A power series being given as the solution of a linear differential equation with appropriate initial conditions, minimization consists in finding a non-trivial linear differential equation of minimal order having this power series as a solution. This problem exists in both homogeneous and inhomogeneous variants; it is distinct from, but related to, the classical problem of factorization of differential operators. Recently, minimization has found applications in Transcendental Number Theory, more specifically in the computation of non-zero algebraic points where Siegel's $E$-functions take algebraic values. We present algorithms and implementations for these questions, and discuss examples and experiments.

翻译：给定一个幂级数作为具有适当初始条件的线性微分方程的解，极小化问题旨在寻找一个以该幂级数为解的非平凡最小阶线性微分方程。该问题同时存在于齐次与非齐次两种情形中，它与经典的微分算子分解问题不同但相互关联。近年来，极小化问题在超越数论中得到了应用，具体而言，用于计算Siegel $E$函数取代数值的非零代数点。我们针对这些问题提出了算法与实现，并讨论了相关实例与实验。