Multivariate Difference-Differential Dimension Polynomials
Commutative Algebra
2012-07-20 v1
Abstract
In this paper we generalize the Ritt-Kolchin method of characteristic sets and the classical Gr\"obner basis technique to prove the existence and obtain methods of computation of multivariate difference-differential dimension polynomials associated with a finitely generated difference-differential field extension. We also give an interpretation of such polynomials in the spirit of the A. Einstein's concept of strength of a system of PDEs and determine their invariants, that is, characteristics of a finitely generated difference-differential field extension carried by every its dimension polynomial.
Cite
@article{arxiv.1207.4757,
title = {Multivariate Difference-Differential Dimension Polynomials},
author = {Alexander Levin},
journal= {arXiv preprint arXiv:1207.4757},
year = {2012}
}
Comments
28 pages