Univariate real root isolation in an extension field and applications

Autor: Adam Strzebonski, Elias P. Tsigaridas

Publikováno v: Journal of Symbolic Computation
Journal of Symbolic Computation, Elsevier, In press, ⟨10.1016/j.jsc.2017.12.001⟩
Journal of Symbolic Computation, In press, ⟨10.1016/j.jsc.2017.12.001⟩

We present algorithmic, complexity and implementation results for the problem of isolating the real roots of a univariate polynomial in B α ∈ L [ y ] , where L = Q ( α ) is a simple algebraic extension of the rational numbers. We revisit two appr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b56ca1e5c7b959f89dc5134bc4ff1310
https://doi.org/10.1016/j.jsc.2017.12.001

CAD Adjacency Computation Using Validated Numerics

Autor: Adam Strzebonski

Publikováno v: ISSAC

We present an algorithm for computation of cell adjacencies for well-based cylindrical algebraic decomposition. Cell adjacency information can be used to compute topological operations e.g. closure, boundary, connected components, and topological pro

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dfbb398541bb0cb1b40e780be66af679

Univariate real root isolation over a single logarithmic extension of real algebraic numbers

Autor: Adam Strzebonski, Elias P. Tsigaridas

Publikováno v: Applications of Computer Algebra: July 20-23, 2015, Kalamata, Greece
ACA 2015-Applications of Computer Algebra
ACA 2015-Applications of Computer Algebra, Jul 2015, Kalamata, Greece. pp.425-445, ⟨10.1007/978-3-319-56932-1_27⟩
Applications of Computer Algebra ISBN: 9783319569307

We present algorithmic, complexity, and implementation results for the problem of isolating the real roots of a univariate polynomial \(B \in L[x]\), where \(L=\mathbb {Q} [ \lg (\alpha )]\) and \(\alpha \) is a positive real algebraic number. The al

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9def2a8203434efcfbb77d59d26c84fd
https://inria.hal.science/hal-01001820v3/file/st-rs-log.pdf

A Comparative Study of Two Real Root Isolation Methods

Autor: Adam Strzebonski, Alkiviadis G. Akritas

Publikováno v: Nonlinear Analysis, Vol 10, Iss 4 (2005)

Recent progress in polynomial elimination has rendered the computation of the real roots of ill-conditioned polynomials of high degree (over 1000) with huge coefficients (several thousand digits) a critical operation in computer algebra. To rise to t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d4dc534616fba058eefe9860957384f
https://doi.org/10.15388/na.2005.10.4.15110

Solving Systems of Strict Polynomial Inequalities

Autor: Adam Strzebonski

Publikováno v: Journal of Symbolic Computation. 29(3):471-480

We present an algorithm for finding an explicit description of solution sets of systems of strict polynomial inequalities, correct up to lower dimensional algebraic sets. Such a description is sufficient for many practical purposes, such as volume in

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6046d2df5edcb23b7b309d0300275e01