On Wednesday, August 5, 2020 at 10:19:57 AM UTC-7, john_perry_usm wrote:
>
>
> It's possible that you want a local term ordering. Unlike global term 
> orderings, in a local ordering 1>t for any monomial t.
>
> TO = TermOrder("negdegrevlex",3)
> R = PolynomialRing(GF(2),'x',3,order=TO)
> R.inject_variables()
> >>>> Defining x0, x1, x2
> I = R.ideal([x0*x1+x2])
> x2.reduce(I)
> >>>> x0*x1
>
>
In which case you need to realize that you're not working in a polynomial 
ring but in its localization! This has been the source of many bug reports 
already, and is currently not sufficiently documented.

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