Yes, but the polynomial form generalizes to coefficients of an arbitrary field, not just naturals. If your vector were, say, [1.3, 2.197656, pi, -1/2, 3*2i] the

Yes, but the polynomial form generalizes to coefficients of an arbitrary field, not just naturals. If your vector were, say, [1.3, 2.197656, pi, -1/2, 3*2i] then there wouldn’t be a reasonable base you could pick for a place-value representation.