Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond
Seiten
2016
Cambridge University Press (Verlag)
978-1-107-10963-6 (ISBN)
Cambridge University Press (Verlag)
978-1-107-10963-6 (ISBN)
In this fourth and final volume the author covers extensions of Buchberger's Algorithm, including a discussion of the most promising recent alternatives to Gröbner bases: Gerdt's involutive bases and Faugère's F4 and F5 algorithms. This completes the author's comprehensive treatise, which is a fundamental reference for any mathematical library.
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.
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.
Teo Mora is a Professor of Algebra in the Department of Mathematics at the University of Genoa.
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.
| Erscheint lt. Verlag | 1.4.2016 |
|---|---|
| Reihe/Serie | Encyclopedia of Mathematics and its Applications |
| Zusatzinfo | Worked examples or Exercises; 40 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 163 x 240 mm |
| Gewicht | 1470 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-107-10963-9 / 1107109639 |
| ISBN-13 | 978-1-107-10963-6 / 9781107109636 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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