Upper bound for the norm of the factors of a polynomial: case where all the roots of the polynomial are real. (Majoration de la norme des facteurs d’un polynôme: Cas où toutes les racines du polynôme sont réelles.) (French) Zbl 0778.12001

Author’s abstract: In the first part of this paper, we give upper bounds for the norm of factors of polynomials whose zeros are real. These bounds are very useful in polynomial factorization algorithms. In the second part, we prove an upper bound for the number of real roots of any polynomial, and also a lower bound for the norm of a polynomial, depending on the distribution of its roots in the complex plane.


12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
12D05 Polynomials in real and complex fields: factorization
26C10 Real polynomials: location of zeros
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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