微分多项式系统的约化算法理论<英>

An Algorithmic Theory of Reduction of Differential Polynomials System

本文中,作者推广了纯代数形式的特征列集理论(吴方法)为微分形式的相应理论,即建立了在机器证明和诸多微分问题中非常重要的微分多项式组的约化算法理论。引入了一些新的概念和观点使函数微分(导数)具有直观的代数几何表示。给出了Coherent条件下的特征列集的算法。给出的算法易于在计算机上实现并适合应用于广泛的微分问题,如微分方程对称计算,各种微分关系的自动推理等问题。

In this article, the characteristic set theory (Wu's method) of pure algebraic polynomial system is generalized to differential case. An algorithmic theory for reduction of differential polynomials system which is essential in mechanical theorem proving and various applications in differential fields is given. Some new concepts and view are introduced as a result the derivatives of functions have corresponding simple multi-index interpretations and geometry partners. Also under Coherent conditions a algorithm of differential Characteristic set for differential polynomial system is given. The generalized algorithm is more constructive and easily carried out on computer and adapts to apply in wide rang of differential problems, such as calculating of symmetries of differential equations, automatic reasoning of variety transformations in differential cases.