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 <[email protected] 
> <javascript:>> 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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