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Functions | Variables
facBivar.h File Reference

bivariate factorization over Q(a) More...

#include "cf_assert.h"
#include "timing.h"
#include "facFqBivarUtil.h"
#include "DegreePattern.h"
#include "cf_util.h"
#include "facFqSquarefree.h"
#include "cf_map.h"
#include "cf_algorithm.h"
#include "cfNewtonPolygon.h"
#include "fac_util.h"

Go to the source code of this file.

Functions

 TIMING_DEFINE_PRINT (fac_bi_sqrf) TIMING_DEFINE_PRINT(fac_bi_factor_sqrf) CFList biFactorize(const CanonicalForm &F
 
CFList ratBiSqrfFactorize (const CanonicalForm &G, const Variable &v=Variable(1))
 factorize a squarefree bivariate polynomial over $ Q(\alpha) $. More...
 
CFFList ratBiFactorize (const CanonicalForm &G, const Variable &v=Variable(1), bool substCheck=true)
 factorize a bivariate polynomial over $ Q(\alpha) $ More...
 
CFList conv (const CFFList &L)
 convert a CFFList to a CFList by dropping the multiplicity More...
 
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) More...
 
void findGoodPrime (const CanonicalForm &f, int &start)
 find a big prime p from our tables such that no term of f vanishes mod p More...
 
modpk coeffBound (const CanonicalForm &f, int p)
 compute p^k larger than the bound on the coefficients of a factor of f over Z More...
 

Variables

const Variablev
 < [in] a sqrfree bivariate poly More...
 

Detailed Description

bivariate factorization over Q(a)

Author
Martin Lee

Definition in file facBivar.h.

Function Documentation

◆ coeffBound() [1/2]

modpk coeffBound ( const CanonicalForm f,
int  p 
)

compute p^k larger than the bound on the coefficients of a factor of f over Z

Parameters
[in]fpoly over Z
[in]psome positive integer

◆ coeffBound() [2/2]

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)

Parameters
[in]fpoly over Z[a]
[in]psome positive integer
[in]mipominimal polynomial with denominator 1

Definition at line 97 of file facBivar.cc.

98 {
99  int * degs = degrees( f );
100  int M = 0, i, k = f.level();
101  CanonicalForm K= 1;
102  for ( i = 1; i <= k; i++ )
103  {
104  M += degs[i];
105  K *= degs[i] + 1;
106  }
107  DELETE_ARRAY(degs);
108  K /= power (CanonicalForm (2), k/2);
109  K *= power (CanonicalForm (2), M);
110  int N= degree (mipo);
112  b= 2*power (maxNorm (f), N)*power (maxNorm (mipo), 4*N)*K*
113  power (CanonicalForm (2), N)*
114  power (CanonicalForm (N+1), 4*N);
115  b /= power (abs (lc (mipo)), N);
116 
117  CanonicalForm B = p;
118  k = 1;
119  while ( B < b ) {
120  B *= p;
121  k++;
122  }
123  return modpk( p, k );
124 }
Rational abs(const Rational &a)
Definition: GMPrat.cc:436
CanonicalForm power(const CanonicalForm &f, int n)
exponentiation
CanonicalForm lc(const CanonicalForm &f)
int degree(const CanonicalForm &f)
int * degrees(const CanonicalForm &f, int *degs=0)
int * degrees ( const CanonicalForm & f, int * degs )
Definition: cf_ops.cc:493
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:56
CanonicalForm maxNorm(const CanonicalForm &f)
CanonicalForm maxNorm ( const CanonicalForm & f )
FILE * f
Definition: checklibs.c:9
factory's main class
Definition: canonicalform.h:86
CanonicalForm mipo
Definition: facAlgExt.cc:57
return modpk(p, k)
CanonicalForm b
Definition: facBivar.cc:42
int p
Definition: facBivar.cc:39
int M
Definition: facBivar.cc:41
DELETE_ARRAY(degs)
int i
Definition: facBivar.cc:41
b *CanonicalForm B
Definition: facBivar.cc:52
int k
Definition: facBivar.cc:41

◆ conv()

CFList conv ( const CFFList L)

convert a CFFList to a CFList by dropping the multiplicity

Parameters
[in]La CFFList

Definition at line 126 of file facBivar.cc.

