mjo-common: prevent \Sn[1] and \Hn[1] from dropping their superscripts.

[mjotex.git] / examples.tex

diff --git a/examples.tex b/examples.tex
index e1f375fdc68d219d144010732030850d31cd5869..a2e9cf34cb704826ed403907e2034eba952aeec6 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -112,11 +112,16 @@
     \begin{equation*}
       \directsummany{k=1}{\infty}{V_{k}} \ne \cartprodmany{k=1}{\infty}{V_{k}}.
     \end{equation*}
+    %
     Here are a few common tuple spaces that should not have a
     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
@@ -130,8 +135,9 @@
     \begin{equation*}
       \unionmany{k=1}{\infty}{A_{k}} = \intersectmany{k=1}{\infty}{B_{k}}
     \end{equation*}
-
-    Finally, we have the four standard types of intervals in $\Rn[1]$,
+    %
+    The powerset of $X$ displays nicely, as $\powerset{X}$. Finally,
+    we have the four standard types of intervals in $\Rn[1]$,
     %
     \begin{align*}
       \intervaloo{a}{b} &= \setc{ x \in \Rn[1]}{ a < x < b },\\