  We consider the problem of finding a condition for a univariate polynomial
having a given multiplicity structure when the number of distinct roots is
given. It is well known that such conditions can be written as conjunctions of
several polynomial equations and one inequation in the coefficients, by using
repeated parametric gcd's. In this paper, we give a novel condition which is
not based on repeated gcd's. Furthermore, it is shown that the number of
polynomials in the condition is optimal and the degree of polynomials is
smaller than that in the previous condition based on repeated gcd's.
