Very recent work introduces an asymptotically fast subdivision algorithm, denoted ANewDsc,
for isolating the real roots of a univariate real polynomial. The method combines Descartes …

Computing the roots of a univariate polynomial is a fundamental and long-studied problem
of computational algebra with applications in mathematics, engineering, computer science …

We describe a subdivision algorithm for isolating the complex roots of a polynomial F∈ C [x].
Given an oracle that provides approximations of each of the coefficients of F to any absolute …

We present an algorithm for isolating all roots of an arbitrary complex polynomial p that also
works in the presence of multiple roots provided that (1) the number of distinct roots is given …

Let F (z) be an arbitrary complex polynomial. We introduce the {local root clustering
problem}, to compute a set of natural epsilon-clusters of roots of F (z) in some box region B0 …

We introduce a novel algorithm denoted NewDsc to isolate the real roots of a univariate
square-free polynomial f with integer coefficients. The algorithm iteratively subdivides an …

Given two coprime polynomials P and Q in Z [x, y] of degree bounded by d and bitsize
bounded by τ, we address the problem of solving the system {P, Q}. We are interested in …

We present a certified and complete algorithm to compute arrangements of real planar
algebraic curves. It computes the decomposition of the plane induced by a finite number of …

We propose to design new algorithms for motion planning problems using the well-known
Domain Subdivision paradigm, coupled with" soft" predicates. Unlike the traditional exact …

We study the complexity of computing the real solutions of a bivariate polynomial system
using the recently presented algorithm Bisolve [2]. Bisolve is an elimination method which, in …