Revision history [back]

I am not sure this trick is formally correct (pleases tell us), but you can try to make c1 and c2 transcendental, by creating a fraction field around them:

sage: R.<c1,c2> = PolynomialRing(QQ)
sage: F = R.fraction_field()
sage: S.<x,y,z> = PolynomialRing(F)
sage: I = ideal(y^2 + z - c1, x*y^2 - c2 - 2)
sage: I.groebner_basis()
[y^2 + z - c1, x*z + (-c1)*x + c2 + 2]


I am not sure this trick is formally correct (pleases (please tell us), but you can try to make c1 and c2 transcendental, by creating a fraction field around them:

sage: R.<c1,c2> = PolynomialRing(QQ)
sage: F = R.fraction_field()
sage: S.<x,y,z> = PolynomialRing(F)
sage: I = ideal(y^2 + z - c1, x*y^2 - c2 - 2)
sage: I.groebner_basis()
[y^2 + z - c1, x*z + (-c1)*x + c2 + 2]


I am not sure this trick is formally correct (please tell us), us!), but you can try to make c1 and c2 transcendental, by creating a fraction field around them:

sage: R.<c1,c2> = PolynomialRing(QQ)
sage: F = R.fraction_field()
sage: S.<x,y,z> = PolynomialRing(F)
sage: I = ideal(y^2 + z - c1, x*y^2 - c2 - 2)
sage: I.groebner_basis()
[y^2 + z - c1, x*z + (-c1)*x + c2 + 2]