How to align a system of multiline equations?

Question

I've got a system of equations, each of them doesn't fit the page width, so I'm searching the way to align them so that:

• the brace should appear to the left with no indentation
• the first line of each equation should be left-aligned
• the last line of each equation should be right-aligned

I reached the following: but I don't like the huge spacing between the brace and the 1-st letter of each equation.

The code I used is the following:

\[
\setlength{\multlinegap}{0pt}
\left\{
\begin{array}{c}
\shoveleft{A_{PP}\sin\alpha_{P1} - A_{PS}\cos\alpha_{S1} +B_{PP} \sin\alpha_{P2} +B_{PS} \cos\alpha_{S2} =} \\ \shoveright{=\sin\alpha_{P1},} \\
% 2-nd equation
\shoveleft{ A_{PP}\cos\alpha_{P1}  +A_{PS} \sin\alpha_{S1} -B_{PP}\cos\alpha_{P2} + B_{PS} \sin\alpha_{S2} = } \\
\shoveright{ =\cos\alpha_{P1},} \\
% 3-rd equation
\shoveleft{ A_{PP}\gamma_{P1} \cos 2\alpha_{S1} +A_{PS}  \gamma_{S1} \sin 2\alpha_{S1} +B_{PP}  \gamma_{P2} \cos 2\alpha_{S2} -} \\
\shoveright{- B_{PS}   \gamma_{S2} \sin 2\alpha_{S2} = \gamma_{P1} \cos 2\alpha_{S1},} \\
% 4-th equation
\shoveleft{ -A_{PP}n_1 \gamma_{S1} \sin 2\alpha_{P1} +A_{PS}  \gamma_{S1} \cos 2\alpha_{S1} +B_{PP} n_2 \gamma_{S2} \sin 2\alpha_{P2} +} \\
\shoveright{+ B_{PS} \gamma_{S2} \cos 2\alpha_{S2} = n_1 \gamma_{S1} \sin 2\alpha_{P1}.}\end{array}
\right.
\] 

Any help will be appreciated. Thanks!

Answer 1

the multlined environment from mathtools is your friend. (it loads amsmath, so there's no need to do that).

two things to note about this example:

• \mathindent is set to zero width within a group so it will disappear after the display ends.
• since multlined (like multline) automatically sets the first line flush left and the last line flush right, you don't want the \shove... commands on those lines. in fact, the spacing will be compromised if you do wrap those lines in \shove... arguments.

here's the code:

\documentclass{article}
\usepackage[fleqn]{mathtools}

\begin{document}

\noindent some text here
{\mathindent=0pt
\[
\setlength{\multlinegap}{0pt}
\left\{
\begin{multlined}
A_{PP}\sin\alpha_{P1} - A_{PS}\cos\alpha_{S1} +B_{PP} \sin\alpha_{P2} +B_{PS} \cos\alpha_{S2} = \\
\shoveright{=\sin\alpha_{P1},} \\
% 2-nd equation
\shoveleft{ A_{PP}\cos\alpha_{P1}  +A_{PS} \sin\alpha_{S1} -B_{PP}\cos\alpha_{P2} + B_{PS} \sin\alpha_{S2} = } \\
\shoveright{ =\cos\alpha_{P1},} \\
% 3-rd equation
\shoveleft{ A_{PP}\gamma_{P1} \cos 2\alpha_{S1} +A_{PS}  \gamma_{S1} \sin 2\alpha_{S1} +B_{PP}  \gamma_{P2} \cos 2\alpha_{S2} -} \\
\shoveright{- B_{PS}   \gamma_{S2} \sin 2\alpha_{S2} = \gamma_{P1} \cos 2\alpha_{S1},} \\
% 4-th equation
\shoveleft{ -A_{PP}n_1 \gamma_{S1} \sin 2\alpha_{P1} +A_{PS}  \gamma_{S1} \cos 2\alpha_{S1} +B_{PP} n_2 \gamma_{S2} \sin 2\alpha_{P2} +} \\
+ B_{PS} \gamma_{S2} \cos 2\alpha_{S2} = n_1 \gamma_{S1} \sin 2\alpha_{P1}.
\end{multlined}
\right.
\] }

\end{document}

Answer 2

This is not directly addressing your question, but more about making the information easier to parse. I would suggest the following changes to make the pattern easier to see:

• Eliminate the double equal signs
• align the terms across multiple lines

Notes:

• The leading minus sign on the last equation has non-standard spacing but I think it looks better in this case
• You could also consider aligning the middle +/- signs (and perhaps even the equal signs) to make the pattern ever more obvious.

