facFqBivar.cc File Reference

This file provides functions for factorizing a bivariate polynomial over , 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. More...

#include "config.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"
#include "NTLconvert.h"
#include "FLINTconvert.h"

Go to the source code of this file.

Functions
	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
else	if (L.length()==1) return mod(L.getFirst()(0
else L	getLast ()(0
	for (int j=1;j<=l;j++, i++) tmp1.append(i.getItem())
return	mod (mulNTL(buf1, buf2, b), M)
CanonicalForm	evalPoint (const CanonicalForm &F, CanonicalForm &eval, const Variable &alpha, CFList &list, const bool &GF, bool &fail)
	find an evaluation point p, s.t. F(p,y) is squarefree and . More...
CFList	uniFactorizer (const CanonicalForm &A, const Variable &alpha, const bool &GF)
	Univariate factorization of squarefree monic polys over finite fields via NTL. If the characteristic is even special GF2 routines of NTL are used. More...
CFList	extFactorRecombination (CFList &factors, CanonicalForm &F, const CanonicalForm &N, const ExtensionInfo &info, DegreePattern &degs, const CanonicalForm &eval, int s, int thres)
	naive factor recombination as decribed in "Factoring multivariate polynomials over a finite field" by L Bernardin. More...
CFList	factorRecombination (CFList &factors, CanonicalForm &F, const CanonicalForm &N, DegreePattern &degs, const CanonicalForm &eval, int s, int thres, const modpk &b, const CanonicalForm &den)
	naive factor recombination as decribed in "Factoring multivariate polynomials over a finite field" by L Bernardin. More...
Variable	chooseExtension (const Variable &alpha, const Variable &beta, int k)
	chooses a field extension. More...
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)
void	earlyFactorDetection (CFList &reconstructedFactors, CanonicalForm &F, CFList &factors, int &adaptedLiftBound, int *&factorsFoundIndex, DegreePattern &degs, bool &success, int deg, const CanonicalForm &eval, const modpk &b)
	detects factors of F at stage deg of Hensel lifting. No combinations of more than one factor are tested. Lift bound and possible degree pattern are updated. More...
void	extEarlyFactorDetection (CFList &reconstructedFactors, CanonicalForm &F, CFList &factors, int &adaptedLiftBound, int *&factorsFoundIndex, DegreePattern &degs, bool &success, const ExtensionInfo &info, const CanonicalForm &eval, int deg)
	detects factors of F at stage deg of Hensel lifting. No combinations of more than one factor are tested. Lift bound and possible degree pattern are updated. More...
int *	getCombinations (int *rightSide, int sizeOfRightSide, int &sizeOfOutput, int degreeLC)
int *	getLiftPrecisions (const CanonicalForm &F, int &sizeOfOutput, int degreeLC)
	compute lifting precisions from the shape of the Newton polygon of F More...
void	deleteFactors (CFList &factors, int *factorsFoundIndex)
CFList	henselLiftAndEarly (CanonicalForm &A, bool &earlySuccess, CFList &earlyFactors, DegreePattern &degs, int &liftBound, const CFList &uniFactors, const ExtensionInfo &info, const CanonicalForm &eval, modpk &b, CanonicalForm &den)
	hensel Lifting and early factor detection More...
CFList	henselLiftAndEarly (CanonicalForm &A, bool &earlySuccess, CFList &earlyFactors, DegreePattern &degs, int &liftBound, const CFList &uniFactors, const ExtensionInfo &info, const CanonicalForm &eval)
	hensel Lifting and early factor detection More...
long	isReduced (const mat_zz_p &M)
long	isReduced (const nmod_mat_t M)
long	isReduced (const mat_zz_pE &M)
int *	extractZeroOneVecs (const mat_zz_p &M)
int *	extractZeroOneVecs (const nmod_mat_t M)
int *	extractZeroOneVecs (const mat_zz_pE &M)
void	reconstructionTry (CFList &reconstructedFactors, CanonicalForm &F, const CFList &factors, const int liftBound, int &factorsFound, int *&factorsFoundIndex, mat_zz_pE &N, const CanonicalForm &eval, bool beenInThres)
void	reconstructionTry (CFList &reconstructedFactors, CanonicalForm &F, const CFList &factors, const int liftBound, int &factorsFound, int *&factorsFoundIndex, mat_zz_p &N, const CanonicalForm &eval, bool beenInThres)
void	reconstructionTry (CFList &reconstructedFactors, CanonicalForm &F, const CFList &factors, const int liftBound, int &factorsFound, int *&factorsFoundIndex, nmod_mat_t N, const CanonicalForm &eval, bool beenInThres)
CFList	reconstruction (CanonicalForm &G, CFList &factors, int *zeroOneVecs, int precision, const mat_zz_pE &N, const CanonicalForm &eval)
CFList	monicReconstruction (CanonicalForm &G, CFList &factors, int *zeroOneVecs, int precision, const mat_zz_pE &N)
CFList	extReconstruction (CanonicalForm &G, CFList &factors, int *zeroOneVecs, int precision, const mat_zz_p &N, const ExtensionInfo &info, const CanonicalForm &evaluation)
CFList	extReconstruction (CanonicalForm &G, CFList &factors, int *zeroOneVecs, int precision, const nmod_mat_t N, const ExtensionInfo &info, const CanonicalForm &evaluation)
CFList	reconstruction (CanonicalForm &G, CFList &factors, int *zeroOneVecs, int precision, const mat_zz_p &N, const CanonicalForm &eval)
CFList	reconstruction (CanonicalForm &G, CFList &factors, int *zeroOneVecs, int precision, const nmod_mat_t N, const CanonicalForm &eval)
void	extReconstructionTry (CFList &reconstructedFactors, CanonicalForm &F, const CFList &factors, const int liftBound, int &factorsFound, int *&factorsFoundIndex, mat_zz_p &N, bool beenInThres, const ExtensionInfo &info, const CanonicalForm &evaluation)
void	extReconstructionTry (CFList &reconstructedFactors, CanonicalForm &F, const CFList &factors, const int liftBound, int &factorsFound, int *&factorsFoundIndex, nmod_mat_t N, bool beenInThres, const ExtensionInfo &info, const CanonicalForm &evaluation)
int	liftAndComputeLattice (const CanonicalForm &F, int *bounds, int sizeBounds, int start, int liftBound, int minBound, CFList &factors, mat_zz_p &NTLN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, bool &irreducible)
int	liftAndComputeLattice (const CanonicalForm &F, int *bounds, int sizeBounds, int start, int liftBound, int minBound, CFList &factors, nmod_mat_t FLINTN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, bool &irreducible)
int	extLiftAndComputeLattice (const CanonicalForm &F, int *bounds, int sizeBounds, int liftBound, int minBound, int start, CFList &factors, mat_zz_p &NTLN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, bool &irreducible, const CanonicalForm &evaluation, const ExtensionInfo &info, CFList &source, CFList &dest)
int	extLiftAndComputeLattice (const CanonicalForm &F, int *bounds, int sizeBounds, int liftBound, int minBound, int start, CFList &factors, nmod_mat_t FLINTN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, bool &irreducible, const CanonicalForm &evaluation, const ExtensionInfo &info, CFList &source, CFList &dest)
int	liftAndComputeLattice (const CanonicalForm &F, int *bounds, int sizeBounds, int start, int liftBound, int minBound, CFList &factors, mat_zz_pE &NTLN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, bool &irreducible)
int	liftAndComputeLatticeFq2Fp (const CanonicalForm &F, int *bounds, int sizeBounds, int start, int liftBound, int minBound, CFList &factors, nmod_mat_t FLINTN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, bool &irreducible, const Variable &alpha)
CFList	increasePrecision (CanonicalForm &F, CFList &factors, int factorsFound, int oldNumCols, int oldL, int precision, const CanonicalForm &eval)
CFList	increasePrecision (CanonicalForm &F, CFList &factors, int factorsFound, int oldNumCols, int oldL, const Variable &, int precision, const CanonicalForm &eval)
CFList	extIncreasePrecision (CanonicalForm &F, CFList &factors, int factorsFound, int oldNumCols, int oldL, const CanonicalForm &evaluation, const ExtensionInfo &info, CFList &source, CFList &dest, int precision)
CFList	increasePrecision2 (const CanonicalForm &F, CFList &factors, const Variable &alpha, int precision)
CFList	increasePrecisionFq2Fp (CanonicalForm &F, CFList &factors, int factorsFound, int oldNumCols, int oldL, const Variable &alpha, int precision, const CanonicalForm &eval)
CFList	increasePrecision (CanonicalForm &F, CFList &factors, int oldL, int l, int d, int *bounds, CFArray &bufQ, nmod_mat_t FLINTN, const CanonicalForm &eval)
CFList	increasePrecision (CanonicalForm &F, CFList &factors, int oldL, int l, int d, int *bounds, CFArray &bufQ, mat_zz_pE &NTLN, const CanonicalForm &eval)
CFList	extIncreasePrecision (CanonicalForm &F, CFList &factors, int oldL, int l, int d, int *bounds, CFArray &bufQ, nmod_mat_t FLINTN, const CanonicalForm &evaluation, const ExtensionInfo &info, CFList &source, CFList &dest)
CFList	increasePrecisionFq2Fp (CanonicalForm &F, CFList &factors, int oldL, int l, int d, int *bounds, CFArray &bufQ, nmod_mat_t FLINTN, const Variable &alpha, const CanonicalForm &eval)
CFList	furtherLiftingAndIncreasePrecision (CanonicalForm &F, CFList &factors, int l, int liftBound, int d, int *bounds, nmod_mat_t FLINTN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, const CanonicalForm &eval)
CFList	furtherLiftingAndIncreasePrecision (CanonicalForm &F, CFList &factors, int l, int liftBound, int d, int *bounds, mat_zz_pE &NTLN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, const CanonicalForm &eval)
CFList	extFurtherLiftingAndIncreasePrecision (CanonicalForm &F, CFList &factors, int l, int liftBound, int d, int *bounds, nmod_mat_t FLINTN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, const CanonicalForm &evaluation, const ExtensionInfo &info, CFList &source, CFList &dest)
CFList	furtherLiftingAndIncreasePrecisionFq2Fp (CanonicalForm &F, CFList &factors, int l, int liftBound, int d, int *bounds, nmod_mat_t FLINTN, CFList &diophant, CFMatrix &M, CFArray &Pi, CFArray &bufQ, const Variable &alpha, const CanonicalForm &eval)
void	refineAndRestartLift (const CanonicalForm &F, const nmod_mat_t FLINTN, int liftBound, int l, CFList &factors, CFMatrix &M, CFArray &Pi, CFList &diophant)
void	refineAndRestartLift (const CanonicalForm &F, const mat_zz_pE &NTLN, int liftBound, int l, CFList &factors, CFMatrix &M, CFArray &Pi, CFList &diophant)
CFList	earlyReconstructionAndLifting (const CanonicalForm &F, const nmod_mat_t N, CanonicalForm &bufF, CFList &factors, int &l, int &factorsFound, bool beenInThres, CFMatrix &M, CFArray &Pi, CFList &diophant, bool symmetric, const CanonicalForm &evaluation)
CFList	earlyReconstructionAndLifting (const CanonicalForm &F, const mat_zz_pE &N, CanonicalForm &bufF, CFList &factors, int &l, int &factorsFound, bool beenInThres, CFMatrix &M, CFArray &Pi, CFList &diophant, bool symmetric, const CanonicalForm &evaluation)
CFList	extEarlyReconstructionAndLifting (const CanonicalForm &F, const nmod_mat_t N, CanonicalForm &bufF, CFList &factors, int &l, int &factorsFound, bool beenInThres, CFMatrix &M, CFArray &Pi, CFList &diophant, const ExtensionInfo &info, const CanonicalForm &evaluation)
CFList	sieveSmallFactors (const CanonicalForm &G, CFList &uniFactors, DegreePattern &degPat, CanonicalForm &H, CFList &diophant, CFArray &Pi, CFMatrix &M, bool &success, int d, const CanonicalForm &eval)
CFList	extSieveSmallFactors (const CanonicalForm &G, CFList &uniFactors, DegreePattern &degPat, CanonicalForm &H, CFList &diophant, CFArray &Pi, CFMatrix &M, bool &success, int d, const CanonicalForm &evaluation, const ExtensionInfo &info)
CFList	henselLiftAndLatticeRecombi (const CanonicalForm &G, const CFList &uniFactors, const Variable &alpha, const DegreePattern &degPat, bool symmetric, const CanonicalForm &eval)
ExtensionInfo	init4ext (const ExtensionInfo &info, const CanonicalForm &evaluation, int &degMipo)
CFList	extHenselLiftAndLatticeRecombi (const CanonicalForm &G, const CFList &uniFactors, const ExtensionInfo &extInfo, const DegreePattern &degPat, const CanonicalForm &eval)
CFList	extBiFactorize (const CanonicalForm &F, const ExtensionInfo &info)
	Factorization over an extension of initial field. More...
CFList	biFactorize (const CanonicalForm &F, const ExtensionInfo &info)
	bivariate factorization over finite fields as decribed in "Factoring multivariate polynomials over a finite field" by L Bernardin. More...

Variables
const CanonicalForm &	M
const CanonicalForm const modpk &	b
	else
CFListIterator	i = L
CFList	tmp1
CFList	tmp2 = Difference (L, tmp1)
CanonicalForm	buf1 = prodMod0 (tmp1, M, b)
CanonicalForm	buf2 = prodMod0 (tmp2, M, b)

Detailed Description

This file provides functions for factorizing a bivariate polynomial over , 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

Definition in file facFqBivar.cc.

Function Documentation

biFactorize()

CFList biFactorize	(	const CanonicalForm &	F,
		const ExtensionInfo &	info
	)

bivariate factorization over finite fields as decribed in "Factoring multivariate polynomials over a finite field" by L Bernardin.

Factorization of a squarefree bivariate polynomials over an arbitrary finite field, information on the current field we work over is in info. info may also contain information about the initial field if initial and current field do not coincide. In this case the current field is an extension of the initial field and the factors returned are factors of F over the initial field.

Parameters

[in]	F	a sqrfree bivariate poly
[in]	info	information about extension

Definition at line 8303 of file facFqBivar.cc.

{
  if (F.inCoeffDomain())
    return CFList(F);
 
  CanonicalForm A= F;
  bool GF= (CFFactory::gettype() == GaloisFieldDomain);
 
  Variable alpha= info.getAlpha();
  Variable beta= info.getBeta();
  CanonicalForm gamma= info.getGamma();
  CanonicalForm delta= info.getDelta();
  int k= info.getGFDegree();
  bool extension= info.isInExtension();
  if (A.isUnivariate())
  {
    if (extension == false)
      return uniFactorizer (F, alpha, GF);
    else
    {
      CFList source, dest;
      A= mapDown (A, info, source, dest);
      return uniFactorizer (A, beta, GF);
    }
  }
 
  CFMap N;
  A= compress (A, N);
  Variable y= A.mvar();
 
  if (y.level() > 2) return CFList (F);
  Variable x= Variable (1);
 
  //remove and factorize content
  CanonicalForm contentAx= content (A, x);
  CanonicalForm contentAy= content (A);
 
  A= A/(contentAx*contentAy);
  CFList contentAxFactors, contentAyFactors;
 
  if (!extension)
  {
    contentAxFactors= uniFactorizer (contentAx, alpha, GF);
    contentAyFactors= uniFactorizer (contentAy, alpha, GF);
  }
 
  //trivial case
  CFList factors;
  if (A.inCoeffDomain())
  {
    append (factors, contentAxFactors);
    append (factors, contentAyFactors);
    decompress (factors, N);
    return factors;
  }
  else if (A.isUnivariate())
  {
    factors= uniFactorizer (A, alpha, GF);
    append (factors, contentAxFactors);
    append (factors, contentAyFactors);
    decompress (factors, N);
    return factors;
  }
 
 
  //check trivial case
  if (degree (A) == 1 || degree (A, 1) == 1 ||
      (size (A) == 2 && igcd (degree (A), degree (A,1))==1))
  {
    factors.append (A);
 
    appendSwapDecompress (factors, contentAxFactors, contentAyFactors,
                          false, false, N);
 
    if (!extension)
      normalize (factors);
    return factors;
  }
 
  // check derivatives
  bool derivXZero= false;
  CanonicalForm derivX= deriv (A, x);
  CanonicalForm gcdDerivX;
  if (derivX.isZero())
    derivXZero= true;
  else
  {
    gcdDerivX= gcd (A, derivX);
    if (degree (gcdDerivX) > 0)
    {
      CanonicalForm g= A/gcdDerivX;
      CFList factorsG=
      Union (biFactorize (g, info), biFactorize (gcdDerivX, info));
      append (factorsG, contentAxFactors);
      append (factorsG, contentAyFactors);
      decompress (factorsG, N);
      if (!extension)
        normalize (factorsG);
      return factorsG;
    }
  }
  bool derivYZero= false;
  CanonicalForm derivY= deriv (A, y);
  CanonicalForm gcdDerivY;
  if (derivY.isZero())
    derivYZero= true;
  else
  {
    gcdDerivY= gcd (A, derivY);
    if (degree (gcdDerivY) > 0)
    {
      CanonicalForm g= A/gcdDerivY;
      CFList factorsG=
      Union (biFactorize (g, info), biFactorize (gcdDerivY, info));
      append (factorsG, contentAxFactors);
      append (factorsG, contentAyFactors);
      decompress (factorsG, N);
      if (!extension)
        normalize (factorsG);
      return factorsG;
    }
  }
  //main variable is chosen s.t. the degree in x is minimal
  bool swap= false;
  if ((degree (A) > degree (A, x)) || derivXZero)
  {
    if (!derivYZero)
    {
      A= swapvar (A, y, x);
      swap= derivXZero;
      derivXZero= derivYZero;
      derivYZero= swap;
      swap= true;
    }
  }
 
  int boundsLength;
  bool isIrreducible= false;
  int * bounds= computeBounds (A, boundsLength, isIrreducible);
  if (isIrreducible)
  {
    delete [] bounds;
    factors.append (A);
 
    appendSwapDecompress (factors, contentAxFactors, contentAyFactors,
                          swap, false, N);
 
    if (!extension)
      normalize (factors);
    return factors;
  }
 
  int minBound= bounds[0];
  for (int i= 1; i < boundsLength; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
 
  int boundsLength2;
  int * bounds2= computeBoundsWrtDiffMainvar (A, boundsLength2, isIrreducible);
  int minBound2= bounds2[0];
  for (int i= 1; i < boundsLength2; i++)
  {
    if (bounds2[i] != 0)
      minBound2= tmin (minBound2, bounds2[i]);
  }
 
 
  bool fail= false;
  CanonicalForm Aeval, evaluation, bufAeval, bufEvaluation, buf, tmp;
  CFList uniFactors, list, bufUniFactors;
  DegreePattern degs;
  DegreePattern bufDegs;
 
  bool fail2= false;
  CanonicalForm Aeval2, evaluation2, bufAeval2, bufEvaluation2;
  CFList bufUniFactors2, list2, uniFactors2;
  DegreePattern degs2;
  DegreePattern bufDegs2;
  bool swap2= false;
 
  // several univariate factorizations to obtain more information about the
  // degree pattern therefore usually less combinations have to be tried during
  // the recombination process
  int factorNums= 3;
  int subCheck1= substituteCheck (A, x);
  int subCheck2= substituteCheck (A, y);
  bool symmetric= false;
 
  TIMING_START (fac_fq_uni_total);
  for (int i= 0; i < factorNums; i++)
  {
    bufAeval= A;
    TIMING_START (fac_fq_bi_evaluation);
    bufEvaluation= evalPoint (A, bufAeval, alpha, list, GF, fail);
    TIMING_END_AND_PRINT (fac_fq_bi_evaluation, "time to find eval point: ");
    if (!derivXZero && !fail2 && !symmetric)
    {
      if (i == 0)
      {
        buf= swapvar (A, x, y);
        symmetric= (A/Lc (A) == buf/Lc (buf));
      }
      bufAeval2= buf;
      TIMING_START (fac_fq_bi_evaluation);
      bufEvaluation2= evalPoint (buf, bufAeval2, alpha, list2, GF, fail2);
      TIMING_END_AND_PRINT (fac_fq_bi_evaluation,
                            "time to find eval point wrt y: ");
    }
    // first try to change main variable if there is no valid evaluation point
    if (fail && (i == 0))
    {
      if (!derivXZero && !fail2 && !symmetric)
      {
        bufEvaluation= bufEvaluation2;
        int dummy= subCheck2;
        subCheck2= subCheck1;
        subCheck1= dummy;
        tmp= A;
        A= buf;
        buf= tmp;
        bufAeval= bufAeval2;
        swap2= true;
        fail= false;
      }
      else
        fail= true;
    }
 
    // if there is no valid evaluation point pass to a field extension
    if (fail && (i == 0))
    {
      factors= extBiFactorize (A, info);
      appendSwapDecompress (factors, contentAxFactors, contentAyFactors,
                            swap, swap2, N);
      normalize (factors);
      delete [] bounds;
      delete [] bounds2;
      return factors;
    }
 
    // there is at least one valid evaluation point
    // but we do not compute more univariate factorization over an extension
    if (fail && (i != 0))
      break;
 
    // univariate factorization
    TIMING_START (fac_fq_uni_factorizer);
    bufUniFactors= uniFactorizer (bufAeval, alpha, GF);
    TIMING_END_AND_PRINT (fac_fq_uni_factorizer,
                          "time for univariate factorization over Fq: ");
    DEBOUTLN (cerr, "Lc (bufAeval)*prod (bufUniFactors)== bufAeval " <<
              (prod (bufUniFactors)*Lc (bufAeval) == bufAeval));
 
    if (!derivXZero && !fail2 && !symmetric)
    {
      TIMING_START (fac_fq_uni_factorizer);
      bufUniFactors2= uniFactorizer (bufAeval2, alpha, GF);
      TIMING_END_AND_PRINT (fac_fq_uni_factorizer,
                            "time for univariate factorization in y over Fq: ");
      DEBOUTLN (cerr, "Lc (bufAeval2)*prod (bufUniFactors2)== bufAeval2 " <<
                (prod (bufUniFactors2)*Lc (bufAeval2) == bufAeval2));
    }
 
    if (bufUniFactors.length() == 1 ||
        (!fail2 && !derivXZero && !symmetric && (bufUniFactors2.length() == 1)))
    {
      if (extension)
      {
        CFList source, dest;
        appendMapDown (factors, A, info, source, dest);
      }
      else
        factors.append (A);
 
      appendSwapDecompress (factors, contentAxFactors, contentAyFactors,
                            swap, swap2, N);
 
      if (!extension)
        normalize (factors);
      delete [] bounds;
      delete [] bounds2;
      return factors;
    }
 
    if (i == 0 && !extension)
    {
      if (subCheck1 > 0)
      {
        int subCheck= substituteCheck (bufUniFactors);
 
        if (subCheck > 1 && (subCheck1%subCheck == 0))
        {
          CanonicalForm bufA= A;
          subst (bufA, bufA, subCheck, x);
          factors= biFactorize (bufA, info);
          reverseSubst (factors, subCheck, x);
          appendSwapDecompress (factors, contentAxFactors, contentAyFactors,
                                swap, swap2, N);
          if (!extension)
            normalize (factors);
          delete [] bounds;
          delete [] bounds2;
          return factors;
        }
      }
 
      if (!derivXZero && !fail2 && !symmetric && subCheck2 > 0)
      {
        int subCheck= substituteCheck (bufUniFactors2);
 
        if (subCheck > 1 && (subCheck2%subCheck == 0))
        {
          CanonicalForm bufA= A;
          subst (bufA, bufA, subCheck, y);
          factors= biFactorize (bufA, info);
          reverseSubst (factors, subCheck, y);
          appendSwapDecompress (factors, contentAxFactors, contentAyFactors,
                                swap, swap2, N);
          if (!extension)
            normalize (factors);
          delete [] bounds;
          delete [] bounds2;
          return factors;
        }
      }
    }
 
    // degree analysis
    bufDegs = DegreePattern (bufUniFactors);
    if (!derivXZero && !fail2 && !symmetric)
      bufDegs2= DegreePattern (bufUniFactors2);
 
    if (i == 0)
    {
      Aeval= bufAeval;
      evaluation= bufEvaluation;
      uniFactors= bufUniFactors;
      degs= bufDegs;
      if (!derivXZero && !fail2 && !symmetric)
      {
        Aeval2= bufAeval2;
        evaluation2= bufEvaluation2;
        uniFactors2= bufUniFactors2;
        degs2= bufDegs2;
      }
    }
    else
    {
      degs.intersect (bufDegs);
      if (!derivXZero && !fail2 && !symmetric)
      {
        degs2.intersect (bufDegs2);
        if (bufUniFactors2.length() < uniFactors2.length())
        {
          uniFactors2= bufUniFactors2;
          Aeval2= bufAeval2;
          evaluation2= bufEvaluation2;
        }
      }
      if (bufUniFactors.length() < uniFactors.length())
      {
        uniFactors= bufUniFactors;
        Aeval= bufAeval;
        evaluation= bufEvaluation;
      }
    }
    list.append (bufEvaluation);
    if (!derivXZero && !fail2 && !symmetric)
      list2.append (bufEvaluation2);
  }
  TIMING_END_AND_PRINT (fac_fq_uni_total,
                        "total time for univariate factorizations: ");
 
  if (!derivXZero && !fail2 && !symmetric)
  {
    if ((uniFactors.length() > uniFactors2.length() && minBound2 <= minBound)||
        (uniFactors.length() == uniFactors2.length()
         && degs.getLength() > degs2.getLength() && minBound2 <= minBound))
    {
      degs= degs2;
      uniFactors= uniFactors2;
      evaluation= evaluation2;
      Aeval= Aeval2;
      A= buf;
      swap2= true;
    }
  }
 
  if (degs.getLength() == 1) // A is irreducible
  {
    if (extension)
    {
      CFList source, dest;
      appendMapDown (factors, A, info, source, dest);
    }
    else
      factors.append (A);
    appendSwapDecompress (factors, contentAxFactors, contentAyFactors,
                            swap, swap2, N);
    if (!extension)
      normalize (factors);
    delete [] bounds;
    delete [] bounds2;
    return factors;
  }
 
  int liftBound= degree (A, y) + 1;
 
  if (swap2)
  {
    delete [] bounds;
    bounds= bounds2;
    minBound= minBound2;
  }
 
  TIMING_START (fac_fq_bi_shift_to_zero);
  A= A (y + evaluation, y);
  TIMING_END_AND_PRINT (fac_fq_bi_shift_to_zero,
                        "time to shift eval to zero: ");
 
  int degMipo= 1;
  if (extension && alpha.level() != 1 && k==1)
    degMipo= degree (getMipo (alpha));
 
  DEBOUTLN (cerr, "uniFactors= " << uniFactors);
 
  if ((GF && !extension) || (GF && extension && k != 1))
  {
    bool earlySuccess= false;
    CFList earlyFactors;
    TIMING_START (fac_fq_bi_hensel_lift);
    uniFactors= henselLiftAndEarly
               (A, earlySuccess, earlyFactors, degs, liftBound,
                uniFactors, info, evaluation);
    TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift,
                          "time for bivariate hensel lifting over Fq: ");
    DEBOUTLN (cerr, "lifted factors= " << uniFactors);
 
    CanonicalForm MODl= power (y, liftBound);
 
