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Invar: computer algebra for the invariants of the Riemanntensor

Published online by Cambridge University Press:  30 September 2008

A. Oscoz ,
E. Mediavilla ,
M. Serra-Ricart ,
J.M. Martín-García ,
D. Yllanes  and
R. Portugal
J.M. Martín-García
Affiliation:
Instituto de Estructura de la Materia, CSIC, C/ Serrano 123, 28006 Madrid, Spain
D. Yllanes
Affiliation:
Instituto de Estructura de la Materia, CSIC, C/ Serrano 123, 28006 Madrid, Spain
R. Portugal
Affiliation:
Laboratório Nacional de Computação Científica (LNCC), Av. Getúlio Vargas 333, Petrópolis, RJ, CEP 25651-075, Brazil
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Abstract

We report on the systematic listing of polynomial relations among the algebraic invariants of a Riemann tensor. We construct all such relations for the 3 × 1029 invariants with up to seven Riemann tensors, and provide the computer algebra system Invar (both for Mathematica and Maple) which uses them to maximally simplify any invariant within seconds. We also report work in progress to extend Invar and its database to handle all differential Riemann invariants up to 12 derivatives of the metric.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 30: Spanish Relativity Meeting - Encuentros Relativistas Españoles , ERE2007: Relativistic Astrophysics and Cosmology , 2008 , pp. 223 - 226
Copyright
© EAS, EDP Sciences, 2008

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