variable-sized "such that" pipe

Question

I am looking for a pipe symbol that can be made to vary in height automatically.

One of the common ways of writing "such that" in mathematics is with the pipe symbol (|). The pipe can be represented in LaTeX directly as the character | or as \vert, but neither of these expands vertically in math presentation mode. I can adjust it manually this way:

\[\mathcal{H}=\left\lbrace h(x)=\sum_{i=0}^{k-1}a_{i}x_{i}\mod m\ \Bigg\vert
     \ a_{i}\in\mathbb{Z}_{m^{k}}\right\rbrace\]

but I am looking for a true variable-sized option, parallel to \lbrace etc.

The amsmath package provides \lvert and \rvert, but I do not find them expanding as expected, and the amsmath documentation specifies that they should be used as binary delimiters (one on each side of something else), rather than alone.

Answer 1

You can use the braket package for this kind of thing.

\documentclass{article}
\usepackage{braket}
\usepackage{amsmath}
\usepackage{bbold}
\begin{document}

\[
\mathcal{H}=\Set{ h(x)=\sum_{i=0}^{k-1}a_{i}x_{i}\mod m\ |
     \ a_{i}\in\mathbb{Z}_{m^{k}}}
\]

\end{document}

It defines a \Set macro which automatically puts its contents in variable sized braces, and any instance of the | symbol inside will adjust accordingly. This solution also has the advantage of making your source code more semantic.

Answer 2

You can also use \middle which goes with \left and \right:

\[
\mathcal{H}=\left\{ h(x)=\sum_{i=0}^{k-1}a_{i}x_{i}\mod m\ \middle|\ 
     a_{i}\in\mathbb{Z}_{m^{k}}\right\}
\]

This saves you having to use \left. or \right. unnecessarily.

Answer 3

You could use \left| stuff \right. or \left. stuff \right| depending on where you want the | and where it should take it's size from. For instance:

\[
  \left.\sum_{i \in I} x_i \right| x_i > 2
\]

takes the size from the sum. (Yes, I realize its a stupid example). Whereas

\[
  \sum_{i \in I} x_i \left| x_i > 2 \right.
\]

takes the size of the x_i > 2.

I see you added an example, that would become:

\[
  \mathcal{H}=\left\lbrace h(x)=\left.\sum_{i=0}^{k-1}a_{i}x_{i}\mod m\ \right|\ a_{i}\in\mathbb{Z}_{m^{k}}\right\rbrace
\]

With the result:

Answer 4

Here is my solution with a syntax much closer to the mathematical meaning

\usepackage{mathtools}
\providecommand\given{} % is redefined in \Set
\newcommand\SetSymbol[1][]{\nonscript\:#1\vert \allowbreak\nonscript\:\mathopen{}}
\DeclarePairedDelimiterX\Set[1]{\{}{\}}{
  \renewcommand\given{\SetSymbol[\delimsize]}
  #1
}

Now we can simply use

\Set{ x\in A \given x^2 > 1 }

much much closer to the mathematical meaning.

In the OPs case, I'd use

\Set[\Big]{ h(x)=\sum_{i=0}^{k-1}a_{i}x_{i}\mod m \given  a_{i}\in\mathbb{Z}_{m^{k}} }

as there is no reason to scale the fences excessively.

I use the separate \SetSymbol macro, because there are very complicated set constructions, where one cannot use \Set (as in \{ and \} on separate lines), and thus in that case one may want to be able to refer to the given symbol for sets, just in case one want change the symbol later on.

Update: March 2015, added \mathopen{} and \allowbreak