Aligned equations with comments/explanations

Question

In many cases I want to write some aligned equation that goes through multiple lines and add a comment for some of the lines (I think if the comments are short enough then it's clearer than explaining everything at the end of the equation). Ideally, all the comments should start on the same vertical line. This is achieved by what's shown in the following example:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
    This is just some text to show where the margin is. Some more and more text yay text is good.
    \begin{align*}
    a + b + c + d + e &= an-expression \\
    &= some-very-longgggggggggg-expression && \text{comment} \\
    &= another-expression && \text{a little longer comment} \\
    &= 0
    \end{align*}
\end{document}

The problem is when some of the equation's lines are too long:

The second comment is inside the right margin, which should not be allowed.

I know it happens because the align environment creates a table and each & sign adds a column, so the second comment cannot be on a different column than the first comment (which is pushed by the equation on its row).

But still, what I would like to happen is that the second comment would end by the right margin. Is there a simple way to achieve that? If possible, I would prefer to not define too complicated commands, even if it means I'll not get exactly what I asked for, but something else that kinda solves the problem.

Answer 1

You cannot have all the comments vertically aligned at their left margin, because the wide equation and the wide comment simply don't fit the line.

You can save space by setting the first term on a line by itself and still have the look of a display, avoiding to go to the left margin:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

This is just some text to show where the margin is.
Some more and more text yay text is good.
This is just some text to show where the margin is.
Some more and more text yay text is good.
\begin{align*}
\lefteqn{a + b + c + d + e}\quad \\
&= an-expression \\
&= some-very-longgggggggggg-expression && \text{comment} \\
&= another-expression && \text{a little longer comment} \\
&= 0
\end{align*}

\end{document}

With \lefteqn you hide the width of the term; I added \quad in order not to have the=` signs at the left margin and it turns out that still a tad of space is available.

Another possibility you can explore, but this depends on the actual equations and comments, is breaking the long comment across lines.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

This is just some text to show where the margin is. 
Some more and more text yay text is good.
This is just some text to show where the margin is. 
Some more and more text yay text is good.
\begin{align*}
a + b + c + d + e
&= an-expression \\
&= some-very-longgggggggggg-expression && \text{comment} \\
&= another-expression && \begin{tabular}[t]{@{}l@{}}
                         a little \\
                         longer \\
                         comment
                         \end{tabular} \\
&= 0
\end{align*}

\end{document}

Answer 2

Well, the following is a very simple trick that “kinda solves the problem”:

% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly 
                                 % declare the paper format.

\usepackage[T1]{fontenc}         % Not always necessary, but recommended.
% End of standard header.  What follows pertains to the problem at hand.

\usepackage{amsmath}



\begin{document}

% \slshape % if uncommented, will the reference to the Magic Theorem be slanted?

Some text before the equation, to show where the right margin lies.  Oh, no, 
that was not enough: \emph{now} it is enough!
\begin{flalign*}
    \textit{formula\_result} &= \textit{short\_term} \\
        &= \textit{muuuuch\_loooonger\_term} + \textit{another\_one}
                && \text{by \ldots} && \\
        &= x-x
                && && \makebox[0pt][r]{by the Magic Theorem} \\
        &= 0
\end{flalign*}
Some text after the equation, to show again the position of the right margin of
the text block.

\end{document}

This is the output I get (on a TeXLive 2016, sorry, but that’s what I’ve got at the moment):

Addition: An even simpler solution using \hidewidth, which, however, does not yield exactly the same printout as the previous one:

% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly 
                                 % declare the paper format.

\usepackage[T1]{fontenc}         % Not always necessary, but recommended.
% End of standard header.  What follows pertains to the problem at hand.

\usepackage{amsmath}



\begin{document}

Some text before the equation, to show where the right margin lies.  Oh, no, 
that was not enough: \emph{now} it is enough!
\begin{flalign*}
    \textit{formula\_result} &= \textit{short\_term} \\
        &= \textit{muuuuch\_loooonger\_term} + \textit{another\_one}
                & \text{by \ldots} & \\
        &= x-x
                & \hidewidth\text{by the Magic Theorem} & \\
        &= 0
\end{flalign*}
Some text after the equation, to show again the position of the right margin of
the text block.

\end{document}

Indeed, IMHO the output is actually better, with both explanations aligned along the right margin:

Second addition: If you object to using plain TeX commands like \hidewidth, you can replace the second example with the following code

% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly 
                                 % declare the paper format.

\usepackage[T1]{fontenc}         % Not always necessary, but recommended.
% End of standard header.  What follows pertains to the problem at hand.

\usepackage{amsmath}



\begin{document}

% \slshape

Some text before the equation, to show where the right margin lies.  Oh, no, 
that was not enough: \emph{now} it is enough!
\begin{flalign*}
    \textit{formula\_result} &= \textit{short\_term} \\
        &= \textit{muuuuch\_loooonger\_term} + \textit{another\_one}
                & \text{by \ldots} & \\
        &= x-x
                & \makebox[0pt][r]{by the Magic Theorem} & \\
        &= 0
\end{flalign*}
Some text after the equation, to show again the position of the right margin of
the text block.

\end{document}

with no change in the output.

Answer 3

Googling \lefteqn from egreg's answer I found this answer which is about \MoveEqLeft - a command from mathtools (see 3.4.4 here). So the example becomes:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}

\begin{document}
    This is just some text to show where the margin is. Some more and more text yay text is good.
    \begin{align*}
    \MoveEqLeft[1] a + b + c + d + e \\
    &= an-expression \\
    &= some-very-longgggggggggg-expression && \text{comment} \\
    &= another-expression && \text{a little longer comment} \\
    &= 0
    \end{align*}
\end{document}

Which yields the following output (same as egreg's):

I think this solution is a bit better than using \lefteqn since \MoveEqLeft was made specifically to solve this problem (according to the documentation).

Answer 4

Here are two possibilities, with the flalign* environment, and \mathrlap from mathtools, or with a simple align* and the fleqn environment from nccmath:

\documentclass{article}
\usepackage{mathtools, nccmath}
\usepackage{showframe}
 \renewcommand{\ShowFrameLinethickness}{0.3pt}

\begin{document}

    This is just some text to show where the margin is. Some more and more text yay text is good.
    \begin{flalign*}
   \mathrlap{ a + b + c + d + e} \\
    &= an-expression \\
    &= some-very-longgggggggggg-expression && \text{comment} \\
    &= another-expression && \text{a little longer comment} \\
    &= 0
    \end{flalign*}
Some other text and another possibility:
\begin{fleqn}
    \begin{align*}
    a + b &+ c + d + e\\
    &= an-expression \\
    &= some-very-longgggggggggg-expression && \text{comment} \\
    &= another-expression && \text{a little longer comment} \\
    &= 0
    \end{align*}
\end{fleqn}

\end{document}