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The syntax of the procedure is:
INT Descartes_Lemma_Interval(int Degree,VECTOR &Coeff)
with: This procedure returns the number of positive real roots up to an even number. If the procedure returns $m$ the number of positive roots is $m-2k$ with $k\in[0,m/2]$.

There is an implementation of this method for interval polynomial. Here it is necessary to introduce an additional parameter to indicate the confidence we have in the result. The procedure is implemented as:

INT Descartes_Lemma_Interval(int Degree,INTERVAL_VECTOR &Coeff,int *Confidence);
Confidence is a quality index: Similar algorithms for negative roots are available:
INT Descartes_Lemma_Negative_Interval(int Degree,VECTOR &Coeff)
INT Descartes_Lemma_Negative_Interval(int Degree,INTERVAL_VECTOR &Coeff,int *Confidence)

Jean-Pierre Merlet 2012-12-20