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Mathematical background

Let $P$ the polynomial:


with $a_0a_n \not=0$. Let the sequence $\{a_0,a_1,\ldots,a_n\}$ and the $n$ the number of change of sign in this sequence. Then the number of positive real roots, counted with their order of multiplicity is equal to $n-2k$ with $k\in [0,n/2]$ [13].

Jean-Pierre Merlet 2012-12-20