X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-common.tex;h=1a8f6fe4ac45f7ce32fe64106ffa15ccc486addd;hb=db9108a5c69e72667f4731880f1e3173459675fd;hp=5c0162a76b575e8336bad47740cdeec47f90d1c7;hpb=f45c3c41f01e5c0adc6ac1638456fc6e7c0e3111;p=mjotex.git

diff --git a/mjo-common.tex b/mjo-common.tex
index 5c0162a..1a8f6fe 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -38,6 +38,9 @@
 % 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}! }
 
@@ -75,19 +78,23 @@
   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
 
+% The space of symmetric n-by-n matrices.
+\providecommand*{\Sn}[1][n]{
+  \mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
 
 %
 % Basic set operations
 %
 
 % The union of its two arguments.
-\providecommand*{\union}[2]{ {#1} \cup {#2} }
+\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} }
+\providecommand*{\intersect}[2]{ {#1}\cap{#2} }
 
 % A three-argument intersection.
 \providecommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
@@ -99,12 +106,13 @@
 % 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} }
+  \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} }
+\providecommand*{\cartprodmany}[3]{ \binopmany{\times}{#1}{#2}{#3} }
+\providecommand*{\directsummany}[3]{ \binopmany{\oplus}{#1}{#2}{#3} }
+\providecommand*{\unionmany}[3]{ \binopmany{\cup}{#1}{#2}{#3} }