## Section: Software

### Isotop : Topology and Geometry of Planar Algebraic Curves

Participants : Jinsan Cheng, Sylvain Lazard, Luis Peñaranda, Marc Pouget.

Isotop is a Maple software for computing the topology of an algebraic plane curve, that is, for computing an arrangement of polylines isotopic to the input curve. This problem is a necessary key step for computing arrangements of algebraic curves and has also applications for curve plotting. This software has been developed since 2007 in collaboration with F. Rouillier from INRIA Paris - Rocquencourt (SALSA). It is based on the method described in [20] which incorporates several improvements over previous methods. In particular, our approach does not require generic position (nor shearing) and avoids the computations of sub-resultant sequences. Our preliminary implementation is competitive with other implementations (such as AlciX and Insulate developed at MPII Saarbrücken, Germany and top developed at Santander Univ., Spain). It performs similarly for small-degree curves and performs significantly better for higher degrees, in particular when the curves are not in generic position.