Zero parameters in command definition

Question

Let us say I want to define a command for typesetting (a+b)^2:

\newcommand{\sumsquare}[2]{\ensuremath{(#1+#2)^2}}

How can I modify it so that \sumsquare{a}{0} will produce a^2?

Answer 1

I would suggest you change the syntax to \sumsquare{a}{}:

This can be coded either this way:

\newcommand{\sumsquare}[2]{%
   \ifx\\#2\\%
     \ensuremath{#1^2}}%
   \else
     \ensuremath{(#1+#2)^2}}%
   \fi
}

or:

\newcommand{\sumsquare}[2]{%
   \begingroup
   \def\tempvar{#2}%
   \ifx\tempvar\empty
     \endgroup
     \ensuremath{#1^2}}%
   \else
     \endgroup
     \ensuremath{(#1+#2)^2}}%
   \fi
}

If your really want 0 as the no-operant indicator you can define it like this:

\newcommand{\sumsquare}[2]{%
   \begingroup
   \def\tempvara{#2}%
   \def\tempvarb{0}%
   \ifx\tempvara\tempvarb
     \endgroup
     \ensuremath{#1^2}}%
   \else
     \endgroup
     \ensuremath{(#1+#2)^2}}%
   \fi
}

(I named the temporary variables this way to avoid \makeatletter. Normally \@tempa and \@tempb are used.)

Explanation:

The \ifx command compares the next to tokens (e.g. macros, characters, ...) if the hold the same definition. In the last example the 0 and the #2 are both defined to a macro each, which are then compared. This requires assignments and is therefore not expandable, i.e. doesn't work inside an \edef.

In the first code \ifx\\#2\\ is used to test if #2 is empty. If #2 contains something, \ifx compares the first token in it with \\, which does not match as long #2 doesn't start with \\. All other tokens are then simply taken as part of the true part and simply discarded with it. If \\ is a valid value for #2 simply use some other macro like \relax or \@nnil instead.

However, if #2 is empty the expression is reduced to \ifx\\\\, i.e. \ifx compares two \\, which are of course defined identical.

Answer 2

A solution using xparse

\documentclass{article}
\usepackage{xparse}
\NewDocumentCommand\sumsquare{mg}{%
  \IfNoValueTF{#2}
    {\ensuremath{#1^2}}
    {\ensuremath{(#1+#2)^2}}
}

Answer 3

It can also be done with an optional second argument, but it is not really shorter than typing it

\documentclass{article}
\newcommand{\sumsquare}[2]{\ensuremath{\ifx\relax#2\relax#1\else(#1+#2)\fi^2}}
\begin{document}

\sumsquare{a}{b} \sumsquare{a}{}

\end{document}