Finite fields in Axiom: a few questions

"Alasdair McAndrew" <[email protected]>
Newsgroups gmane.comp.mathematics.axiom.user
Message-ID <[email protected]>
It was playing around with finite fields which got me to investigate Axiom
in the first place.  Here are a few questions, arising from this input:

(1) -> F16:=FiniteField(2,4)

   (1)  FiniteField(2,4)
                                                                 Type:
Domain
(2) -> random()$F16

          3     2
   (2)  %A  + %A  + 1
                                                       Type:
FiniteField(2,4)
(3) -> definingPolynomial()$F16

         4
   (3)  ?  + ? + 1
                                Type: SparseUnivariatePolynomial PrimeField
2


All well and good, but

- how to I get output in terms of a nice variable (say x) rather than "?"
and "%A"?

- is there any way of forcing a particular defining polynomial?  (This is
good for working through examples.)

Thanks,
Alasdair

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