What's the difference between split and aligned?

Question

I don't understand the difference between the split and aligned environments introduced by amsmath, so I'm posting this question as a place to collect what subtle details there may be. One thing observable straight off is that split only works with two columns, whereas aligned works with an arbitrary number of columns. But they are similar in other immediately visible ways:

• Both have to be wrapped in another math-introducing environment, like \begin{equation}...\end{equation}
• Both permit only a single \tag{...} for the entire group, not one tag for each line (EDIT: not sure where I got that impression, in fact neither permits any \tag, though aligned's friend gathered does permit a single \tag, as described here)

I searched existing questions on this site about what differences there may be between these environments. I did find this question: Difference between (split, align) and (gather, aligned)?, where---despite the title and phrasing of the question---most of the answers focus just on the difference between the split and aligned environments themselves.

EDIT: Collecting the differences noted so far.

• As one answer to the above question points out, inside equation environments (but not inside gather or align environments), the split and aligned environments have different vertical spacing from the surrounding text.

• As another answer to that question points out, when the body of these environments gets very long, their horizontal placement starts to diverge.

• As Mico noted in comments, section 3.7 of the amsmath User Guide notes that aligned (together with alignedat and gathered) accepts an optional [t] or [b] argument, for explicit vertical placement of any equation tags. split does not accept any such argument.

• As egreg notes in his answer, split will on the other hand honor the tbtags or (default) centertags option to the amsmath package. Whereas aligned and its friends will not.

• As Mico's comments also suggested, but I did not immediately appreciate, split is not supposed to go together with any other typeset material on the same display line. On the other hand, aligned and its friends can be freely combined with other unaligned materials, or even other blocks of aligned and so on. They will be horizontally juxtaposed and vertically centered. I've explained this further in an answer below.

Perhaps that exhausts the differences between split and aligned: though if others know of other differences, please point them out.

Answer 1

One important difference is that split obeys to the centertags (default) or tbtags option. Here is an example

\documentclass[twocolumn]{article}
\usepackage[
%  tbtags,
%  leqno,
]{amsmath}
\begin{document}
\begin{align}
a&=b\\
\begin{split}
c&=d+{}\\
 &=e+{}\\
 &=f
\end{split}\\
g&=h
\end{align}
\end{document}

Now the same with uncommented tbtags:

Now also leqno is uncommented:

To the contrary, aligned will have the equation number according to the vertical alignment option: centered for \begin{aligned}...\end{aligned}, at the top for \begin{aligned}[t]...\end{aligned}, at the bottom for \begin{aligned}[b]...\end{aligned}. Thus it's better to use split whenever possible, if equation numbers are involved. (I rarely use equation numbers, so I usually don't bother.)

Answer 2

Here's another difference I notice. According to the AMS User Guide (p. 6 and p. 29 in the Version 2.0 copy I have):

The split structure should constitute the entire body of the enclosing struc- ture, apart from commands like \label that produce no visible material.

The split environment is designed to serve as the entire body of an equation, or an entire line of an align or gather environment. There cannot be any printed material before or after it within the same enclosing structure:

\begin{equation}
\left\{ % <-- Not allowed
\begin{split}
...
\end{split}
\right. % <-- Not allowed
\end{equation}

However, in my testing (conducted before reading these passages), this constraint seems nowadays often not to be enforced. Here's an example that doesn't work:

\documentclass[]{article}
\usepackage{amssymb,amsmath}
\begin{document}

\begin{equation}
\begin{aligned}
y=0
\end{aligned}
\qquad
\left. \begin{aligned}
B'&=-\partial\times E,\\
E'&=\partial\times B - 4\pi j,
\end{aligned}
\right\}
\qquad \text{Maxwell’s equations}
\qquad
\begin{aligned}
x=0
\end{aligned}
\end{equation}

\begin{equation}
% \begin{split}
% y=0
% \end{split}
% \qquad
\left. \begin{split}
B'&=-\partial\times E,\\
E'&=\partial\times B - 4\pi j,
\end{split}
\right\}
\qquad \text{Maxwell’s equations}
\enspace
\begin{split}
x=0
\end{split}
\end{equation}

\end{document}

which produces:

and in the log we see a related error message:

Package amsmath Warning: Cannot use `split' here; (amsmath) trying to recover with `aligned' on input line 31.

However, if the comments are removed from the previous source, then it typesets fine (and there is no Warning in the log):

The horizontal spacing is just a bit different from that of aligned. I wish I understood better why multiple splits on the same display line works in the second case but not the first. Still, it is clear that the docs say this is not its intended use, and as the first example shows, it can't be expected to perform that use reliably. If you want an aligned block of equations on a line together with additional material (including but not only including other aligned blocks), you're supposed to use aligned and friends (alignedat, gathered).

Answer 3

I was referred here from a search engine. I assume this might still be actively viewed question and might be worth pointing out another difference I found between aligned and split.

I can't confirm this in documentation but split seems to respect binary alignment in a particular column from the surrounding environment align. This may be useful if one wants to give a separate tag to a inner group of expressions. I couldn't get it worked this with aligned.

For instance, in this example, there are two groups of some inner expressions (top and bottom), which received a separate tag and can still respects a mutual alignment in a particular column. It seems very easy to achieve with split

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
  \begin{split}
    a                  &= b \
    cc                 &= dd
  \end{split} \[2ex]
  \begin{split}
    z_{1}              &= a + b + c + d \
    z_{\mathrm{LONGT}} &= x_1 + x_2 + x_3 + x_4 \
    z_{234}            &= a + b + c + d \
    z_{56}             &= a + b + c + d 
  \end{split} \[2ex]
  a                    &= b & c &= d & e &= f \[2ex]
                       &    & \begin{split}
                                z_{1}             &= a + b + c + d \
                                z_{\mathrm{LONG}} &= x_1 + x_2 + x_3 + x_4 \
                                z_{234}           &= a + b + c + d \
                                z_{56}            &= a + b + c + d 
                              \end{split} \[3ex]
                       &    & g &= h &   &
\end{align}
\end{document}