A useful program when you do General Relativity is GR-Tensor. It runs under Maple (there exists also a Mathematica version) and it calculates the Christoffel symbol, the Riemann tensor, the Ricci tensor, the curvature, etc. all you need in order to deal with a physical problem in General Relativity. It was created at Queen's University (Ontario) and you can download it from the web at http://astro.queensu.ca/ grtensor/
This was a great help in doing computation such as
having an explicit form of the Raychaudhuri equation
(
page ) in the case of the
de Sitter metrics.
Here I will introduce this program that I used (MapleV version).