->Shdl))
3164	{
3165	printf(" %d. ",oo+1);
3166	pWrite(pHead(strat->Shdl->m[oo]));
3167	oo++;
3168	}
3169	#endif
3170	#if SBA_PRINT_ZERO_REDUCTIONS
3171	printf("----------------------------------------------------------\n");
3172	printf("ZERO REDUCTIONS: %ld\n",zeroreductions);
3173	zeroreductions = 0;
3174	#endif
3175	#if SBA_PRINT_REDUCTION_STEPS
3176	printf("----------------------------------------------------------\n");
3177	printf("S-REDUCTIONS: %ld\n",sba_reduction_steps);
3178	#endif
3179	#if SBA_PRINT_OPERATIONS
3180	printf("OPERATIONS: %ld\n",sba_operations);
3181	#endif
3182	#if SBA_PRINT_REDUCTION_STEPS
3183	printf("- - - - - - - - - - - - - - - - - - - - - - - - - - - - - \n");
3184	printf("INTERREDUCTIONS: %ld\n",sba_interreduction_steps);
3185	#endif
3186	#if SBA_PRINT_OPERATIONS
3187	printf("INTERREDUCTION OPERATIONS: %ld\n",sba_interreduction_operations);
3188	#endif
3189	#if SBA_PRINT_REDUCTION_STEPS
3190	printf("- - - - - - - - - - - - - - - - - - - - - - - - - - - - - \n");
3191	printf("ALL REDUCTIONS: %ld\n",sba_reduction_steps+sba_interreduction_steps);
3192	sba_interreduction_steps = 0;
3193	sba_reduction_steps = 0;
3194	#endif
3195	#if SBA_PRINT_OPERATIONS
3196	printf("ALL OPERATIONS: %ld\n",sba_operations+sba_interreduction_operations);
3197	sba_interreduction_operations = 0;
3198	sba_operations = 0;
3199	#endif
3200	#if SBA_PRINT_SIZE_G
3201	printf("----------------------------------------------------------\n");
3202	printf("SIZE OF G: %d / %d\n",size_g,size_g_non_red);
3203	size_g = 0;
3204	size_g_non_red = 0;
3205	#endif
3206	#if SBA_PRINT_SIZE_SYZ
3207	printf("SIZE OF SYZ: %ld\n",size_syz);
3208	printf("----------------------------------------------------------\n");
3209	size_syz = 0;
3210	#endif
3211	#if SBA_PRINT_PRODUCT_CRITERION
3212	printf("PRODUCT CRITERIA: %ld\n",product_criterion);
3213	product_criterion = 0;
3214	#endif
3215	return (strat->Shdl);
3216	}
3217
3218	poly kNF2 (ideal F,ideal Q,poly q,kStrategy strat, int lazyReduce)
3219	{
3220	assume(q!=NULL);
3221	assume(!(idIs0(F)&&(Q==NULL))); // NF(q, std(0) in polynomial ring?
3222
3223	// lazy_reduce flags: can be combined by \|
3224	//#define KSTD_NF_LAZY 1
3225	// do only a reduction of the leading term
3226	//#define KSTD_NF_NONORM 4
3227	// only global: avoid normalization, return a multiply of NF
3228	poly p;
3229
3230	//if ((idIs0(F))&&(Q==NULL))
3231	// return pCopy(q); /F=0/
3232	//strat->ak = idRankFreeModule(F);
3233	/- creating temp data structures------------------- -/
3234	BITSET save1;
3235	SI_SAVE_OPT1(save1);
3236	si_opt_1\|=Sy_bit(OPT_REDTAIL);
3237	initBuchMoraCrit(strat);
3238	strat->initEcart = initEcartBBA;
3239	strat->enterS = enterSBba;
3240	#ifndef NO_BUCKETS
3241	strat->use_buckets = (!TEST_OPT_NOT_BUCKETS) && (!rIsPluralRing(currRing));
3242	#endif
3243	/- set S -/
3244	strat->sl = -1;
3245	/- init local data struct.---------------------------------------- -/
3246	/Shdl=/initS(F,Q,strat);
3247	/- compute------------------------------------------------------- -/
3248	//if ((TEST_OPT_INTSTRATEGY)&&(lazyReduce==0))
3249	//{
3250	// for (i=strat->sl;i>=0;i--)
3251	// pNorm(strat->S[i]);
3252	//}
3253	kTest(strat);
3254	if (TEST_OPT_PROT) { PrintS("r"); mflush(); }
3255	if (BVERBOSE(23)) kDebugPrint(strat);
3256	int max_ind;
3257	p = redNF(pCopy(q),max_ind,lazyReduce & KSTD_NF_NONORM,strat);
3258	if ((p!=NULL)&&((lazyReduce & KSTD_NF_LAZY)==0))
3259	{
3260	if (TEST_OPT_PROT) { PrintS("t"); mflush(); }
3261	if (rField_is_Ring(currRing))
3262	{
3263	p = redtailBba_Z(p,max_ind,strat);
3264	}
3265	else
3266	{
3267	si_opt_1 &= ~Sy_bit(OPT_INTSTRATEGY);
3268	p = redtailBba(p,max_ind,strat,(lazyReduce & KSTD_NF_NONORM)==0);
3269	}
3270	}
3271	/- release temp data------------------------------- -/
3272	assume(strat->L==NULL); /* strat->L unused */
3273	assume(strat->B==NULL); /* strat->B unused */
3274	omFree(strat->sevS);
3275	omFree(strat->ecartS);
3276	assume(strat->T==NULL);//omfree(strat->T);
3277	assume(strat->sevT==NULL);//omfree(strat->sevT);
3278	assume(strat->R==NULL);//omfree(strat->R);
3279	omfree(strat->S_2_R);
3280	omfree(strat->fromQ);
3281	idDelete(&strat->Shdl);
3282	SI_RESTORE_OPT1(save1);
3283	if (TEST_OPT_PROT) PrintLn();
3284	return p;
3285	}
3286
3287	poly kNF2Bound (ideal F,ideal Q,poly q,int bound,kStrategy strat, int lazyReduce)
3288	{
3289	assume(q!=NULL);
3290	assume(!(idIs0(F)&&(Q==NULL))); // NF(q, std(0) in polynomial ring?
