automatic size adjustment for nested parentheses

Question

As I prefer outer parentheses to grow larger in nested expressions, I happen to insert \bigl and \bigr and its larger cousins a lot. I have always wondered whether there is a way to do this automagically.

Inserting \left and \right prophylacticly before all opening and closing parentheses and hoping that it sorts things out doesn't do the trick in all cases as seen below.

The left column is without any size changing commands. The middle column as a \left \right pair at every parentheses/brace/bracket and the rightmost column shows my preferred version.

As seen in the middle column of the second and third line the \left and \right pair sometimes makes the outer parentheses larger, on the cost of an extra horizontal space between \Pr and (. The extra space is fine in case of really big opening parentheses but here I'd prefer the regular spacing.

\documentclass{scrartcl}
\usepackage{amsmath}
\usepackage{amsfonts}
\begin{document}
\begin{align*}
&1-(1-F(x))^n&&1-\left(1-F(x)\right)^n&&1-\bigl(1-F(x)\bigr)^n\\
&\Pr(X_{(1)}\le x)&&\Pr\left(X_{(1)}\le x\right)&&\Pr\bigl(X_{(1)}\le x\bigr)\\
&\mathbb{E}[\min\{X_1,X_2\}]&&\mathbb{E}\left[\min\left\{X_1,X_2\right\}\right]&&\mathbb{E}\bigl[\min\left\{X_1,X_2\right\}\bigr]\\
&\left(\pi-\arccos(\frac{y}{r})\right)&&(\pi-\arccos\left(\frac{y}{r}\right))&&\left(\pi-\arccos \left(\frac{y}{r}\right)\right)
\end{align*}
\end{document}

As mathematical expressions can be arbitrarly complex there is probably no general way to do this. But I’m not asking for a solution of the general case. A partial solution that works in the simple cases shown above would be a big help. The simple rule could be, that parentheses never shrink below the size of an inner pair. Of course you can immediately think of extensions like a \mid in a conditional expectation that grows with the size of the expectation’s brackets.

What is your preference regarding the size of nested parentheses? Is there a better way to archieve your preferred style despite inserting \bigl \bigr manually?

---

EDIT:

A colleague pointed me to section 8.3 of Herbert Voß’ mathmode document where size problems with parentheses are solved by playing with two TeX parameters within a group around the expression in question. This led naturally to appendix G of the TeXbook where the mechanics of \delimitershortfall and \delimiterfactor are explained.

\delimitershortfall specifies the maximum space not covered by a delimiter (default 5pt) and \delimiterfactor is the ratio for variable delimiters, times 1000 (default 901).

I used them to implement the never shrink below a subformular size idea from above by setting the shortfall to 0pt and the ratio to 1.0.

While it works nicely in line one and three, in line two and four the parentheses now grow too much, and still there is the extra horizontal space introduced by \left.

Answer 1

The nath package with \delimgrowth=1 is very close to your preferred style.

\documentclass{article}
\usepackage{amssymb}
\usepackage{nath}
\delimgrowth=1

\begin{document}
  \begin{equation}
     1 - (1-F(x))^n \\
     \Pr(X_{(1)} \le x) \\
     \mathbb{E}[\min\{X_1, X_2\} ] \\
     ( \pi - \arccos (\frac {y}{r}) )
  \end{equation}
\end{document}

Read the nath guide for details, especially the part about incompatibility with amsmath.

