Quaternions : a mathematica package for quaternionic analysis

Abstract

This paper describes new issues of the Mathematica standard package Quaternions for implementing Hamilton's Quaternion Algebra. This work attempts to endow the original package with the ability to perform operations on symbolic expressions involving quaternion-valued functions. A collection of new functions is introduced in order to provide basic mathematical tools necessary for dealing with regular functions in $\mathbb{R}^{n+1}$, for $n\geq2$. The performance of the package is illustrated by presenting several examples and applications.