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Solving Polynomial Equation Systems IV

Volume 4. Buchberger Theory and Beyond

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: April 2016
  • availability: Available
  • format: Hardback
  • isbn: 9781107109636


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About the Authors
  • 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
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    Product details

    • Date Published: April 2016
    • format: Hardback
    • isbn: 9781107109636
    • length: 834 pages
    • dimensions: 240 x 163 x 57 mm
    • weight: 1.47kg
    • contains: 40 b/w illus.
    • availability: 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

  • Author

    Teo Mora, University of Genoa
    Teo Mora is a Professor of Algebra in the Department of Mathematics at the University of Genoa.

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