Subresultants and generic monomial bases

Given n polynomials in n variables of respective degrees d1,…,dn, and a set of monomials of cardinality d1⋯dn, we give an explicit subresultant-based polynomial expression in the coefficients of the input polynomials whose non-vanishing is a necessary and sufficient condition for this set of monomials to be a basis of the ring of polynomials in n variables modulo the ideal generated by the system of polynomials. This approach allows us to clarify the algorithms for the Bézout construction of the resultant.