#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:
-------------------------------------+-------------------------------------
Comment (by 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.
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?
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).
Thanks for your work on this,[[BR]]
Travis
--
Ticket URL: <http://trac.sagemath.org/ticket/15948#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
