DifferentialGeometry swMATH ID: 7593 Software Authors: Anderson, I.M.; Torre, C.G. Description: New symbolic tools for differential geometry, gravitation, and field theory. 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. Homepage: http://www.maplesoft.com/support/help/Maple/view.aspx?path=DifferentialGeometry Dependencies: Maple Keywords: Maple software package DifferentialGeometry Related Software: Maple; GeM; LieAlgebrasOfVectorFields; SADE; Rif; Vessiot; CLUCalc; MapDE; CRACK; REDUCE; Mathematica; Cartan; Maxima; xTerior; Redberry; xTensor; Invar; GRTensorII; Cadabra; ATENSOR Cited in: 30 Publications all top 5 Cited by 35 Authors 11 Tychkov, Sergey N. 10 Duyunova, Anna Andreevna 10 Lychagin, Valentin V. 4 Anderson, Ian M. 4 Torre, Charles G. 2 Hereman, Willy A. 2 Hrdina, Jaroslav 2 Huang, S.-L. Tracy 2 Mohammadi, Zahra 2 Reid, Gregory John 2 Vassiliou, Peter John 2 Zalabová, Lenka 1 Adams, Paul J. 1 De Doná, José A. 1 Doubrov, Boris M. 1 Eklund, Holly L. 1 Fels, Mark E. 1 Furutani, Kenro 1 Galaev, Anton S. 1 Godoy Molina, Mauricio 1 Herbst, Barend M. 1 Hickman, Mark S. 1 Huang, Tracy Shih-lung 1 Hubert, Evelyne 1 Lisle, Ian G. 1 Markina, Irina 1 Medvedev, Aleksandr Vladislavovich 1 Morimoto, Tohru 1 Návrat, Aleš 1 Poole, Douglas 1 Sagerschnig, Katja 1 Tehseen, Naghmana 1 The, Dennis 1 Vasilev, Alexander 1 Willse, Travis all top 5 Cited in 16 Serials 5 Journal of Geometry and Physics 3 Lobachevskii Journal of Mathematics 2 Journal of Mathematical Physics 2 Journal of Symbolic Computation 2 Journal of Dynamical and Control Systems 2 Analysis and Mathematical Physics 1 General Relativity and Gravitation 1 Letters in Mathematical Physics 1 Archivum Mathematicum 1 Journal of Pure and Applied Algebra 1 Mathematics and Computers in Simulation 1 Programming and Computer Software 1 SIAM Journal on Control and Optimization 1 The Journal of Geometric Analysis 1 Journal of Lie Theory 1 Mathematics in Computer Science all top 5 Cited in 20 Fields 16 Differential geometry (53-XX) 13 Partial differential equations (35-XX) 10 Fluid mechanics (76-XX) 8 Computer science (68-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Topological groups, Lie groups (22-XX) 4 Systems theory; control (93-XX) 3 Field theory and polynomials (12-XX) 3 Nonassociative rings and algebras (17-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Relativity and gravitational theory (83-XX) 2 Ordinary differential equations (34-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Associative rings and algebras (16-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) Citations by Year