1 | /* emacs edit mode for this file is -*- C++ -*- */ |
---|
2 | /* $Id: fac_multivar.cc,v 1.14 2008-03-17 17:44:04 Singular Exp $ */ |
---|
3 | |
---|
4 | #include <config.h> |
---|
5 | |
---|
6 | #include "assert.h" |
---|
7 | #include "debug.h" |
---|
8 | #include "timing.h" |
---|
9 | |
---|
10 | #include "cf_defs.h" |
---|
11 | #include "cf_algorithm.h" |
---|
12 | #include "fac_multivar.h" |
---|
13 | #include "fac_univar.h" |
---|
14 | #include "cf_reval.h" |
---|
15 | #include "cf_map.h" |
---|
16 | #include "fac_util.h" |
---|
17 | #include "cf_binom.h" |
---|
18 | #include "cf_iter.h" |
---|
19 | #include "cf_primes.h" |
---|
20 | #include "fac_distrib.h" |
---|
21 | |
---|
22 | void out_cf(char *s1,const CanonicalForm &f,char *s2); |
---|
23 | void out_cff(CFFList &L); |
---|
24 | |
---|
25 | TIMING_DEFINE_PRINT(fac_content); |
---|
26 | TIMING_DEFINE_PRINT(fac_findeval); |
---|
27 | TIMING_DEFINE_PRINT(fac_distrib); |
---|
28 | TIMING_DEFINE_PRINT(fac_hensel); |
---|
29 | |
---|
30 | static CFArray |
---|
31 | conv_to_factor_array( const CFFList & L ) |
---|
32 | { |
---|
33 | int n; |
---|
34 | CFFListIterator I = L; |
---|
35 | bool negate = false; |
---|
36 | |
---|
37 | if ( ! I.hasItem() ) |
---|
38 | n = 0; |
---|
39 | else if ( I.getItem().factor().inBaseDomain() ) { |
---|
40 | negate = I.getItem().factor().sign() < 0; |
---|
41 | I++; |
---|
42 | n = L.length(); |
---|
43 | } |
---|
44 | else |
---|
45 | n = L.length() + 1; |
---|
46 | CFFListIterator J = I; |
---|
47 | while ( J.hasItem() ) { |
---|
48 | n += J.getItem().exp() - 1; |
---|
49 | J++; |
---|
50 | } |
---|
51 | CFArray result( 1, n-1 ); |
---|
52 | int i, j, k; |
---|
53 | i = 1; |
---|
54 | while ( I.hasItem() ) { |
---|
55 | k = I.getItem().exp(); |
---|
56 | for ( j = 1; j <= k; j++ ) { |
---|
57 | result[i] = I.getItem().factor(); |
---|
58 | i++; |
---|
59 | } |
---|
60 | I++; |
---|
61 | } |
---|
62 | if ( negate ) |
---|
63 | result[1] = -result[1]; |
---|
64 | return result; |
---|
65 | } |
---|
66 | |
---|
67 | static modpk |
---|
68 | coeffBound ( const CanonicalForm & f, int p ) |
---|
69 | { |
---|
70 | int * degs = degrees( f ); |
---|
71 | int M = 0, i, k = f.level(); |
---|
72 | for ( i = 1; i <= k; i++ ) |
---|
73 | M += degs[i]; |
---|
74 | CanonicalForm b = 2 * maxNorm( f ) * power( CanonicalForm( 3 ), M ); |
---|
75 | CanonicalForm B = p; |
---|
76 | k = 1; |
---|
77 | while ( B < b ) { |
---|
78 | B *= p; |
---|
79 | k++; |
---|
80 | } |
---|
81 | return modpk( p, k ); |
---|
82 | } |
---|
83 | |
---|
84 | // static bool |
---|
85 | // nonDivisors ( CanonicalForm omega, CanonicalForm delta, const CFArray & F, CFArray & d ) |
---|
86 | // { |
---|
87 | // DEBOUTLN( cerr, "nondivisors omega = " << omega ); |
