Subresultants and Generic Monomial Bases

Given n polynomials in n variables of respective degrees d_1,…,d_n, and a set of monomials of cardinality d_1…d_n, 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 Bezout construction of the resultant.