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Mathematical background

Let $P(x)$ be an univariate polynomial of degree $n$:

\begin{displaymath}
P(x)= a_0 x^n + a_{1} x^{n-1}+.....a_n=0
\end{displaymath}

and $x_1,\ldots,x_n$ the real and complex roots of $P$. Let define $S_p$ as

\begin{displaymath}
S_p=\sum_{i =1}^{i =n} x_i^p
\end{displaymath}

We have [4]:

\begin{eqnarray*}
&& a_0S_1+a_1=0\\
&& a_0S_2+a_1S_1+2a_2=0\\
&& \ldots\\
&& ...
..._p=0\\
&&\ldots\\
&& a_0S_n+a_1S_{n-1}+\ldots+a_{n-1}S_1+a_n=0
\end{eqnarray*}



Jean-Pierre Merlet 2012-12-20