Equal size underbraces at a lower position

Question

I am writing a markdown document and I want to have underbraces of equal size under each term, like the one here:

I could only do it manually by adding a bunch of empty spaces (\ ) around the terms:

$$
\underbrace{\ \ \ \ X_t \ \ \ \ }_\text{Population at time $t$} =
\underbrace{\alpha \circ X_{t-1}}_\text{Survivors from time $t-1$} +
\underbrace{\ \ \ \ \epsilon_t \ \ \ \ }_\text{Immigration} 
$$

Though, it is not efficient to add spaces manually (and investigating visually whether they end up of equal size), and they do not look nice and need to be lowered a bit.:

How can I fix it?

(Please ignore the mismatch of the circle operators; I have posted it elsewhere.)

Answer 1

You use a \parbox-based approach along the following lines:

\documentclass{article}
\usepackage{amsmath}
\usepackage{newtxtext,newtxmath} % optional - Times Roman text and math fonts
\newlength\mylen
\settowidth\mylen{$\displaystyle\alpha\circ X_{t-1}$} % measure width of widest element
\newcommand\mybox[1]{\parbox{\mylen}{\centering$\displaystyle #1$}}
\begin{document}
\[
\underbrace{\mybox{X_t}}_{\text{Population at time $t$}} =
\underbrace{\mybox{\alpha\circ X_{t-1}}}_{\text{Survivors from time $t-1$}} +
\underbrace{\mybox{P\epsilon_t}}_{\text{Immigration}}
\]
\end{document}

Answer 2

One very ugly way to do it is to cheat with some \vphantom. Please note that you can also insert horizontal spaces with \hspace* instead of a series of backslashes. There is probably a better way to achieve all this but, for a start...

\documentclass{article}
\usepackage{amsmath}
\begin{document}
$$
\underbrace{\vphantom{\Big|} \hspace{5mm} X_t \hspace{5mm}}\text{Population at time $t$} =
\underbrace{\vphantom{\Big|}\alpha \circ X{t-1}}\text{Survivors from time $t-1$} +
\underbrace{\vphantom{\Big|} \hspace{5mm} \epsilon_t \hspace{5mm}}\text{Immigration} 
$$
\end{document}

Answer 3

You can define \ubrace macro and use \def\ubracew{max-width-formula} before each such formula inside math mode.

\def\ubrace#1#2{%
   \setbox0=\hbox{$\displaystyle\ubracew$}%
   \underbrace{\hbox to\wd0{\hss$\displaystyle#1$\lower.8ex\hbox{}\hss}}%
   _{\text{#2}}%
}
$$
\def\ubracew{\alpha\circ X_{t-1}}
\ubrace{X_t}{Population at time $t$} =
\ubrace{\alpha \circ X_{t-1}}{Survivors from time $t-1$} +
\ubrace{\epsilon_t}{Immigration}
$$

Answer 4

eqparbox can help with this via it's \eqmakebox[<tag>][<align>]{<stuff>} macro. All <stuff> with the same <tag> is set in a box that is of maximum width. Additional <align>ment can be specified (left, centre or right) on a per-use basis. Not sure whether this will work in Markdown, as it requires at least two compilations with any change in the maximum width of elements using the same <tag>.

I've added \eqmathbox that translates the definition into a math-friendly environment (since there are different styles of display within math mode). If you don't have an up-to-date LaTeX, you should also include xparse (...or update your LaTeX distribution).

\documentclass{article}
\usepackage{eqparbox,amsmath}
%\usepackage{xparse}% If you have LaTeX2e < 2020-10-01
% https://tex.stackexchange.com/a/34412/5764
\makeatletter
% \eqmathbox[<tag>][<align>]{<math>}
\NewDocumentCommand{\eqmathbox}{o O{c} m}{%
  \IfValueTF{#1}
    {\def\eqmathbox@##1##2{\eqmakebox[#1][#2]{$##1##2$}}}
    {\def\eqmathbox@##1##2{\eqmakebox{$##1##2$}}}
  \mathpalette\eqmathbox@{\vphantom{\Big|} #3} % \vphantom{\Big|} added to push the braces lower
}
\makeatother
\begin{document}
[
  \underbrace{\eqmathbox[Xt]{          X_t         }}\text{Population at time $t$} =
    \underbrace{\eqmathbox[Xt]{\alpha \circ X{t - 1}}}\text{Survivors from time $t - 1$} +
    \underbrace{\eqmathbox[Xt]{      \epsilon_t      }}\text{Immigration} 
]
\end{document}