# Octonions and Quaternions

## Documentation for package ‘onion’ version 1.5-3

- 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 Z misc

onion-package | Octonions and Quaternions

## -- A --

abs-method | Various logarithmic and circular functions for onions
acos | Various logarithmic and circular functions for onions
acos-method | Various logarithmic and circular functions for onions
acosh | Various logarithmic and circular functions for onions
acosh-method | Various logarithmic and circular functions for onions
ad | The adjoint map
adjoint | The adjoint map
Arith | Methods for Function Arith in package Onion
Arith-method | Methods for Function Arith in package Onion
Arith-methods | Methods for Function Arith in package Onion
as.matrix | Basic onion functions
as.matrix-method | Basic onion functions
as.numeric-method | Basic onion functions
as.octonion | Basic onion functions
as.octonionmat | Onionic matrices
as.onion | Basic onion functions
as.onionmat | Onionic matrices
as.orthogonal | Orthogonal matrix equivalents
as.quaternion | Basic onion functions
as.quaternionmat | Onionic matrices
asin | Various logarithmic and circular functions for onions
asin-method | Various logarithmic and circular functions for onions
asinh | Various logarithmic and circular functions for onions
asinh-method | Various logarithmic and circular functions for onions
associator | Various non-field diagnostics
atan | Various logarithmic and circular functions for onions
atan-method | Various logarithmic and circular functions for onions
atanh | Various logarithmic and circular functions for onions
atanh-method | Various logarithmic and circular functions for onions

## -- B --

biggest | Returns the biggest type of a set of onions
bind | Binding of onionmats
bind_onion | Binding of onionmats
bind_onionmat_onion | Binding of onionmats
bind_onionmat_onionmat | Binding of onionmats
bind_onion_matrix | Binding of onionmats
bind_onion_onion | Binding of onionmats
bind_onion_onionmat | Binding of onionmats
bunny | The Stanford Bunny

## -- C --

c | Concatenation
c-method | Concatenation
c.onion | Concatenation
cbind | Binding of onionmats
cbind2-method | Binding of onionmats
colnames | Names of an onionic vector
colnames-method | Names of an onionic vector
colnames<- | Onionic matrices
colnames<--method | Names of an onionic vector
commutator | Various non-field diagnostics
Compare-method | Methods for compare S4 group
Compare-methods | Methods for compare S4 group
comp_names | Print method for onions
concatenate.onion | Concatenation
condense | Condense an onionic vector into a short form
condense.onion | Condense an onionic vector into a short form
Conj | Complex functionality for onions
Conj-method | Complex functionality for onions
cos | Various logarithmic and circular functions for onions
cos-method | Various logarithmic and circular functions for onions
cosh | Various logarithmic and circular functions for onions
cosh-method | Various logarithmic and circular functions for onions
cprod | Onionic matrices
cprod-method | Onionic matrices
cumsum | Cumulative sums and products of onions
c_onionpair | Concatenation

## -- D --

diag | Onionic matrices
diag-method | Onionic matrices
diag.onion | Onionic matrices
diag.onionmat | Onionic matrices
diag<--method | Onionic matrices
diag<-.onionmat | Onionic matrices
dim | Names of an onionic vector
dim-method | Names of an onionic vector
dim<- | Names of an onionic vector
dim<--method | Names of an onionic vector
dimnames-method | Names of an onionic vector
dimnames<--method | Names of an onionic vector
dot | Class "dot"
dot-class | Class "dot"
dotprod | Various products of two onions
dot_error | Class "dot"
drop | Drop zero imaginary parts of an onionic vector
drop-method | Drop zero imaginary parts of an onionic vector
drop.onion | Drop zero imaginary parts of an onionic vector

## -- E --

exp | Various logarithmic and circular functions for onions
exp-method | Various logarithmic and circular functions for onions
extract | Class "dot"
e_even.onion | Various products of two onions
e_odd.onion | Various products of two onions

## -- G --

getd | Onionic matrices
getM | Onionic matrices
g_even.onion | Various products of two onions
g_odd.onion | Various products of two onions

## -- H --

H0 | Unit onions
H1 | Unit onions
Hall | Unit onions
harmonize_on | Methods for Function Arith in package Onion
harmonize_oo | Methods for Function Arith in package Onion
herm_onion_mat | Onionic matrices
Hi | Unit onions
Him | Unit onions
Hj | Unit onions
Hk | Unit onions
ht | Onionic matrices
ht-method | Onionic matrices

