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[Licence| Download | New Version Template] adzk_v2_0.tar.gz(31862 Kbytes)
Manuscript Title: The Invar Tensor Package: Differential invariants of Riemann
Authors: J.M. Martín-García, D. Yllanes, R. Portugal
Program title: Invar Tensor Package v2.0
Catalogue identifier: ADZK_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 179(2008)586
Programming language: Mathematica and Maple.
Computer: Any computer running Mathematica versions 5.0 to 6.0 or Maple versions 9 and 11.
Operating system: Linux, Unix, Windows XP, MacOS.
RAM: 100 Mb
Word size: 64 or 32 bits
Supplementary material: The new database of relations is much larger than that for the previous version and therefore has not been included in the distribution. To obtain the Mathematica and Maple database files click on this link.
Keywords: Riemann tensor, tensor calculus, Mathematica, Maple, computer algebra.
PACS: 02.70.Wz, 04.20.-q, 02.40.Ky.
Classification: 1.5, 5.

Does the new version supersede the previous version?: Yes. The previous version (1.0) only handled algebraic invariants. The current version (2.0) has been extended to cover differential invariants as well.

Nature of problem:
Manipulation and simplification of scalar polynomial expressions formed from the Riemann tensor and its covariant derivatives.

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.

Reasons for new version:
With this new version, the user can manipulate differential invariants of the Riemann tensor. Differential invariants are required in many physical problems in classical and quantum gravity.

Summary of revisions:
The database of syzygies has been expanded by a factor of 30. New commands were added in order to deal with the enlarged database and to manipulate the covariant derivative.

The present version only handles scalars, and not expressions with free indices.

Running time:
One second to fully reduce any monomial of the Riemann tensor up to degree 7 or order 10 in terms of independent invariants. The Mathematica notebook included in the distribution takes approximately 5 minutes to run.