Interesting. It seems the problem is that
cm.discover_action(GF(5), ZZ, operator.div)
tries to look for a right action on of
cm.discover_action(GF(5), Frac(ZZ), operator.mul)
which doesn't exist as there are no coercions between GF(5) and QQ.
I posted a patch to http://trac.sagemath.org/ticket/17740 .
On Thu, Feb 5, 2015 at 1:39 PM, Jonas Jermann <jjerma...@gmail.com> wrote:
> Hi
>
> Set x=GF(5)['x'].gen()
> I dunno if this helps but here is an explanation why one gets a
> different behavior for x/7 than cm.bin_op(x,7,operator.div):
>
> If you do "x/7" then I think it calls __div__ from polynomial_element
> (Polynomial class):
>
> try:
> if not isinstance(right, Element) or right.parent() != self.parent():
> R = self.parent().base_ring()
> x = R._coerce_(right)
> return self * ~x
> except (TypeError, ValueError):
> pass
> return RingElement.__div__(self, right)
>
> Here right=ZZ(7), self=x, so right.parent() != self.parent()
> so it does x = GF(5)._coerce_(7)
> which is why you end up without the Fraction Field...
>
> If on the other hand you do cm.bin_op(x,7,operator.div) or x._div_(7) you
> get a Fraction Field element at the moment.
>
>
> Best
> Jonas
>
>
> On 05.02.2015 22:08, Vincent Delecroix wrote:
>>
>> 2015-02-05 21:38 UTC+01:00, John Cremona <john.crem...@gmail.com>:
>>>
>>> If you ask for operator.mul instead of operator.div then you get the
>>> poly ring. Is that it, perhaps?
>>
>>
>> Nope. I want to get rid of many hacks in rings/polynomial. In order to
>> do that I need the div operation to be correctly handled by the
>> coercion (or perhaps I missed something about the aim of coercion?).
>> Namely, if p is an element of GF(5)['x,y'] then (p/Integer(2)) should
>> be an element of GF(5)['x,y']. You can argue that this is what you get
>> in Sage
>>
>> sage: R = GF(5)['x','y']
>> sage: (R.an_element() / 2).parent()
>> Multivariate Polynomial Ring in x, y over Finite Field of size 5
>>
>> But the reason why is a bit of a hack that actually introduce many
>> bugs in other places:
>>
>> sage: R = GF(5)['x,y']
>> sage: (R.one() / R.one()).parent()
>> Multivariate Polynomial Ring in x, y over Finite Field of size 5
>>
>> the above should be an element of the fraction field! And you can
>> build more involved examples.
>>
>> Vincent
>>
>
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