mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
75 lines
1.7 KiB
C
75 lines
1.7 KiB
C
/*
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Copyright (C) 2017 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_elliptic.h"
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#include "acb_modular.h"
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void
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acb_elliptic_roots(acb_t e1, acb_t e2, acb_t e3, const acb_t tau, slong prec)
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{
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acb_t t1, t2, t3, t4;
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int e1r, e23r;
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if (!arb_is_positive(acb_imagref(tau)) || !arb_is_finite(acb_realref(tau)))
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{
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acb_indeterminate(e1);
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acb_indeterminate(e2);
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acb_indeterminate(e3);
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return;
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}
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acb_init(t1);
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acb_init(t2);
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acb_init(t3);
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acb_init(t4);
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e1r = e23r = 0;
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if (arb_is_int(acb_realref(tau)))
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e1r = e23r = 1;
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else if (arb_is_int_2exp_si(acb_realref(tau), -1))
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e1r = 1;
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acb_modular_theta(t1, t2, t3, t4, t1, tau, prec);
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acb_pow_ui(t2, t2, 4, prec);
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acb_pow_ui(t4, t4, 4, prec);
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acb_sub(e2, t2, t4, prec);
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acb_mul_2exp_si(t3, t4, 1);
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acb_add(e1, t2, t3, prec);
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acb_mul_2exp_si(t3, t2, 1);
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acb_add(e3, t3, t4, prec);
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acb_const_pi(t3, prec);
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acb_mul(t3, t3, t3, prec);
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acb_div_ui(t3, t3, 3, prec);
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acb_mul(e1, e1, t3, prec);
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acb_mul(e2, e2, t3, prec);
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acb_mul(e3, e3, t3, prec);
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acb_neg(e3, e3);
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if (e1r)
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arb_zero(acb_imagref(e1));
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if (e23r)
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{
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arb_zero(acb_imagref(e2));
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arb_zero(acb_imagref(e3));
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}
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acb_clear(t1);
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acb_clear(t2);
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acb_clear(t3);
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acb_clear(t4);
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}
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