Algorithms for D-modules and their applications

用一个函数所满足的微分方程来研究它是分析的一个主要目的。因此，首先，我们必须找到给定函数所满足的微分方程。我将我已经介绍过的d模块（微分方程的代数对应物）的一般算法应用于一些特定的函数，并获得了计算函数微分方程的算法，例如多项式的对数和多项式不等式定义的域上的积分。我还使用了一个日本的软件系统来实现这些算法。

It is a primary purpose of analysis to study a function by using the differential equations which it satisfies. Hence one must find, first of all, the differential equations which a given function satisfies. I applied general algorithms for D-modules (algebraic counterpart of differential equations), which I had introduced, to some specific functions and obtained algorithms for computing the differential equations for functions such as the logarithm of a polynomial and the integral over a domain defined by polynomial inequalities. I also implemented these algorithms by using a Japanese software system.