A Symbolic-Numeric Algorithm for Computing the Alexander Polynomial of a Plane Curve Singularity - Hodorog, M; Mourrain, B; Schicho, J (2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2010)
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.