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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_newton_convergence_factor(arf_t convergence_factor,
arb_srcptr poly, slong len,
const arb_t convergence_interval, slong prec)
{
arb_ptr deriv;
arb_t t, u;
arb_init(t);
arb_init(u);
deriv = _arb_vec_init(len - 1);
_arb_poly_derivative(deriv, poly, len, prec);
_arb_poly_evaluate(t, deriv, len - 1, convergence_interval, prec);
_arb_poly_derivative(deriv, deriv, len - 1, prec);
_arb_poly_evaluate(u, deriv, len - 2, convergence_interval, prec);
arb_div(t, u, t, prec);
arb_mul_2exp_si(t, t, -1);
arb_get_abs_ubound_arf(convergence_factor, t, prec);
_arb_vec_clear(deriv, len - 1);
arb_clear(t);
arb_clear(u);
}
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