87 lines
2.4 KiB
C
87 lines
2.4 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 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 "ulong_extras.h"
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#include "nmod_vec.h"
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#include "nmod_poly.h"
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void
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_nmod_poly_atan_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod)
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{
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mp_ptr t, u;
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t = _nmod_vec_init(n);
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u = _nmod_vec_init(n);
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/* atan(h(x)) = integral(h'(x)/(1+h(x)^2)) */
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_nmod_poly_mullow(u, h, n, h, n, n, mod); u[0] = UWORD(1);
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_nmod_poly_derivative(t, h, n, mod); t[n-1] = UWORD(0);
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_nmod_poly_div_series(g, t, u, n, mod);
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_nmod_poly_integral(g, g, n, mod);
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_nmod_vec_clear(t);
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_nmod_vec_clear(u);
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}
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void
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nmod_poly_atan_series(nmod_poly_t g, const nmod_poly_t h, slong n)
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{
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mp_ptr h_coeffs;
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slong h_len = h->length;
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if (h_len > 0 && h->coeffs[0] != UWORD(0))
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{
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flint_printf("Exception (nmod_poly_atan_series): Constant term != 0.\n");
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abort();
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}
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if (h_len == 1 || n < 2)
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{
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nmod_poly_zero(g);
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return;
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}
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nmod_poly_fit_length(g, n);
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if (h_len < n)
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{
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h_coeffs = _nmod_vec_init(n);
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flint_mpn_copyi(h_coeffs, h->coeffs, h_len);
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flint_mpn_zero(h_coeffs + h_len, n - h_len);
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}
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else
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h_coeffs = h->coeffs;
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_nmod_poly_atan_series(g->coeffs, h_coeffs, n, h->mod);
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if (h_len < n)
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_nmod_vec_clear(h_coeffs);
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g->length = n;
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_nmod_poly_normalise(g);
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}
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