    TIMING_START (fac_fq_bi_factor_recombination);
    if (extension)
      factors= extFactorRecombination (uniFactors, A, MODl, info, degs,
                                       evaluation, 1, uniFactors.length()/2);
    else
      factors= factorRecombination (uniFactors, A, MODl, degs, evaluation, 1,
                                    uniFactors.length()/2);
    TIMING_END_AND_PRINT (fac_fq_bi_factor_recombination,
                          "time for naive bivariate factor recombi over Fq: ");
 
    if (earlySuccess)
      factors= Union (earlyFactors, factors);
    else if (!earlySuccess && degs.getLength() == 1)
      factors= earlyFactors;
  }
  else if (degree (A) > 4 && beta.level() == 1 && (2*minBound)/degMipo < 32)
  {
    TIMING_START (fac_fq_bi_hensel_lift);
    if (extension)
    {
      CFList lll= extHenselLiftAndLatticeRecombi (A, uniFactors, info, degs,
                                                  evaluation
                                                 );
      factors= Union (lll, factors);
    }
    else if (alpha.level() == 1 && !GF)
    {
      CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs,
                                               symmetric, evaluation);
      factors= Union (lll, factors);
    }
    else if (!extension && (alpha != x || GF))
    {
      CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs,
                                               symmetric, evaluation);
      factors= Union (lll, factors);
    }
    TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift,
                          "time to bivar lift and LLL recombi over Fq: ");
    DEBOUTLN (cerr, "lifted factors= " << uniFactors);
  }
  else
  {
    bool earlySuccess= false;
    CFList earlyFactors;
    TIMING_START (fac_fq_bi_hensel_lift);
    uniFactors= henselLiftAndEarly
               (A, earlySuccess, earlyFactors, degs, liftBound,
                uniFactors, info, evaluation);
    TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift,
                          "time for bivar hensel lifting over Fq: ");
    DEBOUTLN (cerr, "lifted factors= " << uniFactors);
 
    CanonicalForm MODl= power (y, liftBound);
    if (!extension)
    {
      TIMING_START (fac_fq_bi_factor_recombination);
      factors= factorRecombination (uniFactors, A, MODl, degs, evaluation, 1, 3);
      TIMING_END_AND_PRINT (fac_fq_bi_factor_recombination,
                            "time for small subset naive recombi over Fq: ");
 
      int oldUniFactorsLength= uniFactors.length();
      if (degree (A) > 0)
      {
        CFList tmp;
        TIMING_START (fac_fq_bi_hensel_lift);
        if (alpha.level() == 1)
          tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1,
                                  liftBound, evaluation
                                 );
        else
        {
          if (degree (A) > getCharacteristic())
            tmp= increasePrecisionFq2Fp (A, uniFactors, 0, uniFactors.length(),
                                         1, alpha, liftBound, evaluation
                                        );
          else
            tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1,
                                    alpha, liftBound, evaluation
                                   );
        }
        TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift,
                              "time to increase precision: ");
        factors= Union (factors, tmp);
        if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0
                                  && uniFactors.length() != oldUniFactorsLength)
           )
        {
          DegreePattern bufDegs= DegreePattern (uniFactors);
          degs.intersect (bufDegs);
          degs.refine ();
          factors= Union (factors, factorRecombination (uniFactors, A, MODl,
                                                        degs, evaluation, 4,
                                                        uniFactors.length()/2
                                                       )
                         );
        }
      }
    }
    else
    {
      if (beta.level() != 1 || k > 1)
      {
        if (k > 1)
        {
          factors= extFactorRecombination (uniFactors, A, MODl, info, degs,
                                           evaluation, 1, uniFactors.length()/2
                                          );
        }
        else
        {
          factors= extFactorRecombination (uniFactors, A, MODl, info, degs,
                                           evaluation, 1, 3
                                          );
          if (degree (A) > 0)
          {
            CFList tmp= increasePrecision2 (A, uniFactors, alpha, liftBound);
            DegreePattern bufDegs= DegreePattern (tmp);
            degs.intersect (bufDegs);
            degs.refine ();
            factors= Union (factors, extFactorRecombination (tmp, A, MODl, info,
                                                             degs, evaluation,
                                                             1, tmp.length()/2
                                                            )
                           );
          }
        }
      }
      else
      {
        factors= extFactorRecombination (uniFactors, A, MODl, info, degs,
                                         evaluation, 1, 3
                                        );
        int oldUniFactorsLength= uniFactors.length();
        if (degree (A) > 0)
        {
          int degMipo;
          ExtensionInfo info2= init4ext (info, evaluation, degMipo);
 
          CFList source, dest;
          CFList tmp= extIncreasePrecision (A, uniFactors, 0,
                                            uniFactors.length(), 1, evaluation,
                                            info2, source, dest, liftBound
                                           );
          factors= Union (factors, tmp);
          if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0
                                  && uniFactors.length() != oldUniFactorsLength)
             )
          {
            DegreePattern bufDegs= DegreePattern (uniFactors);
            degs.intersect (bufDegs);
            degs.refine ();
            factors= Union (factors,extFactorRecombination (uniFactors, A, MODl,
                                                        info, degs, evaluation,
                                                        4, uniFactors.length()/2
                                                            )
                           );
          }
        }
      }
    }
 
    if (earlySuccess)
      factors= Union (earlyFactors, factors);
    else if (!earlySuccess && degs.getLength() == 1)
      factors= earlyFactors;
  }
 
  if (!swap2)
    delete [] bounds2;
  delete [] bounds;
 
  appendSwapDecompress (factors, contentAxFactors, contentAyFactors,
                        swap, swap2, N);
  if (!extension)
    normalize (factors);
 
  return factors;
}

chooseExtension()

Variable chooseExtension	(	const Variable &	alpha,
		const Variable &	beta,
		int	k
	)

chooses a field extension.

Returns

chooseExtension returns an extension specified by beta of appropiate size

Parameters

[in]	alpha	some algebraic variable
[in]	beta	some algebraic variable
[in]	k	some int

Definition at line 806 of file facFqBivar.cc.

{
  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);
}

deleteFactors()

void deleteFactors	(	CFList &	factors,
		int *	factorsFoundIndex
	)

Definition at line 1136 of file facFqBivar.cc.

{
  CFList result;
  int i= 0;
  for (CFListIterator iter= factors; iter.hasItem(); iter++, i++)
  {
    if (factorsFoundIndex[i] == 1)
      continue;
    else
      result.append (iter.getItem());
  }
  factors= result;
}

earlyFactorDetection() [1/2]

void earlyFactorDetection	(	CFList &	reconstructedFactors,
		CanonicalForm &	F,
		CFList &	factors,
		int &	adaptedLiftBound,
		int *&	factorsFoundIndex,
		DegreePattern &	degs,
		bool &	success,
		int	deg,
		const CanonicalForm &	eval,
		const modpk &	b = modpk()
	)

detects factors of F at stage deg of Hensel lifting. No combinations of more than one factor are tested. Lift bound and possible degree pattern are updated.

See also

factorRecombination(), extEarlyFactorDetection()

Parameters

[in,out]	reconstructedFactors	list of reconstructed factors
[in,out]	F	poly to be factored, returns poly divided by detected factors in case of success
[in,out]	factors	list of factors lifted up to deg, returns a list of factors without detected factors
[in,out]	adaptedLiftBound	adapted lift bound
[in,out]	factorsFoundIndex	factors already considered
[in,out]	degs	degree pattern, is updated whenever we find a factor
[in,out]	success	indicating success
[in]	deg	stage of Hensel lifting
[in]	eval	evaluation point
[in]	b	coeff bound

Definition at line 971 of file facFqBivar.cc.

{
  CanonicalForm den= 1;
  earlyFactorDetection (reconstructedFactors, F, factors, adaptedLiftBound,
                        factorsFoundIndex, degs, success, deg, eval, b, den);
}

earlyFactorDetection() [2/2]

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
	)

Definition at line 852 of file facFqBivar.cc.

{
  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;
}

earlyReconstructionAndLifting() [1/2]

CFList earlyReconstructionAndLifting	(	const CanonicalForm &	F,
		const mat_zz_pE &	N,
		CanonicalForm &	bufF,
		CFList &	factors,
		int &	l,
		int &	factorsFound,
		bool	beenInThres,
		CFMatrix &	M,
		CFArray &	Pi,
		CFList &	diophant,
		bool	symmetric,
		const CanonicalForm &	evaluation
	)

Definition at line 6419 of file facFqBivar.cc.

{
  int sizeOfLiftPre;
  int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2));
  Variable y= F.mvar();
  factorsFound= 0;
  CanonicalForm LCF= LC (F, 1);
  CFList result;
  int smallFactorDeg= 11;
  mat_zz_pE NTLN= N;
  int * factorsFoundIndex= new int [NTLN.NumCols()];
  for (long i= 0; i < NTLN.NumCols(); i++)
    factorsFoundIndex [i]= 0;
 
  if (degree (F) + 1 > smallFactorDeg)
  {
    if (l < smallFactorDeg)
    {
      TIMING_START (fac_fq_lift);
      factors.insert (LCF);
      henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M);
      TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction0: ");
      l= smallFactorDeg;
    }
    TIMING_START (fac_fq_reconstruction);
    reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound,
                       factorsFoundIndex, NTLN, evaluation, beenInThres
                      );
    TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct0: ");
    if (result.length() == NTLN.NumCols())
    {
      delete [] liftPre;
      delete [] factorsFoundIndex;
      return result;
    }
  }
 
  int i= sizeOfLiftPre - 1;
  int dummy= 1;
  if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30)
  {
    while (i > 0)
    {
      if (l < liftPre[i-1] + 1)
      {
        factors.insert (LCF);
        TIMING_START (fac_fq_lift);
        henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M);
        TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction1: ");
        l= liftPre[i-1] + 1;
      }
      else
      {
        i--;
        if (i != 0)
          continue;
      }
      TIMING_START (fac_fq_reconstruction);
      reconstructionTry (result, bufF, factors, l, factorsFound,
                         factorsFoundIndex, NTLN, evaluation, beenInThres
                        );
      TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct1: ");
      if (result.length() == NTLN.NumCols())
      {
        delete [] liftPre;
        delete [] factorsFoundIndex;
        return result;
      }
      i--;
    }
  }
  else
  {
    i= 1;
    while ((degree (F,y)/4+1)*i + 4 <= smallFactorDeg)
      i++;
    while (i < 5)
    {
      dummy= tmin (degree (F,y)+1, (degree (F,y)/4+1)*i+4);
      if (l < dummy)
      {
        factors.insert (LCF);
        TIMING_START (fac_fq_lift);
        henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M);
        TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction2: ");
        l= dummy;
        if (i == 1 && degree (F)%4==0 && symmetric && factors.length() == 2 &&
            LC (F,1).inCoeffDomain() &&
           (degree (factors.getFirst(), 1) == degree (factors.getLast(),1)))
        {
          Variable x= Variable (1);
          CanonicalForm g, h, gg, hh, multiplier1, multiplier2, check1, check2;
          int m= degree (F)/4+1;
          g= factors.getFirst();
          h= factors.getLast();
          g= mod (g, power (y,m));
          h= mod (h, power (y,m));
          g= g (y-evaluation, y);
          h= h (y-evaluation, y);
          gg= mod (swapvar (g,x,y),power (x,m));
          gg= gg (y + evaluation, y);
          multiplier1= factors.getLast()[m-1][0]/gg[m-1][0];
          gg= div (gg, power (y,m));
          gg= gg*power (y,m);
          hh= mod (swapvar (h,x,y),power (x,m));
          hh= hh (y + evaluation, y);
          multiplier2= factors.getFirst()[m-1][0]/hh[m-1][0];
          hh= div (hh, power (y,m));
          hh= hh*power (y,m);
          gg= multiplier1*gg+mod (factors.getLast(), power (y,m));
          hh= multiplier2*hh+mod (factors.getFirst(), power (y,m));
          check1= gg (y-evaluation,y);
          check2= hh (y-evaluation,y);
          CanonicalForm oldcheck1= check1;
          check1= swapvar (check1, x, y);
          if (check1/Lc (check1) == check2/Lc (check2))
          {
            result.append (oldcheck1);
            result.append (check2);
            delete [] liftPre;
            delete [] factorsFoundIndex;
            return result;
          }
        }
      }
      else
      {
        i++;
        if (i < 5)
          continue;
      }
      TIMING_START (fac_fq_reconstruction);
      reconstructionTry (result, bufF, factors, l, factorsFound,
                         factorsFoundIndex, NTLN, evaluation, beenInThres
                        );
      TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct2: ");
      if (result.length() == NTLN.NumCols())
      {
        delete [] liftPre;
        delete [] factorsFoundIndex;
        return result;
      }
      i++;
    }
  }
 
  delete [] liftPre;
  delete [] factorsFoundIndex;
  return result;
}

earlyReconstructionAndLifting() [2/2]

CFList earlyReconstructionAndLifting	(	const CanonicalForm &	F,
		const nmod_mat_t	N,
		CanonicalForm &	bufF,
		CFList &	factors,
		int &	l,
		int &	factorsFound,
		bool	beenInThres,
		CFMatrix &	M,
		CFArray &	Pi,
		CFList &	diophant,
		bool	symmetric,
		const CanonicalForm &	evaluation
	)

Definition at line 6205 of file facFqBivar.cc.

{
  int sizeOfLiftPre;
  int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2));
 
  Variable y= F.mvar();
  factorsFound= 0;
  CanonicalForm LCF= LC (F, 1);
  CFList result;
  int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1);
#ifdef HAVE_FLINT
  nmod_mat_t FLINTN;
  nmod_mat_init_set (FLINTN, N);
  int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
  for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
  mat_zz_p NTLN= N;
  int * factorsFoundIndex= new int [NTLN.NumCols()];
  for (long i= 0; i < NTLN.NumCols(); i++)
#endif
    factorsFoundIndex [i]= 0;
 
  if (degree (F) + 1 > smallFactorDeg)
  {
    if (l < smallFactorDeg)
    {
      TIMING_START (fac_fq_lift);
      factors.insert (LCF);
      henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M);
      TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction0: ");
      l= smallFactorDeg;
    }
#ifdef HAVE_FLINT
    TIMING_START (fac_fq_reconstruction);
    reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound,
                       factorsFoundIndex, FLINTN, evaluation, beenInThres
                      );
    TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct0: ");
    if (result.length() == nmod_mat_ncols (FLINTN))
    {
      nmod_mat_clear (FLINTN);
#else
    TIMING_START (fac_fq_reconstruction);
    reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound,
                       factorsFoundIndex, NTLN, evaluation, beenInThres
                      );
    TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct0: ");
    if (result.length() == NTLN.NumCols())
    {
#endif
      delete [] liftPre;
      delete [] factorsFoundIndex;
      return result;
    }
  }
 
  int i= sizeOfLiftPre - 1;
  int dummy= 1;
  if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30)
  {
    while (i > 0)
    {
      if (l < liftPre[i-1] + 1)
      {
        factors.insert (LCF);
        TIMING_START (fac_fq_lift);
        henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M);
        TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction1: ");
        l= liftPre[i-1] + 1;
      }
      else
      {
        i--;
        if (i != 0)
          continue;
      }
#ifdef HAVE_FLINT
      TIMING_START (fac_fq_reconstruction);
      reconstructionTry (result, bufF, factors, l, factorsFound,
                         factorsFoundIndex, FLINTN, evaluation, beenInThres
                        );
      TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct1: ");
      if (result.length() == nmod_mat_ncols (FLINTN))
      {
        nmod_mat_clear (FLINTN);
#else
      TIMING_START (fac_fq_reconstruction);
      reconstructionTry (result, bufF, factors, l, factorsFound,
                         factorsFoundIndex, NTLN, evaluation, beenInThres
                        );
      TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct1: ");
      if (result.length() == NTLN.NumCols())
      {
#endif
        delete [] liftPre;
        delete [] factorsFoundIndex;
        return result;
      }
      i--;
    }
  }
  else
  {
    i= 1;
    while (((degree (F,y)/4)*i+1) + 4 <= smallFactorDeg)
      i++;
    while (i < 5)
    {
      dummy= tmin (degree (F,y)+1, ((degree (F,y)/4)+1)*i+4);
      if (l < dummy)
      {
        factors.insert (LCF);
        TIMING_START (fac_fq_lift);
        henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M);
        TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction2: ");
        l= dummy;
        if (i == 1 && degree (F)%4==0 && symmetric && factors.length() == 2 &&
            LC (F,1).inCoeffDomain() &&
           (degree (factors.getFirst(), 1) == degree (factors.getLast(),1)))
        {
          Variable x= Variable (1);
          CanonicalForm g, h, gg, hh, multiplier1, multiplier2, check1, check2;
          int m= degree (F)/4+1;
          g= factors.getFirst();
          h= factors.getLast();
          g= mod (g, power (y,m));
          h= mod (h, power (y,m));
          g= g (y-evaluation, y);
          h= h (y-evaluation, y);
          gg= mod (swapvar (g,x,y),power (x,m));
          gg= gg (y + evaluation, y);
          multiplier1= factors.getLast()[m-1][0]/gg[m-1][0];
          gg= div (gg, power (y,m));
          gg= gg*power (y,m);
          hh= mod (swapvar (h,x,y),power (x,m));
          hh= hh (y + evaluation, y);
          multiplier2= factors.getFirst()[m-1][0]/hh[m-1][0];
          hh= div (hh, power (y,m));
          hh= hh*power (y,m);
          gg= multiplier1*gg+mod (factors.getLast(), power (y,m));
          hh= multiplier2*hh+mod (factors.getFirst(), power (y,m));
          check1= gg (y-evaluation,y);
          check2= hh (y-evaluation,y);
          CanonicalForm oldcheck1= check1;
          check1= swapvar (check1, x, y);
          if (check1/Lc (check1) == check2/Lc (check2))
          {
#ifdef HAVE_FLINT
            nmod_mat_clear (FLINTN);
#endif
            result.append (oldcheck1);
            result.append (check2);
            delete [] liftPre;
            delete [] factorsFoundIndex;
            return result;
          }
        }
      }
      else
      {
        i++;
        if (i < 5)
          continue;
      }
#ifdef HAVE_FLINT
      TIMING_START (fac_fq_reconstruction);
      reconstructionTry (result, bufF, factors, l, factorsFound,
                         factorsFoundIndex, FLINTN, evaluation, beenInThres
                        );
      TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct2: ");
      if (result.length() == nmod_mat_ncols (FLINTN))
      {
        nmod_mat_clear (FLINTN);
#else
      TIMING_START (fac_fq_reconstruction);
      reconstructionTry (result, bufF, factors, l, factorsFound,
                         factorsFoundIndex, NTLN, evaluation, beenInThres
                        );
      TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct2: ");
      if (result.length() == NTLN.NumCols())
      {
#endif
        delete [] liftPre;
        delete [] factorsFoundIndex;
        return result;
      }
      i++;
    }
  }
 
#ifdef HAVE_FLINT
  nmod_mat_clear (FLINTN);
#endif
  delete [] liftPre;
  delete [] factorsFoundIndex;
  return result;
}

evalPoint()

CanonicalForm evalPoint	(	const CanonicalForm &	F,
		CanonicalForm &	eval,
		const Variable &	alpha,
		CFList &	list,
		const bool &	GF,
		bool &	fail
	)

find an evaluation point p, s.t. F(p,y) is squarefree and .

Returns

evalPoint returns an evaluation point, which is valid if and only if fail == false.

Parameters

[in]	F	compressed, bivariate poly
[in,out]	eval	F (p, y)
[in]	alpha	algebraic variable
[in]	list	list of points already considered
[in]	GF	GaloisFieldDomain?
[in,out]	fail	equals true, if there is no valid evaluation point

Definition at line 84 of file facFqBivar.cc.

{
  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;
}

extBiFactorize()

CFList extBiFactorize	(	const CanonicalForm &	F,
		const ExtensionInfo &	info
	)

Factorization over an extension of initial field.

Returns

extBiFactorize returns factorization of F over initial field

See also

biFactorize()

Parameters

[in]	F	poly to be factored
[in]	info	info about extension

Definition at line 8928 of file facFqBivar.cc.

{
 
  CanonicalForm A= F;
  Variable alpha= info.getAlpha();
  Variable beta= info.getBeta();
  int k= info.getGFDegree();
  char cGFName= info.getGFName();
  CanonicalForm delta= info.getDelta();
 
  bool GF= (CFFactory::gettype() == GaloisFieldDomain);
  Variable x= Variable (1);
  CFList factors;
  if (!GF && alpha == x)  // we are in F_p
  {
    bool extension= true;
    int p= getCharacteristic();
    if (p*p < (1<<16)) // pass to GF if possible
    {
      setCharacteristic (getCharacteristic(), 2, 'Z');
      A= A.mapinto();
      ExtensionInfo info2= ExtensionInfo (extension);
      factors= biFactorize (A, info2);
 
      CanonicalForm mipo= gf_mipo;
      setCharacteristic (getCharacteristic());
      Variable vBuf= rootOf (mipo.mapinto());
      for (CFListIterator j= factors; j.hasItem(); j++)
        j.getItem()= GF2FalphaRep (j.getItem(), vBuf);
      prune (vBuf);
    }
    else // not able to pass to GF, pass to F_p(\alpha)
    {
      CanonicalForm mipo= randomIrredpoly (2, x);
      Variable v= rootOf (mipo);
      ExtensionInfo info2= ExtensionInfo (v);
      factors= biFactorize (A, info2);
      prune (v);
    }
    return factors;
  }
  else if (!GF && (alpha != x)) // we are in F_p(\alpha)
  {
    if (k == 1) // need factorization over F_p
    {
      int extDeg= degree (getMipo (alpha));
      extDeg++;
      CanonicalForm mipo= randomIrredpoly (extDeg, x);
      Variable v= rootOf (mipo);
      ExtensionInfo info2= ExtensionInfo (v);
      factors= biFactorize (A, info2);
      prune (v);
    }
    else
    {
      if (beta == x)
      {
        Variable v= chooseExtension (alpha, beta, k);
        CanonicalForm primElem, imPrimElem;
        bool primFail= false;
        Variable vBuf;
        primElem= primitiveElement (alpha, vBuf, primFail);
        ASSERT (!primFail, "failure in integer factorizer");
        if (primFail)
          ; //ERROR
        else
          imPrimElem= mapPrimElem (primElem, alpha, v);
 
        CFList source, dest;
        CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem,
                                   source, dest);
        ExtensionInfo info2= ExtensionInfo (v, alpha, imPrimElem, primElem);
        factors= biFactorize (bufA, info2);
        prune (v);
      }
      else
      {
        Variable v= chooseExtension (alpha, beta, k);
        CanonicalForm primElem, imPrimElem;
        bool primFail= false;
        Variable vBuf;
        ASSERT (!primFail, "failure in integer factorizer");
        if (primFail)
          ; //ERROR
        else
          imPrimElem= mapPrimElem (delta, beta, v);
 
        CFList source, dest;
        CanonicalForm bufA= mapDown (A, info, source, dest);
        source= CFList();
        dest= CFList();
        bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest);
        ExtensionInfo info2= ExtensionInfo (v, beta, imPrimElem, delta);
        factors= biFactorize (bufA, info2);
        prune (v);
      }
    }
    return factors;
  }
  else // we are in GF (p^k)
  {
    int p= getCharacteristic();
    int extensionDeg= getGFDegree();
    bool extension= true;
    if (k == 1) // need factorization over F_p
    {
      extensionDeg++;
      if (ipower (p, extensionDeg) < (1<<16))
      // pass to GF(p^k+1)
      {
        CanonicalForm mipo= gf_mipo;
        setCharacteristic (p);
        Variable vBuf= rootOf (mipo.mapinto());
        A= GF2FalphaRep (A, vBuf);
        setCharacteristic (p, extensionDeg, 'Z');
        ExtensionInfo info2= ExtensionInfo (extension);
        factors= biFactorize (A.mapinto(), info2);
        prune (vBuf);
      }
      else // not able to pass to another GF, pass to F_p(\alpha)
      {
        CanonicalForm mipo= gf_mipo;
        setCharacteristic (p);
        Variable vBuf= rootOf (mipo.mapinto());
        A= GF2FalphaRep (A, vBuf);
        Variable v= chooseExtension (vBuf, beta, k);
        ExtensionInfo info2= ExtensionInfo (v, extension);
        factors= biFactorize (A, info2);
        prune (vBuf);
      }
    }
    else // need factorization over GF (p^k)
    {
      if (ipower (p, 2*extensionDeg) < (1<<16))
      // pass to GF (p^2k)
      {
        setCharacteristic (p, 2*extensionDeg, 'Z');
        ExtensionInfo info2= ExtensionInfo (k, cGFName, extension);
        factors= biFactorize (GFMapUp (A, extensionDeg), info2);
        setCharacteristic (p, extensionDeg, cGFName);
      }
      else // not able to pass to GF (p^2k), pass to F_p (\alpha)
      {
        CanonicalForm mipo= gf_mipo;
        setCharacteristic (p);
        Variable v1= rootOf (mipo.mapinto());
        A= GF2FalphaRep (A, v1);
        Variable v2= chooseExtension (v1, v1, k);
        CanonicalForm primElem, imPrimElem;
        bool primFail= false;
        Variable vBuf;
        primElem= primitiveElement (v1, vBuf, primFail);
        ASSERT (!primFail, "failure in integer factorizer");
        if (primFail)
          ; //ERROR
        else
          imPrimElem= mapPrimElem (primElem, v1, v2);
 
        CFList source, dest;
        CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem,
                                     source, dest);
        ExtensionInfo info2= ExtensionInfo (v2, v1, imPrimElem, primElem);
        factors= biFactorize (bufA, info2);
        setCharacteristic (p, k, cGFName);
        for (CFListIterator i= factors; i.hasItem(); i++)
          i.getItem()= Falpha2GFRep (i.getItem());
        prune (v1);
      }
    }
    return factors;
  }
}

extEarlyFactorDetection()

void extEarlyFactorDetection	(	CFList &	reconstructedFactors,
		CanonicalForm &	F,
		CFList &	factors,
		int &	adaptedLiftBound,
		int *&	factorsFoundIndex,
		DegreePattern &	degs,
		bool &	success,
		const ExtensionInfo &	info,
		const CanonicalForm &	eval,
		int	deg
	)

detects factors of F at stage deg of Hensel lifting. No combinations of more than one factor are tested. Lift bound and possible degree pattern are updated.

See also

factorRecombination(), earlyFactorDetection()

Parameters

[in,out]	reconstructedFactors	list of reconstructed factors
[in,out]	F	poly to be factored, returns poly divided by detected factors in case of success
[in,out]	factors	list of factors lifted up to deg, returns a list of factors without detected factors
[in,out]	adaptedLiftBound	adapted lift bound
[in,out]	factorsFoundIndex	factors already considered
[in,out]	degs	degree pattern, is updated whenever we find a factor
[in,out]	success	indicating success
[in]	info	information about extension
[in]	eval	evaluation point
[in]	deg	stage of Hensel lifting

Definition at line 982 of file facFqBivar.cc.

{
  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);
  CanonicalForm buf= F, LCBuf= LC (buf, x), g, buf2;
  CanonicalForm M= power (y, deg);
  adaptedLiftBound= 0;
  bool trueFactor= false;
  int d= degree (F), l= 0;
  CFList source, dest;
  int degMipoBeta= 1;
  if (!k && beta.level() != 1)
    degMipoBeta= degree (getMipo (beta));
  CanonicalForm quot;
  for (CFListIterator i= factors; i.hasItem(); i++, l++)
  {
    if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1)
      continue;
    else
    {
      g= mulMod2 (i.getItem(), LCBuf, M);
      g /= content (g, x);
      if (fdivides (g, buf, quot))
      {
        buf2= g (y - eval, y);
        buf2 /= Lc (buf2);
 
        if (!k && beta == x)
        {
          if (degree (buf2, alpha) < degMipoBeta)
          {
            appendTestMapDown (reconstructedFactors, buf2, info, source, dest);
            factorsFoundIndex[l]= 1;
            buf= quot;
            d -= degree (g);
            LCBuf= LC (buf, x);
            trueFactor= true;
          }
        }
        else
        {
          if (!isInExtension (buf2, gamma, k, delta, source, dest))
          {
            appendTestMapDown (reconstructedFactors, buf2, info, source, dest);
            factorsFoundIndex[l]= 1;
            buf= quot;
            d -= degree (g);
            LCBuf= LC (buf, x);
            trueFactor= true;
          }
        }
        if (trueFactor)
        {
          T= Difference (T, CFList (i.getItem()));
          F= buf;
 
          // compute new possible degree pattern
          bufDegs2= DegreePattern (T);
          bufDegs1.intersect (bufDegs2);
          bufDegs1.refine ();
          trueFactor= false;
          if (bufDegs1.getLength() <= 1)
          {
            if (!buf.inCoeffDomain())
            {
              buf= buf (y - eval, y);
              buf /= Lc (buf);
              appendMapDown (reconstructedFactors, buf, info, source, dest);
              F= 1;
            }
            break;
          }
        }
      }
    }
  }
  adaptedLiftBound= d + 1;
  if (adaptedLiftBound < deg)
  {
    degs= bufDegs1;
    success= true;
  }
  if (bufDegs1.getLength() <= 1)
    degs= bufDegs1;
}

extEarlyReconstructionAndLifting()

CFList extEarlyReconstructionAndLifting	(	const CanonicalForm &	F,
		const nmod_mat_t	N,
		CanonicalForm &	bufF,
		CFList &	factors,
		int &	l,
		int &	factorsFound,
		bool	beenInThres,
		CFMatrix &	M,
		CFArray &	Pi,
		CFList &	diophant,
		const ExtensionInfo &	info,
		const CanonicalForm &	evaluation
	)

Definition at line 6579 of file facFqBivar.cc.

