#17886: Faster qqbar operations using resultants
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Reporter: gagern | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.6
Component: number fields | Resolution:
Keywords: qqbar resultant | Merged in:
exactify minpoly | Reviewers:
Authors: Martin von Gagern | Work issues:
Report Upstream: N/A | Commit:
Branch: | 234b2c4f3435531007c095d278a4c02da8ee2365
u/gagern/ticket/17886 | Stopgaps:
Dependencies: |
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Comment (by gagern):
OK, the doctests look a lot better now. Mostly arbitrary choices made
differently, like sign changes or using a different root as the reference
generator, stuff like that. In several cases I obtain simpler results,
i.e. polynomials of lower degree and the likes.
One thing that has me worried are cyclotomics. If both arguments are from
cyclotomic fields, then we should do the union (which is fast in that
case) instead of the minpoly and resultant. I haven't figured out how best
to check for that case, though.
Another thing I fail is that test taken from that ARPREC paper. That
example is really fast in current implementation, precisely because it's
only operating in a single number field, so it doesn't really require any
unions at all. Should we try to detect this fact, i.e. see if both
arguments are either rational or elements of the same number field? My
failure is only later on, where the original code somehow magically knows
that the difference of two equal numbers is zero. I guess that if we did
introduce a special case for equal number field, we might get that for
free even though I don't know exactly how it works.
--
Ticket URL: <http://trac.sagemath.org/ticket/17886#comment:4>
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