Elimination Methods in Polynomial Computer Algebra

✍ Scribed by Valery Bykov, Alexander Kytmanov, Mark Lazman (auth.), Mikael Passare (eds.)

• Publisher: Springer Netherlands
• Year: 1998
• Tongue: English
• Leaves: 253
• Series: Mathematics and Its Applications 448
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xi
Basic Mathematical Facts....Pages 1-30
A Modified Elimination Method....Pages 31-98
Applications in Mathematical Kinetics....Pages 99-171
Computer Realizations....Pages 173-224
Back Matter....Pages 225-244

✦ Subjects

Several Complex Variables and Analytic Spaces; Math. Applications in Chemistry; Symbolic and Algebraic Manipulation; Numeric Computing