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facFqBivar.cc
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facFqBivar.cc
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/*****************************************************************************\
* Computer Algebra System SINGULAR
\*****************************************************************************/
/** @file facFqBivar.cc
*
* This file provides functions for factorizing a bivariate polynomial over
* \f$ F_{p} \f$ , \f$ F_{p}(\alpha ) \f$ or GF, based on "Modern Computer
* Algebra, Chapter 15" by J. von zur Gathen & J. Gerhard and "Factoring
* multivariate polynomials over a finite field" by L. Bernardin.
* Factor Recombination is described in "Factoring polynomials over global
* fields" by K. Belabas, M. van Hoeij, J. Klueners, A. Steel
*
*
* @author Martin Lee
*
**/
/*****************************************************************************/
#include "config.h"
#include <math.h>
#include "cf_assert.h"
#include "cf_util.h"
#include "debug.h"
#include "timing.h"
#include "canonicalform.h"
#include "cf_defs.h"
#include "cf_map_ext.h"
#include "cf_random.h"
#include "facHensel.h"
#include "facMul.h"
#include "cf_map.h"
#include "cf_irred.h"
#include "facFqBivarUtil.h"
#include "facFqBivar.h"
#include "cfNewtonPolygon.h"
#ifdef HAVE_NTL
#include "NTLconvert.h"
#endif
#ifdef HAVE_FLINT
#include "FLINTconvert.h"
#include "flint/nmod_poly_factor.h"
#include "flint/fq_nmod_poly_factor.h"
#endif
TIMING_DEFINE_PRINT(fac_fq_uni_factorizer)
TIMING_DEFINE_PRINT(fac_fq_bi_hensel_lift)
TIMING_DEFINE_PRINT(fac_fq_bi_factor_recombination)
TIMING_DEFINE_PRINT(fac_fq_bi_evaluation)
TIMING_DEFINE_PRINT(fac_fq_bi_shift_to_zero)
TIMING_DEFINE_PRINT(fac_fq_logarithmic)
TIMING_DEFINE_PRINT(fac_fq_compute_lattice_lift)
TIMING_DEFINE_PRINT(fac_fq_till_reduced)
TIMING_DEFINE_PRINT(fac_fq_reconstruction)
TIMING_DEFINE_PRINT(fac_fq_lift)
TIMING_DEFINE_PRINT(fac_fq_uni_total)
CanonicalForm prodMod0 (const CFList& L, const CanonicalForm& M, const modpk& b)
{
if (L.isEmpty())
return 1;
else if (L.length() == 1)
return mod (L.getFirst()(0, 1) , M);
else if (L.length() == 2)
return mod (mulNTL (L.getFirst()(0, 1),L.getLast()(0, 1), b), M);
else
{
int l= L.length()/2;
CFListIterator i= L;
CFList tmp1, tmp2;
CanonicalForm buf1, buf2;
for (int j= 1; j <= l; j++, i++)
tmp1.append (i.getItem());
tmp2= Difference (L, tmp1);
buf1= prodMod0 (tmp1, M, b);
buf2= prodMod0 (tmp2, M, b);
return mod (mulNTL (buf1,buf2, b), M);
}
}
#if defined(HAVE_NTL) || defined(HAVE_FLINT)
CanonicalForm evalPoint (const CanonicalForm& F, CanonicalForm & eval,
const Variable& alpha, CFList& list, const bool& GF,
bool& fail)
{
fail= false;
Variable x= Variable(2);
Variable y= Variable(1);
FFRandom genFF;
GFRandom genGF;
CanonicalForm random, mipo;
double bound;
int p= getCharacteristic ();
if (alpha.level() != 1)
{
mipo= getMipo (alpha);
int d= degree (mipo);
bound= pow ((double) p, (double) d);
}
else if (GF)
{
int d= getGFDegree();
bound= ipower (p, d);
}
else
bound= p;
random= 0;
do
{
if (list.length() >= bound)
{
fail= true;
break;
}
if (list.isEmpty())
random= 0;
