The Octonion RPN Calculator

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

Calculator Description

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.

Definition of basis elements

\(e_0=(1,0)=1\)

\(e_1=(0,1)=i\)

\(e_2=(e_1,0)=j\)

\(e_3=(0,e_1)=k\)

\(e_4=(e_2,0)\)

\(e_5=(0,e_2)\)

\(e_6=(e_3,0)\)

\(e_7=(0,e_3)\)

Multiplication Table

A worked example of use

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

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