---|
88 | // DEBOUTLN( cerr, "nondivisors delta = " << delta ); |
---|
89 | // DEBOUTLN( cerr, "nondivisors F = " << F ); |
---|
90 | // CanonicalForm q, r; |
---|
91 | // int k = F.size(); |
---|
92 | // d = CFArray( 0, k ); |
---|
93 | // d[0] = delta * omega; |
---|
94 | // for ( int i = 1; i <= k; i++ ) { |
---|
95 | // q = abs(F[i]); |
---|
96 | // for ( int j = i-1; j >= 0; j-- ) { |
---|
97 | // r = d[j]; |
---|
98 | // do { |
---|
99 | // r = gcd( r, q ); |
---|
100 | // q = q / r; |
---|
101 | // } while ( r != 1 ); |
---|
102 | // if ( q == 1 ) |
---|
103 | // return false; |
---|
104 | // } |
---|
105 | // d[i] = q; |
---|
106 | // } |
---|
107 | // return true; |
---|
108 | // } |
---|
109 | |
---|
110 | static void |
---|
111 | findEvaluation ( const CanonicalForm & U, const CanonicalForm & V, const CanonicalForm & omega, const CFFList & F, Evaluation & A, CanonicalForm & U0, CanonicalForm & delta, CFArray & D, int r ) |
---|
112 | { |
---|
113 | DEBINCLEVEL( cerr, "findEvaluation" ); |
---|
114 | CanonicalForm Vn; |
---|
115 | CFFListIterator I; |
---|
116 | int j; |
---|
117 | bool found = false; |
---|
118 | CFArray FF = CFArray( 1, F.length() ); |
---|
119 | if ( r > 0 ) |
---|
120 | A.nextpoint(); |
---|
121 | while ( ! found ) |
---|
122 | { |
---|
123 | Vn = A( V ); |
---|
124 | if ( Vn != 0 ) |
---|
125 | { |
---|
126 | U0 = A( U ); |
---|
127 | DEBOUTLN( cerr, "U0 = " << U0 ); |
---|
128 | if ( isSqrFree( U0 ) ) |
---|
129 | { |
---|
130 | delta = content( U0 ); |
---|
131 | DEBOUTLN( cerr, "content( U0 ) = " << delta ); |
---|
132 | for ( I = F, j = 1; I.hasItem(); I++, j++ ) |
---|
133 | FF[j] = A( I.getItem().factor() ); |
---|
134 | found = nonDivisors( omega, delta, FF, D ); |
---|
135 | } |
---|
136 | else |
---|
137 | { |
---|
138 | DEBOUTLN( cerr, "not sqrfree : " << sqrFree( U0 ) ); |
---|
139 | } |
---|
140 | } |
---|
141 | if ( ! found ) |
---|
142 | A.nextpoint(); |
---|
143 | } |
---|
144 | DEBDECLEVEL( cerr, "findEvaluation" ); |
---|
145 | } |
---|
146 | |
---|
147 | #ifdef HAVE_NTL |
---|
148 | int prime_number=0; |
---|
149 | void find_good_prime(const CanonicalForm &f, int &start) |
---|
150 | { |
---|
151 | if (! f.inBaseDomain() ) |
---|
152 | { |
---|
153 | int l = f.level(); |
---|
154 | CFIterator i = f; |
---|
155 | for(;;) |
---|
156 | { |
---|
157 | if ( i.hasTerms() ) |
---|
158 | { |
---|
159 | find_good_prime(i.coeff(),start); |
---|
160 | if((i.exp()!=0) && ((i.exp() % cf_getSmallPrime(start))==0)) |
---|
161 | { |
---|
162 | start++; |
---|
163 | i=f; |
---|
164 | } |
---|
165 | else i++; |
---|
166 | } |
---|
167 | else break; |
---|
168 | } |
---|
169 | } |
---|
170 | else |
---|
171 | { |
---|
172 | if (f.inZ()) |
---|
173 | { |
