1 | /*****************************************************************************\ |
---|
2 | * Computer Algebra System SINGULAR |
---|
3 | \*****************************************************************************/ |
---|
4 | /** @file facFqBivar.cc |
---|
5 | * |
---|
6 | * This file provides functions for factorizing a bivariate polynomial over |
---|
7 | * \f$ F_{p} \f$ , \f$ F_{p}(\alpha ) \f$ or GF, based on "Modern Computer |
---|
8 | * Algebra, Chapter 15" by J. von zur Gathen & J. Gerhard and "Factoring |
---|
9 | * multivariate polynomials over a finite field" by L. Bernardin. |
---|
10 | * Factor Recombination is described in "Factoring polynomials over global |
---|
11 | * fields" by K. Belabas, M. van Hoeij, J. Klueners, A. Steel |
---|
12 | * |
---|
13 | * |
---|
14 | * @author Martin Lee |
---|
15 | * |
---|
16 | **/ |
---|
17 | /*****************************************************************************/ |
---|
18 | |
---|
19 | #include "config.h" |
---|
20 | |
---|
21 | #include "cf_assert.h" |
---|
22 | #include "debug.h" |
---|
23 | #include "timing.h" |
---|
24 | |
---|
25 | #include "canonicalform.h" |
---|
26 | #include "cf_defs.h" |
---|
27 | #include "cf_map_ext.h" |
---|
28 | #include "cf_random.h" |
---|
29 | #include "facHensel.h" |
---|
30 | #include "facMul.h" |
---|
31 | #include "cf_map.h" |
---|
32 | #include "cf_gcd_smallp.h" |
---|
33 | #include "facFqBivarUtil.h" |
---|
34 | #include "facFqBivar.h" |
---|
35 | #include "cfNewtonPolygon.h" |
---|
36 | #include "algext.h" |
---|
37 | |
---|
38 | #ifdef HAVE_NTL |
---|
39 | #include "NTLconvert.h" |
---|
40 | |
---|
41 | #ifdef HAVE_FLINT |
---|
42 | #include "FLINTconvert.h" |
---|
43 | #endif |
---|
44 | |
---|
45 | TIMING_DEFINE_PRINT(fac_fq_uni_factorizer) |
---|
46 | TIMING_DEFINE_PRINT(fac_fq_bi_hensel_lift) |
---|
47 | TIMING_DEFINE_PRINT(fac_fq_bi_factor_recombination) |
---|
48 | |
---|
49 | CanonicalForm prodMod0 (const CFList& L, const CanonicalForm& M, const modpk& b) |
---|
50 | { |
---|
51 | if (L.isEmpty()) |
---|
52 | return 1; |
---|
53 | else if (L.length() == 1) |
---|
54 | return mod (L.getFirst()(0, 1) , M); |
---|
55 | else if (L.length() == 2) |
---|
56 | return mod (mulNTL (L.getFirst()(0, 1),L.getLast()(0, 1), b), M); |
---|
57 | else |
---|
58 | { |
---|
59 | int l= L.length()/2; |
---|
60 | CFListIterator i= L; |
---|
61 | CFList tmp1, tmp2; |
---|
62 | CanonicalForm buf1, buf2; |
---|
63 | for (int j= 1; j <= l; j++, i++) |
---|
64 | tmp1.append (i.getItem()); |
---|
65 | tmp2= Difference (L, tmp1); |
---|
66 | buf1= prodMod0 (tmp1, M, b); |
---|
67 | buf2= prodMod0 (tmp2, M, b); |
---|
68 | return mod (mulNTL (buf1,buf2, b), M); |
---|
69 | } |
---|
70 | } |
---|
71 | |
---|
72 | CanonicalForm evalPoint (const CanonicalForm& F, CanonicalForm & eval, |
---|
73 | const Variable& alpha, CFList& list, const bool& GF, |
---|
74 | bool& fail) |
---|
75 | { |
---|
76 | fail= false; |
---|
77 | Variable x= Variable(2); |
---|
78 | Variable y= Variable(1); |
---|
79 | FFRandom genFF; |
---|
80 | GFRandom genGF; |
---|
81 | CanonicalForm random, mipo; |
---|
82 | double bound; |
---|
83 | int p= getCharacteristic (); |
---|
84 | if (alpha.level() != 1) |
---|
85 | { |
---|
86 | mipo= getMipo (alpha); |
---|
87 | int d= degree (mipo); |
---|
88 | bound= ipower (p, d); |
---|
89 | } |
---|
90 | else if (GF) |
---|
91 | { |
---|
92 | int d= getGFDegree(); |
---|
93 | bound= ipower (p, d); |
---|
94 | } |
---|
95 | else |
---|
96 | bound= p; |
---|
97 | |
---|
98 | random= 0; |
---|
99 | do |
---|
100 | { |
---|
101 | if (list.length() >= bound) |
---|
102 | { |
---|
103 | fail= true; |
---|
104 | break; |
---|
105 | } |
---|
106 | if (list.isEmpty()) |
---|
107 | random= 0; |
---|
108 | else if (GF) |
---|
109 | { |
---|
110 | if (list.length() == 1) |
---|
111 | random= getGFGenerator(); |
---|
112 | else |
---|
113 | random= genGF.generate(); |
---|
114 | } |
---|
115 | else if (list.length() < p || alpha.level() == 1) |
---|
116 | random= genFF.generate(); |
---|
117 | else if (alpha != x && list.length() >= p) |
---|
118 | { |
---|
119 | if (list.length() == p) |
---|
120 | random= alpha; |
---|
121 | else |
---|
122 | { |
---|
123 | AlgExtRandomF genAlgExt (alpha); |
---|
124 | random= genAlgExt.generate(); |
---|
125 | } |
---|
126 | } |
---|
127 | if (find (list, random)) continue; |
---|
128 | eval= F (random, x); |
---|
129 | if (degree (eval) != degree (F, y)) |
---|
130 | { //leading coeff vanishes |
---|
131 | if (!find (list, random)) |
---|
132 | list.append (random); |
---|
133 | continue; |
---|
134 | } |
---|
135 | if (degree (gcd (deriv (eval, eval.mvar()), eval), eval.mvar()) > 0) |
---|
136 | { //evaluated polynomial is not squarefree |
---|
137 | if (!find (list, random)) |
---|
138 | list.append (random); |
---|
139 | continue; |
---|
140 | } |
---|
141 | } while (find (list, random)); |
---|
142 | |
---|
143 | return random; |
---|
144 | } |
---|
145 | |
---|
146 | CFList |
---|
147 | uniFactorizer (const CanonicalForm& A, const Variable& alpha, const bool& GF) |
---|
148 | { |
---|
149 | Variable x= A.mvar(); |
---|
150 | if (A.inCoeffDomain()) |
---|
151 | return CFList(); |
---|
152 | ASSERT (A.isUnivariate(), |
---|
153 | "univariate polynomial expected or constant expected"); |
---|
154 | CFFList factorsA; |
---|
155 | zz_p::init (getCharacteristic()); |
---|
156 | if (GF) |
---|
157 | { |
---|
158 | int k= getGFDegree(); |
---|
159 | char cGFName= gf_name; |
---|
160 | CanonicalForm mipo= gf_mipo; |
---|
161 | setCharacteristic (getCharacteristic()); |
---|
162 | Variable beta= rootOf (mipo.mapinto()); |
---|
163 | CanonicalForm buf= GF2FalphaRep (A, beta); |
---|
164 | if (getCharacteristic() > 2) |
---|
165 | { |
---|
166 | zz_pX NTLMipo= convertFacCF2NTLzzpX (mipo.mapinto()); |
---|
167 | zz_pE::init (NTLMipo); |
---|
168 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (buf, NTLMipo); |
---|
169 | MakeMonic (NTLA); |
---|
170 | vec_pair_zz_pEX_long NTLFactorsA= CanZass (NTLA); |
---|
171 | zz_pE multi= to_zz_pE (1); |
---|
172 | factorsA= convertNTLvec_pair_zzpEX_long2FacCFFList (NTLFactorsA, multi, |
---|
173 | x, beta); |
---|
174 | } |
---|
175 | else |
---|
176 | { |
---|
177 | GF2X NTLMipo= convertFacCF2NTLGF2X (mipo.mapinto()); |
---|
178 | GF2E::init (NTLMipo); |
---|
179 | GF2EX NTLA= convertFacCF2NTLGF2EX (buf, NTLMipo); |
---|
180 | MakeMonic (NTLA); |
---|
181 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
---|
182 | GF2E multi= to_GF2E (1); |
---|
183 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
---|
184 | x, beta); |
---|
185 | } |
---|
186 | setCharacteristic (getCharacteristic(), k, cGFName); |
---|
187 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
---|
188 | { |
---|
189 | buf= i.getItem().factor(); |
---|
190 | buf= Falpha2GFRep (buf); |
---|
191 | i.getItem()= CFFactor (buf, i.getItem().exp()); |
---|
192 | } |
---|
193 | } |
---|
194 | else if (alpha.level() != 1) |
---|
195 | { |
---|
196 | if (getCharacteristic() > 2) |
---|
197 | { |
---|
198 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
199 | zz_pE::init (NTLMipo); |
---|
200 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (A, NTLMipo); |
---|
201 | MakeMonic (NTLA); |
---|
202 | vec_pair_zz_pEX_long NTLFactorsA= CanZass (NTLA); |
---|
203 | zz_pE multi= to_zz_pE (1); |
---|
204 | factorsA= convertNTLvec_pair_zzpEX_long2FacCFFList (NTLFactorsA, multi, |
---|
205 | x, alpha); |
---|
206 | } |
---|
207 | else |
---|
208 | { |
---|
209 | GF2X NTLMipo= convertFacCF2NTLGF2X (getMipo (alpha)); |
---|
210 | GF2E::init (NTLMipo); |
---|
211 | GF2EX NTLA= convertFacCF2NTLGF2EX (A, NTLMipo); |
---|
212 | MakeMonic (NTLA); |
---|
213 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
---|
214 | GF2E multi= to_GF2E (1); |
---|
215 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
---|
216 | x, alpha); |
---|
217 | } |
---|
218 | } |
---|
219 | else |
---|
220 | { |
---|
221 | #ifdef HAVE_FLINT |
---|
222 | nmod_poly_t FLINTA; |
---|
223 | convertFacCF2nmod_poly_t (FLINTA, A); |
---|
224 | nmod_poly_factor_t result; |
---|
225 | nmod_poly_factor_init (result); |
---|
226 | mp_limb_t leadingCoeff= nmod_poly_factor (result, FLINTA); |
---|
227 | factorsA= convertFLINTnmod_poly_factor2FacCFFList (result, leadingCoeff, x); |
---|
228 | if (factorsA.getFirst().factor().inCoeffDomain()) |
---|
229 | factorsA.removeFirst(); |
---|
230 | nmod_poly_factor_clear (result); |
---|
231 | nmod_poly_clear (FLINTA); |
---|
232 | #else |
---|
233 | if (getCharacteristic() > 2) |
---|
234 | { |
---|
235 | zz_pX NTLA= convertFacCF2NTLzzpX (A); |
---|
236 | MakeMonic (NTLA); |
---|
237 | vec_pair_zz_pX_long NTLFactorsA= CanZass (NTLA); |
---|
238 | zz_p multi= to_zz_p (1); |
---|
239 | factorsA= convertNTLvec_pair_zzpX_long2FacCFFList (NTLFactorsA, multi, |
---|
240 | x); |
---|
241 | } |
---|
242 | else |
---|
243 | { |
---|
244 | GF2X NTLA= convertFacCF2NTLGF2X (A); |
---|
245 | vec_pair_GF2X_long NTLFactorsA= CanZass (NTLA); |
---|
246 | GF2 multi= to_GF2 (1); |
---|
247 | factorsA= convertNTLvec_pair_GF2X_long2FacCFFList (NTLFactorsA, multi, |
---|
248 | x); |
---|
249 | } |
---|
250 | #endif |
---|
251 | } |
---|
252 | CFList uniFactors; |
---|
253 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
---|
254 | uniFactors.append (i.getItem().factor()); |
---|
255 | return uniFactors; |
---|
256 | } |
---|
257 | |
---|
258 | /// naive factor recombination as decribed in "Factoring |
---|
259 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
260 | CFList |
---|
261 | extFactorRecombination (CFList& factors, CanonicalForm& F, |
---|
262 | const CanonicalForm& N, const ExtensionInfo& info, |
---|
263 | DegreePattern& degs, const CanonicalForm& eval, int s, |
---|
264 | int thres) |
---|
265 | { |
---|
266 | if (factors.length() == 0) |
---|
267 | { |
---|
268 | F= 1; |
---|
269 | return CFList(); |
---|
270 | } |
---|
271 | if (F.inCoeffDomain()) |
---|
272 | return CFList(); |
---|
273 | |
---|
274 | Variable alpha= info.getAlpha(); |
---|
275 | Variable beta= info.getBeta(); |
---|
276 | CanonicalForm gamma= info.getGamma(); |
---|
277 | CanonicalForm delta= info.getDelta(); |
---|
278 | int k= info.getGFDegree(); |
---|
279 | |
---|
280 | CanonicalForm M= N; |
---|
281 | int l= degree (N); |
---|
282 | Variable y= F.mvar(); |
---|
283 | Variable x= Variable (1); |
---|
284 | CFList source, dest; |
---|
285 | if (degs.getLength() <= 1 || factors.length() == 1) |
---|
286 | { |
---|
287 | CFList result= CFList(mapDown (F(y-eval, y), info, source, dest)); |
---|
288 | F= 1; |
---|
289 | return result; |
---|
290 | } |
---|
291 | |
---|
292 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, M) == F " << |
---|
293 | (mod (LC (F, 1)*prodMod (factors, M), M)/Lc (mod (LC (F, 1)*prodMod (factors, M), M)) == F/Lc (F))); |
---|
294 | int degMipoBeta= 1; |
---|
295 | if (!k && beta.level() != 1) |
---|
296 | degMipoBeta= degree (getMipo (beta)); |
---|
297 | |
---|
298 | CFList T, S, Diff; |
---|
299 | T= factors; |
---|
300 | |
---|
301 | CFList result; |
---|
302 | CanonicalForm buf, buf2, quot; |
---|
303 | |
---|
304 | buf= F; |
---|
305 | |
---|
306 | CanonicalForm g, LCBuf= LC (buf, x); |
---|
307 | int * v= new int [T.length()]; |
---|
308 | for (int i= 0; i < T.length(); i++) |
---|
309 | v[i]= 0; |
---|
310 | |
---|
311 | CFArray TT; |
---|
312 | DegreePattern bufDegs1, bufDegs2; |
---|
313 | bufDegs1= degs; |
---|
314 | int subsetDeg; |
---|
315 | TT= copy (factors); |
---|
316 | bool nosubset= false; |
---|
317 | bool recombination= false; |
---|
318 | bool trueFactor= false; |
---|
319 | CanonicalForm test; |
---|
320 | CanonicalForm buf0= buf (0, x)*LCBuf; |
---|
321 | while (T.length() >= 2*s && s <= thres) |
---|
322 | { |
---|
323 | while (nosubset == false) |
---|
324 | { |
---|
325 | if (T.length() == s) |
---|
326 | { |
---|
327 | delete [] v; |
---|
328 | if (recombination) |
---|
329 | { |
---|
330 | T.insert (LCBuf); |
---|
331 | g= prodMod (T, M); |
---|
332 | T.removeFirst(); |
---|
333 | g /= content(g); |
---|
334 | g= g (y - eval, y); |
---|
335 | g /= Lc (g); |
---|
336 | appendTestMapDown (result, g, info, source, dest); |
---|
337 | F= 1; |
---|
338 | return result; |
---|
339 | } |
---|
340 | else |
---|
341 | { |
---|
342 | appendMapDown (result, F (y - eval, y), info, source, dest); |
---|
343 | F= 1; |
---|
344 | return result; |
---|
345 | } |
---|
346 | } |
---|
347 | S= subset (v, s, TT, nosubset); |
---|
348 | if (nosubset) break; |
---|
349 | subsetDeg= subsetDegree (S); |
---|
350 | // skip those combinations that are not possible |
---|
351 | if (!degs.find (subsetDeg)) |
---|
352 | continue; |
---|
353 | else |
---|
354 | { |
---|
355 | test= prodMod0 (S, M); |
---|
356 | test *= LCBuf; |
---|
357 | test = mod (test, M); |
---|
358 | if (fdivides (test, buf0)) |
---|
359 | { |
---|
360 | S.insert (LCBuf); |
---|
361 | g= prodMod (S, M); |
---|
362 | S.removeFirst(); |
---|
363 | g /= content (g, x); |
---|
364 | if (fdivides (g, buf, quot)) |
---|
365 | { |
---|
366 | buf2= g (y - eval, y); |
---|
367 | buf2 /= Lc (buf2); |
---|
368 | |
---|
369 | if (!k && beta.level() == 1) |
---|
370 | { |
---|
371 | if (degree (buf2, alpha) < degMipoBeta) |
---|
372 | { |
---|
373 | buf= quot; |
---|
374 | LCBuf= LC (buf, x); |
---|
375 | recombination= true; |
---|
376 | appendTestMapDown (result, buf2, info, source, dest); |
---|
377 | trueFactor= true; |
---|
378 | } |
---|
379 | } |
---|
380 | else |
---|
381 | { |
---|
382 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
383 | { |
---|
384 | buf= quot; |
---|
385 | LCBuf= LC (buf, x); |
---|
386 | recombination= true; |
---|
387 | appendTestMapDown (result, buf2, info, source, dest); |
---|
388 | trueFactor= true; |
---|
389 | } |
---|
390 | } |
---|
391 | if (trueFactor) |
---|
392 | { |
---|
393 | T= Difference (T, S); |
---|
394 | l -= degree (g); |
---|
395 | M= power (y, l); |
---|
396 | buf0= buf (0, x)*LCBuf; |
---|
397 | |
---|
398 | // compute new possible degree pattern |
---|
399 | bufDegs2= DegreePattern (T); |
---|
400 | bufDegs1.intersect (bufDegs2); |
---|
401 | bufDegs1.refine (); |
---|
402 | if (T.length() < 2*s || T.length() == s || |
---|
403 | bufDegs1.getLength() == 1) |
---|
404 | { |
---|
405 | delete [] v; |
---|
406 | if (recombination) |
---|
407 | { |
---|
408 | appendTestMapDown (result, buf (y - eval, y), info, source, |
---|
409 | dest); |
---|
410 | F= 1; |
---|
411 | return result; |
---|
412 | } |
---|
413 | else |
---|
414 | { |
---|
415 | appendMapDown (result, F (y - eval, y), info, source, dest); |
---|
416 | F= 1; |
---|
417 | return result; |
---|
418 | } |
---|
419 | } |
---|
420 | trueFactor= false; |
---|
421 | TT= copy (T); |
---|
422 | indexUpdate (v, s, T.length(), nosubset); |
---|
423 | if (nosubset) break; |
---|
424 | } |
---|
425 | } |
---|
426 | } |
---|
427 | } |
---|
428 | } |
---|
429 | s++; |
---|
430 | if (T.length() < 2*s || T.length() == s) |
---|
431 | { |
---|
432 | delete [] v; |
---|
433 | if (recombination) |
---|
434 | { |
---|
435 | appendTestMapDown (result, buf (y - eval, y), info, source, dest); |
---|
436 | F= 1; |
---|
437 | return result; |
---|
438 | } |
---|
439 | else |
---|
440 | { |
---|
441 | appendMapDown (result, F (y - eval, y), info, source, dest); |
---|
442 | F= 1; |
---|
443 | return result; |
---|
444 | } |
---|
445 | } |
---|
446 | for (int i= 0; i < T.length(); i++) |
---|
447 | v[i]= 0; |
---|
448 | nosubset= false; |
---|
449 | } |
---|
450 | if (T.length() < 2*s) |
---|
451 | { |
---|
452 | appendMapDown (result, F (y - eval, y), info, source, dest); |
---|
453 | F= 1; |
---|
454 | delete [] v; |
---|
455 | return result; |
---|
456 | } |
---|
457 | |
---|
458 | if (s > thres) |
---|
459 | { |
---|
460 | factors= T; |
---|
461 | F= buf; |
---|
462 | degs= bufDegs1; |
---|
463 | } |
---|
464 | |
---|
465 | delete [] v; |
---|
466 | return result; |
---|
467 | } |
---|
468 | |
---|
469 | /// naive factor recombination as decribed in "Factoring |
---|
470 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
471 | CFList |
---|
472 | factorRecombination (CFList& factors, CanonicalForm& F, |
---|
473 | const CanonicalForm& N, DegreePattern& degs, int s, |
---|
474 | int thres, const modpk& b |
---|
475 | ) |
---|
476 | { |
---|
477 | if (factors.length() == 0) |
---|
478 | { |
---|
479 | F= 1; |
---|
480 | return CFList (); |
---|
481 | } |
---|
482 | if (F.inCoeffDomain()) |
---|
483 | return CFList(); |
---|
484 | if (degs.getLength() <= 1 || factors.length() == 1) |
---|
485 | { |
---|
486 | CFList result= CFList (F); |
---|
487 | F= 1; |
---|
488 | return result; |
---|
489 | } |
---|
490 | #ifdef DEBUGOUTPUT |
---|
491 | if (b.getp() == 0) |
---|
492 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, N) == F " << |
---|
493 | (mod (LC (F, 1)*prodMod (factors, N),N)/Lc (mod (LC (F, 1)*prodMod (factors, N),N)) == F/Lc(F))); |
---|
494 | else |
---|
495 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, N) == F " << |
---|
496 | (mod (b(LC (F, 1)*prodMod (factors, N)),N)/Lc (mod (b(LC (F, 1)*prodMod (factors, N)),N)) == F/Lc(F))); |
---|
497 | #endif |
---|
498 | |
---|
499 | CFList T, S; |
---|
500 | |
---|
501 | CanonicalForm M= N; |
---|
502 | int l= degree (N); |
---|
503 | T= factors; |
---|
504 | CFList result; |
---|
505 | Variable y= Variable (2); |
---|
506 | Variable x= Variable (1); |
---|
507 | CanonicalForm LCBuf= LC (F, x); |
---|
508 | CanonicalForm g, quot, buf= F; |
---|
509 | int * v= new int [T.length()]; |
---|
510 | for (int i= 0; i < T.length(); i++) |
---|
511 | v[i]= 0; |
---|
512 | bool nosubset= false; |
---|
513 | CFArray TT; |
---|
514 | DegreePattern bufDegs1, bufDegs2; |
---|
515 | bufDegs1= degs; |
---|
516 | int subsetDeg; |
---|
517 | TT= copy (factors); |
---|
518 | bool recombination= false; |
---|
519 | CanonicalForm test; |
---|
520 | bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) || |
---|
521 | getCharacteristic() > 0; |
---|
522 | if (!isRat) |
---|
523 | On (SW_RATIONAL); |
---|
524 | CanonicalForm buf0= mulNTL (buf (0, x), LCBuf); |
---|
525 | if (!isRat) |
---|
526 | Off (SW_RATIONAL); |
---|
527 | while (T.length() >= 2*s && s <= thres) |
---|
528 | { |
---|
529 | while (nosubset == false) |
---|
530 | { |
---|
531 | if (T.length() == s) |
---|
532 | { |
---|
533 | delete [] v; |
---|
534 | if (recombination) |
---|
535 | { |
---|
536 | T.insert (LCBuf); |
---|
537 | g= prodMod (T, M); |
---|
538 | if (b.getp() != 0) |
---|
539 | g= b(g); |
---|
540 | T.removeFirst(); |
---|
541 | result.append (g/content (g, x)); |
---|
542 | F= 1; |
---|
543 | return result; |
---|
544 | } |
---|
545 | else |
---|
546 | { |
---|
547 | result= CFList (F); |
---|
548 | F= 1; |
---|
549 | return result; |
---|
550 | } |
---|
551 | } |
---|
552 | S= subset (v, s, TT, nosubset); |
---|
553 | if (nosubset) break; |
---|
554 | subsetDeg= subsetDegree (S); |
---|
555 | // skip those combinations that are not possible |
---|
556 | if (!degs.find (subsetDeg)) |
---|
557 | continue; |
---|
558 | else |
---|
559 | { |
---|
560 | if (!isRat) |
---|
561 | On (SW_RATIONAL); |
---|
562 | test= prodMod0 (S, M); |
---|
563 | if (!isRat) |
---|
564 | { |
---|
565 | test *= bCommonDen (test); |
---|
566 | Off (SW_RATIONAL); |
---|
567 | } |
---|
568 | test= mulNTL (test, LCBuf, b); |
---|
569 | test= mod (test, M); |
---|
570 | if (uniFdivides (test, buf0)) |
---|
571 | { |
---|
572 | if (!isRat) |
---|
573 | On (SW_RATIONAL); |
---|
574 | S.insert (LCBuf); |
---|
575 | g= prodMod (S, M); |
---|
576 | S.removeFirst(); |
---|
577 | if (!isRat) |
---|
578 | { |
---|
579 | g *= bCommonDen(g); |
---|
580 | Off (SW_RATIONAL); |
---|
581 | } |
---|
582 | if (b.getp() != 0) |
---|
583 | g= b(g); |
---|
584 | if (!isRat) |
---|
585 | On (SW_RATIONAL); |
---|
586 | g /= content (g, x); |
---|
587 | if (fdivides (g, buf, quot)) |
---|
588 | { |
---|
589 | recombination= true; |
---|
590 | result.append (g); |
---|
591 | if (b.getp() != 0) |
---|
592 | buf= quot*bCommonDen (quot); |
---|
593 | else |
---|
594 | buf= quot; |
---|
595 | LCBuf= LC (buf, x); |
---|
596 | T= Difference (T, S); |
---|
597 | l -= degree (g); |
---|
598 | M= power (y, l); |
---|
599 | buf0= mulNTL (buf (0, x), LCBuf); |
---|
600 | if (!isRat) |
---|
601 | Off (SW_RATIONAL); |
---|
602 | // compute new possible degree pattern |
---|
603 | bufDegs2= DegreePattern (T); |
---|
604 | bufDegs1.intersect (bufDegs2); |
---|
605 | bufDegs1.refine (); |
---|
606 | if (T.length() < 2*s || T.length() == s || |
---|
607 | bufDegs1.getLength() == 1) |
---|
608 | { |
---|
609 | delete [] v; |
---|
610 | if (recombination) |
---|
611 | { |
---|
612 | result.append (buf); |
---|
613 | F= 1; |
---|
614 | return result; |
---|
615 | } |
---|
616 | else |
---|
617 | { |
---|
618 | result= CFList (F); |
---|
619 | F= 1; |
---|
620 | return result; |
---|
621 | } |
---|
622 | } |
---|
623 | TT= copy (T); |
---|
624 | indexUpdate (v, s, T.length(), nosubset); |
---|
625 | if (nosubset) break; |
---|
626 | } |
---|
627 | if (!isRat) |
---|
628 | Off (SW_RATIONAL); |
---|
629 | } |
---|
630 | } |
---|
631 | } |
---|
632 | s++; |
---|
633 | if (T.length() < 2*s || T.length() == s) |
---|
634 | { |
---|
635 | delete [] v; |
---|
636 | if (recombination) |
---|
637 | { |
---|
638 | result.append (buf); |
---|
639 | F= 1; |
---|
640 | return result; |
---|
641 | } |
---|
642 | else |
---|
643 | { |
---|
644 | result= CFList (F); |
---|
645 | F= 1; |
---|
646 | return result; |
---|
647 | } |
---|
648 | } |
---|
649 | for (int i= 0; i < T.length(); i++) |
---|
650 | v[i]= 0; |
---|
651 | nosubset= false; |
---|
652 | } |
---|
653 | delete [] v; |
---|
654 | if (T.length() < 2*s) |
---|
655 | { |
---|
656 | result.append (F); |
---|
657 | F= 1; |
---|
658 | return result; |
---|
659 | } |
---|
660 | |
---|
661 | if (s > thres) |
---|
662 | { |
---|
663 | factors= T; |
---|
664 | F= buf; |
---|
665 | degs= bufDegs1; |
---|
666 | } |
---|
667 | |
---|
668 | return result; |
---|
669 | } |
---|
670 | |
---|
671 | Variable chooseExtension (const Variable & alpha, const Variable& beta, int k) |
---|
672 | { |
---|
673 | zz_p::init (getCharacteristic()); |
---|
674 | zz_pX NTLIrredpoly; |
---|
675 | int i=1, m= 2; |
---|
676 | // extension of F_p needed |
---|
677 | if (alpha.level() == 1 && beta.level() == 1 && k == 1) |
---|
678 | { |
---|
679 | i= 1; |
---|
680 | m= 2; |
---|
681 | } //extension of F_p(alpha) needed but want to factorize over F_p |
---|
682 | else if (alpha.level() != 1 && beta.level() == 1 && k == 1) |
---|
683 | { |
---|
684 | i= 1; |
---|
685 | m= degree (getMipo (alpha)) + 1; |
---|
686 | } //extension of F_p(alpha) needed for first time |
---|
687 | else if (alpha.level() != 1 && beta.level() == 1 && k != 1) |
---|
688 | { |
---|
689 | i= 2; |
---|
690 | m= degree (getMipo (alpha)); |
---|
691 | } |
---|
692 | else if (alpha.level() != 1 && beta.level() != 1 && k != 1) |
---|
693 | { |
---|
694 | m= degree (getMipo (beta)); |
---|
695 | i= degree (getMipo (alpha))/m + 1; |
---|
696 | } |
---|
697 | BuildIrred (NTLIrredpoly, i*m); |
---|
698 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
699 | return rootOf (newMipo); |
---|
700 | } |
---|
701 | |
---|
702 | void |
---|
703 | earlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
704 | factors, int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
705 | DegreePattern& degs, bool& success, int deg, |
---|
706 | const modpk& b) |
---|
707 | { |
---|
708 | DegreePattern bufDegs1= degs; |
---|
709 | DegreePattern bufDegs2; |
---|
710 | CFList T= factors; |
---|
711 | CanonicalForm buf= F; |
---|
712 | Variable x= Variable (1); |
---|
713 | CanonicalForm g, quot; |
---|
714 | CanonicalForm M= power (F.mvar(), deg); |
---|
715 | adaptedLiftBound= 0; |
---|
716 | int d= degree (F), l= 0; |
---|
717 | bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) || getCharacteristic() > 0; |
---|
718 | if (!isRat) |
---|
719 | On (SW_RATIONAL); |
---|
720 | if (b.getp() != 0) |
---|
721 | buf *= bCommonDen (buf); |
---|
722 | CanonicalForm LCBuf= LC (buf, x); |
---|
723 | CanonicalForm buf0= mulNTL (buf (0,x), LCBuf); |
---|
724 | CanonicalForm buf1= mulNTL (buf (1,x), LCBuf); |
---|
725 | if (!isRat) |
---|
726 | Off (SW_RATIONAL); |
---|
727 | CanonicalForm test0, test1; |
---|
728 | |
---|
729 | for (CFListIterator i= factors; i.hasItem(); i++, l++) |
---|
730 | { |
---|
731 | if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1) |
---|
732 | continue; |
---|
733 | else |
---|
734 | { |
---|
735 | test1= mod (mulNTL (i.getItem() (1,x), LCBuf, b), M); |
---|
736 | if (uniFdivides (test1, buf1)) |
---|
737 | { |
---|
738 | test0= mod (mulNTL (i.getItem() (0,x), LCBuf, b), M); |
---|
739 | if (uniFdivides (test0, buf0)) |
---|
740 | { |
---|
741 | if (!isRat) |
---|
742 | On (SW_RATIONAL); |
---|
743 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
744 | if (!isRat) |
---|
745 | { |
---|
746 | g *= bCommonDen(g); |
---|
747 | Off (SW_RATIONAL); |
---|
748 | } |
---|
749 | if (b.getp() != 0) |
---|
750 | g= b(g); |
---|
751 | if (!isRat) |
---|
752 | On (SW_RATIONAL); |
---|
753 | g /= content (g, x); |
---|
754 | if (fdivides (g, buf, quot)) |
---|
755 | { |
---|
756 | reconstructedFactors.append (g); |
---|
757 | factorsFoundIndex[l]= 1; |
---|
758 | if (b.getp() != 0) |
---|
759 | buf= quot*bCommonDen(quot); |
---|
760 | else |
---|
761 | buf= quot; |
---|
762 | d -= degree (g); |
---|
763 | LCBuf= LC (buf, x); |
---|
764 | buf0= mulNTL (buf (0,x), LCBuf); |
---|
765 | buf1= mulNTL (buf (1,x), LCBuf); |
---|
766 | if (!isRat) |
---|
767 | Off (SW_RATIONAL); |
---|
768 | T= Difference (T, CFList (i.getItem())); |
---|
769 | F= buf; |
---|
770 | |
---|
771 | // compute new possible degree pattern |
---|
772 | bufDegs2= DegreePattern (T); |
---|
773 | bufDegs1.intersect (bufDegs2); |
---|
774 | bufDegs1.refine (); |
---|
775 | if (bufDegs1.getLength() <= 1) |
---|
776 | { |
---|
777 | if (!buf.inCoeffDomain()) |
---|
778 | reconstructedFactors.append (buf); |
---|
779 | break; |
---|
780 | } |
---|
781 | } |
---|
782 | if (!isRat) |
---|
783 | Off (SW_RATIONAL); |
---|
784 | } |
---|
785 | } |
---|
786 | } |
---|
787 | } |
---|
788 | adaptedLiftBound= d + 1; |
---|
789 | if (adaptedLiftBound < deg) |
---|
790 | { |
---|
791 | degs= bufDegs1; |
---|
792 | success= true; |
---|
793 | } |
---|
794 | if (bufDegs1.getLength() <= 1) |
---|
795 | degs= bufDegs1; |
---|
796 | } |
---|
797 | |
---|
798 | void |
---|
799 | extEarlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
800 | factors,int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
801 | DegreePattern& degs, bool& success, const |
---|
802 | ExtensionInfo& info, const CanonicalForm& eval, int deg |
---|
803 | ) |
---|
804 | { |
---|
805 | Variable alpha= info.getAlpha(); |
---|
806 | Variable beta= info.getBeta(); |
---|
807 | CanonicalForm gamma= info.getGamma(); |
---|
808 | CanonicalForm delta= info.getDelta(); |
---|
809 | int k= info.getGFDegree(); |
---|
810 | DegreePattern bufDegs1= degs, bufDegs2; |
---|
811 | CFList result; |
---|
812 | CFList T= factors; |
---|
813 | Variable y= F.mvar(); |
---|
814 | Variable x= Variable (1); |
---|
815 | CanonicalForm buf= F, LCBuf= LC (buf, x), g, buf2; |
---|
816 | CanonicalForm M= power (y, deg); |
---|
817 | adaptedLiftBound= 0; |
---|
818 | bool trueFactor= false; |
---|
819 | int d= degree (F), l= 0; |
---|
820 | CFList source, dest; |
---|
821 | int degMipoBeta= 1; |
---|
822 | if (!k && beta.level() != 1) |
---|
823 | degMipoBeta= degree (getMipo (beta)); |
---|
824 | CanonicalForm quot; |
---|
825 | for (CFListIterator i= factors; i.hasItem(); i++, l++) |
---|
826 | { |
---|
827 | if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1) |
