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A Mathematica package for calculation covariant series expansions of fundamental bitensors http://www.barrywardell.net/research/…
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=============================================================================== 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>.