3291
3292	// lazy_reduce flags: can be combined by \|
3293	//#define KSTD_NF_LAZY 1
3294	// do only a reduction of the leading term
3295	//#define KSTD_NF_NONORM 4
3296	// only global: avoid normalization, return a multiply of NF
3297	poly p;
3298
3299	//if ((idIs0(F))&&(Q==NULL))
3300	// return pCopy(q); /F=0/
3301	//strat->ak = idRankFreeModule(F);
3302	/- creating temp data structures------------------- -/
3303	BITSET save1;
3304	SI_SAVE_OPT1(save1);
3305	si_opt_1\|=Sy_bit(OPT_REDTAIL);
3306	initBuchMoraCrit(strat);
3307	strat->initEcart = initEcartBBA;
3308	strat->enterS = enterSBba;
3309	#ifndef NO_BUCKETS
3310	strat->use_buckets = (!TEST_OPT_NOT_BUCKETS) && (!rIsPluralRing(currRing));
3311	#endif
3312	/- set S -/
3313	strat->sl = -1;
3314	/- init local data struct.---------------------------------------- -/
3315	/Shdl=/initS(F,Q,strat);
3316	/- compute------------------------------------------------------- -/
3317	//if ((TEST_OPT_INTSTRATEGY)&&(lazyReduce==0))
3318	//{
3319	// for (i=strat->sl;i>=0;i--)
3320	// pNorm(strat->S[i]);
3321	//}
3322	kTest(strat);
3323	if (TEST_OPT_PROT) { PrintS("r"); mflush(); }
3324	if (BVERBOSE(23)) kDebugPrint(strat);
3325	int max_ind;
3326	p = redNFBound(pCopy(q),max_ind,lazyReduce & KSTD_NF_NONORM,strat,bound);
3327	if ((p!=NULL)&&((lazyReduce & KSTD_NF_LAZY)==0))
3328	{
3329	if (TEST_OPT_PROT) { PrintS("t"); mflush(); }
3330	if (rField_is_Ring(currRing))
3331	{
3332	p = redtailBba_Z(p,max_ind,strat);
3333	}
3334	else
3335	{
3336	si_opt_1 &= ~Sy_bit(OPT_INTSTRATEGY);
3337	p = redtailBbaBound(p,max_ind,strat,bound,(lazyReduce & KSTD_NF_NONORM)==0);
3338	//p = redtailBba(p,max_ind,strat,(lazyReduce & KSTD_NF_NONORM)==0);
3339	}
3340	}
3341	/- release temp data------------------------------- -/
3342	assume(strat->L==NULL); /* strat->L unused */
3343	assume(strat->B==NULL); /* strat->B unused */
3344	omFree(strat->sevS);
3345	omFree(strat->ecartS);
3346	assume(strat->T==NULL);//omfree(strat->T);
3347	assume(strat->sevT==NULL);//omfree(strat->sevT);
3348	assume(strat->R==NULL);//omfree(strat->R);
3349	omfree(strat->S_2_R);
3350	omfree(strat->fromQ);
3351	idDelete(&strat->Shdl);
3352	SI_RESTORE_OPT1(save1);
3353	if (TEST_OPT_PROT) PrintLn();
3354	return p;
3355	}
3356
3357	ideal kNF2 (ideal F,ideal Q,ideal q,kStrategy strat, int lazyReduce)
3358	{
3359	assume(!idIs0(q));
3360	assume(!(idIs0(F)&&(Q==NULL)));
3361	// lazy_reduce flags: can be combined by \|
3362	//#define KSTD_NF_LAZY 1
3363	// do only a reduction of the leading term
3364	//#define KSTD_NF_NONORM 4
3365	// only global: avoid normalization, return a multiply of NF
3366	poly p;
3367	int i;
3368	ideal res;
3369	int max_ind;
3370
3371	//if (idIs0(q))
3372	// return idInit(IDELEMS(q),si_max(q->rank,F->rank));
3373	//if ((idIs0(F))&&(Q==NULL))
3374	// return idCopy(q); /F=0/
3375	//strat->ak = idRankFreeModule(F);
3376	/- creating temp data structures------------------- -/
3377	BITSET save1;
3378	SI_SAVE_OPT1(save1);
3379	si_opt_1\|=Sy_bit(OPT_REDTAIL);
3380	initBuchMoraCrit(strat);
3381	strat->initEcart = initEcartBBA;
3382	strat->enterS = enterSBba;
3383	/- set S -/
3384	strat->sl = -1;
3385	#ifndef NO_BUCKETS
3386	strat->use_buckets = (!TEST_OPT_NOT_BUCKETS) && (!rIsPluralRing(currRing));
3387	#endif
3388	/- init local data struct.---------------------------------------- -/
3389	/Shdl=/initS(F,Q,strat);
3390	/- compute------------------------------------------------------- -/
3391	res=idInit(IDELEMS(q),si_max(q->rank,F->rank));
3392	si_opt_1 &= ~Sy_bit(OPT_INTSTRATEGY);
3393	for (i=IDELEMS(q)-1; i>=0; i--)
3394	{
3395	if (q->m[i]!=NULL)
3396	{
3397	if (TEST_OPT_PROT) { PrintS("r");mflush(); }
3398	p = redNF(pCopy(q->m[i]),max_ind,lazyReduce & KSTD_NF_NONORM,strat);
3399	if ((p!=NULL)&&((lazyReduce & KSTD_NF_LAZY)==0))
3400	{
3401	if (TEST_OPT_PROT) { PrintS("t"); mflush(); }
3402	if (rField_is_Ring(currRing))
3403	{
3404	p = redtailBba_Z(p,max_ind,strat);
3405	}
3406	else
3407	{
3408	p = redtailBba(p,max_ind,strat,(lazyReduce & KSTD_NF_NONORM)==0);
3409	}
3410	}
3411	res->m[i]=p;
3412	}
3413	//else
3414	// res->m[i]=NULL;
3415	}
3416	/- release temp data------------------------------- -/
3417	assume(strat->L==NULL); /* strat->L unused */
3418	assume(strat->B==NULL); /* strat->B unused */
3419	omFree(strat->sevS);
3420	omFree(strat->ecartS);
3421	assume(strat->T==NULL);//omfree(strat->T);
3422	assume(strat->sevT==NULL);//omfree(strat->sevT);
3423	assume(strat->R==NULL);//omfree(strat->R);
3424	omfree(strat->S_2_R);
3425	omfree(strat->fromQ);
3426	idDelete(&strat->Shdl);
3427	SI_RESTORE_OPT1(save1);
3428	if (TEST_OPT_PROT) PrintLn();
3429	return res;
3430	}
3431
3432	ideal kNF2Bound (ideal F,ideal Q,ideal q,int bound,kStrategy strat, int lazyReduce)
3433	{
3434	assume(!idIs0(q));
3435	assume(!(idIs0(F)&&(Q==NULL)));
3436	// lazy_reduce flags: can be combined by \|
3437	//#define KSTD_NF_LAZY 1
3438	// do only a reduction of the leading term
3439	//#define KSTD_NF_NONORM 4
3440	// only global: avoid normalization, return a multiply of NF
