Solving polynomial equation systems. Volume 4, Buchberger's theory and beyond / Teo Mora.
Material type: TextSeries: 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
- computer
- online resource
- 9781316271902 (ebook)
- 512.9/4 21
- QA218 .M64 2016
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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