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/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2010 Sebastian Pancratz
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"
void
_fmpz_poly_resultant(fmpz_t res, const fmpz * poly1, slong len1,
const fmpz * poly2, slong len2)
{
if (len2 == 1)
{
fmpz_pow_ui(res, poly2, len1 - 1);
}
else
{
fmpz_t a, b, g, h, t;
fmpz *A, *B, *W;
const slong alloc = len1 + len2;
slong sgn = 1;
fmpz_init(a);
fmpz_init(b);
fmpz_init(g);
fmpz_init(h);
fmpz_init(t);
A = W = _fmpz_vec_init(alloc);
B = W + len1;
_fmpz_poly_content(a, poly1, len1);
_fmpz_poly_content(b, poly2, len2);
_fmpz_vec_scalar_divexact_fmpz(A, poly1, len1, a);
_fmpz_vec_scalar_divexact_fmpz(B, poly2, len2, b);
fmpz_one(g);
fmpz_one(h);
fmpz_pow_ui(a, a, len2 - 1);
fmpz_pow_ui(b, b, len1 - 1);
fmpz_mul(t, a, b);
do
{
const slong d = len1 - len2;
if (!(len1 & WORD(1)) & !(len2 & WORD(1)))
sgn = -sgn;
_fmpz_poly_pseudo_rem_cohen(A, A, len1, B, len2);
FMPZ_VEC_NORM(A, len1);
if (len1 == 0)
{
fmpz_zero(res);
goto cleanup;
}
{
fmpz * T;
slong len;
T = A, A = B, B = T;
len = len1, len1 = len2, len2 = len;
}
fmpz_pow_ui(a, h, d);
fmpz_mul(b, g, a);
_fmpz_vec_scalar_divexact_fmpz(B, B, len2, b);
fmpz_pow_ui(g, A + (len1 - 1), d);
fmpz_mul(b, h, g);
fmpz_divexact(h, b, a);
fmpz_set(g, A + (len1 - 1));
} while (len2 > 1);
fmpz_pow_ui(g, h, len1 - 1);
fmpz_pow_ui(b, B + (len2 - 1), len1 - 1);
fmpz_mul(a, h, b);
fmpz_divexact(h, a, g);
fmpz_mul(res, t, h);
if (sgn < 0)
fmpz_neg(res, res);
cleanup:
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(g);
fmpz_clear(h);
fmpz_clear(t);
_fmpz_vec_clear(W, alloc);
}
}
void
fmpz_poly_resultant(fmpz_t res, const fmpz_poly_t poly1,
const fmpz_poly_t poly2)
{
const slong len1 = poly1->length, len2 = poly2->length;
if (len1 == 0 || len2 == 0)
{
fmpz_zero(res);
return;
}
if (len1 >= len2)
_fmpz_poly_resultant(res, poly1->coeffs, len1, poly2->coeffs, len2);
else
{
_fmpz_poly_resultant(res, poly2->coeffs, len2, poly1->coeffs, len1);
if ((len1 > 1) && (!(len1 & WORD(1)) & !(len2 & WORD(1))))
fmpz_neg(res, res);
}
}
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