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.
General
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