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 ${\partial }_i\mathit{j}=M_i\mathit{j}$ 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.

Program summary

Program title: Libra

CPC Library link to program files: https://doi.org/10.17632/69d5cd7hb4.1

Licensing provisions: GPLv3

Programming language: Wolfram Mathematica

Nature of problem: Transformation of the first-order linear differential systems with respect to one or several variables: reduction to fuchsian form, to ϵ-form, formal solution in terms of the Goncharov's polylogarithms and in terms of generalized power series.

Solution method: Algorithms described in Refs. [1], [2], and [3, Section E.8].

中文翻译：

---

Libra：用于多环积分的微分系统变换的包

我们为Mathematica系统提供了一个名为Libra的新包。其目的是为一阶微分系统的变换提供方便的工具${\partial }_{\mathrm{一世}}\mathit{j}={米}_{\mathrm{一世}}\mathit{j}$对于一个或多个变量。特别是，Libra旨在将出现在多循环计算中的微分系统简化为ϵ形式。该软件包还包含一些用于构建通用解的工具：通过路径有序指数的微扰展开和通过规则奇异点附近的广义幂级数展开。Libra还具有确定原始主积分渐近线中系数的最小列表的工具，足以固定边界条件。

程序概要

项目名称： 天秤座

CPC 库程序文件链接： https : //doi.org/10.17632/69d5cd7hb4.1

许可条款： GPLv3

编程语言：Wolfram Mathematica

问题的性质：关于一个或多个变量的一阶线性微分系统的变换：归约到 fuchsian 形式，到ϵ形式，根据 Goncharov 多对数和广义幂级数的形式解。

解决方法：参考文献中描述的算法。[1]、[2] 和 [3，第 E.8 节]。