Solving Polynomial Equation Systems

Erscheinungsjahr 2016
ISBN: 978-1-107-10963-6
Verlag: Cambridge University Press

Buch, Englisch, Band 158, 834 Seiten, HC gerader Rücken kaschiert, Format (B × H): 161 mm x 240 mm, Gewicht: 1555 g

Reihe: Encyclopedia of Mathematics and its Applications

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.

Autoren/Hrsg.

Mora, Teo

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

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.

Über Autor(innen)

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