#13757: The conversion from E to E.abelian_group() does not perserve group order
for elliptic curves over finite fields.
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Reporter: mderickx | Owner: tbd
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-5.6
Component: PLEASE CHANGE | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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One would expect that the following code is deterministic and prints 10
times the same:
{{{
sub_gens=[(542, 488, 1)]
p=709
for i in xrange(10):
E2=EllipticCurve(GF(p),[606,486])
ab=E2.abelian_group()
sub_gens=[E2(i) for i in sub_gens]
index=ab.order()/ab.submodule([ab(i) for i in sub_gens]).order()
sub=ab.submodule([ab(i) for i in sub_gens])
print index,[(ab(i),i.order(),ab(i).order()) for i in sub_gens]
}}}
However the output is:
{{{
6 [((542 : 488 : 1), 57, 114)]
228 [((542 : 488 : 1), 57, 3)]
6 [((542 : 488 : 1), 57, 114)]
3 [((542 : 488 : 1), 57, 228)]
3 [((542 : 488 : 1), 57, 228)]
6 [((542 : 488 : 1), 57, 114)]
6 [((542 : 488 : 1), 57, 114)]
3 [((542 : 488 : 1), 57, 228)]
228 [((542 : 488 : 1), 57, 3)]
6 [((542 : 488 : 1), 57, 114)]
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13757>
Sage <http://www.sagemath.org>
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