-% The direct sum of three things.
-\newcommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
+% A free-form tuple of things. Useful for when the exact number is not
+% known, such as when \ldots will be stuck in the middle of the list,
+% and when you don't want to think in column-vector terms, e.g. with
+% elements of an abstract Cartesian product space.
+\newcommand*{\tuple}[1]{ \left({#1}\right) }
+
+% The "least common multiple of" function. Takes a nonempty set of
+% things that can be multiplied and ordered as its argument. Name
+% chosen for synergy with \gcd, which *does* exist already.
+\newcommand*{\lcm}[1]{ \operatorname{lcm}\of{{#1}} }
+\ifdefined\newglossaryentry
+ \newglossaryentry{lcm}{
+ name={\ensuremath{\lcm{X}}},
+ description={the least common multiple of the elements of $X$},
+ sort=l
+ }
+\fi