How to change the mathmode font

Question

I'm looking for a way to get the textfont (lmodern for my case) into mathmode as in 2) but without using \text{} each time I need to write text in math mode. How do we change the font of mathmode in such a way?

EDIT : I put an image to be more explicit, I hope you understand better what I mean. It's simple in fact, I don't want the standard mathmode font at all whether it is between $…$ or in an equation environment or anywhere else. I don't want to use \text{} command each time I need to write something on a line in math mode.

Answer 1

If you're willing and able to use LuaLaTeX to compile your document, the following solution may (should?) be of interest to you. It defines a Lua function which, if activated, renders subscript and superscript terms with \mathrm if there is no whitespace between the _ and ^ characters and the sub/super-script arguments.

The solution also provides two utility macros, named \SubSupToMathrmOn and \SubSupToMathrmOff, respectively, to activate and deactivate the Lua function. By "activate", I mean "assign the Lua function to LuaTeX's process_input_buffer callback so that it functions as a preprocessor."

If you want to render a subscript or superscript term in upright letters without deactivating the Lua function, just make sure to leave whitespace immediately after the _ and ^ characters.

% !TEX TS-program = lualatex
% see also https://tex.stackexchange.com/a/630382/5001

\documentclass{article}
\usepackage{luacode} % for 'luacode' environment
\begin{luacode} 

  -- Define the Lua function that does all of the work:
  function subsup2mathrm ( s )
    s = s:gsub ( "_(%b{})"  , "_{\\mathrm%1}" )
    s = s:gsub ( "_(%a)"    , "_{\\mathrm{%1}}" )
    s = s:gsub ( "%^(%b{})" , "^{\\mathrm%1}" )
    s = s:gsub ( "%^(%a)"   , "^{\\mathrm{%1}}" )
    return s
  end

\end{luacode}

%% LaTeX utility macros to activate and deactivate the Lua function:
\newcommand\SubSupToMathrmOn{\directlua{luatexbase.add_to_callback ( 
   "process_input_buffer" , subsup2mathrm , "subsup2mathrm" )}}
\newcommand\SubSupToMathrmOff{\directlua{luatexbase.remove_from_callback ( 
   "process_input_buffer" , "subsup2mathrm" )}}

\begin{document}
$u_v^w$ $\mu_{something}^{anything}$ % Lua function isn't activated yet

\medskip
\SubSupToMathrmOn % now activate the Lua function
$u_v^w$ $\mu_{something} ^{anything}$ \quad $u_ v ^ w$
\end{document}