---|
828 | continue; |
---|
829 | else |
---|
830 | { |
---|
831 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
832 | g /= content (g, x); |
---|
833 | if (fdivides (g, buf, quot)) |
---|
834 | { |
---|
835 | buf2= g (y - eval, y); |
---|
836 | buf2 /= Lc (buf2); |
---|
837 | |
---|
838 | if (!k && beta == x) |
---|
839 | { |
---|
840 | if (degree (buf2, alpha) < degMipoBeta) |
---|
841 | { |
---|
842 | appendTestMapDown (reconstructedFactors, buf2, info, source, dest); |
---|
843 | factorsFoundIndex[l]= 1; |
---|
844 | buf= quot; |
---|
845 | d -= degree (g); |
---|
846 | LCBuf= LC (buf, x); |
---|
847 | trueFactor= true; |
---|
848 | } |
---|
849 | } |
---|
850 | else |
---|
851 | { |
---|
852 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
853 | { |
---|
854 | appendTestMapDown (reconstructedFactors, buf2, info, source, dest); |
---|
855 | factorsFoundIndex[l]= 1; |
---|
856 | buf= quot; |
---|
857 | d -= degree (g); |
---|
858 | LCBuf= LC (buf, x); |
---|
859 | trueFactor= true; |
---|
860 | } |
---|
861 | } |
---|
862 | if (trueFactor) |
---|
863 | { |
---|
864 | T= Difference (T, CFList (i.getItem())); |
---|
865 | F= buf; |
---|
866 | |
---|
867 | // compute new possible degree pattern |
---|
868 | bufDegs2= DegreePattern (T); |
---|
869 | bufDegs1.intersect (bufDegs2); |
---|
870 | bufDegs1.refine (); |
---|
871 | trueFactor= false; |
---|
872 | if (bufDegs1.getLength() <= 1) |
---|
873 | { |
---|
874 | if (!buf.inCoeffDomain()) |
---|
875 | { |
---|
876 | buf= buf (y - eval, y); |
---|
877 | buf /= Lc (buf); |
---|
878 | appendMapDown (reconstructedFactors, buf, info, source, dest); |
---|
879 | } |
---|
880 | break; |
---|
881 | } |
---|
882 | } |
---|
883 | } |
---|
884 | } |
---|
885 | } |
---|
886 | adaptedLiftBound= d + 1; |
---|
887 | if (adaptedLiftBound < deg) |
---|
888 | { |
---|
889 | degs= bufDegs1; |
---|
890 | success= true; |
---|
891 | } |
---|
892 | if (bufDegs1.getLength() <= 1) |
---|
893 | degs= bufDegs1; |
---|
894 | } |
---|
895 | |
---|
896 | int* |
---|
897 | getCombinations (int * rightSide, int sizeOfRightSide, int& sizeOfOutput, |
---|
898 | int degreeLC) |
---|
899 | { |
---|
900 | Variable x= Variable (1); |
---|
901 | int p= getCharacteristic(); |
---|
902 | int d= getGFDegree(); |
---|
903 | char cGFName= gf_name; |
---|
904 | setCharacteristic(0); |
---|
905 | CanonicalForm buf= 1; |
---|
906 | for (int i= 0; i < sizeOfRightSide; i++) |
---|
907 | buf *= (power (x, rightSide [i]) + 1); |
---|
908 | |
---|
909 | int j= 0; |
---|
910 | for (CFIterator i= buf; i.hasTerms(); i++, j++) |
---|
911 | { |
---|
912 | if (i.exp() < degreeLC) |
---|
913 | { |
---|
914 | j++; |
---|
915 | break; |
---|
916 | } |
---|
917 | } |
---|
918 | |
---|
919 | ASSERT ( j > 1, "j > 1 expected" ); |
---|
920 | |
---|
921 | int* result = new int [j - 1]; |
---|
922 | sizeOfOutput= j - 1; |
---|
923 | |
---|
924 | int i= 0; |
---|
925 | for (CFIterator m = buf; i < j - 1; i++, m++) |
---|
926 | result [i]= m.exp(); |
---|
927 | |
---|
928 | if (d > 1) |
---|
929 | setCharacteristic (p, d, cGFName); |
---|
930 | else |
---|
931 | setCharacteristic (p); |
---|
932 | return result; |
---|
933 | } |
---|
934 | |
---|
935 | int * |
---|
936 | getLiftPrecisions (const CanonicalForm& F, int& sizeOfOutput, int degreeLC) |
---|
937 | { |
---|
938 | int sizeOfNewtonPoly; |
---|
939 | int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPoly); |
---|
940 | int sizeOfRightSide; |
---|
941 | int * rightSide= getRightSide(newtonPolyg, sizeOfNewtonPoly, sizeOfRightSide); |
---|
942 | int * result= getCombinations(rightSide, sizeOfRightSide, sizeOfOutput, |
---|
943 | degreeLC); |
---|
944 | delete [] rightSide; |
---|
945 | for (int i= 0; i < sizeOfNewtonPoly; i++) |
---|
946 | delete [] newtonPolyg[i]; |
---|
947 | delete [] newtonPolyg; |
---|
948 | return result; |
---|
949 | } |
---|
950 | |
---|
951 | void |
---|
952 | deleteFactors (CFList& factors, int* factorsFoundIndex) |
---|
953 | { |
---|
954 | CFList result; |
---|
955 | int i= 0; |
---|
956 | for (CFListIterator iter= factors; iter.hasItem(); iter++, i++) |
---|
957 | { |
---|
958 | if (factorsFoundIndex[i] == 1) |
---|
959 | continue; |
---|
960 | else |
---|
961 | result.append (iter.getItem()); |
---|
962 | } |
---|
963 | factors= result; |
---|
964 | } |
---|
965 | |
---|
966 | CFList |
---|
967 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
968 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
969 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
970 | const CanonicalForm& eval, modpk& b) |
---|
971 | { |
---|
972 | Variable alpha= info.getAlpha(); |
---|
973 | Variable beta= info.getBeta(); |
---|
974 | CanonicalForm gamma= info.getGamma(); |
---|
975 | CanonicalForm delta= info.getDelta(); |
---|
976 | bool extension= info.isInExtension(); |
---|
977 | |
---|
978 | int sizeOfLiftPre; |
---|
979 | int * liftPre= getLiftPrecisions (A, sizeOfLiftPre, degree (LC (A, 1), 2)); |
---|
980 | |
---|
981 | Variable x= Variable (1); |
---|
982 | Variable y= Variable (2); |
---|
983 | CFArray Pi; |
---|
984 | CFList diophant; |
---|
985 | CFList bufUniFactors= uniFactors; |
---|
986 | CanonicalForm bufA= A; |
---|
987 | CanonicalForm lcA0= 0; |
---|
988 | bool mipoHasDen= false; |
---|
989 | if (getCharacteristic() == 0 && b.getp() != 0) |
---|
990 | { |
---|
991 | if (alpha.level() == 1) |
---|
992 | { |
---|
993 | lcA0= lc (A (0, 2)); |
---|
994 | A *= b.inverse (lcA0); |
---|
995 | A= b (A); |
---|
996 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
997 | i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem()))); |
---|
998 | } |
---|
999 | else |
---|
1000 | { |
---|
1001 | lcA0= Lc (A (0,2)); |
---|
1002 | On (SW_RATIONAL); |
---|
1003 | mipoHasDen= !bCommonDen(getMipo(alpha)).isOne(); |
---|
1004 | Off (SW_RATIONAL); |
---|
1005 | CanonicalForm lcA0inverse= b.inverse (lcA0); |
---|
1006 | A *= lcA0inverse; |
---|
1007 | A= b (A); |
---|
1008 | // Lc of bufUniFactors is in Z |
---|
1009 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
1010 | i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem()))); |
---|
1011 | } |
---|
1012 | } |
---|
1013 | bufUniFactors.insert (LC (A, x)); |
---|
1014 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1); |
---|
1015 | earlySuccess= false; |
---|
1016 | int newLiftBound= 0; |
---|
1017 | |
---|
1018 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1);//this is a tunable parameter |
---|
1019 | int dummy; |
---|
1020 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
1021 | for (int i= 0; i < uniFactors.length(); i++) |
---|
1022 | factorsFoundIndex [i]= 0; |
---|
1023 | |
---|
1024 | CFList bufBufUniFactors; |
---|
1025 | Variable v= alpha; |
---|
1026 | if (smallFactorDeg >= liftBound || degree (A,y) <= 4) |
---|
1027 | henselLift12 (A, bufUniFactors, liftBound, Pi, diophant, M, b, true); |
---|
1028 | else if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
1029 | { |
---|
1030 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true); |
---|
1031 | if (mipoHasDen) |
---|
1032 | { |
---|
1033 | for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++) |
---|
1034 | if (hasFirstAlgVar (iter.getItem(), v)) |
---|
1035 | break; |
---|
1036 | if (v != alpha) |
---|
1037 | { |
---|
1038 | bufBufUniFactors= bufUniFactors; |
---|
1039 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1040 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1041 | A= replacevar (A, alpha, v); |
---|
1042 | } |
---|
1043 | } |
---|
1044 | |
---|
1045 | if (!extension) |
---|
1046 | { |
---|
1047 | if (v==alpha) |
---|
1048 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1049 | factorsFoundIndex, degs, earlySuccess, |
---|
1050 | smallFactorDeg, b); |
---|
1051 | else |
---|
1052 | earlyFactorDetection(earlyFactors, bufA, bufBufUniFactors, newLiftBound, |
---|
1053 | factorsFoundIndex, degs, earlySuccess, |
---|
1054 | smallFactorDeg, b); |
---|
1055 | } |
---|
1056 | else |
---|
1057 | extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1058 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1059 | eval, smallFactorDeg); |
---|
1060 | if (degs.getLength() > 1 && !earlySuccess && |
---|
1061 | smallFactorDeg != liftPre [sizeOfLiftPre-1] + 1) |
---|
1062 | { |
---|
1063 | if (newLiftBound >= liftPre[sizeOfLiftPre-1]+1) |
---|
1064 | { |
---|
1065 | bufUniFactors.insert (LC (A, x)); |
---|
1066 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
1067 | liftPre[sizeOfLiftPre-1] + 1, Pi, diophant, M, b); |
---|
1068 | if (v!=alpha) |
---|
1069 | { |
---|
1070 | bufBufUniFactors= bufUniFactors; |
---|
1071 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1072 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1073 | } |
---|
1074 | if (!extension) |
---|
1075 | { |
---|
1076 | if (v==alpha) |
---|
1077 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1078 | factorsFoundIndex, degs, earlySuccess, |
---|
1079 | liftPre[sizeOfLiftPre-1] + 1, b); |
---|
1080 | else |
---|
1081 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
1082 | factorsFoundIndex, degs, earlySuccess, |
---|
1083 | liftPre[sizeOfLiftPre-1] + 1, b); |
---|
1084 | } |
---|
1085 | else |
---|
1086 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
1087 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1088 | eval, liftPre[sizeOfLiftPre-1] + 1); |
---|
1089 | } |
---|
1090 | } |
---|
1091 | else if (earlySuccess) |
---|
1092 | liftBound= newLiftBound; |
---|
1093 | |
---|
1094 | int i= sizeOfLiftPre - 1; |
---|
1095 | while (degs.getLength() > 1 && !earlySuccess && i - 1 >= 0) |
---|
1096 | { |
---|
1097 | if (newLiftBound >= liftPre[i] + 1) |
---|
1098 | { |
---|
1099 | bufUniFactors.insert (LC (A, x)); |
---|
1100 | henselLiftResume12 (A, bufUniFactors, liftPre[i] + 1, |
---|
1101 | liftPre[i-1] + 1, Pi, diophant, M, b); |
---|
1102 | if (v!=alpha) |
---|
1103 | { |
---|
1104 | bufBufUniFactors= bufUniFactors; |
---|
1105 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1106 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1107 | } |
---|
1108 | if (!extension) |
---|
1109 | { |
---|
1110 | if (v==alpha) |
---|
1111 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1112 | factorsFoundIndex, degs, earlySuccess, |
---|
1113 | liftPre[i-1] + 1, b); |
---|
1114 | else |
---|
1115 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
1116 | factorsFoundIndex, degs, earlySuccess, |
---|
1117 | liftPre[i-1] + 1, b); |
---|
1118 | } |
---|
1119 | else |
---|
1120 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
1121 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1122 | eval, liftPre[i-1] + 1); |
---|
1123 | } |
---|
1124 | else |
---|
1125 | { |
---|
1126 | liftBound= newLiftBound; |
---|
1127 | break; |
---|
1128 | } |
---|
1129 | i--; |
---|
1130 | } |
---|
1131 | if (earlySuccess) |
---|
1132 | liftBound= newLiftBound; |
---|
1133 | //after here all factors are lifted to liftPre[sizeOfLiftPre-1] |
---|
1134 | } |
---|
1135 | else |
---|
1136 | { |
---|
1137 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true); |
---|
1138 | if (mipoHasDen) |
---|
1139 | { |
---|
1140 | for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++) |
---|
1141 | if (hasFirstAlgVar (iter.getItem(), v)) |
---|
1142 | break; |
---|
1143 | if (v != alpha) |
---|
1144 | { |
---|
1145 | bufBufUniFactors= bufUniFactors; |
---|
1146 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1147 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1148 | A= replacevar (A, alpha, v); |
---|
1149 | } |
---|
1150 | } |
---|
1151 | if (!extension) |
---|
1152 | { |
---|
1153 | if (v==alpha) |
---|
1154 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1155 | factorsFoundIndex, degs, earlySuccess, |
---|
1156 | smallFactorDeg, b); |
---|
1157 | else |
---|
1158 | earlyFactorDetection (earlyFactors, bufA, bufBufUniFactors, newLiftBound, |
---|
1159 | factorsFoundIndex, degs, earlySuccess, |
---|
1160 | smallFactorDeg, b); |
---|
1161 | } |
---|
1162 | else |
---|
1163 | extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1164 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1165 | eval, smallFactorDeg); |
---|
1166 | int i= 1; |
---|
1167 | while ((degree (A,y)/4)*i + 4 <= smallFactorDeg) |
---|
1168 | i++; |
---|
1169 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*i+4); |
---|
1170 | if (degs.getLength() > 1 && !earlySuccess && dummy > smallFactorDeg) |
---|
1171 | { |
---|
1172 | bufUniFactors.insert (LC (A, x)); |
---|
1173 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
1174 | dummy, Pi, diophant, M, b); |
---|
1175 | if (v!=alpha) |
---|
1176 | { |
---|
1177 | bufBufUniFactors= bufUniFactors; |
---|
1178 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1179 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1180 | } |
---|
1181 | if (!extension) |
---|
1182 | { |
---|
1183 | if (v==alpha) |
---|
1184 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1185 | factorsFoundIndex, degs, earlySuccess, dummy, b); |
---|
1186 | else |
---|
1187 | earlyFactorDetection (earlyFactors, bufA,bufBufUniFactors, newLiftBound, |
---|
1188 | factorsFoundIndex, degs, earlySuccess, dummy, b); |
---|
1189 | } |
---|
1190 | else |
---|
1191 | extEarlyFactorDetection (earlyFactors, bufA,bufUniFactors, newLiftBound, |
---|
1192 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1193 | eval, dummy); |
---|
1194 | } |
---|
1195 | while (degs.getLength() > 1 && !earlySuccess && i < 4) |
---|
1196 | { |
---|
1197 | if (newLiftBound >= dummy) |
---|
1198 | { |
---|
1199 | bufUniFactors.insert (LC (A, x)); |
---|
1200 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*(i+1)+4); |
---|
1201 | henselLiftResume12 (A, bufUniFactors, (degree (A,y)/4)*i + 4, |
---|
1202 | dummy, Pi, diophant, M, b); |
---|
1203 | if (v!=alpha) |
---|
1204 | { |
---|
1205 | bufBufUniFactors= bufUniFactors; |
---|
1206 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1207 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1208 | } |
---|
1209 | if (!extension) |
---|
1210 | { |
---|
1211 | if (v==alpha) |
---|
1212 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1213 | factorsFoundIndex, degs, earlySuccess, dummy,b); |
---|
1214 | else |
---|
1215 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
1216 | factorsFoundIndex, degs, earlySuccess, dummy,b); |
---|
1217 | } |
---|
1218 | else |
---|
1219 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
1220 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1221 | eval, dummy); |
---|
1222 | } |
---|
1223 | else |
---|
1224 | { |
---|
1225 | liftBound= newLiftBound; |
---|
1226 | break; |
---|
1227 | } |
---|
1228 | i++; |
---|
1229 | } |
---|
1230 | if (earlySuccess) |
---|
1231 | liftBound= newLiftBound; |
---|
1232 | } |
---|
1233 | |
---|
1234 | A= bufA; |
---|
1235 | if (earlyFactors.length() > 0 && degs.getLength() > 1) |
---|
1236 | { |
---|
1237 | liftBound= degree (A,y) + 1; |
---|
1238 | earlySuccess= true; |
---|
1239 | deleteFactors (bufUniFactors, factorsFoundIndex); |
---|
1240 | } |
---|
1241 | |
---|
1242 | delete [] factorsFoundIndex; |
---|
1243 | delete [] liftPre; |
---|
1244 | |
---|
1245 | return bufUniFactors; |
---|
1246 | } |
---|
1247 | |
---|
1248 | CFList |
---|
1249 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
1250 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
1251 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
1252 | const CanonicalForm& eval) |
---|
1253 | { |
---|
1254 | modpk dummy= modpk(); |
---|
1255 | return henselLiftAndEarly (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
1256 | uniFactors, info, eval, dummy); |
---|
1257 | } |
---|
1258 | |
---|
1259 | long isReduced (const mat_zz_p& M) |
---|
1260 | { |
---|
1261 | long i, j, nonZero; |
---|
1262 | for (i = 1; i <= M.NumRows(); i++) |
---|
1263 | { |
---|
1264 | nonZero= 0; |
---|
1265 | for (j = 1; j <= M.NumCols(); j++) |
---|
1266 | { |
---|
1267 | if (!IsZero (M (i,j))) |
---|
1268 | nonZero++; |
---|
1269 | } |
---|
1270 | if (nonZero != 1) |
---|
1271 | return 0; |
---|
1272 | } |
---|
1273 | return 1; |
---|
1274 | } |
---|
1275 | |
---|
1276 | long isReduced (const mat_zz_pE& M) |
---|
1277 | { |
---|
1278 | long i, j, nonZero; |
---|
1279 | for (i = 1; i <= M.NumRows(); i++) |
---|
1280 | { |
---|
1281 | nonZero= 0; |
---|
1282 | for (j = 1; j <= M.NumCols(); j++) |
---|
1283 | { |
---|
1284 | if (!IsZero (M (i,j))) |
---|
1285 | nonZero++; |
---|
1286 | } |
---|
1287 | if (nonZero != 1) |
---|
1288 | return 0; |
---|
1289 | } |
---|
1290 | return 1; |
---|
1291 | } |
---|
1292 | |
---|
1293 | int * extractZeroOneVecs (const mat_zz_p& M) |
---|
1294 | { |
---|
1295 | long i, j; |
---|
1296 | bool nonZeroOne= false; |
---|
1297 | int * result= new int [M.NumCols()]; |
---|
1298 | for (i = 1; i <= M.NumCols(); i++) |
---|
1299 | { |
---|
1300 | for (j = 1; j <= M.NumRows(); j++) |
---|
1301 | { |
---|
1302 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
1303 | { |
---|
1304 | nonZeroOne= true; |
---|
1305 | break; |
---|
1306 | } |
---|
1307 | } |
---|
1308 | if (!nonZeroOne) |
---|
1309 | result [i - 1]= 1; |
---|
1310 | else |
---|
1311 | result [i - 1]= 0; |
---|
1312 | nonZeroOne= false; |
---|
1313 | } |
---|
1314 | return result; |
---|
1315 | } |
---|
1316 | |
---|
1317 | int * extractZeroOneVecs (const mat_zz_pE& M) |
---|
1318 | { |
---|
1319 | long i, j; |
---|
1320 | bool nonZeroOne= false; |
---|
1321 | int * result= new int [M.NumCols()]; |
---|
1322 | for (i = 1; i <= M.NumCols(); i++) |
---|
1323 | { |
---|
1324 | for (j = 1; j <= M.NumRows(); j++) |
---|
1325 | { |
---|
1326 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
1327 | { |
---|
1328 | nonZeroOne= true; |
---|
1329 | break; |
---|
1330 | } |
---|
1331 | } |
---|
1332 | if (!nonZeroOne) |
---|
1333 | result [i - 1]= 1; |
---|
1334 | else |
---|
1335 | result [i - 1]= 0; |
---|
1336 | nonZeroOne= false; |
---|
1337 | } |
---|
1338 | return result; |
---|
1339 | } |
---|
1340 | |
---|
1341 | void |
---|
1342 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
1343 | factors, const int liftBound, int& factorsFound, int*& |
---|
1344 | factorsFoundIndex, mat_zz_pE& N, bool beenInThres |
---|
1345 | ) |
---|
1346 | { |
---|
1347 | Variable y= Variable (2); |
---|
1348 | Variable x= Variable (1); |
---|
1349 | CanonicalForm yToL= power (y, liftBound); |
---|
1350 | if (factors.length() == 2) |
---|
1351 | { |
---|
1352 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1353 | tmp1= factors.getFirst(); |
---|
1354 | tmp2= factors.getLast(); |
---|
1355 | tmp1 *= LC (F, x); |
---|
1356 | tmp1= mod (tmp1, yToL); |
---|
1357 | tmp1 /= content (tmp1, x); |
---|
1358 | tmp2 *= LC (F, x); |
---|
1359 | tmp2= mod (tmp2, yToL); |
---|
1360 | tmp2 /= content (tmp2, x); |
---|
1361 | tmp3 = tmp1*tmp2; |
---|
1362 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
1363 | { |
---|
1364 | factorsFound++; |
---|
1365 | F= 1; |
---|
1366 | reconstructedFactors.append (tmp1); |
---|
1367 | reconstructedFactors.append (tmp2); |
---|
1368 | return; |
---|
1369 | } |
---|
1370 | } |
---|
1371 | CanonicalForm quot, buf; |
---|
1372 | CFListIterator iter; |
---|
1373 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1374 | { |
---|
1375 | if (factorsFoundIndex [i - 1] == 1) |
---|
1376 | continue; |
---|
1377 | iter= factors; |
---|
1378 | if (beenInThres) |
---|
1379 | { |
---|
1380 | int count= 1; |
---|
1381 | while (count < i) |
---|
1382 | { |
---|
1383 | count++; |
---|
1384 | iter++; |
---|
1385 | } |
---|
1386 | buf= iter.getItem(); |
---|
1387 | } |
---|
1388 | else |
---|
1389 | { |
---|
1390 | buf= 1; |
---|
1391 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1392 | { |
---|
1393 | if (!IsZero (N (j,i))) |
---|
1394 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1395 | } |
---|
1396 | } |
---|
1397 | buf *= LC (F, x); |
---|
1398 | buf= mod (buf, yToL); |
---|
1399 | buf /= content (buf, x); |
---|
1400 | if (fdivides (buf, F, quot)) |
---|
1401 | { |
---|
1402 | factorsFoundIndex[i - 1]= 1; |
---|
1403 | factorsFound++; |
---|
1404 | F= quot; |
---|
1405 | F /= Lc (F); |
---|
1406 | reconstructedFactors.append (buf); |
---|
1407 | } |
---|
1408 | if (degree (F) <= 0) |
---|
1409 | return; |
---|
1410 | if (factorsFound + 1 == N.NumCols()) |
---|
1411 | { |
---|
1412 | reconstructedFactors.append (F); |
---|
1413 | return; |
---|
1414 | } |
---|
1415 | } |
---|
1416 | } |
---|
1417 | |
---|
1418 | void |
---|
1419 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
1420 | factors, const int liftBound, int& factorsFound, int*& |
---|
1421 | factorsFoundIndex, mat_zz_p& N, bool beenInThres |
---|
1422 | ) |
---|
1423 | { |
---|
1424 | Variable y= Variable (2); |
---|
1425 | Variable x= Variable (1); |
---|
1426 | CanonicalForm yToL= power (y, liftBound); |
---|
1427 | if (factors.length() == 2) |
---|
1428 | { |
---|
1429 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1430 | tmp1= factors.getFirst(); |
---|
1431 | tmp2= factors.getLast(); |
---|
1432 | tmp1 *= LC (F, x); |
---|
1433 | tmp1= mod (tmp1, yToL); |
---|
1434 | tmp1 /= content (tmp1, x); |
---|
1435 | tmp2 *= LC (F, x); |
---|
1436 | tmp2= mod (tmp2, yToL); |
---|
1437 | tmp2 /= content (tmp2, x); |
---|
1438 | tmp3 = tmp1*tmp2; |
---|
1439 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
1440 | { |
---|
1441 | factorsFound++; |
---|
1442 | F= 1; |
---|
1443 | reconstructedFactors.append (tmp1); |
---|
1444 | reconstructedFactors.append (tmp2); |
---|
1445 | return; |
---|
1446 | } |
---|
1447 | } |
---|
1448 | CanonicalForm quot, buf; |
---|
1449 | CFListIterator iter; |
---|
1450 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1451 | { |
---|
1452 | if (factorsFoundIndex [i - 1] == 1) |
---|
1453 | continue; |
---|
1454 | iter= factors; |
---|
1455 | if (beenInThres) |
---|
1456 | { |
---|
1457 | int count= 1; |
---|
1458 | while (count < i) |
---|
1459 | { |
---|
1460 | count++; |
---|
1461 | iter++; |
---|
1462 | } |
---|
1463 | buf= iter.getItem(); |
---|
1464 | } |
---|
1465 | else |
---|
1466 | { |
---|
1467 | buf= 1; |
---|
1468 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1469 | { |
---|
1470 | if (!IsZero (N (j,i))) |
---|
1471 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1472 | } |
---|
1473 | } |
---|
1474 | buf *= LC (F, x); |
---|
1475 | buf= mod (buf, yToL); |
---|
1476 | buf /= content (buf, x); |
---|
1477 | if (fdivides (buf, F, quot)) |
---|
1478 | { |
---|
1479 | factorsFoundIndex[i - 1]= 1; |
---|
1480 | factorsFound++; |
---|
1481 | F= quot; |
---|
1482 | F /= Lc (F); |
---|
1483 | reconstructedFactors.append (buf); |
---|
1484 | } |
---|
1485 | if (degree (F) <= 0) |
---|
1486 | return; |
---|
1487 | if (factorsFound + 1 == N.NumCols()) |
---|
1488 | { |
---|
1489 | reconstructedFactors.append (F); |
---|
1490 | return; |
---|
1491 | } |
---|
1492 | } |
---|
1493 | } |
---|
1494 | |
---|
1495 | CFList |
---|
1496 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
1497 | precision, const mat_zz_pE& N |
---|
1498 | ) |
---|
1499 | { |
---|
1500 | Variable y= Variable (2); |
---|
1501 | Variable x= Variable (1); |
---|
1502 | CanonicalForm F= G; |
---|
1503 | CanonicalForm yToL= power (y, precision); |
---|
1504 | CanonicalForm quot, buf; |
---|
1505 | CFList result, factorsConsidered; |
---|
1506 | CFList bufFactors= factors; |
---|
1507 | CFListIterator iter; |
---|
1508 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1509 | { |
---|
1510 | if (zeroOneVecs [i - 1] == 0) |
---|
1511 | continue; |
---|
1512 | iter= factors; |
---|
1513 | buf= 1; |
---|
1514 | factorsConsidered= CFList(); |
---|
1515 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1516 | { |
---|
1517 | if (!IsZero (N (j,i))) |
---|
1518 | { |
---|
1519 | factorsConsidered.append (iter.getItem()); |
---|
1520 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1521 | } |
---|
1522 | } |
---|
1523 | buf *= LC (F, x); |
---|
1524 | buf= mod (buf, yToL); |
---|
1525 | buf /= content (buf, x); |
---|
1526 | if (fdivides (buf, F, quot)) |
---|
1527 | { |
---|
1528 | F= quot; |
---|
1529 | F /= Lc (F); |
---|
1530 | result.append (buf); |
---|
1531 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1532 | } |
---|
1533 | if (degree (F) <= 0) |
---|
1534 | { |
---|
1535 | G= F; |
---|
1536 | factors= bufFactors; |
---|
1537 | return result; |
---|
1538 | } |
---|
1539 | } |
---|
1540 | G= F; |
---|
1541 | factors= bufFactors; |
---|
1542 | return result; |
---|
1543 | } |
---|
1544 | |
---|
1545 | CFList |
---|
1546 | monicReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
1547 | int precision, const mat_zz_pE& N |
---|
1548 | ) |
---|
1549 | { |
---|
1550 | Variable y= Variable (2); |
---|
1551 | Variable x= Variable (1); |
---|
1552 | CanonicalForm F= G; |
---|
1553 | CanonicalForm yToL= power (y, precision); |
---|
1554 | CanonicalForm quot, buf, buf2; |
---|
1555 | CFList result; |
---|
1556 | CFList bufFactors= factors; |
---|
1557 | CFList factorsConsidered; |
---|
1558 | CFListIterator iter; |
---|
1559 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1560 | { |
---|
1561 | if (zeroOneVecs [i - 1] == 0) |
---|
1562 | continue; |
---|
1563 | iter= factors; |
---|
1564 | buf= 1; |
---|
1565 | factorsConsidered= CFList(); |
---|
1566 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1567 | { |
---|
1568 | if (!IsZero (N (j,i))) |
---|
1569 | { |
---|
1570 | factorsConsidered.append (iter.getItem()); |
---|
1571 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1572 | } |
---|
1573 | } |
---|
1574 | buf2= buf; |
---|
1575 | buf *= LC (F, x); |
---|
1576 | buf= mod (buf, yToL); |
---|
1577 | buf /= content (buf, x); |
---|
1578 | if (fdivides (buf, F, quot)) |
---|
1579 | { |
---|
1580 | F= quot; |
---|
1581 | F /= Lc (F); |
---|
1582 | result.append (buf2); |
---|
1583 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1584 | } |
---|
1585 | if (degree (F) <= 0) |
---|
1586 | { |
---|
1587 | G= F; |
---|
1588 | factors= bufFactors; |
---|
1589 | return result; |
---|
1590 | } |
---|
1591 | } |
---|
1592 | G= F; |
---|
1593 | factors= bufFactors; |
---|
1594 | return result; |
---|
1595 | } |
---|
1596 | |
---|
1597 | CFList |
---|
1598 | extReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
1599 | precision, const mat_zz_p& N, const ExtensionInfo& info, |
---|
1600 | const CanonicalForm& evaluation |
---|
1601 | ) |
---|
1602 | { |
---|
1603 | Variable y= Variable (2); |
---|
1604 | Variable x= Variable (1); |
---|
1605 | Variable alpha= info.getAlpha(); |
---|
1606 | Variable beta= info.getBeta(); |
---|
1607 | int k= info.getGFDegree(); |
---|
1608 | CanonicalForm gamma= info.getGamma(); |
---|
1609 | CanonicalForm delta= info.getDelta(); |
---|
1610 | CanonicalForm F= G; |
---|
1611 | CanonicalForm yToL= power (y, precision); |
---|
1612 | CFList result; |
---|
1613 | CFList bufFactors= factors; |
---|
1614 | CFList factorsConsidered; |
---|
1615 | CanonicalForm buf2, quot, buf; |
---|
1616 | CFListIterator iter; |
---|
1617 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1618 | { |
---|
1619 | if (zeroOneVecs [i - 1] == 0) |
---|
1620 | continue; |
---|
1621 | iter= factors; |
---|
1622 | buf= 1; |
---|
1623 | factorsConsidered= CFList(); |
---|
1624 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1625 | { |
---|
1626 | if (!IsZero (N (j,i))) |
---|
1627 | { |
---|
1628 | factorsConsidered.append (iter.getItem()); |
---|
1629 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1630 | } |
---|
1631 | } |
---|
1632 | buf *= LC (F, x); |
---|
1633 | buf= mod (buf, yToL); |
---|
1634 | buf /= content (buf, x); |
---|
1635 | buf2= buf (y-evaluation, y); |
---|
1636 | if (!k && beta == x) |
---|
1637 | { |
---|
