" tommy quaternion "

[tommy1729]

ok here is a 5 dim candidate

the coefficients are " magnitudes " ; nonnegative reals.


1 + a + b + c + d + e = 0.

so when " reduced " not all magnitudes can be nonzero.

mod ( 1 + a + b + c + d + e ) if you want.
( so the dimension reduces from 6 ( 5 letters and real ) to 5 )


a^2 = b^2  = ... = 1.

a b = c
a c = d
a d = e
a e = b

b c = e
b d = a
b e = d

c d = b
c e = a

d e = c

som and products are commutative.

som and product behave distributive.



regards

tommy1729