  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.
