X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-common.tex;h=b269417749dcf12738b968645a0083c7aa033ed2;hb=90b275219d518d1c851c71c87484c1a3385f3b70;hp=26e761bda919ae79d587a16e8b435f49cd019694;hpb=90f73298ec65ab89af5131ec8473f9c5909d333c;p=mjotex.git

diff --git a/mjo-common.tex b/mjo-common.tex
index 26e761b..b269417 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -3,32 +3,41 @@
 %
 
 % 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
 %
@@ -62,3 +71,20 @@
 \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} }