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The Cassini bounds may be obtained with the procedure:

int Cassini_Simplification(INTERVAL_MATRIX &A,int Size, 
                  int Type_Matrix, INTERVAL &Input)
where The procedure will return -1 if there is no intersection between Input and the Cassini bounds, 1 if there Input has been improved, 0 otherwise.

This procedure may also be called with:

int Cassini_Simplification(int (* TheMatrix)(INTERVAL_VECTOR &, INTERVAL_MATRIX &),
      INTERVAL_VECTOR &Param,int Size, int Type_Matrix, INTERVAL &Input)
where TheMatrix is a procedure that compute the elements of the matrix according to the interval value of the parameters Param.

Jean-Pierre Merlet 2012-12-20