{"title":"FIRE 6.5: Feynman integral reduction with new simplification library","authors":"Alexander V. Smirnov , Mao Zeng","doi":"10.1016/j.cpc.2024.109261","DOIUrl":null,"url":null,"abstract":"<div><p>FIRE is a program which performs integration-by-parts (IBP) reductions of Feynman integrals. Originally, the C++ version of FIRE relies on the computer algebra system Fermat by Robert Lewis to simplify rational functions. We present an upgrade of FIRE which incorporates a new library FUEL initially described in a separate publication, which enables a flexible choice of third-party computer algebra systems as simplifiers, as well as efficient communications with some of the simplifiers as C++ libraries rather than through Unix pipes. We achieve significant speedups for IBP reductions of Feynman integrals involving many kinematic variables, when using an open source backend based on FLINT newly added in this work, or the Symbolica backend developed by Ben Ruijl as a potential successor of FORM.</p></div><div><h3>Program summary</h3><p><em>Program title:</em> FIRE, version 6.5 (FIRE 6.5)</p><p><em>CPC Library link to program files:</em> <span>https://doi.org/10.17632/cy6k69pb3y.2</span><svg><path></path></svg></p><p><em>Developer's repository link:</em> <span>https://gitlab.com/feynmanintegrals/fire.git</span><svg><path></path></svg></p><p><em>Licensing provisions:</em> GPLv2</p><p><em>Programming language:</em> <span>Wolfram Mathematica</span> 8.0 or higher, <span>C++17</span></p><p><em>Supplementary material:</em> See linked repository for installation instructions.</p><p><em>Journal reference of previous version:</em> Comput. Phys. Commun. 247 (2020) 106877</p><p><em>Does the new version supersede the previous version?:</em> Yes.</p><p><em>Reasons for the new version:</em> The new version no longer relies on a single computer algebra system, <span>Fermat</span> [1], but instead allows a flexible choice of several systems, some of which offer higher performance, especially when the number of variables is large.</p><p><em>Summary of revisions:</em> A new library <span>FUEL</span> [2] is used as a core component of the new version of <span>FIRE</span> to access different computer algebra systems as simplifiers of rational function expressions. Since the first release of <span>FUEL</span> described elsewhere, <span>FUEL</span> version 1.0 here has been enhanced with a new backend based on the open source library <span>FLINT</span> [3] that provides highly performant simplification of rational functions.</p><p><em>Nature of problem:</em> Feynman integrals of a given family are reduced to a finite set of master integrals, by solving linear equations arising from integration by parts, using Gaussian elimination. The coefficients of the linear equations are generally rational functions in kinematic variables and the spacetime dimension, and the simplification of such rational functions during Gaussian elimination is a key task that is improved in this upgrade of <span>FIRE</span>.</p><p><em>Solution method:</em> Computer algebra systems with state-of-the-art capabilities for polynomial GCD computations are used as simplification backends, or simplifiers in short. Due to the design of <span>FIRE</span>, text strings are used as the exchange format for rational functions before and after simplification. A fast <span>C++</span> parser is written to parse strings into the internal format of an external simplifer, <span>FLINT</span> [3], with state-of-the-art performance for multivariate polynomial calculations. Similarly, the simplifier <span>Symbolica</span> [4] has high performance in both GCD computations and parsing, and has been integrated into FIRE.</p></div><div><h3>References</h3><p></p><ul><li><span>[1]</span><span><p><span>https://home.bway.net/lewis/</span><svg><path></path></svg>, free–ware with some restrictions.</p></span></li><li><span>[2]</span><span><p><span>https://doi.org/10.26089/NumMet.v24r425</span><svg><path></path></svg>, open source.</p></span></li><li><span>[3]</span><span><p><span>https://flintlib.org/</span><svg><path></path></svg>, open source.</p></span></li><li><span>[4]</span><span><p><span>https://symbolica.io/</span><svg><path></path></svg>, commercial software with free licenses for students and hobbyists.</p></span></li></ul></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":null,"pages":null},"PeriodicalIF":7.2000,"publicationDate":"2024-05-24","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/S001046552400184X","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}
引用次数: 0
Abstract
FIRE is a program which performs integration-by-parts (IBP) reductions of Feynman integrals. Originally, the C++ version of FIRE relies on the computer algebra system Fermat by Robert Lewis to simplify rational functions. We present an upgrade of FIRE which incorporates a new library FUEL initially described in a separate publication, which enables a flexible choice of third-party computer algebra systems as simplifiers, as well as efficient communications with some of the simplifiers as C++ libraries rather than through Unix pipes. We achieve significant speedups for IBP reductions of Feynman integrals involving many kinematic variables, when using an open source backend based on FLINT newly added in this work, or the Symbolica backend developed by Ben Ruijl as a potential successor of FORM.
