Approaches to the implementation of generalized complex numbers in the Julia language

In problems of mathematical physics in order to study the structures of spaces by using the Cayley-Klein models in theoretical calculations, the generalized complex numbers are essential. In the case of computational experiments, such tasks require their high-quality implementation in a programming language. The proposed small deployment of generalized complex numbers in modern programming languages have several disadvantages. In this article we propose to use the Julia language as the language for generalized complex numbers implemention, 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 introduce a new numerical type. The resulting implementation of dual numbers can be considered as a prototype for a complete software module supporting generalized complex numbers. © 2020 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org)