onion (version 1.2-7)

onion: Basic onion functions

Description

Construct, coerce to, test for, and print onions

Usage

octonion(length.out = NULL, names = NULL, Re = 0, i = 0, j = 0, 
    k = 0, l = 0, il = 0, jl = 0, kl = 0)
as.octonion(x, single = FALSE, names=NULL)
is.octonion(x)
quaternion(length.out = NULL, names = NULL, Re = 0, i = 0, j = 0, k = 0)
as.quaternion(x, single = FALSE, names=NULL)
is.quaternion(x)
is.onion(x)
as.onion(x,type,names=NULL,single=FALSE)
type(x)

Arguments

length.out

In functions quaternion() and octonion(), the length of the onionic vector returned.

names

In functions quaternion() and octonion(), the names of the octonionic vector returned.

Re

The real part of the onionic vector returned.

i

Component \(i\) of the onionic vector returned.

j

Component \(j\) of the onionic vector returned.

k

In function octonion(), component \(k\) of the octonionic vector returned.

l

In function octonion(), component \(l\) of the octonionic vector returned.

il

In function octonion(), component \(il\) of the octonionic vector returned.

jl

In function octonion(), component \(jl\) of the octonionic vector returned.

kl

In function octonion(), component \(kl\) of the octonionic vector returned.

x

Onion to be tested or printed

single

In functions as.octonion() and as.quaternion(), a Boolean variable with default FALSE meaning to interpret x as a vector of reals to be coerced into an onionic vector with zero imaginary part; and TRUE meaning to interpret x as a length 4 (or length 8) vector and return the corresponding single onion.

type

In function as.onion() a string either “quaternion” or “octonion” denoting the algebra to be forced into

Details

Functions quaternion() and octonion() use standard recycling where possible; rbind() is used.

Functions as.quaternion() and as.octonion() coerce to quaternions and octonions respectively. If given a complex vector, the real and imaginary components are interpreted as Re and i respectively.

The output of type() is accepted as the type argument of function as.onion(); thus as.onion(out,type=type(x)) works as expected.

Examples

# NOT RUN {
x <- octonion(Re=1,il=1:3)
x
kl(x) <- 100
x

as.quaternion(diag(4))
# }

Run the code above in your browser using DataCamp Workspace