#17337: Use the empty set to generate IntegerModRing(1)
----------------------------+-------------------------------
Reporter: pbruin | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.4
Component: finite rings | Keywords: unit group
Merged in: | Authors: Peter Bruin
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies: #17317
Stopgaps: |
----------------------------+-------------------------------
The following choice of generators for two trivial groups is somewhat
inconsistent:
{{{
sage: Zmod(1).unit_gens()
(0,)
sage: Zmod(2).unit_gens()
()
}}}
It would be better to use the empty set as a set of generators for the
unit group of `Zmod(1)` as well.
The main adaptation that this requires is that `DirichletGroup(1).0` no
longer works (this group is also generated by the empty set) and needs to
be changed to `DirichletGroup(1)[0]`.
--
Ticket URL: <http://trac.sagemath.org/ticket/17337>
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