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Quaternions: A Mathematica Package for Quaternionic Analysis

  • M. I. Falcão
  • Fernando Miranda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6784)

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 ℝ n + 1, for n ≥ 2. The performance of the package is illustrated by presenting several examples and applications.

Keywords

Quaternions Clifford Analysis monogenic functions symbolic computation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • M. I. Falcão
    • 1
  • Fernando Miranda
    • 2
  1. 1.Departamento de Matemática e AplicaçõesUniversidade do MinhoPortugal
  2. 2.Departamento de Matemática e Aplicações and Centro de MatemáticaUniversidade do MinhoPortugal

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