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View all- Poteaux AWeimann M(2020)Computing the equisingularity type of a pseudo-irreducible polynomialApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-020-00451-xOnline publication date: 24-Aug-2020
A regularization method for computing approximate invariants of plane curves singularities
Pages 44 - 53
Abstract
We approach the algebraic problem of computing topological invariants for the singularities of a plane complex algebraic curve defined by a squarefree polynomial with inexactly-known 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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Index Terms
- A regularization method for computing approximate invariants of plane curves singularities
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Published: 07 June 2012
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ISSAC '11: International Symposium on Symbolic and Algebraic Computation
June 7, 2011 - June 9, 2012
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View all- Poteaux AWeimann M(2020)Computing the equisingularity type of a pseudo-irreducible polynomialApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-020-00451-xOnline publication date: 24-Aug-2020
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