There are many ways to achieve this, so this is just to show one method.

Code:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\Phantom}{\phantom{{}+{}}}%
\newcommand{\Plus}{{}+{}}%
\newcommand{\Minus}{{}-{}}%

\begin{document}
\[\begin{cases}
\Phantom A_{PP}\sin\alpha_{P1} - A_{PS}\cos\alpha_{S1} \\
        \Plus B_{PP}\sin\alpha_{P2} + B_{PS}\cos\alpha_{S2} =
         \sin\alpha_{P1}, \\[7pt]
% 2-nd equation
\Phantom A_{PP}\cos\alpha_{P1}  +A_{PS} \sin\alpha_{S1} \\
\Minus B_{PP}\cos\alpha_{P2} + B_{PS} \sin\alpha_{S2} = \cos\alpha_{P1}, \\[7pt]
% 3-rd equation
\Phantom A_{PP}\gamma_{P1} \cos 2\alpha_{S1} +A_{PS}  \gamma_{S1} \sin 2\alpha_{S1} \\
\Plus B_{PP}  \gamma_{P2} \cos 2\alpha_{S2}
- B_{PS}   \gamma_{S2} \sin 2\alpha_{S2} = \gamma_{P1} \cos 2\alpha_{S1}, \\[7pt]
% 4-th equation
\Minus A_{PP}n_1 \gamma_{S1} \sin 2\alpha_{P1} +A_{PS}  \gamma_{S1} \cos 2\alpha_{S1} \\
\Plus B_{PP} n_2 \gamma_{S2} \sin 2\alpha_{P2} +
       B_{PS} \gamma_{S2} \cos 2\alpha_{S2} = n_1 \gamma_{S1} \sin 2\alpha_{P1}.
\end{cases}\]
\end{document}

Answer 3

To remove the space between the row and the brace you can use the declaration @{}. The declaration @{} is described here:

Spaces between rows and cols in a table - Better ways than mine?

To provide an equation about the whole contents you can use the command \resizebox. Note this results in an unwanted size of the equation.

\documentclass{article}
\usepackage{showframe}
\usepackage{array}
\usepackage{amsmath}
\usepackage{graphicx}
\begin{document}
\[
\setlength{\multlinegap}{0pt}
\left\{
\begin{array}{c}
\shoveleft{A_{PP}\sin\alpha_{P1} - A_{PS}\cos\alpha_{S1} +B_{PP} \sin\alpha_{P2} +B_{PS} \cos\alpha_{S2} =} \\ \shoveright{=\sin\alpha_{P1},} \\
% 2-nd equation
\shoveleft{ A_{PP}\cos\alpha_{P1}  +A_{PS} \sin\alpha_{S1} -B_{PP}\cos\alpha_{P2} + B_{PS} \sin\alpha_{S2} = } \\
\shoveright{ =\cos\alpha_{P1},} \\
% 3-rd equation
\shoveleft{ A_{PP}\gamma_{P1} \cos 2\alpha_{S1} +A_{PS}  \gamma_{S1} \sin 2\alpha_{S1} +B_{PP}  \gamma_{P2} \cos 2\alpha_{S2} -} \\
\shoveright{- B_{PS}   \gamma_{S2} \sin 2\alpha_{S2} = \gamma_{P1} \cos 2\alpha_{S1},} \\
% 4-th equation
\shoveleft{ -A_{PP}n_1 \gamma_{S1} \sin 2\alpha_{P1} +A_{PS}  \gamma_{S1} \cos 2\alpha_{S1} +B_{PP} n_2 \gamma_{S2} \sin 2\alpha_{P2} +} \\
\shoveright{+ B_{PS} \gamma_{S2} \cos 2\alpha_{S2} = n_1 \gamma_{S1} \sin 2\alpha_{P1}.}\end{array}
\right.
\] 


