#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):
I will trust you that there are cases where this is all that the users
needs.
Can we add to the documentation more from the documentation of pari's
ellgroup() function? As I understand that, if ellgroup()[2] has length 1
then the group is cyclic and this point does generate it; while if it has
length 2 then the first point has order d1 = exponent, the structure is
[d1,d2] with d2>1 and d1|d1, and the Weil pairing between the points has
order exactly d2 even though the second "generator" may have order not d2
(its order must then be a multiple of d2 and a divisor of d1).
As the pari doc says, this avoids the possibly expensive Weil pairing
step.
I will be testing this shortly.
--
Ticket URL: <http://trac.sagemath.org/ticket/16949#comment:5>
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