Macro factory, passing on star arguments

Question

I want to define a set of macros, with similar behaviour but applied to different symbols. To avoid repetitions, I thought it would be a good idea to generate them programmatically from a template.

I have a bunch of quantities

1. with general indices (\idx) applied to them,
2. but I occasionally need variations of this index (e.g., for defining recurrence relations);
3. or to scrap the automatic index altogether and replace it with something else.

I thought of using a O{\idx} argument type, but I do not like this solution, as I would like to especially restate \idx for 2.. It seems like a star argument could be useful here.

This is why I came up with:

\documentclass[12pt]{article}

\usepackage{amsmath}

\NewDocumentCommand\idx{}{j}
\NewDocumentCommand\pmatstar{mm}{#1_{#2}}
\NewDocumentCommand\pmatnostar{mm}{#1_{\idx#2}}
\NewDocumentCommand\matnum{smO{}}{
    \IfBooleanTF{#1}{
        \pmatstar{#2}{#3}
    }{
        \pmatnostar{#2}{#3}
    }
}

%%%%%
% What I do not know how to do
%
% \NewDocumentCommand\specmatnum{mm}{...}
% \spectmatnum{mlow}{L}
% \spectmatnum{mupp}{U}
% ...
%
%%%%%

%%%%%
% This is what I want to avoid
%
% \NewDocumentCommand\mlow{sO{}}{
%     \IfBooleanTF{#1}{
%         \pmatstar{L}{#2}
%     }{
%         \pmatnostar{L}{#2}
%     }
% }
% \NewDocumentCommand\mupp{sO{}}{
%     \IfBooleanTF{#1}{
%         \pmatstar{U}{#2}
%     }{
%         \pmatnostar{U}{#2}
%     }
% }
% ...
%
%%%%%
\begin{document}

\begin{align*}
\text{Default: } &\matnum{L}\\
\text{No star, modified default: } &\matnum{L}[+1]\\
\text{Star, no optional argument: } &\matnum*{L}\\
\text{Star, optional '2': } &\matnum*{L}[2]
\end{align*}

%%%%%
% How I would like to be able to replicate the above example without calling \matnum directly
%
% \mlow
% \mlow[+1]
% \mlow*
% \mlow*[2]
%
%%%%%

\end{document}

My question being, how not to duplicate the definition of \matnum for all my symbols? The main difficulty for me being the passing of the *, without rewriting the \IfBooleanTF{}{}{}; which nullifies the point of having \matnum in the first place. I think the rest is straightforward.

Answer 1

\documentclass[12pt]{article}

\usepackage{amsmath}

\NewDocumentCommand\idx{}{j}
\NewDocumentCommand\matnum{msO{}}{#1_{\IfBooleanF{#2}{\idx}#3}}

\NewDocumentCommand\specmatnum{mm}{%
 \ExpandArgs{c}\NewDocumentCommand{#1}{}{\matnum{#2}}}

\specmatnum{mlow}{L}
\specmatnum{mupp}{U}

\begin{document}

\begin{align*}
\text{Default: } &\mlow\\
\text{No star, modified default: } &\mlow[+1]\\
\text{Star, no optional argument: } &\mlow*\\
\text{Star, optional '2': } &\mlow*[2]
\end{align*}


\end{document}

Answer 2

Write down what you want to abstract and it becomes simpler:

\documentclass{article}
\usepackage{amsmath}

% we want that
% \spectmatnum{\mlow}{L}
% defines \mlow so
% \mlow -> L_{j}
% \mlow[+1] -> L_{j+1}
% \mlow* -> L
% \mlow*[2] -> L_{2}
%
% \NewDocumentCommand{\mlow}{so}{%
%   L%
%   \IfBooleanTF{#1}{%
%     \IfValueT{#2}{_{#2}}%
%   }{%
%     _{\idx\IfValueT{#2}{#2}}%
%   }%
% }

\NewDocumentCommand{\spectmatnum}{mm}{%
  % #1 = command name
  % #2 = letter
  \NewDocumentCommand{#1}{so}{%
    #2%
    \IfBooleanTF{##1}{%
      \IfValueT{##2}{_{##2}}%
    }{%
      _{\idx\IfValueT{##2}{##2}}%
    }%
  }%
}

\NewDocumentCommand{\idx}{}{j}

\spectmatnum{\mlow}{L}
\spectmatnum{\mupp}{U}



\begin{document}

$\mlow\quad\mlow[+1]\quad\mlow*\quad\mlow*[2]$

$\mupp\quad\mupp[+1]\quad\mupp*\quad\mupp*[2]$

%%% comparison with \matnum
\NewDocumentCommand\matnum{msO{}}{#1_{\IfBooleanF{#2}{\idx}#3}}
\NewDocumentCommand{\MLOW}{}{\matnum{L}}

$\mlow*|$

$\MLOW*|$

\end{document}

The parameters in the inner \NewDocumentCommand become ##1 and ##2, whereas #1 and #2 refer to the argument to the outer one.

Since \spectmatnum defines a command, just give the command as argument, not just the name.

Why not sO{\idx} as the argument specifier? You can see the reason at the bottom, where the presence of an unwanted space is shown.