Maple

Quaternions

Intended Audience:

• Researchers and engineers interested in modeling systems using quaternions.
• Educators may use the package to supplement their notes and text for a course, one of the topics of which is spinors or quaternions for which the help pages could replace a text book. The Maple™ environment is easy to use, it does not require compilation, and many students may already be familiar with it if Maple™ is used to help teach first and second year mathematics courses.
• Students at either the undergraduate or the graduate level will get a solid introduction to quaternions and their use with this package. It requires very little time to start constructing quaternions and to begin manipulating them.

Product Description:

Quaternions for Maple™ is an easy-to-use toolbox for Maple which allows professionals, researchers, and students to learn about, experiment with, and model systems through quaternions in the Maple worksheet environment. It transforms Maple into a system which works with quaternions as seamlessly as the basic system deals with complex numbers. The functionality covers many of the basic principles of quaternions including an environment where the multiplication operator (*) is no longer commutative.

Features list:

• Arithmetic operations (+, -, *, /, ^) on quaternions both for numeric and symbolic computations, including noncommutative multiplication.
• Over 70 routines, including:
  • Quaternion-related functions (conjugate, abs, etc.);
  • Exponential, trigonometric, and hyperbolic functions and their inverses on quaternions;
  • Overloaded Maple routines to make the manipulation of quaternions equivalent to the manipulation of Maple's complex numbers (op, nops, select, map, etc.); and
  • Plotting of quaternions.
• An emphasis on an efficient numeric implementation based on Maple's numerics on complex numbers.
• Example worksheets for quaternion fractals and rotation sequences.

Technical Requirements

• Maple 8 or higher

Author Information

• Douglas Harder was a developer in the Mathematics Group at Maplesoft for four years. He is the author of the MapleConnect FuzzySets package and the Units package and the co-author of numerous library packages including Maplets, MathML, and Student[Calculus1]. He has contributed a number of packages to the Maple Applications Center, most notably the Warnings package. He maintains other packages of interest on his Maplesque web site. He is now a lecturer at the University of Waterloo in the Department of Electrical and Computer Engineering. As an undergraduate student, he studied properties of quaternionic fractals.

  Douglas Wilhelm Harder
  Department of Electrical and Computer Engineering,
  University of Waterloo
  200 University Avenue West
  Waterloo, ON
  N2L 3G1
  dwharder@alumni.uwaterloo.ca

Technical Support

• Terms: Standard
• Technical support for the Quaternions package includes:
• The customer will receive installation instructions with the product.
• For a period of one year, the consumer may send installation help requests, questions, bug reports, feature requests, etc. to dwharder@alumni.uwaterloo.ca. After one year, the author reserves the right not to respond to e-mails.
• In general, response time to emails will be less than three business days, though this will not always be possible.
• For a period of one year after purchase, all bug fixes and updates will be made available to the customer.
• For a period of four months after purchase, all feature upgrades will be made available free of charge to the customer.