# Octonions and Quaternions

## Documentation for package ‘onion’ version 1.2-7

- DESCRIPTION file.
- User guides, package vignettes and other documentation.

## Help Pages

A B C D E G H I J K L M N O P Q R S T misc

onion-package | Manipulation of quaternions and octonions

## -- A --

acos | Elementary transcendental functions
acos.octonion | Elementary transcendental functions
acos.onion | Elementary transcendental functions
acosh | Elementary transcendental functions
acosh.octonion | Elementary transcendental functions
acosh.onion | Elementary transcendental functions
AequalsA | Arithmetic Ops Group Methods for Octonions
Ainv | Arithmetic Ops Group Methods for Octonions
Amassage | Arithmetic Ops Group Methods for Octonions
Aneg | Arithmetic Ops Group Methods for Octonions
Apower | Arithmetic Ops Group Methods for Octonions
AprodA | Arithmetic Ops Group Methods for Octonions
AprodS | Arithmetic Ops Group Methods for Octonions
as.matrix.onion | Coerces an onionic vector into a matrix
as.octonion | Basic onion functions
as.onion | Basic onion functions
as.quaternion | Basic onion functions
asin | Elementary transcendental functions
asin.octonion | Elementary transcendental functions
asin.onion | Elementary transcendental functions
asinh | Elementary transcendental functions
asinh.octonion | Elementary transcendental functions
asinh.onion | Elementary transcendental functions
associator | Various non-field diagnostics
AsumA | Arithmetic Ops Group Methods for Octonions
atan | Elementary transcendental functions
atan.octonion | Elementary transcendental functions
atan.onion | Elementary transcendental functions
atanh | Elementary transcendental functions
atanh.octonion | Elementary transcendental functions
atanh.onion | Elementary transcendental functions

## -- B --

biggest | Returns the biggest type of a set of onions
bunny | The Stanford Bunny

## -- C --

c.onion | Combine onionic vectors into a single vector
commutator | Various non-field diagnostics
condense | Condense an onionic vector into a short form
condense.onion | Condense an onionic vector into a short form
Conj.onion | Onionic conjugation
cos | Elementary transcendental functions
cos.octonion | Elementary transcendental functions
cos.onion | Elementary transcendental functions
cosh | Elementary transcendental functions
cosh.octonion | Elementary transcendental functions
cosh.onion | Elementary transcendental functions
cumsum.onion | Cumulative sums for onions

## -- D --

dotprod | Euclidean even product

## -- E --

e.even | Various products of two onionic vectors
e.even.onion | Various products of two onionic vectors
e.odd | Various products of two onionic vectors
e.odd.onion | Various products of two onionic vectors
exp | Elementary transcendental functions
exp.octonion | Elementary transcendental functions
exp.onion | Elementary transcendental functions

## -- G --

g.even | Various products of two onionic vectors
g.even.onion | Various products of two onionic vectors
g.odd | Various products of two onionic vectors
g.odd.onion | Various products of two onionic vectors
get.comp | Octonion components
get.comp.onion | Octonion components

## -- H --

H0 | Unit onions
H1 | Unit onions
Hall | Unit onions
harmonize | Arithmetic Ops Group Methods for Octonions
Hi | Unit onions
Him | Unit onions
Hj | Unit onions
Hk | Unit onions
HprodH | Arithmetic Ops Group Methods for Octonions

## -- I --

i | Octonion components
i.octonion | Octonion components
i.quaternion | Octonion components
i<- | Octonion components
i<-.octonion | Octonion components
i<-.quaternion | Octonion components
il | Octonion components
il.octonion | Octonion components
il<- | Octonion components
il<-.octonion | Octonion components
Im | Octonion components
Im.default | Octonion components
Im.octonion | Octonion components
Im.quaternion | Octonion components
Im<- | Octonion components
Im<-.octonion | Octonion components
Im<-.quaternion | Octonion components
is.octonion | Basic onion functions
is.onion | Basic onion functions
is.quaternion | Basic onion functions

## -- J --

j | Octonion components
j.octonion | Octonion components
j.quaternion | Octonion components
j<- | Octonion components
j<-.octonion | Octonion components
j<-.quaternion | Octonion components
jl | Octonion components
jl.octonion | Octonion components
jl<- | Octonion components
jl<-.octonion | Octonion components

## -- K --

k | Octonion components
k.octonion | Octonion components
k.quaternion | Octonion components
k<- | Octonion components
k<-.octonion | Octonion components
k<-.quaternion | Octonion components
kl | Octonion components
kl.octonion | Octonion components
kl<- | Octonion components
kl<-.octonion | Octonion components

