#16222: Faster exactification using numeric minpoly
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Reporter: gagern | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Martin von Gagern | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/gagern/ticket/16222 | 8597313c855ce7a413cfcabead498059d2cfcbf6
Dependencies: | Stopgaps:
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Comment (by gagern):
Replying to [comment:8 vdelecroix]:
> So I guess we can produce a candidate quite reliably.
I'm unsure about the relation between “candidate” and “reliable”. The
former implies something that needs to be verified, the latter like I
could rely on it without verification. But I guess what you mean is that
we could construct a candidate which would ''very likely'' be the correct
one. But “very likely” isn't enough in my opinion.
> Right, checking that it is actually an annihilator polynomial is
harder... I do not see anything different from calling `__nonzero__` which
indeed calls `.exactify()`.
In theory, we could go the reverse route: take the descriptor dag and try
building a symbolic expression from this which in turn can be fed to
Maxima for verification. But I'm far from certain that this is a good idea
for those cases which didn't originate in a symbolic expression in the
first place. Which brings us back to the request as it currently stands,
right?
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Ticket URL: <http://trac.sagemath.org/ticket/16222#comment:9>
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