3441	poly p;
3442	int i;
3443	ideal res;
3444	int max_ind;
3445
3446	//if (idIs0(q))
3447	// return idInit(IDELEMS(q),si_max(q->rank,F->rank));
3448	//if ((idIs0(F))&&(Q==NULL))
3449	// return idCopy(q); /F=0/
3450	//strat->ak = idRankFreeModule(F);
3451	/- creating temp data structures------------------- -/
3452	BITSET save1;
3453	SI_SAVE_OPT1(save1);
3454	si_opt_1\|=Sy_bit(OPT_REDTAIL);
3455	initBuchMoraCrit(strat);
3456	strat->initEcart = initEcartBBA;
3457	strat->enterS = enterSBba;
3458	/- set S -/
3459	strat->sl = -1;
3460	#ifndef NO_BUCKETS
3461	strat->use_buckets = (!TEST_OPT_NOT_BUCKETS) && (!rIsPluralRing(currRing));
3462	#endif
3463	/- init local data struct.---------------------------------------- -/
3464	/Shdl=/initS(F,Q,strat);
3465	/- compute------------------------------------------------------- -/
3466	res=idInit(IDELEMS(q),si_max(q->rank,F->rank));
3467	si_opt_1 &= ~Sy_bit(OPT_INTSTRATEGY);
3468	for (i=IDELEMS(q)-1; i>=0; i--)
3469	{
3470	if (q->m[i]!=NULL)
3471	{
3472	if (TEST_OPT_PROT) { PrintS("r");mflush(); }
3473	p = redNFBound(pCopy(q->m[i]),max_ind,lazyReduce & KSTD_NF_NONORM,strat,bound);
3474	if ((p!=NULL)&&((lazyReduce & KSTD_NF_LAZY)==0))
3475	{
3476	if (TEST_OPT_PROT) { PrintS("t"); mflush(); }
3477	if (rField_is_Ring(currRing))
3478	{
3479	p = redtailBba_Z(p,max_ind,strat);
3480	}
3481	else
3482	{
3483	p = redtailBbaBound(p,max_ind,strat,bound,(lazyReduce & KSTD_NF_NONORM)==0);
3484	}
3485	}
3486	res->m[i]=p;
3487	}
3488	//else
3489	// res->m[i]=NULL;
3490	}
3491	/- release temp data------------------------------- -/
3492	assume(strat->L==NULL); /* strat->L unused */
3493	assume(strat->B==NULL); /* strat->B unused */
3494	omFree(strat->sevS);
3495	omFree(strat->ecartS);
3496	assume(strat->T==NULL);//omfree(strat->T);
3497	assume(strat->sevT==NULL);//omfree(strat->sevT);
3498	assume(strat->R==NULL);//omfree(strat->R);
3499	omfree(strat->S_2_R);
3500	omfree(strat->fromQ);
3501	idDelete(&strat->Shdl);
3502	SI_RESTORE_OPT1(save1);
3503	if (TEST_OPT_PROT) PrintLn();
3504	return res;
3505	}
3506
3507	#if F5C
3508	/*********************************************************************
3509	* interrreduction step of the signature-based algorithm:
3510	* 1. all strat->S are interpreted as new critical pairs
3511	* 2. those pairs need to be completely reduced by the usual (non sig-
3512	* safe) reduction process (including tail reductions)
3513	* 3. strat->S and strat->T are completely new computed in these steps
3514	********************************************************************/
3515	void f5c (kStrategy strat, int& olddeg, int& minimcnt, int& hilbeledeg,
3516	int& hilbcount, int& srmax, int& lrmax, int& reduc, ideal Q,
3517	intvec w,intvec hilb )
3518	{
3519	int Ll_old, red_result = 1;
3520	int pos = 0;
3521	hilbeledeg=1;
3522	hilbcount=0;
3523	minimcnt=0;
3524	srmax = 0; // strat->sl is 0 at this point
3525	reduc = olddeg = lrmax = 0;
3526	// we cannot use strat->T anymore
3527	//cleanT(strat);
3528	//strat->tl = -1;
3529	Ll_old = strat->Ll;
3530	while (strat->tl >= 0)
3531	{
3532	if(!strat->T[strat->tl].is_redundant)
3533	{
3534	LObject h;
3535	h.p = strat->T[strat->tl].p;
3536	h.tailRing = strat->T[strat->tl].tailRing;
3537	h.t_p = strat->T[strat->tl].t_p;
3538	if (h.p!=NULL)
3539	{
3540	if (currRing->OrdSgn==-1)
3541	{
3542	cancelunit(&h);
3543	deleteHC(&h, strat);
3544	}
3545	if (h.p!=NULL)
3546	{
3547	if (TEST_OPT_INTSTRATEGY)
3548	{
3549	h.pCleardenom(); // also does remove Content
3550	}
3551	else
3552	{
3553	h.pNorm();
3554	}
3555	strat->initEcart(&h);
3556	if(rField_is_Ring(currRing))
3557	pos = posInLF5CRing(strat->L, Ll_old+1,strat->Ll,&h,strat);
3558	else
3559	pos = strat->Ll+1;
3560	h.sev = pGetShortExpVector(h.p);
3561	enterL(&strat->L,&strat->Ll,&strat->Lmax,h,pos);
3562	}
3563	}
3564	}
3565	strat->tl--;
3566	}
3567	strat->sl = -1;
3568	#if 0
3569	//#ifdef HAVE_TAIL_RING
3570	if(!rField_is_Ring()) // create strong gcd poly computes with tailring and S[i] ->to be fixed
3571	kStratInitChangeTailRing(strat);
3572	#endif
3573	//enterpairs(pOne(),0,0,-1,strat,strat->tl);
3574	//strat->sl = -1;
3575	/* picks the last element from the lazyset L */
3576	while (strat->Ll>Ll_old)
3577	{
3578	strat->P = strat->L[strat->Ll];
3579	strat->Ll--;
3580	//#if 1
3581	#ifdef DEBUGF5
3582	PrintS("NEXT PAIR TO HANDLE IN INTERRED ALGORITHM\n");
3583	PrintS("-------------------------------------------------\n");
3584	pWrite(pHead(strat->P.p));
3585	pWrite(pHead(strat->P.p1));
3586	pWrite(pHead(strat->P.p2));
3587	printf("%d\n",strat->tl);
3588	PrintS("-------------------------------------------------\n");
3589	#endif
3590	if (pNext(strat->P.p) == strat->tail)
3591	{
3592	// deletes the short spoly
3593	if (rField_is_Ring(currRing))
3594	pLmDelete(strat->P.p);
3595	else
3596	pLmFree(strat->P.p);
3597
3598	// TODO: needs some masking
3599	// TODO: masking needs to vanish once the signature
3600	// sutff is completely implemented
3601	strat->P.p = NULL;
3602	poly m1 = NULL, m2 = NULL;
