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Make u and v be in the Fraction field:

sage: B.<u,v> = Frac(QQ['u,v'])
sage: R.<x,y> = PolynomialRing(B, 'x', 'y')
sage: I = R.ideal(v * x^2 + y, u* x * y + y^2) 
sage: g = I.groebner_basis()
sage: g
[y^3 + u^2/v*y^2, x^2 + 1/v*y, x*y + 1/u*y^2]

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