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This package provide a massively parallel framework for partial fraction decomposition of rational functions based on the Singular/GPI-Space framework.
Our implementation is based on a combination of the following two algorithms:
- the approach described in the paper
Janko Boehm, Marcel Wittmann, Zihao Wu, Yingxuan Xu, and Yang Zhang: IBP reduction coefficients made simple, JHEP 12 (2020) 054,
which has been implemened in Singular in the library pfd.lib.
- MultivariateApart algorithm
Matthias Heller, Andreas von Manteuffel, Comput.Phys.Commun. 271 (2022) 108174
Although applicable in general, its primary aim is the partial fraction decomposition of integration-by-parts coefficients in high energy physics.
Our package relies on code developed in the repository framework implemented primarily by Lukas Ristau.
Since most useful in applications in high energy physics, the main function of our framework applies the partial fraction decoposition function to a specified subset of entries of a two-dimensional array of rational functions.
To use the framework, it is required to install Singular, GPI-Space, some of their dependencies and the project code itself. The preferable way is the use the supercomputing package manager Spack, which will take care of all dependencies automatically. We also provide an instruction for a manual installation of all components, which can be used in case the installation with Spack is not possible on the target system.
Installation of pfd parallel using Spack
Appendix: Manual installation from sources
We provide an example how to use pfd-parallel. We also discuss the options of the implementation, e.g. input formats, output formats, choice of parallelization strategy, and algorithmic options available. In the appendix section, we provide some scripts which are useful to run computations in an automatic manner.
Appendix: Convenient scripts to run a computation in pfd parallel