Flush left all math display equations, including $$

Question

I plan to write a package to adapt a document for visually impaired persons. My wish is that all works out of the box, independently of of the user habits or class, just with \usepackage{my-package}, without adaptation of the latex code of the document.

One of the adaptation needed for some visually impaired persons is to flush left all content, including equations.

For display math equations created with amsmath environments, I plan to use the fleqn and leqno options

\PassOptionsToPackage{fleqn, leqno}{amsmath}
\RequirePackage{amsmath}

and since I'm not sure if amsmath was already loaded before my package, I'm going to force some settings:

\tagsleft@true
\@fleqntrue
\let\mathindent=\@mathmargin
\@mathmargin\leftmargini minus\leftmargini

I tested many display environments: \[...\], displaymath, equation, align and gather; this works.

The problem arises with $$...$$ formulas. I know that \[...\] is preferable to $$...$$ but some users still use double dollars to write formulas. Worse, maybe some of them mix amsmath environments and $$.

I managed to flush left $$...$$ equations, with

\def\leftdisplay#1$${\leftline{\indent$\displaystyle{#1}$}$$}
\everydisplay{\leftdisplay}

taken in the TeXbook (answer to the exercise 19.4). But it's incompatible with amsmath display environments, and generate errors:

Paragraph ended before \leftdisplay was complete.
Missing $ inserted.
Display math should end with $$.

The best I did is to add \noexpand before \leftdisplay. This suppresses the errors, but $$...$$ are no more flushed left.

So is it possible to flush left all display equations, whether they are created with $$...$$ or amsmath environments?

Here where I am:

\documentclass{article}
\usepackage[fleqn, leqno]{amsmath}
\def\leftdisplay#1$${\leftline{\indent$\displaystyle{#1}$}$$}
\everydisplay{\noexpand\leftdisplay}
\begin{document}
$$ double~dollars $$
[
  brackets
]
\begin{displaymath}
  displaymath~env
\end{displaymath}
\begin{equation}
  \label{eq:equation}
  equation~env
\end{equation}
\begin{align}
  \label{eq:align}
  align
\end{align}
\begin{gather}
  \label{eq:gather}
  gather
\end{gather}
\end{document}

EDIT

From David Carlisle's comment I understand that it's not possible without risking to break something else. I will then abandon my request and implement an option for evil users that still use $$ (with an exhortation in the doc to use \[...\] instead - but who reads the doc?).

Answer 1

Whilst I strongly recommend not doing this, the code being developed for tagging needs to handle 'raw' $$ (because there are millions of documents on arXiv and a good percentage will use it, even though it's never been supported in LaTeX). As such, we can use an internal of the tagging code to make the adjustment

\DocumentMetadata{testphase = {math}}
\documentclass{article}
\usepackage[fleqn, leqno]{amsmath}
\ExplSyntaxOn
\cs_gset_protected:Npn __math_grab_dollardollar:w % $$
  #1 $$
  {
    \tl_if_blank:nF {#1}
      {
        __math_process:nn { equation* } {#1}
        \socket_use:n {tagsupport/math/display/begin}
        \socket_use:nn{tagsupport/math/display/formula/begin}
          { \leftline{$\indent\displaystyle{#1}$} }
        $$
      }
  }
\ExplSyntaxOff
\begin{document}
$$ double~dollars $$
[
  brackets
]
\begin{displaymath}
  displaymath~env
\end{displaymath}
\begin{equation}
  \label{eq:equation}
  equation~env
\end{equation}
\begin{align}
  \label{eq:align}
  align
\end{align}
\begin{gather}
  \label{eq:gather}
  gather
\end{gather}
\end{document}

Note that this is very much not supported: the internal might change, we might revise how we do grabbing, etc. Use at your own risk!