Vertical and horizontal curly brackets (braces)

This is a semi-automatic translation from the french version. Please comment if you find any translation errors. I will be happy to fix them, thanks!

Horizontal curly brackets

To display curly brackets on a text, it is possible to use the command \overbrace:

5+5 = \overbrace{10_{10}}^{1010_2}

$$5+5 = \overbrace{10_{10}}^{1010_2}$$

The analogous command is \underbrace:

5+5 = \underbrace{10_{10}}_{1010_2}

To display a vertical curly bracket on the left of a text, you can use the following command:

\left\{ 1+1=2

$$\begin{cases} 1+1=2\end{cases}$$

For a curly bracket on the right, you can use the \right command.

But \left and \right are really useful when writing systems or functions. Here are 2 examples:

\left\{
\begin{array}{rcr}
4x + 8y & = & 54 \\
2x + 7y & = & 39 
\end{array}
\right.

$$\begin{cases} 4x + 8y = & 54 \cr 2x + 7y = & 39 \end{cases}$$

Another example :

g(i,j) = \left\{
\begin{array}{ll}
 255 & \mbox{si} f(i,j) \leq s \\
 0 & \mbox{sinon} 
\end{array}
\right.

$$g(i,j) =\begin{cases}255&\text{si}; f(i,j)\leq s\cr0 &\text{sinon.}\end{cases}$$

Alternatively, you can use the \begin{cases} environment:

g(i,j) =
\begin{cases}  
255 & \text{si} f(i,j) \leq s \\
0 & \text{sinon.}    
\end{cases}