SimpleTensor -- a user-friendly Mathematica package for elementary tensor and differential-geometric calculations

TL;DR

SimpleTensor is a Mathematica package that simplifies elementary tensor and differential geometry calculations, emphasizing ease of use, versatility, and hackability for users.

Contribution

It introduces a user-friendly, all-purpose Mathematica package for tensor and differential geometry calculations, contrasting with more complex existing tools.

Findings

Supports tensor contractions with Einstein notation

Enables basis transformations and tensor derivatives

Includes exterior derivative and interior product functions

Abstract

In this paper we present a short overview of the new Wolfram Mathematica package intended for elementary "in-basis" tensor and differential-geometric calculations. In contrast to alternatives our package is designed to be easy-to-use, short, all-purpose, and hackable. It supports tensor contractions using Einstein notation, transformations between different bases, tensor derivative operator, expansion in basis vectors and forms, exterior derivative, and interior product.