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source: git/factory/facAbsBiFact.cc @ c13ebd

spielwiese

Last change on this file since c13ebd was c13ebd, checked in by Hans Schoenemann <hannes@…>, 3 years ago
factory: discriminant from FLINT
Property mode set to `100644`
File size: 21.0 KB

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1	/*****************************************************************************\
2	* Computer Algebra System SINGULAR
3	\*****************************************************************************/
4	/** @file facAbsBiFact.cc
5	*
6	* @author Martin Lee
7	*
8	**/
9	/*****************************************************************************/
10
11
12	#include "config.h"
13
14
15	#include "timing.h"
16	#include "debug.h"
17
18	#include "facAbsBiFact.h"
19	#include "facBivar.h"
20	#include "facFqBivar.h"
21	#include "cf_reval.h"
22	#include "cf_primes.h"
23	#include "cf_algorithm.h"
24	#ifdef HAVE_FLINT
25	#include "FLINTconvert.h"
26	#include <flint/fmpz_poly_factor.h>
27	#endif
28	#ifdef HAVE_NTL
29	#include "NTLconvert.h"
30	#include <NTL/LLL.h>
31	#endif
32
33	#if defined(HAVE_NTL) \|\| defined(HAVE_FLINT)
34	TIMING_DEFINE_PRINT(fac_Qa_factorize)
35	TIMING_DEFINE_PRINT(fac_evalpoint)
36
37	CFAFList uniAbsFactorize (const CanonicalForm& F, bool full)
38	{
39	CFAFList result;
40	if (degree (F) == 1)
41	{
42	bool isRat= isOn (SW_RATIONAL);
43	On (SW_RATIONAL);
44	result= CFAFList (CFAFactor (F/Lc(F), 1, 1));
45	result.insert (CFAFactor (Lc (F), 1, 1));
46	if (!isRat)
47	Off (SW_RATIONAL);
48	return result;
49	}
50	CanonicalForm LcF= 1;
51	Variable alpha;
52	CFFList QaFactors;
53	CFFListIterator iter;
54	alpha= rootOf (F);
55	QaFactors= factorize (F, alpha);
56	iter= QaFactors;
57	if (iter.getItem().factor().inCoeffDomain())
58	{
59	LcF = iter.getItem().factor();
60	iter++;
61	}
62	for (;iter.hasItem(); iter++)
63	{
64	if (full)
65	result.append (CFAFactor (iter.getItem().factor(), getMipo (alpha),
66	iter.getItem().exp()));
67	if (!full && degree (iter.getItem().factor()) == 1)
68	{
69	result.append (CFAFactor (iter.getItem().factor(), getMipo (alpha),
70	iter.getItem().exp()));
71	break;
72	}
73	}
74	result.insert (CFAFactor (LcF, 1, 1));
75	return result;
76	}
77
78	//TODO optimize choice of p -> choose p as large as possible (better than small p since factorization mod p does not require field extension, also less lifting)
79	int
80	choosePoint (const CanonicalForm& F, int tdegF, CFArray& eval, bool rec,
81	int absValue)
82	{
83	REvaluation E1 (1, 1, IntRandom (absValue));
84	REvaluation E2 (2, 2, IntRandom (absValue));
85	if (rec)
86	{
87	E1.nextpoint();
88	E2.nextpoint();
89	}
90
91	CanonicalForm f, f1, f2, Fp;
92	int i, p;
93	CFFList f1Factors, f2Factors;
94	CFFListIterator iter;
95	int count= 0;
96	while (1)
97	{
98	count++;
99	f1= E1 (F);
100	if (!f1.isZero() && degree (f1) == degree (F,2))
101	{
102	f1Factors= factorize (f1);
103	if (f1Factors.getFirst().factor().inCoeffDomain())
104	f1Factors.removeFirst();
