How to align a set of multiline equations

Question

I am trying to align a set of long equations, that are themselves align environments as most of them are spreading on multiple lines.

Currently I just have a sequence of align environments, with each equation inside in order to align the pieces of each equations. I am attaching a screenshot of the result:

What would like to get instead is something looking more like

which is the same set of equations after going through the copyediting office of a journal and looks much better.

Here is a MWE. I would like all three equations to align on the equal sign.

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{align}
a & =  b + c + d \nonumber \\
  & \qquad + e + f + g
\label{eq:1}
\end{align}
\begin{align}
k & = l + m + n + m + n + m + n \nonumber \\
  & \qquad + o + p + q
\label{eq:2}
\end{align}
\begin{equation}
r = s + t (u + v + w)
\label{eq:3}
\end{equation}
\end{document}

Answer 1

without an actual example, here's how i interpret what you want.

and here is the input:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
This example shows \verb|aligned| equations within
an \verb|align| environment.
\begin{align}
  \phantom{i + j + k}
  &\begin{aligned}
    \mathllap{a} &= b + c + d\\
      &\qquad + e + f + g + x + y + z
  \end{aligned}\\
  &\begin{aligned}
    \mathllap{i + j + k} &= l + m + n\\
      &\qquad + o + p + q
  \end{aligned}
\end{align}
\end{document}

the longest left-hand element is inserted at the beginning as a \phantom and the lengths of the left-hand elements of the individual aligned segments are made "invisible" by lapping them to the left using \mathllap from the mathtools package.

the original answer was (correctly) noted to align the segments properly only when the left-hand sides had the same length. this modification overcomes that problem.

Answer 2

You can also use the split environment inside the align environment, using an ampersand (&) where you want the alignment to take place. Here is a MWE:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{align}
\begin{split}\label{eq:1}
    a ={}& b + c + d\\
         & + e + f + g
\end{split}\\
\begin{split}\label{eq:2}
    k ={}& l + m + n + m + n + m + n\\
         & + o + p + q
\end{split}\\
    r ={}& s + t (u + v + w)\label{eq:3}
\end{align}
\end{document}

Notice that the last equation is not inside a split environment, but still aligns with the rest, since it's still inside the align environment.

The output looks like this:

Note the empty groups ({}) before the ampersands. Without these, there would be no kerning applied between the equals signs and the character afterwards, because the alignment breaks the box. While the empty groups don't do anything themselves, in math mode the symbols before them add kerning as though the empty groups were ordinary characters. This enables TeX to choose the most appropriate spacing. If the ampersands were placed before the equal signs, the align environment would kern around the equal signs as it should with no such hassle, but then the addition sign of the split equation would lie uncomfortably far back, requiring some sort of manual tweaking of its own.

Answer 3

As an extension to barbara's answer, you could wrap only the right-hand side of your equations into aligned subenvironments. This allows you to align the equal signs of the separate equations independent of the size of left- or right-hand sides.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
This example shows \verb|aligned| equations within
an \verb|align| environment.
\begin{align}
  a &= \begin{aligned}[t]
      &b + c + d +\\
      &c + e + f + g + h + i
       \end{aligned}\\
  k &= \begin{aligned}[t]
      &l + m + n\\
      &+ o + p + q
       \end{aligned}
\end{align}
\end{document}

The plus sign on the second line of the second equation does not exactly match up because it's a mathbin symbol. Maybe someone with more TeX knowledge could comment on how to best fix that.

Answer 4

Here is an align-only version of your equations:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\newcommand{\myvec}[1]{\hat{\mathbf{#1}}}% Vector notation
\begin{document}
\begin{align}
  f_{\textit{P},\textit{P}}\left(\myvec{n};\myvec{m}\right) &= \frac{\omega^2}{4\pi\rho\alpha^4} \textit{AF}\left(k_\alpha\left(\myvec{n}-\myvec{m}\right)\right) \nonumber \\
    &\mathrel{\phantom{=}} \times\left\{\left(\lambda+\mu\right)^2\eta_N+\left(\lambda+\mu\right)\mu\eta_N\left(\cos 2\phi+\cos 2\theta\right)\right. \nonumber \\
    &\mathrel{\phantom{=}} \left.\kern-\nulldelimiterspace +\;\mu^2\eta_N\cos 2\phi\cos 2\theta+\mu^2\eta_T\sin 2\phi\sin 2\theta\cos\varphi\vphantom{\left(\lambda\right)^2}\right\}, \\
  f_{\textit{P},\textit{SH}}\left(\myvec{n};\myvec{m},\myvec{q}\right) &= \frac{\omega^2}{4\pi\rho\alpha\beta^3} \textit{AF}\left(k_\alpha\myvec{n}-k_\beta\myvec{m}\right) \nonumber \\
    &\mathrel{\phantom{=}} \times\left(-\mu^2\eta_T\right)\sin 2\phi\cos\theta\sin\varphi, \\
  f_{\textit{P},\textit{SV}}\left(\myvec{n};\myvec{m},\myvec{q}\right) &= \frac{\omega^2}{4\pi\rho\alpha\beta^3} \textit{AF}\left(k_\alpha\myvec{n}-k_\beta\myvec{m}\right) \nonumber \\
    &\mathrel{\phantom{=}} \times\left\{\left(\lambda+\mu\right)\mu\eta_N\sin 2\theta+\mu^2\eta_N\cos 2\phi\sin 2\theta\right. \nonumber \\
    &\mathrel{\phantom{=}} \left.\kern-\nulldelimiterspace -\;\mu^2\eta_T\sin 2\phi\cos 2\theta\cos\varphi\right\},
\end{align}
\end{document}
​

