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The simplest implementation of the Miranda theorem is

int Miranda(int Dim,INTERVAL_VECTOR (* F)(int,int,INTERVAL_VECTOR &),
           INTERVAL_VECTOR &Input)
where Dim is the number of equations, Input is a ball for the variables and F is a procedure in MakeF format that allows to compute an interval evaluation of the equations. This procedure returns 1 if Miranda theorem is satisfied for Input, 0 otherwise. This implementation is embedded in the Solve_General_Interval solving algorithm.

Another implementation uses the derivatives for improving the interval evaluation:

int Miranda(int Dim,
           INTERVAL_VECTOR (* F)(int,int,INTERVAL_VECTOR &),
           INTERVAL_MATRIX (* J)(int,int,INTERVAL_VECTOR &),
           INTERVAL_VECTOR &Input)
J is a procedure in MakeJ format that allows to compute the derivative of the equations.

Jean-Pierre Merlet 2012-12-20