source: git/factory/NTLconvert.cc @ d07137

/* $Id: NTLconvert.cc,v 1.12 2003-10-15 17:19:38 Singular Exp $ */
#include <config.h>

#include "cf_gmp.h"

#include "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"

#ifdef HAVE_NTL
#include <string.h>
#include <NTL/ZZXFactoring.h>
#include <NTL/ZZ_pXFactoring.h>
#include <NTL/GF2XFactoring.h>
#include <NTL/ZZ_pEXFactoring.h>
#include <NTL/GF2EXFactoring.h>
#include <NTL/tools.h>
#include "int_int.h"
#include <limits.h>
#include "NTLconvert.h"

#ifdef HAVE_OMALLOC
#define Alloc(L) omAlloc(L)
#define Free(A,L) omFreeSize(A,L)
#elif defined(USE_MEMUTIL)
#include "memutil.h"
#define Alloc(L) getBlock(L)
#define Free(A,L) freeBlock(A,L)
#else
#define Alloc(L) malloc(L)
#define Free(A,L) free(A)
#endif

#ifdef NTL_CLIENT               // in <NTL/tools.h>: using of name space NTL
NTL_CLIENT
#endif

////////////////////////////////////////////////////////////////////////////////
// NAME: convertFacCF2NTLZZpX                                                 //
//                                                                            //
// DESCRIPTION:                                                               //
// Conversion routine for Factory-type canonicalform into ZZpX of NTL,        //
// i.e. polynomials over F_p. As a precondition for correct execution,        //
// the characteristic has to a a prime number.                                //
//                                                                            //
// INPUT:  A canonicalform f                                                  //
// OUTPUT: The converted NTL-polynomial over F_p of type ZZpX                 //
////////////////////////////////////////////////////////////////////////////////

#if 0
void out_cf(char *s1,const CanonicalForm &f,char *s2)
{
  printf("%s",s1);
  if (f==0) printf("+0");
  else if (! f.inCoeffDomain() )
  {
    int l = f.level();
    for ( CFIterator i = f; i.hasTerms(); i++ )
    {
      int e=i.exp();
      printf("+(");out_cf("+(",i.coeff(),")*v(");printf("%d)^%d",l,e);
    }
  }
  else
  {
    if ( f.isImm() )
    {
      printf("+%d(",f.intval());
    }
    else printf("+...(");
    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);
}
#endif

ZZ_pX convertFacCF2NTLZZpX(CanonicalForm f)
{
  ZZ_pX ntl_poly;

  CFIterator i;
  i=f;

  int j=0;
  int NTLcurrentExp=i.exp();
  int largestExp=i.exp();
  int k;

  // we now build up the NTL-polynomial
  ntl_poly.SetMaxLength(largestExp+1);

  for (;i.hasTerms();i++)
  {
    for (k=NTLcurrentExp;k>i.exp();k--)
    {
      SetCoeff(ntl_poly,k,0);
    }
    NTLcurrentExp=i.exp();

    CanonicalForm c=i.coeff();
    if (!c.isImm()) c.mapinto(); //c%= getCharacteristic();
    if (!c.isImm())
    {  //This case will never happen if the characteristic is in fact a prime
       // number, since all coefficients are represented as immediates
       #ifndef NOSTREAMIO
       cout<<"convertFacCF2NTLZZ_pX: coefficient not immediate! : "<<f<<"\n";
       #else
       printf("convertFacCF2NTLZZ_pX: coefficient not immediate!, char=%d\n",
              getCharacteristic());
       #endif
       exit(1);
    }
    else
    {
      SetCoeff(ntl_poly,NTLcurrentExp,c.intval());
    }
    NTLcurrentExp--;
  }

  //Set the remaining coefficients of ntl_poly to zero.
  // This is necessary, because NTL internally
  // also stores powers with zero coefficient,
  // whereas factory stores tuples of degree and coefficient
  //leaving out tuples if the coefficient equals zero
  for (k=NTLcurrentExp;k>=0;k--)
  {
    SetCoeff(ntl_poly,k,0);
  }

