In , Cariolaro et al. demonstrated how colorability problems can be approached numerically by the use of computer algebra systems and the Combinatorial Nullstellensatz. In particular, they verified a case of the List Coloring Conjecture by proving that the list-chromatic index of K6 is 5. In this short note, we show that using the coefficient formula of Schauz  is much more efficient than using partial derivatives. As a consequence we are able to show that list-chromatic index of K8 is 7 and the list-chromatic index of K10 is 9.
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