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101 0 $aeng
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181   $ctxt
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200 10$aComputer Algebra Methods for Equivariant Dynamical Systems /$fby Karin Gatermann
205   $a1st ed. 2000.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000.
215   $a1 online resource (XVIII, 162 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1728
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-67161-7 
320   $aIncludes bibliographical references (pages [139]-149) and index.
327   $aGröbner 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.
330   $aThis book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1728
606   $aAlgebra
606   $aComputer science?Mathematics
606   $aComputer mathematics
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000
606   $aMathematics of Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/I17001
606   $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026
606   $aMath Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17044
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
606   $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082
615  0$aAlgebra.
615  0$aComputer science?Mathematics.
615  0$aComputer mathematics.
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615  0$aGlobal analysis (Mathematics).
615  0$aManifolds (Mathematics).
615 14$aAlgebra.
615 24$aMathematics of Computing.
615 24$aComputational Science and Engineering.
615 24$aMath Applications in Computer Science.
615 24$aAnalysis.
615 24$aGlobal Analysis and Analysis on Manifolds.
676   $a510
700   $aGatermann$b Karin$4aut$4http://id.loc.gov/vocabulary/relators/aut$065494
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910146313803321
996   $aComputer algebra methods for equivariant dynamical systems$978811
997   $aUNINA