Polynomial real root isolation by differentiation
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Some problems about polynomials
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
On the sign of a real algebraic number
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Algorithms for exact polynomial root calculation
Algorithms for exact polynomial root calculation
Algorithms for polynomials over a real algebraic number field.
Algorithms for polynomials over a real algebraic number field.
Univariate real root isolation in an extension field
Proceedings of the 36th international symposium on Symbolic and algebraic computation
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Several algorithms are known to separate the real zeros of a polynomial. In his thesis Heindel [He70] showed, that the computing time of his algorithm using Sturm sequences is polynomially bounded in the length of the coefficients. The polynomials are assumed to have integral coefficients. In his Diplomarbeit [Lü76] Ludicke gave a modified Sturm algorithm for real algebraic polynomials with a polynomially bounded, but very high computing time. He described and analyzed the algorithm, but did not implement it. In the present paper we extend the Collins/Loos - algorithm [CL76] from integral to real algebraic coefficients and gain empirical computing times.