int main()
{
slong iter;
flint_rand_t state;
flint_printf("l....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t s, t, u;
dirichlet_group_t G;
dirichlet_char_t chi;
ulong q, k;
slong prec;
acb_init(s);
acb_init(t);
acb_init(u);
q = 1 + n_randint(state, 50);
prec = 2 + n_randint(state, 100);
k = n_randint(state, n_euler_phi(q));
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
dirichlet_char_index(chi, G, k);
if (n_randint(state, 2))
acb_set_si(s, n_randint(state, 50) - 25);
else
acb_randtest(s, state, 2 + n_randint(state, 200), 2);
acb_dirichlet_l_hurwitz(t, s, NULL, G, chi, prec);
acb_dirichlet_l(u, s, G, chi, prec);
if (!acb_overlaps(t, u))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("iter = %ld q = %lu k = %lu prec = %ld\n\n", iter, q, k, prec);
flint_printf("s = "); acb_printn(s, 100, 0); flint_printf("\n\n");
flint_printf("t = "); acb_printn(t, 100, 0); flint_printf("\n\n");
flint_printf("u = "); acb_printn(u, 100, 0); flint_printf("\n\n");
abort();
}
dirichlet_char_clear(chi);
dirichlet_group_clear(G);
acb_clear(s);
acb_clear(t);
acb_clear(u);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
arith_cos_minpoly(fmpz_poly_t poly, ulong n)
{
if (n == 0)
{
fmpz_poly_set_ui(poly, UWORD(1));
}
else
{
slong d = (n <= 2) ? 1 : n_euler_phi(n) / 2;
fmpz_poly_fit_length(poly, d + 1);
_arith_cos_minpoly(poly->coeffs, d, n);
_fmpz_poly_set_length(poly, d + 1);
}
}
void arith_euler_phi(fmpz_t res, const fmpz_t n)
{
fmpz_factor_t factors;
fmpz_t t;
ulong exp;
slong i;
if (fmpz_sgn(n) <= 0)
{
fmpz_zero(res);
return;
}
if (fmpz_abs_fits_ui(n))
{
fmpz_set_ui(res, n_euler_phi(fmpz_get_ui(n)));
return;
}
fmpz_factor_init(factors);
fmpz_factor(factors, n);
fmpz_one(res);
fmpz_init(t);
for (i = 0; i < factors->num; i++)
{
fmpz_sub_ui(t, factors->p + i, UWORD(1));
fmpz_mul(res, res, t);
exp = factors->exp[i];
if (exp != 1)
{
fmpz_pow_ui(t, factors->p + i, exp - UWORD(1));
fmpz_mul(res, res, t);
}
}
fmpz_clear(t);
fmpz_factor_clear(factors);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("chi....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t zn1, zn2, zn1n2, zn1zn2;
dirichlet_group_t G;
dirichlet_char_t chi;
ulong q, m, n1, n2, iter2;
int res;
q = 1 + n_randint(state, 1000);
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
acb_init(zn1);
acb_init(zn2);
acb_init(zn1n2);
acb_init(zn1zn2);
/* check chi(n1) chi(n2) = chi(n1 n2) */
for (iter2 = 0; iter2 < 10; iter2++)
{
do {
m = 1 + n_randint(state, q);
} while (n_gcd(q, m) != 1);
dirichlet_char_log(chi, G, m);
n1 = n_randint(state, 1000);
n2 = n_randint(state, 1000);
acb_dirichlet_chi(zn1, G, chi, n1, 53);
acb_dirichlet_pairing(zn2, G, m, n1, 53);
if (!acb_overlaps(zn1, zn2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("n = %wu\n\n", n1);
flint_printf("char = "); acb_printd(zn1, 15); flint_printf("\n\n");
flint_printf("pairing = "); acb_printd(zn2, 15); flint_printf("\n\n");
dirichlet_char_print(G, chi);
dirichlet_char_log(chi, G, m);
flint_printf("log(m) = "); dirichlet_char_print(G, chi);
dirichlet_char_log(chi, G, n1);
flint_printf("log(n1) = "); dirichlet_char_print(G, chi);
