mjo-convex: add \faceof and \properfaceof.

[mjotex.git] / examples.tex

diff --git a/examples.tex b/examples.tex
index 897396c1061d05706da5b7d21cd187aa6199b76b..a1605c11bd311340a5212754fe0cc7453220f662 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -80,6 +80,11 @@
     \end{align*}
   \end{section}
 
+  \begin{section}{Complex}
+    We sometimes want to conjugate complex numbers like
+    $\compconj{a+bi} = a - bi$.
+  \end{section}
+
   \begin{section}{Cone}
     The dual cone of $K$ is $\dual{K}$. Some familiar symmetric cones
     are $\Rnplus$, $\Lnplus$, $\Snplus$, and $\Hnplus$.  If cones
@@ -94,7 +99,9 @@
     The conic hull of a set $X$ is $\cone{X}$; its affine hull is
     $\aff{X}$, and its convex hull is $\conv{X}$. If $K$ is a cone,
     then its lineality space is $\linspace{K}$, its lineality is
-    $\lin{K}$, and its extreme directions are $\Ext{K}$.
+    $\lin{K}$, and its extreme directions are $\Ext{K}$. The fact that
+    $F$ is a face of $K$ is denoted by $F \faceof K$; if $F$ is a
+    proper face, then we write $F \properfaceof K$.
   \end{section}
 
   \begin{section}{Font}
@@ -232,6 +239,10 @@
       fox
     \end{theorem}
 
+    \begin{exercise}
+      jumps
+    \end{exercise}
+
     \begin{definition}
       quod
     \end{definition}
@@ -262,6 +273,10 @@
       fox
     \end{theorem*}
 
+    \begin{exercise*}
+      jumps
+    \end{exercise*}
+
     \begin{definition*}
       quod
     \end{definition*}