Hi,
when I type example below...

R.<x,y>=PolynomialRing(ZZ,2)
I=R*(4*x^2*y^2+2*x*y^3+3*x*y,2*x^2+x*y,2*y^2)
I.groebner_basis()

 [x^2*y, x*y^2, 2*x^2 + x*y, 3*x*y, 2*y^2]
... this is wrong result.
Right one is  [x*y^3, 2*x^2 + x*y, 3*x*y, 2*y^2] (from the book, and
calculating by hand).
How can I find the bug?

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