xAct:  Efficient tensor computer algebra for Mathematica

José M. Martín-García, GPL 2002-2013

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 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:

• 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: high-order 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 algebra-valued forms
• xTras: Additions to xAct
• TexAct: Tex code to format xAct expressions
• xPand: Cosmological perturbation theory

A single file with the current versions (30 January 2013) of all packages can be downloaded: xAct_1.0.5.tgz for linux/unix/mac, or xAct_1.0.5.zip 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 jose@xact.es

News

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).

25 October 2011: Version 1.0.3 of xAct released:

• This is another bug-fix version.
• Updated Spinors for publication.
• Added messages reporting non-standard configuration in some packages.

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.