math shorthand macro: avoid extra space from empty superscript

Question

I find myself writing $\{0,1\}^x$ a whole lot, so I want to define a shorthand macro:

\def\zo#1{\{0,1\}^{#1}}

However, sometimes I need $\{0,1\}$ with no superscript. If I write \zo{} I get a tiny bit of extra space after the close brace (because there's an empty superscript in there). The only way I have found to get rid of it is

\def\zo#1{\{0,1\}\if\relax\detokenize{#1}\relax\else^{#1}\fi}

which is rather a mouthful. Is there a more elegant way to accomplish this? Note that the actual document I am writing is in LaTeX, so if amsmath (for instance) has something to the purpose, that would be a fine answer. I have expressed the question in plain TeX because it is fundamentally a question about the core math engine.

If you can't see the tiny bit of extra space, this MWE (requires (pdf)etex) will make it obvious:

\def\a#1{\{0,1\}^{#1}}
\def\b#1{\{0,1\}\if\relax\detokenize{#1}\relax\else^{#1}\fi}
\leavevmode\rlap{$\a{}\a{}\a{}\a{}$}$\b{}\b{}\b{}\b{}$
\bye

→ (400% zoom)

Answer 1

Solution A

Use

\def\a{\{0,1\}}

and add ^{<stuff>} if needed.

Solution B

Notes

• \csname <something else>\endcsname expands to \relax if \<something else> is not defined.
• No other macro must be named \qrrgobbletwo<something> where <something> could be an argument for \a.
• All other “tricks” and helpers used in the other answers ( \newcommand with optional argument/\@ifnextchar) can still be applied. (But then I would use an conditional anyway!)

Reference

• Does the \relax side-effect of \csname...\endcsname still have a use?

Code

\def\qrrgobbletwo#1#2{}
\def\a#1{%
    \{0,1\}\csname qrrgobbletwo\detokenize{#1}\endcsname^{#1}%
}
\def\b#1{\{0,1\}\if\relax\detokenize{#1}\relax\else^{#1}\fi}
\leavevmode\rlap{$\a{}\a{}\a{}\a{}$}$\b{}\b{}\b{}\b{}$

\leavevmode\rlap{$\a{a}\a{a}\a{a}\a{a}$}$\b{a}\b{a}\b{a}\b{a}$
\bye

Output

Answer 2

This seems to be an optional feature so should be an optional argument:

 \newcommand\zo[1][]{\{0,1\}\ifx\relax#1\relax\else^{#1}\fi}

    \zo   \zo[x]

Answer 3

Using e.g. xparse you'll get more readable code:

\usepackage{xparse}
\DeclareDocumentCommand\zo{g}{%
  \ensuremath{%
    \{0,1\}%
    \IfNoValueTF{#1}{}{^{#1}}%
  }%
}

Using {o} as an argument specifier instead of {g} would make the command use an optional ([]-delimited) argument instead, which may be more appropriate.

Answer 4

You can use the clever conditional tests by Donald Arsenau discussed in Is "conditionals" name of package?

{\catcode`\@=11 % @ is a letter
 \catcode`\!=8  % funny catcode so ! will be a delimiter
 \catcode`\Q=3  % funny catcode so Q will be a delimiter
 \long\gdef\given#1{88\fi\Ifbl@nk#1QQQ\empty!}
 \long\gdef\blank#1{88\fi\Ifbl@nk#1QQ..!}% if null or spaces
 \long\gdef\nil#1{\IfN@Ught#1* {#1}!}% if null
 \long\gdef\IfN@Ught#1 #2!{\blank{#2}}
 \long\gdef\Ifbl@nk#1#2Q#3!{\ifx#3}% same as above
}
\def\kmsp{\kern-\scriptspace}

\def\zo#1{\{0,1\}^{\if\blank{#1}\aftergroup\kmsp\else#1\fi}}

$\zo{}\zo{}$\quad$\zo{2}\zo{2}$

$\{0,1\}\{0,1\}$\quad$\{0,1\}^2\{0,1\}^2$

\bye

Of course this is overkill, but shows why a small space creeps in: it's called \scriptspace and is added by TeX when there's a (possibly empty) superscript or subscript.

