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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:

&&-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

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:
    X(1) = (-0.1+0.25*x(1))*Sqr(x(1));
    X(2) = (-0.1+0.55*x(2))*Sqr(x(2));

Jean-Pierre Merlet 2012-12-20