  //normalize the polynomial and return it
  ntl_poly.normalize();

  return ntl_poly;
}

////////////////////////////////////////////////////////////////////////////////
// NAME: convertFacCF2NTLGF2X                                                 //
//                                                                            //
// DESCRIPTION:                                                               //
// Conversion routine for Factory-type canonicalform into GF2X of NTL,        //
// i.e. polynomials over F_2. As precondition for correct execution,          //
// the characteristic must equal two.                                         //
// This is a special case of the more general conversion routine for          //
// canonicalform to ZZpX. It is included because NTL provides additional      //
// support and faster algorithms over F_2, moreover the conversion code       //
// can be optimized, because certain steps are either completely obsolent     //
// (like normalizing the polynomial) or they can be made significantly        //
// faster (like building up the NTL-polynomial).                              //
//                                                                            //
// INPUT:  A canonicalform f                                                  //
// OUTPUT: The converted NTL-polynomial over F_2 of type GF2X                 //
////////////////////////////////////////////////////////////////////////////////

GF2X convertFacCF2NTLGF2X(CanonicalForm f)
{
  //printf("convertFacCF2NTLGF2X\n");
  GF2X ntl_poly;

  CFIterator i;
  i=f;

  int j=0;
  int NTLcurrentExp=i.exp();
  int largestExp=i.exp();
  int k;

  //building the NTL-polynomial
  ntl_poly.SetMaxLength(largestExp+1);

  for (;i.hasTerms();i++)
  {

    for (k=NTLcurrentExp;k>i.exp();k--)
    {
      SetCoeff(ntl_poly,k,0);
    }
    NTLcurrentExp=i.exp();

    if (!i.coeff().isImm()) i.coeff()=i.coeff().mapinto();
    if (!i.coeff().isImm())
    {
      #ifndef NOSTREAMIO
      cout<<"convertFacCF2NTLGF2X: coefficient not immidiate! : " << f << "\n";
      #else
      printf("convertFacCF2NTLGF2X: coefficient not immidiate!");
      #endif
      exit(1);
    }
    else
    {
      SetCoeff(ntl_poly,NTLcurrentExp,i.coeff().intval());
    }
    NTLcurrentExp--;
  }
  for (k=NTLcurrentExp;k>=0;k--)
  {
    SetCoeff(ntl_poly,k,0);
  }
  //normalization is not necessary of F_2

  return ntl_poly;
}


////////////////////////////////////////////////////////////////////////////////
// NAME: convertNTLZZpX2CF                                                    //
//                                                                            //
// DESCRIPTION:                                                               //
// Conversion routine for NTL-Type ZZpX to Factory-Type canonicalform.        //
// Additionally a variable x is needed as a parameter indicating the          //
// main variable of the computed canonicalform. To guarantee the correct      //
// execution of the algorithm, the characteristic has a be an arbitrary       //
// prime number.                                                              //
//                                                                            //
// INPUT:  A canonicalform f, a variable x                                    //
// OUTPUT: The converted Factory-polynomial of type canonicalform,            //
//         built by the main variable x                                       //
////////////////////////////////////////////////////////////////////////////////

CanonicalForm convertNTLZZpX2CF(ZZ_pX poly,Variable x)
{
  //printf("convertNTLZZpX2CF\n");
  CanonicalForm bigone;


  if (deg(poly)>0)
  {
    // poly is non-constant
    bigone=0;
    bigone.mapinto();
    // Compute the canonicalform coefficient by coefficient,
    // bigone summarizes the result.
    for (int j=0;j<deg(poly)+1;j++)
    {
      if (coeff(poly,j)!=0)
      {
        bigone+=(power(x,j)*CanonicalForm(to_long(rep(coeff(poly,j)))));
      }
    }
  }
  else
  {
    // poly is immediate
    bigone=CanonicalForm(to_long(rep(coeff(poly,0))));
    bigone.mapinto();
  }
  return bigone;
}


