\downarrow is not centered in table when using tex4ht with column type centered paragraph

Question

I am making a table, with one column. The table is centered. The column type is centered paragraph.

I am using \downarrow for annotation between each row to indicate transformation made.

In pdf, everything is centered. But in HTML, the math is centered, but the arrows are not. This happens only when I use column type as centered paragraph. If I use just c, then the arrows are centered.

But I have to use centered paragraph and not c for column type, because I am using displayed math in table, which needs paragraph. I am using displayed math because the math is little larger and easier to read.

Here is an example that works same way in PDF and HTML, which using c. Then below that I show an example which does not work in HTML when I change the column type to centered paragraph

\documentclass[12pt,oneside]{book}  

%added nov 23, 2023 to enlarge vertical arrow.
%https://tex.stackexchange.com/questions/213811/how-to-elongate-down-arrow
\newcommand{\xdownarrow}[1]{%
  {\left\downarrow\vbox to #1{}\right.\kern-\nulldelimiterspace}
}
\usepackage{amsmath}

\begin{document}

\begin{table}
\centering
\begin{tabular}{c}
$\int \frac{e^{x+e^x} \left(e^x+1\right)}{x+e^x} \, dx$\\
$\Big\downarrow$ \rlap{7258}\\
$\int \frac{e^{x+e^x}}{x+e^x}d\left(x+e^x\right)$\\
$\Big\downarrow$ \rlap{2609}\\
$\operatorname{ExpIntegralEi}\left(x+e^x\right)$
\end{tabular}
\end{table} 

\end{document}

Compiling with lualatex gives

Compiling with tex4ht using

make4ht -ulm default -a debug foo.tex "mathjax,htm,nostyle"

Gives

Output is similar. arrows are centered

Now I modified the MWE to using column type centered paragraph so I can use display math

\documentclass[12pt,oneside]{book}  
%added nov 23, 2023 to enlarge vertical arrow.
%https://tex.stackexchange.com/questions/213811/how-to-elongate-down-arrow
\newcommand{\xdownarrow}[1]{%
  {\left\downarrow\vbox to #1{}\right.\kern-\nulldelimiterspace}
}

\usepackage{array}
%see https://tex.stackexchange.com/questions/12703/how-to-create-fixed-width-table-columns-with-text-raggedright-centered-raggedlef
\newcolumntype{C}[1]{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}m{#1}}

\usepackage{amsmath}    
\begin{document}
\begin{table}
\centering
\begin{tabular}{C{\textwidth}}
$\displaystyle \int \frac{e^{x+e^x} \left(e^x+1\right)}{x+e^x} \, dx$\\
$\Big\downarrow$ \rlap{7258}\\
$\displaystyle \int \frac{e^{x+e^x}}{x+e^x}d\left(x+e^x\right)$\\
$\Big\downarrow$ \rlap{2609}\\
$\displaystyle \operatorname{ExpIntegralEi}\left(x+e^x\right)$
\end{tabular}
\end{table}

\end{document}

Now lualatex gives

But tex4ht gives using same command as above this:

The arrows for some reason no longer centered as in PDF.

Is there an easy workaround for this?

TL 2023 updated about 2 months ago.

Tex4ht tracking number

Answer 1

Try this configuration file:

\Preamble{xhtml}

\catcode`\:=11
\Configure{halignTD} {}{}
   {<}{\HCode{ style="white-space:nowrap; text-align:left;"}}
   {-}{\HCode{ style="white-space:nowrap; text-align:center;"}}
   {>}{\HCode{ style="white-space:nowrap; text-align:right;"}}
   {^}{\HCode{ style="vertical-align:top; white-space:nowrap;"}}
   {=}{\HCode{ style="vertical-align:baseline; white-space:nowrap;"}}
   {|}{\HCode{ style="vertical-align:middle; white-space:nowrap;"}}
   {_}{\HCode{ style="vertical-align:bottom; white-space:nowrap;"}}
   {p}{\HCode{ style="white-space:normal; text-align:left;"}\Protect\a:HColWidth}
   {m}{\HCode{ style="white-space:normal; text-align:center; vertical-align:middle;"}\Protect\a:HColWidth}
   {b}{\HCode{ style="white-space:normal; text-align:left; vertical-align:bottom;"}\Protect\a:HColWidth}
   {}
\catcode`\:=12
\begin{document}
\EndPreamble

It is a configuration for possible values of table column specifications. In theory, it should be possible to add line for your C specification here, but it seems that it is converted to m specification by array internally. So I've changed the configuration for m to align to center: {m}{\HCode{ style="white-space:normal; text-align:center; vertical-align:middle;"}\Protect\a:HColWidth}. I won't change it in TeX4ht sources, because m columns should be normally left aligned. Hopefully, this won't cause issues in your other tables.

This is the result: