On Fri, Oct 15, 2010 at 05:57:37AM -0700, Christian Stump wrote:
> I do not yet understand your idea of having this hierarchy of classes.
> What is the advantage for multiple classification objects to have the
> common ancestor "ClassificationObject"?
- To make it easy to share, or not, whatever makes sense to be.
- To foster a uniform implementation of this kind of things
> Also, I think that it might get chaotic (in the negative sense) to
> attach properties to an object just because you can define this
> property for another object with the "same" classification type. Two
> examples
Having a single hierarchy of classes does not impose that
Cartan-Killing types for cluster algebra need be the same as
Cartan-types for Coxeter groups. There can be distinct classes
CartanTypeForCluster / CartanType which possibly can have a common
super-class if we want to share things like the drawing of the
diagram.
> I thought of the following: you have a class ComplexReflectionGroup
> having all properties you think of, including a classification_type.
> And then, it could as well have methods to_CoxeterGroup() returning
> the CoxeterGroup of this type if possible and an error saying there is
> no Coxeter group of this type otherwise.
(or just coxeter_group()). I don't have a good feeling yet whether
there should be a distinction or, e.g., G(1,1,m) should just return
the symmetric group.
> The only objects (I see at the moment) which I would handle in a
> hierarchy are CoxeterGroup containing FiniteCoxeterGroup containing
> WeylGroup, and CoxeterGroup containing as well AffineCoxeterGroup
> containing AffineWeylGroup, and CoxeterGroups containing
> HyperbolicCoxeterGroups.
Yup. except for HyperbolicCoxeterGroups which does not exist yet, this
is what the current hierarchy of categories (which is something
different from the hierarchy of classes of classification types) does.
> But having CoxeterGroups and (finite) ComplexReflectionGroups, they
> have FiniteCoxeterGroups as an overlap, but beside this, they behave
> very different (think of hyperbolic Coxeter groups or even worse).
Sure. We can have FiniteCoxeterGroups be a subcategory of Both
CoxeterGroups and ComplexReflectionGroups, with the last two being
otherwise independent.
> I would suggest, we set up a skype meeting these days and discuss
> all this on the phone!
Yup. I am for example home until 6pm Paris time tonight. My skype
login is "Nicolas M. Thiery". I hope my skype is working though.
I also have a free (or cheap enough) phone plan to call Canada.
Best,
Nicolas
--
Nicolas M. Thiéry "Isil" <[email protected]>
http://Nicolas.Thiery.name/
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