### Roots of a Polynomial in a PolynomialRing

If I do:

`R.<x,y>= PolynomialRing(QQ,2)`

`f=x^2-y^2`

`f.roots()`

Why it doesn't work?
And next code work:

`R.<x>= PolynomialRing(QQ)`

`f=x^2-1`

`f.roots()`

I don't understand why.

And one more things,
If I want to define all polinomials as this form -> a*x^2 - b*y^2 where $a$ and $b$ are constants.
Have I do this?

`R.<a,b,x,y>=PolynomialRing(QQ,4)`

`I=R.Ideal([a*x^2 - b*y^2])`

`f= 2*x^2 - 3*y^2`

How can I do that?

Thank you so much.