Possibly incorrect result in groebner basis over the integers

[Georgi Guninski]

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]

[G. M.-S.]

This result is correct, as you are working over ℤ.

If you try over ℚ, you will get [1].

Guillermo

[Emmanuel Briand]

Not a bug, but a (nice) feature: Gröbner bases for rings of polynomials with integers coefficients, documented in:

https://doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/multi_polynomial_ideal.html

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