## -- I --

i | Extract or Replace Parts of onions or glubs
i-method | Extract or Replace Parts of onions or glubs
i.octonion | Extract or Replace Parts of onions or glubs
i.quaternion | Extract or Replace Parts of onions or glubs
i<- | Extract or Replace Parts of onions or glubs
i<--method | Extract or Replace Parts of onions or glubs
i<-.octonion | Extract or Replace Parts of onions or glubs
i<-.quaternion | Extract or Replace Parts of onions or glubs
il | Extract or Replace Parts of onions or glubs
il-method | Extract or Replace Parts of onions or glubs
il.octonion | Extract or Replace Parts of onions or glubs
il<- | Extract or Replace Parts of onions or glubs
il<--method | Extract or Replace Parts of onions or glubs
il<-.octonion | Extract or Replace Parts of onions or glubs
Im | Complex functionality for onions
Im-method | Complex functionality for onions
Im<- | Complex functionality for onions
Im<--method | Complex functionality for onions
Im<-.quaternion | Extract or Replace Parts of onions or glubs
index-class | Class "onion"
is.octonion | Basic onion functions
is.onion | Basic onion functions
is.onionmat | Onionic matrices
is.quaternion | Basic onion functions
is_orthogonal | Orthogonal matrix equivalents

## -- J --

j | Extract or Replace Parts of onions or glubs
j-method | Extract or Replace Parts of onions or glubs
j.octonion | Extract or Replace Parts of onions or glubs
j.quaternion | Extract or Replace Parts of onions or glubs
j<- | Extract or Replace Parts of onions or glubs
j<--method | Extract or Replace Parts of onions or glubs
j<-.octonion | Extract or Replace Parts of onions or glubs
j<-.quaternion | Extract or Replace Parts of onions or glubs
jacobi | Class "dot"
jl | Extract or Replace Parts of onions or glubs
jl-method | Extract or Replace Parts of onions or glubs
jl.octonion | Extract or Replace Parts of onions or glubs
jl<- | Extract or Replace Parts of onions or glubs
jl<--method | Extract or Replace Parts of onions or glubs
jl<-.octonion | Extract or Replace Parts of onions or glubs

## -- K --

k | Extract or Replace Parts of onions or glubs
k-method | Extract or Replace Parts of onions or glubs
k.octonion | Extract or Replace Parts of onions or glubs
k.quaternion | Extract or Replace Parts of onions or glubs
k<- | Extract or Replace Parts of onions or glubs
k<--method | Extract or Replace Parts of onions or glubs
k<-.octonion | Extract or Replace Parts of onions or glubs
k<-.quaternion | Extract or Replace Parts of onions or glubs
kl | Extract or Replace Parts of onions or glubs
kl-method | Extract or Replace Parts of onions or glubs
kl.octonion | Extract or Replace Parts of onions or glubs
kl<- | Extract or Replace Parts of onions or glubs
kl<--method | Extract or Replace Parts of onions or glubs
kl<-.octonion | Extract or Replace Parts of onions or glubs

## -- L --

l | Extract or Replace Parts of onions or glubs
l-method | Extract or Replace Parts of onions or glubs
l.octonion | Extract or Replace Parts of onions or glubs
l<- | Extract or Replace Parts of onions or glubs
l<--method | Extract or Replace Parts of onions or glubs
l<-.octonion | Extract or Replace Parts of onions or glubs
length | Length of an octonionic vector
length-method | Length of an octonionic vector
length.onion | Length of an octonionic vector
length<- | Length of an octonionic vector
length<--method | Length of an octonionic vector
length<-.onion | Length of an octonionic vector
log | Various logarithmic and circular functions for onions
log-method | Various logarithmic and circular functions for onions
Logic-method | Logical operations on onions
logic.onion | Logical operations on onions

## -- M --

matrix-method | Onionic matrices
matrix2quaternion | Orthogonal matrix equivalents
matrix_arith_onion | Onionic matrices
matrix_arith_onionmat | Onionic matrices
matrix_plus_onion | Onionic matrices
matrix_plus_onionmat | Onionic matrices
matrix_prod_onion | Onionic matrices
max | Various summary statistics for onions
min | Various summary statistics for onions
Mod | Complex functionality for onions
Mod-method | Complex functionality for onions

## -- N --

names-method | Names of an onionic vector
names.onion | Names of an onionic vector
names.onion<- | Names of an onionic vector
names<- | Names of an onionic vector
names<--method | Names of an onionic vector
names<-.onion | Names of an onionic vector
ncol | Onionic matrices
ncol-method | Names of an onionic vector
ncol-method | Onionic matrices
ncol-methods | Onionic matrices
ncol.onionmat | Onionic matrices
newonionmat | Onionic matrices
Norm | Complex functionality for onions
Norm-method | Complex functionality for onions
Norm.onion | Complex functionality for onions
nrow | Onionic matrices
nrow-method | Names of an onionic vector
nrow-method | Onionic matrices
nrow-methods | Onionic matrices
nrow.onionmat | Onionic matrices
numeric_arith_onion | Methods for Function Arith in package Onion
numeric_arith_onionmat | Onionic matrices
numeric_matrixprod_onionmat | Onionic matrices

