Long summation symbol

Question

I need to put a long expression under summation symbol in single row. For example like this $(i_1,\ldots,i_n)\in\mathcal{P}(\overline{1,n})$. How can I get a long summation symbol? Long but not tall. Minimal working example is

    \documentclass{article}
    \begin{document}
    \[\sum_{(i_1,\ldots,i_n)\in\mathcal{P}(\overline{1,n})}\]
    \end{document}

I want summation symbol have same length as string under it. Something like this

But, maybe, I ask something unusual and unapplicable.

Answer 1

Don't do this.

Not making it intelligent on purpose. But it could be made intelligent.

\documentclass{article}

\usepackage{adjustbox,expl3,etoolbox}

\letcs\replicate{prg_replicate:nn}

\newcommand*\longsum[1][1]{%
  \mathop{\textnormal{%
    \clipbox{0pt 0pt {.5\width} 0pt}{$\displaystyle\sum$}%
    \replicate{#1}{\clipbox{{.5\width} 0pt {.4\width} 0pt}{$\displaystyle\sum$}}%
    \clipbox{{.6\width} 0pt 0pt 0pt}{$\displaystyle\sum$}}}%
}

\begin{document}

\[
  \longsum[31]_{(i_1,\ldots,i_n)\in\mathcal{P}(\overline{1,n})}
\]

\end{document}

Here you use \longsum_{like always} but it has an optional argument which repeats a part of the sum to be longer. In your particular case \longsum[31]_{..} seems to do.

---

Oh, or may be what you want is to reduce space around the \sum symbol? You can do that automatically with \smashoperator, see How to extend the text under summation symbol without making extra space, or manually for middle grounds with \kern-1em \sum_{long expression} \kern-1em (adjust -1em to the size you want).

Answer 2

Instead of having one fairly long line below the summation symbol, you may want to insert a line break. This can be done with the help of the \substack macro of the amsmath package.

Observe that it isn't really necessary to surround i_1,\dots,i_n with round parentheses.

\documentclass{article}
\usepackage{amsmath} % for "\substack" macro
%% decicated macro "\Pset" -- note the extra spacing around "\overline{...}`
\newcommand\Pset{\mathcal{P}(\mkern1.5mu \overline{1,n} \mkern1.5mu)}

\begin{document}
\[
\sum_{\substack{i_1,\dots,i_n\\ \in\,\Pset}}
\]
\end{document}

Answer 3

Are you looking for something like this?

\documentclass{article}
\begin{document}
\[\sum_{(i_1,\ldots,i_n)\in\mathcal{P}(\overline{1,n})}\]
\end{document}

Or this?

\documentclass{article}
\begin{document}
\(\sum_{(i_1,\ldots,i_n)\in\mathcal{P}(\overline{1,n})}\)
\end{document}

Edit

I'm wondering... Are you bothered by the length of the subscript because of the white space between the sum and the next variable? Because if this is the case, then the command \mathclap from mathtools allow to overlap the subscript to the sum symbol. The difference with respect to the original is shown in the following image.

And this is the code to reproduce it:

\documentclass[convert]{article}
\usepackage{mathtools}
\begin{document}
\[\sum_{i_1,\ldots,i_n\in\mathcal{P}(\overline{1,n})}x_i\]
\[\sum_{\mathclap{i_1,\ldots,i_n\in\mathcal{P}(\overline{1,n})}}x_i\]
\end{document}

Answer 4

In case you want to stretch the summation symbol horizontally, you can use the \hstretch command from the scalerel package. You can measure the width of the summation symbol and the subscript using \settowidth and use pgf to calculate the scaling factor that needs to be supplied to \hstretch. Note that the widths are not fully consistent with the actual width of the symbol so you have to adjust the factor (by 0.6 in the example below). The summation itself is displayed using \underset from the amsmath package.

MWE:

\documentclass{article}
\usepackage{scalerel}
\usepackage{pgf}
\usepackage{amsmath}
\begin{document}

\def\mysubscript{(i_1,\ldots,i_n)\in\mathcal{P}(\overline{1,n})}

\newlength\mylen
\settowidth\mylen{${}_\mysubscript$}

\newlength\mysumlen
\settowidth\mysumlen{$\sum$}

\pgfmathsetmacro\scalefactor{\mylen / \mysumlen * 0.6}

\noindent width of subscript: \the\mylen\\
width of sum: \the\mysumlen\\
scale factor: \scalefactor\\


\[\underset{\mysubscript}{\hstretch{\scalefactor}{\sum}}\]

\end{document}

Result:

Note that the result is aesthetically rather questionable and I would advise against using it in any situation whatsoever.