---|
174 | while((f!=0) && (mod(f,cf_getSmallPrime(start))==0)) |
---|
175 | { |
---|
176 | start++; |
---|
177 | } |
---|
178 | } |
---|
179 | /* should not happen! |
---|
180 | else if (f.inQ()) |
---|
181 | { |
---|
182 | while((f.den()!=0) && (mod(f.den(),cf_getSmallPrime(start))==0)) |
---|
183 | { |
---|
184 | start++; |
---|
185 | } |
---|
186 | while((f.num()!=0) && (mod(f.num(),cf_getSmallPrime(start))==0)) |
---|
187 | { |
---|
188 | start++; |
---|
189 | } |
---|
190 | } |
---|
191 | else |
---|
192 | cout <<"??"<< f <<"\n"; |
---|
193 | */ |
---|
194 | } |
---|
195 | } |
---|
196 | #endif |
---|
197 | |
---|
198 | static CFArray ZFactorizeMulti ( const CanonicalForm & arg ) |
---|
199 | { |
---|
200 | DEBINCLEVEL( cerr, "ZFactorizeMulti" ); |
---|
201 | CFMap M; |
---|
202 | CanonicalForm UU, U = compress( arg, M ); |
---|
203 | CanonicalForm delta, omega, V = LC( U, 1 ); |
---|
204 | int t = U.level(); |
---|
205 | CFFList F = factorize( V ); |
---|
206 | CFFListIterator I, J; |
---|
207 | CFArray G, lcG, D; |
---|
208 | int i, j, k, m, r, maxdeg, h; |
---|
209 | REvaluation A( 2, t, IntRandom( 50 ) ); |
---|
210 | CanonicalForm U0; |
---|
211 | CanonicalForm ft, ut, gt, d; |
---|
212 | modpk b; |
---|
213 | bool negate = false; |
---|
214 | |
---|
215 | DEBOUTLN( cerr, "-----------------------------------------------------" ); |
---|
216 | DEBOUTLN( cerr, "trying to factorize U = " << U ); |
---|
217 | DEBOUTLN( cerr, "U is a polynomial of level = " << arg.level() ); |
---|
218 | DEBOUTLN( cerr, "U will be factorized with respect to variable " << Variable(1) ); |
---|
219 | DEBOUTLN( cerr, "the leading coefficient of U with respect to that variable is " << V ); |
---|
220 | DEBOUTLN( cerr, "which is factorized as " << F ); |
---|
221 | |
---|
222 | maxdeg = 0; |
---|
223 | for ( i = 2; i <= t; i++ ) |
---|
224 | { |
---|
225 | j = U.degree( Variable( i ) ); |
---|
226 | if ( j > maxdeg ) maxdeg = j; |
---|
227 | } |
---|
228 | |
---|
229 | if ( F.getFirst().factor().inCoeffDomain() ) |
---|
230 | { |
---|
231 | omega = F.getFirst().factor(); |
---|
232 | F.removeFirst(); |
---|
233 | if ( omega < 0 ) |
---|
234 | { |
---|
235 | negate = true; |
---|
236 | omega = -omega; |
---|
237 | U = -U; |
---|
238 | } |
---|
239 | } |
---|
240 | else |
---|
241 | omega = 1; |
---|
242 | |
---|
243 | bool goodeval = false; |
---|
244 | r = 0; |
---|
245 | |
---|
246 | // for ( i = 0; i < 10*t; i++ ) |
---|
247 | // A.nextpoint(); |
---|
248 | |
---|
249 | while ( ! goodeval ) |
---|
250 | { |
---|
251 | TIMING_START(fac_findeval); |
---|
252 | findEvaluation( U, V, omega, F, A, U0, delta, D, r ); |
---|
253 | TIMING_END(fac_findeval); |
---|
254 | DEBOUTLN( cerr, "the evaluation point to reduce to an univariate problem is " << A ); |