Some of the adjustments include

• Using \mathrel for proper spacing around hidden = (included via \phantom);
• Some negative \nulldelimiter kerning around missing \left. delimiters (otherwise there would be additional spacing introduced between operator/operand);
• Height adjustment for multi-line \left\{ and \right\} pairs.

As a common thread, it may be useful to peruse Herbert Voß' mathmode document.

Answer 5

This is a way to accomplish this for small amounts of text by using the \intertext command.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
This example shows \verb|aligned| equations within
an \verb|align| environment.
\begin{align}
  \begin{aligned}
a &= b + c + d\\
  &\qquad + e + f + g
  \end{aligned}\\
  \begin{aligned}
k &= l + m + n + m + n + m + n\\
  &\qquad + o + p + q
  \end{aligned}
\end{align}

This example shows text and  equations within
an \verb|align| environment.
\begin{align}
a &= b + c + d\\
  &\qquad + e + f + g
\intertext{A small amount of text can go here with $x=2$ inline math
 and     $$\int_a^b f(x)\,dx=F(b)-F(a)$$ (even inline math). But not a lot 
of text. }
k &= l + m + n + m + n + m + n\\
  &\qquad + o + p + q
\end{align}

\end{document}

Answer 6

If instead of aligning the trailing equations you wish to right-justify them (similarly to the way the \multiline environment handles trailing equations), you can use the following trick, which I picked up from this answer by Ulrike Fischer.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
a & = b + c + d + e + f + g + h \nonumber \\
  & \hspace{7cm} + i + j + k \\
a & = b + c + d + e + f + g + h \nonumber \\
  & \omit\hfill ${} + i + j + k$
\end{align}
\end{document}

Answer 7

This answer works when you use the fleqn package. The example below defines two LaTeX macros \mymidline and \mylastline. Both macros essentially expand to their first argument within align* environments. The \mymidline macro centers it and the \mylastline macro right-aligns it. Thereby, the width of the stuff in the second argument is subtracted from the available "display width". For align* environments that should just be the (longest) left-hand side of the equation. The example below shows how you can do that most efficiently with a macro \LHS.

\documentclass{article}
\usepackage[DIV15]{typearea}
\usepackage{amsmath,amsfonts}
\usepackage{fleqn}
\usepackage{ulem}
\makeatletter
\newdimen\@tzadima
\newdimen\@tzadimb
\newbox\@tzaboxa
\def\mylinemeasures#1#2{%
  \@tzadima\displaywidth%
  \advance\@tzadima-\tagwidth@%
  \advance\@tzadima-\alignsep@%
  \setbox\@tzaboxa\hbox{$\displaystyle#1$}%
  \@tzadimb\wd\@tzaboxa%
  \advance\@tzadima-\@tzadimb%
  \setbox\@tzaboxa\hbox{$\displaystyle#2$}%
  \@tzadimb\wd\@tzaboxa%
  \advance\@tzadima-\@tzadimb%
}
\def\mymidline#1#2{%
  \mylinemeasures{#1}{#2}%
  \divide\@tzadima2%
  \hbox to \@tzadima{}#1\notag
}
\def\mylastline#1#2{%
  \mylinemeasures{#1}{#2}%
  \hbox to \@tzadima{}#1%
}
\makeatother
\begin{document}
\begin{align*}
  \gdef\LHS{(L\cdot R)^{(i)}[i+1:n,i+1:n]}\LHS
  &= \underbrace{L^{(i-1)}[i+1:n,1:i-1]\cdot R^{(i-1)}[1:i-1,i+1:n]}_{\text{untouched}}+\\
  &\mymidline{+ L^{(i)}[i+1:n,i] \underbrace{R^{(i)}[i,i+1:n]}_{\text{untouched pivot row}}+}\LHS\\
  &\mylastline{+ \underbrace{L^{(i)}[i+1:n,i+1:n]}_{=1_{n-i-1}}\cdot R^{(i)}[i+1:n,i+1:n]}\LHS\\
  &= L^{(i-1)}[i+1:n,1:i-1]\cdot R^{(i-1)}[1:i-1,i+1:n]
    +\\
  &\mymidline{+ \uwave{L^{(i)}[i+1:n,i]\cdot R^{(i-1)}[i,i+1:n]}+}\LHS\\
  &\mylastline{+R^{(i-1)}[i+1:n,i+1:n]\uwave{\strut- L^{(i)}[i+1:n,i]\cdot R^{(i-1)}[i,i+1:n]}}\LHS\\
  &=L^{(i-1)}[i+1:n,1:i-1]\cdot R^{(i-1)}[1:i-1,i+1:n] +\\
  &\mymidline{+ \underbrace{L^{(i-1)}[i+1:n,i]}_{=0}\cdot R^{(i-1)}[i,i+1:n] +}\LHS\\
  &\mylastline{+ \underbrace{L^{(i-1)}[i+1:n,i+1:n]}_{=1_{n-i}}\cdot R^{(i-1)}[i+1:n,i+1:n]}\LHS\\
  &= A[i+1:n,i+1:n].
\end{align*}
\end{document}

