xAct:  Efficient tensor computer algebra for the Wolfram Language

José M. Martín-García, GPL 2002-2024

Main collaborators: Alfonso García-Parrado, Alessandro Stecchina, Barry Wardell, Cyril Pitrou, David Brizuela, David Yllanes, Guillaume Faye, Leo Stein, Renato Portugal, Teake Nutma, Thomas Bäckdahl.

Introduction

xAct is a suite of free packages for tensor computer algebra in the Wolfram Language. xAct implements state-of-the-art algorithms for fast manipulations of indices and has been modelled on the current geometric approach to General Relativity. It is highly programmable and configurable. Since its first public release in March 2004, xAct has been intensively tested and has solved a number of hard problems in GR.

There are four packages acting as a kernel for the rest:

• xCore: generic programming tools
• xPerm: manipulation of large groups of permutations
• xTensor: abstract tensor computations, the flagship of the system
• xCoba: component tensor computations

Other packages include:

• xPert: high-order perturbation theory in GR, by David Brizuela, JMMG and Guillermo Mena Marugán.
• Harmonics: tensor spherical harmonics, by David Brizuela, JMMG and Guillermo Mena Marugán.
• Invar: polynomial invariants of the Riemann tensor, by JMMG, David Yllanes, Renato Portugal and Leon Manssur.
• Spinors: spinor computations in GR, by Alfonso García-Parrado and JMMG.
• xPrint: Formatted input for xAct, by Alessandro Stecchina.
• SymManipulator: Symmetrized expressions in xAct, by Thomas Bäckdahl.
• AVF: Exterior calculus with algebra-valued forms, by Hugo D. Wahlquist.
• xTras: Additions to xAct, by Teake Nutma.
• TexAct: Tex code to format xAct expressions, by Thomas Bäckdahl, JMMG and Barry Wardell.
• xPand: Cosmological perturbation theory, by Cyril Pitrou, Xavier Roy and Obinna Umeh.
• xTerior: Exterior calculus, by Alfonso García-Parrado and Leo C. Stein.
• SpinFrames: NP and GHP form of spinor equations, by Thomas Bäckdahl and Steffen Aksteiner.
• xIST/COPPER: General scalar-tensor theories and perturbations, by Johannes Noller.
• EFTofPNG:: Effective field theory of post-Newtonian gravity, by Michele Levi and Jan Steinhoff.
• bimEX: 3 + 1 Bimetric relativity, by Francesco Torsello.
• FieldsX: Fermions, gauge fields and BRST cohomology, by Markus B. Fröb.
• xPPN: Parametrized post-Newtonian formalism, by Manuel Hohmann.
• SymSpin: Symmetric spinors, by Steffen Aksteiner and Thomas Bäckdahl.
• HiGGS: Hamiltonian analysis of Poincaré gauge theory, by Will Barker.
• xBrauer: Brauer algebra for tensor calculus, by Thomas Helpin.
• PSALTer: Particle spectrum for any tensor Lagrangian, by Will Barker, Carlo Marzo and Claire Rigouzzo.

A single file with the current versions (17 October 2021) of all packages can be downloaded: xAct_1.2.0.tgz for linux/unix/mac, or xAct_1.2.0.zip for windows. See the Installation notes.

Check http://contrib.xact.es for possible updates of some of those packages, or entirely new packages. See also there the page of contributed example notebooks.

Examples: very simple session, check of the Bianchi identities for a connection with torsion, benchmarking examples.

xAct is free software. Please cite the associated publications and this web page if you use it.

For comments or questions, please contact jose@xact.es, or send your questions to the xAct forum.

News

4 March 2024: xAct is 20 years old!

• Watch a series of talks by xAct developers to celebrate two decades of tensor computation.

22 November 2023: 1000 documents with xAct.

• The articles page has collected 1000 articles or theses acknowleging the use of xAct in their computations. Many thanks to all developers and authors who have contributed to reaching this milestone!

17 October 2021: Version 1.2.0 of xAct release.

• Added new package SymSpin by Steffen Aksteiner and Thomas Bäckdahl.

28 February 2021: Version 1.1.5 of xAct release.

16 February 2020: Version 1.1.4 of xAct release:

• Added examples section in xCobaDoc.nb on CTensor computation in flat space.
• New symbol ATensor to use abstract tensors without the need of DefTensor.
• Bug fixes.

Previous news

CopyLeft

The programs in this page are distributed as free software under the GNU General Public License. They are distributed in the hope that they wil be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.