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

Abstract

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 ∂ij=Mij 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 summaryProgram title:LibraCPC Library link to program files:https://doi.org/10.17632/69d5cd7hb4.1Licensing provisions: GPLv3Programming language: Wolfram MathematicaNature 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].