#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:39 jdemeyer]:
> The problem is that I don't really know how this "checking for equality"
works. If it works well, then why bother with intervals in the first
place?
Checking for equality means turning the symbolic expression into an
algebraic number. Which in turn means building a tree of algebraic number
descriptors. Comparing them with the input number will work by the usual
comparison of algebraic numbers, which starts by a few rounds of
increasing precision but in the end boils down to finding a common number
field to accomodate both values and doing the arithmetic there. Which can
be really slow. So it works, it may be unavoidable as a last resort, but
it comes with a severe performance penalty. In comment:12 Nils Bruin
explained why that operation is so slow. #16222 (which resulted from
comment:13) and #16964 might reduce that penalty somewhat, but it would
still be better to avoid that.
--
Ticket URL: <http://trac.sagemath.org/ticket/14239#comment:40>
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