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Invar: computer algebra for the invariantsof 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 relationsamong the algebraic invariants of a Riemann tensor. We constructall such relations for the 3 × 1029 invariants with upto seven Riemann tensors, and provide the computer algebra systemInvar (both for Mathematica and Maple)which uses them to maximally simplify any invariant within seconds.We also report work in progress to extend Invarand its database to handle all differential Riemann invariants upto 12 derivatives of the metric.

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