2011/03/08 by I. M. Anderson, C. G. Torre · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Black Holes and Theoretical Physics #Differential (mechanical device) #Differential algebraic geometry #Differential geometry #Field (mathematics) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Symbolic computation #Tensor calculus #Tensor field #Vector field #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/1.3676296
42 pages
arxiv created 2011/03/08 · openalex publication_date 2012/01/01 · arxiv updated 2015/05/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations.