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.Read more
- Covers extensions, applications and alternatives to Gröbner bases
- Discusses pre- and post-Buchberger approaches to 'solving'
- Completes the author's comprehensive treatise
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- Date Published: April 2016
- format: Hardback
- isbn: 9781107109636
- length: 834 pages
- dimensions: 240 x 163 x 57 mm
- weight: 1.47kg
- contains: 40 b/w illus.
- availability: Available
Table of Contents
Part VII. Beyond:
51. Weispfenning II
54. Hironaka II
56. Macaulay V
57. Gerdt and Faugère
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