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/* This file is public domain. Author: Fredrik Johansson. */
#include <string.h>
#include <stdlib.h>
#include <flint/profiler.h>
#include <flint/acb.h>
#include <flint/acb_dirichlet.h>
int main(int argc, char *argv[])
{
dirichlet_group_t G;
dirichlet_char_t chi;
acb_t s;
acb_ptr z;
slong prec, i, len;
ulong q, n;
int zfunction, deflate;
if (argc < 2)
{
flint_printf("lvalue [-character q n] [-re a] [-im b] [-prec p] [-z] [-deflate] [-len l]\n\n");
flint_printf("Print value of Dirichlet L-function at s = a+bi.\n");
flint_printf("Default a = 0.5, b = 0, p = 53, (q, n) = (1, 0) (Riemann zeta)\n");
flint_printf("[-z] - compute Z(s) instead of L(s)\n");
flint_printf("[-deflate] - remove singular term at s = 1\n");
flint_printf("[-len l] - compute l terms in Taylor series at s\n");
return 1;
}
acb_init(s);
zfunction = 0;
prec = 53;
q = 1;
n = 0;
len = 1;
deflate = 0;
acb_set_d(s, 0.5);
for (i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "-prec"))
{
prec = atol(argv[i+1]);
}
}
for (i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "-character"))
{
q = atol(argv[i+1]);
n = atol(argv[i+2]);
}
else if (!strcmp(argv[i], "-len"))
{
len = atol(argv[i+1]);
}
else if (!strcmp(argv[i], "-z"))
{
zfunction = 1;
}
else if (!strcmp(argv[i], "-deflate"))
{
deflate = 1;
}
else if (!strcmp(argv[i], "-re"))
{
arb_set_str(acb_realref(s), argv[i+1], prec);
}
else if (!strcmp(argv[i], "-im"))
{
arb_set_str(acb_imagref(s), argv[i+1], prec);
}
}
if (n_gcd(q, n) != 1)
{
flint_printf("need gcd(q,n) = 1 to define a character\n");
flint_abort();
}
z = _acb_vec_init(len);
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
dirichlet_char_log(chi, G, n);
TIMEIT_ONCE_START;
if (zfunction)
acb_dirichlet_hardy_z(z, s, G, chi, len, prec);
else
acb_dirichlet_l_jet(z, s, G, chi, deflate, len, prec);
for (i = 0; i < len; i++)
{
if (i == 0)
flint_printf("%s(s) = ", zfunction ? "Z" : "L");
else if (i == 1)
flint_printf("%s'(s) = ", zfunction ? "Z" : "L");
else
flint_printf("[x^%wd] %s(s+x) = ", i, zfunction ? "Z" : "L");
acb_printn(z + i, prec * 0.333 + 1, 0);
flint_printf("\n");
}
TIMEIT_ONCE_STOP;
print_memory_usage();
_acb_vec_clear(z, len);
acb_clear(s);
dirichlet_char_clear(chi);
dirichlet_group_clear(G);
flint_cleanup();
return 0;
}
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