\noindent\resizebox{\linewidth}{!}{%
$\setlength{\multlinegap}{0pt}
\left\{
\begin{array}{@{}c@{}}
\shoveleft{A_{PP}\sin\alpha_{P1} - A_{PS}\cos\alpha_{S1} +B_{PP} \sin\alpha_{P2} +B_{PS} \cos\alpha_{S2} =} \\ \shoveright{=\sin\alpha_{P1},} \\
% 2-nd equation
\shoveleft{ A_{PP}\cos\alpha_{P1}  +A_{PS} \sin\alpha_{S1} -B_{PP}\cos\alpha_{P2} + B_{PS} \sin\alpha_{S2} = } \\
\shoveright{ =\cos\alpha_{P1},} \\
% 3-rd equation
\shoveleft{ A_{PP}\gamma_{P1} \cos 2\alpha_{S1} +A_{PS}  \gamma_{S1} \sin 2\alpha_{S1} +B_{PP}  \gamma_{P2} \cos 2\alpha_{S2} -} \\
\shoveright{- B_{PS}   \gamma_{S2} \sin 2\alpha_{S2} = \gamma_{P1} \cos 2\alpha_{S1},} \\
% 4-th equation
\shoveleft{ -A_{PP}n_1 \gamma_{S1} \sin 2\alpha_{P1} +A_{PS}  \gamma_{S1} \cos 2\alpha_{S1} +B_{PP} n_2 \gamma_{S2} \sin 2\alpha_{P2} +} \\
\shoveright{+ B_{PS} \gamma_{S2} \cos 2\alpha_{S2} = n_1 \gamma_{S1} \sin 2\alpha_{P1}.}\end{array}
\right.
$} 
\end{document}

Answer 4

\documentclass[a4paper]{article}
\usepackage{amsmath,tabularx}
\renewcommand\tabularxcolumn[1]{m{#1}}
\begin{document}

\noindent
\begin{tabularx}{\linewidth}{@{}l@{\kern-10pt}X@{}}
$\left\{\rule{0pt}{4\normalbaselineskip}\right.$
&
\begin{multline}
A_{PP}\sin\alpha_{P1} - A_{PS}\cos\alpha_{S1} +B_{PP} \sin\alpha_{P2} 
           +B_{PS} \cos\alpha_{S2} = \sin\alpha_{P1}, \\
% 2-nd equation
\shoveleft A_{PP}\cos\alpha_{P1}  +A_{PS} \sin\alpha_{S1} -B_{PP}\cos\alpha_{P2} 
           + B_{PS} \sin\alpha_{S2} =\cos\alpha_{P1}, \\
% 3-rd equation
\shoveleft A_{PP}\gamma_{P1} \cos 2\alpha_{S1} +A_{PS}  \gamma_{S1} \sin 2\alpha_{S1} +B_{PP}  \gamma_{P2} \cos 2\alpha_{S2} - \\
\shoveright{-B_{PS}   \gamma_{S2} \sin 2\alpha_{S2} = \gamma_{P1} \cos 2\alpha_{S1},} \\
% 4-th equation
\shoveleft -A_{PP}n_1 \gamma_{S1} \sin 2\alpha_{P1} +A_{PS}  \gamma_{S1} \cos 2\alpha_{S1} +B_{PP} n_2 \gamma_{S2} \sin 2\alpha_{P2} + \\
+ B_{PS} \gamma_{S2} \cos 2\alpha_{S2} = n_1 \gamma_{S1} \sin 2\alpha_{P1}.
\end{multline}
\end{tabularx}

\end{document}

Answer 5

Analyzing the problem carefully, it is a dcases environment of multi-line equations, whose second parts should be right justified (or right aligned, or \shoveright, or \MoveEqRight... you name it).

You need the nested multline environment multilined[t] for each equation, inside an \aligned environment, inside a dcases environment.

I am against this practice:

the brace should appear to the left with no indentation

Thus, I haven't included it in my code.

In the following example, Eq. (1) is not aligned while Eq. (2) is.

