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Algorithms for computer algebra
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Fast algorithms for Taylor shifts and certain difference equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Asymptotically fast computation of subresultants
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A core library for robust numeric and geometric computation
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Subresultants and Reduced Polynomial Remainder Sequences
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Fundamental problems of algorithmic algebra
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New structure theorem for subresultants
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On the complexity of real root isolation using continued fractions
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Subdivision methods for solving polynomial equations
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Journal of Computational and Applied Mathematics
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Univariate real root isolation in an extension field
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Real and complex polynomial root-finding by means of eigen-solving
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Data exchange with arithmetic operations
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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 a polynomial of degree d, with integer coefficients of bit size ≤ 驴, 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 $\mathcal{\tilde O}_B(d^4 \tau^2)$. This matches the best known bounds for binary subdivision solvers. Moreover, we generalize this to cover the non square-free polynomials and show that within the same complexity we can also compute the multiplicities of the roots. We also consider algorithms for sign evaluation, comparison of real algebraic numbers and simultaneous inequalities, and we improve the known bounds at least by a factor of d.Finally, we present our C++implementation in synapsand some preliminary experiments on various data sets.