We describe a new subdivision method to efficiently compute the topology and the
arrangement of implicit planar curves. We emphasize that the output topology and …

We present a complete numerical algorithm of isolating all the real zeros of a zero-
dimensional triangular polynomial system F n Z [x 1…, xn]. Our system F n is general, with …

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 …

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 …

In this paper we give a new projection-based algorithm for computing the topology of a real
algebraic space curve given implicitly by a set of equations. Under some genericity …

We present a method to compute the exact topology of a real algebraic surface S, implicitly
given by a polynomial f∈ Q [x, y, z] of arbitrary total degree N. Additionally, our analysis …

In this paper, we address the problem of determining a real finite set of z-values where the
topology type of the level curves of a (maybe singular) algebraic surface may change. We …

We describe a new algorithm for the visualisation of implicit algebraic curves, which isolates
the singular points, compute the topological degree around these points in order to check …

We present a method to compute the exact topology of a real algebraic surface S, implicitly
given by a polynomial f∈ Q [x; y; z] of arbitrary degree N. Additionally, our analysis provides …

Based on an efficient generic position checking method and on a method to solve bivariate
polynomial systems, we give a new algorithm to compute the topology of an algebraic space …