Creating a large "such that" symbol

Question

I'm using the following macro in my LaTeX document:

\newcommand{\suchthat}{\, \mid \,} % nice "such that"

so that set notation like the following looks nice:

\{x_n \suchthat n \in \mathbb{N}}

However, when I use such definitions of sets inside \[...\] and when I need to make the brackets bigger, the \suchthat symbol looks way to small. Try compiling the following MWE as an example:

\documentclass{article}
\usepackage{amssymb}                % for \mathbb font
\newcommand{\suchthat}{\, \mid \,}  % nice "such that"
\begin{document}

\noindent This looks fine:
\[ S = \left\{ x_n \suchthat n \in \mathbb{N} \right\} \]

\noindent But this does not:
\[ S = \left\{ x_n \suchthat \frac{1}{n} \in \mathbb{N} \right\} \]

\end{document}

Is there something I can include in my macro to automatically resize the suchthat symbol as necessary?

Answer 1

Use \middle only if there's a \left before it; we can check this using \currentgrouptype (texdoc etex for more information):

\documentclass{article}
\newcommand{\suchthat}{\;\ifnum\currentgrouptype=16 \middle\fi|\;}

\begin{document}
\[
a \suchthat b\qquad\left\{\frac{a}{b}\suchthat x\right\}
\]
\end{document}

Answer 2

This can be done with the \middle construction, which goes between \left and \right and resizes it to match:

\documentclass{article}

\makeatletter
\newcommand\suchthat{%
 \@ifstar
  {\mathrel{}\middle|\mathrel{}}
  {\mid}%
}
\makeatother

\begin{document}
 \[ \left\{ \frac{a}{b} \suchthat* (a,b) = 1 \right\} \qquad \{ x \suchthat y \} \]
\end{document}

I have also handled the outer spaces a little more elegantly than with direct \, directives using the \mathrel primitive, which declares its operand to be a "relation", which I think "such that" is.

For convenience, my \suchthat takes a star that makes it resizable, since \middle is invalid outside \left...\right. (In my opinion, fixed size is the default, so it is the unstarred version.)

Answer 3

One way would be to pass a parameter to the \suchthat macro so that it can use a \vphantom to re size. This requires you to determine what portion should be used to re-size.

A better approach would be to pass the entire right hand side to the \suchthat macro.

Both produce similar results. Here is a comparison of the original on the left and new version on the right:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\newcommand{\Oldsuchthat}{\, \mid \,}
\newcommand*{\suchthat}[1]{\left|\vphantom{#1}\right.}
\begin{document}
\begin{alignat}{2}
  &S = \left\{ x_n \Oldsuchthat n \in \mathbb{N} \right\} &\quad
  &S = \left\{ x_n \suchthat{n} n \in \mathbb{N} \right\} \\[2.0ex]
  %
  &S = \left\{ x_n \Oldsuchthat \frac{1}{n} \in \mathbb{N} \right\} &\quad
  &S = \left\{ x_n \suchthat{\frac{1}{n}} \frac{1}{n} \in \mathbb{N} \right\}
\end{alignat}
\end{document}

Alternate:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\newcommand{\Oldsuchthat}{\, \mid \,}
\newcommand*{\suchthat}[1]{\,\left|\, #1 \right.}
\begin{document}
\begin{alignat}{2}
&S = \left\{ x_n \Oldsuchthat n \in \mathbb{N} \right\} &\quad
%
&S = \left\{ x_n \suchthat{n \in \mathbb{N}}  \right\} \\[2.0ex]
&S = \left\{ x_n \Oldsuchthat \frac{1}{n} \in \mathbb{N} \right\} &\quad
&S = \left\{ x_n \suchthat{\frac{1}{n} \in \mathbb{N}} \right\}
\end{alignat}
\end{document}