This package implements the Hermite norm form. It can be used to compute the
unimodular extension of an integer matrix. In the following example, we compute
the unimodular matrix Uinv which shares rows with the given rectangular matrix
A.
Reference: https://math.stackexchange.com/a/4397337/662983
julia> using HermiteNormalForm, LinearAlgebra
julia> A = [
-2 -1 0 3 0
-3 0 -2 -1 1
3 -1 1 -3 -1
];
julia> H, U = hnf(A); @assert all(isone, diag(H))
julia> Uinv = Int.(inv(U.//1))
5×5 Matrix{Int64}:
-2 -1 0 3 0
-3 0 -2 -1 1
3 -1 1 -3 -1
-7 0 -4 0 0
3 0 2 1 0
julia> Int(det(Uinv.//1))
1