Mathematica中的参数化类型定义：方法和优点
Parameterized Type Definitions in Mathematica: Methods and Advantages
摘要：
代数范畴中的符号计算这一主题在过去的十年中变得极其重要，因为它使现代代数理论的自动建模成为可能。在此理论背景下，本文揭示了实用的参数化的分类方法，通过推导出一个多元多项式类别（在各种系数域），这是使用我们的Mathematica实现的Buchberger的算法，用于确定Groebner基础。这些实现是根据域和类别参数化原则设计的，突出了它们的优点：操作保护，继承，通用性，易于扩展。特别是对广泛使用的符号计算系统Mathematica进行扩展，使之成为一种新型系统，具有一定的实际意义。我们为Mathematica提出的方法受到D. Gruntz和M.莫纳根在高斯为梅普尔工作
英文摘要：
The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the utility of the parameterized categorical approach by deriving a multivariate polynomial category (over various coefficient domains), which is used by our Mathematica implementation of Buchberger's algorithms for determining the Groebner basis. These implementations are designed according to domain and category parameterization principles underlining their advantages: operation protection, inheritance, generality, easy extendibility. In particular, such an extension of Mathematica, a widely used symbolic computation system, with a new type system has a certain practical importance. The approach we propose for Mathematica is inspired from D. Gruntz and M. Monagan's work in Gauss, for Maple.
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