////////////////////////////////////////////////////////////////////////////////
// NAME: convertNTLGF2X2CF                                                    //
//                                                                            //
// DESCRIPTION:                                                               //
// Conversion routine for NTL-Type GF2X to Factory-Type canonicalform,        //
// the routine is again an optimized special case of the more general         //
// conversion to ZZpX. Additionally a variable x is needed as a               //
// parameter indicating the main variable of the computed canonicalform.      //
// To guarantee the correct execution of the algorithm the characteristic     //
// has a be an arbitrary prime number.                                        //
//                                                                            //
// INPUT:  A canonicalform f, a variable x                                    //
// OUTPUT: The converted Factory-polynomial of type canonicalform,            //
//         built by the main variable x                                       //
////////////////////////////////////////////////////////////////////////////////

CanonicalForm convertNTLGF2X2CF(GF2X poly,Variable x)
{
  //printf("convertNTLGF2X2CF\n");
  CanonicalForm bigone;

  if (deg(poly)>0)
  {
    // poly is non-constant
    bigone=0;
    bigone.mapinto();
    // Compute the canonicalform coefficient by coefficient,
    // bigone summarizes the result.
    // In constrast to the more general conversion to ZZpX
    // the only possible coefficients are zero
    // and one yielding the following simplified loop
    for (int j=0;j<deg(poly)+1;j++)
    {
      if (coeff(poly,j)!=0) bigone+=power(x,j);
     // *CanonicalForm(to_long(rep(coeff(poly,j))))) is not necessary any more;
    }
  }
  else
  {
    // poly is immediate
    bigone=CanonicalForm(to_long(rep(coeff(poly,0))));
    bigone.mapinto();
  }

  return bigone;
}

int NTLcmpCF( 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;
}

////////////////////////////////////////////////////////////////////////////////
// NAME: convertNTLvec_pair_ZZpX_long2FacCFFList                              //
//                                                                            //
// DESCRIPTION:                                                               //
// Routine for converting a vector of polynomials from ZZpX to                //
// a CFFList of Factory. This routine will be used after a successful         //
// factorization of NTL to convert the result back to Factory.                //
//                                                                            //
// Additionally a variable x and the computed multiplicity, as a type ZZp     //
// of NTL, is needed as parameters indicating the main variable of the        //
// computed canonicalform and the multiplicity of the original polynomial.    //
// To guarantee the correct execution of the algorithm the characteristic     //
// has a be an arbitrary prime number.                                        //
//                                                                            //
// INPUT:  A vector of polynomials over ZZp of type vec_pair_ZZ_pX_long and   //
//         a variable x and a multiplicity of type ZZp                        //
// OUTPUT: The converted list of polynomials of type CFFList, all polynomials //
//         have x as their main variable                                      //
////////////////////////////////////////////////////////////////////////////////

CFFList convertNTLvec_pair_ZZpX_long2FacCFFList
                                  (vec_pair_ZZ_pX_long e,ZZ_p multi,Variable x)
{
  //printf("convertNTLvec_pair_ZZpX_long2FacCFFList\n");
  CFFList rueckgabe;
  ZZ_pX polynom;
  long exponent;
  CanonicalForm bigone;

  // Maybe, e may additionally be sorted with respect to increasing degree of x
  // but this is not
  //important for the factorization, but nevertheless would take computing time,
  // so it is omitted


  // Go through the vector e and compute the CFFList
  // again bigone summarizes the result
  for (int i=e.length()-1;i>=0;i--)
  {
    rueckgabe.append(CFFactor(convertNTLZZpX2CF(e[i].a,x),e[i].b));
  }
  if(isOn(SW_USE_NTL_SORT)) rueckgabe.sort(NTLcmpCF);
  // the multiplicity at pos 1
  if (!IsOne(multi))
    rueckgabe.insert(CFFactor(CanonicalForm(to_long(rep(multi))),1));
  return rueckgabe;
}

