#14239: symbolic radical expression for algebraic number
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Reporter: gagern | Owner: davidloeffler
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Martin von Gagern | Reviewers: Marc Mezzarobba,
Report Upstream: N/A | Jeroen Demeyer
Branch: | Work issues:
u/jdemeyer/ticket/14239 | Commit:
Dependencies: #17495, #16964 | 24b00c640ccc096afa24da92e29cf2c1372628e2
| Stopgaps:
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Comment (by gagern):
Replying to [comment:61 jdemeyer]:
> 3. My code works in cases where the generator of the field doesn't have
a radical expression, but the element does.
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. 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 and
plug that into the polynomial.
--
Ticket URL: <http://trac.sagemath.org/ticket/14239#comment:67>
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