On Tuesday, November 22, 2016 at 12:19:37 PM UTC, Sho Takemori wrote:
>
> 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.
>
In fact, Singular 4.0.3 (now in Sage 7.5.beta3)
does the right thing:
> ring r=0,(a),ls;
> (1/2+a)/(1+2*a);
1/2
(same if I use more variables while defining r, not just one)
Thus I guess Sage does not get from Singular the data right...
> 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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