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Symbolic expression from a polynomial in a quotient ring

sage: R.<t> = PolynomialRing(ZZ)
sage: I = R.ideal([t^2-2])
sage: S.<z> = R.quotient_ring(I)
sage: eq_z = (z+1)^2-5; eq_z
2*z - 2
sage: SR(eq_z.lift()).variables()
sage: SR(eq_z).variables()

I'd expect the last tuple to contain the variable z, what am I missing?