Latex: Nice abs

Question

I have this expression: |x-|x-|x-4||| Now, every | sign has the same size, but I'd like to make the outward pairs bigger.

Is it possible to do it automatically, or do I have to define the size of each | sign manually? It doesn't work with $\left| \right|$. In this case I have 3 abs signs. But what if there would be for example 12? Is it possible to do it automatically?

This works fine:

\[
\abs*{\VPhantomL x-\abs*{\VPhantomM x-\abs{x-4}}}
\]

But the inline version doesn't:

$\abs*{\VPhantomL x-\abs*{\VPhantomM x-\abs{x-4}}}$

Answer 1

TeX also offers a primitive parameter to always make delimiters grow.

\documentclass{article}
\delimitershortfall-1sp
\newcommand\abs[1]{\left|#1\right|}
\begin{document}
\[
\abs{ x-\abs{ x-\abs{x-4}}}
\]
\end{document}

gives the desired output.

\delimitershortfall is meant to measure how much larger the content is allowed to get before the delimiters start growing, but by setting it to a negative value delimiters always grow.

Answer 2

As egreg commented, for this specific case you could also use the optional parameter to the commands declared with DeclarePairedDelimiter and specify the size:

 \abs[\Big]{x-\abs[\big]{x-\abs{x-4}}}

Note:

• The \left|, \right| pair only resize when there is content in between that has different vertical height. In your case, the content all had the same vertical size and hence no resizing took place.

---

As an alternate, which might be useful in other cases (but does require more work), you could insert a \vphantom{<content with larger vertical size>}.

Here is a solution that inserts a different \vphatom{} between the pairs of \abs to yield:

Notes:

• As declared below with DeclarePairedDelimiter, you need to use \abs*{} if you want the delimiter resized based on the vertical size of the content.
• You can tweak the content of the \VPhamtomL (large), and \VPhantomM (medium), to control the size of the delimiter.

---

Code:

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}%
\begin{document}
You can use the optional paramater to \verb|\abs|:
\[
\abs[\Big]{x-\abs[\big]{x-\abs{x-4}}}
\]

With inline math $\abs[\Big]{x-\abs[\big]{x-\abs{x-4}}}$.

%------------------
\newcommand{\VPhantomL}{\vphantom{x^{2^2}}}%
\newcommand{\VPhantomM}{\vphantom{x^{2}}}%
%
or you can insert a \verb|\vphantom{}|
\[
\abs*{\VPhantomL x-\abs*{\VPhantomM x-\abs{x-4}}}
\]

With inline math $\abs*{\VPhantomL x-\abs*{\VPhantomM x-\abs{x-4}}}$.
\end{document}

Answer 3

The low-TeX (pun obviously irresistible) solution:

\documentclass{article}
\begin{document}
$\Bigl| x - \bigl| x - | x-4 | \bigr| \Bigr|$
\end{document}

Answer 4

You can use nath for automatic scaling of delimiters, but keep in mind that it is incompatible with amsmath (although it does provide its own version of multiline display math environments)

\documentclass[border=3pt]{standalone}
\usepackage{nath}
\delimgrowth=1
\def\abs#1{\lvert#1\rvert} 

\begin{document}
\begin{equation*}
\abs{x \abs{x - \abs{x-4}}}
\end{equation*}
\end{document}