Computing with ordinal expressions like $(\omega^{\omega^2+1}+\omega)^{\omega+2}$ is not very different from handling polynomials, at least if we restrict to ordinals below $\epsilon_0$ written in Cantor Normal Form.
I did not see ordinals mentioned in the manual. Does SAGE know how to do such computations?
I'm interested in basic operations like addition, multiplication, exponentiation, comparison, and it is painful (and risky) to do them by hand.