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xAct:  Efficient tensor computer algebra for the Wolfram Language

José M. Martín-García, GPL 2002-2018

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 Mathematica. 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:

Application packages include:

Contributed packages:

A single file with the current versions (28 February 2018) of all packages can be downloaded: xAct_1.1.3.tgz for linux/unix/mac, or for windows. See the Installation notes.

Check for possible updates of some of those packages.

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.


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.
23 August 2015: Version 1.1.2 of xAct released:
  • New package SpinFrames, by T. Bäckdahl and S. Aksteiner, for the Newman-Penrose (NP) and Geroch-Held-Penrose (GHP) form of spinor equations.
  • Better support for the CTensor framework in xTerior.
  • Various improvements in TexAct.
  • LieDToCovD now handles connections with torsion.
28 September 2014: Version 1.1.1 of xAct released:
  • xAct is now compatible with Mathematica 10.
  • SymManipulator: Some group theoretical algorithms are now coded in the external xperm C executable.
  • TexAct: Better handling of parentheses and support for xTerior.
  • xCoba: Simplification in MetricCompute is now parallelizable.
  • xPert: Perturbation of the metric determinant is now computed using the trace-log formula.
  • xTras: Much faster version of AllContractions and improved symmetrized derivatives.
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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.