xAct: Efficient tensor computer algebra for the Wolfram Language
José M. MartínGarcía, GPL 20022016
Main collaborators: Alfonso GarcíaParrado, 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 Mathematica. xAct implements stateoftheart 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
Application packages include:
 xPert: highorder perturbation theory in GR
 Harmonics: tensor spherical harmonics
 Invar: polynomial invariants of the Riemann tensor
 Spinors: spinor computations in GR
Contributed packages:
 xPrint: Formatted input for xAct
 SymManipulator: Symmetrized expressions in xAct
 AVF: Exterior calculus with algebravalued forms
 xTras: Additions to xAct
 TexAct: Tex code to format xAct expressions
 xPand: Cosmological perturbation theory
 xTerior: Exterior calculus
 SpinFrames: NP and GHP form of spinor equations
A single file with the current versions (23 August 2015) of all packages can be downloaded: xAct_1.1.2.tgz for linux/unix/mac, or xAct_1.1.2.zip for windows. See the Installation notes.
Check http://contrib.xact.es 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 jose@xact.es, or send your questions to the xAct forum.
News
 23 August 2015: Version 1.1.2 of xAct released:

 New package SpinFrames, by T. Bäckdahl and S. Aksteiner, for the NewmanPenrose (NP) and GerochHeldPenrose (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 tracelog formula.
 xTras: Much faster version of AllContractions and improved symmetrized derivatives.
 15 February 2014: Version 1.1.0 of xAct released: (Very many thanks to Alfonso GarcíaParrado, who was fully in charge of this release.)

 New package xTerior, by A. GarcíaParrado 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 contrib.xact.es for development of new packages in xAct, mantained by L. C. Stein and and T. Nutma.
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.