MultivariateApart: Generalized Partial Fractions

TL;DR

MultivariateApart is a software package that performs advanced partial fraction decompositions of multivariate rational functions, ensuring unique and simplified results across different computer algebra systems.

Contribution

It introduces an algorithm that systematically avoids spurious factors and guarantees unique decompositions, enhancing the capabilities of existing algebraic tools.

Findings

Provides a systematic method for avoiding spurious denominator factors.

Ensures unique partial fraction decompositions for sums of terms.

Compatible with Mathematica, Form, and Singular.

Abstract

We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied to terms of a sum separately. The package is designed to work in Mathematica, but also provides interfaces to the Form and Singular computer algebra systems.