Ore Polynomials in Sage

TL;DR

This paper introduces a SageMath package for Ore algebras, providing tools for algebraic operations, transformations, guessing, desingularization, and solving related polynomial and series problems, with a tutorial focus.

Contribution

It offers the first comprehensive SageMath implementation of Ore algebras, including advanced features like desingularization and natural transformations.

Findings

Provides basic arithmetic and actions for Ore algebras

Includes solvers for polynomials, rational functions, and power series

Enables algebraic transformations and guessing techniques

Abstract

We present a Sage implementation of Ore algebras. The main features for the most common instances include basic arithmetic and actions; gcrd and lclm; D-finite closure properties; natural transformations between related algebras; guessing; desingularization; solvers for polynomials, rational functions and (generalized) power series. This paper is a tutorial on how to use the package.