#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/gagern/ticket/14239 | Commit:
Dependencies: | d2f72c655cc22f18c9029da5feff12f35eb0dbf8
| Stopgaps:
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Comment (by gagern):
Replying to [comment:38 jdemeyer]:
> I think it's much more natural to combine code the other way around:
implement everything on the level of `NumberFieldElement` and then call
that code from `AA`/`QQbar`.
I disagree. With `AA` resp. `QQbar` the computation is available for
''any'' element of the field, and is ''always'' based on the minimal
polynomial (for the sake of consistency), even for cyclotomic elements.
For `NumberFieldElement` the computation is only performed for the
generator, and only for non-cyaclotomic fields, so the code we're talking
about is one of may possible cases in a larger control flow structure.
What is more, the cast from `NumberFieldElement` to `AA` resp. `QQbar` is
easy and cheap. The converse has quite a bulky syntax, as you can see in
comment:3, and can be quite costly, as I mentioned in comment:26 item 2.
Or, to put it differently, this is not about converting number field
elements. This is about converting the ''generator'' of a number field,
which itself is an algebraic number, into a symbolic expression. This
involves finding solutions of a symbolic polynomial, comparing isolating
intervals (which is a thing of algebraic numbers not number field
elements), and if that fails, casting to an algebraic number and comparing
the result for equality. Seems to me a lot closer to algebraic numbers
than to number field elements.
--
Ticket URL: <http://trac.sagemath.org/ticket/14239#comment:41>
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