Computer algebra: symbolic and algebraic computation (2nd ed.)
Bounds for positive roots of polynomials
Journal of Computational and Applied Mathematics
There is no “Uspensky's method.”
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Elements of computer algebra with applications
Elements of computer algebra with applications
Mathematics for computer algebra
Mathematics for computer algebra
Fast algorithms for Taylor shifts and certain difference equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
A Comparative Study of Algorithms for Computing Continued Fractions of Algebraic Numbers
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
The predicates for the Voronoi diagram of ellipses
Proceedings of the twenty-second annual symposium on Computational geometry
Almost tight recursion tree bounds for the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
New bounds for the Descartes method
Journal of Symbolic Computation
Complexity of real root isolation using continued fractions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
On the complexity of real root isolation using continued fractions
Theoretical Computer Science
Real Algebraic Numbers: Complexity Analysis and Experimentation
Reliable Implementation of Real Number Algorithms: Theory and Practice
Complexity of real root isolation using continued fractions
Theoretical Computer Science
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Real root isolation of multi-exponential polynomials with application
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Advances on the continued fractions method using better estimations of positive root bounds
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Bounds for real roots and applications to orthogonal polynomials
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Improved bounds for the CF algorithm
Theoretical Computer Science
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We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real numbers. We improve the previously known bound by a factor of d T, where d is the polynomial degree and T bounds the coefficient bitsize, thus matching the current record complexity for real root isolation by exact methods. Namely, the complexity bound is O˜B(d4T2) using a standard bound on the expected bitsize of the integers in the continued fraction expansion. We show how to compute the multiplicities within the same complexity and extend the algorithm to non square-free polynomials. Finally, we present an efficient open-source C++ implementation in the algebraic library synaps, and illustrate its efficiency as compared to other available software. We use polynomials with coefficient bitsize up to 8000 and degree up to 1000.