## -- O --

O0 | Unit onions
O1 | Unit onions
Oall | Unit onions
Octonion | Basic onion functions
octonion | Basic onion functions
octonion-class | Class "onion"
octonion_prod_octonion | Methods for Function Arith in package Onion
octonion_to_quaternion | 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
om_cprod | Onionic matrices
om_ht | Onionic matrices
om_prod | Onionic matrices
om_tcprod | Onionic matrices
onion | Basic onion functions
onion-class | Class "onion"
onionmat | Onionic matrices
onionmat-class | Class "onion"
onionmatprod | Onionic matrices
onionmat_allsum | Various summary statistics for onions
onionmat_arith_matrix | Onionic matrices
onionmat_arith_onion | Onionic matrices
onionmat_arith_onionmat | Onionic matrices
onionmat_arith_single | Onionic matrices
onionmat_compare_onionmat | Methods for compare S4 group
onionmat_compare_single | Methods for compare S4 group
onionmat_complex | Onionic matrices
onionmat_conjugate | Onionic matrices
onionmat_equal_onionmat | Methods for compare S4 group
onionmat_equal_single | Methods for compare S4 group
onionmat_imag | Onionic matrices
onionmat_inv | Onionic matrices
onionmat_inverse | Onionic matrices
onionmat_matrixprod_numeric | Onionic matrices
onionmat_matrixprod_onion | Onionic matrices
onionmat_matrixprod_onionmat | Onionic matrices
onionmat_mod | Onionic matrices
onionmat_neg | Onionic matrices
onionmat_negative | Onionic matrices
onionmat_plus_matrix | Onionic matrices
onionmat_plus_onionmat | Onionic matrices
onionmat_plus_single | Onionic matrices
onionmat_power_matrix | Onionic matrices
onionmat_power_onionmat | Onionic matrices
onionmat_power_single | Onionic matrices
onionmat_prod_matrix | Onionic matrices
onionmat_prod_onionmat | Onionic matrices
onionmat_prod_single | Onionic matrices
onionmat_re | Onionic matrices
onionmat_show | Print method for onions
onionmat_unary | Onionic matrices
onion_abs | Complex functionality for onions
onion_acos | Various logarithmic and circular functions for onions
onion_acosh | Various logarithmic and circular functions for onions
onion_allsum | Various summary statistics for onions
onion_arith_matrix | Onionic matrices
onion_arith_numeric | Methods for Function Arith in package Onion
onion_arith_onion | Methods for Function Arith in package Onion
onion_arith_onionmat | Onionic matrices
onion_arith_single | Onionic matrices
onion_asin | Various logarithmic and circular functions for onions
onion_asinh | Various logarithmic and circular functions for onions
onion_atan | Various logarithmic and circular functions for onions
onion_atanh | Various logarithmic and circular functions for onions
onion_compare | Methods for compare S4 group
onion_complex | Complex functionality for onions
onion_conjugate | Complex functionality for onions
onion_cos | Various logarithmic and circular functions for onions
onion_cosh | Various logarithmic and circular functions for onions
onion_cumprod | Cumulative sums and products of onions
onion_cumsum | Cumulative sums and products of onions
onion_exp | Various logarithmic and circular functions for onions
onion_e_even | Various products of two onions
onion_e_odd | Various products of two onions
onion_g_even | Various products of two onions
onion_g_odd | Various products of two onions
onion_imag | Complex functionality for onions
onion_inverse | Methods for Function Arith in package Onion
onion_log | Various logarithmic and circular functions for onions
onion_logic | Logical operations on onions
onion_matrixprod_onionmat | Onionic matrices
onion_mod | Complex functionality for onions
onion_negative | Methods for Function Arith in package Onion
onion_plus_numeric | Methods for Function Arith in package Onion
onion_plus_onion | Methods for Function Arith in package Onion
onion_power_matrix | Onionic matrices
onion_power_numeric | Methods for Function Arith in package Onion
onion_power_singleinteger | Methods for Function Arith in package Onion
onion_prod_numeric | Methods for Function Arith in package Onion
onion_prod_onion | Methods for Function Arith in package Onion
onion_re | Complex functionality for onions
onion_show | Print method for onions
onion_sign | Various logarithmic and circular functions for onions
onion_sin | Various logarithmic and circular functions for onions
onion_sinh | Various logarithmic and circular functions for onions
onion_sqrt | Various logarithmic and circular functions for onions
onion_tan | Various logarithmic and circular functions for onions
onion_tanh | Various logarithmic and circular functions for onions
onion_to_string | Print method for onions
onion_to_string_lowlevel | Print method for onions
Ops.onionmat | Onionic matrices
orthogonal | Orthogonal matrix equivalents

