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xAct:  Efficient tensor computer algebra for Mathematica

José M. Martín-García, GPL 2002-2014

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 (23 February 2014) of all packages can be downloaded: xAct_1.1.0.tgz for linux/unix/mac, or for windows. See the Installation notes.

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.


15 February 2014: Version 1.1.0 of xAct released:
(Very many thanks to Alfonso García-Parrado, who was fully in charge of this release.)
  • New package xTerior, by A. García-Parrado and L. C. Stein, for exterior calculus.
  • Optimized Windows binaries of xperm.c prepared by T. Bäckdahl.
  • More functionality for tensors by components in xCoba.
  • Improved functionality in TexAct by T. Bäckdahl.
  • Improved functionality in xTras by T. Nutma.
  • There is a new page for development of new packages in xAct, mantained by L. C. Stein and and T. Nutma.
27 January 2013: Version 1.0.5 of xAct released:
(Thanks to Teake Nutma and Cyril Pitrou for much help with this release!)
  • xAct is now compatible with Mathematica 9.
  • New package xPand, by C. Pitrou, X. Roy and O. Umeh, for cosmological perturbation theory around homogeneous spacetimes.
  • The xTras package is now included in the xAct distribution.
  • Functions Permute and PowerPermute respectively renamed PermProduct and PermPower in xPerm.
  • Improved some basic functionality in the area of induced metrics in xTensor.
  • Started new notation for tensors by components in xCoba.
5 May 2012: Version 1.0.4 of xAct released:
(Thanks to Thomas Bäckdahl for much help with this release!)
  • Yet another bug-fix version.
  • Package TexAct excised from xTensor and SymManipulator to handle conversion to Tex output.
  • Package AVF now included in the xAct distribution.
  • Added command xTension to provide hooks to modify the action of the Def/Undef commands.
  • The SymManipulator package can now do irreducible decompositions of spinor expressions.
  • Added partial support for SeriesData expressions (everything but ToCanonical).
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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.