We present OGRe, a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. The package can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but it is especially suitable for general relativity. By implementing an object-oriented design paradigm, OGRe allows calculating arbitrarily complicated tensor formulas easily, and automatically transforms between index configurations and coordinate systems behind the scenes as needed, eliminating user errors by making it impossible for the user to combine tensors in inconsistent ways. Other features include displaying tensors in various forms, automatic calculation of curvature tensors and geodesic equations, easy importing and exporting of tensors between sessions, optimized algorithms and parallelization for improved performance, and more.

翻译：我们提出了“OGRe ” ( OGRe ), 这是一种现代的用于高分微积分的现代数学软件包,设计得既强大又方便用户。该软件包可用于数学和物理两方面,在数学和物理两方面都需要“高”计算,但特别适合一般相对性。通过实施一个面向目标的设计范式, OGRe 允许简单计算任意复杂的“高”公式,并根据需要自动转换指数配置和幕后协调系统,消除用户错误,使用户无法以不一致的方式将“高分数”组合在一起。其他功能包括以各种形式显示“高分数 ” 、 自动计算“ 曲线” 和“ 大地方程式 ” 、 在会话之间轻松进出口“ ” 、 “ 优化算法” 和“ 平行法”, 以便改进性能,等等。