Save and reapply math class after boxing

Question

Is there an easy way to capture the math class (\mathord, \mathrel, …) before boxing a term and then reapply it to the box when using it?

In the following example I’d like to have the same spacing in both equations.

\documentclass{article}

\usepackage{xparse}

\ExplSyntaxOn

\NewDocumentCommand{ \highlight }{ m }{
   \hbox_set:Nn \l_tmpa_box { #1 }
   \box_use:N \l_tmpa_box
}

\ExplSyntaxOff

\begin{document}
\[ a + b \]

\[ a \highlight{+} b \]
\end{document}

I know that bm.sty knows a trick (see also David’s answer on Non-invasive replacement for \fbox?) to do it but I didn’t get how it works and could figure out how to transfer it to my code.

Note: I know that my example is kind of wrong as a box doesn’t allow math content and it only works because + can also be in text mode (\int e.g. would fail here). In my real code if have a test for the correct mode and also math style while saving the box, but I omitted it here to keep the example as short as possible. I’m just looking for a solution to capture the class and apply it like \mathCLASS { \box_use:N \l_tmpa_box }.

---

Background: I need this for the following: The \highlight should color it’s content but as I use a light font, for the highlight three should also be a bolder font choosen. To make it non-invasive I used something like

\NewDocumentCommand{ \highlight }{ m }{
   \begingroup
     \color { red }
     \bfseries
     #1
   \endgroup
}

but this won't work for math as \bfseries is forbidden in math mode. There is \boldmath but it can’t be applied for only a part of an equation so I cam up with code like this

\NewDocumentCommand{ \highlight }{ m }{
   \tobi_set_text_or_math_hbox:Nnn \l_tmpa_box { \color { red } \bfseries \boldmath } { #1 }
   \box_use:N \l_tmpa_box
}

Where \tobi_set_text_or_math_hbox cares for setting the box content in the right font and mode and also applies the right math style if necessary. But then the spacing in math mode doesn’t work anymore so I’m searching for a way to add the correct \mathord, \mathrel etc.

These are the definitions of my math style saving (requires LuaTeX) and boxing macros:

\cs_new_eq:NN \tobi_saved_math_style: \textstyle
\cs_new:Npn \tobi_save_math_style: {
  \int_case:nn { \mathstyle } {
     { \displaystyle } { \cs_set_eq:NN \tobi_saved_math_style: \displaystyle }
     { \textstyle } { \cs_set_eq:NN \tobi_saved_math_style: \textstyle }
     { \scriptstyle } { \cs_set_eq:NN \tobi_saved_math_style: \scriptstyle }
     { \scriptscriptstyle } { \cs_set_eq:NN \tobi_saved_math_style: \scriptscriptstyle }
  }
}

% #1 = box register
% #2 = font macros (always outside math mode)
% #3 = box content
\cs_new:Npn \tobi_set_text_or_math_hbox:nnn #1#2#3 {
  \mode_if_math:TF {
     \tobi_save_math_style:
     \hbox_gset:Nn #1 {
        #2
        \(
           \m@th
           \tobi_saved_math_style:
           #3
        \)
     }
  } {
     \hbox_set:Nn #1 {
        #2 #3
     }
  }
}

Answer 1

This is what I came up with: Do a simple test what the box contains and then apply the correct math class. The test will certainly not always give the correct/desired result and therefore \highlight has an optional argument to manually set the class.

% !TeX program = lualatex
\documentclass[11pt]{scrartcl}

\usepackage{xparse}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{tikz}

\ExplSyntaxOn\makeatletter

\cs_new_eq:NN \tobi_saved_math_style: \textstyle
\cs_new:Npn \tobi_save_math_style: {
   \int_case:nn { \mathstyle } {
      { \displaystyle } { \cs_set_eq:NN \tobi_saved_math_style: \displaystyle }
      { \textstyle } { \cs_set_eq:NN \tobi_saved_math_style: \textstyle }
      { \scriptstyle } { \cs_set_eq:NN \tobi_saved_math_style: \scriptstyle }
      { \scriptscriptstyle } { \cs_set_eq:NN \tobi_saved_math_style: \scriptscriptstyle }
   }
}


% - #1: Box register
% - #2: font switches (always outside math)
% - #3: box content
\cs_new:Npn \tobi_set_text_or_math_hbox:nnn #1#2#3 {
   \mode_if_math:TF {
      \tobi_save_math_style:
      \hbox_gset:Nn #1 {
         #2
         \(
            \m@th
            \tobi_saved_math_style:
            #3
         \)
      }
   } {
      \hbox_set:Nn #1 {
         #2 #3
      }
   }
}
\cs_generate_variant:Nn \tobi_set_text_or_math_hbox:nnn { Nnn, NNN, NnN, NNn }


\tikzset {
   highlight~node/.style = {
      fill = yellow,
      inner~sep = \z@,
   },
}

\tl_new:N \tobi_current_math_class_tl
\tl_set:Nn \tobi_current_math_class_tl { ord }

