I would like to use an open source computer algebra system (CAS) for research in general relativity. Kindly suggest a good choice between Ipython and Sage. I am more interested in the theoretical aspect rather than numerical computations.
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I would not recommend either of the choices you mentioned. If you have Mathematica, and your needs in general relativity are fairly basic (computing connections, curvature, geodesics), then I recommend using the notebooks from Hartle's text freely available here.
If your needs are more advanced, or you need something more capable, I would suggest using xAct and all its packages which include features such as,
- Generic tensor manipulation
- High order gravitational perturbation theory
- Tensor spherical harmonics
- Spinor computations in G.R.
- Exterior calculus
I have used the packages several times for computations, and not only is xAct capable of many feats, it is also quite fast$^\dagger$ and very well-documented. Every package comes with examples as well and notebooks to help you get started. The only downside: there's a bit of a learning curve. However, the authors created a Google group/forum for users to help each other.
$\dagger$ I can attest to this given that I had to use it for computations in $d=26$.
Recently this paper came out on arXiv: Symbolic tensor calculus on manifolds: a SageMath implementation.
It describes how differentiable manifolds, vector and tensor fields classes are implemented in SageMath (via the SageManifold project) and how you can use them.
I have been developing a toolkit; spacetimeengine as a research tool. It is extremely lightweight but fully focused on General Relativity.