Introduction

MultivariateCreativeTelescoping.jl is a Julia package for computing linear differential equations satisfied by parametric integrals using creative telescoping (see, e.g., this reference for an introduction).

The package implements:

  • the integration algorithm introduced in this article, and
  • an algorithm for approximating the Weyl closure, presented in my PhD thesis.

Combined, these algorithms make it possible to compute integrals with natural boundaries of the form

\[I(t) = \int f(t,\boldsymbol{x})\,\mathrm{d}\boldsymbol{x},\]

where $\boldsymbol{x} = (x_1,\dots,x_n)$ and $f$ is a D-finite/holonomic function satisfying a system of partial differential equations with coefficients in $\mathbb{Q}(t,\boldsymbol{x})$.

Installation

Open Julia in a terminal and execute the following line to install the package.

] add MultivariateCreativeTelescoping

Then you should be able to load the package in Julia's REPL with the command

using MultivariateCreativeTelescoping