Ricci

Ricci — A Mathematica package for doing tensor calculations in differential geometry. Ricci is a Mathematica package for doing symbolic tensor computations that arise in differential geometry. It has the following features and capabilities: Manipulation of tensor expressions with and without indices; Implicit use of the Einstein summation convention; Correct manipulation of dummy indices; Display of results in mathematical notation, with upper and lower indices; Automatic calculation of covariant derivatives; Automatic application of tensor symmetries; Riemannian metrics and curvatures; Differential forms; Any number of vector bundles with user-defined characteristics; Names of indices indicate which bundles they refer to; Complex bundles and tensors; Conjugation indicated by barred indices; Connections with and without torsion.