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Mathematical background

Let $P$ the polynomial:

\begin{displaymath}
P=a_0+a_1x+\ldots+a_nx^n
\end{displaymath}

and let $\vert P\vert$ be:

\begin{displaymath}
\vert P\vert={\rm Max}_{i =0}^{i =n} \vert a_i\vert
\end{displaymath}

The minimal distance $\Delta$ between the real roots of $P$ is such that [26]:

\begin{displaymath}
\Delta > \sqrt{\frac{8}{n^{n+2}}}\frac{1}{1+\vert P\vert^n}
\end{displaymath}



Jean-Pierre Merlet 2012-12-20