1638 | if (degree (buf2, alpha) < 1) |
---|
1639 | { |
---|
1640 | if (fdivides (buf, F, quot)) |
---|
1641 | { |
---|
1642 | F= quot; |
---|
1643 | F /= Lc (F); |
---|
1644 | result.append (buf2); |
---|
1645 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1646 | } |
---|
1647 | } |
---|
1648 | } |
---|
1649 | else |
---|
1650 | { |
---|
1651 | CFList source, dest; |
---|
1652 | |
---|
1653 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
1654 | { |
---|
1655 | if (fdivides (buf, F, quot)) |
---|
1656 | { |
---|
1657 | F= quot; |
---|
1658 | F /= Lc (F); |
---|
1659 | result.append (buf2); |
---|
1660 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1661 | } |
---|
1662 | } |
---|
1663 | } |
---|
1664 | if (degree (F) <= 0) |
---|
1665 | { |
---|
1666 | G= F; |
---|
1667 | factors= bufFactors; |
---|
1668 | return result; |
---|
1669 | } |
---|
1670 | } |
---|
1671 | G= F; |
---|
1672 | factors= bufFactors; |
---|
1673 | return result; |
---|
1674 | } |
---|
1675 | |
---|
1676 | CFList |
---|
1677 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
1678 | int precision, const mat_zz_p& N) |
---|
1679 | { |
---|
1680 | Variable y= Variable (2); |
---|
1681 | Variable x= Variable (1); |
---|
1682 | CanonicalForm F= G; |
---|
1683 | CanonicalForm yToL= power (y, precision); |
---|
1684 | CanonicalForm quot, buf; |
---|
1685 | CFList result; |
---|
1686 | CFList bufFactors= factors; |
---|
1687 | CFList factorsConsidered; |
---|
1688 | CFListIterator iter; |
---|
1689 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1690 | { |
---|
1691 | if (zeroOneVecs [i - 1] == 0) |
---|
1692 | continue; |
---|
1693 | iter= factors; |
---|
1694 | buf= 1; |
---|
1695 | factorsConsidered= CFList(); |
---|
1696 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1697 | { |
---|
1698 | if (!IsZero (N (j,i))) |
---|
1699 | { |
---|
1700 | factorsConsidered.append (iter.getItem()); |
---|
1701 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1702 | } |
---|
1703 | } |
---|
1704 | buf *= LC (F, x); |
---|
1705 | buf= mod (buf, yToL); |
---|
1706 | buf /= content (buf, x); |
---|
1707 | if (fdivides (buf, F, quot)) |
---|
1708 | { |
---|
1709 | F= quot; |
---|
1710 | F /= Lc (F); |
---|
1711 | result.append (buf); |
---|
1712 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1713 | } |
---|
1714 | if (degree (F) <= 0) |
---|
1715 | { |
---|
1716 | G= F; |
---|
1717 | factors= bufFactors; |
---|
1718 | return result; |
---|
1719 | } |
---|
1720 | } |
---|
1721 | G= F; |
---|
1722 | factors= bufFactors; |
---|
1723 | return result; |
---|
1724 | } |
---|
1725 | |
---|
1726 | void |
---|
1727 | extReconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const |
---|
1728 | CFList& factors, const int liftBound, int& factorsFound, |
---|
1729 | int*& factorsFoundIndex, mat_zz_p& N, bool beenInThres, |
---|
1730 | const ExtensionInfo& info, const CanonicalForm& evaluation |
---|
1731 | ) |
---|
1732 | { |
---|
1733 | Variable y= Variable (2); |
---|
1734 | Variable x= Variable (1); |
---|
1735 | Variable alpha= info.getAlpha(); |
---|
1736 | Variable beta= info.getBeta(); |
---|
1737 | int k= info.getGFDegree(); |
---|
1738 | CanonicalForm gamma= info.getGamma(); |
---|
1739 | CanonicalForm delta= info.getDelta(); |
---|
1740 | CanonicalForm yToL= power (y, liftBound); |
---|
1741 | CFList source, dest; |
---|
1742 | if (factors.length() == 2) |
---|
1743 | { |
---|
1744 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1745 | tmp1= factors.getFirst(); |
---|
1746 | tmp2= factors.getLast(); |
---|
1747 | tmp1 *= LC (F, x); |
---|
1748 | tmp1= mod (tmp1, yToL); |
---|
1749 | tmp1 /= content (tmp1, x); |
---|
1750 | tmp2 *= LC (F, x); |
---|
1751 | tmp2= mod (tmp2, yToL); |
---|
1752 | tmp2 /= content (tmp2, x); |
---|
1753 | tmp3 = tmp1*tmp2; |
---|
1754 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
1755 | { |
---|
1756 | tmp1= tmp1 (y - evaluation, y); |
---|
1757 | tmp2= tmp2 (y - evaluation, y); |
---|
1758 | if (!k && beta == x && degree (tmp2, alpha) < 1 && |
---|
1759 | degree (tmp1, alpha) < 1) |
---|
1760 | { |
---|
1761 | factorsFound++; |
---|
1762 | F= 1; |
---|
1763 | tmp1= mapDown (tmp1, info, source, dest); |
---|
1764 | tmp2= mapDown (tmp2, info, source, dest); |
---|
1765 | reconstructedFactors.append (tmp1); |
---|
1766 | reconstructedFactors.append (tmp2); |
---|
1767 | return; |
---|
1768 | } |
---|
1769 | else if (!isInExtension (tmp2, gamma, k, delta, source, dest) && |
---|
1770 | !isInExtension (tmp1, gamma, k, delta, source, dest)) |
---|
1771 | { |
---|
1772 | factorsFound++; |
---|
1773 | F= 1; |
---|
1774 | tmp1= mapDown (tmp1, info, source, dest); |
---|
1775 | tmp2= mapDown (tmp2, info, source, dest); |
---|
1776 | reconstructedFactors.append (tmp1); |
---|
1777 | reconstructedFactors.append (tmp2); |
---|
1778 | return; |
---|
1779 | } |
---|
1780 | } |
---|
1781 | } |
---|
1782 | CanonicalForm quot, buf, buf2; |
---|
1783 | CFListIterator iter; |
---|
1784 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1785 | { |
---|
1786 | if (factorsFoundIndex [i - 1] == 1) |
---|
1787 | continue; |
---|
1788 | iter= factors; |
---|
1789 | if (beenInThres) |
---|
1790 | { |
---|
1791 | int count= 1; |
---|
1792 | while (count < i) |
---|
1793 | { |
---|
1794 | count++; |
---|
1795 | iter++; |
---|
1796 | } |
---|
1797 | buf= iter.getItem(); |
---|
1798 | } |
---|
1799 | else |
---|
1800 | { |
---|
1801 | buf= 1; |
---|
1802 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1803 | { |
---|
1804 | if (!IsZero (N (j,i))) |
---|
1805 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1806 | } |
---|
1807 | } |
---|
1808 | buf *= LC (F, x); |
---|
1809 | buf= mod (buf, yToL); |
---|
1810 | buf /= content (buf, x); |
---|
1811 | buf2= buf (y - evaluation, y); |
---|
1812 | if (!k && beta == x) |
---|
1813 | { |
---|
1814 | if (degree (buf2, alpha) < 1) |
---|
1815 | { |
---|
1816 | if (fdivides (buf, F, quot)) |
---|
1817 | { |
---|
1818 | factorsFoundIndex[i - 1]= 1; |
---|
1819 | factorsFound++; |
---|
1820 | F= quot; |
---|
1821 | F /= Lc (F); |
---|
1822 | buf2= mapDown (buf2, info, source, dest); |
---|
1823 | reconstructedFactors.append (buf2); |
---|
1824 | } |
---|
1825 | } |
---|
1826 | } |
---|
1827 | else |
---|
1828 | { |
---|
1829 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
1830 | { |
---|
1831 | if (fdivides (buf, F, quot)) |
---|
1832 | { |
---|
1833 | factorsFoundIndex[i - 1]= 1; |
---|
1834 | factorsFound++; |
---|
1835 | F= quot; |
---|
1836 | F /= Lc (F); |
---|
1837 | buf2= mapDown (buf2, info, source, dest); |
---|
1838 | reconstructedFactors.append (buf2); |
---|
1839 | } |
---|
1840 | } |
---|
1841 | } |
---|
1842 | if (degree (F) <= 0) |
---|
1843 | return; |
---|
1844 | if (factorsFound + 1 == N.NumCols()) |
---|
1845 | { |
---|
1846 | CanonicalForm tmp= F (y - evaluation, y); |
---|
1847 | tmp= mapDown (tmp, info, source, dest); |
---|
1848 | reconstructedFactors.append (tmp); |
---|
1849 | return; |
---|
1850 | } |
---|
1851 | } |
---|
1852 | } |
---|
1853 | |
---|
1854 | //over Fp |
---|
1855 | int |
---|
1856 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, int |
---|
1857 | start, int liftBound, int minBound, CFList& factors, |
---|
1858 | mat_zz_p& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
1859 | Pi, CFArray& bufQ, bool& irreducible |
---|
1860 | ) |
---|
1861 | { |
---|
1862 | CanonicalForm LCF= LC (F, 1); |
---|
1863 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
1864 | bool wasInBounds= false; |
---|
1865 | bool hitBound= false; |
---|
1866 | int l= (minBound+1)*2; |
---|
1867 | int stepSize= 2; |
---|
1868 | int oldL= l/2; |
---|
1869 | bool reduced= false; |
---|
1870 | mat_zz_p NTLK, *NTLC; |
---|
1871 | CFMatrix C; |
---|
1872 | CFArray buf; |
---|
1873 | CFListIterator j; |
---|
1874 | CanonicalForm truncF; |
---|
1875 | Variable y= F.mvar(); |
---|
1876 | while (l <= liftBound) |
---|
1877 | { |
---|
1878 | if (start) |
---|
1879 | { |
---|
1880 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
1881 | start= 0; |
---|
1882 | } |
---|
1883 | else |
---|
1884 | { |
---|
1885 | if (wasInBounds) |
---|
1886 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
1887 | else |
---|
1888 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
1889 | } |
---|
1890 | |
---|
1891 | factors.insert (LCF); |
---|
1892 | j= factors; |
---|
1893 | j++; |
---|
1894 | |
---|
1895 | truncF= mod (F, power (y, l)); |
---|
1896 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
1897 | { |
---|
1898 | if (!wasInBounds) |
---|
1899 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
1900 | else |
---|
1901 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
1902 | bufQ[i]); |
---|
1903 | } |
---|
1904 | |
---|
1905 | for (int i= 0; i < sizeBounds; i++) |
---|
1906 | { |
---|
1907 | if (bounds [i] + 1 <= l/2) |
---|
1908 | { |
---|
1909 | wasInBounds= true; |
---|
1910 | int k= tmin (bounds [i] + 1, l/2); |
---|
1911 | C= CFMatrix (l - k, factors.length() - 1); |
---|
1912 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
1913 | { |
---|
1914 | if (A[ii].size() - 1 >= i) |
---|
1915 | { |
---|
1916 | buf= getCoeffs (A[ii] [i], k); |
---|
1917 | writeInMatrix (C, buf, ii + 1, 0); |
---|
1918 | } |
---|
1919 | } |
---|
1920 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
1921 | NTLK= (*NTLC)*NTLN; |
---|
1922 | transpose (NTLK, NTLK); |
---|
1923 | kernel (NTLK, NTLK); |
---|
1924 | transpose (NTLK, NTLK); |
---|
1925 | NTLN *= NTLK; |
---|
1926 | |
---|
1927 | if (NTLN.NumCols() == 1) |
---|
1928 | { |
---|
1929 | irreducible= true; |
---|
1930 | break; |
---|
1931 | } |
---|
1932 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
1933 | { |
---|
1934 | reduced= true; |
---|
1935 | break; |
---|
1936 | } |
---|
1937 | } |
---|
1938 | } |
---|
1939 | |
---|
1940 | if (irreducible) |
---|
1941 | break; |
---|
1942 | if (reduced) |
---|
1943 | break; |
---|
1944 | oldL= l; |
---|
1945 | l += stepSize; |
---|
1946 | stepSize *= 2; |
---|
1947 | if (l > liftBound) |
---|
1948 | { |
---|
1949 | if (!hitBound) |
---|
1950 | { |
---|
1951 | l= liftBound; |
---|
1952 | hitBound= true; |
---|
1953 | } |
---|
1954 | else |
---|
1955 | break; |
---|
1956 | } |
---|
1957 | } |
---|
1958 | delete [] A; |
---|
1959 | return l; |
---|
1960 | } |
---|
1961 | |
---|
1962 | //over field extension |
---|
1963 | int |
---|
1964 | extLiftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
1965 | int liftBound, int minBound, int start, CFList& |
---|
1966 | factors, mat_zz_p& NTLN, CFList& diophant, |
---|
1967 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, bool& |
---|
1968 | irreducible, const CanonicalForm& evaluation, const |
---|
1969 | ExtensionInfo& info, CFList& source, CFList& dest |
---|
1970 | ) |
---|
1971 | { |
---|
1972 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
1973 | CanonicalForm LCF= LC (F, 1); |
---|
1974 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
1975 | bool wasInBounds= false; |
---|
1976 | bool hitBound= false; |
---|
1977 | int degMipo; |
---|
1978 | Variable alpha; |
---|
1979 | alpha= info.getAlpha(); |
---|
1980 | degMipo= degree (getMipo (alpha)); |
---|
1981 | |
---|
1982 | Variable gamma= info.getBeta(); |
---|
1983 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
1984 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
1985 | |
---|
1986 | int stepSize= 2; |
---|
1987 | int l= ((minBound+1)/degMipo+1)*2; |
---|
1988 | l= tmax (l, 2); |
---|
1989 | if (start > l) |
---|
1990 | l= start; |
---|
1991 | int oldL= l/2; |
---|
1992 | bool reduced= false; |
---|
1993 | Variable y= F.mvar(); |
---|
1994 | Variable x= Variable (1); |
---|
1995 | CanonicalForm powX, imBasis, truncF; |
---|
1996 | CFMatrix Mat, C; |
---|
1997 | CFArray buf; |
---|
1998 | CFIterator iter; |
---|
1999 | mat_zz_p* NTLMat, *NTLC, NTLK; |
---|
2000 | CFListIterator j; |
---|
2001 | while (l <= liftBound) |
---|
2002 | { |
---|
2003 | if (start) |
---|
2004 | { |
---|
2005 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
2006 | start= 0; |
---|
2007 | } |
---|
2008 | else |
---|
2009 | { |
---|
2010 | if (wasInBounds) |
---|
2011 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
2012 | else |
---|
2013 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
2014 | } |
---|
2015 | |
---|
2016 | factors.insert (LCF); |
---|
2017 | |
---|
2018 | if (GF) |
---|
2019 | setCharacteristic (getCharacteristic()); |
---|
2020 | |
---|
2021 | powX= power (y-gamma, l); |
---|
2022 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
2023 | for (int i= 0; i < l*degMipo; i++) |
---|
2024 | { |
---|
2025 | imBasis= mod (power (y, i), powX); |
---|
2026 | imBasis= imBasis (power (y, degMipo), y); |
---|
2027 | imBasis= imBasis (y, gamma); |
---|
2028 | iter= imBasis; |
---|
2029 | for (; iter.hasTerms(); iter++) |
---|
2030 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
2031 | } |
---|
2032 | |
---|
2033 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
2034 | *NTLMat= inv (*NTLMat); |
---|
2035 | |
---|
2036 | if (GF) |
---|
2037 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2038 | |
---|
2039 | j= factors; |
---|
2040 | j++; |
---|
2041 | |
---|
2042 | truncF= mod (F, power (y, l)); |
---|
2043 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
2044 | { |
---|
2045 | if (!wasInBounds) |
---|
2046 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
2047 | else |
---|
2048 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
2049 | bufQ[i]); |
---|
2050 | } |
---|
2051 | |
---|
2052 | for (int i= 0; i < sizeBounds; i++) |
---|
2053 | { |
---|
2054 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
2055 | { |
---|
2056 | wasInBounds= true; |
---|
2057 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
2058 | C= CFMatrix (l*degMipo - k, factors.length() - 1); |
---|
2059 | |
---|
2060 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
2061 | { |
---|
2062 | if (A[ii].size() - 1 >= i) |
---|
2063 | { |
---|
2064 | if (GF) |
---|
2065 | { |
---|
2066 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2067 | setCharacteristic (getCharacteristic()); |
---|
2068 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
2069 | if (alpha != gamma) |
---|
2070 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2071 | gamma, source, dest |
---|
2072 | ); |
---|
2073 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
2074 | } |
---|
2075 | else |
---|
2076 | { |
---|
2077 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2078 | if (alpha != gamma) |
---|
2079 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2080 | gamma, source, dest |
---|
2081 | ); |
---|
2082 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
2083 | } |
---|
2084 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2085 | } |
---|
2086 | if (GF) |
---|
2087 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2088 | } |
---|
2089 | |
---|
2090 | if (GF) |
---|
2091 | setCharacteristic(getCharacteristic()); |
---|
2092 | |
---|
2093 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2094 | NTLK= (*NTLC)*NTLN; |
---|
2095 | transpose (NTLK, NTLK); |
---|
2096 | kernel (NTLK, NTLK); |
---|
2097 | transpose (NTLK, NTLK); |
---|
2098 | NTLN *= NTLK; |
---|
2099 | |
---|
2100 | if (GF) |
---|
2101 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2102 | |
---|
2103 | if (NTLN.NumCols() == 1) |
---|
2104 | { |
---|
2105 | irreducible= true; |
---|
2106 | break; |
---|
2107 | } |
---|
2108 | if (isReduced (NTLN)) |
---|
2109 | { |
---|
2110 | reduced= true; |
---|
2111 | break; |
---|
2112 | } |
---|
2113 | } |
---|
2114 | } |
---|
2115 | |
---|
2116 | if (NTLN.NumCols() == 1) |
---|
2117 | { |
---|
2118 | irreducible= true; |
---|
2119 | break; |
---|
2120 | } |
---|
2121 | if (reduced) |
---|
2122 | break; |
---|
2123 | oldL= l; |
---|
2124 | l += stepSize; |
---|
2125 | stepSize *= 2; |
---|
2126 | if (l > liftBound) |
---|
2127 | { |
---|
2128 | if (!hitBound) |
---|
2129 | { |
---|
2130 | l= liftBound; |
---|
2131 | hitBound= true; |
---|
2132 | } |
---|
2133 | else |
---|
2134 | break; |
---|
2135 | } |
---|
2136 | } |
---|
2137 | delete [] A; |
---|
2138 | return l; |
---|
2139 | } |
---|
2140 | |
---|
2141 | // over Fq |
---|
2142 | int |
---|
2143 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
2144 | int start, int liftBound, int minBound, CFList& factors, |
---|
2145 | mat_zz_pE& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
2146 | Pi, CFArray& bufQ, bool& irreducible |
---|
2147 | ) |
---|
2148 | { |
---|
2149 | CanonicalForm LCF= LC (F, 1); |
---|
2150 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
2151 | bool wasInBounds= false; |
---|
2152 | bool hitBound= false; |
---|
2153 | int l= (minBound+1)*2; |
---|
2154 | int stepSize= 2; |
---|
2155 | int oldL= l/2; |
---|
2156 | bool reduced= false; |
---|
2157 | CFListIterator j; |
---|
2158 | mat_zz_pE* NTLC, NTLK; |
---|
2159 | CFArray buf; |
---|
2160 | CFMatrix C; |
---|
2161 | Variable y= F.mvar(); |
---|
2162 | CanonicalForm truncF; |
---|
2163 | while (l <= liftBound) |
---|
2164 | { |
---|
2165 | if (start) |
---|
2166 | { |
---|
2167 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
2168 | start= 0; |
---|
2169 | } |
---|
2170 | else |
---|
2171 | { |
---|
2172 | if (wasInBounds) |
---|
2173 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
2174 | else |
---|
2175 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
2176 | } |
---|
2177 | |
---|
2178 | factors.insert (LCF); |
---|
2179 | j= factors; |
---|
2180 | j++; |
---|
2181 | |
---|
2182 | truncF= mod (F, power (y,l)); |
---|
2183 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
2184 | { |
---|
2185 | if (l == (minBound+1)*2) |
---|
2186 | { |
---|
2187 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
2188 | } |
---|
2189 | else |
---|
2190 | { |
---|
2191 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
2192 | bufQ[i] |
---|
2193 | ); |
---|
2194 | } |
---|
2195 | } |
---|
2196 | |
---|
2197 | for (int i= 0; i < sizeBounds; i++) |
---|
2198 | { |
---|
2199 | if (bounds [i] + 1 <= l/2) |
---|
2200 | { |
---|
2201 | wasInBounds= true; |
---|
2202 | int k= tmin (bounds [i] + 1, l/2); |
---|
2203 | C= CFMatrix (l - k, factors.length() - 1); |
---|
2204 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
2205 | { |
---|
2206 | |
---|
2207 | if (A[ii].size() - 1 >= i) |
---|
2208 | { |
---|
2209 | buf= getCoeffs (A[ii] [i], k); |
---|
2210 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2211 | } |
---|
2212 | } |
---|
2213 | |
---|
2214 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
2215 | NTLK= (*NTLC)*NTLN; |
---|
2216 | transpose (NTLK, NTLK); |
---|
2217 | kernel (NTLK, NTLK); |
---|
2218 | transpose (NTLK, NTLK); |
---|
2219 | NTLN *= NTLK; |
---|
2220 | |
---|
2221 | if (NTLN.NumCols() == 1) |
---|
2222 | { |
---|
2223 | irreducible= true; |
---|
2224 | break; |
---|
2225 | } |
---|
2226 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
2227 | { |
---|
2228 | reduced= true; |
---|
2229 | break; |
---|
2230 | } |
---|
2231 | } |
---|
2232 | } |
---|
2233 | |
---|
2234 | if (NTLN.NumCols() == 1) |
---|
2235 | { |
---|
2236 | irreducible= true; |
---|
2237 | break; |
---|
2238 | } |
---|
2239 | if (reduced) |
---|
2240 | break; |
---|
2241 | oldL= l; |
---|
2242 | l += stepSize; |
---|
2243 | stepSize *= 2; |
---|
2244 | if (l > liftBound) |
---|
2245 | { |
---|
2246 | if (!hitBound) |
---|
2247 | { |
---|
2248 | l= liftBound; |
---|
2249 | hitBound= true; |
---|
2250 | } |
---|
2251 | else |
---|
2252 | break; |
---|
2253 | } |
---|
2254 | } |
---|
2255 | delete [] A; |
---|
2256 | return l; |
---|
2257 | } |
---|
2258 | |
---|
2259 | int |
---|
2260 | liftAndComputeLatticeFq2Fp (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
2261 | int start, int liftBound, int minBound, CFList& |
---|
2262 | factors, mat_zz_p& NTLN, CFList& diophant, CFMatrix& |
---|
2263 | M, CFArray& Pi, CFArray& bufQ, bool& irreducible, |
---|
2264 | const Variable& alpha |
---|
2265 | ) |
---|
2266 | { |
---|
2267 | CanonicalForm LCF= LC (F, 1); |
---|
2268 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
2269 | bool wasInBounds= false; |
---|
2270 | int l= (minBound+1)*2; |
---|
2271 | int oldL= l/2; |
---|
2272 | int stepSize= 2; |
---|
2273 | bool hitBound= false; |
---|
2274 | int extensionDeg= degree (getMipo (alpha)); |
---|
2275 | bool reduced= false; |
---|
2276 | CFListIterator j; |
---|
2277 | CFMatrix C; |
---|
2278 | CFArray buf; |
---|
2279 | mat_zz_p* NTLC, NTLK; |
---|
2280 | Variable y= F.mvar(); |
---|
2281 | CanonicalForm truncF; |
---|
2282 | while (l <= liftBound) |
---|
2283 | { |
---|
2284 | if (start) |
---|
2285 | { |
---|
2286 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
2287 | start= 0; |
---|
2288 | } |
---|
2289 | else |
---|
2290 | { |
---|
2291 | if (wasInBounds) |
---|
2292 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
2293 | else |
---|
2294 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
2295 | } |
---|
2296 | |
---|
2297 | factors.insert (LCF); |
---|
2298 | j= factors; |
---|
2299 | j++; |
---|
2300 | |
---|
2301 | truncF= mod (F, power (y,l)); |
---|
2302 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
2303 | { |
---|
2304 | if (l == (minBound+1)*2) |
---|
2305 | { |
---|
2306 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
2307 | } |
---|
2308 | else |
---|
2309 | { |
---|
2310 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
2311 | bufQ[i] |
---|
2312 | ); |
---|
2313 | } |
---|
2314 | } |
---|
2315 | |
---|
2316 | for (int i= 0; i < sizeBounds; i++) |
---|
2317 | { |
---|
2318 | if (bounds [i] + 1 <= l/2) |
---|
2319 | { |
---|
2320 | wasInBounds= true; |
---|
2321 | int k= tmin (bounds [i] + 1, l/2); |
---|
2322 | C= CFMatrix ((l - k)*extensionDeg, factors.length() - 1); |
---|
2323 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
2324 | { |
---|
2325 | if (A[ii].size() - 1 >= i) |
---|
2326 | { |
---|
2327 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
2328 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2329 | } |
---|
2330 | } |
---|
2331 | |
---|
2332 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2333 | NTLK= (*NTLC)*NTLN; |
---|
2334 | transpose (NTLK, NTLK); |
---|
2335 | kernel (NTLK, NTLK); |
---|
2336 | transpose (NTLK, NTLK); |
---|
2337 | NTLN *= NTLK; |
---|
2338 | |
---|
2339 | if (NTLN.NumCols() == 1) |
---|
2340 | { |
---|
2341 | irreducible= true; |
---|
2342 | break; |
---|
2343 | } |
---|
2344 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
2345 | { |
---|
2346 | reduced= true; |
---|
2347 | break; |
---|
2348 | } |
---|
2349 | } |
---|
2350 | } |
---|
2351 | |
---|
2352 | if (NTLN.NumCols() == 1) |
---|
2353 | { |
---|
2354 | irreducible= true; |
---|
2355 | break; |
---|
2356 | } |
---|
2357 | if (reduced) |
---|
2358 | break; |
---|
2359 | oldL= l; |
---|
2360 | l += stepSize; |
---|
2361 | stepSize *= 2; |
---|
2362 | if (l > liftBound) |
---|
2363 | { |
---|
2364 | if (!hitBound) |
---|
2365 | { |
---|
2366 | l= liftBound; |
---|
2367 | hitBound= true; |
---|
2368 | } |
---|
2369 | else |
---|
2370 | break; |
---|
2371 | } |
---|
2372 | } |
---|
2373 | delete [] A; |
---|
2374 | return l; |
---|
2375 | } |
---|
2376 | |
---|
2377 | CFList |
---|
2378 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
2379 | int oldNumCols, int oldL, int precision |
---|
2380 | ) |
---|
2381 | { |
---|
2382 | int d; |
---|
2383 | bool isIrreducible= false; |
---|
2384 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
2385 | if (isIrreducible) |
---|
2386 | { |
---|
2387 | delete [] bounds; |
---|
2388 | CanonicalForm G= F; |
---|
2389 | F= 1; |
---|
2390 | return CFList (G); |
---|
2391 | } |
---|
2392 | CFArray * A= new CFArray [factors.length()]; |
---|
2393 | CFArray bufQ= CFArray (factors.length()); |
---|
2394 | mat_zz_p NTLN; |
---|
2395 | ident (NTLN, factors.length()); |
---|
2396 | int minBound= bounds[0]; |
---|
2397 | for (int i= 1; i < d; i++) |
---|
2398 | { |
---|
2399 | if (bounds[i] != 0) |
---|
2400 | minBound= tmin (minBound, bounds[i]); |
---|
2401 | } |
---|
2402 | int l= tmax (2*(minBound + 1), oldL); |
---|
2403 | int oldL2= l/2; |
---|
2404 | int stepSize= 2; |
---|
2405 | bool useOldQs= false; |
---|
2406 | bool hitBound= false; |
---|
2407 | CFListIterator j; |
---|
2408 | CFMatrix C; |
---|
2409 | CFArray buf; |
---|
2410 | mat_zz_p* NTLC, NTLK; |
---|
2411 | Variable y= F.mvar(); |
---|
2412 | CanonicalForm truncF; |
---|
2413 | while (l <= precision) |
---|
2414 | { |
---|
2415 | j= factors; |
---|
2416 | truncF= mod (F, power (y,l)); |
---|
2417 | if (useOldQs) |
---|
2418 | { |
---|
2419 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2420 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
2421 | bufQ[i] |
---|
2422 | ); |
---|
2423 | } |
---|
2424 | else |
---|
2425 | { |
---|
2426 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2427 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
2428 | } |
---|
2429 | useOldQs= true; |
---|
2430 | for (int i= 0; i < d; i++) |
---|
2431 | { |
---|
2432 | if (bounds [i] + 1 <= l/2) |
---|
2433 | { |
---|
2434 | int k= tmin (bounds [i] + 1, l/2); |
---|
2435 | C= CFMatrix (l - k, factors.length()); |
---|
2436 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2437 | { |
---|
2438 | if (A[ii].size() - 1 >= i) |
---|
2439 | { |
---|
2440 | buf= getCoeffs (A[ii] [i], k); |
---|
2441 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2442 | } |
---|
2443 | } |
---|
2444 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2445 | NTLK= (*NTLC)*NTLN; |
---|
2446 | transpose (NTLK, NTLK); |
---|
2447 | kernel (NTLK, NTLK); |
---|
2448 | transpose (NTLK, NTLK); |
---|
2449 | NTLN *= NTLK; |
---|
2450 | if (NTLN.NumCols() == 1) |
---|
2451 | { |
---|
2452 | delete [] A; |
---|
2453 | delete [] bounds; |
---|
2454 | CanonicalForm G= F; |
---|
2455 | F= 1; |
---|
2456 | return CFList (G); |
---|
2457 | } |
---|
2458 | } |
---|
2459 | } |
---|
2460 | |
---|
2461 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
2462 | { |
---|
2463 | if (isReduced (NTLN)) |
---|
2464 | { |
---|
2465 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
2466 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
2467 | factorsFoundIndex[i]= 0; |
---|
2468 | int factorsFound2= 0; |
---|
2469 | CFList result; |
---|
2470 | CanonicalForm bufF= F; |
---|
2471 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
2472 | factorsFoundIndex, NTLN, false |
---|
2473 | ); |
---|
2474 | if (result.length() == NTLN.NumCols()) |
---|
2475 | { |
---|
2476 | delete [] factorsFoundIndex; |
---|
2477 | delete [] A; |
---|
2478 | delete [] bounds; |
---|
2479 | F= 1; |
---|
2480 | return result; |
---|
2481 | } |
---|
2482 | delete [] factorsFoundIndex; |
---|
2483 | } |
---|
2484 | else if (l == precision) |
---|
2485 | { |
---|
2486 | CanonicalForm bufF= F; |
---|
2487 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
2488 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
2489 | F= bufF; |
---|
2490 | delete [] zeroOne; |
---|
2491 | delete [] A; |
---|
2492 | delete [] bounds; |
---|
2493 | return result; |
---|
2494 | } |
---|
2495 | } |
---|
2496 | oldL2= l; |
---|
2497 | l += stepSize; |
---|
2498 | stepSize *= 2; |
---|
2499 | if (l > precision) |
---|
2500 | { |
---|
2501 | if (!hitBound) |
---|
2502 | { |
---|
2503 | l= precision; |
---|
2504 | hitBound= true; |
---|
2505 | } |
---|
2506 | else |
---|
2507 | break; |
---|
2508 | } |
---|
2509 | } |
---|
2510 | delete [] bounds; |
---|
2511 | delete [] A; |
---|
2512 | return CFList(); |
---|
2513 | } |
---|
2514 | |
---|
2515 | CFList |
---|
2516 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
2517 | int oldNumCols, int oldL, const Variable&, |
---|
2518 | int precision |
