We present an approach to construct all the regular solutions of systems of linear ordinary differential equations using the desingularization algorithm of Abramov & Bronstein (2001) as an auxiliary tool.Expand

An algorithm for finding a universal denominator of rational solutions of a system of linear difference equations with polynomial coefficients is proposed.Expand

We consider systems of linear ordinary differential equations containing m unknown functions of a single variable x. The coefficients of the systems are polynomials over a field k of characteristic… Expand

We discuss the algorithms which, given a linear difference equation with rational function coefficients over a field k of characteristic 0, compute a polynomial U(x) ∈ k[x] (a universal denominator) such that the denominator of each of rational solutions (if exist) of the given equation dividesU(x).Expand

Complexities of some well-known algorithms for finding rational solutions of linear difference equations with polynomial coefficients are studied.Expand

We define the width of a given full rank system S with formal power series coefficients as the smallest non-negative integer w such that any l -truncation of S with l ⩾ w is a full Rank system.Expand

The following problem is considered: given a system of linear ordinary differential equations of arbitrary order with power series coefficients, to recognize whether it has regular solutions at point 0 and, if it does, find them.Expand

Construction of Laurent, regular, and formal (exponential–logarithmic) solutions of full-rank linear ordinary differential systems with the coefficients given by infinite, rather than truncated, series.Expand