Partial fraction decompositions on hyperplane arrangements
Commutative Algebra
2026-03-25 v2 High Energy Physics - Theory
Combinatorics
Abstract
We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained by examining the primary decomposition of ideals coming from hyperplane arrangements. We then present an algorithm for finding a PFD that satisfies properties desired for simplifying the calculation of scattering amplitudes. We demonstrate the effectiveness of this algorithm by computing practical examples coming from Feynman integrals.
Cite
@article{arxiv.2602.06531,
title = {Partial fraction decompositions on hyperplane arrangements},
author = {Claire de Korte and Teresa Yu},
journal= {arXiv preprint arXiv:2602.06531},
year = {2026}
}
Comments
18 pages, comments welcome, section 2 re-written and other minor revisions