#11474: Elliptic curves should be unique parent structures
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Reporter: SimonKing | Owner: cremona
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.2
Component: elliptic curves | Resolution:
Keywords: unique parent | Merged in:
Authors: Simon King | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by defeo):
> - the group of points `E(K)` (or more generally `E(L)` for an extension
`L` of `K`), which does not care about the group structure but is the
parent of (the Sage objects representing the) ''K''-rational points of
''E'' (type `SchemeHomset_points_abelian_variety_field`);
> - if ''K'' is a finite field, there is also `E.abelian_group()`, which
returns an object of type `AdditiveAbelianGroupWrapper`.
I haven't dug enough into the way Sage represents groups, but do these two
objects need to be different ? If groups in Sage need to have explicitly
set generators, then obviously yes: we don't want to compute generators
unless the user asks us to.
But if a group can be represented abstractly (by its elements and an
algorithm for the group operation), then it seems to me that these two
should be the same, with the generators computed lazily when the user asks
for them.
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Ticket URL: <http://trac.sagemath.org/ticket/11474#comment:15>
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