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arxiv 1908.04301 v2 pith:MVL2ZEI2 submitted 2019-08-12 hep-th hep-phmath.AG

Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space

Dominik Bendle , Janko Boehm , Wolfram Decker , Alessandro Georgoudis , Franz-Josef Pfreundt , Mirko Rahn , Pascal Wasser , Yang Zhang This is my paper
classification hep-th hep-phmath.AG
keywords gpi-spacealgebraintegralsbasiscomputerfeynmanframeworkintegration-by-parts
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We introduce an algebro-geometrically motived integration-by-parts (IBP) reduction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines the computer algebra system Singular with the workflow management system GPI-Space, which is being developed at the Fraunhofer Institute for Industrial Mathematics (ITWM). In our approach, the IBP relations are first trimmed by modern algebraic geometry tools and then solved by sparse linear algebra and our new interpolation methods. These steps are efficiently automatized and automatically parallelized by modeling the algorithm in GPI-Space using the language of Petri-nets. We demonstrate the potential of our method at the nontrivial example of reducing two-loop five-point nonplanar double-pentagon integrals. We also use GPI-Space to convert the basis of IBP reductions, and discuss the possible simplification of IBP coefficients in a uniformly transcendental basis.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding

    hep-ph 2026-06 unverdicted novelty 8.0

    Machine learning discovers a tube-seeding strategy for IBP reduction of Feynman integrals that scales linearly with numerator power, demonstrated on rank-20 2-loop 5-point integrals.

  2. Integral Reduction with Kira 2.0 and Finite Field Methods

    hep-ph 2020-08 conditional novelty 7.0

    Kira 2.0 implements finite-field coefficient reconstruction for IBP reductions and improved user-equation handling, yielding lower memory use and faster performance on state-of-the-art problems.

  3. LinApart3: efficient algorithm for multivariate partial fraction decomposition with linear denominators

    hep-ph 2026-06 unverdicted novelty 6.0

    LinApart3 performs multivariate partial fraction decomposition for linear-denominator rational functions using linear algebra and residue extraction on hyperplane arrangements, with guarantees on term structure, no sp...

  4. Feynman Integral Reduction without Integration-By-Parts

    hep-th 2024-12 unverdicted novelty 5.0

    Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.