Computing the equisingularity type of a pseudo-irreducible polynomial

Abstract

Germs of plane curve singularities can be classified accordingly to their equisingularity type. For singularities over $$\mathbb {C}$$ , this important data coincides with the topological class. In this paper, we characterise a family of singularities, containing irreducible ones, whose equisingularity type can be computed in an expected quasi-linear time with respect to the discriminant valuation of a Weierstrass equation.