Vertical bar notations

The amsmath package provides commands lvert, rvert, lVert, rVert (compare langle, rangle) to address the problem of overloading for the vert bar character . This character is currently used in / documents to represent a wide variety of mathematical objects: the `divides' relation in a number-theory expression like , or the absolute-value operation , or the `such that' condition in set notation, or the `evaluated at' notation . The multiplicity of uses in itself is not so bad; what is bad, however, is that fact that not all of the uses take the same typographical treatment, and that the complex discriminatory powers of a knowledgeable reader cannot be replicated in computer processing of mathematical documents, at least not without a significant cost in processing speed, and even then not without falling somewhat short of human readers' abilities. It is recommended therefore that there should be a one-to-one correspondence in any given document between the vert bar character and a selected mathematical notation, and similarly for the double-bar command . This immediately rules out the use of | and   for delimiters, as in the notations for absolute value or norm, because left and right delimiters are distinct usages that do not relate in the same way to adjacent symbols; recommended practice is therefore to define suitable commands in the document preamble for any paired-delimiter use of vert bar symbols:

\newcommand{\abs}[1]{\lvert#1\rvert}
\newcommand{\norm}[1]{\lVert#1\rVert}