NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions

TL;DR

NumGfun is a software package that implements classical and advanced algorithms for numerical and symbolic computations involving D-finite functions, including the first general implementation of fast high-precision evaluation algorithms.

Contribution

It provides the first comprehensive implementation of algorithms for D-finite functions, including improvements and references to related methods.

Findings

Implementation of classical algorithms for D-finite functions

First general implementation of fast high-precision evaluation algorithms

Includes improvements over existing algorithms

Abstract

This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be the first general implementation of the fast high-precision numerical evaluation algorithms of Chudnovsky & Chudnovsky. In some cases, our descriptions contain improvements over existing algorithms. We also provide references to relevant ideas not currently used in NumGfun.