コード例 #1
0
void
acb_poly_agm1_series(acb_poly_t res, const acb_poly_t z, long n, long prec)
{
    if (n == 0)
    {
        acb_poly_zero(res);
        return;
    }

    acb_poly_fit_length(res, n);

    if (z->length == 0)
    {
        acb_t t;
        acb_init(t);
        _acb_poly_agm1_series(res->coeffs, t, 1, n, prec);
        acb_clear(t);
    }
    else
    {
        _acb_poly_agm1_series(res->coeffs, z->coeffs, z->length, n, prec);
    }

    _acb_poly_set_length(res, n);
    _acb_poly_normalise(res);
}
コード例 #2
0
void
acb_poly_revert_series_lagrange_fast(acb_poly_t Qinv,
                                    const acb_poly_t Q, slong n, slong prec)
{
    slong Qlen = Q->length;

    if (Qlen < 2 || !acb_is_zero(Q->coeffs)
                 || acb_contains_zero(Q->coeffs + 1))
    {
        flint_printf("Exception (acb_poly_revert_series_lagrange_fast). Input \n"
               "must have zero constant term and nonzero coefficient of x^1.\n");
        abort();
    }

    if (Qinv != Q)
    {
        acb_poly_fit_length(Qinv, n);
        _acb_poly_revert_series_lagrange_fast(Qinv->coeffs, Q->coeffs, Qlen, n, prec);
    }
    else
    {
        acb_poly_t t;
        acb_poly_init2(t, n);
        _acb_poly_revert_series_lagrange_fast(t->coeffs, Q->coeffs, Qlen, n, prec);
        acb_poly_swap(Qinv, t);
        acb_poly_clear(t);
    }

    _acb_poly_set_length(Qinv, n);
    _acb_poly_normalise(Qinv);
}
コード例 #3
0
ファイル: inv_series.c プロジェクト: fredrik-johansson/arb
void
acb_poly_inv_series(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec)
{
    if (n == 0)
    {
        acb_poly_zero(Qinv);
        return;
    }

    if (Q->length == 0)
    {
        acb_poly_fit_length(Qinv, n);
        _acb_vec_indeterminate(Qinv->coeffs, n);
        _acb_poly_set_length(Qinv, n);
        return;
    }

    if (Qinv == Q)
    {
        acb_poly_t t;
        acb_poly_init(t);
        acb_poly_inv_series(t, Q, n, prec);
        acb_poly_swap(Qinv, t);
        acb_poly_clear(t);
        return;
    }

    acb_poly_fit_length(Qinv, n);
    _acb_poly_inv_series(Qinv->coeffs, Q->coeffs, Q->length, n, prec);
    _acb_poly_set_length(Qinv, n);
    _acb_poly_normalise(Qinv);
}
コード例 #4
0
ファイル: add_si.c プロジェクト: argriffing/arb
void
acb_poly_add_si(acb_poly_t res, const acb_poly_t x, slong y, slong prec)
{
    slong len = x->length;

    if (len == 0)
    {
        acb_poly_set_si(res, y);
    }
    else
    {
        acb_poly_fit_length(res, len);

        if (y >= 0)
            acb_add_ui(res->coeffs, x->coeffs, y, prec);
        else
            acb_sub_ui(res->coeffs, x->coeffs, -y, prec);

        if (res != x)
            _acb_vec_set(res->coeffs + 1, x->coeffs + 1, len - 1);

        _acb_poly_set_length(res, len);
        _acb_poly_normalise(res);
    }
}
コード例 #5
0
void
acb_dirichlet_hardy_z_series(acb_poly_t res, const acb_poly_t s,
    const dirichlet_group_t G, const dirichlet_char_t chi,
    slong len, slong prec)
{
    if (len == 0)
    {
        acb_poly_zero(res);
        return;
    }

    acb_poly_fit_length(res, len);

    if (s->length == 0)
    {
        acb_t t;
        acb_init(t);
        _acb_dirichlet_hardy_z_series(res->coeffs, t, 1, G, chi, len, prec);
        acb_clear(t);
    }
    else
    {
        _acb_dirichlet_hardy_z_series(res->coeffs, s->coeffs, s->length, G, chi, len, prec);
    }