127 {
128  CFList result;
129  for (CFFListIterator i= L; i.hasItem(); i++)
130  result.append (i.getItem().factor());
131  return result;
132 }
return result
Definition: facAbsBiFact.cc:75

◆ findGoodPrime()

void findGoodPrime ( const CanonicalForm f,
int &  start 
)

find a big prime p from our tables such that no term of f vanishes mod p

Parameters
[in]fpoly over Z or Z[a]
[in,out]startindex of big prime in cf_primetab.h

Definition at line 61 of file facBivar.cc.

62 {
63  if (! f.inBaseDomain() )
64  {
65  CFIterator i = f;
66  for(;;)
67  {
68  if ( i.hasTerms() )
69  {
70  findGoodPrime(i.coeff(),start);
71  if (0==cf_getBigPrime(start)) return;
72  if((i.exp()!=0) && ((i.exp() % cf_getBigPrime(start))==0))
73  {
74  start++;
75  i=f;
76  }
77  else i++;
78  }
79  else break;
80  }
81  }
82  else
83  {
84  if (f.inZ())
85  {
86  if (0==cf_getBigPrime(start)) return;
87  while((!f.isZero()) && (mod(f,cf_getBigPrime(start))==0))
88  {
89  start++;
90  if (0==cf_getBigPrime(start)) return;
91  }
92  }
93  }
94 }
CF_NO_INLINE FACTORY_PUBLIC CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
int cf_getBigPrime(int i)
Definition: cf_primes.cc:39
class to iterate through CanonicalForm's
Definition: cf_iter.h:44
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

◆ ratBiFactorize()

CFFList ratBiFactorize ( const CanonicalForm G,
const Variable v = Variable (1),
bool  substCheck = true 
)
inline

factorize a bivariate polynomial over $ Q(\alpha) $

Returns
ratBiFactorize returns a list of monic factors with multiplicity, the first element is the leading coefficient.
Parameters
[in]Ga bivariate poly
[in]valgebraic variable
[in]substCheckenables substitute check

Definition at line 129 of file facBivar.h.

