X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-common.tex;h=8ead1233ece6d100f632c6f390d391d7bd957142;hp=e19d7883e6d9a7c70a5865d314cc9dabf1762f46;hb=fc7cfa7f3d02715cb09eae2e1c6bc501dc2d8d50;hpb=38147a40c34416d5dbd87f44d8786e3dd73a132f

diff --git a/mjo-common.tex b/mjo-common.tex
index e19d788..8ead123 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -1,8 +1,17 @@
 %
 % Only the most commonly-used macros. Needed by everything else.
 %
+\ifx\havemjocommon\undefined
+\def\havemjocommon{1}
 
-% Place the argument in matching left/right parntheses.
+
+% Needed for \mathbb.
+\usepackage{amsfonts}
+
+% Needed for \bigtimes.
+\usepackage{mathtools}
+
+% Place the argument in matching left/right parentheses.
 \providecommand*{\of}[1]{ \left({#1}\right) }
 
 % Group terms using parentheses.
@@ -23,12 +32,24 @@
 % 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 direct sum of three things.
+\providecommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
+
+% The factorial operator.
+\providecommand*{\factorial}[1]{ {#1}! }
+
 %
 % Product spaces
 %
@@ -62,3 +83,58 @@
 \providecommand*{\Cn}[1][n]{
   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
+
+% The space of real symmetric n-by-n matrices.
+\providecommand*{\Sn}[1][n]{
+  \mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+
+% The space of complex Hermitian n-by-n matrices.
+\providecommand*{\Hn}[1][n]{
+  \mathcal{H}\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*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
+\providecommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
+\providecommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
+\providecommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
+
+
+% The four standard (UNLESS YOU'RE FRENCH) types of intervals along
+% the real line.
+\providecommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
+\providecommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
+\providecommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
+\providecommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
+
+
+\fi