horizontal centering within \valign cells

Question

I'm trying to use \valign to make an array of items. (See my self-answer to another question.) I'm doing this because I want to specify the items per column instead of per row, and because I want control over the spacing. I'm using LaTeX but these are plain-tex macros.

I'm happy with the following, except that the items are not vertically centred within their column, so this question is about how to achieve that.

\documentclass{article}
\usepackage{amsmath}

% this can't be an environment because the code for \end can't have parameters.
\newcommand{\colarray}[3]{
\vcenter{\hbox{\valign{&\vfil\vbox{\parindent=0pt\tabskip=#2\hsize=#1##}\vfil\cr%
#3%
}}\vskip-#2}%
}

\newcommand*\col[1]{#1\cr}

\begin{document}

\begin{equation}
    x = \colarray{4mm}{2mm}{
        \col{1 & 2 & 3}
        \col{4 & 5 & \Big(6\Big)}
    }
\end{equation}

\end{document}

This produces

From my current rather hazy understanding, centering the items should involve putting each one in an \hbox and using \vfil. However, if I try that the results are not as expected:

\documentclass{article}
\usepackage{amsmath}

% this can't be an environment because the code for \end can't have parameters.
\newcommand{\colarray}[3]{
\vcenter{\hbox{\valign{&\vfil\vbox{\parindent=0pt\tabskip=#2\hsize=#1\hbox to #1{\hfil##\hfil}}\vfil\cr%
#3%
}}\vskip-#2}%
}

\newcommand*\col[1]{#1\cr}

\begin{document}

\begin{equation}
    x = \colarray{4mm}{2mm}{
        \col{1 & 2 & 3}
        \col{4 & 5 & \Big(6\Big)}
    }
\end{equation}

\end{document}

Here's the result:

As you can see the '3' is horizontally aligned differently from the '1' and '2', and the '(6)' is not horizontally centred with respect to the '4' and '5'.

I am not able to work out why this is, so my questions are (1) why is this happening, and (2) how can I fix it?

Answer 1

You need to remove the spaces before each & in your usage of \colarray, as they are significant when they get substituted in the inner \hbox. Alternatively, replace ## with $##$ in the definition of \colarray. Also, I don't think 4mm is big enough for the parenthesized "6"; to align the columns, you will need to increase it.

By the way, you do not need to set \parindent and \hsize in your second attempted solution.

Answer 2

This is similar to RobertR's suggestions, but as a full example.

\documentclass{article}
\usepackage{amsmath}

% this can't be an environment because the code for \end can't have parameters.
% ?? It would be more natural as an environment with \\ like array
\newcommand{\colarray}[3]{%
\vcenter{\hbox{\valign{&\vfil\tabskip=#2\hbox to #1{\strut\hfil$##$\hfil}\vfil\cr%
#3%
}}\vskip-#2}}

\newcommand*\col[1]{#1\cr}

\begin{document}

\begin{equation}
    x = \colarray{5mm}{2mm}{
        \col{1 & 2 & 3}
        \col{4 & 5 & \Bigl(6\Bigr)}
    }
\end{equation}

\end{document}