associator: Various non-field diagnostics
In onion: Octonions and Quaternions

Description Usage Arguments Details Value Author(s) Examples

Diagnostics of non-field behaviour: threeform, associator, commutator

1
2
3

threeform(x1, x2, x3)
associator(x1, x2, x3)
commutator(x1, x2)

x1,x2,x3

onionic vectors

The threeform is defined as Re(x1 * (Conj(x2) * x3) - x3 * (Conj(x2) * x1))/2;

the associator is (x1 * x2) * x3 - x1 * (x2 * x3);

the commutator is x1 * x2 - x2 * x1.

Returns an octonionic vector.

Robin K. S. Hankin

1 2	x <- roct(7) ; y <- roct(7) ; z <- roct(7) associator(x,y,z)

    [1]  [2]  [3]  [4]  [5]  [6]  [7]
Re    0    0    0    0    0    0    0
i   678 -250 -186  150  214  746  -76
j  1098 -540  -66  610   20 -484 -502
k  -264 -438 -110 -848 -148  278  238
l   360   86  214   58  -64  178   -2
il -426  564  298  116  -58 -304   34
jl -654  130 -412  -68   -6 -134   96
kl -264  168   96  -58   20  -16   52