We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with the help of FireFly. This procedure can be parallelized on computer clusters with MPI. Furthermore, the support for user-provided systems of equations has been significantly improved. This mode provides the flexibility to integrate Kira into projects that employ specialized reduction formulas, direct reduction of amplitudes, or to problems involving linear system of equations not limited to relations among standard Feynman integrals. We show examples from state-of-the-art Feynman integral reduction problems and provide benchmarks of the new features, demonstrating significantly reduced main memory usage and improved performance w.r.t. previous versions of Kira.
Symbolic Reduction of Multi-loop Feynman Integrals via Generating Functions
South China Normal University（华南师范大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）；School of Physics, Peking University（北京大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学理论交叉研究中心）
Two decades of algorithmic Feynman integral reduction
Moscow State University（莫斯科国立大学）；Skobeltsyn Institute of Nuclear Physics of Moscow State University（莫斯科国立大学斯科别尔岑核物理研究所）；Moscow Center for Fundamental and Applied Mathematics, Moscow State University（莫斯科国立大学莫斯科基础与应用数学中心）
An Algorithm for the Symbolic Reduction of Multi-loop Feynman Integrals via Generating Functions
State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University（华南师范大学量子物质研究所核物理与技术国家重点实验室）；Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science（广东省核科学重点实验室物质结构与基本相互作用卓越基础研究广东基地）；Beijing Computational Science Research Center（北京计算科学研究中心）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）；School of Physics, Peking University（北京大学物理学院）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学理论交叉研究中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
Resonance and Differential Reduction of Feynman Integrals
School of Mathematics and Hamilton Mathematics Institute, Trinity College（三一学院数学与汉密尔顿数学研究所）；Institute for Theoretical Physics, Utrecht University（乌得勒支大学理论物理研究所）；Center of Mathematical Sciences and Applications Harvard University（哈佛大学数学科学与应用中心）；Jefferson Physical Laboratory, Harvard University（哈佛大学杰斐逊物理实验室）
The geometric bookkeeping guide to Feynman integral reduction and $\varepsilon$-factorised differential equations
Bethe Center for Theoretical Physics, Universität Bonn（波恩大学）；Paul Scherrer Institut（保罗谢尔研究所）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Wuhan University（武汉大学）；Xiamen University（厦门大学）
Reduction of Feynman Integrals in the Parametric Representation II: Reduction of Tensor Integrals
在作者最近的一篇论文中（Chen in JHEP 02：115，2020），考虑了参数表示中费曼积分的约化。利用生成元方法直接对张量积分进行参数化。通过构造和求解参数分部积分（IBP）恒等式，将所得的参数积分降阶。在本文中，我们进一步表明，多项式方程的运营商，产生张量积分可以推导出来。在此基础上，提出了两种简化张量积分的方法。第一种方法是通过引入一些辅助参数，在不改变时空维数的情况下将张量积分参数化。由此产生的参数积分可以通过使用标准IBP方法来减少。在第二种方法中，张量积分（部分）约化是通过使用Gröbner基技术结合符号规则的应用。未约化积分可通过求解参数IBP恒等式进一步约化。
