FIRE 6.5: Feynman Integral Reduction with New Simplification Library

TL;DR

This paper introduces FIRE 6.5, an upgraded Feynman integral reduction program that incorporates a new flexible simplification library, enabling faster IBP reductions with various computer algebra systems.

Contribution

The paper presents FIRE 6.5 with a new library FUEL that allows flexible integration of third-party algebra systems and improves reduction speed for complex Feynman integrals.

Findings

Significant speedups in IBP reduction for integrals with many kinematic variables.

Successful integration of FLINT and Symbolica backends for enhanced performance.

Flexible use of different algebra systems through the new library FUEL.

Abstract

FIRE is a program which performs integration-by-parts (IBP) reduction of Feynman integrals. Originally, the C++ version of FIRE relies on the computer algebra system Fermat by Robert Lewis to simplify rational functions. We present an upgrade of FIRE which incorporates a new library FUEL initially described in a separate publication, which enables a flexible choice of third-party computer algebra systems as simplifiers, as well as efficient communications with some of the simplifiers as C++ libraries rather than through Unix pipes. We achieve significant speedups for IBP reduction of Feynman integrals involving many kinematic variables, when using an open source backend based on FLINT newly added in this work, or the Symbolica backend developed by Ben Ruijl as a potential successor of FORM.