## -- P --

p3d | Three dimensional plotting
plot | Plot onions
plot-method | Plot onions
plot.onion | Plot onions
print | Print method for onions
print-method | Print method for onions
print.octonion | Print method for onions
print.onion | Print method for onions
print.onionmat | Print method for onions
print.quaternion | Print method for onions
prod | Various summary statistics for onions
prod-method | Various summary statistics for onions
prods | Various products of two onions

## -- Q --

Quaternion | Basic onion functions
quaternion | Basic onion functions
quaternion-class | Class "onion"
quaternion_allprod | Various summary statistics for onions
quaternion_prod_quaternion | Methods for Function Arith in package Onion
quaternion_to_octonion | Basic onion functions

## -- R --

range | Various summary statistics for onions
rbind | Binding of onionmats
rbind2-method | Binding of onionmats
Re | Complex functionality for onions
Re-method | Complex functionality for onions
Re<- | Complex functionality for onions
Re<--method | Complex functionality for onions
Re<-.quaternion | Extract or Replace Parts of onions or glubs
rep | Replicate elements of onionic vectors
rep-method | Replicate elements of onionic vectors
rep.onion | Replicate elements of onionic vectors
roct | Random onionic vectors
romat | Random onionic vectors
ronionmat | Random onionic vectors
rotate | Rotates 3D vectors using quaternions
round | Rounding of onions
round-method | Rounding of onions
rownames | Names of an onionic vector
rownames-method | Names of an onionic vector
rownames-method | Onionic matrices
rownames-methods | Onionic matrices
rownames.onionmat | Onionic matrices
rownames<- | Onionic matrices
rownames<--method | Names of an onionic vector
rownames<--method | Onionic matrices
rownames<--methods | Onionic matrices
rownames<-.onionmat | Onionic matrices
rquat | Random onionic vectors
rsoct | Random onionic vectors
rsomat | Random onionic vectors
rsquat | Random onionic vectors

## -- S --

seq | seq method for onions
seq-method | seq method for onions
seq.onion | seq method for onions
seq_onion | seq method for onions
show | Print method for onions
show-method | Print method for onions
sign-method | Complex functionality for onions
sin | Various logarithmic and circular functions for onions
sin-method | Various logarithmic and circular functions for onions
single_arith_onionmat | Onionic matrices
single_compare_onionmat | Methods for compare S4 group
single_power_onionmat | Onionic matrices
single_prod_onionmat | Onionic matrices
sinh | Various logarithmic and circular functions for onions
sinh-method | Various logarithmic and circular functions for onions
SLERP | seq method for onions
slerp | seq method for onions
sqrt | Various logarithmic and circular functions for onions
str-method | Various summary statistics for onions
str_onion | Various summary statistics for onions
sum | Various summary statistics for onions
sum-method | Various summary statistics for onions
Summary-method | Various summary statistics for onions

## -- T --

t-method | Onionic matrices
t.onion | Onionic matrices
t.onionmat | Onionic matrices
tan | Various logarithmic and circular functions for onions
tan-method | Various logarithmic and circular functions for onions
tanh | Various logarithmic and circular functions for onions
tanh-method | Various logarithmic and circular functions for onions
tcprod | Onionic matrices
tcprod-method | Onionic matrices
threeform | Various non-field diagnostics
type | Basic onion functions

## -- Z --

zap | Concatenation
zapsmall | Concatenation
zapsmall-method | Concatenation

## -- misc --

%*% | Onionic matrices
%*%-method | Onionic matrices
%.% | Various products of two onions
%<*>% | Various products of two onions
%<*>%.onion | Various products of two onions
%<.>% | Various products of two onions
%<.>%.onion | Various products of two onions
%>*<% | Various products of two onions
%>*<%.onion | Various products of two onions
%>.<% | Various products of two onions
%>.<%.onion | Various products of two onions
+-method | Onionic matrices
--method | Onionic matrices
. | Class "dot"
[ | Extract or Replace Parts of onions or glubs
[-method | Extract or Replace Parts of onions or glubs
[-method | Class "dot"
[.dot | Class "dot"
[.onion | Extract or Replace Parts of onions or glubs
[.onionmat | Onionic matrices
[<- | Extract or Replace Parts of onions or glubs
[<--method | Extract or Replace Parts of onions or glubs
[<-.onion | Extract or Replace Parts of onions or glubs
[<-.onionmat | Onionic matrices