My good friend and colleague Christian Ikenmeyer and I wrote this cute preprint about polynomials and how they can be written as the determinant of a matrix with entries equal to zero, one and indeterminantes. Go ahead and read it if you know even just a little math, it's quite straightforward. The algorithm described in section 3 has been implemented and you can download the code from my website at the TU Berlin. Compilation instructions are in
ptest.c, but you will need to get nauty to perform the entire computerized proof.