Symbolic tensor calculus on manifolds: a SageMath implementation
arXiv:1804.07346 · doi:10.5802/ccirm.26
Abstract
These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on non-parallelizable manifolds and (iv) is independent of the symbolic backend used to perform calculus at the level of coordinate expressions. In addition to the main ideas, we discuss some details of the implementation in the open-source mathematics software system SageMath, which has been performed via the SageManifolds project.
Lectures at JNCF 2018, CIRM, Marseille (France); 58 pages; to appear in "Les Cours du CIRM" (cedram.org); changes with respect to v1: cedram format, some updates, LaTeX rendering of Jupyter cells
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