An double arrows between two systems

I'm trying to have 2 equations systems separated by a double arrow, something like this :

I'm actually using 3 minipage : the first and the third with and array and the arrow at the center... I've tried with a table, but I can't add the second big bracket...

It doesn't look good, especially fot the arrows, that's not centered...

Here is the code I use...

\begin{center}
\begin{minipage}{.3\linewidth}
\begin{equation*}
\left\{
\begin{array}{r c l}
\omega_{s}^{-}  &=& 8.43 \\
\omega_{s}^{+} &=& 4.43 \\
\omega_{c}^{-} &=& -500\\
\omega_{c}^{+} &=& 500\\
\end{array}
\right.
\end{equation*}
\end{minipage}%
\begin{minipage}{.1\linewidth}
$\Longrightarrow$
\end{minipage}%
\begin{minipage}{.3\linewidth}
\begin{equation*}
\left\{
\begin{array}{r c l}
\Omega_{s}^{-}  &=& 9 \\
\Omega_{s}^{+} &=& 5 \\
\Omega_{c}^{-} &=& -1\\
\Omega_{c}^{+} &=& 1\\
\end{array}
\right.
\end{equation*}
\end{minipage}
\end{center}

-

It's much simpler if you use amsmath:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\left\{ \begin{aligned} \omega_{s}^{-} &= 8.43 \\ \omega_{s}^{+} &= 4.43 \\ \omega_{c}^{-} &= -500\\ \omega_{c}^{+} &= 500\\ \end{aligned} \right. \qquad\Longrightarrow\qquad \left\{ \begin{aligned} \Omega_{s}^{-} &= 9 \\ \Omega_{s}^{+} &= 5 \\ \Omega_{c}^{-} &= -1\\ \Omega_{c}^{+} &= 1\\ \end{aligned} \right.
\end{document}


If you want right alignment of the numbers:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\left\{ \begin{alignedat}{2} \omega_{s}^{-} &={}& 8.43 \\ \omega_{s}^{+} &={}& 4.43 \\ \omega_{c}^{-} &={}& -500\\ \omega_{c}^{+} &={}& 500\\ \end{alignedat} \right. \qquad\Longrightarrow\qquad \left\{ \begin{alignedat}{2} \Omega_{s}^{-} &={}& 9 \\ \Omega_{s}^{+} &={}& 5 \\ \Omega_{c}^{-} &={}& -1\\ \Omega_{c}^{+} &={}& 1\\ \end{alignedat} \right.
\end{document}


-
\begin{equation*}
\begin{cases}
\omega_{s}^{-} = 8.43 \\
\omega_{s}^{+} = 4.43 \\
\omega_{c}^{-} = -500\\
\omega_{c}^{+} = 500\\
\end{cases}
\begin{cases}
\Omega_{s}^{-} = 9 \\
\Omega_{s}^{+} = 5 \\
\Omega_{c}^{-} = -1\\
\Omega_{c}^{+} = 1\\
\end{cases}
\end{equation*}


Remember that you need \usepackage{mathtools} for this.

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Here is a plain TeX version. I'm not saying this is better in anyway, it's just to show you what can be done with an old fashioned \halign. Note that on the left I've used \openup to increase the line spacing and a \strut to make the left brace more "inclusive"; compare to the cramped version on the right without them. Obviously you'd make them the same once you were happy with the spacing.

\left\{\vcenter{\openup4pt\halign{\strut\hfil\omega^#={}&\hfil#\cr -_s & 8.43\cr +_s & 4.43\cr -_c & -500\cr +_c & 500\cr}}\right. \quad\Longrightarrow\quad \left\{\vcenter{\halign{\hfil\Omega^#={}&\hfil#\cr -_s & 9\cr +_s & 5\cr -_c & -1\cr +_c & 1\cr}}\right.


Note that you have to wrap an \halign in vertical box to include it in an equation; a \vcenter is normally the right choice.

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It's much simpler than what you did : use the cases environment:

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

\begin{document}
$\begin{cases} \omega_{s}^{-} = 8.43 \\ \omega_{s}^{+} = 4.43 \\ \omega_{c}^{-} = -500\\ \omega_{c}^{+} = 500 \end{cases} \Longrightarrow\enspace \begin{cases} \Omega_{s}^{-} = 9 \\ \Omega_{s}^{+} = 5 \\ \Omega_{c}^{-} = -1\\ \Omega_{c}^{+} = 1 \end{cases}$

\end{document}


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There are many ways, one of them:

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}

\begin{document}
$\left\{ \begin{array}{@{}l@{}>{{}}l@{}} \omega_s^- &= 8.43 \\ \omega_s^+ &= 4.43 \\ \omega_c^- &= -500 \\ \omega_c^+ &= 500 \end{array} \right.\kern-\nulldelimiterspace \quad \Rightarrow \quad \left\{ \begin{array}{@{}l@{}>{{}}l@{}} \Omega_s^- &= 9 \\ \Omega_s^+ &= 5 \\ \Omega_c^- &= -1 \\ \Omega_c^+ &= 1 \end{array} \right.\kern-\nulldelimiterspace$
\end{document}


Remarks:

• \kern-\nulldelimiterspace: TeX sets the space \nulldelimiterspace at the place of the invisible delimiter. It is removed to avoid an asymmetry around \Rightarrow.

• @{} inside the table specification removes the space that TeX insert at the sides of a column.

• >{{}} inside the table specification before the second column adds an empty math atom before =. Then TeX also inserts space at the left side of the equals symbol.

• The alignment of the = is not really needed here, because the left sides have the same widths anyway. Thus this solution handles the more general case, where the left sides might have different widths.

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