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/*
Copyright (C) 2016 Fredrik Johansson
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"
/* Laurent expansions at s = 1 of first 10 principal L-functions */
/* with mpmath:
chis = [[1],[0,1],[0,1,1],[0,1,0,1],[0,1,1,1,1],[0,1,0,0,0,1],[0,1,1,1,1,1,1],
[0,1,0,1,0,1,0,1],[0,1,1,0,1,1,0,1,1],[0,1,0,1,0,0,0,1,0,1]]
mp.dps = 40
for chi in chis:
phi = chi.count(1); q = len(chi)
L = lambda s: dirichlet(s, chi) - phi/((s-1)*q)
c0 = taylor(L, 1, 0, method="quad")
c1 = taylor(L, 1, 5, singular=True)[1:]
for c in c0 + c1:
print nstr(c, 20) + ",",
print
*/
#define TESTQ 10
#define TESTLEN 6
static const double laurent_data[TESTQ][TESTLEN] = {
{0.57721566490153286061, 0.072815845483676724861, -0.0048451815964361592423,
-0.00034230573671722431103, 0.000096890419394470835728, -6.6110318108421891813e-6},
{0.63518142273073908501, 0.11634237461305384831, -0.018765738937942729408,
0.00061334298434914532242, 0.00042338142025747308027, -0.00010545096447379519004},
{0.7510145394903918042, 0.058764477744540050414, -0.019011359100973296683,
0.0056382252365739175151, -0.0009550480622176659462, 0.000021808301216554848718},
{0.63518142273073908501, 0.11634237461305384831, -0.018765738937942729408,
0.00061334298434914532242, 0.00042338142025747308027, -0.00010545096447379519004},
{0.78366011440804636341, -0.014977808062405260803, 0.0090104707969118845102,
0.003603799084856807634, -0.0029351216034181476022, 0.00093077685173004747355},
{0.60655632993184433857, 0.2095885418562151802, -0.060844893711330538429,
0.0068080382961291386117, 0.0022236616427578346453, -0.0013581825996235430782},
{0.77274344835207292411, -0.047596894381510269689, 0.035406039531261788462,
-0.0054159870134630085898, -0.0019749752308692423114, 0.0014492998471928196325},
{0.63518142273073908501, 0.11634237461305384831, -0.018765738937942729408,
0.00061334298434914532242, 0.00042338142025747308027, -0.00010545096447379519004},
{0.7510145394903918042, 0.058764477744540050414, -0.019011359100973296683,
0.0056382252365739175151, -0.0009550480622176659462, 0.000021808301216554848718},
{0.66908892942800130547, 0.16801639259476784034, -0.072611999814034642781,
0.024624650443138705595, -0.004951850872731033514, -0.00020178815459414925709}
};
int main()
{
slong iter;
flint_rand_t state;
flint_printf("l_jet....");
fflush(stdout);
flint_randinit(state);
/* test Laurent series at s = 1 */
{
acb_t s, t;
dirichlet_group_t G;
dirichlet_char_t chi;
acb_ptr vec;
ulong q;
slong i;
acb_init(s);
acb_init(t);
vec = _acb_vec_init(TESTLEN);
acb_one(s);
for (q = 1; q <= TESTQ; q++)
{
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
acb_dirichlet_l_jet(vec, s, G, chi, 1, TESTLEN, 100);
for (i = 0; i < TESTLEN; i++)
{
acb_set_d(t, laurent_data[q - 1][i]);
mag_set_d(arb_radref(acb_realref(t)),
fabs(laurent_data[q - 1][i]) * 1e-14);
if (!acb_overlaps(vec + i, t))
{
flint_printf("FAIL: Laurent series\n\n");
flint_printf("q = %wu i = %wd\n\n", q, i);
flint_printf("r1 = "); acb_printn(vec + i, 50, 0); flint_printf("\n\n");
flint_printf("r2 = "); acb_printn(t, 50, 0); flint_printf("\n\n");
flint_abort();
}
}
dirichlet_char_clear(chi);
dirichlet_group_clear(G);
}
acb_clear(s);
acb_clear(t);
_acb_vec_clear(vec, TESTLEN);
}
/* test self-consistency */
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t s;
dirichlet_group_t G;
dirichlet_char_t chi;
acb_ptr vec1, vec2;
slong len1, len2;
slong prec1, prec2;
int deflate1, deflate2;
ulong q, k;
slong i;
len1 = n_randint(state, 5);
len2 = n_randint(state, 5);
prec1 = 2 + n_randint(state, 100);
prec2 = 2 + n_randint(state, 100);
deflate1 = n_randint(state, 2);
deflate2 = n_randint(state, 2);
q = 1 + n_randint(state, 20);
k = n_randint(state, n_euler_phi(q));
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
dirichlet_char_index(chi, G, k);
acb_init(s);
vec1 = _acb_vec_init(len1);
vec2 = _acb_vec_init(len2);
if (n_randint(state, 4) == 0)
acb_one(s);
else
acb_randtest(s, state, 2 + n_randint(state, 200), 2);
acb_dirichlet_l_jet(vec1, s, G, chi, deflate1, len1, prec1);
acb_dirichlet_l_jet(vec2, s, G, chi, deflate2, len2, prec2);
if (deflate1 != deflate2 && dirichlet_char_is_principal(G, chi))
{
/* add or subtract phi(q)/((s+x-1)q) */
acb_t t, u;
acb_init(t);
acb_init(u);
acb_set_ui(t, n_euler_phi(q));
acb_div_ui(t, t, q, prec1);
acb_sub_ui(u, s, 1, prec1);
for (i = 0; i < len1; i++)
{
acb_div(t, t, u, prec1);
if (deflate1)
acb_add(vec1 + i, vec1 + i, t, prec1);
else
acb_sub(vec1 + i, vec1 + i, t, prec1);
acb_neg(t, t);
}
acb_clear(t);
acb_clear(u);
}
for (i = 0; i < FLINT_MIN(len1, len2); i++)
{
if (!acb_overlaps(vec1 + i, vec2 + i))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("iter = %wd q = %wu k = %wu i = %wd\n\n", iter, q, k, i);
flint_printf("s = "); acb_printn(s, 50, 0); flint_printf("\n\n");
flint_printf("r1 = "); acb_printn(vec1 + i, 50, 0); flint_printf("\n\n");
flint_printf("r2 = "); acb_printn(vec2 + i, 50, 0); flint_printf("\n\n");
flint_abort();
}
}
dirichlet_char_clear(chi);
dirichlet_group_clear(G);
acb_clear(s);
_acb_vec_clear(vec1, len1);
_acb_vec_clear(vec2, len2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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