Computations of tensor on a Riemannian Manifold.

Question

I am trying to get some practice in computing tensors in Riemannian and Pseudo-Riemannian manifolds. Is there somewhere that I can check my results? For example right now I am computing the Christoffel symbols, Riemann tensor, Ricci tensor and scalar, Einstein and Weyl tensor and the expressions that solve the Killing equations of the pseudosphere $t^2-x^2-y^2=R^2$ in $R^{3,2}$ with metric $dl^2=dt^2-dx^2-dy^2$. The pullback metric is in pseudospherical coordinates with expression $dl^2=R^2(d\chi^2+sinh^2(\chi)d\phi^2)$. I know about sage but i do not have the time to familiarize. I am asking for some cross checking if exists. Thank you