The computation of Groebner basis not correct?
I was trying to compute a Groebner basis for the ideal
I=<xz-y, y^2+z,x+1/2yz>, using lex order.
I used the following code:
P.<x,y,z>=PolynomialRing(QQ,'lex') I=ideal(x*z-y,y^2+z,x+(1/2)*y*z) G=I.groebner_basis();G
The result is
[z^3 + 2*z, x^2 - 1/2*z, x*y - 1/2*z^2, y^2 + z, x*z - y, y*z + 2*x]
Since the computation is easy, I checked by hands but got different result. So I checked by Singular and got the same result as mine, which is
> groebner(I); _=z3+2z _=yz2+2y _=y2+z _=2x+yz
So the result from Sage is wrong, since
yz^2+2y is in the ideal
I, but is not in the Groebner basis from the first computation using
I.groebner_basis(). Did I miss something in my command? Or is there a bug that needs to be fixed?