Customized summation symbol

Question

I am interested in defining some customized math symbols out of existing ones. For example I would like to distinguish between different types of sums, so beside the usual symbol

I would like to have something of the form

so there are some circles in the corners. It should work just like the usual \sum command and look exactly like it (except the modification).

How could I create such a symbol in the most painless way? Is Metafont the answer? Is it possible to modify existing symbols in Metafont without too much work and expertise?

Answer 1

You could create your own symbol using ooalign

as demonstrated in

• What is the command for a sum symbol superimposed on an integral sign?
• \subseteq + \circ as a single symbol ("open subset") which contains a great tutorial on ooalign

The subtle thing in the code below is that I've used a \phantom{sum} in the displaystyle version to make sure that limits of the sum are displayed correctly. Without it, you loose the correct display of the upper limit.

If the circles aren't exactly where you want them, you can move them around by playing with the numbers in the code.

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}

% a new command to draw the little circle
\newcommand{\smallcirc}[1]{\scalebox{#1}{$\circ$}}

\DeclareMathOperator*{\SumCircles}{%
\mathchoice%
  {\ooalign{\phantom{$\displaystyle\sum$}\cr\hidewidth\raisebox{1.2\height}{$\mkern22mu\smallcirc{0.7}$}\hidewidth\cr%
                                  \raisebox{-0.7\height}{$\mkern22mu\smallcirc{0.7}$}\cr
                                  \hidewidth$\displaystyle\sum$}}
  {\ooalign{$\textstyle\sum$\cr%
                                \hidewidth\raisebox{1.9\height}{$\mkern16mu\smallcirc{0.4}$}\hidewidth\cr
                                \hidewidth\raisebox{-.3\height}{$\mkern16mu\smallcirc{0.4}$}\hidewidth\cr}}
  {\ooalign{\raisebox{0\height}{\scalebox{.6}{$\scriptstyle\sum$}}\cr%
                                \hidewidth\raisebox{1.6\height}{$\mkern7.5mu\smallcirc{0.2}$}\hidewidth\cr
                                \hidewidth\raisebox{-0.2\height}{$\mkern7.5mu\smallcirc{0.2}$}\hidewidth\cr}}
  {\ooalign{\raisebox{.2\height}{\scalebox{.6}{$\scriptstyle\sum$}}\cr%
                                \hidewidth\raisebox{2.2\height}{$\mkern7.5mu\smallcirc{0.2}$}\hidewidth\cr
                                \hidewidth\raisebox{0.4\height}{$\mkern7.5mu\smallcirc{0.2}$}\hidewidth\cr}}
}


\begin{document}

$\SumCircles_{\SumCircles} \displaystyle\SumCircles$

\[
    \SumCircles_{n=1}^\infty
    \sum_{n=1}^\infty
\]

\end{document}