Invar` is currently a package for efficient simplification of the algebraic and differential polynomial scalars (usually known as invariants) of the Riemann tensor of a metric-compatible connection. The medium term goal is generalizing Invar` to simplify generic polynomial expressions (with free indices) of the Riemann tensor.
Invar` requires the tensor computer algebra system xTensor` when running on Mathematica. There is a twin version for Maple, based on the tensor system Canon. It can be downloaded, under the General Public Licence, from
    http://www.lncc.br/~portugal/        (Maple version)

For further information, see the articles
     The Invar tensor package, J.M. Martín-García, R. Portugal and L.R.U. Manssur, Comp. Phys. Comm. 177, 640 (2007)
     The Invar tensor package: Differential invariants of Riemann, J.M. Martín-García, D. Yllanes and R. Portugal, Comp. Phys. Comm. (2008)

Subsection 6.3 contains a number of tests designed to check most capabilities of Invar`. They all should give zero.

Load the package and configure

1. Example session

2. General concepts and definitions

3. Canonical invariants

4. Inv -> Permutation -> Riemann

5. Riemann -> Permutation -> Inv

6. Simplification

7. Working with order 12 invariants

8. The (algebraic) Narlikar and Karmarkar basis

9. Final comments

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