From 5c4f67545f0988d065f1d52f90eed9233562c9fc Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 22 Sep 2016 16:04:34 -0400
Subject: [PATCH] Use a slightly better orthogonal direct sum implementation.

---
 examples.tex           |  9 +++++----
 mjo-linear_algebra.tex | 16 ++++++++++++----
 2 files changed, 17 insertions(+), 8 deletions(-)

diff --git a/examples.tex b/examples.tex
index fbbe860..98ddfd5 100644
--- a/examples.tex
+++ b/examples.tex
@@ -107,23 +107,24 @@
     The direct sum of $V$ and $W$ is $\directsum{V}{W}$, of course,
     but what if $W = V^{\perp}$? Then we wish to indicate that fact by
     writing $\directsumperp{V}{W}$. That operator should survive a
-    display equation, too:
+    display equation, too, and the weight of the circle should match
+    that of the usual direct sum operator.
     %
     \begin{align*}
       Z = \directsumperp{V}{W}\\
-      \oplus\oplusperp\oplus\oplusperp
+      \oplus \oplusperp \oplus \oplusperp
     \end{align*}
     %
     Its form should also survive in different font sizes...
     \Large
     \begin{align*}
       Z = \directsumperp{V}{W}\\
-      \oplus\oplusperp\oplus\oplusperp
+      \oplus \oplusperp \oplus \oplusperp
     \end{align*}
     \Huge
     \begin{align*}
       Z = \directsumperp{V}{W}\\
-      \oplus\oplusperp\oplus\oplusperp
+      \oplus \oplusperp \oplus \oplusperp
     \end{align*}
     \normalsize
   \end{section}
diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 5fce75a..0480229 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -5,6 +5,12 @@
 % Needed for \lvert, \rVert, etc. and \operatorname.
 \usepackage{amsmath}
 
+% Wasysym contains the \ocircle that we use in \directsumperp.
+\usepackage{wasysym}
+
+% Part of the adjustbox package; needed to clip the \perp sign.
+\usepackage{trimclip}
+
 \input{mjo-common}
 
 % Absolute value (modulus) of a scalar.
@@ -76,14 +82,16 @@
 %
 % Orthogonal direct sum.
 %
-% Wasysym contains the \ocircle that we use in \directsumperp.
-\usepackage{wasysym}
-\usepackage{scalerel}
+% First declare my ``perp in a circle'' operator, which is meant to be
+% like an \obot or an \operp except has the correct weight circle. It's
+% achieved by overlaying an \ocircle with a \perp, but only after we
+% clip off the top half of the \perp sign and shift it up.
 \DeclareMathOperator{\oplusperp}{\mathbin{
   \ooalign{
     $\ocircle$\cr
-    \raisebox{\noexpand{0.65\height}}{${\vstretch{0.5}{\perp}}$}\cr
+    \raisebox{0.65\height}{$\clipbox{0pt 0pt 0pt 0.5\height}{$\perp$}$}\cr
   }
 }}
 
+% Now declare an orthogonal direct sum in terms of \oplusperp.
 \newcommand*{\directsumperp}[2]{ {#1}\oplusperp{#2} }
-- 
2.44.2