SageMath 8.9 has just been released. It has new features regarding symbolic calculus on manifolds. In particular, some tutorials about vector calculus have been added and computations related to the extrinsic geometry of hypersurfaces have been improved. For more details, see
SageMath is a Python-based free computer algebra system, with some differential geometry and tensor calculus capabilities implemented via the SageManifolds project (https://sagemanifolds.obspm.fr/). See https://sagemanifolds.obspm.fr/examples.html for examples of use, in particular in the context of general relativity.