{
  int sizeOfLiftPre;
  int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2));
  Variable y= F.mvar();
  factorsFound= 0;
  CanonicalForm LCF= LC (F, 1);
  CFList result;
  int smallFactorDeg= 11;
#ifdef HAVE_FLINT
  nmod_mat_t FLINTN;
  nmod_mat_init_set (FLINTN, N);
  int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
  for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
  mat_zz_p NTLN= N;
  int * factorsFoundIndex= new int [NTLN.NumCols()];
  for (long i= 0; i < NTLN.NumCols(); i++)
#endif
    factorsFoundIndex [i]= 0;
 
  if (degree (F) + 1 > smallFactorDeg)
  {
    if (l < smallFactorDeg)
    {
      TIMING_START (fac_fq_lift);
      factors.insert (LCF);
      henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M);
      TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction0: ");
      l= smallFactorDeg;
    }
    TIMING_START (fac_fq_reconstruction);
#ifdef HAVE_FLINT
    extReconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound,
                          factorsFoundIndex, FLINTN, beenInThres, info,
                          evaluation
                      );
#else
    extReconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound,
                          factorsFoundIndex, NTLN, beenInThres, info,
                          evaluation
                      );
#endif
    TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct0: ");
#ifdef HAVE_FLINT
    if (result.length() == nmod_mat_ncols (FLINTN))
    {
      nmod_mat_clear (FLINTN);
#else
    if (result.length() == NTLN.NumCols())
    {
#endif
      delete [] liftPre;
      delete [] factorsFoundIndex;
      return result;
    }
  }
 
  int i= sizeOfLiftPre - 1;
  int dummy= 1;
  if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30)
  {
    while (i > 0)
    {
      if (l < liftPre[i-1] + 1)
      {
        factors.insert (LCF);
        TIMING_START (fac_fq_lift);
        henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M);
        TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction1: ");
        l= liftPre[i-1] + 1;
      }
      else
      {
        i--;
        if (i != 0)
          continue;
      }
      TIMING_START (fac_fq_reconstruction);
#ifdef HAVE_FLINT
      extReconstructionTry (result, bufF, factors, l, factorsFound,
                            factorsFoundIndex, FLINTN, beenInThres, info,
                            evaluation
                           );
#else
      extReconstructionTry (result, bufF, factors, l, factorsFound,
                            factorsFoundIndex, NTLN, beenInThres, info,
                            evaluation
                           );
#endif
      TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct1: ");
#ifdef HAVE_FLINT
      if (result.length() == nmod_mat_ncols (FLINTN))
      {
        nmod_mat_clear (FLINTN);
#else
      if (result.length() == NTLN.NumCols())
      {
#endif
        delete [] liftPre;
        delete [] factorsFoundIndex;
        return result;
      }
      i--;
    }
  }
  else
  {
    i= 1;
    while ((degree (F,y)/4+1)*i + 4 <= smallFactorDeg)
      i++;
    while (i < 5)
    {
      dummy= tmin (degree (F,y)+1, (degree (F,y)/4+1)*i+4);
      if (l < dummy)
      {
        factors.insert (LCF);
        TIMING_START (fac_fq_lift);
        henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M);
        TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction2: ");
        l= dummy;
      }
      else
      {
        i++;
        if (i < 5)
          continue;
      }
      TIMING_START (fac_fq_reconstruction);
#ifdef HAVE_FLINT
      extReconstructionTry (result, bufF, factors, l, factorsFound,
                            factorsFoundIndex, FLINTN, beenInThres, info,
                            evaluation
                           );
#else
      extReconstructionTry (result, bufF, factors, l, factorsFound,
                            factorsFoundIndex, NTLN, beenInThres, info,
                            evaluation
                           );
#endif
      TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct2: ");
#ifdef HAVE_FLINT
      if (result.length() == nmod_mat_ncols (FLINTN))
      {
        nmod_mat_clear (FLINTN);
#else
      if (result.length() == NTLN.NumCols())
      {
#endif
        delete [] liftPre;
        delete [] factorsFoundIndex;
        return result;
      }
      i++;
    }
  }
 
#ifdef HAVE_FLINT
  nmod_mat_clear (FLINTN);
#endif
  delete [] liftPre;
  delete [] factorsFoundIndex;
  return result;
}

extFactorRecombination()

CFList extFactorRecombination	(	CFList &	factors,
		CanonicalForm &	F,
		const CanonicalForm &	N,
		const ExtensionInfo &	info,
		DegreePattern &	degs,
		const CanonicalForm &	eval,
		int	s,
		int	thres
	)

naive factor recombination as decribed in "Factoring multivariate polynomials over a finite field" by L Bernardin.

naive factor recombination over an extension of the initial field. Uses precomputed data to exclude combinations that are not possible.

Parameters

[in,out]	factors	list of lifted factors that are monic wrt Variable (1), original factors-factors found
[in,out]	F	poly to be factored, F/factors found
[in]	N	Variable (2)^liftBound
[in]	info	contains information about extension
[in]	eval	evaluation point
[in]	s	algorithm starts checking subsets of size s
[in]	thres	threshold for the size of subsets which are checked, for a full factor recombination choose thres= factors.length()/2

Definition at line 370 of file facFqBivar.cc.

{
  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;
}

extFurtherLiftingAndIncreasePrecision()

CFList extFurtherLiftingAndIncreasePrecision	(	CanonicalForm &	F,
		CFList &	factors,
		int	l,
		int	liftBound,
		int	d,
		int *	bounds,
		nmod_mat_t	FLINTN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		const CanonicalForm &	evaluation,
		const ExtensionInfo &	info,
		CFList &	source,
		CFList &	dest
	)

Definition at line 5557 of file facFqBivar.cc.

{
  CanonicalForm LCF= LC (F, 1);
  CFList result;
  bool irreducible= false;
  CFList bufFactors= factors;
  CFList bufBufFactors;
  CFArray *A = new CFArray [bufFactors.length()];
  bool useOldQs= false;
  bool hitBound= false;
  bool GF= (CFFactory::gettype()==GaloisFieldDomain);
  int degMipo= degree (getMipo (info.getAlpha()));
  Variable alpha= info.getAlpha();
  int oldL= l; //be careful
  int stepSize= 8;
  l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l),2);
  Variable gamma= info.getBeta();
  CanonicalForm primElemAlpha= info.getGamma();
  CanonicalForm imPrimElemAlpha= info.getDelta();
#ifdef HAVE_FLINT
  nmod_mat_clear (FLINTN);
  nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic());
  for (long i=factors.length()-1; i >= 0; i--)
    nmod_mat_entry (FLINTN, i, i)= 1;
#else
  if (NTLN.NumRows() != factors.length()) //refined factors
    ident (NTLN, factors.length());
#endif
  Variable y= F.mvar();
  CanonicalForm powX, imBasis, bufF, truncF;
  CFMatrix Mat, C;
  CFIterator iter;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTMat, FLINTMatInv, FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLMat,*NTLC, NTLK;
#endif
  CFListIterator j;
  CFArray buf;
  while (l <= liftBound)
  {
    bufFactors.insert (LCF);
    henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M);
 
    if (GF)
      setCharacteristic (getCharacteristic());
 
    powX= power (y-gamma, l);
    Mat= CFMatrix (l*degMipo, l*degMipo);
    for (int i= 0; i < l*degMipo; i++)
    {
 
      imBasis= mod (power (y, i), powX);
      imBasis= imBasis (power (y, degMipo), y);
      imBasis= imBasis (y, gamma);
      iter= imBasis;
      for (; iter.hasTerms(); iter++)
        Mat (iter.exp()+ 1, i+1)= iter.coeff();
    }
 
#ifdef HAVE_FLINT
    convertFacCFMatrix2nmod_mat_t (FLINTMat, Mat);
    nmod_mat_init (FLINTMatInv, nmod_mat_nrows (FLINTMat),
                   nmod_mat_nrows (FLINTMat), getCharacteristic());
    nmod_mat_inv (FLINTMatInv, FLINTMat);
#else
    NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat);
    *NTLMat= inv (*NTLMat);
#endif
 
    if (GF)
      setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
    j= bufFactors;
    truncF= mod (F, power (y, l));
    if (useOldQs)
    {
      for (int i= 0; i < bufFactors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]);
    }
    else
    {
      for (int i= 0; i < bufFactors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]);
    }
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix (l*degMipo - k, bufFactors.length());
        for (int ii= 0; ii < bufFactors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            if (GF)
            {
              A [ii] [i]= A [ii] [i] (y-evaluation, y);
              setCharacteristic (getCharacteristic());
              A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha);
              if (alpha != gamma)
                A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                     gamma, source, dest
                                    );
#ifdef HAVE_FLINT
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv);
#else
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat);
#endif
            }
            else
            {
              A [ii] [i]= A [ii] [i] (y-evaluation, y);
              if (alpha != gamma)
                A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                    gamma, source, dest
                                   );
#ifdef HAVE_FLINT
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv);
#else
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat);
#endif
            }
            writeInMatrix (C, buf, ii + 1, 0);
          }
          if (GF)
            setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
        }
 
        if (GF)
          setCharacteristic(getCharacteristic());
 
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
 
        if (GF)
          setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
#ifdef HAVE_FLINT
        if (nmod_mat_ncols (FLINTN) == 1)
#else
        if (NTLN.NumCols() == 1)
#endif
        {
          irreducible= true;
          break;
        }
      }
    }
 
#ifdef HAVE_FLINT
    nmod_mat_clear (FLINTMat);
    nmod_mat_clear (FLINTMatInv);
    if (nmod_mat_ncols (FLINTN) == 1)
#else
    delete NTLMat;
    if (NTLN.NumCols() == 1)
#endif
    {
      irreducible= true;
      break;
    }
 
    bufF= F;
    bufBufFactors= bufFactors;
#ifdef HAVE_FLINT
    int * zeroOneVecs= extractZeroOneVecs (FLINTN);
    result= extReconstruction (bufF, bufFactors, zeroOneVecs, l, FLINTN, info,
                               evaluation
                              );
#else
    int * zeroOneVecs= extractZeroOneVecs (NTLN);
    result= extReconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, info,
                               evaluation
                              );
#endif
    delete [] zeroOneVecs;
    if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l)
    {
      F= bufF;
      factors= bufFactors;
      delete [] A;
      return result;
    }
    else
    {
      bufF= F;
      bufFactors= bufBufFactors;
    }
 
#ifdef HAVE_FLINT
    if (isReduced (FLINTN))
#else
    if (isReduced (NTLN))
#endif
    {
      int factorsFound= 0;
      bufF= F;
#ifdef HAVE_FLINT
      int* factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
      for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
      int* factorsFoundIndex= new int [NTLN.NumCols()];
      for (long i= 0; i < NTLN.NumCols(); i++)
#endif
        factorsFoundIndex[i]= 0;
#ifdef HAVE_FLINT
      if (l < degree (bufF) + 1 + degree (LCF))
        extReconstructionTry (result, bufF, bufFactors, l, factorsFound,
                              factorsFoundIndex, FLINTN, false, info, evaluation
                             );
      else
        extReconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 +
                              degree (LCF), factorsFound, factorsFoundIndex,
                              FLINTN, false, info, evaluation
                             );
      if (nmod_mat_ncols (FLINTN) == result.length())
#else
      if (l < degree (bufF) + 1 + degree (LCF))
        extReconstructionTry (result, bufF, bufFactors, l, factorsFound,
                              factorsFoundIndex, NTLN, false, info, evaluation
                             );
      else
        extReconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 +
                              degree (LCF), factorsFound, factorsFoundIndex,
                              NTLN, false, info, evaluation
                             );
      if (NTLN.NumCols() == result.length())
#endif
      {
        delete [] A;
        delete [] factorsFoundIndex;
        return result;
      }
      delete [] factorsFoundIndex;
    }
    result= CFList();
    oldL= l;
    stepSize *= 2;
    l += stepSize;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  if (irreducible)
  {
    delete [] A;
    Variable y= Variable (2);
    CanonicalForm tmp= F (y - evaluation, y);
    CFList source, dest;
    tmp= mapDown (tmp, info, source, dest);
    return CFList (tmp);
  }
  delete [] A;
  factors= bufFactors;
  return CFList();
}

extHenselLiftAndLatticeRecombi()

CFList extHenselLiftAndLatticeRecombi	(	const CanonicalForm &	G,
		const CFList &	uniFactors,
		const ExtensionInfo &	extInfo,
		const DegreePattern &	degPat,
		const CanonicalForm &	eval
	)

Definition at line 7712 of file facFqBivar.cc.

{
  CanonicalForm evaluation= eval;
  ExtensionInfo info= extInfo;
  Variable alpha;
  DegreePattern degs= degPat;
  CanonicalForm F= G;
  Variable x= Variable (1);
  Variable y= F.mvar();
  CFList bufUniFactors= uniFactors;
 
 
  int degMipo;
  ExtensionInfo info2= init4ext (info, evaluation, degMipo);
 
  CFList source, dest;
  CanonicalForm LCF= LC (F, 1);
 
  int d;
  bool isIrreducible= false;
  int* bounds= computeBounds (F, d, isIrreducible);
  if (isIrreducible)
  {
    delete [] bounds;
    CFList source, dest;
    CanonicalForm tmp= G (y - evaluation, y);
    tmp= mapDown (tmp, info, source, dest);
    return CFList (tmp);
  }
  int minBound= bounds[0];
  for (int i= 1; i < d; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
 
 
  CFArray Pi;
  CFList diophant;
  int liftBound= tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 +
                       degree (LC (F, 1)));
  CFMatrix M= CFMatrix (liftBound, bufUniFactors.length());
 
  CFList smallFactors;
  CanonicalForm H;
  bool success= false;
  smallFactors= extSieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi,
                                      M, success, minBound + 1, evaluation, info
                                     );
 
  if (smallFactors.length() > 0)
  {
    if (smallFactors.length() == 1)
    {
      if (smallFactors.getFirst() == F)
      {
        delete [] bounds;
        CFList source, dest;
        CanonicalForm tmp= G (y - evaluation, y);
        tmp= mapDown (tmp, info, source, dest);
        return CFList (tmp);
      }
    }
    if (degs.getLength() <= 1)
    {
      delete [] bounds;
      return smallFactors;
    }
  }
 
  int index;
  CanonicalForm tmp1, tmp2;
  for (CFListIterator i= smallFactors; i.hasItem(); i++)
  {
    index= 1;
    tmp1= mod (i.getItem(), y - evaluation);
    tmp1 /= Lc (tmp1);
    for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++)
    {
      tmp2= mod (j.getItem(), y);
      tmp2 /= Lc (tmp2);
      if (tmp1 == tmp2)
      {
        index++;
        j.remove(index);
        break;
      }
    }
  }
 
  if (bufUniFactors.isEmpty())
  {
    delete [] bounds;
    return smallFactors;
  }
 
  if (success)
  {
    F= H/Lc(H);
    delete [] bounds;
    bounds= computeBounds (F, d, isIrreducible);
    if (isIrreducible)
    {
      delete [] bounds;
      CFList source, dest;
      CanonicalForm tmp= F (y - evaluation, y);
      tmp= mapDown (tmp, info, source, dest);
      smallFactors.append (tmp);
      return smallFactors;
    }
    LCF= LC (F, 1);
 
    minBound= bounds[0];
    for (int i= 1; i < d; i++)
    {
      if (bounds[i] != 0)
        minBound= tmin (minBound, bounds[i]);
    }
    Pi= CFArray();
    diophant= CFList();
    liftBound=tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 +
                    degree (LC (F, 1)));
    M= CFMatrix (liftBound, bufUniFactors.length());
    DegreePattern bufDegs= DegreePattern (bufUniFactors);
    degs.intersect (bufDegs);
    degs.refine();
    if (degs.getLength() <= 1)
    {
      delete [] bounds;
      CFList source, dest;
      CanonicalForm tmp= F (y - evaluation, y);
      tmp= mapDown (tmp, info, source, dest);
      smallFactors.append (tmp);
      return smallFactors;
    }
  }
 
  bufUniFactors.insert (LCF);
  int l= 1;
 
#ifdef HAVE_FLINT
  nmod_mat_t FLINTN;
  nmod_mat_init (FLINTN, bufUniFactors.length()-1, bufUniFactors.length()-1,
                 getCharacteristic());
  for (long i= bufUniFactors.length()-2; i >= 0; i--)
    nmod_mat_entry (FLINTN, i, i)= 1;
#else
  if (fac_NTL_char != getCharacteristic())
  {
    fac_NTL_char= getCharacteristic();
    zz_p::init (getCharacteristic());
  }
  zz_pX NTLMipo;
  mat_zz_p NTLN;
 
  ident (NTLN, bufUniFactors.length() - 1);
#endif
  bool irreducible= false;
  CFArray bufQ= CFArray (bufUniFactors.length() - 1);
 
  int oldL;
  TIMING_START (fac_fq_till_reduced);
  if (success)
  {
    int start= 0;
#ifdef HAVE_FLINT
    oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, start,
                                    bufUniFactors, FLINTN, diophant,M, Pi, bufQ,
                                    irreducible, evaluation, info2, source, dest
                                   );
#else
    oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, start,
                                    bufUniFactors, NTLN, diophant, M, Pi, bufQ,
                                    irreducible, evaluation, info2, source, dest
                                   );
#endif
  }
  else
  {
#ifdef HAVE_FLINT
    oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound,
                                    minBound+1, bufUniFactors, FLINTN, diophant,
                                    M, Pi, bufQ, irreducible, evaluation, info2,
                                    source, dest
                                   );
#else
    oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound,
                                    minBound + 1, bufUniFactors, NTLN, diophant,
                                    M, Pi, bufQ, irreducible, evaluation, info2,
                                    source, dest
                                   );
#endif
  }
  TIMING_END_AND_PRINT (fac_fq_till_reduced,
                        "time to compute a reduced lattice: ");
 
  bufUniFactors.removeFirst();
  if (oldL > liftBound)
  {
#ifdef HAVE_FLINT
    nmod_mat_clear (FLINTN);
#endif
    delete [] bounds;
    return Union (smallFactors, extFactorRecombination
                                (bufUniFactors, F,
                                 power (y, degree (F) + 1),info,
                                 degs, evaluation, 1, bufUniFactors.length()/2
                                )
                 );
  }
 
  l= oldL;
  if (irreducible)
  {
#ifdef HAVE_FLINT
    nmod_mat_clear (FLINTN);
#endif
    delete [] bounds;
    CFList source, dest;
    CanonicalForm tmp= F (y - evaluation, y);
    tmp= mapDown (tmp, info, source, dest);
    return Union (CFList (tmp), smallFactors);
  }
 
  CanonicalForm yToL= power (y,l);
 
  CFList result;
  if (l >= degree (F) + 1)
  {
    int * factorsFoundIndex;
 
#ifdef HAVE_FLINT
    factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
    for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
    factorsFoundIndex= new int [NTLN.NumCols()];
    for (long i= 0; i < NTLN.NumCols(); i++)
#endif
      factorsFoundIndex[i]= 0;
 
    int factorsFound= 0;
    CanonicalForm bufF= F;
 
#ifdef HAVE_FLINT
    extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1,
                          factorsFound, factorsFoundIndex, FLINTN, false, info,
                          evaluation
                         );
 
    if (result.length() == nmod_mat_ncols (FLINTN))
    {
      nmod_mat_clear (FLINTN);
#else
    extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1,
                          factorsFound, factorsFoundIndex, NTLN, false, info,
                          evaluation
                         );
 
    if (result.length() == NTLN.NumCols())
    {
#endif
      delete [] factorsFoundIndex;
      delete [] bounds;
      return Union (result, smallFactors);
    }
 
    delete [] factorsFoundIndex;
  }
  if (l >= liftBound)
  {
    int * factorsFoundIndex;
#ifdef HAVE_FLINT
    factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
    for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
    factorsFoundIndex= new int [NTLN.NumCols()];
    for (long i= 0; i < NTLN.NumCols(); i++)
#endif
      factorsFoundIndex[i]= 0;
    CanonicalForm bufF= F;
    int factorsFound= 0;
 
#ifdef HAVE_FLINT
    extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1,
                          factorsFound, factorsFoundIndex, FLINTN, false,
                          info, evaluation
                         );
 
    if (result.length() == nmod_mat_ncols (FLINTN))
    {
      nmod_mat_clear (FLINTN);
#else
    extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1,
                          factorsFound, factorsFoundIndex, NTLN, false,
                          info, evaluation
                         );
 
    if (result.length() == NTLN.NumCols())
    {
#endif
      delete [] factorsFoundIndex;
      delete [] bounds;
      return Union (result, smallFactors);
    }
    delete [] factorsFoundIndex;
  }
 
  result= CFList();
  bool beenInThres= false;
  int thres= 100;
#ifdef HAVE_FLINT
  if (l <= thres && bufUniFactors.length() > nmod_mat_ncols (FLINTN))
  {
    refineAndRestartLift (F, FLINTN, 2*totaldegree (F)-1, l, bufUniFactors, M, Pi,
                         diophant
                        );
#else
  if (l <= thres && bufUniFactors.length() > NTLN.NumCols())
  {
    refineAndRestartLift (F, NTLN, 2*totaldegree (F)-1, l, bufUniFactors, M, Pi,
                         diophant
                        );
#endif
    beenInThres= true;
  }
 
 
  CanonicalForm bufF= F;
  int factorsFound= 0;
 
#ifdef HAVE_FLINT
  result= extEarlyReconstructionAndLifting (F, FLINTN, bufF, bufUniFactors, l,
                                            factorsFound, beenInThres, M, Pi,
                                            diophant, info, evaluation
                                           );
 
  if (result.length() == nmod_mat_ncols (FLINTN))
  {
    nmod_mat_clear (FLINTN);
#else
  result= extEarlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l,
                                            factorsFound, beenInThres, M, Pi,
                                            diophant, info, evaluation
                                           );
 
  if (result.length() == NTLN.NumCols())
  {
#endif
    delete [] bounds;
    return Union (result, smallFactors);
  }
 
  if (result.length() > 0)
  {
   if (beenInThres)
   {
      int index;
      for (CFListIterator i= result; i.hasItem(); i++)
      {
        index= 1;
        tmp1= mod (i.getItem(), y-evaluation);
        tmp1 /= Lc (tmp1);
        for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++)
        {
          tmp2= mod (j.getItem(), y);
          tmp2 /= Lc (tmp2);
          if (tmp1 == tmp2)
          {
            index++;
            j.remove(index);
            break;
          }
        }
      }
    }
    else
    {
#ifdef HAVE_FLINT
      int * zeroOne= extractZeroOneVecs (FLINTN);
#else
      int * zeroOne= extractZeroOneVecs (NTLN);
#endif
      CFList bufBufUniFactors= bufUniFactors;
      CFListIterator iter, iter2;
      CanonicalForm buf;
      CFList factorsConsidered;
#ifdef HAVE_FLINT
      for (int i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
      for (int i= 0; i < NTLN.NumCols(); i++)
#endif
      {
        if (zeroOne [i] == 0)
          continue;
        iter= bufUniFactors;
        buf= 1;
        factorsConsidered= CFList();
#ifdef HAVE_FLINT
        for (int j= 0; j < nmod_mat_nrows (FLINTN); j++, iter++)
        {
          if (!(nmod_mat_entry (FLINTN, j, i) == 0))
#else
        for (int j= 0; j < NTLN.NumRows(); j++, iter++)
        {
          if (!IsZero (NTLN (j + 1,i + 1)))
#endif
          {
            factorsConsidered.append (iter.getItem());
            buf *= mod (iter.getItem(), y);
          }
        }
        buf /= Lc (buf);
        for (iter2= result; iter2.hasItem(); iter2++)
        {
          CanonicalForm tmp= mod (iter2.getItem(), y - evaluation);
          tmp /= Lc (tmp);
          if (tmp == buf)
          {
            bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered);
            break;
          }
        }
      }
      bufUniFactors= bufBufUniFactors;
      delete [] zeroOne;
    }
 
    int oldNumCols;
    CFList resultBufF;
    irreducible= false;
 
#ifdef HAVE_FLINT //TODO
    oldNumCols= nmod_mat_ncols (FLINTN);
    resultBufF= extIncreasePrecision (bufF, bufUniFactors, factorsFound,
                                      oldNumCols, oldL, evaluation, info2,
                                      source, dest, l
                                     );
    nmod_mat_clear (FLINTN);
#else
    oldNumCols= NTLN.NumCols();
    resultBufF= extIncreasePrecision (bufF, bufUniFactors, factorsFound,
                                      oldNumCols, oldL, evaluation, info2,
                                      source, dest, l
                                     );
#endif
    if (bufUniFactors.isEmpty() || degree (bufF) <= 0)
    {
      delete [] bounds;
      result= Union (resultBufF, result);
      return Union (result, smallFactors);
    }
 
    for (CFListIterator i= bufUniFactors; i.hasItem(); i++)
      i.getItem()= mod (i.getItem(), y);
 
    delete [] bounds;
    CFList bufResult;
    DegreePattern bufDegs= DegreePattern (bufUniFactors);
    degs.intersect (bufDegs);
    degs.refine();
    result= Union (result, smallFactors);
    if (degs.getLength() == 1 || bufUniFactors.length() == 1)
    {
      CFList source, dest;
      CanonicalForm tmp= bufF (y - evaluation, y);
      tmp= mapDown (tmp, info, source, dest);
      result.append (tmp);
      return result;
    }
    return Union (result, extHenselLiftAndLatticeRecombi (bufF, bufUniFactors,
                                                          info, degs, evaluation
                                                         )
                 );
  }
 
  if (l/degMipo < liftBound)
  {
#ifdef HAVE_FLINT
    result=extIncreasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ,
                                 FLINTN, evaluation, info2, source, dest
                                );
 
    if (result.length()== nmod_mat_ncols (FLINTN))
    {
      nmod_mat_clear (FLINTN);
#else
    result=extIncreasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ,
                                 NTLN, evaluation, info2, source, dest
                                );
 
    if (result.length()== NTLN.NumCols())
    {
#endif
      delete [] bounds;
      result= Union (result, smallFactors);
      return result;
    }
 
    if (result.isEmpty())
    {
#ifdef HAVE_FLINT
      result= extFurtherLiftingAndIncreasePrecision (F,bufUniFactors, l,
                                                     liftBound, d,bounds,FLINTN,
                                                     diophant, M, Pi, bufQ,
                                                     evaluation, info2, source,
                                                     dest
                                                    );
      if (result.length()== nmod_mat_ncols (FLINTN))
      {
        nmod_mat_clear (FLINTN);
#else
      result= extFurtherLiftingAndIncreasePrecision (F,bufUniFactors, l,
                                                     liftBound, d, bounds, NTLN,
                                                     diophant, M, Pi, bufQ,
                                                     evaluation, info2, source,
                                                     dest
                                                    );
      if (result.length()== NTLN.NumCols())
      {
#endif
        delete [] bounds;
        result= Union (result, smallFactors);
        return result;
      }
    }
  }
 
#ifdef HAVE_FLINT
  nmod_mat_clear (FLINTN);
#endif
 
  DEBOUTLN (cerr, "lattice recombination failed");
 
  DegreePattern bufDegs= DegreePattern (bufUniFactors);
  degs.intersect (bufDegs);
  degs.refine();
 
  delete [] bounds;
  bounds= computeBounds (F, d, isIrreducible);
  if (isIrreducible)
  {
    delete [] bounds;
    CFList source, dest;
    CanonicalForm tmp= F (y - evaluation, y);
    tmp= mapDown (tmp, info, source, dest);
    smallFactors.append (tmp);
    result= Union (result, smallFactors);
    return result;
  }
  minBound= bounds[0];
  for (int i= 1; i < d; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
 
  if (minBound > 16 || result.length() == 0)
  {
    result= Union (result, smallFactors);
    CanonicalForm MODl= power (y, degree (F) + 1);
    delete [] bounds;
    return Union (result, extFactorRecombination (bufUniFactors, F, MODl, info,
                                                  degs, evaluation, 1,
                                                  bufUniFactors.length()/2
                                                 )
                 );
  }
  else
  {
    result= Union (result, smallFactors);
    for (CFListIterator i= bufUniFactors; i.hasItem(); i++)
      i.getItem()= mod (i.getItem(), y);
    delete [] bounds;
    return Union (result, extHenselLiftAndLatticeRecombi (F, bufUniFactors,
                                                          info, degs, evaluation
                                                         )
                 );
  }
}

extIncreasePrecision() [1/2]

CFList extIncreasePrecision	(	CanonicalForm &	F,
		CFList &	factors,
		int	factorsFound,
		int	oldNumCols,
		int	oldL,
		const CanonicalForm &	evaluation,
		const ExtensionInfo &	info,
		CFList &	source,
		CFList &	dest,
		int	precision
	)

Definition at line 3826 of file facFqBivar.cc.

