What is the exact spacing in \begin{gather} environment?

Question

I used to think that \jot is what determines the spacing between rows in gather and align environments.

but setting

\def\jot{0pt}

doesn't remove the spacing completely.

With this MWE I can can specify just the right spacing that I want

\documentclass{article}
\usepackage{amsmath}
\setlength{\fboxsep}{0pt}
\setlength{\fboxrule}{.1pt}
\begin{document}
\renewcommand\arraystretch{0}
[
\begin{array}{c}
\fbox{$a=b$} \[0pt] % exact height between rows
\fbox{$\dfrac22$}
\end{array}
]
\end{document}

---

So my question is what the precise spacing that's used in amsmath environments between rows is? So that I can specify it here \\[...] with array environment in the MWE above to be the same?

Recap:

Everything that I need is a dimension number (like 34.1pt or so), but it must be exact. Eyeballing the spacing isn't acceptable. And the proof based on the source code is required.

Answer 1

Not a completely automatic solution, but to reproduce the distance,

• add a strut of \baselineskip on each row (normally array environment does automatically if \arraystretch is 1, and \baselineskip is equal to \normalbaselineskip; nevertheless we want some adjustment in row distance we will do this manually -- see note below)
• then, the distance is \jot if the lines are "not tall" (in particular if the internal boxes doesn't touch each other), or \jot+\lineskip otherwise.

In this particular case it can be reproduced by:

%! TEX program = lualatex
\documentclass{article}
\usepackage{prettytok}  % ← alternatively comment this out and replace \pretty:x with \tl_show:x. This is just for debug printing
\usepackage{amsmath}
\usepackage{zref-savepos}
\begin{document}
%\def\texta{\dfrac22}
\def\texta{a=b}
\def\textb{\dfrac22}
%\def\textb{a=b}
\begin{gather}
 \texta \zsavepos{a1} \
 \textb \zsavepos{b1}
\end{gather}
[
 \edef\oldlineskip{\the\lineskip}
 \def\arraystretch{0}
 \begin{array}{c}
  \texta \zsavepos{c1} \strut
  \[0pt]\[\dimexpr\jot+\oldlineskip\relax]
  %\[0pt]\[\jot]
  \textb \zsavepos{d1} \strut
 \end{array}
]
\ExplSyntaxOn
\pretty:x{
 \int_eval:n{\zposy{a1} - \zposy{b1}}sp
 =
 \int_eval:n{\zposy{c1} - \zposy{d1}}sp
}
\ExplSyntaxOff
\end{document}

(you need \oldlineskip because \lineskip is set to 0 in array environments. Alternatively just hard code the default value of \lineskip, which is 3pt, in.)

The zref-savepos proves that the vertical length are equal.

Nevertheless if the \textb is a=b instead, the vertical boxes doesn't "touch" each other and you need the second version (\\[\jot]) to get the same spacing.

Note: Struts does not always correctly reproduce TeX's behavior to space the baseline -- for example, I think if in an align environment both rows has height=0 and depth=0.5\baselineskip then the baselineskip will be exactly \baselineskip; nevertheless if the strut is added the height of the row below becomes 0.7\baselineskip and the distance will be something like 1.2\baselineskip+\lineskip instead?

---

---

To determine it automatically... I think there are two ways

• you need to put the content into two boxes, then take the \dp of the row above and the \ht of the row below, add them together and compare with \baselineskip.

• alternatively, use the zref-savepos itself and check if the two lines are \baselineskip apart, in that case add \lineskip.

Example (this may require up to 3 compilation passes however, or maybe 4 in some cases...?)

Make sure you understand what the code does and modify it accordingly. You'll get into trouble if the reference names/auxiliary macro name conflict etc.

%! TEX program = lualatex
\documentclass{article}
\usepackage{prettytok}  % ← alternatively comment this out and replace \pretty:x with \tl_show:x. This is just for debug printing
\usepackage{amsmath}
\usepackage{zref-savepos}
\begin{document}
%\def\texta{\dfrac22}
\def\texta{a=b}
%\def\textb{\dfrac22}
\def\textb{a=b}
\begin{gather}
 \texta \zsavepos{a1} \
 \textb \zsavepos{b1}
\end{gather}
% if this is first run \extradistance will be undefined
\ifx\extradistance\relax
    \gdef\extradistance{0pt}
\fi
% then compute extradistance
\ifdim 
    \dimexpr \zposy{c1}sp - \zposy{d1}sp \relax
    =
    \dimexpr \extradistance+\baselineskip \relax
    % the rows appears to be short, don't need add \lineskip
    \xdef\extradistance{\the\dimexpr\jot\relax}  % \jot is probably not an internal dimen but just in case
\else
    % otherwise, add \lineskip
    \xdef\extradistance{\the\dimexpr\jot+\lineskip\relax}
\fi
\makeatletter
% store the extradistance to aux file
\write@auxout{\gdef\noexpand\extradistance{\extradistance}}
\makeatother
[
    \def\arraystretch{0}
    \begin{array}{c}
        \texta \zsavepos{c1} \strut
        \[0pt]\[\extradistance]
        \textb \zsavepos{d1} \strut
    \end{array}
]
\ExplSyntaxOn
\pretty:x{
 \int_eval:n{\zposy{a1} - \zposy{b1}}sp
 =
 \int_eval:n{\zposy{c1} - \zposy{d1}}sp
}
\pretty:x{
 \dim_to_decimal_in_sp:n {\jot+\baselineskip}sp
}
\ExplSyntaxOff
\end{document}

See also https://tex.stackexchange.com/a/95915/250119.