[Tex/LaTex] How to force \left, \right delimiters to automatically (!) have the same size despite line breaks

Question

This code

\documentclass{article}

\usepackage{amsmath}

\begin{document}
\begin{align*}
\begin{split}
    z = \left( a + b + c \right. \\ 
        \left. + \frac{d}{e} \right)
\end{split} 
\end{align*}
\end{document}

produces the following output:

The two delimiters have different sizes. A common trick to obtain matching sizes is to use \vphantom like so:

\documentclass{article}

\usepackage{amsmath}

\begin{document}
\begin{align*}
\begin{split}
    z = \left( a + b + c +\vphantom{\frac{d}{e}}\right. \\  
        \left. + \frac{d}{e} \right)
\end{split} 
\end{align*}
\end{document}

which produces the following output:

However, such an approach

• becomes rapidly complex as the number of line breaks increases;
• is not maintainable at all (because, if a line's contents change, the argument of \vphantom may have to be modified as well to obtain the desired output).

---

Alternative approach 1: manually size the delimiters (using \big and the likes). Sadly, that's not very maintainable either.

Alternative approach 2: using some math environment provided by the breqn package, which allows for line breaks between two \left/\right delimiters and takes care of delimiter sizing. However, I'd like to stay away from breqn, if possible.

---

Can you think of a way to make associated \left/right\ delimiters to automatically have the same size despite line breaks, without (explicitly) using the \vphantom trick? Ideally, the solution should work for multiple nested pairs of delimiters. For example, in the following, the inner delimiters should have the same size and the outer delimiters should have the same size:

\left( \left( ... \right. \right. \\
\left. \left. ... \right) \right)

Answer 1

The following example uses package zref to remember the size of the math formula in labels. Package mleftright is used to reduce the additional horizontal spacing by \left and \right.

Inside a complex math block, the following macros can be used:

\mzleft{<label>}{<left delimiter>}{<math formula>}
\mzright{<label>}{<math formula>}{<right delimiter>}

The macros can be nested, The <label> is needed to identify the pairs of delimiters. Inside the math block (math environment, ...) the <label> names for the pairs must be unique. After the math block \mzreset can be called. It frees the <label> names and they can be reused.

Example file:

\documentclass{article}

\usepackage{amsmath}
\usepackage{mleftright}
\usepackage{zref-base}

\makeatletter
\zref@newprop{mzheight}[0pt]{\the\ht\z@}
\zref@newprop{mzdepth}[0pt]{\the\dp\z@}
\newcount\c@@mz
\newcommand*{\the@mz}{mz\the\c@@mz}
\newcommand*{\@mz@list}{}    
\let\@mz@do\relax
\newcommand*{\mzreset}{%
  \begingroup
    \def\@mz@do##1{%
      \global\expandafter\let\csname mz@##1\endcsname\relax
    }%
    \@mz@list
    \global\let\@mz@list\@empty
  \endgroup
}
\newcommand*{\mzleft}[3]{%
  \@ifundefined{mz@#1}{%
    \global\advance\c@@mz\@ne
    \expandafter\xdef\csname mz@#1\endcsname{\the@mz}%
    \xdef\@mz@list{\@mz@list\@mz@do{#1}}%
  }{}%
  \expandafter\let\expandafter\@mz\csname mz@#1\endcsname
  \mleft#2%
  \expandafter\mathpalette\expandafter{%
    \expandafter\@mzleft\expandafter{\@mz}%
  }{#3}%
  \mright.\kern-\nulldelimiterspace
}
\newcommand*{\mzright}[3]{%
  \kern-\nulldelimiterspace
  \@ifundefined{mz@#1}{%   
    \@latex@warning{Missing \string\mzleft{#1}}%
    \mleft.#2\mright#3%
  }{%
    \expandafter\let\expandafter\@mz\csname mz@#1\endcsname
    \mleft.%
    \expandafter\mathpalette\expandafter{%
      \expandafter\@mzright\expandafter{\@mz}%
    }{#2}%
    \mright#3%
  }%
}   
\newcommand*{\@mzleft}{%
  \@mzleftright lr%
}
\newcommand*{\@mzright}{%
  \@mzleftright rl%
}
\newcommand*{\@mzleftright}[5]{%
  \sbox0{$\m@th#4{}#5{}$}%
  \ifmeasuring@
  \else
    \begingroup
      \let\@auxout\@mainaux
      \zref@labelbyprops{#3#1}{mzheight,mzdepth}%
    \endgroup
  \fi
  \zifrefundefined{\@mz #2}{%
  }{%
    \dimen@=\zref@extract{#3#2}{mzheight}\relax
    \ifdim\dimen@>\ht0 %
      \ht0=\dimen@
    \fi
    \dimen@=\zref@extract{#3#2}{mzdepth}\relax
    \ifdim\dimen@>\dp0 %
      \dp0=\dimen@
    \fi
  }%   
  \copy0\relax
}
\makeatother

\begin{document}
\begin{align*}
\begin{split}
    z = \mzleft{a}({ a + b + c +} \\
        \mzright{a}{{}+ \frac{d}{e}})
\end{split} 
\end{align*}   

\mzreset

\begin{align*}
\begin{split}
    z = \mzleft{a}{[}{%
          a + b + \frac{c}{d} +
          \mzleft{b}{(}{
            \int_0^\infty \mathrm{d}x
          }   
        } \\  
        \mzright{b}{
          + y}{)
        }
        \mzright{a}{
          + \frac{\displaystyle\sum_{i=0}^{100}i}{e}
        }{]}
\end{split}   
\end{align*}  
\end{document}