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Solving Polynomial Equation Systems III

Volume 3. Algebraic Solving

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: August 2015
  • availability: Available
  • format: Hardback
  • isbn: 9780521811552

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  • This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner bases, which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the 'standard' solutions (Gianni–Kalkbrener Theorem, Stetter Algorithm, Cardinal–Mourrain result) and then moves on to more innovative methods (Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package). The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bézout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.

    • Continues the author's survey of the state of the art for solving univariate polynomials
    • Covers classical results as well as modern methods
    • Third volume of four in the author's comprehensive treatise
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    Product details

    • Date Published: August 2015
    • format: Hardback
    • isbn: 9780521811552
    • length: 294 pages
    • dimensions: 240 x 155 x 25 mm
    • weight: 0.62kg
    • contains: 7 b/w illus.
    • availability: Available
  • Table of Contents

    Preface
    Setting
    Part VI. Algebraic Solving:
    39. Trinks
    40. Stetter
    41. Macaulay IV
    42. Lazard II
    43. Lagrange II
    44. Kronecker IV
    45. Duval II
    Bibliography
    Index.

  • 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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