**
***xAct:*
Efficient tensor computer algebra for the Wolfram Language

*xAct:*Efficient tensor computer algebra for the Wolfram Language

#### José M. Martín-García, GPL 2002-2018

**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*xTerior*: Exterior calculus*SpinFrames*: NP and GHP form of spinor equations

A single file with the current versions (28 February 2018) of all packages can be downloaded: xAct_1.1.3.tgz for linux/unix/mac, or xAct_1.1.3.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

- 28 February 2018: Version 1.1.3 of
*xAct*released: -
- Extended documentation file xCobaDoc.nb, now also covering the
**CTensor**framework. - New version of
*TexAct*, improving parenthesization support, more flexible use of the box typesetting language, and other things. - Bug fixes.

- Extended documentation file xCobaDoc.nb, now also covering the

- 23 August 2015: Version 1.1.2 of
*xAct*released: -
- New package
*SpinFrames*, by T. Bäckdahl and S. Aksteiner, for the Newman-Penrose (NP) and Geroch-Held-Penrose (GHP) form of spinor equations. - Better support for the
**CTensor**framework in*xTerior*. - Various improvements in
*TexAct*. **LieDToCovD**now handles connections with torsion.

- New package

- 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.

# 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.