  The application of computer algebra system Piranha to the investigation of
the planetary problem is described in this work. Piranha is an echeloned
Poisson series processor authored by F. Biscani from Max Planck Institute for
Astronomy in Heidelberg. Using Piranha the averaged semi-analytical motion
theory of four-planetary system is constructed up to the second degree of
planetary masses. In this work we use the algorithm of the Hamiltonian
expansion into the Poisson series in only orbital elements without other
variables. The motion equations are obtained analytically in time-averaged
elements by Hori-Deprit method. Piranha showed high-performance of analytical
manipulations. Different properties of obtained series are discussed. The
numerical integration of the motion equations is performed by Everhart method
for the Solar system's giant-planets and some exoplanetary systems.
