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Elimination Methods in Polynomial Computer Algebra

  • Valery Bykov
  • Alexander Kytmanov
  • Mark Lazman
  • Mikael Passare

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Valery Bykov, Alexander Kytmanov, Mark Lazman
    Pages 1-30
  3. Valery Bykov, Alexander Kytmanov, Mark Lazman
    Pages 31-98
  4. Valery Bykov, Alexander Kytmanov, Mark Lazman
    Pages 99-171
  5. Valery Bykov, Alexander Kytmanov, Mark Lazman
    Pages 173-224
  6. Back Matter
    Pages 225-244

About this book

Introduction

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.

Keywords

Maple Mathematica algebra algorithms computer computer algebra linear algebra

Authors and affiliations

  • Valery Bykov
    • 1
  • Alexander Kytmanov
    • 2
  • Mark Lazman
    • 3
  1. 1.Computer CenterSiberian Branch of the Russian Academy of SciencesKrasnoyarskRussia
  2. 2.Krasnoyarsk State UniversityKrasnoyarskRussia
  3. 3.Institute of CatalysisSiberian Branch of the Russian Academy of SciencesKrasnoyarskRussia

Editors and affiliations

  • Mikael Passare
    • 1
  1. 1.Department of MathematicsStockholm UniversityStockholmSweden

Bibliographic information