In Section 1 we describe classical bounds on the roots of polynomials. In Section 2 we study real roots of univariate polynomials by a method based on Descartes’s law of sign and Bernstein polynomials. These roots are characterized by intervals with rational endpoints. The method presented works only for archimedean real closed fields. In the second part of the chapter we study exact methods working in general real closed fields. Section 3 is devoted to exact sign determination in a real closed field and Section 4 to characterizations of roots in a real closed field.
KeywordsReal Root Binary Complexity Great Common Divisor Bernstein Polynomial Univariate Polynomial
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