The Invar tensor package

Abstract

The Invar package is introduced, a fast manipulator of generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible connection. The package can maximally simplify any polynomial containing tensor products of up to seven Riemann tensors within seconds. It has been implemented both in Mathematica and Maple algebraic systems. Program summary Program title:Invar Tensor Package Catalogue identifier:ADZK_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZK_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 136 240 No. of bytes in distributed program, including test data, etc.:2 711 923 Distribution format:tar.gz Programming language:Mathematica and Maple Computer:Any computer running Mathematica versions 5.0 to 5.2 or Maple versions 9 and 10 Operating system:Linux, Unix, Windows XP RAM:30 Mb Word size:64 or 32 bits Classification:5 External routines:The Mathematica version requires the xTensor and xPerm packages. These are freely available at http://metric.iem.csic.es/Martin-Garcia/xAct Nature of problem:Manipulation and simplification of tensor expressions. Special attention on simplifying scalar polynomial expressions formed from the Riemann tensor on a four-dimensional metric-compatible manifold. Solution method:Algorithms of computational group theory to simplify expressions with tensors that obey permutation symmetries. Tables of syzygies of the scalar invariants of the Riemann tensor. Restrictions:The present versions do not fully address the problem of reducing differential invariants or monomials of the Riemann tensor with free indices. Running time:Less than a second to fully reduce a monomial of the Riemann tensor of degree 7 in terms of independent invariants.