The Octonion multiplication table used for this calculator is explained here.
This is a postfix calculator with a depth 2 stack. To compute R + S*T, for example: R [enter] S [enter] T [times] [plus]
There are ten storage/retrieval registers, X, Y, Z, A, B, C, D, E, F, G accessed by the dropdown icon.
There are various standard register operations, with [push] replaced with [enter].
Numbers may be entered into the main register by hand, or by using the random number generator.
\(e_0=(1,0)=1\)
\(e_1=(0,1)=i\)
\(e_2=(e_1,0)=j\)
\(e_3=(0,e_1)=k\)
\(e_4=(e_2,0)\)
\(e_5=(0,e_2)\)
\(e_6=(e_3,0)\)
\(e_7=(0,e_3)\)
e0 | e1 | e2 | e3 | e4 | e5 | e6 | e7 |
e1 | –e0 | e3 | –e2 | e5 | –e4 | e7 | –e6 |
e2 | –e3 | –e0 | e1 | e6 | –e7 | –e4 | e5 |
e3 | e2 | –e1 | –e0 | –e7 | –e6 | e5 | e4 |
e4 | –e5 | –e6 | e7 | –e0 | e1 | e2 | –e3 |
e5 | e4 | e7 | e6 | –e1 | –e0 | –e3 | –e2 |
e6 | –e7 | e4 | –e5 | –e2 | e3 | –e0 | e1 |
e7 | e6 | –e5 | –e4 | e3 | e2 | –e1 | –e0 |
To illustrate one of the Moufang identities, for example Z(X(ZY)) = ((ZX)Z)Y, perform the following operations:
John Wayland Bales, Department of Mathematics (Retired), Tuskegee University, Tuskegee, AL 36088 USA