> How does one figure it out in code, without looking at the expression?
> (I guess there could be more than one field extension involved)

Maybe like this...

http://axiom-wiki.newsynthesis.org/ExampleIntegration

(26) -> ks := kernels i;

                                      Type:
List(Kernel(Expression(Integer)))
(27) -> [definingPolynomial(k::Expression(Integer)) for k in ks | name
operator k = 'rootOf]


                3
          23%%F0  + %%F0 + 1
   (27)  [------------------]
                  23
                                              Type:
List(Expression(Integer))


Ralf

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