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In this manuscript, which is to appear in the proceedings of the conference"MathemAmplitude 2019" in Padova, Italy, we provide an overview of the moduleintersection method for the the integration-by-parts (IBP) reduction ofmulti-loop Feynman integrals. The module intersection method, based oncomputational algebraic geometry, is a highly efficient way of getting IBPrelations without double propagator or with a bound on the highest propagatordegree. In this manner, trimmed IBP systems which are much shorter than thetraditional ones can be obtained. We apply the modern, Petri net based,workflow management system GPI-Space in combination with the computer algebrasystem Singular to solve the trimmed IBP system via interpolation and efficientparallelization. We show, in particular, how to use the new plugin feature ofGPI-Space to manage a global state of the computation and to efficiently handlemutable data. Moreover, a Mathematica interface to generate IBPs withrestricted propagator degree, which is based on module intersection, ispresented in this review.

Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals