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);
}
void
acb_dirichlet_chi_vec(acb_ptr v, const dirichlet_group_t G, const dirichlet_char_t chi, slong nv, slong prec)
{
slong k;
ulong * a, order;
acb_dirichlet_roots_t t;
a = flint_malloc(nv * sizeof(ulong));
order = dirichlet_order_char(G, chi);
dirichlet_chi_vec_order(a, G, chi, order, nv);
acb_dirichlet_roots_init(t, order, nv, prec);
acb_zero(v + 0);
for (k = 0; k < nv; k++)
{
if (a[k] != DIRICHLET_CHI_NULL)
acb_dirichlet_root(v + k, t, a[k], prec);
else
acb_zero(v + k);
}
acb_dirichlet_roots_clear(t);
flint_free(a);
}
void
acb_dirichlet_theta_arb(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, const arb_t t, slong prec)
{
slong len;
ulong order;
arb_t xt;
mag_t e;
len = acb_dirichlet_theta_length(G->q, t, prec);
arb_init(xt);
_acb_dirichlet_theta_argument_at_arb(xt, G->q, t, prec);
mag_init(e);
mag_tail_kexpk2_arb(e, xt, len);
arb_neg(xt, xt);
arb_exp(xt, xt, prec);
/* TODO: tune this limit */
order = dirichlet_order_char(G, chi);
if (order < 30)
_acb_dirichlet_theta_arb_smallorder(res, G, chi, xt, len, prec);
else
_acb_dirichlet_theta_arb_naive(res, G, chi, xt, len, prec);
arb_add_error_mag(acb_realref(res), e);
arb_add_error_mag(acb_imagref(res), e);
mag_clear(e);
acb_mul_2exp_si(res, res, 1);
arb_clear(xt);
}
static ulong
do_charplusorder(ulong q1, ulong q2)
{
ulong n, q, k;
for (n = 0, q = q1; q <= q2; q++)
{
dirichlet_group_t G;
dirichlet_char_t x;
dirichlet_group_init(G, q);
dirichlet_char_init(x, G);
dirichlet_char_one(x, G);
n++;
for (; dirichlet_char_next(x, G) >= 0; n++)
dirichlet_order_char(G, x);
dirichlet_char_clear(x);
dirichlet_group_clear(G);
}
return n;
}
void
_acb_dirichlet_theta_arb_naive(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, const arb_t xt, slong len, slong prec)
{
ulong order, * a;
acb_dirichlet_roots_t z;
int parity;
parity = dirichlet_parity_char(G, chi);
order = dirichlet_order_char(G, chi);
a = flint_malloc(len * sizeof(ulong));
dirichlet_chi_vec_order(a, G, chi, order, len);
acb_dirichlet_roots_init(z, order, len, prec);
acb_dirichlet_qseries_arb_powers_naive(res, xt, parity, a, z, len, prec);
acb_dirichlet_roots_clear(z);
flint_free(a);
}
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;
}
