source: git/factory/cf_factor.cc @ 72ebdb

/* Emacs edit mode for this file is -*- C++ -*- */
/* $Id$ */

//{{{ docu
//
// cf_factor.cc - factorization and square free algorithms.
//
// Used by: fac_multivar.cc, fac_univar.cc, cf_irred.cc
//
// Header file: cf_algorithm.h
//
//}}}

#include "config.h"

#include "cf_assert.h"

#include "cf_defs.h"
#include "canonicalform.h"
#include "cf_iter.h"
#include "fac_berlekamp.h"
#include "fac_cantzass.h"
#include "fac_univar.h"
#include "fac_multivar.h"
#include "fac_sqrfree.h"
#include "cf_algorithm.h"
#include "facFqFactorize.h"
#include "cf_map.h"
#include "algext.h"
#include "facAlgExt.h"
#include "facFactorize.h"
#include "singext.h"

#include "int_int.h"
#ifdef HAVE_NTL
#include "NTLconvert.h"
#endif

#include "cf_gmp.h"

int getExp(); /* cf_char.cc */

//static bool isUnivariateBaseDomain( const CanonicalForm & f )
//{
//    CFIterator i = f;
//    bool ok = i.coeff().inBaseDomain();
//    i++;
//    while ( i.hasTerms() && ( ok = ok && i.coeff().inBaseDomain() ) ) i++;
//    return ok;
//}

void find_exp(const CanonicalForm & f, int * exp_f)
{
  if ( ! f.inCoeffDomain() )
  {
    int e=f.level();
    CFIterator i = f;
    if (e>=0)
    {
      if (i.exp() > exp_f[e]) exp_f[e]=i.exp();
    }
    for (; i.hasTerms(); i++ )
    {
      find_exp(i.coeff(), exp_f);
    }
  }
}

int find_mvar(const CanonicalForm & f)
{
  int mv=f.level();
  int *exp_f=new int[mv+1];
  int i;
  for(i=mv;i>0;i--) exp_f[i]=0;
  find_exp(f,exp_f);
  for(i=mv;i>0;i--)
  {
    if ((exp_f[i]>0) && (exp_f[i]<exp_f[mv]))
    {
      mv=i;
    }
  }
  delete[] exp_f;
  return mv;
}

#if 0
//#ifndef NOSTREAMIO
void out_cf(const char *s1,const CanonicalForm &f,const char *s2)
{
  printf("%s",s1);
  if (f.isZero()) printf("+0");
  //else if (! f.inCoeffDomain() )
  else if (! f.inBaseDomain() )
  {
    int l = f.level();
    for ( CFIterator i = f; i.hasTerms(); i++ )
    {
      int e=i.exp();
      if (i.coeff().isOne())
      {
        printf("+");
        if (e==0) printf("1");
        else
        {
          printf("v(%d)",l);
          if (e!=1) printf("^%d",e);
        }
      }
      else
      {
        out_cf("+(",i.coeff(),")");
        if (e!=0)
        {
          printf("*v(%d)",l);
          if (e!=1) printf("^%d",e);
        }
      }
    }
  }
  else
  {
    if ( f.isImm() )
    {
      printf("+%d",f.intval());
    }
    else
    {
    #ifdef NOSTREAMIO
      if (f.inZ())
      {
        mpz_t m;
        gmp_numerator(f,m);
        char * str = new char[mpz_sizeinbase( m, 10 ) + 2];
        str = mpz_get_str( str, 10, m );
        printf("%s",str);
        delete[] str;
        mpz_clear(m);
      }
      else if (f.inQ())
      {
        mpz_t m;
        gmp_numerator(f,m);
        char * str = new char[mpz_sizeinbase( m, 10 ) + 2];
        str = mpz_get_str( str, 10, m );
        printf("%s/",str);
        delete[] str;
        mpz_clear(m);
        gmp_denominator(f,m);
        str = new char[mpz_sizeinbase( m, 10 ) + 2];
        str = mpz_get_str( str, 10, m );
        printf("%s",str);
        delete[] str;
        mpz_clear(m);
      }
    #else
       std::cout << f;
    #endif
    }
    //if (f.inZ()) printf("(Z)");
    //else if (f.inQ()) printf("(Q)");
    //else if (f.inFF()) printf("(FF)");
    //else if (f.inPP()) printf("(PP)");
    //else if (f.inGF()) printf("(PP)");
    //else
    if (f.inExtension()) printf("E(%d)",f.level());
  }
  printf("%s",s2);
}
void out_cff(CFFList &L)
{
  //int n = L.length();
  CFFListIterator J=L;
  int j=0;
  for ( ; J.hasItem(); J++, j++ )
  {
    printf("F%d",j);out_cf(":",J.getItem().factor()," ^ ");
    printf("%d\n", J.getItem().exp());
  }
}
void test_cff(CFFList &L,const CanonicalForm & f)
{
  //int n = L.length();
  CFFListIterator J=L;
  CanonicalForm t=1;
  int j=0;
  if (!(L.getFirst().factor().inCoeffDomain()))
    printf("first entry is not const\n");
  for ( ; J.hasItem(); J++, j++ )
  {
    CanonicalForm tt=J.getItem().factor();
    if (tt.inCoeffDomain() && (j!=0))
      printf("other entry is const\n");
    j=J.getItem().exp();
    while(j>0) { t*=tt; j--; }
  }
  if (!(f-t).isZero()) { printf("problem:\n");out_cf("factor:",f," has problems\n");}
}
//#endif
#endif