////////////////////////////////////////////////////////////////////////////////
// NAME: convertNTLvec_pair_GF2X_long2FacCFFList                              //
//                                                                            //
// DESCRIPTION:                                                               //
// Routine for converting a vector of polynomials of type GF2X from           //
// NTL to a list CFFList of Factory. This routine will be used after a        //
// successful factorization of NTL to convert the result back to Factory.     //
// As usual this is simply a special case of the more general conversion      //
// routine but again speeded up by leaving out unnecessary steps.             //
// Additionally a variable x and the computed multiplicity, as type           //
// GF2 of NTL, are needed as parameters indicating the main variable of the   //
// computed canonicalform and the multiplicity of the original polynomial.    //
// To guarantee the correct execution of the algorithm the characteristic     //
// has a be an arbitrary prime number.                                        //
//                                                                            //
// INPUT:  A vector of polynomials over GF2 of type vec_pair_GF2X_long and    //
//         a variable x and a multiplicity of type GF2                        //
// OUTPUT: The converted list of polynomials of type CFFList, all             //
//         polynomials have x as their main variable                          //
////////////////////////////////////////////////////////////////////////////////

CFFList convertNTLvec_pair_GF2X_long2FacCFFList
                               (vec_pair_GF2X_long e,GF2 multi,Variable x)
{
  //printf("convertNTLvec_pair_GF2X_long2FacCFFList\n");
  CFFList rueckgabe;
  GF2X polynom;
  long exponent;
  CanonicalForm bigone;

  // Maybe, e may additionally be sorted with respect to increasing degree of x
  // but this is not
  //important for the factorization, but nevertheless would take computing time
  // so it is omitted.

  //We do not have to worry about the multiplicity in GF2 since it equals one.

  // Go through the vector e and compute the CFFList
  // bigone summarizes the result again
  for (int i=e.length()-1;i>=0;i--)
  {
    bigone=0;

    polynom=e[i].a;
    exponent=e[i].b;
    for (int j=0;j<deg(polynom)+1;j++)
    {
      if (coeff(polynom,j)!=0)
        bigone += (power(x,j)*CanonicalForm(to_long(rep(coeff(polynom,j)))));
    }

    //append the converted polynomial to the CFFList
    rueckgabe.append(CFFactor(bigone,exponent));
  }
  if(isOn(SW_USE_NTL_SORT)) rueckgabe.sort(NTLcmpCF);
  return rueckgabe;
}

////////////////////////////////////////////////////////////////////////////////
// NAME: convertZZ2CF                                                         //
//                                                                            //
// DESCRIPTION:                                                               //
// Routine for conversion of integers represented in NTL as Type ZZ to        //
// integers in Factory represented as canonicalform.                          //
// To guarantee the correct execution of the algorithm the characteristic     //
// has to equal zero.                                                         //
//                                                                            //
// INPUT:  The value coefficient of type ZZ that has to be converted          //
// OUTPUT: The converted Factory-integer of type canonicalform                //
////////////////////////////////////////////////////////////////////////////////

static char *cf_stringtemp=NULL;
static char *cf_stringtemp2=NULL;
static int cf_stringtemp_l=0;
CanonicalForm convertZZ2CF(ZZ coefficient)
{
  long coeff_long;
  //CanonicalForm tmp=0;
  if (cf_stringtemp_l==0)
  {
    cf_stringtemp=(char *)Alloc(1023);
    cf_stringtemp2=(char *)Alloc(1023);
    cf_stringtemp[0]='\0';
    cf_stringtemp2[0]='\0';
    cf_stringtemp_l=1023;
  }
  char dummy[2];
  int minusremainder=0;
  char numbers[]="0123456789abcdef";

  coeff_long=to_long(coefficient);

  //Test whether coefficient can be represented as an immediate integer in Factory
  if ( (NumBits(coefficient)<=NTL_ZZ_NBITS)
  && (coeff_long>MINIMMEDIATE)
  && (coeff_long<MAXIMMEDIATE))
  {
    // coefficient is immediate --> return the coefficient as canonicalform
    return CanonicalForm(coeff_long);
  }
  else
  {
    // coefficient is not immediate (gmp-number)

