From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 12 Mar 2017 23:36:54 +0000 (-0400)
Subject: Add \cartprodmany and \directsummany to mjo-common.
X-Git-Tag: phd-dissertation-submitted~1
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=db9108a5c69e72667f4731880f1e3173459675fd;p=mjotex.git

Add \cartprodmany and \directsummany to mjo-common.
---

diff --git a/examples.tex b/examples.tex
index 6edd538..f33ed74 100644
--- a/examples.tex
+++ b/examples.tex
@@ -36,13 +36,21 @@
     The function $f$ applied to $x$ is $f\of{x}$. We can group terms
     like $a + \qty{b - c}$ or $a + \qty{b - \sqty{c - d}}$. Here's a
     set $\set{1,2,3} = \setc{n \in \Nn[1]}{ n \le 3 }$. Here's a pair
-    of things $\pair{1}{2}$ or a triple of them
-    $\triple{1}{2}{3}$. The Cartesian product of two sets $A$ and $B$
-    is $\cartprod{A}{B}$; if we take the product with $C$ as well,
-    then we obtain $\cartprodthree{A}{B}{C}$. The direct sum of $V$
-    and $W$ is $\directsum{V}{W}$ and the factorial of the number $10$
-    is $\factorial{10}$.
-
+    of things $\pair{1}{2}$ or a triple of them $\triple{1}{2}{3}$,
+    and the factorial of the number $10$ is $\factorial{10}$.
+
+    The Cartesian product of two sets $A$ and $B$ is
+    $\cartprod{A}{B}$; if we take the product with $C$ as well, then
+    we obtain $\cartprodthree{A}{B}{C}$. The direct sum of $V$ and $W$
+    is $\directsum{V}{W}$. Or three things,
+    $\directsumthree{U}{V}{W}$. How about more things? Like
+    $\directsummany{k=1}{\infty}{V_{k}} \ne
+    \cartprodmany{k=1}{\infty}{V_{k}}$. Those direct sums and
+    cartesian products adapt nicely to display equations:
+    %
+    \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
@@ -61,7 +69,6 @@
     \begin{equation*}
       \unionmany{k=1}{\infty}{A_{k}} = \intersectmany{k=1}{\infty}{B_{k}}
     \end{equation*}
-    %
   \end{section}
 
   \begin{section}{Cone}
diff --git a/mjo-common.tex b/mjo-common.tex
index 1e3c69f..1a8f6fe 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -112,5 +112,7 @@
              { {#1}_{#2}^{#3}{#4} }
 }
 
-\providecommand*{\unionmany}[3]{ \binopmany{\cup}{#1}{#2}{#3} }
 \providecommand*{\intersectmany}[3]{ \binopmany{\cap}{#1}{#2}{#3} }
+\providecommand*{\cartprodmany}[3]{ \binopmany{\times}{#1}{#2}{#3} }
+\providecommand*{\directsummany}[3]{ \binopmany{\oplus}{#1}{#2}{#3} }
+\providecommand*{\unionmany}[3]{ \binopmany{\cup}{#1}{#2}{#3} }