mjo-convex: add \faceof and \properfaceof.

diff --git a/examples.tex b/examples.tex
index ef9a0d56f9a29c78a58d6b4cf8534a96ab746731..a1605c11bd311340a5212754fe0cc7453220f662 100644 (file)
--- 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 985731e68db59a8baacbbdd432b920d564daf1a0..a51011f4613ef1e0635d4f73e2b567b2afd3e598 100644 (file)
--- 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 }