Overview

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.

Full Product Details

Author:   V. Bykov ,  A. Kytmanov ,  M. Lazman ,  Mikael Passare
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 1998
Volume:   448
Dimensions:   Width: 16.00cm , Height: 1.40cm , Length: 24.00cm
Weight:   0.421kg
ISBN:  

9789401062305

ISBN 10:   9401062307
Pages:   244
Publication Date:   13 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

1. Basic Mathematical Facts.- 1. The logarithmic residue.- 2. The Newton recursion formulas.- 3. Localization theorems for the real zeros of a polynomial.- 4. The local residue (of Grothendieck).- 5. The multidimensional logarithmic residue.- 6. The classical scheme for elimination of unknowns.- 2. A Modified Elimination Method.- 7. A generalized transformation formula for local residues.- 8. A modified elimination method.- 9. A formula for the logarithmic derivative of the resultant.- 10. Multidimensional analogues of the Newton formulas.- 11. Elimination of unknowns in different variables. Real roots.- 3. Applications in Mathematical Kinetics.- 12. Short schemes.- 13. The search for all stationary solutions.- 14. The kinetic polynomial. Single-route mechanisms.- 15. Construction of the kinetic polynomial in the general case.- 4. Computer Realizations.- 16. Analytic manipulations on the computer.- 17. Basic problems in computer algebra of polynomials.- 18. Realization of the elimination method.- 19. The construction of the resultant.- List of applications.

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