So similarly to how we see algebraic numbers as solutions of polynomials with integer or rational coefficients, it seems like we could make polynomials (in variable "y" say) but use other polynomials (in variable "x") as the coefficients. Then we might get some sort of polynomial type of object (in x) that would solve the polynomial in y.
Is this a thing? I'm not sure what it's called so I don't know how to look it up.
thanks.