-Polynomials are mathematical algebraic structures that play an important role in science and engineering by capturing physical phenomena and by expressing any outcome as a function of some unknown variables. Formally speaking, a polynomial $p(x)$ of degree \textit{n} having $n$ coefficients in the complex plane \textit{C} is :
-%%\begin{center}
-\begin{equation}
- {\Large p(x)=\sum_{i=0}^{n-1}{a_{i}x^{i}}}.
-\end{equation}
-%%\end{center}
-
-The root finding problem consists in finding the values of all the $n$ different values of the variable $x$ for which \textit{p(x)} is null. Such values are called zeros of $p$. If zeros are $\alpha_{i},\textit{i=1,...,n}$ then $p(x)$ can be written as :
+%Polynomials are mathematical algebraic structures that play an important role in science and engineering by capturing physical phenomena and expressing any outcome as a function of some unknown variables. Formally speaking, a polynomial $p(x)$ of degree $n$ having $n$ coefficients in the complex plane $\mathbb{C}$ is:
+%\begin{equation}
+%p(x)=\sum_{i=0}^{n}{a_ix^i}.
+%\end{equation}
+%\LZK{Dans ce cas le polynôme a $n+1$ coefficients et non pas $n$!}
+The issue of finding the roots of polynomials of very high
+degrees arises in many complex problems in various fields,
+such as algebra, biology, finance, physics or climatology [1].
+In algebra for example, finding eigenvalues or eigenvectors of
+any real/complex matrix amounts to that of finding the roots
+of the so-called characteristic polynomial.
+
+The root-finding problem consists in finding the $n$ different values of the unknown variable $x$ for which $p(x)=0$. Such values are called zeros or roots of $p$. If zeros are $\{\alpha_{i}\}_{1\leq i\leq n}$, then $p(x)$ can be written as :