## -- L --

l | Octonion components
l.octonion | Octonion components
l<- | Octonion components
l<-.octonion | Octonion components
length | Length of an octonionic vector
length.onion | Length of an octonionic vector
length.onion<- | Length of an octonionic vector
length<- | Length of an octonionic vector
length<-.onion | Length of an octonionic vector
ln | Elementary transcendental functions
ln.octonion | Elementary transcendental functions
ln.onion | Elementary transcendental functions
log | Elementary transcendental functions
log.octonion | Elementary transcendental functions
log.onion | Elementary transcendental functions

## -- M --

Mod | Norm and modulus of an onionic vector
Mod.onion | Norm and modulus of an onionic vector
Mod<- | Norm and modulus of an onionic vector
Mod<-.onion | Norm and modulus of an onionic vector

## -- N --

names.onion | Names of an onionic vector
names.onion<- | Names of an onionic vector
names<-.onion | Names of an onionic vector
Norm | Norm and modulus of an onionic vector
norm | Norm and modulus of an onionic vector
Norm.onion | Norm and modulus of an onionic vector
norm.onion | Norm and modulus of an onionic vector

## -- O --

O0 | Unit onions
O1 | Unit onions
Oall | Unit onions
Octonion | Basic onion functions
octonion | Basic onion functions
Oi | Unit onions
Oil | Unit onions
Oim | Unit onions
Oj | Unit onions
Ojl | Unit onions
Ok | Unit onions
Okl | Unit onions
Ol | Unit onions
onion | Manipulation of quaternions and octonions
OprodO | Arithmetic Ops Group Methods for Octonions
Ops | Arithmetic Ops Group Methods for Octonions
Ops.onion | Arithmetic Ops Group Methods for Octonions

## -- P --

p3d | Three dimensional plotting
plot.onion | Plot onions
print.octonion | Print method for onions
print.onion | Print method for onions
print.quaternion | Print method for onions
prod | Various products of two onionic vectors
prods | Various products of two onionic vectors

## -- Q --

Quaternion | Basic onion functions
quaternion | Basic onion functions

## -- R --

Re | Octonion components
Re.default | Octonion components
Re.octonion | Octonion components
Re.quaternion | Octonion components
Re<- | Octonion components
Re<-.octonion | Octonion components
Re<-.quaternion | Octonion components
rep.onion | Replicate elements of onionic vectors
roct | Random onionic vector
rotate | Rotates 3D vectors using quaternions
rquat | Random onionic vector
R_HprodH | Arithmetic Ops Group Methods for Octonions
R_OprodO | Arithmetic Ops Group Methods for Octonions

## -- S --

seq.onion | seq method for onions
set.comp<- | Octonion components
set.comp<-.octonion | Octonion components
set.comp<-.onion | Octonion components
set.comp<-.quaternion | Octonion components
Sign | Norm and modulus of an onionic vector
sign | Norm and modulus of an onionic vector
sign.onion | Norm and modulus of an onionic vector
sin | Elementary transcendental functions
sin.octonion | Elementary transcendental functions
sin.onion | Elementary transcendental functions
sinh | Elementary transcendental functions
sinh.octonion | Elementary transcendental functions
sinh.onion | Elementary transcendental functions
SLERP | seq method for onions
slerp | seq method for onions
sqrt | Elementary transcendental functions
sqrt.octonion | Elementary transcendental functions
sqrt.onion | Elementary transcendental functions
str.onion | Compactly display an onion
sum.octonion | Sum of onionic vectors
sum.onion | Sum of onionic vectors
sum.quaternion | Sum of onionic vectors

## -- T --

t.onion | Onion transpose
tan | Elementary transcendental functions
tan.octonion | Elementary transcendental functions
tan.onion | Elementary transcendental functions
tanh | Elementary transcendental functions
tanh.octonion | Elementary transcendental functions
tanh.onion | Elementary transcendental functions
threeform | Various non-field diagnostics
type | Basic onion functions

## -- misc --

%.% | Euclidean even product
%<*>% | Various products of two onionic vectors
%<*>%.onion | Various products of two onionic vectors
%<.>% | Various products of two onionic vectors
%<.>%.onion | Various products of two onionic vectors
%>*<% | Various products of two onionic vectors
%>*<%.onion | Various products of two onionic vectors
%>.<% | Various products of two onionic vectors
%>.<%.onion | Various products of two onionic vectors
[.onion | Extract or Replace Parts of an onion
[<-.onion | Extract or Replace Parts of an onion