On Fri, May 31, 2013 at 04:45:13PM -0400, Mark Shimozono wrote:
> Anyone understand the behavior
>
> sage: RR^2 in Groups()
> False
>
> Certainly (RR^2,+) should be a group.
Abstractly speaking, yes, RR^2 is a group. But on a computer you need
to specify what the notations are for the operations otherwise you
can't call those operations to do anything useful. So Sage makes the
distinction between additive and multiplicative groups. Which indeed
means that there is a lot of duplication between the hierarchy of
categories for additive groups and multiplicative groups. Only the
notation differ ("+", "-", "zero", ...).
> Generally how does one handle the notational difference
> between additive and multiplicative groups?
> I just want to deal with all groups the same way.
It's a can of worm; as far as I know no system has a good way to
handle this. Probably the easiest for your application would be to
have an adapter/view that would take a multiplicative group and wrap
it as an additive group, or the converse.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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