#14300: CyclotomicField's is_isomorphic is mathematically incorrect
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Reporter: robharron | Owner: davidloeffler
Type: defect | Status: positive_review
Priority: critical | Milestone: sage-5.10
Component: number fields | Resolution:
Keywords: CyclotomicField | Work issues:
Report Upstream: N/A | Reviewers: Francis Clarke
Authors: Robert Harron | Merged in:
Dependencies: | Stopgaps:
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Changes (by fwclarke):
* status: needs_work => positive_review
* reviewer: => Francis Clarke
Comment:
Replying to [comment:8 robharron]:
> Since this ticket is for a mathematically incorrect output of sage it
would be great to get it fixed ASAP (my functioning patch has already been
sitting around for three weeks). In view of the examples above, I would
propose worrying about optimizing this function in a separate ticket and
(if there isn't some big problem with what I've written) accepting the
current patch. How does that sound?
After spending some time looking at why the existing code is sometimes
slow, I agree with this suggestion, so a positive review.
----
Using the fact that PARI's `nfisom` runs much faster when one of its
arguments is a number field, rather than a polynomial, it is possible to
make the generic `is_isomorphic` much quicker. It gets a bit complicated
though, because
1. a field's `pari_nf` shouldn't be computed unnecessarily;
2. doing so is much quicker for a cyclotomic field than a general field
of the same degree;
3. for (monic) polynomials with non-integer coefficients PARI's
`nfinit` fails, but `nfisom` works.
I have a draft patch in preparation and will post it soon.
When this is done, it might be sensible to eliminate the cyclotomic
version as the new code will check first whether the defining polynomials
are equal (at the moment `K.is_isomorphic(K)` can be slow). This is
hardly more time-consuming than comparing the values of `zero_order` when
both fields are cyclotomic.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14300#comment:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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