" 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

To solve the sqrt you basically need to solve this set of equation.
See picture.

All variables ( given and solved) need to be non-negative.

The C is not part of input or output But is there to make the reduction ( mod 1 + a + … )

C also nonnegative.

This system was simply obtained by squaring.

regards 

tommy1729

ok. it seems the real part of the square of such a number is always the largest.
Therefore we cannot solve for many numbers including the sqrt of the additive inverse of 1 ( the imaginary )

SO im moving on to dimension 6.

Ill keep you all updated

regards

tommy1729