Desingularization of Ore Operators

TL;DR

This paper introduces a novel method for desingularizing Ore operators by computing a least common left multiple with a random operator, extending classical results and providing a simple algorithm.

Contribution

It generalizes classical desingularization results for differential equations and presents a straightforward algorithm for Ore operator desingularization.

Findings

Desingularization achieved via least common left multiple.

Algorithm is simple and effective.

Generalizes classical differential equation results.

Abstract

We show that Ore operators can be desingularized by calculating a least common left multiple with a random operator of appropriate order. Our result generalizes a classical result about apparent singularities of linear differential equations, and it gives rise to a surprisingly simple desingularization algorithm.