facBivar.h
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1 /*****************************************************************************\
2  * Computer Algebra System SINGULAR
3 \*****************************************************************************/
4 /** @file facBivar.h
5  *
6  * bivariate factorization over Q(a)
7  *
8  * @author Martin Lee
9  *
10  **/
11 /*****************************************************************************/
12 
13 #ifndef FAC_BIVAR_H
14 #define FAC_BIVAR_H
15 
16 // #include "config.h"
17 
18 #include "cf_assert.h"
19 #include "timing.h"
20 
21 #include "facFqBivarUtil.h"
22 #include "DegreePattern.h"
23 #include "cf_util.h"
24 #include "facFqSquarefree.h"
25 #include "cf_map.h"
26 #include "cfNewtonPolygon.h"
27 #include "fac_util.h"
28 
29 TIMING_DEFINE_PRINT(fac_bi_sqrf)
30 TIMING_DEFINE_PRINT(fac_bi_factor_sqrf)
31 
32 /// @return @a biFactorize returns a list of factors of F. If F is not monic
33 /// its leading coefficient is not outputted.
34 CFList
35 biFactorize (const CanonicalForm& F, ///< [in] a sqrfree bivariate poly
36  const Variable& v ///< [in] some algebraic variable
37  );
38 
39 /// factorize a squarefree bivariate polynomial over \f$ Q(\alpha) \f$.
40 ///
41 /// @ return @a ratBiSqrfFactorize returns a list of monic factors, the first
42 /// element is the leading coefficient.
43 #ifdef HAVE_NTL
44 inline
45 CFList
46 ratBiSqrfFactorize (const CanonicalForm & G, ///< [in] a bivariate poly
47  const Variable& v= Variable (1) ///< [in] algebraic variable
48  )
49 {
50  CFMap N;
51  CanonicalForm F= compress (G, N);
52  CanonicalForm contentX= content (F, 1); //erwarte hier primitiven input: primitiv über Z bzw. Z[a]
53  CanonicalForm contentY= content (F, 2);
54  F /= (contentX*contentY);
55  CFFList contentXFactors, contentYFactors;
56  if (v.level() != 1)
57  {
58  contentXFactors= factorize (contentX, v);
59  contentYFactors= factorize (contentY, v);
60  }
61  else
62  {
63  contentXFactors= factorize (contentX);
64  contentYFactors= factorize (contentY);
65  }
66  if (contentXFactors.getFirst().factor().inCoeffDomain())
67  contentXFactors.removeFirst();
68  if (contentYFactors.getFirst().factor().inCoeffDomain())
69  contentYFactors.removeFirst();
70  if (F.inCoeffDomain())
71  {
72  CFList result;
73  for (CFFListIterator i= contentXFactors; i.hasItem(); i++)
74  result.append (N (i.getItem().factor()));
75  for (CFFListIterator i= contentYFactors; i.hasItem(); i++)
76  result.append (N (i.getItem().factor()));
77  if (isOn (SW_RATIONAL))
78  {
79  normalize (result);
80  result.insert (Lc (G));
81  }
82  return result;
83  }
84 
85  mpz_t * M=new mpz_t [4];
86  mpz_init (M[0]);
87  mpz_init (M[1]);
88  mpz_init (M[2]);
89  mpz_init (M[3]);
90 
91  mpz_t * S=new mpz_t [2];
92  mpz_init (S[0]);
93  mpz_init (S[1]);
94 
95  F= compress (F, M, S);
96  CFList result= biFactorize (F, v);
97  for (CFListIterator i= result; i.hasItem(); i++)
98  i.getItem()= N (decompress (i.getItem(), M, S));
99  for (CFFListIterator i= contentXFactors; i.hasItem(); i++)
100  result.append (N(i.getItem().factor()));
101  for (CFFListIterator i= contentYFactors; i.hasItem(); i++)
102  result.append (N (i.getItem().factor()));
103  if (isOn (SW_RATIONAL))
104  {
105  normalize (result);
106  result.insert (Lc (G));
107  }
108 
109  mpz_clear (M[0]);
110  mpz_clear (M[1]);
111  mpz_clear (M[2]);
112  mpz_clear (M[3]);
113  delete [] M;
114 
115  mpz_clear (S[0]);
116  mpz_clear (S[1]);
117  delete [] S;
118 
119  return result;
120 }
121 
122 /// factorize a bivariate polynomial over \f$ Q(\alpha) \f$
123 ///
124 /// @return @a ratBiFactorize returns a list of monic factors with
125 /// multiplicity, the first element is the leading coefficient.
