Argthtjtr

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?

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_nrvert &quad& a_n-|a_n|\

 -abs{a_n} && -abs{a_n} && -|a_n|

end{alignat*}



end{document}

I'd not do it myself, though.