mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
93 lines
2.2 KiB
C
93 lines
2.2 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_elliptic.h"
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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_elliptic_p_jet(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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int real;
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slong k;
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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_elliptic_p(r, z, tau, prec);
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return;
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}
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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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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_jet(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(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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if (real)
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{
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for (k = 0; k < len; k++)
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arb_zero(acb_imagref(r + k));
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}
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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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