23 May 2024 | Xin Guan,1,2,*, Xiao Liu,3,† Yan-Qing Ma,1,4,‡ and Wen-Hao Wu5,§
The article introduces the **Blade** package, which implements the block-triangular form improved Feynman integral reduction method. This method significantly reduces the number of equations compared to traditional integration-by-parts (IBP) systems, leading to faster evaluations and reduced resource consumption. The authors detail the algorithms involved in obtaining the block-triangular form, including a two-step search strategy, polynomial ansatz, and adaptive search techniques. They also introduce novel algorithms for finding the canonical form and symmetry relations of Feynman integrals, as well as for performing spanning-sector reduction. Benchmarks demonstrate that **Blade** is competitive with existing reduction tools and offers several distinctive features, such as support for complex kinematic variables, user-defined Feynman prescriptions, and general integrands. The package is designed to enhance the efficiency of IBP reductions, making intricate physical problems more tractable.The article introduces the **Blade** package, which implements the block-triangular form improved Feynman integral reduction method. This method significantly reduces the number of equations compared to traditional integration-by-parts (IBP) systems, leading to faster evaluations and reduced resource consumption. The authors detail the algorithms involved in obtaining the block-triangular form, including a two-step search strategy, polynomial ansatz, and adaptive search techniques. They also introduce novel algorithms for finding the canonical form and symmetry relations of Feynman integrals, as well as for performing spanning-sector reduction. Benchmarks demonstrate that **Blade** is competitive with existing reduction tools and offers several distinctive features, such as support for complex kinematic variables, user-defined Feynman prescriptions, and general integrands. The package is designed to enhance the efficiency of IBP reductions, making intricate physical problems more tractable.