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fac_multivar.cc
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1/* emacs edit mode for this file is -*- C++ -*- */
2/* $Id: fac_multivar.cc 14377 2011-09-01 13:40:30Z mlee $ */
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#include "fac_multihensel.h"
22#include "facBivar.h"
23
24#ifndef HAVE_NTL
25
26void out_cf(const char *s1,const CanonicalForm &f,const char *s2);
27void out_cff(CFFList &L);
28
29TIMING_DEFINE_PRINT(fac_content);
30TIMING_DEFINE_PRINT(fac_findeval);
31TIMING_DEFINE_PRINT(fac_distrib);
32TIMING_DEFINE_PRINT(fac_hensel);
33
34static CFArray
35conv_to_factor_array( const CFFList & L )
36{
37 int n;
38 CFFListIterator I = L;
39 bool negate = false;
40
41 if ( ! I.hasItem() )
42 n = 0;
43 else if ( I.getItem().factor().inBaseDomain() ) {
44 negate = I.getItem().factor().sign() < 0;
45 I++;
46 n = L.length();
47 }
48 else
49 n = L.length() + 1;
50 CFFListIterator J = I;
51 while ( J.hasItem() ) {
52 n += J.getItem().exp() - 1;
53 J++;
54 }
55 CFArray result( 1, n-1 );
56 int i, j, k;
57 i = 1;
58 while ( I.hasItem() ) {
59 k = I.getItem().exp();
60 for ( j = 1; j <= k; j++ ) {
61 result[i] = I.getItem().factor();
62 i++;
63 }
64 I++;
65 }
66 if ( negate )
67 result[1] = -result[1];
68 return result;
69}
70
71static modpk
72coeffBound_old ( const CanonicalForm & f, int p )
73{
74 int * degs = degrees( f );
75 int M = 0, i, k = f.level();
76 for ( i = 1; i <= k; i++ )
77 M += degs[i];
78 CanonicalForm b = 2 * maxNorm( f ) * power( CanonicalForm( 3 ), M );
80 k = 1;
81 while ( B < b ) {
82 B *= p;
83 k++;
84 }
85 return modpk( p, k );
86}
87
88// static bool
89// nonDivisors ( CanonicalForm omega, CanonicalForm delta, const CFArray & F, CFArray & d )
90// {
91// DEBOUTLN( cerr, "nondivisors omega = " << omega );
92// DEBOUTLN( cerr, "nondivisors delta = " << delta );
93// DEBOUTLN( cerr, "nondivisors F = " << F );
94// CanonicalForm q, r;
95// int k = F.size();
96// d = CFArray( 0, k );
97// d[0] = delta * omega;
98// for ( int i = 1; i <= k; i++ ) {
99// q = abs(F[i]);
100// for ( int j = i-1; j >= 0; j-- ) {
101// r = d[j];
102// do {
103// r = gcd( r, q );
104// q = q / r;
105// } while ( r != 1 );
106// if ( q == 1 )
107// return false;
108// }
109// d[i] = q;
110// }
111// return true;
112// }
113
114static void
115findEvaluation ( const CanonicalForm & U, const CanonicalForm & V, const CanonicalForm & omega, const CFFList & F, Evaluation & A, CanonicalForm & U0, CanonicalForm & delta, CFArray & D, int r )
116{
117 DEBINCLEVEL( cerr, "findEvaluation" );
118 CanonicalForm Vn;
120 int j;
121 bool found = false;
122 CFArray FF = CFArray( 1, F.length() );
123 if ( r > 0 )
124 A.nextpoint();
125 while ( ! found )
126 {
127 Vn = A( V );
128 if ( Vn != 0 )
129 {
130 U0 = A( U );
131 DEBOUTLN( cerr, "U0 = " << U0 );
132 if ( isSqrFree( U0 ) )
133 {
134 delta = content( U0 );
135 DEBOUTLN( cerr, "content( U0 ) = " << delta );
136 for ( I = F, j = 1; I.hasItem(); I++, j++ )
137 FF[j] = A( I.getItem().factor() );
138 found = nonDivisors( omega, delta, FF, D );
139 }
140 else
141 {
142 DEBOUTLN( cerr, "not sqrfree : " << sqrFree( U0 ) );
143 }
144 }
145 if ( ! found )
146 A.nextpoint();
147 }
148 DEBDECLEVEL( cerr, "findEvaluation" );
149}
150
151
152static int prime_number=0;
153void find_good_prime(const CanonicalForm &f, int &start)
154{
155 if (! f.inBaseDomain() )
156 {
157 CFIterator i = f;
158 for(;;)
159 {
160 if ( i.hasTerms() )
161 {
162 find_good_prime(i.coeff(),start);
163 if (start==cf_getNumSmallPrimes()) return;
164 if((i.exp()!=0) && ((i.exp() % cf_getSmallPrime(start))==0))
165 {
166 start++;
167 if (start==cf_getNumSmallPrimes()) return;
168 i=f;
169 }
170 else i++;
171 }
172 else break;
173 }
174 }
175 else
176 {
177 if (f.inZ())
178 {
179 if (start==cf_getNumSmallPrimes()) return;
180 while((!f.isZero()) && (mod(f,cf_getSmallPrime(start))==0))
181 {
182 start++;
183 if (start==cf_getNumSmallPrimes()) return;
184 }
185 }
186/* should not happen!
