![]() ![]() &minus : find the difference between two vectors, differential forms or tensors. &algmult : multiply two vectors in an algebra To display the help page for a particular DifferentialGeometry command, see Getting Help with a Command in a Package. The following is a list of available commands and subpackages.Ī brief description of the package's commands is as follows. Įach command in the DifferentialGeometry package can be accessed by using either the long form or the short form of the command name in the command calling sequence. The redesign and expansion of Vessiot to DifferentialGeometry for Maple 11 was done by I. Anderson, Florin Catrina, Sydney Chamberlain, Cinnamon Hillyard, Jeff Humphries, Jamie Jorgensen, Charles Miller, and Charles Torre at Utah State University. The DifferentialGeometry package is based upon the Vessiot package developed by I. The tutorials present specialized applications of the DifferentialGeometry package. Each lesson contains a set of exercises which range in difficult from simple computational exercises to programming exercises. The lessons worksheets provide a systematic approach to learning the commands in the DifferentialGeometry, Tensor, LieAlgebras, and JetCalculus subpackages. The DifferentialGeometry package includes a comprehensive collection of Lessons and Tutorials. One can also compute with abstract differential forms, that is, with differential forms and their structure equations defined without reference to any underlying system of coordinates.Īlso included are extensive tables of Lie algebras, Lie algebras of vectors, differential equations, and space-time metrics taken from the mathematics and mathematical physics literature. The software includes a variety of homotopy operators for the de Rham and variational bicomplexes extensive capabilities for computing with the Newman-Penrose and spinor formalisms in general relativity programs for analyzing the structure of general and semi-simple Lie algebras programs for finding symmetries of tensor fields and other geometric structures and programs for construction of a solvable Lie group from its Lie algebra.Ĭomputations may be performed in user specified frames. The DifferentialGeometry package is a comprehensive suite of commands and subpackages featuring a collection of tightly integrated tools for computations in the areas of: calculus on manifolds (vector fields, differential forms and transformations) tensor analysis calculus on jet spaces Lie algebras and Lie and transformation groups. ![]() List of the DifferentialGeometry commands and subpackages ![]() Overview of the DifferentialGeometry Package ![]()
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