Buchberger theory and beyond
著者
書誌事項
Buchberger theory and beyond
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 158 . Solving polynomial equation systems ; 4）
Cambridge University Press, c2016
- : hardback
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注記
Includes bibliographical references (p. [803]-812) and index
内容説明・目次
内容説明
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.
目次
- 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 Faugere
- Bibliography
- Index.
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