    _acb_poly_set_length(res, len);
    _acb_poly_normalise(res);
}
コード例 #6
0
ファイル: pow_ui.c プロジェクト: isuruf/arb
void
acb_poly_pow_ui(acb_poly_t res,
    const acb_poly_t poly, ulong exp, slong prec)
{
    slong flen, rlen;

    flen = poly->length;

    if (exp == 0)
    {
        acb_poly_one(res);
    }
    else if (flen == 0)
    {
        acb_poly_zero(res);
    }
    else
    {
        rlen = exp * (flen - 1) + 1;

        if (res != poly)
        {
            acb_poly_fit_length(res, rlen);
            _acb_poly_pow_ui(res->coeffs,
                poly->coeffs, flen, exp, prec);
            _acb_poly_set_length(res, rlen);
            _acb_poly_normalise(res);
        }
        else
        {
            acb_poly_t t;
            acb_poly_init2(t, rlen);
            _acb_poly_pow_ui(t->coeffs,
                poly->coeffs, flen, exp, prec);
            _acb_poly_set_length(t, rlen);
            _acb_poly_normalise(t);
            acb_poly_swap(res, t);
            acb_poly_clear(t);
        }
    }
}
コード例 #7
0
void
acb_poly_pow_ui_trunc_binexp(acb_poly_t res,
    const acb_poly_t poly, ulong exp, long len, long prec)
{
    long flen, rlen;

    flen = poly->length;

    if (exp == 0 && len != 0)
    {
        acb_poly_one(res);
    }
    else if (flen == 0 || len == 0)
    {
        acb_poly_zero(res);
    }
    else
    {
        rlen = poly_pow_length(flen, exp, len);

        if (res != poly)
        {
            acb_poly_fit_length(res, rlen);
            _acb_poly_pow_ui_trunc_binexp(res->coeffs,
                poly->coeffs, flen, exp, rlen, prec);
            _acb_poly_set_length(res, rlen);
            _acb_poly_normalise(res);
        }
        else
        {
            acb_poly_t t;
            acb_poly_init2(t, rlen);
            _acb_poly_pow_ui_trunc_binexp(t->coeffs,
                poly->coeffs, flen, exp, rlen, prec);
            _acb_poly_set_length(t, rlen);
            _acb_poly_normalise(t);
            acb_poly_swap(res, t);
            acb_poly_clear(t);
        }
    }
}
コード例 #8
0
ファイル: lgamma_series.c プロジェクト: argriffing/arb
void
acb_poly_lgamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec)
{
    acb_poly_fit_length(res, n);

    if (f->length == 0 || n == 0)
        _acb_vec_indeterminate(res->coeffs, n);
    else
        _acb_poly_lgamma_series(res->coeffs, f->coeffs, f->length, n, prec);

    _acb_poly_set_length(res, n);
    _acb_poly_normalise(res);
}
コード例 #9
0
ファイル: set_coeff_si.c プロジェクト: argriffing/arb
void
acb_poly_set_coeff_si(acb_poly_t poly, slong n, slong x)
{
    acb_poly_fit_length(poly, n + 1);

    if (n + 1 > poly->length)
    {
        _acb_vec_zero(poly->coeffs + poly->length, n - poly->length);
        poly->length = n + 1;
    }

    acb_set_si(poly->coeffs + n, x);
    _acb_poly_normalise(poly);
}
コード例 #10
0
ファイル: add.c プロジェクト: UBunt14/SourceOfBasicLibraries
void
acb_poly_add(acb_poly_t res, const acb_poly_t poly1,
              const acb_poly_t poly2, long prec)
{
    long max = FLINT_MAX(poly1->length, poly2->length);

    acb_poly_fit_length(res, max);

    _acb_poly_add(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs,
                   poly2->length, prec);

    _acb_poly_set_length(res, max);
    _acb_poly_normalise(res);
}
コード例 #11
0
ファイル: rgamma_series.c プロジェクト: isuruf/arb
void
acb_poly_rgamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec)
{
    if (f->length == 0 || n == 0)
    {
        acb_poly_zero(res);
    }
    else
    {
        acb_poly_fit_length(res, n);
        _acb_poly_rgamma_series(res->coeffs, f->coeffs, f->length, n, prec);
        _acb_poly_set_length(res, n);
        _acb_poly_normalise(res);
    }
}
コード例 #12
0
ファイル: atan_series.c プロジェクト: argriffing/arb
void
acb_poly_atan_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec)
{
    slong hlen = h->length;