bool isPurePoly_m(const CanonicalForm & f)
{
  if (f.inBaseDomain()) return true;
  if (f.level()<0) return false;
  for (CFIterator i=f;i.hasTerms();i++)
  {
    if (!isPurePoly_m(i.coeff())) return false;
  }
  return true;
}
bool isPurePoly(const CanonicalForm & f)
{
  if (f.level()<=0) return false;
  for (CFIterator i=f;i.hasTerms();i++)
  {
    if (!(i.coeff().inBaseDomain())) return false;
  }
  return true;
}


///////////////////////////////////////////////////////////////
// get_max_degree_Variable returns Variable with             //
// highest degree. We assume f is *not* a constant!          //
///////////////////////////////////////////////////////////////
Variable
get_max_degree_Variable(const CanonicalForm & f)
{
  ASSERT( ( ! f.inCoeffDomain() ), "no constants" );
  int max=0, maxlevel=0, n=level(f);
  for ( int i=1; i<=n; i++ )
  {
    if (degree(f,Variable(i)) >= max)
    {
      max= degree(f,Variable(i)); maxlevel= i;
    }
  }
  return Variable(maxlevel);
}

///////////////////////////////////////////////////////////////
// get_Terms: Split the polynomial in the containing terms.  //
// getTerms: the real work is done here.                     //
///////////////////////////////////////////////////////////////
void
getTerms( const CanonicalForm & f, const CanonicalForm & t, CFList & result )
{
  if ( getNumVars(f) == 0 ) result.append(f*t);
  else{
    Variable x(level(f));
    for ( CFIterator i=f; i.hasTerms(); i++ )
      getTerms( i.coeff(), t*power(x,i.exp()), result);
  }
}
CFList
get_Terms( const CanonicalForm & f ){
  CFList result,dummy,dummy2;
  CFIterator i;
  CFListIterator j;

  if ( getNumVars(f) == 0 ) result.append(f);
  else{
    Variable _x(level(f));
    for ( i=f; i.hasTerms(); i++ ){
      getTerms(i.coeff(), 1, dummy);
      for ( j=dummy; j.hasItem(); j++ )
        result.append(j.getItem() * power(_x, i.exp()));

      dummy= dummy2; // have to initalize new
    }
  }
  return result;
}


///////////////////////////////////////////////////////////////
// homogenize homogenizes f with Variable x                  //
///////////////////////////////////////////////////////////////

