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arXiv · 1207.4757

Multivariate Difference-Differential Dimension Polynomials

Alexander Levin
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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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Alexander Levin. 2012-07-19. Multivariate Difference-Differential Dimension Polynomials. https://arxiv.org/abs/1207.4757

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