Rational basis of nullspace

[yewalenikhil65]

This is a note to self ,and would be moved later to an appropriate place.
I was surprised to see MATLAB equipped with ability for calculating rational basis for nullspace and eigenbasis calculations.

Rational basis, according to me is what you obtain if you do reduced echelon form operations on pen-paper ,and then obtain the answer.
This is equivalent but not same as orthonormal basis that you obtain by using default null and eig MATLAB functions.
MATLAB thankfully has rref function for reducing a matrix to echelon form and this is what powers rational basis calculation behind-the-hood in MATLAB.
Julia, for some reasons has removed his rref functionality in their newer versions
Following is my Julia version to calculate nullspace as rational basis using the logic adopted from null.m file from MATLAB built-in function ( Copyright 1984-2017 The MathWorks, Inc.) and a julia library RowEchelon.jl
@pravinjagtap hope this is correct way of citing a MATLAB built-functions !

using LinearAlgebra
using RowEchelon
function rational_basis_nullspace(A::AbstractVecOrMat)
    R,pivcol = rref_with_pivots(A)
    m,n = size(A);
    r = length(pivcol);
    nopiv = collect(1:n);
    deleteat!(nopiv, pivcol)
    Z = zeros(n,n-r);
    if n > r
        Z[nopiv,:] = diagm(0 => ones(n-r));
        if r > 0
            Z[pivcol,:] = -R[1:r,nopiv];
        end
    end
    return Z
end