From: Michael Orlitzky <michael@orlitzky.com>
Date: Tue, 16 Jul 2019 22:59:59 +0000 (-0400)
Subject: mjo-convex: add \faceof and \properfaceof.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=1b921ba1f02499f5784ddb87fd59c0621255042c;p=mjotex.git

mjo-convex: add \faceof and \properfaceof.
---

diff --git a/examples.tex b/examples.tex
index ef9a0d5..a1605c1 100644
--- a/examples.tex
+++ b/examples.tex
@@ -99,7 +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}
diff --git a/mjo-convex.tex b/mjo-convex.tex
index 985731e..a51011f 100644
--- a/mjo-convex.tex
+++ b/mjo-convex.tex
@@ -24,3 +24,7 @@
 
 % The ``Extreme vectors'' (or ``Extreme directions'') operator.
 \newcommand*{\Ext}[1]{ \operatorname{Ext} \of{{#1}} }
+
+% The "is a face of" and "is a proper face of" relations.
+\newcommand*{\faceof}{ \trianglelefteq }
+\newcommand*{\properfaceof}{ \triangleleft }