I am looking for software packages that can be used to do numerical computations on differential manifolds. I know there are several packages to do symbolical calculations, but I am interested in numerical applications. I can deal with Python, Matlab, C/C++ and Fortran. In particular, I am interested in marching forward in time equations of the type
$$ \frac{1}{2}\frac{\partial g}{\partial t}=\widetilde{\nabla T}, $$ where $g$ is the metric, and $\widetilde{\nabla T}$ a symmetric tensor, but also capable of dealing with things like the deRham-Laplace operator, hodge stars, and so on.
