Hi Peter,

On 2014-01-01, Peter Bruin <pjbr...@gmail.com> wrote:
> sage: f = GF(11).convert_map_from(GF(7))
> sage: f
> Conversion map:
>   From: Finite Field of size 7
>   To:   Finite Field of size 11
> sage: f.parent()
> Set of field embeddings from Finite Field of size 7 to Finite Field of size 11

I'd say this is (close to) a bug.

A conversion map is (by definition) a partial map, that in some cases
happens to be an actual map (not just partial), in other cases happens
to even be a morphism, and in the best case is a coerce map.

So, we should think of being more precise, introduce "Set of partial maps from
R to S", and use it as parents of partial maps that aren't maps.
Similarly, one should more consistently distinguish between the set of
all maps and the set of all morphisms.

Cheers,
Simon

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