Complete description
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.
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General info
Publisher & Imprint:
Springer
Edition details
1st ed. Softcover of orig. ed. 1999
City:
Dordrecht
Pages:
439
More info:
height 234 mm
width 156 mm
weight 616 gr
thickness 22 mm
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Age recommended:
Professional and scholarly
Subject Indexing & Classification
Dewey:(DC22) 512.9422
Departments:
Algebra; Differential equations; Combinatorics & graph theory;
Record updated at:
29 March, 2013
time:
14:58
Summary
Differential and Difference Dimension Polynomials
Preface. I. Preliminaries. II. Numerical Polynomials. III. Basic Notion of Differential and Difference Algebra. IV. Grobner 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. Index.
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