Add to subscript in macro definition

Question

I have the following command

\def\pderv#1#2{{#1}_{#2}}

which is supposed to denote partial derivatives. In some documents, I sometimes redefine it as the tradional

\def\pderv#1#2{\frac{\partial #1}{\partial #2}}

This works well in most cases. So that \pderv{f}{x} is either f_x or \frac{\partial f}{\partial x} depending on my definition.

However, sometimes I have a function f_i. In this case, I would like to denote the derivative with either f_{i,x} or \frac{\partial f_i}{\partial x}. The later is doable with the second definition. However, the first definition obviously makes it {f_i}_x.

Is there anyway to to modify the first definition so that if a subscripted expression is passed, like f_i, the output is f_{i,x}? I don't mind modifying the way I call the command (in both definitions) if that's the only way.

Obligatory MWE:

\documentclass{article}

\begin{document}
\def\pderv#1#2{\frac{\partial #1}{\partial #2}}
\[
  \pderv{f}{x},\quad\pderv{f_{i}}{x}
\]

\def\pderv#1#2{{#1}_{#2}}
\[
  \pderv{f}{x},\quad\pderv{f_{i}}{x}
\]
\end{document}

Answer 1

You can kill two birds with a stone using xparse and expl3.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\pderv}{smm}
 {
  \IfBooleanTF{#1}
   {% \pderv* uses the fraction mode
    \frac{\partial #2}{\partial #3}
   }
   {% inline mode
    \tohiko_pderv:nn { #2 } { #3 }
   }
 }

\tl_new:N \tohiko_pderv_function_tl
\tl_new:N \tohiko_pderv_variable_tl

\cs_new_protected:Nn \tohiko_pderv:nn
 {
  \regex_match:nnTF { _ } { #1 }
   {% there is a subscript in the function name
    \tl_set:Nn \tohiko_pderv_function_tl { #1 }
    \tl_set:Nn \tohiko_pderv_variable_tl { #2 }
    \regex_match:nnTF { _ .* \^ } { #1 }
     {% there is a superscript after the subscript
      \regex_replace_once:nnN
       % match everything from _ to ^ and from ^ to the end
       { _ (.*) \^ (.*) \Z }
       % replace with \sb{<subscript>,#2}^{<superscript>}
       { \c{sb}\cB\{\1,\u{tohiko_pderv_variable_tl}\cE\}\c{sp}\cB\{\2\cE\} }
       % in
       \tohiko_pderv_function_tl
      % use the modified token list
      \tl_use:N \tohiko_pderv_function_tl
     }
     {% there is no superscript after the subscript
      \regex_replace_once:nnN
       % match everything from _ to the end
       { _ (.*) \Z }
       % replace with \sb{<subscript>,#2}
       { \c{sb}\cB\{\1,\u{tohiko_pderv_variable_tl}\cE\} }
       % in
       \tohiko_pderv_function_tl
      % use the modified token list
      \tl_use:N \tohiko_pderv_function_tl
     }
   }
   {% no subscript
    #1\sb{#2}
   }
 }

\ExplSyntaxOff

\begin{document}
\[
  \pderv*{f}{x}\quad\pderv*{f_{i}}{x}\quad\pderv*{f_{i}^{2}}{x}\quad\pderv*{f^{2}_{i}}{x}
\]

\[
  \pderv{f}{x}\quad\pderv{f_{i}}{x}\quad\pderv{f_{i}^{2}}{x}\quad\pderv{f^{2}_{i}}{x}
\]

\end{document}

If we use \pderv*{f}{x} we get the fraction form. Without the *, the first argument is scanned for a _. In this case everything from _ to the end of the argument is replaced by _{<whatever>,#2}. However, attention is kept on whether _{<subscript>} is followed by ^{<superscript>} and the appropriate actions are taken.