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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.

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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

R2 v1 2026-06-21T21:38:39.844Z