onionmat.R
In onion: Octonions and Quaternions

## ----setup, include=FALSE-----------------------------------------------------
knitr::opts_chunk$set(echo = TRUE)
options(rmarkdown.html_vignette.check_title = FALSE)
library("onion")
set.seed(1)

## ----out.width='20%', out.extra='style="float:right; padding:10px"',echo=FALSE----
knitr::include_graphics(system.file("help/figures/onion.png", package = "onion"))

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set.seed(0)
options(digits=2)
romat()

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A <- matrix(rquat(21),7,3)  # matrix() calls onion::onionmat()
A

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A[1,]

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A[1,,drop=FALSE]

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Re(A)
k(A)

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j(A) <- -1
A

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sum(A)

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A <- matrix(rquat(21),3,7)
umbral <- state.abb[1:7]
rownames(A) <- letters[1:3]
colnames(A) <- umbral

B <- matrix(rquat(28),7,4)
rownames(B) <- umbral
colnames(B) <- c("H","He","Li","Be")

A %*% B

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C <- matrix(rquat(14),7,2)
rownames(C) <- umbral
colnames(C) <- month.abb[1:2]
cprod(B,C)

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tcprod(A) - A %*% ht(A)

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x <- cprod(matrix(roct(12),4,3))
x

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max(Mod(Im(x+t(x))))

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`%o%` <- function(x,y){(x%*%y + y%*%x)/2}

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x <- cprod(matrix(roct(12),4,3))
y <- cprod(matrix(roct(12),4,3)) # x and y are 3-by-3 Hermitian octonionic matrices

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jj <- x %o% y
max(Mod(Im(jj+t(jj))))

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LHS <- (x %o% y) %o% (x %o% x)
RHS <- x %o% (y %o% (x %o% x))
max(Mod(LHS-RHS))  # zero to numerical precision

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x <- cprod(matrix(roct(16),4,4))
y <- cprod(matrix(roct(16),4,4)) # x and y are 4-by-4 Hermitian octonionic matrices
LHS <- (x %o% y) %o% (x %o% x)
RHS <- x %o% (y %o% (x %o% x))
max(Mod(LHS-RHS))  # miles off

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o <- rsomat()
o
options(show_onionmats_in_place = TRUE)
o