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2014-11-28 19:07:42 +0200 commented answer Can SAGE compute with ordinals?

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

2014-11-28 16:26:23 +0200 asked a question 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.

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2013-07-11 15:36:09 +0200 asked a question simple(?) exponentiation simplification

I'm beginning with sage. It sure looks great but I still have to understand what is the actual meaning of what I type in :-(

This is where I am currently stuck:

 
sage: simplify( (a/b)^c - (a^c)/(b^c) )
-a^c/b^c + (a/b)^c
   

I would have loved to get a nice clean $0$. What do I need to tell sage so that it sees that $(a/b)^c$ and $a^c/b^c$ are the same?