Same spacing around "\middle|" as around "\mid"

Question

I need to write some equations that contain something like (A | B).

I could write \left( A \middle| \right), but this changes spacing around external parentheses, as expained in many topics like this.

There is a nice working solution with \DeclarePairedLimiterX as explained in this answer. However, for many reasons I would like to use \middle| and fix the spacing around it (so that it is the same as around \mid), in the same way as \left and \right are fixed in this answer or by the package mleftright (see this answer). In other words, I would like | to stretch like \middle| and to have the same spacing as \mid. Is it possible? I'm using mathtools.

Thank you!

Answer 1

An engine-independent solution (albeit one I still have a murky feeling about...)

\documentclass[12pt]{article}

\let\originalmiddle=\middle
\def\middle#1{\mathrel{}\originalmiddle#1\mathrel{}}

\begin{document}

\[
(A \mid B)
\left(A \middle| B\right)
\left(\frac{A}{B} \middle\Vert C_{(A \mid B) \left( A \middle| B \right)} \right)
\]

\end{document}

Answer 2

You can use some Lua magic.

The three snippets below are one file. They are only split up because Stack Exchange does not support mixed highlighting.

\documentclass{article}
\usepackage{luacode}

\begin{luacode*}

local noad_id = node.id("noad")
local fence_id = node.id("fence")
local inner_subtype = 9 -- see texnodes.w
local middle_subtype = 2 -- see texnodes.w

local function is_vert(delim)
    return delim.small_fam == 2
        and delim.small_char == 106
        and delim.large_fam == 3
        and delim.large_char == 12
end

local kern = node.new("kern",99) -- 99 = math kern
kern.kern = 5 * 2^16 -- 5 pt (TODO: load this value from the font)

local function adjust_mid_spacing(head)
    for n in node.traverse(head) do
        if n and n.nucleus and n.nucleus.head then
            adjust_mid_spacing(n.nucleus.head)
        elseif n.id == fence_id and n.subtype == middle_subtype then
            if is_vert(n.delim) then
                node.insert_before(head,n,node.copy(kern))
                node.insert_after(head,n,node.copy(kern))
            end
        end
    end
    return head
end

luatexbase.add_to_callback("mlist_to_hlist",
                           function(head, display_type, need_penalties)
                               head = adjust_mid_spacing(head)
                               return node.mlist_to_hlist(head, display_type, need_penalties)
                           end,
                           "adjust spacing around mid")  

\end{luacode*}

\begin{document}

$\left( A \middle| B \right)_{\left( A \middle| B \right)_{\left( A \middle| B \right)}}$

$(A \mid B)_{(A \mid B)_{(A \mid B)}}$

\end{document}

Answer 3

luatex allows the mathclass to be specified on delimiters and you want 2 (mathbin) here.

\documentclass{article}

\begin{document}


$\left( A \middle| B \right)$



$\Uleft( A \Umiddle class 2 | B \Uright)$



\end{document}