---|
255 | DEBOUTLN( cerr, "corresponding delta = " << delta ); |
---|
256 | DEBOUTLN( cerr, " omega = " << omega ); |
---|
257 | DEBOUTLN( cerr, " D = " << D ); |
---|
258 | DEBOUTLN( cerr, "now factorize the univariate polynomial " << U0 ); |
---|
259 | G = conv_to_factor_array( factorize( U0, false ) ); |
---|
260 | DEBOUTLN( cerr, "which factorizes into " << G ); |
---|
261 | #ifdef HAVE_NTL |
---|
262 | { |
---|
263 | int i=prime_number; |
---|
264 | find_good_prime(arg,i); |
---|
265 | find_good_prime(U0,i); |
---|
266 | find_good_prime(U,i); |
---|
267 | int p=cf_getSmallPrime(i); |
---|
268 | //printf("found:p=%d (%d)\n",p,i); |
---|
269 | if ((i==0)||(i!=prime_number)) |
---|
270 | { |
---|
271 | b = coeffBound( U, p ); |
---|
272 | prime_number=i; |
---|
273 | } |
---|
274 | modpk bb=coeffBound(U0,p); |
---|
275 | if (bb.getk() > b.getk() ) b=bb; |
---|
276 | bb=coeffBound(arg,p); |
---|
277 | if (bb.getk() > b.getk() ) b=bb; |
---|
278 | } |
---|
279 | #else |
---|
280 | b = coeffBound( U, getZFacModulus().getp() ); |
---|
281 | if ( getZFacModulus().getpk() > b.getpk() ) |
---|
282 | b = getZFacModulus(); |
---|
283 | #endif |
---|
284 | //printf("p=%d, k=%d\n",b.getp(),b.getk()); |
---|
285 | DEBOUTLN( cerr, "the coefficient bound of the factors of U is " << b.getpk() ); |
---|
286 | |
---|
287 | r = G.size(); |
---|
288 | lcG = CFArray( 1, r ); |
---|
289 | UU = U; |
---|
290 | DEBOUTLN( cerr, "now trying to distribute the leading coefficients ..." ); |
---|
291 | TIMING_START(fac_distrib); |
---|
292 | goodeval = distributeLeadingCoeffs( UU, G, lcG, F, D, delta, omega, A, r ); |
---|
293 | TIMING_END(fac_distrib); |
---|
294 | #ifdef DEBUGOUTPUT |
---|
295 | if ( goodeval ) |
---|
296 | { |
---|
297 | DEBOUTLN( cerr, "the univariate factors after distribution are " << G ); |
---|
298 | DEBOUTLN( cerr, "the distributed leading coeffs are " << lcG ); |
---|
299 | DEBOUTLN( cerr, "U may have changed and is now " << UU ); |
---|
300 | DEBOUTLN( cerr, "which has leading coefficient " << LC( UU, Variable(1) ) ); |
---|
301 | |
---|
302 | if ( LC( UU, Variable(1) ) != prod( lcG ) || A(UU) != prod( G ) ) |
---|
303 | { |
---|
304 | DEBOUTLN( cerr, "!!! distribution was not correct !!!" ); |
---|
305 | DEBOUTLN( cerr, "product of leading coeffs is " << prod( lcG ) ); |
---|
306 | DEBOUTLN( cerr, "product of univariate factors is " << prod( G ) ); |
---|
307 | DEBOUTLN( cerr, "the new U is evaluated as " << A(UU) ); |
---|
308 | } |
---|
309 | else |
---|
310 | DEBOUTLN( cerr, "leading coeffs correct" ); |
---|
311 | } |
---|
312 | else |
---|
313 | { |
---|
314 | DEBOUTLN( cerr, "we have found a bad evaluation point" ); |
---|
315 | } |
---|
316 | #endif |
