Polynomial to companion matrix

Given the polynomial $p\left(x\right)=a_0+a_{1}t+\cdots +a_{n-1}{t}^{n-1}+a_n{t}^n$

the companion matrix is the square matrix defined as

$C\left(p\right)=\left(\begin{array}{ccccc}0& 0& \cdots & 0& -c_0\\ 1& 0& \cdots & 0& -c_1\\ 0& 1& \cdots & 0& -c_2\\ ⋮& ⋮& \ddots & ⋮& ⋮\\ 0& 0& \cdots & 1& -c_{n-1}\end{array}\right)$

where $c_i=\frac{a_i}{a_n}$.

polynomial_to_companion_matrix(Polynomial)

Description

Given a polynomial, returns the companion matrix as described above.