To illustrate one of the Moufang identities, for example Z(X(ZY)) = ((ZX)Z)Y, perform the following operations:

- Select random vectors X, Y and Z
- RANDOM X STO
- RANDOM Y STO
- RANDOM Z STO
- Perform the operations on the left side of the identity
- Z RCL ENTER (Since Z should already be in the register, you don't actually have to recall it.)
- Y RCL × ENTER
- X RCL SWAP × ENTER
- Z RCL SWAP ×
- Store the result
- A STO
- Perform the operations on the right side of the identity
- Z RCL ENTER
- X RCL × ENTER
- Z RCL × ENTER
- Y RCL × ENTER
- Subtract the result obtained on the left side of the identity. Result should be 0 (allowing for small errors).
- A RCL –

The Octonion multiplication table used for this calculator is explained here.

John Wayland Bales, Department of Mathematics, Tuskegee University, Tuskegee, AL 36088 USA