Missing space with DeclarePairedDelimiter

Question

I’m trying to define an abs command for absolute values using DeclarePairedDelimiter from the mathtools package, but I’m running into some spacing issues.

I’d normall write \sup_n \abs{a_n} defined by \DeclarePairedDelimiter{\abs}{\lvert}{\rvert}. But then there is some space missing.

I would instead expect the following output, which I get using \sup_n |a_n|.

With \sup_n {\abs{a_n}} this issue does not appear, but I find this additional pair of curly braces too cumbersome. I also tried some variations, but both versions of \abs seem to have the same issue.

\documentclass[a4paper,10pt]{scrartcl}

\usepackage{mathtools}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\altabs}{|}{|}

\begin{document}
\[
  \sup_n |a_n|              \quad % expected output
  \sup_n \abs{a_n}          \quad
  \sup_n {\abs{a_n}}        \quad % expected output
  \sup_n \lvert a_n \rvert  \quad
  \sup_n \altabs{a_n}       \quad
  \sup_n {\altabs{a_n}}           % expected output
\]
\end{document}

Where is this problem coming from, and how can I get DeclarePairedDelimiter to give the right spacing?

Answer 1

There should be no space between the operator name and a delimiter, so the output one gets from

\sup_{n}\lvert a_{n}\rvert

is right (and is one of the reasons why amsmath introduced \lvert and \rvert to begin with).

On the other hand, you may like the thin space when the delimiter is a vertical bar. Easy enough: add a dummy \mathop{} before it.

\documentclass[a4paper,10pt]{scrartcl}
\usepackage{mathtools}

\DeclarePairedDelimiter{\absinner}{\lvert}{\rvert}
\DeclarePairedDelimiter{\altabsinner}{|}{|}

\newcommand{\abs}{\mathop{}\absinner}
\newcommand{\altabs}{\mathop{}\altabsinner}

\begin{document}
\[
  \sup_n |a_n|              \quad % expected output
  \sup_n \abs{a_n}          \quad
  \sup_n {\abs{a_n}}        \quad % expected output
  \sup_n \altabs{a_n}       \quad
  \sup_n {\altabs{a_n}}           % expected output
\]

\begin{alignat*}{3}
a_n - \abs{a_n} &\quad& a_n-\lvert a_n\rvert &\quad& a_n-|a_n|\\
 -\abs{a_n} && -\abs{a_n} && -|a_n|
\end{alignat*}

\end{document}

I'd not do it myself, though.