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/*
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_lambertw_series(arb_ptr res,
arb_srcptr z, slong zlen, int flags, slong len, slong prec)
{
arb_ptr w, ew, t, u;
arb_t ew0;
zlen = FLINT_MIN(zlen, len);
if (zlen == 1)
{
arb_lambertw(res, z, flags, prec);
_arb_vec_zero(res + 1, len - 1);
return;
}
w = _arb_vec_init(len);
ew = _arb_vec_init(len);
t = _arb_vec_init(len);
u = _arb_vec_init(len);
arb_init(ew0);
arb_lambertw(w, z, flags, prec);
if (arb_contains_zero(w))
arb_exp(ew0, w, prec);
else
arb_div(ew0, z, w, prec);
arb_add(t, ew0, z, prec);
arb_div(w + 1, z + 1, t, prec);
NEWTON_INIT(2, len)
NEWTON_LOOP(m, n)
/* _arb_poly_exp_series(ew, w, m, n, prec); */
arb_zero(t);
_arb_vec_set(t + 1, w + 1, m - 1);
_arb_poly_exp_series(ew, t, m, n, prec);
_arb_vec_scalar_mul(ew, ew, n, ew0, prec);
_arb_poly_mullow(t, ew, n, w, m, n, prec);
_arb_poly_sub(u, t, n, z, FLINT_MIN(zlen, n), prec);
_arb_vec_add(t, t, ew, n, prec);
_arb_poly_div_series(ew, u, n, t, n, n, prec);
_arb_vec_neg(w + m, ew + m, n - m);
NEWTON_END_LOOP
NEWTON_END
_arb_vec_set(res, w, len);
_arb_vec_clear(w, len);
_arb_vec_clear(ew, len);
_arb_vec_clear(t, len);
_arb_vec_clear(u, len);
arb_clear(ew0);
}
void
arb_poly_lambertw_series(arb_poly_t res,
const arb_poly_t z, int flags, slong len, slong prec)
{
if (len == 0 || (flags == 0 && z->length == 0))
{
arb_poly_zero(res);
return;
}
if (z->length == 0)
{
arb_poly_fit_length(res, len);
_arb_vec_indeterminate(res->coeffs, len);
_arb_poly_set_length(res, len);
return;
}
arb_poly_fit_length(res, len);
_arb_poly_lambertw_series(res->coeffs, z->coeffs, z->length, flags, len, prec);
_arb_poly_set_length(res, len);
_arb_poly_normalise(res);
}
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