187 else if (f.inQ())
188 {
189 while((f.den()!=0) && (mod(f.den(),cf_getSmallPrime(start))==0))
190 {
191 start++;
192 }
193 while((f.num()!=0) && (mod(f.num(),cf_getSmallPrime(start))==0))
194 {
195 start++;
196 }
197 }
198 else
199 cout <<"??"<< f <<"\n";
200*/
201 }
202}
203static CFArray ZFactorizeMulti ( const CanonicalForm & arg )
204{
205 prime_number=0;
206 bool is_rat=isOn(SW_RATIONAL);
208 DEBINCLEVEL( cerr, "ZFactorizeMulti" );
209 CFMap M;
210 CanonicalForm UU, U = compress( arg, M );
211 CanonicalForm delta, omega, V = LC( U, 1 );
212 int t = U.level();
213 CFFList F = factorize( V );
214 CFFListIterator I, J;
215 CFArray G, lcG, D;
216 int i, j, r, maxdeg;
217 REvaluation A( 2, t, IntRandom( 50 ) );
218 CanonicalForm U0;
219 CanonicalForm ft, ut, gt, d;
220 modpk b;
221 bool negate = false;
222
223 DEBOUTLN( cerr, "-----------------------------------------------------" );
224 DEBOUTLN( cerr, "trying to factorize U = " << U );
225 DEBOUTLN( cerr, "U is a polynomial of level = " << arg.level() );
226 DEBOUTLN( cerr, "U will be factorized with respect to variable " << Variable(1) );
227 DEBOUTLN( cerr, "the leading coefficient of U with respect to that variable is " << V );
228 DEBOUTLN( cerr, "which is factorized as " << F );
229
230 maxdeg = 0;
231 for ( i = 2; i <= t; i++ )
232 {
233 j = U.degree( Variable( i ) );
234 if ( j > maxdeg ) maxdeg = j;
235 }
236
237 if ( F.getFirst().factor().inCoeffDomain() )
238 {
239 omega = F.getFirst().factor();
240 F.removeFirst();
241 if ( omega < 0 )
242 {
243 negate = true;
244 omega = -omega;
245 U = -U;
246 }
247 }
248 else
249 omega = 1;
250
251 bool goodeval = false;
252 r = 0;
253
254// for ( i = 0; i < 10*t; i++ )
255// A.nextpoint();
256
257 while ( ! goodeval )
258 {
259 TIMING_START(fac_findeval);
260 findEvaluation( U, V, omega, F, A, U0, delta, D, r );
261 TIMING_END(fac_findeval);
262 DEBOUTLN( cerr, "the evaluation point to reduce to an univariate problem is " << A );
263 DEBOUTLN( cerr, "corresponding delta = " << delta );
264 DEBOUTLN( cerr, " omega = " << omega );
265 DEBOUTLN( cerr, " D = " << D );
266 DEBOUTLN( cerr, "now factorize the univariate polynomial " << U0 );
267 G = conv_to_factor_array( factorize( U0, false ) );
268 DEBOUTLN( cerr, "which factorizes into " << G );
269 {
270 int i=prime_number;
271 find_good_prime(arg,i);
272 find_good_prime(U0,i);
273 find_good_prime(U,i);
274 int p;
275 if (i==cf_getNumSmallPrimes()) p=0;
276 else p=cf_getSmallPrime(i);
277 //printf("found:p=%d (%d)\n",p,i);
278 if (p==0)
279 {
280 return conv_to_factor_array(CFFactor(arg,1));
281 //printf("out of primes - switch to non-NTL\n");
282 }
283 else if (((i==0)||(i!=prime_number)))
284 {
285 b = coeffBound_old( U, p );
286 prime_number=i;
287 }
288 else prime_number++;
289 // p!=0:
290 modpk bb=coeffBound_old(U0,p);
291 if (bb.getk() > b.getk() ) b=bb;
292 bb=coeffBound_old(arg,p);
293 if (bb.getk() > b.getk() ) b=bb;
294 }
295 if ( getZFacModulus().getpk() > b.getpk() )
296 b = getZFacModulus();
297 //printf("p=%d, k=%d\n",b.getp(),b.getk());
298 DEBOUTLN( cerr, "the coefficient bound of the factors of U is " << b.getpk() );
299
300 r = G.size();
301 lcG = CFArray( 1, r );
302 UU = U;
303 DEBOUTLN( cerr, "now trying to distribute the leading coefficients ..." );
304 TIMING_START(fac_distrib);
305 goodeval = distributeLeadingCoeffs( UU, G, lcG, F, D, delta, omega, A, r );
306 TIMING_END(fac_distrib);
307#ifdef DEBUGOUTPUT
308 if ( goodeval )
309 {
