### 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 *x*^{2}−4*x*+4.