---|
2519 | ) |
---|
2520 | { |
---|
2521 | int d; |
---|
2522 | bool isIrreducible= false; |
---|
2523 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
2524 | if (isIrreducible) |
---|
2525 | { |
---|
2526 | delete [] bounds; |
---|
2527 | CanonicalForm G= F; |
---|
2528 | F= 1; |
---|
2529 | return CFList (G); |
---|
2530 | } |
---|
2531 | CFArray * A= new CFArray [factors.length()]; |
---|
2532 | CFArray bufQ= CFArray (factors.length()); |
---|
2533 | mat_zz_pE NTLN; |
---|
2534 | ident (NTLN, factors.length()); |
---|
2535 | int minBound= bounds[0]; |
---|
2536 | for (int i= 1; i < d; i++) |
---|
2537 | { |
---|
2538 | if (bounds[i] != 0) |
---|
2539 | minBound= tmin (minBound, bounds[i]); |
---|
2540 | } |
---|
2541 | int l= tmax (2*(minBound + 1), oldL); |
---|
2542 | int oldL2= l/2; |
---|
2543 | int stepSize= 2; |
---|
2544 | bool useOldQs= false; |
---|
2545 | bool hitBound= false; |
---|
2546 | CFListIterator j; |
---|
2547 | CFMatrix C; |
---|
2548 | mat_zz_pE* NTLC, NTLK; |
---|
2549 | CFArray buf; |
---|
2550 | Variable y= F.mvar(); |
---|
2551 | CanonicalForm truncF; |
---|
2552 | while (l <= precision) |
---|
2553 | { |
---|
2554 | j= factors; |
---|
2555 | truncF= mod (F, power (y,l)); |
---|
2556 | if (useOldQs) |
---|
2557 | { |
---|
2558 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2559 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
2560 | bufQ[i] |
---|
2561 | ); |
---|
2562 | } |
---|
2563 | else |
---|
2564 | { |
---|
2565 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2566 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
2567 | } |
---|
2568 | useOldQs= true; |
---|
2569 | for (int i= 0; i < d; i++) |
---|
2570 | { |
---|
2571 | if (bounds [i] + 1 <= l/2) |
---|
2572 | { |
---|
2573 | int k= tmin (bounds [i] + 1, l/2); |
---|
2574 | C= CFMatrix (l - k, factors.length()); |
---|
2575 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2576 | { |
---|
2577 | if (A[ii].size() - 1 >= i) |
---|
2578 | { |
---|
2579 | buf= getCoeffs (A[ii] [i], k); |
---|
2580 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2581 | } |
---|
2582 | } |
---|
2583 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
2584 | NTLK= (*NTLC)*NTLN; |
---|
2585 | transpose (NTLK, NTLK); |
---|
2586 | kernel (NTLK, NTLK); |
---|
2587 | transpose (NTLK, NTLK); |
---|
2588 | NTLN *= NTLK; |
---|
2589 | if (NTLN.NumCols() == 1) |
---|
2590 | { |
---|
2591 | delete [] A; |
---|
2592 | delete [] bounds; |
---|
2593 | CanonicalForm G= F; |
---|
2594 | F= 1; |
---|
2595 | return CFList (G); |
---|
2596 | } |
---|
2597 | } |
---|
2598 | } |
---|
2599 | |
---|
2600 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
2601 | { |
---|
2602 | if (isReduced (NTLN)) |
---|
2603 | { |
---|
2604 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
2605 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
2606 | factorsFoundIndex[i]= 0; |
---|
2607 | int factorsFound2= 0; |
---|
2608 | CFList result; |
---|
2609 | CanonicalForm bufF= F; |
---|
2610 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
2611 | factorsFoundIndex, NTLN, false); |
---|
2612 | if (result.length() == NTLN.NumCols()) |
---|
2613 | { |
---|
2614 | delete [] factorsFoundIndex; |
---|
2615 | delete [] A; |
---|
2616 | delete [] bounds; |
---|
2617 | F= 1; |
---|
2618 | return result; |
---|
2619 | } |
---|
2620 | delete [] factorsFoundIndex; |
---|
2621 | } |
---|
2622 | else if (l == precision) |
---|
2623 | { |
---|
2624 | CanonicalForm bufF= F; |
---|
2625 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
2626 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
2627 | F= bufF; |
---|
2628 | delete [] zeroOne; |
---|
2629 | delete [] A; |
---|
2630 | delete [] bounds; |
---|
2631 | return result; |
---|
2632 | } |
---|
2633 | } |
---|
2634 | oldL2= l; |
---|
2635 | l += stepSize; |
---|
2636 | stepSize *= 2; |
---|
2637 | if (l > precision) |
---|
2638 | { |
---|
2639 | if (!hitBound) |
---|
2640 | { |
---|
2641 | l= precision; |
---|
2642 | hitBound= true; |
---|
2643 | } |
---|
2644 | else |
---|
2645 | break; |
---|
2646 | } |
---|
2647 | } |
---|
2648 | delete [] bounds; |
---|
2649 | delete [] A; |
---|
2650 | return CFList(); |
---|
2651 | } |
---|
2652 | |
---|
2653 | //over field extension |
---|
2654 | CFList |
---|
2655 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
2656 | int oldNumCols, int oldL, const CanonicalForm& evaluation, |
---|
2657 | const ExtensionInfo& info, CFList& source, CFList& dest, |
---|
2658 | int precision |
---|
2659 | ) |
---|
2660 | { |
---|
2661 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
2662 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
2663 | Variable alpha= info.getAlpha(); |
---|
2664 | int d; |
---|
2665 | bool isIrreducible= false; |
---|
2666 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
2667 | if (isIrreducible) |
---|
2668 | { |
---|
2669 | delete [] bounds; |
---|
2670 | CanonicalForm G= F; |
---|
2671 | F= 1; |
---|
2672 | return CFList (G); |
---|
2673 | } |
---|
2674 | |
---|
2675 | CFArray * A= new CFArray [factors.length()]; |
---|
2676 | CFArray bufQ= CFArray (factors.length()); |
---|
2677 | zz_p::init (getCharacteristic()); |
---|
2678 | mat_zz_p NTLN; |
---|
2679 | ident (NTLN, factors.length()); |
---|
2680 | int minBound= bounds[0]; |
---|
2681 | for (int i= 1; i < d; i++) |
---|
2682 | { |
---|
2683 | if (bounds[i] != 0) |
---|
2684 | minBound= tmin (minBound, bounds[i]); |
---|
2685 | } |
---|
2686 | int l= tmax (oldL, 2*((minBound+1)/degMipo+1)); |
---|
2687 | int oldL2= l/2; |
---|
2688 | int stepSize= 2; |
---|
2689 | bool useOldQs= false; |
---|
2690 | bool hitBound= false; |
---|
2691 | Variable gamma= info.getBeta(); |
---|
2692 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
2693 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
2694 | CFListIterator j; |
---|
2695 | Variable y= F.mvar(); |
---|
2696 | CanonicalForm powX, imBasis, truncF; |
---|
2697 | CFMatrix Mat, C; |
---|
2698 | CFIterator iter; |
---|
2699 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
2700 | CFArray buf; |
---|
2701 | while (l <= precision) |
---|
2702 | { |
---|
2703 | j= factors; |
---|
2704 | if (GF) |
---|
2705 | setCharacteristic (getCharacteristic()); |
---|
2706 | powX= power (y-gamma, l); |
---|
2707 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
2708 | for (int i= 0; i < l*degMipo; i++) |
---|
2709 | { |
---|
2710 | imBasis= mod (power (y, i), powX); |
---|
2711 | imBasis= imBasis (power (y, degMipo), y); |
---|
2712 | imBasis= imBasis (y, gamma); |
---|
2713 | iter= imBasis; |
---|
2714 | for (; iter.hasTerms(); iter++) |
---|
2715 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
2716 | } |
---|
2717 | |
---|
2718 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
2719 | *NTLMat= inv (*NTLMat); |
---|
2720 | if (GF) |
---|
2721 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2722 | |
---|
2723 | truncF= mod (F, power (y, l)); |
---|
2724 | if (useOldQs) |
---|
2725 | { |
---|
2726 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2727 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
2728 | bufQ[i] |
---|
2729 | ); |
---|
2730 | } |
---|
2731 | else |
---|
2732 | { |
---|
2733 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2734 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
2735 | } |
---|
2736 | useOldQs= true; |
---|
2737 | for (int i= 0; i < d; i++) |
---|
2738 | { |
---|
2739 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
2740 | { |
---|
2741 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
2742 | C= CFMatrix (l*degMipo - k, factors.length()); |
---|
2743 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2744 | { |
---|
2745 | if (A[ii].size() - 1 >= i) |
---|
2746 | { |
---|
2747 | if (GF) |
---|
2748 | { |
---|
2749 | A[ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2750 | setCharacteristic (getCharacteristic()); |
---|
2751 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
2752 | if (alpha != gamma) |
---|
2753 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2754 | gamma, source, dest |
---|
2755 | ); |
---|
2756 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
2757 | } |
---|
2758 | else |
---|
2759 | { |
---|
2760 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2761 | if (alpha != gamma) |
---|
2762 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2763 | gamma, source, dest |
---|
2764 | ); |
---|
2765 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
2766 | } |
---|
2767 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2768 | } |
---|
2769 | if (GF) |
---|
2770 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2771 | } |
---|
2772 | |
---|
2773 | if (GF) |
---|
2774 | setCharacteristic(getCharacteristic()); |
---|
2775 | |
---|
2776 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2777 | NTLK= (*NTLC)*NTLN; |
---|
2778 | transpose (NTLK, NTLK); |
---|
2779 | kernel (NTLK, NTLK); |
---|
2780 | transpose (NTLK, NTLK); |
---|
2781 | NTLN *= NTLK; |
---|
2782 | |
---|
2783 | if (GF) |
---|
2784 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2785 | |
---|
2786 | if (NTLN.NumCols() == 1) |
---|
2787 | { |
---|
2788 | Variable y= Variable (2); |
---|
2789 | CanonicalForm tmp= F (y - evaluation, y); |
---|
2790 | CFList source, dest; |
---|
2791 | tmp= mapDown (tmp, info, source, dest); |
---|
2792 | delete [] A; |
---|
2793 | delete [] bounds; |
---|
2794 | F= 1; |
---|
2795 | return CFList (tmp); |
---|
2796 | } |
---|
2797 | } |
---|
2798 | } |
---|
2799 | |
---|
2800 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
2801 | { |
---|
2802 | if (isReduced (NTLN)) |
---|
2803 | { |
---|
2804 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
2805 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
2806 | factorsFoundIndex[i]= 0; |
---|
2807 | int factorsFound2= 0; |
---|
2808 | CFList result; |
---|
2809 | CanonicalForm bufF= F; |
---|
2810 | extReconstructionTry (result, bufF, factors,degree (F)+1, factorsFound2, |
---|
2811 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
2812 | ); |
---|
2813 | if (result.length() == NTLN.NumCols()) |
---|
2814 | { |
---|
2815 | delete [] factorsFoundIndex; |
---|
2816 | delete [] A; |
---|
2817 | delete [] bounds; |
---|
2818 | F= 1; |
---|
2819 | return result; |
---|
2820 | } |
---|
2821 | delete [] factorsFoundIndex; |
---|
2822 | } |
---|
2823 | else if (l == precision) |
---|
2824 | { |
---|
2825 | CanonicalForm bufF= F; |
---|
2826 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
2827 | CFList result= extReconstruction (bufF, factors, zeroOne, precision, |
---|
2828 | NTLN, info, evaluation |
---|
2829 | ); |
---|
2830 | F= bufF; |
---|
2831 | delete [] zeroOne; |
---|
2832 | delete [] A; |
---|
2833 | delete [] bounds; |
---|
2834 | return result; |
---|
2835 | } |
---|
2836 | } |
---|
2837 | oldL2= l; |
---|
2838 | l += stepSize; |
---|
2839 | stepSize *= 2; |
---|
2840 | if (l > precision) |
---|
2841 | { |
---|
2842 | if (!hitBound) |
---|
2843 | { |
---|
2844 | hitBound= true; |
---|
2845 | l= precision; |
---|
2846 | } |
---|
2847 | else |
---|
2848 | break; |
---|
2849 | } |
---|
2850 | } |
---|
2851 | delete [] bounds; |
---|
2852 | delete [] A; |
---|
2853 | return CFList(); |
---|
2854 | } |
---|
2855 | |
---|
2856 | CFList |
---|
2857 | increasePrecision2 (const CanonicalForm& F, CFList& factors, |
---|
2858 | const Variable& alpha, int precision) |
---|
2859 | { |
---|
2860 | int d; |
---|
2861 | bool isIrreducible= false; |
---|
2862 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
2863 | if (isIrreducible) |
---|
2864 | { |
---|
2865 | delete [] bounds; |
---|
2866 | return CFList (F); |
---|
2867 | } |
---|
2868 | CFArray * A= new CFArray [factors.length()]; |
---|
2869 | CFArray bufQ= CFArray (factors.length()); |
---|
2870 | zz_p::init (getCharacteristic()); |
---|
2871 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
2872 | zz_pE::init (NTLMipo); |
---|
2873 | mat_zz_pE NTLN; |
---|
2874 | ident (NTLN, factors.length()); |
---|
2875 | int minBound= bounds[0]; |
---|
2876 | for (int i= 1; i < d; i++) |
---|
2877 | { |
---|
2878 | if (bounds[i] != 0) |
---|
2879 | minBound= tmin (minBound, bounds[i]); |
---|
2880 | } |
---|
2881 | int l= tmin (2*(minBound + 1), precision); |
---|
2882 | int oldL= l/2; |
---|
2883 | int stepSize= 2; |
---|
2884 | bool useOldQs= false; |
---|
2885 | bool hitBound= false; |
---|
2886 | CFListIterator j; |
---|
2887 | CFMatrix C; |
---|
2888 | CFArray buf; |
---|
2889 | mat_zz_pE* NTLC, NTLK; |
---|
2890 | Variable y= F.mvar(); |
---|
2891 | CanonicalForm truncF; |
---|
2892 | while (l <= precision) |
---|
2893 | { |
---|
2894 | j= factors; |
---|
2895 | truncF= mod (F, power (y, l)); |
---|
2896 | if (useOldQs) |
---|
2897 | { |
---|
2898 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2899 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], bufQ[i]); |
---|
2900 | } |
---|
2901 | else |
---|
2902 | { |
---|
2903 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2904 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
2905 | } |
---|
2906 | useOldQs= true; |
---|
2907 | for (int i= 0; i < d; i++) |
---|
2908 | { |
---|
2909 | if (bounds [i] + 1 <= l/2) |
---|
2910 | { |
---|
2911 | int k= tmin (bounds [i] + 1, l/2); |
---|
2912 | C= CFMatrix (l - k, factors.length()); |
---|
2913 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2914 | { |
---|
2915 | if (A[ii].size() - 1 >= i) |
---|
2916 | { |
---|
2917 | buf= getCoeffs (A[ii] [i], k); |
---|
2918 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2919 | } |
---|
2920 | } |
---|
2921 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
2922 | NTLK= (*NTLC)*NTLN; |
---|
2923 | transpose (NTLK, NTLK); |
---|
2924 | kernel (NTLK, NTLK); |
---|
2925 | transpose (NTLK, NTLK); |
---|
2926 | NTLN *= NTLK; |
---|
2927 | if (NTLN.NumCols() == 1) |
---|
2928 | { |
---|
2929 | delete [] A; |
---|
2930 | delete [] bounds; |
---|
2931 | return CFList (F); |
---|
2932 | } |
---|
2933 | } |
---|
2934 | } |
---|
2935 | |
---|
2936 | if (isReduced (NTLN) || l == precision) |
---|
2937 | { |
---|
2938 | CanonicalForm bufF= F; |
---|
2939 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
2940 | CFList bufFactors= factors; |
---|
2941 | CFList result= monicReconstruction (bufF, factors, zeroOne, precision, |
---|
2942 | NTLN |
---|
2943 | ); |
---|
2944 | if (result.length() != NTLN.NumCols() && l != precision) |
---|
2945 | factors= bufFactors; |
---|
2946 | if (result.length() == NTLN.NumCols()) |
---|
2947 | { |
---|
2948 | delete [] zeroOne; |
---|
2949 | delete [] A; |
---|
2950 | delete [] bounds; |
---|
2951 | return result; |
---|
2952 | } |
---|
2953 | if (l == precision) |
---|
2954 | { |
---|
2955 | delete [] zeroOne; |
---|
2956 | delete [] A; |
---|
2957 | delete [] bounds; |
---|
2958 | return Union (result, factors); |
---|
2959 | } |
---|
2960 | } |
---|
2961 | oldL= l; |
---|
2962 | l += stepSize; |
---|
2963 | stepSize *= 2; |
---|
2964 | if (l > precision) |
---|
2965 | { |
---|
2966 | if (!hitBound) |
---|
2967 | { |
---|
2968 | l= precision; |
---|
2969 | hitBound= true; |
---|
2970 | } |
---|
2971 | else |
---|
2972 | break; |
---|
2973 | } |
---|
2974 | } |
---|
2975 | delete [] bounds; |
---|
2976 | delete [] A; |
---|
2977 | return CFList(); |
---|
2978 | } |
---|
2979 | |
---|
2980 | CFList |
---|
2981 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
2982 | int oldNumCols, int oldL, const Variable& alpha, |
---|
2983 | int precision |
---|
2984 | ) |
---|
2985 | { |
---|
2986 | int d; |
---|
2987 | bool isIrreducible= false; |
---|
2988 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
2989 | if (isIrreducible) |
---|
2990 | { |
---|
2991 | delete [] bounds; |
---|
2992 | CanonicalForm G= F; |
---|
2993 | F= 1; |
---|
2994 | return CFList (G); |
---|
2995 | } |
---|
2996 | int extensionDeg= degree (getMipo (alpha)); |
---|
2997 | CFArray * A= new CFArray [factors.length()]; |
---|
2998 | CFArray bufQ= CFArray (factors.length()); |
---|
2999 | mat_zz_p NTLN; |
---|
3000 | ident (NTLN, factors.length()); |
---|
3001 | int minBound= bounds[0]; |
---|
3002 | for (int i= 1; i < d; i++) |
---|
3003 | { |
---|
3004 | if (bounds[i] != 0) |
---|
3005 | minBound= tmin (minBound, bounds[i]); |
---|
3006 | } |
---|
3007 | int l= tmax (2*(minBound + 1), oldL); |
---|
3008 | int oldL2= l/2; |
---|
3009 | int stepSize= 2; |
---|
3010 | bool useOldQs= false; |
---|
3011 | bool hitBound= false; |
---|
3012 | CFListIterator j; |
---|
3013 | CFMatrix C; |
---|
3014 | mat_zz_p* NTLC, NTLK; |
---|
3015 | CFArray buf; |
---|
3016 | Variable y= F.mvar(); |
---|
3017 | CanonicalForm truncF; |
---|
3018 | while (l <= precision) |
---|
3019 | { |
---|
3020 | j= factors; |
---|
3021 | truncF= mod (F, power (y, l)); |
---|
3022 | if (useOldQs) |
---|
3023 | { |
---|
3024 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3025 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
3026 | bufQ[i] |
---|
3027 | ); |
---|
3028 | } |
---|
3029 | else |
---|
3030 | { |
---|
3031 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3032 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3033 | } |
---|
3034 | useOldQs= true; |
---|
3035 | for (int i= 0; i < d; i++) |
---|
3036 | { |
---|
3037 | if (bounds [i] + 1 <= l/2) |
---|
3038 | { |
---|
3039 | int k= tmin (bounds [i] + 1, l/2); |
---|
3040 | C= CFMatrix ((l - k)*extensionDeg, factors.length()); |
---|
3041 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3042 | { |
---|
3043 | if (A[ii].size() - 1 >= i) |
---|
3044 | { |
---|
3045 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
3046 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3047 | } |
---|
3048 | } |
---|
3049 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3050 | NTLK= (*NTLC)*NTLN; |
---|
3051 | transpose (NTLK, NTLK); |
---|
3052 | kernel (NTLK, NTLK); |
---|
3053 | transpose (NTLK, NTLK); |
---|
3054 | NTLN *= NTLK; |
---|
3055 | if (NTLN.NumCols() == 1) |
---|
3056 | { |
---|
3057 | delete [] A; |
---|
3058 | delete [] bounds; |
---|
3059 | CanonicalForm G= F; |
---|
3060 | F= 1; |
---|
3061 | return CFList (G); |
---|
3062 | } |
---|
3063 | } |
---|
3064 | } |
---|
3065 | |
---|
3066 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
3067 | { |
---|
3068 | if (isReduced (NTLN)) |
---|
3069 | { |
---|
3070 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3071 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3072 | factorsFoundIndex[i]= 0; |
---|
3073 | int factorsFound2= 0; |
---|
3074 | CFList result; |
---|
3075 | CanonicalForm bufF= F; |
---|
3076 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
3077 | factorsFoundIndex, NTLN, false |
---|
3078 | ); |
---|
3079 | if (result.length() == NTLN.NumCols()) |
---|
3080 | { |
---|
3081 | delete [] factorsFoundIndex; |
---|
3082 | delete [] A; |
---|
3083 | delete [] bounds; |
---|
3084 | F= 1; |
---|
3085 | return result; |
---|
3086 | } |
---|
3087 | delete [] factorsFoundIndex; |
---|
3088 | } |
---|
3089 | else if (l == precision) |
---|
3090 | { |
---|
3091 | CanonicalForm bufF= F; |
---|
3092 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
3093 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
3094 | F= bufF; |
---|
3095 | delete [] zeroOne; |
---|
3096 | delete [] A; |
---|
3097 | delete [] bounds; |
---|
3098 | return result; |
---|
3099 | } |
---|
3100 | } |
---|
3101 | oldL2= l; |
---|
3102 | l += stepSize; |
---|
3103 | stepSize *= 2; |
---|
3104 | if (l > precision) |
---|
3105 | { |
---|
3106 | if (!hitBound) |
---|
3107 | { |
---|
3108 | hitBound= true; |
---|
3109 | l= precision; |
---|
3110 | } |
---|
3111 | else |
---|
3112 | break; |
---|
3113 | } |
---|
3114 | } |
---|
3115 | delete [] bounds; |
---|
3116 | delete [] A; |
---|
3117 | return CFList(); |
---|
3118 | } |
---|
3119 | |
---|
3120 | CFList |
---|
3121 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
3122 | l, int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN |
---|
3123 | ) |
---|
3124 | { |
---|
3125 | CFList result= CFList(); |
---|
3126 | CFArray * A= new CFArray [factors.length()]; |
---|
3127 | int oldL2= oldL/2; |
---|
3128 | bool hitBound= false; |
---|
3129 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3130 | { |
---|
3131 | ident (NTLN, factors.length()); |
---|
3132 | bufQ= CFArray (factors.length()); |
---|
3133 | } |
---|
3134 | bool useOldQs= false; |
---|
3135 | CFListIterator j; |
---|
3136 | CFMatrix C; |
---|
3137 | CFArray buf; |
---|
3138 | mat_zz_p* NTLC, NTLK; |
---|
3139 | CanonicalForm bufF, truncF; |
---|
3140 | CFList bufUniFactors; |
---|
3141 | Variable y= F.mvar(); |
---|
3142 | while (oldL <= l) |
---|
3143 | { |
---|
3144 | j= factors; |
---|
3145 | truncF= mod (F, power (y, oldL)); |
---|
3146 | if (useOldQs) |
---|
3147 | { |
---|
3148 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3149 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
3150 | bufQ[i] |
---|
3151 | ); |
---|
3152 | } |
---|
3153 | else |
---|
3154 | { |
---|
3155 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3156 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
3157 | } |
---|
3158 | useOldQs= true; |
---|
3159 | |
---|
3160 | for (int i= 0; i < d; i++) |
---|
3161 | { |
---|
3162 | if (bounds [i] + 1 <= oldL/2) |
---|
3163 | { |
---|
3164 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
3165 | C= CFMatrix (oldL - k, factors.length()); |
---|
3166 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3167 | { |
---|
3168 | if (A[ii].size() - 1 >= i) |
---|
3169 | { |
---|
3170 | buf= getCoeffs (A[ii] [i], k); |
---|
3171 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3172 | } |
---|
3173 | } |
---|
3174 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3175 | NTLK= (*NTLC)*NTLN; |
---|
3176 | transpose (NTLK, NTLK); |
---|
3177 | kernel (NTLK, NTLK); |
---|
3178 | transpose (NTLK, NTLK); |
---|
3179 | NTLN *= NTLK; |
---|
3180 | if (NTLN.NumCols() == 1) |
---|
3181 | { |
---|
3182 | delete [] A; |
---|
3183 | return CFList (F); |
---|
3184 | } |
---|
3185 | } |
---|
3186 | } |
---|
3187 | if (NTLN.NumCols() == 1) |
---|
3188 | { |
---|
3189 | delete [] A; |
---|
3190 | return CFList (F); |
---|
3191 | } |
---|
3192 | int * zeroOneVecs; |
---|
3193 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3194 | bufF= F; |
---|
3195 | bufUniFactors= factors; |
---|
3196 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
3197 | delete [] zeroOneVecs; |
---|
3198 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < oldL && result.length() > 0) |
---|
3199 | { |
---|
3200 | F= bufF; |
---|
3201 | factors= bufUniFactors; |
---|
3202 | delete [] A; |
---|
3203 | return result; |
---|
3204 | } |
---|
3205 | |
---|
3206 | result= CFList(); |
---|
3207 | oldL2= oldL; |
---|
3208 | oldL *= 2; |
---|
3209 | if (oldL > l) |
---|
3210 | { |
---|
3211 | if (!hitBound) |
---|
3212 | { |
---|
3213 | oldL= l; |
---|
3214 | hitBound= true; |
---|
3215 | } |
---|
3216 | else |
---|
3217 | break; |
---|
3218 | } |
---|
3219 | } |
---|
3220 | delete [] A; |
---|
3221 | return result; |
---|
3222 | } |
---|
3223 | |
---|
3224 | CFList |
---|
3225 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
3226 | l, int d, int* bounds, CFArray& bufQ, mat_zz_pE& NTLN |
---|
3227 | ) |
---|
3228 | { |
---|
3229 | CFList result= CFList(); |
---|
3230 | CFArray * A= new CFArray [factors.length()]; |
---|
3231 | int oldL2= oldL/2; |
---|
3232 | bool hitBound= false; |
---|
3233 | bool useOldQs= false; |
---|
3234 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3235 | ident (NTLN, factors.length()); |
---|
3236 | CFListIterator j; |
---|
3237 | CFMatrix C; |
---|
3238 | CFArray buf; |
---|
3239 | mat_zz_pE* NTLC, NTLK; |
---|
3240 | CanonicalForm bufF, truncF; |
---|
3241 | CFList bufUniFactors; |
---|
3242 | Variable y= F.mvar(); |
---|
3243 | while (oldL <= l) |
---|
3244 | { |
---|
3245 | j= factors; |
---|
3246 | truncF= mod (F, power (y, oldL)); |
---|
3247 | if (useOldQs) |
---|
3248 | { |
---|
3249 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3250 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
3251 | bufQ[i] |
---|
3252 | ); |
---|
3253 | } |
---|
3254 | else |
---|
3255 | { |
---|
3256 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3257 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
3258 | } |
---|
3259 | useOldQs= true; |
---|
3260 | |
---|
3261 | for (int i= 0; i < d; i++) |
---|
3262 | { |
---|
3263 | if (bounds [i] + 1 <= oldL/2) |
---|
3264 | { |
---|
3265 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
3266 | C= CFMatrix (oldL - k, factors.length()); |
---|
3267 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3268 | { |
---|
3269 | if (A[ii].size() - 1 >= i) |
---|
3270 | { |
---|
3271 | buf= getCoeffs (A[ii] [i], k); |
---|
3272 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3273 | } |
---|
3274 | } |
---|
3275 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
3276 | NTLK= (*NTLC)*NTLN; |
---|
3277 | transpose (NTLK, NTLK); |
---|
3278 | kernel (NTLK, NTLK); |
---|
3279 | transpose (NTLK, NTLK); |
---|
3280 | NTLN *= NTLK; |
---|
3281 | if (NTLN.NumCols() == 1) |
---|
3282 | { |
---|
3283 | delete [] A; |
---|
3284 | return CFList (F); |
---|
3285 | } |
---|
3286 | } |
---|
3287 | } |
---|
3288 | if (NTLN.NumCols() == 1) |
---|
3289 | { |
---|
3290 | delete [] A; |
---|
3291 | return CFList (F); |
---|
3292 | } |
---|
3293 | |
---|
3294 | int * zeroOneVecs; |
---|
3295 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3296 | bufF= F; |
---|
3297 | bufUniFactors= factors; |
---|
3298 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
3299 | delete [] zeroOneVecs; |
---|
3300 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
3301 | { |
---|
3302 | F= bufF; |
---|
3303 | factors= bufUniFactors; |
---|
3304 | delete [] A; |
---|
3305 | return result; |
---|
3306 | } |
---|
3307 | |
---|
3308 | result= CFList(); |
---|
3309 | oldL2= oldL; |
---|
3310 | oldL *= 2; |
---|
3311 | if (oldL > l) |
---|
3312 | { |
---|
3313 | if (!hitBound) |
---|
3314 | { |
---|
3315 | oldL= l; |
---|
3316 | hitBound= true; |
---|
3317 | } |
---|
3318 | else |
---|
3319 | break; |
---|
3320 | } |
---|
3321 | } |
---|
3322 | delete [] A; |
---|
3323 | return result; |
---|
3324 | } |
---|
3325 | |
---|
3326 | //over field extension |
---|
3327 | CFList |
---|
3328 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int oldL, int l, int d, |
---|
3329 | int* bounds, CFArray& bufQ, mat_zz_p& NTLN, const |
---|
3330 | CanonicalForm& evaluation, const ExtensionInfo& info, |
---|
3331 | CFList& source, CFList& dest |
---|
3332 | ) |
---|
3333 | { |
---|
3334 | CFList result= CFList(); |
---|
3335 | CFArray * A= new CFArray [factors.length()]; |
---|
3336 | int oldL2= oldL/2; //be careful |
---|
3337 | bool hitBound= false; |
---|
3338 | bool useOldQs= false; |
---|
3339 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
3340 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
3341 | Variable alpha= info.getAlpha(); |
---|
3342 | |
---|
3343 | Variable gamma= info.getBeta(); |
---|
3344 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
3345 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
3346 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3347 | ident (NTLN, factors.length()); |
---|
3348 | Variable y= F.mvar(); |
---|
3349 | CFListIterator j; |
---|
3350 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
3351 | CFMatrix Mat, C; |
---|
3352 | CFIterator iter; |
---|
3353 | mat_zz_p* NTLMat; |
---|
3354 | CFArray buf; |
---|
3355 | mat_zz_p* NTLC, NTLK; |
---|
3356 | CFList bufUniFactors; |
---|
3357 | while (oldL <= l) |
---|
3358 | { |
---|
3359 | j= factors; |
---|
3360 | if (GF) |
---|
