Geodesic
Rational Function Simplification for Integration-by-Parts Reduction and Beyond
Numerical methods and programming, Tome 24 (2023) no. 4, pp. 352-367

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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.
Keywords: Feynman integrals; integration by parts; computer algebra. 
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     author = {K. S. Mokrov and A. V. Smirnov and M. Zeng},
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K. S. Mokrov; A. V. Smirnov; M. Zeng. Rational Function Simplification for Integration-by-Parts Reduction and Beyond. Numerical methods and programming, Tome 24 (2023) no. 4, pp. 352-367. http://geodesic.mathdoc.fr/item/VMP_2023_24_4_a1/