#16743: Extend IsogenyClass_EC to work over number fields
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Reporter: cremona | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: elliptic curves | Resolution:
Keywords: isogeny class | Merged in:
Authors: John Cremona | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/cremona/ticket/16743 | 06d9eb2226151a35bb2d3779e5309f4d066af8ca
Dependencies: #11327, #16764, | Stopgaps:
#16806 |
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Comment (by cremona):
OK, so here is an example:
{{{
sage: K.<i> = QuadraticField(-1)
sage: I = K.ideal(4+i)
sage: J = K.ideal(4-i)
sage: HI = I.pari_hnf()
sage: HJ = J.pari_hnf()
sage: HIS = HI.sage()
sage: HJS = HJ.sage()
sage: cmp(HI,HJ)
1
sage: cmp(HIS,HJS)
-1
}}}
so they diagree. We have
{{{
sage: HI, HJ
([17, 4; 0, 1], [17, 13; 0, 1])
sage: HIS, HJS
(
[17 4] [17 13]
[ 0 1], [ 0 1]
)
}}}
and I think that I should come before J but using the pari_hnf as is gives
the reverse.
Background: I am making databases of things like elliptic curves over
number fields, and am having to be very explicit indeed about how various
objects are ordered. This is a special case: two conjugate primes above a
rational prime p which plsits in a quadratic field. I need to order
these, and want to do so using the HNFs which only differ in one entry.
Using pari_hnf is not consistent! (Try the ideals (2+i) and (2-i) and the
pari_hnf's compare "correctly".)
I'll have to look at those two other tickets, certainly. Yet another
quagmire!
--
Ticket URL: <http://trac.sagemath.org/ticket/16743#comment:15>
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