#15740: Better support for root systems which do not come from a Cartan type
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: sage-combinat
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/combinat/root_systems/non_typed-15740|
1c0a6c7549966eb34e76931d7833a16dc5d36a4c
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'Travis Scrimshaw', 'oldvalue': ''}):
* status: new => needs_review
* commit: => 1c0a6c7549966eb34e76931d7833a16dc5d36a4c
* branch: => public/combinat/root_systems/non_typed-15740
* author: => Travis Scrimshaw
Old description:
> {{{
> sage: d = DynkinDiagram()
> sage: d.add_edge(1,2,3)
> sage: d.add_edge(2,3)
> sage: d.add_edge(3,4,3)
> sage: d.cartan_matrix()
> [ 2 -1 0 0]
> [-3 2 -1 0]
> [ 0 -1 2 -1]
> [ 0 0 -3 2]
> sage: Q = d.root_system().root_lattice()
> sage: Q
> Root lattice of the Root system of type Dynkin diagram of rank 4
> sage: al = Q.simple_roots()
> sage: al[1].reflection(al[2]) # Boom
> }}}
>
> This shouldn't be too hard to fix, just check if the Cartan type is
> `None` (where applicable) and if so, call the corresponding Cartan
> matrix.
New description:
{{{
sage: d = DynkinDiagram()
sage: d.add_edge(1,2,3)
sage: d.add_edge(2,3)
sage: d.add_edge(3,4,3)
sage: d.cartan_matrix()
[ 2 -1 0 0]
[-3 2 -1 0]
[ 0 -1 2 -1]
[ 0 0 -3 2]
sage: Q = d.root_system().root_lattice()
sage: Q
Root lattice of the Root system of type Dynkin diagram of rank 4
sage: al = Q.simple_roots()
sage: al[1].reflection(al[2]) # Boom
}}}
--
Comment:
I fixed this by giving a method `symmetrizer` to the Dynkin diagrams. This
uncovered another small bug in that the index set wasn't being taking from
the Dynkin diagram (i.e. its vertices) which is also fixed here.
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=1c0a6c7549966eb34e76931d7833a16dc5d36a4c
1c0a6c7]||{{{Added symmetrizer method to Dynkin diagrams and fixed the
index set for the corresp. Cartan matrix.}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/15740#comment:1>
Sage <http://www.sagemath.org>
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