Set specifications and Dirac brackets

One of the few glaring omissions from TeX’s mathematical typesetting capabilities is a means of setting separators in the middle of mathematical expressions. TeX provides primitives called \left and \right, which can be used to modify brackets (of whatever sort) around a mathematical expression, as in: \left( \right) — the size of the parentheses is matched to the vertical extent of the expression.

However, in all sorts of mathematical enterprises one may find oneself needing a \middle command, to be used in expressions like

\left\{ x \in \mathbb{N} \middle| x \mbox{ even} \right\}
to specify the set of even natural numbers. The e-TeX system defines just such a command, but users of Knuth’s original need some support. Donald Arseneau’s braket package provides commands for set specifications (as above) and for Dirac brackets (and bras and kets). The package uses the e-TeX built-in command if it finds itself running under e-TeX.