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Erschienen in:
2020 | OriginalPaper | Buchkapitel
The Lie Algebra of Vector Fields Package with Applications to Mappings of Differential Equations
verfasst von : Zahra Mohammadi, Gregory J. Reid, S.-L. Tracy Huang
Erschienen in: Maple in Mathematics Education and Research
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Abstract
Lie symmetry groups of transformations (mappings) of differential equations leave them invariant, and are most conveniently studied through their Lie algebra of vector fields (essentially the linearization of the mappings around the identity transformation). Maple makes powerful and frequent use of such Lie algebras, mostly through routines that are dependent on Maple’s powerful exact integration routines, that essentially automate traditional hand-calculation strategies. However these routines are usually heuristic, and algorithmic approaches require a deeper integration of differential elimination (differential algebraic) approaches in applications to differential equations. This is the underlying motivation of the LieAlgebrasOfVectorFields (
LAVF) package of Huang and Lisle. The LAVF package introduces a powerful algorithmic calculus for doing calculations with differential equations without the heuristics of integration to calculate efficiently many properties of such systems.