Comments on the evaluation of massless scattering

The goal of this work is threefold. First, we give an expression of the most general five point integral on M0,n in terms of Chebyshev polynomials. Second, we choose a special kinematics that transforms the polynomial form of the scattering equations to a linear system of symmetric polynomials. We then explain how this can be used to explicitly evaluate arbitrary point integrals on M0,n . Third, we comment on the recently presented method of companion matrices and we show its equivalence to the elimination theory and an algorithm previously developed by one of the authors.