Initial population.

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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input quat.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1991.
+@
+<<*>>=
+<<license>>
+
+-- This file demonstrates some operations with quaternions.
+ 
+)clear all
+ 
+-- The basic function for creating quaternions is "quatern". This is
+-- a quaternion over the rational numbers.
+q := quatern(2/11,-8,3/4,1)
+ 
+-- The four arguments are the real part, the i imaginary part, the
+-- j imaginary part and the k imaginary part, respectively. These are
+-- extracted with the following functions.
+ 
+real q
+imagI q
+imagJ q
+imagK q
+ 
+-- Because q is over the rationals (and nonzero), you can invert it ...
+inv q
+ 
+-- in addition to the normal arithmetic (ring) operations.
+q**6
+r := quatern(-2,3,23/9,-89)
+q + r
+q - r
+ 
+-- In general, multiplication is not commutative.
+q * r
+r * q
+ 
+-- There are no predefined constants for the imaginary i, j and k but
+-- you can easily define them.
+ 
+i := quatern(0,1,0,0)
+j := quatern(0,0,1,0)
+k := quatern(0,0,0,1)
+ 
+i*i
+j*j
+k*k
+i*j
+j*k
+k*i
+q * i
+ 
+-- The norm is the quaternion times its conjugate
+norm q
+conjugate q
+q * %
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}