Libra: A package for transformation of differential systems for multiloop integrals

We present a new package for Mathematica system, called Libra. Its purpose is to provide convenient tools for the transformation of the first-order differential systems ∂_i j = M_i j for one or several variables. In particular, Libra is designed for the reduction to ϵ-form of the differential systems which appear in multiloop calculations. The package also contains some tools for the construction of general solution: both via perturbative expansion of path-ordered exponent and via generalized power series expansion near regular singular points. Libra also has tools to determine the minimal list of coefficients in the asymptotics of the original master integrals, sufficient for fixing the boundary conditions.我们推出了一款面向Mathematica系统的全新软件包，命名为Libra。其核心功能是为单变量或多变量情形下的一阶微分方程组∂_i j = M_{ij}的变换提供便捷工具。具体而言，Libra专为处理多圈计算中出现的微分方程组、将其约化为ϵ形式（ϵ-form）而设计。该软件包还提供了若干用于构造通解的工具：既支持通过路径有序指数（path-ordered exponent）的微扰展开来获取通解，也支持在正则奇点附近开展广义幂级数展开以构造通解。此外，Libra还配备了用于确定原始主积分（master integrals）渐近行为中的最小系数集的工具，该系数集足以确定边界条件。