April 11, 2018

• A general remark: the constructs ("environments") discussed below require the use of the amsart style or \usepackage{amsmath} and are of two types:
  1. the align, gather, multline and alignat encironments concern the whole equations, i.e. they replace equation (an exception: align can be used inside gather);
  2. split, aligned, gathered and alignedat are "subsidiary environments": they can only appear inside others, like equation, align or gather, and may embrace only some part of a displayed line.
  Some constructs below require \usepackage{mathtools} or \usepackage{enumitem}.
• A piece of advice: forget eqnarray!

1. One multiline formula

• Quite often one formula (i.e. a sequence of expressions connected by binary operations and relations) takes more than one line. As a rule, one formula (in this sense) should have one number; numbering parts of it separately is seldom necessary. In case of need, you can refer to a specific line of a formula by writing e.g. (1.1)₂.
  
  If equation numbers are placed on the left (as in the amsart style, and also in IMPAN journals), the number is normally on the first line of a multiline formula; if the numbers are on the right, it is on the last line. (Warning: this convention is followed by many publishers, but not all: sometimes the number is centred.)
• If there are no natural places for alignment, use multline: \[ \begin{multline}\label{E:m1} aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa \\ + bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb \\ \leq dddddddddddddddddddddddddddddddddddddd. \end{multline} \]
  latex source

   
  \begin{multline}\label{E:m1}
      aaaaaaaaaaaaaaaaaaaaaaaaaaaa\\
      + bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\
      \leq dddddddddddddddddddddddddd.
  \end{multline}
  
  

  The first line is set (almost) flush left, the last line is (almost) flush right, and the middle lines (if any) are centred.
• You can shove any middle line within multline to the right or to the left by making it the argument of \shoveright or \shoveleft: \[ \begin{multline}\label{E:m2} aaaaaaaaaaaaaaaaaaaaaaaaaaaa\\ \shoveleft{+bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb+dddddddddd}\\ \shoveright{\times eeeeeeeeeeeeeeeeeeeeeeee}\\ \leq dddddddddddddddddddddddddd. \end{multline} \]
  latex source

   
  \begin{multline}\label{E:m2}
      aaaaaaaaaaaaaaaaaaaaaaaaaaaa\\
      \shoveleft{+bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb+dddddddddd}\\
      \shoveright{\times eeeeeeeeeeeeeeeeeeeeeeee}\\
      \leq dddddddddddddddddddddddddd.
  \end{multline}
  
  

• You can align a group of lines within multline, using aligned: \[ \begin{multline}\label{E:m3} aaaaaaaaaaaaaaaaa + xxxxxxxxxxxx\\ \begin{aligned} &< bbbbbbbbbbbbbbbbbbbbbbb\\ &\quad + ddddddddddddddddddddddddddddddddddddd\\ &< ccccccccccccccccccc. \end{aligned} \end{multline} \]
  latex source

   
  \begin{multline}\label{E:m3}
      aaaaaaaaaaaaaaaaa + xxxxxxxxxxxx\\  
      \begin{aligned}
          &< bbbbbbbbbbbbbbbbbbbbbbb\\
          &\quad + ddddddddddddddddddddddddddddddddddddd\\
          &< ccccccccccccccccccc.  
      \end{aligned}
  \end{multline}
  
  

• To code an "object" consisting of centred lines within a formula, use gathered: \[ \begin{equation}\label{E:pasc} \mathrm{Pascal}_{4} = \begin{gathered} 1\\ 1\ 2\ 1\\ 1\ 3\ 3\ 1\\ 1\ 4\ 6\ 4\ 1 \end{gathered} \end{equation} \]
  latex source

   
  \begin{equation}\label{E:pasc}
      \mathrm{Pascal}_{4} =
      \begin{gathered}
          1\\
          1\ 2\ 1\\
          1\ 3\ 3\ 1\\
          1\ 4\ 6\ 4\ 1
      \end{gathered}
  \end{equation}
  