3361 | setCharacteristic (getCharacteristic()); |
---|
3362 | |
---|
3363 | powX= power (y-gamma, oldL); |
---|
3364 | Mat= CFMatrix (oldL*degMipo, oldL*degMipo); |
---|
3365 | for (int i= 0; i < oldL*degMipo; i++) |
---|
3366 | { |
---|
3367 | imBasis= mod (power (y, i), powX); |
---|
3368 | imBasis= imBasis (power (y, degMipo), y); |
---|
3369 | imBasis= imBasis (y, gamma); |
---|
3370 | iter= imBasis; |
---|
3371 | for (; iter.hasTerms(); iter++) |
---|
3372 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
3373 | } |
---|
3374 | |
---|
3375 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
3376 | *NTLMat= inv (*NTLMat); |
---|
3377 | if (GF) |
---|
3378 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3379 | |
---|
3380 | truncF= mod (F, power (y, oldL)); |
---|
3381 | if (useOldQs) |
---|
3382 | { |
---|
3383 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3384 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
3385 | bufQ[i]); |
---|
3386 | } |
---|
3387 | else |
---|
3388 | { |
---|
3389 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3390 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
3391 | } |
---|
3392 | useOldQs= true; |
---|
3393 | |
---|
3394 | for (int i= 0; i < d; i++) |
---|
3395 | { |
---|
3396 | if (bounds [i] + 1 <= oldL/2) |
---|
3397 | { |
---|
3398 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
3399 | C= CFMatrix (oldL*degMipo - k, factors.length()); |
---|
3400 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3401 | { |
---|
3402 | if (A[ii].size() - 1 >= i) |
---|
3403 | { |
---|
3404 | if (GF) |
---|
3405 | { |
---|
3406 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3407 | setCharacteristic (getCharacteristic()); |
---|
3408 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
3409 | if (alpha != gamma) |
---|
3410 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3411 | gamma, source, dest |
---|
3412 | ); |
---|
3413 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
3414 | } |
---|
3415 | else |
---|
3416 | { |
---|
3417 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3418 | if (alpha != gamma) |
---|
3419 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3420 | gamma, source, dest |
---|
3421 | ); |
---|
3422 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
3423 | } |
---|
3424 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3425 | } |
---|
3426 | if (GF) |
---|
3427 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3428 | } |
---|
3429 | |
---|
3430 | if (GF) |
---|
3431 | setCharacteristic(getCharacteristic()); |
---|
3432 | |
---|
3433 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3434 | NTLK= (*NTLC)*NTLN; |
---|
3435 | transpose (NTLK, NTLK); |
---|
3436 | kernel (NTLK, NTLK); |
---|
3437 | transpose (NTLK, NTLK); |
---|
3438 | NTLN *= NTLK; |
---|
3439 | |
---|
3440 | if (GF) |
---|
3441 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3442 | |
---|
3443 | if (NTLN.NumCols() == 1) |
---|
3444 | { |
---|
3445 | Variable y= Variable (2); |
---|
3446 | CanonicalForm tmp= F (y - evaluation, y); |
---|
3447 | CFList source, dest; |
---|
3448 | tmp= mapDown (tmp, info, source, dest); |
---|
3449 | delete [] A; |
---|
3450 | return CFList (tmp); |
---|
3451 | } |
---|
3452 | } |
---|
3453 | } |
---|
3454 | if (NTLN.NumCols() == 1) |
---|
3455 | { |
---|
3456 | Variable y= Variable (2); |
---|
3457 | CanonicalForm tmp= F (y - evaluation, y); |
---|
3458 | CFList source, dest; |
---|
3459 | tmp= mapDown (tmp, info, source, dest); |
---|
3460 | delete [] A; |
---|
3461 | return CFList (tmp); |
---|
3462 | } |
---|
3463 | |
---|
3464 | int * zeroOneVecs; |
---|
3465 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3466 | bufF= F; |
---|
3467 | bufUniFactors= factors; |
---|
3468 | result= extReconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, |
---|
3469 | info, evaluation |
---|
3470 | ); |
---|
3471 | delete [] zeroOneVecs; |
---|
3472 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
3473 | { |
---|
3474 | F= bufF; |
---|
3475 | factors= bufUniFactors; |
---|
3476 | return result; |
---|
3477 | } |
---|
3478 | |
---|
3479 | result= CFList(); |
---|
3480 | oldL2= oldL; |
---|
3481 | oldL *= 2; |
---|
3482 | if (oldL > l) |
---|
3483 | { |
---|
3484 | if (!hitBound) |
---|
3485 | { |
---|
3486 | oldL= l; |
---|
3487 | hitBound= true; |
---|
3488 | } |
---|
3489 | else |
---|
3490 | break; |
---|
3491 | } |
---|
3492 | } |
---|
3493 | delete [] A; |
---|
3494 | return result; |
---|
3495 | } |
---|
3496 | |
---|
3497 | CFList |
---|
3498 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int oldL, int l, |
---|
3499 | int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN, |
---|
3500 | const Variable& alpha |
---|
3501 | ) |
---|
3502 | { |
---|
3503 | CFList result= CFList(); |
---|
3504 | CFArray * A= new CFArray [factors.length()]; |
---|
3505 | int extensionDeg= degree (getMipo (alpha)); |
---|
3506 | int oldL2= oldL/2; |
---|
3507 | bool hitBound= false; |
---|
3508 | bool useOldQs= false; |
---|
3509 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3510 | ident (NTLN, factors.length()); |
---|
3511 | CFListIterator j; |
---|
3512 | CFMatrix C; |
---|
3513 | CFArray buf; |
---|
3514 | mat_zz_p* NTLC, NTLK; |
---|
3515 | CanonicalForm bufF, truncF; |
---|
3516 | CFList bufUniFactors; |
---|
3517 | Variable y= F.mvar(); |
---|
3518 | while (oldL <= l) |
---|
3519 | { |
---|
3520 | j= factors; |
---|
3521 | truncF= mod (F, power (y, oldL)); |
---|
3522 | if (useOldQs) |
---|
3523 | { |
---|
3524 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3525 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
3526 | bufQ[i] |
---|
3527 | ); |
---|
3528 | } |
---|
3529 | else |
---|
3530 | { |
---|
3531 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3532 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
3533 | } |
---|
3534 | useOldQs= true; |
---|
3535 | |
---|
3536 | for (int i= 0; i < d; i++) |
---|
3537 | { |
---|
3538 | if (bounds [i] + 1 <= oldL/2) |
---|
3539 | { |
---|
3540 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
3541 | C= CFMatrix ((oldL - k)*extensionDeg, factors.length()); |
---|
3542 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3543 | { |
---|
3544 | if (A[ii].size() - 1 >= i) |
---|
3545 | { |
---|
3546 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
3547 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3548 | } |
---|
3549 | } |
---|
3550 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3551 | NTLK= (*NTLC)*NTLN; |
---|
3552 | transpose (NTLK, NTLK); |
---|
3553 | kernel (NTLK, NTLK); |
---|
3554 | transpose (NTLK, NTLK); |
---|
3555 | NTLN *= NTLK; |
---|
3556 | if (NTLN.NumCols() == 1) |
---|
3557 | { |
---|
3558 | delete [] A; |
---|
3559 | return CFList (F); |
---|
3560 | } |
---|
3561 | } |
---|
3562 | } |
---|
3563 | |
---|
3564 | int * zeroOneVecs; |
---|
3565 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3566 | |
---|
3567 | bufF= F; |
---|
3568 | bufUniFactors= factors; |
---|
3569 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
3570 | delete [] zeroOneVecs; |
---|
3571 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
3572 | { |
---|
3573 | F= bufF; |
---|
3574 | factors= bufUniFactors; |
---|
3575 | delete [] A; |
---|
3576 | return result; |
---|
3577 | } |
---|
3578 | |
---|
3579 | result= CFList(); |
---|
3580 | oldL2= oldL; |
---|
3581 | oldL *= 2; |
---|
3582 | if (oldL > l) |
---|
3583 | { |
---|
3584 | if (!hitBound) |
---|
3585 | { |
---|
3586 | oldL= l; |
---|
3587 | hitBound= true; |
---|
3588 | } |
---|
3589 | else |
---|
3590 | break; |
---|
3591 | } |
---|
3592 | } |
---|
3593 | delete [] A; |
---|
3594 | return result; |
---|
3595 | } |
---|
3596 | |
---|
3597 | CFList |
---|
3598 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
3599 | factors, int l, int liftBound, int d, int* |
---|
3600 | bounds, mat_zz_p& NTLN, CFList& diophant, |
---|
3601 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
3602 | ) |
---|
3603 | { |
---|
3604 | CanonicalForm LCF= LC (F, 1); |
---|
3605 | CFList result; |
---|
3606 | bool irreducible= false; |
---|
3607 | CFList bufFactors= factors; |
---|
3608 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
3609 | bool useOldQs= false; |
---|
3610 | bool hitBound= false; |
---|
3611 | int oldL= l; |
---|
3612 | int stepSize= 8; //TODO choose better step size? |
---|
3613 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
3614 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3615 | ident (NTLN, factors.length()); |
---|
3616 | CFListIterator j; |
---|
3617 | CFMatrix C; |
---|
3618 | CFArray buf; |
---|
3619 | mat_zz_p* NTLC, NTLK; |
---|
3620 | CanonicalForm bufF, truncF; |
---|
3621 | Variable y= F.mvar(); |
---|
3622 | while (l <= liftBound) |
---|
3623 | { |
---|
3624 | bufFactors.insert (LCF); |
---|
3625 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
3626 | bufFactors.insert (LCF); |
---|
3627 | bufFactors.removeFirst(); |
---|
3628 | j= bufFactors; |
---|
3629 | truncF= mod (F, power (y, l)); |
---|
3630 | if (useOldQs) |
---|
3631 | { |
---|
3632 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3633 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
3634 | bufQ[i]); |
---|
3635 | } |
---|
3636 | else |
---|
3637 | { |
---|
3638 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3639 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3640 | } |
---|
3641 | for (int i= 0; i < d; i++) |
---|
3642 | { |
---|
3643 | if (bounds [i] + 1 <= l/2) |
---|
3644 | { |
---|
3645 | int k= tmin (bounds [i] + 1, l/2); |
---|
3646 | C= CFMatrix (l - k, bufFactors.length()); |
---|
3647 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
3648 | { |
---|
3649 | if (A[ii].size() - 1 >= i) |
---|
3650 | { |
---|
3651 | buf= getCoeffs (A[ii] [i], k); |
---|
3652 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3653 | } |
---|
3654 | } |
---|
3655 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3656 | NTLK= (*NTLC)*NTLN; |
---|
3657 | transpose (NTLK, NTLK); |
---|
3658 | kernel (NTLK, NTLK); |
---|
3659 | transpose (NTLK, NTLK); |
---|
3660 | NTLN *= NTLK; |
---|
3661 | if (NTLN.NumCols() == 1) |
---|
3662 | { |
---|
3663 | irreducible= true; |
---|
3664 | break; |
---|
3665 | } |
---|
3666 | } |
---|
3667 | } |
---|
3668 | |
---|
3669 | if (NTLN.NumCols() == 1) |
---|
3670 | { |
---|
3671 | irreducible= true; |
---|
3672 | break; |
---|
3673 | } |
---|
3674 | |
---|
3675 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3676 | bufF= F; |
---|
3677 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
3678 | delete [] zeroOneVecs; |
---|
3679 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
3680 | { |
---|
3681 | F= bufF; |
---|
3682 | factors= bufFactors; |
---|
3683 | delete [] A; |
---|
3684 | return result; |
---|
3685 | } |
---|
3686 | |
---|
3687 | if (isReduced (NTLN)) |
---|
3688 | { |
---|
3689 | int factorsFound= 0; |
---|
3690 | bufF= F; |
---|
3691 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3692 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3693 | factorsFoundIndex[i]= 0; |
---|
3694 | if (l < liftBound) |
---|
3695 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
3696 | factorsFoundIndex, NTLN, false |
---|
3697 | ); |
---|
3698 | else |
---|
3699 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
3700 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
3701 | NTLN, false |
---|
3702 | ); |
---|
3703 | |
---|
3704 | if (NTLN.NumCols() == result.length()) |
---|
3705 | { |
---|
3706 | delete [] A; |
---|
3707 | delete [] factorsFoundIndex; |
---|
3708 | return result; |
---|
3709 | } |
---|
3710 | delete [] factorsFoundIndex; |
---|
3711 | } |
---|
3712 | result= CFList(); |
---|
3713 | oldL= l; |
---|
3714 | stepSize *= 2; |
---|
3715 | l += stepSize; |
---|
3716 | if (l > liftBound) |
---|
3717 | { |
---|
3718 | if (!hitBound) |
---|
3719 | { |
---|
3720 | l= liftBound; |
---|
3721 | hitBound= true; |
---|
3722 | } |
---|
3723 | else |
---|
3724 | break; |
---|
3725 | } |
---|
3726 | } |
---|
3727 | if (irreducible) |
---|
3728 | { |
---|
3729 | delete [] A; |
---|
3730 | return CFList (F); |
---|
3731 | } |
---|
3732 | delete [] A; |
---|
3733 | factors= bufFactors; |
---|
3734 | return CFList(); |
---|
3735 | } |
---|
3736 | |
---|
3737 | //Fq |
---|
3738 | CFList |
---|
3739 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
3740 | factors, int l, int liftBound, int d, int* |
---|
3741 | bounds, mat_zz_pE& NTLN, CFList& diophant, |
---|
3742 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
3743 | ) |
---|
3744 | { |
---|
3745 | CanonicalForm LCF= LC (F, 1); |
---|
3746 | CFList result; |
---|
3747 | bool irreducible= false; |
---|
3748 | CFList bufFactors= factors; |
---|
3749 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
3750 | bool useOldQs= false; |
---|
3751 | bool hitBound= false; |
---|
3752 | int oldL= l; |
---|
3753 | int stepSize= 8; //TODO choose better step size? |
---|
3754 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
3755 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3756 | ident (NTLN, factors.length()); |
---|
3757 | CFListIterator j; |
---|
3758 | CFArray buf; |
---|
3759 | mat_zz_pE* NTLC, NTLK; |
---|
3760 | CanonicalForm bufF, truncF; |
---|
3761 | Variable y= F.mvar(); |
---|
3762 | while (l <= liftBound) |
---|
3763 | { |
---|
3764 | bufFactors.insert (LCF); |
---|
3765 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
3766 | j= bufFactors; |
---|
3767 | truncF= mod (F, power (y, l)); |
---|
3768 | if (useOldQs) |
---|
3769 | { |
---|
3770 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3771 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
3772 | bufQ[i]); |
---|
3773 | } |
---|
3774 | else |
---|
3775 | { |
---|
3776 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3777 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3778 | } |
---|
3779 | for (int i= 0; i < d; i++) |
---|
3780 | { |
---|
3781 | if (bounds [i] + 1 <= l/2) |
---|
3782 | { |
---|
3783 | int k= tmin (bounds [i] + 1, l/2); |
---|
3784 | CFMatrix C= CFMatrix (l - k, bufFactors.length()); |
---|
3785 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
3786 | { |
---|
3787 | if (A[ii].size() - 1 >= i) |
---|
3788 | { |
---|
3789 | buf= getCoeffs (A[ii] [i], k); |
---|
3790 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3791 | } |
---|
3792 | } |
---|
3793 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
3794 | NTLK= (*NTLC)*NTLN; |
---|
3795 | transpose (NTLK, NTLK); |
---|
3796 | kernel (NTLK, NTLK); |
---|
3797 | transpose (NTLK, NTLK); |
---|
3798 | NTLN *= NTLK; |
---|
3799 | if (NTLN.NumCols() == 1) |
---|
3800 | { |
---|
3801 | irreducible= true; |
---|
3802 | break; |
---|
3803 | } |
---|
3804 | } |
---|
3805 | } |
---|
3806 | if (NTLN.NumCols() == 1) |
---|
3807 | { |
---|
3808 | irreducible= true; |
---|
3809 | break; |
---|
3810 | } |
---|
3811 | |
---|
3812 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3813 | bufF= F; |
---|
3814 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
3815 | delete [] zeroOneVecs; |
---|
3816 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
3817 | { |
---|
3818 | F= bufF; |
---|
3819 | factors= bufFactors; |
---|
3820 | delete [] A; |
---|
3821 | return result; |
---|
3822 | } |
---|
3823 | |
---|
3824 | if (isReduced (NTLN)) |
---|
3825 | { |
---|
3826 | int factorsFound= 0; |
---|
3827 | bufF= F; |
---|
3828 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3829 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3830 | factorsFoundIndex[i]= 0; |
---|
3831 | if (l < liftBound) |
---|
3832 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
3833 | factorsFoundIndex, NTLN, false |
---|
3834 | ); |
---|
3835 | else |
---|
3836 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
3837 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
3838 | NTLN, false |
---|
3839 | ); |
---|
3840 | if (NTLN.NumCols() == result.length()) |
---|
3841 | { |
---|
3842 | delete [] A; |
---|
3843 | delete [] factorsFoundIndex; |
---|
3844 | return result; |
---|
3845 | } |
---|
3846 | delete [] factorsFoundIndex; |
---|
3847 | } |
---|
3848 | result= CFList(); |
---|
3849 | oldL= l; |
---|
3850 | stepSize *= 2; |
---|
3851 | l += stepSize; |
---|
3852 | if (l > liftBound) |
---|
3853 | { |
---|
3854 | if (!hitBound) |
---|
3855 | { |
---|
3856 | l= liftBound; |
---|
3857 | hitBound= true; |
---|
3858 | } |
---|
3859 | else |
---|
3860 | break; |
---|
3861 | } |
---|
3862 | } |
---|
3863 | if (irreducible) |
---|
3864 | { |
---|
3865 | delete [] A; |
---|
3866 | return CFList (F); |
---|
3867 | } |
---|
3868 | delete [] A; |
---|
3869 | factors= bufFactors; |
---|
3870 | return CFList(); |
---|
3871 | } |
---|
3872 | |
---|
3873 | //over field extension |
---|
3874 | CFList |
---|
3875 | extFurtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& factors, int l, |
---|
3876 | int liftBound, int d, int* bounds, |
---|
3877 | mat_zz_p& NTLN, CFList& diophant, |
---|
3878 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
3879 | const CanonicalForm& evaluation, const |
---|
3880 | ExtensionInfo& info, CFList& source, |
---|
3881 | CFList& dest |
---|
3882 | ) |
---|
3883 | { |
---|
3884 | CanonicalForm LCF= LC (F, 1); |
---|
3885 | CFList result; |
---|
3886 | bool irreducible= false; |
---|
3887 | CFList bufFactors= factors; |
---|
3888 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
3889 | bool useOldQs= false; |
---|
3890 | bool hitBound= false; |
---|
3891 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
3892 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
3893 | Variable alpha= info.getAlpha(); |
---|
3894 | int oldL= l; //be careful |
---|
3895 | int stepSize= 8; |
---|
3896 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l),2); |
---|
3897 | Variable gamma= info.getBeta(); |
---|
3898 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
3899 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
3900 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3901 | ident (NTLN, factors.length()); |
---|
3902 | Variable y= F.mvar(); |
---|
3903 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
3904 | CFMatrix Mat, C; |
---|
3905 | CFIterator iter; |
---|
3906 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
3907 | CFListIterator j; |
---|
3908 | CFArray buf; |
---|
3909 | while (l <= liftBound) |
---|
3910 | { |
---|
3911 | bufFactors.insert (LCF); |
---|
3912 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
3913 | |
---|
3914 | if (GF) |
---|
3915 | setCharacteristic (getCharacteristic()); |
---|
3916 | |
---|
3917 | powX= power (y-gamma, l); |
---|
3918 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
3919 | for (int i= 0; i < l*degMipo; i++) |
---|
3920 | { |
---|
3921 | |
---|
3922 | imBasis= mod (power (y, i), powX); |
---|
3923 | imBasis= imBasis (power (y, degMipo), y); |
---|
3924 | imBasis= imBasis (y, gamma); |
---|
3925 | iter= imBasis; |
---|
3926 | for (; iter.hasTerms(); iter++) |
---|
3927 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
3928 | } |
---|
3929 | |
---|
3930 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
3931 | *NTLMat= inv (*NTLMat); |
---|
3932 | |
---|
3933 | if (GF) |
---|
3934 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3935 | |
---|
3936 | j= bufFactors; |
---|
3937 | truncF= mod (F, power (y, l)); |
---|
3938 | if (useOldQs) |
---|
3939 | { |
---|
3940 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3941 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
3942 | bufQ[i]); |
---|
3943 | } |
---|
3944 | else |
---|
3945 | { |
---|
3946 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3947 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3948 | } |
---|
3949 | for (int i= 0; i < d; i++) |
---|
3950 | { |
---|
3951 | if (bounds [i] + 1 <= l/2) |
---|
3952 | { |
---|
3953 | int k= tmin (bounds [i] + 1, l/2); |
---|
3954 | C= CFMatrix (l*degMipo - k, bufFactors.length()); |
---|
3955 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
3956 | { |
---|
3957 | if (A[ii].size() - 1 >= i) |
---|
3958 | { |
---|
3959 | if (GF) |
---|
3960 | { |
---|
3961 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3962 | setCharacteristic (getCharacteristic()); |
---|
3963 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
3964 | if (alpha != gamma) |
---|
3965 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3966 | gamma, source, dest |
---|
3967 | ); |
---|
3968 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
3969 | } |
---|
3970 | else |
---|
3971 | { |
---|
3972 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3973 | if (alpha != gamma) |
---|
3974 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3975 | gamma, source, dest |
---|
3976 | ); |
---|
3977 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
3978 | } |
---|
3979 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3980 | } |
---|
3981 | if (GF) |
---|
3982 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3983 | } |
---|
3984 | |
---|
3985 | if (GF) |
---|
3986 | setCharacteristic(getCharacteristic()); |
---|
3987 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3988 | NTLK= (*NTLC)*NTLN; |
---|
3989 | transpose (NTLK, NTLK); |
---|
3990 | kernel (NTLK, NTLK); |
---|
3991 | transpose (NTLK, NTLK); |
---|
3992 | NTLN *= NTLK; |
---|
3993 | if (GF) |
---|
3994 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3995 | |
---|
3996 | if (NTLN.NumCols() == 1) |
---|
3997 | { |
---|
3998 | irreducible= true; |
---|
3999 | break; |
---|
4000 | } |
---|
4001 | } |
---|
4002 | } |
---|
4003 | if (NTLN.NumCols() == 1) |
---|
4004 | { |
---|
4005 | irreducible= true; |
---|
4006 | break; |
---|
4007 | } |
---|
4008 | |
---|
4009 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
4010 | bufF= F; |
---|
4011 | result= extReconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, info, |
---|
4012 | evaluation |
---|
4013 | ); |
---|
4014 | delete [] zeroOneVecs; |
---|
4015 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
4016 | { |
---|
4017 | F= bufF; |
---|
4018 | factors= bufFactors; |
---|
4019 | delete [] A; |
---|
4020 | return result; |
---|
4021 | } |
---|
4022 | |
---|
4023 | if (isReduced (NTLN)) |
---|
4024 | { |
---|
4025 | int factorsFound= 0; |
---|
4026 | bufF= F; |
---|
4027 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4028 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4029 | factorsFoundIndex[i]= 0; |
---|
4030 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
4031 | extReconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
4032 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
4033 | ); |
---|
4034 | else |
---|
4035 | extReconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
4036 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
4037 | NTLN, false, info, evaluation |
---|
4038 | ); |
---|
4039 | if (NTLN.NumCols() == result.length()) |
---|
4040 | { |
---|
4041 | delete [] A; |
---|
4042 | delete [] factorsFoundIndex; |
---|
4043 | return result; |
---|
4044 | } |
---|
4045 | delete [] factorsFoundIndex; |
---|
4046 | } |
---|
4047 | result= CFList(); |
---|
4048 | oldL= l; |
---|
4049 | stepSize *= 2; |
---|
4050 | l += stepSize; |
---|
4051 | if (l > liftBound) |
---|
4052 | { |
---|
4053 | if (!hitBound) |
---|
4054 | { |
---|
4055 | l= liftBound; |
---|
4056 | hitBound= true; |
---|
4057 | } |
---|
4058 | else |
---|
4059 | break; |
---|
4060 | } |
---|
4061 | } |
---|
4062 | if (irreducible) |
---|
4063 | { |
---|
4064 | delete [] A; |
---|
4065 | Variable y= Variable (2); |
---|
4066 | CanonicalForm tmp= F (y - evaluation, y); |
---|
4067 | CFList source, dest; |
---|
4068 | tmp= mapDown (tmp, info, source, dest); |
---|
4069 | return CFList (tmp); |
---|
4070 | } |
---|
4071 | delete [] A; |
---|
4072 | factors= bufFactors; |
---|
4073 | return CFList(); |
---|
4074 | } |
---|
4075 | |
---|
4076 | CFList |
---|
4077 | furtherLiftingAndIncreasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int |
---|
4078 | l, int liftBound, int d, int* bounds, |
---|
4079 | mat_zz_p& NTLN, CFList& diophant, |
---|
4080 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
4081 | const Variable& alpha |
---|
4082 | ) |
---|
4083 | { |
---|
4084 | CanonicalForm LCF= LC (F, 1); |
---|
4085 | CFList result; |
---|
4086 | bool irreducible= false; |
---|
4087 | CFList bufFactors= factors; |
---|
4088 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
4089 | bool useOldQs= false; |
---|
4090 | int extensionDeg= degree (getMipo (alpha)); |
---|
4091 | bool hitBound= false; |
---|
4092 | int oldL= l; |
---|
4093 | int stepSize= 8; //TODO choose better step size? |
---|
4094 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
4095 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
4096 | ident (NTLN, factors.length()); |
---|
4097 | CFListIterator j; |
---|
4098 | CFMatrix C; |
---|
4099 | mat_zz_p* NTLC, NTLK; |
---|
4100 | CanonicalForm bufF, truncF; |
---|
4101 | Variable y= F.mvar(); |
---|
4102 | while (l <= liftBound) |
---|
4103 | { |
---|
4104 | bufFactors.insert (LCF); |
---|
4105 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
4106 | j= bufFactors; |
---|
4107 | truncF= mod (F, power (y, l)); |
---|
4108 | if (useOldQs) |
---|
4109 | { |
---|
4110 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
4111 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
4112 | bufQ[i]); |
---|
4113 | } |
---|
4114 | else |
---|
4115 | { |
---|
4116 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
4117 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
4118 | } |
---|
4119 | for (int i= 0; i < d; i++) |
---|
4120 | { |
---|
4121 | if (bounds [i] + 1 <= l/2) |
---|
4122 | { |
---|
4123 | int k= tmin (bounds [i] + 1, l/2); |
---|
4124 | C= CFMatrix ((l - k)*extensionDeg, bufFactors.length()); |
---|
4125 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
4126 | { |
---|
4127 | CFArray buf; |
---|
4128 | if (A[ii].size() - 1 >= i) |
---|
4129 | { |
---|
4130 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
4131 | writeInMatrix (C, buf, ii + 1, 0); |
---|
4132 | } |
---|
4133 | } |
---|
4134 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
4135 | NTLK= (*NTLC)*NTLN; |
---|
4136 | transpose (NTLK, NTLK); |
---|
4137 | kernel (NTLK, NTLK); |
---|
4138 | transpose (NTLK, NTLK); |
---|
4139 | NTLN *= NTLK; |
---|
4140 | if (NTLN.NumCols() == 1) |
---|
4141 | { |
---|
4142 | irreducible= true; |
---|
4143 | break; |
---|
4144 | } |
---|
4145 | } |
---|
4146 | } |
---|
4147 | if (NTLN.NumCols() == 1) |
---|
4148 | { |
---|
4149 | irreducible= true; |
---|
4150 | break; |
---|
4151 | } |
---|
4152 | |
---|
4153 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
4154 | CanonicalForm bufF= F; |
---|
4155 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
4156 | delete [] zeroOneVecs; |
---|
4157 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
4158 | { |
---|
4159 | F= bufF; |
---|
4160 | factors= bufFactors; |
---|
4161 | delete [] A; |
---|
4162 | return result; |
---|
4163 | } |
---|
4164 | |
---|
4165 | if (isReduced (NTLN)) |
---|
4166 | { |
---|
4167 | int factorsFound= 0; |
---|
4168 | bufF= F; |
---|
4169 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4170 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4171 | factorsFoundIndex[i]= 0; |
---|
4172 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
4173 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
4174 | factorsFoundIndex, NTLN, false |
---|
4175 | ); |
---|
4176 | else |
---|
4177 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
4178 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
4179 | NTLN, false |
---|
4180 | ); |
---|
4181 | if (NTLN.NumCols() == result.length()) |
---|
4182 | { |
---|
4183 | delete [] A; |
