Esempio n. 1
0
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);
    }
}
Esempio n. 3
0
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);
}
Esempio n. 4
0
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;
}
Esempio n. 5
0
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;
}