else if (GF)
{
if (list.length() == 1)
random= getGFGenerator();
else
random= genGF.generate();
}
else if (list.length() < p || alpha.level() == 1)
random= genFF.generate();
else if (alpha != x && list.length() >= p)
{
if (list.length() == p)
random= alpha;
else
{
AlgExtRandomF genAlgExt (alpha);
random= genAlgExt.generate();
}
}
if (find (list, random)) continue;
eval= F (random, x);
if (degree (eval) != degree (F, y))
{ //leading coeff vanishes
if (!find (list, random))
list.append (random);
continue;
}
if (degree (gcd (deriv (eval, eval.mvar()), eval), eval.mvar()) > 0)
{ //evaluated polynomial is not squarefree
if (!find (list, random))
list.append (random);
continue;
}
} while (find (list, random));
return random;
}
#if defined(HAVE_NTL) || defined(HAVE_FLINT)
CFList
uniFactorizer (const CanonicalForm& A, const Variable& alpha, const bool& GF)
{
Variable x= A.mvar();
if (A.inCoeffDomain())
return CFList();
ASSERT (A.isUnivariate(),
"univariate polynomial expected or constant expected");
CFFList factorsA;
if (GF)
{
int k= getGFDegree();
char cGFName= gf_name;
CanonicalForm mipo= gf_mipo;
setCharacteristic (getCharacteristic());
Variable beta= rootOf (mipo.mapinto());
CanonicalForm buf= GF2FalphaRep (A, beta);
#ifdef HAVE_NTL
if (getCharacteristic() > 2)
#else
if (getCharacteristic() > 0)
#endif
{
#if (HAVE_FLINT && __FLINT_RELEASE >= 20400)
nmod_poly_t FLINTmipo, leadingCoeff;
fq_nmod_ctx_t fq_con;
fq_nmod_poly_t FLINTA;
fq_nmod_poly_factor_t FLINTFactorsA;
nmod_poly_init (FLINTmipo, getCharacteristic());
convertFacCF2nmod_poly_t (FLINTmipo, mipo.mapinto());
fq_nmod_ctx_init_modulus (fq_con, FLINTmipo, "Z");
convertFacCF2Fq_nmod_poly_t (FLINTA, buf, fq_con);
fq_nmod_poly_make_monic (FLINTA, FLINTA, fq_con);
fq_nmod_poly_factor_init (FLINTFactorsA, fq_con);
nmod_poly_init (leadingCoeff, getCharacteristic());
fq_nmod_poly_factor (FLINTFactorsA, leadingCoeff, FLINTA, fq_con);
factorsA= convertFLINTFq_nmod_poly_factor2FacCFFList (FLINTFactorsA, x,
beta, fq_con);
fq_nmod_poly_factor_clear (FLINTFactorsA, fq_con);
fq_nmod_poly_clear (FLINTA, fq_con);
nmod_poly_clear (FLINTmipo);
nmod_poly_clear (leadingCoeff);
fq_nmod_ctx_clear (fq_con);
#else
if (fac_NTL_char != getCharacteristic())
{
fac_NTL_char= getCharacteristic();
zz_p::init (getCharacteristic());
}
zz_pX NTLMipo= convertFacCF2NTLzzpX (mipo.mapinto());
zz_pE::init (NTLMipo);
zz_pEX NTLA= convertFacCF2NTLzz_pEX (buf, NTLMipo);
MakeMonic (NTLA);
vec_pair_zz_pEX_long NTLFactorsA= CanZass (NTLA);
zz_pE multi= to_zz_pE (1);
factorsA= convertNTLvec_pair_zzpEX_long2FacCFFList (NTLFactorsA, multi,
x, beta);
#endif
}
#ifdef HAVE_NTL
else
{
GF2X NTLMipo= convertFacCF2NTLGF2X (mipo.mapinto());
GF2E::init (NTLMipo);
GF2EX NTLA= convertFacCF2NTLGF2EX (buf, NTLMipo);
MakeMonic (NTLA);
vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA);
GF2E multi= to_GF2E (1);
factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi,
x, beta);
}
#endif
setCharacteristic (getCharacteristic(), k, cGFName);
for (CFFListIterator i= factorsA; i.hasItem(); i++)
{
buf= i.getItem().factor();
buf= Falpha2GFRep (buf);
i.getItem()= CFFactor (buf, i.getItem().exp());
}
