#15948: DynkinDiagram with crossed nodes and labels
-------------------------------------+-------------------------------------
Reporter: vittucek | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Vít Tuček | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vittucek/ticket/15948 | 454c0ac306ca5ab92951fb72099fd8ce94985785
Dependencies: | Stopgaps:
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Comment (by vittucek):
Replying to [comment:10 tscrim]:
> Replying to [comment:7 vittucek]:
> > The labels which are implemented so far are intended for people who
doesn't want to use Bourbaki convention. I think, this feature is not very
well documented. My labels are purely a decoration of nodes, which can be
used i.e. to denote a homogeneous vector bundle over $G/P$. So I guess the
correct thing to do here is to change `node_labels[i]` to
`node_labels[label(i)]`, right?
> >
> > As for immutability issue, will it be OK, if I just add crossed_nodes
and node_labels to the constructor and get rid of the setters?
>
> If you feel the `label` is not well documented, then you should document
it better. However the best thing to do would be to override the Dynkin
diagram's relabel as
> {{{#!python
> def relabel(self, relabeling):
> return DynkinDiagram(self._cartan_type.relabel(relabeling))
> }}}
> This would result in:
> {{{
> sage: D = DynkinDiagram(['A',4,1])
> sage: DL = DynkinDiagram(D._cartan_type.relabel([2,-1,-2,-3,4])) # This
would be D.relabel([2,-1,-2,-3,4])
> sage: DL
> 2
> O-----------+
> | |
> | |
> O---O---O---O
> -1 -2 -3 4
> A4~ relabelled by {0: 2, 1: -1, 2: -2, 3: -3, 4: 4}
> sage: latex(_)
> \begin{tikzpicture}[scale=0.5]
> \draw (-1,0) node[anchor=east] {$A_{4}^{(1)} \text{ relabelled by }
\left\{0 : 2, 1 : -1, 2 : -2, 3 : -3, 4 : 4\right\}$};
> \draw (0 cm,0) -- (6 cm,0);
> \draw (0 cm,0) -- (3.0 cm, 1.2 cm);
> \draw (3.0 cm, 1.2 cm) -- (6 cm, 0);
> \draw[fill=white] (0 cm, 0) circle (.25cm) node[below=4pt]{$-1$};
> \draw[fill=white] (2 cm, 0) circle (.25cm) node[below=4pt]{$-2$};
> \draw[fill=white] (4 cm, 0) circle (.25cm) node[below=4pt]{$-3$};
> \draw[fill=white] (6 cm, 0) circle (.25cm) node[below=4pt]{$4$};
> \draw[fill=white] (3.0 cm, 1.2 cm) circle (.25cm) node[anchor=south
east]{$2$};
> \end{tikzpicture}
> }}}
> I agree that we should add the following semantic to `CartanType`:
> {{{
> sage: CartanType(['A',2], labels=[-1,-2])
> }}}
> (or perhaps `label` or `labeling` or...) and for `crossed_nodes`. Yet we
should also have an additional method which allows us to set the crossed
nodes.
There are two problems. First that I do not understand current labeling
mechanism properly (code nor use cases -- does anybode use `label` at
all?) and second that the semantics here are really different. My
`node_labels` represent some other object that has a priori nothing to do
with how we label the basis of our Cartan algebra. In reality these
`node_labels` denote a highest weight of the Levi part of a standard
parabolic subalgebra and thus it should really be a mapping that assigns
natural numbers to labels. So perhaps `node_labels` should really be a
dictionary with keys `label(i) for i in self.index_set()` What about
this?
{{{#!python
def set_node_labels(self, node_labels):
if isinstance(node_labels, list):
self.node_labels = {i : node_labels[label(i)-1] for i in
self.index_set()}
else:
self.node_labels = node_labels
}}}
>
> I feel like we should add `type_crossed.py` which keeps/prints this data
and uses the same mechanic that the relabeled Cartan types use. Nicolas,
do you agree?
As with `label` I am not sure what is the use case here. What is wrong
with CartanType having labels, node_labels and crossed out nodes as
instance variables?
>
> Furthermore, I don't like the current state of your printing method.
Your iteration of the string is wrong because your assuming your labeling
is nice (i.e. `[0, 1, ..., k]`). However that is somewhat moot because I
think you should only have one method for printing the individual nodes,
as per Nicolas' suggestion, because it is overkill (it's basically just a
for loop).
Did you look at my last commit?
(http://git.sagemath.org/sage.git/commit/?id=454c0ac306ca5ab92951fb72099fd8ce94985785)
>
> Thanks for your work on this,[[BR]]
> Travis
Thanks for feedback. ;)
--
Ticket URL: <http://trac.sagemath.org/ticket/15948#comment:11>
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