#17317: Add unit_group() method to IntegerModRing
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Reporter: pbruin | Owner:
Type: enhancement | Status: needs_work
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|
7f38953bdbc38709a218533934d759abc5325f76
Dependencies: #17315 | Stopgaps:
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Comment (by 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_`.
--
Ticket URL: <http://trac.sagemath.org/ticket/17317#comment:7>
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