310 DEBOUTLN( cerr, "the univariate factors after distribution are " << G );
311 DEBOUTLN( cerr, "the distributed leading coeffs are " << lcG );
312 DEBOUTLN( cerr, "U may have changed and is now " << UU );
313 DEBOUTLN( cerr, "which has leading coefficient " << LC( UU, Variable(1) ) );
314
315 if ( LC( UU, Variable(1) ) != prod( lcG ) || A(UU) != prod( G ) )
316 {
317 DEBOUTLN( cerr, "!!! distribution was not correct !!!" );
318 DEBOUTLN( cerr, "product of leading coeffs is " << prod( lcG ) );
319 DEBOUTLN( cerr, "product of univariate factors is " << prod( G ) );
320 DEBOUTLN( cerr, "the new U is evaluated as " << A(UU) );
321 }
322 else
323 DEBOUTLN( cerr, "leading coeffs correct" );
324 }
325 else
326 {
327 DEBOUTLN( cerr, "we have found a bad evaluation point" );
328 }
329#endif
330 if ( goodeval )
331 {
332 TIMING_START(fac_hensel);
333 goodeval = Hensel( UU, G, lcG, A, b, Variable(1) );
334 TIMING_END(fac_hensel);
335 }
336 }
337 for ( i = 1; i <= r; i++ )
338 {
339 G[i] /= icontent( G[i] );
340 G[i] = M(G[i]);
341 }
342 // negate noch beachten !
343 if ( negate )
344 G[1] = -G[1];
345 DEBDECLEVEL( cerr, "ZFactorMulti" );
346 if(is_rat) On(SW_RATIONAL);
347 return G;
348}
349
350CFFList ZFactorizeMultivariate ( const CanonicalForm & f, bool issqrfree )
351{
352 CFFList G, F, R;
353 CFArray GG;
355 CFMap M;
356 CanonicalForm g, cont;
357 Variable v1, vm;
358 int k, m, n;
359
360 v1 = Variable(1);
361 if ( issqrfree )
362 F = CFFactor( f, 1 );
363 else
364 F = sqrFree( f );
365
366 for ( i = F; i.hasItem(); i++ )
367 {
368 if ( i.getItem().factor().inCoeffDomain() )
369 {
370 if ( ! i.getItem().factor().isOne() )
371 R.append( CFFactor( i.getItem().factor(), i.getItem().exp() ) );
372 }
373 else
374 {
375 TIMING_START(fac_content);
376 g = compress( i.getItem().factor(), M );
377 // now after compress g contains Variable(1)
378 vm = g.mvar();
379 g = swapvar( g, v1, vm );
380 cont = content( g );
381 g = swapvar( g / cont, v1, vm );
382 cont = swapvar( cont, v1, vm );
383 n = i.getItem().exp();
384 TIMING_END(fac_content);
385 DEBOUTLN( cerr, "now after content ..." );
386 if ( g.isUnivariate() )
387 {
388 G = factorize( g, true );
389 for ( j = G; j.hasItem(); j++ )
390 if ( ! j.getItem().factor().isOne() )
391 R.append( CFFactor( M( j.getItem().factor() ), n ) );
392 }
393 else
394 {
395 GG = ZFactorizeMulti( g );
396 m = GG.max();
397 for ( k = GG.min(); k <= m; k++ )
398 if ( ! GG[k].isOne() )
399 R.append( CFFactor( M( GG[k] ), n ) );
400 }
401 G = factorize( cont, true );
402 for ( j = G; j.hasItem(); j++ )
403 if ( ! j.getItem().factor().isOne() )
404 R.append( CFFactor( M( j.getItem().factor() ), n ) );
405 }
406 }
407 return R;
408}
409#endif
bool isOn(int sw)
switches
void On(int sw)
switches
void Off(int sw)
switches
CanonicalForm power(const CanonicalForm &f, int n)
exponentiation
CanonicalForm FACTORY_PUBLIC content(const CanonicalForm &)
CanonicalForm content ( const CanonicalForm & f )
Definition: cf_gcd.cc:603
CanonicalForm FACTORY_PUBLIC icontent(const CanonicalForm &f)
CanonicalForm icontent ( const CanonicalForm & f )
Definition: cf_gcd.cc:74
int * degrees(const CanonicalForm &f, int *degs=0)
int * degrees ( const CanonicalForm & f, int * degs )
Definition: cf_ops.cc:493
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
Array< CanonicalForm > CFArray
CanonicalForm FACTORY_PUBLIC swapvar(const CanonicalForm &, const Variable &, const Variable &)
swapvar() - swap variables x1 and x2 in f.