105	if (f1Factors.length() == 1 && f1Factors.getFirst().exp() == 1)
106	{
107	f= E2(f1);
108	f2= E2 (F);
109	f2Factors= factorize (f2);
110	Off (SW_RATIONAL);
111	if (f2Factors.getFirst().factor().inCoeffDomain())
112	f2Factors.removeFirst();
113	if (f2Factors.length() == 1 && f2Factors.getFirst().exp() == 1)
114	{
115	#ifdef HAVE_FLINT
116	// init
117	fmpz_t FLINTD1,FLINTD2;
118	fmpz_init(FLINTD1);
119	fmpz_init(FLINTD2);
120	fmpz_poly_t FLINTf1;
121	fmpz_poly_t FLINTf2;
122	// conversion
123	convertFacCF2Fmpz_poly_t(FLINTf1,f1);
124	convertFacCF2Fmpz_poly_t(FLINTf2,f2);
125	// discriminant
126	fmpz_poly_discriminant(FLINTD1,FLINTf1);
127	fmpz_poly_discriminant(FLINTD2,FLINTf2);
128	// conversion
129	CanonicalForm D1= convertFmpz2CF(FLINTD1);
130	CanonicalForm D2= convertFmpz2CF(FLINTD2);
131	// clean up
132	fmpz_poly_clear(FLINTf1);
133	fmpz_poly_clear(FLINTf2);
134	fmpz_clear(FLINTD1);
135	fmpz_clear(FLINTD2);
136	#elif defined(HAVE_NTL)
137	ZZX NTLf1= convertFacCF2NTLZZX (f1);
138	ZZX NTLf2= convertFacCF2NTLZZX (f2);
139	ZZ NTLD1= discriminant (NTLf1);
140	ZZ NTLD2= discriminant (NTLf2);
141	CanonicalForm D1= convertZZ2CF (NTLD1);
142	CanonicalForm D2= convertZZ2CF (NTLD2);
143	#endif
144	if ((!f.isZero()) &&
145	(abs(f)>cf_getSmallPrime (cf_getNumSmallPrimes()-1)))
146	{
147	for (i= cf_getNumPrimes()-1; i >= 0; i--)
148	{
149	if (f % CanonicalForm (cf_getPrime (i)) == 0)
150	{
151	p= cf_getPrime(i);
152	Fp= mod (F,p);
153	if (totaldegree (Fp) == tdegF &&
154	degree (mod (f2,p), 1) == degree (F,1) &&
155	degree (mod (f1, p),2) == degree (F,2))
156	{
157	if (mod (D1, p) != 0 && mod (D2, p) != 0)
158	{
159	eval[0]= E1[1];
160	eval[1]= E2[2];
161	return p;
162	}
163	}
164	}
165	}
166	}
167	else if (!f.isZero())
168	{
169	for (i= cf_getNumSmallPrimes()-1; i >= 0; i--)
170	{
171	if (f % CanonicalForm (cf_getSmallPrime (i)) == 0)
172	{
173	p= cf_getSmallPrime (i);
174	Fp= mod (F,p);
175	if (totaldegree (Fp) == tdegF &&
176	degree (mod (f2, p),1) == degree (F,1) &&
177	degree (mod (f1,p),2) == degree (F,2))
178	{
179	if (mod (D1, p) != 0 && mod (D2, p) != 0)
180	{
181	eval[0]= E1[1];
182	eval[1]= E2[2];
183	return p;
184	}
185	}
186	}
187	}
188	}
189	}
190	E2.nextpoint();
191	On (SW_RATIONAL);
192	}
193	}
194	E1.nextpoint();
195	if (count == 2)
196	{
197	count= 0;
198	absValue++;
199	E1=REvaluation (1, 1, IntRandom (absValue));
200	E2=REvaluation (2, 2, IntRandom (absValue));
201	E1.nextpoint();
202	E2.nextpoint();
203	}
204	}
205	return 0;
206	}
207
208	#ifdef HAVE_NTL
209	//G is assumed to be bivariate, irreducible over Q, primitive wrt x and y, compressed
210	CFAFList absBiFactorizeMain (const CanonicalForm& G, bool full)
211	{
212	CanonicalForm F= bCommonDen (G)*G;
213	bool isRat= isOn (SW_RATIONAL);
214	Off (SW_RATIONAL);
215	F /= icontent (F);
216	On (SW_RATIONAL);
217
218	mpz_t * M=new mpz_t [4];
219	mpz_init (M[0]);
220	mpz_init (M[1]);
221	mpz_init (M[2]);
222	mpz_init (M[3]);
223
224	mpz_t * S=new mpz_t [2];
225	mpz_init (S[0]);
226	mpz_init (S[1]);
227
228	F= compress (F, M, S);
229
230	if (F.isUnivariate())
