Sagemath simplifies general relativistic calculation and can replace Maple completely. Sagemath is built on a solid mathematical framework and all functions follow a robust geometrical hierarchy. It is easy to define metric spaces and calculate the Riemann tensor and other geometric quantities in curved space. The main strength of this package is in visualizing embedding spaces. For example, a graphical representation of the Bondi coordinates shows that it is only a tiny patch on the deSitter hyperboloid in a higher dimensional embedding space. It does not cover the entire spacetime. We explore this in #4 below.
The following are Sagemath tutorials which are rendered live by GitHub nbviewer.
The files can be directly accessed from my GitHub page.
If we want to download and run these files locally then we will need to install Sagemath. Each notebook is written in the language of SageManifold and requires Sage to run. You can install Sagemath from here. On Ubuntu use
apt install sagemath