Definition: cf_ops.cc:168
Factor< CanonicalForm > CFFactor
CanonicalForm LC(const CanonicalForm &f)
int m
Definition: cfEzgcd.cc:128
static int Hensel(const CanonicalForm &UU, CFArray &G, const Evaluation &AA, const CFArray &LeadCoeffs)
Definition: cfEzgcd.cc:302
int i
Definition: cfEzgcd.cc:132
int k
Definition: cfEzgcd.cc:99
int p
Definition: cfModGcd.cc:4078
g
Definition: cfModGcd.cc:4090
const CanonicalForm & GG
Definition: cfModGcd.cc:4076
CanonicalForm b
Definition: cfModGcd.cc:4103
CanonicalForm maxNorm(const CanonicalForm &f)
CanonicalForm maxNorm ( const CanonicalForm & f )
declarations of higher level algorithms.
CFFList FACTORY_PUBLIC sqrFree(const CanonicalForm &f, bool sort=false)
squarefree factorization
Definition: cf_factor.cc:957
CFFList FACTORY_PUBLIC factorize(const CanonicalForm &f, bool issqrfree=false)
factorization over or
Definition: cf_factor.cc:405
factory switches.
static const int SW_RATIONAL
set to 1 for computations over Q
Definition: cf_defs.h:31
void out_cff(CFFList &L)
Definition: cf_factor.cc:202
Iterators for CanonicalForm's.
CanonicalForm compress(const CanonicalForm &f, CFMap &m)
CanonicalForm compress ( const CanonicalForm & f, CFMap & m )
Definition: cf_map.cc:210
map polynomials
int cf_getNumSmallPrimes()
Definition: cf_primes.cc:34
int cf_getSmallPrime(int i)
Definition: cf_primes.cc:28
access to prime tables
generate random evaluation points
FILE * f
Definition: checklibs.c:9
void out_cf(const char *s1, const CanonicalForm &f, const char *s2)
Definition: cf_factor.cc:99
class to iterate through CanonicalForm's
Definition: cf_iter.h:44
class CFMap
Definition: cf_map.h:85
factory's main class
Definition: canonicalform.h:86
int degree() const
Returns -1 for the zero polynomial and 0 if CO is in a base domain.
int level() const
level() returns the level of CO.
class to evaluate a polynomial at points
Definition: cf_eval.h:32
generate random integers
Definition: cf_random.h:56
T & getItem() const
Definition: ftmpl_list.cc:431
T getFirst() const
Definition: ftmpl_list.cc:279
void removeFirst()
Definition: ftmpl_list.cc:287
int length() const
Definition: ftmpl_list.cc:273
class to generate random evaluation points
Definition: cf_reval.h:26
factory's class for variables
Definition: variable.h:33
class to do operations mod p^k for int's p and k
Definition: fac_util.h:23
int getk() const
Definition: fac_util.h:36
functions to print debug output
#define DEBINCLEVEL(stream, msg)
Definition: debug.h:44
#define DEBOUTLN(stream, objects)
Definition: debug.h:49
#define DEBDECLEVEL(stream, msg)
Definition: debug.h:45
return result
Definition: facAbsBiFact.cc:75
b *CanonicalForm B
Definition: facBivar.cc:52
bivariate factorization over Q(a)
bool found
Definition: facFactorize.cc:55
int j
Definition: facHensel.cc:110
fq_nmod_poly_t prod
Definition: facHensel.cc:100
bool nonDivisors(CanonicalForm omega, CanonicalForm delta, const CFArray &F, CFArray &d)
bool distributeLeadingCoeffs(CanonicalForm &U, CFArray &G, CFArray &lcG, const CFFList &F, const CFArray &D, CanonicalForm &delta, CanonicalForm &omega, const Evaluation &A, int r)
CFFList ZFactorizeMultivariate(const CanonicalForm &f, bool issqrfree)
bool isSqrFree(const CanonicalForm &f)
modpk getZFacModulus()
operations mod p^k and some other useful functions for factorization
#define D(A)
Definition: gentable.cc:131
STATIC_VAR TreeM * G
Definition: janet.cc:31
bool delta(X x, Y y, D d)
Definition: TestSuite.h:160
#define R
Definition: sirandom.c:27
#define A
Definition: sirandom.c:24
#define M
Definition: sirandom.c:25
#define TIMING_DEFINE_PRINT(t)
Definition: timing.h:95
#define TIMING_END(t)
Definition: timing.h:93
#define TIMING_START(t)
Definition: timing.h:92