231	{
232	if (degree (F) == 1)
233	{
234	mpz_clear (M[0]);
235	mpz_clear (M[1]);
236	mpz_clear (M[2]);
237	mpz_clear (M[3]);
238	delete [] M;
239
240	mpz_clear (S[0]);
241	mpz_clear (S[1]);
242	delete [] S;
243	if (!isRat)
244	Off (SW_RATIONAL);
245	return CFAFList (CFAFactor (G, 1, 1));
246	}
247	CFAFList result= uniAbsFactorize (F, full);
248	if (result.getFirst().factor().inCoeffDomain())
249	result.removeFirst();
250	for (CFAFListIterator iter=result; iter.hasItem(); iter++)
251	iter.getItem()= CFAFactor (decompress (iter.getItem().factor(), M, S),
252	iter.getItem().minpoly(),iter.getItem().exp());
253	mpz_clear (M[0]);
254	mpz_clear (M[1]);
255	mpz_clear (M[2]);
256	mpz_clear (M[3]);
257	delete [] M;
258
259	mpz_clear (S[0]);
260	mpz_clear (S[1]);
261	delete [] S;
262	if (!isRat)
263	Off (SW_RATIONAL);
264	return result;
265	}
266
267	if (degree (F, 1) == 1 \|\| degree (F, 2) == 1)
268	{
269	mpz_clear (M[0]);
270	mpz_clear (M[1]);
271	mpz_clear (M[2]);
272	mpz_clear (M[3]);
273	delete [] M;
274
275	mpz_clear (S[0]);
276	mpz_clear (S[1]);
277	delete [] S;
278	if (!isRat)
279	Off (SW_RATIONAL);
280	return CFAFList (CFAFactor (G, 1, 1));
281	}
282	int minTdeg, tdegF= totaldegree (F);
283	CanonicalForm Fp, smallestFactor;
284	int p;
285	CFFList factors;
286	Variable alpha;
287	bool rec= false;
288	Variable x= Variable (1);
289	Variable y= Variable (2);
290	CanonicalForm bufF= F;
291	CFFListIterator iter;
292	CFArray eval= CFArray (2);
293	int absValue= 1;
294	differentevalpoint:
295	while (1)
296	{
297	TIMING_START (fac_evalpoint);
298	p= choosePoint (F, tdegF, eval, rec, absValue);
299	TIMING_END_AND_PRINT (fac_evalpoint, "time to find eval point: ");
300
301	//after here isOn (SW_RATIONAL)==false
302	setCharacteristic (p);
303	Fp=F.mapinto();
304	factors= factorize (Fp);
305
306	if (factors.getFirst().factor().inCoeffDomain())
307	factors.removeFirst();
308
309	if (factors.length() == 1 && factors.getFirst().exp() == 1)
310	{
311	if (absIrredTest (Fp))
312	{
313	if (isRat)
314	On (SW_RATIONAL);
315	setCharacteristic(0);
316	mpz_clear (M[0]);
317	mpz_clear (M[1]);
318	mpz_clear (M[2]);
319	mpz_clear (M[3]);
320	delete [] M;
321
322	mpz_clear (S[0]);
323	mpz_clear (S[1]);
324	delete [] S;
325	return CFAFList (CFAFactor (G, 1, 1));
326	}
327	else
328	{
329	setCharacteristic (0);
330	if (modularIrredTestWithShift (F))
331	{
332	if (isRat)
333	On (SW_RATIONAL);
334	mpz_clear (M[0]);
335	mpz_clear (M[1]);
336	mpz_clear (M[2]);
337	mpz_clear (M[3]);
338	delete [] M;
339
340	mpz_clear (S[0]);
341	mpz_clear (S[1]);
342	delete [] S;
343	return CFAFList (CFAFactor (G, 1, 1));
344	}
345	rec= true;
346	continue;
347	}
348	}
349	iter= factors;
350	smallestFactor= iter.getItem().factor();
351	while (smallestFactor.isUnivariate() && iter.hasItem())
352	{
353	iter++;
354	if (!iter.hasItem())
355	break;
356	smallestFactor= iter.getItem().factor();
357	}
358
359	minTdeg= totaldegree (smallestFactor);
360	if (iter.hasItem())
361	iter++;
362	for (; iter.hasItem(); iter++)
363	{
