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