Solving Polynomial Equation Systems IV
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.
- Covers extensions, applications and alternatives to Gröbner bases
- Discusses pre- and post-Buchberger approaches to 'solving'
- Completes the author's comprehensive treatise
Product details
April 2016Hardback
9781107109636
834 pages
240 × 163 × 57 mm
1.47kg
40 b/w illus.
Available
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 Faugère
- Bibliography
- Index.