3603
3604	// check that spoly creation is ok
3605	while (strat->tailRing != currRing &&
3606	!kCheckSpolyCreation(&(strat->P), strat, m1, m2))
3607	{
3608	assume(m1 == NULL && m2 == NULL);
3609	// if not, change to a ring where exponents are at least
3610	// large enough
3611	if (!kStratChangeTailRing(strat))
3612	{
3613	WerrorS("OVERFLOW...");
3614	break;
3615	}
3616	}
3617	// create the real one
3618	ksCreateSpoly(&(strat->P), NULL, strat->use_buckets,
3619	strat->tailRing, m1, m2, strat->R);
3620	}
3621	else if (strat->P.p1 == NULL)
3622	{
3623	if (strat->minim > 0)
3624	strat->P.p2=p_Copy(strat->P.p, currRing, strat->tailRing);
3625	// for input polys, prepare reduction
3626	if(!rField_is_Ring(currRing))
3627	strat->P.PrepareRed(strat->use_buckets);
3628	}
3629
3630	if (strat->P.p == NULL && strat->P.t_p == NULL)
3631	{
3632	red_result = 0;
3633	}
3634	else
3635	{
3636	if (TEST_OPT_PROT)
3637	message((strat->honey ? strat->P.ecart : 0) + strat->P.pFDeg(),
3638	&olddeg,&reduc,strat, red_result);
3639
3640	#ifdef DEBUGF5
3641	PrintS("Poly before red: ");
3642	pWrite(strat->P.p);
3643	#endif
3644	/* complete reduction of the element chosen from L */
3645	red_result = strat->red2(&strat->P,strat);
3646	if (errorreported) break;
3647	}
3648
3649	if (strat->overflow)
3650	{
3651	if (!kStratChangeTailRing(strat)) { WerrorS("OVERFLOW.."); break;}
3652	}
3653
3654	// reduction to non-zero new poly
3655	if (red_result == 1)
3656	{
3657	// get the polynomial (canonicalize bucket, make sure P.p is set)
3658	strat->P.GetP(strat->lmBin);
3659	// in the homogeneous case FDeg >= pFDeg (sugar/honey)
3660	// but now, for entering S, T, we reset it
3661	// in the inhomogeneous case: FDeg == pFDeg
3662	if (strat->homog) strat->initEcart(&(strat->P));
3663
3664	/* statistic */
3665	if (TEST_OPT_PROT) PrintS("s");
3666	int pos;
3667	#if 1
3668	if(!rField_is_Ring(currRing))
3669	pos = posInS(strat,strat->sl,strat->P.p,strat->P.ecart);
3670	else
3671	pos = posInSMonFirst(strat,strat->sl,strat->P.p);
3672	#else
3673	pos = posInS(strat,strat->sl,strat->P.p,strat->P.ecart);
3674	#endif
3675	// reduce the tail and normalize poly
3676	// in the ring case we cannot expect LC(f) = 1,
3677	// therefore we call pCleardenom instead of pNorm
3678	#if F5CTAILRED
3679	BOOLEAN withT = TRUE;
3680	if ((TEST_OPT_INTSTRATEGY) \|\| (rField_is_Ring(currRing)))
3681	{
3682	strat->P.pCleardenom();
3683	if ((TEST_OPT_REDSB)\|\|(TEST_OPT_REDTAIL))
3684	{
3685	strat->P.p = redtailBba(&(strat->P),pos-1,strat, withT);
3686	strat->P.pCleardenom();
3687	}
3688	}
3689	else
3690	{
3691	strat->P.pNorm();
3692	if ((TEST_OPT_REDSB)\|\|(TEST_OPT_REDTAIL))
3693	strat->P.p = redtailBba(&(strat->P),pos-1,strat, withT);
3694	}
3695	#endif
3696	#ifdef KDEBUG
3697	if (TEST_OPT_DEBUG){PrintS("new s:");strat->P.wrp();PrintLn();}
3698	#endif /* KDEBUG */
3699
3700	// min_std stuff
3701	if ((strat->P.p1==NULL) && (strat->minim>0))
3702	{
3703	if (strat->minim==1)
3704	{
3705	strat->M->m[minimcnt]=p_Copy(strat->P.p,currRing,strat->tailRing);
3706	p_Delete(&strat->P.p2, currRing, strat->tailRing);
3707	}
3708	else
3709	{
3710	strat->M->m[minimcnt]=strat->P.p2;
3711	strat->P.p2=NULL;
3712	}
3713	if (strat->tailRing!=currRing && pNext(strat->M->m[minimcnt])!=NULL)
3714	pNext(strat->M->m[minimcnt])
3715	= strat->p_shallow_copy_delete(pNext(strat->M->m[minimcnt]),
3716	strat->tailRing, currRing,
3717	currRing->PolyBin);
3718	minimcnt++;
3719	}
3720
3721	// enter into S, L, and T
3722	// here we need to recompute new signatures, but those are trivial ones
3723	if ((!TEST_OPT_IDLIFT) \|\| (pGetComp(strat->P.p) <= strat->syzComp))
3724	{
3725	enterT(strat->P, strat);
3726	// posInS only depends on the leading term
3727	strat->enterS(strat->P, pos, strat, strat->tl);
3728	//#if 1
3729	#ifdef DEBUGF5
3730	PrintS("ELEMENT ADDED TO GCURR DURING INTERRED: ");
3731	pWrite(pHead(strat->S[strat->sl]));
3732	pWrite(strat->sig[strat->sl]);
3733	#endif
3734	if (hilb!=NULL) khCheck(Q,w,hilb,hilbeledeg,hilbcount,strat);
3735	}
3736	// Print("[%d]",hilbeledeg);
3737	kDeleteLcm(&strat->P);
3738	if (strat->sl>srmax) srmax = strat->sl;
3739	}
3740	else
3741	{
3742	// adds signature of the zero reduction to
3743	// strat->syz. This is the leading term of
3744	// syzygy and can be used in syzCriterion()
3745	// the signature is added if and only if the
3746	// pair was not detected by the rewritten criterion in strat->red = redSig
3747	if (strat->P.p1 == NULL && strat->minim > 0)
3748	{
3749	p_Delete(&strat->P.p2, currRing, strat->tailRing);
3750	}
3751	}
3752
3753	#ifdef KDEBUG
3754	memset(&(strat->P), 0, sizeof(strat->P));
3755	#endif /* KDEBUG */
3756	}
3757	int cc = 0;
3758	while (cc<strat->tl+1)
3759	{
3760	strat->T[cc].sig = pOne();
3761	p_SetComp(strat->T[cc].sig,cc+1,currRing);
3762	strat->T[cc].sevSig = pGetShortExpVector(strat->T[cc].sig);
3763	strat->sig[cc] = strat->T[cc].sig;
3764	strat->sevSig[cc] = strat->T[cc].sevSig;
3765	strat->T[cc].is_sigsafe = TRUE;
3766	cc++;
3767	}
