On Wed, Jan 1, 2014 at 2:17 PM, Peter Bruin <[email protected]> wrote:

> Hi Simon,
>
>
>> I'd say this is (close to) a bug.
>>
>
> It is a bug, without qualification.
>

Yes, it is a bug.

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.
>>
>
> That seems to be the only reasonable solution.
>

We have this already: sage.categories.sets_with_partial_maps.  But it looks
like there are lots of places where it's not used appropriately:

sage: ZZ.convert_map_from(QQ).parent().category()
Category of hom sets in Category of rings


>
> I would like to add that in my opinion the first line of this example,
>
> sage: f = GF(11).convert_map_from(GF(7))
>
> should not be assumed to work at all, and it would be preferable to raise
> an error rather than returning something that is mathematically completely
> arbitrary.
>
> Given the principle that no conditions are imposed on conversions (except
> that if a coercion exists, the conversion equals the coercion), it should
> in particular be perfectly fine if some of them do not satisfy the property
> of existing at all.
>
> Peter
>
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