# Roots of Polynomials over finite Fields

Hi guys,

How can I define all polynomial as this form -> `a*x^2+b*y-1`

over QQ where `a`

and `b`

are constants.
for examples polynomials as : `2*x^2+3*y-1`

or `5*x^2+y-1`

, ...
I know that I have to create a PolynomialRing, but I don't understand how exactly.

Thank you so much.

What do you want to do with that set, apart from just "definiing" it ?

The title of your question says "roots of polynomials over finite fields", while the body of your question asks about creating polynomials over QQ. Could you explain the relationship?

I want to do the addition of 2 points of this equations (a point of this equation is a P=[x,y] such that f(P)=0) The addition for example would be -> [x1+x2, y1,y2]