C++ (Cpp) acb_dirichlet_chi Examples

Example #1

File: l.c Project: argriffing/arb

void
acb_dirichlet_l(acb_t res, const acb_t s,
    const acb_dirichlet_group_t G, ulong m, slong prec)
{
    acb_t chi, t, u, a;
    ulong k;

    acb_init(chi);
    acb_init(t);
    acb_init(u);
    acb_init(a);

    acb_zero(t);

    for (k = 1; k <= G->q; k++)
    {
        acb_dirichlet_chi(chi, G, m, k, prec);

        if (!acb_is_zero(chi))
        {
            acb_set_ui(a, k);
            acb_div_ui(a, a, G->q, prec);
            acb_hurwitz_zeta(u, s, a, prec);
            acb_addmul(t, chi, u, prec);
        }
    }

    acb_set_ui(u, G->q);
    acb_neg(a, s);
    acb_pow(u, u, a, prec);
    acb_mul(res, t, u, prec);

    acb_clear(chi);
    acb_clear(t);
    acb_clear(u);
    acb_clear(a);
}

Example #2

File: t-chi.c Project: fredrik-johansson/arb

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;
}