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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