[math-fun] cubic quaternions - zero divisors

30 Apr 2003

      Thanks for the suggestions!

In the special case Q = cbrt 2, R = cbrt 3, I spotted a zero divisor.

(Q-R)^3 = Q^3 - R^3  since the cross terms cancel out.

        =  2 - 3  =  -1  in the special case.

So  1 + (Q-R)^3 = 0,  and it's the product of  1 + Q - R with

1 - (Q-R) + (Q-R)^2.

This construction seems to work on a lot of cases.

Rich   rcs@cs.arizona.edu

[math-fun] cubic quaternions - zero divisors

Richard Schroeppel