    // convert coefficient to char* (input for gmp)
    dummy[1]='\0';

    if (coefficient<0)
    {
      // negate coefficient, but store the sign in minusremainder
      minusremainder=1;
      coefficient=-coefficient;
    }

    int l=0;
    while (coefficient>15)
    {
      ZZ quotient,remaind;
      ZZ ten;ten=16;
      DivRem(quotient,remaind,coefficient,ten);
      dummy[0]=numbers[to_long(remaind)];
      //tmp*=10; tmp+=to_long(remaind);

      l++;
      if (l>=cf_stringtemp_l-2)
      {
        Free(cf_stringtemp2,cf_stringtemp_l);
        char *p=(char *)Alloc(cf_stringtemp_l*2);
        memcpy(p,cf_stringtemp,cf_stringtemp_l);
        Free(cf_stringtemp,cf_stringtemp_l);
        cf_stringtemp_l*=2;
        cf_stringtemp=p;
        cf_stringtemp2=(char *)Alloc(cf_stringtemp_l);
      }
      cf_stringtemp[l-1]=dummy[0];
      cf_stringtemp[l]='\0';
      //strcat(stringtemp,dummy);

      coefficient=quotient;
    }
    //built up the string in dummy[0]
    dummy[0]=numbers[to_long(coefficient)];
    strcat(cf_stringtemp,dummy);
    //tmp*=10; tmp+=to_long(coefficient);

    if (minusremainder==1)
    {
      //Check whether coefficient has been negative at the start of the procedure
      cf_stringtemp2[0]='-';
      //tmp*=(-1);
    }

    //reverse the list to obtain the correct string
    int len=strlen(cf_stringtemp);
    for (int i=len-1;i>=0;i--)
    {
      cf_stringtemp2[len-i-1+minusremainder]=cf_stringtemp[i];
    }
    cf_stringtemp2[len+minusremainder]='\0';
  }

  //convert the string to canonicalform using the char*-Constructor
  return CanonicalForm(cf_stringtemp2,16);
  //return tmp;
}

////////////////////////////////////////////////////////////////////////////////
// NAME: convertFacCF2NTLZZX                                                  //
//                                                                            //
// DESCRIPTION:                                                               //
// Routine for conversion of canonicalforms in Factory to polynomials         //
// of type ZZX of NTL. To guarantee the correct execution of the              //
// algorithm the characteristic has to equal zero.                            //
//                                                                            //
// INPUT:  The canonicalform that has to be converted                         //
// OUTPUT: The converted NTL-polynom of type ZZX                              //
////////////////////////////////////////////////////////////////////////////////

ZZX convertFacCF2NTLZZX(CanonicalForm f)
{
    ZZX ntl_poly;

    CFIterator i;
    i=f;

    int j=0;
    int NTLcurrentExp=i.exp();
    int largestExp=i.exp();
    int k;

    //set the length of the NTL-polynomial
    ntl_poly.SetMaxLength(largestExp+1);

    //Go through the coefficients of the canonicalform and build up the NTL-polynomial
    for (;i.hasTerms();i++)
    {
      for (k=NTLcurrentExp;k>i.exp();k--)
      {
        SetCoeff(ntl_poly,k,0);
      }
      NTLcurrentExp=i.exp();

      if (!i.coeff().isImm())
      {
        //Coefficient is a gmp-number
        mpz_t gmp_val;
        ZZ temp;
        char* stringtemp;

        gmp_val[0]=getmpi(i.coeff().getval());
        int l=mpz_sizeinbase(gmp_val,10)+2;
        stringtemp=(char*)Alloc(l);
        stringtemp=mpz_get_str(stringtemp,10,gmp_val);
        conv(temp,stringtemp);
        Free(stringtemp,l);

        //set the computed coefficient
        SetCoeff(ntl_poly,NTLcurrentExp,temp);
      }
      else
      {
        //Coefficient is immediate --> use its value
        SetCoeff(ntl_poly,NTLcurrentExp,i.coeff().intval());
      }

