Implementation

The Weyl filter is implemented to manage univariate polynomial (with numerical or interval coefficients) or parametric polynomial. A basic tool of this filter is

 
int Weyl_Filter_Utility(int Degree, double maxroot,
                      INTERVAL_VECTOR &b,INTERVAL_VECTOR &Input)

where Input(1) is the range for the polynom variable and b the $b_i$ coefficients. A more general implementation is

 
int Weyl_Filter(int Degree, INTERVAL_VECTOR &Coeff,double maxroot,
                int (* GetB)(int,INTERVAL_VECTOR &,INTERVAL &,INTERVAL_VECTOR &), 
		INTERVAL_VECTOR &Input)

Here GetB is a procedure that calculates the $b_i$ coefficients. Its arguments are the degree of the polynomial, its coefficients, $z_0$ and the $b_i$ coefficients. It should return 1 if the calculation has been successfull, 0 otherwise. An example of such procedure is Derive_Polynomial_Expansion. Degree is the degree of the polynomial, Coeff its coefficients and Input(1) is the range for the polynomial unknown.

This procedure has several variants:

 
int Weyl_Filter(int Degree, INTERVAL_VECTOR &Coeff,double max_root,
                INTERVAL_VECTOR &Input)

here the GetB procedure will be Derive_Polynomial_Expansion. In

 
int Weyl_Filter(int Degree, INTERVAL_VECTOR &Coeff,
                INTERVAL_VECTOR &Input)

here the GetB procedure will be Derive_Polynomial_Expansion and maxroot will be computed by an ALIAS procedure. The same procedure will be used in

 
int Weyl_Filter(int Degree, INTERVAL_VECTOR &Coeff,
                int (* GetB)(int,INTERVAL_VECTOR &,INTERVAL &,INTERVAL_VECTOR &), 
                INTERVAL_VECTOR &Input)