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);
}
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);
}