---|
317 | if ( goodeval ) |
---|
318 | { |
---|
319 | TIMING_START(fac_hensel); |
---|
320 | goodeval = Hensel( UU, G, lcG, A, b, Variable(1) ); |
---|
321 | TIMING_END(fac_hensel); |
---|
322 | } |
---|
323 | } |
---|
324 | for ( i = 1; i <= r; i++ ) |
---|
325 | { |
---|
326 | G[i] /= icontent( G[i] ); |
---|
327 | G[i] = M(G[i]); |
---|
328 | } |
---|
329 | // negate noch beachten ! |
---|
330 | if ( negate ) |
---|
331 | G[1] = -G[1]; |
---|
332 | DEBDECLEVEL( cerr, "ZFactorMulti" ); |
---|
333 | return G; |
---|
334 | } |
---|
335 | |
---|
336 | CFFList ZFactorizeMultivariate ( const CanonicalForm & f, bool issqrfree ) |
---|
337 | { |
---|
338 | CFFList G, F, R; |
---|
339 | CFArray GG; |
---|
340 | CFFListIterator i, j; |
---|
341 | CFMap M; |
---|
342 | CanonicalForm g, cont; |
---|
343 | Variable v1, vm; |
---|
344 | int k, m, n; |
---|
345 | |
---|
346 | v1 = Variable(1); |
---|
347 | if ( issqrfree ) |
---|
348 | F = CFFactor( f, 1 ); |
---|
349 | else |
---|
350 | F = sqrFree( f ); |
---|
351 | |
---|
352 | for ( i = F; i.hasItem(); i++ ) |
---|
353 | { |
---|
354 | if ( i.getItem().factor().inCoeffDomain() ) |
---|
355 | { |
---|
356 | if ( ! i.getItem().factor().isOne() ) |
---|
357 | R.append( CFFactor( i.getItem().factor(), i.getItem().exp() ) ); |
---|
358 | } |
---|
359 | else |
---|
360 | { |
---|
361 | TIMING_START(fac_content); |
---|
362 | g = compress( i.getItem().factor(), M ); |
---|
363 | // now after compress g contains Variable(1) |
---|
364 | vm = g.mvar(); |
---|
365 | g = swapvar( g, v1, vm ); |
---|
366 | cont = content( g ); |
---|
367 | g = swapvar( g / cont, v1, vm ); |
---|
368 | cont = swapvar( cont, v1, vm ); |
---|
369 | n = i.getItem().exp(); |
---|
370 | TIMING_END(fac_content); |
---|
371 | DEBOUTLN( cerr, "now after content ..." ); |
---|
372 | if ( g.isUnivariate() ) |
---|
373 | { |
---|
374 | G = factorize( g, true ); |
---|
375 | for ( j = G; j.hasItem(); j++ ) |
---|
376 | if ( ! j.getItem().factor().isOne() ) |
---|
377 | R.append( CFFactor( M( j.getItem().factor() ), n ) ); |
---|
378 | } |
---|
379 | else |
---|
380 | { |
---|
381 | GG = ZFactorizeMulti( g ); |
---|
382 | m = GG.max(); |
---|
383 | for ( k = GG.min(); k <= m; k++ ) |
---|
384 | if ( ! GG[k].isOne() ) |
---|
385 | R.append( CFFactor( M( GG[k] ), n ) ); |
---|
386 | } |
---|
387 | G = factorize( cont, true ); |
---|
388 | for ( j = G; j.hasItem(); j++ ) |
---|
389 | if ( ! j.getItem().factor().isOne() ) |
---|
390 | R.append( CFFactor( M( j.getItem().factor() ), n ) ); |
---|
391 | } |
---|
392 | } |
---|
393 | return R; |
---|
394 | } |
---|
395 | |
---|
396 | static CFArray FpFactorizeMulti ( const CanonicalForm & arg ) |
---|
397 | { |
---|
398 | out_cf("FpFactorizeMulti:",arg,"\n"); |
