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


© 2002-2008, under the GNU General Public License (GPL)
     José M. Martín-García
    Instituto de Estructura de la Materia, CSIC, Spain

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


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]

Load the package

0. Basics

1. Manifolds, vector bundles and parameters

2. Indices

3. Tensors and tensor slots

4. Canonicalization

5. Rules and patterns

6. Derivatives

7. Metrics

8. More on rules

9. Manipulation of expressions

10. Final comments

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