Hi,
i guess the actual issue is that groups.misc.AdditiveCyclic(10) produces a
ring, not a group, hence the confusion:
sage: G = groups.misc.AdditiveCyclic(10)
sage: G is IntegerModRing(10)
True
sage: G in Groups()
False
sage: G in Rings()
True
sage: Groups()(G)
NotImplementedError:
I am not sure we have to pollute rings with various *_cayley_graph in
order to work around a wrong pointer lazily introduced in the groups.misc
catalog (#15369).
As long as the category framework is not able to handle that with two
appropriate forgetful functors from rings to groups, i would prefer
groups.misc.AdditiveCyclic to either point to some actual group or even
not to exist at all, than to point the IntegerModRing, just to avoid such
confusion. Note that it is currently not used within Sage source code,
except a single doctest in categories/additive_magmas.py.
Also, the distinction between "additive" and "mutiplicative" for groups
(which by definition have only one law) looks weird. In paricular, we
could not have a uniform name for the neutral element.
Just in case, note that for multiplication in rings, you can already do:
sage: IntegerModRing(10).unit_group().cayley_graph()
Ciao,
Thierry
On Sun, Sep 27, 2015 at 03:32:54PM +0200, Nathann Cohen wrote:
> Hello everybody,
>
> Playing with products of groups today, I was not able to obtain what I
> expected from the 'cayley graph' function, as it seems to use (by
> default) the multiplicative operation defined on my group (my group is
> groups.misc.AdditiveCyclic(10))
>
> What do you think is the cayley graph generated by '1' in the additive
> group Z/10Z? - A cycle? - 10 non-adjacent vertices with a loop
> attached to each?
>
> The second wins. Check it out:
>
> sage:
> groups.misc.AdditiveCyclic(10).cayley_graph(generators=[1]).show()
>
> If anybody knows how that could be fixed "cleanly"...
>
> Thaaaanks,
>
> Nathann
>
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