      NTLcurrentExp--;
    }
    for (k=NTLcurrentExp;k>=0;k--)
    {
      SetCoeff(ntl_poly,k,0);
    }

    //normalize the polynomial
    ntl_poly.normalize();

    return ntl_poly;
}

////////////////////////////////////////////////////////////////////////////////
// NAME: convertNTLvec_pair_ZZX_long2FacCFFList                               //
//                                                                            //
// DESCRIPTION:                                                               //
// Routine for converting a vector of polynomials from ZZ to a list           //
// CFFList of Factory. This routine will be used after a successful           //
// factorization of NTL to convert the result back to Factory.                //
// Additionally a variable x and the computed multiplicity, as a type         //
// ZZ of NTL, is needed as parameters indicating the main variable of the     //
// computed canonicalform and the multiplicity of the original polynomial.    //
// To guarantee the correct execution of the algorithm the characteristic     //
// has to equal zero.                                                         //
//                                                                            //
// INPUT:  A vector of polynomials over ZZ of type vec_pair_ZZX_long and      //
//         a variable x and a multiplicity of type ZZ                         //
// OUTPUT: The converted list of polynomials of type CFFList, all             //
//         have x as their main variable                                      //
////////////////////////////////////////////////////////////////////////////////

CFFList convertNTLvec_pair_ZZX_long2FacCFFList(vec_pair_ZZX_long e,ZZ multi,Variable x)
{
  CFFList rueckgabe;
  ZZX polynom;
  long exponent;
  CanonicalForm bigone;

  // Maybe, e may additionally be sorted with respect to increasing degree of x, but this is not
  //important for the factorization, but nevertheless would take computing time, so it is omitted


  // Go through the vector e and build up the CFFList
  // As usual bigone summarizes the result
  for (int i=e.length()-1;i>=0;i--)
  {
    bigone=0;
    ZZ coefficient;
    polynom=e[i].a;
    exponent=e[i].b;
    long coeff_long;

    for (int j=0;j<deg(polynom)+1;j++)
    {
      coefficient=coeff(polynom,j);
      if (!IsZero(coefficient))
      {
        bigone += (power(x,j)*convertZZ2CF(coefficient));
      }
    }

    //append the converted polynomial to the list
    rueckgabe.append(CFFactor(bigone,exponent));
  }
  if(isOn(SW_USE_NTL_SORT)) rueckgabe.sort(NTLcmpCF);
  // the multiplicity at pos 1
  //if (!IsOne(multi))
    rueckgabe.insert(CFFactor(convertZZ2CF(multi),1));

  //return the converted list
  return rueckgabe;
}


////////////////////////////////////////////////////////////////////////////////
// NAME: convertNTLZZpX2CF                                                    //
//                                                                            //
// DESCRIPTION:                                                               //
// Routine for conversion of elements of arbitrary extensions of ZZp,         //
// having type ZZpE, of NTL to their corresponding values of type             //
// canonicalform in Factory.                                                  //
// To guarantee the correct execution of the algorithm the characteristic     //
// has to be an arbitrary prime number and Factory has to compute in an       //
// extension of F_p.                                                          //
//                                                                            //
// INPUT:  The coefficient of type ZZpE and the variable x indicating the main//
//         variable of the computed canonicalform                             //
// OUTPUT: The converted value of coefficient as type canonicalform           //
////////////////////////////////////////////////////////////////////////////////

CanonicalForm convertNTLZZpE2CF(ZZ_pE coefficient,Variable x)
{
  return convertNTLZZpX2CF(rep(coefficient),x);
}