---|
4184 | delete [] factorsFoundIndex; |
---|
4185 | return result; |
---|
4186 | } |
---|
4187 | delete [] factorsFoundIndex; |
---|
4188 | } |
---|
4189 | result= CFList(); |
---|
4190 | oldL= l; |
---|
4191 | stepSize *= 2; |
---|
4192 | l += stepSize; |
---|
4193 | if (l > liftBound) |
---|
4194 | { |
---|
4195 | if (!hitBound) |
---|
4196 | { |
---|
4197 | l= liftBound; |
---|
4198 | hitBound= true; |
---|
4199 | } |
---|
4200 | else |
---|
4201 | break; |
---|
4202 | } |
---|
4203 | } |
---|
4204 | if (irreducible) |
---|
4205 | { |
---|
4206 | delete [] A; |
---|
4207 | return CFList (F); |
---|
4208 | } |
---|
4209 | delete [] A; |
---|
4210 | factors= bufFactors; |
---|
4211 | return CFList(); |
---|
4212 | } |
---|
4213 | |
---|
4214 | void |
---|
4215 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_p& NTLN, int |
---|
4216 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
4217 | Pi, CFList& diophant |
---|
4218 | ) |
---|
4219 | { |
---|
4220 | CFList bufFactors; |
---|
4221 | Variable y= Variable (2); |
---|
4222 | CanonicalForm LCF= LC (F, 1); |
---|
4223 | CFListIterator iter; |
---|
4224 | CanonicalForm buf; |
---|
4225 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
4226 | { |
---|
4227 | iter= factors; |
---|
4228 | buf= 1; |
---|
4229 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
4230 | { |
---|
4231 | if (!IsZero (NTLN (j,i))) |
---|
4232 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
4233 | } |
---|
4234 | bufFactors.append (buf); |
---|
4235 | } |
---|
4236 | factors= bufFactors; |
---|
4237 | M= CFMatrix (liftBound, factors.length()); |
---|
4238 | Pi= CFArray(); |
---|
4239 | diophant= CFList(); |
---|
4240 | factors.insert (LCF); |
---|
4241 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
4242 | } |
---|
4243 | |
---|
4244 | void |
---|
4245 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_pE& NTLN, int |
---|
4246 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
4247 | Pi, CFList& diophant |
---|
4248 | ) |
---|
4249 | { |
---|
4250 | CFList bufFactors; |
---|
4251 | Variable y= Variable (2); |
---|
4252 | CanonicalForm LCF= LC (F, 1); |
---|
4253 | CFListIterator iter; |
---|
4254 | CanonicalForm buf; |
---|
4255 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
4256 | { |
---|
4257 | iter= factors; |
---|
4258 | buf= 1; |
---|
4259 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
4260 | { |
---|
4261 | if (!IsZero (NTLN (j,i))) |
---|
4262 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
4263 | } |
---|
4264 | bufFactors.append (buf); |
---|
4265 | } |
---|
4266 | factors= bufFactors; |
---|
4267 | M= CFMatrix (liftBound, factors.length()); |
---|
4268 | Pi= CFArray(); |
---|
4269 | diophant= CFList(); |
---|
4270 | factors.insert (LCF); |
---|
4271 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
4272 | } |
---|
4273 | |
---|
4274 | CFList |
---|
4275 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
4276 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
4277 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
4278 | CFArray& Pi, CFList& diophant, bool symmetric, |
---|
4279 | const CanonicalForm& evaluation |
---|
4280 | ) |
---|
4281 | { |
---|
4282 | int sizeOfLiftPre; |
---|
4283 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
4284 | |
---|
4285 | Variable y= F.mvar(); |
---|
4286 | factorsFound= 0; |
---|
4287 | CanonicalForm LCF= LC (F, 1); |
---|
4288 | CFList result; |
---|
4289 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1); |
---|
4290 | mat_zz_p NTLN= N; |
---|
4291 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4292 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4293 | factorsFoundIndex [i]= 0; |
---|
4294 | |
---|
4295 | if (degree (F) + 1 > smallFactorDeg) |
---|
4296 | { |
---|
4297 | if (l < smallFactorDeg) |
---|
4298 | { |
---|
4299 | factors.insert (LCF); |
---|
4300 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
4301 | l= smallFactorDeg; |
---|
4302 | } |
---|
4303 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
4304 | factorsFoundIndex, NTLN, beenInThres |
---|
4305 | ); |
---|
4306 | if (result.length() == NTLN.NumCols()) |
---|
4307 | { |
---|
4308 | delete [] liftPre; |
---|
4309 | delete [] factorsFoundIndex; |
---|
4310 | return result; |
---|
4311 | } |
---|
4312 | } |
---|
4313 | |
---|
4314 | int i= sizeOfLiftPre - 1; |
---|
4315 | int dummy= 1; |
---|
4316 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
4317 | { |
---|
4318 | while (i > 0) |
---|
4319 | { |
---|
4320 | if (l < liftPre[i-1] + 1) |
---|
4321 | { |
---|
4322 | factors.insert (LCF); |
---|
4323 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
4324 | l= liftPre[i-1] + 1; |
---|
4325 | } |
---|
4326 | else |
---|
4327 | { |
---|
4328 | i--; |
---|
4329 | if (i != 0) |
---|
4330 | continue; |
---|
4331 | } |
---|
4332 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4333 | factorsFoundIndex, NTLN, beenInThres |
---|
4334 | ); |
---|
4335 | if (result.length() == NTLN.NumCols()) |
---|
4336 | { |
---|
4337 | delete [] liftPre; |
---|
4338 | delete [] factorsFoundIndex; |
---|
4339 | return result; |
---|
4340 | } |
---|
4341 | i--; |
---|
4342 | } |
---|
4343 | } |
---|
4344 | else |
---|
4345 | { |
---|
4346 | i= 1; |
---|
4347 | while ((degree (F,y)/4)*i + 4 <= smallFactorDeg) |
---|
4348 | i++; |
---|
4349 | while (i < 5) |
---|
4350 | { |
---|
4351 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4)*i+4); |
---|
4352 | if (l < dummy) |
---|
4353 | { |
---|
4354 | factors.insert (LCF); |
---|
4355 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
4356 | l= dummy; |
---|
4357 | if (i == 1 && degree (F)%4==0 && symmetric && factors.length() == 2 && |
---|
4358 | LC (F,1).inCoeffDomain() && |
---|
4359 | (degree (factors.getFirst(), 1) == degree (factors.getLast(),1))) |
---|
4360 | { |
---|
4361 | Variable x= Variable (1); |
---|
4362 | CanonicalForm g, h, gg, hh, multiplier1, multiplier2, check1, check2; |
---|
4363 | int m= degree (F)/4+1; |
---|
4364 | g= factors.getFirst(); |
---|
4365 | h= factors.getLast(); |
---|
4366 | g= mod (g, power (y,m)); |
---|
4367 | h= mod (h, power (y,m)); |
---|
4368 | g= g (y-evaluation, y); |
---|
4369 | h= h (y-evaluation, y); |
---|
4370 | gg= mod (swapvar (g,x,y),power (x,m)); |
---|
4371 | gg= gg (y + evaluation, y); |
---|
4372 | multiplier1= factors.getLast()[m-1][0]/gg[m-1][0]; |
---|
4373 | gg= div (gg, power (y,m)); |
---|
4374 | gg= gg*power (y,m); |
---|
4375 | hh= mod (swapvar (h,x,y),power (x,m)); |
---|
4376 | hh= hh (y + evaluation, y); |
---|
4377 | multiplier2= factors.getFirst()[m-1][0]/hh[m-1][0]; |
---|
4378 | hh= div (hh, power (y,m)); |
---|
4379 | hh= hh*power (y,m); |
---|
4380 | gg= multiplier1*gg+mod (factors.getLast(), power (y,m)); |
---|
4381 | hh= multiplier2*hh+mod (factors.getFirst(), power (y,m)); |
---|
4382 | check1= gg (y-evaluation,y); |
---|
4383 | check2= hh (y-evaluation,y); |
---|
4384 | check1= swapvar (check1, x, y); |
---|
4385 | if (check1/Lc (check1) == check2/Lc (check2)) |
---|
4386 | { |
---|
4387 | result.append (gg); |
---|
4388 | result.append (hh); |
---|
4389 | delete [] liftPre; |
---|
4390 | delete [] factorsFoundIndex; |
---|
4391 | return result; |
---|
4392 | } |
---|
4393 | } |
---|
4394 | } |
---|
4395 | else |
---|
4396 | { |
---|
4397 | i++; |
---|
4398 | if (i < 5) |
---|
4399 | continue; |
---|
4400 | } |
---|
4401 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4402 | factorsFoundIndex, NTLN, beenInThres |
---|
4403 | ); |
---|
4404 | if (result.length() == NTLN.NumCols()) |
---|
4405 | { |
---|
4406 | delete [] liftPre; |
---|
4407 | delete [] factorsFoundIndex; |
---|
4408 | return result; |
---|
4409 | } |
---|
4410 | i++; |
---|
4411 | } |
---|
4412 | } |
---|
4413 | |
---|
4414 | delete [] liftPre; |
---|
4415 | delete [] factorsFoundIndex; |
---|
4416 | return result; |
---|
4417 | } |
---|
4418 | |
---|
4419 | CFList |
---|
4420 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_pE& N, |
---|
4421 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
4422 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
4423 | CFArray& Pi, CFList& diophant, bool symmetric, |
---|
4424 | const CanonicalForm& evaluation |
---|
4425 | ) |
---|
4426 | { |
---|
4427 | int sizeOfLiftPre; |
---|
4428 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
4429 | Variable y= F.mvar(); |
---|
4430 | factorsFound= 0; |
---|
4431 | CanonicalForm LCF= LC (F, 1); |
---|
4432 | CFList result; |
---|
4433 | int smallFactorDeg= 11; |
---|
4434 | mat_zz_pE NTLN= N; |
---|
4435 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4436 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4437 | factorsFoundIndex [i]= 0; |
---|
4438 | |
---|
4439 | if (degree (F) + 1 > smallFactorDeg) |
---|
4440 | { |
---|
4441 | if (l < smallFactorDeg) |
---|
4442 | { |
---|
4443 | factors.insert (LCF); |
---|
4444 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
4445 | l= smallFactorDeg; |
---|
4446 | } |
---|
4447 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
4448 | factorsFoundIndex, NTLN, beenInThres |
---|
4449 | ); |
---|
4450 | if (result.length() == NTLN.NumCols()) |
---|
4451 | { |
---|
4452 | delete [] liftPre; |
---|
4453 | delete [] factorsFoundIndex; |
---|
4454 | return result; |
---|
4455 | } |
---|
4456 | } |
---|
4457 | |
---|
4458 | int i= sizeOfLiftPre - 1; |
---|
4459 | int dummy= 1; |
---|
4460 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
4461 | { |
---|
4462 | while (i > 0) |
---|
4463 | { |
---|
4464 | if (l < liftPre[i-1] + 1) |
---|
4465 | { |
---|
4466 | factors.insert (LCF); |
---|
4467 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
4468 | l= liftPre[i-1] + 1; |
---|
4469 | } |
---|
4470 | else |
---|
4471 | { |
---|
4472 | i--; |
---|
4473 | if (i != 0) |
---|
4474 | continue; |
---|
4475 | } |
---|
4476 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4477 | factorsFoundIndex, NTLN, beenInThres |
---|
4478 | ); |
---|
4479 | if (result.length() == NTLN.NumCols()) |
---|
4480 | { |
---|
4481 | delete [] liftPre; |
---|
4482 | delete [] factorsFoundIndex; |
---|
4483 | return result; |
---|
4484 | } |
---|
4485 | i--; |
---|
4486 | } |
---|
4487 | } |
---|
4488 | else |
---|
4489 | { |
---|
4490 | i= 1; |
---|
4491 | while ((degree (F,y)/4)*i + 4 <= smallFactorDeg) |
---|
4492 | i++; |
---|
4493 | while (i < 5) |
---|
4494 | { |
---|
4495 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4)*i+4); |
---|
4496 | if (l < dummy) |
---|
4497 | { |
---|
4498 | factors.insert (LCF); |
---|
4499 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
4500 | l= dummy; |
---|
4501 | if (i == 1 && degree (F)%4==0 && symmetric && factors.length() == 2 && |
---|
4502 | LC (F,1).inCoeffDomain() && |
---|
4503 | (degree (factors.getFirst(), 1) == degree (factors.getLast(),1))) |
---|
4504 | { |
---|
4505 | Variable x= Variable (1); |
---|
4506 | CanonicalForm g, h, gg, hh, multiplier1, multiplier2, check1, check2; |
---|
4507 | int m= degree (F)/4+1; |
---|
4508 | g= factors.getFirst(); |
---|
4509 | h= factors.getLast(); |
---|
4510 | g= mod (g, power (y,m)); |
---|
4511 | h= mod (h, power (y,m)); |
---|
4512 | g= g (y-evaluation, y); |
---|
4513 | h= h (y-evaluation, y); |
---|
4514 | gg= mod (swapvar (g,x,y),power (x,m)); |
---|
4515 | gg= gg (y + evaluation, y); |
---|
4516 | multiplier1= factors.getLast()[m-1][0]/gg[m-1][0]; |
---|
4517 | gg= div (gg, power (y,m)); |
---|
4518 | gg= gg*power (y,m); |
---|
4519 | hh= mod (swapvar (h,x,y),power (x,m)); |
---|
4520 | hh= hh (y + evaluation, y); |
---|
4521 | multiplier2= factors.getFirst()[m-1][0]/hh[m-1][0]; |
---|
4522 | hh= div (hh, power (y,m)); |
---|
4523 | hh= hh*power (y,m); |
---|
4524 | gg= multiplier1*gg+mod (factors.getLast(), power (y,m)); |
---|
4525 | hh= multiplier2*hh+mod (factors.getFirst(), power (y,m)); |
---|
4526 | check1= gg (y-evaluation,y); |
---|
4527 | check2= hh (y-evaluation,y); |
---|
4528 | check1= swapvar (check1, x, y); |
---|
4529 | if (check1/Lc (check1) == check2/Lc (check2)) |
---|
4530 | { |
---|
4531 | result.append (gg); |
---|
4532 | result.append (hh); |
---|
4533 | delete [] liftPre; |
---|
4534 | delete [] factorsFoundIndex; |
---|
4535 | return result; |
---|
4536 | } |
---|
4537 | } |
---|
4538 | } |
---|
4539 | else |
---|
4540 | { |
---|
4541 | i++; |
---|
4542 | if (i < 5) |
---|
4543 | continue; |
---|
4544 | } |
---|
4545 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4546 | factorsFoundIndex, NTLN, beenInThres |
---|
4547 | ); |
---|
4548 | if (result.length() == NTLN.NumCols()) |
---|
4549 | { |
---|
4550 | delete [] liftPre; |
---|
4551 | delete [] factorsFoundIndex; |
---|
4552 | return result; |
---|
4553 | } |
---|
4554 | i++; |
---|
4555 | } |
---|
4556 | } |
---|
4557 | |
---|
4558 | delete [] liftPre; |
---|
4559 | delete [] factorsFoundIndex; |
---|
4560 | return result; |
---|
4561 | } |
---|
4562 | |
---|
4563 | //over field extension |
---|
4564 | CFList |
---|
4565 | extEarlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
4566 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
4567 | int& factorsFound, bool beenInThres, CFMatrix& |
---|
4568 | M, CFArray& Pi, CFList& diophant, const |
---|
4569 | ExtensionInfo& info, const CanonicalForm& |
---|
4570 | evaluation |
---|
4571 | ) |
---|
4572 | { |
---|
4573 | int sizeOfLiftPre; |
---|
4574 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
4575 | Variable y= F.mvar(); |
---|
4576 | factorsFound= 0; |
---|
4577 | CanonicalForm LCF= LC (F, 1); |
---|
4578 | CFList result; |
---|
4579 | int smallFactorDeg= 11; |
---|
4580 | mat_zz_p NTLN= N; |
---|
4581 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4582 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4583 | factorsFoundIndex [i]= 0; |
---|
4584 | |
---|
4585 | if (degree (F) + 1 > smallFactorDeg) |
---|
4586 | { |
---|
4587 | if (l < smallFactorDeg) |
---|
4588 | { |
---|
4589 | factors.insert (LCF); |
---|
4590 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
4591 | l= smallFactorDeg; |
---|
4592 | } |
---|
4593 | extReconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
4594 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
4595 | evaluation |
---|
4596 | ); |
---|
4597 | if (result.length() == NTLN.NumCols()) |
---|
4598 | { |
---|
4599 | delete [] liftPre; |
---|
4600 | delete [] factorsFoundIndex; |
---|
4601 | return result; |
---|
4602 | } |
---|
4603 | } |
---|
4604 | |
---|
4605 | int i= sizeOfLiftPre - 1; |
---|
4606 | int dummy= 1; |
---|
4607 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
4608 | { |
---|
4609 | while (i > 0) |
---|
4610 | { |
---|
4611 | if (l < liftPre[i-1] + 1) |
---|
4612 | { |
---|
4613 | factors.insert (LCF); |
---|
4614 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
4615 | l= liftPre[i-1] + 1; |
---|
4616 | } |
---|
4617 | else |
---|
4618 | { |
---|
4619 | i--; |
---|
4620 | if (i != 0) |
---|
4621 | continue; |
---|
4622 | } |
---|
4623 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4624 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
4625 | evaluation |
---|
4626 | ); |
---|
4627 | if (result.length() == NTLN.NumCols()) |
---|
4628 | { |
---|
4629 | delete [] liftPre; |
---|
4630 | delete [] factorsFoundIndex; |
---|
4631 | return result; |
---|
4632 | } |
---|
4633 | i--; |
---|
4634 | } |
---|
4635 | } |
---|
4636 | else |
---|
4637 | { |
---|
4638 | i= 1; |
---|
4639 | while ((degree (F,y)/4)*i + 4 <= smallFactorDeg) |
---|
4640 | i++; |
---|
4641 | while (i < 5) |
---|
4642 | { |
---|
4643 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4)*i+4); |
---|
4644 | if (l < dummy) |
---|
4645 | { |
---|
4646 | factors.insert (LCF); |
---|
4647 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
4648 | l= dummy; |
---|
4649 | } |
---|
4650 | else |
---|
4651 | { |
---|
4652 | i++; |
---|
4653 | if (i < 5) |
---|
4654 | continue; |
---|
4655 | } |
---|
4656 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4657 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
4658 | evaluation |
---|
4659 | ); |
---|
4660 | if (result.length() == NTLN.NumCols()) |
---|
4661 | { |
---|
4662 | delete [] liftPre; |
---|
4663 | delete [] factorsFoundIndex; |
---|
4664 | return result; |
---|
4665 | } |
---|
4666 | i++; |
---|
4667 | } |
---|
4668 | } |
---|
4669 | |
---|
4670 | delete [] liftPre; |
---|
4671 | delete [] factorsFoundIndex; |
---|
4672 | return result; |
---|
4673 | } |
---|
4674 | |
---|
4675 | CFList |
---|
4676 | sieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
4677 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
4678 | CFMatrix& M, bool& success, int d |
---|
4679 | ) |
---|
4680 | { |
---|
4681 | CanonicalForm F= G; |
---|
4682 | CFList bufUniFactors= uniFactors; |
---|
4683 | bufUniFactors.insert (LC (F, 1)); |
---|
4684 | int smallFactorDeg= d; |
---|
4685 | DegreePattern degs= degPat; |
---|
4686 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
4687 | int adaptedLiftBound; |
---|
4688 | success= false; |
---|
4689 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
4690 | for (int i= 0; i < uniFactors.length(); i++) |
---|
4691 | factorsFoundIndex [i]= 0; |
---|
4692 | CFList earlyFactors; |
---|
4693 | earlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound, |
---|
4694 | factorsFoundIndex, degs, success, smallFactorDeg); |
---|
4695 | delete [] factorsFoundIndex; |
---|
4696 | if (degs.getLength() == 1) |
---|
4697 | { |
---|
4698 | degPat= degs; |
---|
4699 | return earlyFactors; |
---|
4700 | } |
---|
4701 | if (success) |
---|
4702 | { |
---|
4703 | H= F; |
---|
4704 | return earlyFactors; |
---|
4705 | } |
---|
4706 | int sizeOldF= size (G); |
---|
4707 | if (size (F) < sizeOldF) |
---|
4708 | { |
---|
4709 | H= F; |
---|
4710 | success= true; |
---|
4711 | return earlyFactors; |
---|
4712 | } |
---|
4713 | else |
---|
4714 | { |
---|
4715 | uniFactors= bufUniFactors; |
---|
4716 | return CFList(); |
---|
4717 | } |
---|
4718 | } |
---|
4719 | |
---|
4720 | CFList |
---|
4721 | extSieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
4722 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
4723 | CFMatrix& M, bool& success, int d, const CanonicalForm& |
---|
4724 | evaluation, const ExtensionInfo& info |
---|
4725 | ) |
---|
4726 | { |
---|
4727 | CanonicalForm F= G; |
---|
4728 | CFList bufUniFactors= uniFactors; |
---|
4729 | bufUniFactors.insert (LC (F, 1)); |
---|
4730 | int smallFactorDeg= d; |
---|
4731 | DegreePattern degs= degPat; |
---|
4732 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
4733 | int adaptedLiftBound; |
---|
4734 | success= false; |
---|
4735 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
4736 | for (int i= 0; i < uniFactors.length(); i++) |
---|
4737 | factorsFoundIndex [i]= 0; |
---|
4738 | CFList earlyFactors; |
---|
4739 | extEarlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound, |
---|
4740 | factorsFoundIndex, degs, success, info, evaluation, |
---|
4741 | smallFactorDeg); |
---|
4742 | delete [] factorsFoundIndex; |
---|
4743 | if (degs.getLength() == 1) |
---|
4744 | { |
---|
4745 | degPat= degs; |
---|
4746 | return earlyFactors; |
---|
4747 | } |
---|
4748 | if (success) |
---|
4749 | { |
---|
4750 | H= F; |
---|
4751 | return earlyFactors; |
---|
4752 | } |
---|
4753 | Variable y= F.mvar(); |
---|
4754 | int sizeOldF= size (G); |
---|
4755 | if (size (F) < sizeOldF) |
---|
4756 | { |
---|
4757 | H= F; |
---|
4758 | success= true; |
---|
4759 | return earlyFactors; |
---|
4760 | } |
---|
4761 | else |
---|
4762 | { |
---|
4763 | uniFactors= bufUniFactors; |
---|
4764 | return CFList(); |
---|
4765 | } |
---|
4766 | } |
---|
4767 | |
---|
4768 | CFList |
---|
4769 | henselLiftAndLatticeRecombi (const CanonicalForm& G, const CFList& uniFactors, |
---|
4770 | const Variable& alpha, const DegreePattern& degPat, |
---|
4771 | bool symmetric, const CanonicalForm& evaluation |
---|
4772 | ) |
---|
4773 | { |
---|
4774 | DegreePattern degs= degPat; |
---|
4775 | CanonicalForm F= G; |
---|
4776 | CanonicalForm LCF= LC (F, 1); |
---|
4777 | Variable y= F.mvar(); |
---|
4778 | Variable x= Variable (1); |
---|
4779 | int d; |
---|
4780 | bool isIrreducible= false; |
---|
4781 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
4782 | if (isIrreducible) |
---|
4783 | { |
---|
4784 | delete [] bounds; |
---|
4785 | return CFList (G); |
---|
4786 | } |
---|
4787 | int minBound= bounds[0]; |
---|
4788 | for (int i= 1; i < d; i++) |
---|
4789 | { |
---|
4790 | if (bounds[i] != 0) |
---|
4791 | minBound= tmin (minBound, bounds[i]); |
---|
4792 | } |
---|
4793 | |
---|
4794 | CFList bufUniFactors= uniFactors; |
---|
4795 | CFArray Pi; |
---|
4796 | CFList diophant; |
---|
4797 | int liftBound= 2*totaldegree (F) - 1; |
---|
4798 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
4799 | |
---|
4800 | CFList smallFactors; |
---|
4801 | CanonicalForm H; |
---|
4802 | bool success= false; |
---|
4803 | smallFactors= sieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, M, |
---|
4804 | success, minBound + 1 |
---|
4805 | ); |
---|
4806 | |
---|
4807 | if (smallFactors.length() > 0) |
---|
4808 | { |
---|
4809 | if (smallFactors.length() == 1) |
---|
4810 | { |
---|
4811 | if (smallFactors.getFirst() == F) |
---|
4812 | { |
---|
4813 | delete [] bounds; |
---|
4814 | return CFList (G); |
---|
4815 | } |
---|
4816 | } |
---|
4817 | if (degs.getLength() <= 1) |
---|
4818 | { |
---|
4819 | delete [] bounds; |
---|
4820 | return smallFactors; |
---|
4821 | } |
---|
4822 | } |
---|
4823 | |
---|
4824 | int index; |
---|
4825 | CanonicalForm tmp1, tmp2; |
---|
4826 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
4827 | { |
---|
4828 | index= 1; |
---|
4829 | tmp1= mod (i.getItem(),y); |
---|
4830 | tmp1 /= Lc (tmp1); |
---|
4831 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
4832 | { |
---|
4833 | tmp2= mod (j.getItem(), y); |
---|
4834 | tmp2 /= Lc (tmp2); |
---|
4835 | if (tmp1 == tmp2) |
---|
4836 | { |
---|
4837 | index++; |
---|
4838 | j.remove(index); |
---|
4839 | break; |
---|
4840 | } |
---|
4841 | } |
---|
4842 | } |
---|
4843 | |
---|
4844 | if (bufUniFactors.isEmpty()) |
---|
4845 | { |
---|
4846 | delete [] bounds; |
---|
4847 | return smallFactors; |
---|
4848 | } |
---|
4849 | |
---|
4850 | if (success) |
---|
4851 | { |
---|
4852 | F= H; |
---|
4853 | delete [] bounds; |
---|
4854 | bounds= computeBounds (F, d, isIrreducible); |
---|
4855 | if (isIrreducible) |
---|
4856 | { |
---|
4857 | smallFactors.append (F); |
---|
4858 | delete [] bounds; |
---|
4859 | return smallFactors; |
---|
4860 | } |
---|
4861 | LCF= LC (F, 1); |
---|
4862 | |
---|
4863 | minBound= bounds[0]; |
---|
4864 | for (int i= 1; i < d; i++) |
---|
4865 | { |
---|
4866 | if (bounds[i] != 0) |
---|
4867 | minBound= tmin (minBound, bounds[i]); |
---|
4868 | } |
---|
4869 | Pi= CFArray(); |
---|
4870 | diophant= CFList(); |
---|
4871 | liftBound= 2*totaldegree (F) - 1; |
---|
4872 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
4873 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
4874 | degs.intersect (bufDegs); |
---|
4875 | degs.refine(); |
---|
4876 | if (degs.getLength() <= 1) |
---|
4877 | { |
---|
4878 | smallFactors.append (F); |
---|
4879 | delete [] bounds; |
---|
4880 | return smallFactors; |
---|
4881 | } |
---|
4882 | } |
---|
4883 | |
---|
4884 | bool reduceFq2Fp= (degree (F) > getCharacteristic()); |
---|
4885 | bufUniFactors.insert (LCF); |
---|
4886 | int l= 1; |
---|
4887 | |
---|
4888 | zz_p::init (getCharacteristic()); |
---|
4889 | mat_zz_p NTLN; |
---|
4890 | if (alpha.level() != 1) |
---|
4891 | { |
---|
4892 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
4893 | zz_pE::init (NTLMipo); |
---|
4894 | } |
---|
4895 | mat_zz_pE NTLNe; |
---|
4896 | if (alpha.level() == 1) |
---|
4897 | ident (NTLN, bufUniFactors.length() - 1); |
---|
4898 | else |
---|
4899 | { |
---|
4900 | if (reduceFq2Fp) |
---|
4901 | ident (NTLN, bufUniFactors.length() - 1); |
---|
4902 | else |
---|
4903 | ident (NTLNe, bufUniFactors.length() - 1); |
---|
4904 | } |
---|
4905 | bool irreducible= false; |
---|
4906 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
4907 | |
---|
4908 | int oldL; |
---|
4909 | if (success) |
---|
4910 | { |
---|
4911 | int start= 0; |
---|
4912 | if (alpha.level() == 1) |
---|
4913 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
4914 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
4915 | irreducible |
---|
4916 | ); |
---|
4917 | else |
---|
4918 | { |
---|
4919 | if (reduceFq2Fp) |
---|
4920 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, start, liftBound, |
---|
4921 | minBound, bufUniFactors, NTLN, |
---|
4922 | diophant, M, Pi, bufQ, irreducible, |
---|
4923 | alpha |
---|
4924 | ); |
---|
4925 | else |
---|
4926 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
4927 | bufUniFactors, NTLNe, diophant, M, Pi, bufQ, |
---|
4928 | irreducible |
---|
4929 | ); |
---|
4930 | } |
---|
4931 | } |
---|
4932 | else |
---|
4933 | { |
---|
4934 | if (alpha.level() == 1) |
---|
4935 | oldL= liftAndComputeLattice (F, bounds, d, minBound + 1, liftBound, |
---|
4936 | minBound, bufUniFactors, NTLN, diophant, M, |
---|
4937 | Pi, bufQ, irreducible |
---|
4938 | ); |
---|
4939 | else |
---|
4940 | { |
---|
4941 | if (reduceFq2Fp) |
---|
4942 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, minBound + 1, |
---|
4943 | liftBound, minBound, bufUniFactors, |
---|
4944 | NTLN, diophant, M, Pi, bufQ, |
---|
4945 | irreducible, alpha |
---|
4946 | ); |
---|
4947 | else |
---|
4948 | oldL= liftAndComputeLattice (F, bounds, d, minBound + 1, liftBound, |
---|
4949 | minBound, bufUniFactors, NTLNe, diophant, |
---|
4950 | M, Pi, bufQ, irreducible |
---|
4951 | ); |
---|
4952 | } |
---|
4953 | } |
---|
4954 | |
---|
4955 | bufUniFactors.removeFirst(); |
---|
4956 | if (oldL > liftBound) |
---|
4957 | { |
---|
4958 | delete [] bounds; |
---|
4959 | return Union (smallFactors, |
---|
4960 | factorRecombination (bufUniFactors, F, |
---|
4961 | power (y, degree (F) + 1 + degree (LCF)), |
---|
4962 | degs, 1, bufUniFactors.length()/2 |
---|
4963 | ) |
---|
4964 | ); |
---|
4965 | } |
---|
4966 | |
---|
4967 | l= oldL; |
---|
4968 | if (irreducible) |
---|
4969 | { |
---|
4970 | delete [] bounds; |
---|
4971 | return Union (CFList (F), smallFactors); |
---|
4972 | } |
---|
4973 | |
---|
4974 | CanonicalForm yToL= power (y,l); |
---|
4975 | |
---|
4976 | CFList result; |
---|
4977 | if (l >= degree (F) + 1) |
---|
4978 | { |
---|
4979 | int * factorsFoundIndex; |
---|
4980 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4981 | { |
---|
4982 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4983 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4984 | factorsFoundIndex[i]= 0; |
---|
4985 | } |
---|
4986 | else |
---|
4987 | { |
---|
4988 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
4989 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
4990 | factorsFoundIndex[i]= 0; |
---|
4991 | } |
---|
4992 | int factorsFound= 0; |
---|
4993 | CanonicalForm bufF= F; |
---|
4994 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4995 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
4996 | factorsFound, factorsFoundIndex, NTLN, false |
---|
4997 | ); |
---|
4998 | else |
---|
4999 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
5000 | factorsFound, factorsFoundIndex, NTLNe, false |
---|
5001 | ); |
---|
5002 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
5003 | { |
---|
5004 | if (result.length() == NTLN.NumCols()) |
---|
5005 | { |
---|
5006 | delete [] factorsFoundIndex; |
---|
5007 | delete [] bounds; |
---|
5008 | return Union (result, smallFactors); |
---|
5009 | } |
---|
5010 | } |
---|
5011 | else |
---|
5012 | { |
