Hi,

I'm forwarding this to sage-combinat-devel, where most root system related
discussions take place.

Cheers,

Florent

Hi there,

I am the author of the original question, freshly joined the group.

Cheers,
Jesús

        Hi Jesus,

Good catch! Thanks for the feedback.

Actually, the problem is that ``cartan_matrix`` is implemented for
crystalographic cartan types (in the class
sage.combinat.root_system.cartan_type.CartanType_crystalographic).
However, when constructing a relabeled cartan type, that information
is lost; A3r is not put in the right class::

    sage: A3.__class__.mro()
    [<class 'sage.combinat.root_system.type_A.CartanType'>,  ...
     <class 'sage.combinat.root_system.cartan_type.CartanType_finite'>,
     <class 'sage.combinat.root_system.cartan_type.CartanType_simply_laced'>,
     <class 'sage.combinat.root_system.cartan_type.CartanType_crystalographic'>,
     <class 'sage.combinat.root_system.cartan_type.CartanType_simple'>, ...
     <class 'sage.combinat.root_system.cartan_type.CartanType_abstract'>, ...]
    sage: A3r.__class__.mro()
    [<class 'sage.combinat.root_system.type_relabel.CartanType'>, ...
     <class 'sage.combinat.root_system.cartan_type.CartanType_abstract'>, ...]

There is already a hook in the constructor for relabelled cartan types
to handle this for affine cartan types. In
sage.combinat.root_system.type_relabel.CartanType.__init__, you will find:

        if type.is_affine():
            self._add_abstract_superclass(CartanType_affine)

And indeed this works::

    sage: C = CartanType(["A",3,1])
    sage: Cr = C.relabel({0:0,1:2,2:3,3:1})
    sage: Cr.cartan_matrix()
    [ 2 -1 -1  0]
    [-1  2  0 -1]
    [-1  0  2 -1]
    [ 0 -1 -1  2]

So the right fix would be to add similar hooks for finite, simply
laced, crystalographic, and simple cartan types.

Please! I'd be happy to review a patch if you would be willing to
write one.

Cheers,
                                Nicolas
--
Nicolas M. Thi ry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/

Hi Nicolas,

I will put my hands on it, then. This will be my first contribution to
Sage, so I would ask some patience from you ;)

Cheers,
Jesús

Great, thanks!

Even better: we love when new contributors come in, and this is a
perfect fit for a first contribution.

Certainly! We all know the hurdles ...

By the way, instead of a:

        if type.is_affine():
            self._add_abstract_superclass(CartanType_affine)
        if ...

you may want to use something less redundant like:

        for cls in [CartanType_affine, ...]:
            if isinstance(type, cls) and not isinstance(self, cls):
                self._add_abstract_superclass(cls)

Probably the list of classes should be ordered from most specific to
most general.

Cheers,
                                Nicolas
--
Nicolas M. Thi ry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/

Ok, this is shameful, but I have been a few weeks absolutely overloaded
with work.

Is it too late to fix it?

Cheers, ans sorry!
Jesús

Am Freitag, 5. Oktober 2012 09:24:38 UTC+2 schrieb Nicolas M. Thiery:

FInally! http://trac.sagemath.org/sage_trac/ticket/13724

There are still broken things, seems to behave correctly:

{{{
sage: A3 =
CartanType("A3")                                                                                      

sage:
A3.cartan_matrix()                                                                                        

[ 2 -1  0]
[-1  2 -1]
[ 0 -1  2]
sage: A3r =
A3.relabel({1:2,2:3,3:1})                                                                            

sage: A3r.cartan_matrix()            
[ 2  0 -1]
[ 0  2 -1]
[-1 -1  2]

Mainly, the doctest of type_relabel.py compains about some not correctly
inherited methods. I have the impression that it has to do with dynamic
classes, which are beyond my knowledge. Could I get any hint, please?

Cheers,
Jesús Torrado