MathGroup Archive 1992

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Has anyone implemented quaternions?  I have an ugly
implementation using lists: p = {p0,p1,p2,p3}, but would
like something better than:
p = {p0,p1,p2,p3};
q = {q0,q1,q2,q3};

p ~qTimes~ q - q ~qTimes~ p //Simplify

   {0, 2 (-(p3 q2) + p2 q3), 2 (p3 q1 - p1 q3),
   	2 (-(p2 q1) + p1 q2)}

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