Here is another discovery after 15 minutes of debugging:

sage: K1 = GF(8,'x')
sage: K2 = GF(8,'y')
sage: K1(1) == K2(1)
False

Nathann

On 17 September 2015 at 12:15, Vincent Delecroix
<20100.delecr...@gmail.com> wrote:
>
>
> On 17/09/15 06:53, Simon King wrote:
>>
>> Hi!
>>
>> On 2015-09-17, Jeroen Demeyer <jdeme...@cage.ugent.be> wrote:
>>>
>>> On 2015-09-16 16:43, Jean-Pierre Flori wrote:
>>>>
>>>> Hi,
>>>>
>>>> I guess one of the issue is that there is no canonical map between two
>>>> different representations of the same finite field (so no coercion).
>>>
>>>
>>> The question is really: is the map between representations of the same
>>> finite field, which differ only in variable name, "canonical"?
>>
>>
>> I think that it is in the same way canonical as we have a
>> name-preserving map between polynomial rings.
>>
>> The real problem here is that *conversion* gives rise to an error
>> that mentions *coercion*.
>>
>>    sage: K.<x> = GF(25)
>>    sage: L.<y> = GF(25)
>>    sage: K(y)
>>    Traceback (most recent call last):
>>    ...
>>    TypeError: unable to coerce from a finite field other than the prime
>> subfield
>>
>> That's clearly a bug. Conversion should work, even if it isn't canonical
>> and thus doesn't qualify as coercion!
>>
>> Is there no ticket for it already? I think I have seen that issue
>> before.
>
>
> +1
>
> The behavior should be similar to
>
> sage: Rx.<x> = ZZ[]
> sage: Ry.<y> = ZZ[]
> sage: Rx(3*y**2 + 1)
> 3*x^2 + 1
> sage: x+y
> Traceback (most recent call last):
> ...
> TypeError: unsupported operand parent(s) for '+': 'Univariate Polynomial
> Ring in x over Integer Ring' and 'Univariate Polynomial Ring in y over
> Integer Ring'
>
> Vincent
>
>
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