Invar: computer algebra for the invariants of the Riemann tensor

¹ Instituto de Estructura de la Materia, CSIC, C/ Serrano 123, 28006 Madrid, Spain
² Laboratório Nacional de Computação Científica (LNCC), Av. Getúlio Vargas 333, Petrópolis, RJ, CEP 25651-075, Brazil

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.