126 inline
127 CFFList
128 ratBiFactorize (const CanonicalForm & G, ///< [in] a bivariate poly
129  const Variable& v= Variable (1), ///< [in] algebraic variable
130  bool substCheck= true ///< [in] enables substitute check
131  )
132 {
133  CFMap N;
134  CanonicalForm F= compress (G, N);
135 
136  if (substCheck)
137  {
138  bool foundOne= false;
139  int * substDegree= new int [F.level()];
140  for (int i= 1; i <= F.level(); i++)
141  {
142  substDegree[i-1]= substituteCheck (F, Variable (i));
143  if (substDegree [i-1] > 1)
144  {
145  foundOne= true;
146  subst (F, F, substDegree[i-1], Variable (i));
147  }
148  }
149  if (foundOne)
150  {
151  CFFList result= ratBiFactorize (F, v, false);
152  CFFList newResult, tmp;
154  newResult.insert (result.getFirst());
155  result.removeFirst();
156  for (CFFListIterator i= result; i.hasItem(); i++)
157  {
158  tmp2= i.getItem().factor();
159  for (int j= 1; j <= F.level(); j++)
160  {
161  if (substDegree[j-1] > 1)
162  tmp2= reverseSubst (tmp2, substDegree[j-1], Variable (j));
163  }
164  tmp= ratBiFactorize (tmp2, v, false);
165  tmp.removeFirst();
166  for (CFFListIterator j= tmp; j.hasItem(); j++)
167  newResult.append (CFFactor (j.getItem().factor(),
168  j.getItem().exp()*i.getItem().exp()));
169  }
170  decompress (newResult, N);
171  delete [] substDegree;
172  return newResult;
173  }
174  delete [] substDegree;
175  }
176 
177  CanonicalForm LcF= Lc (F);
178  CanonicalForm contentX= content (F, 1);
179  CanonicalForm contentY= content (F, 2);
180  F /= (contentX*contentY);
181  CFFList contentXFactors, contentYFactors;
182  if (v.level() != 1)
183  {
184  contentXFactors= factorize (contentX, v);
185  contentYFactors= factorize (contentY, v);
186  }
187  else
188  {
189  contentXFactors= factorize (contentX);
190  contentYFactors= factorize (contentY);
191  }
192  if (contentXFactors.getFirst().factor().inCoeffDomain())
193  contentXFactors.removeFirst();
194  if (contentYFactors.getFirst().factor().inCoeffDomain())
195  contentYFactors.removeFirst();
196  decompress (contentXFactors, N);
197  decompress (contentYFactors, N);
198  CFFList result, resultRoot;
199  if (F.inCoeffDomain())
200  {
201  result= Union (contentXFactors, contentYFactors);
202  if (isOn (SW_RATIONAL))
203  {
204  normalize (result);
205  if (v.level() == 1)
206  {
207  for (CFFListIterator i= result; i.hasItem(); i++)
208  {
209  LcF /= power (bCommonDen (i.getItem().factor()), i.getItem().exp());
210  i.getItem()= CFFactor (i.getItem().factor()*
211  bCommonDen(i.getItem().factor()), i.getItem().exp());
212  }
213  }
214  result.insert (CFFactor (LcF, 1));
215  }
216  return result;
217  }
218 
219  mpz_t * M=new mpz_t [4];
220  mpz_init (M[0]);
221  mpz_init (M[1]);
222  mpz_init (M[2]);
223  mpz_init (M[3]);
224 
225  mpz_t * S=new mpz_t [2];
226  mpz_init (S[0]);
227  mpz_init (S[1]);
228 
229  F= compress (F, M, S);
230  TIMING_START (fac_bi_sqrf);
231  CFFList sqrfFactors= sqrFree (F);
