User:Roman Czyborra

Sedenion Multiplication
$ \begin{bmatrix} +P0&-P1&-P2&-P3&-P4&-P5&-P6&-P7&-P8&-P9&-PA&-PB&-PC&-PD&-PE&-PF \\ +P1&+P0&-P3&+P2&-P5&+P4&+P7&-P6&-P9&+P8&+PB&-PA&+PD&-PC&-PF&+PE \\ +P2&+P3&+P0&-P1&-P6&-P7&+P4&+P5&-PA&-PB&+P8&+P9&+PE&+PF&-PC&-PD \\ +P3&-P2&+P1&+P0&-P7&+P6&-P5&+P4&-PB&+PA&-P9&+P8&+PF&-PE&+PD&-PC \\ +P4&+P5&+P6&+P7&+P0&-P1&-P2&-P3&-PC&-PD&-PE&-PF&+P8&+P9&+PA&+PB \\ +P5&-P4&+P7&-P6&+P1&+P0&+P3&-P2&-PD&+PC&-PF&+PE&-P9&+P8&-PB&+PA \\ +P6&-P7&-P4&+P5&+P2&-P3&+P0&+P1&-PE&+PF&+PC&-PD&-PA&+PB&+P8&-P9 \\ +P7&+P6&-P5&-P4&+P3&+P2&-P1&+P0&-PF&-PE&+PD&+PC&-PB&-PA&+P9&+P8 \\ +P8&+P9&+PA&+PB&+PC&+PD&+PE&+PF&+P0&-P1&-P2&-P3&-P4&-P5&-P6&-P7 \\ +P9&-P8&+PB&-PA&+PD&-PC&-PF&+PE&+P1&+P0&+P3&-P2&+P5&-P4&-P7&+P6 \\ +PA&-PB&-P8&+P9&+PE&+PF&-PC&-PD&+P2&-P3&+P0&+P1&+P6&+P7&-P4&-P5 \\ +PB&+PA&-P9&-P8&+PF&-PE&+PD&-PC&+P3&+P2&-P1&+P0&+P7&-P6&+P5&-P4 \\ +PC&-PD&-PE&-PF&-P8&+P9&+PA&+PB&+P4&-P5&-P6&-P7&+P0&+P1&+P2&+P3 \\ +PD&+PC&-PF&+PE&-P9&-P8&-PB&+PA&+P5&+P4&-P7&+P6&-P1&+P0&-P3&+P2 \\ +PE&+PF&+PC&-PD&-PA&+PB&-P8&-P9&+P6&+P7&+P4&-P5&-P2&+P3&+P0&-P1 \\ +PF&-PE&+PD&+PC&-PB&-PA&+P9&-P8&+P7&-P6&+P5&+P4&-P3&-P2&+P1&+P0 \\ \end{bmatrix} \begin{bmatrix} Q0\\Q1\\Q2\\Q3\\Q4\\Q5\\Q6\\Q7\\Q8\\Q9\\QA\\QB\\QC\\QD\\QE\\QF \end{bmatrix} =: \begin{bmatrix} P0\\P1\\P2\\P3\\P4\\P5\\P6\\P7\\P8\\P9\\PA\\PB\\PC\\PD\\PE\\PF \end{bmatrix} \begin{bmatrix} Q0\\Q1\\Q2\\Q3\\Q4\\Q5\\Q6\\Q7\\Q8\\Q9\\QA\\QB\\QC\\QD\\QE\\QF \end{bmatrix}$

open-axiom octon(p0,p1,p2,p3,p4,p5,p6,p7)*octon(q0,q1,q2,q3,q4,q5,q6,q7)-conjugate(octon(q8,q9,qa,qb,qc,qd,qe,qf))*octon(p8,p9,pa,pb,pc,pd,pe,pf) octon(q8,q9,qa,qb,qc,qd,qe,qf)*octon(p0,p1,p2,p3,p4,p5,p6,p7)+octon(p8,p9,pa,pb,pc,pd,pe,pf)*conjugate(octon(q0,q1,q2,q3,q4,q5,q6,q7))