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  3. Solving Polynomial Equation Systems I
  • Cited by 22
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    • Publisher:
      Cambridge University Press
      Publication date:
      October 2009
      March 2003
      ISBN:
      9780511542831
      9780521811545
      DOI:
      https://doi.org/10.1017/CBO9780511542831
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.747kg, 438 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Algebra
      Series:
      Encyclopedia of Mathematics and its Applications (88)
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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 (88)
    Information

    Book description

    Polynomial equations have been long studied, both theoretically and with a view to solving them. Until recently, manual computation was the only solution method and the theory was developed to accommodate it. With the advent of computers, the situation changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasising computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.

    Reviews

    ‘This is an excellent book for readers interested in algebraic methods.‘

    Source: European Mathematical Society Newsletter

    ‘The book [is] a thorough success …‘.

    Source: Zentralblatt MATH

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