Mathematical Problems in Engineering
Volume 2004 (2004), Issue 5, Pages 411-451

Asymptotic-group analysis of algebraic equations

A. D. Shamrovskii,1 I. V. Andrianov,2 and J. Awrejcewicz3

1Zaporoshye State Engineering Academy, Department of Software for Automatic Systems, pr. Lenina 226, Zaporoshye UA-69006, Ukraine
2Institut für Allgemeine Mechanik der RWTH Aachen, Templergraben 64, Aachen 52062, Germany
3Department of Automatics and Biomechanics, Technical University of Łódź, Łódź 90-924, Poland

Received 15 June 2004

Copyright © 2004 A. D. Shamrovskii et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Both the method of asymptotic analysis and the theory of extension group are applied to study the Descates equation. The proposed algorithm allows to obtain various variants of simplification and can be easily generalized to their algebraic and differential equations.