A mathematica notebook to compute relevant GR quantities
The notebook computes the metric inverse, Christoffel symbols, Riemann tensor, Ricci tensor and scalar and Einstein tensor once it is provided with coordinates and the covariant metric
An example notebook for a 3-sphere in hyperspherical coordinates (Read more here: https://www.wikiwand.com/en/3-sphere#/Coordinate_systems_on_the_3-sphere)
An example notebook for the Schwarzschild metric in the usual Schwarzschild coordinates (Read more at: https://www.wikiwand.com/en/Schwarzschild_metric#/The_Schwarzschild_metric)