This is the doc file xTensorDoc.nb of version 0.9.5 of xTensor`. Last update on 13 May 2008.

Author

© 2002-2008, under the GNU General Public License (GPL)

José M. Martín-García

Instituto de Estructura de la Materia, CSIC, Spain

jmm@iem.cfmac.csic.es

http://metric.iem.csic.es/Martin-Garcia/

Helped by:

Alfonso García-Parrado (algar@mai.liu.se): design of vector bundles and complex structure from version 0.9.0.

Intro

xTensor` extends Mathematica capabilities in abstract tensor calculus, specially in General Relativity. It works with tensors with arbitrary symmetries under permutations of indices, defined on several different manifolds and direct products of them. It computes covariant derivatives, Lie derivatives, parametric derivatives and variational derivatives. It allows the presence of a metric in each manifold and defines all the associated tensors (Riemann, Ricci, Einstein, Weyl, etc.)

xTensor` does not perform component calculations. See the twin package xCoba` or use another package like GRTensorM` for that purpose.

xTensor` needs the twin package xPerm` in order to compute the canonical form of a list of indices under certain symmetry group.

xTensor` has been designed with the following priorities in mind:

1.- Mathematical structure

2.- Efficiency

3.- Compliance with Mathematica style

4.- Simplicity of input/output

In particular, concerning the mathematical structure, xTensor` imitates the usual cycle in mathematics ``let X be a (Type) with properties props; then use it to do some computations´´ with the general form of declaration

DefType[X, props]

computations

1. Manifolds, vector bundles and parameters

9. Manipulation of expressions

Created by Mathematica (May 16, 2008) |