### 2.46.10 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+an−1xn−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,....,−an−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]]`