Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form

We present Fuchsia — an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂xJ(x,ϵ)=A(x,ϵ)J(x,ϵ) finds a basis transformation T(x,ϵ), i.e., J(x,ϵ)=T(x,ϵ)J′(x,ϵ), such that the system turns into the epsilon form : ∂xJ′(x,ϵ)=ϵS(x)J′(x,ϵ), where S(x) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ϵ. That makes the construction of the transformation T(x,ϵ) crucial for obtaining solutions of the initial system.