#14239: symbolic radical expression for algebraic number
-------------------------------------+-------------------------------------
Reporter: gagern | Owner: davidloeffler
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Martin von Gagern | Reviewers: Marc Mezzarobba,
Report Upstream: N/A | Jeroen Demeyer
Branch: | Work issues:
u/gagern/ticket/14239 | Commit:
Dependencies: #17495, #16964 | 09683145989c437b59e02c02409d1dac05ac379d
| Stopgaps:
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Comment (by jdemeyer):
Replying to [comment:67 gagern]:
> However, it fails in cases where we are unable to find a radical
expression for the element even though we would have been able to find one
for the generator. Case in point:
>
> {{{
> sage: K.<a> = NumberField(QQ['x']([6, -65, 163, -185, 81, -15, 1]),
embedding=4.9)
> sage: b = a + a^3
> sage: SR(b)
> 120.55238677055798?
> sage: b.polynomial()(SR(a))
> 1/8*((sqrt(4*(1/9*sqrt(109)*sqrt(3) + 2)^(1/3) -
4/3/(1/9*sqrt(109)*sqrt(3) + 2)^(1/3) + 17) + 5)^2 +
4)*(sqrt(4*(1/9*sqrt(109)*sqrt(3) + 2)^(1/3) - 4/3/(1/9*sqrt(109)*sqrt(3)
+ 2)^(1/3) + 17) + 5)
> }}}
>
> Not sure how to proceed here.
I would just live with it for now.
> One approach would be to try conversion of the non-generator element
first, and if that fails (as evidenced by `x.radical_expression().parent()
!= SR`) try again for the generator
I don't like it because it makes things depend again on the choice of
generator...
--
Ticket URL: <http://trac.sagemath.org/ticket/14239#comment:75>
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