This result is correct, as you are working over ℤ.
If you try over ℚ, you will get [1].

Guillermo

On Fri, 10 Mar 2023 at 11:57, Georgi Guninski <ggunin...@gmail.com> wrote:

> I think grobner basis which contain non-zero constant and polynomials
> is a bug.
>
> sage: K.<x,y>=ZZ[]
> sage: l=[x^2+y^2+x+4,x^2+y^2+4*y+2,x^2-13*y^2+x]
> sage: I=Ideal(l);gb=I.groebner_basis();gb
> [y^2 + 4*y + 198, x + 1036*y + 2, 8*y + 544, 1040]
>

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