Software that computes Riemann curvature tensor from data

Question

I have a 3-manifold (climate variable, f(latitude,longitude,time)).

I would like to compute Ricci/Riemann curvature tensors from the data and thus obtain their result in the real space not symbolic terms.

I have mathematica, maple, matlab and R. So far the mathematica and maple differential geometry add on i have only work in symbolic. On Matalb i have a function that calculates principal curvatures for a 2D surface so i was wondering if there exists the same kind of functions for 3-manifolds?

Answer 1

An update after many researches, advices etc..

One should look at discrete differential geometry and probably the most promising axis is triangular/quadrilateral surfaces i.e: meshes.

Several differential geometry quantities are described on and between vertices,edges and faces.

While in my case, the problem finally converged to a 2D problem (thus not needing to compute ricci/riemann curvature tensors) one can then tackle the problem in higher dimensions by calculating discrete sectional curvatures from tangent planes in chosen directions.