#14239: symbolic radical expression for algebraic number
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Reporter: gagern | Owner: davidloeffler
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.1
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: | Reviewers: Marc Mezzarobba
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by mmezzarobba):
* status: needs_review => needs_work
* reviewer: => Marc Mezzarobba
Comment:
I think the feature you are looking for sort of exists. But it is
available for elements of number fields, not algebraic numbers. And it is
pretty inconvenient to use with algebraic numbers because
`alg.as_number_field_element()` returns `alg` as an element of an abstract
number field (plus an embedding of that number field into `QQbar` or
`AA`), while conversion to symbolic expressions expects a number field
with a registered embedding into `CC` or `RR`.
Yet, with the example from your question on AskSage, one can do:
{{{
sage: a = N[0][0]
sage: nf, val, nf2alg = a.as_number_field_element()
sage: approx = CC(nf2alg(nf.gen()))
sage: embedded_nf = NumberField(nf.polynomial(), 'a', embedding=approx)
sage: nf2nf =
sage.rings.number_field.number_field_morphisms.NumberFieldEmbedding(nf,
embedded_nf, embedded_nf.gen())
sage: SR(nf2nf(val))
1/5*sqrt(5)
}}}
So I disagree with the approach you take in your patch: IMO, we should
make something like the example work automatically and share the actual
conversion code between algebraic numbers and number fields instead of
implementing essentially the same feature twice.
--
Ticket URL: <http://trac.sagemath.org/ticket/14239#comment:3>
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