Function primitiveElement

factory/cf_map_ext.cc:342–429

}

CanonicalForm
primitiveElement (const Variable& alpha, Variable& beta, bool& fail)
{
  bool primitive= false;
  fail= false;
  primitive= isPrimitive (alpha, fail);
  if (fail)
    return 0;
  if (primitive)
  {
    beta= alpha;
    return alpha;
  }
  CanonicalForm mipo= getMipo (alpha);
  int d= degree (mipo);
  int p= getCharacteristic ();
  #if defined(HAVE_FLINT) && (__FLINT_RELEASE >= 20503)
  nmod_poly_t FLINT_mipo;
  nmod_poly_init(FLINT_mipo,p);
  #elif defined(HAVE_NTL)
  if (fac_NTL_char != p)
  {
    fac_NTL_char= p;
    zz_p::init (p);
  }
  zz_pX NTL_mipo;
  #else
  factoryError("NTL/FLINT missing: primitiveElement");
  return CanonicalForm(0);
  #endif
  CanonicalForm mipo2;
  primitive= false;
  fail= false;
  bool initialized= false;
  do
  {
    #if defined(HAVE_FLINT) && (__FLINT_RELEASE >= 20503)
    nmod_poly_randtest_monic_irreducible(FLINT_mipo, FLINTrandom, d+1);
    mipo2=convertnmod_poly_t2FacCF(FLINT_mipo,Variable(1));
    #elif defined(HAVE_NTL)
    BuildIrred (NTL_mipo, d);
    mipo2= convertNTLzzpX2CF (NTL_mipo, Variable (1));
    #endif
    if (!initialized)
      beta= rootOf (mipo2);
    else
      setMipo (beta, mipo2);
    primitive= isPrimitive (beta, fail);
    if (primitive)
      break;
    if (fail)
      return 0;
  } while (1);
  #if defined(HAVE_FLINT) && (__FLINT_RELEASE >= 20503)
  nmod_poly_clear(FLINT_mipo);
  // convert alpha_mipo
  nmod_poly_t alpha_mipo;
  convertFacCF2nmod_poly_t(alpha_mipo,mipo);