[Tex/LaTex] scalebox / resizebox shifts fraction component

Question

I have the following code in my document:

$$ \frac{\displaystyle \sum_i \min(A_i,B_i)}
        {\displaystyle \sum_i \max(A_i,B_i)} $$

resulting in:
                                                
I prefer "display style" here, but the size of the contents in the numerator and denominator are a bit too large for my liking in the context where they appear, so I decided to scale down.

$$ \frac{\scalebox{0.75}{\text{$\displaystyle \sum_i \min(A_i,B_i)$}}}
        {\scalebox{0.75}{\text{$\displaystyle \sum_i \max(A_i,B_i)$}}} $$

but for some reason, this causes an unwanted shift:

                                                

so I'm forced to go back to standard "text style" mode in the meantime…

I can't spot why this might be happening based on the code above; I've also tried resizebox but it has the same issue … has anyone got any idea why it's happening or how I could fix it?

(EDIT: I solved my particular problem by scaling down the fraction as a whole rather than its constituent parts; but the question remains. Is this a latex bug? Thanks.)

Answer 1

In my opinion you don't really want \displaystyle, but neither you want \scalebox.

The size of \min and the other letters is right, it's just the summation symbol that grow too large:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\frac{\sum\limits_i \min(A_i,B_i)}
     {\sum\limits_i \max(A_i,B_i)}
\qquad
\frac{\displaystyle\sum_i \min(A_i,B_i)}
     {\displaystyle\sum_i \max(A_i,B_i)}
\]
\end{document}

If you really want to go the \scalebox way, enclose them in \mbox:

\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}
\begin{document}
\[
\frac{\mbox{\scalebox{0.75}{$\displaystyle \sum_i \min(A_i,B_i)$}}}
     {\mbox{\scalebox{0.75}{$\displaystyle \sum_i \max(A_i,B_i)$}}}
\]
\end{document}

The issue is apparently due to how TeX typesets fractions, putting aside the numerator until it decides the size; the assignments performed by \scalebox get wrong without this further level of boxing.

Or, maybe better, use \mfrac from the nccmath package:

\documentclass{article}
\usepackage{amsmath}
\usepackage{nccmath}
\begin{document}
\[
\mfrac{\displaystyle \sum_i \min(A_i,B_i)}
      {\displaystyle \sum_i \max(A_i,B_i)}
\qquad
\frac{\displaystyle \sum_i \min(A_i,B_i)}
      {\displaystyle \sum_i \max(A_i,B_i)}
\]
\end{document}