3768	strat->max_lower_index = strat->tl;
3769	// set current signature index of upcoming iteration step
3770	// NOTE: this needs to be set here, as otherwise initSyzRules cannot compute
3771	// the corresponding syzygy rules correctly
3772	strat->currIdx = cc+1;
3773	for (int cd=strat->Ll; cd>=0; cd--)
3774	{
3775	p_SetComp(strat->L[cd].sig,cc+1,currRing);
3776	cc++;
3777	}
3778	for (cc=strat->sl+1; cc<IDELEMS(strat->Shdl); ++cc)
3779	strat->Shdl->m[cc] = NULL;
3780	#if 0
3781	printf("\nAfter f5c sorting\n");
3782	for(int i=0;i<=strat->sl;i++)
3783	pWrite(pHead(strat->S[i]));
3784	getchar();
3785	#endif
3786	//#if 1
3787	#if DEBUGF5
3788	PrintS("------------------- STRAT S ---------------------\n");
3789	cc = 0;
3790	while (cc<strat->tl+1)
3791	{
3792	pWrite(pHead(strat->S[cc]));
3793	pWrite(strat->sig[cc]);
3794	printf("- - - - - -\n");
3795	cc++;
3796	}
3797	PrintS("-------------------------------------------------\n");
3798	PrintS("------------------- STRAT T ---------------------\n");
3799	cc = 0;
3800	while (cc<strat->tl+1)
3801	{
3802	pWrite(pHead(strat->T[cc].p));
3803	pWrite(strat->T[cc].sig);
3804	printf("- - - - - -\n");
3805	cc++;
3806	}
3807	PrintS("-------------------------------------------------\n");
3808	PrintS("------------------- STRAT L ---------------------\n");
3809	cc = 0;
3810	while (cc<strat->Ll+1)
3811	{
3812	pWrite(pHead(strat->L[cc].p));
3813	pWrite(pHead(strat->L[cc].p1));
3814	pWrite(pHead(strat->L[cc].p2));
3815	pWrite(strat->L[cc].sig);
3816	printf("- - - - - -\n");
3817	cc++;
3818	}
3819	PrintS("-------------------------------------------------\n");
3820	printf("F5C DONE\nSTRAT SL: %d -- %d\n",strat->sl, strat->currIdx);
3821	#endif
3822
3823	}
3824	#endif
3825
3826	/* shiftgb stuff */
3827	#ifdef HAVE_SHIFTBBA
3828
3829
3830	ideal bbaShift(ideal F, ideal Q,intvec w,intvec hilb,kStrategy strat, int uptodeg, int lV)
3831	{
3832	int red_result = 1;
3833	int olddeg,reduc;
3834	int hilbeledeg=1,hilbcount=0,minimcnt=0;
3835	BOOLEAN withT = TRUE; // very important for shifts
3836
3837	initBuchMoraCrit(strat); /set Gebauer, honey, sugarCrit, NO CHANGES /
3838	if(rField_is_Ring(currRing))
3839	initBuchMoraPosRing(strat);
3840	else
3841	initBuchMoraPos(strat); /NO CHANGES YET: perhaps later/
3842	initHilbCrit(F,Q,&hilb,strat); /NO CHANGES/
3843	initBbaShift(strat); /* DONE */
3844	/set enterS, spSpolyShort, reduce, red, initEcart, initEcartPair/
3845	/Shdl=/initBuchMoraShift(F, Q,strat); /* updateS with no toT, i.e. no init for T */
3846	updateSShift(strat,uptodeg,lV); /* initializes T */
3847
3848	if (strat->minim>0) strat->M=idInit(IDELEMS(F),F->rank);
3849	reduc = olddeg = 0;
3850	strat->lV=lV;
3851
3852	#ifndef NO_BUCKETS
3853	if (!TEST_OPT_NOT_BUCKETS)
3854	strat->use_buckets = 1;
3855	#endif
3856
3857	// redtailBBa against T for inhomogenous input
3858	// if (!TEST_OPT_OLDSTD)
3859	// withT = ! strat->homog;
3860
3861	// strat->posInT = posInT_pLength;
3862	kTest_TS(strat);
3863
3864	#ifdef HAVE_TAIL_RING
3865	// kStratInitChangeTailRing(strat);
3866	strat->tailRing=currRing;
3867	#endif
3868
3869	/* compute------------------------------------------------------- */
3870	while (strat->Ll >= 0)
3871	{
3872	#ifdef KDEBUG
3873	if (TEST_OPT_DEBUG) messageSets(strat);
3874	#endif
3875	if (strat->Ll== 0) strat->interpt=TRUE;
3876	if (TEST_OPT_DEGBOUND
3877	&& ((strat->honey && (strat->L[strat->Ll].ecart+currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))
3878	\|\| ((!strat->honey) && (currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))))
3879	{
3880	/*
3881	*stops computation if
3882	* 24 IN test and the degree +ecart of L[strat->Ll] is bigger then
3883	*a predefined number Kstd1_deg
3884	*/
3885	while ((strat->Ll >= 0)
3886	&& (strat->L[strat->Ll].p1!=NULL) && (strat->L[strat->Ll].p2!=NULL)
3887	&& ((strat->honey && (strat->L[strat->Ll].ecart+currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg))
3888	\|\| ((!strat->honey) && (currRing->pFDeg(strat->L[strat->Ll].p,currRing)>Kstd1_deg)))
3889	)
3890	deleteInL(strat->L,&strat->Ll,strat->Ll,strat);
3891	if (strat->Ll<0) break;
3892	else strat->noClearS=TRUE;
3893	}
3894	/* picks the last element from the lazyset L */
3895	strat->P = strat->L[strat->Ll];
3896	strat->Ll--;
3897
3898	if (pNext(strat->P.p) == strat->tail)
3899	{
3900	// deletes the short spoly
3901	pLmFree(strat->P.p);
3902	strat->P.p = NULL;
3903	poly m1 = NULL, m2 = NULL;
3904
3905	// check that spoly creation is ok
3906	while (strat->tailRing != currRing &&
3907	!kCheckSpolyCreation(&(strat->P), strat, m1, m2))
3908	{
3909	assume(m1 == NULL && m2 == NULL);
3910	// if not, change to a ring where exponents are at least
3911	// large enough
3912	kStratChangeTailRing(strat);
3913	}
3914	// create the real one
3915	ksCreateSpoly(&(strat->P), NULL, strat->use_buckets,
3916	strat->tailRing, m1, m2, strat->R);
3917	}
3918	else if (strat->P.p1 == NULL)
3919	{
3920	if (strat->minim > 0)
3921	strat->P.p2=p_Copy(strat->P.p, currRing, strat->tailRing);
3922	// for input polys, prepare reduction