prune (beta);
}
else if (alpha.level() != 1)
{
#ifdef HAVE_NTL
if (getCharacteristic() > 2)
#else
if (getCharacteristic() > 0)
#endif
{
#if (HAVE_FLINT && __FLINT_RELEASE >= 20400)
nmod_poly_t FLINTmipo, leadingCoeff;
fq_nmod_ctx_t fq_con;
fq_nmod_poly_t FLINTA;
fq_nmod_poly_factor_t FLINTFactorsA;
nmod_poly_init (FLINTmipo, getCharacteristic());
convertFacCF2nmod_poly_t (FLINTmipo, getMipo (alpha));
fq_nmod_ctx_init_modulus (fq_con, FLINTmipo, "Z");
convertFacCF2Fq_nmod_poly_t (FLINTA, A, fq_con);
fq_nmod_poly_make_monic (FLINTA, FLINTA, fq_con);
fq_nmod_poly_factor_init (FLINTFactorsA, fq_con);
nmod_poly_init (leadingCoeff, getCharacteristic());
fq_nmod_poly_factor (FLINTFactorsA, leadingCoeff, FLINTA, fq_con);
factorsA= convertFLINTFq_nmod_poly_factor2FacCFFList (FLINTFactorsA, x,
alpha, fq_con);
fq_nmod_poly_factor_clear (FLINTFactorsA, fq_con);
fq_nmod_poly_clear (FLINTA, fq_con);
nmod_poly_clear (FLINTmipo);
nmod_poly_clear (leadingCoeff);
fq_nmod_ctx_clear (fq_con);
#else
if (fac_NTL_char != getCharacteristic())
{
fac_NTL_char= getCharacteristic();
zz_p::init (getCharacteristic());
}
zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha));
zz_pE::init (NTLMipo);
zz_pEX NTLA= convertFacCF2NTLzz_pEX (A, NTLMipo);
MakeMonic (NTLA);
vec_pair_zz_pEX_long NTLFactorsA= CanZass (NTLA);
zz_pE multi= to_zz_pE (1);
factorsA= convertNTLvec_pair_zzpEX_long2FacCFFList (NTLFactorsA, multi,
x, alpha);
#endif
}
#ifdef HAVE_NTL
else
{
GF2X NTLMipo= convertFacCF2NTLGF2X (getMipo (alpha));
GF2E::init (NTLMipo);
GF2EX NTLA= convertFacCF2NTLGF2EX (A, NTLMipo);
MakeMonic (NTLA);
vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA);
GF2E multi= to_GF2E (1);
factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi,
x, alpha);
}
#endif
}
else
{
#ifdef HAVE_FLINT
#ifdef HAVE_NTL
if (degree (A) < 300)
#endif
{
nmod_poly_t FLINTA;
convertFacCF2nmod_poly_t (FLINTA, A);
nmod_poly_factor_t result;
nmod_poly_factor_init (result);
mp_limb_t leadingCoeff= nmod_poly_factor (result, FLINTA);
factorsA= convertFLINTnmod_poly_factor2FacCFFList (result, leadingCoeff, x);
if (factorsA.getFirst().factor().inCoeffDomain())
factorsA.removeFirst();
nmod_poly_factor_clear (result);
nmod_poly_clear (FLINTA);
}
#ifdef HAVE_NTL
else
#endif
#endif /* HAVE_FLINT */
#ifdef HAVE_NTL
if (getCharacteristic() > 2)
{
if (fac_NTL_char != getCharacteristic())
{
fac_NTL_char= getCharacteristic();
zz_p::init (getCharacteristic());
}
zz_pX NTLA= convertFacCF2NTLzzpX (A);
MakeMonic (NTLA);
vec_pair_zz_pX_long NTLFactorsA= CanZass (NTLA);
zz_p multi= to_zz_p (1);
factorsA= convertNTLvec_pair_zzpX_long2FacCFFList (NTLFactorsA, multi,
x);
}
else
{
GF2X NTLA= convertFacCF2NTLGF2X (A);
vec_pair_GF2X_long NTLFactorsA= CanZass (NTLA);
GF2 multi= to_GF2 (1);
factorsA= convertNTLvec_pair_GF2X_long2FacCFFList (NTLFactorsA, multi,
x);
}
#endif
}
CFList uniFactors;
for (CFFListIterator i= factorsA; i.hasItem(); i++)
uniFactors.append (i.getItem().factor());
return uniFactors;
}
#endif
#if defined(HAVE_NTL) || defined(HAVE_FLINT)
/// naive factor recombination as decribed in "Factoring
/// multivariate polynomials over a finite field" by L Bernardin.
