Computing with ordinal expressions like (ωω2+1+ω)ω+2 is not very different from handling polynomials, at least if we restrict to ordinals below ϵ0 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.
Unfortunately Sage does not handle ordinals yet. That said, if you show up with some implementation, i am pretty sure someone will help you to insert it within Sage source code. It should also be possible to interface with existing software such as http://www.mtnmath.com/ord/index.html (whose dependencies MPIR and readline are already satisfied within Sage).
Thanks a 1.0E06 for the pointer to the Ordinal Calculator ! I'll try it right away...
Note that i did not check its pertinence, i just found it from a web search.
Asked: 10 years ago
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Last updated: Nov 28 '14
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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.