Computer modeling of exponential and logarithmic functions of generalized quaternions in symbolic computation system

TL;DR

This paper develops a mathematical model for exponential and logarithmic functions within generalized quaternions, utilizing symbolic computation in Maple to explore their properties and relations to non-commutative hypercomplex systems.

Contribution

It introduces a differential equation approach to model these functions in hypercomplex systems and analyzes their properties and exponential representations.

Findings

Derived differential equations for hypercomplex exponential and logarithmic functions

Explored properties and relations to non-commutative hypercomplex systems

Implemented symbolic simulations in Maple

Abstract

The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex coefficients. Simulation is performed using symbolic computation system Maple. Some properties of these concepts and their relation to the exponential representations of specific non-commutative hypercomplex number systems of dimension four.