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系统的全新扩展包，命名为Libra。其核心功能是为单变量或多变量下的一阶微分系统∂_i j = M_{i j} 提供便捷的变换工具。具体而言，Libra专为多圈计算（multiloop calculations）中出现的微分系统的ε形式约化流程设计。该扩展包还内置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）的微扰展开来构建通解，也支持在正则奇点（regular singular points）附近开展广义幂级数展开以获取通解。此外，Libra还配备了用于确定原始主积分（master integrals）渐近行为中最小系数集合的工具，该集合足以用于固定边界条件。