Rational Function Simplification for Integration-by-Parts Reduction and Beyond

Abstract

We present FUEL (Fractional Universal Evaluation Library), a C++ library for performing rational function arithmetic with a flexible choice of third-party computer algebra systems as simplifiers. FUEL is an outgrowth of a C++ interface to Fermat which was originally part of the FIRE code for integration-by-parts (IBP) reduction for Feynman integrals, now promoted to be a standalone library and with access to simplifiers other than Fermat. We compare the performance of various simplifiers for standalone benchmark problems as well as IBP reduction runs with FIRE. A speedup of more than 10 times is achieved for an example IBP problem related to off-shell three-particle form factors in $\mathcal{N}=4$ super-Yang-Mills theory.

19 pages, 2 figure, 6 tables. v2 update: significant enhancements to the code

References in corpus (6)

• FIRE5: a C++ implementation of Feynman Integral REduction
• Integral Reduction with Kira 2.0 and Finite Field Methods
• Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
• Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language
• The $n_f^2$ contributions to fermionic four-loop form factors
• Off-shell form factor in N=4 sYM at three loops