33 citations · 106 across the 19 of their papers we have counts for
5 papers · 1 filter
When Newton meets Descartes: A Simple and Fast Algorithm to Isolate the Real Roots of a Polynomial
Michael Sagraloff
We introduce a new algorithm denoted DSC2 to isolate the real roots of a univariate square-free polynomial f with integer coefficients. The algorithm iteratively subdivides an init…
On the Complexity of Solving a Bivariate Polynomial System
Pavel Emeliyanenko, Michael Sagraloff
We study the complexity of computing the real solutions of a bivariate polynomial system using the recently proposed algorithm BISOLVE. BISOLVE is a classical elimination method wh…
A Worst-case Bound for Topology Computation of Algebraic Curves
Michael Kerber, Michael Sagraloff
Computing the topology of an algebraic plane curve means to compute a combinatorial graph that is isotopic to and thus represents its topology in $\math…
Root Refinement for Real Polynomials
Michael Kerber, Michael Sagraloff
We consider the problem of approximating all real roots of a square-free polynomial . Given isolating intervals, our algorithm refines each of them to a width of or les…
Arrangement Computation for Planar Algebraic Curves
Eric Berberich, Pavel Emeliyanenko, Alexander Kobel +1
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposit…