Hi David,

First, thank you for technical explanations. They are compelling.

On Thursday, October 13, 2016 at 9:59:50 PM UTC+2, David Roe wrote:
> In order to create finite fields with arbitrary variable names that fit 
> into a lattice of fields, one possibility would be able to give an 
> algebraic closure explicitly as an argument to GF.  Is that what you're 
> suggesting?
> sage: F = GF(3).algebraic_closure('custom')
> sage: K9 = GF(9,'b',Fpbar=F)
> sage: K81 = GF(81,'c',Fpbar=F)
> sage: K81.has_coerce_map_from(K9)
> True

Still speaking from a user's point of view, is there also a technical 
difficulty in keeping just one lattice of fields? So a new creation of a 
finite field gets automatically fitted into the canonical lattice? 

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