X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-common.tex;h=b269417749dcf12738b968645a0083c7aa033ed2;hb=90b275219d518d1c851c71c87484c1a3385f3b70;hp=e19d7883e6d9a7c70a5865d314cc9dabf1762f46;hpb=38147a40c34416d5dbd87f44d8786e3dd73a132f;p=mjotex.git

diff --git a/mjo-common.tex b/mjo-common.tex
index e19d788..b269417 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -23,12 +23,21 @@
 % A pair of things.
 \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} }
 
 % 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} }