mjo-eja.tex: add the Jordan-automorphism group operator, \JAut{}.

[mjotex.git] / examples.tex

diff --git a/examples.tex b/examples.tex
index babc886abe26b31ef223cb783e2fa43d4d848d79..d59975eb872bd2f635f9635756518df236e64f74 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -57,7 +57,7 @@
           \State{Rearrange $M$ randomly}
         \EndWhile{}
 
-        \Return{$M$}
+        \State{\Return{$M$}}
       \end{algorithmic}
     \end{algorithm}
   \end{section}
@@ -79,7 +79,8 @@
     The function $f$ applied to $x$ is $f\of{x}$, and the restriction
     of $f$ to a subset $X$ of its domain is $\restrict{f}{X}$. We can
     group terms like $a + \qty{b - c}$ or $a + \qty{b - \sqty{c -
-        d}}$. The tuples go up to seven, for now:
+        d}}$. The tuples go up to seven, for now, and then we give up
+    and use the general construct:
     %
     \begin{itemize}
       \begin{item}
@@ -100,6 +101,9 @@
       \begin{item}
         Septuple: $\septuple{1}{2}{3}{4}{5}{6}{7}$.
       \end{item}
+      \begin{item}
+        Tuple: $\tuple{1,2,\ldots,8675309}$.
+      \end{item}
     \end{itemize}
     %
     The factorial of the number $10$ is $\factorial{10}$, and the
@@ -139,12 +143,12 @@
 
   \begin{section}{Cone}
     The dual cone of $K$ is $\dual{K}$. Some familiar symmetric cones
-    are $\Rnplus$, $\Lnplus$, $\Snplus$, and $\Hnplus$.  If cones
-    $K_{1}$ and $K_{2}$ are given, we can define $\posops{K_{1}}$,
-    $\posops[K_{2}]{K_{1}}$, $\Sof{K_{1}}$, $\Zof{K_{1}}$,
-    $\LL{K_{1}}$, and $\lyapunovrank{K_{1}}$. We can also define $x
-    \gecone_{K} y$, $x \gtcone_{K} y$, $x \lecone_{K} y$, and $x
-    \ltcone_{K} y$ with respect to a cone $K$.
+    are $\Rnplus$, $\Rnplusplus$, $\Lnplus$, $\Snplus$, and $\Hnplus$.
+    If cones $K_{1}$ and $K_{2}$ are given, we can define
+    $\posops{K_{1}}$, $\posops[K_{2}]{K_{1}}$, $\Sof{K_{1}}$,
+    $\Zof{K_{1}}$, $\LL{K_{1}}$, and $\lyapunovrank{K_{1}}$. We can
+    also define $x \gecone_{K} y$, $x \gtcone_{K} y$, $x \lecone_{K}
+    y$, and $x \ltcone_{K} y$ with respect to a cone $K$.
   \end{section}
 
   \begin{section}{Convex}
@@ -157,8 +161,8 @@
   \end{section}
 
   \begin{section}{Euclidean Jordan algebras}
-    The Jordan product of $x$ and $y$ in some Euclidean Jordan algebra
-    is $\jp{x}{y}$.
+    The Jordan product of $x$ and $y$ in some Euclidean Jordan algebra $V$
+    is $\jp{x}{y}$. The Jordan-automorphism group of $V$ is $\JAut{V}$.
   \end{section}
 
   \begin{section}{Font}
@@ -172,6 +176,11 @@
     \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