mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
109 lines
2.4 KiB
C
109 lines
2.4 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 acb_modular_transform(acb_t w, const psl2z_t g, const acb_t z, slong prec)
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{
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#define a (&g->a)
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#define b (&g->b)
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#define c (&g->c)
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#define d (&g->d)
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#define x acb_realref(z)
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#define y acb_imagref(z)
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if (fmpz_is_zero(c))
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{
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/* (az+b)/d, where we must have a = d = 1 */
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acb_add_fmpz(w, z, b, prec);
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}
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else if (fmpz_is_zero(a))
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{
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/* b/(cz+d), where -bc = 1, c = 1 => -1/(z+d) */
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acb_add_fmpz(w, z, d, prec);
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acb_inv(w, w, prec);
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acb_neg(w, w);
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}
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else if (0)
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{
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acb_t t, u;
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acb_init(t);
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acb_init(u);
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acb_set_fmpz(t, b);
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acb_addmul_fmpz(t, z, a, prec);
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acb_set_fmpz(u, d);
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acb_addmul_fmpz(u, z, c, prec);
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acb_div(w, t, u, prec);
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acb_clear(t);
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acb_clear(u);
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}
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else
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{
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/* (az+b)/(cz+d) = (re+im*i)/den where
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re = bd + (bc+ad)x + ac(x^2+y^2)
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im = (ad-bc)y
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den = c^2(x^2+y^2) + 2cdx + d^2
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*/
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fmpz_t t;
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arb_t re, im, den;
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arb_init(re);
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arb_init(im);
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arb_init(den);
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fmpz_init(t);
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arb_mul(im, x, x, prec);
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arb_addmul(im, y, y, prec);
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fmpz_mul(t, b, d);
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arb_set_fmpz(re, t);
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fmpz_mul(t, b, c);
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fmpz_addmul(t, a, d);
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arb_addmul_fmpz(re, x, t, prec);
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fmpz_mul(t, a, c);
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arb_addmul_fmpz(re, im, t, prec);
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fmpz_mul(t, d, d);
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arb_set_fmpz(den, t);
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fmpz_mul(t, c, d);
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fmpz_mul_2exp(t, t, 1);
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arb_addmul_fmpz(den, x, t, prec);
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fmpz_mul(t, c, c);
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arb_addmul_fmpz(den, im, t, prec);
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fmpz_mul(t, a, d);
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fmpz_submul(t, b, c);
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arb_mul_fmpz(im, y, t, prec);
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arb_div(acb_realref(w), re, den, prec);
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arb_div(acb_imagref(w), im, den, prec);
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arb_clear(re);
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arb_clear(im);
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arb_clear(den);
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fmpz_clear(t);
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}
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#undef a
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#undef b
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#undef c
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#undef d
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#undef x
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#undef y
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}
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