How do I create the following macros?

Question

I would like to define the following macros.

\newcommand{\NC}{\ensuremath{\mathbf{NC}}}
\newcommand{\NC}[1]{\ensuremath{\mathbf{NC^{#1}}}}

But LaTeX complains that \NC is already defined. So, I only define \NC with optional arguments as follows.

\newcommand{\NC}[1][\phantom{0}]{\ensuremath{\mathbf{NC^{#1}}}}

And now \NC works, but \NC1 doesn't work as expected.

Answer 1

There are two ways to solve your problem: If you are willing to type \NC[1] etc., then the following works

\newcommand{\NC}[1][]{{\def\NCexponent{#1}%
  \ifx\NCexponent\empty{\ensuremath{\mathbf{NC}}}\else
    \ensuremath{\mathbf{NC^{#1}}}\fi}}

Here, the \ifx\exponent\empty tests whether the optional argument was present and then uses \mathbf{NC^{#1}} if the argument was there and \mathbf{NC} otherwise. This makes both \NC and \NC[1] work as expected. (The extra layer of braces {{...}} is there to prevent the auxiliary macro \NCexponent from leaking outside this macro.) As for all TeX macros, spaces after a macro are swallowed by TeX, so you need to use constructions like \NC\ and\NC[1] to get a space after \NC.

If you insist to be able to type \NC as well as \NC1, this can also be done, but the solution is more complicated. Here is a complete example:

(updated to use \noexpand#2 as suggested by @egreg)

\documentclass{article}

\def\NC{\NCa{}}
\def\NCa#1#2{\def\next{\NCa{#1#2}}%
  % test whether #2 is a digit:
  \if0\noexpand#2\else\if1\noexpand#2\else\if2\noexpand#2\else
  \if3\noexpand#2\else\if4\noexpand#2\else\if5\noexpand#2\else
  \if6\noexpand#2\else\if7\noexpand#2\else\if8\noexpand#2\else
  \if9\noexpand#2\else
  \def\next{\NCb{#1}#2}%
  \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\next}
\def\NCb#1{{\def\exponent{#1}\ifx\exponent\empty
    \ensuremath{\mathbf{NC}}\else\ensuremath{\mathbf{NC^{#1}}}\fi}}

\begin{document}
There is \NC, \NC1, \NC 2\ and \NC345, as well as \NC a and again
\NC.
\end{document}

This version of the macro \NC checks all the following tokens: as long as they are digits, they are incorporated into the exponents, the first non-digit stops the argument. To achieve this, two auxiliary macros are used. \NCa constructs the exponent; it takes two arguments, the exponent constructed so far (#1) and the next token in the input stream (#2). If the next token is equal to 0, 1, ..., 9, we call \NCa again, with #2 added to the exponent. Otherwise, we call \NCb for typesetting (testing for empty exponents as above) and put back #2 into the input stream behind the expansion of \NCb (by writing \NCb{#1}#2).

One quirk of the second solution is, that all spaces encountered by \NCa are swallowed by the TeX parser. Thus, \NC 1 2 3 is the same as \NC123.