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Given a lattice basis of n vectors in Z^n, we propose an algorithm using 12n^3+O(n^2) floating point operations for checking whether the basis is LLL-reduced. If the basis is reduced then the algorithm will hopefully answer "yes". If the basis is not reduced, or if the precision used is not sufficient with respect to n, and to the numerical properties of the basis, the algorithm will answer "failed". Hence a positive answer is a rigorous certificate. For implementing the certificate itself, wearXiv:cs/0701183v1 fatcat:cfmuh472wje45b7ymthlc2ag2e