论文标题
在朱莉娅语言中实施广义复数的方法
Approaches to the implementation of generalized complex numbers in the Julia language
论文作者
论文摘要
在数学物理学问题中，要在理论计算中使用Cayley-Klein模型研究空间的结构，则需要使用广义复数。在计算实验的情况下，此类任务需要以编程语言的高质量实现。拟议的现代编程语言中广义复数的少量实施具有多种缺点。在本文中，我们建议使用朱莉娅语言作为实施通用复数的语言，尤其是因为它支持多重调度机制。该论文证明了实施一般复数类型之一的方法，即双数数字。我们特别强调了使用多重调度机制实现新数值类型的描述。最终的双重数字实现可以将其视为用于支持广义复数的完整软件模块的原型。
In problems of mathematical physics, to study the structures of spaces using the Cayley-Klein models in theoretical calculations, the use of generalized complex numbers is required. In the case of computational experiments, such tasks require their high-quality implementation in a programming language. The proposed small implementation of generalized complex numbers in modern programming languages have several disadvantages. In this article, we propose using the Julia language as the language for implementing generalized complex numbers, not least because it supports the multiple dispatch mechanism. The paper demonstrates the approach to the implementation of one of the types of generalized complex numbers, namely dual numbers. We place particular emphasis on the description of the use of the multiple dispatch mechanism to implement a new numerical type. The resulting implementation of dual numbers can be considered as a prototype for a complete software module for supporting generalized complex numbers.
