Given a finite collection S of geometric objects such as hyperplanes or spheres in Rd, the
arrangement A (S) is the decomposition of Rd into connected open cells of dimensions 0 …

Let Z be a two dimensional irreducible complex component of the solution set of a system of
polynomial equations with real coefficients in N complex variables. This work presents a …

We present an exact and complete algorithm to isolate the real solutions of a zero-
dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination …

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 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 …

Computing the topology of an algebraic plane curve C means computing a combinatorial
graph that is isotopic to C and thus represents its topology in R2. We prove that, for a …

Given a zero-dimensional polynomial system consisting of n integer polynomials in n
variables, we propose a certified and complete method to compute all complex solutions of …

Bertini_real is a compiled command line program for numerically decomposing the real
portion of a positive-dimensional complex component of an algebraic set. The software uses …

In this paper, a linear univariate representation for the roots of a zero-dimensional
polynomial equation system is presented, where the complex roots of the polynomial system …

This work presents novel geometric algorithms dealing with algebraic curves and surfaces of
arbitrary degree. These algorithms are exact and complete—they return the mathematically …