From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 20 Jan 2023 23:30:02 +0000 (-0500)
Subject: mjo-cone.tex: add the strictly positive orthant, \Rnplusplus.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=4d76b8a320e183fc1fcae6f0c55d7af96806a00b;p=mjotex.git

mjo-cone.tex: add the strictly positive orthant, \Rnplusplus.
---

diff --git a/examples.tex b/examples.tex
index f23b9e9..e70e0e1 100644
--- a/examples.tex
+++ b/examples.tex
@@ -139,12 +139,12 @@
 
   \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}
diff --git a/mjo-cone.tex b/mjo-cone.tex
index 78e8741..00a1309 100644
--- a/mjo-cone.tex
+++ b/mjo-cone.tex
@@ -23,8 +23,10 @@
 % Common cones.
 %
 
-% The nonnegative orthant in the given number of dimensions.
+% The nonnegative and strictly positive orthants in the given number
+% of dimensions.
 \newcommand*{\Rnplus}[1][n]{ \Rn[#1]_{+} }
+\newcommand*{\Rnplusplus}[1][n]{ \Rn[#1]_{++} }
 
 % The Lorentz ``ice-cream'' cone in the given number of dimensions.
 \newcommand*{\Lnplus}[1][n]{ \mathcal{L}^{{#1}}_{+} }