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/*
Copyright (C) 2013 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_pow_series(arb_ptr h,
arb_srcptr f, slong flen,
arb_srcptr g, slong glen, slong len, slong prec)
{
if (glen == 1)
{
_arb_poly_pow_arb_series(h, f, flen, g, len, prec);
return;
}
/* f^g = exp(g * log(f)) */
if (flen == 1)
{
arb_t t;
arb_init(t);
arb_log(t, f, prec);
_arb_vec_scalar_mul(h, g, glen, t, prec);
_arb_poly_exp_series(h, h, glen, len, prec);
arb_clear(t);
}
else
{
arb_ptr t;
t = _arb_vec_init(len);
_arb_poly_log_series(t, f, flen, len, prec);
_arb_poly_mullow(h, t, len, g, glen, len, prec);
_arb_poly_exp_series(h, h, len, len, prec);
_arb_vec_clear(t, len);
}
}
void
arb_poly_pow_series(arb_poly_t h,
const arb_poly_t f, const arb_poly_t g, slong len, slong prec)
{
slong flen, glen;
flen = f->length;
glen = g->length;
flen = FLINT_MIN(flen, len);
glen = FLINT_MIN(glen, len);
if (len == 0)
{
arb_poly_zero(h);
return;
}
if (glen == 0)
{
arb_poly_one(h);
return;
}
if (flen == 0)
{
arb_poly_zero(h);
return;
}
if (flen == 1 && glen == 1)
{
arb_poly_fit_length(h, 1);
arb_pow(h->coeffs, f->coeffs, g->coeffs, prec);
_arb_poly_set_length(h, 1);
_arb_poly_normalise(h);
return;
}
if (f == h || g == h)
{
arb_poly_t t;
arb_poly_init2(t, len);
_arb_poly_pow_series(t->coeffs,
f->coeffs, flen, g->coeffs, glen, len, prec);
_arb_poly_set_length(t, len);
_arb_poly_normalise(t);
arb_poly_swap(t, h);
arb_poly_clear(t);
}
else
{
arb_poly_fit_length(h, len);
_arb_poly_pow_series(h->coeffs,
f->coeffs, flen, g->coeffs, glen, len, prec);
_arb_poly_set_length(h, len);
_arb_poly_normalise(h);
}
}
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