  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.
