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 MultivariateCreativeTelescopingThen you should be able to load the package in Julia's REPL with the command
using MultivariateCreativeTelescoping