For the Allee example, we currently randomize the generators of the radical ideal by multiplying with a completely generic matrix. This gives rise to many extraneous solutions that we then have to discard. Usually, it's better to multiply with a triangular matrix, given an appropriate ordering of the polynomials, as explained in Chapter 13.5 of Sommese–Wampler. I think we should try this!
For the Allee example, we currently randomize the generators of the radical ideal by multiplying with a completely generic matrix. This gives rise to many extraneous solutions that we then have to discard. Usually, it's better to multiply with a triangular matrix, given an appropriate ordering of the polynomials, as explained in Chapter 13.5 of Sommese–Wampler. I think we should try this!