How do I get what's been printed by {align}?

Question

I was trying to figure out an automatic answer to Sharing alignment between equations in two different items by way of typesetting an {align} inside a \vbox and then using \unvbox and \lastbox repeatedly to get the lines of the alignment. Alas, this does not work, as this session with latex shows:

>latex
**\relax
*\documentclass{article}\usepackage{amsmath}\begin{document}

*\setbox0=\vbox{\begin{align*} a&=b \end{align*}}

*\tracingonline=1

*\showbox0
> \box0= []

! OK.
<*> \showbox0

? 

*

*\unvbox0

*\unskip

*\setbox1=\lastbox

*\showbox1
> \box1=void

! OK.
<*> \showbox1

? 

How can there be nothing in the box? Doesn't TeX typeset something? This is surely a mathmode thing, except that the following does work:

> tex
**\relax

*\setbox0=\vbox{$$\eqalign{a&=b}$$}

*\tracingonline=1

*\showbox0
> \box0=
\vbox(22.5+0.0)x469.75499
.\hbox(0.0+0.0)x469.75499, glue set 449.75499fil
..\hbox(0.0+0.0)x20.0
..\penalty 10000
..\glue(\parfillskip) 0.0 plus 1.0fil
..\glue(\rightskip) 0.0
.\penalty 10000
.\glue(\abovedisplayshortskip) 0.0 plus 3.0
.\glue(\baselineskip) 3.5
.\hbox(8.5+3.5)x26.24402, shifted 221.7555
..\hbox(0.0+0.0)x0.0
..\glue 1.66663
..\vbox(8.5+3.5)x22.91077
...\hbox(8.5+3.5)x22.91077 []
..\glue 1.66663
.etc.

! OK.
<*> \showbox0

? 

*

(\eqalign is the TeX version of {align}, to some extent). Perhaps it is more that the AMS environments do what the TikZ documentation refers to as "wicked things", but I don't see how they could trick TeX itself into thinking the box were empty. I do notice that even in the \eqalign example, the innermost box of the alignment is \hbox(8.5+3.5)x22.91077 []; going by the dimensions \hbox(0.0+0.0)x469.75499, glue set 449.75499fil, this is the text (i.e. a = b) but the empty brackets indicate that there is nothing inside the box. So maybe it is a mathmode thing after all and the AMS' wickedness is just hiding the surrounding material as well?

So, is there any way to unwrap an {align}?

Answer 1

The column width in an align are kept in the macro \maxcolumn@widths that's set after the first pass over the environment's contents: in your case

> \maxcolumn@widths=macro:
-> \or 5.28589pt \or 17.62488pt \or 0.0pt.

One can access to the values with \ifcase. Of course it's necessary to "export" the macro, which can be done by saying in any of the cells

\ifmeasuring@
  \global\let\lastmaxcolumn@width\maxcolumn@widths
\fi

(maybe this can be added to the code for \end{align*}, but I'm not sure).

Answer 2

Turns out that the main thing I was asking about is the result of a misunderstanding: if you set \showboxdepth large enough, then everything will be displayed as expected. No empty boxes.

As for unwrapping an {align}: Presumably some combination of \unskip and \unpenalty will reveal the actual list of lines, after which \lastbox will work. See my second answer to Sharing alignment between equations in two different items for the easy version of this.