PFD-PARALLEL, a Singular/GPI-Space package for massively parallel multivariate partial fractioning

Multivariate partial fractioning is a powerful tool for simplifying rational function coefficients in scattering amplitude computations. Since current research problems lead to large sets of complicated rational functions, performance of the partial fractioning as well as size of the obtained expressions are a prime concern. We develop a large scale parallel framework for multivariate partial fractioning, which implements and combines an improved version of Leinartas' algorithm and the MULTIVARIATEAPART algorithm. Our approach relies only on open source software. It combines parallelism over the different rational function coefficients with parallelism for individual expressions. The implementation is based on the SINGULAR/GPI-SPACE FRAMEWORK for massively parallel computer algebra, which formulates parallel algorithms in terms of Petri nets. The modular nature of this approach allows for easy incorporation of future algorithmic developments into our package. We demonstrate the performance of our framework by simplifying expressions arising from current multiloop scattering amplitude problems. We also provide a Mathematica interface to our package, which is available on https://github .com / Wu -Zihao /PfdParallelM. Program summary Program Title: pfd-parallel CPC Library link to program files: https://doi .org /10 .17632 /r99gdp9v76 .1 Developer's repository link: https://github .com /singular-gpispace /pfd-parallel Licensing provisions: GPLv3 Programming language: Singular language, GPI-Space Petri net Nature of problem: In scattering amplitude computation, we often encounter complicated rational functions, which may be simplified using the multivariate partial fraction decomposition. With the consideration of the increasing complexity of the problems, an efficient implementation of such a method is needed. Solution method: We present the package PFD -PARALLEL, which is a large-scale parallelized framework for multivariate partial fractioning. Our package relies only on open source software. It combines different algorithms and provides parallelization based on the SINGULAR/GPI-SPACE FRAMEWORK [1-3]. The package combines both the improved Leinartars' algorithm [4], as well as the MULTIVARIATEAPART algorithm [5], and combines parallelism over the different rational function coefficients and parallelism for individual expressions. Using this approach cutting-edge computations can be handled in an efficient way. Additional comments including restrictions and unusual features: The software, including all dependencies like Singular, GPI-2, GPI-Space, and the Singular/GPI-Space framework, is distributed via the supercomputing package manager Spack, which allows for convenient installation of scientific software, in particular in HPC environments. The code has been tested on Centos 7 and 8, Ubuntu 18.04 LTS and 20.04 LTS.