onion (version 1.5-3)

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)

Value

Returns an octonionic vector

Arguments

x1,x2,x3

onionic vectors

Author

Robin K. S. Hankin

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.

See Also

dot

Examples

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