MultivariateCreativeTelescoping.jl

MultivariateCreativeTelescoping is a package to compute linear differential equations satisfied by parametric integrals using a method called creative telescoping (see e.g. here for an introduction to creative telescoping). This package implements an algorithm recently presented at the JNCF conference [slides] and an article is being written.

This algorithm is dedicated to integrals with natural boundaries of the form

$$I(t) = \int f(t,\boldsymbol{x})\boldsymbol{dx}$$

where $\boldsymbol{x}=(x_1,\dots,x_n)$ and $f$ is a D-finite/holonomic function that satisfies PDEs with coefficients in $\mathbb{Q}(t,\boldsymbol{x})$.

This package is still in developpement but an early version is available. The documentation of the package can be found here.