\documentclass{article}

\usepackage{mathtools}
\usepackage[nopar]{lipsum} % for dummy text only
\begin{document}

\lipsum[66] 
%%                  FIRST EQ
\begin{equation}
    \begin{dcases}
        \begin{multlined}[t]
            A_{PP}\sin\alpha_{P1} - A_{PS}\cos\alpha_{S1} +B_{PP} \sin\alpha_{P2} +B_{PS} \cos\alpha_{S2} =\\
            =\sin\alpha_{P1},
        \end{multlined}
        \\
        \begin{multlined}[t]
            A_{PP}\cos\alpha_{P1}  +A_{PS} \sin\alpha_{S1} -B_{PP}\cos\alpha_{P2} + B_{PS} \sin\alpha_{S2} = \\
            =\cos\alpha_{P1},
        \end{multlined}
        \\
        \begin{multlined}[t]
            A_{PP}\gamma_{P1} \cos 2\alpha_{S1} +A_{PS}  \gamma_{S1} \sin 2\alpha_{S1} +B_{PP}  \gamma_{P2} \cos 2\alpha_{S2} -\\
            - B_{PS}   \gamma_{S2} \sin 2\alpha_{S2} = \gamma_{P1} \cos 2\alpha_{S1},
        \end{multlined}
        \\
        \begin{multlined}[t]
            -A_{PP}n_1 \gamma_{S1} \sin 2\alpha_{P1} +A_{PS}  \gamma_{S1} \cos 2\alpha_{S1} +B_{PP} n_2 \gamma_{S2} \sin 2\alpha_{P2} + \\
            + B_{PS} \gamma_{S2} \cos 2\alpha_{S2} = n_1 \gamma_{S1} \sin 2\alpha_{P1}.
        \end{multlined}
    \end{dcases}
\end{equation}
\lipsum[66]
%%                  SECOND EQ
\begin{equation}
\begin{dcases}
    \begin{aligned}
        \begin{multlined}[t]
            A_{PP}\sin\alpha_{P1} - A_{PS}\cos\alpha_{S1} +B_{PP} \sin\alpha_{P2} +B_{PS} \cos\alpha_{S2} =\\
            =\sin\alpha_{P1},
        \end{multlined}
        \\
        \begin{multlined}[t]
            A_{PP}\cos\alpha_{P1}  +A_{PS} \sin\alpha_{S1} -B_{PP}\cos\alpha_{P2} + B_{PS} \sin\alpha_{S2} = \\
            =\cos\alpha_{P1},
        \end{multlined}
        \\
        \begin{multlined}[t]
            A_{PP}\gamma_{P1} \cos 2\alpha_{S1} +A_{PS}  \gamma_{S1} \sin 2\alpha_{S1} +B_{PP}  \gamma_{P2} \cos 2\alpha_{S2} -\\
            - B_{PS}   \gamma_{S2} \sin 2\alpha_{S2} = \gamma_{P1} \cos 2\alpha_{S1},
        \end{multlined}
        \\
        \begin{multlined}[t]
            -A_{PP}n_1 \gamma_{S1} \sin 2\alpha_{P1} +A_{PS}  \gamma_{S1} \cos 2\alpha_{S1} +B_{PP} n_2 \gamma_{S2} \sin 2\alpha_{P2} + \\
            + B_{PS} \gamma_{S2} \cos 2\alpha_{S2} = n_1 \gamma_{S1} \sin 2\alpha_{P1}.
        \end{multlined}
    \end{aligned}
\end{dcases}
\end{equation}
\lipsum[66]
\end{document}

I came across the solution after two hours of playing around with align, gather, multline, split, alignat, flalign and all its variants; just before I was about to contact Lars Mad­sen (main­tainer of the mathtools package) for an upgrade. It had to be something with an automated format, in pure LaTeX style, not through the use of \quad or \hspace or \vphantom or the like.

It is amazing how such a basic typesetting feature is so unknown. I mean, I couldn't find a solution on the whole Internet. It ought to be included in the the guides and tutorials. Multi-line equations are so common!

I knew there had to be more people demanding a solution to this, which I'm now sharing throughout the forum. It also proves how robust the coding of the mathtools package is, responding successfully to this workaround.