A Symbolic-Numeric Algorithm for Computing the Alexander Polynomial of a Plane Curve Singularity

Mădălina Hodorog (1) , Bernard Mourrain (2) , Josef Schicho (1)

1 RICAM - Johann Radon Institute for Computational and Applied Mathematics
2 GALAAD - Geometry, algebra, algorithms

We report on a symbolic-numeric algorithm for computing the Alexander polynomial of each singularity of a plane complex algebraic curve defined by a polynomial with coefficients of limited accuracy, i.e. the coefficients are both exact and inexact data. We base the algorithm on combinatorial methods from knot theory which we combine with computational geometry algorithms in order to compute efficient and accurate results. Nonetheless the problem we are dealing with is ill-posed, in the sense that tiny perturbations in the coefficients of the defining polynomial cause huge errors in the computed results.

Domaines: Géométrie algébrique [math.AG]

Mădălina Hodorog, Bernard Mourrain, Josef Schicho. A Symbolic-Numeric Algorithm for Computing the Alexander Polynomial of a Plane Curve Singularity. International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), Sep 2010, Timisoara, Romania. pp.21-28. ⟨inria-00542193⟩