  

  If you want to bottom-align two such objects, apply gathered[b] (then you have to add split to centre the equation number): \[ \begin{equation} \begin{split} \begin{gathered}[b] 1\\ 1\ 2\ 1\\ 1\ 3\ 3\ 1 \end{gathered} \qquad \begin{gathered}[b] 1\\ 1\ 2\ 1\\ 1\ 3\ 3\ 1\\ 1\ 4\ 6\ 4\ 1 \end{gathered} \end{split} \end{equation} \]
  latex source

   
  \begin{equation}
  \begin{split}
      \begin{gathered}[b]
      1\\
      1\ 2\ 1\\
      1\ 3\ 3\ 1
      \end{gathered}
      \qquad
      \begin{gathered}[b]
      1\\
      1\ 2\ 1\\
      1\ 3\ 3\ 1\\
      1\ 4\ 6\ 4\ 1
      \end{gathered}
  \end{split}
  \end{equation}
  
  

  With gathered[t], you get top alignment: \[ \begin{equation*} \begin{gathered}[t] 1\\ 1\ 2\ 1\\ 1\ 3\ 3\ 1 \end{gathered} \qquad \begin{gathered}[t] 1\\ 1\ 2\ 1\\ 1\ 3\ 3\ 1\\ 1\ 4\ 6\ 4\ 1 \end{gathered} \end{equation*} \]
  latex source

   
  \begin{equation*}
      \begin{gathered}[t]
      1\\
      1\ 2\ 1\\
      1\ 3\ 3\ 1
      \end{gathered}
      \qquad
      \begin{gathered}[t]
      1\\
      1\ 2\ 1\\
      1\ 3\ 3\ 1\\
      1\ 4\ 6\ 4\ 1
      \end{gathered}
  \end{equation*}
  
  

• The aligned[t] and aligned[b] constructions enable independent and/or nested alignments, e.g., aligned[t] inside aligned: \[ \begin{equation}\label{E:top} \begin{aligned}[t] A &= xyzt = ztuv + \begin{aligned}[t] [& f_1(a,b,c,d,e,f,g,h),\\ & f_2(a,b,c,d,e,f,g,h),\\ & f_3(a,b,c,d,e,f,g,h)] \end{aligned}\\ &= cccccccccccccc \end{aligned} \end{equation} \]
  latex source

   
  \begin{equation}\label{E:top}
  \begin{aligned}[t]
      A &= xyzt = ztuv + 
          \begin{aligned}[t]           
              [& f_1(a,b,c,d,e,f,g,h),\\
              & f_2(a,b,c,d,e,f,g,h),\\
              & f_3(a,b,c,d,e,f,g,h)]
          \end{aligned}\\
      &= cccccccccccccc
  \end{aligned}
  \end{equation}
  
  

  or aligned[b] inside aligned: \[ \begin{equation*} \begin{aligned} \begin{aligned}[b] xxxxxxx + [& f_1(a,b,c,d,e,f,g,h),\\ & f_2(a,b,c,d,e,f,g,h),\\ & f_3(a,b,c,d,e,f,g,h)] \end{aligned} &= tttttttttttttttttttttttttt\\ &= bbbbbbbbbbbbbb. \end{aligned} \end{equation*} \]
  latex source

   
  \begin{equation*}      
  \begin{aligned}
      \begin{aligned}[b]
          xxxxxxx + [& f_1(a,b,c,d,e,f,g,h),\\
          & f_2(a,b,c,d,e,f,g,h),\\
          & f_3(a,b,c,d,e,f,g,h)]
      \end{aligned} 
      &= tttttttttttttttttttttttttt\\
      &= bbbbbbbbbbbbbb.
  \end{aligned}
  \end{equation*}
  
  

