Better transitive closure of labelled arrow

Question

I think the answer will be easy, but I haven't found it yet:

I use labelled arrows like \xrightarrow\tau a lot. Sometimes, I need the transitive closure of such relations, which I write \xrightarrow\tau^* but then, the star is way to high, quite above the \tau.

How can I put the star at the same height as if I had written \rightarrow^*, even when I have a label?

Figures:

Answer 1

\documentclass{article}
\usepackage{amsmath}
\def\Xrightarrow#1#2{\xrightarrow#1{}\negthickspace^#2}
\begin{document}

$ \rightarrow^*$

$ \xrightarrow\tau{}\!\!^* $  

$ \Xrightarrow\tau* $  
\end{document}

\!\! is the same as \negthickspace

Answer 2

You can use \raisebox to adjust the height of the *. Here is the original and one with \raisebox:

I have also define a macro \myxrightarrow that you can use as \myxrightarrow{\tau} to get the same effect.

\documentclass[border=2pt]{standalone}
\usepackage{amsmath}
\newcommand*{\myxrightarrow}[1]{{\xrightarrow{#1}}\raisebox{0.4ex}{\scriptsize*}}%
\begin{document}
$\xrightarrow\tau^*$

${\xrightarrow\tau}\raisebox{0.4ex}{\scriptsize *}$

$\myxrightarrow{\tau}$
\end{document}

Answer 3

Here's another version which defines a new arrow, \xrighttransarrow (maybe there's a better name ...). This is an extensible arrow modelled on the definition of \xrightarrow which makes the * a part of the arrow, rather than a decoration to be added on afterwards. There's a bit of jiggery-pokery to get the spacing right: the * has to be ignored as far as the placement of the \tau is concerned, but then it has to be taken into account when positioning the arrow with its surrounding text. I may well have messed up those bits as I'm no expert on lengths. It's also possible that it would go wrong in different maths styles.

Here's the code:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newdimen\arrow@ht
\setbox\@tempboxa\hbox{\(\rightarrow\)}
\arrow@ht\ht\@tempboxa
\newdimen\star@wd
\setbox\@tempboxa\hbox{\(\scriptstyle *\)}
\star@wd\wd\@tempboxa
\def\righttransarrowfill@{\arrowfill@\relbar\relbar{\raisebox{0pt}[\arrow@ht][0pt]{\(\rightarrow^*\hskip-\star@wd\)}}}
\setbox\@tempboxa\hbox{\(\rightarrow\)}
\arrow@ht\ht\@tempboxa
\newcommand{\xrighttransarrow}[2][]{\ext@arrow 0359\righttransarrowfill@{#1}{#2}\hskip\star@wd}
\makeatother

\begin{document}
\(
a\rightarrow^* b
a\xrightarrow\tau^* b
a\xrightarrow{\raisebox{0pt}[0pt][0pt]{\(\scriptstyle\tau\)}}^* b
a \xrighttransarrow\tau b
\)
\end{document}

Here's the result (note that there's also another \raisebox solution in the middle there):

Answer 4

Here is a simpler definition

\newcommand{\tto}[1][]{\mathrel{
  \vphantom{\xrightarrow{#1}}
  \smash{\xrightarrow{#1}}
  \vphantom{\to}^*}
}

$\tto$
$\tto[\tau]$