# The Octonion RPN Calculator

CAUTION: You must RE-INITIALIZE the calculator after changing any of the default settings in the top row.

 C= 1 2 3 4 5 6 7 Triads: Octonion RPN Calculator Random integer entry [-9,9] Random real entry (-1,1) Register 2 Register 1 Top Register e0 e1 e2 e3 e4 e5 e6 e7 X Y Z A B C D E F G H I J K L M X Y Z A B C D E F G H I J K L M

Fano Plane Code compliments of Bruce Gray at https://github.com/Util

#### A worked example of use

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

1. Select random vectors X, Y and Z
1. INPUT X STO
2. INPUT Y STO
3. INPUT 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 tiny round off errors of order 10-14).
1. A RCL –

Contact:John Wayland Bales, Department of Mathematics (Retired), Tuskegee University, Tuskegee, AL 36088 USA

This is a 'Reverse Polish octonion calculator' with a level three pushdown stack. The top of the stack is the rightmost column.

The traditional 'PUSH' operation is here rendered as 'ENTER'

Octonions may be entered by hand in the top register or you may generate random entries and store them for reuse.

To perform an operation such as x + y you would do x enter y plus and the result will appear in the top register.

An example of a more complex calculation is given below the calculator.

There are sixteen memory registers X,Y,Z plus A through M accessible from a dropdown list.

There are 480 different octonion triad sets which specify the product of the seven octonion basis vectors.

You may replace the seven default triads with your preferred set of triads, but must re-initialize the calculator after doing so.

Feel free to contact me with questions or comments using my email at the bottom of the calculator page.

If you find a bug, please send me a bug report with instructions on how to reproduce the error.

The default triads in the top row are based on Degan's Eight Square Identity.

You may change the default triads to any of the other 480 Octonion triads but you must re-initialize the calculator after doing so.

You may select the value of the 'center' position in the Fano plane by changing the value of C from the drop down list.

### Software © (2009, 2023) John Wayland Bales under the GNU General Public License

You may use or modify this software for any non-commercial use so long as you include this copyright notice.

Also check out the Sedenion calculator.