Program summary
Program title: FIRE, version 6.5 (FIRE 6.5)
CPC Library link to program files:https://doi.org/10.17632/cy6k69pb3y.2
Does the new version supersede the previous version?: Yes.
Reasons for the new version: The new version no longer relies on a single computer algebra system, Fermat [1], but instead allows a flexible choice of several systems, some of which offer higher performance, especially when the number of variables is large.
Summary of revisions: A new library FUEL [2] is used as a core component of the new version of FIRE to access different computer algebra systems as simplifiers of rational function expressions. Since the first release of FUEL described elsewhere, FUEL version 1.0 here has been enhanced with a new backend based on the open source library FLINT [3] that provides highly performant simplification of rational functions.
Nature of problem: Feynman integrals of a given family are reduced to a finite set of master integrals, by solving linear equations arising from integration by parts, using Gaussian elimination. The coefficients of the linear equations are generally rational functions in kinematic variables and the spacetime dimension, and the simplification of such rational functions during Gaussian elimination is a key task that is improved in this upgrade of FIRE.
Solution method: Computer algebra systems with state-of-the-art capabilities for polynomial GCD computations are used as simplification backends, or simplifiers in short. Due to the design of FIRE, text strings are used as the exchange format for rational functions before and after simplification. A fast C++ parser is written to parse strings into the internal format of an external simplifer, FLINT [3], with state-of-the-art performance for multivariate polynomial calculations. Similarly, the simplifier Symbolica [4] has high performance in both GCD computations and parsing, and has been integrated into FIRE.
References
[1]
https://home.bway.net/lewis/, free–ware with some restrictions.
[2]
https://doi.org/10.26089/NumMet.v24r425, open source.
[3]
https://flintlib.org/, open source.
[4]
https://symbolica.io/, commercial software with free licenses for students and hobbyists.
FIRE 是一个对费曼积分进行逐部积分（IBP）还原的程序。最初，FIRE 的 C++ 版本依赖于罗伯特-刘易斯（Robert Lewis）的计算机代数系统费马（Fermat）来简化有理函数。我们介绍了 FIRE 的升级版，它集成了一个新库 FUEL（最初在另一出版物中介绍），可以灵活选择第三方计算机代数系统作为简化器，并以 C++ 库的形式而不是通过 Unix 管道与某些简化器进行高效通信。在使用本研究中新添加的基于 FLINT 的开源后端，或 Ben Ruijl 开发的作为 FORM 潜在后继者的 Symbolica 后端时，我们在涉及许多运动学变量的费曼积分的 IBP 简化方面取得了显著的加速：FIRE, version 6.5 (FIRE 6.5)CPC Library program files link: https://doi.org/10.17632/cy6k69pb3y.2Developer's repository link: https://gitlab.com/feynmanintegrals/fire.gitLicensing provisions：GPLv2 编程语言Wolfram Mathematica 8.0 或更高版本，C++17补充材料：有关安装说明，请参见链接的资源库：Comput.Phys.247 (2020) 106877新版本是否取代旧版本？是：新版本不再依赖于单一的计算机代数系统费马[1]，而是允许灵活选择多个系统，其中一些系统性能更高，尤其是当变量数量较多时：新版 FIRE 的核心组件是一个新库 FUEL [2]，用于访问不同的计算机代数系统，作为有理函数表达式的简化器。问题的性质：通过使用高斯消元法求解分部积分所产生的线性方程组，将给定族的费曼积分简化为一组有限的主积分。线性方程的系数通常是运动变量和时空维度的有理函数，在高斯消元过程中简化这些有理函数是 FIRE 升级版改进的一项关键任务：解决方法：计算机代数系统具有最先进的多项式 GCD 计算能力，可用作简化后端，简称简化器。由于 FIRE 的设计，文本字符串被用作有理函数简化前后的交换格式。我们编写了一个快速 C++ 解析器，用于将字符串解析为外部化简器 FLINT [3] 的内部格式，该化简器在多变量多项式计算方面性能一流。同样，简化器 Symbolica [4] 在 GCD 计算和解析方面也有很高的性能，并已集成到 FIRE 中。参考文献[1]https://home.bway.net/lewis/，免费软件，有一些限制。[2]https://doi.org/10.26089/NumMet.v24r425，开源软件。[3]https://flintlib.org/，开源软件。[4]https://symbolica.io/，商业软件，有免费许可证，供学生和业余爱好者使用。
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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