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Solving Polynomial Equation Systems II

Solving Polynomial Equation Systems II
Macaulay's Paradigm and Gröbner Technology


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: May 2005
  • availability: Available
  • format: Hardback
  • isbn: 9780521811569

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About the Authors
  • The second volume of this comprehensive treatise focusses on Buchberger theory and its application to the algorithmic view of commutative algebra. In distinction to other works, the presentation here is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in issues of implementation. The same language describes the applications of Groebner technology to the central problems of commutative algebra. The book can be also used as a reference on elementary ideal theory and a source for the state-of-the-art in its algorithmization. Aiming to provide a complete survey on Groebner bases and their applications, the author also includes advanced aspects of Buchberger theory, such as the complexity of the algorithm, Galligo's theorem, the optimality of degrevlex, the Gianni-Kalkbrener theorem, the FGLM algorithm, and so on. Thus it will be essential for all workers in commutative algebra, computational algebra and algebraic geometry.

    • Elementary introduction to Groebner bases and Buchberger's Algorithm which also discusses the state-of-the-art of the best implementations
    • Survey of last twenty years work on applying Groebner technology to commutative algebra
    • Unique in stressing modern framework for computational work and solution methods
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    Reviews & endorsements

    'The author treats all relevant steps and results in great detail also including advanced and most recent developments respectively, both of the theoretical and the algorithmic side … an abundance of worked out examples shows the effectivity of the various algorithms.' Monatshefte für Mathematik

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    Product details

    • Date Published: May 2005
    • format: Hardback
    • isbn: 9780521811569
    • length: 784 pages
    • dimensions: 242 x 165 x 42 mm
    • weight: 1.261kg
    • availability: Available
  • Table of Contents

    Part III. Gauss, Euclid, Buchberger - Elementary Gröbner Bases:
    20. Hilbert
    21. Gauss
    22. Buchberger
    23. Macaulay I
    24. Gröbner I
    25. Gebauer and Traverso
    26. Spear
    Part IV. Duality:
    27. Noether
    28. Möller I
    29. Lazard
    30. Macaulay II
    31. Gröbner II
    32. Gröbner III
    33. Möller II
    Part IV. Beyond Dimension Zero:
    34. Gröbner IV
    35. Gianni Trager Zacharias
    36. Macaulay III
    37. Galligo
    38. Giusti

  • Author

    Teo Mora, University of Genoa

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