mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
59 lines
1.4 KiB
C
59 lines
1.4 KiB
C
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/*
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Copyright (C) 2021 Daniel Schultz
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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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void
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acb_elliptic_p_prime(acb_t r, const acb_t z, const acb_t tau, slong prec)
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{
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acb_struct tz[4];
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acb_t t1, t2, t3;
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int i, 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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acb_init(t1);
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acb_init(t2);
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acb_init(t3);
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for (i = 0; i < 4; i++)
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acb_init(tz + i);
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acb_modular_theta(tz + 0, tz + 1, tz + 2, tz + 3, z, tau, prec);
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/* (-2*pi*eta^2/theta1)^3*theta2*theta3*theta4 */
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acb_const_pi(t2, prec);
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acb_mul_2exp_si(t2, t2, 1);
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acb_neg(t2, t2);
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acb_modular_eta(t3, tau, prec);
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acb_mul(t1, t3, t3, prec);
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acb_mul(t3, t1, t2, prec);
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acb_div(t1, t3, tz + 0, prec);
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acb_mul(t2, t1, t1, prec);
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acb_mul(t3, t1, t2, prec);
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acb_mul(t1, tz + 1, tz + 2, prec);
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acb_mul(t2, t1, tz + 3, prec);
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acb_mul(r, t3, t2, prec);
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if (real)
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arb_zero(acb_imagref(r));
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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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for (i = 0; i < 4; i++)
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acb_clear(tz + i);
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}
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