Multivariate Difference-Differential Dimension Polynomials and New Invariants of Difference-Differential Field Extensions

摘要

In this paper we introduce a method of characteristic sets with respect toseveral term orderings for difference-differential polynomials. Using thistechnique, we obtain a method of computation of multivariate dimensionpolynomials of finitely generated difference-differential field extensions.Furthermore, we find new invariants of such extensions and show how thecomputation of multivariate difference-differential polynomials is applied tothe equivalence problem for systems of algebraic difference-differentialequations.