  We prove that the polynomial form of the scattering equations is a Macaulay
H-basis. We demonstrate that this H-basis facilitates integrand reduction and
global residue computations in a way very similar to using a Gr\"obner basis,
but circumvents the heavy computation of the latter. As an example, we apply
the H-basis to prove the conjecture that the dual basis of the polynomial
scattering equations must contain one constant term.
