A CGAL-based Univariate Algebraic Kernel and Application to Arrangements (2009)
Sylvain Lazard, Luis Peñar, A Elias Tsigaridas
Solving univariate polynomials and multivariate polynomial systems is critical in geometric computing with curved objects. Moreover, the real roots need to be computed in a certified way in order to...
On the Topology of Planar Algebraic Curves (2009)
Jinsan Cheng, Sylvain Lazard, Luis Peñar, Marc Pouget, Fabrice Rouillier, Elias Tsigaridas
We introduce a method to compute the topology of planar algebraic curves. The curve may not be in generic position and may have vertical asymptotes. The algebraic tools are rational univariate...
On the topology of planar algebraic curves (2008)
Jinsan Cheng, Sylvain Lazard, Luis Peñar, Marc Pouget, Fabrice Rouillier, Elias Tsigaridas
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and...