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Constructive Ideal Theory

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Computational Invariant Theory

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS))

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Abstract

In this chapter we provide the basic algorithmic tools which will be used in later chapters. More precisely, we introduce some algorithms of constructive ideal theory, almost all of which are based on Gröbner bases. As the reader will find out, these algorithms and thus Gröbner bases literally permeate this book. We restrict ourselves to giving a rather short overview of the part of the theory that we require. The chapter covers Gröbner bases, elimination ideals, syzygies, Hilbert series, radical ideals, and normalization.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    Harm Derksen

  2. Zentrum Mathematik - M11, Technische Universität München, Garching, Germany

    Gregor Kemper

Authors
  1. Harm Derksen
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  2. Gregor Kemper
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Derksen, H., Kemper, G. (2015). Constructive Ideal Theory. In: Computational Invariant Theory. Encyclopaedia of Mathematical Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48422-7_1

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