Overview

This monograph is 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. This book should 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.

Full Product Details

Author:   Alexander V. Mikhalev ,  A.B. Levin ,  E.V. Pankratiev ,  M.V. Kondratieva
Publisher:   Springer
Imprint:   Springer
Edition:   1999 ed.
Volume:   461
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   1.760kg
ISBN:  

9780792354840

ISBN 10:   0792354842
Pages:   422
Publication Date:   30 November 1998
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I. Preliminaries.- II. Numerical Polynomials.- III. Basic Notion of Differential and Difference Algebra.- IV. Gröbner Bases.- V. Differential Dimension Polynomials.- VI. Dimension Polynomials in Difference and Difference-Differential Algebra.- VII. Some Application of Dimension Polynomials in Difference-Differential Algebra.- VIII. Dimension Polynomials of Filtered G-modules and Finitely Generated G-fields Extensions.- IX. Computation of Dimension Polynomials.- References.

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