long explanation in align environment; would like to split over two lines

Question

I have an align environment as follows:

\documentclass{article}
\usepackage{amsmath}
\newcommand\compose{\circ}
\newcommand\bd{\mathbf{d}}

\begin{document}
\begin{align*}
\sum_i [\int_M (\phi_i f)\,\bd V] &= \sum_i [\int_A (\phi_i\compose \alpha)(f\compose\alpha)V(D\alpha)] && \text{by definition} \\
&= \int_A [\sum_i (\phi_i\compose \alpha)(f\compose\alpha)V(D\alpha)] &&  \text{because the sum converges uniformly on compact subsets of $A$} \\
&= \int_A [\sum_i (f\compose\alpha)V(D\alpha)] && \text{because $\sum_i (\phi_i\compose\alpha)=1$ on $A$} \\
&= \int_M f\,\bd V && \text{by definition.}
\end{align*}
\end{document}

The second explanation is too long. I would like to split it over two lines. If I make a whole new line in the align environment it looks terrible:

What's the best way to do this well? A minipage? How would I deal with the fact that align chooses widths itself whereas I need to provide a fixed width for minipage?

Answer 1

What do you think of this? (I made a few more edits to the code. Some comments explain the rationale, or give appropriate credits.)

\documentclass{article}
\usepackage{amsmath}
\newcommand*\compose{\circ}
\newcommand*{\diff}{\mathop{}\!\mathbf{d}} % Thanks to Heiko Oberdiek

\begin{document}
\begin{align*}
    \sum_i \biggl[\int_M (\phi_i f)\diff V\biggr]
        &= \sum_i \biggl[\int_A
            (\phi_i\compose\alpha)(f\compose\alpha)V(D\alpha)\biggr]
            && \mbox{by definition} \\
            % \mbox, for consistency.  Here I do not think it is wrong (see 
            % below), and it avoids the recourse to \mathchoice, which is 
            % relatively cumbersome since it typesets the argument four times 
            % (but who cares of such things nowadays?).
        &= \int_A \biggl[\sum_i
            (\phi_i\compose \alpha)(f\compose\alpha)V(D\alpha)\biggr]
            && \parbox[t]{10pc}{because the sum converges uniformly
                on compact subsets of~$A$\strut} \\ % please note the \strut
        &= \int_A \biggl[\sum_i (f\compose\alpha)V(D\alpha)\biggr]
            && \mbox{because $\sum_i (\phi_i\compose\alpha)=1$ on $A$} \\
            % Note the \textstyle \sum, automatic since \mbox does not patch 
            % \everymath as \text does.
        &= \int_M f\diff V
            && \mbox{by definition.}
\end{align*}
\end{document}

This is the output:

Answer 2

Something like this?

just put equation description in tabular environment:

\documentclass{article}
\usepackage{amsmath}
\newcommand\compose{\circ}
\newcommand\bd{\mathbf{d}}

    \begin{document}
\begin{align*}
\sum_i [\int_M (\phi_i f)\,\bd V]
    &= \sum_i [\int_A (\phi_i\compose \alpha)(f\compose\alpha)V(D\alpha)]
        && \text{by definition} \\
    &= \int_A [\sum_i (\phi_i\compose \alpha)(f\compose\alpha)V(D\alpha)]
        &&  \begin{tabular}[t]{@{}l}
            because the sum converges uniformly\\
            on compact subsets of $A$
            \end{tabular}\\
&= \int_A [\sum_i (f\compose\alpha)V(D\alpha)] && \text{because $\sum_i (\phi_i\compose\alpha)=1$ on $A$} \\
&= \int_M f\,\bd V && \text{by definition.}
\end{align*}
    \end{document}

Edit: As @egreg say, spurious space before description you can eliminate with \begin{tabular}[t]{@{}l}.

Answer 3

A tabular can be used, for example:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mleftright}
\newcommand\compose{\circ}
\newcommand*{\diff}{\mathop{}\!\mathbf{d}}

\begin{document}
\begin{align*}
\sum_i \mleft[\int_M (\phi_i f)\diff V\mright]
  &= \sum_i \mleft[\int_A (\phi_i\compose \alpha)
     (f\compose\alpha)V(D\alpha)\mright]
  && \text{by definition} \\
  &= \int_A \Bigl[\sum_i (\phi_i\compose \alpha)
     (f\compose\alpha)V(D\alpha)\Bigr]
  && \text{\begin{tabular}{@{}l@{}}
    because the sum\\
    converges uniformly on\\
    compact subsets of $A$\end{tabular}} \\
  &= \int_A \Bigl[\sum_i
     (f\compose\alpha)V(D\alpha)\Bigr]
  && \text{\begin{tabular}{@{}l@{}}
    because\\ $\textstyle\sum_i (\phi_i\compose\alpha)=1$
    on $A$\end{tabular}} \\
  &= \int_M f\diff V && \text{by definition.}
\end{align*}
\end{document}

Remarks:

• The square brackets are enlarged via the \left and \right feature. Actually package mleftright with \mleft and \mright provides a version of \left and \right that avoids additional horizontal space.

• The square brackets in the second and third line are enlarged with \Bigl and \Bigr to avoid too large brackets, which would also cover the subscript.

• Macro \diff is defined instead of \bd. The definition with the starting \mathop{} here avoids the manual setting of \, before.

• The sum symbol in the explanation is set in \textstyle instead of \displaystyle, because it is part of the text and not of the displayed equation. This form fits better into text lines.