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\centerline{\bf Tools for Symbolic-Numeric Solving of Differential Equations}
\centerline{\bf with Polynomial Nonlinearity in APS System}

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\centerline{V.Bilenko, P.Denisenko, A.Letichevsky, and V. Volkov}
\centerline{Glushkov Institute of Cybernetics of}
\centerline{National Academy of Sciences of Ukraine}
\centerline{Glushkov prospekt 40}
\centerline{252650 Kiev, Ukraine}
\centerline{Email: vlad@d105.icyb.kiev.ua}

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     The presented method gives the optimal by accuracy approximation in
Chebyshev metric for Linear Differential Equations with a singular
point and Differential Equations with Polynomial Nonlinearity.
In the solving process of the last case appears the system of algebraic
equations. The technique of Grobner Basis may be applied successfully for
finding of roots.
     Algorithms developed for solving DE  have been designed
by means of special packages of APS which supports the various computation
in a polynomial algebra. The main programming technique used in APS is
rewriting-rule-based programming.

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