论文标题
差异代数依赖和诺维科夫依赖
Differential algebraic dependence and Novikov dependence
论文作者
论文摘要
我们为差分多项式代数定义了FOX衍生物的类似物，并为有限元系统的差异代数依赖性提供了标准。特别是，我们证明，差异多项式代数的有限元对具有构建性差异字段$ k $ k $的特征性零元素的有限元组的差分代数依赖性在算法上是可以识别的。使用差分多项式代表自由的Novikov代数代表，我们还提供了Novikov依赖的标准，即Free Novikov代数的有限元系统。
We define an analogue of the Fox derivatives for differential polynomial algebras and give a criterion for differential algebraic dependence of a finite system of elements. In particular, we prove that differential algebraic dependence of a finite set of elements of a differential polynomial algebra over a constructive differential field $k$ of characteristic zero is algorithmically recognizable. Using a representation of free Novikov algebras by differential polynomials we also give a criterion of Novikov dependence of a finite system of elements of free Novikov algebras.
