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Functions | Variables
facBivar.h File Reference
#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 "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]f[in] poly over Z
[in]p[in] some 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]f[in] poly over Z[a]
[in]p[in] some positive integer
[in]mipo[in] minimal 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 }

◆ conv()

CFList conv ( const CFFList L)

convert a CFFList to a CFList by dropping the multiplicity

Parameters
[in]L[in] a 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 }

◆ 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]f[in] poly over Z or Z[a]
[in,out]start[in,out] index 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 }

◆ 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]G[in] a bivariate poly
[in]v[in] algebraic variable
[in]substCheck[in] enables substitute check

Definition at line 128 of file facBivar.h.

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 }

◆ 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]G[in] a bivariate poly
[in]v[in] algebraic variable

Definition at line 46 of file facBivar.h.

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 }

◆ 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 36 of file facBivar.h.

i
int i
Definition: facBivar.cc:41
SW_RATIONAL
static const int SW_RATIONAL
set to 1 for computations over Q
Definition: cf_defs.h:28
isOn
bool isOn(int sw)
switches
Definition: canonicalform.cc:1912
j
int j
Definition: facHensel.cc:105
f
FILE * f
Definition: checklibs.c:9
CFIterator
class to iterate through CanonicalForm's
Definition: cf_iter.h:44
result
return result
Definition: facAbsBiFact.cc:76
degrees
int * degrees(const CanonicalForm &f, int *degs=0)
int * degrees ( const CanonicalForm & f, int * degs )
Definition: cf_ops.cc:493
CFMap
class CFMap
Definition: cf_map.h:85
power
CanonicalForm power(const CanonicalForm &f, int n)
exponentiation
Definition: canonicalform.cc:1837
mod
CF_NO_INLINE CanonicalForm mod(const CanonicalForm &, const CanonicalForm &)
Definition: cf_inline.cc:564
N
const CanonicalForm CFMap CFMap & N
Definition: cfEzgcd.cc:49
cf_getBigPrime
int cf_getBigPrime(int i)
Definition: cf_primes.cc:39
CanonicalForm
factory's main class
Definition: canonicalform.h:83
reverseSubst
CanonicalForm reverseSubst(const CanonicalForm &F, const int d, const Variable &x)
reverse a substitution x^d->x
Definition: facFqBivarUtil.cc:1295
maxNorm
CanonicalForm maxNorm(const CanonicalForm &f)
CanonicalForm maxNorm ( const CanonicalForm & f )
Definition: cf_algorithm.cc:534
i
int i
Definition: cfEzgcd.cc:125
Lc
CanonicalForm Lc(const CanonicalForm &f)
Definition: canonicalform.h:300
abs
Rational abs(const Rational &a)
Definition: GMPrat.cc:439
M
#define M
Definition: sirandom.c:24
k
int k
Definition: facBivar.cc:41
content
CanonicalForm content(const CanonicalForm &)
CanonicalForm content ( const CanonicalForm & f )
Definition: cf_gcd.cc:180
TIMING_START
TIMING_START(fac_alg_resultant)
lc
CanonicalForm lc(const CanonicalForm &f)
Definition: canonicalform.h:297
M
int M
Definition: facBivar.cc:41
compress
CanonicalForm compress(const CanonicalForm &f, CFMap &m)
CanonicalForm compress ( const CanonicalForm & f, CFMap & m )
Definition: cf_map.cc:210
LcF
CanonicalForm LcF
Definition: facAbsBiFact.cc:51
ratBiSqrfFactorize
CFList ratBiSqrfFactorize(const CanonicalForm &G, const Variable &v=Variable(1))
factorize a squarefree bivariate polynomial over .
Definition: facBivar.h:46
Variable::level
int level() const
Definition: factory.h:134
factorize
CFFList factorize(const CanonicalForm &f, bool issqrfree=false)
factorization over or
Definition: cf_factor.cc:390
decompress
CanonicalForm decompress(const CanonicalForm &F, const mpz_t *inverseM, const mpz_t *A)
decompress a bivariate poly
Definition: cfNewtonPolygon.cc:853
List::removeFirst
void removeFirst()
Definition: ftmpl_list.cc:287
substituteCheck
int substituteCheck(const CanonicalForm &F, const Variable &x)
check if a substitution x^n->x is possible
Definition: facFqBivarUtil.cc:1089
List::getFirst
T getFirst() const
Definition: ftmpl_list.cc:279
Factor
Definition: ftmpl_factor.h:18
p
int p
Definition: facBivar.cc:39
bCommonDen
CanonicalForm bCommonDen(const CanonicalForm &f)
CanonicalForm bCommonDen ( const CanonicalForm & f )
Definition: cf_algorithm.cc:293
CanonicalForm::inCoeffDomain
bool inCoeffDomain() const
Definition: canonicalform.cc:119
TIMING_END_AND_PRINT
TIMING_END_AND_PRINT(fac_alg_resultant, "time to compute resultant0: ")
normalize
static poly normalize(poly next_p, ideal add_generators, syStrategy syzstr, int *g_l, int *p_l, int crit_comp)
Definition: syz3.cc:1027
Variable
factory's class for variables
Definition: factory.h:118
B
b *CanonicalForm B
Definition: facBivar.cc:52
b
CanonicalForm b
Definition: facBivar.cc:42
sqrFree
CFFList sqrFree(const CanonicalForm &f, bool sort=false)
squarefree factorization
Definition: cf_factor.cc:757
Union
template List< Variable > Union(const List< Variable > &, const List< Variable > &)
v
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:37
mipo
CanonicalForm mipo
Definition: facAlgExt.cc:57
List< CanonicalForm >
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
Definition: facBivar.cc:61
tmp2
CFList tmp2
Definition: facFqBivar.cc:70
biFactorize
CFList biFactorize(const CanonicalForm &F, const Variable &v)
Definition: facBivar.cc:187
ratBiFactorize
CFFList ratBiFactorize(const CanonicalForm &G, const Variable &v=Variable(1), bool substCheck=true)
factorize a bivariate polynomial over
Definition: facBivar.h:128
G
static TreeM * G
Definition: janet.cc:32
CanonicalForm::level
int level() const
level() returns the level of CO.
Definition: canonicalform.cc:543
CFFactor
Factor< CanonicalForm > CFFactor
Definition: canonicalform.h:385
List::append
void append(const T &)
Definition: ftmpl_list.cc:256
subst
CanonicalForm subst(const CanonicalForm &f, const CFList &a, const CFList &b, const CanonicalForm &Rstar, bool isFunctionField)
Definition: facAlgFuncUtil.cc:120
modpk
return modpk(p, k)
degree
int degree(const CanonicalForm &f)
Definition: canonicalform.h:309
List::insert
void insert(const T &)
Definition: ftmpl_list.cc:193
ListIterator
Definition: ftmpl_list.h:17
DELETE_ARRAY
DELETE_ARRAY(degs)