CanonicalForm
homogenize( const CanonicalForm & f, const Variable & x)
{
#if 0
  int maxdeg=totaldegree(f), deg;
  CFIterator i;
  CanonicalForm elem, result(0);

  for (i=f; i.hasTerms(); i++)
  {
    elem= i.coeff()*power(f.mvar(),i.exp());
    deg = totaldegree(elem);
    if ( deg < maxdeg )
      result += elem * power(x,maxdeg-deg);
    else
      result+=elem;
  }
  return result;
#else
  CFList Newlist, Termlist= get_Terms(f);
  int maxdeg=totaldegree(f), deg;
  CFListIterator i;
  CanonicalForm elem, result(0);

  for (i=Termlist; i.hasItem(); i++)
  {
    elem= i.getItem();
    deg = totaldegree(elem);
    if ( deg < maxdeg )
      Newlist.append(elem * power(x,maxdeg-deg));
    else
      Newlist.append(elem);
  }
  for (i=Newlist; i.hasItem(); i++) // rebuild
    result += i.getItem();

  return result;
#endif
}

CanonicalForm
homogenize( const CanonicalForm & f, const Variable & x, const Variable & v1, const Variable & v2)
{
#if 0
  int maxdeg=totaldegree(f), deg;
  CFIterator i;
  CanonicalForm elem, result(0);

  for (i=f; i.hasTerms(); i++)
  {
    elem= i.coeff()*power(f.mvar(),i.exp());
    deg = totaldegree(elem);
    if ( deg < maxdeg )
      result += elem * power(x,maxdeg-deg);
    else
      result+=elem;
  }
  return result;
#else
  CFList Newlist, Termlist= get_Terms(f);
  int maxdeg=totaldegree(f), deg;
  CFListIterator i;
  CanonicalForm elem, result(0);

  for (i=Termlist; i.hasItem(); i++)
  {
    elem= i.getItem();
    deg = totaldegree(elem,v1,v2);
    if ( deg < maxdeg )
      Newlist.append(elem * power(x,maxdeg-deg));
    else
      Newlist.append(elem);
  }
  for (i=Newlist; i.hasItem(); i++) // rebuild
    result += i.getItem();

  return result;
#endif
}

int singular_homog_flag=1;

int cmpCF( const CFFactor & f, const CFFactor & g )
{
  if (f.exp() > g.exp()) return 1;
  if (f.exp() < g.exp()) return 0;
  if (f.factor() > g.factor()) return 1;
  return 0;
}