\cs_generate_variant:Nn \tl_if_in:NnT { Nf }
\cs_generate_variant:Nn \tl_if_in:NnF { Nf }
\cs_generate_variant:Nn \tl_if_in:NnTF { Nf }

\tl_const:Nx \c_tobi_math_rel_symbols_tl { \tl_to_str:n { = < > \neq } }
\tl_const:Nx \c_tobi_math_bin_symbols_tl { \tl_to_str:n { + - \cdot \times } }
\tl_const:Nx \c_tobi_math_open_symbols_tl { \tl_to_str:n { ( [ \{ } }
\tl_const:Nx \c_tobi_math_close_symbols_tl { \tl_to_str:n { ) ] \} } }
\tl_const:Nx \c_tobi_math_operator_symbols_tl { \tl_to_str:n { \int \sum \prod } }

% - #1: content (text or math)
% - #2 (optional): manual math class = rel|op|bin|ord|close|open
\NewDocumentCommand{ \highlight }{ m o }{
   \tobi_set_text_or_math_hbox:Nnn \l_tmpa_box { \color { red } \bfseries \boldmath } { #1 }
   \tl_set:Nn \tobi_current_math_class_tl { ord }
   \IfNoValueTF { #2 } {
      \tl_if_in:NfTF \c_tobi_math_rel_symbols_tl { \tl_to_str:n { #1 } } {
         \tl_set:Nn \tobi_current_math_class_tl { rel }
      } {
         \tl_if_in:NfTF \c_tobi_math_bin_symbols_tl { \tl_to_str:n { #1 } } {
            \tl_set:Nn \tobi_current_math_class_tl { bin }
         } {
            \tl_if_in:NfTF \c_tobi_math_open_symbols_tl { \tl_to_str:n { #1 } } {
               \tl_set:Nn \tobi_current_math_class_tl { open }
            } {
               \tl_if_in:NfTF \c_tobi_math_close_symbols_tl { \tl_to_str:n { #1 } } {
                  \tl_set:Nn \tobi_current_math_class_tl { close }
               } {
                  \tl_if_in:NfT \c_tobi_math_operator_symbols_tl { \tl_to_str:n { #1 } } {
                     \tl_set:Nn \tobi_current_math_class_tl { operator }
                  }
               }
            }
         }
      }
   } {
      \tl_set:Nn \tobi_current_math_class_tl { #2 }
   }
   \tobi_add_math_class_maybe_if_math_mode:Vn \tobi_current_math_class_tl {
      \begin{tikzpicture} [ baseline = (N.base) ]
         \node [ highlight~node ] (N) {
            \box_use:N \l_tmpa_box
%            \textsubscript{\tobi_current_math_class_tl}
         };
      \end{tikzpicture}
   }
}

\cs_new:Npn \tobi_add_math_class_maybe_if_math_mode:nn #1#2 {
   \mode_if_math:TF {
      \use:c { math #1 } { #2 }
   } {
      #2
   }
}
\cs_generate_variant:Nn \tobi_add_math_class_maybe_if_math_mode:nn { Vn }

\ExplSyntaxOff\makeatother

\begin{document}

%\tl_const:Nx \c_tobi_math_rel_symbols_tl { \tl_to_str:n { = < > \neq } }
$\highlight{=}$
$\highlight{<}$
$\highlight{>}$
$\highlight{\neq}$

%\tl_const:Nx \c_tobi_math_bin_symbols_tl { \tl_to_str:n { + - \cdot \times } }
$\highlight{+}$
$\highlight{-}$
$\highlight{\cdot}$
$\highlight{\times}$

%\tl_const:Nx \c_tobi_math_open_symbols_tl { \tl_to_str:n { ( [ \{ } }
$\highlight{(}$
$\highlight{[}$
$\highlight{\{}$

%\tl_const:Nx \c_tobi_math_close_symbols_tl { \tl_to_str:n { ) ] \} } }
$\highlight{)}$
$\highlight{]}$
$\highlight{\}}$

%\tl_const:Nx \c_tobi_math_operator_symbols_tl { \tl_to_str:n { \int \sum \prod } }
$\highlight{\int}$
$\highlight{\sum}$
$\highlight{\prod}$

$\highlight{a+b}$

$\highlight{=}[ord]$

Text \highlight{highlighted} Text

\[ \highlight{-}3  m\highlight{2a}th \highlight{+} math = \highlight{\int}_0^5 math \, \highlight{\mathrm{d}x} \]
\[ -3  m2ath + math = \int_0^5 math \, \mathrm{d}x \]

\end{document}

Answer 2

It turns out that this works on operators and variables.

\documentclass{article}
\usepackage{xcolor}
\usepackage{mathtools}

\newcommand\highlight[1]% #1 = math
  {\mathmbox{\color{red}{}#1{}}}

\begin{document}
\[ a + b c d \]

\[ a \highlight{+} b \highlight{c} d \]
\end{document}