364	if (!iter.getItem().factor().isUnivariate() &&
365	(totaldegree (iter.getItem().factor()) < minTdeg))
366	{
367	smallestFactor= iter.getItem().factor();
368	minTdeg= totaldegree (smallestFactor);
369	}
370	}
371	if (tdegF % minTdeg == 0)
372	break;
373	setCharacteristic(0);
374	rec=true;
375	}
376	CanonicalForm Gp= Fp/smallestFactor;
377	Gp= Gp /Lc (Gp);
378
379	CanonicalForm Gpy= Gp (eval[0].mapinto(), 1);
380	CanonicalForm smallestFactorEvaly= smallestFactor (eval[0].mapinto(),1);
381	CanonicalForm Gpx= Gp (eval[1].mapinto(), 2);
382	CanonicalForm smallestFactorEvalx= smallestFactor (eval[1].mapinto(),2);
383
384	bool xValid= !(Gpx.inCoeffDomain() \|\| smallestFactorEvalx.inCoeffDomain() \|\|
385	!gcd (Gpx, smallestFactorEvalx).inCoeffDomain());
386	bool yValid= !(Gpy.inCoeffDomain() \|\| smallestFactorEvaly.inCoeffDomain() \|\|
387	!gcd (Gpy, smallestFactorEvaly).inCoeffDomain());
388	if (!xValid \|\| !yValid)
389	{
390	rec= true;
391	setCharacteristic (0);
392	goto differentevalpoint;
393	}
394
395	setCharacteristic (0);
396
397	CanonicalForm mipo;
398
399	CFArray mipos= CFArray (2);
400	CFFList mipoFactors;
401	for (int i= 1; i < 3; i++)
402	{
403	CanonicalForm Fi= F(eval[i-1],i);
404
405	int s= tdegF/minTdeg + 1;
406	CanonicalForm bound= power (maxNorm (Fi), 2*(s-1));
407	bound *= power (CanonicalForm (s),s-1);
408	bound = power (CanonicalForm (2), ((s-1)(s-1))/2); //possible int overflow
409
410	CanonicalForm B = p;
411	long k = 1L;
412	while ( B < bound ) {
413	B *= p;
414	k++;
415	}
416
417	//TODO take floor (log2(k))
418	k= k+1;
419	#ifdef HAVE_FLINT
420	fmpz_poly_t FLINTFi;
421	convertFacCF2Fmpz_poly_t (FLINTFi, Fi);
422	setCharacteristic (p);
423	nmod_poly_t FLINTFpi, FLINTGpi;
424	if (i == 2)
425	{
426	convertFacCF2nmod_poly_t (FLINTFpi,
427	smallestFactorEvalx/lc (smallestFactorEvalx));
428	convertFacCF2nmod_poly_t (FLINTGpi, Gpx/lc (Gpx));
429	}
430	else
431	{
432	convertFacCF2nmod_poly_t (FLINTFpi,
433	smallestFactorEvaly/lc (smallestFactorEvaly));
434	convertFacCF2nmod_poly_t (FLINTGpi, Gpy/lc (Gpy));
435	}
436	nmod_poly_factor_t nmodFactors;
437	nmod_poly_factor_init (nmodFactors);
438	nmod_poly_factor_insert (nmodFactors, FLINTFpi, 1L);
439	nmod_poly_factor_insert (nmodFactors, FLINTGpi, 1L);
440
441	// the following fix is due to interface changes from FLINT 2.3 -> FLINT 2.4
442	# ifndef slong
443	# define slong long
444	# endif
445
446	slong * link= new slong [2];
447	fmpz_poly_t *v= new fmpz_poly_t[2];
448	fmpz_poly_t *w= new fmpz_poly_t[2];
449	fmpz_poly_init(v[0]);
450	fmpz_poly_init(v[1]);
451	fmpz_poly_init(w[0]);
452	fmpz_poly_init(w[1]);
453
454	fmpz_poly_factor_t liftedFactors;
455	fmpz_poly_factor_init (liftedFactors);
456	_fmpz_poly_hensel_start_lift (liftedFactors, link, v, w, FLINTFi,
457	nmodFactors, k);
458
459	nmod_poly_factor_clear (nmodFactors);
460	nmod_poly_clear (FLINTFpi);
461	nmod_poly_clear (FLINTGpi);
462
463	setCharacteristic(0);
464	CanonicalForm liftedSmallestFactor=
465	convertFmpz_poly_t2FacCF ((fmpz_poly_t &)liftedFactors->p[0],x);
466
