Thanks for the answers.  By the way:

> Infinite fields of characteristic p aren't perfect,

Isn't the algebraic closure of F_p perfect?  For fields of
characteristic p, perfect should mean that every element has a pth
root.  (I agree that some infinite fields of characteristic p aren't
perfect, but this is not true for all of them.)

  John

> because the definition
> of perfect is that "every finite extension is separable".
> In any case, Sage is I think very limited regarding non-finite characteristic
> p fields, unfortunately (e.g., function fields of curves over finite fields).
> This is one of those things that Magma is unusually good at.
>
> William
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