Thank you very much for your explanation. I have seen your post at
sage-devel before, but completely forgot it.
I guess it would be better to raise an error or print a message than to
return a wrong result, if it is a known bug and not fixed yet.
Sho Takemori
2016年11月22日火曜日 19時27分58秒 UTC+9 Enrique Artal:
>
> This is an old bug affecting polynomials with local or semilocal orders.
> The problem is that at some point, the definition of the division by a
> polynomial checks first if the polynomial is a unit and in that case it
> identifies it with the constant term. This works for global orderings, but
> it causes this problems with local ones. Some people suggested to create a
> new class of rings to take into account that when considering non global
> rings the actual ring is bigger than the polynomial ring. For me, this is
> beyond my sage abilities.
>
> El viernes, 18 de noviembre de 2016, 3:03:01 (UTC+1), Sho Takemori
> escribió:
>>
>> Dear all,
>>
>> I created a polynomial ring with the "neglex" term order and computed the
>> division of polynomials as follows.
>>
>> sage: R.<a> = PolynomialRing(QQ, 1, order=TermOrder('neglex'))
>> sage: (1/2 + a) / (1 + 2 * a)
>> 1/2 + a
>>
>> I expected the result was 1/2.
>> The Sage version is 7.4 and Sage is running on Ubuntu 16.04.
>>
>> Best regards,
>> Sho Takemori
>>
>>
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