3923	strat->P.PrepareRed(strat->use_buckets);
3924	}
3925
3926	poly qq;
3927
3928	/* here in the nonhomog case we shrink the new spoly */
3929
3930	if ( ! strat->homog)
3931	{
3932	strat->P.GetP(strat->lmBin); // because shifts are counted with .p structure
3933	/* in the nonhomog case we have to shrink the polynomial */
3934	qq = p_Shrink(strat->P.p, lV, currRing); // direct shrink
3935	if (qq != NULL)
3936	{
3937	/* we're here if Shrink is nonzero */
3938	strat->P.p = qq;
3939	strat->P.t_p = NULL;
3940	strat->P.GetP(strat->lmBin);
3941	// update sev and length
3942	strat->initEcart(&(strat->P));
3943	strat->P.sev = pGetShortExpVector(strat->P.p);
3944	// strat->P.FDeg = strat->P.pFDeg();
3945	// strat->P.length = strat->P.pLDeg();
3946	// strat->P.pLength =strat->P.GetpLength(); //pLength(strat->P.p);
3947	}
3948	else
3949	{
3950	/* Shrink is zero, like y(1)y(2) - y(1)y(3)*/
3951	#ifdef KDEBUG
3952	if (TEST_OPT_DEBUG){PrintS("nonzero s shrinks to 0\n");}
3953	#endif
3954	strat->P.p = NULL;
3955	strat->P.t_p = NULL;
3956	}
3957	}
3958	/* end shrinking poly in the nonhomog case */
3959
3960	if (strat->P.p == NULL && strat->P.t_p == NULL)
3961	{
3962	red_result = 0;
3963	}
3964	else
3965	{
3966	if (TEST_OPT_PROT)
3967	message((strat->honey ? strat->P.ecart : 0) + strat->P.pFDeg(),
3968	&olddeg,&reduc,strat, red_result);
3969
3970	/* reduction of the element chosen from L */
3971	red_result = strat->red(&strat->P,strat);
3972	}
3973
3974	// reduction to non-zero new poly
3975	if (red_result == 1)
3976	{
3977	/* statistic */
3978	if (TEST_OPT_PROT) PrintS("s");
3979
3980	// get the polynomial (canonicalize bucket, make sure P.p is set)
3981	strat->P.GetP(strat->lmBin);
3982
3983	int pos=posInS(strat,strat->sl,strat->P.p,strat->P.ecart);
3984
3985	// reduce the tail and normalize poly
3986	if (TEST_OPT_INTSTRATEGY)
3987	{
3988	strat->P.pCleardenom();
3989	if ((TEST_OPT_REDSB)\|\|(TEST_OPT_REDTAIL))
3990	{
3991	strat->P.p = redtailBba(&(strat->P),pos-1,strat, withT);
3992	strat->P.pCleardenom();
3993	}
3994	}
3995	else
3996	{
3997	strat->P.pNorm();
3998	if ((TEST_OPT_REDSB)\|\|(TEST_OPT_REDTAIL))
3999	strat->P.p = redtailBba(&(strat->P),pos-1,strat, withT);
4000	}
4001
4002	// here we must shrink again! and optionally reduce again
4003	// or build shrink into redtailBba!
4004
4005	#ifdef KDEBUG
4006	if (TEST_OPT_DEBUG){PrintS("new s:");strat->P.wrp();PrintLn();}
4007	#endif
4008
4009	// min_std stuff
4010	if ((strat->P.p1==NULL) && (strat->minim>0))
4011	{
4012	if (strat->minim==1)
4013	{
4014	strat->M->m[minimcnt]=p_Copy(strat->P.p,currRing,strat->tailRing);
4015	p_Delete(&strat->P.p2, currRing, strat->tailRing);
4016	}
4017	else
4018	{
4019	strat->M->m[minimcnt]=strat->P.p2;
4020	strat->P.p2=NULL;
4021	}
4022	if (strat->tailRing!=currRing && pNext(strat->M->m[minimcnt])!=NULL)
4023	pNext(strat->M->m[minimcnt])
4024	= strat->p_shallow_copy_delete(pNext(strat->M->m[minimcnt]),
4025	strat->tailRing, currRing,
4026	currRing->PolyBin);
4027	minimcnt++;
4028	}
4029
4030	/* here in the nonhomog case we shrink the reduced poly AGAIN */
4031
4032	if ( ! strat->homog)
4033	{
4034	strat->P.GetP(strat->lmBin); // because shifts are counted with .p structure
4035	/* in the nonhomog case we have to shrink the polynomial */
4036	if (strat->P.p!=NULL)
4037	{
4038	qq = p_Shrink(strat->P.p, lV, currRing); // direct shrink
4039	if (qq != NULL)
4040	{
4041	/* we're here if Shrink is nonzero */
4042	strat->P.p = qq; // is not set by Delete
4043	strat->P.t_p = NULL;
4044	strat->P.GetP(strat->lmBin);
4045	// update sev and length
4046	strat->initEcart(&(strat->P));
4047	strat->P.sev = pGetShortExpVector(strat->P.p);
4048	}
4049	else
4050	{
4051	/* Shrink is zero, like y(1)y(2) - y(1)y(3)*/
4052	#ifdef PDEBUG
4053	if (TEST_OPT_DEBUG){PrintS("nonzero s shrinks to 0");PrintLn();}
4054	#endif
4055	strat->P.p = NULL;
4056	strat->P.t_p = NULL;
4057	goto red_shrink2zero;
4058	}
4059	}
4060	else
4061	{
4062	qq = p_Shrink(strat->P.p, lV, currRing); // direct shrink
4063	if (qq != NULL)
4064	{
4065	/* we're here if Shrink is nonzero */
4066	strat->P.p = qq;
4067	strat->P.t_p = NULL;
4068	// update sev and length
4069	strat->initEcart(&(strat->P));
4070	strat->P.sev = pGetShortExpVector(strat->P.p);
4071	}
4072	else
4073	{
4074	/* Shrink is zero, like y(1)y(2) - y(1)y(3)*/
4075	#ifdef PDEBUG
4076	if (TEST_OPT_DEBUG){PrintS("nonzero s shrinks to 0");PrintLn();}
4077	#endif
4078	strat->P.p = NULL;
4079	strat->P.t_p = NULL;
4080	goto red_shrink2zero;
4081	}
4082	}
4083	}
4084	/* end shrinking poly AGAIN in the nonhomog case */
4085
4086
4087	// enter into S, L, and T
4088	//if ((!TEST_OPT_IDLIFT) \|\| (pGetComp(strat->P.p) <= strat->syzComp))
4089	// enterT(strat->P, strat); // this was here before Shift stuff
4090	//enterTShift(LObject p, kStrategy strat, int atT, int uptodeg, int lV); // syntax
4091	// the default value for atT = -1 as in bba
4092	/* strat->P.GetP(); */
4093	// because shifts are counted with .p structure // done before, but ?
