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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.


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:

Other packages include:

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 for windows. See the Installation notes.

Check 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, or send your questions to the xAct forum.


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.
28 February 2018: Version 1.1.3 of xAct released:
  • Extended documentation file xCobaDoc.nb, now also covering the CTensor framework.
  • New version of TexAct, improving parenthesization support, more flexible use of the box typesetting language, and other things.
  • Bug fixes.
Previous news


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.