Writing (mixed) tensors

Question

Does anybody know about a specific package for handling tensors? Consider, for example, a contraction of the type

$g^{\alpha\beta}g^{\gamma\delta}R_{\alpha\mu\gamma\nu}=R^{\beta\;delta}_{\;\mu\;\nu}$

Handling the indices in the mixed tensor in the r.h.s. appears particularly annoying and the result is not aesthetically satisfying. Any suggestion?

Answer 1

Is the result you are looking for?

\documentclass{article}
\usepackage{amsmath}
\usepackage{tensor}

\begin{document}
$g^{\alpha\beta}g^{\gamma\delta}R_{\alpha\mu\gamma\nu}=R^{\beta\;\delta}_{\;\mu\;\nu}$

$g^{\alpha\beta}g^{\gamma\delta}R_{\alpha\mu\gamma\nu}
    =\tensor{R}{^\beta_\mu^\delta_\nu}$
\end{document}