The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E. Kolchin in 1964 KoI64]' but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. Actually, one can say that the differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the...
The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar rol...
Alexander V. Mikhalev A. B. Levin E. V. Pankratiev
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...
This book is the first monograph wholly devoted to the investigation of differential and difference dimension theory. The differential dimension po...
