Implementation of hyperbolic complex numbers in Julia language

Abstract

Background: Hyperbolic complex numbers are used in the description of hyperbolic spaces. One of the well-known examples of such spaces is the Minkowski space, which plays a leading role in the problems of the special theory of relativity and electrodynamics. However, such numbers are not very common in different programming languages. Purpose: Of interest is the implementation of hyperbolic complex in scientific programming languages, in particular, in the Julia language. Methods: The Julia language is based on the concept of multiple dispatch. This concept is an extension of the concept of polymorphism for object-oriented programming languages. To implement hyperbolic complex numbers, the multiple dispatching approach of the Julia language was used. Results: The result is a library that implements hyperbolic numbers. Conclusions: Based on the results of the study, we can conclude that the concept of multiple dispatching in scientific programming languages is convenient and natural.