    if (hlen == 0 || n == 0)
    {
        acb_poly_zero(g);
        return;
    }

    acb_poly_fit_length(g, n);
    _acb_poly_atan_series(g->coeffs, h->coeffs, hlen, n, prec);
    _acb_poly_set_length(g, n);
    _acb_poly_normalise(g);
}
コード例 #13
0
ファイル: interpolate_fast.c プロジェクト: argriffing/arb
void
acb_poly_interpolate_fast(acb_poly_t poly,
        acb_srcptr xs, acb_srcptr ys, slong n, slong prec)
{
    if (n == 0)
    {
        acb_poly_zero(poly);
    }
    else
    {
        acb_poly_fit_length(poly, n);
        _acb_poly_set_length(poly, n);
        _acb_poly_interpolate_fast(poly->coeffs, xs, ys, n, prec);
        _acb_poly_normalise(poly);
    }
}
コード例 #14
0
ファイル: add_series.c プロジェクト: fredrik-johansson/arb
void
acb_poly_add_series(acb_poly_t res, const acb_poly_t poly1,
              const acb_poly_t poly2, slong len, slong prec)
{
    slong len1, len2;

    len1 = poly1->length;
    len2 = poly2->length;

    len1 = FLINT_MIN(len1, len);
    len2 = FLINT_MIN(len2, len);
    len = FLINT_MAX(len1, len2);

    acb_poly_fit_length(res, len);
    _acb_poly_add(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec);
    _acb_poly_set_length(res, len);
    _acb_poly_normalise(res);
}
コード例 #15
0
ファイル: mullow.c プロジェクト: isuruf/arb
void
acb_poly_mullow(acb_poly_t res, const acb_poly_t poly1,
                                            const acb_poly_t poly2,
                                                slong n, slong prec)
{
    slong len1, len2;

    len1 = poly1->length;
    len2 = poly2->length;

    if (len1 == 0 || len2 == 0 || n == 0)
    {
        acb_poly_zero(res);
        return;
    }

    n = FLINT_MIN((len1 + len2 - 1), n);
    len1 = FLINT_MIN(len1, n);
    len2 = FLINT_MIN(len2, n);

    if (res == poly1 || res == poly2)
    {
        acb_poly_t t;
        acb_poly_init2(t, n);
        _acb_poly_mullow(t->coeffs, poly1->coeffs, len1,
                                poly2->coeffs, len2, n, prec);
        acb_poly_swap(res, t);
        acb_poly_clear(t);
    }
    else
    {
        acb_poly_fit_length(res, n);
        _acb_poly_mullow(res->coeffs, poly1->coeffs, len1,
                                poly2->coeffs, len2, n, prec);
    }

    _acb_poly_set_length(res, n);
    _acb_poly_normalise(res);
}
コード例 #16
0
ファイル: compose.c プロジェクト: argriffing/arb
void acb_poly_compose(acb_poly_t res,
              const acb_poly_t poly1, const acb_poly_t poly2, slong prec)
{
    const slong len1 = poly1->length;
    const slong len2 = poly2->length;
    
    if (len1 == 0)
    {
        acb_poly_zero(res);
    }
    else if (len1 == 1 || len2 == 0)
    {
        acb_poly_set_acb(res, poly1->coeffs);
    }
    else
    {
        const slong lenr = (len1 - 1) * (len2 - 1) + 1;
        
        if (res != poly1 && res != poly2)
        {
            acb_poly_fit_length(res, lenr);
            _acb_poly_compose(res->coeffs, poly1->coeffs, len1,
                                                   poly2->coeffs, len2, prec);
        }
        else
        {
            acb_poly_t t;
            acb_poly_init2(t, lenr);
            _acb_poly_compose(t->coeffs, poly1->coeffs, len1,
                                                 poly2->coeffs, len2, prec);
            acb_poly_swap(res, t);
            acb_poly_clear(t);
        }

        _acb_poly_set_length(res, lenr);
        _acb_poly_normalise(res);
    }
}
コード例 #17
0
ファイル: mullow_classical.c プロジェクト: isuruf/arb
void
acb_poly_mullow_classical(acb_poly_t res, const acb_poly_t poly1,
                                            const acb_poly_t poly2,
                                                slong n, slong prec)
{
    slong len_out;

    if (poly1->length == 0 || poly2->length == 0 || n == 0)
    {
        acb_poly_zero(res);
        return;
    }

    len_out = poly1->length + poly2->length - 1;
    if (n > len_out)
        n = len_out;

    if (res == poly1 || res == poly2)
    {
        acb_poly_t t;
        acb_poly_init2(t, n);
        _acb_poly_mullow_classical(t->coeffs, poly1->coeffs, poly1->length,
                                    poly2->coeffs, poly2->length, n, prec);
        acb_poly_swap(res, t);
        acb_poly_clear(t);
    }
    else
    {
        acb_poly_fit_length(res, n);
        _acb_poly_mullow_classical(res->coeffs, poly1->coeffs, poly1->length,
                                    poly2->coeffs, poly2->length, n, prec);
    }

