TensoriaCalc: A User-Friendly Tensor Calculus Package for the Wolfram Language

Abstract

We describe TensoriaCalc, a tensor calculus package written to be smoothly consistent with the Wolfram Language, so as to ensure ease of usage. It allows multiple metrics to be defined in a given session; and, once a metric is computed, associated standard differential geometry operations to be carried out - covariant derivatives, Hodge duals, index raising and lowering, derivation of geodesic equations, etc. Other non-metric operations, such as the Lie and exterior derivatives, coordinate transformation on tensors, etc. are also part of its built-in functionality.

126 pages. Many figures. The TensoriaCalc code and user guide can be found http://www.stargazing.net/yizen/Tensoria.html and https://github.com/tensoria/TensoriaCalc