def inRadical(f, s):
    sum = f
    for g in s:
        sum += g
    R = parent(sum)
    variables = [ str(v) for v in R.gens() ]
    # print(variables)
    variables.append("yyy")
    H = PolynomialRing(CC, variables)
    yyy = H.gens()[-1]
    s1 =  s.copy()
    s1.append(1 - yyy*f)
    # print(s1)
    J = ideal(s1).groebner_basis()
    # print("J:", J)
    return J == [1.]