xAct: Efficient tensor computer algebra for Mathematica
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
A single file with the current versions (10 January 2010) of all packages can be downloaded: xAct_0.9.9.tgz for linux/unix/mac, or xAct_0.9.9.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 a scientific project, and hence free software. Please cite the associated publications and this web page if you use it. I would be happy to collaborate in your project, offering my expertise with the system and developing new tools if they were required to solve it.
News
- 10 January 2010: Version 0.9.9 of xAct rereleased with more bug fixes.
- 24 November 2009: Version 0.9.9 of xAct rereleased with some bug fixes.
- 9 September 2009: Version 0.9.9 of xAct released, on the same day of the celebration honoring the 65th birthday of Prof. Jesús Martín. This version of xAct will be nicknamed "Chus" after him.
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- Note that now the xAct.tar.gz bundle contains all packages.
- Documentation of Spinors enlarged and rearranged.
- xCoba has a command MetricCompute to construct sequentially components of curvature tensors. See file KerrNewmanExamples.nb.
- Added Leibnitz operator, following Jan's suggestion.
- Support for LaTeX printing of tensor expressions, with commands Tex, TexPrint and TexBreak.
- Safer code for NoScalar.
- Fixed some problems with VarD.
- 1 December 2008: Version 0.9.1 of Spinors released.
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- Added command IrreducibleDecomposition decomposing spinors in their symmetric-tracefree parts.
- The package now handles spacetimes with torsion.
- 23 November 2008: Version 0.9.8 of xAct released.
- Transition version with many small improvements in xTensor:
- Better treatment of 1-dimensional spaces.
- New functions for ADM-like decompositions: commands GaussCodazzi, ToInducedDerivative and DirCovDToLieD.
- Fixed a number of problems with variational derivatives.
- New command Cyclize, similar to Symmetrize, etc.
- Faster manipulations of products of delta's.
- Added option Method in ToCanonical, to choose how to deal with metric-incompatible derivatives.
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.