breqn: dgroup environment not aligning properly

Question

I'm trying to align a set of equations at the equal signs, with one of them breaking. This is the MWE.

\documentclass{article}
\usepackage{amsmath,mathtools,breqn}
\usepackage{amssymb}
\begin{document}
\begin{dgroup}
    \begin{dmath}
        (A \times B) \cup (B \times A)= {(1,3),(1,4),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3)},
    \end{dmath}
    \begin{dmath}
        (A \times B) \cap (B \times A)= {(3,3)},
    \end{dmath}
    \begin{dmath}
        (A \times B) \smallsetminus (B \times A)= {(1,3),(1,4),(2,3),(2,4),(3,4)}.
    \end{dmath}
\end{dgroup}
\end{document}

The first equation should break somewhere in the middle of the set. However, dgroup* breaks it at the equal sign, completely ruining its alignment. I suspect it's because breqn doesn't like breaking lines at commas; I tried following this solution to a related question but it didn't work.

score 0 · Accepted Answer · answered Sep 30 '20 at 15:43

breqn has some heuristics for breaking at some places. It will never break at commas, because it cannot distinguish between the two commas in (1,3),: the first comma must not be used for a break, while in your case the second one might be used.

Since breqn, as well as LaTeX, doesn't really know mathematics, breaking such a display has to be done by somebody who knows.

You can set a break point manually, though. Compare the following two displays and decide which style to adopt.

\documentclass{article}
\usepackage{amsmath,mathtools}
\usepackage{breqn}
\usepackage{amssymb}
\begin{document}
\begin{dgroup}
    \begin{dmath}
        (A \times B) \cup (B \times A)=
        {(1,3),(1,4),(2,3),(2,4),\penalty0
        (3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3)},
    \end{dmath}
    \begin{dmath}
        (A \times B) \cap (B \times A)= {(3,3)},
    \end{dmath}
    \begin{dmath}
        (A \times B) \smallsetminus (B \times A)= {(1,3),(1,4),(2,3),(2,4),(3,4)}.
    \end{dmath}
\end{dgroup}
\begin{align}
(A \times B) \cup (B \times A) &= {
  \begin{aligned}[t]
  &(1,3),(1,4),(2,3),(2,4),\
  &(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3)},
  \end{aligned}
\
(A \times B) \cap (B \times A) &= {(3,3)},
\
(A \times B) \smallsetminus (B \times A) &= {(1,3),(1,4),(2,3),(2,4),(3,4)}.
\end{align}
\end{document}

breqn: dgroup environment not aligning properly

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