{
  bool GF= (CFFactory::gettype()==GaloisFieldDomain);
  int degMipo= degree (getMipo (info.getAlpha()));
  Variable alpha= info.getAlpha();
  int d;
  bool isIrreducible= false;
  int* bounds= computeBounds (F, d, isIrreducible);
  if (isIrreducible)
  {
    delete [] bounds;
    Variable y= Variable (2);
    CanonicalForm tmp= F (y - evaluation, y);
    CFList source, dest;
    tmp= mapDown (tmp, info, source, dest);
    F= 1;
    return CFList (tmp);
  }
 
  CFArray * A= new CFArray [factors.length()];
  CFArray bufQ= CFArray (factors.length());
#ifdef HAVE_FLINT
  nmod_mat_t FLINTN;
  nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic());
  for (long i=factors.length()-1; i >= 0; i--)
    nmod_mat_entry (FLINTN, i, i)= 1;
#else
  if (fac_NTL_char != getCharacteristic())
  {
    fac_NTL_char= getCharacteristic();
    zz_p::init (getCharacteristic());
  }
  mat_zz_p NTLN;
  ident (NTLN, factors.length());
#endif
  int minBound= bounds[0];
  for (int i= 1; i < d; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
  int l= tmax (oldL, 2*((minBound+1)/degMipo+1));
  int oldL2= l/2;
  int stepSize= 2;
  bool useOldQs= false;
  bool hitBound= false;
  Variable gamma= info.getBeta();
  CanonicalForm primElemAlpha= info.getGamma();
  CanonicalForm imPrimElemAlpha= info.getDelta();
  CFListIterator j;
  Variable y= F.mvar();
  CanonicalForm powX, imBasis, truncF;
  CFMatrix Mat, C;
  CFIterator iter;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTMat, FLINTMatInv, FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLMat,*NTLC, NTLK;
#endif
  CFArray buf;
  while (l <= precision)
  {
    j= factors;
    if (GF)
      setCharacteristic (getCharacteristic());
    powX= power (y-gamma, l);
    Mat= CFMatrix (l*degMipo, l*degMipo);
    for (int i= 0; i < l*degMipo; i++)
    {
      imBasis= mod (power (y, i), powX);
      imBasis= imBasis (power (y, degMipo), y);
      imBasis= imBasis (y, gamma);
      iter= imBasis;
      for (; iter.hasTerms(); iter++)
          Mat (iter.exp()+ 1, i+1)= iter.coeff();
    }
 
#ifdef HAVE_FLINT
    convertFacCFMatrix2nmod_mat_t (FLINTMat, Mat);
    nmod_mat_init (FLINTMatInv, nmod_mat_nrows (FLINTMat),
                   nmod_mat_nrows (FLINTMat), getCharacteristic());
    nmod_mat_inv (FLINTMatInv, FLINTMat);
#else
    NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat);
    *NTLMat= inv (*NTLMat);
#endif
 
    if (GF)
      setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
    truncF= mod (F, power (y, l));
    if (useOldQs)
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i],
                                     bufQ[i]
                                    );
    }
    else
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]);
    }
    useOldQs= true;
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= (l/2)*degMipo)
      {
        int k= tmin (bounds [i] + 1, (l/2)*degMipo);
        C= CFMatrix (l*degMipo - k, factors.length());
        for (int ii= 0; ii < factors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            if (GF)
            {
              A[ii] [i]= A [ii] [i] (y-evaluation, y);
              setCharacteristic (getCharacteristic());
              A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha);
              if (alpha != gamma)
                A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                     gamma, source, dest
                                    );
#ifdef HAVE_FLINT
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv);
#else
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat);
#endif
            }
            else
            {
              A [ii] [i]= A [ii] [i] (y-evaluation, y);
              if (alpha != gamma)
                A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                    gamma, source, dest
                                   );
#ifdef HAVE_FLINT
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv);
#else
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat);
#endif
            }
            writeInMatrix (C, buf, ii + 1, 0);
          }
          if (GF)
            setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
        }
 
        if (GF)
          setCharacteristic(getCharacteristic());
 
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
 
        if (GF)
          setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
#ifdef HAVE_FLINT
        if (nmod_mat_ncols (FLINTN) == 1)
        {
          nmod_mat_clear (FLINTMat);
          nmod_mat_clear (FLINTMatInv);
          nmod_mat_clear (FLINTN);
#else
        if (NTLN.NumCols() == 1)
        {
          delete NTLMat;
#endif
          Variable y= Variable (2);
          CanonicalForm tmp= F (y - evaluation, y);
          CFList source, dest;
          tmp= mapDown (tmp, info, source, dest);
          delete [] A;
          delete [] bounds;
          F= 1;
          return CFList (tmp);
        }
      }
    }
 
#ifdef HAVE_FLINT
    nmod_mat_clear (FLINTMat);
    nmod_mat_clear (FLINTMatInv);
#else
    delete NTLMat;
#endif
 
#ifdef HAVE_FLINT
    if (nmod_mat_ncols (FLINTN) < oldNumCols - factorsFound)
    {
      if (isReduced (FLINTN))
      {
        int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
        for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
    if (NTLN.NumCols() < oldNumCols - factorsFound)
    {
      if (isReduced (NTLN))
      {
        int * factorsFoundIndex= new int [NTLN.NumCols()];
        for (long i= 0; i < NTLN.NumCols(); i++)
#endif
          factorsFoundIndex[i]= 0;
        int factorsFound2= 0;
        CFList result;
        CanonicalForm bufF= F;
#ifdef HAVE_FLINT
        extReconstructionTry (result, bufF, factors,degree (F)+1, factorsFound2,
                              factorsFoundIndex, FLINTN, false, info, evaluation
                             );
        if (result.length() == nmod_mat_ncols (FLINTN))
        {
          nmod_mat_clear (FLINTN);
#else
        extReconstructionTry (result, bufF, factors,degree (F)+1, factorsFound2,
                              factorsFoundIndex, NTLN, false, info, evaluation
                             );
        if (result.length() == NTLN.NumCols())
        {
#endif
          delete [] factorsFoundIndex;
          delete [] A;
          delete [] bounds;
          F= 1;
          return result;
        }
        delete [] factorsFoundIndex;
      }
      else if (l == precision)
      {
        CanonicalForm bufF= F;
#ifdef HAVE_FLINT
        int * zeroOne= extractZeroOneVecs (FLINTN);
        CFList result= extReconstruction (bufF, factors, zeroOne, precision,
                                          FLINTN, info, evaluation
                                         );
        nmod_mat_clear (FLINTN);
#else
        int * zeroOne= extractZeroOneVecs (NTLN);
        CFList result= extReconstruction (bufF, factors, zeroOne, precision,
                                          NTLN, info, evaluation
                                         );
#endif
        F= bufF;
        delete [] zeroOne;
        delete [] A;
        delete [] bounds;
        return result;
      }
    }
    oldL2= l;
    l += stepSize;
    stepSize *= 2;
    if (l > precision)
    {
      if (!hitBound)
      {
        hitBound= true;
        l= precision;
      }
      else
        break;
    }
  }
 
#ifdef HAVE_FLINT
  nmod_mat_clear (FLINTN);
#endif
  delete [] bounds;
  delete [] A;
  return CFList();
}

extIncreasePrecision() [2/2]

CFList extIncreasePrecision	(	CanonicalForm &	F,
		CFList &	factors,
		int	oldL,
		int	l,
		int	d,
		int *	bounds,
		CFArray &	bufQ,
		nmod_mat_t	FLINTN,
		const CanonicalForm &	evaluation,
		const ExtensionInfo &	info,
		CFList &	source,
		CFList &	dest
	)

Definition at line 4756 of file facFqBivar.cc.

{
  CFList result= CFList();
  CFArray * A= new CFArray [factors.length()];
  int oldL2= oldL/2; //be careful
  bool hitBound= false;
  bool useOldQs= false;
  bool GF= (CFFactory::gettype()==GaloisFieldDomain);
  int degMipo= degree (getMipo (info.getAlpha()));
  Variable alpha= info.getAlpha();
 
  Variable gamma= info.getBeta();
  CanonicalForm primElemAlpha= info.getGamma();
  CanonicalForm imPrimElemAlpha= info.getDelta();
#ifdef HAVE_FLINT
  nmod_mat_clear (FLINTN);
  nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic());
  for (long i=factors.length()-1; i >= 0; i--)
    nmod_mat_entry (FLINTN, i, i)= 1;
#else
  if (NTLN.NumRows() != factors.length()) //refined factors
    ident (NTLN, factors.length());
#endif
  Variable y= F.mvar();
  CFListIterator j;
  CanonicalForm powX, imBasis, bufF, truncF;
  CFMatrix Mat, C;
  CFIterator iter;
  CFArray buf;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTMat, FLINTMatInv, FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLC, NTLK, *NTLMat;
#endif
  CFList bufUniFactors;
  while (oldL <= l)
  {
    j= factors;
    if (GF)
      setCharacteristic (getCharacteristic());
 
    powX= power (y-gamma, oldL);
    Mat= CFMatrix (oldL*degMipo, oldL*degMipo);
    for (int i= 0; i < oldL*degMipo; i++)
    {
      imBasis= mod (power (y, i), powX);
      imBasis= imBasis (power (y, degMipo), y);
      imBasis= imBasis (y, gamma);
      iter= imBasis;
      for (; iter.hasTerms(); iter++)
        Mat (iter.exp()+ 1, i+1)= iter.coeff();
    }
 
#ifdef HAVE_FLINT
    convertFacCFMatrix2nmod_mat_t (FLINTMat, Mat);
    nmod_mat_init (FLINTMatInv, nmod_mat_nrows (FLINTMat),
                   nmod_mat_nrows (FLINTMat), getCharacteristic());
    nmod_mat_inv (FLINTMatInv, FLINTMat);
#else
    NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat);
    *NTLMat= inv (*NTLMat);
#endif
 
    if (GF)
      setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
    truncF= mod (F, power (y, oldL));
    if (useOldQs)
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i],
                                     bufQ[i]);
    }
    else
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]);
    }
    useOldQs= true;
 
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= oldL/2)
      {
        int k= tmin (bounds [i] + 1, oldL/2);
        C= CFMatrix (oldL*degMipo - k, factors.length());
        for (int ii= 0; ii < factors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            if (GF)
            {
              A [ii] [i]= A [ii] [i] (y-evaluation, y);
              setCharacteristic (getCharacteristic());
              A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha);
              if (alpha != gamma)
                A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                     gamma, source, dest
                                    );
#ifdef HAVE_FLINT
              buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, FLINTMatInv);
#else
              buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat);
#endif
            }
            else
            {
              A [ii] [i]= A [ii] [i] (y-evaluation, y);
              if (alpha != gamma)
                A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                    gamma, source, dest
                                   );
#ifdef HAVE_FLINT
              buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, FLINTMatInv);
#else
              buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat);
#endif
            }
            writeInMatrix (C, buf, ii + 1, 0);
          }
          if (GF)
            setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
        }
 
        if (GF)
          setCharacteristic(getCharacteristic());
 
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
 
        if (GF)
          setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
#ifdef HAVE_FLINT
        if (nmod_mat_ncols (FLINTN) == 1)
        {
          nmod_mat_clear (FLINTMat);
          nmod_mat_clear (FLINTMatInv);
#else
        if (NTLN.NumCols() == 1)
        {
          delete NTLMat;
#endif
          Variable y= Variable (2);
          CanonicalForm tmp= F (y - evaluation, y);
          CFList source, dest;
          tmp= mapDown (tmp, info, source, dest);
          delete [] A;
          return CFList (tmp);
        }
      }
    }
 
#ifdef HAVE_FLINT
    nmod_mat_clear (FLINTMat);
    nmod_mat_clear (FLINTMatInv);
#else
    delete NTLMat;
#endif
 
#ifdef HAVE_FLINT
    if (nmod_mat_ncols (FLINTN) == 1)
#else
    if (NTLN.NumCols() == 1)
#endif
    {
      Variable y= Variable (2);
      CanonicalForm tmp= F (y - evaluation, y);
      CFList source, dest;
      tmp= mapDown (tmp, info, source, dest);
      delete [] A;
      return CFList (tmp);
    }
 
    int * zeroOneVecs;
    bufF= F;
    bufUniFactors= factors;
#ifdef HAVE_FLINT
    zeroOneVecs= extractZeroOneVecs (FLINTN);
    result= extReconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, FLINTN,
                               info, evaluation
                              );
#else
    zeroOneVecs= extractZeroOneVecs (NTLN);
    result= extReconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN,
                               info, evaluation
                              );
#endif
    delete [] zeroOneVecs;
    if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0)
    {
      F= bufF;
      factors= bufUniFactors;
      return result;
    }
 
    result= CFList();
    oldL2= oldL;
    oldL *= 2;
    if (oldL > l)
    {
      if (!hitBound)
      {
        oldL= l;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  return result;
}

extLiftAndComputeLattice() [1/2]

int extLiftAndComputeLattice	(	const CanonicalForm &	F,
		int *	bounds,
		int	sizeBounds,
		int	liftBound,
		int	minBound,
		int	start,
		CFList &	factors,
		mat_zz_p &	NTLN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		bool &	irreducible,
		const CanonicalForm &	evaluation,
		const ExtensionInfo &	info,
		CFList &	source,
		CFList &	dest
	)

Definition at line 2749 of file facFqBivar.cc.

{
  bool GF= (CFFactory::gettype()==GaloisFieldDomain);
  CanonicalForm LCF= LC (F, 1);
  CFArray *A= new CFArray [factors.length() - 1];
  bool wasInBounds= false;
  bool hitBound= false;
  int degMipo;
  Variable alpha;
  alpha= info.getAlpha();
  degMipo= degree (getMipo (alpha));
 
  Variable gamma= info.getBeta();
  CanonicalForm primElemAlpha= info.getGamma();
  CanonicalForm imPrimElemAlpha= info.getDelta();
 
  int stepSize= 2;
  int l= ((minBound+1)/degMipo+1)*2;
  l= tmax (l, 2);
  if (start > l)
    l= start;
  int oldL= l/2;
  bool reduced= false;
  Variable y= F.mvar();
  Variable x= Variable (1);
  CanonicalForm powX, imBasis, truncF;
  CFMatrix Mat, C;
  CFArray buf;
  CFIterator iter;
  mat_zz_p* NTLMat, *NTLC, NTLK;
  CFListIterator j;
  while (l <= liftBound)
  {
    TIMING_START (fac_fq_compute_lattice_lift);
    if (start)
    {
      henselLiftResume12 (F, factors, start, l, Pi, diophant, M);
      start= 0;
    }
    else
    {
      if (wasInBounds)
        henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M);
      else
        henselLift12 (F, factors, l, Pi, diophant, M);
    }
    TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift,
                          "time to lift in compute lattice: ");
 
    factors.insert (LCF);
 
    if (GF)
      setCharacteristic (getCharacteristic());
 
    powX= power (y-gamma, l);
    Mat= CFMatrix (l*degMipo, l*degMipo);
    for (int i= 0; i < l*degMipo; i++)
    {
      imBasis= mod (power (y, i), powX);
      imBasis= imBasis (power (y, degMipo), y);
      imBasis= imBasis (y, gamma);
      iter= imBasis;
      for (; iter.hasTerms(); iter++)
        Mat (iter.exp()+ 1, i+1)= iter.coeff();
    }
 
    NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat);
    *NTLMat= inv (*NTLMat);
 
    if (GF)
      setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
    j= factors;
    j++;
 
    truncF= mod (F, power (y, l));
    TIMING_START (fac_fq_logarithmic);
    for (int i= 0; i < factors.length() - 1; i++, j++)
    {
      if (!wasInBounds)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]);
      else
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]);
    }
    TIMING_END_AND_PRINT (fac_fq_logarithmic,
                          "time to compute logarithmic derivative: ");
 
    for (int i= 0; i < sizeBounds; i++)
    {
      if (bounds [i] + 1 <= (l/2)*degMipo)
      {
        wasInBounds= true;
        int k= tmin (bounds [i] + 1, (l/2)*degMipo);
        C= CFMatrix (l*degMipo - k, factors.length() - 1);
 
        for (int ii= 0; ii < factors.length() - 1; ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            if (GF)
            {
              A [ii] [i]= A [ii] [i] (y-evaluation, y);
              setCharacteristic (getCharacteristic());
              A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha);
              if (alpha != gamma)
                A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                     gamma, source, dest
                                    );
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat);
            }
            else
            {
              A [ii] [i]= A [ii] [i] (y-evaluation, y);
              if (alpha != gamma)
                A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                    gamma, source, dest
                                   );
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat);
            }
            writeInMatrix (C, buf, ii + 1, 0);
          }
          if (GF)
            setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
        }
 
        if (GF)
          setCharacteristic(getCharacteristic());
 
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
 
        if (GF)
          setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
        if (NTLN.NumCols() == 1)
        {
          irreducible= true;
          break;
        }
        if (isReduced (NTLN))
        {
          reduced= true;
          break;
        }
      }
    }
 
    delete NTLMat;
 
    if (NTLN.NumCols() == 1)
    {
      irreducible= true;
      break;
    }
    if (reduced)
      break;
    oldL= l;
    l += stepSize;
    stepSize *= 2;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  if (!wasInBounds)
  {
    if (start)
      henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M);
    else
      henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M);
    factors.insert (LCF);
  }
  return l;
}

extLiftAndComputeLattice() [2/2]

int extLiftAndComputeLattice	(	const CanonicalForm &	F,
		int *	bounds,
		int	sizeBounds,
		int	liftBound,
		int	minBound,
		int	start,
		CFList &	factors,
		nmod_mat_t	FLINTN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		bool &	irreducible,
		const CanonicalForm &	evaluation,
		const ExtensionInfo &	info,
		CFList &	source,
		CFList &	dest
	)

Definition at line 2948 of file facFqBivar.cc.

{
  bool GF= (CFFactory::gettype()==GaloisFieldDomain);
  CanonicalForm LCF= LC (F, 1);
  CFArray *A= new CFArray [factors.length() - 1];
  bool wasInBounds= false;
  bool hitBound= false;
  int degMipo;
  Variable alpha;
  alpha= info.getAlpha();
  degMipo= degree (getMipo (alpha));
 
  Variable gamma= info.getBeta();
  CanonicalForm primElemAlpha= info.getGamma();
  CanonicalForm imPrimElemAlpha= info.getDelta();
 
  int stepSize= 2;
  int l= ((minBound+1)/degMipo+1)*2;
  l= tmax (l, 2);
  if (start > l)
    l= start;
  int oldL= l/2;
  bool reduced= false;
  Variable y= F.mvar();
  Variable x= Variable (1);
  CanonicalForm powX, imBasis, truncF;
  CFMatrix Mat, C;
  CFArray buf;
  CFIterator iter;
  long rank;
  nmod_mat_t FLINTMat, FLINTMatInv, FLINTC, FLINTK, null;
  CFListIterator j;
  while (l <= liftBound)
  {
    if (start)
    {
      henselLiftResume12 (F, factors, start, l, Pi, diophant, M);
      start= 0;
    }
    else
    {
      if (wasInBounds)
        henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M);
      else
        henselLift12 (F, factors, l, Pi, diophant, M);
    }
 
    factors.insert (LCF);
 
    if (GF)
      setCharacteristic (getCharacteristic());
 
    powX= power (y-gamma, l);
    Mat= CFMatrix (l*degMipo, l*degMipo);
    for (int i= 0; i < l*degMipo; i++)
    {
      imBasis= mod (power (y, i), powX);
      imBasis= imBasis (power (y, degMipo), y);
      imBasis= imBasis (y, gamma);
      iter= imBasis;
      for (; iter.hasTerms(); iter++)
        Mat (iter.exp()+ 1, i+1)= iter.coeff();
    }
 
    convertFacCFMatrix2nmod_mat_t (FLINTMat, Mat);
    nmod_mat_init (FLINTMatInv, nmod_mat_nrows (FLINTMat),
                   nmod_mat_nrows (FLINTMat), getCharacteristic());
    nmod_mat_inv (FLINTMatInv, FLINTMat);
 
    if (GF)
      setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
    j= factors;
    j++;
 
    truncF= mod (F, power (y, l));
    for (int i= 0; i < factors.length() - 1; i++, j++)
    {
      if (!wasInBounds)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]);
      else
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]);
    }
 
    for (int i= 0; i < sizeBounds; i++)
    {
      if (bounds [i] + 1 <= (l/2)*degMipo)
      {
        wasInBounds= true;
        int k= tmin (bounds [i] + 1, (l/2)*degMipo);
        C= CFMatrix (l*degMipo - k, factors.length() - 1);
 
        for (int ii= 0; ii < factors.length() - 1; ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            if (GF)
            {
              A [ii] [i]= A [ii] [i] (y-evaluation, y);
              setCharacteristic (getCharacteristic());
              A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha);
              if (alpha != gamma)
                A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                     gamma, source, dest
                                    );
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv);
            }
            else
            {
              A [ii] [i]= A [ii] [i] (y-evaluation, y);
              if (alpha != gamma)
                A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha,
                                    gamma, source, dest
                                   );
              buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv);
            }
            writeInMatrix (C, buf, ii + 1, 0);
          }
          if (GF)
            setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
        }
 
        if (GF)
          setCharacteristic(getCharacteristic());
 
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
 
        if (GF)
          setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
 
        if (nmod_mat_ncols (FLINTN) == 1)
        {
          irreducible= true;
          break;
        }
        if (isReduced (FLINTN))
        {
          reduced= true;
          break;
        }
      }
    }
 
    nmod_mat_clear (FLINTMat);
    nmod_mat_clear (FLINTMatInv);
 
    if (nmod_mat_ncols (FLINTN) == 1)
    {
      irreducible= true;
      break;
    }
    if (reduced)
      break;
    oldL= l;
    l += stepSize;
    stepSize *= 2;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  if (!wasInBounds)
  {
    if (start)
      henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M);
    else
      henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M);
    factors.insert (LCF);
  }
  return l;
}

extractZeroOneVecs() [1/3]

int * extractZeroOneVecs

(

const mat_zz_p &

M

)

Definition at line 1525 of file facFqBivar.cc.

{
  long i, j;
  bool nonZeroOne= false;
  int * result= new int [M.NumCols()];
  for (i = 1; i <= M.NumCols(); i++)
  {
    for (j = 1; j <= M.NumRows(); j++)
    {
      if (!(IsOne (M (j,i)) || IsZero (M (j,i))))
      {
        nonZeroOne= true;
        break;
      }
    }
    if (!nonZeroOne)
      result [i - 1]= 1;
    else
      result [i - 1]= 0;
    nonZeroOne= false;
  }
  return result;
}

extractZeroOneVecs() [2/3]

int * extractZeroOneVecs

(

const mat_zz_pE &

M

)

Definition at line 1577 of file facFqBivar.cc.

{
  long i, j;
  bool nonZeroOne= false;
  int * result= new int [M.NumCols()];
  for (i = 1; i <= M.NumCols(); i++)
  {
    for (j = 1; j <= M.NumRows(); j++)
    {
      if (!(IsOne (M (j,i)) || IsZero (M (j,i))))
      {
        nonZeroOne= true;
        break;
      }
    }
    if (!nonZeroOne)
      result [i - 1]= 1;
    else
      result [i - 1]= 0;
    nonZeroOne= false;
  }
  return result;
}

extractZeroOneVecs() [3/3]

int * extractZeroOneVecs

(

const nmod_mat_t

M

)

Definition at line 1551 of file facFqBivar.cc.

