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, bits;
flint_rand_t state;
flint_printf("properties....");
fflush(stdout);
flint_randinit(state);
for (bits = 5; bits <= 30; bits += 5)
{
for (iter = 0; iter < 50; iter++)
{
dirichlet_group_t G;
dirichlet_char_t chi, psi;
ulong q, iter2;
q = 2 + n_randint(state, 1 << bits);
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
dirichlet_char_init(psi, G);
/* check number char properties */
for (iter2 = 0; iter2 < 100; iter2++)
{
ulong m, n;
ulong p1, p2, pairing, cm, cn, q2, q3;
dirichlet_group_t G2, G3;
dirichlet_char_t chi2, chi3;
if (iter2 == 50)
dirichlet_group_dlog_precompute(G, 5);
/* one random character */
do
m = n_randint(state, q);
while (n_gcd(q, m) > 1);
dirichlet_char_log(chi, G, m);
p1 = dirichlet_order_ui(G, m);
p2 = dirichlet_order_char(G, chi);
check_eq(p1, p2, q, m, "order m", "order chi");
p1 = dirichlet_conductor_ui(G, m);
p2 = dirichlet_conductor_char(G, chi);
check_eq(p1, p2, q, m, "conductor m", "conductor chi");
p1 = dirichlet_parity_ui(G, m);
p2 = dirichlet_parity_char(G, chi);
check_eq(p1, p2, q, m, "parity m", "parity chi");
p1 = dirichlet_char_is_real(G, chi);
p2 = (dirichlet_order_char(G, chi) <= 2);
check_eq(p1, p2, q, m, "is_real", "(order <= 2)");
/* check index */
p1 = dirichlet_index_char(G, chi);
dirichlet_char_index(psi, G, p1);
if (!dirichlet_char_eq_deep(G, chi, psi))
{
flint_printf("FAIL: index\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("chi = "); dirichlet_char_print(G, chi);
flint_printf("\n\nindex(chi) = %wu\n\n", p1);
flint_printf("psi(index) = %wu\n\n", psi->n);
flint_printf("psi = "); dirichlet_char_print(G, psi);
flint_printf("\n\n");
abort();
}
/* lift to higher modulus */
q2 = q * (1 + n_randint(state, 100));
dirichlet_group_init(G2, q2);
dirichlet_char_init(chi2, G2);
dirichlet_char_lift(chi2, G2, chi, G);
p1 = dirichlet_conductor_char(G, chi);
p2 = dirichlet_conductor_char(G2, chi2);
check_eq(p1, p2, q, m, "conductor chi", "conductor lift");
p1 = dirichlet_order_char(G, chi);
p2 = dirichlet_order_char(G2, chi2);
check_eq(p1, p2, q, m, "order chi", "order lift");
/* and lower */
dirichlet_char_lower(psi, G, chi2, G2);
if (!dirichlet_char_eq_deep(G, chi, psi))
{
flint_printf("FAIL: lift and lower back\n\n");
flint_printf("q = %wu\n\nchi = ", q);
dirichlet_char_print(G, chi);
flint_printf("\n\nq2 = %wu\n\nchi2 = ", q2);
dirichlet_char_print(G2, chi2);
flint_printf("\n\nq = %wu\n\npsi = ", q);
dirichlet_char_print(G, psi);
flint_printf("\n\n");
abort();
}
q3 = dirichlet_conductor_char(G, chi) * random_divisor(state, G);
q3 = n_gcd(q, q3);
dirichlet_group_init(G3, q3);
dirichlet_char_init(chi3, G3);
dirichlet_char_lower(chi3, G3, chi2, G2);
p1 = dirichlet_conductor_char(G, chi);
p2 = dirichlet_conductor_char(G3, chi3);
check_eq(p1, p2, q, m, "conductor chi", "conductor lower");
p1 = dirichlet_order_char(G, chi);
p2 = dirichlet_order_char(G3, chi3);
check_eq(p1, p2, q, m, "order chi", "order lower");
dirichlet_char_clear(chi3);
dirichlet_group_clear(G3);
dirichlet_char_clear(chi2);
dirichlet_group_clear(G2);
/* another random character */
do
n = n_randint(state, q);
while (n_gcd(q, n) > 1);
dirichlet_char_log(psi, G, n);
pairing = dirichlet_pairing(G, m, n);
cn = dirichlet_chi(G, chi, n);
cm = dirichlet_chi(G, psi, m);
if (pairing != cn || pairing != cm)
{
flint_printf("FAIL: pairing\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("n = %wu\n\n", n);
flint_printf("chi(m,n) = %wu\n\n", pairing);
flint_printf("chi(m)(n) = %wu\n\n", cn);
flint_printf("chi(n)(m) = %wu\n\n", cm);
abort();
}
}
dirichlet_group_dlog_clear(G);
dirichlet_char_clear(chi);
dirichlet_char_clear(psi);
dirichlet_group_clear(G);
}
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
