What is the difference between \empty and \@empty?

Question

I want to elaborate a command that would print differently simple differential dx and multidimensional differential d^3x. For this purpose I invented the command \dif with one optional argument. It is defined as follows:

\newcommand{\dif}[1][]{%
    \def\@tmp@a{#1}%
    \ifx\@tmp@a\@empty
        [b1]\mathrm{d}
    \else
        [b2]\mathrm{d}^{#1}{} \!
    \fi
}

Here [b1] and [b2] are added for debugging. Branch [b1] is intended for the case when the command is called without any argument, e.g. \dif{x}. Second branch [b2] should be taken in case where, e.g., the command \dif[3]{x} is used to print d^3x. The definition, shown above, seems to work fine. However, if \@empty is substituted with \empty first branch is always ignored.

The command \empty is explained in The TeXBook, so that initially I tried it for this code and only occasionally reverted to \@empty having remembered a post at this site where it was said that the \end command of Plain TeX is redefined to \@@end in LaTeX.

Can somebody explain what is the difference between \empty and \@empty in LaTeX and, perhaps, suggest a better solution for my problem?

Answer 1

I get the same output either with \@empty or with \empty. I suggest you another definition:

\newcommand{\dif}[1][]{\mathop{}\!\mathrm{d}
  \if\relax\detokenize{#1}\relax
  \else
    ^{#1}\mkern-1.5mu
  \fi}

This has two advantages over yours:

1. It takes care automatically of the thin space before the d
2. It uses a slight smaller backspace in case there's an exponent to the d.

Of course I'd prefer an italic d, but that's another story. :)

Answer 2

The \@empty and \empty macros are defined in the source file for the LaTeX format latex.ltx on line 122 and 441, respectively:

\def\@empty{}

\let\empty\@empty

So both are actually identical. I as well wondered about having two names for the same thing around. I guess the LaTeX developers wanted a macro which is safer for being redefined by the user or other packages.

You code actually should work with both \@empty and \empty. Put a \show\@empty and \show\empty before your \ifx to debug the issue. Maybe one gets redefined somewhere. In that case you could place a \tracingall\tracingassigns=1\relax \tracingonline=0\relax very early of your document preamble and then search for the redefinition in the log file.

Answer 3

For the purpose of testing whether the argument of a command is empty I would recommend using the \@ifmtarg switch provided by the ifmtarg package. Thus:

\documentclass{article}

\usepackage{ifmtarg}

\makeatletter

\newcommand*{\dif}[1][]{%
  \@ifmtarg{#1}{[b1]\mathrm{d}}{[b2]\mathrm{d}^{#1}{} \!}%
}

\makeatother

...

The \@ifmtarg switch relies on neither \empty nor \@empty.