{
  long i, j;
  bool nonZeroOne= false;
  int * result= new int [nmod_mat_ncols (M)];
  for (i = 0; i < nmod_mat_ncols (M); i++)
  {
    for (j = 0; j < nmod_mat_nrows (M); j++)
    {
      if (!((nmod_mat_entry (M, j, i) == 1) || (nmod_mat_entry (M, j,i) == 0)))
      {
        nonZeroOne= true;
        break;
      }
    }
    if (!nonZeroOne)
      result [i]= 1;
    else
      result [i]= 0;
    nonZeroOne= false;
  }
  return result;
}

extReconstruction() [1/2]

CFList extReconstruction	(	CanonicalForm &	G,
		CFList &	factors,
		int *	zeroOneVecs,
		int	precision,
		const mat_zz_p &	N,
		const ExtensionInfo &	info,
		const CanonicalForm &	evaluation
	)

Definition at line 1960 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  Variable alpha= info.getAlpha();
  Variable beta= info.getBeta();
  int k= info.getGFDegree();
  CanonicalForm gamma= info.getGamma();
  CanonicalForm delta= info.getDelta();
  CanonicalForm F= G;
  CanonicalForm yToL= power (y, precision);
  CFList result;
  CFList bufFactors= factors;
  CFList factorsConsidered;
  CanonicalForm buf2, quot, buf;
  CFListIterator iter;
  for (long i= 1; i <= N.NumCols(); i++)
  {
    if (zeroOneVecs [i - 1] == 0)
      continue;
    iter= factors;
    buf= 1;
    factorsConsidered= CFList();
    for (long j= 1; j <= N.NumRows(); j++, iter++)
    {
      if (!IsZero (N (j,i)))
      {
        factorsConsidered.append (iter.getItem());
        buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    buf2= buf (y-evaluation, y);
    buf2 /= Lc (buf2);
    if (!k && beta == x)
    {
      if (degree (buf2, alpha) < 1)
      {
        if (fdivides (buf, F, quot))
        {
          F= quot;
          F /= Lc (F);
          result.append (buf2);
          bufFactors= Difference (bufFactors, factorsConsidered);
        }
      }
    }
    else
    {
      CFList source, dest;
 
      if (!isInExtension (buf2, gamma, k, delta, source, dest))
      {
        if (fdivides (buf, F, quot))
        {
          F= quot;
          F /= Lc (F);
          result.append (buf2);
          bufFactors= Difference (bufFactors, factorsConsidered);
        }
      }
    }
    if (degree (F) <= 0)
    {
      G= F;
      factors= bufFactors;
      return result;
    }
  }
  G= F;
  factors= bufFactors;
  return result;
}

extReconstruction() [2/2]

CFList extReconstruction	(	CanonicalForm &	G,
		CFList &	factors,
		int *	zeroOneVecs,
		int	precision,
		const nmod_mat_t	N,
		const ExtensionInfo &	info,
		const CanonicalForm &	evaluation
	)

Definition at line 2041 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  Variable alpha= info.getAlpha();
  Variable beta= info.getBeta();
  int k= info.getGFDegree();
  CanonicalForm gamma= info.getGamma();
  CanonicalForm delta= info.getDelta();
  CanonicalForm F= G;
  CanonicalForm yToL= power (y, precision);
  CFList result;
  CFList bufFactors= factors;
  CFList factorsConsidered;
  CanonicalForm buf2, quot, buf;
  CFListIterator iter;
  for (long i= 0; i < nmod_mat_ncols(N); i++)
  {
    if (zeroOneVecs [i] == 0)
      continue;
    iter= factors;
    buf= 1;
    factorsConsidered= CFList();
    for (long j= 0; j < nmod_mat_nrows(N); j++, iter++)
    {
      if (!(nmod_mat_entry (N, j, i) == 0))
      {
        factorsConsidered.append (iter.getItem());
        buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    buf2= buf (y-evaluation, y);
    buf2 /= Lc (buf2);
    if (!k && beta == x)
    {
      if (degree (buf2, alpha) < 1)
      {
        if (fdivides (buf, F, quot))
        {
          F= quot;
          F /= Lc (F);
          result.append (buf2);
          bufFactors= Difference (bufFactors, factorsConsidered);
        }
      }
    }
    else
    {
      CFList source, dest;
 
      if (!isInExtension (buf2, gamma, k, delta, source, dest))
      {
        if (fdivides (buf, F, quot))
        {
          F= quot;
          F /= Lc (F);
          result.append (buf2);
          bufFactors= Difference (bufFactors, factorsConsidered);
        }
      }
    }
    if (degree (F) <= 0)
    {
      G= F;
      factors= bufFactors;
      return result;
    }
  }
  G= F;
  factors= bufFactors;
  return result;
}

extReconstructionTry() [1/2]

void extReconstructionTry	(	CFList &	reconstructedFactors,
		CanonicalForm &	F,
		const CFList &	factors,
		const int	liftBound,
		int &	factorsFound,
		int *&	factorsFoundIndex,
		mat_zz_p &	N,
		bool	beenInThres,
		const ExtensionInfo &	info,
		const CanonicalForm &	evaluation
	)

Definition at line 2224 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  Variable alpha= info.getAlpha();
  Variable beta= info.getBeta();
  int k= info.getGFDegree();
  CanonicalForm gamma= info.getGamma();
  CanonicalForm delta= info.getDelta();
  CanonicalForm yToL= power (y, liftBound);
  CFList source, dest;
  if (factors.length() == 2)
  {
    CanonicalForm tmp1, tmp2, tmp3;
    tmp1= factors.getFirst();
    tmp2= factors.getLast();
    tmp1= mulMod2 (tmp1, LC (F,x), yToL);
    tmp1 /= content (tmp1, x);
    tmp2= mulMod2 (tmp2, LC (F,x), yToL);
    tmp2 /= content (tmp2, x);
    tmp3 = tmp1*tmp2;
    if (tmp3/Lc (tmp3) == F/Lc (F))
    {
      tmp1= tmp1 (y - evaluation, y);
      tmp2= tmp2 (y - evaluation, y);
      tmp1 /= Lc (tmp1);
      tmp2 /= Lc (tmp2);
      if (!k && beta == x && degree (tmp2, alpha) < 1 &&
          degree (tmp1, alpha) < 1)
      {
        factorsFound++;
        F= 1;
        tmp1= mapDown (tmp1, info, source, dest);
        tmp2= mapDown (tmp2, info, source, dest);
        reconstructedFactors.append (tmp1);
        reconstructedFactors.append (tmp2);
        return;
      }
      else if (!isInExtension (tmp2, gamma, k, delta, source, dest) &&
               !isInExtension (tmp1, gamma, k, delta, source, dest))
      {
        factorsFound++;
        F= 1;
        tmp1= mapDown (tmp1, info, source, dest);
        tmp2= mapDown (tmp2, info, source, dest);
        reconstructedFactors.append (tmp1);
        reconstructedFactors.append (tmp2);
        return;
      }
    }
  }
  CanonicalForm quot, buf, buf2;
  CFListIterator iter;
  for (long i= 1; i <= N.NumCols(); i++)
  {
    if (factorsFoundIndex [i - 1] == 1)
      continue;
    iter= factors;
    if (beenInThres)
    {
      int count= 1;
      while (count < i)
      {
        count++;
        iter++;
      }
      buf= iter.getItem();
    }
    else
    {
      buf= 1;
      for (long j= 1; j <= N.NumRows(); j++, iter++)
      {
        if (!IsZero (N (j,i)))
          buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    buf2= buf (y - evaluation, y);
    buf2 /= Lc (buf2);
    if (!k && beta == x)
    {
      if (degree (buf2, alpha) < 1)
      {
        if (fdivides (buf, F, quot))
        {
          factorsFoundIndex[i - 1]= 1;
          factorsFound++;
          F= quot;
          F /= Lc (F);
          buf2= mapDown (buf2, info, source, dest);
          reconstructedFactors.append (buf2);
        }
      }
    }
    else
    {
      if (!isInExtension (buf2, gamma, k, delta, source, dest))
      {
        if (fdivides (buf, F, quot))
        {
          factorsFoundIndex[i - 1]= 1;
          factorsFound++;
          F= quot;
          F /= Lc (F);
          buf2= mapDown (buf2, info, source, dest);
          reconstructedFactors.append (buf2);
        }
      }
    }
    if (degree (F) <= 0)
      return;
    if (factorsFound + 1 == N.NumCols())
    {
      CanonicalForm tmp= F (y - evaluation, y);
      tmp= mapDown (tmp, info, source, dest);
      reconstructedFactors.append (tmp);
      return;
    }
  }
}

extReconstructionTry() [2/2]

void extReconstructionTry	(	CFList &	reconstructedFactors,
		CanonicalForm &	F,
		const CFList &	factors,
		const int	liftBound,
		int &	factorsFound,
		int *&	factorsFoundIndex,
		nmod_mat_t	N,
		bool	beenInThres,
		const ExtensionInfo &	info,
		const CanonicalForm &	evaluation
	)

Definition at line 2354 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  Variable alpha= info.getAlpha();
  Variable beta= info.getBeta();
  int k= info.getGFDegree();
  CanonicalForm gamma= info.getGamma();
  CanonicalForm delta= info.getDelta();
  CanonicalForm yToL= power (y, liftBound);
  CFList source, dest;
  if (factors.length() == 2)
  {
    CanonicalForm tmp1, tmp2, tmp3;
    tmp1= factors.getFirst();
    tmp2= factors.getLast();
    tmp1= mulMod2 (tmp1, LC (F,x), yToL);
    tmp1 /= content (tmp1, x);
    tmp2= mulMod2 (tmp2, LC (F,x), yToL);
    tmp2 /= content (tmp2, x);
    tmp3 = tmp1*tmp2;
    if (tmp3/Lc (tmp3) == F/Lc (F))
    {
      tmp1= tmp1 (y - evaluation, y);
      tmp2= tmp2 (y - evaluation, y);
      tmp1 /= Lc (tmp1);
      tmp2 /= Lc (tmp2);
      if (!k && beta == x && degree (tmp2, alpha) < 1 &&
          degree (tmp1, alpha) < 1)
      {
        factorsFound++;
        F= 1;
        tmp1= mapDown (tmp1, info, source, dest);
        tmp2= mapDown (tmp2, info, source, dest);
        reconstructedFactors.append (tmp1);
        reconstructedFactors.append (tmp2);
        return;
      }
      else if (!isInExtension (tmp2, gamma, k, delta, source, dest) &&
               !isInExtension (tmp1, gamma, k, delta, source, dest))
      {
        factorsFound++;
        F= 1;
        tmp1= mapDown (tmp1, info, source, dest);
        tmp2= mapDown (tmp2, info, source, dest);
        reconstructedFactors.append (tmp1);
        reconstructedFactors.append (tmp2);
        return;
      }
    }
  }
  CanonicalForm quot, buf, buf2;
  CFListIterator iter;
  for (long i= 0; i < nmod_mat_ncols (N); i++)
  {
    if (factorsFoundIndex [i] == 1)
      continue;
    iter= factors;
    if (beenInThres)
    {
      int count= 0;
      while (count < i)
      {
        count++;
        iter++;
      }
      buf= iter.getItem();
    }
    else
    {
      buf= 1;
      for (long j= 0; j < nmod_mat_nrows (N); j++, iter++)
      {
        if (!(nmod_mat_entry (N, j, i) == 0))
          buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    buf2= buf (y - evaluation, y);
    buf2 /= Lc (buf2);
    if (!k && beta == x)
    {
      if (degree (buf2, alpha) < 1)
      {
        if (fdivides (buf, F, quot))
        {
          factorsFoundIndex[i]= 1;
          factorsFound++;
          F= quot;
          F /= Lc (F);
          buf2= mapDown (buf2, info, source, dest);
          reconstructedFactors.append (buf2);
        }
      }
    }
    else
    {
      if (!isInExtension (buf2, gamma, k, delta, source, dest))
      {
        if (fdivides (buf, F, quot))
        {
          factorsFoundIndex[i]= 1;
          factorsFound++;
          F= quot;
          F /= Lc (F);
          buf2= mapDown (buf2, info, source, dest);
          reconstructedFactors.append (buf2);
        }
      }
    }
    if (degree (F) <= 0)
      return;
    if (factorsFound + 1 == nmod_mat_nrows (N))
    {
      CanonicalForm tmp= F (y - evaluation, y);
      tmp= mapDown (tmp, info, source, dest);
      reconstructedFactors.append (tmp);
      return;
    }
  }
}

extSieveSmallFactors()

CFList extSieveSmallFactors	(	const CanonicalForm &	G,
		CFList &	uniFactors,
		DegreePattern &	degPat,
		CanonicalForm &	H,
		CFList &	diophant,
		CFArray &	Pi,
		CFMatrix &	M,
		bool &	success,
		int	d,
		const CanonicalForm &	evaluation,
		const ExtensionInfo &	info
	)

Definition at line 6809 of file facFqBivar.cc.

{
  CanonicalForm F= G;
  CFList bufUniFactors= uniFactors;
  bufUniFactors.insert (LC (F, 1));
  int smallFactorDeg= d;
  DegreePattern degs= degPat;
  henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M);
  int adaptedLiftBound;
  success= false;
  int * factorsFoundIndex= new int [uniFactors.length()];
  for (int i= 0; i < uniFactors.length(); i++)
    factorsFoundIndex [i]= 0;
  CFList earlyFactors;
  extEarlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound,
                           factorsFoundIndex, degs, success, info, evaluation,
                           smallFactorDeg);
  delete [] factorsFoundIndex;
  if (degs.getLength() == 1)
  {
    degPat= degs;
    return earlyFactors;
  }
  if (success)
  {
    H= F;
    return earlyFactors;
  }
  Variable y= F.mvar();
  int sizeOldF= size (G);
  if (size (F) < sizeOldF)
  {
    H= F;
    success= true;
    return earlyFactors;
  }
  else
  {
    uniFactors= bufUniFactors;
    return CFList();
  }
}

factorRecombination()

CFList factorRecombination	(	CFList &	factors,
		CanonicalForm &	F,
		const CanonicalForm &	N,
		DegreePattern &	degs,
		const CanonicalForm &	eval,
		int	s,
		int	thres,
		const modpk &	b,
		const CanonicalForm &	den
	)

naive factor recombination as decribed in "Factoring multivariate polynomials over a finite field" by L Bernardin.

naive factor recombination. Uses precomputed data to exclude combinations that are not possible.

Parameters

[in,out]	factors	list of lifted factors that are monic wrt Variable (1)
[in,out]	F	poly to be factored
[in]	N	Variable (2)^liftBound
[in]	degs	degree pattern
[in]	eval	evaluation point
[in]	s	algorithm starts checking subsets of size s
[in]	thres	threshold for the size of subsets which are checked, for a full factor recombination choose thres= factors.length()/2
[in]	b	coeff bound
[in]	den	bound on the den if over Q (a)

Definition at line 586 of file facFqBivar.cc.

{
  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;
}

for()

for	(	int	j = 1;j<=l;j++,
		i++
	)

furtherLiftingAndIncreasePrecision() [1/2]

CFList furtherLiftingAndIncreasePrecision	(	CanonicalForm &	F,
		CFList &	factors,
		int	l,
		int	liftBound,
		int	d,
		int *	bounds,
		mat_zz_pE &	NTLN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		const CanonicalForm &	eval
	)

Definition at line 5409 of file facFqBivar.cc.

{
  CanonicalForm LCF= LC (F, 1);
  CFList result;
  bool irreducible= false;
  CFList bufFactors= factors;
  CFList bufBufFactors;
  CFArray *A = new CFArray [bufFactors.length()];
  bool useOldQs= false;
  bool hitBound= false;
  int oldL= l;
  int stepSize= 8; //TODO choose better step size?
  l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2);
  if (NTLN.NumRows() != factors.length()) //refined factors
    ident (NTLN, factors.length());
  CFListIterator j;
  CFArray buf;
  mat_zz_pE* NTLC, NTLK;
  CanonicalForm bufF, truncF;
  Variable y= F.mvar();
  while (l <= liftBound)
  {
    bufFactors.insert (LCF);
    henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M);
    j= bufFactors;
    truncF= mod (F, power (y, l));
    if (useOldQs)
    {
      for (int i= 0; i < bufFactors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]);
    }
    else
    {
      for (int i= 0; i < bufFactors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]);
    }
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        int k= tmin (bounds [i] + 1, l/2);
        CFMatrix C= CFMatrix (l - k, bufFactors.length());
        for (int ii= 0; ii < bufFactors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
        NTLC= convertFacCFMatrix2NTLmat_zz_pE(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
        if (NTLN.NumCols() == 1)
        {
          irreducible= true;
          break;
        }
      }
    }
    if (NTLN.NumCols() == 1)
    {
      irreducible= true;
      break;
    }
 
    int * zeroOneVecs= extractZeroOneVecs (NTLN);
    bufF= F;
    bufBufFactors= bufFactors;
    result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, eval);
    delete [] zeroOneVecs;
    if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l)
    {
      F= bufF;
      factors= bufFactors;
      delete [] A;
      return result;
    }
    else
    {
      bufF= F;
      bufFactors= bufBufFactors;
    }
 
    if (isReduced (NTLN))
    {
      int factorsFound= 0;
      bufF= F;
      int* factorsFoundIndex= new int [NTLN.NumCols()];
      for (long i= 0; i < NTLN.NumCols(); i++)
        factorsFoundIndex[i]= 0;
      if (l < liftBound)
        reconstructionTry (result, bufF, bufFactors, l, factorsFound,
                           factorsFoundIndex, NTLN, eval, false
                          );
      else
        reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 +
                           degree (LCF), factorsFound, factorsFoundIndex,
                           NTLN, eval, false
                          );
      if (NTLN.NumCols() == result.length())
      {
        delete [] A;
        delete [] factorsFoundIndex;
        return result;
      }
      delete [] factorsFoundIndex;
    }
    result= CFList();
    oldL= l;
    stepSize *= 2;
    l += stepSize;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  if (irreducible)
  {
    delete [] A;
    return CFList (F (y-eval,y));
  }
  delete [] A;
  factors= bufFactors;
  return CFList();
}

furtherLiftingAndIncreasePrecision() [2/2]

CFList furtherLiftingAndIncreasePrecision	(	CanonicalForm &	F,
		CFList &	factors,
		int	l,
		int	liftBound,
		int	d,
		int *	bounds,
		nmod_mat_t	FLINTN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		const CanonicalForm &	eval
	)

Definition at line 5174 of file facFqBivar.cc.

{
  CanonicalForm LCF= LC (F, 1);
  CFList result;
  bool irreducible= false;
  CFList bufFactors= factors;
  CFList bufBufFactors;
  CFArray *A = new CFArray [bufFactors.length()];
  bool useOldQs= false;
  bool hitBound= false;
  int oldL= l;
  int stepSize= 8; //TODO choose better step size?
  l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2);
#ifdef HAVE_FLINT
  if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors
  {
    nmod_mat_clear (FLINTN);
    nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic());
    for (long i=factors.length()-1; i >= 0; i--)
      nmod_mat_entry (FLINTN, i, i)= 1;
  }
#else
  if (NTLN.NumRows() != factors.length()) //refined factors
    ident (NTLN, factors.length());
#endif
  CFListIterator j;
  CFMatrix C;
  CFArray buf;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLC, NTLK;
#endif
  CanonicalForm bufF, truncF;
  Variable y= F.mvar();
  while (l <= liftBound)
  {
    bufFactors.insert (LCF);
    henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M);
    j= bufFactors;
    truncF= mod (F, power (y, l));
    if (useOldQs)
    {
      for (int i= 0; i < bufFactors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]);
    }
    else
    {
      for (int i= 0; i < bufFactors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]);
    }
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix (l - k, bufFactors.length());
        for (int ii= 0; ii < bufFactors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
#ifdef HAVE_FLINT
        if (nmod_mat_ncols (FLINTN) == 1)
#else
        if (NTLN.NumCols() == 1)
#endif
        {
          irreducible= true;
          break;
        }
      }
    }
 
#ifdef HAVE_FLINT
    if (nmod_mat_ncols (FLINTN) == 1)
#else
    if (NTLN.NumCols() == 1)
#endif
    {
      irreducible= true;
      break;
    }
 
#ifdef HAVE_FLINT
    int * zeroOneVecs= extractZeroOneVecs (FLINTN);
#else
    int * zeroOneVecs= extractZeroOneVecs (NTLN);
#endif
    bufF= F;
    bufBufFactors= bufFactors;
#ifdef HAVE_FLINT
    result= reconstruction (bufF, bufFactors, zeroOneVecs, l, FLINTN, eval);
#else
    result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, eval);
#endif
    delete [] zeroOneVecs;
    if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l)
    {
      F= bufF;
      factors= bufFactors;
      delete [] A;
      return result;
    }
    else
    {
      bufF= F;
      bufFactors= bufBufFactors;
    }
 
#ifdef HAVE_FLINT
    if (isReduced (FLINTN))
#else
    if (isReduced (NTLN))
#endif
    {
      int factorsFound= 0;
      bufF= F;
#ifdef HAVE_FLINT
      int* factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
      for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
      int* factorsFoundIndex= new int [NTLN.NumCols()];
      for (long i= 0; i < NTLN.NumCols(); i++)
#endif
        factorsFoundIndex[i]= 0;
#ifdef HAVE_FLINT
      if (l < liftBound)
        reconstructionTry (result, bufF, bufFactors, l, factorsFound,
                           factorsFoundIndex, FLINTN, eval, false
                          );
      else
        reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 +
                           degree (LCF), factorsFound, factorsFoundIndex,
                           FLINTN, eval, false
                          );
 
      if (nmod_mat_ncols (FLINTN) == result.length())
#else
      if (l < liftBound)
        reconstructionTry (result, bufF, bufFactors, l, factorsFound,
                           factorsFoundIndex, NTLN, eval, false
                          );
      else
        reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 +
                           degree (LCF), factorsFound, factorsFoundIndex,
                           NTLN, eval, false
                          );
 
      if (NTLN.NumCols() == result.length())
#endif
      {
        delete [] A;
        delete [] factorsFoundIndex;
        return result;
      }
      delete [] factorsFoundIndex;
    }
    result= CFList();
    oldL= l;
    stepSize *= 2;
    l += stepSize;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  if (irreducible)
  {
    delete [] A;
    return CFList (F (y-eval,y));
  }
  delete [] A;
  factors= bufFactors;
  return CFList();
}

furtherLiftingAndIncreasePrecisionFq2Fp()

CFList furtherLiftingAndIncreasePrecisionFq2Fp	(	CanonicalForm &	F,
		CFList &	factors,
		int	l,
		int	liftBound,
		int	d,
		int *	bounds,
		nmod_mat_t	FLINTN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		const Variable &	alpha,
		const CanonicalForm &	eval
	)

Definition at line 5873 of file facFqBivar.cc.

{
  CanonicalForm LCF= LC (F, 1);
  CFList result;
  bool irreducible= false;
  CFList bufFactors= factors;
  CFList bufBufFactors;
  CFArray *A = new CFArray [bufFactors.length()];
  bool useOldQs= false;
  int extensionDeg= degree (getMipo (alpha));
  bool hitBound= false;
  int oldL= l;
  int stepSize= 8; //TODO choose better step size?
  l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2);
#ifdef HAVE_FLINT
  if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors
  {
    nmod_mat_clear (FLINTN);
    nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic());
    for (long i=factors.length()-1; i >= 0; i--)
      nmod_mat_entry (FLINTN, i, i)= 1;
  }
#else
  if (NTLN.NumRows() != factors.length()) //refined factors
    ident (NTLN, factors.length());
#endif
  CFListIterator j;
  CFMatrix C;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLC, NTLK;
#endif
  CanonicalForm bufF, truncF;
  Variable y= F.mvar();
  while (l <= liftBound)
  {
    bufFactors.insert (LCF);
    henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M);
    j= bufFactors;
    truncF= mod (F, power (y, l));
    if (useOldQs)
    {
      for (int i= 0; i < bufFactors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]);
    }
    else
    {
      for (int i= 0; i < bufFactors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]);
    }
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix ((l - k)*extensionDeg, bufFactors.length());
        for (int ii= 0; ii < bufFactors.length(); ii++)
        {
          CFArray buf;
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k, alpha);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
#ifdef HAVE_FLINT
        if (nmod_mat_ncols (FLINTN) == 1)
#else
        if (NTLN.NumCols() == 1)
#endif
        {
          irreducible= true;
          break;
        }
      }
    }
#ifdef HAVE_FLINT
    if (nmod_mat_ncols (FLINTN) == 1)
#else
    if (NTLN.NumCols() == 1)
#endif
    {
      irreducible= true;
      break;
    }
 
#ifdef HAVE_FLINT
    int * zeroOneVecs= extractZeroOneVecs (FLINTN);
#else
    int * zeroOneVecs= extractZeroOneVecs (NTLN);
#endif
    CanonicalForm bufF= F;
    bufBufFactors= bufFactors;
#ifdef HAVE_FLINT
    result= reconstruction (bufF, bufFactors, zeroOneVecs, l, FLINTN, eval);
#else
    result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN,  eval);
#endif
    delete [] zeroOneVecs;
    if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l)
    {
      F= bufF;
      factors= bufFactors;
      delete [] A;
      return result;
    }
    else
    {
      bufF= F;
      bufFactors= bufBufFactors;
    }
 
#ifdef HAVE_FLINT
    if (isReduced (FLINTN))
#else
    if (isReduced (NTLN))
#endif
    {
      int factorsFound= 0;
      bufF= F;
#ifdef HAVE_FLINT
      int* factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
      for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
      int* factorsFoundIndex= new int [NTLN.NumCols()];
      for (long i= 0; i < NTLN.NumCols(); i++)
#endif
        factorsFoundIndex[i]= 0;
#ifdef HAVE_FLINT
      if (l < degree (bufF) + 1 + degree (LCF))
        reconstructionTry (result, bufF, bufFactors, l, factorsFound,
                           factorsFoundIndex, FLINTN, eval, false
                          );
      else
        reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 +
                           degree (LCF), factorsFound, factorsFoundIndex,
                           FLINTN, eval, false
                          );
      if (nmod_mat_ncols (FLINTN) == result.length())
#else
      if (l < degree (bufF) + 1 + degree (LCF))
        reconstructionTry (result, bufF, bufFactors, l, factorsFound,
                           factorsFoundIndex, NTLN, eval, false
                          );
      else
        reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 +
                           degree (LCF), factorsFound, factorsFoundIndex,
                           NTLN, eval, false
                          );
      if (NTLN.NumCols() == result.length())
#endif
      {
        delete [] A;
        delete [] factorsFoundIndex;
        return result;
      }
      delete [] factorsFoundIndex;
    }
    result= CFList();
    oldL= l;
    stepSize *= 2;
    l += stepSize;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  if (irreducible)
  {
    delete [] A;
    return CFList (F (y-eval,y));
  }
  delete [] A;
  factors= bufFactors;
  return CFList();
}

getCombinations()

int * getCombinations	(	int *	rightSide,
		int	sizeOfRightSide,
		int &	sizeOfOutput,
		int	degreeLC
	)

Definition at line 1081 of file facFqBivar.cc.

{
  Variable x= Variable (1);
  int p= getCharacteristic();
  int d= getGFDegree();
  char cGFName= gf_name;
  setCharacteristic(0);
  CanonicalForm buf= 1;
  for (int i= 0; i < sizeOfRightSide; i++)
    buf *= (power (x, rightSide [i]) + 1);
 
  int j= 0;
  for (CFIterator i= buf; i.hasTerms(); i++, j++)
  {
    if (i.exp() < degreeLC)
    {
      j++;
      break;
    }
  }
 
  ASSERT ( j > 1, "j > 1 expected" );
 
  int* result = new int  [j - 1];
  sizeOfOutput= j - 1;
 
  int i= 0;
  for (CFIterator m = buf; i < j - 1; i++, m++)
    result [i]= m.exp();
 
  if (d > 1)
    setCharacteristic (p, d, cGFName);
  else
    setCharacteristic (p);
  return result;
}

getLast()

else L getLast

(

)

getLiftPrecisions()

int * getLiftPrecisions	(	const CanonicalForm &	F,
		int &	sizeOfOutput,
		int	degreeLC
	)

compute lifting precisions from the shape of the Newton polygon of F

Returns

getLiftPrecisions returns lifting precisions computed from the shape of the Newton polygon of F

Parameters

[in]	F	a bivariate poly
[in,out]	sizeOfOutput	size of the output
[in]	degreeLC	degree of the leading coeff [in] of F wrt. Variable (1)

Definition at line 1120 of file facFqBivar.cc.

{
  int sizeOfNewtonPoly;
  int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPoly);
  int sizeOfRightSide;
  int * rightSide= getRightSide(newtonPolyg, sizeOfNewtonPoly, sizeOfRightSide);
  int * result= getCombinations(rightSide, sizeOfRightSide, sizeOfOutput,
                                degreeLC);
  delete [] rightSide;
  for (int i= 0; i < sizeOfNewtonPoly; i++)
    delete [] newtonPolyg[i];
  delete [] newtonPolyg;
  return result;
}

henselLiftAndEarly() [1/2]

CFList henselLiftAndEarly	(	CanonicalForm &	A,
		bool &	earlySuccess,
		CFList &	earlyFactors,
		DegreePattern &	degs,
		int &	liftBound,
		const CFList &	uniFactors,
		const ExtensionInfo &	info,
		const CanonicalForm &	eval
	)

hensel Lifting and early factor detection

Returns

henselLiftAndEarly returns monic (wrt Variable (1)) lifted factors without factors which have been detected at an early stage of Hensel lifting

See also

earlyFactorDetection(), extEarlyFactorDetection()

Parameters

[in,out]	A	poly to be factored, returns poly divided by detected factors in case of success
[in,out]	earlySuccess	indicating success
[in,out]	earlyFactors	list of factors detected at early stage of Hensel lifting
[in,out]	degs	degree pattern
[in,out]	liftBound	(adapted) lift bound
[in]	uniFactors	univariate factors
[in]	info	information about extension
[in]	eval	evaluation point

Definition at line 1455 of file facFqBivar.cc.

{
  modpk dummy= modpk();
  CanonicalForm den= 1;
  return henselLiftAndEarly (A, earlySuccess, earlyFactors, degs, liftBound,
                             uniFactors, info, eval, dummy, den);
}

henselLiftAndEarly() [2/2]

CFList henselLiftAndEarly	(	CanonicalForm &	A,
		bool &	earlySuccess,
		CFList &	earlyFactors,
		DegreePattern &	degs,
		int &	liftBound,
		const CFList &	uniFactors,
		const ExtensionInfo &	info,
		const CanonicalForm &	eval,
		modpk &	b,
		CanonicalForm &	den
	)

hensel Lifting and early factor detection

Returns

henselLiftAndEarly returns monic (wrt Variable (1)) lifted factors without factors which have been detected at an early stage of Hensel lifting

See also

earlyFactorDetection(), extEarlyFactorDetection()

Parameters

[in,out]	A	poly to be factored, returns poly divided by detected factors in case of success
[in,out]	earlySuccess	indicating success
[in,out]	earlyFactors	list of factors detected at early stage of Hensel lifting
[in,out]	degs	degree pattern
[in,out]	liftBound	(adapted) lift bound
[in]	uniFactors	univariate factors
[in]	info	information about extension
[in]	eval	evaluation point
[in]	b	coeff bound
[in]	den	bound on the den if over Q(a)

Definition at line 1152 of file facFqBivar.cc.

