Computation of unimodular matrices

Here we give an algorithm for solving the following problem. Let $m<n$ integer vectors be given in the $n$-dimensional real space. Their linear span forms a linear subspace $L$ in $\mathbb{R}^n$. It is required to calculate such an unimodular matrix that a linear transformation with it transforms the subspace $L$ into a coordinate one. Also, programs that implement the algorithms and power transformations, for which they are needed, are given.