165 lines
4.6 KiB
C
165 lines
4.6 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 Sebastian Pancratz
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******************************************************************************/
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#include <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "fmpz_vec.h"
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#include "fmpq_poly.h"
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void _fmpq_poly_resultant(fmpz_t rnum, fmpz_t rden,
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const fmpz *poly1, const fmpz_t den1, slong len1,
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const fmpz *poly2, const fmpz_t den2, slong len2)
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{
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if (len2 == 1)
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{
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if (len1 == 1)
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{
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fmpz_one(rnum);
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fmpz_one(rden);
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}
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else if (len1 == 2)
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{
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fmpz_set(rnum, poly2);
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fmpz_set(rden, den2);
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}
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else
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{
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fmpz_pow_ui(rnum, poly2, len1 - 1);
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if (fmpz_is_one(den2))
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{
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fmpz_one(rden);
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}
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else
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{
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fmpz_pow_ui(rden, den2, len1 - 1);
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}
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}
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}
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else /* len1 >= len2 >= 2 */
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{
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fmpz_t c1, c2;
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fmpz *prim1, *prim2, *g;
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slong lenG = len2;
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fmpz_init(c1);
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fmpz_init(c2);
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_fmpz_vec_content(c1, poly1, len1);
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_fmpz_vec_content(c2, poly2, len2);
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prim1 = _fmpz_vec_init(len1);
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prim2 = _fmpz_vec_init(len2);
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g = _fmpz_vec_init(len2);
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_fmpz_vec_scalar_divexact_fmpz(prim1, poly1, len1, c1);
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_fmpz_vec_scalar_divexact_fmpz(prim2, poly2, len2, c2);
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_fmpz_poly_gcd(g, prim1, len1, prim2, len2);
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FMPZ_VEC_NORM(g, lenG);
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if (lenG > 1)
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{
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fmpz_zero(rnum);
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fmpz_one(rden);
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}
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else /* prim1, prim2 are coprime */
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{
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fmpz_t t;
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fmpz_init(t);
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_fmpz_poly_resultant(rnum, prim1, len1, prim2, len2);
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if (!fmpz_is_one(c1))
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{
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fmpz_pow_ui(t, c1, len2 - 1);
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fmpz_mul(rnum, rnum, t);
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}
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if (!fmpz_is_one(c2))
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{
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fmpz_pow_ui(t, c2, len1 - 1);
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fmpz_mul(rnum, rnum, t);
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}
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if (fmpz_is_one(den1))
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{
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if (fmpz_is_one(den2))
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fmpz_one(rden);
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else
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fmpz_pow_ui(rden, den2, len1 - 1);
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}
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else
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{
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if (fmpz_is_one(den2))
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fmpz_pow_ui(rden, den1, len2 - 1);
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else
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{
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fmpz_pow_ui(rden, den1, len2 - 1);
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fmpz_pow_ui(t, den2, len1 - 1);
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fmpz_mul(rden, rden, t);
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}
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}
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_fmpq_canonicalise(rnum, rden);
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fmpz_clear(t);
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}
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fmpz_clear(c1);
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fmpz_clear(c2);
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_fmpz_vec_clear(prim1, len1);
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_fmpz_vec_clear(prim2, len2);
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_fmpz_vec_clear(g, len2);
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}
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}
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void fmpq_poly_resultant(fmpq_t r, const fmpq_poly_t f, const fmpq_poly_t g)
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{
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const slong len1 = f->length;
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const slong len2 = g->length;
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if (len1 == 0 || len2 == 0)
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{
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fmpq_zero(r);
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}
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else
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{
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if (len1 >= len2)
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{
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_fmpq_poly_resultant(fmpq_numref(r), fmpq_denref(r),
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f->coeffs, f->den, len1,
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g->coeffs, g->den, len2);
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}
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else
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{
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_fmpq_poly_resultant(fmpq_numref(r), fmpq_denref(r),
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g->coeffs, g->den, len2,
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f->coeffs, f->den, len1);
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if (((len1 | len2) & WORD(1)) == WORD(0))
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fmpq_neg(r, r);
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}
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}
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}
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