[Axiom-developer] A quick question about finite fields and polynomials

[Alasdair McAndrew]

Hello,

I'm just looking at axiom again after some years, and I've run into a little conundrum.  I have two objects, an element u of the finite field FF(7,4), and the defining polynomial f of that field.  Thus:

(67) -> u

(67) -> 

            3      2

   (67)  5%A  + 5%A  + %A

                                                       Type: FiniteField(7,4)

68) -> f

(68) -> 

          4

   (68)  ?  + ? + 1

                                Type: SparseUnivariatePolynomial PrimeField 7

What I want to do is to coerce both objects to polynomials over PF 7, so that I can factorize the result.  I want something like

(69) -> factor(5*b^3+5*b^2+b+b^4+b+1::POLY PF 7)

(69) -> 

   (69)  (b + 1)(b + 2)(b + 3)(b + 6)

                                       Type: Factored Polynomial PrimeField 7

But how can I obtain the polynomial in _expression_ (69) without typing it in; that is, from u and f directly?

Thanks,

Alasdair

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