Generalized characteristic sets and new multivariate difference dimension polynomials
Generalized characteristic sets and new multivariate difference dimension polynomials
复制标题
广义特征集和新的多元差分维多项式
DOI：
10.1007/s00200-023-00628-0
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发表时间：
2024
期刊：
影响因子：
--
通讯作者：
Levin, Alexander
中科院分区：
文献类型：
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作者：
Levin, Alexander
我们使用有效阶概念对偏差分多项式的情况的推广以及基本平移集的划分，引入了一种新型的差分多项式特征集。利用这些特征集的性质，我们证明了有限生成差分域扩展的多元维多项式的存在性并概述了一种计算方法，该方法描述了通过生成器的邻接变换获得的中间域的超越度，这些生成器的阶数相对于分区的分量受两个自然数序列的限制。我们证明，与先前已知的差分维多项式相比，此类维多项式本质上具有更多的不变量（即不依赖于其差分生成器集合的扩展特征）。特别是，与代数差分方程组相关的新型维数多项式比经典的单变量差分维数多项式提供了更多关于该系统的信息。
We introduce a new type of characteristic sets of difference polynomials using a generalization of the concept of effective order to the case of partial difference polynomials and a partition of the basic set of translations. Using properties of these characteristic sets, we prove the existence and outline a method of computation of a multivariate dimension polynomial of a finitely generated difference field extension that describes the transcendence degrees of intermediate fields obtained by adjoining transforms of the generators whose orders with respect to the components of the partition ofare bounded by two sequences of natural numbers. We show that such dimension polynomials carry essentially more invariants (that is, characteristics of the extension that do not depend on the set of its difference generators) than previously known difference dimension polynomials. In particular, a dimension polynomial of the new type associated with a system of algebraic difference equations gives more information about the system than the classical univariate difference dimension polynomial.
影响因子：
0.8
作者：
Levin, Alexander
通讯作者：
Levin, Alexander
有效阶数的约简及一类新型差分模维数多项式
DOI：
10.1145/3476446.3535497
发表时间：
2022
期刊：
2022 International Symposium on Symbolic and Algebraic Computation
影响因子：
--
作者：
Levin, Alexander
通讯作者：
Levin, Alexander