4094	int atR=strat->tl+1; // enterTShift introduces T[tl+1], T[tl+2]...
4095	// with T[tl+1]=P.p
4096	enterTShift(strat->P,strat,-1,uptodeg, lV);
4097	enterpairsShift(strat->P.p,strat->sl,strat->P.ecart,pos,strat, atR,uptodeg,lV);
4098	// enterpairsShift(vw,strat->sl,strat->P.ecart,pos,strat, strat->tl,uptodeg,lV);
4099	// posInS only depends on the leading term
4100	strat->enterS(strat->P, pos, strat, atR);
4101
4102	if (hilb!=NULL) khCheck(Q,w,hilb,hilbeledeg,hilbcount,strat);
4103	// Print("[%d]",hilbeledeg);
4104	kDeleteLcm(&strat->P);
4105	}
4106	else
4107	{
4108	red_shrink2zero:
4109	if (strat->P.p1 == NULL && strat->minim > 0)
4110	{
4111	p_Delete(&strat->P.p2, currRing, strat->tailRing);
4112	}
4113	}
4114	#ifdef KDEBUG
4115	memset(&(strat->P), 0, sizeof(strat->P));
4116	#endif
4117	kTest_TS(strat);
4118	}
4119	#ifdef KDEBUG
4120	if (TEST_OPT_DEBUG) messageSets(strat);
4121	#endif
4122	/* complete reduction of the standard basis--------- */
4123	/* shift case: look for elt's in S such that they are divisible by elt in T */
4124	// if (TEST_OPT_SB_1)
4125	if (TEST_OPT_REDSB)
4126	{
4127	int k=0;
4128	int j=-1;
4129	while(k<=strat->sl)
4130	{
4131	// loop
4132	// {
4133	// if (j>=k) break;
4134	// clearS(strat->S[j],strat->sevS[j],&k,&j,strat);
4135	// j++;
4136	// }
4137	LObject Ln (strat->S[k],currRing, strat->tailRing);
4138	Ln.SetShortExpVector();
4139	j = kFindDivisibleByInT(strat, &Ln, j+1);
4140	if (j<0) { k++; j=-1;}
4141	else
4142	{
4143	if ( pLmCmp(strat->S[k],strat->T[j].p) == 0)
4144	{
4145	j = kFindDivisibleByInT(strat, &Ln, j+1);
4146	if (j<0) { k++; j=-1;}
4147	else
4148	{
4149	deleteInS(k,strat);
4150	}
4151	}
4152	else
4153	{
4154	deleteInS(k,strat);
4155	}
4156	}
4157	}
4158	}
4159
4160	if (TEST_OPT_REDSB)
4161	{ completeReduce(strat, TRUE); //shift: withT = TRUE
4162	if (strat->completeReduce_retry)
4163	{
4164	// completeReduce needed larger exponents, retry
4165	// to reduce with S (instead of T)
4166	// and in currRing (instead of strat->tailRing)
4167	#ifdef HAVE_TAIL_RING
4168	if(currRing->bitmask>strat->tailRing->bitmask)
4169	{
4170	strat->completeReduce_retry=FALSE;
4171	cleanT(strat);strat->tailRing=currRing;
4172	int i;
4173	for(i=strat->sl;i>=0;i--) strat->S_2_R[i]=-1;
4174	completeReduce(strat);
4175	}
4176	if (strat->completeReduce_retry)
4177	#endif
4178	Werror("exponent bound is %ld",currRing->bitmask);
4179	}
4180	}
4181	else if (TEST_OPT_PROT) PrintLn();
4182
4183	/* release temp data-------------------------------- */
4184	exitBuchMora(strat);
4185	// if (TEST_OPT_WEIGHTM)
4186	// {
4187	// pRestoreDegProcs(currRing,pFDegOld, pLDegOld);
4188	// if (ecartWeights)
4189	// {
4190	// omFreeSize((ADDRESS)ecartWeights,((currRing->N)+1)*sizeof(short));
4191	// ecartWeights=NULL;
4192	// }
4193	// }
4194	if (TEST_OPT_PROT) messageStat(hilbcount,strat);
4195	if (Q!=NULL) updateResult(strat->Shdl,Q,strat);
4196	return (strat->Shdl);
4197	}
4198
4199
4200	ideal freegb(ideal I, int uptodeg, int lVblock)
4201	{
4202	/* todo main call */
4203
4204	/* assume: ring is prepared, ideal is copied into shifted ring */
4205	/* uptodeg and lVblock are correct - test them! */
4206
4207	/* check whether the ideal is in V */
4208
4209	// if (0)
4210	if (! ideal_isInV(I,lVblock) )
4211	{
4212	WerrorS("The input ideal contains incorrectly encoded elements! ");
4213	return(NULL);
4214	}
4215
4216	// kStrategy strat = new skStrategy;
4217	/* ideal bbaShift(ideal F, ideal Q,intvec w,intvec hilb,kStrategy strat, int uptodeg, int lV) */
4218	/* at the moment:
4219	- no quotient (check)
4220	- no w, no hilb
4221	*/
4222	/* ideal F, ideal Q, tHomog h,intvec ** w, intvec *hilb,int syzComp,
4223	int newIdeal, intvec vw) /
4224	ideal RS = kStdShift(I,NULL, testHomog, NULL,NULL,0,0,NULL, uptodeg, lVblock);
4225	//bbaShift(I,NULL, NULL, NULL, strat, uptodeg, lVblock);
4226	idSkipZeroes(RS);
4227	return(RS);
4228	}
4229
4230	/*2
4231	*reduces h with elements from T choosing the first possible
4232	* element in t with respect to the given pDivisibleBy
4233	*/
4234	int redFirstShift (LObject* h,kStrategy strat)
4235	{
4236	if (h->IsNull()) return 0;
4237
4238	int at, reddeg,d;
4239	int pass = 0;
