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/*
Copyright (C) 2016 Pascal Molin
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
void
acb_dirichlet_jacobi_sum_naive(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec)
{
ulong k1, k2, m1, m2, g, e, m;
ulong * v1, * v2;
slong *v;
nmod_t expo;
acb_t z;
v1 = flint_malloc(G->q * sizeof(ulong));
v2 = flint_malloc(G->q * sizeof(ulong));
dirichlet_vec_set_null(v1, G, G->q);
dirichlet_chi_vec_loop(v1, G, chi1, G->q);
dirichlet_vec_set_null(v2, G, G->q);
dirichlet_chi_vec_loop(v2, G, chi2, G->q);
nmod_init(&expo, G->expo);
m1 = dirichlet_order_char(G, chi1);
m2 = dirichlet_order_char(G, chi2);
g = m1 * m2 / n_gcd(m1, m2);
m = G->expo / g;
v = flint_malloc(g * sizeof(slong));
for (e = 0; e < g; e++)
v[e] = 0;
for (k1 = 2, k2 = G->q - 1; k2 > 1; k1++, k2--)
{
if (v1[k1] == DIRICHLET_CHI_NULL ||
v2[k2] == DIRICHLET_CHI_NULL)
continue;
e = nmod_add(v1[k1], v2[k2], expo) / m;
v[e]++;
}
acb_init(z);
acb_unit_root(z, g, prec);
acb_dirichlet_si_poly_evaluate(res, v, g, z, prec);
acb_clear(z);
flint_free(v);
flint_free(v2);
flint_free(v1);
}
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