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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 $Z_p$ as:

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

We have [4]:

\begin{eqnarray*}
&& a_0Z_1+a_1=0\\
&& a_0Z_2-a_2=0\\
&& \ldots\\
&& a_0Z_k+(-1)^ka_k=0\\
&&\ldots\\
&& a_0\prod_{i =1}^{i =n}x_i+(-1)^na_n=0
\end{eqnarray*}



Jean-Pierre Merlet 2012-12-20