232  TIMING_END_AND_PRINT (fac_bi_sqrf,
233  "time for bivariate sqrf factors over Q: ");
234  for (CFFListIterator i= sqrfFactors; i.hasItem(); i++)
235  {
236  TIMING_START (fac_bi_factor_sqrf);
237  CFList tmp= ratBiSqrfFactorize (i.getItem().factor(), v);
238  TIMING_END_AND_PRINT (fac_bi_factor_sqrf,
239  "time to factor bivariate sqrf factors over Q: ");
240  for (CFListIterator j= tmp; j.hasItem(); j++)
241  {
242  if (j.getItem().inCoeffDomain()) continue;
243  result.append (CFFactor (N (decompress (j.getItem(), M, S)),
244  i.getItem().exp()));
245  }
246  }
247  result= Union (result, contentXFactors);
248  result= Union (result, contentYFactors);
249  if (isOn (SW_RATIONAL))
250  {
251  normalize (result);
252  if (v.level() == 1)
253  {
254  for (CFFListIterator i= result; i.hasItem(); i++)
255  {
256  LcF /= power (bCommonDen (i.getItem().factor()), i.getItem().exp());
257  i.getItem()= CFFactor (i.getItem().factor()*
258  bCommonDen(i.getItem().factor()), i.getItem().exp());
259  }
260  }
261  result.insert (CFFactor (LcF, 1));
262  }
263 
264  mpz_clear (M[0]);
265  mpz_clear (M[1]);
266  mpz_clear (M[2]);
267  mpz_clear (M[3]);
268  delete [] M;
269 
270  mpz_clear (S[0]);
271  mpz_clear (S[1]);
272  delete [] S;
273 
274  return result;
275 }
276 
277 #endif
278 
279 /// convert a CFFList to a CFList by dropping the multiplicity
280 CFList conv (const CFFList& L ///< [in] a CFFList
281  );
282 
283 /// compute p^k larger than the bound on the coefficients of a factor of @a f
284 /// over Q (mipo)
285 modpk
286 coeffBound (const CanonicalForm & f, ///< [in] poly over Z[a]
287  int p, ///< [in] some positive integer
288  const CanonicalForm& mipo ///< [in] minimal polynomial with
289  ///< denominator 1
290  );
291 
292 /// find a big prime p from our tables such that no term of f vanishes mod p
293 void findGoodPrime(const CanonicalForm &f, ///< [in] poly over Z or Z[a]
294  int &start ///< [in,out] index of big prime in
295  /// cf_primetab.h
296  );
297 
298 /// compute p^k larger than the bound on the coefficients of a factor of @a f
299 /// over Z
300 modpk
301 coeffBound (const CanonicalForm & f, ///< [in] poly over Z
302  int p ///< [in] some positive integer
303  );
304 
305 #endif
306 
TIMING_END_AND_PRINT(fac_alg_resultant, "time to compute resultant0: ")
CanonicalForm power(const CanonicalForm &f, int n)
exponentiation
void findGoodPrime(const CanonicalForm &f, int &start)
find a big prime p from our tables such that no term of f vanishes mod p
Definition: facBivar.cc:61
int j
Definition: facHensel.cc:105
CFFList ratBiFactorize(const CanonicalForm &G, const Variable &v=Variable(1), bool substCheck=true)
factorize a bivariate polynomial over
Definition: facBivar.h:128
static poly normalize(poly next_p, ideal add_generators, syStrategy syzstr, int *g_l, int *p_l, int crit_comp)
Definition: syz3.cc:1027
This file provides functions to compute the Newton polygon of a bivariate polynomial.
