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ccgrg - the symbolic tensor analysis package, with tools for general relativity
Authors

Andrzej Woszczyna
Organization: Copernicus Center for Interdisciplinary Studies, Krakow
Wojciech Czaja
Krzysztof Głód
Zdzisław A. Golda
Andrzej Odrzywołek
Piotr Plaszczyk
Lech Sokołowski
Sebastian Szybka
Organization: Jagiellonian University
Radosław Kycia
Organization: Jagiellonian University
Revision date

2014-03-05
Description

Riemann and Weyl curvature, covariant derivative, Lie derivative, the first and the second fundamental form on hyper-surfaces, as well as basic notions of relativistic hydrodynamics (expansion, vorticity, shear) are predefined functions of the package. New tensors are easy to define. Instructions, basic examples, and some more advanced examples are attached to the package.

Characteristic feature of the ccgrg package is the specific coupling between the functional programming and the Parker-Christensen index convention. This causes that no particular tools to rising/lowering tensor indices neither to the tensor contractions are needed. Tensor formulas are written in the form close to that of classical textbooks in GRG, with the only difference that the summation symbol appears explicitly. Tensors are functions, not matrixes, and their components are evaluated lazily. This means that only these components which are indispensable to realize the final task are computed. The memoization technique prevents repetitive evaluation of the same quantities. This saves both, time and memory.
Subjects

*Mathematica Technology > Application Packages > Applications from Independent Developers > Tensors in Physics
*Mathematica Technology > Programming > Symbolic Computation
*Mathematics > Calculus and Analysis > Differential Geometry
*Science > Physics > Astrophysics
*Science > Physics > Relativity Theory
Keywords

symbolic, dynamic programming, tensor, relativity, gravitation, cosmology, astrophysics, perturbations, relativistic fluids
Downloads

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ccgrg_pack.zip (888.2 KB) - ZIP archive