FIRE 6.5: Feynman integral reduction with new simplification library

FIRE is a program which performs integration-by-parts (IBP) reductions 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 reductions 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. Program summary Program title: FIRE, version 6.5 (FIRE 6.5)CPC Library link to program files: https://doi.org/10.17632/cy6k69pb3y.2Developer's repository link: https://gitlab.com/feynmanintegrals/fire.gitLicensing provisions: GPLv2Programming language: Wolfram Mathematica 8.0 or higher, C++17Supplementary material: See linked repository for installation instructions.Journal reference of previous version: Comput. Phys. Commun. 247 (2020) 106877Does the new version supersede the previous version?: Yes.Reasons for the new version: The new version no longer relies on a single computer algebra system, Fermat [1], but instead allows a flexible choice of several systems, some of which offer higher performance, especially when the number of variables is large.Summary of revisions: A new library FUEL [2] is used as a core component of the new version of FIRE to access different computer algebra systems as simplifiers of rational function expressions. Since the first release of FUEL described elsewhere, FUEL version 1.0 here has been enhanced with a new backend based on the open source library FLINT [3] that provides highly performant simplification of rational functions.Nature of problem: Feynman integrals of a given family are reduced to a finite set of master integrals, by solving linear equations arising from integration by parts, using Gaussian elimination. The coefficients of the linear equations are generally rational functions in kinematic variables and the spacetime dimension, and the simplification of such rational functions during Gaussian elimination is a key task that is improved in this upgrade of FIRE.Solution method: Computer algebra systems with state-of-the-art capabilities for polynomial GCD computations are used as simplification backends, or simplifiers in short. Due to the design of FIRE, text strings are used as the exchange format for rational functions before and after simplification. A fast C++ parser is written to parse strings into the internal format of an external simplifer, FLINT [3], with state-of-the-art performance for multivariate polynomial calculations. Similarly, the simplifier Symbolica [4] has high performance in both GCD computations and parsing, and has been integrated into FIRE. References [1]https://home.bway.net/lewis/, free–ware with some restrictions.[2]https://doi.org/10.26089/NumMet.v24r425, open source.[3]https://flintlib.org/, open source.[4]https://symbolica.io/, commercial software with free licenses for students and hobbyists.