Note: The information below, and more details, can be found in our wiki
Documentation of the pfd-parallel project
This package provide a massively parallel framework for partial fraction decomposition of rational functions based on the Singular/GPI-Space framework.
The project is supported by Project B5 of SFB-TRR 195 and SymbTools of Forschungsinitiative RLP.
The accompaning paper of pfd-parallel is:
Dominik Bendle, Janko Boehm, Murray Heymann, Rourou Ma, Mirko Rahn, Lukas Ristau, Marcel Wittmann, Zihao Wu, Hefeng Xu, and Yang Zhang: pfd-parallel, a Singular/GPI-Space package for massively parallel multivariate partial fractioning, Comput. Phys. Commun. 294 (2024) 108942
Our implementation is based on a combination of the following two algorithms:
- the enhanced Leinartas' algorithm 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.
- the MultivariateApart algorithm as described in
Matthias Heller, Andreas von Manteuffel, Comput. Phys. Commun. 271 (2022) 108174
Although applicable in general, the primary aim of our package 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.