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

In problems of mathematical physics in order to study the structures ofspaces by using the Cayley–Klein models in theoretical calculations, the generalized complex numbers are essential. In the case ofcompu- tational 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 mech- anism. 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.