• To move a line within an aligned structure to the left or to the right, use MoveEqLeft with a positive or negative parameter (this requires \usepackage{mathtools}): \[ \begin{equation}\label{E:shove1} \begin{aligned}[t] xxxxx &= yyyyyyyyyyyyyy + [eeee \\ \MoveEqLeft \hspace{12em} \times zzzzzzzzzzzzzzzzzz] \\ &= tttttttttttttttttt \\ &= vvvvvvvvvvv. \end{aligned} \end{equation} \]
  latex source

   
  \begin{equation}\label{E:shove1}
  \begin{aligned}[t]
      xxxxx &= yyyyyyyyyyyyyy + [eeee \\
      \MoveEqLeft[-10] \times zzzzzzzzzzzzzzzzzz] \\
      &= tttttttttttttttttt \\
      &= vvvvvvvvvvv.
  \end{aligned}
  \end{equation}
  
  

  ⚠ Warning: breaks in Mathjax

• If the formulas are left-numbered, you can also label a longer statement as a "formula", by treating it as an item of an itemized list (this requires \usepackage{enumitem}; the "leftmargin" parameter has to be adjusted according to the width of the formula number):

  $\begin{equation}\end{equation}$

  Here you can place any statement, even taking several lines of text and including displayed formulas, like \[ aaaa=bbb. \]

  $\begin{equation}\end{equation}$

  Next item.

  
  
  latex source

   
  \newcommand{\Item}{\refstepcounter{equation}\item}
  \begin{enumerate}[label=(\theequation), ref=\theequation, leftmargin=2.5em]
      \Item\label{E:text4} Here you can place any statement, even taking several 
      lines of text and including displayed formulas, like
      \[
      aaaa=bbb.
      \]
      \Item\label{E:text5} Next item.
  \end{enumerate}
  
  

  ⚠ Warning: breaks in Mathjax

2. Several formulas or sets of displayed equations

• Separate formulas should end with a comma or semicolon—to make it clear that the next line is not a continuation of the preceding one.
• If there are no natural places for vertical alignment, use gather: \[ \begin{gather} aaaaaaaaaa=b, \quad\ cc=xxx, \quad\ dd=yyy, \label{E:g1}\\ mmmmmmmmmmmmm=0 \quad\ \text{for all }i=1,\ldots,n. \label{E:g2} \end{gather} \]
  latex source

   
  \begin{gather}
      aaaaaaaaaa=b,  \quad\  cc=xxx,  \quad\  dd=yyy, \label{E:g1}\\
      mmmmmmmmmmmmm=0  \quad\  \text{for all }i=1,\ldots,n. \label{E:g2}
  \end{gather}
  
  

  Note the spacing between parts of a formula on the same line; you can use \quad (small space), \quad\  (medium space) or \qquad (large space).
• If a formula number is unnecessary, you can "switch it off", using \notag: \[ \begin{gather} aaaaaaaaaa=b, \quad\ cc=xxx, \quad\ dd=yyy, \notag\\ mmmmmmmmmmmmm=0 \quad\ \text{for all }i=1,\ldots,n. \label{E:g3} \end{gather} \]
  latex source

   
  \begin{gather}
      aaaaaaaaaa=b,  \quad\  cc=xxx,  \quad\  dd=yyy, \notag\\
      mmmmmmmmmmmmm=0  \quad\  \text{for all }i=1,\ldots,n. \label{E:g3}
  \end{gather}
  
  

  (A formula number not cited in text is "information noise"; also, the number takes some space and often causes the formula to occupy one line more. As a rule, number only those formulas that are referred to later.)
• If no number is necessary, use gather*: \[ \begin{gather*} aaaaaaaaaa=b, \quad\ cc=xxx, \quad\ dd=yyy,\\ mmmmmmmmmmmmm=0 \quad\ \text{for all }i=1,\ldots,n. \end{gather*} \]
  latex source

   
  \begin{gather*}
      aaaaaaaaaa=b,  \quad\  cc=xxx,  \quad\  dd=yyy,\\
      mmmmmmmmmmmmm=0  \quad\  \text{for all }i=1,\ldots,n.
  \end{gather*}
  
