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  3. Solving Polynomial Equation Systems II
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    • Publisher:
      Cambridge University Press
      Publication date:
      June 2013
      May 2005
      ISBN:
      9781107340954
      9780521811569
      DOI:
      https://doi.org/10.1017/CBO9781107340954
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      1.261kg, 784 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Algebra
      Series:
      Encyclopedia of Mathematics and its Applications (99)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (99)
    Information

    Book description

    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.

    Reviews

    '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.'

    Source: Monatshefte für Mathematik

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