CFList
extFactorRecombination (CFList& factors, CanonicalForm& F,
const CanonicalForm& N, const ExtensionInfo& info,
DegreePattern& degs, const CanonicalForm& eval, int s,
int thres)
{
if (factors.length() == 0)
{
F= 1;
return CFList();
}
if (F.inCoeffDomain())
return CFList();
Variable alpha= info.getAlpha();
Variable beta= info.getBeta();
CanonicalForm gamma= info.getGamma();
CanonicalForm delta= info.getDelta();
int k= info.getGFDegree();
CanonicalForm M= N;
int l= degree (N);
Variable y= F.mvar();
Variable x= Variable (1);
CFList source, dest;
if (degs.getLength() <= 1 || factors.length() == 1)
{
CFList result= CFList(mapDown (F(y-eval, y), info, source, dest));
F= 1;
return result;
}
DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, M) == F " <<
(mod (LC (F, 1)*prodMod (factors, M), M)/Lc (mod (LC (F, 1)*prodMod (factors, M), M)) == F/Lc (F)));
int degMipoBeta= 1;
if (!k && beta.level() != 1)
degMipoBeta= degree (getMipo (beta));
CFList T, S, Diff;
T= factors;
CFList result;
CanonicalForm buf, buf2, quot;
buf= F;
CanonicalForm g, LCBuf= LC (buf, x);
int * v= new int [T.length()];
for (int i= 0; i < T.length(); i++)
v[i]= 0;
CFArray TT;
DegreePattern bufDegs1, bufDegs2;
bufDegs1= degs;
int subsetDeg;
TT= copy (factors);
bool nosubset= false;
bool recombination= false;
bool trueFactor= false;
CanonicalForm test;
CanonicalForm buf0= buf (0, x)*LCBuf;
while (T.length() >= 2*s && s <= thres)
{
while (nosubset == false)
{
if (T.length() == s)
{
delete [] v;
if (recombination)
{
T.insert (LCBuf);
g= prodMod (T, M);
T.removeFirst();
g /= content(g);
g= g (y - eval, y);
g /= Lc (g);
appendTestMapDown (result, g, info, source, dest);
F= 1;
return result;
}
else
{
appendMapDown (result, F (y - eval, y), info, source, dest);
F= 1;
return result;
}
}
S= subset (v, s, TT, nosubset);
if (nosubset) break;
subsetDeg= subsetDegree (S);
// skip those combinations that are not possible
if (!degs.find (subsetDeg))
continue;
else
{
test= prodMod0 (S, M);
test *= LCBuf;
test = mod (test, M);
if (fdivides (test, buf0))
{
S.insert (LCBuf);
g= prodMod (S, M);
S.removeFirst();
g /= content (g, x);
if (fdivides (g, buf, quot))
{
buf2= g (y - eval, y);
buf2 /= Lc (buf2);
if (!k && beta.level() == 1)
{
if (degree (buf2, alpha) < degMipoBeta)
{
buf= quot;
LCBuf= LC (buf, x);
recombination= true;
appendTestMapDown (result, buf2, info, source, dest);
trueFactor= true;
}
}
else
{
if (!isInExtension (buf2, gamma, k, delta, source, dest))
{
buf= quot;
LCBuf= LC (buf, x);
recombination= true;
appendTestMapDown (result, buf2, info, source, dest);
trueFactor= true;
}
}
if (trueFactor)
{
T= Difference (T, S);
l -= degree (g);
M= power (y, l);
buf0= buf (0, x)*LCBuf;
// compute new possible degree pattern
bufDegs2= DegreePattern (T);
bufDegs1.intersect (bufDegs2);
bufDegs1.refine ();
if (T.length() < 2*s || T.length() == s ||
bufDegs1.getLength() == 1)
{
delete [] v;
if (recombination)
{
buf= buf (y-eval,y);
buf /= Lc (buf);
appendTestMapDown (result, buf, info, source,
dest);
F= 1;
return result;
}
else
{
appendMapDown (result, F (y - eval, y), info, source, dest);
