Sagemath: primary decomposition in a number ring

Question

I am trying to factorise the ideal $2R$ in $R = Z[\alpha,\beta]$ where $\alpha$ is a root of some polynomial and $\beta$ as a root of polynomial in $Q[\alpha]$. How do we represent $R$ in a way that factor(2R) or $I.primary_decomposition$ works?

Here is my current code: R.<alpha, beta> = PolynomialRing(ZZ, order='lex') S.<a,b> = QuotientRing(R,R.ideal(alpha^3+alpha^2-2*alpha+8)) T.<x,y> = QuotientRing(S,S.ideal(2*b-a^2-a)) I = T(2) I.primary_decomposition()