Sturm's Theorem for Polynomials

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Let be the number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval and are not or . Then , the difference between the number of sign changes of the Sturm chain evaluated at and at .

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By subdividing an interval until every subinterval contains at most one root, one can locate subintervals containing all the real roots in the original interval.

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Contributed by: Izidor Hafner (January 2017)