flint_abort();
}
acb_dirichlet_pairing(zn2, G, m, n2, 53);
acb_dirichlet_pairing(zn1n2, G, m, n1 * n2, 53);
acb_mul(zn1zn2, zn1, zn2, 53);
if (!acb_overlaps(zn1n2, zn1zn2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("n1 = %wu\n\n", n1);
flint_printf("n2 = %wu\n\n", n2);
flint_printf("zn1 = "); acb_printd(zn1, 15); flint_printf("\n\n");
flint_printf("zn2 = "); acb_printd(zn2, 15); flint_printf("\n\n");
flint_printf("zn1n2 = "); acb_printd(zn1n2, 15); flint_printf("\n\n");
flint_printf("zn1zn2 = "); acb_printd(zn1zn2, 15); flint_printf("\n\n");
flint_abort();
}
}
if (iter % 10 == 0)
{
/* check orthogonality */
acb_zero(zn1);
n1 = n_randint(state, 1000);
for (m = 1; m <= q; m++)
{
if (n_gcd(q, m) == 1)
{
acb_dirichlet_pairing(zn2, G, m, n1, 53);
acb_add(zn1, zn1, zn2, 53);
}
}
if (n1 % q == 1 % q)
res = arb_contains_si(acb_realref(zn1), n_euler_phi(q)) &&
arb_contains_zero(acb_imagref(zn1));
else
res = acb_contains_zero(zn1);
if (!res)
{
flint_printf("FAIL: orthogonality\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("phi = %wu\n\n", n_euler_phi(q));
flint_printf("n1 = %wu\n\n", n1);
flint_printf("zn1 = "); acb_printd(zn1, 15); flint_printf("\n\n");
flint_abort();
}
}
dirichlet_group_clear(G);
dirichlet_char_clear(chi);
acb_clear(zn1);
acb_clear(zn2);
acb_clear(zn1n2);
acb_clear(zn1zn2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("hardy_z....");
fflush(stdout);
flint_randinit(state);
/* test self-consistency */
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t s, s2;
dirichlet_group_t G;
dirichlet_char_t chi;
acb_ptr vec1, vec2;
slong len1, len2;
slong prec1, prec2;
ulong q, k;
slong i;
len1 = n_randint(state, 6);
len2 = n_randint(state, 6);
prec1 = 2 + n_randint(state, 100);
prec2 = 2 + n_randint(state, 100);
do {
q = 1 + n_randint(state, 30);
} while (q % 4 == 2);
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
do {
k = n_randint(state, n_euler_phi(q));
dirichlet_char_index(chi, G, k);
} while (dirichlet_conductor_char(G, chi) != q);
acb_init(s);
acb_init(s2);
vec1 = _acb_vec_init(len1);
vec2 = _acb_vec_init(len2);
acb_randtest(s, state, 2 + n_randint(state, 200), 2);
acb_randtest(s2, state, 2 + n_randint(state, 200), 2);
acb_sub(s2, s2, s2, 200);
acb_add(s2, s, s2, 200);
acb_dirichlet_hardy_z(vec1, s, G, chi, len1, prec1);
acb_dirichlet_hardy_z(vec2, s2, G, chi, len2, prec2);
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();
}
}
if (arb_contains_zero(acb_imagref(s)))
{
for (i = 0; i < len1; i++)
{
if (!arb_contains_zero(acb_imagref(vec1 + i)))
{
flint_printf("FAIL: real 1\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_abort();
}
}
}
if (arb_contains_zero(acb_imagref(s2)))
{
for (i = 0; i < len2; i++)
{
if (!arb_contains_zero(acb_imagref(vec2 + i)))
{
flint_printf("FAIL: real 1\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(vec2 + i, 50, 0); flint_printf("\n\n");
flint_abort();
}
}
}
dirichlet_char_clear(chi);
dirichlet_group_clear(G);
acb_clear(s);
acb_clear(s2);
_acb_vec_clear(vec1, len1);
_acb_vec_clear(vec2, len2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}