[Axiom-developer] About finite fields

[Fabio S.]

I realized that when constructing finite fields providing a user choosen 
polynomial, Axiom doesn't check whether the used polynomial is 
irreducible or not.

For example:

(10) -> factor(x^8+x^4+x^2+x+1::PF 2)
(10) ->
           4    3       4    3    2
   (10)  (x  + x  + 1)(x  + x  + x  + x + 1)
                               Type: Factored(Polynomial(PrimeField(2)))
                                                             Time: 0 sec
(11) -> K:=FFP(PF 2,x^8+x^4+x^2+x+1)
(11) ->
   (11)  FiniteFieldExtensionByPolynomial(PrimeField(2),?^8+?^4+?^2+?+1)
                                                         Type: Domain
                                               Time: 0.01 (IN) = 0.01 sec
(12) -> size()$K
(12) ->
   (12)  256
                                                Type: NonNegativeInteger
                                                             Time: 0 sec
(13) -> a:=index(2)$K
(13) ->
   (13)  %A
   Type: FiniteFieldExtensionByPolynomial(PrimeField(2),?^8+?^4+?^2+?+1)
                                              Time: 0.01 (OT) = 0.01 sec
(14) -> minimalPolynomial a
(14) ->
          8    4    2
   (14)  ?  + ?  + ?  + ? + 1
                         Type: SparseUnivariatePolynomial(PrimeField(2))
                                                             Time: 0 sec
(15) -> (a^4+a^3+1)*(a^4+a^3+a^2+a+1)
(15) ->
   (15)  0
   Type: FiniteFieldExtensionByPolynomial(PrimeField(2),?^8+?^4+?^2+?+1)
                                                             Time: 0 sec


I am surprised that FiniteFieldByPolynomial allows a contruction which, 
clearly, has no sense and I am wondering if this has to be considered a 
bug to be fixed.

Fabio