Como posso preservar o espaçamento vertical em torno de uma equação em uma minipágina?

Question

O exemplo a seguir:

\documentclass{standalone}

\begin{document}
% outer minipages are not part of the test, and just demonstrate the inconsistency
\begin{minipage}[t]{0.5\textwidth}
    
    This is an equation
    \begin{equation}
        x = 1,
    \end{equation}
    which ends in a comma.
    
\end{minipage}%
\begin{minipage}[t]{0.5\textwidth}
    
    This is a minipage equation\par
    \begin{minipage}[t]{\textwidth}
        \begin{equation}
            x = 1,
        \end{equation}
        \par\nointerlineskip\xdef\tpd{\the\prevdepth}
    \end{minipage}%
    \par\prevdepth\tpd\noindent
    which ends in a comma.
    
\end{minipage}%

\end{document}

de onde as prevdepthcoisas são tiradashttps://tex.stackexchange.com/a/34982/41112, renderiza como

Como posso fazer com que a coluna da direita corresponda à da esquerda, sem remover a minipágina? Observe que a linha $x=1$ também está desalinhada, embora apenas ligeiramente.

---

Editar: Acontece que este é um problema XY, e a solução para minha pergunta acima não funciona para um problema real. Aquilo é:

\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}

\begin{document}

This is some text that is long enough to wrap across multiple lines, or at least it ought to be. This gap is too big:\par\nointerlineskip\noindent
\begin{minipage}[t]{.5\textwidth}%
    \begin{subequations}\label{eq:tensor_tensor_tensor_left}%
    \begin{alignat}{2}%
    &
        (M \otimes_{\color{red} R} N) \otimes_{\color{blue} A} (P \otimes_{\color{red} R} Q) \nonumber \\
    \cong_{\color{blue} A} {}&
        ((M \otimes_{\color{red} R} N) \otimes_{\color{blue} A} P) \otimes_{\color{red} R} Q) \label{eq:ttt-left-assoc-1}
    \end{alignat}%
    \end{subequations}%
\end{minipage}%
\begin{minipage}[t]{.5\textwidth}%
    \begin{subequations}\label{eq:tensor_tensor_tensor_right}%
    \begin{alignat}{2}%
    &
        (M \otimes_{\color{red} R} N) \otimes_{\color{blue} A} (P \otimes_{\color{red} R} Q) \nonumber \\
    \cong_{\color{blue} A} {}&
        M \otimes_{\color{red} R} (N \otimes_{\color{blue} A} (P \otimes_{\color{red} R} Q) \label{eq:ttt-right-assoc-1}
    \end{alignat}%
    \end{subequations}%
  \par\xdef\tpd{\the\prevdepth}%
  \vspace*{\belowdisplayskip}\vspace*{-\baselineskip}%
  \end{minipage}\par\prevdepth=\tpd\noindent
and some more unindented text. The gap above is too small. Toegther they add to the right amount.
\begin{alignat}{2}%
&
    (M \otimes_{\color{red} R} N) \otimes_{\color{blue} A} (P \otimes_{\color{red} R} Q) \nonumber \\
\cong_{\color{blue} A} {}&
    M \otimes_{\color{red} R} (N \otimes_{\color{blue} A} (P \otimes_{\color{red} R} Q) \label{eq:ttt-right-assoc-1}
\end{alignat}%
These two gaps are just right, and is a bit bigger than the one above

\end{document}

que dá:

Answer 1

Deixe-me modificar seu exemplo, para que a segunda minipágina externa seja apenas para mostrar o efeito lado a lado com a primeira minipágina. Na segunda minipágina, a primeira linha e a equação estão em uma minipágina e o texto a seguir fica fora.

\documentclass{article}

\begin{document}
% outer minipages are not part of the test, and just demonstrate the inconsistency
\noindent
\begin{minipage}[t]{0.5\textwidth}
  This is an equation
  \begin{equation}
    x = 1,
  \end{equation}
  which ends in a comma.
\end{minipage}%
\begin{minipage}[t]{0.5\textwidth}
  \begin{minipage}[t]{\linewidth}
    This is a minipage equation
        \begin{equation}
            x = 1,
        \end{equation}
  \par\xdef\tpd{\the\prevdepth}%
  \vspace*{\belowdisplayskip}\vspace*{-\baselineskip}
  \end{minipage}\par\prevdepth=\tpd
   which ends in a comma.
\end{minipage}

\end{document}

No entanto, isso poderia falhar de várias maneiras, porque o salto após a equação poderia ser \belowdisplayshortskipe seria necessária uma rotina bastante complexa para verificá-lo.

