mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
81 lines
2.2 KiB
C
81 lines
2.2 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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/* eta1 = (-1/6) theta1'''(0) / theta1'(0) */
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static void
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eta1(acb_t res, acb_t theta1, const acb_t tau, slong prec)
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{
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acb_ptr theta;
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acb_t z;
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acb_init(z);
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theta = _acb_vec_init(16);
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acb_modular_theta_jet(theta,
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theta + 4, theta + 8, theta + 12, z, tau, 4, prec);
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if (theta1 != NULL)
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acb_set(theta1, theta + 1);
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acb_div(res, theta + 3, theta + 1, prec);
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acb_neg(res, res);
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_acb_vec_clear(theta, 16);
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acb_clear(z);
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}
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/* zeta(z) = 2 eta1 z + theta1'(z,q) / theta1(z,q) */
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void
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acb_elliptic_zeta(acb_t res, const acb_t z, const acb_t tau, slong prec)
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{
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acb_ptr t;
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int real;
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real = acb_is_real(z) && arb_is_int_2exp_si(acb_realref(tau), -1) &&
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arb_is_positive(acb_imagref(tau));
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t = _acb_vec_init(8);
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acb_modular_theta_jet(t, t + 2, t + 4, t + 6, z, tau, 2, prec);
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eta1(t + 2, NULL, tau, prec);
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acb_mul_2exp_si(t + 2, t + 2, 1);
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acb_mul(t + 2, t + 2, z, prec);
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acb_div(t, t + 1, t, prec);
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acb_add(res, t, t + 2, prec);
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if (real)
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arb_zero(acb_imagref(res));
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_acb_vec_clear(t, 8);
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}
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/* sigma(z) = exp(eta1 z^2) theta1(z) / theta1'(0) */
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void
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acb_elliptic_sigma(acb_t res, const acb_t z, const acb_t tau, slong prec)
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{
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acb_ptr t;
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int real;
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real = acb_is_real(z) && arb_is_int_2exp_si(acb_realref(tau), -1) &&
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arb_is_positive(acb_imagref(tau));
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t = _acb_vec_init(8);
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acb_modular_theta_jet(t, t + 2, t + 4, t + 6, z, tau, 2, prec);
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eta1(t + 2, t + 3, tau, prec);
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acb_mul(t + 4, z, z, prec);
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acb_mul(t + 2, t + 2, t + 4, prec);
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acb_exp(t + 2, t + 2, prec);
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acb_div(t, t, t + 3, prec);
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acb_mul(res, t, t + 2, prec);
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if (real)
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arb_zero(acb_imagref(res));
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_acb_vec_clear(t, 8);
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}
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