O1 {onion}

Unit onions

Description

Each of the eight unit quaternions and octonions

Usage

H1
Hi
Hj
Hk
H0
Him
Hall
O1
Oi
Oj
Ok
Ol
Oil
Ojl
O0
Oim
Oall

Format

Each one is an onionic vector of length one.

Details

Try Hi (=quaternion(i=1)) to get the pattern for the first four. The next ones are the zero quaternion, the pure imaginary quaternion with all components 1, and the quaternion with all components 1. The ones beginning with “O” follow a similar pattern.

These are just variables that may be overwritten and thus resemble T and F whose value may be changed.

Value

A length-one onion, either a quaternion or an octonion

Examples

Oall
seq_onion(from=O1,to=Oil,len=6)

stopifnot(Hj*Hk ==  Hi)
stopifnot(Okl*Oil == -Oj )  # See tests/test_aaa.R for the full set