If you have the numbered version align* you should also consider the width of the equation label and the label separator in the second argument of \mymidline and \mylastline. I didn't find a predefined measure for the label width. After some tests it turned out that \quad\quad(1) is an appropriate placeholder for the label.

\documentclass{article}
\usepackage[DIV15]{typearea}
\usepackage{amsmath,amsfonts}
\usepackage{fleqn}
\usepackage{ulem}
\makeatletter
\newdimen\@tzadima
\newdimen\@tzadimb
\newbox\@tzaboxa
\def\mylinemeasures#1#2{%
  \@tzadima\displaywidth%
  \advance\@tzadima-\tagwidth@%
  \advance\@tzadima-\alignsep@%
  \setbox\@tzaboxa\hbox{$\displaystyle#1$}%
  \@tzadimb\wd\@tzaboxa%
  \advance\@tzadima-\@tzadimb%
  \setbox\@tzaboxa\hbox{$\displaystyle#2$}%
  \@tzadimb\wd\@tzaboxa%
  \advance\@tzadima-\@tzadimb%
}
\def\mymidline#1#2{%
  \mylinemeasures{#1}{#2}%
  \divide\@tzadima2%
  \hbox to \@tzadima{}#1\notag
}
\def\mylastline#1#2{%
  \mylinemeasures{#1}{#2}%
  \hbox to \@tzadima{}#1%
}
\makeatother
\begin{document}
\begin{align}
  \gdef\LHS{(L\cdot R)^{(i)}[i+1:n,i+1:n]}\LHS
  &= \underbrace{L^{(i-1)}[i+1:n,1:i-1]\cdot R^{(i-1)}[1:i-1,i+1:n]}_{\text{untouched}}+\notag\\
  &\mymidline{+ L^{(i)}[i+1:n,i] \underbrace{R^{(i)}[i,i+1:n]}_{\text{untouched pivot row}}+}\LHS\\
  &\mylastline{+ \underbrace{L^{(i)}[i+1:n,i+1:n]}_{=1_{n-i-1}}\cdot R^{(i)}[i+1:n,i+1:n]}{\LHS\quad\quad(1)}\\
  &= L^{(i-1)}[i+1:n,1:i-1]\cdot R^{(i-1)}[1:i-1,i+1:n] +\notag\\
  &\mymidline{+ \uwave{L^{(i)}[i+1:n,i]\cdot R^{(i-1)}[i,i+1:n]}+}{(L\cdot R)^{(i)}[i+1:n,i+1:n]}\\
  &\mylastline{+R^{(i-1)}[i+1:n,i+1:n]\uwave{\strut- L^{(i)}[i+1:n,i]\cdot R^{(i-1)}[i,i+1:n]}}{\LHS\quad\quad(1)}\\
  &=L^{(i-1)}[i+1:n,1:i-1]\cdot R^{(i-1)}[1:i-1,i+1:n] +\notag\\
  &\mymidline{+ \underbrace{L^{(i-1)}[i+1:n,i]}_{=0}\cdot R^{(i-1)}[i,i+1:n] +}{(L\cdot R)^{(i)}[i+1:n,i+1:n]}\\
  &\mylastline{+ \underbrace{L^{(i-1)}[i+1:n,i+1:n]}_{=1_{n-i}}\cdot R^{(i-1)}[i+1:n,i+1:n]}{\LHS\quad\quad(1)}\\
  &= A[i+1:n,i+1:n].
\end{align}
\end{document}

Answer 8

\begin{align}
\ni Tdij (Ti,Tj,Sk,t) & = Tdij(Ti,Tj,Sk,t) \nonumber \\
 & Tddir (Ti,Tj,Sk,t) \bigoplus \nonumber \\
& Tdrecom (Ti,Tj,Sk,t) \bigoplus \nonumber \\
& Tdiv (Ti,Tj,Sk,t)
\label{eq:1}
\end{align}

will provide following output