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:
- 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
- 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
- xTerior: Exterior calculus
Check http://contrib.xact.es for possible updates of some of those packages.
xAct is free software. Please cite the associated publications and this web page if you use it.
- 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.
- 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 contrib.xact.es 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.
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.