LatticeReduce
LatticeReduce[{v1, v2, ...}] gives a reduced basis for the set of vectors v_i using the LLL algorithm.
Examples
Reduce a lattice basis:
LatticeReduce[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}]2D example:
LatticeReduce[{{1, 0}, {3, 4}}]
(* {{1, 0}, {0, 4}} *)Please visit the official Wolfram Language Reference for more details.