Making equations copyable in pdf

Question

I would like to write a .pdf, where my readers could copy the rendered formulae and paste them directly in their TeX documents.

And the copied text would automatically be:

\int x\sin ax\;\mathrm{d}x = \frac{\sin ax}{a^2}-\frac{x\cos ax}{a}+C

Is this possible?

Answer 1

The PDF format supports a feature "ActualText" that is used for copy-paste instead of the actual typeset text. However, it is not supported by all PDF viewers, but Acrobat Reader does support it.

\documentclass{article}
\usepackage{accsupp}

\newcommand*{\copyable}[1]{%
  \BeginAccSupp{%
    ActualText=\detokenize{#1},%
    method=escape,
  }%
  #1%
  \EndAccSupp{}%
}

\begin{document}
\[
  \copyable{\int x\sin ax\;\mathrm{d}x = \frac{\sin ax}{a^2}-\frac{x\cos ax}{a}+C}
\]
\end{document}

Copy-paste result (\detokenize adds spaces after command names):

\int x\sin ax\;\mathrm {d}x = \frac {\sin ax}{a^2}-\frac {x\cos ax}{a}+C

A more verbatim-like copy is much more complicated:

\documentclass{article}
\usepackage{accsupp}

\makeatletter
\newcommand*{\copyable}{%
  \begingroup
  \@sanitize
  \catcode`\%=14 % allow % as comment char, also needed for \%
  \@copyable
}
\newcommand*{\@copyable}[1]{%
  \endgroup
  \BeginAccSupp{%
    ActualText=\detokenize{#1},%
    method=escape,
  }%
  \scantokens{#1}%
  \EndAccSupp{}%
}
\makeatother

\begin{document}
\[
  \copyable{\int x\sin ax\;\mathrm{d}x = \frac{\sin ax}{a^2}-\frac{x\cos ax}{a}+C}
\]
\end{document}

Copy-paste result:

\int x\sin ax\;\mathrm{d}x = \frac{\sin ax}{a^2}-\frac{x\cos ax}{a}+C

However, the argument of \copyable is read with verbatim catcodes. Therefore this trick will not work, if \copyable is inside an argument of another macro (or in environments of package amsmath). In this case the \detokenize has a function to get the previous version with spaces after command names at least.

Discussion about areas

\copyable inserts whatsits that does not influence the mathematical spacing. Thus the whole equation can be split:

\[
  \copyable{\int x\sin ax\;\mathrm{d}x}
  \copyable{=}
  \copyable{\frac{\sin ax}{a^2}}
  \copyable{-}
  \copyable{\frac{x\cos ax}{a}}
  \copyable{+}
  \copyable{C}
\]

And where the mapping from formula to copy-paste text is correct, \copyable can be omitted:

\[
  \copyable{\int x\sin ax\;\mathrm{d}x}
  =
  \copyable{\frac{\sin ax}{a^2}}
  -
  \copyable{\frac{x\cos ax}{a}}
  + C
\]

The area that is shown in the PDF viewer for selecting depends on the formula and especially the PDF viewer.

Acrobat Reader usually only shows the area above the first symbol of the formula. In case of the integral sign, a small rectangle above it. The latest example with AR9/Linux:

Evince 3.4.0 is a little better in the coverage of the rectangle. The first equation with the whole equation in \copyable:

But Evince has problems in the separation of the equations. Here I wanted to select the second equation only, but it gets mixed up with the third:

Okular 0.14.3 has a nicer selecting tool, but if the \copyable is split up into terms (second and third equations of the latest example), then the terms get mixed up. - Fatal for mathematicians.

Answer 2

It is also possible to use the Mathpix desktop app (for Mac and PC(beta)) to take a screenshot of the PDF and it will render the LaTeX instantly (and already have it copied to your clipboard, all you have to do is paste into your editor of choice).

Here is a brief demo using Mathpix to extract LaTeX from a PDF and pasting into Overleaf:

Answer 3

Using https://tex.stackexchange.com/a/621117/250119, it's possible to redefine various commands in order to make the copypaste work automatically.

Adapted a bit from https://tex.stackexchange.com/a/233397/250119 and the top answer in https://tex.stackexchange.com/a/119718/250119.

Unfortunately, this solution redefines various standard LaTeX math environments so it can be fragile and breaks other unexpected solutions. If something breaks, first step to debug is to comment out this part.

Only \(...\), \[...\], \begin{align*}, \begin{gather*} are handled.

---

\documentclass{article}
\usepackage{amsmath}
\usepackage{accsupp}
\newcommand\copypaste[2]{%
    \BeginAccSupp{method=escape,ActualText={\detokenize{#2}}}%
        #1%
    \EndAccSupp{}%
}
\ExplSyntaxOn
% ======== redefine $...$
\char_set_catcode_active:N $
\cs_new:Npn $ #1 $ { \c_math_toggle_token \copypaste{#1}{$#1$} \c_math_toggle_token }
\char_set_catcode_other:N $
\AtBeginDocument{ \char_set_catcode_active:N $ }
% ======== redefine (...)
\cs_new_eq:NN \jonas__old_open_parenthesis: (
\cs_gset:Npn ( #1 ) {
    \jonas__old_open_parenthesis: \copypaste{#1}{( #1 )} )
}
% ======== redefine [...]
\cs_new_eq:NN \jonas__old_open_square_bracket: [
\cs_gset:Npn [ #1 ] {
    \jonas__old_open_square_bracket: \copypaste{#1}{[ #1 ]} ]
}
% ======== redefine align*
\ProvideDocumentCommand \NewEnvironmentCopy {mm} { % lines taken from https://tex.stackexchange.com/a/680717/250119, can be deleted if LaTeX version is new enough
    \expandafter \NewCommandCopy \csname#1\expandafter\endcsname \csname#2\endcsname
\expandafter \NewCommandCopy \csname end#1\expandafter\endcsname \csname end#2\endcsname }
\ProvideDocumentCommand \RenewEnvironmentCopy {mm} {
    \expandafter \RenewCommandCopy \csname#1\expandafter\endcsname \csname#2\endcsname
\expandafter \RenewCommandCopy \csname end#1\expandafter\endcsname \csname end#2\endcsname }
\clist_map_inline:nn {
    align,gather
} {
    \message{======== #1}
\NewEnvironmentCopy{old-#1}{#1} % backup the old definition
\RenewDocumentEnvironment{#1}{b}{
    \copypaste{
        \begin{old-#1}
            ##1
        \end{old-#1}
    }{
        \begin{#1} ^^J
            ##1 ^^J
        \end{#1}
    }
}{}
}
% ======== done
\ExplSyntaxOff
\begin{document}
What I have is $x^2 + y^2 = z^2$ and (\frac{1}{2}).
Try to copy/paste me.
[
y = \frac{\cos{x}}{1+\cos{x}}
]
Some aligned equations:
\begin{align}
    1+2 &= 3 \
    4+5 &= 9
\end{align}
Gather environment:
\begin{gather}
    1+2 = 3 \
    4+5 = 8+1
\end{gather}
Other environments (not handled):
\begin{align}
    1+2 &= 3
\end{align}
\begin{equation}
    1+2=3
\end{equation}
\begin{equation}
    1+2=3
\end{equation}
\end{document}