////////////////////////////////////////////////////////////////////////////////
// NAME: convertNTLvec_pair_ZZpEX_long2FacCFFList                             //
//                                                                            //
// DESCRIPTION:                                                               //
// Routine for converting a vector of polynomials from ZZpEX to a CFFList     //
// of Factory. This routine will be used after a successful factorization     //
// of NTL to convert the result back to Factory.                              //
// Additionally a variable x and the computed multiplicity, as a type         //
// ZZpE of NTL, is needed as parameters indicating the main variable of the   //
// computed canonicalform and the multiplicity of the original polynomial.    //
// To guarantee the correct execution of the algorithm the characteristic     //
// has a be an arbitrary prime number p and computations have to be done      //
// in an extention of F_p.                                                    //
//                                                                            //
// INPUT:  A vector of polynomials over ZZpE of type vec_pair_ZZ_pEX_long and //
//         a variable x and a multiplicity of type ZZpE                       //
// OUTPUT: The converted list of polynomials of type CFFList, all polynomials //
//         have x as their main variable                                      //
////////////////////////////////////////////////////////////////////////////////

CFFList convertNTLvec_pair_ZZpEX_long2FacCFFList(vec_pair_ZZ_pEX_long e,ZZ_pE multi,Variable x,Variable alpha)
{
  CFFList rueckgabe;
  ZZ_pEX polynom;
  long exponent;
  CanonicalForm bigone;

  // Maybe, e may additionally be sorted with respect to increasing degree of x, but this is not
  //important for the factorization, but nevertheless would take computing time, so it is omitted

  // Go through the vector e and build up the CFFList
  // As usual bigone summarizes the result during every loop
  for (int i=e.length()-1;i>=0;i--)
  {
    bigone=0;

    polynom=e[i].a;
    exponent=e[i].b;

    for (int j=0;j<deg(polynom)+1;j++)
    {
      if (IsOne(coeff(polynom,j)))
      {
        bigone+=power(x,j);
      }
      else
      {
        CanonicalForm coefficient=convertNTLZZpE2CF(coeff(polynom,j),alpha);
        if (coeff(polynom,j)!=0)
        {
          bigone += (power(x,j)*coefficient);
        }
      }
    }
    //append the computed polynomials together with its exponent to the CFFList
    rueckgabe.append(CFFactor(bigone,exponent));
  }
  if(isOn(SW_USE_NTL_SORT)) rueckgabe.sort(NTLcmpCF);
  // Start by appending the multiplicity
  if (!IsOne(multi))
    rueckgabe.insert(CFFactor(convertNTLZZpE2CF(multi,alpha),1));

  //return the computed CFFList
  return rueckgabe;
}

////////////////////////////////////////////////////////////////////////////////
// NAME: convertNTLGF2E2CF                                                    //
//                                                                            //
// DESCRIPTION:                                                               //
// Routine for conversion of elements of extensions of GF2, having type       //
// GF2E, of NTL to their corresponding values of type canonicalform in        //
// Factory.                                                                   //
// To guarantee the correct execution of the algorithm, the characteristic    //
// must equal two and Factory has to compute in an extension of F_2.          //
// As usual this is an optimized special case of the more general conversion  //
// routine from ZZpE to Factory.                                              //
//                                                                            //
// INPUT:  The coefficient of type GF2E and the variable x indicating the     //
//         main variable of the computed canonicalform                        //
// OUTPUT: The converted value of coefficient as type canonicalform           //
////////////////////////////////////////////////////////////////////////////////

CanonicalForm convertNTLGF2E2CF(GF2E coefficient,Variable x)
{
  return convertNTLGF2X2CF(rep(coefficient),x);
}

////////////////////////////////////////////////////////////////////////////////
// NAME: convertNTLvec_pair_GF2EX_long2FacCFFList                             //
//                                                                            //
// DESCRIPTION:                                                               //
// Routine for converting a vector of polynomials from GF2EX to a CFFList     //
// of Factory. This routine will be used after a successful factorization     //
// of NTL to convert the result back to Factory.                              //
// This is a special, but optimized case of the more general conversion       //
// from ZZpE to canonicalform.                                                //
// Additionally a variable x and the computed multiplicity, as a type GF2E    //
// of NTL, is needed as parameters indicating the main variable of the        //
// computed canonicalform and the multiplicity of the original polynomial.    //
// To guarantee the correct execution of the algorithm the characteristic     //
// has to equal two and computations have to be done in an extention of F_2.  //
//                                                                            //
// INPUT:  A vector of polynomials over GF2E of type vec_pair_GF2EX_long and  //
//         a variable x and a multiplicity of type GF2E                       //
// OUTPUT: The converted list of polynomials of type CFFList, all polynomials //
//         have x as their main variable                                      //
////////////////////////////////////////////////////////////////////////////////

