Implementation

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

$$Z_p= \sum_{i<j<\ldots<k,i =1,\ldots,n} x_ix_j\ldots x_k$$

This procedure enable to compute the $n$ elements $Z_1,\ldots,Z_n$ ($Z_1$ is the sum of the roots, $Z_n$ the product of the roots). The syntax is:

 
VECTOR ProdN_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 ProdN_Polynomial_Interval(int Degree,INTERVAL_VECTOR &Coeff)

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