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[Licence| Download | New Version Template] adzk_v1_0.tar.gz(2648 Kbytes)
Manuscript Title: The Invar Tensor Package
Authors: J.M. Martín-García, R. Portugal, L.R.U. Manssur
Program title: Invar Tensor Package
Catalogue identifier: ADZK_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 177(2007)640
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
Keywords: Riemann tensor, tensor calculus, Mathematica, Maple, computer algebra.
PACS: 02.70.Wz, 04.20.-q, 02.40.Ky.
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.

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.