---|
399 | DEBINCLEVEL( cerr, "FpFactorizeMulti" ); |
---|
400 | CFMap M; |
---|
401 | CanonicalForm UU, U = compress( arg, M ); |
---|
402 | CanonicalForm delta, omega, V = LC( U, 1 ); |
---|
403 | int t = U.level(); |
---|
404 | CFFList F = factorize( V ); |
---|
405 | CFFListIterator I, J; |
---|
406 | CFArray G, lcG, D; |
---|
407 | int i, j, k, m, r, maxdeg, h; |
---|
408 | REvaluation A( 2, t, FFRandom() ); |
---|
409 | CanonicalForm U0; |
---|
410 | CanonicalForm ft, ut, gt, d; |
---|
411 | modpk b; |
---|
412 | bool negate = false; |
---|
413 | |
---|
414 | DEBOUTLN( cerr, "-----------------------------------------------------" ); |
---|
415 | DEBOUTLN( cerr, "trying to factorize U = " << U ); |
---|
416 | DEBOUTLN( cerr, "U is a polynomial of level = " << arg.level() ); |
---|
417 | DEBOUTLN( cerr, "U will be factorized with respect to variable " << Variable(1) ); |
---|
418 | DEBOUTLN( cerr, "the leading coefficient of U with respect to that variable is " << V ); |
---|
419 | DEBOUTLN( cerr, "which is factorized as " << F ); |
---|
420 | |
---|
421 | maxdeg = 0; |
---|
422 | out_cf("try:",U,"\n"); |
---|
423 | for ( i = 2; i <= t; i++ ) |
---|
424 | { |
---|
425 | j = U.degree( Variable( i ) ); |
---|
426 | if ( j > maxdeg ) maxdeg = j; |
---|
427 | } |
---|
428 | |
---|
429 | if ( F.getFirst().factor().inCoeffDomain() ) |
---|
430 | { |
---|
431 | omega = F.getFirst().factor(); |
---|
432 | F.removeFirst(); |
---|
433 | if ( omega < 0 ) |
---|
434 | { |
---|
435 | negate = true; |
---|
436 | omega = -omega; |
---|
437 | U = -U; |
---|
438 | } |
---|
439 | } |
---|
440 | else |
---|
441 | omega = 1; |
---|
442 | |
---|
443 | bool goodeval = false; |
---|
444 | r = 0; |
---|
445 | |
---|
446 | // for ( i = 0; i < 10*t; i++ ) |
---|
447 | // A.nextpoint(); |
---|
448 | |
---|
449 | while ( ! goodeval ) |
---|
450 | { |
---|
451 | TIMING_START(fac_findeval); |
---|
452 | findEvaluation( U, V, omega, F, A, U0, delta, D, r ); |
---|
453 | out_cf("univ.U0:",U0,"\n"); |
---|
454 | TIMING_END(fac_findeval); |
---|
455 | DEBOUTLN( cerr, "the evaluation point to reduce to an univariate problem is " << A ); |
---|
456 | DEBOUTLN( cerr, "corresponding delta = " << delta ); |
---|
457 | DEBOUTLN( cerr, " omega = " << omega ); |
---|
458 | DEBOUTLN( cerr, " D = " << D ); |
---|
459 | DEBOUTLN( cerr, "now factorize the univariate polynomial " << U0 ); |
---|
460 | G = conv_to_factor_array( factorize( U0, false ) ); |
---|
461 | printf("conv_to_factor_array\n"); |
---|
462 | DEBOUTLN( cerr, "which factorizes into " << G ); |
---|
463 | |
---|
464 | r = G.size(); |
---|
465 | lcG = CFArray( 1, r ); |
---|
466 | UU = U; |
---|
467 | //if ( goodeval ) |
---|
468 | { |
---|
469 | printf("start hensel\n"); |
