title: How to solve a system of linear equations over the nonnegative integers?
body: <p>Given a linear system <code>Ax = b</code>, where matrix <code>A</code> and vector <code>b</code> have integer values, I want to find all <strong>nonnegative integer</strong> vectors <code>x</code> that solve this equation.</p>
  
  <p>So far, I have found some techniques such as the <a href="https://en.wikipedia.org/wiki/Smith_normal_form" rel="noreferrer">Smith normal form</a> or the <a href="https://en.wikipedia.org/wiki/Hermite_normal_form" rel="noreferrer">Hermite normal form</a> of a matrix to find integer solutions, and I guess I could then use a linear solver to find nonnegative solutions. Is there a library that could make this easier?</p>
  
  <p>Python solutions would be ideal, but if a library exists in another language I want to know about it.</p>