467	CanonicalForm otherFactor=
468	convertFmpz_poly_t2FacCF ((fmpz_poly_t &)liftedFactors->p[1],x);
469	modpk pk= modpk (p, k);
470	#else
471	modpk pk= modpk (p, k);
472	ZZX NTLFi=convertFacCF2NTLZZX (pk (Fi*pk.inverse (lc(Fi))));
473	setCharacteristic (p);
474
475	if (fac_NTL_char != p)
476	{
477	fac_NTL_char= p;
478	zz_p::init (p);
479	}
480	zz_pX NTLFpi, NTLGpi;
481	if (i == 2)
482	{
483	NTLFpi=convertFacCF2NTLzzpX (smallestFactorEvalx/lc(smallestFactorEvalx));
484	NTLGpi=convertFacCF2NTLzzpX (Gpx/lc (Gpx));
485	}
486	else
487	{
488	NTLFpi=convertFacCF2NTLzzpX (smallestFactorEvaly/lc(smallestFactorEvaly));
489	NTLGpi=convertFacCF2NTLzzpX (Gpy/lc (Gpy));
490	}
491	vec_zz_pX modFactors;
492	modFactors.SetLength(2);
493	modFactors[0]= NTLFpi;
494	modFactors[1]= NTLGpi;
495	vec_ZZX liftedFactors;
496	MultiLift (liftedFactors, modFactors, NTLFi, (long) k);
497	setCharacteristic(0);
498	CanonicalForm liftedSmallestFactor=
499	convertNTLZZX2CF (liftedFactors[0], x);
500
501	CanonicalForm otherFactor=
502	convertNTLZZX2CF (liftedFactors[1], x);
503	#endif
504
505	Off (SW_SYMMETRIC_FF);
506	liftedSmallestFactor= pk (liftedSmallestFactor);
507	if (i == 2)
508	liftedSmallestFactor= liftedSmallestFactor (eval[0],1);
509	else
510	liftedSmallestFactor= liftedSmallestFactor (eval[1],1);
511
512	On (SW_SYMMETRIC_FF);
513	CFMatrix *M= new CFMatrix (s, s);
514	(*M)(s,s)= power (CanonicalForm (p), k);
515	for (int j= 1; j < s; j++)
516	{
517	(*M) (j,j)= 1;
518	(*M) (j+1,j)= -liftedSmallestFactor;
519	}
520
521	mat_ZZ * NTLM= convertFacCFMatrix2NTLmat_ZZ (*M);
522
523	ZZ det;
524
525	transpose (NTLM, NTLM);
526	(void) LLL (det, *NTLM, 1L, 1L); //use floating point LLL ?
527	transpose (NTLM, NTLM);
528	delete M;
529	M= convertNTLmat_ZZ2FacCFMatrix (*NTLM);
530	delete NTLM;
531
532	mipo= 0;
533	for (int j= 1; j <= s; j++)
534	mipo += (M) (j,1)power (x,s-j);
535
536	delete M;
537	mipoFactors= factorize (mipo);
538	if (mipoFactors.getFirst().factor().inCoeffDomain())
539	mipoFactors.removeFirst();
540
541	#ifdef HAVE_FLINT
542	fmpz_poly_clear (v[0]);
543	fmpz_poly_clear (v[1]);
544	fmpz_poly_clear (w[0]);
545	fmpz_poly_clear (w[1]);
546	delete [] v;
547	delete [] w;
548	delete [] link;
549	fmpz_poly_factor_clear (liftedFactors);
550	#endif
551
552	if (mipoFactors.length() > 1 \|\|
553	(mipoFactors.length() == 1 && mipoFactors.getFirst().exp() > 1) \|\|
554	mipo.inCoeffDomain())
555	{
556	rec=true;
557	goto differentevalpoint;
558	}
559	else
560	mipos[i-1]= mipo;
561	}
562
563	if (degree (mipos[0]) != degree (mipos[1]))
564	{
565	rec=true;
566	goto differentevalpoint;
567	}
568
569	On (SW_RATIONAL);
570	if (maxNorm (mipos[0]) < maxNorm (mipos[1]))
571	alpha= rootOf (mipos[0]);
572	else
573	alpha= rootOf (mipos[1]);
574
575	int wrongMipo= 0;
576
577	Variable beta;
578	if (maxNorm (mipos[0]) < maxNorm (mipos[1]))
579	{
580	mipoFactors= factorize (mipos[1], alpha);
581	if (mipoFactors.getFirst().factor().inCoeffDomain())
582	mipoFactors.removeFirst();
583	for (iter= mipoFactors; iter.hasItem(); iter++)
584	{
