ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 28 Nov 2014 18:23:29 -0600Can SAGE compute with ordinals?https://ask.sagemath.org/question/25035/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.
Fri, 28 Nov 2014 09:26:23 -0600https://ask.sagemath.org/question/25035/can-sage-compute-with-ordinals/Comment by slelievre for <p>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.</p>
<p>I did not see ordinals mentioned in the manual. Does SAGE know how to do such computations? </p>
<p>I'm interested in basic operations like addition, multiplication, exponentiation, comparison, and it is painful (and risky) to do them by hand. </p>
https://ask.sagemath.org/question/25035/can-sage-compute-with-ordinals/?comment=25044#post-id-25044Nice 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.Fri, 28 Nov 2014 14:38:01 -0600https://ask.sagemath.org/question/25035/can-sage-compute-with-ordinals/?comment=25044#post-id-25044Answer by tmonteil for <p>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.</p>
<p>I did not see ordinals mentioned in the manual. Does SAGE know how to do such computations? </p>
<p>I'm interested in basic operations like addition, multiplication, exponentiation, comparison, and it is painful (and risky) to do them by hand. </p>
https://ask.sagemath.org/question/25035/can-sage-compute-with-ordinals/?answer=25036#post-id-25036Unfortunately 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).
Fri, 28 Nov 2014 09:37:09 -0600https://ask.sagemath.org/question/25035/can-sage-compute-with-ordinals/?answer=25036#post-id-25036Comment by tmonteil for <p>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 <a href="http://www.mtnmath.com/ord/index.html">http://www.mtnmath.com/ord/index.html</a> (whose dependencies MPIR and readline are already satisfied within Sage).</p>
https://ask.sagemath.org/question/25035/can-sage-compute-with-ordinals/?comment=25047#post-id-25047Note that i did not check its pertinence, i just found it from a web search.Fri, 28 Nov 2014 18:23:29 -0600https://ask.sagemath.org/question/25035/can-sage-compute-with-ordinals/?comment=25047#post-id-25047Comment by phs for <p>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 <a href="http://www.mtnmath.com/ord/index.html">http://www.mtnmath.com/ord/index.html</a> (whose dependencies MPIR and readline are already satisfied within Sage).</p>
https://ask.sagemath.org/question/25035/can-sage-compute-with-ordinals/?comment=25038#post-id-25038Thanks a 1.0E06 for the pointer to the Ordinal Calculator ! I'll try it right away...Fri, 28 Nov 2014 12:07:42 -0600https://ask.sagemath.org/question/25035/can-sage-compute-with-ordinals/?comment=25038#post-id-25038