{
  Variable alpha= info.getAlpha();
  Variable beta= info.getBeta();
  CanonicalForm gamma= info.getGamma();
  CanonicalForm delta= info.getDelta();
  bool extension= info.isInExtension();
 
  int sizeOfLiftPre;
  int * liftPre= getLiftPrecisions (A, sizeOfLiftPre, degree (LC (A, 1), 2));
 
  Variable x= Variable (1);
  Variable y= Variable (2);
  CFArray Pi;
  CFList diophant;
  CFList bufUniFactors= uniFactors;
  On (SW_RATIONAL);
  CanonicalForm bufA= A;
  if (!Lc (A).inBaseDomain())
  {
    bufA /= Lc (A);
    CanonicalForm denBufA= bCommonDen (bufA);
    bufA *= denBufA;
    Off (SW_RATIONAL);
    den /= gcd (den, denBufA);
  }
  else
  {
    bufA= A;
    Off (SW_RATIONAL);
    den /= gcd (den, Lc (A));
  }
  CanonicalForm lcA0= 0;
  bool mipoHasDen= false;
  if (getCharacteristic() == 0 && b.getp() != 0)
  {
    if (alpha.level() == 1)
    {
      lcA0= lc (A (0, 2));
      A *= b.inverse (lcA0);
      A= b (A);
      for (CFListIterator i= bufUniFactors; i.hasItem(); i++)
        i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem())));
    }
    else
    {
      lcA0= Lc (A (0,2));
      On (SW_RATIONAL);
      mipoHasDen= !bCommonDen(getMipo(alpha)).isOne();
      Off (SW_RATIONAL);
      CanonicalForm lcA0inverse= b.inverse (lcA0);
      A *= lcA0inverse;
      A= b (A);
      // Lc of bufUniFactors is in Z
      for (CFListIterator i= bufUniFactors; i.hasItem(); i++)
        i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem())));
    }
  }
  bufUniFactors.insert (LC (A, x));
  CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1);
  earlySuccess= false;
  int newLiftBound= 0;
 
  int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1);//this is a tunable parameter
  int dummy;
  int * factorsFoundIndex= new int [uniFactors.length()];
  for (int i= 0; i < uniFactors.length(); i++)
    factorsFoundIndex [i]= 0;
 
  CFList bufBufUniFactors;
  Variable v= alpha;
  if (smallFactorDeg >= liftBound || degree (A,y) <= 4)
    henselLift12 (A, bufUniFactors, liftBound, Pi, diophant, M, b, true);
  else if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30)
  {
    henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true);
    if (mipoHasDen)
    {
      for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++)
        if (hasFirstAlgVar (iter.getItem(), v))
          break;
      if (v != alpha)
      {
        bufBufUniFactors= bufUniFactors;
        for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++)
          iter.getItem()= replacevar (iter.getItem(), v, alpha);
        A= replacevar (A, alpha, v);
      }
    }
 
    if (!extension)
    {
      if (v==alpha)
        earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound,
                              factorsFoundIndex, degs, earlySuccess,
                              smallFactorDeg, eval, b, den);
      else
        earlyFactorDetection(earlyFactors, bufA, bufBufUniFactors, newLiftBound,
                             factorsFoundIndex, degs, earlySuccess,
                             smallFactorDeg, eval, b, den);
    }
    else
      extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound,
                               factorsFoundIndex, degs, earlySuccess, info,
                               eval, smallFactorDeg);
    if (degs.getLength() > 1 && !earlySuccess &&
        smallFactorDeg != liftPre [sizeOfLiftPre-1] + 1)
    {
      if (newLiftBound >= liftPre[sizeOfLiftPre-1]+1)
      {
        bufUniFactors.insert (LC (A, x));
        henselLiftResume12 (A, bufUniFactors, smallFactorDeg,
                            liftPre[sizeOfLiftPre-1] + 1, Pi, diophant, M, b);
        if (v!=alpha)
        {
          bufBufUniFactors= bufUniFactors;
          for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++)
            iter.getItem()= replacevar (iter.getItem(), v, alpha);
        }
        if (!extension)
        {
          if (v==alpha)
          earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound,
                                factorsFoundIndex, degs, earlySuccess,
                                liftPre[sizeOfLiftPre-1] + 1, eval, b, den);
          else
          earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound,
                                factorsFoundIndex, degs, earlySuccess,
                                liftPre[sizeOfLiftPre-1] + 1, eval, b, den);
        }
        else
          extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound,
                                   factorsFoundIndex, degs, earlySuccess, info,
                                   eval, liftPre[sizeOfLiftPre-1] + 1);
      }
    }
    else if (earlySuccess)
      liftBound= newLiftBound;
 
    int i= sizeOfLiftPre - 1;
    while (degs.getLength() > 1 && !earlySuccess && i - 1 >= 0)
    {
      if (newLiftBound >= liftPre[i] + 1)
      {
        bufUniFactors.insert (LC (A, x));
        henselLiftResume12 (A, bufUniFactors, liftPre[i] + 1,
                            liftPre[i-1] + 1, Pi, diophant, M, b);
        if (v!=alpha)
        {
          bufBufUniFactors= bufUniFactors;
          for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++)
            iter.getItem()= replacevar (iter.getItem(), v, alpha);
        }
        if (!extension)
        {
          if (v==alpha)
          earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound,
                                factorsFoundIndex, degs, earlySuccess,
                                liftPre[i-1] + 1, eval, b, den);
          else
          earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound,
                                factorsFoundIndex, degs, earlySuccess,
                                liftPre[i-1] + 1, eval, b, den);
        }
        else
          extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound,
                                   factorsFoundIndex, degs, earlySuccess, info,
                                   eval, liftPre[i-1] + 1);
      }
      else
      {
        liftBound= newLiftBound;
        break;
      }
      i--;
    }
    if (earlySuccess)
      liftBound= newLiftBound;
    //after here all factors are lifted to liftPre[sizeOfLiftPre-1]
  }
  else
  {
    henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true);
    if (mipoHasDen)
    {
      for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++)
        if (hasFirstAlgVar (iter.getItem(), v))
          break;
      if (v != alpha)
      {
        bufBufUniFactors= bufUniFactors;
        for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++)
          iter.getItem()= replacevar (iter.getItem(), v, alpha);
        A= replacevar (A, alpha, v);
      }
    }
    if (!extension)
    {
      if (v==alpha)
      earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound,
                            factorsFoundIndex, degs, earlySuccess,
                            smallFactorDeg, eval, b, den);
      else
      earlyFactorDetection (earlyFactors, bufA, bufBufUniFactors, newLiftBound,
                            factorsFoundIndex, degs, earlySuccess,
                            smallFactorDeg, eval, b, den);
    }
    else
      extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound,
                               factorsFoundIndex, degs, earlySuccess, info,
                               eval, smallFactorDeg);
    int i= 1;
    while ((degree (A,y)/4)*i + 4 <= smallFactorDeg)
      i++;
    dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*i+4);
    if (degs.getLength() > 1 && !earlySuccess && dummy > smallFactorDeg)
    {
      bufUniFactors.insert (LC (A, x));
      henselLiftResume12 (A, bufUniFactors, smallFactorDeg,
                          dummy, Pi, diophant, M, b);
      if (v!=alpha)
      {
        bufBufUniFactors= bufUniFactors;
        for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++)
          iter.getItem()= replacevar (iter.getItem(), v, alpha);
      }
      if (!extension)
      {
        if (v==alpha)
        earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound,
                              factorsFoundIndex, degs, earlySuccess, dummy,eval,
                              b, den);
        else
        earlyFactorDetection (earlyFactors, bufA,bufBufUniFactors, newLiftBound,
                              factorsFoundIndex, degs, earlySuccess, dummy,eval,
                              b, den);
      }
      else
        extEarlyFactorDetection (earlyFactors, bufA,bufUniFactors, newLiftBound,
                                 factorsFoundIndex, degs, earlySuccess, info,
                                 eval, dummy);
    }
    while (degs.getLength() > 1 && !earlySuccess && i < 4)
    {
      if (newLiftBound >= dummy)
      {
        bufUniFactors.insert (LC (A, x));
        dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*(i+1)+4);
        henselLiftResume12 (A, bufUniFactors, (degree (A,y)/4)*i + 4,
                            dummy, Pi, diophant, M, b);
        if (v!=alpha)
        {
          bufBufUniFactors= bufUniFactors;
          for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++)
            iter.getItem()= replacevar (iter.getItem(), v, alpha);
        }
        if (!extension)
        {
          if (v==alpha)
          earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound,
                                factorsFoundIndex, degs, earlySuccess, dummy,
                                eval, b, den);
          else
          earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound,
                                factorsFoundIndex, degs, earlySuccess, dummy,
                                eval, b, den);
        }
        else
          extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound,
                                   factorsFoundIndex, degs, earlySuccess, info,
                                   eval, dummy);
      }
      else
      {
        liftBound= newLiftBound;
        break;
      }
      i++;
    }
    if (earlySuccess)
      liftBound= newLiftBound;
  }
 
  A= bufA;
  if (earlyFactors.length() > 0 && degs.getLength() > 1)
  {
    liftBound= degree (A,y) + 1;
    earlySuccess= true;
    deleteFactors (bufUniFactors, factorsFoundIndex);
  }
 
  delete [] factorsFoundIndex;
  delete [] liftPre;
 
  return bufUniFactors;
}

henselLiftAndLatticeRecombi()

CFList henselLiftAndLatticeRecombi	(	const CanonicalForm &	G,
		const CFList &	uniFactors,
		const Variable &	alpha,
		const DegreePattern &	degPat,
		bool	symmetric,
		const CanonicalForm &	eval
	)

Definition at line 6859 of file facFqBivar.cc.

{
  DegreePattern degs= degPat;
  CanonicalForm F= G;
  CanonicalForm LCF= LC (F, 1);
  Variable y= F.mvar();
  Variable x= Variable (1);
  int d;
  bool isIrreducible= false;
  int* bounds= computeBounds (F, d, isIrreducible);
  if (isIrreducible)
  {
    delete [] bounds;
    return CFList (G);
  }
  int minBound= bounds[0];
  for (int i= 1; i < d; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
 
  CFList bufUniFactors= uniFactors;
  CFArray Pi;
  CFList diophant;
  int liftBound= 2*totaldegree (F) - 1;
  CFMatrix M= CFMatrix (liftBound, bufUniFactors.length());
 
  CFList smallFactors;
  CanonicalForm H;
  bool success= false;
  smallFactors= sieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, M,
                                   success, minBound + 1, eval
                                  );
 
  if (smallFactors.length() > 0)
  {
    if (smallFactors.length() == 1)
    {
      if (smallFactors.getFirst() == F)
      {
        delete [] bounds;
        return CFList (G (y-eval,y));
      }
    }
    if (degs.getLength() <= 1)
    {
      delete [] bounds;
      return smallFactors;
    }
  }
 
  int index;
  CanonicalForm tmp1, tmp2;
  for (CFListIterator i= smallFactors; i.hasItem(); i++)
  {
    index= 1;
    tmp1= mod (i.getItem(),y-eval);
    tmp1 /= Lc (tmp1);
    for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++)
    {
      tmp2= mod (j.getItem(), y);
      tmp2 /= Lc (tmp2);
      if (tmp1 == tmp2)
      {
        index++;
        j.remove(index);
        break;
      }
    }
  }
 
  if (bufUniFactors.isEmpty())
  {
    delete [] bounds;
    return smallFactors;
  }
 
  if (success)
  {
    F= H;
    delete [] bounds;
    bounds= computeBounds (F, d, isIrreducible);
    if (isIrreducible)
    {
      smallFactors.append (F (y-eval,y));
      delete [] bounds;
      return smallFactors;
    }
    LCF= LC (F, 1);
 
    minBound= bounds[0];
    for (int i= 1; i < d; i++)
    {
      if (bounds[i] != 0)
        minBound= tmin (minBound, bounds[i]);
    }
    Pi= CFArray();
    diophant= CFList();
    liftBound= 2*totaldegree (F) - 1;
    M= CFMatrix (liftBound, bufUniFactors.length());
    DegreePattern bufDegs= DegreePattern (bufUniFactors);
    degs.intersect (bufDegs);
    degs.refine();
    if (degs.getLength() <= 1)
    {
      smallFactors.append (F (y-eval,y));
      delete [] bounds;
      return smallFactors;
    }
  }
 
  bool reduceFq2Fp= (degree (F) > getCharacteristic());
  bufUniFactors.insert (LCF);
  int l= 1;
 
#ifdef HAVE_FLINT
  nmod_mat_t FLINTN;
#endif
 
  if (fac_NTL_char != getCharacteristic())
  {
    fac_NTL_char= getCharacteristic();
    zz_p::init (getCharacteristic());
  }
  mat_zz_p NTLN;
 
  if (alpha.level() != 1)
  {
    zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha));
    zz_pE::init (NTLMipo);
  }
  mat_zz_pE NTLNe;
 
  if (alpha.level() == 1)
  {
#ifdef HAVE_FLINT
    nmod_mat_init (FLINTN, bufUniFactors.length()-1, bufUniFactors.length()-1, getCharacteristic());
    for (long i= bufUniFactors.length()-2; i >= 0; i--)
      nmod_mat_entry (FLINTN, i, i)= 1;
#else
    ident (NTLN, bufUniFactors.length() - 1);
#endif
  }
  else
  {
    if (reduceFq2Fp)
#ifdef HAVE_FLINT
    {
      nmod_mat_init (FLINTN, bufUniFactors.length()-1, bufUniFactors.length()-1, getCharacteristic());
      for (long i= bufUniFactors.length()-2; i >= 0; i--)
        nmod_mat_entry (FLINTN, i, i)= 1;
    }
#else
      ident (NTLN, bufUniFactors.length() - 1);
#endif
    else
      ident (NTLNe, bufUniFactors.length() - 1);
  }
  bool irreducible= false;
  CFArray bufQ= CFArray (bufUniFactors.length() - 1);
 
  int oldL;
  TIMING_START (fac_fq_till_reduced);
  if (success)
  {
    int start= 0;
    if (alpha.level() == 1)
      oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound,
#ifdef HAVE_FLINT
                                   bufUniFactors, FLINTN, diophant, M, Pi, bufQ,
#else
                                   bufUniFactors, NTLN, diophant, M, Pi, bufQ,
#endif
                                   irreducible
                                  );
    else
    {
      if (reduceFq2Fp)
        oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, start, liftBound,
#ifdef HAVE_FLINT
                                          minBound, bufUniFactors, FLINTN,
#else
                                          minBound, bufUniFactors, NTLN,
#endif
                                          diophant, M, Pi, bufQ, irreducible,
                                          alpha
                                         );
      else
        oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound,
                                    bufUniFactors, NTLNe, diophant, M, Pi, bufQ,
                                    irreducible
                                    );
    }
  }
  else
  {
    if (alpha.level() == 1)
    {
      oldL= liftAndComputeLattice (F, bounds, d, minBound + 1, liftBound,
#ifdef HAVE_FLINT
                                   minBound, bufUniFactors, FLINTN, diophant, M,
#else
                                   minBound, bufUniFactors, NTLN, diophant, M,
#endif
                                   Pi, bufQ, irreducible
                                  );
    }
    else
    {
      if (reduceFq2Fp)
        oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, minBound + 1,
                                          liftBound, minBound, bufUniFactors,
#ifdef HAVE_FLINT
                                          FLINTN, diophant, M, Pi, bufQ,
#else
                                          NTLN, diophant, M, Pi, bufQ,
#endif
                                          irreducible, alpha
                                         );
      else
        oldL= liftAndComputeLattice (F, bounds, d, minBound + 1, liftBound,
                                     minBound, bufUniFactors, NTLNe, diophant,
                                     M, Pi, bufQ, irreducible
                                    );
    }
  }
 
  TIMING_END_AND_PRINT (fac_fq_till_reduced,
                        "time to compute a reduced lattice: ");
  bufUniFactors.removeFirst();
  if (oldL > liftBound)
  {
#ifdef HAVE_FLINT
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
      nmod_mat_clear (FLINTN);
#endif
    delete [] bounds;
    return Union (smallFactors,
                  factorRecombination (bufUniFactors, F,
                                       power (y, degree (F) + 1),
                                       degs, eval, 1, bufUniFactors.length()/2
                                      )
                 );
  }
 
  l= oldL;
  if (irreducible)
  {
#ifdef HAVE_FLINT
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
      nmod_mat_clear (FLINTN);
#endif
    delete [] bounds;
    return Union (CFList (F(y-eval,y)), smallFactors);
  }
 
  CanonicalForm yToL= power (y,l);
 
  CFList result;
  if (l >= degree (F) + 1)
  {
    int * factorsFoundIndex;
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
    {
#ifdef HAVE_FLINT
      factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
      for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
      factorsFoundIndex= new int [NTLN.NumCols()];
      for (long i= 0; i < NTLN.NumCols(); i++)
#endif
        factorsFoundIndex[i]= 0;
    }
    else
    {
      factorsFoundIndex= new int [NTLNe.NumCols()];
      for (long i= 0; i < NTLNe.NumCols(); i++)
        factorsFoundIndex[i]= 0;
    }
    int factorsFound= 0;
    CanonicalForm bufF= F;
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
      reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1,
#ifdef HAVE_FLINT
                         factorsFound, factorsFoundIndex, FLINTN, eval, false
#else
                         factorsFound, factorsFoundIndex, NTLN, eval, false
#endif
                        );
    else
        reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1,
                           factorsFound, factorsFoundIndex, NTLNe, eval, false
                          );
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
    {
#ifdef HAVE_FLINT
      if (result.length() == nmod_mat_ncols (FLINTN))
      {
        if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
          nmod_mat_clear (FLINTN);
#else
      if (result.length() == NTLN.NumCols())
      {
#endif
        delete [] factorsFoundIndex;
        delete [] bounds;
        return Union (result, smallFactors);
      }
    }
    else
    {
      if (result.length() == NTLNe.NumCols())
      {
        delete [] factorsFoundIndex;
        delete [] bounds;
        return Union (result, smallFactors);
      }
    }
    delete [] factorsFoundIndex;
  }
  if (l >= liftBound)
  {
    int * factorsFoundIndex;
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
    {
#ifdef HAVE_FLINT
      factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
      for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
      factorsFoundIndex= new int [NTLN.NumCols()];
      for (long i= 0; i < NTLN.NumCols(); i++)
#endif
        factorsFoundIndex[i]= 0;
    }
    else
    {
      factorsFoundIndex= new int [NTLNe.NumCols()];
      for (long i= 0; i < NTLNe.NumCols(); i++)
        factorsFoundIndex[i]= 0;
    }
    CanonicalForm bufF= F;
    int factorsFound= 0;
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
      reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1,
#ifdef HAVE_FLINT
                         factorsFound, factorsFoundIndex, FLINTN, eval, false
#else
                         factorsFound, factorsFoundIndex, NTLN, eval, false
#endif
                        );
    else
      reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1,
                         factorsFound, factorsFoundIndex, NTLNe, eval, false
                        );
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
    {
#ifdef HAVE_FLINT
      if (result.length() == nmod_mat_ncols(FLINTN))
      {
        nmod_mat_clear (FLINTN);
#else
      if (result.length() == NTLN.NumCols())
      {
#endif
        delete [] factorsFoundIndex;
        delete [] bounds;
        return Union (result, smallFactors);
      }
    }
    else
    {
      if (result.length() == NTLNe.NumCols())
      {
        delete [] factorsFoundIndex;
        delete [] bounds;
        return Union (result, smallFactors);
      }
    }
    delete [] factorsFoundIndex;
  }
 
  result= CFList();
  bool beenInThres= false;
  int thres= 100;
  if (l <= thres)
  {
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
    {
#ifdef HAVE_FLINT
      if (nmod_mat_ncols (FLINTN) < bufUniFactors.length())
      {
        refineAndRestartLift (F, FLINTN, liftBound, l, bufUniFactors, M, Pi,
#else
      if (NTLN.NumCols() < bufUniFactors.length())
      {
        refineAndRestartLift (F, NTLN, liftBound, l, bufUniFactors, M, Pi,
#endif
                              diophant
                             );
        beenInThres= true;
      }
    }
    else
    {
      if (NTLNe.NumCols() < bufUniFactors.length())
      {
        refineAndRestartLift (F, NTLNe, liftBound, l, bufUniFactors, M, Pi,
                              diophant
                             );
        beenInThres= true;
      }
    }
  }
 
  CanonicalForm bufF= F;
  int factorsFound= 0;
  if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
  {
#ifdef HAVE_FLINT
    result= earlyReconstructionAndLifting (F, FLINTN, bufF, bufUniFactors, l,
#else
    result= earlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l,
#endif
                                           factorsFound, beenInThres, M, Pi,
                                           diophant, symmetric, eval
                                          );
 
#ifdef HAVE_FLINT
    if (result.length() == nmod_mat_ncols (FLINTN))
    {
      nmod_mat_clear (FLINTN);
#else
    if (result.length() == NTLN.NumCols())
    {
#endif
      delete [] bounds;
      return Union (result, smallFactors);
    }
  }
  else
  {
    result= earlyReconstructionAndLifting (F, NTLNe, bufF, bufUniFactors, l,
                                           factorsFound, beenInThres, M, Pi,
                                           diophant, symmetric, eval
                                          );
 
    if (result.length() == NTLNe.NumCols())
    {
      delete [] bounds;
      return Union (result, smallFactors);
    }
  }
 
  if (result.length() > 0)
  {
    if (beenInThres)
    {
      int index;
      for (CFListIterator i= result; i.hasItem(); i++)
      {
        index= 1;
        tmp1= mod (i.getItem(), y-eval);
        tmp1 /= Lc (tmp1);
        for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++)
        {
          tmp2= mod (j.getItem(), y);
          tmp2 /= Lc (tmp2);
          if (tmp1 == tmp2)
          {
            index++;
            j.remove(index);
            break;
          }
        }
      }
    }
    else
    {
      int * zeroOne;
      long numCols, numRows;
      if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
      {
#ifdef HAVE_FLINT
        numCols= nmod_mat_ncols (FLINTN);
        numRows= nmod_mat_nrows (FLINTN);
        zeroOne= extractZeroOneVecs (FLINTN);
#else
        numCols= NTLN.NumCols();
        numRows= NTLN.NumRows();
        zeroOne= extractZeroOneVecs (NTLN);
#endif
      }
      else
      {
        numCols= NTLNe.NumCols();
        numRows= NTLNe.NumRows();
        zeroOne= extractZeroOneVecs (NTLNe);
      }
      CFList bufBufUniFactors= bufUniFactors;
      CFListIterator iter, iter2;
      CanonicalForm buf;
      CFList factorsConsidered;
      CanonicalForm tmp;
      for (int i= 0; i < numCols; i++)
      {
        if (zeroOne [i] == 0)
          continue;
        iter= bufUniFactors;
        buf= 1;
        factorsConsidered= CFList();
        for (int j= 0; j < numRows; j++, iter++)
        {
          if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
          {
#ifdef HAVE_FLINT
            if (!(nmod_mat_entry (FLINTN, j,i) == 0))
#else
            if (!IsZero (NTLN (j + 1,i + 1)))
#endif
            {
              factorsConsidered.append (iter.getItem());
              buf *= mod (iter.getItem(), y);
            }
          }
          else
          {
            if (!IsZero (NTLNe (j + 1,i + 1)))
            {
              factorsConsidered.append (iter.getItem());
              buf *= mod (iter.getItem(), y);
            }
          }
        }
        buf /= Lc (buf);
        for (iter2= result; iter2.hasItem(); iter2++)
        {
          tmp= mod (iter2.getItem(), y-eval);
          tmp /= Lc (tmp);
          if (tmp == buf)
          {
            bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered);
            break;
          }
        }
      }
      bufUniFactors= bufBufUniFactors;
      delete [] zeroOne;
    }
 
    int oldNumCols;
    CFList resultBufF;
    irreducible= false;
 
    if (alpha.level() == 1)
    {
#ifdef HAVE_FLINT
      oldNumCols= nmod_mat_ncols (FLINTN);
#else
      oldNumCols= NTLN.NumCols();
#endif
      resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound,
                                     oldNumCols, oldL, l, eval
                                    );
    }
    else
    {
      if (reduceFq2Fp)
      {
#ifdef HAVE_FLINT
        oldNumCols= nmod_mat_ncols (FLINTN);
#else
        oldNumCols= NTLN.NumCols();
#endif
 
        resultBufF= increasePrecisionFq2Fp (bufF, bufUniFactors, factorsFound,
                                            oldNumCols, oldL, alpha, l, eval
                                           );
      }
      else
      {
        oldNumCols= NTLNe.NumCols();
 
        resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound,
                                       oldNumCols, oldL, alpha, l, eval
                                      );
      }
    }
 
    if (bufUniFactors.isEmpty() || degree (bufF) <= 0)
    {
#ifdef HAVE_FLINT
      if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
        nmod_mat_clear (FLINTN);
#endif
      delete [] bounds;
      result= Union (resultBufF, result);
      return Union (result, smallFactors);
    }
 
    for (CFListIterator i= bufUniFactors; i.hasItem(); i++)
      i.getItem()= mod (i.getItem(), y);
 
    result= Union (result, resultBufF);
    result= Union (result, smallFactors);
    delete [] bounds;
    DegreePattern bufDegs= DegreePattern (bufUniFactors);
    degs.intersect (bufDegs);
    degs.refine();
    if (degs.getLength() == 1 || bufUniFactors.length() == 1)
    {
#ifdef HAVE_FLINT
      if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
        nmod_mat_clear (FLINTN);
#endif
      result.append (bufF (y-eval,y));
      return result;
    }
#ifdef HAVE_FLINT
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
      nmod_mat_clear (FLINTN);
#endif
    return Union (result, henselLiftAndLatticeRecombi (bufF, bufUniFactors,
                                                       alpha, degs, symmetric,
                                                       eval
                                                      )
                 );
  }
 
  if (l < liftBound)
  {
    if (alpha.level() == 1)
    {
        result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ,
#ifdef HAVE_FLINT
                                  FLINTN, eval
#else
                                  NTLN, eval
#endif
                                 );
    }
    else
    {
      if (reduceFq2Fp)
      {
          result=increasePrecisionFq2Fp (F, bufUniFactors, oldL, l, d, bounds,
#ifdef HAVE_FLINT
                                         bufQ, FLINTN, alpha, eval
#else
                                         bufQ, NTLN, alpha, eval
#endif
                                        );
      }
      else
      {
          result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ,
                                    NTLNe, eval
                                   );
      }
    }
    if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
    {
#ifdef HAVE_FLINT
      if (result.length()== nmod_mat_ncols (FLINTN))
      {
        nmod_mat_clear (FLINTN);
#else
      if (result.length()== NTLN.NumCols())
      {
#endif
        delete [] bounds;
        result= Union (result, smallFactors);
        return result;
      }
    }
    else
    {
      if (result.length()== NTLNe.NumCols())
      {
        delete [] bounds;
        result= Union (result, smallFactors);
        return result;
      }
    }
 
    if (result.isEmpty())
    {
      if (alpha.level() == 1)
        result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l,
#ifdef HAVE_FLINT
                                                    liftBound,d,bounds,FLINTN,
#else
                                                    liftBound, d, bounds, NTLN,
#endif
                                                    diophant, M, Pi, bufQ, eval
                                                   );
      else
      {
        if (reduceFq2Fp)
          result= furtherLiftingAndIncreasePrecisionFq2Fp (F,bufUniFactors, l,
                                                           liftBound, d, bounds,
#ifdef HAVE_FLINT
                                                           FLINTN, diophant, M,
#else
                                                           NTLN, diophant, M,
#endif
                                                           Pi, bufQ, alpha, eval
                                                          );
        else
          result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l,
                                                      liftBound, d, bounds,
                                                      NTLNe, diophant, M,
                                                      Pi, bufQ, eval
                                                     );
      }
 
      if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
      {
#ifdef HAVE_FLINT
        if (result.length() == nmod_mat_ncols (FLINTN))
        {
          nmod_mat_clear (FLINTN);
#else
        if (result.length() == NTLN.NumCols())
        {
#endif
          delete [] bounds;
          result= Union (result, smallFactors);
          return result;
        }
      }
      else
      {
        if (result.length() == NTLNe.NumCols())
        {
          delete [] bounds;
          result= Union (result, smallFactors);
          return result;
        }
      }
    }
  }
 
  DEBOUTLN (cerr, "lattice recombination failed");
 
  DegreePattern bufDegs= DegreePattern (bufUniFactors);
  degs.intersect (bufDegs);
  degs.refine();
 
  delete [] bounds;
  bounds= computeBounds (F, d, isIrreducible);
#ifdef HAVE_FLINT
  if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp))
    nmod_mat_clear (FLINTN);
#endif
  if (isIrreducible)
  {
    delete [] bounds;
    result= Union (result, smallFactors);
    result.append (F (y-eval,y));
    return result;
  }
  minBound= bounds[0];
  for (int i= 1; i < d; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
 
  if (minBound > 16 || result.length() == 0)
  {
    result= Union (result, smallFactors);
    CanonicalForm MODl= power (y, degree (F) + 1);
    delete [] bounds;
    return Union (result, factorRecombination (bufUniFactors, F, MODl, degs,
                                               eval, 1, bufUniFactors.length()/2
                                              )
                 );
  }
  else
  {
    result= Union (result, smallFactors);
    for (CFListIterator i= bufUniFactors; i.hasItem(); i++)
      i.getItem()= mod (i.getItem(), y);
    delete [] bounds;
    return Union (result, henselLiftAndLatticeRecombi (F, bufUniFactors, alpha,
                                                       degs,symmetric, eval
                                                      )
                 );
  }
}

if()

else if

(

L.

length() = = 1

)

increasePrecision() [1/4]

CFList increasePrecision	(	CanonicalForm &	F,
		CFList &	factors,
		int	factorsFound,
		int	oldNumCols,
		int	oldL,
		const Variable &	,
		int	precision,
		const CanonicalForm &	eval
	)

Definition at line 3684 of file facFqBivar.cc.