  

• If you need one centred number (for a group of equations), instead of gather use gathered inside equation: \[ \begin{equation}\label{E:g4} \begin{gathered} aaaaaaaaaa=b, \quad\ cc=xxx, \quad\ dd=yyy,\\ mmmmmmmmmmmmm=0 \quad\ \text{for all }i=1,\ldots,n. \end{gathered} \end{equation} \]
  latex source

   
  \begin{equation}\label{E:g4}
  \begin{gathered}
      aaaaaaaaaa=b,  \quad\  cc=xxx,  \quad\  dd=yyy,\\
      mmmmmmmmmmmmm=0  \quad\  \text{for all }i=1,\ldots,n.
  \end{gathered}
  \end{equation}
  
  

• You can also "gather" several "multlines", using the subsidiary construct multlined, available in mathtools, with optional parameters indicating the placement of formula numbers and the width of the formulas: \[ \begin{gather} \begin{multlined}[t][10cm] aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\ +bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\ \shoveright{\times yyyyyyyyyyy}\\ =xxxxxxxxxxxxxxxxxxxxxxxxxxxx, \notag \end{multlined}\label{E:m4}\\ \begin{multlined}[t][10cm] cccccccccccccccccccccccccccccccccccccccc\\ =ddddddddddddddddddddddddddddddddddddddddd. \notag \end{multlined}\label{E:m5} \end{gather} \]
  latex source

   
  \begin{gather}
      \begin{multlined}[t][10cm] 
          aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\
          +bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\
          \shoveright{\times yyyyyyyyyyy}\\
          =xxxxxxxxxxxxxxxxxxxxxxxxxxxx, \notag
      \end{multlined}\label{E:m4}\\
      \begin{multlined}[t][10cm] 
          cccccccccccccccccccccccccccccccccccccccc\\
          =ddddddddddddddddddddddddddddddddddddddddd. \notag
      \end{multlined}\label{E:m5}
  \end{gather}
  
  

• In most cases, however, we want to align something, and then we use align: \[ \begin{align} xxxxx &= yyyyyyyyyyyyyy \label{E:a1}\\ &\quad + zzzzzzzzzzzzzzzzzz, \notag\\ bbb &= tttttttttttttttttt, \label{E:a2}\\ hh &= vvvvvvvvvvv. \label{E:a3} \end{align} \]
  latex source

   
  \begin{align}
      xxxxx &= yyyyyyyyyyyyyy \label{E:a1}\\
            &\quad + zzzzzzzzzzzzzzzzzz, \notag\\
      bbb   &= tttttttttttttttttt, \label{E:a2}\\
      hh    &= vvvvvvvvvvv. \label{E:a3}
  \end{align}
  
  

  Note that the alignment symbols, called ampersands (&), should be placed to the left of binary relation signs; if, as above, part of an expression is continued on the next line, put &\quad before the binary operation sign.
  
  Remember that you cannot place & signs anywhere: the parts between two & signs and between & and \\ should be "separate formulas" (in the $\TeX$ sense), so you cannot e.g. put a & inside { } or inside \left - \right.
• If you need one centred number for a group of aligned equations, use split or aligned inside equation: \[ \begin{equation}\label{E:a4} \begin{split} xxxxx &= yyyyyyyyyyyyyy\\ &\quad + zzzzzzzzzzzzzzzzzz,\\ bbb &= tttttttttttttttttt,\\ hh &= vvvvvvvvvvv. \end{split} \end{equation} \]
  latex source

   
  \begin{equation}\label{E:a4}
  \begin{split}
      xxxxx &= yyyyyyyyyyyyyy\\
            &\quad + zzzzzzzzzzzzzzzzzz,\\
      bbb   &= tttttttttttttttttt,\\
      hh    &= vvvvvvvvvvv.
  \end{split}
  \end{equation}
  
  

