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.
| ISBN: | 9781107109636 |
| Publication date: | 1st April 2016 |
| Author: | Teo University of Genoa Mora |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 834 pages |
| Series: | Encyclopedia of Mathematics and its Applications |
| Genres: |
Algebra |
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.
Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond features in the following genres: Algebra
Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond is available in Hardback
Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond was written by Teo University of Genoa Mora and published by Cambridge University Press
Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond has 834 pages
Yes it is part of Encyclopedia of Mathematics and its Applications series