Computing almost-commuting basis of Ordinary Differential Operators

An effective computation of a basis of a nontrivial centralizer of a differential operator is the first step towards a Picard-Vessiot theory for spectral problems of ordinary differential operators. The set of almost-commuting operators enjoys a richer structure that allows the computation of these centralizers. We present a method to calculate a basis of almost-commuting operators. Its application to the computation of nontrivial centralizers is illustrated by examples.