threeform {onion}

Various non-field diagnostics

Description

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

Usage

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

Arguments

x1, x2, x3

onionic vectors

Details

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.

Value

Returns an octonionic vector

Author(s)

Robin K. S. Hankin

See Also

dot

Examples

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