The Lenstra Lenstra Lovász algorithm is massively used in the MAGMA computational algebra system, making it crucial to have a LLL routine which is as reliable and as fast as possible. For this purpose, the underlying code has been almost entirely rewritten, and the user interface has been changed.

In this talk, we will stress the improvements over the previous version by considering a few examples, explain what are the new algorithms and heuristics that have been implemented and finally describe the user interface and a few LLL-based routines that have been updated/added.