Tensor calculations

Question

During my current work, I want to calculate expression $\nabla_{\gamma}\nabla_{\beta}\nabla_{\alpha}\left(\frac{1}{R}\right)$, where $R\equiv\sqrt{x^2+y^2+z^2}$ and $\alpha$, $\beta$, $\gamma$ are 3D-indices (1,2,3) and metric is euclidean, $\nabla_{\alpha}\equiv\frac{\partial}{\partial x^{\alpha}}$. I try to use Ricci package, but I did not find any suitable examples in documentation. Does anybody try to calculate expressions like that?

On https://en.wikipedia.org/wiki/Tensor_software I find some similar packages, but I have not got enough experience in Mathematica and can not choose the simplest way to solve my problem.

Answer 1

Perhaps you can use my answer to Cartesian tensor gradient? For instance:

D[1/R, R[α], R[β], R[γ], NonConstants->{R}] //TeXForm

$\frac{3 R_{\alpha } \delta _{\beta ,\gamma }}{R^5}+\frac{3 R_{\beta } \delta _{\alpha ,\gamma }}{R^5}+\frac{3 R_{\gamma } \delta _{\alpha ,\beta }}{R^5}-\frac{15 R_{\alpha } R_{\beta } R_{\gamma }}{R^7}$