From 1b921ba1f02499f5784ddb87fd59c0621255042c Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Tue, 16 Jul 2019 18:59:59 -0400 Subject: [PATCH] mjo-convex: add \faceof and \properfaceof. --- examples.tex | 4 +++- mjo-convex.tex | 4 ++++ 2 files changed, 7 insertions(+), 1 deletion(-) 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 } -- 2.44.2