---

Sobre arealproblema, sugiro administrar de acordo com as linhas dehttps://tex.stackexchange.com/a/550010/4427

Prefiro .\mathcolor{red}{R}​\color{red} R

\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}

\newcommand{\sidebysidesubequations}[5][0.5]{%
  $$% Yes! We're consciously doing it
  \begin{minipage}{#1\displaywidth}%
  \setlength{\abovedisplayskip}{0pt}%
  \begin{subequations}\label{#2}
  \noindent#3
  \end{subequations}
  \end{minipage}
  \begin{minipage}{\dimeval{\displaywidth-#1\displaywidth}}
  \setlength{\abovedisplayskip}{0pt}%
  \begin{subequations}\label{#4}
  \noindent#5
  \end{subequations}
  \end{minipage}
  $$%
}

\begin{document}

This is some text that is long enough to wrap across multiple lines, or 
at least it ought to be.
\sidebysidesubequations{eq:tensor_tensor_tensor_left}{
  \begin{align}
    & (M \otimes_{\mathcolor{red}{R}} N)
    \otimes_{\mathcolor{blue}{A}}
    (P \otimes_{\mathcolor{red}{R}} Q) \nonumber \\
  \cong_{\mathcolor{blue}{A}} {}&
    M \otimes_{\mathcolor{red}{R}}
    (N \otimes_{\mathcolor{blue}{A}} (P \otimes_{\mathcolor{red}{R}} Q) \label{eq:ttt-left-assoc-1}
 \\
    & (M \otimes_{\mathcolor{red}{R}} N)
    \otimes_{\mathcolor{blue}{A}}
    (P \otimes_{\mathcolor{red}{R}} Q) \nonumber \\
  \cong_{\mathcolor{blue}{A}} {}&
    M \otimes_{\mathcolor{red}{R}}
    (N \otimes_{\mathcolor{blue}{A}} (P \otimes_{\mathcolor{red}{R}} Q) \label{foo1}
  \end{align}
}{eq:tensor_tensor_tensor_right}{
  \begin{align}
    & (M \otimes_{\mathcolor{red}{R}} N)
    \otimes_{\mathcolor{blue}{A}} (P \otimes_{\mathcolor{red}{R}} Q) \nonumber \\
  \cong_{\mathcolor{blue}{A}} {}&
      M \otimes_{\mathcolor{red}{R}}
  (N \otimes_{\mathcolor{blue}{A}} (P \otimes_{\mathcolor{red}{R}} Q) \label{eq:ttt-right-assoc-1}
  \\
    & (M \otimes_{\mathcolor{red}{R}} N)
    \otimes_{\mathcolor{blue}{A}} (P \otimes_{\mathcolor{red}{R}} Q) \nonumber \\
  \cong_{\mathcolor{blue}{A}} {}&
      M \otimes_{\mathcolor{red}{R}}
  (N \otimes_{\mathcolor{blue}{A}} (P \otimes_{\mathcolor{red}{R}} Q) \label{foo2}
  \end{align}
}
and some more unindented text
and some more unindented text
and some more unindented text
and some more unindented text.
\begin{align}
  & (M \otimes_{\mathcolor{red}{R}} N)
    \otimes_{\mathcolor{blue}{A}} (P \otimes_{\mathcolor{red}{R}} Q) \nonumber \\
  \cong_{\mathcolor{blue}{A}} {}&
    M \otimes_{\mathcolor{red}{R}}
    (N \otimes_{\mathcolor{blue}{A}}
    (P \otimes_{\mathcolor{red}{R}} Q) \label{eq:ttt-right-assoc-2}
  \end{align}
These two gaps are just right, and is a bit bigger than the one above

\end{document}