mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
127 lines
3.4 KiB
C
127 lines
3.4 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2014 Fredrik Johansson
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******************************************************************************/
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#include "acb_modular.h"
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#include "acb_poly.h"
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void
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acb_modular_theta_zpx_notransform(acb_ptr theta1, acb_ptr theta2,
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acb_ptr theta3, acb_ptr theta4, const acb_t z, const acb_t tau,
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slong len, slong prec)
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{
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acb_t q, q4, w;
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int w_is_unit;
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acb_init(q);
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acb_init(q4);
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acb_init(w);
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/* compute q_{1/4}, q */
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acb_mul_2exp_si(q4, tau, -2);
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acb_exp_pi_i(q4, q4, prec);
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acb_pow_ui(q, q4, 4, prec);
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/* compute w */
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acb_exp_pi_i(w, z, prec);
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w_is_unit = arb_is_zero(acb_imagref(z));
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/* evaluate theta functions */
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acb_modular_theta_sum(theta1, theta2, theta3, theta4,
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w, w_is_unit, q, len, prec);
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_acb_vec_scalar_mul(theta1, theta1, len, q4, prec);
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_acb_vec_scalar_mul(theta2, theta2, len, q4, prec);
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acb_clear(q);
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acb_clear(q4);
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acb_clear(w);
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}
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void
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acb_modular_elliptic_p_zpx(acb_ptr r, const acb_t z, const acb_t tau, slong len, slong prec)
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{
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acb_t t01, t02, t03, t04;
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acb_ptr tz1, tz2, tz3, tz4;
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acb_t t;
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if (len < 1)
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return;
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if (len == 1)
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{
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acb_modular_elliptic_p(r, z, tau, prec);
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return;
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}
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acb_init(t);
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acb_init(t01);
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acb_init(t02);
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acb_init(t03);
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acb_init(t04);
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tz1 = _acb_vec_init(len);
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tz2 = _acb_vec_init(len);
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tz3 = _acb_vec_init(len);
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tz4 = _acb_vec_init(len);
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acb_modular_theta_zpx_notransform(tz1, tz2, tz3, tz4, z, tau, len, prec);
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/* [theta_4(z) / theta_1(z)]^2 */
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_acb_poly_div_series(tz2, tz4, len, tz1, len, len, prec);
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_acb_poly_mullow(tz1, tz2, len, tz2, len, len, prec);
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acb_zero(t);
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acb_modular_theta_notransform(t01, t02, t03, t04, t, tau, prec);
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/* [theta_2(0) * theta_3(0)] ^2 */
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acb_mul(t, t02, t03, prec);
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acb_mul(t, t, t, prec);
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_acb_vec_scalar_mul(tz1, tz1, len, t, prec);
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/* - [theta_2(0)^4 + theta_3(0)^4] / 3 */
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acb_pow_ui(t02, t02, 4, prec);
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acb_pow_ui(t03, t03, 4, prec);
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acb_add(t, t02, t03, prec);
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acb_div_ui(t, t, 3, prec);
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acb_sub(tz1, tz1, t, prec);
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/* times pi^2 */
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acb_const_pi(t, prec);
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acb_mul(t, t, t, prec);
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_acb_vec_scalar_mul(r, tz1, len, t, prec);
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acb_clear(t);
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acb_clear(t01);
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acb_clear(t02);
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acb_clear(t03);
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acb_clear(t04);
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_acb_vec_clear(tz1, len);
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_acb_vec_clear(tz2, len);
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_acb_vec_clear(tz3, len);
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_acb_vec_clear(tz4, len);
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}
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