TIMING_START(fac_alg_resultant)
factory&#39;s class for variables
Definition: factory.h:117
factory&#39;s main class
Definition: canonicalform.h:77
assertions for Factory
void insert(const T &)
Definition: ftmpl_list.cc:193
static TreeM * G
Definition: janet.cc:32
CanonicalForm Lc(const CanonicalForm &f)
CanonicalForm compress(const CanonicalForm &f, CFMap &m)
CanonicalForm compress ( const CanonicalForm & f, CFMap & m )
Definition: cf_map.cc:210
CanonicalForm LcF
Definition: facAbsBiFact.cc:51
void removeFirst()
Definition: ftmpl_list.cc:287
map polynomials
CanonicalForm subst(const CanonicalForm &f, const CFList &a, const CFList &b, const CanonicalForm &Rstar, bool isFunctionField)
CanonicalForm content(const CanonicalForm &)
CanonicalForm content ( const CanonicalForm & f )
Definition: cf_gcd.cc:180
T getFirst() const
Definition: ftmpl_list.cc:279
template List< Variable > Union(const List< Variable > &, const List< Variable > &)
This file provides functions for squarefrees factorizing over , or GF.
modpk coeffBound(const CanonicalForm &f, int p, const CanonicalForm &mipo)
compute p^k larger than the bound on the coefficients of a factor of f over Q (mipo) ...
Definition: facBivar.cc:97
#define M
Definition: sirandom.c:24
CFFList factorize(const CanonicalForm &f, bool issqrfree=false)
factorization over or
Definition: cf_factor.cc:390
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:48
CanonicalForm decompress(const CanonicalForm &F, const mpz_t *inverseM, const mpz_t *A)
decompress a bivariate poly
int level() const
Definition: factory.h:134
static const int SW_RATIONAL
set to 1 for computations over Q
Definition: cf_defs.h:28
bool isOn(int sw)
switches
int substituteCheck(const CanonicalForm &F, const Variable &x)
check if a substitution x^n->x is possible
FILE * f
Definition: checklibs.c:9
int i
Definition: cfEzgcd.cc:125
CFList tmp2
Definition: facFqBivar.cc:70
CanonicalForm bCommonDen(const CanonicalForm &f)
CanonicalForm bCommonDen ( const CanonicalForm & f )
CFList biFactorize(const CanonicalForm &F, const Variable &v)
Definition: facBivar.cc:187
class CFMap
Definition: cf_map.h:84
This file provides utility functions for bivariate factorization.
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:37
CFList ratBiSqrfFactorize(const CanonicalForm &G, const Variable &v=Variable(1))
factorize a squarefree bivariate polynomial over .
Definition: facBivar.h:46
CanonicalForm mipo
Definition: facAlgExt.cc:57
CFList conv(const CFFList &L)
convert a CFFList to a CFList by dropping the multiplicity
Definition: facBivar.cc:126
Factor< CanonicalForm > CFFactor
This file provides a class to handle degree patterns.
CanonicalForm reverseSubst(const CanonicalForm &F, const int d, const Variable &x)
reverse a substitution x^d->x
int level() const
level() returns the level of CO.
operations mod p^k and some other useful functions for factorization
void append(const T &)
Definition: ftmpl_list.cc:256
int p
Definition: cfModGcd.cc:4019
class to do operations mod p^k for int&#39;s p and k
Definition: fac_util.h:22
CFFList sqrFree(const CanonicalForm &f, bool sort=false)
squarefree factorization
Definition: cf_factor.cc:757
return result
Definition: facAbsBiFact.cc:76
TIMING_DEFINE_PRINT(fac_bi_sqrf) TIMING_DEFINE_PRINT(fac_bi_factor_sqrf) CFList biFactorize(const CanonicalForm &F
bool inCoeffDomain() const