CFFList convertNTLvec_pair_GF2EX_long2FacCFFList(vec_pair_GF2EX_long e,GF2E multi,Variable x,Variable alpha)
{
  CFFList rueckgabe;
  GF2EX polynom;
  long exponent;
  CanonicalForm bigone;

  // Maybe, e may additionally be sorted with respect to increasing degree of x, but this is not
  //important for the factorization, but nevertheless would take computing time, so it is omitted

  // multiplicity is always one, so we do not have to worry about that

  // Go through the vector e and build up the CFFList
  // As usual bigone summarizes the result during every loop
  for (int i=e.length()-1;i>=0;i--)
  {
    bigone=0;

    polynom=e[i].a;
    exponent=e[i].b;

    for (int j=0;j<deg(polynom)+1;j++)
    {
      if (IsOne(coeff(polynom,j)))
      {
        bigone+=power(x,j);
      }
      else
      {
        CanonicalForm coefficient=convertNTLGF2E2CF(coeff(polynom,j),alpha);
        if (coeff(polynom,j)!=0)
        {
          bigone += (power(x,j)*coefficient);
        }
      }
    }

    // append the computed polynomial together with its multiplicity
    rueckgabe.append(CFFactor(bigone,exponent));

  }
  if(isOn(SW_USE_NTL_SORT)) rueckgabe.sort(NTLcmpCF);
  // return the computed CFFList
  return rueckgabe;
}

////////////////////////////////////////////////////
// CanonicalForm in Z_2(a)[X] to NTL GF2EX        //
////////////////////////////////////////////////////
GF2EX convertFacCF2NTLGF2EX(CanonicalForm f,GF2X mipo)
{
  GF2E::init(mipo);
  GF2EX result;
  CFIterator i;
  i=f;

  int j=0;
  int NTLcurrentExp=i.exp();
  int largestExp=i.exp();
  int k;

  result.SetMaxLength(largestExp+1);
  for(;i.hasTerms();i++)
  {
    for(k=NTLcurrentExp;k>i.exp();k--) SetCoeff(result,k,0);
    NTLcurrentExp=i.exp();
    CanonicalForm c=i.coeff();
    GF2X cc=convertFacCF2NTLGF2X(c);
    //ZZ_pE ccc;
    //conv(ccc,cc);
    SetCoeff(result,NTLcurrentExp,to_GF2E(cc));
    NTLcurrentExp--;
  }
  for(k=NTLcurrentExp;k>=0;k--) SetCoeff(result,k,0);
  result.normalize();
  return result;
}
////////////////////////////////////////////////////
// CanonicalForm in Z_p(a)[X] to NTL ZZ_pEX       //
////////////////////////////////////////////////////
ZZ_pEX convertFacCF2NTLZZ_pEX(CanonicalForm f, ZZ_pX mipo)
{
  ZZ_pE::init(mipo);
  ZZ_pEX result;
  CFIterator i;
  i=f;

  int j=0;
  int NTLcurrentExp=i.exp();
  int largestExp=i.exp();
  int k;

  result.SetMaxLength(largestExp+1);
  for(;i.hasTerms();i++)
  {
    for(k=NTLcurrentExp;k>i.exp();k--) SetCoeff(result,k,0);
    NTLcurrentExp=i.exp();
    CanonicalForm c=i.coeff();
    ZZ_pX cc=convertFacCF2NTLZZpX(c);
    //ZZ_pE ccc;
    //conv(ccc,cc);
    SetCoeff(result,NTLcurrentExp,to_ZZ_pE(cc));
    NTLcurrentExp--;
  }
  for(k=NTLcurrentExp;k>=0;k--) SetCoeff(result,k,0);
  result.normalize();
  return result;
}
#endif