The fields R, C, and H have 1, 2, and 4 degrees of freedom. To represent all possible functional mappings, 1, 2, and 4 automorphic functions are required for each field.
R: Identity (z).
C: Identity, conjugate (z, z*).
H: Identity, 3 conjugates (q, q*, q*1, q*2) where
Any quaternion function on the R4 manifold
can be represented on the manifold H1 using a combination of q, q*, q*1,and q*2.
sweetser@alum.mit.edu copyright 2003, all rights reserved.
