As others have remarked, vertical bars can be obtained with different commands and one should use the correct one in each case:
\mid
when it's a relation symbol, for instance in set notation or for “divides”;
\lvert
or \rvert
when it's a (left or right) delimiter; note that this requires amsmath
that's recommended anyway when a document needs math.
Just typing |
can work, but there are some subtleties, so it's better to use the above commands. Similarly, for the double bar is
You can exploit mathtools
for your symbol for expectation, but with some more tricks in order to make the bar doing the right thing.
\documentclass{article}
\usepackage{mathtools}
\newcommand{\expect}{\operatorname{E}\expectarg}
\DeclarePairedDelimiterX{\expectarg}[1]{[}{]}{%
\ifnum\currentgrouptype=16 \else\begingroup\fi
\activatebar#1
\ifnum\currentgrouptype=16 \else\endgroup\fi
}
\newcommand{\innermid}{\nonscript\;\delimsize\vert\nonscript\;}
\newcommand{\activatebar}{%
\begingroup\lccode`\~=`\|
\lowercase{\endgroup\let~}\innermid
\mathcode`|=\string"8000
}
\begin{document}
$\expect{X|Y}$
$\expect[\big]{X|Y}$
$\expect*{\dfrac{1}{2}X|Y}$
\end{document}
In the same style as macros declared with \DeclaredPairedDelimiter
, you can give \expect
an optional argument that can be one among \big
, \Big
, \bigg
or \Bigg
for manually sizing the delimiters or use \expect*
in order to get automatic sizing (use it sparingly).
Here you can use |
for conditional expectation, because the macros take care of its relation nature.
UPDATE
A revamped definition that uses new features of expl3
and xparse
. This also allows to specify the measure of the expectation.
\documentclass{article}
\usepackage{mathtools}
\NewDocumentCommand{\expect}{ e{^} s o >{\SplitArgument{1}{|}}m }{%
\operatorname{E}% the expectation operator
\IfValueT{#1}{{\!}^{#1}}% the measure of the expectation
\IfBooleanTF{#2}{% *-variant
\expectarg*{\expectvar#4}%
}{% no *-variant
\IfNoValueTF{#3}{% no optional argument
\expectarg{\expectvar#4}%
}{% optional argument
\expectarg[#3]{\expectvar#4}%
}%
}%
}
\NewDocumentCommand{\expectvar}{mm}{%
#1\IfValueT{#2}{\nonscript\;\delimsize\vert\nonscript\;#2}%
}
\DeclarePairedDelimiterX{\expectarg}[1]{[}{]}{#1}
\linespread{1.1}
\begin{document}
$\expect{X}$ $\expect^P{X}$
$\expect{X|Y}$ $\expect^P{X|Y}$
$\expect[\big]{X|Y}$ $\expect^P[\big]{X|Y}$
$\expect*{\dfrac{1}{2}X|Y}$ $\expect^P*{\dfrac{1}{2}X|Y}$
\end{document}
You can try with \vline
MWE:
\documentclass[aps]{revtex4}
\usepackage{amsmath,amssymb}
\begin{document}
Your attempt
\[\left|\frac{S}{\sum\limits^{N}_{a=1}T_{a}}\right|\]
With \verb|\vline|
\[\vline\,\frac{S}{\sum\limits^{N}_{a=1}T_{a}}\,\vline\]
\end{document}
Output:
Some remarks:
- Use
\[...\]\
instead of $$
. See Why is \[ ... \] preferable to $$ ... $$?
- Use
\limits
instead of \overset
and \underset
to obtain subscripts and superscrips as in \displaystyle
.
Best Answer
According to
texdoc symbols
:\mvert
and\mid
are identical and produce a relation.\vert
is a synonym for|
and both produce the same symbol, but should be used in the context of an ordinal, and should be used as an operator, not as a delimiter (p54, bottom).\divides
once again produces the same symbol but should be used as a binary “divides” operator.\lvert
and\rvert
are left and right delimiters, respectively.