Re: Finite fields in Axiom: a few questions

"Alasdair McAndrew" <[email protected]> writes:

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

(1) -> )se me au of
(1) ->  F16:=FiniteField(2,4)

   (1)  FiniteField(2,4)
                                                                 Type: Domain
(2) -> (definingPolynomial()$F16).x

         4
   (2)  x  + x + 1


> and "%A"?

this one I do not know (currently), since

(10) -> p := random()$F16

           3     2
   (10)  %A  + %A  + 1
                                                       Type: FiniteField(2,4)

is *not* a polynomial. It's an element of FiniteField(2,4). But maybe you like:

(12) -> minimalPolynomial(p).x

          4    3
   (12)  x  + x  + 1
                                            Type: Fraction Polynomial Integer

(It would be rather easy to modify the output of FiniteField wo use something
else as output, but I don't think this would make sense)

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

Is this what FiniteFieldExtensionByPolynomial is for? I guess one would have to
do a little maths here. I'll look into it today afternoon.

Martin