How to define a new math operator with \mathclap in its arguments?

Question

I would like to define a math operator with \mathop and I would like its arguments to be automatically put in a zero width box with \mathclap. Defining an operator, e.g. \sum, with \newcommand

\newcommand{\Sum}[2]{\sum_{\mathclap{#1}}^{\mathclap{#2}}}

would do, but it would force me to provide every time two arguments. If I define the new command with an optional argument, that wouldn't solve the matter, since the mandatory argument is still to be provided (and I may need only the optional in some occurrences). Besides \mathop doesn't require a specific order of the arguments, while \newcommand does.

Any ideas?

Answer 1

You can look ahead for _ and ^ by hand.I'm not sure it's a good idea but something like

\documentclass{article}
\usepackage{mathtools}

\makeatletter
\def\Sum{%
  \let\Sum@subarg\relax
  \let\Sum@suparg\relax
  \Sum@testsub}

\def\Sum@sub_#1{%
  \def\Sum@subarg{#1}%
  \ifx\Sum@suparg\relax
   \expandafter\Sum@testsup
  \else
  \expandafter\Sum@doit
  \fi}

\def\Sum@sup^#1{%
  \def\Sum@suparg{#1}%
  \Sum@testsub@b
}


\def\Sum@testsup{%
  \let\Sum@suparg\@empty
  \@ifnextchar^\Sum@sup\Sum@testsub}

\def\Sum@testsup@b{%
  \let\Sum@suparg\@empty
  \@ifnextchar^\Sum@sup\Sum@doit}

\def\Sum@testsub{%
  \@ifnextchar_\Sum@sub\Sum@testsup@b}

\def\Sum@testsub@b{%
  \@ifnextchar_\Sum@sub\Sum@doit}


\def\Sum@doit{%
\sum_{\mathclap{\Sum@subarg}}^{\mathclap{\Sum@suparg}}}

\makeatletter


\begin{document}

\[\sum_{aaaaa+aaaaa}^{bbbbbb}x_i\]
\[\Sum_{aaaaa+aaaaa}^{bbbbbb}x_i\]
\[\Sum^{bbbbbb}_{aaaaa+aaaaa}x_i\]
\[\Sum_{aaaaa+aaaaa}x_i\]
\[\Sum^{bbbbbb}x_i\]
\[\Sum x_i\]

\end{document}