Minimal polynomial : pmin

### 2.46.8 Minimal polynomial : `pmin`

`pmin` takes one (resp two) argument(s): a square matrix A of size n and optionnaly the name of a symbolic variable.
`pmin` returns the minimal polynomial of A written as a list of its coefficients if no variable was provided, or written in symbolic form with respect to the variable name given as second argument. The minimal polynomial of A is the polynomial P having minimal degree such that P(A)=0.
Input :

`pmin([[1,0],[0,1]])`

Output :

`[1,-1]`

Input :

`pmin([[1,0],[0,1]],x)`

Output :

`x-1`

Hence the minimal polynomial of [[1,0],[0,1]] is `x-1`.
Input :

`pmin([[2,1,0],[0,2,0],[0,0,2]])`

Output :

`[1,-4,4]`

Input :

`pmin([[2,1,0],[0,2,0],[0,0,2]],x)`

Output :

`x```^```2-4*x+4`

Hence, the minimal polynomial of [[2,1,0],[0,2,0],[0,0,2]] is x2−4x+4.