We assume that $\mathbb{K} = \mathbb{C}$, that $(\mathrm{Id}, f, f^2, \ldots, f^{n-1})$ is free, and that $x_0 = u_1 + u_{m_1+1} + \cdots + u_{m_1 + \cdots + m_{p-1}+1}$ where $(u_1, \ldots, u_n)$ is the basis described in Q17. Justify that $f$ is cyclic.