# The Sedenion RPN Calculator

## Before using the calculator one must (1) **SELECT** and (2) **INITIALIZE** one of the eight doubling products.

### If you get NaN, you probably forgot to INITIALIZE the doubling product which you selected.

Those who are unfamiliar with postfix (reverse Polish) calculation may consult the Wikipedia article.

Please read the notice about the numbering of basis vectors below.

This calculator uses eight doubling products for multiplying two ordered pairs \((a,b)\) and \((c,d)\). The Cayley-Dickson products are P, Q and their transposes.

One's choice of doubling product may be selected from the drop-down product list at the top of the first column.

Products P and its transpose are the two traditional Cayley-Dickson products. The two Q Cayley-Dickson products were developed by this researcher.

All four P, Q products produce mutually isomorphic algebras.

The B products are mutually isomorphic to each other but not to the P, Q products. All eight products satisfy the quaternion rules for the basis vectors.

That is, for \(0\ne p\ne q\ne0\quad\)
(1) \(e_p\cdot e_q=-e_q\cdot e_p\) and (2) \(e_p\cdot e_q=e_r \leftrightarrow e_q\cdot e_r=e_p\).

**Important notice about the numbering of unit basis vectors**

The basis vectors satisfy \(e_{2p}=(e_p,0)\) and \(e_{2p+1}=(0,e_p)\). This differs from traditional numbering.

To translate between numbering systems, write the basis vector subscripts in reverse-binary order.

For sedenions \(e_3=e_{0011}\to e_{1100}=e_{12}\) in traditional numbering.

For octonions (using only \(e_0\) to \(e_7\)), \(e_3=e_{011}\to e_{110}=e_{6}\) in traditional numbering.

For quaternions \(e_3=e_{11}\to e_{11}=e_3\) but \(e_1=e_{01}\to e_{10}=e_2\).

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

Contact me by email for questions about the calculator.