F= 1;
return result;
}
}
trueFactor= false;
TT= copy (T);
indexUpdate (v, s, T.length(), nosubset);
if (nosubset) break;
}
}
}
}
}
s++;
if (T.length() < 2*s || T.length() == s)
{
delete [] v;
if (recombination)
{
buf= buf (y-eval,y);
buf /= Lc (buf);
appendTestMapDown (result, buf, info, source, dest);
F= 1;
return result;
}
else
{
appendMapDown (result, F (y - eval, y), info, source, dest);
F= 1;
return result;
}
}
for (int i= 0; i < T.length(); i++)
v[i]= 0;
nosubset= false;
}
if (T.length() < 2*s)
{
appendMapDown (result, F (y - eval, y), info, source, dest);
F= 1;
delete [] v;
return result;
}
if (s > thres)
{
factors= T;
F= buf;
degs= bufDegs1;
}
delete [] v;
return result;
}
#endif
/// naive factor recombination as decribed in "Factoring
/// multivariate polynomials over a finite field" by L Bernardin.
CFList
factorRecombination (CFList& factors, CanonicalForm& F,
const CanonicalForm& N, DegreePattern& degs, const
CanonicalForm& eval, int s, int thres, const modpk& b,
const CanonicalForm& den
)
{
if (factors.length() == 0)
{
F= 1;
return CFList ();
}
if (F.inCoeffDomain())
return CFList();
Variable y= Variable (2);
if (degs.getLength() <= 1 || factors.length() == 1)
{
CFList result= CFList (F(y-eval,y));
F= 1;
return result;
}
#ifdef DEBUGOUTPUT
if (b.getp() == 0)
DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, N) == F " <<
(mod (LC (F, 1)*prodMod (factors, N),N)/Lc (mod (LC (F, 1)*prodMod (factors, N),N)) == F/Lc(F)));
else
DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, N) == F " <<
(mod (b(LC (F, 1)*prodMod (factors, N)),N)/Lc (mod (b(LC (F, 1)*prodMod (factors, N)),N)) == F/Lc(F)));
#endif
CFList T, S;
CanonicalForm M= N;
int l= degree (N);
T= factors;
CFList result;
Variable x= Variable (1);
CanonicalForm denom= den, denQuot;
CanonicalForm LCBuf= LC (F, x)*denom;
CanonicalForm g, quot, buf= F;
int * v= new int [T.length()];
for (int i= 0; i < T.length(); i++)
v[i]= 0;
bool nosubset= false;
CFArray TT;
DegreePattern bufDegs1, bufDegs2;
bufDegs1= degs;
int subsetDeg;
TT= copy (factors);
bool recombination= false;
CanonicalForm test;
bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) ||
getCharacteristic() > 0;
if (!isRat)
On (SW_RATIONAL);
CanonicalForm buf0= mulNTL (buf (0, x), LCBuf);
if (!isRat)
Off (SW_RATIONAL);
while (T.length() >= 2*s && s <= thres)
{
while (nosubset == false)
{
if (T.length() == s)
{
delete [] v;
if (recombination)
{
T.insert (LCBuf);
g= prodMod (T, M);
if (b.getp() != 0)
g= b(g);
T.removeFirst();
g /= content (g,x);
result.append (g(y-eval,y));
F= 1;
return result;
}
else
{
result= CFList (F(y-eval,y));
F= 1;
return result;
}
}
S= subset (v, s, TT, nosubset);
if (nosubset) break;
subsetDeg= subsetDegree (S);
// skip those combinations that are not possible
if (!degs.find (subsetDeg))
continue;
else
{
if (!isRat)
On (SW_RATIONAL);
test= prodMod0 (S, M);
if (!isRat)
{
test *= bCommonDen (test);
Off (SW_RATIONAL);
}
test= mulNTL (test, LCBuf, b);
test= mod (test, M);
if (uniFdivides (test, buf0))
{
if (!isRat)
On (SW_RATIONAL);
S.insert (LCBuf);
