Implementation of hyperbolic complex numbers in Julia language

TL;DR

This paper presents a Julia library for hyperbolic complex numbers, leveraging multiple dispatch to facilitate their implementation in scientific computing, with potential applications in physics and geometry.

Contribution

The paper introduces a novel implementation of hyperbolic complex numbers in Julia using multiple dispatch, filling a gap in scientific programming tools.

Findings

The library successfully implements hyperbolic complex numbers in Julia.

Multiple dispatch proves to be an effective approach for such implementations.

The approach simplifies the integration of hyperbolic numbers into scientific computations.

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.