133 {
134  CFMap N;
135  CanonicalForm F= compress (G, N);
136 
137  if (substCheck)
138  {
139  bool foundOne= false;
140  int * substDegree= new int [F.level()];
141  for (int i= 1; i <= F.level(); i++)
142  {
143  substDegree[i-1]= substituteCheck (F, Variable (i));
144  if (substDegree [i-1] > 1)
145  {
146  foundOne= true;
147  subst (F, F, substDegree[i-1], Variable (i));
148  }
149  }
150  if (foundOne)
151  {
152  CFFList result= ratBiFactorize (F, v, false);
153  CFFList newResult, tmp;
155  newResult.insert (result.getFirst());
156  result.removeFirst();
157  for (CFFListIterator i= result; i.hasItem(); i++)
158  {
159  tmp2= i.getItem().factor();
160  for (int j= 1; j <= F.level(); j++)
161  {
162  if (substDegree[j-1] > 1)
163  tmp2= reverseSubst (tmp2, substDegree[j-1], Variable (j));
164  }
165  tmp= ratBiFactorize (tmp2, v, false);
166  tmp.removeFirst();
167  for (CFFListIterator j= tmp; j.hasItem(); j++)
168  newResult.append (CFFactor (j.getItem().factor(),
169  j.getItem().exp()*i.getItem().exp()));
170  }
171  decompress (newResult, N);
172  delete [] substDegree;
173  return newResult;
174  }
175  delete [] substDegree;
176  }
177 
178  CanonicalForm LcF= Lc (F);
179  CanonicalForm contentX= content (F, 1);
180  CanonicalForm contentY= content (F, 2);
181  F /= (contentX*contentY);
182  CFFList contentXFactors, contentYFactors;
183  if (v.level() != 1)
184  {
185  contentXFactors= factorize (contentX, v);
186  contentYFactors= factorize (contentY, v);
187  }
188  else
189  {
190  contentXFactors= factorize (contentX);
191  contentYFactors= factorize (contentY);
192  }
193  if (contentXFactors.getFirst().factor().inCoeffDomain())
194  contentXFactors.removeFirst();
195  if (contentYFactors.getFirst().factor().inCoeffDomain())
196  contentYFactors.removeFirst();
197  decompress (contentXFactors, N);
198  decompress (contentYFactors, N);
199  CFFList result, resultRoot;
200  if (F.inCoeffDomain())
201  {
202  result= Union (contentXFactors, contentYFactors);
203  if (isOn (SW_RATIONAL))
204  {
205  normalize (result);
206  if (v.level() == 1)
207  {
208  for (CFFListIterator i= result; i.hasItem(); i++)
209  {
210  LcF /= power (bCommonDen (i.getItem().factor()), i.getItem().exp());
211  i.getItem()= CFFactor (i.getItem().factor()*
212  bCommonDen(i.getItem().factor()), i.getItem().exp());
213  }
214  }
215  result.insert (CFFactor (LcF, 1));
216  }
217  return result;
218  }
219 
220  mpz_t * M=new mpz_t [4];
221  mpz_init (M[0]);
222  mpz_init (M[1]);
223  mpz_init (M[2]);
224  mpz_init (M[3]);
225 
226  mpz_t * S=new mpz_t [2];
227  mpz_init (S[0]);
228  mpz_init (S[1]);
229 
230  F= compress (F, M, S);
231  TIMING_START (fac_bi_sqrf);
232  CFFList sqrfFactors= sqrFree (F);
233  TIMING_END_AND_PRINT (fac_bi_sqrf,
234  "time for bivariate sqrf factors over Q: ");
235  for (CFFListIterator i= sqrfFactors; i.hasItem(); i++)
236  {
237  TIMING_START (fac_bi_factor_sqrf);
238  CFList tmp= ratBiSqrfFactorize (i.getItem().factor(), v);
239  TIMING_END_AND_PRINT (fac_bi_factor_sqrf,
240  "time to factor bivariate sqrf factors over Q: ");
241  for (CFListIterator j= tmp; j.hasItem(); j++)
242  {
243  if (j.getItem().inCoeffDomain()) continue;
244  result.append (CFFactor (N (decompress (j.getItem(), M, S)),
245  i.getItem().exp()));
246  }
247  }
248  result= Union (result, contentXFactors);
249  result= Union (result, contentYFactors);
250  if (isOn (SW_RATIONAL))
251  {
252  normalize (result);
253  if (v.level() == 1)
254  {
255  for (CFFListIterator i= result; i.hasItem(); i++)
256  {
257  LcF /= power (bCommonDen (i.getItem().factor()), i.getItem().exp());
258  i.getItem()= CFFactor (i.getItem().factor()*
259  bCommonDen(i.getItem().factor()), i.getItem().exp());
260  }
261  }
262  result.insert (CFFactor (LcF, 1));
263  }
264 
265  mpz_clear (M[0]);
266  mpz_clear (M[1]);
267  mpz_clear (M[2]);
268  mpz_clear (M[3]);
269  delete [] M;
270 
271  mpz_clear (S[0]);
272  mpz_clear (S[1]);
273  delete [] S;
274 
275  return result;
276 }
bool isOn(int sw)
switches
CanonicalForm FACTORY_PUBLIC content(const CanonicalForm &)
CanonicalForm content ( const CanonicalForm & f )
Definition: cf_gcd.cc:603
CanonicalForm Lc(const CanonicalForm &f)
Factor< CanonicalForm > CFFactor
int i
Definition: cfEzgcd.cc:132
CanonicalForm decompress(const CanonicalForm &F, const mpz_t *inverseM, const mpz_t *A)
decompress a bivariate poly
CanonicalForm bCommonDen(const CanonicalForm &f)
CanonicalForm bCommonDen ( const CanonicalForm & f )
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
static const int SW_RATIONAL
set to 1 for computations over Q
Definition: cf_defs.h:31
CanonicalForm compress(const CanonicalForm &f, CFMap &m)
CanonicalForm compress ( const CanonicalForm & f, CFMap & m )
Definition: cf_map.cc:210
class CFMap
Definition: cf_map.h:85
bool inCoeffDomain() const
int level() const
level() returns the level of CO.
T getFirst() const
Definition: ftmpl_list.cc:279
void removeFirst()
Definition: ftmpl_list.cc:287
void append(const T &)
Definition: ftmpl_list.cc:256
void insert(const T &)
Definition: ftmpl_list.cc:193
factory's class for variables
Definition: factory.h:127
int level() const
Definition: factory.h:143
CanonicalForm LcF
Definition: facAbsBiFact.cc:50
TIMING_END_AND_PRINT(fac_alg_resultant, "time to compute resultant0: ")
TIMING_START(fac_alg_resultant)
CanonicalForm subst(const CanonicalForm &f, const CFList &a, const CFList &b, const CanonicalForm &Rstar, bool isFunctionField)
CFList ratBiSqrfFactorize(const CanonicalForm &G, const Variable &v=Variable(1))
factorize a squarefree bivariate polynomial over .
Definition: facBivar.h:47
CFFList ratBiFactorize(const CanonicalForm &G, const Variable &v=Variable(1), bool substCheck=true)
factorize a bivariate polynomial over
Definition: facBivar.h:129
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
CanonicalForm reverseSubst(const CanonicalForm &F, const int d, const Variable &x)
reverse a substitution x^d->x
int substituteCheck(const CanonicalForm &F, const Variable &x)
check if a substitution x^n->x is possible
CFList tmp2
Definition: facFqBivar.cc:72
int j
Definition: facHensel.cc:110
template List< Variable > Union(const List< Variable > &, const List< Variable > &)
STATIC_VAR TreeM * G
Definition: janet.cc:31
#define M
Definition: sirandom.c:25
static poly normalize(poly next_p, ideal add_generators, syStrategy syzstr, int *g_l, int *p_l, int crit_comp)
Definition: syz3.cc:1026

