#17317: Add unit_group() method to IntegerModRing
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Reporter: pbruin | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: number theory | Resolution:
Keywords: unit group | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pbruin/17317-IntegerModRing_unit_group|
7e046ddd5ddf66209daf7dd4755e76e4dbbedf56
Dependencies: #17315 | Stopgaps:
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Comment (by pbruin):
Replying to [comment:7 fwclarke]:
> For number fields, we have
> {{{
> sage: QuadraticField(5).unit_group(5)
> Unit group with structure C2 x Z of Number Field in a with defining
polynomial x^2 - 5
> sage: QuadraticField(5).unit_group(5).number_field()
> Number Field in a with defining polynomial x^2 - 5
> }}}
> But in the current case:
> {{{
> sage: Zmod(1000).unit_group()
> Multiplicative Abelian group isomorphic to C2 x C2 x C100
> }}}
> Though we can see which ring we're working with via
> {{{
> sage: Zmod(1000).unit_group().values_group()
> Ring of integers modulo 1000
> }}}
> this terminology is very non-intuitive. I think it would be worth
having a class for these groups, with a `ring` method and a more complete
`_repr_`.
I agree, but this should probably be done on a different ticket. I think
it won't cause problems if we change the precise type of group output by
`unit_group()` in the future. (Maybe we could just make it a subclass of
`AbelianGroupWithValues`.)
--
Ticket URL: <http://trac.sagemath.org/ticket/17317#comment:12>
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