Explicit Criterion to Determine the Number of Positive Roots of a Polynomial 1)
Lu Yang, Bican Xia · 1997
In a recent article, a complete discrimination system was given for a poly- nomial with symbolic/literal coecients. Such a system is a set of explicit expressions in terms of the coecients, which is sucient for determining the numbers and multiplici- ties of the real and imaginary roots. Sometimes, however, one wants to know the number of roots in a certain range, especially, in a interval. We give here an explicit criterion to determine the number of positive roots of a real polynomial, and hence an ecient algorithm is introduced for determining the number of roots in a general interval.