mirror of
https://github.com/vale981/arb
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66 lines
1.6 KiB
C
66 lines
1.6 KiB
C
/*
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Copyright (C) 2014 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_modular.h"
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void
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acb_modular_eta(acb_t z, const acb_t tau, slong prec)
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{
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psl2z_t g;
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fmpq_t t;
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arf_t one_minus_eps;
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acb_t tau_prime, eta, q, q24;
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psl2z_init(g);
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fmpq_init(t);
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arf_init(one_minus_eps);
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acb_init(tau_prime);
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acb_init(eta);
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acb_init(q);
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acb_init(q24);
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arf_set_ui_2exp_si(one_minus_eps, 63, -6);
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acb_modular_fundamental_domain_approx(tau_prime, g, tau,
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one_minus_eps, prec);
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acb_div_ui(q24, tau_prime, 12, prec);
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acb_exp_pi_i(q24, q24, prec);
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acb_pow_ui(q, q24, 24, prec);
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acb_modular_eta_sum(eta, q, prec);
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acb_mul(eta, eta, q24, prec);
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/* epsilon^-1 */
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fmpq_set_si(t, -acb_modular_epsilon_arg(g), 12);
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arb_sin_cos_pi_fmpq(acb_imagref(q), acb_realref(q), t, prec);
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acb_mul(eta, eta, q, prec);
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/* (c*tau+d)^(-1/2) */
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if (!fmpz_is_zero(&g->c))
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{
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acb_mul_fmpz(q, tau, &g->c, prec);
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acb_add_fmpz(q, q, &g->d, prec);
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acb_rsqrt(q, q, prec);
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acb_mul(eta, eta, q, prec);
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}
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acb_set(z, eta);
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psl2z_clear(g);
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fmpq_clear(t);
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arf_clear(one_minus_eps);
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acb_clear(tau_prime);
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acb_clear(eta);
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acb_clear(q);
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acb_clear(q24);
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}
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