4240	int j = 0;
4241
4242	if (! strat->homog)
4243	{
4244	d = h->GetpFDeg() + h->ecart;
4245	reddeg = strat->LazyDegree+d;
4246	}
4247	h->SetShortExpVector();
4248	loop
4249	{
4250	j = kFindDivisibleByInT(strat, h);
4251	if (j < 0)
4252	{
4253	h->SetDegStuffReturnLDeg(strat->LDegLast);
4254	return 1;
4255	}
4256
4257	if (!TEST_OPT_INTSTRATEGY)
4258	strat->T[j].pNorm();
4259	#ifdef KDEBUG
4260	if (TEST_OPT_DEBUG)
4261	{
4262	PrintS("reduce ");
4263	h->wrp();
4264	PrintS(" with ");
4265	strat->T[j].wrp();
4266	}
4267	#endif
4268	ksReducePoly(h, &(strat->T[j]), strat->kNoetherTail(), NULL, strat);
4269	if (!h->IsNull())
4270	{
4271	poly qq=p_Shrink(h->GetP(),strat->lV,currRing);
4272	h->p=qq;
4273	h->t_p=NULL;
4274	}
4275
4276	#ifdef KDEBUG
4277	if (TEST_OPT_DEBUG)
4278	{
4279	PrintS("\nto ");
4280	wrp(h->p);
4281	PrintLn();
4282	}
4283	#endif
4284	if (h->IsNull())
4285	{
4286	kDeleteLcm(h);
4287	h->Clear();
4288	return 0;
4289	}
4290	h->SetShortExpVector();
4291
4292	#if 0
4293	if ((strat->syzComp!=0) && !strat->honey)
4294	{
4295	if ((strat->syzComp>0) &&
4296	(h->Comp() > strat->syzComp))
4297	{
4298	assume(h->MinComp() > strat->syzComp);
4299	#ifdef KDEBUG
4300	if (TEST_OPT_DEBUG) PrintS(" > syzComp\n");
4301	#endif
4302	if (strat->homog)
4303	h->SetDegStuffReturnLDeg(strat->LDegLast);
4304	return -2;
4305	}
4306	}
4307	#endif
4308	if (!strat->homog)
4309	{
4310	if (!TEST_OPT_OLDSTD && strat->honey)
4311	{
4312	h->SetpFDeg();
4313	if (strat->T[j].ecart <= h->ecart)
4314	h->ecart = d - h->GetpFDeg();
4315	else
4316	h->ecart = d - h->GetpFDeg() + strat->T[j].ecart - h->ecart;
4317
4318	d = h->GetpFDeg() + h->ecart;
4319	}
4320	else
4321	d = h->SetDegStuffReturnLDeg(strat->LDegLast);
4322	/- try to reduce the s-polynomial -/
4323	pass++;
4324	/*
4325	*test whether the polynomial should go to the lazyset L
4326	*-if the degree jumps
4327	*-if the number of pre-defined reductions jumps
4328	*/
4329	if (!TEST_OPT_REDTHROUGH && (strat->Ll >= 0)
4330	&& ((d >= reddeg) \|\| (pass > strat->LazyPass)))
4331	{
4332	h->SetLmCurrRing();
4333	if (strat->posInLDependsOnLength)
4334	h->SetLength(strat->length_pLength);
4335	at = strat->posInL(strat->L,strat->Ll,h,strat);
4336	if (at <= strat->Ll)
4337	{
4338	//int dummy=strat->sl;
4339	/* if (kFindDivisibleByInS(strat,&dummy, h) < 0) */
4340	//if (kFindDivisibleByInT(strat->T,strat->sevT, dummy, h) < 0)
4341	if (kFindDivisibleByInT(strat, h) < 0)
4342	return 1;
4343	enterL(&strat->L,&strat->Ll,&strat->Lmax,*h,at);
4344	#ifdef KDEBUG
4345	if (TEST_OPT_DEBUG) Print(" degree jumped; ->L%d\n",at);
4346	#endif
4347	h->Clear();
4348	return -1;
4349	}
4350	}
4351	if ((TEST_OPT_PROT) && (strat->Ll < 0) && (d >= reddeg))
4352	{
4353	reddeg = d+1;
4354	Print(".%d",d);mflush();
4355	}
4356	}
4357	}
4358	}
4359
4360	void initBbaShift(kStrategy strat)
4361	{
4362	/* setting global variables ------------------- */
4363	strat->enterS = enterSBba; /* remains as is, we change enterT! */
4364
4365	strat->red = redFirstShift; /* no redHomog ! */
4366
4367	if (currRing->pLexOrder && strat->honey)
4368	strat->initEcart = initEcartNormal;
4369	else
4370	strat->initEcart = initEcartBBA;
4371	if (strat->honey)
4372	strat->initEcartPair = initEcartPairMora;
4373	else
4374	strat->initEcartPair = initEcartPairBba;
4375	// if ((TEST_OPT_WEIGHTM)&&(F!=NULL))
4376	// {
4377	// //interred machen Aenderung
4378	// pFDegOld=currRing->pFDeg;
4379	// pLDegOld=pLDeg;
4380	// //h=ggetid("ecart");
4381	// //if ((h!=NULL) /&& (IDTYP(h)==INTVEC_CMD)/)
4382	// //{
4383	// // ecartWeights=iv2array(IDINTVEC(h));
4384	// //}
4385	// //else
4386	// {
4387	// ecartWeights=(short )omAlloc(((currRing->N)+1)sizeof(short));
4388	// /uses automatic computation of the ecartWeights to set them/
4389	// kEcartWeights(F->m,IDELEMS(F)-1,ecartWeights,currRing);
4390	// }
4391	// pRestoreDegProcs(currRing,totaldegreeWecart, maxdegreeWecart);
4392	// if (TEST_OPT_PROT)
4393	// {
4394	// for(int i=1; i<=rVar(currRing); i++)
4395	// Print(" %d",ecartWeights[i]);
4396	// PrintLn();
4397	// mflush();
4398	// }
4399	// }
4400	}
4401	#endif

Note: See TracBrowser for help on using the repository browser.

Download in other formats: