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Solving Polynomial Equation Systems IV : Volume 4, Buchberger Theory and Beyond.
・ISBN 978-1-107-10963-6 hard GB£ 189.00
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-316-27190-2
| 著者・編者 | Mora, Teo, |
|---|---|
| シリーズ | Encyclopedia of Mathematics and its Applications |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2016 |
| ページ数 | 834 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-15909＞ |
解説
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.