Abstract
The book "Handbook of Finsler geometry" has been included with a CD containing an elegant Maple package, FINSLER, for calculations in Finsler geometry. Using this package, an example concerning a Finsler generalization of Einstein's vacuum field equations was treated. In this example, the calculation of the components of the hv-curvature of Cartan connection leads to wrong expressions. On the other hand, the FINSLER package works only in dimension four. We introduce a new Finsler package in which we fix the two problems and solve them. Moreover, we extend this package to compute not only the geometric objects associated with Cartan connection but also those associated with Berwald, Chern and Hashiguchi connections in any dimension. These improvements have been illustrated by a concrete example. Furthermore, the problem of simplifying tensor expressions is treated. This paper is intended to make calculations in Finsler geometry more easier and simpler.
Program summary
Program title: Finsler
Catalogue identifier: AERE_v1_0
Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AERE_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.: 18401
No. of bytes in distributed program, including test data, etc.: 233369
Distribution format: tar.gz
Programming language: Maple 12 or higher.
Computer: any computer where the Maple program can be installed.
Operating system: any system running Maple.
RAM: the computer should possess sufficient RAM comparable with the complexity of the performed computations; it is preferable to have 2 GB or more.
Classification: 1.5, 1.9, 4.12.
Nature of problem:
the FINSLER package [2] (included with [1]) has some problems: the wrong calculations of the hv-curvature components of Cartan connection and the non-ability of computing some curvature tensors in dimensions different from four. Moreover, it computes some geometric objects in a non-simplified form.
Solution method:
in the new package, the above mentioned problems have been solved. The FINSLER package has been extended to be able to compute the geometric objects associated with Berwald, Chern and Hashiguchi connections (besides those associated with Cartan connection) in any dimension. A technique for tensor simplification has been introduced.
Additional comments:
other new tensors or geometric objects not defined in the package can be added in a similar manner.
Running time:
the examples provided take only a few seconds to run.
References:
[1] P.L. Antonelli (Ed.), Handbook of Finsler geometry I, II, Kluwer Acad. publ., 2003.
[2] S.F. Rutz and R. Portugal, FINSLER: A computer algebra package for Finsler geometries, Nonlinear Analysis, 47 (2001) 6121-6134. (C) 2013 Elsevier B.V. All rights reserved.