Higher quotation marks in equations

Question

I want to use quotation marks in equations (using \begin{equation} ... \end{equation}) and I want them to be adapted to the height of the text in between. Something like:

\begin{equation}
    x = \left''\frac12\right``
\end{equation}

or

\begin{equation}
    x = \Big{''}\frac12\Big{``}
\end{equation}

But none of these two, not any other I could attempt worked like I wanted.

Please, if someone can help.

Answer 1

You raise quotes the required amount, but never lower them.

\documentclass{article}

\makeatletter

\NewDocumentCommand{\mathquotes}{m}{% #1 = subformula to be quoted
  {\mathpalette\mathquotes@{#1}}%
}

\newcommand{\mathquotes@}[2]{%
  \begingroup
  \sbox\z@{$\m@th#1#2$}%
  \sbox\tw@{\normalfont``}%
  \ifdim\ht\tw@>\ht\z@
    \dimen@=0pt
  \else
    \dimen@=\dimexpr\ht\z@-\ht\tw@\relax
  \fi
  \raisebox{\dimen@}{\normalfont``}\box\z@\raisebox{\dimen@}{\normalfont''}%
  \endgroup
}

\makeatother

\begin{document}

\[
\mathquotes{a}+\mathquotes{\frac{1}{2}}
\]

\end{document}

Here's a version where \mathquotes* uses single quotes.

\documentclass{article}

\makeatletter

\NewDocumentCommand{\mathquotes}{sm}{{% #2 = subformula to be quoted
  \IfBooleanTF{#1}{%
    \mathpalette\mathquotes@{{`}{#2}{'}}%
  }{%
    \mathpalette\mathquotes@{{``}{#2}{''}}%
  }%
}}

\newcommand{\mathquotes@}[2]{\mathquotes@@#1#2}
\newcommand{\mathquotes@@}[4]{%
  \begingroup
  \sbox\z@{$\m@th#1#3$}%
  \sbox\tw@{\normalfont#2}%
  \ifdim\ht\tw@>\ht\z@
    \dimen@=0pt
  \else
    \dimen@=\dimexpr\ht\z@-\ht\tw@\relax
  \fi
  \raisebox{\dimen@}{\normalfont#2}\box\z@\raisebox{\dimen@}{\normalfont#4}%
  \endgroup
}

\makeatother

\begin{document}

\[
\mathquotes{a}+\mathquotes{\frac{1}{2}}+\mathquotes*{A}
\]

\end{document}

Answer 2

Quotation marks are not delimiters so you can't use \left...\right or \Big and friends. And these only work on single characters, which '' is not.

This solution will raise the quotation marks to the height of the fraction:

\catcode`\@=11
% \raisearound{<left material>}{<right material>}{<center material>}
\def\raisearound#1#2#3{\mathpalette\raisearoundA{{#1}{#2}{#3}}}
\def\raisearoundA#1#2{\raisearoundB#1#2}
\def\raisearoundB#1#2#3#4{{%
    \setbox0=\hbox{#2}%
    \setbox1=\hbox{#3}%
    \setbox2=\hbox{$\m@th#1#4$}%
    \raise\dimexpr\ht2-\ht0\relax\box0%
    \copy2%
    \raise\dimexpr\ht2-\ht1\relax\box1%
}}
\catcode`\@=12

$A+\raisearound{``}{''}{\frac12}+B$

$\displaystyle A+\raisearound{``}{''}{\frac12}+B$