Line breaking in equation

Question

This is the equation I want to write in LaTex:

I have read these advices, but for split and multilined commands it says that they are undefined (and also for multiline, but nevertheless this is not suitable for me). Is there another possibility how to break line?

Answer 1

The empheqpackage (which loads mathtools and amsmath) lets put whatever you want on the left or on the right of a group of equations. So here is another solution, with the gather*environment:

    \documentclass[12pt,a4paper,bothsides]{article}
    \usepackage[utf8]{inputenc}
    \usepackage[showframe, nomarginpar]{geometry}
    \usepackage[overload]{empheq}


    \begin{document}

    \begin{gather*}[left ={ V_{i,j} = \empheqlbrace},  right = \empheqrbrace ]
           a + b  = c + d \\
            ∫_0¹ x² \ \mathrm{d}x   = \dfrac{1}{3}\\
           \nabla u  =  0
    \end{gather*}

    \end{document}

Answer 2

Since you've noted in a comment that the semicolons are there to denote an "if ..." relationship, I would suggest that you display the material in two separate columns, with ; replaced with if at the start of the second column.

Furthermore, since the same, fairly complicated expression occurs five times between the curly braces, I suggest you define it beforehand and give it a shorthand, say, \widehat{W}. (You're obviously free to come up with a more suitable shorthand symbol!) Then use either an array environment or a dcases environment to state what V_{ij} is, with \widehat{W} -- or whatever symbol you end up choosing -- making its appearance five times.

This setup -- first, define the complicated expression; second, use it repeatedly in the statement of what V_{ij} is -- should let the reader focus more easily on the structure of the argument.

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}    
\begin{document}
Let $\displaystyle\widehat{W}\equiv W_{j}\ln\biggl( 1 + 
  \frac{G_{i,j} \abs{h_{i,j}}^2 P_{i,j}} {\sigma_{i,j}^2} \biggr)$. Then
\[
\renewcommand\arraystretch{1.5} % more space between lines to mimic display style
  V_{i,j} =
  \left\{\begin{array}{ll}
     (Q_{1}D_{i}^{d} + Q_{2}D_{i}^{o}) \widehat{W}
        & \text{if } D_{i}^{d} + D_{i}^{o} \leq \widehat{W}\\
     Q_{1}D_{i}^{d} \widehat{W}
        & \text{if } D_{i}^{d} \leq \widehat{W} < D_{i}^{d} + D_{i}^{o}\\
     0 
        & \text{if } \widehat{W} < D_{i}^{d}
  \end{array}\right\}
\]

Or, using the \texttt{dcases} environment:
\[
  V_{i,j} =
  \begin{dcases} % dcases environment is provided by the mathtools package
     (Q_{1}D_{i}^{d} + Q_{2}D_{i}^{o}) \widehat{W}
        & \text{if } D_{i}^{d} + D_{i}^{o} \leq \widehat{W}\\
     Q_{1}D_{i}^{d} \widehat{W}
        & \text{if } D_{i}^{d} \leq \widehat{W} < D_{i}^{d} + D_{i}^{o}\\
     0 
        & \text{if } \widehat{W} < D_{i}^{d}      
  \end{dcases}
\]
\end{document}

Answer 3

Another solution:

\documentclass{article}

\usepackage{geometry}
\usepackage{mathtools}

\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}


\begin{document}

\begin{equation*}
  V_{i,j} =
  \begin{Bmatrix}
    \displaystyle (Q_{1}D_{i}^{d} + Q_{2}D_{i}^{o})W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu}; D_{i}^{d} + D_{i}^{o} \leq W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu}\\[3ex]
    \displaystyle Q_{1}D_{i}^{d}W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu}; D_{i}^{d} \leq W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu} < D_{i}^{d} + D_{i}^{o}\\[3ex]
    \displaystyle 0; W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu} < D_{i}^{d}
  \end{Bmatrix}
\end{equation*}

\end{document}

P.S. I've added geometry to avoid the equation going into the margin.

Update

If you want all the math in the document to be written in display style, you can declare \everymath{\displaystyle};

\documentclass{article}

\usepackage{geometry}
\usepackage{mathtools}

\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\everymath{\displaystyle}


\begin{document}

\begin{equation*}
  V_{i,j} =
  \begin{Bmatrix}
    (Q_{1}D_{i}^{d} + Q_{2}D_{i}^{o})W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu}; D_{i}^{d} + D_{i}^{o} \leq W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu}\\[3ex]
    Q_{1}D_{i}^{d}W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu}; D_{i}^{d} \leq W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu} < D_{i}^{d} + D_{i}^{o}\\[3ex]
    0; W_{j}\ln{\mkern -7mu}\left(1 + \frac{G_{i,j}\abs{h_{i,j}}^{2}P_{i,j}}{\sigma_{i,j}^{2}}\right){\mkern -5mu} < D_{i}^{d}
  \end{Bmatrix}
\end{equation*}

\end{document}

Answer 4

You have to load the mathtools package to obtain the multlined environment.

Anyway, the Bmatrix environment from the same package (and from amsmath, of which mathtools is an extension) may be suitable to you:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
V_{i,j}=\begin{Bmatrix} Q_1 \\ Q_2 \\ Q_3\end{Bmatrix}
\]
\end{document}

Instead of Q_1, Q_2 and Q_3, you may enter your own formulas.

Answer 5

You could use an array:

\begin{align*}
    V_{i,j}=\left\lbrace\begin{array}{c}%
                First line\\
                Second line\\
                Third line
             \end{array}\right\rbrace
\end{align*}