Real Algebraic Numbers: Complexity Analysis and Experimentation

  title={Real Algebraic Numbers: Complexity Analysis and Experimentation},
  author={Ioannis Z. Emiris and Bernard Mourrain and Elias P. Tsigaridas},
  booktitle={Reliable Implementation of Real Number Algorithms},
We present algorithmic, complexity and implementation results concerning real root isolation of a polynomial of degree d, with integer coefficients of bit size ≤ τ , using Sturm (-Habicht) sequences and the Bernstein subdivision solver. In particular, we unify and simplify the analysis of both methods and we give an asymptotic complexity bound of e OB(d τ). This matches the best known bounds for binary subdivision solvers. Moreover, we generalize this to cover the non square-free polynomials… CONTINUE READING
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