How to redefine spacing of a symbol inside a macro?

Question

When writing mathematics expression, I would like to remove the space around the symbol +.

For a simple expression a+b, I can do it by enclosing + like a{+}b. But it requires more labor work for complex expression like: a+b+c+d+e.

I would like to ask whether there is a programmable way so that I can define a macro fooplus:

\newcommand{\fooplus}[1]{do some thing here about +}

so that \fooplus{a+b+c+d+e} produces the same result likea{+}b{+}c{+}d{+}e?

Thanks for spending time to take a look at my question.

Answer 1

For simple cases it's sufficient to change the math code of + (in a group):

\documentclass{article}

\newcommand\fooplus[1]{%
  \begingroup\mathcode`+=\numexpr\mathcode`+-"2000\relax
  #1
  \endgroup
}

\begin{document}
$\fooplus{a+b+c+d+e}\neq x+y$

$a+b+c+d+e\neq x+y$
\end{document}

Explanation. Since + should be a binary operation symbol, its mathcode is of the form "2abc, so subtracting "2000 we turn it into an ordinary symbol.

Answer 2

If you can use LuaLaTeX, it's not too much work to set up a Lua function that changes the status of + -- as well as -, *, and = -- to math-ordinary. (Lua provides powerful and flexible string handling functions.) The LaTeX macro \fooplus below simply invokes the Lua function.

% !TeX program = lualatex
\documentclass{article}
\usepackage{luacode} % for 'luacode' environment and '\luastring' macro
\begin{luacode}
function fooplus ( s )
  tex.sprint (( string.gsub ( s , "[%+%-%*%=]" , "{%0}" ) ))
end
\end{luacode}
\newcommand\fooplus[1]{\directlua{fooplus(\luastring{#1})}}

\begin{document}
$\fooplus{a+b+c+d+e=f-g*h}$

$a+b+c+d+e=f-g*h$
\end{document}