Finding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo Approach

Abstract

The reduction of a large number of scalar integrals to a small set of master integrals via Laporta's algorithm is common practice in multi-loop calculations. It is also a major bottleneck in terms of running time and memory consumption. It involves solving a large set of linear equations where many of the equations are linearly dependent. We propose a simple algorithm that eliminates all linearly dependent equations from a given system, reducing the time and space requirements of a subsequent run of Laporta's algorithm.

8 pages, 1 figure. Added references. Some minor additions

References in corpus (3)

• Algorithm FIRE -- Feynman Integral REduction
• FIRE4, LiteRed and accompanying tools to solve integration by parts relations
• Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals

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