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https://github.com/vale981/arb
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52 lines
1.3 KiB
C
52 lines
1.3 KiB
C
/*
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Copyright (C) 2012 Fredrik Johansson
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_poly.h"
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void
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_acb_poly_root_inclusion(acb_t r, const acb_t m,
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acb_srcptr poly,
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acb_srcptr polyder, slong len, slong prec)
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{
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acb_t t;
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arf_t u, v;
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acb_init(t);
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arf_init(u);
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arf_init(v);
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acb_set(r, m);
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mag_zero(arb_radref(acb_realref(r)));
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mag_zero(arb_radref(acb_imagref(r)));
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_acb_poly_evaluate(t, poly, len, r, prec);
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acb_get_abs_ubound_arf(u, t, MAG_BITS);
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/* it could happen that we have an exact root, in which case
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we should avoid dividing by the derivative */
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if (!arf_is_zero(u))
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{
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_acb_poly_evaluate(t, polyder, len - 1, r, prec);
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acb_inv(t, t, MAG_BITS);
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acb_get_abs_ubound_arf(v, t, MAG_BITS);
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arf_mul(u, u, v, MAG_BITS, ARF_RND_UP);
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arf_mul_ui(u, u, len - 1, MAG_BITS, ARF_RND_UP);
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}
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arf_get_mag(arb_radref(acb_realref(r)), u);
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arf_get_mag(arb_radref(acb_imagref(r)), u);
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arf_clear(u);
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arf_clear(v);
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acb_clear(t);
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}
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