I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2008, VOLUME 14, NUMBER 4, PAGES 167-180
Dimension polynomials of intermediate differential fields and the
strength of a system of differential equations with group action
A. B. Levin
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a differential field of zero characteristic with a basic set
and let denote the free
commutative semigroup of all elements of the form
Let the order of such an element be defined as , and for
any , let
a differential field extension of generated by
a finite set
and let be an intermediate
differential field of the extension .
Furthermore, for any , let
We prove the existence and describe some properties of
a polynomial such that
for all sufficiently large .
This result implies the existence of a dimension polynomial that
describes the strength of a system of differential equations with
group action in the sense of A. Einstein.
We shall also present a more general result, a theorem on
a multivariate dimension polynomial associated with an
intermediate differential field and partitions of the
basic set .
Last modified: February 28, 2009