On Sun, May 24, 2009 at 01:44:40PM +0100, John Cremona wrote:
> I also would not use "ring" unless it had both a 0 and a 1.
Sorry, if I was unclearn. I was not doubting the a consensus about this.
The question I was raising was about the names we wanted to use for
"rings" without 0 resp. 1.
> 2009/5/24 William Stein <wst...@gmail.com>:
> > For me rings always have both 1 and 0.
> > I would call a "ring without 1" an algebra.
Possibly. Although "algebra" is very often taken for a ring with a
vector space structure (and this is the current convention in
Sage/Axiom/MuPAD). Darn, no internet access to check what Wikipedia
says.
> I have not looked at the rest of what has been done in any one
> detail. But I hope that all the functionality for abelian groups
> will be available for both additive and multiplicative groups,
> something which is certainly not the case at present.
This certainly is very much desirable. The current patch is just about
setting up the overall framework. Now it needs to be filled up, in
particular by abstracting out generic code spread over the Sage library.
I will leave this to the experts, and (finally!) focus back on my
favorite topics (hopf algebras, combinatorics, representation theory, ...).
By the way: as in Axiom/MuPAD/... the current setup does not do
anything special to factor out generic code that work the same for
both additive and multiplicative groups except for the *names* of the
operations. We need good ideas for handling this nicely!
Best,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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