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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