% 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}! }