    _acb_poly_set_length(res, n);
    _acb_poly_normalise(res);
}
コード例 #18
0
void
acb_hypgeom_pfq_series_direct(acb_poly_t res,
    const acb_poly_struct * a, long p,
    const acb_poly_struct * b, long q,
    const acb_poly_t z, int regularized,
    long n, long len, long prec)
{
    acb_poly_t s, t, err;
    arb_poly_t C, T;
    long i;
    int is_real;

    /* default algorithm to choose number of terms */
    if (n < 0)
    {
        n = acb_hypgeom_pfq_series_choose_n(a, p, b, q, z, len, prec);
    }

    acb_poly_init(s);
    acb_poly_init(t);
    acb_poly_init(err);
    arb_poly_init(C);
    arb_poly_init(T);

    acb_hypgeom_pfq_series_sum_forward(s, t, a, p, b, q, z, regularized, n, len, prec);

    if (acb_poly_length(t) != 0)
    {
        is_real = acb_poly_is_real(z);
        for (i = 0; i < p; i++)
            is_real = is_real && acb_poly_is_real(a + i);
        for (i = 0; i < q; i++)
            is_real = is_real && acb_poly_is_real(b + i);

        acb_poly_majorant(T, t, MAG_BITS);
        acb_hypgeom_pfq_series_bound_factor(C, a, p, b, q, z, n, len, MAG_BITS);

        arb_poly_mullow(T, T, C, len, MAG_BITS);

        /* create polynomial of errors */
        acb_poly_fit_length(err, len);

        for (i = 0; i < FLINT_MIN(len, T->length); i++)
        {
            arb_add_error(acb_realref(err->coeffs + i), T->coeffs + i);
            if (!is_real)
                arb_add_error(acb_imagref(err->coeffs + i), T->coeffs + i);
        }

        _acb_poly_set_length(err, len);
        _acb_poly_normalise(err);

        acb_poly_add(s, s, err, prec);
    }

    acb_poly_set(res, s);

    acb_poly_clear(s);
    acb_poly_clear(t);
    acb_poly_clear(err);
    arb_poly_clear(C);
    arb_poly_clear(T);
}
コード例 #19
0
ファイル: pfq_sum_fme.c プロジェクト: fredrik-johansson/arb
static void
evaluate(acb_poly_t A, acb_srcptr a, slong p, const acb_t z, slong n, slong prec)
{
    acb_poly_fit_length(A, p + 1);

    if (p == 1)
    {
        acb_add_ui(A->coeffs, a, n, prec);
        if (z != NULL)
            acb_mul(A->coeffs, A->coeffs, z, prec);
    }
    else if (p == 2)
    {
        acb_add(A->coeffs, a + 0, a + 1, prec);
        acb_add_ui(A->coeffs + 1, A->coeffs, 2 * n, prec);
        acb_add_ui(A->coeffs, A->coeffs, n, prec);
        acb_mul_ui(A->coeffs, A->coeffs, n, prec);
        acb_addmul(A->coeffs, a + 0, a + 1, prec);
        if (z != NULL)
        {
            acb_mul(A->coeffs, A->coeffs, z, prec);
            acb_mul(A->coeffs + 1, A->coeffs + 1, z, prec);
        }
    }
    else if (p == 3)
    {
        acb_t t, u;
        acb_init(t);
        acb_init(u);

        acb_add(t, a + 0, a + 1, prec);
        acb_add(t, t, a + 2, prec);

        acb_mul(u, a + 0, a + 1, prec);
        acb_mul(A->coeffs, u, a + 2, prec);

        acb_addmul(u, a + 0, a + 2, prec);
        acb_addmul(u, a + 1, a + 2, prec);

        /*
        (a0 + n)(a1 + n)(a2 + n) = a0 a1 a2 + (a0 a1 + a0 a2 + a1 a2) n + (a0 + a1 + a2) n^2 + n^3
        (a0 a1 + a0 a2 + a1 a2) + 2 (a0 + a1 + a2) n + 3 n^2
        (a0 + a1 + a2) + 3n
        1
        */

        acb_addmul_ui(A->coeffs, u, n, prec);
        acb_addmul_ui(A->coeffs, t, n * n, prec);
        acb_add_ui(A->coeffs, A->coeffs, n * n * n, prec);

