How can I make every occurrence of `+` and `-` be replaced by a macro, but only in math mode?

Question

I decided to hack together an answer by using an existing answer: https://tex.stackexchange.com/a/127507/49339

So, my MnotWE looks like this, after much simplification:

\documentclass[12pt,letterpaper]{article}

\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{amsmath}

\makeatletter
% LaTeX's \@ifnextchar gobbles spaces, therefore
% \msh@ifnextchar is defined that keeps spaces
\newcommand*{\msh@ifnextchar}[3]{%
    \def\msh@temp{\msh@@ifnextchar{#1}{#2}{#3}}%
    \futurelet\msh@token\msh@temp
}
\newcommand*{\msh@@ifnextchar}[1]{%
    \ifx\msh@token#1%
    \expandafter\@firstoftwo
    \else
    \expandafter\@secondoftwo
    \fi
}

% Commands that take the original meanings of the special characters
\mathchardef\msh@code@minus=\mathcode`\-\relax
\mathchardef\msh@code@plus=\mathcode`\+\relax

% Macro \setmathshorthands activates and defines the special
% characters
\begingroup
\@ifdefinable{\setmathshorthands}{%
    \xdef\setmathshorthands{%
        \let\noexpand-\noexpand\msh@minus
        \let\noexpand+\noexpand\msh@plus
    }%
}%
\endgroup

\newcommand*{\msh@minus}{\&}

\newcommand*{\msh@plus}{\$}

\makeatother

% Activate math shorthands in the math modes
\everymath{\setmathshorthands}
\everydisplay{\setmathshorthands}


\begin{document}
    \begin{equation*}
        a + b - c = 0
    \end{equation*}
\end{document}

The macros I am using at the moment are toy examples, I have some more complicated macros I will eventually replace these with. However, for the moment, let's just work with these toys.

Anyway, compiling this example, I get the error:

line 50: Missing control sequence inserted. \begin{equation*}

What do?

Answer 1

In the group, you needed

  \catcode`\-=\active
  \catcode`\+=\active

and in \setmathshorthands, you needed

  \mathcode\number`\-="8000 %
  \mathcode\number`\+="8000 %

The \catcode changes are necessary so that - and + are [temporarily] treated as active characters, so as to define their math-active behavior in future invocations of \setmathshorthands.

Thanks to the OP for citing the \mathcode information at What is the differences between mathcode and catcode and how can I use mathcode?, which is a way to make these characters be treated as active in math mode only, even when they are not actually active:

\mathcode"8000 is a special code that is not looked up in the usual way. If a character has that mathcode, the definition of the active (catcode 13) token is used instead, even though the character itself is not active. this is used in plain and LaTeX to allow ' to work as a normal non-active apostrophe in text but in math it has catcode hex 8000 so the active definition is used, which expands to ^{\prime}

The MWE (which also tests the use of - in text mode):

\documentclass[12pt,letterpaper]{article}

\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{amsmath}

\makeatletter
% LaTeX's \@ifnextchar gobbles spaces, therefore
% \msh@ifnextchar is defined that keeps spaces
\newcommand*{\msh@ifnextchar}[3]{%
    \def\msh@temp{\msh@@ifnextchar{#1}{#2}{#3}}%
    \futurelet\msh@token\msh@temp
}
\newcommand*{\msh@@ifnextchar}[1]{%
    \ifx\msh@token#1%
    \expandafter\@firstoftwo
    \else
    \expandafter\@secondoftwo
    \fi
}

% Commands that take the original meanings of the special characters
\mathchardef\msh@code@minus=\mathcode`\-\relax
\mathchardef\msh@code@plus=\mathcode`\+\relax

% Macro \setmathshorthands activates and defines the special
% characters
\begingroup
  \catcode`\-=\active
  \catcode`\+=\active
\@ifdefinable{\setmathshorthands}{%
    \xdef\setmathshorthands{%
      \mathcode\number`\-="8000 %
      \mathcode\number`\+="8000 %
        \let\noexpand-\noexpand\msh@minus
        \let\noexpand+\noexpand\msh@plus
    }%
}%
\endgroup

\newcommand*{\msh@minus}{\&}

\newcommand*{\msh@plus}{\$}

\makeatother

% Activate math shorthands in the math modes
\everymath{\setmathshorthands}
\everydisplay{\setmathshorthands}


\begin{document}
A-b--c---d dddddddddddd dddddddddddd ddddddddddddd dddddddd fffff\-ggg
    \begin{equation*}
        a + b - c = 0 \quad \text{ravings of a mad-man}
    \end{equation*}
\end{document}