The paper describes an evaluation of c~clicity for a planar system of ODF, with a cubic polynomial right side.This problem is the important, as it is a suhproblem of the famous XIrI-th Hilbert problem.Estimations of cyclicity and c'onditious for a center art! calculated by direct computer alge}]ra methods for the cubic homogeneous and some extrnsirmsof thrhomogmrmuscase.In particular the 5 (complex) parametm case is investigated for the first time.For a lligllor{ter Lya~}llllov focllsclllantitiesc alculation a modular arithmetic is used, The NORT and GROEBNER packages under REDUCE-3.6systcm wet-e applied.

This article describes the Standard LISP program for building a normal form and a corresponding normalizing transformation of a system of ordinary differential equations (ODE) in Bruno's notation [1] up to the specified order.This program includes also a complete set of procedures of arithmetic for the truncated power series and input/output services.This gives us an opportunity to continue a treatment of obtained results autonomically or in a REDUCE environment.The program can work in a rational arithmetic or in an approximate rational arithmetic, or in a float point arithmetic.The program usage is illustrated by treating systems of weakly nonlinear ODES in the language of the truncated series.The approximate solution is produced from the normal form calculated up to enough high order and from the corresponding normalizing transformation.This method demonstrates rather good agreement with numerical solutions of some well known equations.