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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_revert_series_lagrange(arb_ptr Qinv,
arb_srcptr Q, slong Qlen, slong n, slong prec)
{
slong i;
arb_ptr R, S, T, tmp;
if (n <= 2)
{
if (n >= 1)
arb_zero(Qinv);
if (n == 2)
arb_inv(Qinv + 1, Q + 1, prec);
return;
}
R = _arb_vec_init(n - 1);
S = _arb_vec_init(n - 1);
T = _arb_vec_init(n - 1);
arb_zero(Qinv);
arb_inv(Qinv + 1, Q + 1, prec);
_arb_poly_inv_series(R, Q + 1, FLINT_MIN(Qlen, n) - 1, n - 1, prec);
_arb_vec_set(S, R, n - 1);
for (i = 2; i < n; i++)
{
_arb_poly_mullow(T, S, n - 1, R, n - 1, n - 1, prec);
arb_div_ui(Qinv + i, T + i - 1, i, prec);
tmp = S; S = T; T = tmp;
}
_arb_vec_clear(R, n - 1);
_arb_vec_clear(S, n - 1);
_arb_vec_clear(T, n - 1);
}
void
arb_poly_revert_series_lagrange(arb_poly_t Qinv,
const arb_poly_t Q, slong n, slong prec)
{
slong Qlen = Q->length;
if (Qlen < 2 || !arb_is_zero(Q->coeffs)
|| arb_contains_zero(Q->coeffs + 1))
{
flint_printf("Exception (arb_poly_revert_series_lagrange). Input must \n"
"have zero constant term and nonzero coefficient of x^1.\n");
flint_abort();
}
if (Qinv != Q)
{
arb_poly_fit_length(Qinv, n);
_arb_poly_revert_series_lagrange(Qinv->coeffs, Q->coeffs, Qlen, n, prec);
}
else
{
arb_poly_t t;
arb_poly_init2(t, n);
_arb_poly_revert_series_lagrange(t->coeffs, Q->coeffs, Qlen, n, prec);
arb_poly_swap(Qinv, t);
arb_poly_clear(t);
}
_arb_poly_set_length(Qinv, n);
_arb_poly_normalise(Qinv);
}
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