How to insert a counter inside math mode?

Question

I am looking for a way to insert a counter in the math mode $ .* $. In particular, I am writing a document in LaTex and I want to check the grammar within the document with a language tool. First, I removed all the math by following the answer to the following question: remove everything in math mode. However, by removing all the math, the language tool reports errors because of the empty string between words. Therefore, I would like to insert a counter in order to have something between words. I tried the following

\newcounter{equat}
\setcounter{equat}{1}
\newcommand{\newEQ}{\refstepcounter{equat}\Alph{equat}}
\def$#1${\newEQ}

but apparently, I cannot use \stepcounter, \refstepcounter or \addtocounter in \def$#1${.*}. Does anyone know how I can increase the above counter? I thought about inserting the \refstepcounter before (or after) the math mode, but I cannot find how to do it.

I thank everyone in advance!

---

Working example

I have this:

\documentclass{article}
\usepackage{comment}
\usepackage{verbatim}
\def[#1]{}
\def(#1){}
\catcode`$=13
\def$$#1$${}
\def$#1${}
\makeatletter
\renewenvironment{subequations}{\comment}{\endcomment}
\renewenvironment{equation}{\comment}{\endcomment}
\renewenvironment{alignat}{\comment}{\endcomment}
\renewenvironment{align}{\comment}{\endcomment}
\renewenvironment{equation}{\comment}{\endcomment}
\renewenvironment{alignat}{\comment}{\endcomment}
\renewenvironment{align*}{\comment}{\endcomment}
\makeatother
\begin{document}
    This is an example with $ E = m c^2 $ and 
    \begin{equation}
        \cos^2(\alpha) + \sin^2(\alpha) = 1.
    \end{equation}
\end{document}

If I compile the above code, I get:

This is an example with and 

However, I want something like the following

This is an example A with B.

where A and B are the alphabetic conversion of a counter.

If I put the command \newEQ inside the redefinition of the above environment, the I solve this problem only for the environments:

\makeatletter
\renewenvironment{subequations}{\newEQ\comment}{\endcomment\ }
\renewenvironment{equation}{\newEQ\comment}{\endcomment\ }
\renewenvironment{alignat}{\newEQ\comment}{\endcomment\ }
\renewenvironment{align}{\newEQ\comment}{\endcomment\ }
\renewenvironment{equation*}{\newEQ\comment}{\endcomment\ }
\renewenvironment{alignat*}{\newEQ\comment}{\endcomment\ }
\renewenvironment{align*}{\newEQ\comment}{\endcomment\ }
\makeatother

Indeed, I got the following result

This is an example with A

Answer 1

The following works in the minimal example. Please note that \def$#1${} does overwrite the prior \def$$#1$${}, instead the following defines only $ and uses LaTeX's \@ifnextchar to see if the following char is another $, based on that it either gobbles until the next $ or $$.

Also I used the alphalph package so that your document can contain more than 26 equations.

\documentclass{article}
\usepackage{amsmath}
\usepackage{alphalph}
\newcounter{myequat}
\renewcommand\themyequat{\AlphAlph{\value{myequat}}}
\newcommand\newEQ{}
\protected\def\newEQ{\refstepcounter{myequat}\themyequat}
\usepackage{comment}
\usepackage{verbatim}
\protected\def[#1]{\newEQ}
\protected\def(#1){\newEQ}
\makeatletter
\catcode`$=13
\protected\def${\newEQ@ifnextchar$@gobbledisplay@gobbleinline}
\def@gobbledisplay$#1$${}
\def@gobbleinline#1${}
\makeatother
\makeatletter
\renewenvironment{subequations}{\newEQ\comment}{\endcomment}
\renewenvironment{equation}{\newEQ\comment}{\endcomment}
\renewenvironment{alignat}{\newEQ\comment}{\endcomment}
\renewenvironment{align}{\newEQ\comment}{\endcomment}
\renewenvironment{equation}{\newEQ\comment}{\endcomment}
\renewenvironment{alignat}{\newEQ\comment}{\endcomment}
\renewenvironment{align*}{\newEQ\comment}{\endcomment}
\makeatother
\begin{document}
    This is an example with $ E = m c^2 $ and 
    \begin{equation}
        \cos^2(\alpha) + \sin^2(\alpha) = 1.
    \end{equation}
\end{document}