onion (version 1.2-7)

threeform: 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

Value

Returns an octonionic vector.

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.

Examples

# NOT RUN {
x <- roct(7) ; y <- roct(7) ; z <- roct(7)
associator(x,y,z)
# }