计算多项式对数微分方程的算法
An algorithm to compute the differential equations for the logarithm of a polynomial
摘要：
我们提出了一个算法来计算的零化子（即，多项式系数微分算子环中多项式的对数的线性微分方程。该算法包括关于多项式f的零化子的参数s的微分和商计算。更一般地说，对于复数s和正整数m，f^s（log f）^m的零化子可以计算，这构成了D-模理论中所谓的完整系统。这使我们能够计算一个完整的系统的积分的函数涉及一个多项式的对数，通过使用积分算法的D-模。
英文摘要：
We present an algorithm to compute the annihilator of (i.e., the linear differential equations for) the logarithm of a polynomial in the ring of differential operators with polynomial coefficients. The algorithm consists of differentiation with respect to the parameter s of the annihilator of f^s for a polynomial f and quotient computation. More generally, the annihilator of f^s(log f)^m for a complex number s and a positive integer m can be computed, which constitutes what is called a holonomic system in D-module theory. This enables us to compute a holonomic system for the integral of a function involving the logarithm of a polynomial by using integration algorithm for D-modules.
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