GRUMPS
GRUMPS: General Relativity Using Multiple Processors and Symmetries
GRUMPS is a Mathematica package for coordinate basis calculations of curvature tensors and related objects that show up in general relativity and other gravitational theories. It is designed to be fast and easy to use. Most modern CPUs are multi-core, meaning Mathematica can run multiple kernels simultaneously. GRUMPS takes advantage of this by distributing calculations and simplifications across all available kernels.
GRUMPS is meant to be used as a scratchpad for quick calculations. It is not intended to take the place of more advanced systems. If you are using Mathematica for complicated tensor calculations I strongly recommend the xAct suite of packages. They have a bit of a learning curve, but they define the state-of-the-art in tensor computer algebra.
In its present form GRUMPS can calculate Christoffel symbols, curvature tensors, and certain scalar invariants. It can also format and display the results using standard notation. The package is alpha software in the early stages of development (the current version number is 0.1.6). Many features have yet to be implemented. However, it's pretty handy and you might find it useful.
Most of this package was written by Alex Gilman during his senior year (2015) at Loyola University Chicago.