Computing a lattice basis from a system of generating vectors
In this paper we describe how the LLL-algorithm can be used to compute a basis of a lattice L in R n from a system of k generating vectors and a lower bound for the lengths of the non zero vectors in L. The algorithm which we present is proved to be polynomial time in n + k and the size of the input data. The algorithm is applied to the problem of finding multiplicative relations between units of algebraic number fields. Numerical results show that our method works very efficiently.
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