---|
5013 | if (result.length() == NTLNe.NumCols()) |
---|
5014 | { |
---|
5015 | delete [] factorsFoundIndex; |
---|
5016 | delete [] bounds; |
---|
5017 | return Union (result, smallFactors); |
---|
5018 | } |
---|
5019 | } |
---|
5020 | delete [] factorsFoundIndex; |
---|
5021 | } |
---|
5022 | if (l >= liftBound) |
---|
5023 | { |
---|
5024 | int * factorsFoundIndex; |
---|
5025 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
5026 | { |
---|
5027 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5028 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5029 | factorsFoundIndex[i]= 0; |
---|
5030 | } |
---|
5031 | else |
---|
5032 | { |
---|
5033 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
5034 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
5035 | factorsFoundIndex[i]= 0; |
---|
5036 | } |
---|
5037 | CanonicalForm bufF= F; |
---|
5038 | int factorsFound= 0; |
---|
5039 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
5040 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
5041 | (LCF), factorsFound, factorsFoundIndex, NTLN, false |
---|
5042 | ); |
---|
5043 | else |
---|
5044 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
5045 | (LCF), factorsFound, factorsFoundIndex, NTLNe, false |
---|
5046 | ); |
---|
5047 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
5048 | { |
---|
5049 | if (result.length() == NTLN.NumCols()) |
---|
5050 | { |
---|
5051 | delete [] factorsFoundIndex; |
---|
5052 | delete [] bounds; |
---|
5053 | return Union (result, smallFactors); |
---|
5054 | } |
---|
5055 | } |
---|
5056 | else |
---|
5057 | { |
---|
5058 | if (result.length() == NTLNe.NumCols()) |
---|
5059 | { |
---|
5060 | delete [] factorsFoundIndex; |
---|
5061 | delete [] bounds; |
---|
5062 | return Union (result, smallFactors); |
---|
5063 | } |
---|
5064 | } |
---|
5065 | delete [] factorsFoundIndex; |
---|
5066 | } |
---|
5067 | |
---|
5068 | result= CFList(); |
---|
5069 | bool beenInThres= false; |
---|
5070 | int thres= 100; |
---|
5071 | if (l <= thres) |
---|
5072 | { |
---|
5073 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
5074 | { |
---|
5075 | if (NTLN.NumCols() < bufUniFactors.length()) |
---|
5076 | { |
---|
5077 | refineAndRestartLift (F, NTLN, liftBound, l, bufUniFactors, M, Pi, |
---|
5078 | diophant |
---|
5079 | ); |
---|
5080 | beenInThres= true; |
---|
5081 | } |
---|
5082 | } |
---|
5083 | else |
---|
5084 | { |
---|
5085 | if (NTLNe.NumCols() < bufUniFactors.length()) |
---|
5086 | { |
---|
5087 | refineAndRestartLift (F, NTLNe, liftBound, l, bufUniFactors, M, Pi, |
---|
5088 | diophant |
---|
5089 | ); |
---|
5090 | beenInThres= true; |
---|
5091 | } |
---|
5092 | } |
---|
5093 | } |
---|
5094 | |
---|
5095 | CanonicalForm bufF= F; |
---|
5096 | int factorsFound= 0; |
---|
5097 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
5098 | { |
---|
5099 | result= earlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
5100 | factorsFound, beenInThres, M, Pi, |
---|
5101 | diophant, symmetric, evaluation |
---|
5102 | ); |
---|
5103 | |
---|
5104 | if (result.length() == NTLN.NumCols()) |
---|
5105 | { |
---|
5106 | delete [] bounds; |
---|
5107 | return Union (result, smallFactors); |
---|
5108 | } |
---|
5109 | } |
---|
5110 | else |
---|
5111 | { |
---|
5112 | result= earlyReconstructionAndLifting (F, NTLNe, bufF, bufUniFactors, l, |
---|
5113 | factorsFound, beenInThres, M, Pi, |
---|
5114 | diophant, symmetric, evaluation |
---|
5115 | ); |
---|
5116 | |
---|
5117 | if (result.length() == NTLNe.NumCols()) |
---|
5118 | { |
---|
5119 | delete [] bounds; |
---|
5120 | return Union (result, smallFactors); |
---|
5121 | } |
---|
5122 | } |
---|
5123 | |
---|
5124 | if (result.length() > 0) |
---|
5125 | { |
---|
5126 | if (beenInThres) |
---|
5127 | { |
---|
5128 | int index; |
---|
5129 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
5130 | { |
---|
5131 | index= 1; |
---|
5132 | tmp1= mod (i.getItem(), y); |
---|
5133 | tmp1 /= Lc (tmp1); |
---|
5134 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
5135 | { |
---|
5136 | tmp2= mod (j.getItem(), y); |
---|
5137 | tmp2 /= Lc (tmp2); |
---|
5138 | if (tmp1 == tmp2) |
---|
5139 | { |
---|
5140 | index++; |
---|
5141 | j.remove(index); |
---|
5142 | break; |
---|
5143 | } |
---|
5144 | } |
---|
5145 | } |
---|
5146 | } |
---|
5147 | else |
---|
5148 | { |
---|
5149 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
5150 | CFList bufBufUniFactors= bufUniFactors; |
---|
5151 | CFListIterator iter, iter2; |
---|
5152 | CanonicalForm buf; |
---|
5153 | CFList factorsConsidered; |
---|
5154 | CanonicalForm tmp; |
---|
5155 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
5156 | { |
---|
5157 | if (zeroOne [i] == 0) |
---|
5158 | continue; |
---|
5159 | iter= bufUniFactors; |
---|
5160 | buf= 1; |
---|
5161 | factorsConsidered= CFList(); |
---|
5162 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
5163 | { |
---|
5164 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
5165 | { |
---|
5166 | factorsConsidered.append (iter.getItem()); |
---|
5167 | buf *= mod (iter.getItem(), y); |
---|
5168 | } |
---|
5169 | } |
---|
5170 | buf /= Lc (buf); |
---|
5171 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
5172 | { |
---|
5173 | tmp= mod (iter2.getItem(), y); |
---|
5174 | tmp /= Lc (tmp); |
---|
5175 | if (tmp == buf) |
---|
5176 | { |
---|
5177 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
5178 | break; |
---|
5179 | } |
---|
5180 | } |
---|
5181 | } |
---|
5182 | bufUniFactors= bufBufUniFactors; |
---|
5183 | delete [] zeroOne; |
---|
5184 | } |
---|
5185 | |
---|
5186 | int oldNumCols; |
---|
5187 | CFList resultBufF; |
---|
5188 | irreducible= false; |
---|
5189 | |
---|
5190 | if (alpha.level() == 1) |
---|
5191 | { |
---|
5192 | oldNumCols= NTLN.NumCols(); |
---|
5193 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
5194 | oldNumCols, oldL, l |
---|
5195 | ); |
---|
5196 | } |
---|
5197 | else |
---|
5198 | { |
---|
5199 | if (reduceFq2Fp) |
---|
5200 | { |
---|
5201 | oldNumCols= NTLN.NumCols(); |
---|
5202 | |
---|
5203 | resultBufF= increasePrecisionFq2Fp (bufF, bufUniFactors, factorsFound, |
---|
5204 | oldNumCols, oldL, alpha, l |
---|
5205 | ); |
---|
5206 | } |
---|
5207 | else |
---|
5208 | { |
---|
5209 | oldNumCols= NTLNe.NumCols(); |
---|
5210 | |
---|
5211 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
5212 | oldNumCols, oldL, alpha, l |
---|
5213 | ); |
---|
5214 | } |
---|
5215 | } |
---|
5216 | |
---|
5217 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
5218 | { |
---|
5219 | delete [] bounds; |
---|
5220 | result= Union (resultBufF, result); |
---|
5221 | return Union (result, smallFactors); |
---|
5222 | } |
---|
5223 | |
---|
5224 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
5225 | i.getItem()= mod (i.getItem(), y); |
---|
5226 | |
---|
5227 | result= Union (result, resultBufF); |
---|
5228 | result= Union (result, smallFactors); |
---|
5229 | delete [] bounds; |
---|
5230 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
5231 | degs.intersect (bufDegs); |
---|
5232 | degs.refine(); |
---|
5233 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
5234 | { |
---|
5235 | result.append (bufF); |
---|
5236 | return result; |
---|
5237 | } |
---|
5238 | return Union (result, henselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
5239 | alpha, degs, symmetric, |
---|
5240 | evaluation |
---|
5241 | ) |
---|
5242 | ); |
---|
5243 | } |
---|
5244 | |
---|
5245 | if (l < liftBound) |
---|
5246 | { |
---|
5247 | if (alpha.level() == 1) |
---|
5248 | { |
---|
5249 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
5250 | NTLN |
---|
5251 | ); |
---|
5252 | } |
---|
5253 | else |
---|
5254 | { |
---|
5255 | if (reduceFq2Fp) |
---|
5256 | { |
---|
5257 | result=increasePrecisionFq2Fp (F, bufUniFactors, oldL, l, d, bounds, |
---|
5258 | bufQ, NTLN, alpha |
---|
5259 | ); |
---|
5260 | } |
---|
5261 | else |
---|
5262 | { |
---|
5263 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
5264 | NTLNe |
---|
5265 | ); |
---|
5266 | } |
---|
5267 | } |
---|
5268 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
5269 | { |
---|
5270 | if (result.length()== NTLN.NumCols()) |
---|
5271 | { |
---|
5272 | delete [] bounds; |
---|
5273 | result= Union (result, smallFactors); |
---|
5274 | return result; |
---|
5275 | } |
---|
5276 | } |
---|
5277 | else |
---|
5278 | { |
---|
5279 | if (result.length()== NTLNe.NumCols()) |
---|
5280 | { |
---|
5281 | delete [] bounds; |
---|
5282 | result= Union (result, smallFactors); |
---|
5283 | return result; |
---|
5284 | } |
---|
5285 | } |
---|
5286 | |
---|
5287 | if (result.isEmpty()) |
---|
5288 | { |
---|
5289 | if (alpha.level() == 1) |
---|
5290 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
5291 | liftBound, d, bounds, NTLN, |
---|
5292 | diophant, M, Pi, bufQ |
---|
5293 | ); |
---|
5294 | else |
---|
5295 | { |
---|
5296 | if (reduceFq2Fp) |
---|
5297 | result= furtherLiftingAndIncreasePrecisionFq2Fp (F,bufUniFactors, l, |
---|
5298 | liftBound, d, bounds, |
---|
5299 | NTLN, diophant, M, |
---|
5300 | Pi, bufQ, alpha |
---|
5301 | ); |
---|
5302 | else |
---|
5303 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
5304 | liftBound, d, bounds, |
---|
5305 | NTLNe, diophant, M, |
---|
5306 | Pi, bufQ |
---|
5307 | ); |
---|
5308 | } |
---|
5309 | |
---|
5310 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
5311 | { |
---|
5312 | if (result.length() == NTLN.NumCols()) |
---|
5313 | { |
---|
5314 | delete [] bounds; |
---|
5315 | result= Union (result, smallFactors); |
---|
5316 | return result; |
---|
5317 | } |
---|
5318 | } |
---|
5319 | else |
---|
5320 | { |
---|
5321 | if (result.length() == NTLNe.NumCols()) |
---|
5322 | { |
---|
5323 | delete [] bounds; |
---|
5324 | result= Union (result, smallFactors); |
---|
5325 | return result; |
---|
5326 | } |
---|
5327 | } |
---|
5328 | } |
---|
5329 | } |
---|
5330 | |
---|
5331 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
5332 | |
---|
5333 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
5334 | degs.intersect (bufDegs); |
---|
5335 | degs.refine(); |
---|
5336 | |
---|
5337 | delete [] bounds; |
---|
5338 | bounds= computeBounds (F, d, isIrreducible); |
---|
5339 | if (isIrreducible) |
---|
5340 | { |
---|
5341 | delete [] bounds; |
---|
5342 | result= Union (result, smallFactors); |
---|
5343 | result.append (F); |
---|
5344 | return result; |
---|
5345 | } |
---|
5346 | minBound= bounds[0]; |
---|
5347 | for (int i= 1; i < d; i++) |
---|
5348 | { |
---|
5349 | if (bounds[i] != 0) |
---|
5350 | minBound= tmin (minBound, bounds[i]); |
---|
5351 | } |
---|
5352 | |
---|
5353 | if (minBound > 16 || result.length() == 0) |
---|
5354 | { |
---|
5355 | result= Union (result, smallFactors); |
---|
5356 | CanonicalForm MODl= power (y, degree (F) + 1 + degree (LC (F, 1))); |
---|
5357 | delete [] bounds; |
---|
5358 | return Union (result, factorRecombination (bufUniFactors, F, MODl, degs, 1, |
---|
5359 | bufUniFactors.length()/2 |
---|
5360 | ) |
---|
5361 | ); |
---|
5362 | } |
---|
5363 | else |
---|
5364 | { |
---|
5365 | result= Union (result, smallFactors); |
---|
5366 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
5367 | i.getItem()= mod (i.getItem(), y); |
---|
5368 | delete [] bounds; |
---|
5369 | return Union (result, henselLiftAndLatticeRecombi (F, bufUniFactors, alpha, |
---|
5370 | degs,symmetric, evaluation |
---|
5371 | ) |
---|
5372 | ); |
---|
5373 | } |
---|
5374 | } |
---|
5375 | |
---|
5376 | ExtensionInfo |
---|
5377 | init4ext (const ExtensionInfo& info, const CanonicalForm& evaluation, |
---|
5378 | int& degMipo |
---|
5379 | ) |
---|
5380 | { |
---|
5381 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
5382 | Variable alpha= info.getAlpha(); |
---|
5383 | if (GF) |
---|
5384 | { |
---|
5385 | degMipo= getGFDegree(); |
---|
5386 | CanonicalForm GFMipo= gf_mipo; |
---|
5387 | setCharacteristic (getCharacteristic()); |
---|
5388 | GFMipo.mapinto(); |
---|
5389 | alpha= rootOf (GFMipo); |
---|
5390 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
5391 | } |
---|
5392 | else |
---|
5393 | { |
---|
5394 | alpha= info.getAlpha(); |
---|
5395 | degMipo= degree (getMipo (alpha)); |
---|
5396 | } |
---|
5397 | |
---|
5398 | Variable gamma; |
---|
5399 | CanonicalForm primElemAlpha, imPrimElemAlpha; |
---|
5400 | if ((!GF && evaluation != alpha) || (GF && evaluation != getGFGenerator())) |
---|
5401 | { |
---|
5402 | CanonicalForm bufEvaluation; |
---|
5403 | if (GF) |
---|
5404 | { |
---|
5405 | setCharacteristic (getCharacteristic()); |
---|
5406 | bufEvaluation= GF2FalphaRep (evaluation, alpha); |
---|
5407 | } |
---|
5408 | else |
---|
5409 | bufEvaluation= evaluation; |
---|
5410 | CanonicalForm mipo= findMinPoly (bufEvaluation, alpha); |
---|
5411 | gamma= rootOf (mipo); |
---|
5412 | Variable V_buf; |
---|
5413 | bool fail= false; |
---|
5414 | primElemAlpha= primitiveElement (alpha, V_buf, fail); |
---|
5415 | imPrimElemAlpha= map (primElemAlpha, alpha, bufEvaluation, gamma); |
---|
5416 | |
---|
5417 | if (GF) |
---|
5418 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
5419 | } |
---|
5420 | else |
---|
5421 | gamma= alpha; |
---|
5422 | ExtensionInfo info2= ExtensionInfo (alpha, gamma, primElemAlpha, |
---|
5423 | imPrimElemAlpha, 1, info.getGFName(), true |
---|
5424 | ); |
---|
5425 | |
---|
5426 | return info2; |
---|
5427 | } |
---|
5428 | |
---|
5429 | CFList |
---|
5430 | extHenselLiftAndLatticeRecombi(const CanonicalForm& G, const CFList& uniFactors, |
---|
5431 | const ExtensionInfo& extInfo, const |
---|
5432 | DegreePattern& degPat, const CanonicalForm& eval |
---|
5433 | ) |
---|
5434 | { |
---|
5435 | CanonicalForm evaluation= eval; |
---|
5436 | ExtensionInfo info= extInfo; |
---|
5437 | Variable alpha; |
---|
5438 | DegreePattern degs= degPat; |
---|
5439 | CanonicalForm F= G; |
---|
5440 | Variable x= Variable (1); |
---|
5441 | Variable y= F.mvar(); |
---|
5442 | CFList bufUniFactors= uniFactors; |
---|
5443 | |
---|
5444 | |
---|
5445 | int degMipo; |
---|
5446 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
5447 | |
---|
5448 | CFList source, dest; |
---|
5449 | CanonicalForm LCF= LC (F, 1); |
---|
5450 | |
---|
5451 | int d; |
---|
5452 | bool isIrreducible= false; |
---|
5453 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
5454 | if (isIrreducible) |
---|
5455 | { |
---|
5456 | delete [] bounds; |
---|
5457 | CFList source, dest; |
---|
5458 | CanonicalForm tmp= G (y - evaluation, y); |
---|
5459 | tmp= mapDown (tmp, info, source, dest); |
---|
5460 | return CFList (tmp); |
---|
5461 | } |
---|
5462 | int minBound= bounds[0]; |
---|
5463 | for (int i= 1; i < d; i++) |
---|
5464 | { |
---|
5465 | if (bounds[i] != 0) |
---|
5466 | minBound= tmin (minBound, bounds[i]); |
---|
5467 | } |
---|
5468 | |
---|
5469 | |
---|
5470 | CFArray Pi; |
---|
5471 | CFList diophant; |
---|
5472 | int liftBound= tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
5473 | degree (LC (F, 1))); |
---|
5474 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
5475 | |
---|
5476 | CFList smallFactors; |
---|
5477 | CanonicalForm H; |
---|
5478 | bool success= false; |
---|
5479 | smallFactors= extSieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, |
---|
5480 | M, success, minBound + 1, evaluation, info |
---|
5481 | ); |
---|
5482 | |
---|
5483 | if (smallFactors.length() > 0) |
---|
5484 | { |
---|
5485 | if (smallFactors.length() == 1) |
---|
5486 | { |
---|
5487 | if (smallFactors.getFirst() == F) |
---|
5488 | { |
---|
5489 | delete [] bounds; |
---|
5490 | CFList source, dest; |
---|
5491 | CanonicalForm tmp= G (y - evaluation, y); |
---|
5492 | tmp= mapDown (tmp, info, source, dest); |
---|
5493 | return CFList (tmp); |
---|
5494 | } |
---|
5495 | } |
---|
5496 | if (degs.getLength() <= 1) |
---|
5497 | { |
---|
5498 | delete [] bounds; |
---|
5499 | return smallFactors; |
---|
5500 | } |
---|
5501 | } |
---|
5502 | |
---|
5503 | int index; |
---|
5504 | CanonicalForm tmp1, tmp2; |
---|
5505 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
5506 | { |
---|
5507 | index= 1; |
---|
5508 | tmp1= mod (i.getItem(), y - evaluation); |
---|
5509 | tmp1 /= Lc (tmp1); |
---|
5510 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
5511 | { |
---|
5512 | tmp2= mod (j.getItem(), y); |
---|
5513 | tmp2 /= Lc (tmp2); |
---|
5514 | if (tmp1 == tmp2) |
---|
5515 | { |
---|
5516 | index++; |
---|
5517 | j.remove(index); |
---|
5518 | break; |
---|
5519 | } |
---|
5520 | } |
---|
5521 | } |
---|
5522 | |
---|
5523 | if (bufUniFactors.isEmpty()) |
---|
5524 | { |
---|
5525 | delete [] bounds; |
---|
5526 | return smallFactors; |
---|
5527 | } |
---|
5528 | |
---|
5529 | if (success) |
---|
5530 | { |
---|
5531 | F= H; |
---|
5532 | delete [] bounds; |
---|
5533 | bounds= computeBounds (F, d, isIrreducible); |
---|
5534 | if (isIrreducible) |
---|
5535 | { |
---|
5536 | delete [] bounds; |
---|
5537 | CFList source, dest; |
---|
5538 | CanonicalForm tmp= F (y - evaluation, y); |
---|
5539 | tmp= mapDown (tmp, info, source, dest); |
---|
5540 | smallFactors.append (tmp); |
---|
5541 | return smallFactors; |
---|
5542 | } |
---|
5543 | LCF= LC (F, 1); |
---|
5544 | |
---|
5545 | minBound= bounds[0]; |
---|
5546 | for (int i= 1; i < d; i++) |
---|
5547 | { |
---|
5548 | if (bounds[i] != 0) |
---|
5549 | minBound= tmin (minBound, bounds[i]); |
---|
5550 | } |
---|
5551 | Pi= CFArray(); |
---|
5552 | diophant= CFList(); |
---|
5553 | liftBound=tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
5554 | degree (LC (F, 1))); |
---|
5555 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
5556 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
5557 | degs.intersect (bufDegs); |
---|
5558 | degs.refine(); |
---|
5559 | if (degs.getLength() <= 1) |
---|
5560 | { |
---|
5561 | delete [] bounds; |
---|
5562 | CFList source, dest; |
---|
5563 | CanonicalForm tmp= F (y - evaluation, y); |
---|
5564 | tmp= mapDown (tmp, info, source, dest); |
---|
5565 | smallFactors.append (tmp); |
---|
5566 | return smallFactors; |
---|
5567 | } |
---|
5568 | } |
---|
5569 | |
---|
5570 | bufUniFactors.insert (LCF); |
---|
5571 | int l= 1; |
---|
5572 | |
---|
5573 | zz_p::init (getCharacteristic()); |
---|
5574 | zz_pX NTLMipo; |
---|
5575 | mat_zz_p NTLN; |
---|
5576 | |
---|
5577 | ident (NTLN, bufUniFactors.length() - 1); |
---|
5578 | bool irreducible= false; |
---|
5579 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
5580 | |
---|
5581 | int oldL; |
---|
5582 | if (success) |
---|
5583 | { |
---|
5584 | int start= 0; |
---|
5585 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, start, |
---|
5586 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
5587 | irreducible, evaluation, info2, source, dest |
---|
5588 | ); |
---|
5589 | } |
---|
5590 | else |
---|
5591 | { |
---|
5592 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, |
---|
5593 | minBound + 1, bufUniFactors, NTLN, diophant, |
---|
5594 | M, Pi, bufQ, irreducible, evaluation, info2, |
---|
5595 | source, dest |
---|
5596 | ); |
---|
5597 | } |
---|
5598 | |
---|
5599 | bufUniFactors.removeFirst(); |
---|
5600 | if (oldL > liftBound) |
---|
5601 | { |
---|
5602 | delete [] bounds; |
---|
5603 | return Union (smallFactors, extFactorRecombination |
---|
5604 | (bufUniFactors, F, |
---|
5605 | power (y, degree (F) + 1 + degree (LCF)),info, |
---|
5606 | degs, evaluation, 1, bufUniFactors.length()/2 |
---|
5607 | ) |
---|
5608 | ); |
---|
5609 | } |
---|
5610 | |
---|
5611 | l= oldL; |
---|
5612 | if (irreducible) |
---|
5613 | { |
---|
5614 | delete [] bounds; |
---|
5615 | CFList source, dest; |
---|
5616 | CanonicalForm tmp= F (y - evaluation, y); |
---|
5617 | tmp= mapDown (tmp, info, source, dest); |
---|
5618 | return Union (CFList (tmp), smallFactors); |
---|
5619 | } |
---|
5620 | |
---|
5621 | CanonicalForm yToL= power (y,l); |
---|
5622 | |
---|
5623 | CFList result; |
---|
5624 | if (l >= degree (F) + 1) |
---|
5625 | { |
---|
5626 | int * factorsFoundIndex; |
---|
5627 | |
---|
5628 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5629 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5630 | factorsFoundIndex[i]= 0; |
---|
5631 | |
---|
5632 | int factorsFound= 0; |
---|
5633 | CanonicalForm bufF= F; |
---|
5634 | |
---|
5635 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
5636 | factorsFound, factorsFoundIndex, NTLN, false, info, |
---|
5637 | evaluation |
---|
5638 | ); |
---|
5639 | |
---|
5640 | if (result.length() == NTLN.NumCols()) |
---|
5641 | { |
---|
5642 | delete [] factorsFoundIndex; |
---|
5643 | delete [] bounds; |
---|
5644 | return Union (result, smallFactors); |
---|
5645 | } |
---|
5646 | |
---|
5647 | delete [] factorsFoundIndex; |
---|
5648 | } |
---|
5649 | if (l >= liftBound) |
---|
5650 | { |
---|
5651 | int * factorsFoundIndex; |
---|
5652 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5653 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5654 | factorsFoundIndex[i]= 0; |
---|
5655 | CanonicalForm bufF= F; |
---|
5656 | int factorsFound= 0; |
---|
5657 | |
---|
5658 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
5659 | (LCF), factorsFound, factorsFoundIndex, NTLN, false, |
---|
5660 | info, evaluation |
---|
5661 | ); |
---|
5662 | |
---|
5663 | if (result.length() == NTLN.NumCols()) |
---|
5664 | { |
---|
5665 | delete [] factorsFoundIndex; |
---|
5666 | delete [] bounds; |
---|
5667 | return Union (result, smallFactors); |
---|
5668 | } |
---|
5669 | delete [] factorsFoundIndex; |
---|
5670 | } |
---|
5671 | |
---|
5672 | result= CFList(); |
---|
5673 | bool beenInThres= false; |
---|
5674 | int thres= 100; |
---|
5675 | if (l <= thres && bufUniFactors.length() > NTLN.NumCols()) |
---|
5676 | { |
---|
5677 | refineAndRestartLift (F, NTLN, 2*totaldegree (F)-1, l, bufUniFactors, M, Pi, |
---|
5678 | diophant |
---|
5679 | ); |
---|
5680 | beenInThres= true; |
---|
5681 | } |
---|
5682 | |
---|
5683 | |
---|
5684 | CanonicalForm bufF= F; |
---|
5685 | int factorsFound= 0; |
---|
5686 | |
---|
5687 | result= extEarlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
5688 | factorsFound, beenInThres, M, Pi, |
---|
5689 | diophant, info, evaluation |
---|
5690 | ); |
---|
5691 | |
---|
5692 | if (result.length() == NTLN.NumCols()) |
---|
5693 | { |
---|
5694 | delete [] bounds; |
---|
5695 | return Union (result, smallFactors); |
---|
5696 | } |
---|
5697 | |
---|
5698 | if (result.length() > 0) |
---|
5699 | { |
---|
5700 | if (beenInThres) |
---|
5701 | { |
---|
5702 | int index; |
---|
5703 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
5704 | { |
---|
5705 | index= 1; |
---|
5706 | tmp1= mod (i.getItem(), y-evaluation); |
---|
5707 | tmp1 /= Lc (tmp1); |
---|
5708 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
5709 | { |
---|
5710 | tmp2= mod (j.getItem(), y); |
---|
5711 | tmp2 /= Lc (tmp2); |
---|
5712 | if (tmp1 == tmp2) |
---|
5713 | { |
---|
5714 | index++; |
---|
5715 | j.remove(index); |
---|
5716 | break; |
---|
5717 | } |
---|
5718 | } |
---|
5719 | } |
---|
5720 | } |
---|
5721 | else |
---|
5722 | { |
---|
5723 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
5724 | CFList bufBufUniFactors= bufUniFactors; |
---|
5725 | CFListIterator iter, iter2; |
---|
5726 | CanonicalForm buf; |
---|
5727 | CFList factorsConsidered; |
---|
5728 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
5729 | { |
---|
5730 | if (zeroOne [i] == 0) |
---|
5731 | continue; |
---|
5732 | iter= bufUniFactors; |
---|
5733 | buf= 1; |
---|
5734 | factorsConsidered= CFList(); |
---|
5735 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
5736 | { |
---|
5737 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
5738 | { |
---|
5739 | factorsConsidered.append (iter.getItem()); |
---|
5740 | buf *= mod (iter.getItem(), y); |
---|
5741 | } |
---|
5742 | } |
---|
5743 | buf /= Lc (buf); |
---|
5744 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
5745 | { |
---|
5746 | CanonicalForm tmp= mod (iter2.getItem(), y - evaluation); |
---|
5747 | tmp /= Lc (tmp); |
---|
5748 | if (tmp == buf) |
---|
5749 | { |
---|
5750 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
5751 | break; |
---|
5752 | } |
---|
5753 | } |
---|
5754 | } |
---|
5755 | bufUniFactors= bufBufUniFactors; |
---|
5756 | delete [] zeroOne; |
---|
5757 | } |
---|
5758 | |
---|
5759 | int oldNumCols; |
---|
5760 | CFList resultBufF; |
---|
5761 | irreducible= false; |
---|
5762 | |
---|
5763 | oldNumCols= NTLN.NumCols(); |
---|
5764 | resultBufF= extIncreasePrecision (bufF, bufUniFactors, factorsFound, |
---|
5765 | oldNumCols, oldL, evaluation, info2, |
---|
5766 | source, dest, l |
---|
5767 | ); |
---|
5768 | |
---|
5769 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
5770 | { |
---|
5771 | delete [] bounds; |
---|
5772 | result= Union (resultBufF, result); |
---|
5773 | return Union (result, smallFactors); |
---|
5774 | } |
---|
5775 | |
---|
5776 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
5777 | i.getItem()= mod (i.getItem(), y); |
---|
5778 | |
---|
5779 | delete [] bounds; |
---|
5780 | CFList bufResult; |
---|
5781 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
5782 | degs.intersect (bufDegs); |
---|
5783 | degs.refine(); |
---|
5784 | result= Union (result, smallFactors); |
---|
5785 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
5786 | { |
---|
5787 | result.append (bufF); |
---|
5788 | return result; |
---|
5789 | } |
---|
5790 | return Union (result, extHenselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
5791 | info, degs, evaluation |
---|
5792 | ) |
---|
5793 | ); |
---|
5794 | } |
---|
5795 | |
---|
5796 | if (l/degMipo < liftBound) |
---|
5797 | { |
---|
5798 | result=extIncreasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
5799 | NTLN, evaluation, info2, source, dest |
---|
5800 | ); |
---|
5801 | |
---|
5802 | if (result.length()== NTLN.NumCols()) |
---|
5803 | { |
---|
5804 | delete [] bounds; |
---|
5805 | result= Union (result, smallFactors); |
---|
5806 | return result; |
---|
5807 | } |
---|
5808 | |
---|
5809 | if (result.isEmpty()) |
---|
5810 | { |
---|
5811 | result= extFurtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
5812 | liftBound, d, bounds, NTLN, |
---|
5813 | diophant, M, Pi, bufQ, |
---|
5814 | evaluation, info2, source, |
---|
5815 | dest |
---|
5816 | ); |
---|
5817 | if (result.length()== NTLN.NumCols()) |
---|
5818 | { |
---|
5819 | delete [] bounds; |
---|
5820 | result= Union (result, smallFactors); |
---|
5821 | return result; |
---|
5822 | } |
---|
5823 | } |
---|
5824 | } |
---|
5825 | |
---|
5826 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
5827 | |
---|
5828 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
5829 | degs.intersect (bufDegs); |
---|
5830 | degs.refine(); |
---|
5831 | |
---|
5832 | delete [] bounds; |
---|
5833 | bounds= computeBounds (F, d, isIrreducible); |
---|
5834 | if (isIrreducible) |
---|
5835 | { |
---|
5836 | delete [] bounds; |
---|
5837 | CFList source, dest; |
---|
5838 | CanonicalForm tmp= F (y - evaluation, y); |
---|
5839 | tmp= mapDown (tmp, info, source, dest); |
---|
5840 | smallFactors.append (tmp); |
---|
5841 | result= Union (result, smallFactors); |
---|
5842 | return result; |
---|
5843 | } |
---|
5844 | minBound= bounds[0]; |
---|
5845 | for (int i= 1; i < d; i++) |
---|
5846 | { |
---|
5847 | if (bounds[i] != 0) |
---|
5848 | minBound= tmin (minBound, bounds[i]); |
---|
5849 | } |
---|
5850 | |
---|
5851 | if (minBound > 16 || result.length() == 0) |
---|
5852 | { |
---|
5853 | result= Union (result, smallFactors); |
---|
5854 | CanonicalForm MODl= power (y, degree (F) + 1 + degree (LC (F, 1))); |
---|
5855 | delete [] bounds; |
---|
