Bug(?) in the division of polynomials with the TermOrder('neglex')

[Sho Takemori]

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

[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.

[Sho Takemori]

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:

[Dima Pasechnik]

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...

[Justin C. Walker]

On Nov 22, 2016, at 05:40 , Dima Pasechnik wrote:

>
> 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...

I see the same with Singular 3.1.3:
$ Singular
SINGULAR / Development
A Computer Algebra System for Polynomial Computations / version 3-1-3
0<
by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ March 2011
FB Mathematik der Universitaet, D-67653 Kaiserslautern \
// ** executing /SandBox/Justin/sb/Singular/3-1-3/LIB/.singularrc
> ring R=0,x,dp;
// ** redefining R **
> poly f1=(1/2)+x;
> poly f2=1+2*x;
> f1/f2;
1/2

FWIW.

Justin

--
Justin C. Walker, Curmudgeon at Large
Institute for the Absorption of Federal Funds
-----------
I want to die, peacefully in my sleep, like my grandfather;
not screaming in terror, like his passengers.

[Enrique Artal]

I think the problem was not in Singular but in the Sage code for division of polynomials. There is a ticket, https://trac.sagemath.org/ticket/17638. I may help but my skills are not enough to solve the problem.