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Elimination Methods in Polynomial Computer Algebra

  • Book
  • © 1998

Overview

Authors:
  1. Valery Bykov

    1. Computer Center, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

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  2. Alexander Kytmanov

    1. Krasnoyarsk State University, Krasnoyarsk, Russia

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  3. Mark Lazman

    1. Institute of Catalysis, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

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Editors:
  1. Mikael Passare

    1. Department of Mathematics, Stockholm University, Stockholm, Sweden

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Part of the book series: Mathematics and Its Applications (MAIA, volume 448)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xi
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  2. Basic Mathematical Facts

    • Valery Bykov, Alexander Kytmanov, Mark Lazman
    Pages 1-30

  3. A Modified Elimination Method

    • Valery Bykov, Alexander Kytmanov, Mark Lazman
    Pages 31-98

  4. Applications in Mathematical Kinetics

    • Valery Bykov, Alexander Kytmanov, Mark Lazman
    Pages 99-171

  5. Computer Realizations

    • Valery Bykov, Alexander Kytmanov, Mark Lazman
    Pages 173-224

  6. Back Matter

    Pages 225-244
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Keywords

About this book

The subject of this book is connected with a new direction in mathematics, which has been actively developed over the last few years, namely the field of polynomial computer algebra, which lies at the intersection point of algebra, mathematical analysis and programming. There were several incentives to write the book. First of all, there has lately been a considerable interest in applied nonlinear problems characterized by multiple sta­ tionary states. Practical needs have then in their turn led to the appearance of new theoretical results in the analysis of systems of nonlinear algebraic equations. And finally, the introduction of various computer packages for analytic manipulations has made it possible to use complicated elimination-theoretical algorithms in prac­ tical research. The structure of the book is accordingly represented by three main parts: Mathematical results driven to constructive algorithms, computer algebra realizations of these algorithms, and applications. Nonlinear systems of algebraic equations arise in diverse fields of science. In particular, for processes described by systems of differential equations with a poly­ nomial right hand side one is faced with the problem of determining the number (and location) of the stationary states in certain sets.

Authors, Editors and Affiliations

  • Department of Mathematics, Stockholm University, Stockholm, Sweden

    Mikael Passare

  • Computer Center, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

    Valery Bykov

  • Krasnoyarsk State University, Krasnoyarsk, Russia

    Alexander Kytmanov

  • Institute of Catalysis, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

    Mark Lazman

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