Implementation

Let $x_i$ be the $n$ roots (either complex or real) of a polynomial of degree $n$. Let $S_p$ be:

$$S_p=\sum_{i =1}^{i =n} x_i^p$$

This procedure enable to compute the $n$ elements $S_1,\ldots,S_n$. The syntax is:

 
VECTOR SumN_Polynomial_Interval(int Degree,VECTOR &Coeff)

with:

• Degree: degree of the polynomial
• Coeff: coefficients of the polynomial ordered along increasing degree

This procedure returns 0 if the leading coefficient is equal to 0, 1 otherwise. There is an equivalent procedure for interval polynomial:

 
INTERVAL_VECTOR SumN_Polynomial_Interval(int Degree,INTERVAL_VECTOR &Coeff)

which returns intervals including the $S_p$. This procedure returns 0 if 0 is included in the leading interval.