| onion-package {onion} | R Documentation |
Octonions and Quaternions
Description
Quaternions and Octonions are four- and eight- dimensional extensions of the complex numbers. They are normed division algebras over the real numbers and find applications in spatial rotations (quaternions), and string theory and relativity (octonions). The quaternions are noncommutative and the octonions nonassociative. See the package vignette for more details.
Details
| Package: | onion |
| Version: | 1.5-3 |
| Title: | Octonions and Quaternions |
| LazyData: | TRUE |
| Authors@R: | person(given=c("Robin", "K. S."), family="Hankin", role = c("aut","cre"), email="hankin.robin@gmail.com", comment = c(ORCID = "0000-0001-5982-0415")) |
| Description: | Quaternions and Octonions are four- and eight- dimensional extensions of the complex numbers. They are normed division algebras over the real numbers and find applications in spatial rotations (quaternions), and string theory and relativity (octonions). The quaternions are noncommutative and the octonions nonassociative. See the package vignette for more details. |
| Maintainer: | Robin K. S. Hankin <hankin.robin@gmail.com> |
| License: | GPL-2 |
| Depends: | methods, R (>= 3.5.0) |
| Suggests: | testthat,knitr,rmarkdown,covr |
| VignetteBuilder: | knitr |
| Imports: | emulator, Matrix, freealg (>= 1.0-4), mathjaxr |
| URL: | https://github.com/RobinHankin/onion |
| BugReports: | https://github.com/RobinHankin/onion/issues |
| RdMacros: | mathjaxr |
| Author: | Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>) |
Index of help topics:
adjoint The adjoint map
Arith Methods for Function Arith in package Onion
biggest Returns the biggest type of a set of onions
bind Binding of onionmats
bunny The Stanford Bunny
c Concatenation
Compare-methods Methods for compare S4 group
condense Condense an onionic vector into a short form
cumsum Cumulative sums and products of onions
dot-class Class "dot"
drop Drop zero imaginary parts of an onionic vector
i Extract or Replace Parts of onions or glubs
length Length of an octonionic vector
log Various logarithmic and circular functions for
onions
logic.onion Logical operations on onions
names.onion Names of an onionic vector
O1 Unit onions
onion Basic onion functions
onion-class Class "onion"
onion-package Octonions and Quaternions
onionmat Onionic matrices
orthogonal Orthogonal matrix equivalents
p3d Three dimensional plotting
plot Plot onions
prods Various products of two onions
Re Complex functionality for onions
rep Replicate elements of onionic vectors
roct Random onionic vectors
rotate Rotates 3D vectors using quaternions
round Rounding of onions
seq seq method for onions
show Print method for onions
sum Various summary statistics for onions
threeform Various non-field diagnostics
zapsmall Concatenation
There are precisely four normed division algebras over the reals: the reals themselves, the complex numbers, the quaternions, and the octonions. The R system is well equipped to deal with the first two: the onion package provides some functionality for the third and fourth.
Author(s)
Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)
Maintainer: Robin K. S. Hankin <hankin.robin@gmail.com>
References
R. K. S. Hankin 2006. “Normed division algebras in R: introducing the onion package”. R News, Volume 6, number 2
Examples
rquat(10) # random quaternions
Ok + (Oi + Ojl)/(Oj-Oil) # basic octonions
x <- roct(10)
y <- roct(10)
z <- roct(10)
x*(y*z) - (x*y)*z # nonassociative!