{
  int d;
  bool isIrreducible= false;
  Variable y= F.mvar();
  int* bounds= computeBounds (F, d, isIrreducible);
  if (isIrreducible)
  {
    delete [] bounds;
    CanonicalForm G= F;
    F= 1;
    return CFList (G (y-eval,y));
  }
  CFArray * A= new CFArray [factors.length()];
  CFArray bufQ= CFArray (factors.length());
  mat_zz_pE NTLN;
  ident (NTLN, factors.length());
  int minBound= bounds[0];
  for (int i= 1; i < d; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
  int l= tmax (2*(minBound + 1), oldL);
  int oldL2= l/2;
  int stepSize= 2;
  bool useOldQs= false;
  bool hitBound= false;
  CFListIterator j;
  CFMatrix C;
  mat_zz_pE* NTLC, NTLK;
  CFArray buf;
  CanonicalForm truncF;
  while (l <= precision)
  {
    j= factors;
    truncF= mod (F, power (y,l));
    if (useOldQs)
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i],
                                     bufQ[i]
                                    );
    }
    else
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]);
    }
    useOldQs= true;
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix (l - k, factors.length());
        for (int ii= 0; ii < factors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
        NTLC= convertFacCFMatrix2NTLmat_zz_pE(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
        if (NTLN.NumCols() == 1)
        {
          delete [] A;
          delete [] bounds;
          CanonicalForm G= F;
          F= 1;
          return CFList (G (y-eval,y));
        }
      }
    }
 
    if (NTLN.NumCols() < oldNumCols - factorsFound)
    {
      if (isReduced (NTLN))
      {
        int * factorsFoundIndex= new int [NTLN.NumCols()];
        for (long i= 0; i < NTLN.NumCols(); i++)
          factorsFoundIndex[i]= 0;
        int factorsFound2= 0;
        CFList result;
        CanonicalForm bufF= F;
        reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2,
                           factorsFoundIndex, NTLN, eval, false);
        if (result.length() == NTLN.NumCols())
        {
          delete [] factorsFoundIndex;
          delete [] A;
          delete [] bounds;
          F= 1;
          return result;
        }
        delete [] factorsFoundIndex;
      }
      else if (l == precision)
      {
        CanonicalForm bufF= F;
        int * zeroOne= extractZeroOneVecs (NTLN);
        CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN, eval);
        F= bufF;
        delete [] zeroOne;
        delete [] A;
        delete [] bounds;
        return result;
      }
    }
    oldL2= l;
    l += stepSize;
    stepSize *= 2;
    if (l > precision)
    {
      if (!hitBound)
      {
        l= precision;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] bounds;
  delete [] A;
  return CFList();
}

increasePrecision() [2/4]

CFList increasePrecision	(	CanonicalForm &	F,
		CFList &	factors,
		int	factorsFound,
		int	oldNumCols,
		int	oldL,
		int	precision,
		const CanonicalForm &	eval
	)

Definition at line 3475 of file facFqBivar.cc.

{
  int d;
  bool isIrreducible= false;
  int* bounds= computeBounds (F, d, isIrreducible);
  Variable y= F.mvar();
  if (isIrreducible)
  {
    delete [] bounds;
    CanonicalForm G= F;
    F= 1;
    return CFList (G (y-eval, y));
  }
  CFArray * A= new CFArray [factors.length()];
  CFArray bufQ= CFArray (factors.length());
#ifdef HAVE_FLINT
  nmod_mat_t FLINTN;
  nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic());
  for (long i=factors.length()-1; i >= 0; i--)
    nmod_mat_entry (FLINTN, i, i)= 1;
#else
  mat_zz_p NTLN;
  ident (NTLN, factors.length());
#endif
  int minBound= bounds[0];
  for (int i= 1; i < d; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
  int l= tmax (2*(minBound + 1), oldL);
  int oldL2= l/2;
  int stepSize= 2;
  bool useOldQs= false;
  bool hitBound= false;
  CFListIterator j;
  CFMatrix C;
  CFArray buf;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLC, NTLK;
#endif
  CanonicalForm truncF;
  while (l <= precision)
  {
    j= factors;
    truncF= mod (F, power (y,l));
    if (useOldQs)
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i],
                                     bufQ[i]
                                    );
    }
    else
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]);
    }
    useOldQs= true;
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix (l - k, factors.length());
        for (int ii= 0; ii < factors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
#ifdef HAVE_FLINT
        if (nmod_mat_ncols (FLINTN) == 1)
        {
          nmod_mat_clear (FLINTN);
#else
        if (NTLN.NumCols() == 1)
        {
#endif
          delete [] A;
          delete [] bounds;
          CanonicalForm G= F;
          F= 1;
          return CFList (G (y-eval,y));
        }
      }
    }
 
#ifdef HAVE_FLINT
    if (nmod_mat_ncols (FLINTN) < oldNumCols - factorsFound)
    {
      if (isReduced (FLINTN))
      {
        int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
        for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
    if (NTLN.NumCols() < oldNumCols - factorsFound)
    {
      if (isReduced (NTLN))
      {
        int * factorsFoundIndex= new int [NTLN.NumCols()];
        for (long i= 0; i < NTLN.NumCols(); i++)
#endif
          factorsFoundIndex[i]= 0;
        int factorsFound2= 0;
        CFList result;
        CanonicalForm bufF= F;
#ifdef HAVE_FLINT
        reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2,
                           factorsFoundIndex, FLINTN, eval, false
                          );
        if (result.length() == nmod_mat_ncols (FLINTN))
        {
          nmod_mat_clear (FLINTN);
#else
        reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2,
                           factorsFoundIndex, NTLN, eval, false
                          );
        if (result.length() == NTLN.NumCols())
        {
#endif
          delete [] factorsFoundIndex;
          delete [] A;
          delete [] bounds;
          F= 1;
          return result;
        }
        delete [] factorsFoundIndex;
      }
      else if (l == precision)
      {
        CanonicalForm bufF= F;
#ifdef HAVE_FLINT
        int * zeroOne= extractZeroOneVecs (FLINTN);
        CFList result= reconstruction (bufF,factors,zeroOne,precision,FLINTN, eval);
        nmod_mat_clear (FLINTN);
#else
        int * zeroOne= extractZeroOneVecs (NTLN);
        CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN, eval);
#endif
        F= bufF;
        delete [] zeroOne;
        delete [] A;
        delete [] bounds;
        return result;
      }
    }
    oldL2= l;
    l += stepSize;
    stepSize *= 2;
    if (l > precision)
    {
      if (!hitBound)
      {
        l= precision;
        hitBound= true;
      }
      else
        break;
    }
  }
#ifdef HAVE_FLINT
  nmod_mat_clear (FLINTN);
#endif
  delete [] bounds;
  delete [] A;
  return CFList();
}

increasePrecision() [3/4]

CFList increasePrecision	(	CanonicalForm &	F,
		CFList &	factors,
		int	oldL,
		int	l,
		int	d,
		int *	bounds,
		CFArray &	bufQ,
		mat_zz_pE &	NTLN,
		const CanonicalForm &	eval
	)

Definition at line 4647 of file facFqBivar.cc.

{
  CFList result= CFList();
  CFArray * A= new CFArray [factors.length()];
  int oldL2= oldL/2;
  bool hitBound= false;
  bool useOldQs= false;
  if (NTLN.NumRows() != factors.length()) //refined factors
    ident (NTLN, factors.length());
  CFListIterator j;
  CFMatrix C;
  CFArray buf;
  mat_zz_pE* NTLC, NTLK;
  CanonicalForm bufF, truncF;
  CFList bufUniFactors;
  Variable y= F.mvar();
  while (oldL <= l)
  {
    j= factors;
    truncF= mod (F, power (y, oldL));
    if (useOldQs)
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i],
                                     bufQ[i]
                                    );
    }
    else
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]);
    }
    useOldQs= true;
 
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= oldL/2)
      {
        int k= tmin (bounds [i] + 1, oldL/2);
        C= CFMatrix (oldL - k, factors.length());
        for (int ii= 0; ii < factors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
        NTLC= convertFacCFMatrix2NTLmat_zz_pE(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
 
        if (NTLN.NumCols() == 1)
        {
          delete [] A;
          return CFList (F (y-eval,y));
        }
      }
    }
    if (NTLN.NumCols() == 1)
    {
      delete [] A;
      return CFList (F (y-eval,y));
    }
 
    int * zeroOneVecs;
    zeroOneVecs= extractZeroOneVecs (NTLN);
    bufF= F;
    bufUniFactors= factors;
    result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, eval);
    delete [] zeroOneVecs;
    if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0)
    {
      F= bufF;
      factors= bufUniFactors;
      delete [] A;
      return result;
    }
 
    result= CFList();
    oldL2= oldL;
    oldL *= 2;
    if (oldL > l)
    {
      if (!hitBound)
      {
        oldL= l;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  return result;
}

increasePrecision() [4/4]

CFList increasePrecision	(	CanonicalForm &	F,
		CFList &	factors,
		int	oldL,
		int	l,
		int	d,
		int *	bounds,
		CFArray &	bufQ,
		nmod_mat_t	FLINTN,
		const CanonicalForm &	eval
	)

Definition at line 4478 of file facFqBivar.cc.

{
  CFList result= CFList();
  CFArray * A= new CFArray [factors.length()];
  int oldL2= oldL/2;
  bool hitBound= false;
#ifdef HAVE_FLINT
  if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors
  {
    nmod_mat_clear (FLINTN);
    nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic());
    for (long i=factors.length()-1; i >= 0; i--)
      nmod_mat_entry (FLINTN, i, i)= 1;
    bufQ= CFArray (factors.length());
  }
#else
  if (NTLN.NumRows() != factors.length()) //refined factors
  {
    ident (NTLN, factors.length());
    bufQ= CFArray (factors.length());
  }
#endif
  bool useOldQs= false;
  CFListIterator j;
  CFMatrix C;
  CFArray buf;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLC, NTLK;
#endif
  CanonicalForm bufF, truncF;
  CFList bufUniFactors;
  Variable y= F.mvar();
  while (oldL <= l)
  {
    j= factors;
    truncF= mod (F, power (y, oldL));
    if (useOldQs)
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i],
                                     bufQ[i]
                                    );
    }
    else
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]);
    }
    useOldQs= true;
 
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= oldL/2)
      {
        int k= tmin (bounds [i] + 1, oldL/2);
        C= CFMatrix (oldL - k, factors.length());
        for (int ii= 0; ii < factors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
#ifdef HAVE_FLINT
        if (nmod_mat_ncols (FLINTN) == 1)
#else
        if (NTLN.NumCols() == 1)
#endif
        {
          delete [] A;
          return CFList (F (y-eval,y));
        }
      }
    }
#ifdef HAVE_FLINT
    if (nmod_mat_ncols (FLINTN) == 1)
#else
    if (NTLN.NumCols() == 1)
#endif
    {
      delete [] A;
      return CFList (F (y-eval,y));
    }
    int * zeroOneVecs;
#ifdef HAVE_FLINT
    zeroOneVecs= extractZeroOneVecs (FLINTN);
#else
    zeroOneVecs= extractZeroOneVecs (NTLN);
#endif
    bufF= F;
    bufUniFactors= factors;
#ifdef HAVE_FLINT
    result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, FLINTN, eval);
#else
    result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, eval);
#endif
    delete [] zeroOneVecs;
    if (degree (bufF) + 1 + degree (LC (bufF, 1)) < oldL && result.length() > 0)
    {
      F= bufF;
      factors= bufUniFactors;
      delete [] A;
      return result;
    }
 
    result= CFList();
    oldL2= oldL;
    oldL *= 2;
    if (oldL > l)
    {
      if (!hitBound)
      {
        oldL= l;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  return result;
}

increasePrecision2()

CFList increasePrecision2	(	const CanonicalForm &	F,
		CFList &	factors,
		const Variable &	alpha,
		int	precision
	)

Definition at line 4134 of file facFqBivar.cc.

{
  int d;
  bool isIrreducible= false;
  int* bounds= computeBounds (F, d, isIrreducible);
  if (isIrreducible)
  {
    delete [] bounds;
    return CFList (F);
  }
  CFArray * A= new CFArray [factors.length()];
  CFArray bufQ= CFArray (factors.length());
  if (fac_NTL_char != getCharacteristic())
  {
    fac_NTL_char= getCharacteristic();
    zz_p::init (getCharacteristic());
  }
  zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha));
  zz_pE::init (NTLMipo);
  mat_zz_pE NTLN;
  ident (NTLN, factors.length());
  int minBound= bounds[0];
  for (int i= 1; i < d; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
  int l= tmin (2*(minBound + 1), precision);
  int oldL= l/2;
  int stepSize= 2;
  bool useOldQs= false;
  bool hitBound= false;
  CFListIterator j;
  CFMatrix C;
  CFArray buf;
  mat_zz_pE* NTLC, NTLK;
  Variable y= F.mvar();
  CanonicalForm truncF;
  while (l <= precision)
  {
    j= factors;
    truncF= mod (F, power (y, l));
    if (useOldQs)
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], bufQ[i]);
    }
    else
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]);
    }
    useOldQs= true;
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix (l - k, factors.length());
        for (int ii= 0; ii < factors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
        NTLC= convertFacCFMatrix2NTLmat_zz_pE(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
 
        if (NTLN.NumCols() == 1)
        {
          delete [] A;
          delete [] bounds;
          return CFList (F);
        }
      }
    }
 
    if (isReduced (NTLN) || l == precision)
    {
      CanonicalForm bufF= F;
      int * zeroOne= extractZeroOneVecs (NTLN);
      CFList bufFactors= factors;
      CFList result= monicReconstruction (bufF, factors, zeroOne, precision,
                                          NTLN
                                         );
      if (result.length() != NTLN.NumCols() && l != precision)
        factors= bufFactors;
      if (result.length() == NTLN.NumCols())
      {
        delete [] zeroOne;
        delete [] A;
        delete [] bounds;
        return result;
      }
      if (l == precision)
      {
        delete [] zeroOne;
        delete [] A;
        delete [] bounds;
        return Union (result, factors);
      }
      delete [] zeroOne;
    }
    oldL= l;
    l += stepSize;
    stepSize *= 2;
    if (l > precision)
    {
      if (!hitBound)
      {
        l= precision;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] bounds;
  delete [] A;
  return CFList();
}

increasePrecisionFq2Fp() [1/2]

CFList increasePrecisionFq2Fp	(	CanonicalForm &	F,
		CFList &	factors,
		int	factorsFound,
		int	oldNumCols,
		int	oldL,
		const Variable &	alpha,
		int	precision,
		const CanonicalForm &	eval
	)

Definition at line 4267 of file facFqBivar.cc.

{
  int d;
  bool isIrreducible= false;
  Variable y= F.mvar();
  int* bounds= computeBounds (F, d, isIrreducible);
  if (isIrreducible)
  {
    delete [] bounds;
    CanonicalForm G= F;
    F= 1;
    return CFList (G (y-eval,y));
  }
  int extensionDeg= degree (getMipo (alpha));
  CFArray * A= new CFArray [factors.length()];
  CFArray bufQ= CFArray (factors.length());
#ifdef HAVE_FLINT
  nmod_mat_t FLINTN;
  nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic());
  for (long i=factors.length()-1; i >= 0; i--)
    nmod_mat_entry (FLINTN, i, i)= 1;
#else
  mat_zz_p NTLN;
  ident (NTLN, factors.length());
#endif
  int minBound= bounds[0];
  for (int i= 1; i < d; i++)
  {
    if (bounds[i] != 0)
      minBound= tmin (minBound, bounds[i]);
  }
  int l= tmax (2*(minBound + 1), oldL);
  int oldL2= l/2;
  int stepSize= 2;
  bool useOldQs= false;
  bool hitBound= false;
  CFListIterator j;
  CFMatrix C;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLC, NTLK;
#endif
  CFArray buf;
  CanonicalForm truncF;
  while (l <= precision)
  {
    j= factors;
    truncF= mod (F, power (y, l));
    if (useOldQs)
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i],
                                     bufQ[i]
                                    );
    }
    else
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]);
    }
    useOldQs= true;
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix ((l - k)*extensionDeg, factors.length());
        for (int ii= 0; ii < factors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k, alpha);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
#ifdef HAVE_FLINT
        if (nmod_mat_ncols (FLINTN) == 1)
        {
          nmod_mat_clear (FLINTN);
#else
        if (NTLN.NumCols() == 1)
        {
#endif
          delete [] A;
          delete [] bounds;
          CanonicalForm G= F;
          F= 1;
          return CFList (G (y-eval,y));
        }
      }
    }
 
#ifdef HAVE_FLINT
    if (nmod_mat_ncols (FLINTN) < oldNumCols - factorsFound)
    {
      if (isReduced (FLINTN))
      {
        int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)];
        for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
#else
    if (NTLN.NumCols() < oldNumCols - factorsFound)
    {
      if (isReduced (NTLN))
      {
        int * factorsFoundIndex= new int [NTLN.NumCols()];
        for (long i= 0; i < NTLN.NumCols(); i++)
#endif
          factorsFoundIndex[i]= 0;
        int factorsFound2= 0;
        CFList result;
        CanonicalForm bufF= F;
#ifdef HAVE_FLINT
        reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2,
                           factorsFoundIndex, FLINTN, eval, false
                          );
        if (result.length() == nmod_mat_ncols (FLINTN))
        {
          nmod_mat_clear (FLINTN);
#else
        reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2,
                           factorsFoundIndex, NTLN, eval, false
                          );
        if (result.length() == NTLN.NumCols())
        {
#endif
          delete [] factorsFoundIndex;
          delete [] A;
          delete [] bounds;
          F= 1;
          return result;
        }
        delete [] factorsFoundIndex;
      }
      else if (l == precision)
      {
        CanonicalForm bufF= F;
#ifdef HAVE_FLINT
        int * zeroOne= extractZeroOneVecs (FLINTN);
        CFList result= reconstruction (bufF,factors,zeroOne,precision,FLINTN, eval);
        nmod_mat_clear (FLINTN);
#else
        int * zeroOne= extractZeroOneVecs (NTLN);
        CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN, eval);
#endif
        F= bufF;
        delete [] zeroOne;
        delete [] A;
        delete [] bounds;
        return result;
      }
    }
    oldL2= l;
    l += stepSize;
    stepSize *= 2;
    if (l > precision)
    {
      if (!hitBound)
      {
        hitBound= true;
        l= precision;
      }
      else
        break;
    }
  }
#ifdef HAVE_FLINT
  nmod_mat_clear (FLINTN);
#endif
  delete [] bounds;
  delete [] A;
  return CFList();
}

increasePrecisionFq2Fp() [2/2]

CFList increasePrecisionFq2Fp	(	CanonicalForm &	F,
		CFList &	factors,
		int	oldL,
		int	l,
		int	d,
		int *	bounds,
		CFArray &	bufQ,
		nmod_mat_t	FLINTN,
		const Variable &	alpha,
		const CanonicalForm &	eval
	)

Definition at line 5014 of file facFqBivar.cc.

{
  CFList result= CFList();
  CFArray * A= new CFArray [factors.length()];
  int extensionDeg= degree (getMipo (alpha));
  int oldL2= oldL/2;
  bool hitBound= false;
  bool useOldQs= false;
#ifdef HAVE_FLINT
  if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors
  {
    nmod_mat_clear (FLINTN);
    nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic());
    for (long i=factors.length()-1; i >= 0; i--)
      nmod_mat_entry (FLINTN, i, i)= 1;
  }
#else
  if (NTLN.NumRows() != factors.length()) //refined factors
    ident (NTLN, factors.length());
#endif
  CFListIterator j;
  CFMatrix C;
  CFArray buf;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLC, NTLK;
#endif
  CanonicalForm bufF, truncF;
  CFList bufUniFactors;
  Variable y= F.mvar();
  while (oldL <= l)
  {
    j= factors;
    truncF= mod (F, power (y, oldL));
    if (useOldQs)
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i],
                                     bufQ[i]
                                    );
    }
    else
    {
      for (int i= 0; i < factors.length(); i++, j++)
        A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]);
    }
    useOldQs= true;
 
    for (int i= 0; i < d; i++)
    {
      if (bounds [i] + 1 <= oldL/2)
      {
        int k= tmin (bounds [i] + 1, oldL/2);
        C= CFMatrix ((oldL - k)*extensionDeg, factors.length());
        for (int ii= 0; ii < factors.length(); ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k, alpha);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
#ifdef HAVE_FLINT
        if (nmod_mat_ncols (FLINTN) == 1)
#else
        if (NTLN.NumCols() == 1)
#endif
        {
          delete [] A;
          return CFList (F(y-eval,y));
        }
      }
    }
 
    int * zeroOneVecs;
#ifdef HAVE_FLINT
    zeroOneVecs= extractZeroOneVecs (FLINTN);
#else
    zeroOneVecs= extractZeroOneVecs (NTLN);
#endif
 
    bufF= F;
    bufUniFactors= factors;
#ifdef HAVE_FLINT
    result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, FLINTN, eval);
#else
    result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, eval);
#endif
    delete [] zeroOneVecs;
    if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0)
    {
      F= bufF;
      factors= bufUniFactors;
      delete [] A;
      return result;
    }
 
    result= CFList();
    oldL2= oldL;
    oldL *= 2;
    if (oldL > l)
    {
      if (!hitBound)
      {
        oldL= l;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  return result;
}

init4ext()

ExtensionInfo init4ext	(	const ExtensionInfo &	info,
		const CanonicalForm &	evaluation,
		int &	degMipo
	)

Definition at line 7657 of file facFqBivar.cc.

{
  bool GF= (CFFactory::gettype() == GaloisFieldDomain);
  Variable alpha= info.getAlpha();
  if (GF)
  {
    degMipo= getGFDegree();
    CanonicalForm GFMipo= gf_mipo;
    setCharacteristic (getCharacteristic());
    GFMipo.mapinto();
    alpha= rootOf (GFMipo);
    setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
  }
  else
  {
    alpha= info.getAlpha();
    degMipo= degree (getMipo (alpha));
  }
 
  Variable gamma;
  CanonicalForm primElemAlpha, imPrimElemAlpha;
  if ((!GF && evaluation != alpha) || (GF && evaluation != getGFGenerator()))
  {
    CanonicalForm bufEvaluation;
    if (GF)
    {
      setCharacteristic (getCharacteristic());
      bufEvaluation= GF2FalphaRep (evaluation, alpha);
    }
    else
      bufEvaluation= evaluation;
    CanonicalForm mipo= findMinPoly (bufEvaluation, alpha);
    gamma= rootOf (mipo);
    Variable V_buf;
    bool fail= false;
    primElemAlpha= primitiveElement (alpha, V_buf, fail);
    imPrimElemAlpha= map (primElemAlpha, alpha, bufEvaluation, gamma);
 
    if (GF)
      setCharacteristic (getCharacteristic(), degMipo, info.getGFName());
  }
  else
    gamma= alpha;
  ExtensionInfo info2= ExtensionInfo (alpha, gamma, primElemAlpha,
                                      imPrimElemAlpha, 1, info.getGFName(), true
                                     );
 
  return info2;
}

isReduced() [1/3]

long isReduced

(

const mat_zz_p &

M

)

Definition at line 1468 of file facFqBivar.cc.

{
  long i, j, nonZero;
  for (i = 1; i <= M.NumRows(); i++)
  {
    nonZero= 0;
    for (j = 1; j <= M.NumCols(); j++)
    {
      if (!IsZero (M (i,j)))
        nonZero++;
    }
    if (nonZero != 1)
      return 0;
  }
  return 1;
}

isReduced() [2/3]

long isReduced

(

const mat_zz_pE &

M

)

Definition at line 1506 of file facFqBivar.cc.

{
  long i, j, nonZero;
  for (i = 1; i <= M.NumRows(); i++)
  {
    nonZero= 0;
    for (j = 1; j <= M.NumCols(); j++)
    {
      if (!IsZero (M (i,j)))
        nonZero++;
    }
    if (nonZero != 1)
      return 0;
  }
  return 1;
}

isReduced() [3/3]

long isReduced

(

const nmod_mat_t

M

)

Definition at line 1487 of file facFqBivar.cc.

{
  long i, j, nonZero;
  for (i = 1; i <= nmod_mat_nrows(M); i++)
  {
    nonZero= 0;
    for (j = 1; j <= nmod_mat_ncols (M); j++)
    {
      if (!(nmod_mat_entry (M, i-1, j-1)==0))
        nonZero++;
    }
    if (nonZero != 1)
      return 0;
  }
  return 1;
}

liftAndComputeLattice() [1/3]

int liftAndComputeLattice	(	const CanonicalForm &	F,
		int *	bounds,
		int	sizeBounds,
		int	start,
		int	liftBound,
		int	minBound,
		CFList &	factors,
		mat_zz_p &	NTLN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		bool &	irreducible
	)

Definition at line 2485 of file facFqBivar.cc.