◆ ratBiSqrfFactorize()

CFList ratBiSqrfFactorize ( const CanonicalForm G,
const Variable v = Variable (1) 
)
inline

factorize a squarefree bivariate polynomial over $ Q(\alpha) $.

@ return ratBiSqrfFactorize returns a list of monic factors, the first element is the leading coefficient.

Parameters
[in]Ga bivariate poly
[in]valgebraic variable

Definition at line 47 of file facBivar.h.

50 {
51  CFMap N;
52  CanonicalForm F= compress (G, N);
53  CanonicalForm contentX= content (F, 1); //erwarte hier primitiven input: primitiv über Z bzw. Z[a]
54  CanonicalForm contentY= content (F, 2);
55  F /= (contentX*contentY);
56  CFFList contentXFactors, contentYFactors;
57  if (v.level() != 1)
58  {
59  contentXFactors= factorize (contentX, v);
60  contentYFactors= factorize (contentY, v);
61  }
62  else
63  {
64  contentXFactors= factorize (contentX);
65  contentYFactors= factorize (contentY);
66  }
67  if (contentXFactors.getFirst().factor().inCoeffDomain())
68  contentXFactors.removeFirst();
69  if (contentYFactors.getFirst().factor().inCoeffDomain())
70  contentYFactors.removeFirst();
71  if (F.inCoeffDomain())
72  {
73  CFList result;
74  for (CFFListIterator i= contentXFactors; i.hasItem(); i++)
75  result.append (N (i.getItem().factor()));
76  for (CFFListIterator i= contentYFactors; i.hasItem(); i++)
77  result.append (N (i.getItem().factor()));
78  if (isOn (SW_RATIONAL))
79  {
80  normalize (result);
81  result.insert (Lc (G));
82  }
83  return result;
84  }
85 
86  mpz_t * M=new mpz_t [4];
87  mpz_init (M[0]);
88  mpz_init (M[1]);
89  mpz_init (M[2]);
90  mpz_init (M[3]);
91 
92  mpz_t * S=new mpz_t [2];
93  mpz_init (S[0]);
94  mpz_init (S[1]);
95 
96  F= compress (F, M, S);
97  CFList result= biFactorize (F, v);
98  for (CFListIterator i= result; i.hasItem(); i++)
99  i.getItem()= N (decompress (i.getItem(), M, S));
100  for (CFFListIterator i= contentXFactors; i.hasItem(); i++)
101  result.append (N(i.getItem().factor()));
102  for (CFFListIterator i= contentYFactors; i.hasItem(); i++)
103  result.append (N (i.getItem().factor()));
104  if (isOn (SW_RATIONAL))
105  {
106  normalize (result);
107  result.insert (Lc (G));
108  }
109 
110  mpz_clear (M[0]);
111  mpz_clear (M[1]);
112  mpz_clear (M[2]);
113  mpz_clear (M[3]);
114  delete [] M;
115 
116  mpz_clear (S[0]);
117  mpz_clear (S[1]);
118  delete [] S;
119 
120  return result;
121 }
CFList biFactorize(const CanonicalForm &F, const Variable &v)
Definition: facBivar.cc:188

◆ TIMING_DEFINE_PRINT()

TIMING_DEFINE_PRINT ( fac_bi_sqrf  ) const &
Returns
biFactorize returns a list of factors of F. If F is not monic its leading coefficient is not outputted.

Variable Documentation

◆ v

< [in] a sqrfree bivariate poly

< [in] some algebraic variable

Definition at line 38 of file facBivar.h.