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Converting polynomials between rings

I have two polynomials, each one explicitly created as members of different multivariate polynomial rings. So for example I might have

R1.<a,b,c,t> = PolynomialRing(QQ) 
L = (a*t^2+b*t+c).subs(a=2,b=3,c=4)

R2.<A,B,C,D,t> = PolynomialRing(QQ)
p = (A*t+B)^2+(C*t+D)^2

Now I want to compare the coefficients of the two polynomials, which means converting L to be a polynomial in the ring R2.

However, I'm not sure (or more to the point, can't remember) how to do this. Is there some simple, canonical way to do this? Thanks!