When to use which alignment environment?

Question

There seem to be a whopping align, aligned, alignedat, alignat, xalignat, xxalignat and falign in amsmath / mathtools - some also in there starred version.

I just find sloppy statements like:

• "The advantage of aligned is the much better horizontal and vertical spacing.", p.52

• "Similar to align, to be used inside another mathematics environment."

When do I use which align environment (best practice)?

What are the exact differences between them?

Why does the environment exist at all (example use case, if applicable)?

Which should I avoid and why?

In particular, what are the differences between

• align and xalignat
• xxalignat and flalign*
• alignat* and alignedat

and what is the semantic difference / different use-case between align* and aligned? When do I use which?

It appears to me as if align is intended to be used to print independent columns whereas alignat is intended to align dependent columns (e.g. equations [rows] aligned by their operators [columns]).

Thanks a lot!

---

Appendix

Source:

\documentclass{scrartcl}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathtools,onlyamsmath}

\newlength{\Short}
\newlength{\LShort}
\newlength{\Long}
\setlength{\Short}{.05\columnwidth}
\setlength{\LShort}{.08\columnwidth}

\newcommand{\env}[2][]{\begin{#2}#1
    \framebox[\Short]{} &= \framebox[\LShort]{} & \framebox[\LShort]{} &= \framebox[\LShort]{} & \framebox[\LShort]{} &= \framebox[\LShort]{}\\
    \framebox[\Short]{} &= \framebox[\Short]{}  & \framebox[\Short]{}  &= \framebox[\Short]{}  & \framebox[\Short]{}  &= \framebox[\Short]{}
\end{#2}}

\newcommand{\Align}[2][]{\paragraph{#2}\env[#1]{#2}}
\newcommand{\mAlign}[2][]{\paragraph{#2}\[\env[#1]{#2}\]}


\begin{document}

\thispagestyle{empty}
\enlargethispage{\baselineskip}

\Align{align*}
\Align{align}

\Align[{3}]{alignat*}
\Align[{3}]{alignat}

\mAlign{aligned}

\mAlign[{3}]{alignedat}

\Align[{3}]{xalignat}
\Align[{3}]{xxalignat}

\Align{flalign*}
\Align{flalign}

\newpage

\Align{align}
\Align[{3}]{xalignat}

\Align[{3}]{xxalignat}
\Align{flalign*}

\Align[{3}]{alignat*}
\mAlign[{3}]{alignedat}

\Align{align*}
\mAlign{aligned}

\end{document}

Answer 1

amsmath is derived from AMSTeX (amstex.tex) which does not have * forms but otherwise has mostly similar naming, including the x- variants. The environments that start math displays are documented in amsmath.pdf as

%    \begin{environment}{align}
%    \begin{environment}{align*}
%    \begin{environment}{flalign}
%    \begin{environment}{flalign*}
%    \begin{environment}{alignat}
%    \begin{environment}{alignat*}
%    \begin{environment}{xalignat}
%    \begin{environment}{xalignat*}
%    \begin{environment}{xxalignat}
%    The definitions of the various \env{align} environments are quite
%    straight-forward.
%
%    \begin{macrocode}
\newenvironment{alignat}{%
  \start@align\z@\st@rredfalse
}{%
  \endalign
}
\newenvironment{alignat*}{%
  \start@align\z@\st@rredtrue
}{%
  \endalign
}
\newenvironment{xalignat}{%
  \start@align\@ne\st@rredfalse
}{%
  \endalign
}
\newenvironment{xalignat*}{%
  \start@align\@ne\st@rredtrue
}{%
  \endalign
}
\newenvironment{xxalignat}{%
  \start@align\tw@\st@rredtrue
}{%
  \endalign
}
\newenvironment{align}{%
  \start@align\@ne\st@rredfalse\m@ne
}{%
  \math@cr \black@\totwidth@
  \egroup
  \ifingather@
    \restorealignstate@
    \egroup
    \nonumber
    \ifnum0=`{\fi\iffalse}\fi
  \else
    $$%
  \fi
  \ignorespacesafterend
}
\newenvironment{align*}{%
  \start@align\@ne\st@rredtrue\m@ne
}{%
  \endalign
}
\newenvironment{flalign}{%
  \start@align\tw@\st@rredfalse\m@ne
}{%
  \endalign
}
\newenvironment{flalign*}{%
  \start@align\tw@\st@rredtrue\m@ne
}{%
  \endalign
}

Where you can see they are all variants of the same underlying code.

Comparing, say xalignat* and align* You see

\start@align\@ne\st@rredtrue
\start@align\@ne\st@rredtrue\m@ne

so align* is just \xalignat* except -1 is supplied as the number of column pairs, which makes the environment not require a {3} argument for 3 column pairs in your example, it just does the right thing. As such, the x... versions are not really needed and are not documented at all in the user level amslguide.pdf documentation.

As documented, the -ed named environments do not start a math display and must be started within an outer math environment. They have more in common with array or matrix, except that they set their entries with left and right, rather than centred, alignment and use displaystyle rather than textstyle.