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Solving polynomial equation systems. Volume 4, Buchberger's theory and beyond / Teo Mora.

By: Material type: TextTextSeries: Encyclopedia of mathematics and its applications ; v. 158.Publisher: Cambridge : Cambridge University Press, 2016Description: 1 online resource (xi, 820 pages) : digital, PDF file(s)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781316271902 (ebook)
Subject(s): Additional physical formats: Print version: : No titleDDC classification:
  • 512.9/4 21
LOC classification:
  • QA218 .M64 2016
Online resources:
Contents:
1. Solving polynomial equation systems -- 2. Macaulay's Paradigm and Gröbner Technology -- 3. Algebraic Solving
Summary: In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
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Title from publisher's bibliographic system (viewed on 05 Apr 2016).

1. Solving polynomial equation systems -- 2. Macaulay's Paradigm and Gröbner Technology -- 3. Algebraic Solving

In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.

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