• If you have two "split" sets of equations and you want them to have a common alignment, you have to use two split's inside align (this is the advantage of split over aligned): \[ \begin{align} \begin{split} aaaaaaaaaaaaaaaaaaaaaaa &= bbbbbbbbbbbbb,\\ bbbb &= xxxxxx, \end{split}\label{Ea5}\\ \begin{split} ccccc &= yyyyyyy, \phantom{bbbbl}\\ dddddddd &= zzzzz.\label{E:a6} \end{split} \end{align} \]
  latex source

   
  \begin{align}
      \begin{split}
          aaaaaaaaaaaaaaaaaaaaaaa &= bbbbbbbbbbbbb,\\
          bbbb &= xxxxxx,
      \end{split}\label{Ea5}\\
      \begin{split}
          ccccc &= yyyyyyy,\\
          dddddddd &= zzzzz.\label{E:a6}
      \end{split}
  \end{align}
  
  

  ⚠ Warning: breaks in Mathjax

  If you do not want "aligned alignments", use split or aligned inside gather: \[ \begin{gather} \begin{split} & aaaaaaaaaaaaaaaaaaaaaaa = bbbbbbbbbbbbb,\\ & bbbbbbbbbbbbbbbbbbbbbbbb = xxxxxx, \end{split}\label{E:a7}\\ \begin{split} & ccccc = yyyyyyy,\\ & dddddddd = zzzzz. \end{split}\label{E:a8} \end{gather} \]
  latex source

   
  \begin{gather}
      \begin{split}
          & aaaaaaaaaaaaaaaaaaaaaaa = bbbbbbbbbbbbb,\\
          & bbbbbbbbbbbbbbbbbbbbbbbb = xxxxxx,
      \end{split}\label{E:a7}\\
      \begin{split}
          & ccccc = yyyyyyy,\\
          & dddddddd = zzzzz.
      \end{split}\label{E:a8}
  \end{gather}
  
  

• If you need several aligned "columns", you can still use align or align*, but you have to add additional ampersands separating the columns: \[ \begin{align*} aa &= bbbbb, & dd &= ee & &\text{(by Lemma 2),}\\ hh &= ii, & ll &= kkkkkk & &\text{(by \eqref{E:a8}).} \end{align*} \]
  latex source

   
  \begin{align*}
      aa &= bbbbb, & dd &= ee     &  &\text{(by Lemma 2),}\\
      hh &= ii,    & ll &= kkkkkk &  &\text{(by \eqref{E:a8}).}
  \end{align*}
  
  

  However, here you do not control the spacing between the columns. If you want to prescribe it, use alignat (or alignat*), which has a parameter (the number of columns) and requires specifying the intercolumn spaces: \[ \begin{alignat}{3} aa &= bbbbb,\quad\ & dd &= ee & &\text{(by Lemma 2),}\label{E:a9}\\ hh &= ii, & ll &= kkkkkk\quad\ & &\text{(by \eqref{E:a8}).}\label{E:a10} \end{alignat} \]
  latex source

   
  \begin{alignat}{3}
      aa &= bbbbb,\quad\ & dd &= ee           &  &\text{(by Lemma 2),}\label{E:a9}\\
      hh &= ii,          & ll &= kkkkkk\quad\ &  &\text{(by \eqref{E:a8}).}\label{E:a10}
  \end{alignat}
  
  

• alignat also has a subsidiary version, alignedat, which you can put inside equation if you need one centred number: \[ \begin{equation}\label{E:a11} \begin{alignedat}{3} aa &= bbbbb,\quad\ & dd &= ee & &\text{(by Lemma 2),}\\ hh &= ii, & ll &= kkkkkk\quad\ & &\text{(by \eqref{E:a8}).} \end{alignedat} \end{equation} \]
  latex source

   
  \begin{equation}\label{E:a11}
  \begin{alignedat}{3}
      aa &= bbbbb,\quad\ & dd &= ee           &  &\text{(by Lemma 2),}\\
      hh &= ii,          & ll &= kkkkkk\quad\ &  &\text{(by \eqref{E:a8}).}
  \end{alignedat}
  \end{equation}
  
