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Differential and Difference Dimension Polynomials : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - A. V. Mikhalev

Differential and Difference Dimension Polynomials

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover

Published: 30th November 1998
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This book is the first monograph wholly devoted to the investigation of differential and difference dimension theory. The differential dimension polynomial describes in exact terms the degree of freedom of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations.

Difference algebra arises from the study of algebraic difference equations and therefore bears a considerable resemblance to its differential counterpart. Difference algebra was developed in the same period as differential algebra and it has the same founder, J. Ritt. It grew to a mathematical area with its own ideas and methods mainly due to the work of R. Cohn, who raised difference algebra to the same level as differential algebra. The relatively new science of computer algebra has given strong impulses to the theory of dimension polynomials, now that packages such as MAPLE enable the solution of many problems which cannot be solved otherwise. Applications of differential and difference dimension theory can be found in many fields of mathematics, as well as in theoretical physics, system theory and other areas of science.

Audience: This book will be of interest to researchers and graduate students whose work involves differential and difference equations, algebra and number theory, partial differential equations, combinatorics and mathematical physics.

Preface
Preliminaries
Numerical Polynomials
Basic Notion of Differential and Difference Algebra
Grobner Bases
Differential Dimension Polynomials
Dimension Polynomials in Difference and Difference-Differential Algebra
Some Application of Dimension Polynomials in Difference-Differential Algebra
Dimension Polynomials of Filtered G-modules and Finitely Generated G-Fields Extensions
Computation of Dimension Polynomials
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792354840
ISBN-10: 0792354842
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER ) : Book 461
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 422
Published: 30th November 1998
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.88  x 2.54
Weight (kg): 0.84