An Algorithm for Nonparametric Decomposition of Differential Polynomials

Abstract

Last decades, one of the most important problems of symbolic computations (see l7r) is the development of algorithms for solving algebraic and differential equations, in particular, those for factoring linear ordinary differential operators (LODO) l1–4r. In this paper, the problems of LODO factorization and decomposition of ordinary polynomials l5, 6r are generalized: an algorithm is proposed for decomposition of differential polynomials that allows one to find a particular solution to a complex algebraic differential equation (an example is provided in the end of the paper).