{"title":"Blade: A package for block-triangular form improved Feynman integrals decomposition","authors":"Xin Guan , Xiao Liu , Yan-Qing Ma , Wen-Hao Wu","doi":"10.1016/j.cpc.2025.109538","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we present the package <span>Blade</span> 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 <span>Blade</span> is remarkably competitive among existing reduction tools. Furthermore, the <span>Blade</span> package offers several distinctive features, including support for complex kinematic variables or masses, user-defined Feynman prescriptions for each propagator, and general integrands.</div></div><div><h3>Program summary</h3><div><em>Program Title:</em> <span>Blade</span></div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/rzfwjzmd26.1</span><svg><path></path></svg></span></div><div><em>Developer's repository link:</em> <span><span>https://gitee.com/multiloop-pku/blade</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> MIT</div><div><em>Programming language:</em> <span>Wolfram Mathematica</span> 11.3 or higher</div><div><em>External routines/libraries used:</em> <span>Wolfram Mathematica</span> [1], <span>FiniteFlow</span> [2]</div><div><em>Nature of problem:</em> Automatically reducing dimensionally regularized Feynman integrals into linear combination of master integrals.</div><div><em>Solution method:</em> The program implements recently proposed block-triangular form to significantly improve the reduction efficiency.</div></div><div><h3>References</h3><div><ul><li><span>[1]</span><span><div><span><span>http://www.wolfram.com/mathematica</span><svg><path></path></svg></span>, commercial algebraic software.</div></span></li><li><span>[2]</span><span><div><span><span>https://github.com/peraro/finiteflow</span><svg><path></path></svg></span>, open source.</div></span></li></ul></div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"310 ","pages":"Article 109538"},"PeriodicalIF":7.2000,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010465525000414","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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Abstract
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.
Program summary
Program Title:Blade
CPC Library link to program files:https://doi.org/10.17632/rzfwjzmd26.1
期刊介绍：
The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper.
Computer Programs in Physics (CPiP)
These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged.
Computational Physics Papers (CP)
These are research papers in, but are not limited to, the following themes across computational physics and related disciplines.
mathematical and numerical methods and algorithms;
computational models including those associated with the design, control and analysis of experiments; and
algebraic computation.
Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.
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