Most often the multiplication in convention descriptions and papers is
described in matrix multiplication style like this:
q · p := Q(q)p
Q(q) :=
[q0 −q1 −q2 −q3]
[q1 q0 −q3 q2]
[q2 q3 q0 −q1]
[q3 −q2 q1 q0]
I'm just rearanging the terms such that it's easily comparable with
these definitions additional to it being clearly described by
documenting we use the hamilton convention.