[Tex/LaTex] Multiple letters without spacing in Math

Question

Is there something I can add to the preamble of my document such that multiple letters without spacing in a Math environment (such as $NP$) do not have extra spacing between them and are not considered multiple distinct variables? Right now, I have to use $\mathit{NP}$ to prevent any extra spacing, but I feel that it is more natural to add a space between the letters if they are a different variable ($N P$).

For example, if I want the multi-letter variable NP, I want to be able to say $NP$ which would automatically be replaced by $\mathit{NP}$. If I want N and P to have the proper inter-variable spacing, I want to do that only when they are separated by a space, like so: $N P$.

Is there a way to achieve this? Would it break something that I'm unaware of?

Edit:

Here's a screenshot that shows what I mean:

So basically, is it possible for line 1 to automatically give me line 3 and for line 2 to give me line 2?

Answer 1

It's theoretically possible to make LaTeX recognize clusters of letters and typeset them as if they were input as argument to \mathit, but it would be deadly slow: each alphabetic character should be turned into a “math active” one, which checks whether the following item is an alphabetic character; if it is it should typeset itself, starting \mathit if it's the first one, and then pass the same control to the next character; if not followed by an alphabetic character it should end \mathit.

It's instead better to do something like

\newcommand{\mli}[1]{\mathit{#1}}

where \mli stands for MultiLetter Identifier; use any control sequence name. Then you'd input

$\mli{P}=\mli{NP}$

that has a good deal of advantages, but mainly keeps information about the input.

_{Note: I have a nice proof of the above statement, but unfortunately there are length limitations for posts on this site.}

---

Heiko's solution in expl3.

\documentclass[fleqn]{article}
\usepackage{xcolor}
\usepackage{amsmath}
\usepackage{xparse}

\ExplSyntaxOn

% 1. Define an equivalent for each letter
\cs_new_protected:Nn \__egreg_letter_loop:nn
 {
  \int_step_inline:nnn { `#1 } { `#2 }
   {
    \exp_args:Nc \mathchardef 
     { __egreg_letter_code_##1: } % generate the old code
     =
     \mathcode##1 % the old code
     \scan_stop:
    \cs_new_protected:cx { __egreg_letter_act_##1: }
     {
      \exp_not:N \__egreg_letter_scan:nw { ##1 }
     }
    \char_set_active_eq:nc { ##1 } { __egreg_letter_act_##1: }
   }
 }
\__egreg_letter_loop:nn { A } { Z }
\__egreg_letter_loop:nn { a } { z }

% 2. Define the main macro that does the scanning
\tl_new:N \l__egreg_letter_scanned_tl

\cs_new_protected:Npn \__egreg_letter_scan:nw #1
 {
  \tl_if_empty:NT \l__egreg_letter_scanned_tl { \c_group_begin_token } % to be closed later
  \tl_put_right:Nx \l__egreg_letter_scanned_tl { \exp_not:c { __egreg_letter_code_#1: } }
  \peek_catcode:NF A
   {% next char is not a letter
    \__egreg_letter_deliver:V \l__egreg_letter_scanned_tl
   }
 }
\cs_new_protected:Nn \__egreg_letter_deliver:n
 {
  \tl_if_single:nTF { #1 }
   {
    \__egreg_letter_single:n { #1 }
   }
   {
    \__egreg_letter_group:n { #1 }
   }
  \c_group_end_token % finish the group
 }
\cs_generate_variant:Nn \__egreg_letter_deliver:n { V }

% 3. The interface for defining the actions
\NewDocumentCommand{\definelettersingle}{m}
 {
  \cs_set_protected:Nn \__egreg_letter_single:n { { #1 } }
 }
\NewDocumentCommand{\definelettergroup}{m}
 {
  \cs_set_protected:Nn \__egreg_letter_group:n { { #1 } }
 }

% 4. Make all letters math active
\int_step_inline:nnn { `A } { `Z } { \mathcode#1="8000 }
\int_step_inline:nnn { `a } { `z } { \mathcode#1="8000 }

\ExplSyntaxOff

% initialize

\definelettersingle{#1}
\definelettergroup{\mathit{#1}}

\begin{document}

First a standard formula $NP\ne N P$

\bigskip

Now \textcolor{blue}{single letters are set in blue},
\textcolor{red}{multiple letters in red}.
\begin{itemize}
\item Multiple letters are put in \verb|\mathit|:
  \definelettersingle{{\color{blue}#1}}%
  \definelettergroup{\mathit{\color{red}#1}}%
  \[ NP \neq N P \]

\item Multiple letters are put in \verb|\mathrm|:
  \definelettersingle{{\color{blue}#1}}%
  \definelettergroup{\mathrm{\color{red}#1}}%
  \[ NP\ (text) \neq N P\ (two\ variables) \]
  \[ F_force = m_mass a_acceleration \]
\end{itemize}
\end{document}