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https://github.com/vale981/arb
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65 lines
1.6 KiB
C
65 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_delta(acb_t z, const acb_t tau, slong prec)
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{
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psl2z_t g;
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arf_t one_minus_eps;
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acb_t tau_prime, t1, t2, t3, t4, q;
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psl2z_init(g);
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arf_init(one_minus_eps);
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acb_init(tau_prime);
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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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acb_init(q);
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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_exp_pi_i(q, tau_prime, prec);
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acb_modular_theta_const_sum(t2, t3, t4, q, prec);
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/* (t2 t3 t4) ^ 8 * q^2 */
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acb_mul(t1, t2, t3, prec);
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acb_mul(t1, t1, t4, prec);
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acb_mul(t1, t1, t1, prec);
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acb_mul(t1, t1, t1, prec);
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acb_mul(t1, t1, q, prec);
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acb_mul(t1, t1, t1, prec);
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acb_mul_2exp_si(t1, t1, -8);
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if (!fmpz_is_zero(&g->c))
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{
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acb_mul_fmpz(t2, tau, &g->c, prec);
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acb_add_fmpz(t2, t2, &g->d, prec);
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acb_pow_ui(t2, t2, 12, prec);
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acb_div(t1, t1, t2, prec);
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}
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acb_set(z, t1);
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psl2z_clear(g);
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arf_clear(one_minus_eps);
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acb_clear(tau_prime);
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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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acb_clear(q);
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}
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