585	if (degree (iter.getItem().factor()) > 1)
586	wrongMipo++;
587	}
588	if (wrongMipo == mipoFactors.length())
589	{
590	rec=true;
591	goto differentevalpoint;
592	}
593	wrongMipo= 0;
594	beta= rootOf (mipos[1]);
595	mipoFactors= factorize (mipos[0], beta);
596	if (mipoFactors.getFirst().factor().inCoeffDomain())
597	mipoFactors.removeFirst();
598	for (iter= mipoFactors; iter.hasItem(); iter++)
599	{
600	if (degree (iter.getItem().factor()) > 1)
601	wrongMipo++;
602	}
603	if (wrongMipo == mipoFactors.length())
604	{
605	rec=true;
606	goto differentevalpoint;
607	}
608	}
609	else
610	{
611	mipoFactors= factorize (mipos[0], alpha);
612	if (mipoFactors.getFirst().factor().inCoeffDomain())
613	mipoFactors.removeFirst();
614	for (iter= mipoFactors; iter.hasItem(); iter++)
615	{
616	if (degree (iter.getItem().factor()) > 1)
617	wrongMipo++;
618	}
619	if (wrongMipo == mipoFactors.length())
620	{
621	rec=true;
622	goto differentevalpoint;
623	}
624	wrongMipo= 0;
625	beta= rootOf (mipos[0]);
626	mipoFactors= factorize (mipos[1], beta);
627	if (mipoFactors.getFirst().factor().inCoeffDomain())
628	mipoFactors.removeFirst();
629	for (iter= mipoFactors; iter.hasItem(); iter++)
630	{
631	if (degree (iter.getItem().factor()) > 1)
632	wrongMipo++;
633	}
634	if (wrongMipo == mipoFactors.length())
635	{
636	rec=true;
637	goto differentevalpoint;
638	}
639	}
640
641
642	CanonicalForm F1;
643	if (degree (F,1) > minTdeg)
644	F1= F (eval[1], 2);
645	else
646	F1= F (eval[0], 1);
647
648	CFFList QaF1Factors;
649	bool swap= false;
650	if (F1.level() == 2)
651	{
652	swap= true;
653	F1=swapvar (F1, x, y);
654	F= swapvar (F, x, y);
655	}
656
657	wrongMipo= 0;
658	QaF1Factors= factorize (F1, alpha);
659	if (QaF1Factors.getFirst().factor().inCoeffDomain())
660	QaF1Factors.removeFirst();
661	for (iter= QaF1Factors; iter.hasItem(); iter++)
662	{
663	if (degree (iter.getItem().factor()) > minTdeg)
664	wrongMipo++;
665	}
666
667	if (wrongMipo == QaF1Factors.length())
668	{
669	rec= true;
670	F= bufF;
671	goto differentevalpoint;
672	}
673
674	CanonicalForm evaluation;
675	if (swap)
676	evaluation= eval[0];
677	else
678	evaluation= eval[1];
679
680	F *= bCommonDen (F);
681	F= F (y + evaluation, y);
682
683	int liftBound= degree (F,y) + 1;
684
685	modpk b= modpk();
686
687	CanonicalForm den= 1;
688
689	mipo= getMipo (alpha);
690
691	CFList uniFactors;
692	for (iter=QaF1Factors; iter.hasItem(); iter++)
693	uniFactors.append (iter.getItem().factor());
694
695	F /= Lc (F1);
696	#ifdef HAVE_FLINT
697	// init
698	fmpz_t FLINTf,FLINTD;
699	fmpz_init(FLINTf);
700	fmpz_init(FLINTD);
701	fmpz_poly_t FLINTmipo;
702	fmpz_poly_t FLINTLcf;
703	//conversion
704	convertFacCF2Fmpz_poly_t(FLINTmipo,mipo);
705	convertFacCF2Fmpz_poly_t(FLINTLcf,Lc (F*bCommonDen (F)));
706	// resultant, discriminant
707	fmpz_poly_resultant(FLINTf,FLINTmipo,FLINTLcf);
708	fmpz_poly_discriminant(FLINTD,FLINTmipo);
709	fmpz_mul(FLINTf,FLINTD,FLINTf);
710	den= abs (convertFmpz2CF(FLINTf));
711	// clean up
712	fmpz_clear(FLINTf);
713	// FLINTD is used below
