The NonLinear procedure

The purpose of the procedure is to compute an interval evaluation of the non linear term of the equations (the $G_i$ terms in the mathematical background). This procedure take as argument a box and the returned evaluation of the non-linear terms. Consider for example the equations:

$$\begin{eqnarray*} &&-0.1 x_1^2+0.25 x_1^3+x_1+0.5 x_2+0.3=0\\ &&-0.1 x_2^2+0.55 x_2^3+2x_1-0.5 x_2+0.2=0 \end{eqnarray*}$$

The non-linear terms of these equations are $-0.1 x_1^2+0.25 x_1^3$ and $-0.1 x_2^2+0.55 x_2^3$ and the NonLinear procedure is written as:

 
void NonLinear(INTERVAL_VECTOR &x,INTERVAL_VECTOR &X)
{
    X(1) = (-0.1+0.25*x(1))*Sqr(x(1));
    X(2) = (-0.1+0.55*x(2))*Sqr(x(2));
}