#10817: implementation of the generalized associahedron as a polyhedral complex
-----------------------------+----------------------------------------------
Reporter: stumpc5 | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: combinatorics | Keywords: associahedra
Work_issues: | Upstream: N/A
Reviewer: | Author: Christian Stump
Merged: | Dependencies:
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Changes (by stumpc5):
* milestone: sage-4.7.2 => sage-4.7.1
Old description:
> The patch contains the implementation of the generalized associahedron,
> as constructed in [CFZ] Chapoton, Fomin, Zelevinsky - Polytopal
> realizations of the generalized associahedra,
> http://arxiv.org/abs/math/0202004.
>
> {{{
> sage: Associahedron(['A',3])
> Generalized associahedron of type ['A', 3] with 14 vertices
> }}}
>
> The class inherits from Polyhedra, and uses several new methods for root
> spaces:
>
> - `RootLatticeRealization`.index_bipartition, returns the bipartition of
> the indices of the Dynkin diagram vertices, if it is bipartite
>
> - `RootLatticeRealization`.almost_positive_roots, returns the sorted list
> of positive and simple negative roots
>
> - `RootLatticeRealization`.tau_plus_minus, returns two piecewise linear
> operators on the root space which are used to define the "tropical
> Coxeter element" in [CFZ]
>
> - `RootLatticeRealization`.almost_positive_root_decomposition, returns
> the orbit decomposition of the almost positive roots under the dihedral
> group action of < tau_plus, tau_minus > as defined above
>
> Apply only trac_10817-generalized_associahedra-cs.patch
New description:
The patch contains the implementation of the generalized associahedron, as
constructed in [CFZ] Chapoton, Fomin, Zelevinsky - Polytopal realizations
of the generalized associahedra, http://arxiv.org/abs/math/0202004.
{{{
sage: Associahedron(['A',3])
Generalized associahedron of type ['A', 3] with 14 vertices
}}}
The class inherits from Polyhedra, and uses several new methods for root
spaces:
- `RootLatticeRealization`.index_bipartition, returns the bipartition of
the indices of the Dynkin diagram vertices, if it is bipartite
- `RootLatticeRealization`.almost_positive_roots, returns the sorted list
of positive and simple negative roots
- `RootLatticeRealization`.tau_plus_minus, returns two piecewise linear
operators on the root space which are used to define the "tropical Coxeter
element" in [CFZ]
- `RootLatticeRealization`.almost_positive_root_decomposition, returns the
orbit decomposition of the almost positive roots under the dihedral group
action of < tau_plus, tau_minus > as defined above
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10817#comment:12>
Sage <http://www.sagemath.org>
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