Compress cases environment horizontally

Question

I currently have the following cases environment:

\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{lipsum}

\begin{document}

\lipsum[66]
\[
G(x,u) = \begin{cases}
-\dfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi + x - u)}{4\sinh \pi} & \text{for \(0 \le x \le u \le \pi\)}\vspace{0.25em}\\
-\dfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi - x + u)}{4\sinh \pi} & \text{\phantom{for} \(0 \le u \le x \le \pi\).}
\end{cases}
\]

\end{document}

but it produces a result that sticks out into the margin:

I think the natural way to fix this would be to intersperse the expressions and conditions in the following way (apologies for bad image editing, but hopefully it's clear what I mean):

Is there a straightforward way of achieving this with cases or similar?

---

This is similar to the desired output in this question, which used a hack to produce something along the right lines. But the answers in that case focused on splitting the expressions, which doesn't work well for me.

Answer 1

You can move the condition to a new line:

\documentclass{article}
\usepackage{mathtools}
\usepackage{lipsum}

\begin{document}

\lipsum[66]
\begin{equation}
G(x,u) = \begin{cases}
-\dfrac{\cosh(\pi-x-u)+\cosh(\pi+x+u)-2\cosh(\pi+x-u)}{4\sinh\pi} & \\
                     & \makebox[0pt][r]{for $0 \le x \le u \le\pi$} \\[2ex]
-\dfrac{\cosh(\pi-x-u)+\cosh(\pi+x+u)-2\cosh(\pi-x+u)}{4\sinh\pi} & \\
                     & \makebox[0pt][r]{$0\le u\le x\le\pi$}
\end{cases}
\end{equation}

\end{document}

Answer 2

Since there is a lengthy common expression, you could do the following:

In the following definition, let $C=\cosh(\pi-x-u)+\cosh(\pi+x+u).$
\[
G(x,u) = \begin{cases}
-\dfrac{C - 2\cosh (\pi + x - u)}{4\sinh \pi} & \text{for \(0 \le x \le u \le \pi\)}\vspace{0.25em}\\
-\dfrac{C - 2\cosh (\pi - x + u)}{4\sinh \pi} & \text{\phantom{for} \(0 \le u \le x \le \pi\).}
\end{cases}
\]

Answer 3

I propose this variant layout, based on the fleqn environment and the mediumsized fractions from nccmath:

    \documentclass[a4paper]{article}
    \usepackage{amsmath, mathtools}
    \usepackage{nccmath}
    \usepackage{lipsum}
    \begin{document}

    \lipsum[66]
    \begin{fleqn}
    \[
    \begin{aligned}
     & G(x,u)= \\
     & \begin{cases}\begin{alignedat}{2}
     & -\mfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi + x - u)}{4\sinh \pi} &\qquad \text{for } & 0 \le x \le u \le \pi, \\[2ex]
     & -\mfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi - x + u)}{4\sinh \pi} & & 0 \le u \le x \le \pi.
    \end{alignedat}
    \end{cases}
    \end{aligned}
    \]
    \end{fleqn}

    \end{document} 

Answer 4

One possible solution is use of the \splitfrac{ defined in the mathtools package:

\documentclass{article}
\usepackage{mathtools}
\usepackage{lipsum}

\begin{document}
\lipsum[66]
\begin{equation}
G(x,u) = \begin{cases}
-\dfrac{\splitfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u)}
                  {- 2\cosh (\pi + x - u)}}
       {4\sinh \pi}     & \text{for \(0 \le x \le u \le \pi\)}\vspace{0.25em}\\[3ex]
-\dfrac{\splitfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u)} 
                  {- 2\cosh (\pi - x + u)}}
       {4\sinh \pi}     & \text{\phantom{for} \(0 \le u \le x \le \pi\).}
\end{cases}
\end{equation}
\end{document}

However, if you define\textwidth with `geometry package, for example, as is done in the next MWE, that your equation nice fit on page:

\documentclass{article}
\usepackage{geometry}
\usepackage{mathtools}
\usepackage{lipsum}

\begin{document}
\lipsum[66]
\begin{equation}
G(x,u) = \begin{cases}
-\dfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi + x - u)}
       {4\sinh \pi}     & \text{for \(0 \le x \le u \le \pi\)}\vspace{0.25em}\\[3ex]
-\dfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi - x + u)}
       {4\sinh \pi}     & \text{\phantom{for} \(0 \le u \le x \le \pi\).}
\end{cases}
\end{equation}
\end{document}

So, please consider my comment below your question!

Answer 5

I endorse your idea, with a few fixes.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
G(x,u) = \left\{
  \begin{aligned}
    -\dfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi + x - u)}{4\sinh \pi}
    \qquad
    \\[-1ex]
    \text{for \(0 \le x \le u \le \pi\),}
    \\[2ex]
    -\dfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi - x + u)}{4\sinh \pi}
    \qquad
    \\[-1ex]
    \text{for \(0 \le u \le x \le \pi\).}
  \end{aligned}
\right.
\]

\end{document}

However, you can do it without cases:

\[
G(x,u)=
  -\frac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi - \lvert x - u\rvert)}
        {4\sinh \pi}
\]