xTensor: Fast abstract tensor computer algebra

Author: José M. Martín-García, © 2002-2020 under GPL

Introduction

xTensor extends Mathematica capabilities in abstract tensor calculus, specially in General Relativity. It works with tensors with arbitrary symmetries under permutations of indices, defined on several different manifolds and products of them. It computes covariant derivatives, Lie derivatives and parametric derivatives. It allows the presence of a metric in each manifold and defines all the associated tensors (Riemann, Ricci, Einstein, Weyl, etc.)

xTensor does not perform component calculations. Use the companion package xCoba.

xTensor needs the package xPerm in order to compute the canonical form of a list of indices under permutation symmetry groups.

See xTensor.History.

Download and installation

Current version: 1.1.4 (as of 16 February 2020). It is recommended to download the main xAct bundle, but you can also download the different files separately:

• xTensor.nb: source file with all definitions and comments. Many examples. You need this file if you want to understand and/or modify the internals of the package. It's almost a Reference file.
• xTensor.m: package file. This file is automatically generated by Mathematica when xTensor.nb is saved. This is the only essential file.
• xTensorDoc.nb: main documentation file.
• xTensorRefGuide.nb: reference guide with details but not examples.
• General Public License

See the Installation notes for instructions.

Other documentation

Notes for a course on xTensor, held in Paris in April 2009:

• Introductory talk (1 hour, pdf).
• Basic concepts (2 hours, mathematica slide show).
• Intermediate concepts (2 hours, mathematica slide show).
• Advanced concepts (2 hours, mathematica slide show).