g= prodMod (S, M);
S.removeFirst();
if (!isRat)
{
g *= bCommonDen(g);
Off (SW_RATIONAL);
}
if (b.getp() != 0)
g= b(g);
if (!isRat)
On (SW_RATIONAL);
g /= content (g, x);
if (!isRat)
{
On (SW_RATIONAL);
if (!Lc (g).inBaseDomain())
g /= Lc (g);
g *= bCommonDen (g);
Off (SW_RATIONAL);
g /= icontent (g);
On (SW_RATIONAL);
}
if (fdivides (g, buf, quot))
{
denom *= abs (lc (g));
recombination= true;
result.append (g (y-eval,y));
if (b.getp() != 0)
{
denQuot= bCommonDen (quot);
buf= quot*denQuot;
Off (SW_RATIONAL);
denom /= gcd (denom, denQuot);
On (SW_RATIONAL);
}
else
buf= quot;
LCBuf= LC (buf, x)*denom;
T= Difference (T, S);
l -= degree (g);
M= power (y, l);
buf0= mulNTL (buf (0, x), LCBuf);
if (!isRat)
Off (SW_RATIONAL);
// compute new possible degree pattern
bufDegs2= DegreePattern (T);
bufDegs1.intersect (bufDegs2);
bufDegs1.refine ();
if (T.length() < 2*s || T.length() == s ||
bufDegs1.getLength() == 1)
{
delete [] v;
if (recombination)
{
result.append (buf (y-eval,y));
F= 1;
return result;
}
else
{
result= CFList (F (y-eval,y));
F= 1;
return result;
}
}
TT= copy (T);
indexUpdate (v, s, T.length(), nosubset);
if (nosubset) break;
}
if (!isRat)
Off (SW_RATIONAL);
}
}
}
s++;
if (T.length() < 2*s || T.length() == s)
{
delete [] v;
if (recombination)
{
result.append (buf(y-eval,y));
F= 1;
return result;
}
else
{
result= CFList (F(y-eval,y));
F= 1;
return result;
}
}
for (int i= 0; i < T.length(); i++)
v[i]= 0;
nosubset= false;
}
delete [] v;
if (T.length() < 2*s)
{
result.append (F(y-eval,y));
F= 1;
return result;
}
if (s > thres)
{
factors= T;
F= buf;
degs= bufDegs1;
}
return result;
}
#if defined(HAVE_NTL) || defined(HAVE_FLINT)
Variable chooseExtension (const Variable & alpha, const Variable& beta, int k)
{
int i=1, m= 2;
// extension of F_p needed
if (alpha.level() == 1 && beta.level() == 1 && k == 1)
{
i= 1;
m= 2;
} //extension of F_p(alpha) needed but want to factorize over F_p
else if (alpha.level() != 1 && beta.level() == 1 && k == 1)
{
i= 1;
m= degree (getMipo (alpha)) + 1;
} //extension of F_p(alpha) needed for first time
else if (alpha.level() != 1 && beta.level() == 1 && k != 1)
{
i= 2;
m= degree (getMipo (alpha));
}
else if (alpha.level() != 1 && beta.level() != 1 && k != 1)
{
m= degree (getMipo (beta));
i= degree (getMipo (alpha))/m + 1;
}
#if defined(HAVE_FLINT)
nmod_poly_t Irredpoly;
nmod_poly_init(Irredpoly,getCharacteristic());
nmod_poly_randtest_monic_irreducible(Irredpoly,FLINTrandom,i*m+1);
CanonicalForm newMipo= convertnmod_poly_t2FacCF(Irredpoly,Variable (1));
#elif defined(HAVE_NTL)
if (fac_NTL_char != getCharacteristic())
{
fac_NTL_char= getCharacteristic();
zz_p::init (getCharacteristic());
}
zz_pX NTLIrredpoly;
BuildIrred (NTLIrredpoly, i*m);
CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1));
#else
factoryError("NTL/FLINT missing: chooseExtension");
#endif
return rootOf (newMipo);
}
#endif
void
earlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList&
factors, int& adaptedLiftBound, int*& factorsFoundIndex,
DegreePattern& degs, bool& success, int deg, const
CanonicalForm& eval, const modpk& b, CanonicalForm& den)
