Programs in Physics & Physical Chemistry
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Programs in Physics & Physical Chemistry |
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| 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. |
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