Hardcover. 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, Groebner 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 Faugere (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. In this fourth and final volume the author covers extensions of Buchberger's Algorithm, including a discussion of the most promising recent alternatives to Groebner bases: Gerdt's involutive bases and Faugere's F4 and F5 algorithms. This completes the author's comprehensive treatise, which is a fundamental reference for any mathematical library. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

Title

Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond (Hardcover)

Publisher

Cambridge University Press, Cambridge

Publication Date

2016

Language

English

ISBN 10

1107109639

ISBN 13

9781107109636

Binding

Hardcover

Condition

new

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About this title

Synopsis

In this fourth and final volume the author covers extensions of Buchberger's Algorithm, including a discussion of the most promising recent alternatives to Gr�bner bases: Gerdt's involutive bases and Faug�re's F4 and F5 algorithms. This completes the author's comprehensive treatise, which is a fundamental reference for any mathematical library.

About the Author

Teo Mora is a Professor of Algebra in the Department of Mathematics at the University of Genoa.

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