Control sequence with arbitrary number of parameters

Question

I want a macro which can generate units consisting of several base units. Let the macro be \unit. For example, I want \unit{kg} to mean \mathrm{kg} and \unit{kg}{m}{s^{-2}} to mean \mathrm{kg \cdot m \cdot s^{-2}} etc. (though how to represent exponentiation is yet to be decided).

First, I tried the following code but this didn't work. The error log says Runway Argument? ! File ended while scanning use of \@unit. <inserted text> \par.

\documentclass[uplatex]{jsarticle}
\makeatletter
\def\unit#1{\@unit#1}
\def\@unit#1{%
    \ifx\bgroup#1
        \mathrm{#1 \cdot}%
    \else
        \relax
    \expandafter\@unit\fi}
\makeatother
%
\begin{document}
\unit{{kg}{m}}
\end{document}

How should I define the desired \unit?

Answer 1

Assuming you want input syntax

\unit{kg}{m}

what you need to do is use the TeX primitive \futurelet to search for an upcoming {. If there is one, we can grab a (braced) argument, typeset it in math mode then loop. Note that this approach requires braces around each argument.

\documentclass{article}
\makeatletter
\def\unit{%
  $%
  \futurelet\@let@token\@unit
}
\def\@unit{%
  \ifx\@let@token\bgroup
    \expandafter\@@unit
  \else
    \expandafter$%
  \fi
}
\def\@@unit#1{%
  \mathrm{#1}%
  \futurelet\@let@token\@@@unit
}
\def\@@@unit{%
  \ifx\@let@token\bgroup
    \cdot
    \expandafter\@@unit
  \else
    \expandafter$%
  \fi
}
\makeatother
\begin{document}
\unit{kg}{m}
\end{document}

To allow for insertion of the \cdot I've used two auxiliaries: one is used only for the first unit an omits the \cdot, the second one inserts the required \cdot.

Answer 2

The problem when you do \def\@unit#1 is that the argument will never be the brace, but all that goes from the open brace to the matching closed one and your test is never successful.

You can do it with \futurelet, but you'll be tied to a very inflexible system of input. Here's an expl3 implementation that's possibly clearer than \futurelet.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\unit}{}
 {
  % if we're not in math mode open it and remember to close it
  \mode_if_math:F { $ \bool_set_true:N \l_merzong_close_bool }
  % clear the container for the units
  \seq_clear:N \merzong_units_seq
  % start looking forward for an open brace
  \merzong_scan_arg:
 }

\cs_new_protected:Npn \merzong_scan_arg:
 {
  \peek_catcode:NTF \c_group_begin_token
   {% the next token is an open brace, absorb the argument
    \merzong_add_unit:n
   }
   {% the next token is not an open brace, deliver the units
    % absorbed so far, with \unitmulti between them
    \seq_use:Nn \merzong_units_seq { \unitmulti }
    % close math mode if we started it
    \bool_if:NT \l_merzong_close_bool { $ }
   }
 }
\cs_new_protected:Npn \merzong_add_unit:n #1
 {
  % absorb the argument and add it to the sequence
  \seq_put_right:Nn \merzong_units_seq { \mathrm{#1} }
  % restart the recursion
  \merzong_scan_arg:
 }

\seq_new:N \merzong_units_seq
\ExplSyntaxOff

\newcommand\useunitmultidot{\let\unitmulti=\cdot}
\newcommand\useunitmultispace{\let\unitmulti=\,}
\useunitmultidot % initialize

\begin{document}

\section{Centered dot}

\unit{kg}{m^2}{s^{-2}}

\section{Space}
\useunitmultispace

\unit{kg}{m^2}{s^{-2}}

\end{document}

What you want to do is already done by siunitx. Using it ensure great consistency in your usage of units.

\documentclass{article}
\usepackage{siunitx}

\begin{document}

\section{Centered dot}

\sisetup{inter-unit-product=\ensuremath{{}\cdot{}}}

\SI{3}{\kilo\gram\meter\squared\per\second\squared} or \SI{3}{kg.m^2.s^{-2}}

\section{Thin space}

\sisetup{inter-unit-product=\,}

\SI{3}{\kilo\gram\meter\squared\per\second\squared} or \SI{3}{kg.m^2.s^{-2}}

\section{Fraction for negative exponent}

\sisetup{per-mode=symbol}

\SI{3}{\kilo\gram\meter\squared\per\second\squared}

\end{document}