Buchberger theory and beyond
Author(s)
Bibliographic Information
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
Available at / 35 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackS||EMA||158200035539936
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
: hardback/M 792080396637
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Note
Includes bibliographical references (p. [803]-812) and index
Description and Table of Contents
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, 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.
Table of Contents
- 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.
by "Nielsen BookData"