{
  CanonicalForm LCF= LC (F, 1);
  CFArray *A= new CFArray [factors.length() - 1];
  bool wasInBounds= false;
  bool hitBound= false;
  int l= (minBound+1)*2;
  int stepSize= 2;
  int oldL= l/2;
  bool reduced= false;
  mat_zz_p NTLK, *NTLC;
  CFMatrix C;
  CFArray buf;
  CFListIterator j;
  CanonicalForm truncF;
  Variable y= F.mvar();
  while (l <= liftBound)
  {
    TIMING_START (fac_fq_compute_lattice_lift);
    if (start)
    {
      henselLiftResume12 (F, factors, start, l, Pi, diophant, M);
      start= 0;
    }
    else
    {
      if (wasInBounds)
        henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M);
      else
        henselLift12 (F, factors, l, Pi, diophant, M);
    }
    TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift,
                          "time to lift in compute lattice: ");
 
    factors.insert (LCF);
    j= factors;
    j++;
 
    truncF= mod (F, power (y, l));
    TIMING_START (fac_fq_logarithmic);
    for (int i= 0; i < factors.length() - 1; i++, j++)
    {
      if (!wasInBounds)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]);
      else
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]);
    }
    TIMING_END_AND_PRINT (fac_fq_logarithmic,
                          "time to compute logarithmic derivative: ");
 
    for (int i= 0; i < sizeBounds; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        wasInBounds= true;
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix (l - k, factors.length() - 1);
        for (int ii= 0; ii < factors.length() - 1; ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
 
        if (NTLN.NumCols() == 1)
        {
          irreducible= true;
          break;
        }
        if (isReduced (NTLN) && l > (minBound+1)*2)
        {
          reduced= true;
          break;
        }
      }
    }
 
    if (irreducible)
      break;
    if (reduced)
      break;
    oldL= l;
    l += stepSize;
    stepSize *= 2;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  if (!wasInBounds)
  {
    if (start)
      henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M);
    else
      henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M);
    factors.insert (LCF);
  }
  return l;
}

liftAndComputeLattice() [2/3]

int liftAndComputeLattice	(	const CanonicalForm &	F,
		int *	bounds,
		int	sizeBounds,
		int	start,
		int	liftBound,
		int	minBound,
		CFList &	factors,
		mat_zz_pE &	NTLN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		bool &	irreducible
	)

Definition at line 3157 of file facFqBivar.cc.

{
  CanonicalForm LCF= LC (F, 1);
  CFArray *A= new CFArray [factors.length() - 1];
  bool wasInBounds= false;
  bool hitBound= false;
  int l= (minBound+1)*2;
  int stepSize= 2;
  int oldL= l/2;
  bool reduced= false;
  CFListIterator j;
  mat_zz_pE* NTLC, NTLK;
  CFArray buf;
  CFMatrix C;
  Variable y= F.mvar();
  CanonicalForm truncF;
  while (l <= liftBound)
  {
    TIMING_START (fac_fq_compute_lattice_lift);
    if (start)
    {
      henselLiftResume12 (F, factors, start, l, Pi, diophant, M);
      start= 0;
    }
    else
    {
      if (wasInBounds)
        henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M);
      else
        henselLift12 (F, factors, l, Pi, diophant, M);
    }
    TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift,
                          "time to lift in compute lattice: ");
 
    factors.insert (LCF);
    j= factors;
    j++;
 
    truncF= mod (F, power (y,l));
    TIMING_START (fac_fq_logarithmic);
    for (int i= 0; i < factors.length() - 1; i++, j++)
    {
      if (l == (minBound+1)*2)
      {
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]);
      }
      else
      {
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]
                                    );
      }
    }
    TIMING_END_AND_PRINT (fac_fq_logarithmic,
                          "time to compute logarithmic derivative: ");
 
    for (int i= 0; i < sizeBounds; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        wasInBounds= true;
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix (l - k, factors.length() - 1);
        for (int ii= 0; ii < factors.length() - 1; ii++)
        {
 
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
 
        NTLC= convertFacCFMatrix2NTLmat_zz_pE(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
 
        if (NTLN.NumCols() == 1)
        {
          irreducible= true;
          break;
        }
        if (isReduced (NTLN) && l > (minBound+1)*2)
        {
          reduced= true;
          break;
        }
      }
    }
 
    if (NTLN.NumCols() == 1)
    {
      irreducible= true;
      break;
    }
    if (reduced)
      break;
    oldL= l;
    l += stepSize;
    stepSize *= 2;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  if (!wasInBounds)
  {
    if (start)
      henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M);
    else
      henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M);
    factors.insert (LCF);
  }
  return l;
}

liftAndComputeLattice() [3/3]

int liftAndComputeLattice	(	const CanonicalForm &	F,
		int *	bounds,
		int	sizeBounds,
		int	start,
		int	liftBound,
		int	minBound,
		CFList &	factors,
		nmod_mat_t	FLINTN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		bool &	irreducible
	)

Definition at line 2610 of file facFqBivar.cc.

{
  CanonicalForm LCF= LC (F, 1);
  CFArray *A= new CFArray [factors.length() - 1];
  bool wasInBounds= false;
  bool hitBound= false;
  int l= (minBound+1)*2;
  int stepSize= 2;
  int oldL= l/2;
  bool reduced= false;
  long rank;
  nmod_mat_t FLINTK, FLINTC, null;
  CFMatrix C;
  CFArray buf;
  CFListIterator j;
  CanonicalForm truncF;
  Variable y= F.mvar();
  while (l <= liftBound)
  {
    TIMING_START (fac_fq_compute_lattice_lift);
    if (start)
    {
      henselLiftResume12 (F, factors, start, l, Pi, diophant, M);
      start= 0;
    }
    else
    {
      if (wasInBounds)
        henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M);
      else
        henselLift12 (F, factors, l, Pi, diophant, M);
    }
    TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift,
                          "time to lift in compute lattice: ");
 
    factors.insert (LCF);
    j= factors;
    j++;
 
    truncF= mod (F, power (y, l));
    TIMING_START (fac_fq_logarithmic);
    for (int i= 0; i < factors.length() - 1; i++, j++)
    {
      if (!wasInBounds)
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]);
      else
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]);
    }
    TIMING_END_AND_PRINT (fac_fq_logarithmic,
                          "time to compute logarithmic derivative: ");
 
    for (int i= 0; i < sizeBounds; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        wasInBounds= true;
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix (l - k, factors.length() - 1);
        for (int ii= 0; ii < factors.length() - 1; ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
 
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
        if (nmod_mat_ncols (FLINTN) == 1)
        {
          irreducible= true;
          break;
        }
        if (isReduced (FLINTN) && l > (minBound+1)*2)
        {
          reduced= true;
          break;
        }
      }
    }
 
    if (irreducible)
      break;
    if (reduced)
      break;
    oldL= l;
    l += stepSize;
    stepSize *= 2;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  if (!wasInBounds)
  {
    if (start)
      henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M);
    else
      henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M);
    factors.insert (LCF);
  }
  return l;
}

liftAndComputeLatticeFq2Fp()

int liftAndComputeLatticeFq2Fp	(	const CanonicalForm &	F,
		int *	bounds,
		int	sizeBounds,
		int	start,
		int	liftBound,
		int	minBound,
		CFList &	factors,
		nmod_mat_t	FLINTN,
		CFList &	diophant,
		CFMatrix &	M,
		CFArray &	Pi,
		CFArray &	bufQ,
		bool &	irreducible,
		const Variable &	alpha
	)

Definition at line 3292 of file facFqBivar.cc.

{
  CanonicalForm LCF= LC (F, 1);
  CFArray *A= new CFArray [factors.length() - 1];
  bool wasInBounds= false;
  int l= (minBound+1)*2;
  int oldL= l/2;
  int stepSize= 2;
  bool hitBound= false;
  int extensionDeg= degree (getMipo (alpha));
  bool reduced= false;
  CFListIterator j;
  CFMatrix C;
  CFArray buf;
#ifdef HAVE_FLINT
  long rank;
  nmod_mat_t FLINTC, FLINTK, null;
#else
  mat_zz_p* NTLC, NTLK;
#endif
  Variable y= F.mvar();
  CanonicalForm truncF;
  while (l <= liftBound)
  {
    TIMING_START (fac_fq_compute_lattice_lift);
    if (start)
    {
      henselLiftResume12 (F, factors, start, l, Pi, diophant, M);
      start= 0;
    }
    else
    {
      if (wasInBounds)
        henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M);
      else
        henselLift12 (F, factors, l, Pi, diophant, M);
    }
    TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift,
                          "time to lift in compute lattice: ");
 
    factors.insert (LCF);
    j= factors;
    j++;
 
    truncF= mod (F, power (y,l));
    TIMING_START (fac_fq_logarithmic);
    for (int i= 0; i < factors.length() - 1; i++, j++)
    {
      if (l == (minBound+1)*2)
      {
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]);
      }
      else
      {
        A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i],
                                     bufQ[i]
                                    );
      }
    }
    TIMING_END_AND_PRINT (fac_fq_logarithmic,
                          "time to compute logarithmic derivative: ");
 
    for (int i= 0; i < sizeBounds; i++)
    {
      if (bounds [i] + 1 <= l/2)
      {
        wasInBounds= true;
        int k= tmin (bounds [i] + 1, l/2);
        C= CFMatrix ((l - k)*extensionDeg, factors.length() - 1);
        for (int ii= 0; ii < factors.length() - 1; ii++)
        {
          if (A[ii].size() - 1 >= i)
          {
            buf= getCoeffs (A[ii] [i], k, alpha);
            writeInMatrix (C, buf, ii + 1, 0);
          }
        }
 
#ifdef HAVE_FLINT
        convertFacCFMatrix2nmod_mat_t (FLINTC, C);
        nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN),
                       getCharacteristic());
        nmod_mat_mul (FLINTK, FLINTC, FLINTN);
        nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        rank= nmod_mat_nullspace (null, FLINTK);
        nmod_mat_clear (FLINTK);
        nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank);
        nmod_mat_clear (FLINTC);
        nmod_mat_init_set (FLINTC, FLINTN);
        nmod_mat_clear (FLINTN);
        nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK),
                       getCharacteristic());
        nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!!
 
        nmod_mat_clear (FLINTC);
        nmod_mat_window_clear (FLINTK);
        nmod_mat_clear (null);
#else
        NTLC= convertFacCFMatrix2NTLmat_zz_p(C);
        NTLK= (*NTLC)*NTLN;
        transpose (NTLK, NTLK);
        kernel (NTLK, NTLK);
        transpose (NTLK, NTLK);
        NTLN *= NTLK;
        delete NTLC;
#endif
 
#ifdef HAVE_FLINT
        if (nmod_mat_nrows (FLINTN) == 1)
#else
        if (NTLN.NumCols() == 1)
#endif
        {
          irreducible= true;
          break;
        }
#ifdef HAVE_FLINT
        if (isReduced (FLINTN) && l > (minBound+1)*2)
#else
        if (isReduced (NTLN) && l > (minBound+1)*2)
#endif
        {
          reduced= true;
          break;
        }
      }
    }
 
#ifdef HAVE_FLINT
    if (nmod_mat_ncols (FLINTN) == 1)
#else
    if (NTLN.NumCols() == 1)
#endif
    {
      irreducible= true;
      break;
    }
    if (reduced)
      break;
    oldL= l;
    l += stepSize;
    stepSize *= 2;
    if (l > liftBound)
    {
      if (!hitBound)
      {
        l= liftBound;
        hitBound= true;
      }
      else
        break;
    }
  }
  delete [] A;
  if (!wasInBounds)
  {
    if (start)
      henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M);
    else
      henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M);
    factors.insert (LCF);
  }
  return l;
}

mod()

return mod	(	mulNTL(buf1, buf2, b)	,
		M
	)

monicReconstruction()

CFList monicReconstruction	(	CanonicalForm &	G,
		CFList &	factors,
		int *	zeroOneVecs,
		int	precision,
		const mat_zz_pE &	N
	)

Definition at line 1907 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  CanonicalForm F= G;
  CanonicalForm yToL= power (y, precision);
  CanonicalForm quot, buf, buf2;
  CFList result;
  CFList bufFactors= factors;
  CFList factorsConsidered;
  CFListIterator iter;
  for (long i= 1; i <= N.NumCols(); i++)
  {
    if (zeroOneVecs [i - 1] == 0)
      continue;
    iter= factors;
    buf= 1;
    factorsConsidered= CFList();
    for (long j= 1; j <= N.NumRows(); j++, iter++)
    {
      if (!IsZero (N (j,i)))
      {
        factorsConsidered.append (iter.getItem());
        buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf2= buf;
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    if (fdivides (buf, F, quot))
    {
      F= quot;
      F /= Lc (F);
      result.append (buf2);
      bufFactors= Difference (bufFactors, factorsConsidered);
    }
    if (degree (F) <= 0)
    {
      G= F;
      factors= bufFactors;
      return result;
    }
  }
  G= F;
  factors= bufFactors;
  return result;
}

reconstruction() [1/3]

CFList reconstruction	(	CanonicalForm &	G,
		CFList &	factors,
		int *	zeroOneVecs,
		int	precision,
		const mat_zz_p &	N,
		const CanonicalForm &	eval
	)

Definition at line 2122 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  CanonicalForm F= G;
  CanonicalForm yToL= power (y, precision);
  CanonicalForm quot, buf;
  CFList result;
  CFList bufFactors= factors;
  CFList factorsConsidered;
  CFListIterator iter;
  for (long i= 1; i <= N.NumCols(); i++)
  {
    if (zeroOneVecs [i - 1] == 0)
      continue;
    iter= factors;
    buf= 1;
    factorsConsidered= CFList();
    for (long j= 1; j <= N.NumRows(); j++, iter++)
    {
      if (!IsZero (N (j,i)))
      {
        factorsConsidered.append (iter.getItem());
        buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    if (fdivides (buf, F, quot))
    {
      F= quot;
      F /= Lc (F);
      result.append (buf (y-eval,y));
      bufFactors= Difference (bufFactors, factorsConsidered);
    }
    if (degree (F) <= 0)
    {
      G= F;
      factors= bufFactors;
      return result;
    }
  }
  G= F;
  factors= bufFactors;
  return result;
}

reconstruction() [2/3]

CFList reconstruction	(	CanonicalForm &	G,
		CFList &	factors,
		int *	zeroOneVecs,
		int	precision,
		const mat_zz_pE &	N,
		const CanonicalForm &	eval
	)

Definition at line 1856 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  CanonicalForm F= G;
  CanonicalForm yToL= power (y, precision);
  CanonicalForm quot, buf;
  CFList result, factorsConsidered;
  CFList bufFactors= factors;
  CFListIterator iter;
  for (long i= 1; i <= N.NumCols(); i++)
  {
    if (zeroOneVecs [i - 1] == 0)
      continue;
    iter= factors;
    buf= 1;
    factorsConsidered= CFList();
    for (long j= 1; j <= N.NumRows(); j++, iter++)
    {
      if (!IsZero (N (j,i)))
      {
        factorsConsidered.append (iter.getItem());
        buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    if (fdivides (buf, F, quot))
    {
      F= quot;
      F /= Lc (F);
      result.append (buf (y-eval,y));
      bufFactors= Difference (bufFactors, factorsConsidered);
    }
    if (degree (F) <= 0)
    {
      G= F;
      factors= bufFactors;
      return result;
    }
  }
  G= F;
  factors= bufFactors;
  return result;
}

reconstruction() [3/3]

CFList reconstruction	(	CanonicalForm &	G,
		CFList &	factors,
		int *	zeroOneVecs,
		int	precision,
		const nmod_mat_t	N,
		const CanonicalForm &	eval
	)

Definition at line 2173 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  CanonicalForm F= G;
  CanonicalForm yToL= power (y, precision);
  CanonicalForm quot, buf;
  CFList result;
  CFList bufFactors= factors;
  CFList factorsConsidered;
  CFListIterator iter;
  for (long i= 0; i < nmod_mat_ncols (N); i++)
  {
    if (zeroOneVecs [i] == 0)
      continue;
    iter= factors;
    buf= 1;
    factorsConsidered= CFList();
    for (long j= 0; j < nmod_mat_nrows (N); j++, iter++)
    {
      if (!(nmod_mat_entry (N, j, i) == 0))
      {
        factorsConsidered.append (iter.getItem());
        buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    if (fdivides (buf, F, quot))
    {
      F= quot;
      F /= Lc (F);
      result.append (buf (y-eval,y));
      bufFactors= Difference (bufFactors, factorsConsidered);
    }
    if (degree (F) <= 0)
    {
      G= F;
      factors= bufFactors;
      return result;
    }
  }
  G= F;
  factors= bufFactors;
  return result;
}

reconstructionTry() [1/3]

void reconstructionTry	(	CFList &	reconstructedFactors,
		CanonicalForm &	F,
		const CFList &	factors,
		const int	liftBound,
		int &	factorsFound,
		int *&	factorsFoundIndex,
		mat_zz_p &	N,
		const CanonicalForm &	eval,
		bool	beenInThres
	)

Definition at line 1688 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  CanonicalForm yToL= power (y, liftBound);
  CanonicalForm bufF= F (y-eval, y);
  if (factors.length() == 2)
  {
    CanonicalForm tmp1, tmp2, tmp3;
    tmp1= factors.getFirst();
    tmp2= factors.getLast();
    tmp1= mulMod2 (tmp1, LC (F,x), yToL);
    tmp1 /= content (tmp1, x);
    tmp1= tmp1 (y-eval, y);
    tmp2= mulMod2 (tmp2, LC (F,x), yToL);
    tmp2 /= content (tmp2, x);
    tmp2= tmp2 (y-eval,y);
    tmp3 = tmp1*tmp2;
    if (tmp3/Lc (tmp3) == bufF/Lc (bufF))
    {
      factorsFound++;
      F= 1;
      reconstructedFactors.append (tmp1);
      reconstructedFactors.append (tmp2);
      return;
    }
  }
  CanonicalForm quot, buf;
  CFListIterator iter;
  for (long i= 1; i <= N.NumCols(); i++)
  {
    if (factorsFoundIndex [i - 1] == 1)
      continue;
    iter= factors;
    if (beenInThres)
    {
      int count= 1;
      while (count < i)
      {
        count++;
        iter++;
      }
      buf= iter.getItem();
    }
    else
    {
      buf= 1;
      for (long j= 1; j <= N.NumRows(); j++, iter++)
      {
        if (!IsZero (N (j,i)))
          buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    buf= buf (y-eval,y);
    if (fdivides (buf, bufF, quot))
    {
      factorsFoundIndex[i - 1]= 1;
      factorsFound++;
      bufF= quot;
      bufF /= Lc (bufF);
      reconstructedFactors.append (buf);
    }
    if (degree (bufF) <= 0)
      return;
    if (factorsFound + 1 == N.NumCols())
    {
      reconstructedFactors.append (bufF);
      F=1;
      return;
    }
  }
  if (reconstructedFactors.length() != 0)
    F= bufF (y+eval,y);
}

reconstructionTry() [2/3]

void reconstructionTry	(	CFList &	reconstructedFactors,
		CanonicalForm &	F,
		const CFList &	factors,
		const int	liftBound,
		int &	factorsFound,
		int *&	factorsFoundIndex,
		mat_zz_pE &	N,
		const CanonicalForm &	eval,
		bool	beenInThres
	)

Definition at line 1604 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  CanonicalForm yToL= power (y, liftBound);
  CanonicalForm bufF= F (y-eval, y);
  if (factors.length() == 2)
  {
    CanonicalForm tmp1, tmp2, tmp3;
    tmp1= factors.getFirst();
    tmp2= factors.getLast();
    tmp1= mulMod2 (tmp1, LC (F,x), yToL);
    tmp1 /= content (tmp1, x);
    tmp1= tmp1 (y-eval, y);
    tmp2= mulMod2 (tmp2, LC (F,x), yToL);
    tmp2 /= content (tmp2, x);
    tmp2= tmp2 (y-eval, y);
    tmp3 = tmp1*tmp2;
    if (tmp3/Lc (tmp3) == bufF/Lc (bufF))
    {
      factorsFound++;
      F= 1;
      reconstructedFactors.append (tmp1);
      reconstructedFactors.append (tmp2);
      return;
    }
  }
  CanonicalForm quot, buf;
  CFListIterator iter;
  for (long i= 1; i <= N.NumCols(); i++)
  {
    if (factorsFoundIndex [i - 1] == 1)
      continue;
    iter= factors;
    if (beenInThres)
    {
      int count= 1;
      while (count < i)
      {
        count++;
        iter++;
      }
      buf= iter.getItem();
    }
    else
    {
      buf= 1;
      for (long j= 1; j <= N.NumRows(); j++, iter++)
      {
        if (!IsZero (N (j,i)))
          buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    buf= buf (y-eval,y);
    if (fdivides (buf, bufF, quot))
    {
      factorsFoundIndex[i - 1]= 1;
      factorsFound++;
      bufF= quot;
      bufF /= Lc (bufF);
      reconstructedFactors.append (buf);
    }
    if (degree (bufF) <= 0)
      return;
    if (factorsFound + 1 == N.NumCols())
    {
      reconstructedFactors.append (bufF);
      F= 1;
      return;
    }
  }
  if (reconstructedFactors.length() != 0)
    F= bufF (y+eval,y);
}

reconstructionTry() [3/3]

void reconstructionTry	(	CFList &	reconstructedFactors,
		CanonicalForm &	F,
		const CFList &	factors,
		const int	liftBound,
		int &	factorsFound,
		int *&	factorsFoundIndex,
		nmod_mat_t	N,
		const CanonicalForm &	eval,
		bool	beenInThres
	)

Definition at line 1772 of file facFqBivar.cc.

{
  Variable y= Variable (2);
  Variable x= Variable (1);
  CanonicalForm yToL= power (y, liftBound);
  CanonicalForm bufF= F (y-eval, y);
  if (factors.length() == 2)
  {
    CanonicalForm tmp1, tmp2, tmp3;
    tmp1= factors.getFirst();
    tmp2= factors.getLast();
    tmp1= mulMod2 (tmp1, LC (F,x), yToL);
    tmp1 /= content (tmp1, x);
    tmp1= tmp1 (y-eval, y);
    tmp2= mulMod2 (tmp2, LC (F,x), yToL);
    tmp2 /= content (tmp2, x);
    tmp2= tmp2 (y-eval, y);
    tmp3 = tmp1*tmp2;
    if (tmp3/Lc (tmp3) == bufF/Lc (bufF))
    {
      factorsFound++;
      F= 1;
      reconstructedFactors.append (tmp1);
      reconstructedFactors.append (tmp2);
      return;
    }
  }
  CanonicalForm quot, buf;
  CFListIterator iter;
  for (long i= 0; i < nmod_mat_ncols (N); i++)
  {
    if (factorsFoundIndex [i] == 1)
      continue;
    iter= factors;
    if (beenInThres)
    {
      int count= 0;
      while (count < i)
      {
        count++;
        iter++;
      }
      buf= iter.getItem();
    }
    else
    {
      buf= 1;
      for (long j= 0; j < nmod_mat_nrows (N); j++, iter++)
      {
        if (!(nmod_mat_entry (N, j, i) == 0))
          buf= mulMod2 (buf, iter.getItem(), yToL);
      }
    }
    buf= mulMod2 (buf, LC (F,x), yToL);
    buf /= content (buf, x);
    buf= buf (y-eval,y);
    if (fdivides (buf, bufF, quot))
    {
      factorsFoundIndex[i]= 1;
      factorsFound++;
      bufF= quot;
      bufF /= Lc (bufF);
      reconstructedFactors.append (buf);
    }
    if (degree (F) <= 0)
      return;
    if (factorsFound + 1 == nmod_mat_ncols (N))
    {
      F= 1;
      reconstructedFactors.append (bufF);
      return;
    }
  }
  if (reconstructedFactors.length() != 0)
    F= bufF (y+eval,y);
}

refineAndRestartLift() [1/2]

void refineAndRestartLift	(	const CanonicalForm &	F,
		const mat_zz_pE &	NTLN,
		int	liftBound,
		int	l,
		CFList &	factors,
		CFMatrix &	M,
		CFArray &	Pi,
		CFList &	diophant
	)

Definition at line 6173 of file facFqBivar.cc.

{
  CFList bufFactors;
  Variable y= Variable (2);
  CanonicalForm LCF= LC (F, 1);
  CFListIterator iter;
  CanonicalForm buf;
  for (long i= 1; i <= NTLN.NumCols(); i++)
  {
    iter= factors;
    buf= 1;
    for (long j= 1; j <= NTLN.NumRows(); j++, iter++)
    {
      if (!IsZero (NTLN (j,i)))
        buf= mulNTL (buf, mod (iter.getItem(), y));
    }
    bufFactors.append (buf);
  }
  factors= bufFactors;
  M= CFMatrix (liftBound, factors.length());
  Pi= CFArray();
  diophant= CFList();
  factors.insert (LCF);
  henselLift12 (F, factors, l, Pi, diophant, M);
}

refineAndRestartLift() [2/2]

void refineAndRestartLift	(	const CanonicalForm &	F,
		const nmod_mat_t	FLINTN,
		int	liftBound,
		int	l,
		CFList &	factors,
		CFMatrix &	M,
		CFArray &	Pi,
		CFList &	diophant
	)

Definition at line 6140 of file facFqBivar.cc.

{
  CFList bufFactors;
  Variable y= Variable (2);
  CanonicalForm LCF= LC (F, 1);
  CFListIterator iter;
  CanonicalForm buf;
  for (long i= 0; i < nmod_mat_ncols (FLINTN); i++)
  {
    iter= factors;
    buf= 1;
    for (long j= 0; j < nmod_mat_nrows (FLINTN); j++, iter++)
    {
      if (!(nmod_mat_entry (FLINTN,j,i) == 0))
        buf= mulNTL (buf, mod (iter.getItem(), y));
    }
    bufFactors.append (buf);
  }
  factors= bufFactors;
  M= CFMatrix (liftBound, factors.length());
  Pi= CFArray();
  diophant= CFList();
  factors.insert (LCF);
  henselLift12 (F, factors, l, Pi, diophant, M);
}

sieveSmallFactors()

CFList sieveSmallFactors	(	const CanonicalForm &	G,
		CFList &	uniFactors,
		DegreePattern &	degPat,
		CanonicalForm &	H,
		CFList &	diophant,
		CFArray &	Pi,
		CFMatrix &	M,
		bool &	success,
		int	d,
		const CanonicalForm &	eval
	)

Definition at line 6762 of file facFqBivar.cc.

{
  CanonicalForm F= G;
  CFList bufUniFactors= uniFactors;
  bufUniFactors.insert (LC (F, 1));
  int smallFactorDeg= d;
  DegreePattern degs= degPat;
  henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M);
  int adaptedLiftBound;
  success= false;
  int * factorsFoundIndex= new int [uniFactors.length()];
  for (int i= 0; i < uniFactors.length(); i++)
    factorsFoundIndex [i]= 0;
  CFList earlyFactors;
  earlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound,
                        factorsFoundIndex, degs, success, smallFactorDeg, eval);
  delete [] factorsFoundIndex;
  if (degs.getLength() == 1)
  {
    degPat= degs;
    return earlyFactors;
  }
  if (success)
  {
    H= F;
    return earlyFactors;
  }
  int sizeOldF= size (G);
  if (size (F) < sizeOldF)
  {
    H= F;
    success= true;
    return earlyFactors;
  }
  else
  {
    uniFactors= bufUniFactors;
    return CFList();
  }
}

TIMING_DEFINE_PRINT()

TIMING_DEFINE_PRINT

(

fac_fq_uni_factorizer

)

const &

uniFactorizer()

CFList uniFactorizer	(	const CanonicalForm &	A,
		const Variable &	alpha,
		const bool &	GF
	)

Univariate factorization of squarefree monic polys over finite fields via NTL. If the characteristic is even special GF2 routines of NTL are used.

Returns

uniFactorizer returns a list of monic factors

Parameters

[in]	A	squarefree univariate poly
[in]	alpha	algebraic variable
[in]	GF	GaloisFieldDomain?

Definition at line 160 of file facFqBivar.cc.

{
  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;
}

Variable Documentation

b

else L b

Initial value:

{
  if (L.isEmpty())
    return 1

Definition at line 60 of file facFqBivar.cc.

buf1

buf1 = prodMod0 (tmp1, M, b)

Definition at line 73 of file facFqBivar.cc.

buf2

buf2 = prodMod0 (tmp2, M, b)

Definition at line 73 of file facFqBivar.cc.

else

else

Initial value:

{
    int l= L.length()/2

Definition at line 68 of file facFqBivar.cc.

i

CFListIterator i = L

Definition at line 71 of file facFqBivar.cc.

M

else L M

Definition at line 60 of file facFqBivar.cc.

tmp1

CFList tmp1

Definition at line 72 of file facFqBivar.cc.

tmp2

tmp2 = Difference (L, tmp1)

Definition at line 72 of file facFqBivar.cc.