Correcting improper use of \left and \right in multi-line LaTeX equations

Question

As a copy editor, my job involves optimizing the layout of scientific articles written by authors directly in LaTeX to ensure they conform to the styles of the journals I work for.

A common issue I encounter is the inappropriate use of the \left and \right macros, especially when equations are split across multiple lines. This often results in mismatched bracket sizes, which is visually unappealing and incorrect.

For instance, in the following equation (real case):

\begin{align}
P^{ij} & = -2 \sqrt{-g}\left\{G^{ijlm}\dot K_{lm} + \alpha K^{ij} K -\alpha g^{ij} K_{lm} K^{lm}+\alpha~\,R^{\hspace{-0.4cm}3\hspace{0.3cm}ij}\right. \nonumber \\
&\left.\qquad \qquad\quad  -g^{ij}\left[\left(\frac{\alpha}3+2\beta\right)(~R^\3-3K_{lm}K^{lm}+K^2)+\gamma\right]\right\}, \label{Pijsol} 
\end{align}

the corresponding brackets are of different sizes.

To speed up the correction of these cases, I thought I could define macros that allow me to replace \left/\right with, for example, \biggl/\biggr without needing to remove the corresponding \right./\left. (to simplify and expedite my work).

For example:

\begin{align*}
x&=\left(y\right.\\
 &\left.\qquad +\frac{1}{2}\right)
\end{align*}

should become something like:

\begin{align*}
x&=\lbiggl(y\right.\\
 &\left.\qquad +\frac{1}{2}\rbiggl)
\end{align*}

and work like the following code:

\begin{align*}
x&=\biggl(\left.y\right.\\
 &\left.\qquad +\frac{1}{2}\right.\biggr)
\end{align*}

The idea is to write a function in Emacs Lisp that automatically performs the replacements \left --> \lbiggl and \right --> \rbiggr for the first corresponding brackets after the cursor, simply ignoring the \right./\left..

Does my idea make sense? How can I define \lbiggl/\rbiggr and similar commands to achieve the desired effect?

I am also open to solutions that address the problem in other ways. (I am aware that alternative methods, such as \vphantom, can be used, but the solution I am looking for should be focused on speed of implementation rather than formal rigor in the code.)

Answer 1

Adopt a better input style, so you can easily add bits.

In the particular case, I believe it's better to use multline rather than align, but it's not the main point.

Balancing \left and \right in input allows to easily spot the appropriate place where inserting a phantom.

I changed some syntactic constructs you use.

1. The “prescript” to R should definitely not added with negative and positive spaces; the \mathop{}\! part guarantees that a thin space will be added if \iiiR follows an ordinary symbol. Using ~ is not really the best and in the second instance, a gap between the parenthesis and ³R would be ambiguous.

2. \frac{\alpha}3 should really be \frac{\alpha}{3}`. You gain two keystrokes at the expense of uniformity and clarity.

3. \dot K must be \dot{K}. Yes, the former syntax works but what about when your text editor takes the initiative and split \dot at the end of a line and K at the start of a new one?

\documentclass{article}
\usepackage{amsmath}

\newcommand{\iiiR}{\mathop{}\!{}^{3\!}R}

\begin{document}

\begin{multline}
P^{ij} =
-2 \sqrt{-g}\left\{ \vphantom{\frac{\alpha}{3}} % <--- for balancing
  G^{ijlm}\dot{K}_{lm} + \alpha K^{ij} K -
  \alpha g^{ij} K_{lm} K^{lm}+\alpha \iiiR^{ij}
\right. \\
\left.
  -g^{ij}\left[
    \left(\frac{\alpha}{3}+2\beta\right)(\iiiR-3K_{lm}K^{lm}+K^2)+\gamma
  \right]
\right\}, \label{Pijsol} 
\end{multline}

\end{document}

Answer 2

You can use the longmath package to create delimiter groups extending over multiple lines or cells.

It allows to link brackets in different (sub)formulas to each other and adapt their sizes to the content between them automatically.

\documentclass{article}
\usepackage{longmath}
\usepackage{amsmath}
\begin{document}
\begin{align*}
   x &= \lleft {label1} ( 1 + 2 + 3 \\
     &  \qquad + 4 + \frac{1}{2} \rright {label1} )
\end{align*}
\end{document}

Here, label1 is a label that links the ( and ) to each other. Alternatively, the two array cells can be linked automatically.

\documentclass{article}
\usepackage{longmath}
\usepackage{amsmath}
\begin{document}
\begin{align*}
   x &= \lleft ( 1 + 2 + 3 \pushdelimiter \\
     &  \pulldelimiter \qquad + 4 + \frac{1}{2} \rright )
\end{align*}
\end{document}

Both examples produce the same output.