5856 | return Union (result, extFactorRecombination (bufUniFactors, F, MODl, info, |
---|
5857 | degs, evaluation, 1, |
---|
5858 | bufUniFactors.length()/2 |
---|
5859 | ) |
---|
5860 | ); |
---|
5861 | } |
---|
5862 | else |
---|
5863 | { |
---|
5864 | result= Union (result, smallFactors); |
---|
5865 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
5866 | i.getItem()= mod (i.getItem(), y); |
---|
5867 | delete [] bounds; |
---|
5868 | return Union (result, extHenselLiftAndLatticeRecombi (F, bufUniFactors, |
---|
5869 | info, degs, evaluation |
---|
5870 | ) |
---|
5871 | ); |
---|
5872 | } |
---|
5873 | } |
---|
5874 | |
---|
5875 | CFList |
---|
5876 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
5877 | |
---|
5878 | /// bivariate factorization over finite fields as decribed in "Factoring |
---|
5879 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
5880 | CFList |
---|
5881 | biFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
5882 | { |
---|
5883 | if (F.inCoeffDomain()) |
---|
5884 | return CFList(F); |
---|
5885 | |
---|
5886 | CanonicalForm A= F; |
---|
5887 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
5888 | |
---|
5889 | Variable alpha= info.getAlpha(); |
---|
5890 | Variable beta= info.getBeta(); |
---|
5891 | CanonicalForm gamma= info.getGamma(); |
---|
5892 | CanonicalForm delta= info.getDelta(); |
---|
5893 | int k= info.getGFDegree(); |
---|
5894 | bool extension= info.isInExtension(); |
---|
5895 | if (A.isUnivariate()) |
---|
5896 | { |
---|
5897 | if (extension == false) |
---|
5898 | return uniFactorizer (F, alpha, GF); |
---|
5899 | else |
---|
5900 | { |
---|
5901 | CFList source, dest; |
---|
5902 | A= mapDown (A, info, source, dest); |
---|
5903 | return uniFactorizer (A, beta, GF); |
---|
5904 | } |
---|
5905 | } |
---|
5906 | |
---|
5907 | CFMap N; |
---|
5908 | A= compress (A, N); |
---|
5909 | Variable y= A.mvar(); |
---|
5910 | |
---|
5911 | if (y.level() > 2) return CFList (F); |
---|
5912 | Variable x= Variable (1); |
---|
5913 | |
---|
5914 | //remove and factorize content |
---|
5915 | CanonicalForm contentAx= content (A, x); |
---|
5916 | CanonicalForm contentAy= content (A); |
---|
5917 | |
---|
5918 | A= A/(contentAx*contentAy); |
---|
5919 | CFList contentAxFactors, contentAyFactors; |
---|
5920 | |
---|
5921 | if (!extension) |
---|
5922 | { |
---|
5923 | contentAxFactors= uniFactorizer (contentAx, alpha, GF); |
---|
5924 | contentAyFactors= uniFactorizer (contentAy, alpha, GF); |
---|
5925 | } |
---|
5926 | |
---|
5927 | //trivial case |
---|
5928 | CFList factors; |
---|
5929 | if (A.inCoeffDomain()) |
---|
5930 | { |
---|
5931 | append (factors, contentAxFactors); |
---|
5932 | append (factors, contentAyFactors); |
---|
5933 | decompress (factors, N); |
---|
5934 | return factors; |
---|
5935 | } |
---|
5936 | else if (A.isUnivariate()) |
---|
5937 | { |
---|
5938 | factors= uniFactorizer (A, alpha, GF); |
---|
5939 | append (factors, contentAxFactors); |
---|
5940 | append (factors, contentAyFactors); |
---|
5941 | decompress (factors, N); |
---|
5942 | return factors; |
---|
5943 | } |
---|
5944 | |
---|
5945 | |
---|
5946 | //check trivial case |
---|
5947 | if (degree (A) == 1 || degree (A, 1) == 1 || |
---|
5948 | (size (A) == 2 && igcd (degree (A), degree (A,1))==1)) |
---|
5949 | { |
---|
5950 | factors.append (A); |
---|
5951 | |
---|
5952 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
5953 | false, false, N); |
---|
5954 | |
---|
5955 | normalize (factors); |
---|
5956 | return factors; |
---|
5957 | } |
---|
5958 | |
---|
5959 | // check derivatives |
---|
5960 | bool derivXZero= false; |
---|
5961 | CanonicalForm derivX= deriv (A, x); |
---|
5962 | CanonicalForm gcdDerivX; |
---|
5963 | if (derivX.isZero()) |
---|
5964 | derivXZero= true; |
---|
5965 | else |
---|
5966 | { |
---|
5967 | gcdDerivX= gcd (A, derivX); |
---|
5968 | if (degree (gcdDerivX) > 0) |
---|
5969 | { |
---|
5970 | CanonicalForm g= A/gcdDerivX; |
---|
5971 | CFList factorsG= |
---|
5972 | Union (biFactorize (g, info), biFactorize (gcdDerivX, info)); |
---|
5973 | append (factorsG, contentAxFactors); |
---|
5974 | append (factorsG, contentAyFactors); |
---|
5975 | decompress (factorsG, N); |
---|
5976 | normalize (factors); |
---|
5977 | return factorsG; |
---|
5978 | } |
---|
5979 | } |
---|
5980 | bool derivYZero= false; |
---|
5981 | CanonicalForm derivY= deriv (A, y); |
---|
5982 | CanonicalForm gcdDerivY; |
---|
5983 | if (derivY.isZero()) |
---|
5984 | derivYZero= true; |
---|
5985 | else |
---|
5986 | { |
---|
5987 | gcdDerivY= gcd (A, derivY); |
---|
5988 | if (degree (gcdDerivY) > 0) |
---|
5989 | { |
---|
5990 | CanonicalForm g= A/gcdDerivY; |
---|
5991 | CFList factorsG= |
---|
5992 | Union (biFactorize (g, info), biFactorize (gcdDerivY, info)); |
---|
5993 | append (factorsG, contentAxFactors); |
---|
5994 | append (factorsG, contentAyFactors); |
---|
5995 | decompress (factorsG, N); |
---|
5996 | normalize (factors); |
---|
5997 | return factorsG; |
---|
5998 | } |
---|
5999 | } |
---|
6000 | //main variable is chosen s.t. the degree in x is minimal |
---|
6001 | bool swap= false; |
---|
6002 | if ((degree (A) > degree (A, x)) || derivXZero) |
---|
6003 | { |
---|
6004 | if (!derivYZero) |
---|
6005 | { |
---|
6006 | A= swapvar (A, y, x); |
---|
6007 | swap= derivXZero; |
---|
6008 | derivXZero= derivYZero; |
---|
6009 | derivYZero= swap; |
---|
6010 | swap= true; |
---|
6011 | } |
---|
6012 | } |
---|
6013 | |
---|
6014 | int boundsLength; |
---|
6015 | bool isIrreducible= false; |
---|
6016 | int * bounds= computeBounds (A, boundsLength, isIrreducible); |
---|
6017 | if (isIrreducible) |
---|
6018 | { |
---|
6019 | delete [] bounds; |
---|
6020 | factors.append (A); |
---|
6021 | |
---|
6022 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
6023 | swap, false, N); |
---|
6024 | |
---|
6025 | normalize (factors); |
---|
6026 | return factors; |
---|
6027 | } |
---|
6028 | |
---|
6029 | bool fail= false; |
---|
6030 | CanonicalForm Aeval, evaluation, bufAeval, bufEvaluation, buf, tmp; |
---|
6031 | CFList uniFactors, list, bufUniFactors; |
---|
6032 | DegreePattern degs; |
---|
6033 | DegreePattern bufDegs; |
---|
6034 | |
---|
6035 | bool fail2= false; |
---|
6036 | CanonicalForm Aeval2, evaluation2, bufAeval2, bufEvaluation2; |
---|
6037 | CFList bufUniFactors2, list2, uniFactors2; |
---|
6038 | DegreePattern degs2; |
---|
6039 | DegreePattern bufDegs2; |
---|
6040 | bool swap2= false; |
---|
6041 | |
---|
6042 | // several univariate factorizations to obtain more information about the |
---|
6043 | // degree pattern therefore usually less combinations have to be tried during |
---|
6044 | // the recombination process |
---|
6045 | int factorNums= 3; |
---|
6046 | int subCheck1= substituteCheck (A, x); |
---|
6047 | int subCheck2= substituteCheck (A, y); |
---|
6048 | bool symmetric= false; |
---|
6049 | for (int i= 0; i < factorNums; i++) |
---|
6050 | { |
---|
6051 | bufAeval= A; |
---|
6052 | bufEvaluation= evalPoint (A, bufAeval, alpha, list, GF, fail); |
---|
6053 | if (!derivXZero && !fail2 && !symmetric) |
---|
6054 | { |
---|
6055 | if (i == 0) |
---|
6056 | { |
---|
6057 | buf= swapvar (A, x, y); |
---|
6058 | symmetric= (A/Lc (A) == buf/Lc (buf)); |
---|
6059 | } |
---|
6060 | bufAeval2= buf; |
---|
6061 | bufEvaluation2= evalPoint (buf, bufAeval2, alpha, list2, GF, fail2); |
---|
6062 | } |
---|
6063 | // first try to change main variable if there is no valid evaluation point |
---|
6064 | if (fail && (i == 0)) |
---|
6065 | { |
---|
6066 | if (!derivXZero && !fail2 && !symmetric) |
---|
6067 | { |
---|
6068 | bufEvaluation= bufEvaluation2; |
---|
6069 | int dummy= subCheck2; |
---|
6070 | subCheck2= subCheck1; |
---|
6071 | subCheck1= dummy; |
---|
6072 | tmp= A; |
---|
6073 | A= buf; |
---|
6074 | buf= tmp; |
---|
6075 | bufAeval= bufAeval2; |
---|
6076 | swap2= true; |
---|
6077 | fail= false; |
---|
6078 | } |
---|
6079 | else |
---|
6080 | fail= true; |
---|
6081 | } |
---|
6082 | |
---|
6083 | // if there is no valid evaluation point pass to a field extension |
---|
6084 | if (fail && (i == 0)) |
---|
6085 | { |
---|
6086 | factors= extBiFactorize (A, info); |
---|
6087 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
6088 | swap, swap2, N); |
---|
6089 | normalize (factors); |
---|
6090 | return factors; |
---|
6091 | } |
---|
6092 | |
---|
6093 | // there is at least one valid evaluation point |
---|
6094 | // but we do not compute more univariate factorization over an extension |
---|
6095 | if (fail && (i != 0)) |
---|
6096 | break; |
---|
6097 | |
---|
6098 | // univariate factorization |
---|
6099 | TIMING_START (fac_fq_uni_factorizer); |
---|
6100 | bufUniFactors= uniFactorizer (bufAeval, alpha, GF); |
---|
6101 | TIMING_END_AND_PRINT (fac_fq_uni_factorizer, |
---|
6102 | "time for univariate factorization: "); |
---|
6103 | DEBOUTLN (cerr, "Lc (bufAeval)*prod (bufUniFactors)== bufAeval " << |
---|
6104 | (prod (bufUniFactors)*Lc (bufAeval) == bufAeval)); |
---|
6105 | |
---|
6106 | if (!derivXZero && !fail2 && !symmetric) |
---|
6107 | { |
---|
6108 | TIMING_START (fac_fq_uni_factorizer); |
---|
6109 | bufUniFactors2= uniFactorizer (bufAeval2, alpha, GF); |
---|
6110 | TIMING_END_AND_PRINT (fac_fq_uni_factorizer, |
---|
6111 | "time for univariate factorization in y: "); |
---|
6112 | DEBOUTLN (cerr, "Lc (bufAeval2)*prod (bufUniFactors2)== bufAeval2 " << |
---|
6113 | (prod (bufUniFactors2)*Lc (bufAeval2) == bufAeval2)); |
---|
6114 | } |
---|
6115 | |
---|
6116 | if (bufUniFactors.length() == 1 || |
---|
6117 | (!fail2 && !derivXZero && !symmetric && (bufUniFactors2.length() == 1))) |
---|
6118 | { |
---|
6119 | if (extension) |
---|
6120 | { |
---|
6121 | CFList source, dest; |
---|
6122 | appendMapDown (factors, A, info, source, dest); |
---|
6123 | } |
---|
6124 | else |
---|
6125 | factors.append (A); |
---|
6126 | |
---|
6127 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
6128 | swap, swap2, N); |
---|
6129 | |
---|
6130 | normalize (factors); |
---|
6131 | return factors; |
---|
6132 | } |
---|
6133 | |
---|
6134 | if (i == 0) |
---|
6135 | { |
---|
6136 | if (subCheck1 > 0) |
---|
6137 | { |
---|
6138 | int subCheck= substituteCheck (bufUniFactors); |
---|
6139 | |
---|
6140 | if (subCheck > 1 && (subCheck1%subCheck == 0)) |
---|
6141 | { |
---|
6142 | CanonicalForm bufA= A; |
---|
6143 | subst (bufA, bufA, subCheck, x); |
---|
6144 | factors= biFactorize (bufA, info); |
---|
6145 | reverseSubst (factors, subCheck, x); |
---|
6146 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
6147 | swap, swap2, N); |
---|
6148 | normalize (factors); |
---|
6149 | return factors; |
---|
6150 | } |
---|
6151 | } |
---|
6152 | |
---|
6153 | if (!derivXZero && !fail2 && !symmetric && subCheck2 > 0) |
---|
6154 | { |
---|
6155 | int subCheck= substituteCheck (bufUniFactors2); |
---|
6156 | |
---|
6157 | if (subCheck > 1 && (subCheck2%subCheck == 0)) |
---|
6158 | { |
---|
6159 | CanonicalForm bufA= A; |
---|
6160 | subst (bufA, bufA, subCheck, y); |
---|
6161 | factors= biFactorize (bufA, info); |
---|
6162 | reverseSubst (factors, subCheck, y); |
---|
6163 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
6164 | swap, swap2, N); |
---|
6165 | normalize (factors); |
---|
6166 | return factors; |
---|
6167 | } |
---|
6168 | } |
---|
6169 | } |
---|
6170 | |
---|
6171 | // degree analysis |
---|
6172 | bufDegs = DegreePattern (bufUniFactors); |
---|
6173 | if (!derivXZero && !fail2 && !symmetric) |
---|
6174 | bufDegs2= DegreePattern (bufUniFactors2); |
---|
6175 | |
---|
6176 | if (i == 0) |
---|
6177 | { |
---|
6178 | Aeval= bufAeval; |
---|
6179 | evaluation= bufEvaluation; |
---|
6180 | uniFactors= bufUniFactors; |
---|
6181 | degs= bufDegs; |
---|
6182 | if (!derivXZero && !fail2 && !symmetric) |
---|
6183 | { |
---|
6184 | Aeval2= bufAeval2; |
---|
6185 | evaluation2= bufEvaluation2; |
---|
6186 | uniFactors2= bufUniFactors2; |
---|
6187 | degs2= bufDegs2; |
---|
6188 | } |
---|
6189 | } |
---|
6190 | else |
---|
6191 | { |
---|
6192 | degs.intersect (bufDegs); |
---|
6193 | if (!derivXZero && !fail2 && !symmetric) |
---|
6194 | { |
---|
6195 | degs2.intersect (bufDegs2); |
---|
6196 | if (bufUniFactors2.length() < uniFactors2.length()) |
---|
6197 | { |
---|
6198 | uniFactors2= bufUniFactors2; |
---|
6199 | Aeval2= bufAeval2; |
---|
6200 | evaluation2= bufEvaluation2; |
---|
6201 | } |
---|
6202 | } |
---|
6203 | if (bufUniFactors.length() < uniFactors.length()) |
---|
6204 | { |
---|
6205 | uniFactors= bufUniFactors; |
---|
6206 | Aeval= bufAeval; |
---|
6207 | evaluation= bufEvaluation; |
---|
6208 | } |
---|
6209 | } |
---|
6210 | list.append (bufEvaluation); |
---|
6211 | if (!derivXZero && !fail2 && !symmetric) |
---|
6212 | list2.append (bufEvaluation2); |
---|
6213 | } |
---|
6214 | |
---|
6215 | if (!derivXZero && !fail2 && !symmetric) |
---|
6216 | { |
---|
6217 | if (uniFactors.length() > uniFactors2.length() || |
---|
6218 | (uniFactors.length() == uniFactors2.length() |
---|
6219 | && degs.getLength() > degs2.getLength())) |
---|
6220 | { |
---|
6221 | degs= degs2; |
---|
6222 | uniFactors= uniFactors2; |
---|
6223 | evaluation= evaluation2; |
---|
6224 | Aeval= Aeval2; |
---|
6225 | A= buf; |
---|
6226 | swap2= true; |
---|
6227 | } |
---|
6228 | } |
---|
6229 | |
---|
6230 | if (degs.getLength() == 1) // A is irreducible |
---|
6231 | { |
---|
6232 | if (extension) |
---|
6233 | { |
---|
6234 | CFList source, dest; |
---|
6235 | appendMapDown (factors, A, info, source, dest); |
---|
6236 | } |
---|
6237 | else |
---|
6238 | factors.append (A); |
---|
6239 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
6240 | swap, swap2, N); |
---|
6241 | normalize (factors); |
---|
6242 | return factors; |
---|
6243 | } |
---|
6244 | |
---|
6245 | int liftBound= degree (A, y) + 1; |
---|
6246 | |
---|
6247 | if (swap2) |
---|
6248 | bounds= computeBounds (A, boundsLength, isIrreducible); |
---|
6249 | |
---|
6250 | int minBound= bounds[0]; |
---|
6251 | for (int i= 1; i < boundsLength; i++) |
---|
6252 | { |
---|
6253 | if (bounds[i] != 0) |
---|
6254 | minBound= tmin (minBound, bounds[i]); |
---|
6255 | } |
---|
6256 | |
---|
6257 | A= A (y + evaluation, y); |
---|
6258 | |
---|
6259 | int degMipo= 1; |
---|
6260 | if (extension && alpha.level() != 1 && k==1) |
---|
6261 | degMipo= degree (getMipo (alpha)); |
---|
6262 | |
---|
6263 | DEBOUTLN (cerr, "uniFactors= " << uniFactors); |
---|
6264 | |
---|
6265 | if ((GF && !extension) || (GF && extension && k != 1)) |
---|
6266 | { |
---|
6267 | bool earlySuccess= false; |
---|
6268 | CFList earlyFactors; |
---|
6269 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
6270 | uniFactors= henselLiftAndEarly |
---|
6271 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
6272 | uniFactors, info, evaluation); |
---|
6273 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, "time for hensel lifting: "); |
---|
6274 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
6275 | |
---|
6276 | CanonicalForm MODl= power (y, liftBound); |
---|
6277 | |
---|
6278 | if (extension) |
---|
6279 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
6280 | evaluation, 1, uniFactors.length()/2); |
---|
6281 | else |
---|
6282 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, |
---|
6283 | uniFactors.length()/2); |
---|
6284 | |
---|
6285 | if (earlySuccess) |
---|
6286 | factors= Union (earlyFactors, factors); |
---|
6287 | else if (!earlySuccess && degs.getLength() == 1) |
---|
6288 | factors= earlyFactors; |
---|
6289 | } |
---|
6290 | else if (degree (A) > 4 && beta.level() == 1 && (2*minBound)/degMipo < 32) |
---|
6291 | { |
---|
6292 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
6293 | if (extension) |
---|
6294 | { |
---|
6295 | CFList lll= extHenselLiftAndLatticeRecombi (A, uniFactors, info, degs, |
---|
6296 | evaluation |
---|
6297 | ); |
---|
6298 | factors= Union (lll, factors); |
---|
6299 | } |
---|
6300 | else if (alpha.level() == 1 && !GF) |
---|
6301 | { |
---|
6302 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs, |
---|
6303 | symmetric, evaluation); |
---|
6304 | factors= Union (lll, factors); |
---|
6305 | } |
---|
6306 | else if (!extension && (alpha != x || GF)) |
---|
6307 | { |
---|
6308 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs, |
---|
6309 | symmetric, evaluation); |
---|
6310 | factors= Union (lll, factors); |
---|
6311 | } |
---|
6312 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, "time for hensel lifting: "); |
---|
6313 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
6314 | } |
---|
6315 | else |
---|
6316 | { |
---|
6317 | bool earlySuccess= false; |
---|
6318 | CFList earlyFactors; |
---|
6319 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
6320 | uniFactors= henselLiftAndEarly |
---|
6321 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
6322 | uniFactors, info, evaluation); |
---|
6323 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, "time for hensel lifting: "); |
---|
6324 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
6325 | |
---|
6326 | CanonicalForm MODl= power (y, liftBound); |
---|
6327 | if (!extension) |
---|
6328 | { |
---|
6329 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, 3); |
---|
6330 | |
---|
6331 | int oldUniFactorsLength= uniFactors.length(); |
---|
6332 | if (degree (A) > 0) |
---|
6333 | { |
---|
6334 | CFList tmp; |
---|
6335 | if (alpha.level() == 1) |
---|
6336 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
6337 | liftBound |
---|
6338 | ); |
---|
6339 | else |
---|
6340 | { |
---|
6341 | if (degree (A) > getCharacteristic()) |
---|
6342 | tmp= increasePrecisionFq2Fp (A, uniFactors, 0, uniFactors.length(), |
---|
6343 | 1, alpha, liftBound |
---|
6344 | ); |
---|
6345 | else |
---|
6346 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
6347 | alpha, liftBound |
---|
6348 | ); |
---|
6349 | } |
---|
6350 | factors= Union (factors, tmp); |
---|
6351 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
6352 | && uniFactors.length() != oldUniFactorsLength) |
---|
6353 | ) |
---|
6354 | { |
---|
6355 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
6356 | degs.intersect (bufDegs); |
---|
6357 | degs.refine (); |
---|
6358 | factors= Union (factors, factorRecombination (uniFactors, A, MODl, |
---|
6359 | degs, 4, |
---|
6360 | uniFactors.length()/2 |
---|
6361 | ) |
---|
6362 | ); |
---|
6363 | } |
---|
6364 | } |
---|
6365 | } |
---|
6366 | else |
---|
6367 | { |
---|
6368 | if (beta.level() != 1 || k > 1) |
---|
6369 | { |
---|
6370 | if (k > 1) |
---|
6371 | { |
---|
6372 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
6373 | evaluation, 1, uniFactors.length()/2 |
---|
6374 | ); |
---|
6375 | } |
---|
6376 | else |
---|
6377 | { |
---|
6378 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
6379 | evaluation, 1, 3 |
---|
6380 | ); |
---|
6381 | if (degree (A) > 0) |
---|
6382 | { |
---|
6383 | CFList tmp= increasePrecision2 (A, uniFactors, alpha, liftBound); |
---|
6384 | DegreePattern bufDegs= DegreePattern (tmp); |
---|
6385 | degs.intersect (bufDegs); |
---|
6386 | degs.refine (); |
---|
6387 | factors= Union (factors, extFactorRecombination (tmp, A, MODl, info, |
---|
6388 | degs, evaluation, |
---|
6389 | 1, tmp.length()/2 |
---|
6390 | ) |
---|
6391 | ); |
---|
6392 | } |
---|
6393 | } |
---|
6394 | } |
---|
6395 | else |
---|
6396 | { |
---|
6397 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
6398 | evaluation, 1, 3 |
---|
6399 | ); |
---|
6400 | int oldUniFactorsLength= uniFactors.length(); |
---|
6401 | if (degree (A) > 0) |
---|
6402 | { |
---|
6403 | int degMipo; |
---|
6404 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
6405 | |
---|
6406 | CFList source, dest; |
---|
6407 | CFList tmp= extIncreasePrecision (A, uniFactors, 0, |
---|
6408 | uniFactors.length(), 1, evaluation, |
---|
6409 | info2, source, dest, liftBound |
---|
6410 | ); |
---|
6411 | factors= Union (factors, tmp); |
---|
6412 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
6413 | && uniFactors.length() != oldUniFactorsLength) |
---|
6414 | ) |
---|
6415 | { |
---|
6416 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
6417 | degs.intersect (bufDegs); |
---|
6418 | degs.refine (); |
---|
6419 | factors= Union (factors,extFactorRecombination (uniFactors, A, MODl, |
---|
6420 | info, degs, evaluation, |
---|
6421 | 4, uniFactors.length()/2 |
---|
6422 | ) |
---|
6423 | ); |
---|
6424 | } |
---|
6425 | } |
---|
6426 | } |
---|
6427 | } |
---|
6428 | |
---|
6429 | if (earlySuccess) |
---|
6430 | factors= Union (earlyFactors, factors); |
---|
6431 | else if (!earlySuccess && degs.getLength() == 1) |
---|
6432 | factors= earlyFactors; |
---|
6433 | } |
---|
6434 | delete [] bounds; |
---|
6435 | if (!extension) |
---|
6436 | { |
---|
6437 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
6438 | i.getItem()= i.getItem() (y - evaluation, y); |
---|
6439 | } |
---|
6440 | |
---|
6441 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
6442 | swap, swap2, N); |
---|
6443 | normalize (factors); |
---|
6444 | |
---|
6445 | return factors; |
---|
6446 | } |
---|
6447 | |
---|
6448 | CFList |
---|
6449 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
6450 | { |
---|
6451 | |
---|
6452 | CanonicalForm A= F; |
---|
6453 | Variable alpha= info.getAlpha(); |
---|
6454 | Variable beta= info.getBeta(); |
---|
6455 | int k= info.getGFDegree(); |
---|
6456 | char cGFName= info.getGFName(); |
---|
6457 | CanonicalForm delta= info.getDelta(); |
---|
6458 | |
---|
6459 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
6460 | Variable x= Variable (1); |
---|
6461 | CFList factors; |
---|
6462 | if (!GF && alpha == x) // we are in F_p |
---|
6463 | { |
---|
6464 | bool extension= true; |
---|
6465 | int p= getCharacteristic(); |
---|
6466 | if (p*p < (1<<16)) // pass to GF if possible |
---|
6467 | { |
---|
6468 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
6469 | A= A.mapinto(); |
---|
6470 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
6471 | factors= biFactorize (A, info2); |
---|
6472 | |
---|
6473 | CanonicalForm mipo= gf_mipo; |
---|
6474 | setCharacteristic (getCharacteristic()); |
---|
6475 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
6476 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
6477 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
6478 | } |
---|
6479 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
6480 | { |
---|
6481 | CanonicalForm mipo= randomIrredpoly (2, x); |
---|
6482 | Variable v= rootOf (mipo); |
---|
6483 | ExtensionInfo info2= ExtensionInfo (v); |
---|
6484 | factors= biFactorize (A, info2); |
---|
6485 | } |
---|
6486 | return factors; |
---|
6487 | } |
---|
6488 | else if (!GF && (alpha != x)) // we are in F_p(\alpha) |
---|
6489 | { |
---|
6490 | if (k == 1) // need factorization over F_p |
---|
6491 | { |
---|
6492 | int extDeg= degree (getMipo (alpha)); |
---|
6493 | extDeg++; |
---|
6494 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, x); |
---|
6495 | Variable v= rootOf (mipo); |
---|
6496 | ExtensionInfo info2= ExtensionInfo (v); |
---|
6497 | factors= biFactorize (A, info2); |
---|
6498 | } |
---|
6499 | else |
---|
6500 | { |
---|
6501 | if (beta == x) |
---|
6502 | { |
---|
6503 | Variable v= chooseExtension (alpha, beta, k); |
---|
6504 | CanonicalForm primElem, imPrimElem; |
---|
6505 | bool primFail= false; |
---|
6506 | Variable vBuf; |
---|
6507 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
6508 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
6509 | if (primFail) |
---|
6510 | ; //ERROR |
---|
6511 | else |
---|
6512 | imPrimElem= mapPrimElem (primElem, alpha, v); |
---|
6513 | |
---|
6514 | CFList source, dest; |
---|
6515 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
6516 | source, dest); |
---|
6517 | ExtensionInfo info2= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
6518 | factors= biFactorize (bufA, info2); |
---|
6519 | } |
---|
6520 | else |
---|
6521 | { |
---|
6522 | Variable v= chooseExtension (alpha, beta, k); |
---|
6523 | CanonicalForm primElem, imPrimElem; |
---|
6524 | bool primFail= false; |
---|
6525 | Variable vBuf; |
---|
6526 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
6527 | if (primFail) |
---|
6528 | ; //ERROR |
---|
6529 | else |
---|
6530 | imPrimElem= mapPrimElem (delta, beta, v); |
---|
6531 | |
---|
6532 | CFList source, dest; |
---|
6533 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
6534 | source= CFList(); |
---|
6535 | dest= CFList(); |
---|
6536 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
6537 | ExtensionInfo info2= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
6538 | factors= biFactorize (bufA, info2); |
---|
6539 | } |
---|
6540 | } |
---|
6541 | return factors; |
---|
6542 | } |
---|
6543 | else // we are in GF (p^k) |
---|
6544 | { |
---|
6545 | int p= getCharacteristic(); |
---|
6546 | int extensionDeg= getGFDegree(); |
---|
6547 | bool extension= true; |
---|
6548 | if (k == 1) // need factorization over F_p |
---|
6549 | { |
---|
6550 | extensionDeg++; |
---|
6551 | if (ipower (p, extensionDeg) < (1<<16)) |
---|
6552 | // pass to GF(p^k+1) |
---|
6553 | { |
---|
6554 | CanonicalForm mipo= gf_mipo; |
---|
6555 | setCharacteristic (p); |
---|
6556 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
6557 | A= GF2FalphaRep (A, vBuf); |
---|
6558 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
6559 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
6560 | factors= biFactorize (A.mapinto(), info2); |
---|
6561 | } |
---|
6562 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
6563 | { |
---|
6564 | CanonicalForm mipo= gf_mipo; |
---|
6565 | setCharacteristic (p); |
---|
6566 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
6567 | A= GF2FalphaRep (A, vBuf); |
---|
6568 | Variable v= chooseExtension (vBuf, beta, k); |
---|
6569 | ExtensionInfo info2= ExtensionInfo (v, extension); |
---|
6570 | factors= biFactorize (A, info2); |
---|
6571 | } |
---|
6572 | } |
---|
6573 | else // need factorization over GF (p^k) |
---|
6574 | { |
---|
6575 | if (ipower (p, 2*extensionDeg) < (1<<16)) |
---|
6576 | // pass to GF (p^2k) |
---|
6577 | { |
---|
6578 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
6579 | ExtensionInfo info2= ExtensionInfo (k, cGFName, extension); |
---|
6580 | factors= biFactorize (GFMapUp (A, extensionDeg), info2); |
---|
6581 | setCharacteristic (p, extensionDeg, cGFName); |
---|
6582 | } |
---|
6583 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
6584 | { |
---|
6585 | CanonicalForm mipo= gf_mipo; |
---|
6586 | setCharacteristic (p); |
---|
6587 | Variable v1= rootOf (mipo.mapinto()); |
---|
6588 | A= GF2FalphaRep (A, v1); |
---|
6589 | Variable v2= chooseExtension (v1, v1, k); |
---|
6590 | CanonicalForm primElem, imPrimElem; |
---|
6591 | bool primFail= false; |
---|
6592 | Variable vBuf; |
---|
6593 | primElem= primitiveElement (v1, vBuf, primFail); |
---|
6594 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
6595 | if (primFail) |
---|
6596 | ; //ERROR |
---|
6597 | else |
---|
6598 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
6599 | |
---|
6600 | CFList source, dest; |
---|
6601 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
6602 | source, dest); |
---|
6603 | ExtensionInfo info2= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
6604 | factors= biFactorize (bufA, info2); |
---|
6605 | setCharacteristic (p, k, cGFName); |
---|
6606 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
6607 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
6608 | } |
---|
6609 | } |
---|
6610 | return factors; |
---|
6611 | } |
---|
6612 | } |
---|
6613 | |
---|
6614 | #endif |
---|
6615 | /* HAVE_NTL */ |
---|
6616 | |
---|
6617 | |
---|