#11836: gens_reduced() does not handle "large" ideals
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Reporter: mirela | Owner: jdemeyer
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.7.2
Component: number fields | Keywords:
Work_issues: | Upstream: N/A
Reviewer: Marco Streng | Author: Jeroen Demeyer
Merged: | Dependencies: #11130
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Comment(by mstreng):
Replying to [comment:15 mstreng]
Wait, why use flag=1 at all in bnfisprincipal? flag=1 is the (only) one
that gives the warning. So if you replace flag=1 by flag=0 or flag=2 on
line 1067, then that removes the warning.
More importantly: flag=2 (as opposed to 0 or 1) makes sure that
{{{__ideal_class_log}}} is really correct by doubling the precision if
necessary. That would fix a bug that we haven't even found yet! It doesn't
slow correct answers down, as it only doubles the precision until we know
{{{__ideal_class_log}}}; it does not continue on until we know a
generator.
{{{
sage: K.<a> = NumberField(x^2+x-58)
sage: p =
613224584287432205092056925860654065041482770538957925076607095244391171340391841
sage: P = K.ideal(p).factor()[0][0]
sage: bnf = P.number_field().pari_bnf()
sage: bnf.bnfisprincipal(P.pari_hnf(), 0)
[]~
sage: bnf.bnfisprincipal(P.pari_hnf(), 1)
*** Warning: precision too low for generators, not given.
[[]~, []~]
sage: bnf.bnfisprincipal(P.pari_hnf(), 2)
[]~
sage: bnf.bnfisprincipal(P.pari_hnf(), 3)
[[]~, [402403512193607551973543413116828658131543,
49582667258207098257547477827105364096774]~]
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11836#comment:17>
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