线性微分理想的维数

The dimension of the linear differential ideal

微分理想的维数是微分代数中一个重要的概念 ,利用 Hilbert多项式来计算微分理想的维数 ,计算量较大 .本文通过吴微分特征列算法和偏微分方程的形式解理论 ,给出了线性微分理想的维数多项式、维数的定义和算法 ,且算法容易实现 .

The dimension of the differential ideal is an important concept in Differential Algebra.Much work has been done in computing the dimension by using Hilbert polynomial.This paper suggests that the definitions of dimension and dimension polynomial to linear differential ideal be given via Wu's algorithm of differential characteristic sequence and the formal theory of partial differential equations,meanwhile the algorithm for finding the dimension polynomial be given,and it is easy to accomplish.