On Mon, Nov 21, 2011 at 11:36 PM, William Stein <wst...@gmail.com> wrote:
> On Mon, Nov 21, 2011 at 4:50 PM, David Roe <r...@math.harvard.edu> wrote:
>> The coercion graph in Sage is supposed to be transitive.  This
>> assumption is explicit in the documentation of sage.structure.coerce
>> for example.  But we have the following:
>>
>> sage: R = Zmod(6)
>> sage: S = Zmod(3)
>> sage: T = GF(3)
>> sage: T.has_coerce_map_from(S)
>> True
>> sage: S.has_coerce_map_from(R)
>> True
>> sage: T.has_coerce_map_from(R)
>> False
>
> I think that should return True, since there is a canonical map from
> Z/6Z to GF(3).
>
>> Any opinions on which of these results should change?  I'm thinking
>> about such coercions between finite rings in the context of residue
>> fields and quotients of p-adic rings, so you can also ask yourself if
>> you want a coercion from Zmod(250) to Zp(5).quotient(5^3).
>
> I want such a coercion, since again there is a canonical map Z/250Z
> --> Z/5^3Z \isom Z_5 / 5^3 Z_5.

+1. My thoughts exactly.

- Robert

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