714	fmpz_poly_clear(FLINTLcf);
715	fmpz_poly_clear(FLINTmipo);
716	#elif defined(HAVE_NTL)
717	ZZX NTLmipo= convertFacCF2NTLZZX (mipo);
718	ZZX NTLLcf= convertFacCF2NTLZZX (Lc (F*bCommonDen (F)));
719	ZZ NTLf= resultant (NTLmipo, NTLLcf);
720	ZZ NTLD= discriminant (NTLmipo);
721	den= abs (convertZZ2CF (NTLD*NTLf));
722	#endif
723
724	// make factors elements of Z(a)[x] disable for modularDiophant
725	CanonicalForm multiplier= 1;
726	for (CFListIterator i= uniFactors; i.hasItem(); i++)
727	{
728	multiplier *= bCommonDen (i.getItem());
729	i.getItem()= i.getItem()*bCommonDen(i.getItem());
730	}
731	F *= multiplier;
732	F *= bCommonDen (F);
733
734	Off (SW_RATIONAL);
735	int ii= 0;
736	#ifdef HAVE_FLINT
737	CanonicalForm discMipo= convertFmpz2CF(FLINTD);
738	fmpz_clear(FLINTD);
739	#elif defined(HAVE_NTL)
740	CanonicalForm discMipo= convertZZ2CF (NTLD);
741	#endif
742	findGoodPrime (bufF*discMipo,ii);
743	findGoodPrime (F1*discMipo,ii);
744	findGoodPrime (F*discMipo,ii);
745
746	int pp=cf_getBigPrime(ii);
747	b = coeffBound( F, pp, mipo );
748	modpk bb= coeffBound (F1, pp, mipo);
749	if (bb.getk() > b.getk() ) b=bb;
750	bb= coeffBound (F, pp, mipo);
751	if (bb.getk() > b.getk() ) b=bb;
752
753	ExtensionInfo dummy= ExtensionInfo (alpha, false);
754	DegreePattern degs= DegreePattern (uniFactors);
755
756	bool earlySuccess= false;
757	CFList earlyFactors;
758	uniFactors= henselLiftAndEarly
759	(F, earlySuccess, earlyFactors, degs, liftBound,
760	uniFactors, dummy, evaluation, b, den);
761
762	DEBOUTLN (cerr, "lifted factors= " << uniFactors);
763
764	CanonicalForm MODl= power (y, liftBound);
765
766	On (SW_RATIONAL);
767	F *= bCommonDen (F);
768	Off (SW_RATIONAL);
769
770	CFList biFactors;
771
772	biFactors= factorRecombination (uniFactors, F, MODl, degs, evaluation, 1,
773	uniFactors.length()/2, b, den);
774
775	On (SW_RATIONAL);
776
777	if (earlySuccess)
778	biFactors= Union (earlyFactors, biFactors);
779	else if (!earlySuccess && degs.getLength() == 1)
780	biFactors= earlyFactors;
781
782	bool swap2= false;
783	appendSwapDecompress (biFactors, CFList(), CFList(), swap, swap2, CFMap());
784	if (isOn (SW_RATIONAL))
785	normalize (biFactors);
786
787	CFAFList result;
788	bool found= false;
789
790	for (CFListIterator i= biFactors; i.hasItem(); i++)
791	{
792	if (full)
793	result.append (CFAFactor (decompress (i.getItem(), M, S),
794	getMipo (alpha), 1));
795
796	if (totaldegree (i.getItem()) == minTdeg)
797	{
798	if (!full)
799	result= CFAFList (CFAFactor (decompress (i.getItem(), M, S),
800	getMipo (alpha), 1));
801	found= true;
802
803	if (!full)
804	break;
805	}
806	}
807
808	if (!found)
809	{
810	rec= true;
811	F= bufF;
812	goto differentevalpoint;
813	}
814
815	if (isRat)
816	On (SW_RATIONAL);
817	else
818	Off (SW_RATIONAL);
819
820	mpz_clear (M[0]);
821	mpz_clear (M[1]);
822	mpz_clear (M[2]);
823	mpz_clear (M[3]);
824	delete [] M;
825
826	mpz_clear (S[0]);
827	mpz_clear (S[1]);
828	delete [] S;
829
830	return result;
831	}
832	#endif
833	#endif

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