Bivariate Dimension Polynomials of Non-Reflexive Prime Difference-Differential Ideals.: The Case of One Translation
Bivariate Dimension Polynomials of Non-Reflexive Prime Difference-Differential Ideals.: The Case of One Translation
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非自反素数差微分理想的二元维多项式。：一种翻译的情况
DOI：
10.1145/3208976.3209008
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
A. Levin
中科院分区：
文献类型：
--
作者：
A. Levin
利用关于二项序的特征集方法证明了具有几个基本导子和一个平移的差-微分多项式代数中与非自反差-微分理想相关的二元多项式的存在性，并得到了一种计算方法。由此得到了一般差域上差多项式代数中非自反素差理想的维多项式的一个新的证明和计算方法。我们还讨论了我们的结果在代数差分微分方程组中的应用。
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 dimension polynomial associated with a non-reflexive difference-differential ideal in the algebra of difference-differential polynomials with several basic derivations and one translation. As a consequence, 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. We also discuss applications of our results to systems of algebraic difference-differential equations.