How to create a document command that has a name that is not known in advance?

Question

I'd like to create a LaTeX3 function, \my_func, that has a single parameter, #1, which is expected to be initialized to a LaTeX3 string. \my_func is to create a new document command using xparse's \NewDocumentCommand, whose name is the one passed as argument to \my_func. How can I do so?

To give a concrete usage example, there's a bunch of mathematical functions that I wish to define. I'm still not sure what symbols I wish to use to represent them, though. So I define macros \func1, \func2, etc. with rather long and expressive names, e.g. \LeftProjectionOfTheSecondDegree. These names won't change, but the symbols that represent them on paper may change later on.

Each of these functions can appear either standalone, or inside a bigger expression. When used inside a bigger expression, the functions always take arguments. However when they are used on their own, I need to express how many arguments they take, so I use subscripts, but these subscripts should not appear when the functions are part of a larger expression, because then the number of arguments can be easily deduced from the context.

Answer 1

You are precisely looking for \ensuremath, I think. \ensuremath ensures that its contents is typeset inside math mode: are you in math mode? ok, just put the code; are you out of math mode? ok, then type $..$ around the expression.

\documentclass{article}

\usepackage{xparse}

\NewDocumentcommand\savelongexpression{mm}{\NewDocumentCommand#1{}{\ensuremath{#2}}

\savelongexpression\nameone{x^2 + y^2}
\savelongexpression\nametwo{\sin x \cos x}

\begin{document}

\nameone{} and \nametwo. Also $\nameone + \nametwo$, and
\[
  \nameone - \nametwo
\]
too.

\end{document}

Note that you need to add {} or any alternative after the command if you want the space tokenized.