Spacing around \left and \right

Question

Why does the addition of a \left and \right introduces an extra space around the formula? Specifically, why do $\cos(\theta)$ and $\cos\left(\theta\right)$ render differently?

Is there a way to use resizable delimiters without introducing the spurious spaces?

Why did Knuth design it like this?

Edit: This occurs too, if \operatorname{MYOP} or some other operator, like \lim, \min etc. is used. (This edit is basically to make it easier to find this answer.)

Answer 1

I've found an answer in a usenet post by Heiko Oberdiek and another by Donald Arseneau. Improved code thanks to shiznick.

The issue is that \left and \right introduces an inner atom (see The TeXbook, chapter 18, section 4), which has different spacing rules than ordinary atoms, produced by ( and ) (and the other delimiters).

To remove this spurious spacing, one has to manually insert opening and closing atoms in the formula. Specifically, $\cos(\theta)$ and $\cos\mathopen{}\left(\theta\right)\mathclose{}$ render exactly the same.

However, inserting it does make your formulas ugly. So a good solution would be to just redefine \left and \right:

\let\originalleft\left
\let\originalright\right
\renewcommand{\left}{\mathopen{}\mathclose\bgroup\originalleft}
\renewcommand{\right}{\aftergroup\egroup\originalright}

Incidentally, this code also fixes the spacing of |, that is very fragile. Check for example $|+x|$ and $\left|+x\right|$. Also $\cos|\theta|$ and $\cos\left|\theta\right|$. This is due to the fact that both delimiters are equal, and TeX doesn't know if they're opening or closing the expression. The same logic applies to \|.

EDIT: The old code had a problem with subscripts and superscripts: they didn't accompany the growth of the delimiters. Fixed now thanks to Philipp Stephani and Heiko Oberdiek.

Answer 2

The package mathtools has implemented a general solution for that problem. It defines the command \DeclarePairedDelimiter that you can use as follows:

\DeclarePairedDelimiter\pars{\lparen}{\rparen}.

With this single declaration you have a new powerful command for several cases:

• \pars{x} just replaces $(x)$
• \pars*{x} will do the right thing with \left and \right (same result as the answer of Mateus Araújo)
• \pars[\big]{x} which replaces $\bigl(x\bigr)$ (all the size commands work)

Answer 3

"As result of the newsgroup thread", which was mentioned in Mateus Araújo' answer, Heiko Oberdiek wrote the mleftright package. "It also adds some error checks (group nesting levels)." (both cited from Heiko's comment to Mateus Araújo' answer)

\mleft and \mright from that package can be used instead of \left and \right and do not insert additional space.

When additional space shall not be used, also \left. and \right. should be looked at (see What does \right. do?). To get rid of the additional space there
\left.\kern-\nulldelimiterspace and \right.\kern-\nulldelimiterspace can be used (probably best by defining those as new commands and using those).

Answer 4

The following code fixes both \left and \right -- put it in the preamble:

\let\originalleft\left
\let\originalright\right
\def\left#1{\mathopen{}\originalleft#1}
\def\right#1{\originalright#1\mathclose{}}

I haven't tested it in all scenarios, of course, but I added it to the preamble of my entire Ph.D. dissertation, and it worked without errors and without any additional modifications to the code.

Answer 5

With LuaTeX you can control the spacing between an op atom (such as \cos) and an inner atom (which is what is generated by a \left...\right pair).

\documentclass{article}

\Umathopinnerspacing\displaystyle=0mu
\Umathopinnerspacing\textstyle=0mu

\begin{document}

$\cos(\theta)$

$\cos\left(\theta\right)$

\end{document}

Answer 6

This is in answer to the particular question of why Knuth designed it like this. I believe it is because opening and closing using \left and \right is often done in conjunction with sums or other big mathematical symbols. Compare the following two formulas:

The bottom one is with the suggested fix from the earlier answer. In my opinion, the top one looks more balanced, which is probably the reason for the functionality being as it is.

Answer 7

I have been using the accepted answer for a while now, but actually I came up with something in the last few days that also gets around the issue that \left \right prevents line breaking.

\def\delim#1#2#3{
  \mathopen{\left#1 \vphantom{#2} \right.}
  \kern-\nulldelimiterspace #2 \kern-\nulldelimiterspace
  \mathclose{ \left. \vphantom{#2} \right#3 }
}

The \kern-\nulldelimiterspace removes the spacing produced by \right. and \left..

It's not too hard to extend this to allow for \middle either.

One note of caution: I think nesting this too much will cause LaTeX to run out of memory.