mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
95 lines
2.3 KiB
C
95 lines
2.3 KiB
C
|
/*
|
||
|
|
Copyright (C) 2017 Fredrik Johansson
|
||
|
|
|
||
|
|
This file is part of Arb.
|
||
|
|
|
||
|
|
Arb is free software: you can redistribute it and/or modify it under
|
||
|
|
the terms of the GNU Lesser General Public License (LGPL) as published
|
||
|
|
by the Free Software Foundation; either version 2.1 of the License, or
|
||
|
|
(at your option) any later version. See <http://www.gnu.org/licenses/>.
|
||
|
|
*/
|
||
|
|
|
||
|
|
#include "arb_poly.h"
|
||
|
|
|
||
|
|
void
|
||
|
|
_arb_poly_log1p_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec)
|
||
|
|
{
|
||
|
|
arb_t a;
|
||
|
|
|
||
|
|
flen = FLINT_MIN(flen, n);
|
||
|
|
|
||
|
|
arb_init(a);
|
||
|
|
arb_log1p(a, f, prec);
|
||
|
|
|
||
|
|
if (flen == 1)
|
||
|
|
{
|
||
|
|
_arb_vec_zero(res + 1, n - 1);
|
||
|
|
}
|
||
|
|
else if (n == 2)
|
||
|
|
{
|
||
|
|
arb_add_ui(res, f + 0, 1, prec);
|
||
|
|
arb_div(res + 1, f + 1, res + 0, prec);
|
||
|
|
}
|
||
|
|
else if (_arb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */
|
||
|
|
{
|
||
|
|
slong i, j, d = flen - 1;
|
||
|
|
|
||
|
|
arb_add_ui(res, f + 0, 1, prec);
|
||
|
|
|
||
|
|
for (i = 1, j = d; j < n; j += d, i++)
|
||
|
|
{
|
||
|
|
if (i == 1)
|
||
|
|
arb_div(res + j, f + d, res, prec);
|
||
|
|
else
|
||
|
|
arb_mul(res + j, res + j - d, res + d, prec);
|
||
|
|
_arb_vec_zero(res + j - d + 1, flen - 2);
|
||
|
|
}
|
||
|
|
_arb_vec_zero(res + j - d + 1, n - (j - d + 1));
|
||
|
|
|
||
|
|
for (i = 2, j = 2 * d; j < n; j += d, i++)
|
||
|
|
arb_div_si(res + j, res + j, i % 2 ? i : -i, prec);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
arb_ptr f_diff, f_inv;
|
||
|
|
slong alloc;
|
||
|
|
|
||
|
|
alloc = n + flen;
|
||
|
|
f_inv = _arb_vec_init(alloc);
|
||
|
|
f_diff = f_inv + n;
|
||
|
|
|
||
|
|
arb_add_ui(f_diff, f, 1, prec);
|
||
|
|
_arb_vec_set(f_diff + 1, f + 1, flen - 1);
|
||
|
|
_arb_poly_inv_series(f_inv, f_diff, flen, n, prec);
|
||
|
|
_arb_poly_derivative(f_diff, f, flen, prec);
|
||
|
|
_arb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
|
||
|
|
_arb_poly_integral(res, res, n, prec);
|
||
|
|
|
||
|
|
_arb_vec_clear(f_inv, alloc);
|
||
|
|
}
|
||
|
|
|
||
|
|
arb_swap(res, a);
|
||
|
|
arb_clear(a);
|
||
|
|
}
|
||
|
|
|
||
|
|
void
|
||
|
|
arb_poly_log1p_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec)
|
||
|
|
{
|
||
|
|
slong flen = f->length;
|
||
|
|
|
||
|
|
if (flen == 0 || n == 0)
|
||
|
|
{
|
||
|
|
arb_poly_zero(res);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (flen == 1 /*&& !arb_contains_si(f->coeffs, -1)*/)
|
||
|
|
n = 1;
|
||
|
|
|
||
|
|
arb_poly_fit_length(res, n);
|
||
|
|
_arb_poly_log1p_series(res->coeffs, f->coeffs, flen, n, prec);
|
||
|
|
_arb_poly_set_length(res, n);
|
||
|
|
_arb_poly_normalise(res);
|
||
|
|
}
|
||
|
|
|