Teo Mora

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

• Format: ePub

Produktbeschreibung

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, Grobner 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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 1. April 2016
• Englisch
• ISBN-13: 9781316379585
• Artikelnr.: 52861726

Autorenporträt

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

Inhaltsangabe

Part VII. Beyond: 46. Zacharias
47. Bergman
48. Ufnarovski
49. Weispfenning
50. Spear2
51. Weispfenning II
52. Sweedler
53. Hironaka
54. Hironaka II
55. Janet
56. Macaulay V
57. Gerdt and Faugère
Bibliography
Index.