#8777: unify the definitions and semantics for elliptic curve and abelian
variety
torsion subgroups
-----------------------------+----------------------------------------------
Reporter: was | Owner: was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.4.1
Component: number theory | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-----------------------------+----------------------------------------------
{{{
Hi,
Maybe this is a frivolous comment, but I'd like to express my surprise at
the use of "torsion_subgroup" to mean two very different things for an
abelian variety and for an elliptic curve:
sage: E=EllipticCurve('11a')
sage: E.torsion_subgroup()
Torsion Subgroup isomorphic to Multiplicative Abelian Group isomorphic to
C5 associated to the Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x
- 20 over Rational Field
sage: A=J0(11)
sage: A.torsion_subgroup()
Traceback (most recent call last):
...
TypeError: torsion_subgroup() takes exactly 2 arguments (1 given)
sage: A.torsion_subgroup(5)
Finite subgroup with invariants [5, 5] over QQ of Abelian variety J0(11)
of dimension 1
sage: A.rational_torsion_subgroup()
Torsion subgroup of Abelian variety J0(11) of dimension 1
sage: A.rational_torsion_subgroup().order()
5
sage: A.rational_torsion_subgroup().abelian_group()
Traceback (most recent call last):
...
AttributeError: 'RationalTorsionSubgroup' object has no attribute
'abelian_group'
I'm surprised that "torsion_subgroup" for an elliptic curve over Q refers
to *rational* torsion while for an abelian variety over Q it refers to
*all* torsion. Further, it's frustrating to me that the rational torsion
subgroup of an abelian variety over Q has an order but not the structure
of an abelian group. I'm sure that there are good reasons for this, but
this end user is kind of amazed. Before the sage session above, I used to
think that elliptic curves and abelian varieties of dimension 1 were the
same thing! Live and learn....
Best,
Ken Ribet
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8777>
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