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020 _a9783540465195
_9978-3-540-46519-5
024 7 _a10.1007/BFb0104059
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
245 1 0 _aComputer Algebra Methods for Equivariant Dynamical Systems
_h[electronic resource] /
_cedited by Karin Gatermann.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2000.
300 _aXVIII, 162 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1728
505 0 _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.
520 _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.
650 0 _aAlgebra.
650 0 _aComputer science.
650 0 _aGlobal analysis (Mathematics).
650 0 _aGlobal analysis.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aMathematics of Computing.
_0http://scigraph.springernature.com/things/product-market-codes/I17001
650 2 4 _aComputational Science and Engineering.
_0http://scigraph.springernature.com/things/product-market-codes/M14026
650 2 4 _aMath Applications in Computer Science.
_0http://scigraph.springernature.com/things/product-market-codes/I17044
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
700 1 _aGatermann, Karin.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662199626
776 0 8 _iPrinted edition:
_z9783540671619
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1728
856 4 0 _uhttps://doi.org/10.1007/BFb0104059
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9636
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