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[Licence| Download | E-mail| 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.

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.