        acb_set(A->coeffs + 1, u);
        acb_addmul_ui(A->coeffs + 1, t, 2 * n, prec);
        acb_add_ui(A->coeffs + 1, A->coeffs + 1, 3 * n * n, prec);

        acb_add_ui(A->coeffs + 2, t, 3 * n, prec);

        if (z != NULL)
        {
            acb_mul(A->coeffs + 0, A->coeffs + 0, z, prec);
            acb_mul(A->coeffs + 1, A->coeffs + 1, z, prec);
            acb_mul(A->coeffs + 2, A->coeffs + 2, z, prec);
        }

        acb_clear(t);
        acb_clear(u);
    }
    else if (p != 0)
    {
        flint_abort();
    }

    if (z != NULL)
        acb_set(A->coeffs + p, z);
    else
        acb_one(A->coeffs + p);

    _acb_poly_set_length(A, p + 1);
    _acb_poly_normalise(A);
}
コード例 #20
0
ファイル: pfq_series_direct.c プロジェクト: jdemeyer/arb
void
acb_hypgeom_pfq_series_direct(acb_poly_t res,
    const acb_poly_struct * a, long p,
    const acb_poly_struct * b, long q,
    const acb_poly_t z, int regularized,
    long n, long len, long prec)
{
    acb_poly_t s, t, err;
    arb_poly_t C, T;
    long i;
    int is_real;
    int terminating;

    /* default algorithm to choose number of terms */
    if (n < 0)
    {
        n = acb_hypgeom_pfq_series_choose_n(a, p, b, q, z, len, prec);
    }

    terminating = 0;

    /* check if it terminates due to a root of the numerator */
    for (i = 0; i < p; i++)
    {
        if (acb_poly_length(a + i) == 0 && n > 0)
        {
            terminating = 1;
        }
        else if (acb_poly_length(a + i) == 1)
        {
            acb_srcptr c = acb_poly_get_coeff_ptr(a + i, 0);

            if (acb_is_int(c) && arb_is_negative(acb_realref(c)) &&
                arf_cmpabs_ui(arb_midref(acb_realref(c)), n) < 0)
            {
                terminating = 1;
            }
        }
    }

    /* check if it terminates (to order n) due to z */
    /* the following tests could be made stronger... */
    if (z->length == 0 && n >= 1)
    {
        terminating = 1;
    }
    else if (!terminating && z->length > 0 && acb_is_zero(z->coeffs) && n >= len)
    {
        if (regularized)
        {
            terminating = 1;
        }
        else
        {
            terminating = 1;

            for (i = 0; i < q; i++)
            {
                acb_srcptr c = acb_poly_get_coeff_ptr(b + i, 0);

                if (!arb_is_positive(acb_realref(c)) && acb_contains_int(c))
                    terminating = 0;
            }
        }
    }

    acb_poly_init(s);
    acb_poly_init(t);
    acb_poly_init(err);
    arb_poly_init(C);
    arb_poly_init(T);

    acb_hypgeom_pfq_series_sum_forward(s, t, a, p, b, q, z, regularized, n, len, prec);

    if (!terminating)
    {
        is_real = acb_poly_is_real(z);
        for (i = 0; i < p; i++)
            is_real = is_real && acb_poly_is_real(a + i);
        for (i = 0; i < q; i++)
            is_real = is_real && acb_poly_is_real(b + i);

        acb_poly_majorant(T, t, MAG_BITS);
        acb_hypgeom_pfq_series_bound_factor(C, a, p, b, q, z, n, len, MAG_BITS);

        if (!_arb_vec_is_finite(T->coeffs, T->length) ||
            !_arb_vec_is_finite(C->coeffs, C->length))
        {
            arb_poly_fit_length(T, len);
            _arb_vec_indeterminate(T->coeffs, len);
            _arb_poly_set_length(T, len);
        }
        else
        {
            arb_poly_mullow(T, T, C, len, MAG_BITS);
        }

        /* create polynomial of errors */
        acb_poly_fit_length(err, len);

        for (i = 0; i < FLINT_MIN(len, T->length); i++)
        {
            arb_add_error(acb_realref(err->coeffs + i), T->coeffs + i);
            if (!is_real)
                arb_add_error(acb_imagref(err->coeffs + i), T->coeffs + i);
        }

        _acb_poly_set_length(err, len);
        _acb_poly_normalise(err);

        acb_poly_add(s, s, err, prec);
    }

    acb_poly_set(res, s);

    acb_poly_clear(s);
    acb_poly_clear(t);
    acb_poly_clear(err);
    arb_poly_clear(C);
    arb_poly_clear(T);
}