onion-package: Octonions and Quaternions

In RobinHankin/onion: Octonions and Quaternions

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

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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 <[e-mail]>

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!

RobinHankin/onion documentation built on April 20, 2024, 2:05 p.m.