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

TL;DR

TensoriaCalc is a user-friendly tensor calculus package integrated with the Wolfram Language, enabling comprehensive differential geometry operations and tensor manipulations within a consistent environment.

Contribution

It introduces a new tensor calculus package that seamlessly integrates with Wolfram Language, supporting multiple metrics and various geometric operations.

Findings

Supports multiple metrics in a session

Enables standard differential geometry computations

Includes non-metric tensor operations

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.