---|
470 | TIMING_START(fac_hensel); |
---|
471 | goodeval = Hensel( UU, G, lcG, A, b, Variable(1) ); |
---|
472 | TIMING_END(fac_hensel); |
---|
473 | } |
---|
474 | } |
---|
475 | for ( i = 1; i <= r; i++ ) |
---|
476 | { |
---|
477 | G[i] /= icontent( G[i] ); |
---|
478 | G[i] = M(G[i]); |
---|
479 | } |
---|
480 | // negate noch beachten ! |
---|
481 | if ( negate ) |
---|
482 | G[1] = -G[1]; |
---|
483 | DEBDECLEVEL( cerr, "ZFactorMulti" ); |
---|
484 | return G; |
---|
485 | } |
---|
486 | CFFList FpFactorizeMultivariate ( const CanonicalForm & f, bool issqrfree ) |
---|
487 | { |
---|
488 | CFFList G, F, R; |
---|
489 | CFArray GG; |
---|
490 | CFFListIterator i, j; |
---|
491 | CFMap M; |
---|
492 | CanonicalForm g, cont; |
---|
493 | Variable v1, vm; |
---|
494 | int k, m, n; |
---|
495 | |
---|
496 | v1 = Variable(1); |
---|
497 | if ( issqrfree ) |
---|
498 | F = CFFactor( f, 1 ); |
---|
499 | else |
---|
500 | F = sqrFree( f ); |
---|
501 | |
---|
502 | printf("nach sqrFree:\n"); |
---|
503 | out_cff(F); |
---|
504 | for ( i = F; i.hasItem(); i++ ) |
---|
505 | { |
---|
506 | out_cf("consider:",i.getItem().factor(),"\n"); |
---|
507 | if ( i.getItem().factor().inCoeffDomain() ) |
---|
508 | { |
---|
509 | if ( ! i.getItem().factor().isOne() ) |
---|
510 | R.append( CFFactor( i.getItem().factor(), i.getItem().exp() ) ); |
---|
511 | } |
---|
512 | else |
---|
513 | { |
---|
514 | TIMING_START(fac_content); |
---|
515 | g = compress( i.getItem().factor(), M ); |
---|
516 | // now after compress g contains Variable(1) |
---|
517 | vm = g.mvar(); |
---|
518 | g = swapvar( g, v1, vm ); |
---|
519 | cont = content( g ); |
---|
520 | g = swapvar( g / cont, v1, vm ); |
---|
521 | cont = swapvar( cont, v1, vm ); |
---|
522 | n = i.getItem().exp(); |
---|
523 | TIMING_END(fac_content); |
---|
524 | DEBOUTLN( cerr, "now after content ..." ); |
---|
525 | if ( g.isUnivariate() ) |
---|
526 | { |
---|
527 | G = factorize( g, true ); |
---|
528 | for ( j = G; j.hasItem(); j++ ) |
---|
529 | if ( ! j.getItem().factor().isOne() ) |
---|
530 | R.append( CFFactor( M( j.getItem().factor() ), n ) ); |
---|
531 | } |
---|
532 | else |
---|
533 | { |
---|
534 | GG = FpFactorizeMulti( g ); |
---|
535 | m = GG.max(); |
---|
536 | for ( k = GG.min(); k <= m; k++ ) |
---|
537 | if ( ! GG[k].isOne() ) |
---|
538 | R.append( CFFactor( M( GG[k] ), n ) ); |
---|
539 | } |
---|
540 | out_cf("try cont:",cont,"\n"); |
---|
541 | G = factorize( cont, true ); |
---|
542 | out_cff(G); |
---|
543 | for ( j = G; j.hasItem(); j++ ) |
---|
544 | if ( ! j.getItem().factor().isOne() ) |
---|
545 | R.append( CFFactor( M( j.getItem().factor() ), n ) ); |
---|
546 | } |
---|
547 | } |
---|
548 | return R; |
---|
549 | } |
---|