Answer 2

Use it this way with a small negative space between two large parentheses:

\documentclass{scrartcl}
\usepackage{amsmath}
\begin{document}
\delimitershortfall=-1pt
\begin{align*}
\left(\pi-\arccos \left(\frac{y}{r}\right)\right)\\
\left(\pi-\arccos \left(\frac{y}{r}\right)\!\right)
\end{align*}
\end{document}

here is an idea how it can be done with a double (( and/or )). It is also possible to use \left((...( and a \right))...). only the number of \left and \right parentheses must correspond to each other

\documentclass{scrartcl}
\usepackage{amsmath}

\delimitershortfall=-1pt
\let\Right\right
\let\Left\left
\makeatletter
\def\right#1{\Right#1\@ifnextchar){\!\right}{}}
\def\left#1{\Left#1\@ifnextchar({\!\left}{}}
\makeatother
\begin{document}
\begin{align*}
\left(\pi-\arccos \left(\frac{y}{r}\right)\right)\\
\left(\pi-\arccos \left(\frac{y}{r}\right))\\
\left((\pi-\arccos \left(\frac{y}{r}\right)))\\
\left(\left(x + \frac12\right)\arccos(\pi)\right)\\
\left((x + \frac12\right)\arccos(\pi)\right)
\end{align*}
\end{document}

Answer 3

You can do this without using external packages, which can simplify things a bit if the solution needs to work e.g. in KaTeX. You can define your own "growing parenthesis" command by using invisibe subscripts around the parenthesis' contents:

\newcommand{\paren}[1]{\mathopen{}\left( {#1}_{{}_{}}\,\negthickspace\right)\mathclose{}}
\newcommand{\bracket}[1]{\mathopen{}\left[ {#1}_{{}_{}}\,\negthickspace\right]\mathclose{}}

Which gets you exactly the look you want when used at the right places (middle column was modified):

\begin{aligned}
&1-(1-F(x))^n&&1-\paren{1-F(x)}^n&&1-\bigl(1-F(x)\bigr)^n\\
&\Pr(X_{(1)}\le x)&&\Pr\left(X_{(1)}\le x\right)&&\Pr\bigl(X_{(1)}\le x\bigr)\\
&\mathbb{E}[\min\{X_1,X_2\}]&&\mathbb{E}\bracket{\min\left\{X_1,X_2\right\}}&&\mathbb{E}\bigl[\min\left\{X_1,X_2\right\}\bigr]\\
&\left(\pi-\arccos(\frac{y}{r})\right)&&\left(\pi-\arccos\left(\frac{y}{r}\right)\right)&&\left(\pi-\arccos \left(\frac{y}{r}\right)\right)
\end{aligned}
\[ \paren{\paren{\paren{\paren{\paren{}}}}} \]
\[ \bracket{\bracket{\bracket{\bracket{\bracket{}}}}} \]

Answer 4

My current solution is to use the mathtools macro \DeclarePairedDelimiter

e.g. \DeclarePairedDelimiter\brac{(}{)} allows me to use \brac*{stuff} for autoexpanding brackets. This probably is preferable to nath with extremely large documents (the readme for nath suggests that it takes up to 3 times the compile time!)

Of course it's somewhat annoying to have to star the command every time, so you can swap the behavior, detailed here: Easily change behavior of \DeclarePairedDelimiter

Also, nath is notorious for being incompatable with almost all math related packages, so it's not actually useful at all.

Answer 5

What I do is declaring a parenthis-function that uses \vphantom with \raisebox to add extra height to the outer delimiter.

The solution is not pretty:

• I use \mathop because else \vphantom does not work and then add negative space to counter the extra space that \mathop adds.

• Also inside \raisebox you need to use \( \) to get into mathmode and \displaystyle to get the right virtual height

But it works for me and you can still tweak \delimtershortfall and \delimiterfactor to your liking (if you then also adjust the raise in \raisebox). Also you can change the value in \raisebox to adjust the growth of the delimiters.

\documentclass[12pt,a4paper]{article}
\usepackage{mleftright}


\global\delimitershortfall=5.5pt
\global\delimiterfactor=880
\renewcommand*{\left}{\mleft}
\renewcommand*{\right}{\mright}
\newcommand{\braced}[1]
    { \left( #1 \right) 
        \mskip-1.5mu \vphantom{ \mathop{
           \raisebox{3pt}{ \(\left(\displaystyle #1 \right)\) } } }
    }

\begin{document}
    \[
    \braced{ x + \braced{\braced{ y }} }
    \]
\end{document}