A Mathematica package for calculation covariant series expansions of fundamental bitensors
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Documentation/English
Kernel
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.MathematicaResources
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AbstractMatrix.m
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CovariantSeries.m
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README

README

===============================================================================
CovariantSeries - Version 1.1
===============================================================================
Copyright 2009-2012 Barry Wardell

The CovariantSeries package and the associated AbstractMatrix package provide
symbolic Mathematica code for calculating covariant series expansions of
fundamental bi-tensors including the world-function, the van Vleck determinant,
the bi-vector of parallel transport, the bi-scalar V(x,x') appearing in the
Hadamard form of the scalar Green function and the DeWitt coefficients.
===============================================================================

Getting the package
-------------------
The latest version of this software will always be available from the project
website:

http://www.barrywardell.net/Research/Code/CovariantSeries/

or directly from the git repository:

http://github.com/barrywardell/CovariantSeries

Install
---------
Extract the zip file and move the CovariantSeries folder into your Mathematica
applications folder. This is typically located in the following places:

Linux: 	/usr/share/Mathematica/Applications/
Mac:   	/Library/Mathematica/Applications/ or ~/Library/Mathematica/Applications/
Windows:Unknown

although any location listed by Mathematica's $Path variable should be fine.
The code can then be loaded into Mathematica using the command:

<< CovariantSeries`

For outputting in explicit Riemann tensor form, xTensor
(http://metric.iem.csic.es/Martin-Garcia/xAct/index.html) is required and the
AvramidiToXTensor package must also be loaded:

<< CovariantSeries`AvramidiToXTensor`

Examples
--------
For example usage, see the documentation which is available by entering "CovariantSeries"
into the search box in the Mathematica documentation.

Changelog
---------
26 Sep  2012: Version 1.1 released
              Add support for computing the bi-tensor U_n.
              Fix problems with interaction with recent versions of xTensor.
              AbstractMatrix package has been moved into CovariantSeries application
              rather than being a separate package.
              Renamed Bitensors variable to $Bitensors.
              Add Mathematica-style documentation.
17 Aug  2009: Version 1.0 released.
              Full support for converting to xTensor notation.
              Correct calculation of SqrtDeltaInvBitensor.
              More efficient calculation of DeWitt coefficients.
              Support for calculating off-diagonal DeWitt coefficients.
              Add support for a potential term in the wave equation.
26 June 2009: Version 0.9.1 released.
              No code changes, but repackaged so that Mathematica will
              actually load the package properly.
 2 June 2009: Initial version (0.9) released.

Known problems
--------------
None.

License
-------
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.

Contact
-------
For any queries, please contact Barry Wardell <CovariantSeries@barrywardell.net>.