What is the difference between ( and \left( in LaTeX? Sometimes, when the content is small, it does not seem to matter which pair I use.
What is the best practice when it comes to which parentheses use?
[Tex/LaTex] “(” or “\left(” parentheses
best practicesbracketsmath-mode
Related Solutions
The \DeclarePairedDelimiter command from mathtools is useful. For example defining an absolute value macro;
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
gives also a starred version with \left and \right
\abs*{\frac{a}{b}}
and the unstarred version takes an optional argument that can be \big, \Big, etc
\abs[\Bigg]{\frac{a}{b}}
Under normal conditions, using \quad inside or outside \text gives the same result, as far as the amount of space is concerned. I'm disregarding what happens when \text is used in a sub/superscript, for the moment.
TeX maintains two current fonts when it's typesetting a math formula: it remembers the font that was current before the formula started and also takes note of the current math family so that math symbols which are given type 7 are typeset using the font corresponding to the current family. Note that the current math family is only saved as a number; this number will be turned into a real font only when the formula is finished and is being converted into a horizontal list.
When an instruction such as \quad is found in a formula, it expands to \hskip1em as usual and the em is converted into a length by examining the fontdimen 6 parameter of the current text font, so the first that was mentioned above. If \mskip18mu were used, the em of the font attached to math family 2 would be used; but it's not.
When \text{text} is processed in math mode, TeX executes (in a group)
\mathchoice
{\textdef@\displaystyle\f@size{text}}%
{\textdef@\textstyle\f@size{\firstchoice@false #1}}%
{\textdef@\textstyle\sf@size{\firstchoice@false #1}}%
{\textdef@\textstyle \ssf@size{\firstchoice@false #1}}%
and we're interested in the first and second arguments to \mathchoice. The \firstchoice@false command is just to avoid executing multiple times commands such as \label or \stepcounter that can possibly sneak in the argument to \text, but it's irrelevant for the problem at hand.
For the sake of simplicity, let's assume we're in \displaystyle (but for \textstyle it would be the same). TeX typesets four boxes, but uses only the one resulting from
\textdef@\displaystyle\f@size{text}
This is turned into
\hbox{{\everymath{\displaystyle}\let\f@size\f@size\selectfont text}}
We have to remember that \f@size, \sf@size and \ssf@size expand to the font sizes LaTeX has determined to be the current overall font size (they are 10pt, 7pt, 5pt when the size is \normalsize in a 10pt document; they are 12pt, 8pt, 6pt when the size is \normalsize in a 12pt document or \large in a 10pt document; and so on). In this case the \let does nothing, but \selectfont is really relevant!
What does it do? It resets the current text font based on the current values of \f@encoding, \f@family, \f@series, \f@shape, \f@size and \f@baselineskip. In this case, since \f@size has not changed, the same font that was current outside \text is carried over inside it.
As a conclusion, \quad will have the same width inside \text as it has outside it.
If \text is used in a first level subscript, only \f@size changes, becoming equivalent to what \sf@size was before, so the \quad will use the width corresponding to the current text font, but at \sf@size.
Of course, using \quad outside \text has another difference: the argument to \text is typeset in a box, so this glue cannot be used as a break point if the formula is inline. (This was remarked by David Carlisle.)
Why the example by Przemysław Scherwentke gives different quads? When we do
\font\meta=logo10 at 20pt \meta
we're overriding the NFSS infrastructure for font selection: \meta will become the current text font, but the values of the \f@... macros is not changed. Therefore for the quads in
\meta $a \quad\text{META}\quad b$
the value corresponding to \meta are used (it is the current text font). Conversely, in
\meta $a \text{\quad META\quad} b$
the determination of 1em happens after \selectfont, so the font is reset to what it was before the \meta instruction, because the \f@... macros are not updated when issuing \meta. Indeed “META” is typeset in the current text font, not using the logo font.
Here's a test.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\font\meta=logo10 at 14.4pt
{\meta $a \quad\text{META}\quad b$}
{\meta $a \quad\mbox{META}\quad b$}
{\meta $a \text{\quad META\quad} b$}
{\meta $a \quad\text{META}\quad b$}
\newcommand{\goodmeta}{%
\fontencoding{U}%
\fontfamily{logo}%
\fontsize{14.4}{14.4}%
\selectfont}
{\goodmeta $a \quad\text{META}\quad b$}
{\goodmeta $a \quad\mbox{META}\quad b$}
{\goodmeta $a \text{\quad META\quad} b$}
{\goodmeta $a \quad\text{META}\quad b$}
\end{document}
One can see that in lines 1, 3 and 4 the word “META” is typeset in Computer Modern, while in line 2 it's in the logo font (because \mbox uses the current font without issuing any \selectfont command).
In the other cases, where \goodmeta is used, the results are identical.
Best Answer
There are in fact four important differences:
\left( ... \right)etc. scales according to the height and depth of its contents. This scaling is "dumb" in the sense that it will always take the full height and depth into account (how much of the expression is covered is controlled by\delimitershortfalland\delimiterfactor): for example, in\left( \rule{1cm}{1cm} \right), the parentheses reach far below the square. A more relevant example is\left( \sum_a^b \right)where the parentheses also cover the sum limits. The simple delimiters(and)and also the manually-sized delimiters\big(etc. don't scale.\left ... \rightforms a group: if you say\newlength\mylength \[ \left( \mylength=1cm \right) \the\mylength \]you get0.0ptbecause the value was reset. More importantly, you cannot have line breaks inside\left ... \rightgroups, neither manual nor automatic ones, without special trickery. Any\leftneeds a matching\right.\leftetc. For example,<produces a less-than sign, while\left<produces an angle bracket.\bigetc. use the same interpretation as\left(because they use\leftinternally). Technically,\leftuses the delimiter code, while unadorned characters use the mathematical code.\left ... \rightinserts an inner node, while(inserts an opening node. This becomes visible in$\sin()$vs.$\sin\left(\right). Therefore you can never simply replace(by\left(and vice versa, you always have to check whether the spacing comes out right. An automatic solution to this issue is offered in Spacing around\leftand\right, but the spacing within\left...\rightcan still be different as explained in this answer.