# Can SAGE compute with ordinals?

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.

Nice question. Juste a note: we write Sage rather than SAGE. Originally it was an acronym standing for "Software for Algebraic and Geometric Exploration", but as it now covers all of mathematics, the acronym was abandoned and Sage became just a plain name, and is written with just an initial capital letter.