145 lines
3.8 KiB
C
145 lines
3.8 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) 2010 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 "fmpz_poly.h"
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void
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_fmpz_poly_resultant(fmpz_t res, const fmpz * poly1, slong len1,
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const fmpz * poly2, slong len2)
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{
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if (len2 == 1)
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{
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fmpz_pow_ui(res, poly2, len1 - 1);
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}
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else
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{
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fmpz_t a, b, g, h, t;
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fmpz *A, *B, *W;
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const slong alloc = len1 + len2;
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slong sgn = 1;
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fmpz_init(a);
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fmpz_init(b);
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fmpz_init(g);
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fmpz_init(h);
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fmpz_init(t);
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A = W = _fmpz_vec_init(alloc);
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B = W + len1;
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_fmpz_poly_content(a, poly1, len1);
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_fmpz_poly_content(b, poly2, len2);
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_fmpz_vec_scalar_divexact_fmpz(A, poly1, len1, a);
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_fmpz_vec_scalar_divexact_fmpz(B, poly2, len2, b);
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fmpz_one(g);
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fmpz_one(h);
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fmpz_pow_ui(a, a, len2 - 1);
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fmpz_pow_ui(b, b, len1 - 1);
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fmpz_mul(t, a, b);
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do
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{
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const slong d = len1 - len2;
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if (!(len1 & WORD(1)) & !(len2 & WORD(1)))
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sgn = -sgn;
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_fmpz_poly_pseudo_rem_cohen(A, A, len1, B, len2);
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FMPZ_VEC_NORM(A, len1);
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if (len1 == 0)
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{
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fmpz_zero(res);
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goto cleanup;
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}
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{
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fmpz * T;
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slong len;
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T = A, A = B, B = T;
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len = len1, len1 = len2, len2 = len;
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}
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fmpz_pow_ui(a, h, d);
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fmpz_mul(b, g, a);
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_fmpz_vec_scalar_divexact_fmpz(B, B, len2, b);
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fmpz_pow_ui(g, A + (len1 - 1), d);
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fmpz_mul(b, h, g);
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fmpz_divexact(h, b, a);
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fmpz_set(g, A + (len1 - 1));
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} while (len2 > 1);
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fmpz_pow_ui(g, h, len1 - 1);
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fmpz_pow_ui(b, B + (len2 - 1), len1 - 1);
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fmpz_mul(a, h, b);
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fmpz_divexact(h, a, g);
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fmpz_mul(res, t, h);
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if (sgn < 0)
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fmpz_neg(res, res);
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cleanup:
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fmpz_clear(a);
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fmpz_clear(b);
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fmpz_clear(g);
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fmpz_clear(h);
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fmpz_clear(t);
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_fmpz_vec_clear(W, alloc);
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}
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}
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void
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fmpz_poly_resultant(fmpz_t res, const fmpz_poly_t poly1,
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const fmpz_poly_t poly2)
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{
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const slong len1 = poly1->length, len2 = poly2->length;
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if (len1 == 0 || len2 == 0)
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{
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fmpz_zero(res);
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return;
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}
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if (len1 >= len2)
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_fmpz_poly_resultant(res, poly1->coeffs, len1, poly2->coeffs, len2);
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else
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{
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_fmpz_poly_resultant(res, poly2->coeffs, len2, poly1->coeffs, len1);
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if ((len1 > 1) && (!(len1 & WORD(1)) & !(len2 & WORD(1))))
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fmpz_neg(res, res);
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}
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}
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