171 lines
4.8 KiB
C
171 lines
4.8 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) 2008, 2009 William Hart
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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_gcd_subresultant(fmpz * 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_t c;
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fmpz_init(c);
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_fmpz_poly_content(c, poly1, len1);
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fmpz_gcd(res, c, poly2);
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fmpz_clear(c);
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}
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else
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{
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fmpz_t a, b, d, g, h;
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fmpz *A, *B, *W;
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slong lenA, lenB;
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fmpz_init(a);
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fmpz_init(b);
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fmpz_init(d);
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fmpz_init(g);
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fmpz_init(h);
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A = W = _fmpz_vec_init(len1 + len2);
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B = W + len1;
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lenA = len1;
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lenB = len2;
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_fmpz_poly_content(a, poly1, lenA);
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_fmpz_poly_content(b, poly2, lenB);
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_fmpz_vec_scalar_divexact_fmpz(A, poly1, lenA, a);
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_fmpz_vec_scalar_divexact_fmpz(B, poly2, lenB, b);
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fmpz_gcd(d, a, b);
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fmpz_one(g);
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fmpz_one(h);
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while (1)
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{
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const slong delta = lenA - lenB;
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_fmpz_poly_pseudo_rem_cohen(A, A, lenA, B, lenB);
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FMPZ_VEC_NORM(A, lenA);
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if (lenA <= 1)
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break;
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{ /* Swap A and B */
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fmpz *T;
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slong len;
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T = A, A = B, B = T, len = lenA, lenA = lenB, lenB = len;
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}
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if (delta == 1)
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{
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fmpz_mul(b, g, h);
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_fmpz_vec_scalar_divexact_fmpz(B, B, lenB, b);
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fmpz_set(g, A + (lenA - 1));
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fmpz_set(h, g);
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}
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else
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{
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fmpz_pow_ui(a, h, delta);
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fmpz_mul(b, g, a);
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_fmpz_vec_scalar_divexact_fmpz(B, B, lenB, b);
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fmpz_pow_ui(b, A + (lenA - 1), delta);
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fmpz_mul(g, h, b);
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fmpz_divexact(h, g, a);
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fmpz_set(g, A + (lenA - 1));
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}
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}
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if (lenA == 1)
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{
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fmpz_set(res, d);
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_fmpz_vec_zero(res + 1, len2 - 1);
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}
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else
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{
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_fmpz_poly_content(b, B, lenB);
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_fmpz_vec_scalar_divexact_fmpz(B, B, lenB, b);
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if (fmpz_sgn(B + (lenB - 1)) < 0)
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fmpz_neg(d, d);
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_fmpz_vec_scalar_mul_fmpz(res, B, lenB, d);
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if (len2 >= lenB)
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_fmpz_vec_zero(res + lenB, len2 - lenB);
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}
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fmpz_clear(a);
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fmpz_clear(b);
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fmpz_clear(d);
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fmpz_clear(g);
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fmpz_clear(h);
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_fmpz_vec_clear(W, len1 + len2);
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}
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}
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void
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fmpz_poly_gcd_subresultant(fmpz_poly_t res, const fmpz_poly_t poly1,
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const fmpz_poly_t poly2)
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{
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if (poly1->length < poly2->length)
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{
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fmpz_poly_gcd_subresultant(res, poly2, poly1);
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}
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else /* len1 >= len2 >= 0 */
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{
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const slong len1 = poly1->length;
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const slong len2 = poly2->length;
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if (len1 == 0) /* len1 = len2 = 0 */
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{
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fmpz_poly_zero(res);
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}
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else if (len2 == 0) /* len1 > len2 = 0 */
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{
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if (fmpz_sgn(poly1->coeffs + (len1 - 1)) > 0)
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fmpz_poly_set(res, poly1);
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else
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fmpz_poly_neg(res, poly1);
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}
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else /* len1 >= len2 >= 1 */
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{
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/* underscore code automatically handles aliasing */
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fmpz_poly_fit_length(res, len2);
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_fmpz_poly_gcd_subresultant(res->coeffs, poly1->coeffs, len1,
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poly2->coeffs, len2);
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_fmpz_poly_set_length(res, len2);
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_fmpz_poly_normalise(res);
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}
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}
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}
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