A complement to \smash, \llap, and \rlap

In both plain TeX and LaTeX, most local alignment issues are addressed using \smash, \phantom, \vphantom, \hphantom, \llap, and \rlap. (LaTeX also provides \makebox. All these macros are reviewed in this article.) However, conspicuously missing is a horizontal version of \smash, which is necessary, for example, to eliminate the excessive whitespace surrounding some large operators. Another snag: whereas \smash and \phantom behave as expected in both horizontal mode and math mode, \llap, \rlap, and \makebox are not suited for use in math mode. This article introduces the macro \clap (simultaneously a centered version of \llap/\rlap and a horizontal version of \smash), and the three macros \mathllap, \mathrlap, and \mathclap (versions of \llap, \rlap, and \clap designed for math mode). Examples involving large operators, polynomial long division, and commutative diagrams are given.