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Titlebook: Algorithms in Invariant Theory; Bernd Sturmfels Book 2008Latest edition Springer-Verlag Vienna 2008 Finite.Invariant.Invariant Theory.alge

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期刊全称Algorithms in Invariant Theory
影响因子2023Bernd Sturmfels
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学科分类Texts & Monographs in Symbolic Computation
图书封面Titlebook: Algorithms in Invariant Theory;  Bernd Sturmfels Book 2008Latest edition Springer-Verlag Vienna 2008 Finite.Invariant.Invariant Theory.alge
影响因子J. Kung and G.-C. Rota, in their 1984 paper, write: “Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics”. The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this “classical and new” area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.
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978-3-211-77416-8Springer-Verlag Vienna 2008
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,Strukturveränderung: Gefahr und Chance,Invariant theory is both a classical and a new area of mathematics. It played a central role in 19th century algebra and geometry, yet many of its techniques and algorithms were practically forgotten by the middle of the 20th century.
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,Strukturveränderung: Gefahr und Chance,emain invariant under the action of a finite matrix group Γ ⊂ .(C.). The main result of this chapter is a collection of algorithms for finding a finite set ., .,...,. of fundamental invariants which generate the invariant subring C[x].. These algorithms make use of the Molien series (Sect. 2.2) and
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Strukturkrisen: Entwicklung und Ursachen,orithm, to be presented in Sect. 4.6, is derived from Hilbert (1893). We will discuss Hilbert’s algorithm from the point of view of Gröbner bases theory. This chapter is less elementary than the previous three. While most of the presentation is self-contained, familiarity with basic notions of commu
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