FIRE 7: Automatic Reduction with Modular Approach

Abstract

FIRE7 is a major update to the FIRE program for integration-by-parts (IBP) reduction of Feynman integrals. A large part of improvements is related to the automatic reduction and reconstruction with the modular arithmetic approach, while the performance of the classical rational polynomial approach is also significantly increased. An improved presolve algorithm performs Gaussian elimination to simplify IBP identities before substituting numerical indices as in the Laporta algorithm. Various new command line tools are included to facilitate tasks such as applying an IBP reduction table to reduce a loop integrand as a linear combination of individual integrals.