On the complexity of the Lickteig-Roy subresultant algorithm

Grégoire Lecerf (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

In their 1996 article, Lickteig and Roy introduced a fast divide and conquer variant of the subresultant algorithm which avoids coefficient growth in defective cases. The present article concerns the complexity analysis of their algorithm over effective rings endowed with the partially defined division routine. This leads to new convenient complexity bounds for gcds, especially when coefficients are in abstract polynomial rings where evaluation/interpolation schemes are not supposed to be available.

Domaines: Calcul formel [cs.SC]

Grégoire Lecerf. On the complexity of the Lickteig-Roy subresultant algorithm. Journal of Symbolic Computation, 2019, 92, pp.243-268. ⟨hal-01450869⟩