  

• If you want the consecutive equations of a group of equations to be numbered e.g. (2a), (2b) etc., use subequations, inside which you can place the previous constructs, e.g., alignat inside subequations:

  $\begin{equation}\label{E:suba}\end{equation}$

  \[ %\begin{equation}\label{E:suba} \begin{alignat}{3} aa &= bbbbb,\quad\ & dd &= ee & &\text{(by Lemma 2),}\tag{2.18a}\label{E:suba1}\\ hh &= ii, & ll &= kkkkkk\quad\ & &\text{(by \eqref{E:a8}).}\tag{2.18b}\label{E:suba2} \end{alignat} %\end{equation} \]
  latex source

   
  \begin{subequations}\label{E:suba}
  \begin{alignat}{3}
      aa &= bbbbb,\quad\ & dd &= ee           &  &\text{(by Lemma 2),}\label{E:suba1}\\
      hh &= ii,          & ll &= kkkkkk\quad\ &  &\text{(by \eqref{E:a8}).}\label{E:suba2}
  \end{alignat}
  \end{subequations}
  
  

  ⚠ Warning: breaks in Mathjax

  or gather inside subequations:

  $\begin{equation}\label{E:subg}\end{equation}$

  \[ %\begin{subequations}\label{E:subg} \begin{gather} \begin{split} & aaaaaaaaaaaaaaaaaaaaaaa = bbbbbbbbbbbbb,\\ & bbbbbbbbbbbbbbbbbbbbbbbb = xxxxxx, \end{split}\tag{2.19a}\label{E:subg1}\\ \begin{split} & ccccc = yyyyyyy,\\ & dddddddd = zzzzz. \end{split}\tag{2.19b}\label{E:subg2} \end{gather} %\end{subequations} \]
  latex source

  
  \begin{subequations}\label{E:subg}
  \begin{gather}
      \begin{split}
          & aaaaaaaaaaaaaaaaaaaaaaa = bbbbbbbbbbbbb,\\
          & bbbbbbbbbbbbbbbbbbbbbbbb = xxxxxx,
      \end{split}\label{E:subg1}\\
      \begin{split}
          & ccccc = yyyyyyy,\\
          & dddddddd = zzzzz.
      \end{split}\label{E:subg2} 
  \end{gather}
  \end{subequations}
  
  

  ⚠ Warning: breaks in Mathjax

  Note the independent labels of the whole group and its parts; writing \eqref{E:suba}, we invoke the whole system \eqref{E:suba}, while writing \eqref{E:suba1} we refer to \eqref{E:suba1}.
• If you want to place a longer comment in the middle of an aligned construction, you can use \intertext (this only works within align or align*, but not with aligned): \[ \begin{align}\label{E:inter} xxxxx &= yyyyyyyyyyyyyy + [eeee \\ \MoveEqLeft \hspace{11em} \times zzzzzzzzzzzzzzzzzz] \notag \end{align} \] (note that we have not used the full strength of $(H)$ here, but only the concavity of $f$) \[ \begin{align} &= tttttttttttttttttt \phantom{zzzzzzzzzzzzzzzzzz} \notag\\ &= vvvvvvvvvvv. \notag \end{align} \]
  latex source

  
  \begin{align}\label{E:inter}
      xxxxx &= yyyyyyyyyyyyyy + [eeee \\
      \MoveEqLeft[-10] \times zzzzzzzzzzzzzzzzzz] \notag\\
      \intertext{(\emph{note that we have not used the full strength 
          of $(H)$ here, but only the concavity of $f$})}
      &= tttttttttttttttttt \notag\\
      &= vvvvvvvvvvv. \notag
  \end{align}
  
  

  ⚠ Warning: breaks in Mathjax

References

[1] G. Grätzer, More Math into $\LaTeX$, 4th ed., Springer, Berlin, 2007.