HermiteNormalForm

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