Center vertically within \left and \right in math mode

Question

I trying to vertically center what's inside a \left and \right, but it keeps centering with what I imagine is the baseline, even if what's below the baseline is much bigger, for example a sum expression, see example. I currently have this minimal working example: \documentclass{article}

\begin{document}
  \[
    D_{P2P} = \max\left\{
        \frac{N}{u_s},
        \frac{F}{d_p},
        \frac{NF}{u_s + \sum\limits_{i=1}^{N} u_i}
      \right\}
  \]
\end{document}

Which renders as:

Which is not too bad, but I'm trying to have this result:

Expected output was extracted from Computer Networking: A Top Down Approach, 6th edition, equation 2.3, which I guess was rendered in Latex as well, so I think it's possible.

Any idea?

EDIT: Here is the output with \nolimits_ which IMO looks good enough, but hypothetically, is there a way to achieve the expected result anyway?

Answer 1

The contents in the braces can be vertically centered around the current math axis by the help of \vcenter. I prefer the solution with \nolimits (that is the default behavior of the sum sign in this context), because it avoids a ragged math axis and baseline.

\documentclass{article}
\usepackage{amsmath}

\begin{document}
  \[
    D_{\text{P2P}} = \max\left\{
        \vcenter{\hbox{$\displaystyle
          \frac{N}{u_s},
          \frac{F}{d_p},
          \frac{NF}{u_s + \sum\limits_{i=1}^{N} u_i}
        $}}
      \right\}
  \]
  \[
    D_{\text{P2P}} = \max\left\{
          \frac{N}{u_s},
          \frac{F}{d_p},
        \vcenter{\hbox{$\displaystyle
          \frac{NF}{u_s + \sum\limits_{i=1}^{N} u_i}
        $}}
      \right\}
  \]
  \[
    D_{\text{P2P}} = \max\left\{
        \frac{N}{u_s},
        \frac{F}{d_p},
        \frac{NF}{u_s + \sum_{i=1}^{N} u_i}
      \right\}
  \]
\end{document}

Answer 2

Another occasion for a three-pronged comparison in the good, the bad and the ugly style.

You could use gathered for obtaining different alignments. The example you have at the top is beyond any classification: nobody would typeset such a thing.

\documentclass{amsart}
\usepackage{amsmath}

\begin{document}

\title{The Good, the Bad, and the Ugly}
\author{Bob Robertson}
\maketitle

\section{The Good}

This is the best way to typeset your formulas, since it places fraction
lines at the same height as the context
\[
D_{\text{P2P}} =
\max\left\{
  \frac{N}{u_s},
  \frac{F}{d_p},
  \frac{NF}{u_s + \sum_{i=1}^{N} u_i}
\right\}
\]

\section{The Bad}

This is bad, because the third fraction is very ambiguous with
regard to the context
\[
D_{\text{P2P}} =
\max\left\{
  \frac{N}{u_s},
  \frac{F}{d_p},
  \begin{gathered}
    \frac{NF}{u_s + \sum\limits_{i=1}^{N} u_i}
  \end{gathered}
\right\}
\]

\section{The Ugly}

This is simply ugly and utterly wrong, no discussion allowed
\[
D_{\text{P2P}} =
\max\left\{
\begin{gathered}
  \frac{N}{u_s},
  \frac{F}{d_p},
  \frac{NF}{u_s + \sum\limits_{i=1}^{N} u_i}
\end{gathered}
\right\}
\]

\end{document}