Automatically prevent extra line spacing because of math

Question

The boxes and glue system seems to be both the strength and weakness of TeX. One of the major problems I often have to deal with is uneven distances between lines as in the example below.

Inserting some \smash commands around the math proves that this extra line spacing is not at all necessary; there is plenty of room for the math on lines of standard height:

Currently, inserting \smash commands manually is the only acceptable solution I have found to this problem, as I doubt messing with the interline glue is a good idea (or what?). I wonder if there is an automatic way to accomplish this? Can I prevent TeX from adjusting the line height based on the size of inline math?

You might think:

But what if you want to place large structures, like matrices, in inline math? Certainly you do not want them to collide with the adjacent lines?

But the fact is that I never place matrices or similar large constructions in inline math. In my opinion, such things belong entirely in displayed math.

\documentclass{article}

\usepackage{mathtools}

\DeclareMathOperator\Ad{Ad}

\usepackage{lipsum}

\begin{document}

Consider the map~$\Ad_{g_0^2}$.
La la la la la la la la la la la la la la la la la.
And the algebra~$\widetilde{A}$.
\lipsum[1]

Consider the map~\smash{$\Ad_{g_0^2}$}.
La la la la la la la la la la la la la la la la la.
And the algebra~\smash{$\widetilde{A}$}.
\lipsum[1]

\end{document}

Answer 1

Posting a second answer as I got drawn back to this page by a comment ping and I see that there is only a luatex answer when a simpler classic tex answer is possible.

If you set \lineskiplimit=-\maxdimen then tex will preserve baseline with no limit on the amount of overlapping that would cause.

\documentclass{article}
\usepackage{mathtools}
\DeclareMathOperator\Ad{Ad}
\usepackage{lipsum}
\begin{document}
\lineskiplimit=-\maxdimen
Consider the map~$\Ad_{g_0^2}$.
La la la la la la la la la la la la la la la la la.
And the algebra~$\widetilde{A}$.
\lipsum[1]
Consider the map~\smash{$\Ad_{g_0^2}$}.
La la la la la la la la la la la la la la la la la.
And the algebra~\smash{$\widetilde{A}$}.
\lipsum[1]
\end{document}

Answer 2

Here's a luatex version that could be made more robust but after the linebreaking it uses a callback to set the height and depth of boxes and (s) replace any baselineskip or lineskip glue by a fixed value. (Probably it should preserve the height of the first box and the depth of the last, left as an exercise..

\documentclass{article}
\usepackage{mathtools}
\DeclareMathOperator\Ad{Ad}
\directlua{
  function fixlines(h,c)
    local pd=0
    print('code: ' .. type(c) .. ':' .. c)
    for n in node.traverse(h) do
      %
      % smash boxes
      if n.id==0 then
        n.depth=0
        n.height=0
      end
      %
      % lineskip or baselineskip set to 12pt
      if n.id==12 and (n.subtype==1 or n.subtype==2) then
        n.width=786432 % 12pt in sp
      end
    end
    return h
  end
  luatexbase.add_to_callback('post_linebreak_filter', fixlines, 'fix line spacing')
}
\usepackage{lipsum}
\begin{document}
Consider the map~$\Ad_{g_0^2}$.
La la la la la la la la la la la la la la la la la.
And the algebra~$\widetilde{A}$.
\lipsum[1]
Consider the map~\smash{$\Ad_{g_0^2}$}.
La la la la la la la la la la la la la la la la la.
And the algebra~\smash{$\widetilde{A}$}.
\lipsum[1]
\end{document}