A simpler definition would be (again using \blank):

\def\zo#1{\{0,1\}\if\blank{#1}\else^{#1}\fi

This works even with \zo{ }.

---

However, I don't find any convenience of writing \zo{2} instead of \zo^{2}, considering also that you are forced to put in the braces when there's no exponent. So, the best definition is, in my opinion,

\def\zo{\{0,1\}}

with following input as

$\zo$
$\zo^{2}$

and so on. No tests, no problems. This is "Solution A" in Qrrbrbirlbel's answer.

---

Simple LaTeX solution:

\usepackage{xparse}
\NewDocumentCommand{\zo} { o } {\{0,1\}\IfValueT{#1}{^{#1}}}

to be used as

$\zo$
$\zo[2]$

Answer 5

\makeatletter
\newcommand\zo[1]{\begingroup\def\x{#1}\ifx\x\@empty\{0,1\}\else\{0,1\}^{\x}\fi\endgroup}
\makeatother

We collect the argument by \def\x{#1} and then test if it's empty by \ifx\x\@empty. The rest should be clear. This solution is a bit better than yours because we read #1 only once. If might be a good idea to make it robust by replacing \newcommand with \DeclareRobustCommand, so that you can use it in strange contexts as section titles as well.

---

To make it purely plainTeX, you can do the following:

\def\zo#1{\begingroup\def\x{#1}\def\y{}\ifx\x\y\{0,1\}\else\{0,1\}^{\x}\fi\endgroup}

---

Example:

\makeatletter
\newcommand\zo[1]{\begingroup\def\x{#1}\ifx\x\@empty\{0,1\}\else\{0,1\}^{\x}\fi\endgroup}
\newcommand\oldzo[1]{\{0,1\}^{#1}}
\makeatother

\noindent
$\zo{}\zo{}\zo{}\zo{}$\\
$\oldzo{}\oldzo{}\oldzo{}\oldzo{}$\\
$\{0,1\}\{0,1\}\{0,1\}\{0,1\}$

---

Variant with an optional argument:

\makeatletter
\def\zo@opt[#1]{\{0,1\}^{#1}}
\newcommand\zo{\@ifnextchar[\zo@opt{\{0,1\}}}
\makeatother

$\zo[2] \neq \zo \zo$

Answer 6

Here is a partially functional solution based on meta-conditionals:

\def\zo{\{0,1\}\xzo}
\def\xzo#1{\xxzo #1\empty^\empty}
\def\xxzo#1#2#3{#3{#1}}

\let\a\zo
\def\b#1{\{0,1\}\if\relax\detokenize{#1}\relax\else^{#1}\fi}
\leavevmode\rlap{$\a{}\a{}\a{}\a{}$}$\b{}\b{}\b{}\b{}$

\def\x{123}
$
\zo{1}
\zo{\x}
\zo\alpha
$
\bye

You can verify (running with etex) that this does not create phantom space with an empty argument. The only catch is that if you want a multi-token exponent, you have to frame it in a temporary macro because the "trick" requires that the argument have exactly zero or one tokens.

The way the trick works is that when TeX picks up undelimited arguments, it doesn't have any way of knowing where the end of one is except by looking at where the next one begins. So we have a meta-conditional, where which arguments become #1, #2, and #3 in \xxzo depends on whether the #1 that is placed in \xzo is empty or one token. If the former, then #1 = \empty, #2 = ^, and #3 = \empty, and \xxzo expands to almost nothing (the braces with no content are a box with zero width). If the latter, then #1 = #1, #2 = \empty, and #3 = ^, and you get the superscript. Effectively, the absence of the putative first argument pushes the ^ into the "ignored" slot.

I tried for a while to make it work with arbitrary arguments to \zo, but that would appear to require a delimited argument, and the entire basis for the trick fails there since you have to place a delimiter that prevents the argument numbers from shifting. Any suggestions would be welcome.