Evaluation of a polynomial

The evaluation of a polynomial for a given value is implemented as:

 
REAL Evaluate_Polynomial_Interval(int Degree,VECTOR &Coeff,REAL P)
INTERVAL Evaluate_Polynomial_Interval(int Degree,INTERVAL_VECTOR &Coeff,REAL P)
INTERVAL Evaluate_Polynomial_Interval(int Degree,VECTOR &Coeff,INTERVAL P)
INTERVAL Evaluate_Polynomial_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL P)
REAL Evaluate_Polynomial_Interval(int Degree,INTEGER_VECTOR &Coeff,REAL P);
int Evaluate_Polynomial_Interval(int Degree,INTEGER_VECTOR &Coeff,INT P);

with:

• Degree: degree of the polynomial
• Coeff: the Degree+1 coefficients (which can be REAL, INT or INTERVAL of the polynomial in increasing degree
• P: the point at which we want to compute the polynomial. It may be REAL, INT or INTERVAL.

These procedures enable to get:

• the value of a polynomial with REAL coefficients at a point
• the interval value of a polynomial with interval coefficients at a real point
• the interval value of a polynomial with REAL coefficients at for an interval value of the unknown. The first and second order derivative of the polynomial are used to get sharp bounds
• the interval value of a polynomial with interval coefficients for an interval value of the unknown. The first and second order derivative of the polynomial are used to get sharp bounds