Enrique, you are right, that doesn't come from the interface, but directely
from Singular. Above, I took the wrong ordering. Here the correction:
sage: R.<x,y>=PolynomialRing(QQ,order='neglex')
sage: R._singular_init_()
polynomial ring, over a field, local ordering
// coefficients: QQ
// number of vars : 2
// block 1 : ordering ls
// : names x y
// block 2 : ordering C
SINGULAR / Development
A Computer Algebra System for Polynomial Computations / version 4.1
.1
0<
by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Feb 2018
FB Mathematik der Universitaet, D-67653 Kaiserslautern \
> ring r = 0,(x, y),ls;
> poly f,g = 1+x, x^2;
> ideal I = (g);
> reduce(f,I);
1
BTW: The ticket you mentioned doesn't seem to adress that problem properly.
The example which Simon inserted is now working. Therefore the ticket just
consists of a doctest for that (I guess that has been made on the Sage Days
in Zaragozza). The only reason that it isn't closed has been a merge
confict, which has disappeared in the meantime.
On Thursday, April 9, 2020 at 9:28:07 AM UTC+2, Enrique Artal wrote:
>
> HI,
> I think it is related with ticket #17638
> <https://trac.sagemath.org/ticket/17638>. There is a mathematical origin
> in this situation. When considering a non local ordering, one is working in
> a localized ideal, where any polynomial whose leading term is a non-zero
> constant is invertible. Singular works silently in this new ring without
> explicit declaration. I think that for Sage, a new structure should be
> constructed, but I do not know how. Best, Enrique.
>
> El lunes, 6 de abril de 2020, 9:46:26 (UTC+2), Yang Zhou escribió:
>>
>> Hi,
>>
>> I am trying to truncate a multi-variable polynomial by moding out higher
>> order term and found
>> the following (simplified) example. I am wondering if it is a bug.
>>
>>
>> *Reproducible Example: *
>>
>>> R.<x,y> = PolynomialRing(QQ, order='negdeglex')
>>>
>> f = 1 + x
>>> I = R.ideal(x^2)
>>> f.mod(I)
>>>
>> *Expected output:*
>>
>>> 1 + x
>>>
>> *Actual output:*
>>
>>> 1
>>>
>>
>>
>> *Note: *
>> The actual output will be 1+x when I omit the "order='negdeglex"
>> parameter.
>>
>> *SageMath version:*
>> SageMath version 9.0, Release Date: 2020-01-01
>>
>> *Operating system:*
>> OS: Ubuntu 19.10 x86_64
>> Kernel: 5.3.0-45-generic
>>
>> Best regards,
>> Yang
>>
>
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