#14239: symbolic radical expression for algebraic number
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Reporter: gagern | Owner: davidloeffler
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.5
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Martin von | Reviewers: Marc Mezzarobba,
Gagern, Jeroen Demeyer | Jeroen Demeyer
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/gagern/ticket/14239 | 4626286463c734f931ecc7405285dc7bc1b58772
Dependencies: #17495, #16964 | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:102 gagern]:
> Yes, you are definitely seeing the patch in the wrong direction. A good
thing that you pasted the patch lines above, otherwise I would have ben
thoroughly confused.
Oups... sorry
> Replying to [comment:100 vdelecroix]:
> > What is the point of looking for an approximation
> >
> > {{{
> > k = ( K._n()*CC(K.gen()).log() / CC(two_pi_i) ).real().round() # n ln
z / (2 pi i)
> > }}}
>
> Are you sure you want this handled with this ticket here? If so I'll
have to work out how to find the right `k` using exact arithmetic. I guess
the integers are all there somewhere, but I'll have to look closer. It's
been a while.
It should be easy, `NumberField_cyclotomic` does have a method
`.zeta_order()`. But then, the exact root of unity depends on the
embedding... and I do not see how to avoid going to `QQbar` (or using in
an ugly way interval approximations). It is really a pity that we use
embedding into `RLF/CLF` by default and not `AA/QQbar` (see also #18103,
#18104).
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/14239#comment:103>
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