104 lines
2.7 KiB
C
104 lines
2.7 KiB
C
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/*=============================================================================
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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 Fredrik Johansson
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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
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_fmpq_poly_sin_series(fmpz * g, fmpz_t gden,
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const fmpz * h, const fmpz_t hden, slong n)
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{
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fmpz * t;
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fmpz * u;
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fmpz_t tden;
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fmpz_t uden;
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t = _fmpz_vec_init(n);
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u = _fmpz_vec_init(n);
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fmpz_init(tden);
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fmpz_init(uden);
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/* sin(x) = 2*tan(x/2)/(1+tan(x/2)^2) */
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fmpz_mul_ui(uden, hden, UWORD(2));
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_fmpq_poly_tan_series(t, tden, h, uden, n);
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_fmpq_poly_mullow(u, uden, t, tden, n, t, tden, n, n);
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fmpz_set(u, uden);
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_fmpq_poly_canonicalise(u, uden, n);
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_fmpq_poly_div_series(g, gden, t, tden, u, uden, n);
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_fmpq_poly_scalar_mul_ui(g, gden, g, gden, n, UWORD(2));
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_fmpq_poly_canonicalise(g, gden, n);
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_fmpz_vec_clear(t, n);
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_fmpz_vec_clear(u, n);
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fmpz_clear(tden);
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fmpz_clear(uden);
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}
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void
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fmpq_poly_sin_series(fmpq_poly_t res, const fmpq_poly_t f, slong n)
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{
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fmpz * f_coeffs;
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slong flen = f->length;
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if (flen && !fmpz_is_zero(f->coeffs))
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{
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flint_printf("Exception (fmpq_poly_sin_series). Constant term != 0.\n");
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abort();
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}
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if (flen == 0 || n < 2)
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{
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fmpq_poly_zero(res);
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return;
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}
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fmpq_poly_fit_length(res, n);
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if (flen < n)
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{
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f_coeffs = _fmpz_vec_init(n);
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_fmpz_vec_set(f_coeffs, f->coeffs, flen);
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}
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else
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{
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f_coeffs = f->coeffs;
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}
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_fmpq_poly_sin_series(res->coeffs, res->den, f_coeffs, f->den, n);
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if (flen < n)
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{
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_fmpz_vec_clear(f_coeffs, n);
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}
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_fmpq_poly_set_length(res, n);
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_fmpq_poly_normalise(res);
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}
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