Companion matrix of a polynomial : companion

companion takes as argument an unitary polynomial P and the name of its variable.
companion returns the matrix whose characteristic polynomial is P.
If P(x) = xⁿ + a_n-1x^n-1 + ... + a_-1x + a₀, this matrix is equal to the unit matrix of size n - 1 bordered with [0, 0.., 0, - a₀] as first row, and with [- a₀, - a₁,...., - a_n-1] as last column.
Input :

companion(x^2+5x-7,x)

Output :

[[0,7],[1,-5]]

Input :

companion(x^4+3x^3+2x^2+4x-1,x)

Output :

[[0,0,0,1],[1,0,0,-4],[0,1,0,-2],[0,0,1,-3]]