CFFList factorize ( const CanonicalForm & f, bool issqrfree )
{
  if ( f.inCoeffDomain() )
        return CFFList( f );
  int mv=f.level();
  int org_v=mv;
  //out_cf("factorize:",f,"==================================\n");
  if (! f.isUnivariate() )
  {
    if ( singular_homog_flag && f.isHomogeneous())
    {
      Variable xn = get_max_degree_Variable(f);
      int d_xn = degree(f,xn);
      CFMap n;
      CanonicalForm F = compress(f(1,xn),n);
      CFFList Intermediatelist;
      Intermediatelist = factorize(F);
      CFFList Homoglist;
      CFFListIterator j;
      for ( j=Intermediatelist; j.hasItem(); j++ )
      {
        Homoglist.append(
            CFFactor( n(j.getItem().factor()), j.getItem().exp()) );
      }
      CFFList Unhomoglist;
      CanonicalForm unhomogelem;
      for ( j=Homoglist; j.hasItem(); j++ )
      {
        unhomogelem= homogenize(j.getItem().factor(),xn);
        Unhomoglist.append(CFFactor(unhomogelem,j.getItem().exp()));
        d_xn -= (degree(unhomogelem,xn)*j.getItem().exp());
      }
      if ( d_xn != 0 ) // have to append xn^(d_xn)
        Unhomoglist.append(CFFactor(CanonicalForm(xn),d_xn));
      if(isOn(SW_USE_NTL_SORT)) Unhomoglist.sort(cmpCF);
      return Unhomoglist;
    }
    mv=find_mvar(f);
    if ( getCharacteristic() == 0 )
    {
      if (mv!=f.level())
      {
        swapvar(f,Variable(mv),f.mvar());
      }
    }
    else
    {
      if (mv!=1)
      {
        swapvar(f,Variable(mv),Variable(1));
        org_v=1;
      }
    }
  }
  CFFList F;
  if ( getCharacteristic() > 0 )
  {
    if (f.isUnivariate())
    {
      #ifdef HAVE_NTL
      if (isOn(SW_USE_NTL) && (isPurePoly(f)))
      {
        // USE NTL
        if (getCharacteristic()!=2)
        {
          if (fac_NTL_char!=getCharacteristic())
          {
            fac_NTL_char=getCharacteristic();
            #ifndef NTL_ZZ
            if (fac_NTL_char >NTL_SP_BOUND)
            {
              ZZ r;
              r=getCharacteristic();
              ZZ_pContext ccc(r);
              ccc.restore();
              ZZ_p::init(r);
            }
            else
            #endif
            {
              #ifdef NTL_ZZ
              ZZ r;
              r=getCharacteristic();
              ZZ_pContext ccc(r);
              #else
              zz_pContext ccc(getCharacteristic());
              #endif
              ccc.restore();
              #ifdef NTL_ZZ
              ZZ_p::init(r);
              #else
              zz_p::init(getCharacteristic());
              #endif
            }
          }
          #ifndef NTL_ZZ
          if (fac_NTL_char >NTL_SP_BOUND)
          {
            // convert to NTL
            ZZ_pX f1=convertFacCF2NTLZZpX(f);
            ZZ_p leadcoeff = LeadCoeff(f1);
            //make monic
            f1=f1 / LeadCoeff(f1);
            // factorize
            vec_pair_ZZ_pX_long factors;
            CanZass(factors,f1);
            // convert back to factory
            F=convertNTLvec_pair_ZZpX_long2FacCFFList(factors,leadcoeff,f.mvar());
          }
          else
          #endif
          {
            // convert to NTL
            #ifdef NTL_ZZ
            ZZ_pX f1=convertFacCF2NTLZZpX(f);
            ZZ_p leadcoeff = LeadCoeff(f1);
            #else
            zz_pX f1=convertFacCF2NTLzzpX(f);
            zz_p leadcoeff = LeadCoeff(f1);
            #endif
            //make monic
            f1=f1 / LeadCoeff(f1);
            // factorize
            #ifdef NTL_ZZ
            vec_pair_ZZ_pX_long factors;
            #else
            vec_pair_zz_pX_long factors;
            #endif
            CanZass(factors,f1);
            // convert back to factory
            #ifdef NTL_ZZ
            F=convertNTLvec_pair_ZZpX_long2FacCFFList(factors,leadcoeff,f.mvar());
            #else
            F=convertNTLvec_pair_zzpX_long2FacCFFList(factors,leadcoeff,f.mvar());
            #endif
          }
          //test_cff(F,f);
        }
        else /*getCharacteristic()==2*/
        {
          // Specialcase characteristic==2
          if (fac_NTL_char!=2)
          {
            fac_NTL_char=2;
            zz_p::init(2);
          }
          // convert to NTL using the faster conversion routine for characteristic 2
          GF2X f1=convertFacCF2NTLGF2X(f);
          // no make monic necessary in GF2
          //factorize
          vec_pair_GF2X_long factors;
          CanZass(factors,f1);

          // convert back to factory again using the faster conversion routine for vectors over GF2X
          F=convertNTLvec_pair_GF2X_long2FacCFFList(factors,LeadCoeff(f1),f.mvar());
        }
      }
      else
      #endif
      {  // Use Factory without NTL
        if ( isOn( SW_BERLEKAMP ) )
          F=FpFactorizeUnivariateB( f, issqrfree );
        else
          F=FpFactorizeUnivariateCZ( f, issqrfree, 0, Variable(), Variable() );
      }
    }
    else
    {
      #ifdef HAVE_NTL
      if (issqrfree)
      {
        CFList factors;
        Variable alpha;
        if (CFFactory::gettype() == GaloisFieldDomain)
          factors= GFSqrfFactorize (f);
        else if (hasFirstAlgVar (f, alpha))
          factors= FqSqrfFactorize (f, alpha);
        else
          factors= FpSqrfFactorize (f);
        for (CFListIterator i= factors; i.hasItem(); i++)
          F.append (CFFactor (i.getItem(), 1));
      }
      else
      {
        Variable alpha;
        if (CFFactory::gettype() == GaloisFieldDomain)
          F= GFFactorize (f);
        else if (hasFirstAlgVar (f, alpha))
          F= FqFactorize (f, alpha);
        else
          F= FpFactorize (f);
      }
      #else
      ASSERT( f.isUnivariate(), "multivariate factorization not implemented" );
      #endif
    }
  }
  else
  {
    bool on_rational = isOn(SW_RATIONAL);
    On(SW_RATIONAL);
    CanonicalForm cd = bCommonDen( f );
    CanonicalForm fz = f * cd;
    Off(SW_RATIONAL);
    if ( f.isUnivariate() )
    {
      #ifdef HAVE_NTL
      if ((isOn(SW_USE_NTL)) && (isPurePoly(f)))
      {
        //USE NTL
        CanonicalForm ic=icontent(fz);
        fz/=ic;
        ZZ c;
        vec_pair_ZZX_long factors;
        //factorize the converted polynomial
        factor(c,factors,convertFacCF2NTLZZX(fz));

