Genom3ck

We approach the algebraic problem of computing topological invariants for the singularities of a plane complex algebraic curve defined by a squarefree polynomial with inexactlyknown coefficients. Consequently, we deal with an ill-posed problem in the sense that, tiny changes in the input data lead to dramatic modifications in the output solution.We present a regularization method for handling the illposedness of the problem. For this purpose, we first design symbolic-numeric algorithms to extract structural information on the plane complex algebraic curve: (i) we compute the link of each singularity by numerical equation solving; (ii) we compute the Alexander polynomial of each link by using algorithms from computational geometry and combinatorial objects from knot theory; (iii) we derive a formula for the delta-invariant and the genus. We then prove the convergence for inexact data of the symbolic-numeric algorithms by using concepts from algebraic geometry and topology.Moreover we perform several numerical experiments, which support the validity for the convergence statement.

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Genom3ck

Cited by 2 publications

References 2 publications

A regularization approach for estimating the type of a plane curve singularity

A regularization approach for estimating the type of a plane curve singularity

A regularization method for computing approximate invariants of plane curves singularities

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