{
DegreePattern bufDegs1= degs;
DegreePattern bufDegs2;
CFList T= factors;
CanonicalForm buf= F;
Variable x= Variable (1);
Variable y= Variable (2);
CanonicalForm g, quot;
CanonicalForm M= power (F.mvar(), deg);
adaptedLiftBound= 0;
int d= degree (F), l= 0;
bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) ||
getCharacteristic() > 0;
if (!isRat)
On (SW_RATIONAL);
if (b.getp() != 0)
buf *= bCommonDen (buf);
CanonicalForm LCBuf= LC (buf, x)*den;
CanonicalForm buf0= mulNTL (buf (0,x), LCBuf);
CanonicalForm buf1= mulNTL (buf (1,x), LCBuf);
if (!isRat)
Off (SW_RATIONAL);
CanonicalForm test0, test1;
CanonicalForm denQuot;
for (CFListIterator i= factors; i.hasItem(); i++, l++)
{
if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1)
continue;
else
{
test1= mod (mulNTL (i.getItem() (1,x), LCBuf, b), M);
if (uniFdivides (test1, buf1))
{
test0= mod (mulNTL (i.getItem() (0,x), LCBuf, b), M);
if (uniFdivides (test0, buf0))
{
if (!isRat)
On (SW_RATIONAL);
g= mulMod2 (i.getItem(), LCBuf, M);
if (!isRat)
{
g *= bCommonDen(g);
Off (SW_RATIONAL);
}
if (b.getp() != 0)
g= b(g);
if (!isRat)
On (SW_RATIONAL);
g /= content (g, x);
if (!isRat)
{
On (SW_RATIONAL);
if (!Lc (g).inBaseDomain())
g /= Lc (g);
g *= bCommonDen (g);
Off (SW_RATIONAL);
g /= icontent (g);
On (SW_RATIONAL);
}
if (fdivides (g, buf, quot))
{
den *= abs (lc (g));
reconstructedFactors.append (g (y-eval,y));
factorsFoundIndex[l]= 1;
if (b.getp() != 0)
{
denQuot= bCommonDen (quot);
buf= quot*denQuot;
Off (SW_RATIONAL);
den /= gcd (den, denQuot);
On (SW_RATIONAL);
}
else
buf= quot;
d -= degree (g);
LCBuf= LC (buf, x)*den;
buf0= mulNTL (buf (0,x), LCBuf);
buf1= mulNTL (buf (1,x), LCBuf);
if (!isRat)
Off (SW_RATIONAL);
T= Difference (T, CFList (i.getItem()));
F= buf;
// compute new possible degree pattern
bufDegs2= DegreePattern (T);
bufDegs1.intersect (bufDegs2);
bufDegs1.refine ();
if (bufDegs1.getLength() <= 1)
{
if (!buf.inCoeffDomain())
{
reconstructedFactors.append (buf (y-eval,y));
F= 1;
}
break;
}
}
if (!isRat)
Off (SW_RATIONAL);
}
}
}
}
adaptedLiftBound= d + 1;
if (adaptedLiftBound < deg)
{
degs= bufDegs1;
success= true;
}
if (bufDegs1.getLength() <= 1)
degs= bufDegs1;
}
void
earlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList&
factors, int& adaptedLiftBound, int*& factorsFoundIndex,
DegreePattern& degs, bool& success, int deg, const
CanonicalForm& eval, const modpk& b)
{
CanonicalForm den= 1;
earlyFactorDetection (reconstructedFactors, F, factors, adaptedLiftBound,
factorsFoundIndex, degs, success, deg, eval, b, den);
}
void
extEarlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList&
factors,int& adaptedLiftBound, int*& factorsFoundIndex,
DegreePattern& degs, bool& success, const
ExtensionInfo& info, const CanonicalForm& eval, int deg
)
{
Variable alpha= info.getAlpha();
Variable beta= info.getBeta();
CanonicalForm gamma= info.getGamma();
CanonicalForm delta= info.getDelta();
int k= info.getGFDegree();
DegreePattern bufDegs1= degs, bufDegs2;
CFList result;
CFList T= factors;
Variable y= F.mvar();
Variable x= Variable (1);