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Can SAGE compute with ordinals?

asked 2014-11-28 09:26:23 -0500

phs gravatar image

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.

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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.

slelievre gravatar imageslelievre ( 2014-11-28 14:38:01 -0500 )edit

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answered 2014-11-28 09:37:09 -0500

tmonteil gravatar image

updated 2014-11-28 09:44:20 -0500

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).

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Thanks a 1.0E06 for the pointer to the Ordinal Calculator ! I'll try it right away...

phs gravatar imagephs ( 2014-11-28 12:07:42 -0500 )edit

Note that i did not check its pertinence, i just found it from a web search.

tmonteil gravatar imagetmonteil ( 2014-11-28 18:23:29 -0500 )edit

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Asked: 2014-11-28 09:26:23 -0500

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Last updated: Nov 28 '14