From 6759e3a5bd5fd13bd239ee851c66d1eac83a7c1b Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 4 Nov 2019 08:59:15 -0500
Subject: [PATCH] mjo-common: prevent \Sn[1] and \Hn[1] from dropping their
 superscripts.

This was a TODO item for a while; a standalone "S" or "H" doesn't have
the same meaning as, say, a standalone \mathbb{R} does. The "n"
doesn't indicate the arity of a Cartesian product, so for example S^2
isn't two copies of S^1. Dropping the superscript was therefore
misleading (and nonstandard notation).
---
 TODO           |  3 ---
 examples.tex   |  6 +++++-
 mjo-common.tex | 19 +++++++++----------
 3 files changed, 14 insertions(+), 14 deletions(-)

diff --git a/TODO b/TODO
index ddde006..a8ef5d8 100644
--- a/TODO
+++ b/TODO
@@ -1,4 +1 @@
 1. Move the set operations from mjo-common and mjo-misc into mjo-set.
-
-2. Having S^{n} or H^{n} reduce to simply "S" or "H" in the case where
-   n=1 doesn't make sense.
diff --git a/examples.tex b/examples.tex
index cd615de..a2e9cf3 100644
--- a/examples.tex
+++ b/examples.tex
@@ -117,7 +117,11 @@
     superscript when that superscript would be one: $\Nn[1]$,
     $\Zn[1]$, $\Qn[1]$, $\Rn[1]$, $\Cn[1]$. However, if the
     superscript is (say) two, then it appears: $\Nn[2]$, $\Zn[2]$,
-    $\Qn[2]$, $\Rn[2]$, $\Cn[2]$.
+    $\Qn[2]$, $\Rn[2]$, $\Cn[2]$. Likewise we have the $n$-by-$n$
+    real-symmetric and complex-Hermitian matrices $\Sn$ and $\Hn$
+    respectively; however $\Sn[1]$ and $\Hn[1]$ do not automatically
+    simplify because the ``$n$'' does not indicate the arity of a
+    Cartesian product in this case.
 
     We also have a few basic set operations, for example the union of
     two or three sets: $\union{A}{B}$, $\unionthree{A}{B}{C}$. And of
diff --git a/mjo-common.tex b/mjo-common.tex
index a8d9aaa..5971547 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -138,11 +138,10 @@
 \fi
 
 
-% The space of real symmetric n-by-n matrices.
-\newcommand*{\Sn}[1][n]{
-  \mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
-}
-
+% The space of real symmetric n-by-n matrices. Does not reduce to
+% merely "S" when n=1 since S^{n} does not mean an n-fold cartesian
+% product of S^{1}.
+\newcommand*{\Sn}[1][n]{ \mathcal{S}^{#1} }
 \ifdefined\newglossaryentry
   \newglossaryentry{Sn}{
     name={\ensuremath{\Sn}},
@@ -151,11 +150,10 @@
   }
 \fi
 
-% The space of complex Hermitian n-by-n matrices.
-\newcommand*{\Hn}[1][n]{
-  \mathcal{H}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
-}
-
+% The space of complex Hermitian n-by-n matrices. Does not reduce to
+% merely "H" when n=1 since H^{n} does not mean an n-fold cartesian
+% product of H^{1}.
+\newcommand*{\Hn}[1][n]{ \mathcal{H}^{#1} }
 \ifdefined\newglossaryentry
   \newglossaryentry{Hn}{
     name={\ensuremath{\Hn}},
@@ -164,6 +162,7 @@
   }
 \fi
 
+
 %
 % Basic set operations
 %
-- 
2.43.2