论文信息 - Tensor calculus with open-source software: the SageManifolds project

Tensor calculus with open-source software: the SageManifolds project

The SageManifolds project aims at extending the mathematics software system Sage towards differential geometry and tensor calculus. Like Sage, SageManifolds is free, open-source and is based on the Python programming language. We discuss here some details of the implementation, which relies on Sage's parent/element framework, and present a concrete example of use.

[1] D. A. Bolotin,et al. Introduction to Redberry: the computer algebra system designed for tensor manipulation , 2013, ArXiv.

[2] Malcolm MacCallum,et al. COMPUTER ALGEBRA IN GENERAL RELATIVITY , 2002 .

[3] José M. Martín-García,et al. xPerm: fast index canonicalization for tensor computer algebra , 2008, Comput. Phys. Commun..

[4] G. Cl'ement,et al. The gravitating ? model in 2 + 1 dimensions: black hole solutions , 1998 .

[5] Kasper Peeters,et al. Cadabra: a field-theory motivated symbolic computer algebra system , 2006, Comput. Phys. Commun..

[6] François Apéry,et al. La surface de Boy , 1986 .

[7] Charles G. Torre,et al. New symbolic tools for diffe rential geometry, gravitation, and field theor y , 2012 .

[8] Richard A. Matzner,et al. Computer programs for calculating general- relativistic curvature tensors. , 1967 .

[9] N. Steenrod. The Topology of Fibre Bundles. (PMS-14) , 1951 .

[10] Guillaume Connan,et al. Calcul mathématique avec Sage , 2013 .

[11] Dmitry S. Kulyabov,et al. Tensor computations in computer algebra systems , 2013, Programming and Computer Software.

[12] Marc Mars. A spacetime characterization of the Kerr metric , 1999 .