Using SageMath 7.4, I do the following:
sage: var('u R omega')
sage: hs = (1+u^R).series(u==omega, 2); hs
(omega^R + 1) + (R*omega^R/omega)*(-omega + u) + Order((omega - u)^2)
sage: hs.subs({omega^R: -1}).simplify()
R*(omega - u)/omega + Order((omega - u)^2) + _SAGE_VAR_(0)
I am wondering what _SAGE_VAR_(0)
shall be and how to get rid of it.