Tensor calculus with open-source software: the SageManifolds project

Abstract

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.

17 pages, 6 figures, many small changes w.r.t. v1; to appear in the Proceedings of "ERE2014: Almost 100 years after Einstein's revolution" (Journal of Physics: Conference Series)

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• xPerm: fast index canonicalization for tensor computer algebra
• A field-theory motivated approach to symbolic computer algebra
• A spacetime characterization of the Kerr metric
• New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory
• Tensor computations in computer algebra systems

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• Compact objects with scalar charge embedded in a magnetic or electric field in Einstein-Maxwell-dilaton theories
• A polynomial affine model of gravity: after ten years
• Symbolic analysis of second-order ordinary differential equations with polynomial coefficients
• de Sitterization via Kerr-Schild
• Radiating solutions in Entangled Relativity