  By solving a problem regarding polynomials in a quotient ring, we obtain the
relative hull and the Hermitian hull of projective Reed-Muller codes over the
projective plane. The dimension of the hull determines the minimum number of
maximally entangled pairs required for the corresponding entanglement-assisted
quantum error-correcting code. Hence, by computing the dimension of the hull we
now have all the parameters of the symmetric and asymmetric
entanglement-assisted quantum error-correcting codes constructed with
projective Reed-Muller codes over the projective plane. As a byproduct, we also
compute the dimension of the Hermitian hull for affine Reed-Muller codes in 2
variables.
