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＜電子ブック＞
Computer Algebra Methods for Equivariant Dynamical Systems / by Karin Gatermann
(Lecture Notes in Mathematics. ISSN:16179692 ; 1728)

版	1st ed. 2000.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2000
本文言語	英語
大きさ	XVIII, 162 p : online resource
著者標目	*Gatermann, Karin author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Mathematical analysis LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Algebra FREE:Mathematics of Computing FREE:Computational Science and Engineering FREE:Mathematical Applications in Computer Science FREE:Analysis FREE:Global Analysis and Analysis on Manifolds
一般注記	Gröbner bases: Buchberger's algorithm -- The consequence of grading -- Definitions and the relation to Gröbner bases -- Computation of a Hilbert series -- The Hilbert series driven Buchberger algorithm -- The computation with algebraic extensions -- Detection of Gröbner bases -- Dynamic Buchberger algorithm -- Elimination -- Algorithms of the computation of invariants and equivariants: Using the Hilbert series -- Invariants -- Equivariants -- Using the nullcone -- Using a homogeneous system of parameters -- Computing uniqueness -- Symmetric bifurcation theory -- Local bifurcation analysis -- An example of secondary Hopf bifurcation -- Orbit space reduction -- Exact computation of steady states -- Differential equations on the orbit space -- Using Noether normalization -- Further reading -- References -- Index This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics HTTP:URL=https://doi.org/10.1007/BFb0104059

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