  We study integrability of the Euler-Poisson equations describing the motion
of a rigid body with one fixed point in a constant gravity field. Using the
Morales-Ramis theory and tools of differential algebra we prove that a
symmetric heavy top is integrable only in the classical cases of Euler,
Lagrange, and Kovalevskaya and is partially integrable only in the
Goryachev-Chaplygin case. Our proof is alternative to that given by Ziglin
({\em Funktsional. Anal. i Prilozhen.}, 17(1):8--23, 1983; {\em Funktsional.
Anal. i Prilozhen.}, 31(1):3--11, 95, 1997).
