Approximate contact factorization of germs of plane curves

Joris van der Hoeven (1, 2) , Grégoire Lecerf (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

Given an algebraic germ of a plane curve at the origin, in terms of a bivariate polynomial, we analyze the complexity of computing an irreducible decomposition up to any given truncation order. With a suitable representation of the irreducible components, and whenever the characteristic of the ground field is zero or larger than the degree of the germ, we design a new algorithm that involves a nearly linear number of arithmetic operations in the ground field plus a small amount of irreducible univariate polynomial factorizations.

Mots clés: contact factorization; approximate root; polynomial factorization; algebraic curve; complexity

Domaines: Logiciel mathématique [cs.MS]

Joris van der Hoeven, Grégoire Lecerf. Approximate contact factorization of germs of plane curves. 2022. ⟨hal-03745581⟩