Aligning fractions with an alignment tab

Question

I don't know whether this is really a good idea or not, but I'm wondering if it's possible to implement a version of \frac where the numerator and denominator can be aligned at an alignment tab (&).

There are many questions about fraction alignment on this site, with the most obvious solution in many cases being to use \hfill. But consider a fraction like this one:

The top one looks, to my eyes, a little messy, but using \hfill moves the numerator too far to the left. What I really want (I think) is to align them exactly at the open bracket. So I'm imagining an \alignedfrac command that would allow me to write

\[
\alignedfrac{q&(x\mid y)}{p_\mathrm{foo}&(w\mid x,y,z)}
\]

and have that align the numerator and denominator at the & characters.

I'm aware that this may or may not actually be a good choice, and that I'm probably solving a non-problem, but still, I'm curious whether it's possible to implement something like this.

Here's the MWE that produces the image above:

\documentclass{article}
\begin{document}

\noindent without any alignment:
\[
\frac{q(x\mid y)}{p_\mathrm{foo}(w\mid x,y,z)}
\]
using hfill:
\[
\frac{q(x\mid y)\hfill}{p_\mathrm{foo}(w\mid x,y,z)}
\]
\end{document}

Answer 1

Here I construct the left portion of the frac (\leftfrac) and the right portion (\rightfrac) independently, using \hfills to achieve the portional justifications. Then, I typeset both adjacently, with a negative \mkern between them.

Per Mico's suggestion, occurrences of | have been replaced with \mid, for better appearance.

EDITED to add \vphantom matching, which I believe will help things if the left and right portions are of different vertical extents.

\documentclass{article}
\begin{document}
\newcommand\alignedfrac[2]{%
  \leftfrac#1\\#2\relax\mkern-4.5mu\rightfrac#1\\#2\relax
}
\def\leftfrac#1&#2\\#3&#4\relax{%
  \frac{\hfill#1\vphantom{#2}}{\hfill#3\vphantom{#4}}}
\def\rightfrac#1&#2\\#3&#4\relax{%
  \frac{\vphantom{#1}#2\hfill}{\vphantom{#3}#4\hfill}}
\noindent without any alignment:
\[
\frac{q(x\mid y)}{p_\mathrm{foo}(w\mid x,y,z)}
\]
using hfill:
\[
\frac{q(x\mid y)\hfill}{p_\mathrm{foo}(w\mid x,y,z)}
\]
using alignedfrac
\[
\alignedfrac{q&(x\mid y)}{p_\mathrm{foo}&(w\mid x,y,z)}
\]

\end{document}

Answer 2

You can do it:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand{\alignedfrac}[2]{%
  \begingroup
  \setbox0=\vbox{%
    \m@th
    \ialign{&$\displaystyle##$\cr#1\cr#2\cr}%
    \setbox2=\lastbox
    \hbox{%
      \unhbox2
      \unskip
      \setbox4=\lastbox
      \unskip
      \setbox6=\lastbox
      \global\dimen1=\wd6
      \global\dimen3=\wd4
    }
  }
  \frac{\af@make#1\@nil}{\af@make#2\@nil}
  \endgroup
}
\def\af@make#1&#2\@nil{%
  \makebox[\dimen1][r]{$\displaystyle#1$}%
  \makebox[\dimen3][l]{$\displaystyle#2$}%
}
\makeatother

\begin{document}

\begin{gather*}
\alignedfrac{q&(x\mid y)}{p_\mathrm{foo}&(w\mid x,y,z)} \\
\frac{q(x\mid y)}{p_\mathrm{foo}(w\mid x,y,z)}
\end{gather*}

\end{document}

What's the deal? I make an alignment with the primitive \halign and then examine its last row by dismantling the built box. I store the dimension of the two parts and use them to make boxes of the right width.

However, I see no improvement with respect to the standard fraction, as the image clearly shows.