2026-10-15T23:11:12Z https://data.mendeley.com/oai

oai:data.mendeley.com/rzfwjzmd26.1 2025-02-20T22:22:34Z

Ballantyne, John Blade: A package for block-triangular form improved Feynman integrals decomposition Mendeley Data In this article, we present the package Blade as the first implementation of the block-triangular form improved Feynman integral reduction method. The block-triangular form has orders of magnitude fewer equations compared to the plain integration-by-parts system, allowing for strictly block-by-block solutions. This results in faster evaluations and reduced resource consumption. We elucidate the algorithms involved in obtaining the block-triangular form along with their implementations. Additionally, we introduce novel algorithms for finding the canonical form and symmetry relations of Feynman integrals, as well as for performing spanning-sector reduction. Our benchmarks for various state-of-the-art problems demonstrate that Blade is remarkably competitive among existing reduction tools. Furthermore, the Blade package offers several distinctive features, including support for complex kinematic variables or masses, user-defined Feynman prescriptions for each propagator, and general integrands. Computational Physics Differential Equation Guan, Xin Liu, Xiao Ma, Yan-Qing Wu, Wen-Hao Dataset doi:10.17632/rzfwjzmd26.1 oai:data.mendeley.com/rzfwjzmd26.1 MIT License http://opensource.org/licenses/MIT https://data.mendeley.com/datasets/rzfwjzmd26 2025-02-20T22:22:34Z