X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-common.tex;h=5c0162a76b575e8336bad47740cdeec47f90d1c7;hp=8dae2cff42f0d75693f2a01b3c853c74b526ef9b;hb=e49da80d1ec7904d4ba8ca0e4bb1a24b14c1d74e;hpb=a32b270207ddd934668e5197d4222113c66ae6ee

diff --git a/mjo-common.tex b/mjo-common.tex
index 8dae2cf..5c0162a 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -2,29 +2,44 @@
 % Only the most commonly-used macros. Needed by everything else.
 %
 
+% Needed for \mathbb.
+\usepackage{amsfonts}
+
 % Place the argument in matching left/right parntheses.
-\providecommand*{\of}[1]{ \left( {#1} \right) }
+\providecommand*{\of}[1]{ \left({#1}\right) }
 
 % Group terms using parentheses.
-\providecommand*{\qty}[1]{ \left( {#1} \right) }
+\providecommand*{\qty}[1]{ \left({#1}\right) }
 
 % Group terms using square brackets.
-\providecommand*{\sqty}[1]{ \left[ {#1} \right] }
+\providecommand*{\sqty}[1]{ \left[{#1}\right] }
 
 % Create a set from the given elements
-\providecommand*{\set}[1]{ \left\lbrace {#1} \right\rbrace }
+\providecommand*{\set}[1]{\left\lbrace{#1}\right\rbrace}
 
 % A set comprehension, where the ``such that...'' bar is added
 % automatically. The bar was chosen over a colon to avoid ambiguity
 % with the L : V -> V notation. We can't leverage \set here because \middle
 % needs \left and \right present.
-\providecommand*{\setc}[2]{ \left\lbrace {#1}\ \middle|\ {#2} \right\rbrace }
+\providecommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
 
 % A pair of things.
-\providecommand*{\pair}[2]{ \left( {#1}, {#2} \right) }
+\providecommand*{\pair}[2]{ \left({#1},{#2}\right) }
+
+% A triple of things.
+\providecommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
 
 % The Cartesian product of two things.
-\providecommand*{\cartprod}[2]{ {#1} \times {#2} }
+\providecommand*{\cartprod}[2]{ {#1}\times{#2} }
+
+% The Cartesian product of three things.
+\providecommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
+
+% The direct sum of two things.
+\providecommand*{\directsum}[2]{ {#1}\oplus{#2} }
+
+% The factorial operator.
+\providecommand*{\factorial}[1]{ {#1}! }
 
 %
 % Product spaces
@@ -59,3 +74,37 @@
 \providecommand*{\Cn}[1][n]{
   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
+
+
+%
+% Basic set operations
+%
+
+% The union of its two arguments.
+\providecommand*{\union}[2]{ {#1} \cup {#2} }
+
+% A three-argument union.
+\providecommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
+
+% The intersection of its two arguments.
+\providecommand*{\intersect}[2]{ {#1} \cap {#2} }
+
+% A three-argument intersection.
+\providecommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
+
+% An indexed arbitrary binary operation such as the union or
+% intersection of an infinite number of sets. The first argument is
+% the operator symbol to use, such as \cup for a union. The second
+% argument is the lower index, for example k=1. The third argument is
+% the upper index, such as \infty. Finally the fourth argument should
+% contain the things (e.g. indexed sets) to be operated on.
+\providecommand*{\binopmany}[4]{
+  \mathchoice
+  { \underset{#2}{\overset{#3}{#1}}{#4} }
+  { {#1}_{#2}^{#3}{#4} }
+  { {#1}_{#2}^{#3}{#4} }
+  { {#1}_{#2}^{#3}{#4} }
+}
+
+\providecommand*{\unionmany}[3]{ \binopmany{\cup}{#1}{#2}{#3} }
+\providecommand*{\intersectmany}[3]{ \binopmany{\cap}{#1}{#2}{#3} }