#16261: Default behaviour of AdditiveAbelianGroup(a_tuple)
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Reporter: | Owner:
ncohen | Status: needs_review
Type: | Milestone: sage-6.2
enhancement | Resolution:
Priority: major | Merged in:
Component: group | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: | 5d78cfc86f64819c0427941c882015dd2e3df73e
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/16261 |
Dependencies: |
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Comment (by nbruin):
Replying to [comment:14 ncohen]:
> Do I misunderstand your question or are you saying that you would like
to use any base you like instead of (1,0),(0,1), or the smith form ?
Basically, yes. The problem is that presently, AdditiveAbelianGroup is a
little too lax in what it accepts as "invariants". In the classification
of (finite) abelian groups, the "invariants" `[a1,a2,...,ar]` are subject
to the additional condition that `ai` divides `a(i+1)`. Otherwise they
aren't really invariants.
If you're going to allow abelian groups to be specified in forms different
from smith normal form, I think it's a little strange to just limit to
these "diagonal" forms. In general, you specify a finitely generated
abelian group using generators and relations, i.e., `ZZ^r` modulo some
submodule. Since the underlying machinery is that of ZZ-modules anyway,
why not do it properly?
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Ticket URL: <http://trac.sagemath.org/ticket/16261#comment:15>
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