void fmpq_poly_derivative(fmpq_poly_t res, const fmpq_poly_t poly)
{
slong len = poly->length;
if (len < 2)
{
fmpq_poly_zero(res);
return;
}
fmpq_poly_fit_length(res, len - 1);
_fmpq_poly_derivative(res->coeffs, res->den, poly->coeffs, poly->den, len);
_fmpq_poly_set_length(res, len - 1);
}
void _fmpq_poly_log_series(fmpz * g, fmpz_t gden,
const fmpz * f, const fmpz_t fden, long n)
{
fmpz * f_diff;
fmpz * f_inv;
fmpz_t f_diff_den;
fmpz_t f_inv_den;
f_diff = _fmpz_vec_init(n);
f_inv = _fmpz_vec_init(n);
fmpz_init(f_diff_den);
fmpz_init(f_inv_den);
_fmpq_poly_derivative(f_diff, f_diff_den, f, fden, n);
_fmpq_poly_inv_series(f_inv, f_inv_den, f, fden, n);
_fmpq_poly_mullow(g, gden, f_diff, f_diff_den, n - 1, f_inv, f_inv_den, n - 1, n - 1);
_fmpq_poly_integral(g, gden, g, gden, n);
_fmpz_vec_clear(f_diff, n);
_fmpz_vec_clear(f_inv, n);
fmpz_clear(f_diff_den);
fmpz_clear(f_inv_den);
}
