MultivariateApart: Generalized partial fractions

We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows systematically avoid spurious denominator factors and is capable producing unique results also when being applied terms sum separately. designed work in Mathematica, but provides interfaces the Form Singular computer algebra systems. Program title: MultivariateApart CPC Library link program files: https://doi.org/10.17632/zbt9tfpkgv.1 Developer's repository link: https://gitlab.msu.edu/vmante/multivariateapart Licensing provisions: GPLv3 Programming language: Mathematica (Wolfram Language) Nature problem: Partial decomposition widely used particle physics bring functions into form. Treating case by applying univariate method iteratively risks introduction singularities. Here, we formulate an that handles non-linear denominators, avoids aims at providing good performance for typical applications physics. It can be obtain decomposing individual separately, independent details input A variant approach reach Leĭnartas' as output Solution method: reformulate problem calculating reducing polynomial with respect specific ideal. reduction based on Gröbner basis calculation guarantees result decomposition. provide complete implementation package. Optionally, included speed up computation. Additional comments including restrictions unusual features: Our does not introduce new singularities were presented input. If, however, contains singularities, our such way cancellation these guaranteed. By default, main function this first putting over common denominator, canceling result.