کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4946024 | 1364079 | 2017 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Algorithmic calculus for Lie determining systems
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
هوش مصنوعی
چکیده انگلیسی
The infinitesimal symmetries of differential equations (DEs) or other geometric objects provide key insight into their analytical structure, including construction of solutions and of mappings between DEs. This article is a contribution to the algorithmic treatment of symmetries of DEs and their applications. Infinitesimal symmetries obey a determining system L of linear homogeneous partial differential equations, with the property that its solution vector fields form a Lie algebra L. We exhibit several algorithms that work directly with the determining system without solving it. A procedure is given that can decide if a system specifies a Lie algebra L, if L is abelian and if a system Lâ² specifies an ideal in L. Algorithms are described that compute determining systems for transporter, Lie product and Killing orthogonal subspace. This gives a systematic calculus for Lie determining systems, enabling computation of the determining systems for normalisers, centralisers, centre, derived algebra, solvable radical and key series (derived series, lower/upper central series). Our methods thereby give algorithmic access to new geometrical invariants of the symmetry action.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 79, Part 2, MarchâApril 2017, Pages 482-498
Journal: Journal of Symbolic Computation - Volume 79, Part 2, MarchâApril 2017, Pages 482-498
نویسندگان
Ian G. Lisle, S.-L. Tracy Huang,