Algorithms for D-modules and their applications

分析的主要目的是利用函数所满足的微分方程来研究函数。因此，首先必须找到一个给定函数所满足的微分方程。我适用于一般算法的D-模块（代数对应的微分方程），我已经介绍了，一些具体的功能和获得算法计算微分方程的功能，如对数的多项式和积分域定义的多项式不等式。我还使用日本的软件系统实现了这些算法。

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.