| Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond Contributor(s): Mora, Teo (Author) |
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ISBN: 1107109639 ISBN-13: 9781107109636 Publisher: Cambridge University Press OUR PRICE: $209.95 Product Type: Hardcover - Other Formats Published: April 2016 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - General - Mathematics | Algebra - Elementary |
| Dewey: 512.94 |
| Series: Encyclopedia of Mathematics and Its Applications |
| Physical Information: 2" H x 6.14" W x 9.21" (3.19 lbs) 834 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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, Gr bner 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 Faug re (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. |
Contributor Bio(s): Mora, Teo: - Teo Mora is a Professor of Algebra in the Department of Mathematics at the University of Genoa. |