Integral reduction with Kira 2.0 and finite field methods

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.本文介绍费曼积分(Feynman integral)约化程序Kira的2.0新版本，并详述其各项新增功能。其核心新增功能为借助FireFly，通过有限域方法重构分部积分(integration-by-parts)约化中的最终系数。该流程可基于MPI（消息传递接口，Message Passing Interface）在计算机集群上实现并行计算。此外，程序对用户自定义方程组的支持功能已得到显著优化。该模式可灵活将Kira集成至各类项目中，包括采用专属约化公式、直接约化散射振幅的项目，以及不限于标准费曼积分间关系的线性方程组相关问题。本文展示了来自当前最前沿费曼积分约化问题的实例，并给出了新增功能的基准测试结果。测试结果表明，相较于Kira的过往版本，新功能的主内存占用显著降低，运行性能也得到了提升。