Making a summation sign adjust to contents of summation

Question

I'd like to make my summations adjust in size just as brackets and parenthesis do when using \left and \right - in principle, something like this:

\left\sum_i \frac{a+b}{x+y}\right.

This example, however, doesn't compile.

I've seen this question, and others like it, that detail how to make the summation sign larger, but it's not dynamic. Is there a way to do this dynamically?

Answer 1

Does this work for you? A command \scalerel intended for math mode that takes two arguments. It scales the first argument's height to match that of the second argument. It also vertically shifts the first argument to match the bounds of the second.

\documentclass{article}
\usepackage{calc}
\usepackage{graphicx}

\global\newlength\thewidth
\global\newlength\theheight
\global\newlength\blobheight
\global\newlength\blobdepth
\newsavebox{\prebox}

\newcommand\finddims[1]{\setbox0\hbox{#1}}

\newcommand\scalerel[2]{%
  \sbox{\prebox}{$#1$}%
  \finddims{$#2$}%
  \setlength\blobheight{\ht0+\dp0}%
  \setlength\blobdepth{\dp0}%
  \finddims{$#1$}%
  \setlength\thewidth{\wd0*\ratio{\blobheight}{\ht0+\dp0}}%
  \setlength\theheight{\ht0*\ratio{\blobheight}{\ht0+\dp0}}%
  \raisebox{-\blobdepth+\dp0*\ratio{\blobheight}{\ht0+\dp0}}%
           {\resizebox{\thewidth}{\theheight}{\usebox{\prebox}}}#2%
}

\begin{document}

\def\preblob{\displaystyle\sum_{i=0}^3}
\def\blob{\displaystyle\frac{\displaystyle\frac{x^3}{z+r^3}}%
          {\displaystyle\frac{y}{x^2}}%
}

Unscaled: $\preblob\blob$\rule{20ex}{0ex}%
Scaled: $\scalerel{\preblob}{\blob}$

\vspace*{1em} Of course, this can be take to crazy extremes

$\scalerel{i}{\blob}$
\end{document}