#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 vdelecroix):
Replying to [comment:7 gagern]:
> Replying to [comment:6 vdelecroix]:
> > Did you try using the magic `algdep` from pari?
>
> My code builds on that, since
[http://git.sagemath.org/sage.git/tree/src/sage/symbolic/expression.pyx?h=develop&id=d27f8497dcd19d70ec08155888e6fec9c74b839a#n10602
expression.minpoly calls calculus.minpoly] which in turn
[http://git.sagemath.org/sage.git/tree/src/sage/calculus/calculus.py?h=develop&id=d27f8497dcd19d70ec08155888e6fec9c74b839a#n957
calls algdep]. But it does come with a verification step, ensuring that
the found polynomial is in fact the one we need. I'm not sure I'd trust
the output from `algdep` directly, particularly not unless I had some very
good ideas of what degree to expect.
Of course we can not believe the output of `algdep`. But at least we can
bound the degree. And once a polynomial is given we can check
irreducibility. So I guess we can produce a candidate quite reliably.
> > The advantage is that it would potentially speed up non symbolic
cases.
>
> Well, one alternative would be to directly feed the descriptor DAG into
`calculus.minpoly`. Computing a `numerical_approx` from these would be
easy enough. The hard part would be the symbolic verification step,
`g(ex).simplify_trig().canonicalize_radical() == 0`. I guess that's done
in Maxima. Do you have an idea how we might either implement this for the
non-symbolic case, or find a rigorous argument why we don't need such a
proof?
Right, checking that it is actually an annihilator polynomial is harder...
I do not see anything different from calling `__nonzero__` which indeed
calls `.exactify()`.
--
Ticket URL: <http://trac.sagemath.org/ticket/16222#comment:8>
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