flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2014 William Hart

    This file is part of FLINT.

    FLINT is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "fmpq.h"
#include "nf_elem.h"

void _nf_elem_norm(fmpz_t rnum, fmpz_t rden, const nf_elem_t a, const nf_t nf)
{
   if (nf->flag & NF_LINEAR)
   {
      const fmpz * const anum = LNF_ELEM_NUMREF(a);
      const fmpz * const aden = LNF_ELEM_DENREF(a);

      fmpz_set(rnum, anum);
      fmpz_set(rden, aden);
   } else if (nf->flag & NF_QUADRATIC)
   {
      const fmpz * const anum = QNF_ELEM_NUMREF(a);
      const fmpz * const aden = QNF_ELEM_DENREF(a);
      fmpz_t pow, one;

      slong alen = 2;
      while (alen > 0 && fmpz_is_zero(anum + alen - 1))
         alen--;

      if (alen == 0)
      {
         fmpz_zero(rnum);
         fmpz_one(rden);

         return;
      }

      fmpz_init_set_ui(one, 1);
      fmpz_init(pow);

      _fmpq_poly_resultant(rnum, rden,
         nf->pol->coeffs, one, 3, anum, aden, alen);

      if (!fmpz_is_one(nf->pol->coeffs + 2) && alen > 1)
      {
         fmpz_pow_ui(pow, nf->pol->coeffs + 2, alen - 1);
         if (fmpz_sgn(pow) < 0)
         {
            fmpz_neg(one, one);
            fmpz_neg(pow, pow);
         }
         _fmpq_mul(rnum, rden, rnum, rden, one, pow);

         if (fmpz_sgn(rden) < 0)
         {
            fmpz_neg(rnum, rnum);
            fmpz_neg(rden, rden);
         }
      }

      fmpz_clear(one);
      fmpz_clear(pow);
   } else /* generic nf_elem */
   {
      const fmpz * const anum = NF_ELEM_NUMREF(a);
      const fmpz * const aden = NF_ELEM_DENREF(a);
      fmpz_t pow, one;

      slong alen = NF_ELEM(a)->length;
      slong len = nf->pol->length;
      fmpz * coeffs = nf->pol->coeffs;

      if (alen == 0)
      {
         fmpz_zero(rnum);
         fmpz_one(rden);

         return;
      }

      fmpz_init_set_ui(one, 1);
      fmpz_init(pow);

      _fmpq_poly_resultant(rnum, rden,
         nf->pol->coeffs, one, len, anum, aden, alen);

      if (!fmpz_is_one(coeffs + len - 1) && alen > 1)
      {
         fmpz_pow_ui(pow, coeffs + len - 1, alen - 1);
         if (fmpz_sgn(pow) < 0)
         {
            fmpz_neg(one, one);
            fmpz_neg(pow, pow);
         }
         _fmpq_mul(rnum, rden, rnum, rden, one, pow);

         if (fmpz_sgn(rden) < 0)
         {
            fmpz_neg(rnum, rnum);
            fmpz_neg(rden, rden);
         }
      }

      fmpz_clear(one);
      fmpz_clear(pow);

   }
}

void nf_elem_norm(fmpq_t res, const nf_elem_t a, const nf_t nf)
{
   _nf_elem_norm(fmpq_numref(res), fmpq_denref(res), a, nf);
}