From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 4 Mar 2021 03:38:29 +0000 (-0500)
Subject: mjo-hurwitz.tex: new file for Hurwitz algebras (quaternions and octonions).
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=07b10e9bcd59b16af1cd6b143f07f0a3cd56d33d;p=mjotex.git

mjo-hurwitz.tex: new file for Hurwitz algebras (quaternions and octonions).
---

diff --git a/GNUmakefile b/GNUmakefile
index 73d8988..61c9eca 100644
--- a/GNUmakefile
+++ b/GNUmakefile
@@ -31,8 +31,8 @@ BIBS = local-references.bib
 #
 MJOTEX  = mjo-algebra.tex mjo-algorithm.tex mjo-arrow.tex mjo-calculus.tex
 MJOTEX += mjo-common.tex mjo-complex.tex mjo-cone.tex mjo-convex.tex
-MJOTEX += mjo-eja.tex mjo-font.tex mjo-linear_algebra.tex mjo-listing.tex
-MJOTEX += mjo-proof_by_cases.tex mjo-set.tex mjo-theorem.tex
+MJOTEX += mjo-eja.tex mjo-font.tex mjo-hurwitz.tex mjo-linear_algebra.tex
+MJOTEX += mjo-listing.tex mjo-proof_by_cases.tex mjo-set.tex mjo-theorem.tex
 MJOTEX += mjo-theorem-star.tex mjo-topology.tex mjo.bst
 
 # Compile a list of raw source code listings (*.listing) and their
diff --git a/examples.tex b/examples.tex
index babc886..2d05431 100644
--- a/examples.tex
+++ b/examples.tex
@@ -172,6 +172,11 @@
     \end{itemize}
   \end{section}
 
+  \begin{section}{Hurwitz}
+    Here lies the Hurwitz algebras, like the quaternions
+    $\quaternions$ and octonions $\octonions$.
+  \end{section}
+
   \begin{section}{Linear algebra}
     The absolute value of $x$ is $\abs{x}$, or its norm is
     $\norm{x}$. The inner product of $x$ and $y$ is $\ip{x}{y}$ and
diff --git a/mjo-hurwitz.tex b/mjo-hurwitz.tex
new file mode 100644
index 0000000..9dca960
--- /dev/null
+++ b/mjo-hurwitz.tex
@@ -0,0 +1,27 @@
+\ifx\havemjohurwitz\undefined
+\def\havemjohurwitz{1}
+
+
+\newcommand*{\quaternions}{\mathbb{H}}
+
+\ifdefined\newglossaryentry
+  \newglossaryentry{quaternions}{
+    name={\ensuremath{\quaternions}},
+    description={the algebra of quaternions},
+    sort=H
+  }
+\fi
+
+
+\newcommand*{\octonions}{\mathbb{O}}
+
+\ifdefined\newglossaryentry
+  \newglossaryentry{octonions}{
+    name={\ensuremath{\octonions}},
+    description={the algebra of octonions},
+    sort=O
+  }
+\fi
+
+
+\fi
diff --git a/mjotex.sty b/mjotex.sty
index f85f779..90db53c 100644
--- a/mjotex.sty
+++ b/mjotex.sty
@@ -8,6 +8,7 @@
 \input{mjo-convex}
 \input{mjo-eja}
 \input{mjo-font}
+\input{mjo-hurwitz}
 \input{mjo-linear_algebra}
 \input{mjo-listing}
 \input{mjo-proof_by_cases}