This difference may be relevant: R.<x,y> = ZZ[] I = R.ideal(4*x^2,9*y^2) I.reduce(x^2*y^2) #correctly returns 0 (x^2*y^2).reduce(I) #does not return 0 (x^2*y^2).reduce(I.groebner_basis()) #does return 0
The documentation of x.reduce suggests that if the argument is an ideal for which sage can compute a strong groebner basis, then the reduction should take place with respect to a strong groebner basis. It looks like it's not doing that. On Wednesday, 26 November 2025 at 07:05:08 UTC-8 [email protected] wrote: > I expect this is a bug related to > https://github.com/sagemath/sage/issues/40301 > > On Tuesday, November 25, 2025 at 2:23:28 PM UTC Georgi Guninski wrote: > >> I am looking for rings with many degree $d$ nilpotent elements and >> non-zero product, for detail check [1]. >> >> While working over ZZ[x,y] I noticed this, is it a bug? >> >> sage: Kx.<x,y>=ZZ[];Kquo.<w1,w2>=Kx.quotient([(2*x)^2,(3*y)^2]) >> sage: w1^2 >> w1^2 >> sage: w1*w2 >> w1*w2 >> sage: (w1*w2)^2 >> 0 #why zero??? >> sage: ((x*y)^2).reduce(Ideal([(2*x)^2,(3*y)^2])) >> x^2*y^2 >> sage: >> >> [1]: >> https://mathoverflow.net/questions/504074/many-degree-d-nilpotent-elements-of-quotients-of-polynomial-rings-and-non-vani >> >> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/sage-devel/d8617349-961c-4bc1-8c25-22c7bbc6980fn%40googlegroups.com.
