Allow me to introduce the Pauli Algebra package for Maple. This package implements the Clifford Algebra of Physical Space Cl3 through the use of complex paravectors. The syntax of the package is similar to the notation popularized by the work of Dr. William E. Baylis. For more information, check out the Wikipedia entry on Paravectors and the APS workbook available on Dr. Baylis' website
To install the Pauli Algebra package while in a Maple session, type
Alternatively, you can find the Pauli Algebra package in the MapleCloud, and choose the install button on the far right.
Upon installation, several help files become available in Maple Help to assist you with the syntax.
As you will see in the Pauli.mpl source code of the package workbook, a number of Maple functions have been overloaded to handle the package's Paravector datatype. If you wish to overload additional Maple functions, let me know, and I'll include them in future updates.
I'll sign off by attaching a Maple worksheet/pdf containing some examples.