%0 Journal Article
%T A probabilistic and deterministic modular algorithm for computing Groebner basis over $\Q$
%A Bernard Parisse
%J Computer Science
%D 2013
%I arXiv
%X Modular algorithm are widely used in computer algebra systems (CAS), for example to compute efficiently the gcd of multivariate polynomials. It is known to work to compute Groebner basis over $\Q$, but it does not seem to be popular among CAS implementers. In this paper, I will show how to check a candidate Groebner basis (obtained by reconstruction of several Groebner basis modulo distinct prime numbers) with a given error probability, that may be 0 if a certified Groebner basis is desired. This algorithm is now the default algorithm used by the Giac/Xcas computer algebra system with competitive timings, thanks to a trick that can accelerate computing Groebner basis modulo a prime once the computation has been done modulo another prime.
%U http://arxiv.org/abs/1309.4044v2