I commented on the ticket that using
R2.<x,y> = PolynomialRing(QQ, 2, order="lp")
makes it work.
So this is a relatively harmless and easy to fix interface bug...

On Mon, Mar 18, 2019 at 4:16 PM Rachel Player <rachelpla...@gmail.com> wrote:
>
> Hi Dima,
>
> Thanks for your reply. I opened the following ticket: 
> https://trac.sagemath.org/ticket/27508#ticket
>
> Cheers,
> Rachel
>
> On Monday, 18 March 2019 13:21:52 UTC, Dima Pasechnik wrote:
>>
>> On Mon, Mar 18, 2019 at 1:01 PM Rachel Player <rachel...@gmail.com> wrote:
>> >
>> > I'd like to "remove squares" in some polynomials living in a polynomial 
>> > ring over QQ, in 2 variables: x,y. I tried to implement this by modding 
>> > out by the ideal (x^2 - x, y^2 - y). However, I have found that depending 
>> > on the ordering, the result of .mod() does not always output the 
>> > polynomial I am looking for.
>>
>> Thanks. This looks like a bug to me.
>> Specifically, a bug in Singular, or in Singular interface to Sage, as
>> if I do
>> R2.<s,t>=PolynomialRing(QQ,2,order="lex", implementation="generic")
>> then things work. (this is a slow Python implementation then)
>>
>> Care to open a trac ticket?
>>
>> Dima
>> >
>> > Please see attached for a code example: in the ring R2, the order is 
>> > specified as lex, and the polynomial x + y^2 does not reduce to x + y I 
>> > would like. This issue does not come up for the ring R1 (no ordering 
>> > specified explicitly), where both x + y^2 and x^2 + y reduce to x + y as 
>> > expected.
>> >
>> > Is there a way to force reduction even for the non-leading terms?
>> >
>> > Thanks,
>> > Rachel
>> >
>> >
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