Re: Analytic Functions in 3D?-


As regards quaternions: the norm in the quaternion skew field yields the
well-known Euclidean metric with its accompanying topology.
Multiplication is not commutative, so one needs to distinguish between
left-division
( p^(-1).q ) and right-division ( q.p^(-1) ), and consequently, between
left- and right-difference and differential quotients.
I am not aware of a fully developed quaternion differential calculus.
Google and Wikipedia might be helpful.


In fact, this isn't very useful. Even the quaternion map z^2 is
not left-differentiable and not right-differentiable.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.