#16949: Improve gens() for elliptic curves over a finite field
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Reporter: jdemeyer | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jdemeyer/improve_abelian_group___for_elliptic_curves_over_a_finite_field|
46393f34e5bf179dfc79a4fa597838ef18910981
Dependencies: | Stopgaps:
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Comment (by cremona):
Perhaps this ticket should be dependent on #16931, which is referred to in
comments in the code?
I would like to see and Example where the product of the orders of the two
generators is greater than the cardinality. But maybe since the gens
returned are random, this cannot be tested deterministically. That is a
pity, but we could have something like
{{{
sage: E = EllipticCurve(GF(41),[2,5])
sage: P,Q = E.gens()
sage: P.order()
22
sage: Q.order()
22
sage: P.order()*Q.order(), E.cardinality()
(484, 44)
}}}
More importantly: suppose that I had done this before calling E.gens():
{{{
sage: E.abelian_group()
Additive abelian group isomorphic to Z/22 + Z/2 embedded in Abelian group
of points on Elliptic Curve defined by y^2 = x^3 + 2*x + 5 over Finite
Field of size 41
sage: E.abelian_group().gens()
((35 : 33 : 1), (10 : 0 : 1))
sage: P,Q = E.abelian_group().gens()
sage: P.order(),Q.order()
(22, 2)
}}}
i.e. I had done the hard work, but it was ignored. Surely the new faster
E.gens() would be even faster in this case if it checked whether
generators were already known?
--
Ticket URL: <http://trac.sagemath.org/ticket/16949#comment:6>
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