On Mon, Mar 8, 2021 at 12:27 PM Alex Braat <alexbr...@gmail.com> wrote:
>
> Small update:
> Replacing Integers(p^2) by QuotientRing(ZZ, p^2) seems to fix the issue.

Could you open a trac ticket on this?
It looks as if multivariate polynomial rings over Integers(p^2) are
directly using Singular,
but I don't think Singular can do such computations (over non-fields)

QuotientRing(ZZ, p^2) does something else.

>
> Op maandag 8 maart 2021 om 10:34:06 UTC+1 schreef dim...@gmail.com:
>>
>> On Mon, Mar 8, 2021 at 9:25 AM Alex Braat <alex...@gmail.com> wrote:
>> >
>> > Hello,
>> >
>> > I have encountered some strange behavior when I evaluate multivariate 
>> > polynomials over the integers modulo n. For instance,
>> >
>> > In:
>> > p = 3
>> > S = Integers(p^2)
>> > R.<x,y> = PolynomialRing(S)
>> > f = x^2 * y^2
>> > print(f([S(p),S(1)]), f([S(1), S(p)]))
>> >
>> > Out:
>> > 1 0
>> >
>> > while both evaluations should ofcourse be equal to 0. This does not depend 
>> > on the prime p, and is consistent in both of these versions of SageMath:
>>
>> looks like a bug (also in the 9.3.beta7)
>> sage: f(S(3),S(1))
>> 1
>>
>>
>> >
>> > 'SageMath version 8.7, Release Date: 2019-03-23'
>> > 'SageMath version 9.2, Release Date: 2020-10-24'
>> >
>> > Am I doing something wrong or is this a bug?
>> >
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