The Maxima computer algebra system, the open-source successor to MACSYMA, the first general-purpose computer algebra system that was initially developed at the Massachusetts Institute of Technology in the late 1960s and later distributed by the United States Department of Energy, has some remarkable capabilities, some of which are implemented in the form of add-on, "share" packages that are distributed along with the core Maxima system. One such share package is itensor, for indicial tensor manipulation. One of the more remarkable features of itensor is functional differentiation. Through this, it is possible to use itensor to develop a Lagrangian field theory and derive the corresponding field equations. In the present note, we demonstrate this capability by deriving Maxwell's equations from the Maxwell Lagrangian, and exploring the properties of the system, including current conservation.

翻译：Maxima计算机代数系统是MACSYMA的开源继承者，后者作为首个通用计算机代数系统，于20世纪60年代末在麻省理工学院（MIT）初步研发，后由美国能源部负责分发。该系统具备若干卓越功能，其中部分以附加“共享”软件包的形式实现，并与核心Maxima系统一同分发。此类共享包之一为itensor，专用于指标张量操作。itensor最显著的特性之一在于其泛函微分能力。借助此功能，可运用itensor构建拉格朗日场论并推导相应的场方程。在本文中，我们通过从麦克斯韦拉格朗日量推导麦克斯韦方程组，并探讨系统的性质（包括电流守恒），来展示这一功能。