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作者 Gatermann, Karin, 1961-
書名 Computer algebra methods for equivariant dynamical systems [electronic resource] / Karin Gatermann
出版項 Berlin ; New York : Springer, ©2000
國際標準書號 9783540465195 (electronic bk.)
3540465197 (electronic bk.)
book jacket
說明 1 online resource (xi, 153 pages) : illustrations
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Lecture notes in mathematics, 0075-8434 ; 1728
Lecture notes in mathematics (Springer-Verlag) ; 1728
附註 Includes bibliographical references (p. [139]-149) and index
Grbner bases: Buchberger's algorithm -- The consequence of grading -- Definitions and the relation to Grbner bases -- Computation of a Hilbert series -- The Hilbert series driven Buchberger algorithm -- The computation with algebraic extensions -- Detection of Grbner 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 Grbner 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
鏈接 Print version: Gatermann, Karin, 1961- Computer algebra methods for equivariant dynamical systems. Berlin ; New York : Springer, ©2000 3540671617 (DLC) 00028453 (OCoLC)43662068
主題 Algebra -- Data processing
Gröbner bases
Differentiable dynamical systems
Algèbre -- Informatique
Gröbner, Bases de
Dynamique différentiable
Algebra -- Data processing. fast (OCoLC)fst00804890
Differentiable dynamical systems. fast (OCoLC)fst00893426
Gröbner bases. fast (OCoLC)fst00948675
Algebra. gtt
Computermethoden. gtt
Dynamische systemen. gtt
Algoritmen. gtt
Algebra comutativa. larpcal
Computeralgebra. swd
Gröbner-Basis. swd
Dynamisches System. swd
Äquivariantes Vektorfeld. swd
Electronic books
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