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 …

In this paper, we give improved bounds for the computational complexity of computing with
planar algebraic curves. More specifically, for arbitrary coprime polynomials f, g∈ Z [x, y] …

We address the problem of solving systems of bivariate polynomials with integer coefficients.
We first present an algorithm for computing a separating linear form of such systems, that is …

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 …

In this paper, an algorithm is given for determining the topology of an algebraic space curve
and to compute a certified G 1 rational parametric approximation of the algebraic space …

The goal of this paper is to measure the non-convexity of compact and smooth connected
components of real algebraic plane curves. We study these curves first in a general setting …

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 …

Abstract Let P∈ Z [X, Y] be a given square-free polynomial of total degree d with integer
coefficients of bitsize less than τ, and let VR (P):={(x, y)∈ R 2∣ P (x, y)= 0} be the real planar …

Recently developed GeoGebra tools for the automated deduction and discovery of
geometric statements combine in a unique way computational (real and complex) algebraic …

We address the problem of solving systems of two bivariate polynomials of total degree at
most d with integer coefficients of maximum bitsize τ We suppose known a linear separating …