        //convert the result back to Factory
        F=convertNTLvec_pair_ZZX_long2FacCFFList(factors,c,fz.mvar());
        if ( ! ic.isOne() )
        {
          if ( F.getFirst().factor().inCoeffDomain() )
          {
            CFFactor new_first( F.getFirst().factor() * ic );
            F.removeFirst();
            F.insert( new_first );
          }
          else
            F.insert( CFFactor( ic ) );
        }
        else
        {
          if ( !F.getFirst().factor().inCoeffDomain() )
          {
            CFFactor new_first( 1 );
            F.insert( new_first );
          }
        }
        //if ( F.getFirst().factor().isOne() )
        //{
        //  F.removeFirst();
        //}
        //printf("NTL:\n");out_cff(F);
        //F=ZFactorizeUnivariate( fz, issqrfree );
        //printf("fac.:\n");out_cff(F);
      }
      else
      #endif
      {
        //Use Factory without NTL
        F = ZFactorizeUnivariate( fz, issqrfree );
      }
    }
    else
    {
      F = ZFactorizeMultivariate( fz, issqrfree );
    }

    if ( on_rational )
      On(SW_RATIONAL);
    if ( ! cd.isOne() )
    {
      if ( F.getFirst().factor().inCoeffDomain() )
      {
        CFFactor new_first( F.getFirst().factor() / cd );
        F.removeFirst();
        F.insert( new_first );
      }
      else
      {
        F.insert( CFFactor( 1/cd ) );
      }
    }
  }

  if ((mv!=org_v) && (! f.isUnivariate() ))
  {
    CFFListIterator J=F;
    for ( ; J.hasItem(); J++)
    {
      swapvar(J.getItem().factor(),Variable(mv),Variable(org_v));
    }
    swapvar(f,Variable(mv),Variable(org_v));
  }
  //out_cff(F);
  if(isOn(SW_USE_NTL_SORT)) F.sort(cmpCF);
  return F;
}

#ifdef HAVE_NTL
CanonicalForm fntl ( const CanonicalForm & f, int j )
{
  ZZX f1=convertFacCF2NTLZZX(f);
  return convertZZ2CF(coeff(f1,j));
}
#endif

CFFList factorize ( const CanonicalForm & f, const Variable & alpha )
{
  if ( f.inCoeffDomain() )
    return CFFList( f );
  //out_cf("factorize:",f,"==================================\n");
  //out_cf("mipo:",getMipo(alpha),"\n");
  CFFList F;
  ASSERT( alpha.level() < 0, "not an algebraic extension" );
  int ch=getCharacteristic();
  if (f.isUnivariate()&& (ch>0))
  {
    #ifdef HAVE_NTL
    if  (isOn(SW_USE_NTL))
    {
      //USE NTL
      if (ch>2)
      {
        // First all cases with characteristic !=2
        // set remainder
        if (fac_NTL_char!=getCharacteristic())
        {
          fac_NTL_char=getCharacteristic();
          #ifdef NTL_ZZ
          ZZ r;
          r=getCharacteristic();
          ZZ_pContext ccc(r);
          #else
          zz_pContext ccc(getCharacteristic());
          #endif
          ccc.restore();
          #ifdef NTL_ZZ
          ZZ_p::init(r);
          #else
          zz_p::init(getCharacteristic());
          #endif
        }

