On Friday, November 8, 2013 3:25:10 PM UTC-8, Travis Scrimshaw wrote:
>
> I think it would be better to make these UniqueRepresentations by sorting
> the list of integer inputs, that way things like
>
>>
>> sage: G1 is G2
>> False
>> sage: G1 == G2
>> False
>>
>> would make sense.
>>
>
> Sorry, I meant to say these would be True and the output from these
> comparisons would make sense.
>
Quoting from the documentation of AdditiveAbelianGroup:
Construct a finitely-generated additive abelian group.
INPUTS:
* "invs" (list of integers): the invariants. These should all be
greater than or equal to zero.
* "remember_generators" (boolean): whether or not to fix a set of
generators (corresponding to the given invariants, which need not
be in Smith form).
I'd agree with you if remember_generators were "false", but it's "true" by
default. So G1 and G2 should really be non-equal. It pretty clear
"remember_generators" was partially implemented:
- It does set the generators properly, so that G2.0, G2.1 etc. do the
right thing
- It prints elements represented wrt. the remembered set of generators
- G2.0.lift() seems to do the right thing
but not fully:
- the group prints in a funny way (it mentions some isomorphic group, but
printing the group that was constructed would make a lot more sense)
- the element construction from lists uses some internal basis
- asking "list(G2.0)" gives the list of coefficients wrt. the internal
basis (that's at least consistent with the previous one)
- indexing on an element works wrt. the internal basis:
sage: (G2.0[0],G2.0[1])
(0, 1)
sage: G2.0
(1, 0)
The best thing is probably to just finish the job.
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