We use the method of characteristic sets with respect to two term orderings to prove the existence and obtain a method of computation of a bivariate Kolchin-type dimension polynomial associated with a non-reflexive difference-differential ideal in the algebra of difference-differential polynomials with several basic derivations and one translation. In particular, we obtain a new proof and a method of computation of the dimension polynomial of a non-reflexive prime difference ideal in the algebra of difference polynomials over an ordinary difference field. As a consequence, it is shown that the reflexive closure of a prime difference polynomial ideal is the inverse image of this ideal under a power of the basic translation. We also discuss applications of our results to the analysis of systems of algebraic difference-differential equations.

我们使用关于两个项排序的特征集方法来证明其存在性，并获得与差分方程式代数中的非自反差分理想方程相关联的二元Kolchin型尺寸多项式的计算方法，其中几个基本派生和一个翻译。特别地，我们获得了新的证明和计算普通多项式域上差分多项式代数中非自反素差分理想的尺寸多项式的方法。结果表明，素差多项式理想的自反闭合是在基本平移力的作用下该理想的逆像。我们还将讨论我们的结果在代数差分-微分方程系统分析中的应用。