        // set minimal polynomial in NTL
        #ifdef NTL_ZZ
        ZZ_pX minPo=convertFacCF2NTLZZpX(getMipo(alpha));
        ZZ_pEContext c(minPo);
        #else
        zz_pX minPo=convertFacCF2NTLzzpX(getMipo(alpha));
        zz_pEContext c(minPo);
        #endif

        c.restore();

        // convert to NTL
        #ifdef NTL_ZZ
        ZZ_pEX f1=convertFacCF2NTLZZ_pEX(f,minPo);
        ZZ_pE leadcoeff= LeadCoeff(f1);
        #else
        zz_pEX f1=convertFacCF2NTLzz_pEX(f,minPo);
        zz_pE leadcoeff= LeadCoeff(f1);
        #endif

        //make monic
        f1=f1 / leadcoeff;

        // factorize using NTL
        #ifdef NTL_ZZ
        vec_pair_ZZ_pEX_long factors;
        #else
        vec_pair_zz_pEX_long factors;
        #endif
        CanZass(factors,f1);

        // return converted result
        #ifdef NTL_ZZ
        F=convertNTLvec_pair_ZZpEX_long2FacCFFList(factors,leadcoeff,f.mvar(),alpha);
        #else
        F=convertNTLvec_pair_zzpEX_long2FacCFFList(factors,leadcoeff,f.mvar(),alpha);
        #endif
      }
      else if (/*getCharacteristic()*/ch==2)
      {
        // special case : GF2

        // remainder is two ==> nothing to do
        // set remainder
        ZZ r;
        r=getCharacteristic();
        ZZ_pContext ccc(r);
        ccc.restore();

        // set minimal polynomial in NTL using the optimized conversion routines for characteristic 2
        GF2X minPo=convertFacCF2NTLGF2X(getMipo(alpha,f.mvar()));
        GF2EContext c(minPo);
        c.restore();

        // convert to NTL again using the faster conversion routines
        GF2EX f1;
        if (isPurePoly(f))
        {
          GF2X f_tmp=convertFacCF2NTLGF2X(f);
          f1=to_GF2EX(f_tmp);
        }
        else
        {
          f1=convertFacCF2NTLGF2EX(f,minPo);
        }

        // make monic (in Z/2(a))
        GF2E f1_coef=LeadCoeff(f1);
        MakeMonic(f1);

        // factorize using NTL
        vec_pair_GF2EX_long factors;
        CanZass(factors,f1);

        // return converted result
        F=convertNTLvec_pair_GF2EX_long2FacCFFList(factors,f1_coef,f.mvar(),alpha);
      }
      else
      {
      }
    }
    else
    #endif
    {
      F=FpFactorizeUnivariateCZ( f, false, 1, alpha, Variable() );
    }
  }
  else if (ch>0)
  {
    #ifdef HAVE_NTL
    F= FqFactorize (f, alpha);
    #else
    ASSERT( f.isUnivariate(), "multivariate factorization not implemented" );
    #endif

  }
  else if (f.isUnivariate() && (ch == 0)) // Q(a)[x]
  {
    F= AlgExtFactorize (f, alpha);
  }
  else //Q(a)[x1,...,xn]
  {
    F= ratFactorize (f, alpha);
  }
  if(isOn(SW_USE_NTL_SORT)) F.sort(cmpCF);
  return F;
}

CFFList sqrFree ( const CanonicalForm & f )
{
//    ASSERT( f.isUnivariate(), "multivariate factorization not implemented" );
    CFFList result;

    if ( getCharacteristic() == 0 )
        result = sqrFreeZ( f );
    else
        result = sqrFreeFp( f );

    //return ( sort ? sortCFFList( result ) : result );
    return result;
}

bool isSqrFree ( const CanonicalForm & f )
{
//    ASSERT( f.isUnivariate(), "multivariate factorization not implemented" );
    if ( getCharacteristic() == 0 )
        return isSqrFreeZ( f );
    else
        return isSqrFreeFp( f );
}