On the complexity of polynomial reduction

Joris van der Hoeven (1)

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

In this paper, we present a new algorithm for reducing a multivariate polynomial with respect to an autoreduced tuple of other polynomials. In a suitable sparse complexity model, it is shown that the execution time is essentially the same (up to a logarithmic factor) as the time needed to verify that the result is correct. This is a first step towards making advantage of fast sparse polynomial arithmetic for the computation of Gröbner bases.

Mots clés: Sparse reduction; complexity; division; Groebner basis; algorithm

Domaines: Logiciel mathématique [cs.MS]

Joris van der Hoeven. On the complexity of polynomial reduction. 2012. ⟨hal-00658704⟩