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

Authors

DOI:

https://doi.org/10.26089/NumMet.v24r425

Keywords:

Feynman integrals, integration by parts, computer algebra

Abstract

We present FUEL (Fractional Universal Evaluation Library), a C++ library for performingrational 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 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 calculation of the off-shell three-particle form factors in N = 4 supersymmetric Yang-Mills theory.

Author Biographies

Kirill S. Mokrov

Alexander V. Smirnov

Mao Zeng

University of Edinburgh,
Higgs Centre for Theoretical Physics
James Clark Maxwell Building, Peter Guthrie Tait Road, EH9 3FD, Edinburgh, United Kingdom
• Royal Society University Research Fellow

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Published

19-10-2023

How to Cite

Mokrov K.S., Smirnov A.V., Zeng M. Rational Function Simplification for Integration-by-Parts Reduction and Beyond // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2023. 24. 352-367. doi 10.26089/NumMet.v24r425

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Methods and algorithms of computational mathematics and their applications